Answers
Answer : see the image attached
Hence proved
Related Questions
A car travels along a straight road for 30 seconds starting at time t = 0. Its acceleration in ft/sec2 is given by the linear graph below for the time interval [0, 30]. At t = 0, the velocity of the car is 0 and its position is 10.
What is the velocity of the car when t = 6? Please show your work and include units in your answer.
Answers
The velocity experimented by the car is equal to - 1 feet per second.
What is the velocity of a car at a given time?
Herein we have the graph of the position of the car (y), in feet, versus time (t), in seconds. The graph shows a linear equation, that is, the position is described by a polynomial of the form:
y = m · t + b
Then, the functions for the velocity and acceleration are shown below:
Velocity
dy / dt = m
The slope represents the velocity of the car.
Acceleration
d²y / dt² = 0
Then, the velocity of the car is found by means of the secant line formula:
dy / dt = (0 ft - 10 ft) / (10 s - 0 s)
dy / dt = - 1 ft / s
The velocity of the car is - 1 feet per second.
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Which of the following statements are true? Select all that apply.
If the equation were graphed, it would be a horizontal line.
Both functions have the same slope.
The origin is the y-intercept for the function expressed in the table.
The linear equation does not have a y-intercept.
The table and the graph express an equivalent function.
Answers
Answer:
Both functions have the same slope.The origin is the y-intercept for the function expressed in the table.The table and the graph express an equivalent function.Step-by-step explanation:
Both functions have the same slope
The slope is m in the equation; y =mx+c which is the formula for a straight line.
m = change in Y/change in x
Using 2 points: (1,3/4) and ( 4,3) from the table;
= (3 - 3/4) / ( 4 - 1)
= 2.25/3
= 0.75 which is 3/4 which is the same as the slope of the function in the equation.
The origin is the y-intercept for the function expressed in the table.
Slope of function in table is known to be 0.75. Find c to complete equation.
3 = 0.75 ( 4) + c
3 = 3 + c
c = 0
c is the y-intercept. The origin of a line is 0 so if c is 0 then the origin is the y intercept.
The table and the graph express an equivalent function.
The function for the table as calculated is;
y = 0.75x + 0
y = 0.75x
This is the same as the function for the equation for the graph which is y = 3/4x.
Answer:Both functions have the same slope.
The origin is the y-intercept for the function expressed in the table.
The table and the graph express an equivalent function.
Step-by-step explanation:
Compare the linear functions expressed below by data in a table and by an equation.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 6, negative four-thirds, 1, 4. Column 2 is labeled y with entries negative StartFraction 9 Over 2 EndFraction, negative 1, three-fourths, 3. y = three-fourths x.
Which of the following statements are true? Select all that apply.
If the equation were graphed, it would be a horizontal line.
Both functions have the same slope.
The origin is the y-intercept for the function expressed in the table.
The linear equation does not have a y-intercept.
The table and the graph express an equivalent function.
O GRAPHS AND FUNCTIONSFinding a difference quotient for a linear or quadratic function
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given difference quotient formula
\(\frac{f(x+h)-f(x)}{h}\)STEP 2: Write the given function f(x)
\(f(x)=-2x^2-4x+7\)STEP 3: Get f(x+h)
\(\begin{gathered} f(x)=-2x^2-4x+7,\text{ we n}eed\text{ to get }f(x+h) \\ f(x+h)=-2(x+h)^2-4(x+h)+7 \\ -2(x+h)^2-4(x+h)+7=-2(x^2+2xh+h^2)-4x-4h+7 \\ \Rightarrow-2x^2-4xh-2h^2-4x-4h+7 \\ \Rightarrow-2x^2-2h^2-4xh-4x-4h+7 \end{gathered}\)STEP 4: Rewrite the expression by substitution
\(\begin{gathered} \frac{f(x+h)-f(x)}{h}\Rightarrow\frac{-2x^2-2h^2-4xh-4x-4h+7-(-2x^2-4x+7)}{h} \\ \Rightarrow\frac{-2x^2-2h^2-4xh-4x-4h+7+2x^2+4x-7_{}}{h} \\ Re-\text{arrange the expression} \\ \frac{-2x^2+2x^2-2h^2-4xh-4x+4x-4h+7-7}{h} \\ \Rightarrow\frac{-2h^2-4xh-4h}{h} \\ \Rightarrow\frac{-h(2h)}{h}-\frac{(4x)h}{h}-\frac{h(4)}{h} \\ \Rightarrow-2h-4x-4 \end{gathered}\)Hence, the result of the simplification is:
\(-2h-4x-4\)Please help will mark Brainly
Answers
The number of tickets day and evening combined should be more then 8 since it says at least 8 tickets. However the cost of the tickets which is 15x+30y (multiply the amount of tickets bought by the cost) should be less then 300 bucks since they have a budget. Hope this helps!
Adriana is excited to go to the used video game store to buy a gaming system later today. The gaming system usually costs x dollars, but today it's on sale for 15% off!
Pick all the expressions that represent the sale price of the gaming system
x-0.15x
1.15x
x(0.15)
0.85x
Answers
Answer:
.85x and x-0.15x
What is the volume in cubic centimeters of the figure below?
Answers
Answer:
so that you will multiply 15 * 4.
Step-by-step explanation:
15*4 = 60 now you divide 60 by 4 and the answer will be 15.
The zeros of a parabola are 6 and -5. If (-1, 3) is a point on the graph, which equation can be solved to find the
value of a in the equation of the parabola?
O3 = a(-1 + 6)-1-5)
O 3 = a(-1-6)(-1 +5)
O -1 = a(3+6)(3-5)
O-1 = a(3-6)(3+5)
Answers
Answer:
3 = a(-1-6)(-1+5).
Step-by-step explanation:
y = a(x - 6)(x + 5)
When x = -1, y = 3 so we have:
3 = a(-1-6)(-1+5).
A rectangular prism is 4 units high 2 units wide and 6 units long What is the surface area in square units
Answers
Answer:
Step-by-step explanation:
surface area=2×l×b+2(l+b)×h=2(lb+lh+bh)
=2(6×2+6×4+2×4)
=2(12+24+8)
=2×44
=88 square units.
The surface area of a given rectangular prism is 88 square units.
Given that, a rectangular prism is 4 units high 2 units wide and 6 units long.
We need to find the surface area of a rectangular prism in square units.
What is the surface area of a rectangular prism?The total area of a rectangular prism's rectangular faces is referred to as the prism's surface area. There are two different kinds of it: lateral surface area and total surface area. In contrast to the lateral surface area, which only includes the lateral faces and excludes the base areas, the total surface area of a rectangular prism refers to the area of all six faces.
The surface area of rectangular prism formula =2×l×b+2(l+b)×h=2(lb+lh+bh)
Now, 2(6×2+6×4+2×4)
=2(12+24+8)
=2×44
=88 square units
Therefore, the surface area of a given rectangular prism is 88 square units.
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what is the theorem of Protagorous
Answers
Answer:
Protagoras is best known for his claim that, "Of all things the measure is Man, of the things that are, that they are, and of the things that are not, that they are not" or, in other words, that everything is relative to individual experience, judgement, and interpretation.
Step-by-step explanation:
Answer:
hypotenuse^2 = base^2 + perpendicular^2
Step-by-step explanation:
Refer the attached file.
Which inequality represents the situation described below?
The distance, d, is less than 200 miles.
A. d ≥ 200
B. d > 200
C. d ≤ 200
D. d < 200
Answers
Hello!
The distance, d, is less than 200 miles.
B. d > 200
The radius of a circle is 4 millimeters. What is the circle's area? Use 3.14 for pi.
(The answer MUST BE ONE OF THE ANSWERS BELOW)
Answers
Answer:
50.24 mm^2
Step-by-step explanation:
The area of a circle is given by
A = pi r^2 where r is the radius
A = 3.14 ( 4)^2
= 50.24 mm^2
Answer:
c. 50.24 square millimeters
Step-by-step explanation:
Radius of circle = 4 milimeters.
Area of a circle = πr²
Area = 3.14 × 4² (π = 3.14)
= 50.24 square millimeters
(HELP)What is the perimeter measured in centimeters of the rectangle pictured below do not include units in your answer
Answers
Answer:
26cm
Step-by-step explanation:
7+7+6+6=26
Answer:
26 cm
Step-by-step explanation:
7x2 because of 2 sides
12x2 because of 2 sides
14+12=26
(5x + 75)
(3x+ 25)
a. x = 80
b. x = 10
c. X= -25
d.x=25
Answers
Answer:
c. x=-25 is the answer
(5x+75)
- (3x+25 )
=2x +50
×=-25
This is the last one
Answers
Answer:
C option SAS is the correct answer of this question .....plz mark my answer as brainlist plzzzz vote me also plzzzz
the area of a rectangle is 40squares inches. The rectangle is 8inches long. How wide is the rectangle
Answers
Answer:5
Step-by-step explanation:
Suav wants to use a sheet of fiberboard 27 inches long to create a skateboard ramp with a 19 degree angle of elevation from the ground. How high will the ramp rise from the ground at its highest end? Round your answer to the nearest hundredth of an inch if necessary.
PLEASE HELPPP!
Answers
The ramp rises 8.79 inches from the lowest point on the ground to the nearest hundredth.
A right angle triangle is what?A right angle triangle has a 90 degree angle as one of its angles. Trigonometric ratios can be used to determine the sides. The length of the fiberboard becomes the hypotenuse of the right triangle that is so constructed. As a result, the ramp rises 8.79 inches from the ground at its tallest point to the closest hundredth.
The opposite side of the right triangle is the height of the ramp that is created.
Hence,
sin 19° = opposite / hypotenuse
sin 19° = h / 27
cross multiply
h = 27 × sin 19°
h = 27 × 0.32556815445
h = 8.79034017034
h = 8.79 inches.
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PLS HELP
2. Write a quadratic function to the model to the graph to the right
Answers
We can use the quadratic function in vertex form, f(x) = a(x - h)^2 + k where:
(h, k) = vertex
a = determines whether the graph opens up or down, and makes the parent function wider or narrower.
* If a is positive, the graph opens up.
* If a is negative, the graph opens down.
h = determines how far left or right the parent function is translated.
k = determines how far up or down the parent function is translated.
Now that we defined each variable in the vertex form, we can plug in the values of the vertex (-4, 3) into the equation:
f(x) = a(x - h)^2 + k
f(x) = a(x + 4)^2 + 3
To solve for the value of “a”, we must choose another point from the graph. The y-intercept of the parabola happens to be (0, 19), so we’ll use its values to solve for “a”:
19 = a(0 + 4)^2 + 3
19 = a(4)^2 + 3
19 = a(16) + 3
Subtract 3 from both sides:
19 - 3 = a(16) + 3- 3
16 = 16a
Divide both sides by 16:
16/16 = 16a/16
1 = a
The value of a = 1. Since it is a positive number, then it confirms that the parabola opens upward.
Therefore, the quadratic function in vertex form is:
f(x) = (x + 4)^2 + 3
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In △JKL , if m∠ J < 90° , then ∠K and ∠L are _____
Answers
Both angle K and angle L must be acute angles, measuring less than 90 degrees, in order to satisfy the conditions of the given triangle.
In triangle JKL, if angle J is less than 90 degrees, then angle K and angle L are both acute angles.
An acute angle is defined as an angle that measures less than 90 degrees. Since angle J is given to be less than 90 degrees, it is an acute angle.
In a triangle, the sum of the interior angles is always 180 degrees. Therefore, if angle J is less than 90 degrees, the sum of angles K and L must be greater than 90 degrees in order to satisfy the condition that the angles of a triangle add up to 180 degrees.
Hence, both angle K and angle L must be acute angles, measuring less than 90 degrees, in order to satisfy the conditions of the given triangle.
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Corsica fills a bucket with water at a constant rate. The equation below represents a proportional relationship between the ounces of the water in the bucket (W) and the time it takes to fill the bucket in seconds (S).
3W = 32S
How many ounces of water were added to the bucket per second.
Answers
Answer:3/32ounces
Step-by-step explanation:
It's Lila's turn to host movie night, and she's picking movies to rent. Flick City Digital Movies is having a sale, so Lila rents 5 movies for a total of $24.75. Each movie costs the same amount, Let c represent the cost to rent a movie. Which equation models the problem? c/5 = 24.75 5c = 24.75
Answers
Answer:
5c = 24.75
Step-by-step explanation:
5c = 24.75 If you divide both sides by 5, you will find out how much each movie cost.
\(\frac{5c}{5}\) = \(\frac{24.75}{5}\)
c = 4.95
Each movie cost $4.95 to rent.
Polygon A is similar to Polygon B.
Find the perimeter of Polygon B.
24
A
PA = 128
15
B
PB = [?]
![Polygon A is similar to Polygon B.Find the perimeter of Polygon B.24APA = 12815BPB = [?]](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/aeAtjpjtmFvriRXC3qTSsaWOypFbLSSs.png)
Answers
Answer:
\(P_{B}\) = 80
Step-by-step explanation:
given 2 similar figures with ratio of sides = a : b
then ratio of perimeters is also a : b
here ratio of sides = 24 : 15 = 8 : 5
the ratio of perimeters is also 8 : 5
then by proportion
\(\frac{ratioA}{P_{A} }\) = \(\frac{ratioB}{P_{B} }\) , that is
\(\frac{8}{128}\) = \(\frac{5}{P_{B} }\) ( cross- multiply )
8 \(P_{B}\) = 5 × 128 = 640 ( divide both sides by 8 )
\(P_{B}\) = 80
The points A, B, C and D lie in order on a straight line
such that
AB:BD = 1:2
AC:CD= 7:2
Find AB:BC:CD
Answers
Answer:
7 + 2 = 9, so AC = 7/9 and CD = 2/9
1 + 2 = 3, so AB = 1/3 = 3/9 and
BD = 2/3 = 6/9
AB + BC = AC
3/9 + BC = 7/9, so BC = 4/9
AB:BC:CD = (3/9):(4/9):(2/9) = 3:4:2
Which fraction is equal to ⅛?
⁴⁄₆ ⁴⁄₃₀ ²⁄₁₆
Answers
Answer:
2/16
Step-by-step explanation:
1/8 * 2/2 = 2/16
Answer:
2/16
Step-by-step explanation:
Hope this helped!!!
L
Question 2 of 10
A triangle has two sides of lengths 7 and 12. What value could the length of
the third side be? Check all that apply.
O A. 3
O B. 17
C. 7
O D. 9
O E. 11
OF. 5
SUBMN
Answers
Answer:
B, C, D, E
Step-by-step explanation:
The length of the third side will be between 12-7 = 5 and 12+7 = 19. The answer choices in that range are ...
B. 17
C. 7
D. 9
E. 11
__
Side lengths A(5) and F(3) are too short.
______
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Does anyone know this ?
Answers
Answer:
I think it is A, C, E I'm. it too sure, sorry if it's wrong
Four different exponential functions are represented below.
Drag the representation of each function into order from greatest y-intercept to least y-
intercept.
Answers
The graph of the function y = 2x⁴ - 5x³ + x² - 2x + 4 is plotted and attached.
How to solve
We have the 4 functions as shown in the image attached.
The y - intercept is the point where the graph intercepts the y - axis.
Function [1] -
y = 4 + 2x
y - intercept is 4
Function [2] -
y = 5ˣ + 1
y - intercept is 2.
Function [3] -
the y-intercept is 1.
Function [4] -
the y - intercept is at -1.
Therefore, the greatest y-intercept is of function -
f(x) = 2x + 4
and the least y-intercept is of the function shown in graph [4] or function [4].
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Answer:
Carlos puts $3 into his bank account and it grows by 50% each year
f(x)=4^x+1
(The Table)
(The Graph)
Estimate and then solve the equation
X - 17 4/5 = - 13 1/5
The estimated equation is
The estimated solution is x =
The actual solution is x =
Answers
Answer: x-18=-13
5
4 3/5
Step-by-step explanation:
Given the formula: D=m/v
Solve for V.
Answers
Answer:
v=m/d
Step-by-step explanation:
D=m/v
D*v=m
d*v/d=m/d
v=m/d
The required solution for v is v = m/D.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign =.
The given equation is,
D = m/v
To solve for v we need to isolate v to one side and other variables to another side.
Therefore multilpying the equation both the side by we get,
Dv = v*m/v
Solving we obtain,
Dv = m
Now divide the equation both side by D we obtain,
Dv/D = m/D
Solving we obtain,
v = m/D
which is the required solution for v.
Thus, the required solution for v is v = m/D.
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Need some help with this :(
(Don’t answer if you don’t know)15 points
Answers
a translation of T2, –7(x, y) is applied to ΔABC, what are the coordinates of B'?
Answers
If a translation of T (2, -7) is applied to the triangle ABC as shown in the figure attached hereby for reference, and B (1, 5) gets repositioned to B', then the current coordinates of B' are (3, -2).
As per the question statement, a translation of T (2, -7) is applied to the triangle ABC as shown in the figure attached hereby for reference, and B (1, 5) gets repositioned to B'.
We are required to calculate the coordinates of B'.
To solve this question, we need to know what Translation (a, b) to (x, y) and (-a, -b) to (x, y) means. Translation (a, b) to (x, y) means the abscissa "x" is to be shifted to the right by "a" units while the ordinate "y" is to be shifted to the right by "b" units, i.e., after translation, the new coordinates become [(a + x), (b + x)]. On the other hand, Translation (-a, -b) to (x, y) means the abscissa "x" is to be shifted to the left by "a" units while the ordinate "y" is to be shifted to the left by "b" units, i.e., after translation, the new coordinates become [(a - x), (b - x)].
Here, as per the above mentioned concept, a translation of T (2, -7) if applied to the point B (1, 5), the new point B' will be at \([(1+2), (5+(-7)]=[3, (-2)]\).
Translation: In Coordinate Geometry, a translation is a repositioning of a point or a figure from one location to another location without changing its size, shape or orientation.Coordinates: The coordinates of a point are a pair of numbers that define its exact location on a two-dimensional coordinate plane by using the horizontal and vertical distances from the two reference axesTo learn more about Translation, click on the link below.
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Answer: D (3,-12)
Step-by-step explanation: