if r(x) = x² and r(x) = 4, then the value of x = ± 2
What is equivalent of value?Equal means same in all aspects, whereas equivalent means similar but not identical. For example, 2 is said to be equal to 2 but equivalent to 1 + 1.
For example y = x+5 and the same y = 2x+7
then we can say that x+5 Is also equal to 2x+7
2x+7 = x+5
then x = -2
similarly r(x) = x²
thesame r(x) = 4
this means that x² = 4
solving for x
we find the square root of both sides
√x² = √4
x= ±2
It is ± because square root value as two possible values of either both positive or both negative.
Therefore the value of x is ±2
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URGENT!!!
Which of the following points best represents the location of -1 5/8 on the number line?
A
B
C
D
Answer:
A
Step-by-step explanation:
[tex]-2<-1 \frac{5}{8}<-1[/tex], and A is the only point between -2 and -1.
Answer: i believe your answer would be C.
Step-by-step explanation: it is located where -1 is and is on the 5th line. between -1 and the letter C there are 8 lines. So answer would be letter C. sorry if that’s wrong.
How do you match a logarithmic function with its graph?
Matching a logarithmic function with its graph can be done by understanding the key characteristics of logarithmic functions and how they are represented on a graph.
A logarithmic function is of the form y = log base b (x), where b is the base of the logarithm (usually 10 or e).
The graph of a logarithmic function is a reflection of the exponential function of the same base b, across the line y=x.
Here are some key characteristics of logarithmic functions and their corresponding graphs:
1) Asymptote: The graph of a logarithmic function has a vertical asymptote at x=0, since the logarithm of a non-positive number is undefined.
2) Domain: The domain of a logarithmic function is x>0, since the logarithm of a negative number is undefined.
3)Range: The range of a logarithmic function is all real numbers
4) Increasing or decreasing: A logarithmic function is increasing over its domain
5) Shape: The graph of a logarithmic function is concave down.
6) x-intercept: The x-intercept of the graph is (1,0), since the logarithm of 1 is always 0.
By keeping these characteristics in mind, you can match a logarithmic function with its graph by observing the shape, asymptote, domain and range of the graph.
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3y+2=2y-5x into y=mx+b form
3y + 2 = 2y - 5x
3y - 2y = -5x -2
y = -5x - 2
49x+ 0.10= 117.90
I need help please
Subtract 0.1 from both sides49x+ 0.10= 117.90
49x+0.1-0.1=117.9-0.1
x=2.404
What is meant by variables?A quantity that may assume any one of a set of values. : a symbol representing a variable. : something that is variable. : a factor in a scientific experiment that may be subject to change.A variable is any characteristics, number, or quantity that can be measured or counted. A variable may also be called a data item. Age, sex, business income and expenses, country of birth, capital expenditure, class grades, eye colour and vehicle type are examples of variables.A variable is a quantity that may change within the context of a mathematical problem or experiment. Typically, we use a single letter to represent a variable. The letters x, y, and z are common generic symbols used for variables49 x+0.1=117.9Move 0.1 to the right side49 x=117.8Divide both sides by 4949 x/49=117.8/49Simplifyx=2.40408To learn more about variables refers to:
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What is the best approximation for the area of this figure?
21+14. 5π units²
21+7. 25π units²
10. 5+7. 25π units²
10. 5+14. 5π units²
Coordinate plane with axes labeled x and y. A closed figure is formed by two segments and a semicircle. A segment extends from negative 5 comma negative 2 to negative 5 comma 1. Another segment extends from negative 5 comma 1 to 2 comma 1. A semicircle extends from 2 comma 1 to negative 5 comma negative 2. What is the area of this polygon?
28. 5 units²
34. 5 units²
37. 5 units²
40. 5 units²
6 sided polygon on a coordinate plane with vertices at (negative 6, negative 2), (negative 5, 1), (negative 1, 4), (1, 1), (5, 3), and (1, negative 2)
1) The best approximation for the area of this figure is 21+14. 5π units².
2) The total area of the closed figure is 10.5 + 19.63 = 30.13 square units.
3) This is a hexagon with vertices at the specified coordinates on a coordinate plane.
FIGURE AND POLYGON1) The best approximation for the area of this figure is 21 + 14.5π units². The area of a semicircle with a radius of 7 is 14.5π units², and the two segments form a rectangle with an area of 21 units². Adding these two values together gives 21 + 14.5π units².
2) This closed figure can be divided into two parts: a triangle and a quarter of a circle. The area of the triangle can be found using the formula for the area of a triangle (base times height divided by 2). The base of the triangle is the length of the segment from negative 5 comma negative 2 to negative 5 comma 1, which is 3 units. The height of the triangle is the length of the segment from negative 5 comma negative 2 to 2 comma 1, which is 7 units. So the area of the triangle is (3*7)/2 = 10.5 square units.
The area of the quarter of a circle can be found using the formula for the area of a circle (pi times the radius squared). The radius of the semicircle is the length of the segment from 2 comma 1 to negative 5 comma negative 2, which is 5 units. So the area of the quarter of the circle is (pi*5²)/4 = 19.63 square units.
So the total area of the closed figure is 10.5 + 19.63 = 30.13 square units.
3) A hexagon is a polygon with six sides and six angles. In this case, the hexagon is placed on a coordinate plane, with each of its vertices (or corners) located at specific x and y coordinates.
The coordinates provided are: (negative 6, negative 2), (negative 5, 1), (negative 1, 4), (1, 1), (5, 3), and (1, negative 2). These coordinates correspond to six points on the plane, and the hexagon is formed by connecting these points in the specified order.
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What is the solution to this system of linear equations 2x 3y equals 3?
The solution to this system of linear equations is x = 3, y = 2.
2x - 3y = 3
2x = 3 + 3y
2x = 3y + 3
x = (3y + 3) / 2
x = 3/2 + 3/2y
x = 3, y = 2
This system of linear equations features two unknown variables, x and y. The equation 2x - 3y = 3 can be rearranged into 2x = 3y + 3. This equation can then be solved for x by dividing both sides by 2, resulting in x = 3y + 3/2. Since 3y + 3/2 must equal 3, this means that y must equal 2. Substituting 2 for y in the original equation yields 2x = 3 + 3(2), or 2x = 9. Dividing both sides by 2 yields x = 9/2, or x = 3. Therefore, the solution to this system of linear equations is x = 3 and y = 2.
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The solution to the system of linear equations 2x + 3y = 3 is x = 1 and y = -1/3.
1. Rewrite the equation in standard form is
2x + 3y = 3
2. Subtract 2x from both sides of the equation:
3y = 3 - 2x
3. Divide both sides by 3:
y = (3 - 2x)/3
4. Solve for x by substituting y in the original equation:
2x + 3(3 - 2x)/3 = 3
5. Simplify and solve for x:
2x + 3 - 2x = 3
x = 1
6. Substitute x into the equation y = (3 - 2x)/3
y = (3 - 2(1))/3
y = -1/3
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Regan has Rs.10,000 in total. He lent a part of it to Sandip and the remaining to Saline. If Saline paid Rs.2160 more interest than Regan at the end of 3 years and at the rate of 18% simple interest rate. Find how much money did Regan give to Sandip and Saline. (Assume 365 days in a year)
The Rs. 10,000 Regan lent to Sandip and Saline and the Rs.2160 more interest Saline paid than Sandip after 3 years at an 18% simple interest rate, indicates by expressing the amounts using equations, that the amount Regan gives to Sandip and Saline is Rs. 3,000 and Rs. 7,000 respectively.
What is an equation?An equation is the presentation of a statement of the equivalence between quantities, or expressions, by joining the expressions with a '=' sign.
The amount Regan has = Rs. 10,000
Let x represent the amount Regan lent to Sandip, we get;
The amount Regan lent to Saline = 10,000 - x
The interest rate of the loan Regan lent to Sandip and Saline = 18% simple interest
The interest Saline paid to Regan after 3 years, using simple interest = Rs. 2160 + The interest Saline paid to Regan
The simple interest formula is; I = P·R·T/100
Where;
P = The principal amount loaned
R = The interest rate = 18%
T = The time or duration of the loan = 3 years
Therefore;
(10000- x) × 18/100 × 3 = 2160 + x × 18/100 × 3
5400 - 0.54·x = 2160 + 0.54·x
5400 - 2160 = 0.54·x + 0.54·x = 1.08·x
3240 = 1.08·x
x = 3240 ÷ 1.08 = 3000
The amount Regan lent to Sandip, x = Rs. 3000
The amount Regan lent to Saline = 10,000 - x
x = 3000
10,000 - x = 10,000 - 3000 = 7,000 (substitution property)
The amount Regan lent to Saline = Rs. 7,000
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a. Kiran tried to double this recipe. He used 2 cups of
yogurt, 6 tablespoons of peanut butter, 5 teaspoons of
chocolate syrup, and 4 cups of crushed ice. He didn't
think it tasted right. Describe how the flavor of Kiran's
recipe compares to Clare's recipe.
Therefore , the solution to this problem of unitary method comes out to be he should use 4 teaspoons of chocolate syrup instead of 5.
Define unitary method.A single or distinct variable is referred to by the word unitary. Therefore, the goal of this strategy is to establish values in reference to a single unit. The unitary technique, for instance, can be used to calculate how many kilometers a car will go on one litre of gas if it travels 44 km on two litres of fuel.
Here,
Given :This recipe was doubled by Kiran. He used 4 cups of crushed ice, 6 tablespoons of chocolate syrup, 6 tablespoons of peanut butter, and 2 cups of yogurt.
1. Kiran's smoothie would be more chocolatey than Clare's. All ingredients are doubled, but there is an extra teaspoon of chocolate syrup in his smoothie.
2. Answers vary. Sample response: he should use 4 teaspoons of chocolate syrup instead of 5.
Therefore , the solution to this problem of unitary method comes out to be he should use 4 teaspoons of chocolate syrup instead of 5.
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Find the measure of the two marked angles NEED HELP ASP!!!!!
The measure of the two marked angles are as follows:
60°60°How to find angles when parallel lines are cut by a transversal?When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate exterior angle, alternate interior angles, linear angles, vertically opposite angles, same side interior angles etc.
According to the diagram the parallel lines are cut by the transversal and formed the angles.
Hence, the angles are alternate exterior angles.
Alternate exterior angles are congruent. Hence, the angles are as follows:
10x - 20 = 7x + 4
10x - 7x = 4 + 20
3x = 24
x = 24 / 3
x = 8
Therefore, the angles are as follows:
10x - 20 = 10(8) - 20 = 80 - 20 = 60 degrees
7x + 4 = 7(8) + 4 = 56 + 4 = 60 degrees.
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Find the volume of the cylinder. Round your answer to the nearest tenth if necessary. Use 3. 14 for pi.
A can of juice has a radius of 5 inches and a height of 6 inches. What is the volume of the can?
The volume of the can based on mentioned radius and height of can is 471 inches³.
Volume of cylinder is defined the capacity or amount of fluid that can be held in the object. The mentioned object is can which is cylindrical in shape.
Use the below mentioned formula to calculate the volume -
V = πr²h, where V is volume, r is radius and h is height.
Keep the values in formula to find the value of volume of cylinder
V = 3.14×5²×6
Next step is to perform multiplication on Right Hand Side of the equation
V = 471 inches³
The obtained volume is already rounded off. Thus, the volume of the can is 471 inches³.
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write an explicit rule for -2, 5, 12, 19
The explicit rule for the sequence -2, 5, 12, 19 is
-2 + (n - 1) 7.
What is an arithmetic sequence?It is a sequence where the difference between each consecutive term is the same.
Example:
2, 4, 6, 8, 10 is an arithmetic sequence.
We have,
-2, 5, 12, 19
This is an arithmetic sequence.
The first term.
a = -2.
The common difference.
d = 5 - (-2) = 7
= 12 - 5 = 7
= 19 - 12 = 7
Now,
The nth term of an arithmetic sequence.
= a + (n -1)d
= -2 + (n - 1)7
Thus,
The explicit rule is -2 + (n -1) 7.
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Find the lengths of the diagonals of rectangle WXYZ.
WY= 16x + 2-
XZ=36x-6
The length of each diagonal is
units.
Therefore , the solution of the given problem of equation comes out to be each diagonal measures 8.4 units in length..
Define equation.An equation is a mathematical representation of two equal variables, one on each side of a "equals" sign. Everyday issues can be resolved with equations. We commonly look for pre algebra help to deal with problems in real life. Pre-algebra contains the fundamental concepts of mathematics.
Here,
Given: 16x + 2 = 36x - 6 8 = 20x x = 8/20, simplifying to 2/5, or 0.4
You would set the two equations equal to one another and find x because a rectangle's diagonals are congruent.
Re-enter the value of x into a single of the equations.
=>16(0.4) + 2
=>6.4 + 2
=>8.4
To make sure, confirm with the other diagonal.
=>36(0.4) - 6
=>14.4 - 6
=>8.4
Each diagonal measures 8.4 units in length..
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The waitress had a table with a bill of $75.29 and received $12.80. What was the percent tip she received?
Answer:
17%
Step-by-step explanation:
Firstly, we can establish that the tip is a percentage of the bill, excluding tips. This means that the $75.29 would be 100%, thus to find the percentage of tip received, we would take
$12.80/$75.29 × 100 = 17%
if x+3=9 whats the answer:)
enjoy
Answer:
x=6
Step-by-step explanation:
then x=6 because replacing x 6+3=9
Condos in Georgetown go up in value by 10% each year. If the Sutton family's condo is now worth $120,000, what will it be worth in 8 years? If necessary, round your answer to the nearest cent.
The Sutton family's condo's worth in 8 years will be $216000.
What is exponential function?An exponential function is a mathematical function in the form f(x) = aˣ, where {x} is a variable and {a} is a constant which is called the base.
Given is that Condos in Georgetown go up in value by 10% each year. Sutton family's condo's current worth is $120,000.
We can write the function to calculate the worth after {T} years as follows.
A{T, R} = A{i} {1 + RT}
A{T, R} = {120000} {1 + (10/100) x 8}
A{T, R} = {120000} {1 + 0.1 x 8}
A{T, R} = {120000} {1 + 0.8}
A{T, R} = {120000 x 1.8}
A{T, R} = 216000
Therefore, the Sutton family's condo's worth in 8 years will be $216000.
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A line passes through the points (–6,5) and (8,–2). What is its equation in point-slope form?
Answer:
y - (-2 ) = 1\2 ( x- 8)
Step-by-step explanation:
The point slope form equation is y-y₁=m(x-x₁)
( -6 , 5 ) ( 8 , -2 )
( x , y ) (x1 , y1 )
Firstly we need to find the slope
y1 - y -2 - 5
we can find the slope by this equation : ------------- = --------------
x1 - x 8 - (-6)
The slope is 1\2
Question 2 (Essay Worth 2 points)
(05.06 HC)
Using f(x) = log x, what is the x-intercept of g(x) = log (x + 4)? Explain your reasoning.
In accordance with comparative comparative, the x-intercept of function g(x) = ㏒ (x + 4) is equal to x = - 4.
How to determine the x-intercept of a logarithmic functionAccording to function theory, a function f(x) has an x-intercept when f(x) exists for x = 0. Besides, logarithms of 1 for any base is equal to zero, that is:
Logarithm of 1 at any base.
㏒ₐ 1 = 0
If ㏒ x = 0, then x = 1. And if ㏒ (x + 4) = 0, then x + 4 = 0, that is, x = - 4.
Then, by direct comparison between the two logarithmic expression, the logarithmic function g(x) = ㏒ (x + 4) has x = - 4 as its x-intercept.
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Convert the number into standard form, please!
Convert from number format to standard form as a decimal multiplied by a power of 10.
What is standard form?Standard form is a way of writing a number so it is easier to read. It is often used for very large or very small numbers. Standard form is like scientific notation and is typically used in science and engineering.A number is written in standard form when it is represented as a decimal number times a power of 10.As an example, consider the speed of light which travels at about 671,000,000 miles per hour. Written in standard form this number is equivalent to 6.71 x 108.step 1
convert 1.5806*10rais to 4
Convert to decimal notation
1.5806*10^4
The exponent is 4, making it 10 to the power of 4. As the exponent is positive, the solution is a number greater than the origin or base number. To find our answer, we move the decimal to the right 4 time(s)
1.5806 ->15806
step 2
final result
15806
Simplify the expression
1.581*10^4
Simplify exponents and square roots
1.581*10^4
10 ^4 = 10 × 10 × 10 × 10 = 10,000
1.581*10000
Perform any multiplication or division, from left to right:
1.581*10000
15806
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The base of an open rectangular box is of length (2x + 5) cm and width x cm.
The area of this base is 58 cm².
The height of the open box is (x - 2) cm.
I have attached a pic
(I already did part (a) and (bi) and you may use the answers to help you do the (bii) question)
+ the answer for (bi) if you can’t see it, it is 4.28 and -6.78
This is the question:
b) (ii) Hence calculate the volume of the box, stating the units of your answer.
A box's volume equals [tex]135.25cm^{3}[/tex] the length (2x + 5) cm and breadth x cm of the base of an open rectangular box.
what is volume?The area occupied within an object's three-dimensional bounds is referred to as its volume. The basic formula for volume is length, width, and height, as opposed to the basic formula for the area of a rectangular shape, which is length, breadth, and height. No matter how you refer to the various dimensions, the calculation remains the same. It is sometimes referred to as the vessel's "capacity" or "volume." infant milk bottle with milliliter measuring indications and juice bottle with a 1 liter capacity.
given
Calculate the box's volume and provide your answer in units.
Due to the fact that x = 4.28, the remaining sides are 2x + 5 = 2(4.28) + 5 = 13.56
and x - 2 = 4.28 -2 = 2.28.
We are aware that volume is calculated as follows: 13.56 (4.28) ( 2.28 )
=[tex]135.25cm^{3}[/tex]
A box's volume equals [tex]135.25cm^{3}[/tex] the length (2x + 5) cm and breadth x cm of the base of an open rectangular box.
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Please help me with my hw
Answer:
9m^8 n^2
Step-by-step explanation:
Open up the parenthesis and simplify to find your answer.
solve by completing the square
-x^2=5x-14
Answer:
Roots: -7, 2
Step-by-step explanation:
-x² = 5x - 14
-x² -5x +14 = 0
x² + 5x - 14 = 0
(x + 7)(x -2) = 0
x = -7 or x = 2
Write an equation in slope-intercept form for each line at the right. Line one goes from (-6,7) to (1,-7) and line two goes from about (1.25,7) to (3.25,-7)
y=-2x-5 and y=-7x+15.75 are equations in slope-intercept form for each line.
What is slope intercept form of line?The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
We need to find equation in slope-intercept form of line passing through of (-6,7) to (1,-7) and one more line passing through (1.25,7) to (3.25,-7)
Slope of line with (-6,7) to (1,-7) is m=-7-7/1+6=-14/7
=-2
y intercept we have to find
7=-2(-6)+b
7=12+b
-5=b
So slope intercept form of line passing through (-6,7) to (1,-7) is y=-2x-5
Now Slope of line with (1.25,7) to (3.25,-7) is
m=-7-7/3.25-1.25
m=-14/2=-7
y intercept we have to find
7=-7(1.25)+b
7=-8.75+b
b=15.75
So slope intercept form of line passing through (1.25,7) to (3.25,-7) is y=-7x+15.75
Hence, y=-2x-5 and y=-7x+15.75 are equations in slope-intercept form for each line.
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There are 200 students, where 86 of them were in the athletics team. Therefore, ___% of the students were in the athletics team.
Answer:
43%
Step-by-step explanation:
calculate percentage as
( number of students in athletics team ÷ total students ) × 100%
= ( 86 ÷ 200) × 100%
= 0.43 × 100%
= 43%
Jared’s monthly income is 4500 Jared spend 11%of his income on grocies
Answer:
Jared's groceries = 495
Step-by-step explanation:
We calculate 11% from Jared monthly income:
11% x 4500 = 495
Jared's groceries = 495
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The dollar value v(t) of a certain car model that is t years old is given by the following exponential function.
v (t)=20,000 (0.86)'
Find the value of the car after 4 years and after 10 years.
Round your answers to the nearest dollar as necessary.
Value after 4 years:
Value after 10 years:
Answer:
4 years: $10,94010 years: $4,426Step-by-step explanation:
Given the value function v(t) = 20000·0.86^t, you want the value after 4 years and 10 years.
EvaluationPut the value of t in the formula where t is, and do the arithmetic.
The attached calculator output tells us ...
value after 4 years: $10,940
value after 10 years: $4,426
__
Additional comment
When you are asked to do the same evaluation with different numbers, it is convenient to process them as a list, or using a spreadsheet.
What is step 3 in problem solving?
Step 3 is Define the problem Goals.
there are 8 steps, which are as follows,
1- Define the Problem
2- Clarification of the Problem
3- Define the problem Goals
4- Identify main Cause of the Problem
5- Develop a Action Plan
6- Execute that Action Plan
7- Analyze the Results
8- Continuous Improvements
Problem solving
Problem solving is the method of determining the problem and then clarify the doubts and prepare a action plan and then execute the action plan and find out the desired results and if the results are not appropriate then improve the action plan and your way of doing until you get the desired results.
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please help: solve for x
Step-by-step explanation:
since the height from M (line MB) to the baseline is splitting the baseline into 2 identical halves, the triangle must be an isoceles triangle (both legs are identical long).
and therefore,
5x - 5 = 3x + 1
2x - 5 = 1
2x = 6
x = 6/2 = 3
Figure ABCD is a parallelogram if point C lies on the line y=-1 what is the x vale of point C
The value of x of point C is 4. The coordinate of C is (4,-1).
What is the coordinate of a point?
The coordinates represent the location of a point in the 2D coordinate plane with respect to the origin. A point's x-coordinate is its perpendicular distance from the y-axis as measured along the x-axis. A point's y-coordinate is the perpendicular distance from the x-axis measured along the y-axis.
The distance between points A and B is 4 units.
The opposite sides of a parallelogram are equal and parallel.
To make parallelogram, the point C lies on the left side of point D.
The distance between point C and D must be 4 unit.
The coordinates of C is (4,-1).
The x value of point C is 4.
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The perimeter of a rectangle is 84cm and it's length is 6cm longer than it's breadth. Find the length and breadth of the rectangle
Answer:
Step-by-step explanation:
The perimeter of a rectangle is the sum of all its sides. Since the perimeter is given as 84 cm, we can set up the following equation to represent the problem:
2l + 2b = 84
Where l is the length of the rectangle and b is the breadth.
We are also told that the length is 6 cm longer than the breadth. We can represent this relationship with the equation:
l = b + 6
Substituting the second equation into the first equation, we get:
2(b + 6) + 2b = 84
Expanding the left side of the equation gives:
2b + 12 + 2b = 84
Combining as terms gives:
4b + 12 = 84
Subtracting 12 from both sides gives:
4b = 72
Dividing both sides by 4 gives:
b = 18
Substituting this value back into the equation l = b + 6 gives us:
l = 18 + 6
l = 24
Therefore, the length of the rectangle is 24 cm and the breadth is 18 cm.
What is the difference between a difference of two squares and a perfect square trinomial?
Depending on whether a and b are real numbers, they can factor as (a + b) (a + b) or (a - b)(a - b). Forms like (a + b)(a - b) are unique products also known as the difference of squares.
what is perfect square ?When you square an integer, you get perfect squares. The number 81, for example, is a perfect square since it can be derived by squaring 9: 99=81. Because 12 can be squared to make 144, 144 is a perfect square. 13 may be squared to make 169, which is a perfect square. Mathematics-related language. Informally: When an integer (a "whole") number is multiplied by itself, whether the result is positive, negative, or zero, the result is referred to as a square number, a perfect square, or simply "a square." All square numbers are therefore 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on.
given
Perfect square trinomials, also referred to as trinomial squares, are the squares of binomial expressions.
Depending on whether a and b are real numbers, they can factor as (a + b)(a + b) or (a - b)(a - b). Forms like (a + b)(a - b) are unique products also known as the difference of squares.
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