To find the circle with center (3, -4) and radius 64, we again replace 64 with 64² in the equation, and get:
(x - 3)² + (y + 4)² = 4096
What would be a circular example?Several everyday items, such as turning ceiling fans, turning car wheels, spinning windmill blades, and turning gas turbine gears, exhibit circular motion. Another is an earth-orbiting satellite that was built by people.
The equation (x + 3)² + (y - 4)² = 64 represents a circle with center (-3, 4) and radius 8.
To find the circle with center (-3, 4) and radius 64, we replace 64 with 64² in the equation and get:
(x + 3)² + (y - 4)² = 4096
This circle has center (-3, 4) and radius 64.
To find the circle with center (3, -4) and radius 8, we replace (x + 3) with (x - 3) and (y - 4) with (y + 4) in the equation, and get:
(x - 3)² + (y + 4)² = 64
This circle has center (3, -4) and radius 8.
To find the circle with center (3, -4) and radius 64, we again replace 64 with 64² in the equation, and get:
(x - 3)² + (y + 4)² = 4096
This circle has center (3, -4) and radius 64.
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some students have a goal of collecting 200 leaves for a science project. what does the 0% mean in this situation?what does 100% mean
0% would indicate that the kids have not gathered any leaves for the scientific project, and 100% would indicate that they have succeeded in collecting 200 leaves.
Why is percentage important?In mathematics, a percentage is a quantity or a ratio that is expressed as a fraction of 100. Calculating a percentage involves multiplying a quantity by 100 and dividing it by the total.
To determine "how much" or "how many," utilise the percentage. Calculating the precise quantity or figure that is being discussed is made easier with the use of a percentage. We compare fractions. determining a percentage rise or fall aids in calculating profit and loss margins.
In this case, 0% would indicate that the kids have not gathered any leaves for the scientific project, and 100% would indicate that they have succeeded in collecting 200 leaves for the project.
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find the x intercept and the y intercept for 6x-3y=-12
The x intercept and the y intercept for 6x - 3y = -12 is x = 0.5y + 2 and y = 2x - 4.
What are intercepts in graphs?The term “intercept” refers to the location where a line or curve crosses a graph's axis. The x-intercept is the point at which the x-axis is crossed. The y-intercept is the point at which the y-axis is crossed.
The line's steepness is measured by its slope (m). It is the difference between the y-coordinate change and the corresponding x-coordinate change. For 6x - 3y = 12, just enter the above coordinates and solve for m to obtain the slope.
To solve for x, we solve the equation so the variable x is by itself on the left side:
6x - 3y = 12
x = 0.5y + 2
To solve for y, we solve the equation so the variable y is by itself on the left side:
6x - 3y = 12
y = 2x - 4
Therefore, the x = 0.5y + 2 and y = 2x - 4.
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Which of these groups of values plugged into the TVM solver of a graphing calculator will return the amount of a 25 year loan with an APR of 16.8% compounded monthly, that is paid off with the monthly payment of 340?
A graphing calculator's tvm solver will calculate the monthly payment for a 25-year loan which comes to
N=300; I%=6.7; PV=-175000; PMT=; FV=0; P/Y=12; C/Y=12; PMT:END
What is TVM ?A TVM solver needs the loan amount as the Present Value (PV), zero as the Future Value (FV), and N as the actual number of payments (25×12 = 300) in order to determine the loan payment.
The annual interest rate is considered by solvers to be I%. The monthly interest rate is used an HP-12C financial calculator.
Here C contains the list of numbers required to calculate the monthly payment for this $175,000 loan at a 6.7% interest rate.
Cash flow typically has a negative sign for amounts paid and a positive sign for quantities received.
Here the available options indicate that the loan amount is negative while the payment amount is positive. Also, we anticipate receiving the loan amount and making the installments.
We are Given the aforementioned standards, the indicators, in this case, are the opposite of what we typically anticipate.
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Evaluate each expression for the set of values given in a table 28-c^3+6
The complete table:
c 1 2 3
28 - c³ + 6 33 26 7.
What is a quadratic function?A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.
Given:
A quadratic expression is 28 - c³ + 6.
Let A = 28 - c³ + 6.
When c = 1,
then A = 28 - 1³ + 6 = 28 - 1 + 6 = 33
When c = 2,
then A = 28 - 2³ + 6 = 28 - 8 + 6 = 26
When c = 3,
then A = 28 - 3³ + 6 = 28 - 27 + 6 = 7.
Therefore, all the required values are given above.
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For a certain are given as to. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.
Since odds in favor of a certain horse finishing in second place are given as 49 to 51 so number of outcomes in favor is m = 49
and number of outcomes not in favor n = 51
and total outcomes are m+n = 49 +51 = 100
The probability of a certain horse finishing in second place is 49 /100 = 0.49.
What is probability?The number of favourable outcomes to all possible outcomes of an event is the ratio, which is known as probability. For an experiment with 'n' number of outcomes, the symbol x can be used to indicate the number of excellent outcomes. The probability of an event can be calculated using the following equation:
x/n, where Probability is Favorable Outcomes/Total Results (Event)
The number of outcomes in favour is m = 49, the number of outcomes not in favour is n = 51, and the total outcomes are m+n = 49 + 51 = 100 because the chances in favour of a particular horse placing in second place are provided as 49 to 51.
The likelihood that a certain horse will place second is 49/100, or 0.49.
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The complete question is:
For a certain are given as to. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.
Orlando went to a game room that charged $3 admission, plus 0.50 per token. The equation which represents his total cost is y=0.50x + 3. What are the ordered pairs for the equation when you use these x-values: 5, 10, 20?
In the equation, the ordered pair for x = 5 is (5, 5.5), the ordered pair for x = 10 is (10, 8), the ordered pair for x = 20 is (20, 13).
What does a linear equation look like in the slope-intercept form?A linear equation has the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept. The line's rate of change, or how steeply it rises or descends as we go down the x-axis, is indicated by the slope. The line's intersection with the y-axis, or the value of y when x is equal to 0, is represented by the y-intercept.
The given equation is:
y=0.50x + 3
Substituting the different values of x we find the required ordered pair as follows:
When x = 5:
y = 0.50(5) + 3 = 5/2 + 6/2 = 11/2 = 5.5
When x = 10:
y = 0.50(10) + 3 = 5 + 3 = 8
When x = 20:
y = 0.50(20) + 3 = 10 + 3 = 13
Therefore, the ordered pair for x = 5 is (5, 5.5), the ordered pair for x = 10 is (10, 8), the ordered pair for x = 20 is (20, 13).
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A petri dish of bacteria grow continuously at a rate of 200% each day. If the petri dish began with 10 bacteria, how many bacteria are there after 5 days? Use the exponential growth function f(t) = aert, and give your answer to the nearest whole number.
Answer: 320
Step-by-step explanation:
Multiply each time by 2 so 10*2=20 then 40, 80, 160, and 320
The figure shows a large square with an area of a^2 that contains a smaller square with an area of b^2. Describe the regions that represent a^2-b^2.
As a result, the total area of these four triangular regions, a2 - b2, represents the disparity between the two squares' surface areas.
what is triangle ?A triangle is a two-dimensional geometric shape with three straight edges and three angles. It is one of the fundamental geometric forms and can be categorised in various ways based on the sides and angles it has. Triangles are typically categorised according to their edges as follows: Equilateral triangles have three identical sides and three equal angles, each measuring 60 degrees. A triangle with an isosceles triangle has two edges that are equal and two angles that are equal.
A triangle called a scalene triangle lacks equal edges and angles.
given
The four triangular areas outside the smaller square but inside the bigger square are the regions that stand for a2 and b2.
Consider the size of the large rectangle, which is a2, to understand why this is the case. Consider the smaller square's size, which is b2.
These two areas vary by (a2) - (b2), which we can also write as:
(a + b)(a - b) (a - b)
According to this formula, the difference between the two squares' areas is equivalent to the product of their side lengths' sum and differences.
We can write the sum and difference of their side lengths as (a + b) and (a - b), respectively, because the big square's side length is a and the smaller square's side length is b.
The area of the four triangular areas outside the smaller square but inside the larger square is represented by the product (a + b)(a - b).
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Need Help Asap pls.........
Answer:
159
Step-by-step explanation:
So first you work on the (3 + 5) which is 8 but don't forget the ^2 so 8^2 is 64. Then you work on your next term which is 10^2 which is 100. So now our equation is 100 + 64 -5 and you can solve this by going left to right. So 100 + 64 is 164 then - 5 is 159.
Select the correct answer from each drop-down menu. The general form of the equation of a circle is 7x2 + 7y2 − 28x + 42y − 35 = 0. The equation of this circle in standard form is . The center of the circle is at the point , and its radius is units.
Answer:
The center of the circle is at the point (2, -3), and its radius is 4 units
Step-by-step explanation:
The equation of the circle in standard form can be obtained by completing the square for both x and y terms as follows:
7x^2 - 28x + 7y^2 + 42y - 35 = 0
7(x^2 - 4x) + 7(y^2 + 6y) = 35
7(x^2 - 4x + 4 - 4) + 7(y^2 + 6y + 9 - 9) = 35
7[(x - 2)^2 - 4] + 7[(y + 3)^2 - 9] = 35
7(x - 2)^2 + 7(y + 3)^2 - 112 = 0
7(x - 2)^2 + 7(y + 3)^2 = 112
Dividing by 112 on both sides, we get:
(x - 2)^2 + (y + 3)^2 / 16 = 1
Therefore, the equation of the circle in standard form is (x - 2)^2 + (y + 3)^2 / 16 = 1.
The center of the circle is at the point (2, -3), and its radius is 4 units.
Suppose you know that the radius of one circle is three times the radius of another circle. Explain how you can determine the ratio of the areas of the circles and the ratio of the circumferences of the circles without knowing the actual measurements.
The ratio for the area and the ratio for the circumferences of the circles are 9 : 1 and 6 : 1 respectively.
What is a circle?
A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the centre.
If the radius of one circle is three times the radius of another circle, then we can use this information to determine the ratio of the areas of the circles and the ratio of the circumferences of the circles without knowing their actual measurements.
Let's call the radius of the smaller circle "r" and the radius of the larger circle "3r".
Ratio of areas -
The area of a circle is proportional to the square of its radius, so the ratio of the areas of the two circles is -
= (area of larger circle) / (area of smaller circle)
= (π(3r)²) / (πr²)
= 9r²/r²
= 9/1
Therefore, the ratio of the areas of the two circles is 9:1.
Ratio of circumferences -
The circumference of a circle is proportional to its radius, so the ratio of the circumferences of the two circles is -
= (circumference of larger circle) / (circumference of smaller circle)
= 2π(3r) / 2πr
= 6r/r
= 6/1
Therefore, the ratio of the circumferences of the two circles is 6:1.
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Determine the exact surface area of the cylinder in terms of TT.
39 1/4
14 1/16
12 1/2
10 15/16
The surface area of the cylinder is 39 1/4
What is a Cylinder?Cylinder is is a three-dimensional solid consisting of two parallel circular bases joined together by a curved surface at a particular distance from the center of the circular bases. Cylinder has two flat ends in the shape of circles.
How to determine the surface area of cylinder
Surface area of cylinder is is the total space occupied by the flat circular bases of the cylinder and the curved surface.
Surface area = 2πrh + 2πr^2
Surface area = 2πr(r + h)
Where π = 22/7
r = 1 1/4 = 5/4
h = 3 3/4 = 15/4
SA = 2 * 22/7 * 5/4(5/4 + 15/4)
SA = 44/7 * 5/4(5)
SA = 44/7 * 6.25
SA = 39.2857 cm^2
Surface Area = 39 1/4 cm^2 is also related to 39.2857 cm^2
Therefore, the exact surface area of cylinder is 39 1/4 cm^2
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PLEASE HELP
Using the recursive formula given, find the first five terms of each sequence.
1.) A1 = 12, An=3An-1 -21, n≥2
2.) A1 = 1/2, An = An-1 + 3/2, n≥2
The first five terms of the given sequence are, 12, -9, 30, -51, -72....
What is a sequence?A sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
Given is the recursive formula, we need to find the first five terms of the sequence,
1) a₁ = 12, aₙ = 3 and aₙ₋₁-21 :-
a₂ = a₂₋₁ -21
= 12-21
= -9
a₃ = a₃₋₁-21
= -9-21
= -30
a₄ = a₄₋₁-21
= -30-21
= -51
a₅ = a₅₋₁-21
= -51-21
= -72
Hence, the first five terms of the given sequence are, 12, -9, 30, -51, -72....
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1. The circumcenter of ARST is A. What is the length of AT?
The correct option is D. For the circumcenter A of the triangle ∆RST, the length of AT is equal to 23.
What is the circumcenter of a triangleThe circumcenter of a triangle is the point where the perpendicular bisectors of the sides of the triangle intersect. This point is equidistant from the three vertices of the triangle and is the center of the circumcircle, which is the circle passing through all three vertices of the triangle.
Hence;
AS = AR = AT
3x - 7 = 2x + 3
3x - 2x = 7 + 3 {collect like terms}
x = 10
so;
AS = 3(10) - 7
AS = 30 - 7
AS = 23 and AT also is = 23.
Thus , for the circumcenter A of the triangle ∆RST, the length of AT is equal to 23.
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The fencing of the left border costs $8 per foot, while the fencing of the lower border costs $2 per foot. (No fencing is required along the river.) You want to spend $320 and enclose as much area as possible. What are the dimensions of your garden, and what area does it enclose?
The dimensions of the garden are 20 feet by 80 feet, and the area enclosed is 1600 square feet.
How is optimization employed in mathematics?
The process of selecting the optimal answer from a range of alternatives is known as optimization. In mathematics, optimization is employed to determine a function's maximum or least value. Typically, an optimization issue entails the optimization of a function under a set of restrictions.
Let's assume that the length of the left border is x feet.
The length of the lower border is y feet.
From the given situation the equation is:
8x + 2y = 320
To maximize the area of the garden, we maximize the product xy.
2y = 320 - 8x
y = 160 - 4x
Substituting this expression for y into the expression for the area, we get:
A = xy = x(160 - 4x) = 160x - 4x²
To find the value of x that maximizes the area, we can take the derivative of A with respect to x and set it equal to zero:
dA/dx = 160 - 8x = 0
x = 20
Substituting x = 20 back into the expression for y, we get:
y = 160 - 4x = 80
Therefore, the dimensions of the garden are 20 feet by 80 feet, and the area enclosed is: A = xy = (20)(80) = 1600 feet².
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Gwen purchased a fruit salad for $12 and two
watermelons to cut up and add to the fruit salad.
The watermelons cost the same amount, and all
the fruit was less than $22 in all. Write an
inequality to represent this situation. Then
complete the sentence.
Answer:27
6574
Step-by-step explanation:
Answer:
2x+12<22
Step-by-step explanation:
Bc I got it correct
Find the equation of the line shown.
I need it quick pls
The equation of the line shown is y = 2x.
What is a proportional relationship?In Mathematics, a proportional relationship can be defined as a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:
y = kx
Where:
x and y represents the variables or data points.k represents the constant of proportionality.Next, we would determine the constant of proportionality (k) as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 2/1 = 4/2
Constant of proportionality, k = 2.
Therefore, the required equation is given by:
y = kx
y = 2x
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How can I show my work for 7.540 - 4.826
PLEASE HELP ASAP !!!!!!
OPTIONS : YES OR NO
Answer:
Below
Step-by-step explanation:
Yes ..... multiply 'x' by '2' then add 3 to get the 'y' value
this is a line of the equation y = 2x + 3 LINEAR
In a board game, Maliq gets x points for landing on a red space, 2x points for landing on a blue
space, and 5x points for going all the way around the board. He lands on 21 red spaces, 19 blue
spaces, and goes around the board twice, for a total of 21x + 19 • 2x + 2 • 5x points. Which
expression also represents Maliq's total points?
a. (21+19) 2x + 10x
b. 42x
C. 69x
d. (21+19+2)(x + 2x + 5x)
The expression that represents Maliq's total points is given as follows:
C. 69x.
How to obtain the expressions?The amount of points for each landing is given as follows:
Red space: x points.Blue space: 2x points.All the way: 5x points.The number of times that Maliq landed on each space is given as follows:
21 red spaces.19 blue spaces.2 around the board.Hence the expression for the total points is given as follows:
21x + 19(2x) + 2(5x) = 21x + 38x + 10x = 69x.
(we multiply the terms and then combine the like terms, as all the terms have the variable x they are like terms).
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The median for the given set of six ordered data values is 31.5.
9 12 23 41 50
What is the missing value?
-
The missing value is
Answer:
Step-by-step explanation:
25
2
The model represents the quotient of two decimals.
PLEASE LOOK AT PIC TO DETERMINE
Which expression does this model represent?
A. 0.875 divided by 3.5
B. 3.5 divided by 0.875
C. 4.0 divided by 0.875
D. 0.875 divided by 4.0
Answer:
The model represents the division of the larger rectangle (3.5 units wide) into 4 equal parts, and shading 1 part of it.
This means that the division is 3.5 divided into 4 parts, with each part being equal to the smaller rectangle with a width of 0.875.
Therefore, the expression represented by the model is:
B. 3.5 divided by 0.875
Step-by-step explanation:
13. If 30% of the pupils in a school are boys, what percentage of the pupils are girls?
Answer:
70%
Step-by-step explanation:
100%-30%=70%
fxbhctcybyvybuninuvtxectb
Refer to the sample data for pre-employment drug screening shown below. If one of the subjects is randomly selected, what is the probability that the test result is a false positive? Who would suffer from a false positive result? Why?
Pre-Employment Drug Screening Results
Positive test result
Negative test result
Drug Use Is Indicated
Drug Use Is Not Indicated
Subject Uses Drugs
46
8
Subject Is Not a Drug User
1
30
Question content area bottom
Part 1
The probability of a false positive test result is enter your response here.
(Round to three decimal places as needed.)
The probability of a false positive test result is approximately 0.267 or 0.267 probability units.
What is probability?Probability is the measure of the likelihood or chance that an event will occur, expressed as a number between 0 and 1.
For example, the probability of rolling a six on a fair dice is 1/6 or approximately 0.167. It is a fundamental concept in statistics and plays a crucial role in many real-life applications, such as decision-making, risk analysis, and scientific research.
To find the probability of a false positive test result, we need to calculate the proportion of individuals who test positive but do not use drugs out of the total number of individuals. This is represented by the ratio of the number of false positives to the total number of negative test results, which is:
(false positives) / (negative test results) = 8 / 30 = 0.267
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The scale of the model is 1 inch = 9 feet. The fountain at the center of the city is 18 1/2 feet wide. How wide is the fountain in the model?
Answer: 2.05 repeating
Step-by-step explanation:
18/2= 2
1/2 feet goes into 9 18 times so 1/18 = .055 repeating
P (5,-4) and Q (-1,-2) are points on a straight line. Find the equation of the perpendicular
bisector of PQ; giving the answer in the form y=mx+c.
To find the equation of the perpendicular bisector of PQ, we need to first find the midpoint of PQ, and then determine the slope of the line perpendicular to PQ that passes through this midpoint.
The midpoint of PQ is given by the formula:
((x1 + x2) / 2, (y1 + y2) / 2)
where (x1, y1) = (5, -4) and (x2, y2) = (-1, -2)
So, the midpoint of PQ is:
((5 - 1) / 2, (-4 - 2) / 2) = (2, -3)
Now, the slope of the line PQ can be found using the formula:
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) = (5, -4) and (x2, y2) = (-1, -2)
So, the slope of PQ is:
(-2 - (-4)) / (-1 - 5) = 2/3
Since the perpendicular bisector of PQ will have a slope that is the negative reciprocal of the slope of PQ, the slope of the perpendicular bisector is:
-1 / (2/3) = -3/2
Finally, we can use the point-slope form of the equation of a line to find the equation of the perpendicular bisector. We know that the line passes through the point (2, -3), and has a slope of -3/2. So, the equation of the line is:
y - (-3) = (-3/2)(x - 2)
Simplifying this equation, we get:
y + 3 = (-3/2)x + 3
y = (-3/2)x + 0
Hence, the equation of the perpendicular bisector of PQ is y = (-3/2)x.
Wyatt earns a base salary of $250 per week and 3% commission on sales. If he sells $10,000 worth of goods this week, what would his paycheck be
Wyatt's paycheck for the week would be $550.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
To calculate Wyatt's paycheck, we need to determine his total earnings for the week.
His earnings from his base salary are simply $250.
To calculate his earnings from commission, we need to determine 3% of his sales.
3% of $10,000 is:
0.03 * 10000 = $300
So Wyatt's earnings from commission would be $300.
Adding his base salary and commission together, we get:
$250 + $300 = $550
Therefore, Wyatt's paycheck for the week would be $550.
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A ball is thrown upward with an initial velocity of 75 feet per second and an initial height of 4 feet. Given h(t) = −16t2 + v0t + h0, complete function h to model the vertical motion of the ball. Then find the ball’s maximum height, to the nearest foot.
The highest height of the ball, to the closest foot, is stated to be around 88 feet.
What is velocity, for instance?Velocity may be referred to as the speed when something moves toward a particular location. as the rate of a car driving northwest on a highway or the pace at which a rocket takes off.
The function h(t) = −16t² + v0t + h0 models the vertical motion of the ball, where t is time in seconds, v0 is the initial velocity in feet per second, and h0 is the initial height in feet.
In this case, the beginning height is 4 feet, and the velocity of the fluid equals 75 feet per second. As a result, the following outlines the function h(t) which it simulates the ball's vertical motion:
h(t) = -16t² + 75t + 4
The point of the concave function h must be located in order to determine the ball's peak (t) = -16t² + 75t + 4.
The t-coordinate of the vertex is given by t = -b/2a, where a = -16 and b = 75. Substituting these values, we get:
t = -75 / (2 x (-16)) = 2.34375
We enter this t quantity into the procedure h(t) to get the maximum height:
h(2.34375) = -16(2.34375)² + 75(2.34375) + 4 = 87.74
To the nearest foot, the ball therefore achieves a peak of 88 feet.
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True or False. The point (-1/5, -3/2)
Lies on the graph of f(x).
True; the point (-1/5, -3/2) does lie on the graph of f(x) = 7.5x.
How to determine the true statementFrom the question, we have the following parameters that can be used in our computation:
f(x) = 7.5x
The point is given as
(x, y) = (-1/5, -3/2)
To determine whether the point (-1/5, -3/2) lies on the graph of f(x) = 7.5x, we can substitute x = -1/5 into the equation and see if it gives us y = -3/2.
f(x) = 7.5x
By substitution, we have
f(-1/5) = 7.5(-1/5)
Evaluate
f(-1/5) = -1.5
Express as fraction
f(-1/5) = -3/2
So, the point (-1/5, -3/2) does lie on the graph of f(x) = 7.5x.
Hence, the statement is false.
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Complete question
True or False. The point (-1/5, -3/2) lies on the graph of f(x).
Where f(x) = 7.5x
Identify the factor pair of ac you could use to rewrite b to factor the trinomial by grouping.
3x²2² +11x-4
The factors of ac are
(Use a comma to separate answers as needed.)
(x+4), (3x-1) are the required factors in the given trinomial solution.
The solution provided below has been developed in a clear step by step manner.
Step: 1
Given polynomial is 3x²2² +11x-4
=3x(x+4)-1(x+4)
=(x+4)(3x-1)
Explanation: Please refer to solution in this step.
Step: 2
(x+4), (3x-1) are the required factors
A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them. Factors can be found using either division or multiplication.
Learn more about factors here brainly.com/question/14549998
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