Answer:
A'(3, 1); B'(-2, 2); C'(-4, 6); D'(1, -4)-----------------------------------
The scale factor k affects the points with the rule:
(x, y) → (kx, ky)Apply the rule to the given points, given k = 1/2:
A(6, 2) → A'(3, 1);B(-4, 4) → B'(-2, 2);C(-8, 12) → C'(-4, 6);D(2, -8) → D'(1, -4)Jason conducted a survey amongst his friends to determine the amount of hours they watch TV each week. Here is the table that Jason found.
What statement is NOT true about the frequency chart?
Only 3 people did not watch TV each week.
The largest group of people were the ones who watched 1 hour per week.
70% of the people spent less than 1 hour watching TV a week
30% watch 2 hours or more on TV a week
The statement that is NOT true about the frequency chart is "70% of the people spent less than 1 hour watching TV a week".
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
The statement that is NOT true about the frequency chart is "70% of the people spent less than 1 hour watching TV a week". This is because according to the table, the percentage of people who spent less than 1 hour watching TV is 50%, which means that half of the people surveyed watched less than 1 hour of TV each week.
Therefore, The statement that is NOT true about the frequency chart is "70% of the people spent less than 1 hour watching TV a week".
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A person places $34300 in an investment account earning an annual rate of 2%, compounded continuously. Using the formula � = � � � � V=Pe rt , where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 17 years.
The amount of money in the account after 17 years is approximately $49,222.26.
Describe Investment?Investment is the act of allocating resources, such as money or time, with the expectation of generating a return or profit in the future. Investment can take many forms, such as investing in stocks, bonds, real estate, or businesses.
Investment is an important tool for individuals and businesses to build wealth and achieve financial goals. By investing in assets that appreciate in value or generate income, investors can increase their net worth and achieve long-term financial stability.
When making investment decisions, investors typically consider factors such as risk, return, liquidity, and diversification. Risk refers to the possibility of losing money, while return refers to the potential profit or income generated by the investment. Liquidity refers to how easily an investment can be converted into cash, while diversification refers to spreading investment across multiple assets to reduce risk.
Using the formula [tex]V= Pe^{rt}[/tex], where P = $34300, r = 0.02, and t = 17, we can find the value of the account after 17 years:
V = 34300 * [tex]e^{0.02*177[/tex]
V ≈ $49,222.26
Therefore, the amount of money in the account after 17 years is approximately $49,222.26.
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The graphs show the same data. Why do they have different appearances?
Hence, they are different because they drawn from the different scales values.
What is the data?Data in math is a collection of facts and figures that can be in any form—numerical or non-numerical.
Numerical data is the one you can calculate, and it is always collected in number form, such as scores of students in class, wages of workers in an organization or height of players on a football team, etc.
As per the given graphs they are different because they drawn with the help of different scales.
Hence, they are different because they drawn from the different scales values.
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A triangular piece of land has base 2 meter and height 10meter. if the land is 15 dolar per square meter what is its value
Answer:
150.00
Step-by-step explanation:
a = 1/2bh
a = 1/2(2)(10)
a = 10 [tex]m^{2}[/tex]
10x15 = 150
Helping in the name of Jesus.
What is the measurement of the fourth angle of a quadrilateral if the other angle’s measure 80 degrees 120 degrees and 65 degrees?
the measurement of the fourth angle of the quadrilateral is 95 degrees.
To find the measurement of the fourth angle of a quadrilateral when the measures of three angles are given, we can use the fact that the sum of the measures of the angles in a quadrilateral is 360 degrees.
Let's denote the measure of the fourth angle as x. Then we can write an equation:
80 + 120 + 65 + x = 360
Simplifying this equation, we get:
x = 360 - 80 - 120 - 65 = 95
Therefore, the measurement of the fourth angle of the quadrilateral is 95 degrees.
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Find an angle in each quadrant with a common reference angle with 165°, from 0°≤θ<360°
Answer:
Here are the angles in each quadrant with a common reference angle of 165°:
First quadrant: angle is 15° (subtract 165° from 180°)
Second quadrant: angle is 195° (subtract 165° from 180° and add the result to 180°)
Third quadrant: angle is 195° (subtract 165° from 180° and then subtract the result from 180°)
Fourth quadrant: angle is 195° (subtract 165° from 360°)
(5 1/2, - 7 1/2) and (5 1/2, - 1 1/2)
Answer:
Step-by-step explanation:
1) -2
2) 0
Please mark me Brainliest!!! <3 <3 <3
Which of the following is not a perfect square trinomial?
Group of answer choices
A. x^2+16x+64
B. x^2+7x+49
C. x^2+10x+25
D. 4x^2+16x+16
Answer:
B
Step-by-step explanation:
[tex]x^{2} +7x+49[/tex] is a prime equation.
Find the total surface area of this cylinder. Give your answer to 1 decimal place. 18 cm Feedback 24 cm
In light of this, the cylinder's total surface area falls between approximately 1017.9 cm²and 1357.2 cm².
Define the cylinder's entire surface area.A cylinder's total surface area is equal to the sum of all of its faces' surface areas. The cylinder's total surface area—the sum of its curved and circular areas—has a radius of "r" and a height of "h." The entire surface area of the cylinder is calculated as follows:
Define cylinder:Total Surface Area of Cylinder = 2r (h + r) square units.
The three-dimensional shape of a cylinder is made up of two parallel circular bases connected by a curved surface. It is seen as a prism since its base is a circular. It is frequently used as a container and can either be solid or hollow 13.
The following formula can be used to get a cylinder's total surface area:
A = 2πr² + 2πrh
where r is the cylinder's base's radius, h is the cylinder's height, and is a mathematical constant roughly equal to 3.14159.
Yet, we can locate a variety of potential surface areas using the provided information. With the assumption that the radius is equal to the feedback's half (9 cm), we can
after which, we can determine the surface area as follows:
A = 2π(9)² + 2π(9)(18) (18)
A= 2π(81) + 2π(2916)
A ≈ 1017.9 cm²
The surface area can be calculated as follows if we assume that the radius is equal to two-thirds of the feedback (i.e., r = 12 cm):
A = 2π(12)² + 2π(12)(18) (18)
A ≈ 1357.2 cm²
Complete question is given below:
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add [-6 -22] + [-3 2 1]
Answer:
-349
Step-by-step explanation:
1)[-6-22]+[-321]
2)(-28)-321
3)-349
How do I make x the subject of y=ax^2 + b
Answer:
Step-by-step explanation:
To make x the subject of y = ax^2 + b, we can use the following steps:
1.Subtract b from both sides to isolate the term with x^2:
y - b = ax^2
2.Divide both sides by a to isolate x^2:
(y - b) / a = x^2
3.Take the square root of both sides to solve for x:
x = ± sqrt((y - b) / a))
Therefore, the expression for x as a subject of y = ax^2 + b is:
x = ± sqrt((y - b) / a))
A(r(t))=\pi(0.25+2t+4t^2)
Explanation:
To write a composite function, we apply one function to another given function. In this case, we want to find area in terms of time; this means that the function A(r) gets applied to the function r(t).
In order to do this, we replace r with r(t). We already know that r(t)=0.5+2t; this means we replace r with 0.5+2t:
A(r(t))=π(0.5+2t)²
To simplify this, we simplify the squared term:
A(r(t)) = π(0.5+2t)(0.5+2t)
A(r(t)) = π(0.5*0.5+0.5*2t+2t*0.5+2t*2t)
A(r(t)) = π(0.25+t+t+4t²)
A(r(t)) = π(0.25+2t+4t²)
Answer:
So the composite function that gives the area of a circle in terms of time is:
A(r(t)) = π(0.25+2t+4t²)
Find the value of the derivative (if it exists) at the indicated extremum. (If an answer does not exist, enter DNE.)
The calculated value of the derivative f'(x) at x = -2/3 if f(x) = 5x√(x + 1) is f'(-2/3) = 0
How to find the value of the derivativeGiven the function
f(x) = 5x√(x + 1)
Factor out 5
So, we have
f(x) = 5[x√(x + 1)]
The derivative is then calculated using the following chain rule
f'(x) = 5[du/dx * dy/du]
When differentiated, we have
f'(x) = 5[√(x + 1) + x/2[√(x + 1)]]
This gives
f'(x) = 5[3x + 2/2[√(x + 1)]]
So, we have
f'(x) = [15x + 10]/[2√(x + 1)]
Substitute -2/3 for x
f'(-2/3) = [15(-2/3) + 10]/[2√((-2/3) + 1)]
Evaluate
f'(-2/3) = [0]/[2√1/3]
Evaluate the quotient
f'(-2/3) = 0
Hence, the value of the derivative is 0
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I need help with this question
The revenue for Jessicas Cafe in 2017 was 1.193 times larger than the revenue in 2016. 2. The revenue for Jessicas Cafe in 2017 represented 119.3% of the revenue in 2016.
What is fraction and percentage?A factor is a number that represents how two quantities are related to one another. It is frequently used to indicate how much one amount exceeds or falls short of another. For instance, if a business's revenue. On the other hand, a percentage is a technique to represent a portion or ratio of something as a fraction of 100. For instance, if a company made money.
The given revenue for the two years is $138200 and $164900.
The factor of the two revenue is:
factor = 164900 / 138200 = 1.193
Hence, the revenue for Jessicas Cafe in 2017 was 1.193 times larger than the revenue in 2016.
percentage = (164900 / 138200) * 100% = 119.3%
Therefore, the revenue for Jessicas Cafe in 2017 represented 119.3% of the revenue in 2016.
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Find the perimeter of 2cm, 4cm, 2cm, 5cm, 4cm, 1cm
Answer:
Step-by-step explanation:
The perimeter is the distance around the edge of the shape.
[tex]P=2+4+2+1+4+5=18cm[/tex]
Solve 2x^2+8x-3 by completing the square
Karen needs to find a courier to deliver a package the first courier charges a fee of $20 plus $2 per pound the second charges $12 plus $3 per pound karen determines that given her packages weight the two courier services are equivalent in terms of cost. how much will it cost? what is the weight?
Answer:
Step-by-step explanation:
Let's call the weight of Karen's package "w" in pounds.
For the first courier, the cost is given by:
Cost = 20 + 2w
For the second courier, the cost is given by:
Cost = 12 + 3w
We know that these costs are equivalent, so we can set them equal to each other:
20 + 2w = 12 + 3w
Simplifying this equation, we get:
8 = w
So the weight of Karen's package is 8 pounds.
To find the cost, we can plug this weight into either of the equations above:
For the first courier:
Cost = 20 + 2(8) = 36
For the second courier:
Cost = 12 + 3(8) = 36
So it will cost Karen $36 to deliver her package, and the weight of the package is 8 pounds.
2 PART QUESTION PLS HELP Harris has a spinner that is divided into three equal sections numbered 1 to 3, and a second spinner that is divided into five equal sections numbered 4 to 8. He spins each spinner and records the sum of the spins. Harris repeats this experiment 500 times.
Part A
Which equation can be solved to predict the number of times Harris will spin a sum less than 10?
A) 3/500 = x/15
B) 12/500 = x/15
C) 12/15 = x/500
D) 3/15 = x/500
QUESTION 2
Part B
How many times should Harris expect to spin a sum that is 10
or greater?
_______
The equation that can be solved to predict the number of times Harris will spin a sum less than 10 is B) 12/500 = x/15
Harris should expect to spin a sum of 10 or greater 240 times.
How to explain the equationIt should be noted that to predict the number of times Harris will spin a sum less than 10, we need to find the probability of getting a sum less than 10 and multiply it by the total number of experiments (500).
The possible sums that can be obtained are: 5, 6, 7, 8, 9, 10, 11, and 12. The probability of getting a sum less than 10 is the sum of the probabilities of getting each of these outcomes, which is:
P(sum less than 10) = P(1 and 4, 1 and 5, 2 and 4, 2 and 5, 3 and 4, 3 and 5)
= 6/15 * 2/5
= 4/25
Multiplying this probability by the total number of experiments (500), we get:
Number of times Harris will spin a sum less than 10 = (4/25) * 500 = 80
Therefore, the correct equation to predict the number of times Harris will spin a sum less than 10 is: 12/500 = x/15
Part B: Based on the information, the possible outcomes that give a sum of 10 or greater are: 10, 11, and 12. The probability of getting a sum of 10 or greater is the sum of the probabilities of getting each of these outcomes, which is:
P(sum of 10 or greater) = P(1 and 9, 2 and 8, 3 and 7, 4 and 6, 5 and 5, 6 and 4, 7 and 3, 8 and 2, 9 and 1, 8 and 3, 7 and 4, 6 and 5)
= 12/15 * 3/5
= 36/75
= 12/25
Multiplying this probability by the total number of experiments (500), we get:
Number of times Harris should expect to spin a sum of 10 or greater = (12/25) * 500 = 240
Therefore, Harris should expect to spin a sum of 10 or greater 240 times.
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Point B (8, -3) has been transformed. After a reflection over the x-axis, what is the coordinate of point B’?
The coordinate of point B' is (8, 3) after reflecting point B (8, -3) over the x-axis.
What is Reflection in geometry?A reflection is an involution: when applied twice in succession, every point returns to its original location, and every geometrical object is restored to its original state.
When a point is reflected over the x-axis, its y-coordinate changes sign while its x-coordinate remains the same.
Therefore, to find the coordinates of point B' after reflecting point B over the x-axis, we simply need to change the sign of the y-coordinate of point B.
Starting with point B at (8, -3), reflecting over the x-axis changes the sign of the y-coordinate, so the new point B' is at:
B' = (8, 3)
Therefore, the coordinate of point B' is (8, 3) after reflecting point B (8, -3) over the x-axis.
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30*8000(5-)1800=?
1500(800-)15000*18000=?
Answer:
1) 2160000000
2) 3.24 * 10^14
Step-by-step explanation:
30*8000(5-)1800
240000 * 5 * 1800
1200000 * 1800
2160000000
1500(800-)15000*18000
1200000 * 15000 * 18000
18000000000 * 18000
3.24 * 10^14
What generalization can you make about the equations?
A whole number by a unit fraction is the same as
About the equation [tex]7 * 3 = 21[/tex], the generalization we can make is that dividing a whole number by a unit fraction is the same as multiplying a whole number by the denominator of the unit fraction.
What is considered as generalization in mathematics?We use generalizations to describe the pattern they see in the relationship of a specific group of numbers. It's a pattern that holds true every time.
In mathematics, generalization can be defined as a statement that is true for an entire class of objects, the process by which we obtain a general statement, or the method by which knowledge is transferred from one setting to another.
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Help with math problems
The expressions whose solutions are represented by the graph are:
A. 5 - X > 4
D. 6x - 7 > 5
Which expressions have solutions on the graph?The mathematical expressions, whose solutions are represented by the graph are those that fall within the shaded region of the graph. For instance, in the mathematical expression, 5 - x > 4, the shaded region points to 4 and values greater than it.
So, this expression satisfies the condition and can be described as a solution represented by the graph.
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find the segment CB, knowing that the angle α is 25° and the segment AB is 8 cm.
After calculating the value of CB, we get a result of 3.45 cm. This means that the segment CB is 3.45 cm, given that the angle α is 25° and the segment AB is 8 cm.
CB = 8 cm * tan(25°)
≈ 3.45 cm
To find the segment CB, we need to use the tangent of the angle α (25°). We also need to know the length of the segment AB, which is 8 cm. To solve for CB, we use the equation CB = 8 cm * tan(25°). After calculating the value of CB, we get a result of 3.45 cm. This means that the segment CB is 3.45 cm, given that the angle α is 25° and the segment AB is 8 cm.
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if x is multiplied by 5 and then 3 is subtracted, then the function is f(x)=5x-3.
If x is multiplied by 5 and then 3 is subtracted, then the function is f(x)=5x-3. the inverse function of f(x) = 5x - 3 is f^(-1)(x) = (x + 3)/5.
How to find the inverse function?To find the inverse function of f(x) = 5x - 3, we need to follow these steps:
Step 1: Replace f(x) with y:
y = 5x - 3
Step 2: Solve for x in terms of y:
y = 5x - 3
y + 3 = 5x
x = (y + 3)/5
Step 3: Replace x with f^(-1)(x) and y with x:
f^(-1)(x) = (x + 3)/5
Step 4: Check if the inverse function is valid by verifying if f(f^(-1)(x)) = x and f^(-1)(f(x)) = x:
f(f^(-1)(x)) = f((x+3)/5) = 5((x+3)/5) - 3 = x + 2
f^(-1)(f(x)) = f^(-1)(5x - 3) = (5x - 3 + 3)/5 = x/5
Since f(f^(-1)(x)) = x + 2 and f^(-1)(f(x)) = x/5, the inverse function is valid.
Therefore, the inverse function of f(x) = 5x - 3 is f^(-1)(x) = (x + 3)/5.
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The complete question is:
if x is multiplied by 5 and then 3 is subtracted, then the function is f(x)=5x-3.
What are the step to find the inverse to this function?
need help
A car was valued at $44,000 in the year 1992. The value depreciated to $15,000 by the year 2006.
A) What was the annual rate of change between 1992 and 2006?
r=---------------Round the rate of decrease to 4 decimal places.
B) What is the correct answer to part A written in percentage form?
r=---------------%
C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2009 ?
value = $ -----------------Round to the nearest 50 dollars.
Rounding to the nearest 50 dollars, we get:
value = $12,550.
What is annual rate of change?The annual rate of change refers to the percentage change in a quantity over a period of one year. It is commonly used to express the growth or decline of economic indicators, such as GDP, inflation, or employment, as well as the performance of financial assets, such as stocks or bonds. To calculate the annual rate of change, you need to take the difference between the initial and final values of the quantity, divide it by the initial value, and multiply the result by 100 to express it as a percentage. For example, if a company's revenue was $1 million in 2021 and $1.2 million in 2022, the annual rate of change in revenue would be (1.2-1)/1 * 100 = 20%.
A) The car depreciated from $44,000 in 1992 to $15,000 in 2006, a period of 14 years.
The annual rate of change can be found using the formula:
[tex]r = (V2/V1)^{(1/n)} - 1[/tex]
where V1 is the initial value, V2 is the final value, and n is the number of years.
Substituting the given values, we get:
[tex]r = ($15,000/$44,000)^{(1/14)} - 1[/tex]
[tex]r = 0.0576[/tex]
So, the annual rate of change (or depreciation) is 0.0576.
B) To express this rate as a percentage, we can multiply it by 100 and add a percent sign:
[tex]r = 0.0576 x 100%[/tex]
[tex]r = 5.76%[/tex]
So, the car depreciated at an annual rate of 5.76%.
C) If we assume that the car value continues to drop by the same percentage, we can use the formula for exponential decay:
[tex]V = V0*(1-r)^t[/tex]
where V0 is the initial value, r is the rate of change, and t is the time elapsed.
Substituting the given values, we get:
[tex]V = $15,000*(1-0.0576)^3[/tex]
[tex]V = $12,527.31[/tex]
Rounding to the nearest 50 dollars, we get:
[tex]value=12,550[/tex]
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Please help brainlesst and pints
The ball will reach its maximum height after 3.5 seconds.
What is projectile motion?
Projectile motion is the motion of an object that is launched into the air and then moves along a curved path under the influence of gravity.
In projectile motion, the object follows a parabolic trajectory, which is a curve described by a quadratic function. The path of the object depends on the initial velocity, angle of projection, and acceleration due to gravity.
The key characteristics of projectile motion are that the object moves in two dimensions, typically horizontally and vertically, and that the motion in each dimension is independent of the other. This means that the horizontal and vertical components of motion can be analyzed separately.
The height function of the ball thrown The key characteristics of projectile motion are that the object moves in two dimensions, typically horizontally and vertically, and that the motion in each dimension is independent of the other. This means that the horizontal and vertical components of motion can be analyzed separately. is given by h(t) = 112t - 16t^2, where t is the time in seconds and h(t) is the height of the ball at time t.
To find the maximum height, we need to find the vertex of the parabolic function h(t). The vertex of a parabola given by the equation y = ax^2 + bx + c is located at x = -b/2a.
In the case of our height function h(t) = -16t^2 + 112t, the coefficient of the squared term is -16, and the coefficient of the linear term is 112. Therefore, the time at which the ball reaches its maximum height is given by:
t = -b/2a = -112/(2*(-16)) = 3.5
So, the ball will reach its maximum height after 3.5 seconds.
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I think you need to make an equation. Help Me!
Answer: h = 7
Step-by-step explanation:
63 = 1/2 * 18 * h
63 = 9 * h
63 = 9h
*Divide 9 on both sides.
7 = h
*Write the slope-intercept equation of the function f whose graph satisfies the given conditions.
The graph of f passes through (-12,7) and is perpendicular to the line that has an x-intercept of 1 and a y-intercept of -3.
What is the equation of the function ?
Answer: Slope-intercept form : y-y₁=m(x-x₁)
Passes through (-12, 7)
Slope = -5/3
m = slope
Simply plug everything in :)
y - y₁ = m(x - x₁)
y - 7 = -5/3(x + 12)
Simplify.
y - 7 = -5/3x - 20
Add 7 to both sides.
y = -5/3x = -13
~Hope I helped~
Step-by-step explanation:
Triangle QRS is shown below. Use the information given to determine the measure of ∠ R.
Angel Q= 38.2
Angel S= 52.7
Angel R=??
I’m so confused please help!
Answer: r=89.1
Step-by-step explanation: It has been given that,
PQ=PR
So, it is an isosceles triangle, hence ∠Q=∠R. let it be x
Now, we know that the sum of the angles of a triangle = is 180
∘
.
So,
∠P+∠Q+∠R=180
38.2+52.7+x=180
90.9+x=180
taking 90.9 in RHS it becomes -, so
x=180-90.9
x=89.1
Question Catherine randomly selects 10 books off of her bookshelf. She records the number of pages in the books in the table below. Use a calculator to create a histogram of the data, and then interpret the plot. Set Xmin to 100, Xmax to 250, and Xscl to 25. Number of Pages 227 142 165 180 145 162 121 195 160 174
1. Data is approx bell-shaped and symmetric
2. Median is between 150 to 175
What is a Histogram?A histogram is a graphical representation of a frequency distribution of a set of continuous data. It is used to display the shape of the data and to show how frequently certain values occur within a given range or interval.
In a histogram, the x-axis represents the range or interval of the data, and the y-axis represents the frequency of occurrence of values within each interval.
The data is divided into a set of bins or intervals, and the height of each bar on the histogram represents the number of data points that fall within that particular bin. The bars of the histogram are typically drawn adjacent to each other, with no gaps between them, to emphasize the continuity of the data.
Therefore, from the histogram used to represent the given data, it can be seen that the data is symmetric and also the median has the values between 150 to 175
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