A police car is located 40 feet to the side of a straight road.
A red car is driving along the road in the direction of the police car and is 140 feet up the road from the location of the police car. The police radar reads that the distance between the police car and the red car is decreasing at a rate of 85 feet per second. How fast is the red car actually traveling along the road?
The actual speed (along the road) of the red car is feet per second
The actual speed (along the road) of the red car is 8.37 feet per second
To solve this problem
Let's call the distance between the police car and the red car "x" at time t. Then, we know that:
x^2 = 40^2 + (140 - vt)^2
Where
v is the velocity of the red car (in feet per second) t is timeWe are given that dx/dt (the rate at which x is decreasing) is -85 ft/s, so:
d/dt [x^2] = d/dt [40^2 + (140 - vt)^2]
2x(dx/dt) = 0 - 2v(140 - vt)
Substituting dx/dt = -85 and solving for v, we get:
2x(−85) = −2v(140−vt)
−170x = −280v + 2v^2t
v^2t = 140v - (85/2)x
Now, we can differentiate the equation x^2 = 40^2 + (140 - vt)^2 with respect to time to get:
2x(dx/dt) = 2(140 - vt)(-v)
Substituting dx/dt = -85 and solving for x, we get:
-170x = -2v(140 - vt)
x = (140v - vt^2)/85
Substituting this expression for x into the equation we derived earlier, we get:
v^2t = 140v - (85/2)((140v - vt^2)/85)
v^2t = 140v - 70(2v - t^2)
v^2t = 140v - 140v + 70t^2
v^2t = 70t^2
v = sqrt(70t^2)/t = sqrt(70) = 8.37 ft/s (rounded to two decimal places)
Therefore, the actual speed (along the road) of the red car is 8.37 feet per second
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Savvas Realize
8-6: MathXL for School: Practice & Problem Solving
★ Start Page
0 Assignment is past due (
The circumference of the hub cap of a tire is 83.90 centimeters. Find the area of this hub cap. Use 3.14 for x. Use pencil and paper. If the circumference
were smaller, explain how this would change the area of the hub cap.
The area of this hub cap is about 560 square centimeters.
(Round the final answer to the nearest whole number as needed. Round all intermediate values to the nearest thousandth as needed.)
It can be seen that if the circumference were smaller, the area would decrease, as it is proportional to the square of the radius.
How to solveGiven the circumference (C) of the hub cap as 83.90 cm, we can find the radius (r) using the formula C = 2 * π * r,
where π = 3.14.
Thus, r ≈ 13.363 cm.
To find the area (A), use the formula A = π * r^2, yielding A ≈ 560.509 cm². Rounded, the area is about 561 cm².
Therefore, it can be seen that if the circumference were smaller, the area would decrease, as it is proportional to the square of the radius.
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Betty has 30 mls of cough medicine with breakfast.
She drinks half of her 4 ounce orange juice, and 25% of her 8 oz cup of coffee. How many mls total
did she consume?
Betty consumed a total of 148.294 milliliters of liquid with her breakfast.
To solve this problemWe can change the volumes of the coffee and orange juice to milliliters so that all of the measurements are in the same unit:
4 ounces = 4 * 29.5735, = 118.294 ml.
8 ounces = 8 x 29.5735, = 236.588 ml.
Half of Betty's 4-ounce glass of orange juice, or:
1/2 * 118.294 mls = 59.147 mls
She consumed 25% of her 8-ounce coffee, which is :
0.25 * 236.588 mls = 59.147 mls.
So, in total, Betty consumed:
30 mls of cough medicine + 59.147 mls of orange juice + 59.147 mls of coffee = 148.294 mls
Therefore, Betty consumed a total of 148.294 milliliters of liquid with her breakfast.
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Find the area of parallelogram WXYZ. Round your answer to the nearest tenth if
necessary.
21 in
18 in
21 in
23.2 in
23.2 in
Answer:
378in^2 i think
Step-by-step explanation:
A scatter plot is shown on a coordinate plane. The x-axis is numbered 0 to 15 and the y-axis is numbered from 2 to 26 in increments of 2. Points shown are located at (7, 2), (9, 1), (11, 3), (7, 6), (5, 8), (8.5, 8), (3, 12), (6, 13), and (4, 16). A line of best fit goes through points (5, 12) and (9, 4) and is extended to show it approaching the points (0, 22) and (11, 0).
Which equation represents the line of best fit?
The equation represents the line of best fit is y = -2x + 22.
What is an equation?A mathematical statement that represents a relationship between two or more quantities is typically expressed using symbols, numbers, and mathematical operations. Equations are used to express mathematical relationships, make predictions, and solve problems. An equation typically consists of an expression on each side of an equal sign (=), indicating that the values on both sides are equivalent.
According to the given information:
To determine the equation of the line of best fit in the scatter plot, we can use the slope-intercept form of a linear equation, which is given by:
y = mx + b
where m is the slope and b is the y-intercept.
Given that the line of best fit goes through points (5, 12) and (9, 4), we can calculate the slope (m) using the formula:
m = [tex]\frac{(y_{2}-y_{1})}{(x_{2}-x_{1} ) }[/tex]
Plugging in the values from the given points, we get:
m = [tex]\frac{(4-12)}{(9-5)}[/tex]
m = -8 / 4
m = -2
So, the slope of the line of best fit is -2.
Next, we can substitute the slope and one of the given points (5, 12) into the slope-intercept form to solve for the y-intercept (b):
12 = -2(5) + b
12 = -10 + b
b = 12 + 10
b = 22
So, the y-intercept of the line of best fit is 22.
Thus, the equation of the line of best fit is:
y = -2x + 22.
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Question
Each answer choice below represents a relation by a set of ordered pairs. In which of the answer choices is the relation a function?
Select all correct answers.
Select all that apply:
{(2,−5),(−2,0),(−3,6),(2,−4)}
{(−1,5),(−4,8),(−4,14),(2,6)}
{(1,3),(−2,−1),(4,3),(8,1)}
{(−2,−5),(7,1),(7,−3),(4,−1)}
{(8,8),(4,1),(1,6),(−5,6)}
Answer:
(c) {(1,3),(−2,−1),(4,3),(8,1)}(e) {(8,8),(4,1),(1,6),(−5,6)}Step-by-step explanation:
You want the lists of ordered pairs that represent a functional relation.
FunctionA function maps an input value to exactly one output value. A set of ordered pairs will represent a function if no input (x-value) is repeated.
We only need to look at the first values of the ordered pairs.
(a) 2 is repeated
(b) -4 is repeated
(c) a function
(d) 7 is repeated
(e) a function
Answer:
(c) {(1,3),(−2,−1),(4,3),(8,1)}(e) {(8,8),(4,1),(1,6),(−5,6)}Step-by-step explanation:
You want the lists of ordered pairs that represent a functional relation.
FunctionA function maps an input value to exactly one output value. A set of ordered pairs will represent a function if no input (x-value) is repeated.
We only need to look at the first values of the ordered pairs.
(a) 2 is repeated
(b) -4 is repeated
(c) a function
(d) 7 is repeated
(e) a function
The histogram below gives the distribution of test scores for a sample of
students in a school in Alaska. Approximately how many students received a
score between 70.5 and 80?
Answer:
B. 200 students
Step-by-step explanation:
An air traffic controller is tracking two planes. To start, Plane A is at altitude of 2639 feet and Plane B is just taking off. Plane A is gaining altitude at 35.25 feet per second and Plane B is gaining altitude at 80.75 feet per second
How many seconds will pass before the planes are at the same altitude?
What will their altitude be when they're at the same altitude?
Answer:
Step-by-step explanation:
To find the number of seconds it will take for the planes to be at the same altitude, we need to set the altitude equations for both planes equal to each other and solve for time:
2639 + 35.25t = h (altitude equation for Plane A)
0 + 80.75t = h (altitude equation for Plane B)
where h is the altitude of both planes when they are at the same altitude, and t is the number of seconds that have passed.
Setting the two equations equal to each other and solving for t, we get:
2639 + 35.25t = 80.75t
45.5t = 2639
t = 58
Therefore, it will take 58 seconds for the planes to be at the same altitude.
To find their altitude at that time, we can substitute t = 58 into either of the altitude equations and solve for h:
2639 + 35.25t = h
2639 + 35.25(58) = h
h = 4818.5
Therefore, when the planes are at the same altitude, their altitude will be approximately 4818.5 feet.
What is the area of a right triangle with a height of 6 1/4 yards and base of 22 yards
Answer:
The area should be 0.5 * b * h
Step-by-step explanation:
B stands for the base of the triangle and H is the height
Find the x-intercept and y-intercept of this equation.
y = 4x + 7
Question 10 options:
x-intercept (4,0), y-intercept (0,7)
x-intercept (-7,0), y-intercept (0,-4)
x-intercept (7/4, 0), y-intercept (0,-4/7)
x-intercept (-7/4, 0), y-intercept (0,7)
The intercepts of the equation are: D. D. x-intercept (-7/4, 0), y-intercept (0,7).
What is the X-intercept and Y-intercept of a Linear Equation?The x-intercept of an equation is simply the value of x when the corresponding value of y equals zero. Also, this is where the line of the equation cuts across the x-axis on a graph.
The y-intercept of an equation, on the other hand, is the value of y when the corresponding value of x equals zero. It is the point where the line of the equation cuts across the y-axis on a graph.
Thus, given the equation y = 4x + 7, the y-intercept is:
y = 4(0) + 7
y = 7
The x-intercept is:
0 = 4x + 7
-4x = 7
x = 7/-4
x = -7/4
The correct option is: D. x-intercept (-7/4, 0), y-intercept (0,7).
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Need help with this problem
The sales tax on 250 dollars purchase is: $3865
How to find the equation model?We are told that sales tax is directly proportional to retail price. Thus:
S ∝ p
Any item that sells for 158 dollars has a sales tax of 10.22 dollars. Thus:
158 = 10.22k
where k is constant of proportionality
Thus:
k = 158/10.22
k = 15.46
Thus, the equation is:
S = 15.46p
Sales tax on 250 dollars purchase is:
S = 15.46 * 250
S = $3865
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Calculus derivatives. Find f(x).
The solution equates to f(x) = 6x + 8.
How to explain the functionReiterating the same statement without reiteration, it is observed that f'(x) equals ƒ""(x), ultimately resulting in a value of 6. Subsequently, we can derive a complete expression for f(x) where C represents an integration constant.
It should be noted that to find this constant, since f(-1) = 2, plugging in x as -1 and f(x) as 2 into the above equation results in:
2 = 6(-1) + C
C = 8
As such, we can confirm that the entire expression of f(x) is simply 6 times x added to 8. Validating this answer, when assessing f(0) or f(1) , either result should match the given values from our initial problem which they do. Hence, the solution equates to:
f(x) = 6x + 8.
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To compare the dry braking distances from 30 to 0 miles per hour for two makes of automobiles, a safety engineer conducts braking tests for 35 models of Make A and 35 models of Make B.
The mean braking distance for Make A is 42 feet. Assume the population standard deviation is 4.6 feet.
The mean braking distance for Make B is 45 feet. Assume the population standard deviation is 4.3 feet.
At α = 0.10, can the engineer support the claim that the mean braking distances are different for the two makes of automobiles?
Assume the samples are random and independent, and the populations are normally distributed.
(a) Identify the claim and state H_0 and H_a
(The mean braking distance is different for the two makes of automobiles.)
What are H_0 and H_a?
(b) Find the critical value(s) and identify the rejection region(s).
(c) Find the standardized test statistic z for μ_1 - μ_2
z = _____
(d) Decide whether to reject or fail to reject the null hypothesis.
(e) Interpret the decision in the context of the original claim.
Upper Critical Value; 1.645
p-Value; 0.0814
Reject the null hypothesis
How to solvea).
claim: A. The mean breaking distance is different for the two makes of automobiles
H0 and Ha.: E
[tex]\ H_0: \mu_1 = \mu_2 \ \ \ H_a: \mu_1 \neq \mu_2[/tex]
b).
critical values are (-1.645, 1.645)
Rejection region: E. z < -1.645 , z >1.645
c)
test statistic z= -1.743
d).
C. Reject H0. The stat statistic falls in the rejection region.
e).
At the 10% significance level, there is sufficient evidence to support the claim that means breaking distance of make A is different from mean breaking distance of making B.
m 2
M1
7t
Z Test for Differences in Two Means
Data
Hypothesized Difference
0
Level of Significance
0.1
Population 1 Sample
Sample Size
35
Sample Mean
42
Population Standard Deviation
4.9
Population 2 Sample
Sample Size
35
Sample Mean
44
Population Standard Deviation
4.7
Intermediate Calculations
Difference in Sample Means
-2
Standard Error of the Difference in Means
1.1477
Z Test Statistic
-1.7427
Two-Tail Test
Lower Critical Value
-1.645
Upper Critical Value
1.645
p-Value
0.0814
Reject the null hypothesis
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Calculate the area of the composite figure shown
The total area of the given figure is 525 cm² respectively.
What is the area?The area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.
The area of a plane figure is the area that its perimeter encloses.
The quantity of unit squares that cover a closed figure's surface is its area.
So, first, we will divide the figure into 2 parts which will be the triangle and the rectangle, and then add their area to get the total area as follows:
Triangle:
1/2 * b * h
1/2 * 15 * 20
15 * 10
150 cm²
Rectangle:
l*b
15*25
375 cm²
The total area of the figure: 375 + 150 = 525 cm²
Therefore, the total area of the given figure is 525 cm² respectively.
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In a different plan for area codes, the first digit could be any number from 1 through 7, the second digit was either 3, 4, 5, 6, and the third digit could be any number except 6, 7, or 8. With this plan, how many different area codes are possible?
Answer:
196
Step-by-step explanation:
There are 7 choices for the first spot.
4 choices for the second spot. And 7 choices for the third spot, which cannot be 6,7,8--so it can be 0,1,2,3,4,5 or 9 (7choices)
7 × 4 × 7 is 196
There are 196 possibilities for the three digit area code with this plan.
Hannah is working in England for 3 months on a project for her company. One weekend Hannah decides to go to France with her car on the ferry, then explore the French countryside. In England, speed limit signs are posted in miles per hour (mph) and Hannah's rental car only shows the speed in miles per hour. In France, speed limit signs are posted in kilometers per hour (kph). Hannah looks up the conversion and learns that 1 kph = 0.62 mph.
On the road that Hannah is currently on, the posted speed limit is 130 kilometers per hour. What is the maximum whole-number speed, in miles per hour, that Hannah can drive without exceeding the speed limit?
A. 82 mph
B. 79 mph
C. 209 mph
D. 80 mph
Answer:
To convert kilometers per hour to miles per hour, we need to multiply by 0.62. Therefore, to find the maximum speed that Hannah can drive without exceeding the speed limit of 130 kilometers per hour, we can multiply 130 by 0.62:
130 km/h * 0.62 = 80.6 mph
Since Hannah needs to stay within the speed limit, the maximum whole-number speed she can drive is 80 mph, which is option D.
Step-by-step explanation:
If a scatter plot has a pattern that is best fit by y=x2, we say that it has a property that displays a linear or a nonlinear pattern?
The scatter plot that has a pattern that is best fit by y = x^2 has a property that displays a nonlinear pattern
Describing the property of the scatter plotFrom the question, we have the following parameters that can be used in our computation:
Equation of the best fit of the scatter plot: y = x^2
As a general rule
Any equation that has a degree other than 1 is a non linear equation
This means that the property it displays is a nonlinear pattern
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it takes 2/3 of a gallon of paint to cover 3/4 of a wall. How many gallons of paint are needed to cover a full wall?
In January, the amount of snowfall was 5 2/3 feet. In February, the amount of snowfall was 3 1/5 feet. What was the amount of snowfall in the two months combined? Write your answer as a mixed number in simplest form.
Answer:
8 13/15
Step-by-step explanation:
Multiply the fractions so they both have the least common denominator:
5 2/3 = 5 10/15
3 1/5 = 3 3/15
Now, you can add the two mixed numbers:
[tex]5 \frac{10}{15} + 3 \frac{3}{15} = 8 \frac{13}{15}[/tex]
This is your final answer.
the angle of elevation from the horizontal to the sun is 38°. How long of a shadow would a 32 foot tree make at this time?
The length of the shadow would be approximately 41.7 feet if the angle of elevation from the horizontal to the sun is 38° at this time.
If the angle of elevation from the horizontal to the sun is 38°, then the tangent of that angle is equal to the opposite side (the height of the tree) divided by the adjacent side (the length of the shadow).
Therefore, we can set up the equation using trigonometric function tangent as,
tan(38°) = height of tree / length of shadow
Solving for the length of the shadow, we get:
length of shadow = height of tree / tan(38°)
Plugging in the given height of the tree (32 feet) and using a calculator to find the tangent of 38°, we get:
length of shadow = 32 / tan(38°) = 41.7 feet (rounded to one decimal place)
Therefore, the length of the shadow would be approximately 41.7 feet at this time.
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This diagram shows a cube. Each edge of the cube is 13 units long. The diagonal of each face is x units long. The diagonal of the cube is y units long.
Find x and y. If necessary, round your answers to the nearest tenth.
The value of x is 18.4 and the value of y is 22.5 in the cube
Finding the values of x and yFrom the question, we have the following parameters that can be used in our computation:
The diagram of a cube.
Each edge of the cube = 13 units.
The diagonal of each face is x units long
So, we have
x^2 = 13^2 + 13^2
Evaluate
x = 18.4
The diagonal of the cube is y units long.
So, we have
y^2 = 13^2 + 13^2 + 13^2
Evaluate
y = 22.5
Hence, the value of x is 18.4 and the value of y is 22.5
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Ms. Shaddai writes 3q = 51 and \{15, 16, 17\} on the board. Tell if each value in the set is a solution of the equation. Show your work.
Only 17 is a solution of the equation 3q = 51 among the values in the set {15, 16, 17}.
How to find out if each value in the set is a solution of the equation?To check if a value is a solution of the equation 3q = 51, we substitute the value for q and check if the equation is true.
Let's check each value in the set {15, 16, 17}:
For q = 15, 3q = 3(15) = 45, which is not equal to 51. Therefore, 15 is not a solution of the equation 3q = 51.
For q = 16, 3q = 3(16) = 48, which is not equal to 51. Therefore, 16 is not a solution of the equation 3q = 51.
For q = 17, 3q = 3(17) = 51, which is equal to 51. Therefore, 17 is a solution of the equation 3q = 51.
Therefore, only 17 is a solution of the equation 3q = 51 among the values in the set {15, 16, 17}.
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Please answer quickly!!! I'll give BRAINLIEST!!!!! I attached the picture.
Answer: No.
Step-by-step explanation:
The graph doesn't represent a linear, exponential, or quadratic function.
An example of a linear function is a straight line.
An example of a quadratic function is like a smile.
An example of an exponential function is a curved line.
So hence, this doesn't represent a function.
Reply below if you have any questions of concerns.
You're welcome!
- Nerdworm
Find the equation of a line parallel to 5x+y=5 that passes through the point (8,-9)
Answer:
y = -5x + 31
Step-by-step explanation:
To find the equation of a line parallel to the line 5x + y = 5, we first need to rearrange it in slope-intercept form, which is
y = -5x + 5. (We see that the slope of this line is -5)
A line parallel to this line will have the same slope of -5. Now, we need to find the equation of a line that passes through the point (8,-9) with slope -5.
We can use the point-slope form of the line to find the equation. The point-slope form of a line is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.
Substituting the values we have, we get:
y - (-9) = -5(x - 8)
Simplifying this equation, we get:
y + 9 = -5x + 40
y = -5x + 31
Therefore, the equation of the line parallel to 5x + y = 5 that passes through the point (8, -9) is y = -5x + 31.
Find the area of the following figure:
Answer: 61,6 in.
Step-by-step explanation:
To find the area of trapezoids with parallel bases, we add the length of the lower base to the length of the upper base.
[tex]12+10=22[/tex]Then we multiply this value by the height.
[tex](5.6).22=123.2[/tex]Finally, we divide the resulting value by [tex]2[/tex].
[tex]123.2/2=61.6[/tex]3 A system of two linear equations is graphed on a coordinate plane. If the system of
equations has infinitely many solutions, which statement must be true?
a. On the graph, there are no points (x, y) that satisfy both equations.
b. On the graph, there is exactly one point (x, y) that satisfies both equations.
c. On the graph, any point (x, y) that satisfies one of the equations cannot satisfy the
other equation.
d.
On the graph, any point (x, y) that satisfies one of the equations must also satisfy
the other equation.
Answer:
d. On the graph, any point (x, y) that satisfies one of the equations must also satisfy the other equation.----------------------
If the system of linear equations has infinitely many solutions, it means the two lines overlap.
In other words, each point of one of the lines also belongs to the second line.
Choices a, b, c give us one or no solutions and therefore not the answer.
Choice d is reflecting the infinitely many solutions and hence is the correct one.
y = -x + 10 y = -x + 12
The solution to the given simultaneous equation y = -x + 10 ; y = -x + 12 is zero.
How to solve simultaneous equation?
y = -x + 10
y = -x + 12
Subtract both equations
y - y = -x -(-x) + 10 -12
0 = -x + x - 2
0 = 0 - 2
0 = -2
In conclusion, zero is the solution to the equation
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Carmine takes a loan for $11,500 at a rate of 8% that is compounded quarterly. Assuming she makes no payments for the first 2 years, what is her loan balance?
Carmine's loan balance after two years would be approximately $13,827.72.
Define the term loan?In mathematics, the term "loan" typically refers to a sum of money that is borrowed by one party from another with the agreement to repay it with interest over time. Loans are a common financial concept used in various areas of mathematics, such as finance, economics, and business.
What does compounded quarterly means?"Compounded quarterly" refers to a method of calculating interest or investment growth where the interest is added to the principal and then reinvested or recalculated at the end of each quarter (every three months) within a given time period.
To calculate Carmine's loan balance after two years, we need to use the compound interest formula, which is given by:
A = P ×[tex](1+r/n)^{nt}[/tex]
Where:
A = the loan balance after t years
P = the initial principal amount (loan amount) = $11,500
r = annual interest rate = 8% or 0.08 (expressed as a decimal)
n = number of times interest is compounded per year = 4 (since it is compounded quarterly)
t = time in years = 2 (since Carmine made no payments for the first two years)
Putting the values into the formula, we get:
A = 11,500 × (1 + 0.08/4)⁸
A = 11,500 × (1 + 0.02)⁸
A = 11,500 × (1.02)⁸
A ≈ $13,827.72
So, Carmine's loan balance after two years would be approximately $13,827.72.
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how do i find the area of this shape?
Answer:
(1/2)(12)(16) + (1/2)π(6^2)
= (96 + 18π) square cm
= about 152.55 square cm
The perimeter of a rectangle is 21.2 m, and its area is 23.68 m².
Find its length and width.
length: m
width: m