The expression which represent consecutive odd integer is 2x+1.
What is odd integer?
Any integer that cannot be divided by two is referred to as an odd number. In other words, integers that take the form 2k+1, where k , are referred to be odd numbers. Integers or sets of integers on a number line can be either odd or even, it should be noted.
Here let us take the odd integer as x.
Now the expression which expression consecutive odd integer is,
=> 2x+1 .
Here x is a real number.
Hence the expression which represent the next consecutive odd integer is 2x+1.
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The expression which represent consecutive odd integer is 2x+1.
What is odd integer?Any integer that cannot be divided by two is referred to as an odd number. In other words, integers that take the form 2k+1, where k , are referred to be odd numbers. Integers or sets of integers on a number line can be either odd or even, it should be noted.
Here let us take the odd integer as x.
Now the expression which expression consecutive odd integer is,
=> 2x+1 .
Here x is a real number.
Hence the expression which represent the next consecutive odd integer is 2x+1.
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What is the sum of 6 of the interior angles of a regular decagon
As a result, there are 1440 degrees total internal angles in a decagon.
What is angle?A figure that is created by two rays or lines that have the same endpoint is known as an angle in plane geometry. From the Latin word "angulus," which meaning "corner," comes the English term "angle." The vertex, which is the shared terminal of the two rays, is referred to as the side of an angle. Two lines intersect at a shared point to produce an angle. Degrees, denoted by the symbol °, are used to measure them. Acute, right, obtuse, and reflex angles are among the four crucial types of angles. 360° makes up a full circle. It has completed two full rotations if the angle is more than 720°.To learn more about angle, refer to:
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In 1986 one of the first video games, the Nintendo, sold for $180. Similar to many items, its value depreciated over time. the function that models how its value has changed over times is: f(x) = 3x^2 - 40x +180,
1. The number shows the video game sold in 1986at $180.
2. The function f(x) = 3x² - 40x +180 which clearly resemble the standard vertex form.
3. The vertex of the given parabola is, (h, k) = (6.667, 46.667)
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
f(x) = 3x² - 40x +180
1. For f(0) put x= 0 we get
f(0) = 3(0)² - 40(0) +180
f(0) = 180
So, the number shows the video game sold in 1986 at $180.
2. We know that the standard form of the parabola is y=ax²+bx+c.
Also we have f(x) = 3x² - 40x +180 which clearly resemble the standard vertex form.
3. Comparing the given equation with y = ax² + bx + c, we have
a = 3, b = -40, and c = 180.
So, x-coordinate is, h = -b/2a = - (-40)/ 2(3)
h= 40/6 = 6.667
and, y-coordinate is, k = 3(6.667)² - 40(6.667) +180 = 46.667.
So, The vertex of the given parabola is, (h, k) = (6.667, 46.667)
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7/6 = 18 x-6 = 18 6x = 18 1. In 6 years, Rosario will be 18 years old. How old is she now? x + 6 = 18
Please help!!! I am so confused and this is due tomorrow!!
f (x+ h) = 4(x+ h) - 6 and f (x+ h) - f (x) = 4(x+ h) - 6 - 4 (x) - 6 are the results of simulating f (x+ h) = 4.
what is function ?The subject of mathematics includes quantities and their variations, equations and related structures, forms and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A relationship between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.
Given
A) f( x+ h ) = 4( x+ h ) - 6
B) f ( x+ h ) - f (x) = 4 (x+ h ) - 6 - 4 (x) - 6
f (x+ h) = 4(x+ h) - 6 and f (x+ h) - f (x) = 4(x+ h) - 6 - 4 (x) - 6 are the results of simulating f (x+ h) = 4.
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What number represents the change in altitude a hiker must complete to return to sea level if he is at an altitude of 25 feet below sea level?
help please ASAP! :)
(PS, you can win 95 points by answering my question! =D)
The number that represents the change in altitude a hiker must complete to return to sea level if he is at an altitude of 25 feet below sea level is 25.
When the hiker is at an altitude of 25 feet below sea level, he needs to go up 25 feet to reach sea level. This represents a change in altitude of 25 feet, regardless of the direction it is going.
So the number that represents the change in altitude to return to sea level is 25.
A is the midpoint of segment bouded by (-2, 3) & (6, -1). B is a point at 3/4 of distance from (4, 3) to (0, -3). Find the equation of AB.
The equation of line segment AB, whose endpoints are A(x, y) = (2, 1) and B(x, y) = (1, - 1.5), is P(x, y) = (1 - k) · (2, 1) + k · (1, - 1.5), for 0 ≤ k ≤ 1.
How to derive the equation of a line segment
In this problem we need to determine the equation that described the line segment AB, whose endpoints are points within other two line segments. The location of a point can be found by means of the following formula:
P''(x, y) = P(x, y) + k · [P'(x, y) - P(x, y)], 0 ≤ k ≤ 1
Where:
P(x, y), P'(x, y) - Endpoints of line segment.k - Length ratio.P''(x, y) - Endpoint within line segment.First, determine the locations of endpoints A and B:
A(x, y) = (- 2, 3) + 0.5 · [(6, - 1) - (- 2, 3)]
A(x, y) = (- 2, 3) + 0.5 · (8, - 4)
A(x, y) = (- 2, 3) + (4, - 2)
A(x, y) = (2, 1)
B(x, y) = (4, 3) + 0.75 · [(0, - 3) - (4, 3)]
B(x, y) = (4, 3) + 0.75 · (- 4, - 6)
B(x, y) = (4, 3) + (- 3, - 4.5)
B(x, y) = (1, - 1.5)
Second, derive the equation of line segment AB:
P(x, y) = A(x, y) + k · [B(x, y) - A(x, y)]
P(x, y) = (2, 1) + k · [(1, - 1.5) - (2, 1)]
P(x, y) = (1 - k) · (2, 1) + k · (1, - 1.5), for 0 ≤ k ≤ 1.
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the bottom angle is also 45 could some one answer this for me
The length of the side opposite to the reference angle is 7.77 units.
What are trigonometric ratios in terms of a right-angle triangle?We know a right-angled triangle has three sides they are -: Hypotenuse,
Opposite and Adjacent.
We can remember SOH CAH TOA which is,
sin = opposite/hypotenuse, cos = adjecen/hypotenuse and
tan = opposite/adjacent.
If we take the reference angle 45°, The side 'x' is opposite and the side having a length of 11 units is the hypotenuse.
We know, sin = opposite/hypotenuse.
Therefore,
sin45° = x/11.
1/√2 = x/11.
x = 11/√2.
x = 7.77 units.
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You randomly select a letter from the letters A, B, C, D, E and flip a coin. The table represents the sample space, where H represents the coin landing heads up and T represents landing tails up. What is the probability of selecting the letter “C” or the coin landing tails up?
To find the probability of selecting the letter "C" or the coin landing tails up, we need to calculate the probability of each event individually and then add the probabilities of the two events together.
The probability of selecting the letter "C" is:
1/5
This is because there are 5 letters in total, A, B, C, D, and E, and "C" is one of them, so the probability of selecting "C" is 1/5.
The probability of the coin landing tails up is:
1/2
This is because there are two possible outcomes when flipping a coin, heads or tails, and since the coin is fair, the probability of getting heads or tails is 1/2.
To find the combined probability of the two events we need to add them together using the rule of "or" in probability which is defined as:
P(A or B) = P(A) + P(B) - P(A and B)
However in this case A and B are mutually exclusive events, meaning they can't happen at the same time. There is no way to have "C" and coin landing tails up at the same time. Then we don't have to subtract P(A and B)
Therefore, the probability of selecting the letter "C" or the coin landing tails up is:
1/5 + 1/2 = 2/5 + 1/2 = 7/10
So the probability of selecting the letter "C" or the coin landing tails up is 7/10
Select the correct answer from each drop-down menu.
How are line segments and rays alike? How are they different?
Both a ray and a line segment
is
✓. A ray is
but a line segment
Both a ray and a line segment have two endpoints . A ray is bounded on one side , but a line segment is not bounded on either side.
What is the difference between a ray and a line?Line extends forever in both directions. 1. Ray starts at one point and continues on forever in one directionA line is a straight path on a plane that extends forever in both directions with no endpoints. A line segment is part of a line that has two endpoints and is finite in length. A ray is a line segment that extends indefinitely in one direction.A line is a simple geometric shape that extends in both the directions, but a line segment has two defined endpoints. Both the figures are also different from a ray, as a ray has only one endpoint and extend infinitely in one direction.To learn more about difference between a ray and a line refers to:
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Write the inequality using interval notation.
A person has to be taller than 55 inches but shorter than 70 inches to ride the Twirly
Swirly ride at an amusement park.
The inequality using interval notation is given as 55 < x < 70
What is an equation?An equation consists of numbers and variables linked together by mathematical operations to form an expression.
Inequalities are used to show that an expression containing numbers and variables are not equal.
Interval notation involves using parentheses for opened ends and square brackets for closed ends.
Let x represent the allowed height to ride at an amusement park. A person has to be taller than 55 inches but shorter than 70 inches, hence:
55 < x < 70
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A blue parallelogram has a height of 6 inches and a base of 10 inches. a scale of 2:1 was applied to the blue parallelogram to create a green parallelogram. what is the area of the green parallelogram? Provide explanation/show work!
the area of the green parallelogram will be 15inch².
What is Area of Parallelogram?
The region in a two-dimensional plane that a parallelogram occupies is known as its area. A parallelogram is a form with four sides with two geometry dimensions. Because the opposing sides are equal and parallel, so it is a unique quadrilateral example. The space bounded by the four sides of a parallelogram is known as its area. A parallelogram's area is calculated as the sum of its length and height.
A blue parallelogram has a height of 6 inches and a base of 10 inches.
a scale of 2:1 was applied to the blue parallelogram to create a green parallelogram.
So the height will be half and the base ill also be.
For the green parallelogram will be 3 inch and 5 inch.
The area will be 3*5 = 15inch²
Hence, the area of the green parallelogram will be 15inch².
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isabella is building a fort.The base is 78 inches wide by 92 inches long. what is the area of the base in square inches show your work
The area of a rectangle is found by multiplying the length by the width.
To find the area of the base of Isabella's fort, we will use the following formula:
Area = length x width
We are given that the base of the fort is 78 inches wide and 92 inches long. So we can plug these values into the formula:
Area = 78 inches x 92 inches = 7176 square inches
Therefore, the area of the base of Isabella's fort is 7176 square inches.
Exercise 21 1. A girl moves from a point P on a bearing of 060° to a point Q, 40m away. She then moves from the point Q, on a bearing of 120° to a point R. The bearing of P from R is 255, Calculate, correct to three significant figures, the distance between P and R.
Therefore , the answer is the distance between P and R is 12,2m.
How far is that?Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending point.
Here,
Using the sine rule, sin a/A = sin b/B in this instance, we can determine the distance between P and R.
Sin angle PQR/PR is equal to Sin angle QRP/PQ.
We are aware that the QRP angle is 45° because:
Since it is an alternative interior angle, angle NPR is 75°.
Since 75° – 60° = 15, the angle QPR would be 15°.
As a result, angle QRP would be 45° since 180° – 120° – 15° = 45°.
When we know the angle QRP, we can quickly calculate the PR by entering the values into a calculator.
Sin 120°/RP = Sin 45°/10
RP = sin(120,10) sin(45,45),
=root 6 × 5
= 12.2m(3s.f) (3s.f)
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Niquelle places signposts along a trail that is 4 1/2 miles long. The signposts divide the
trail into sections that are 3/4 mile long. How many sections does Niquelle create
along the trail?
Using Simple division, Number of sections that Niquelle create along the trail is 6 sections.
One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division.
The other operations are multiplication, addition, and subtraction. Simply write the first fraction, the division symbol (), and the second fraction to divide a fraction. For instance, your issue could be 3/4 5/8. Use horizontal rather than diagonal lines to conveniently divide each fraction's numerator (top number) and denominator (bottom number).
Partitive division and quotative division are the two types of division. In some circumstances, one form may be more beneficial than the other.
Length of the trail = 4 1/2 miles long = 9/2 miles
The signposts divide the trail into sections that are 3/4 mile long.
Number of sections that Niquelle create along the trail = 9/2 miles ÷ 3/4
⇒ 9/2 × 4/3
⇒ 6 sections
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A trader sells eggs at 30naira each or 150naira for six, How much do you save by buying three doten eggs in sixes Instead of separately
He saved 180 naira by buying three dozen eggs in sixes Instead of separately.
What is a dozen?A group of twelve is referred to as a dozen and is frequently abbreviated as doz or dz. Given that there are roughly twelve lunar cycles (or months) in each cycle of the sun (or year), the number twelve may be one of the earliest primitive integer groupings.
Twelve is useful because it has the greatest number of divisors among numbers up to its double, a property shared only by the numbers 1, 2, 6, 12, 60, 360, and 2520.
1 dozen = 12
3 dozen = 36
6 eggs costs 150 naira
36 eggs costs 150 naira = 36/6 × 150
= 900 naira
Each egg costs 30 naira, then 36 eggs costs = 36 × 30
= 1080 naira
Savings = 1080 - 900 = 180 naira
Thus, He saved 180 naira by buying three dozen eggs in sixes Instead of separately.
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The dimensions of the rectangular pool shown below are 60 yards by 30
yards. A fence will be built around the outside of the deck. The ratio of the
dimensions of the pool to the dimensions of the fence is How many yards
of fence should be purchased to enclose the deck?
60 Yards
30 Yards
A. 270 yards
B. 540 yards
C. 200 yards
D. 312 yards
540 yards should be purchased to enclose the deck and option B is correct.
What is rectangle?A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides.
A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.
Pools dimension = 1:3
Length = 60 × 3
= 180
Breadth= 30 × 4
= 90
Perimeter of rectangle = 2(l+b) = 2(90+180)
P = 2(270) = 540 yards
Thus, 540 yards should be purchased to enclose the deck and option B is correct
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All stocks traded in U.S. stock markets are identified by a "ticker symbol" — an abbreviation of one to four letters. For example, Ford is "F," DuPont is "DD," Microsoft is "MSFT," and Harley-Davidson is "HOG." How many different stock ticker symbols are possible?
The answer is 475,254, but I don`t understand how this number was gotten
Answer:
456,754
Step-by-step explanation:
A ticker symbol is an abbreviation of one to four letters, which means it can be one letter, two letters, three letters or four letters. Each letter can be any of the 26 letters in the English alphabet, so there are 26 choices for each position.
For one letter ticker symbols:
26 (number of choices for the first letter) * 1 (number of positions) = 26 different possibilities.
For two letter ticker symbols:
26 (number of choices for the first letter) * 26 (number of choices for the second letter) = 676 different possibilities.
For three letter ticker symbols:
26 (number of choices for the first letter) * 26 (number of choices for the second letter) * 26 (number of choices for the third letter) = 17,576 different possibilities.
For four letter ticker symbols:
26 (number of choices for the first letter) * 26 (number of choices for the second letter) * 26 (number of choices for the third letter) * 26 (number of choices for the fourth letter) = 456976 different possibilities.
So, the total number of different stock ticker symbols that are possible is 26 + 676 + 17,576 + 456976 = 456,754.
What is the solution to the following system?
IM BEING TIMMED!!!!!
(3, 1, 0)
(0, 1, 0)
(2, 1, 0)
(–2, 1, 0)
The solution of the given system of equations is (2, 1, 0).
What is system of equations?
A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, also known as a system of equations or an equation system.
Consider, the given system of equations.
3x + 3y + 6z = 9 ..(1)
x + 3y + 2z = 5 ..(2)
3x + 12y + 12z = 18 ..(3)
Divide equation (1) by 3
x + y + 2z = 3 ..(4)
Subtract equation (4) from equation (2)
x + 3y + 2z = 5
- x + y + 2z = 3
______________
2y = 2
⇒ y = 1
Multiply equation (1) by 2
6x + 6y + 12z = 18 ..(5)
Subtract equation (3) from equation (5)
6x + 6y + 12z = 18
- 3x + 12y + 12z = 18
_______________________
3x - 6y = 0 ..(6)
Multiply equation (2) by 6
6x + 18y + 12z = 30 ..(7)
Subtract equation (3) from equation (7)
6x + 18y + 12z = 30
- 3x + 12 y + 12z = 18
_______________________
3x + 6y = 12 ..(8)
Adding equation (6) and (8)
3x - 6y = 0
+ 3x + 6y = 12
________________
6x = 12
⇒ x = 2
Now plug x = 2, y = 1 in equation (1)
3(2) + 3(1) + 6z = 9
6 + 3 +6z = 9
9 + 6z = 9
6z = 0
z = 0
Hence, the solution of the given system of equations is (2, 1, 0).
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Use the formula d = ( r − c ) t to find c if d = 12 , r = 7 , and t = 2 .
Answer:
30=(12-c)5
30=60-5c multiply 12 and c by 5
-30=-5c Subtract 60 from 30
-30 ÷ -5= c divide -30 by -5
c=6
jessica and her family went to each applebee's. they ordered two appetizers for $15.58 each, 4 sweet teas for $23.67, chiken tenders meal for $10.two pasta meals for $19 each ,4 sweet teas for 1.25. jessica decided that her family should leave an 18% tip. how much wil Jessica's family pay for the meal, including the tip?
Answer: $180.02
Step-by-step explanation:
The total bill for the food will be $178.84 and then add the tip which is 18% to get the total. One method of changing the 18% to money wise is 1.18 and then adding the two numbers together to get a total of $180.02.
What are the features of the quadratic function graphed in the figure?
Vertex (3, -4) with x-intercepts (1, 0), (5, 0), and (0, 5) and an axis of symmetry of 3. As a result, choice B is the right response.
In a graph, what exactly is a vertex?
A node of a graph, or one of the points on which the graph is defined and which may be connected by graph edges, is known as a "vertex" and is a mathematical term for this type of point.The following are some characteristics of the quadratic function:The curve's bottommost point, or vertex, is situated halfway along the curve. The point's x-coordinate is 3 and its y-coordinate is -4. The quadratic's x-axis intersection points are (1, 0) and (5, 0), and its y-axis intersection point is (0,5).The right response is, therefore, option B.
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Full Question-
What characteristics can you see in the graph of the quadratic function in the figure? Options for question 14: A: The vertex is at (-4,3), the y-intercept is at (5,0), the x-intercepts are at (0,1) and (0,5), and the symmetry axis is at (-4,3) B: The vertex is at (-3,-4), the y-intercept is at (0,5), the x-intercepts are at (1,0) and (5,0), and the symmetry axis is at (3); C: Vertex: (3, -4), y-intercepts: (1, 0), and (5, 0), x-intercept: (0, 5), axis of symmetry: (3 D) Axis of symmetry is at x = -3, vertex is at (-3,4), y-intercept is at (0,5), and x-intercepts are at (1,0) and (5,0).
The rectangle on the right is a scaled copy of the rectangle on the left. Identify the
scale factor. Express your answer as a whole number or fraction in simplest form.
3
7
7/3
The scale factor of the rectangle and its copy is [tex]\frac{2}{3}[/tex].
What is scale factor?The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).
The rectangle on right hand side is the scaled copy of the original rectangle. The scaled version of the rectangle is given as follows:
[tex]\frac{42}{63} \text{ and } \frac{15}{\frac{45}{2} } = \frac{30}{45}[/tex]
Rationalize the factors to find the scale factor.
Rationalize the factor [tex]\frac{42}{63}[/tex] by multiplying and dividing by 45.
[tex]\frac{(42)(45)}{(63)(45)}[/tex]
[tex]\frac{1890}{2835}[/tex]
Rationalize [tex]\frac{30}{45}[/tex] by multiplying and dividing by 63.
[tex]\frac{(30)(63)}{(45)(63)}[/tex]
[tex]\frac{1890}{2835}[/tex]
Scale factor = [tex]\frac{1890}{2835} = \frac{2}{3}[/tex]
Hence the scale factor of the rectangle and its copy is [tex]\frac{2}{3}[/tex].
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Is 28/20 equal to 1 2/5?
Answer: Yes
Step-by-step explanation: 28/20 Simplified is 1 2/5
Answer:
Yes
Step-by-step explanation:
Pleas HELP MEEEEEEE :CCC
Answer: 15,24,plan A
Step-by-step explanation: you will need to use the 15 from 150 to see which one costs less because 24+ 15= 39 so its obvious that plan B costs less then plan A the next step is pretty easy because they both cost 24 at the same time but its obvious that plan A costs more so your answer for each of them is
A circle has a radius of 11 ft. Find the radian measure of the central angle θ that intercepts an arc of length 9 ft. Do not round any intermediate computations, and round your answer to the nearest tenth.
The radian measure of the central angle θ is 5.4 radians.
Find the radian measure of the central angle θ that intercepts an arc of length 9 ft.The radian measure of a central angle is the ratio of the arc length to the radius of the circle. To calculate the radian measure of the central angle, we must divide the length of the arc (9 ft) by the radius of the circle (11 ft). 9ft/11ft = 0.818181818Therefore, the radian measure of the central angle θ is 0.818181818. To convert this value to a decimal to the nearest tenth, we must multiply the value by 10 and round to the nearest tenth.0.818181818 x 10 = 8.18181818Rounding to the nearest tenth, the radian measure of the central angle θ is 8.2.The radian measure of the central angle of a circle can be found using the formula θ = s/r, where s is the length of the arc and r is the radius of the circle. In this case, s = 9 ft and r = 11 ft, so θ = 9/11.To find the radian measure of the central angle, we need to convert the fraction 9/11 into decimal form, which yields 0.818181818....To convert this decimal into radians, we can multiply it by 2π and get 5.06544 radians. Finally, to round this answer to the nearest tenth, we can round 5.06544 to 5.1 radians.Therefore, the radian measure of the central angle θ that intercepts an arc of length 9 ft on a circle with a radius of 11 ft is 5.1 radians.To learn more about The radian measure of the central angle refer to:
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Mari suspects that there is a relationship between the number of text messages high school students send and their academic achievement. To explore this, she asks a random sample of 52 students at her school how many text messages they sent yesterday and what their grade point average (GPA) was during the most recent marking period. Her data are summarized in the scatter plot below. The line of best fit is also shown as y=3.8-0.005x.
what is the GPA of someone who texted 200 and 90 times?
Answer:
Interpretation of the slope: For students at this school, the predicted GPA decreases by 0.005 for each additional text message sent OR the GPA decreases by 0.005, on average, for each additional text message sent.
Interpretation of intercept: The model predicts that students at this school who send no text messages have, on average, a GPA of 3.8.
Step-by-step explanation:
The purpose of this task is to assess the ability to interpret the slope and intercept of the line of best fit in context. There are two common errors that students make when interpreting the slope. Students may not make it clear that the slope is the predicted change (not necessarily an actual change) in GPA associated with an increase of 1 in the number of text messages sent. They also often do not communicate that the slope describes the change
You might want to point out that it is not always reasonable to interpret the intercept as the predicted y value when x = 0, as this often involves extrapolation far beyond the range of the x values in the data set. In this example, however, it is appropriate because there are observations with x = 0 in the data set.
You can also point out that the interpretation of the slope and intercept represents a generalization from the sample of 52 students to the population of all students at the school. This is appropriate because the sample was a random sample of students from the school.
Although this task is short and looks simple, some of the points brought out in this task are subtle. It might be a good strategy to engage in a whole class discussion of the correct interpretations.
Todd made $12,800 in interest by placing $40,000 in a savings account with simple interest for 4 years. What was the interest rate?
Answer: The interest rate is 0.16 or 16% ✅
Step-by-step explanation:
The interest rate is the percentage of the principal (the initial amount of money) that is paid as interest over a certain period of time. To find the interest rate in this scenario, we can use the formula:
Interest = Principal x Interest Rate x Time
In this case:
Interest = $12,800
Principal = $40,000
Time = 4 years
So we can set up the equation:
12800 = 40000 x Interest Rate x 4
To find the interest rate, we can divide both sides of the equation by 40000 x 4, which gives us:
12800 / (40000 x 4) = Interest Rate
We can simplify this fraction:
0.16 = Interest Rate
So the interest rate is 0.16 or 16%.
When Todd made $12,800 in interest by placing $40,000 in a savings account with simple interest for 4 years, the interest rate was 7.5%.
Simple interest is a formula for calculating the amount of interest that will be charged on a sum of money at a specific rate and during a specific time frame.
In contrast to compound interest, where the interest of one year's principal is added to the principal of the following year to calculate the interest, the principal sum in the case of simple interest stays the same.
Simple Interest = [tex]$ \frac{ \text P \times \text R \times \text T}{100}[/tex]
where,
P = Principal,
R = Rate of Interest in % per annum, and
T = Time, in years
Here given that,
Todd made $12,800 in interest, i.e. Simple Interest = 12,800
By placing $40,000 in a savings account, i.e. Principal = 40,000
with simple interest for 4 years, i.e. Time = 4 years
To find, interest rate
Substitute the data into the simple interest formula
[tex]$ \Rightarrow 12,800 = \frac{40,000 \times \text R \times 4}{100}[/tex]
[tex]$ \Rightarrow \text R = \frac{ 12,000 \times 100}{40,000 \times 4}[/tex]
[tex]$ \Rightarrow \text R = \frac{1,200,000}{160,000}[/tex]
⇒ R = 7.5%
Thus, the interest rate was 7.5%.
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Which transformations have been performed on the graph of f(x)=√x to obtain the graph of g(x)=√x+3+6?
Select each correct answer.
Otranslate the graph to the left
O compress the graph closer to the x-axis
Otranslate the graph to the right
O translate the graph down
Otranslate the graph up
O reflect the graph over the x-axis
Ostretch the graph away from the x-axis
Therefore , the solution of the given problem of function comes out to be the correct options are B, E and F
What is meant by the word function?A science called mathematics studies numbers, its variations, arithmetic and the local tissue, shapes, and both their existing and projected places. The relationship between a group of inputs, which each have a corresponding output, is described by a function. A function is variable a collection of inputs that together produce a single, recognizable output with each input. A city, municipality, or scope—often referred to as a realm—is assigned to each function.
Here,
By observing the 1/4 placed ahead of the cubed root symbol, we can get the solution B. Every y value is reduced by a factor of 1/4, bringing it closer to the x axis.
By examining the 3 within the cube root symbol, we can determine solution E. The value is always moved left by that many spaces when we add a digit under the cube root symbol.
Finally, if we look at the 6 at the conclusion, we can locate F. Any integer used as a constant at the conclusion of an equation causes the graph to advance by that too many spaces.
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Jorge's trip takes the same amount of time as Zahara's but he traveled a shorter distance. Does Jorge drive faster or slower Zahara's dad
Answer: Slower
Step-by-step explanation:
Speed is a measure of how quickly an object moves, and it is calculated as distance traveled divided by time. Since Jorge and Zahara's dad traveled the same amount of time but Jorge traveled a shorter distance, it can be inferred that Zahara's dad traveled at a faster speed.
Another way to understand this is that, if Jorge and Zahara's dad were driving at the same speed, they would have traveled the same distance in the same amount of time. However, since Jorge traveled a shorter distance than Zahara's dad, it can be inferred that Jorge was driving at a slower speed.
Answer:
Step-by-step explanation:
Find the equation of the line that passes through the point (6,-2) and is parallel to the line 5x+3y
Answer: y=(-5/3)x+8
Step-by-step explanation: earrange 5x+3y=6 in slope intercept form
y=mx=b
5x+3y=6
3y=6-5x
y=2-(5x)/3
then slope for a line parallel is -5/3
Use point slope form y-y1=m(x-x1)
plug un values of (x,y) = (6,-2)
and m=-5/3
y-y1=m(x-x1)
y-(-2)=(-5/3)(x-6)
y+2=(-5/3)x+10
y=(-5/3)x+10-2
y=(-5/3)x+8 <-- solution