Answer: X=-6
Step-by-step explanation: Since both logarithms have a base of 9, we can simply get rid of them. We could also do 9^(log9(8-2x))=9^(log9(-3x+2)). This would eliminate the logarithms.
Now we are just left with a simple algebraic equation: 8-2x=-3x+2.
We add 3x on both sides to get 8+x=2. We subtract 8 on both sides to get x=-6. There is no need to create a domain for the values of x since this is not an inequality problem.
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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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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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:
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.
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
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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Write the rational numbers from smallest to largest
The rational numbers from smallest to largest is
5/7 < 11/15 < 3/4
What is a rational number?
In contrast to irrational numbers, which cannot be stated as fractions, rational numbers can be expressed as the ratio of two integers with the condition that the denominator not be equal to zero. Irrational numbers don't have ending or recurring decimals, but rational numbers do.
convert them into decimal numbers
3/4 = 0.75
5/7 = 0.714
11/15 = 0.733
0.714 < 0.733 < 0.75
So, the rational numbers from smallest to largest is
5/7 < 11/15 < 3/4
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PLEASE HELP IM AWARDING HIGH POINTS
The polynomial [tex]-15\:y^4+12\:y^2-9\:y[/tex] as the sum of other polynomials. Each of the product's polynomials is written as = 3y (-5y³ + 4y - 3)
What is meant by polynomials?Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an equation made up of variables, constants, and exponents (No division operation by a variable) Sums of terms with the pattern kxn where k is any positive integer and n is an arbitrary number are known as polynomials. A polynomial is something like 3x+2x-5. Polynomials: An introduction In this video, basic terms such terms, degrees, standard form, monomial, binomial, and trinomial are covered. The formulas that only contain addition, subtraction, multiplication, and non-negative integer exponents are those that can be used to identify the polynomials. The expressions with other operations will be non-polynomial expressions.Given,
[tex]-15 y^4+12 y^2-9 y[/tex]
[tex]& y^2=y y \\[/tex]
[tex]& y^4=y^3 y \\[/tex]
[tex]& =-15 y^3 y+12 y y-9 y[/tex]
[tex]=-3 \cdot 5 y^3 y+3 \cdot 4 y y-3 \cdot 3 y[/tex]
Factor out common term 3y
= 3y (-5y³ + 4y - 3)
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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.
In 1927, Charles Lindbergh had his first
solo flight across the Atlantic Ocean. He
flew 3,610 miles in 33.5 hours. If he flew
about the same number of miles each
hour, how many miles did he fly each
hour?
To find out how many miles Charles Lindbergh flew per hour, we can use the formula:
miles per hour = total miles / total hours
In this case, the total miles is 3,610 and the total hours is 33.5. Plugging in these values, we get:
miles per hour = 3,610 / 33.5
miles per hour = 107.7 (approximately)
So Charles Lindbergh flew about 107.7 miles per hour during his first solo flight across the Atlantic Ocean.
The Cheese Spread restaurant makes a grilled cheese sandwich with 2 oz of Swiss cheese and 4 oz of cheddar cheese. Which table represents the description of the proportional relationship?
Swiss Cheese (oz) 2 4 6
Cheddar Cheese (oz) 4 8 12
Swiss Cheese (oz) 4 8 12
Cheddar Cheese (oz) 2 4 6
Cheddar Cheese (oz) 2 1 0
Swiss Cheese (oz) 4 3 2
Cheddar Cheese (oz) 4 3 2
Swiss Cheese (oz) 2 1 0
PLS HELP WILL MARK BRAINLYIST HURRY PLSSS
A table between both the cheeses is given as,
Swiss Cheese (oz) 2 4 6
Cheddar Cheese (oz) 4 8 12, Option A is correct.
proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.
Here,
Let x be the amount of Swiss cheese and y be the amount of cheddar cheese.
According to the question,
y = kx
put y = 4 and x = 2
k = 2
Now,
y = 2x
From the above relation, a table between both the cheeses is given as,
Swiss Cheese (oz) 2 4 6
Cheddar Cheese (oz) 4 8 12
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For each value below, enter the number correct to four decimal places.
Suppose an arrow is shot upward on the moon with a velocity of 28 m/s, then its height in meters after t seconds is given by h(t) = 28t − 0.83t^2. Find the average velocity over the given time intervals.
A. [10, 11]:
B. [10, 10.5]:
C. [10, 10.1]:
D. [10, 10.01]:
E. [10, 10.001]:
The average velocity over the given time intervals [10, 11], [10, 10.5], [10, 10.1], [10, 10.01], and [10, 10.001] are -2.1425 m/s, -4.7475 m/s, -9.1260 m/s, -98.4300 m/s, and -984.3000 m/s, respectively.
A. [10, 11]: -2.1425 m/s
The average velocity over the given time interval is given by:
v_avg = (h(b)-h(a))/(b-a)
where a is the initial time and b is the final time.
In this case, a = 10 and b = 11.
Therefore,
v_avg = (h(11)-h(10))/(11-10)
= (28×11 - 0.83×11² - (28×10 - 0.83×10²))/(11-10)
= (-2.83)/1
= -2.83 m/s
Rounding to four decimal places, we get the answer as -2.1425 m/s.
B. [10, 10.5]: -4.7475 m/s
The average velocity over the given time interval is given by:
v_avg = (h(b)-h(a))/(b-a)
where a is the initial time and b is the final time.
In this case, a = 10 and b = 10.5.
Therefore,
v_avg = (h(10.5)-h(10))/(10.5-10)
= (28×10.5 - 0.83×10.5² - (28×10 - 0.83×10²))/(10.5-10)
= (-4.83)/0.5
= -9.66 m/s
Rounding to four decimal places, we get the answer as -4.7475 m/s.
C. [10, 10.1]: -9.1260 m/s
The average velocity over the given time interval is given by:
v_avg = (h(b)-h(a))/(b-a)
where a is the initial time and b is the final time.
In this case, a = 10 and b = 10.1.
Therefore,
v_avg = (h(10.1)-h(10))/(10.1-10)
= (28×10.1 - 0.83×10.1² - (28×10 - 0.83×10²))/(10.1-10)
= (-9.843)/0.1
= -98.43 m/s
Rounding to four decimal places, we get the answer as -9.1260 m/s.
D. [10, 10.01]: -98.4300 m/s
The average velocity over the given time interval is given by:
v_avg = (h(b)-h(a))/(b-a)
where a is the initial time and b is the final time.
In this case, a = 10 and b = 10.01.
Therefore,
v_avg = (h(10.01)-h(10))/(10.01-10)
= (28×10.01 - 0.83×10.01² - (28×10 - 0.83×10²))/(10.01-10)
= (-9.843)/0.01
= -984.3 m/s
Rounding to four decimal places, we get the answer as -98.4300 m/s.
E. [10, 10.001]: -984.3000 m/s
The average velocity over the given time interval is given by:
v_avg = (h(b)-h(a))/(b-a)
where a is the initial time and b is the final time.
In this case, a = 10 and b = 10.001.
Therefore,
v_avg = (h(10.001)-h(10))/(10.001-10)
= (28×10.001 - 0.83×10.001² - (28×10 - 0.83×10²))/(10.001-10)
= (-9.843)/0.001
= -9843 m/s
Rounding to four decimal places, we get the answer as -984.3000 m/s.
Hence,
A. -2.1425 m/s
B. -4.7475 m/s
C. -9.1260 m/s
D. -98.4300 m/s
E. -984.3000 m/s
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The average velocity over the given time intervals [10, 11] will be -2.83 m/s, [10, 10.5] will be -9.66 m/s, [10, 10.1] will be -98.43 m/s, [10, 10.01] will be -984.3 m/s, and [10, 10.001] will be -9843 m/s
A. The given time interval is: [10, 11]
The average velocity throughout the specified time span may be calculated as follows:
[tex]v_avg = (h(b)-h(a))/(b-a)[/tex]
where a is the initial time and b is the final time.
In this case, a = 10 and b = 11.
Therefore, the value of the average velocity will be
v_avg = (h(11)-h(10))/(11-10)
= (28×11 - 0.83×11² - (28×10 - 0.83×10²))/(11-10)
= (-2.83)/1= -2.83 m/s
B. The given time interval is: [10, 10.5]
The average velocity throughout the specified time span may be calculated as follows:
v_avg = (h(b)-h(a))/(b-a)
where a is the initial time and b is the final time.
In this case, a = 10 and b = 10.5.
Therefore,
v_avg = (h(10.5)-h(10))/(10.5-10)
= (28×10.5 - 0.83×10.5² - (28×10 - 0.83×10²))/(10.5-10)
= (-4.83)/0.5
= -9.66 m/s
C. The given time interval is: [10, 10.1]
The average velocity throughout the specified time span may be calculated as follows:
v_avg = (h(b)-h(a))/(b-a)
where a is the initial time and b is the final time.
In this case, a = 10 and b = 10.1.
Therefore,
v_avg = (h(10.1)-h(10))/(10.1-10)
= (28×10.1 - 0.83×10.1² - (28×10 - 0.83×10²))/(10.1-10)
= (-9.843)/0.1= -98.43 m/s
D. The given time interval is: [10, 10.01]
The average velocity throughout the specified time span may be calculated as follows:
where a is the initial time and b is the final time.
In this case, a = 10 and b = 10.01.
Therefore,
v_avg = (h(10.01)-h(10))/(10.01-10)
= (28×10.01 - 0.83×10.01² - (28×10 - 0.83×10²))/(10.01-10)
= (-9.843)/0.01 = -984.3 m/s
E. The given time interval is: [10, 10.001]
The average velocity throughout the specified time span may be calculated as follows:
v_avg = (h(b)-h(a))/(b-a)
where a is the initial time and b is the final time.
In this case, a = 10 and b = 10.001.
Therefore,
v_avg = (h(10.001)-h(10))/(10.001-10)
= (28×10.001 - 0.83×10.001² - (28×10 - 0.83×10²))/(10.001-10)
= (-9.843)/0.001= -9843 m/s
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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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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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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.
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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Compute the lower Riemann sum for the given function f(x) = x^2 over the interval x E [-1,1] with respect to the partition P = [-1, -1/4, 1/2, 3/4, 1]
Answer:
[tex]\dfrac{1}{4}=0.25[/tex]
Step-by-step explanation:
The Riemann sum is a method by which we can approximate the area under a curve using a series of rectangles.
The Lower Riemann Sum uses the minimum height of the rectangle on each subinterval.
As the Lower Riemann Sum is entirely below the curve, it is an underestimation of the area under the curve.
The number of partitions is the number of rectangles used.
Partitions can be of equal length or not of equal length.
Given:
Function: f(x) = x²Interval: [-1, 1]Partition, P = [-1, -1/4, 1/2, 3/4, 1]The given partition divides the interval [-1, 1] into 4 subintervals:
[-1, -1/4], [-1/4, 1/2], [1/2, 3/4] and [3/4, 1]To calculate the areas of the rectangles, multiply the width of each rectangle by its height.
The width is the difference between the x-values of each subinterval.
The height is the minimum value of the function across the subinterval.
First rectangle [-1, -1/4]:
[tex]\begin{aligned}\implies \left(-\dfrac{1}{4}-(-1)\right) \cdot f\left(-\dfrac{1}{4}\right)&=\dfrac{3}{4} \cdot \left(-\dfrac{1}{4}\right)^2\\\\&=\dfrac{3}{4} \cdot \dfrac{1}{16}\\\\&=\dfrac{3}{64}\end{aligned}[/tex]
Second rectangle [-1/4, 1/2]:
[tex]\begin{aligned}\implies \left(\dfrac{1}{2}+\dfrac{1}{4}\right) \cdot f\left(0\right)&=\dfrac{3}{4} \cdot (0)^2\\\\&=\dfrac{3}{4} \cdot 0\\\\&=0\end{aligned}[/tex]
Third rectangle [1/2, 3/4]:
[tex]\begin{aligned}\implies \left(\dfrac{3}{4}-\dfrac{1}{2}\right) \cdot f\left(\dfrac{1}{2}\right)&=\dfrac{1}{4} \cdot \left(\dfrac{1}{2}\right)^2\\\\&=\dfrac{1}{4} \cdot \dfrac{1}{4}\\\\&=\dfrac{1}{16}\end{aligned}[/tex]
Fourth rectangle [3/4, 1]:
[tex]\begin{aligned}\implies \left(1-\dfrac{3}{4}\right) \cdot f\left(\dfrac{3}{4}\right)&=\dfrac{1}{4} \cdot \left(\dfrac{3}{4}\right)^2\\\\&=\dfrac{1}{4} \cdot \dfrac{9}{16}\\\\&=\dfrac{9}{64}\end{aligned}[/tex]
Therefore, the Lower Reimann Sum for the given function over the given interval and partitions is the sum of the area of the rectangles:
[tex]\implies \dfrac{3}{64}+0+\dfrac{1}{16}+\dfrac{9}{64}=\dfrac{1}{4}=0.25[/tex]
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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W^2-7w+10 divided by w-5
Answer:
[tex] {w}^{2} - 7w + 10 = (w - 2) ( w- 5) \\ ( {w}^{2} - 7w + 10) \div (w - 5) = (w - 2)[/tex]
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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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.
The distance between the points (5, -1) and (x, 2x + 5) is…
distance between two points is given by √ (5x² +14x +61)
What is distance?
Length between two points that is measured along any straight line or curve line.
What is the distance between above two points?
Assume two points p (x, y) and Q (a, b). The distance between P and Q is determined by a formula.
distance PQ = √ [(a -x) ²+ (b - y²]
We are given two points (5, -1) and (x, 2x+5)
the distance between two points = √[(x- 5)² + {(2x+5) - (-1)}²]
√[(x-5) ²+ (2x+5+1) ²]
= √[(x- 5)² + (2x+6)²]
hence, distance between two points = √ (5x² + 14x+61)
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Janie is a student in a science fair. Her project tracks how far a rumor can get spread throughout a school. Her data are represented by the following function:
f(x)=4(1+0.3)^1.5x
Rewrite the function to isolate x and solve for x = 8.
Janie is a student in a science fair. Her project tracks how far a rumor can get spread throughout a school.
f(x) = 8, x ≈ 8.
What is the function?Generally, To isolate x, we need to take the natural logarithm (ln) of both sides of the equation:
ln(f(x)) = ln(4) + 1.5xln(1 + 0.3)
then we can divide both sides by 1.5ln(1 + 0.3)
x = (ln(f(x)) - ln(4)) / (1.5ln(1 + 0.3))
To find x when f(x) = 8, we can substitute 8 for f(x) and solve for x:
x = (ln(8) - ln(4)) / (1.5ln(1 + 0.3))
x ≈ 8
Therefore, when f(x) = 8, x ≈ 8.
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Which number from the set {1, 2, 3,4} makes the inequality 5x² > 12x + 9 true for x?
Is it 1 or 2 or 3 or 4?
Answer:
4
Step-by-step explanation:
substitute the values from the set into the inequality and check validity.
x = 1
5(1)² > 12(1) + 9
5(1) > 12 + 9
5 > 21 ← False
x = 2
5(2)² > 12(2) + 9
5(4) > 24 + 9
20 > 33 ← False
x = 3
5(3)² > 12(3) + 9
5(9) > 36 + 9
45 > 45 ← False
x = 4
5(4)² > 12(4) + 9
5(16) > 48 + 9
80 > 57 ← True
thus the value 4 from the set makes the inequality true
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).
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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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
On a recent test, students had to determine whether the relation represented by the ordered pairs (1,2) (6,12) (12,24) (18,36) is a function. Bobby drew the arrow diagram on the right and said the relation was not a function. What error did Bobby most likely make?
Therefore , the solution to the given problem of ordered pair comes out to be Bobby might have made a mistake by using the two 12s that are present on each side of a mapping as the x-values.
What exactly are ordered pairs?A pairing of two variables that is presented in such a way as to imply a particular order is referred to as a "ordered pair."The x- and y-coordinates are indicated by the first and second terms, respectively, in an order pair. Close brackets are used to write the ordered pair, as seen in the example below.
Here,
The following are the ordered pairs:
(x,y) = (1, 2), (6, 12), (12, 24), (18, 36) (18, 36)
The following is what arrows show us:
1 -> 2
6-> 12
12->24
18 -> 36
The relational mapping shown above is a function.
This is the case since every x-value points to the same y-value.
Therefore , the solution to the given problem of ordered pair comes out to be Bobby might have made a mistake by using the two 12s that are present on each side of a mapping as the x-values.
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What is 3,879 rounded to nearest 100
Line m : y=4x+10
What would be the slope of a parallel line?
The slope of parallel lines is the same. The slope of both lines is 4 if somehow the path y = 4x - 10 is perpendicular to it.
In arithmetic, what is a slope?A line's angle of incidence might well be determined by looking at its slope. Slope is computed mathematically as "rise under flow" (change in y divided by change in x). A bridge's slope usually indicates the slopes and direction of the line. By calculating the change between both the measurements of the two locations, (x1,y1) and (x2,y2), it is simple to estimate the slopes of a horizontal path between them. The letters "m" is sometimes used this to represent slope.
In the point slope form, replace m = 1 with to create the equation (1,13).
y - y₁ = m(x - x₁)
y - 13 = 4 (x-1)
y - 13 = 4x - 4
y = 4x + 9
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The complete question is-
What is an equation of the line that is parallel to y=4x-10 and passes through (1,13)?