there are a total of 127 cars and trucks on a lot. if there are four more than twice the number of trucks than cars, how many cars are on the lot

Answers

Answer 1

Answer: C+T=127

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2C+4=T

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C+(2C+4)=127

3C+4=127

3C=123

C=41

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When C=41,

41+T=127

T=127-41

T=86

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Check answer:

86+41=127

Answer 2

Answer: The total amount of cars on the lot are 127

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A sphere and the base of a cone have a radius of 3 inches. The volume of the sphere equals the volume of the cone. what is the height of the cone, in inches?

Answers

So the volume of a sphere is $V= (4)/(3) \pi r^3$ , and the volume of a cone is $V= \pi r^2 (h)/(3)$ (h=height, r=radius). Knowing only the radius, we can solve for the volume of the sphere. (Also I'm going to be leaving answers in pi form.)

$V= (4)/(3) \pi 3^3$
Solve the exponents to get $V= (4)/(3) \pi 9$
Multiply 4/3 and 9 to get $V=13.5 \pi$

Now that we know the volume of the sphere, we can solve for the height of the cone since the volumes for both are the same.

$13.5 \pi = \pi 3^2 (h)/(3)$

Solve the exponents to get $13.5 \pi =9 \pi (h)/(3)$

Divide $9 \pi$ on each side to get $1.5= (h)/(3)$

Multiply 3 on each side, and your answer should be $4.5=h$

Part A. Claire runs 10 km in 1 hour. How many km does she run in half an hour? in 2 1/2 hours? The answer would be : 1.5 km and 2.25 km
Part B. Malia runs 5 miles in 1 hour. How many miles does she run in half an hour? In 2 1/2 hours?
The answer would be : 2.5 and 1.25
Part C. On Tuesday, Claire and Malia both ran for 2 1/2 hours. Who ran the farther distance?
Answer would be : ?

Answers

Part A: Claire ran 5 km in half and hour and 25 km in 2 1/2 hours.
Part B: Malia ran 2.5 miles in half an hour and 12.5 miles in 2 1/2 hours.
Part C: Claire ran 4.8832 km faster than Malia in 2 1/2 hours.

The line tangent to the graph of g(x) = x^{3}-4x+1 at the point (2, 1) is given by the formulaL(x) = 8(x - 2) + 1.

Which of the following statements are true? Select all that apply.
A. The functions are approximately equal on the interval 1.9 smaller than or equal to x larger than or equal to 2.1.
B. The functions have the same y-intercept.
C. The slope of the line equals g'(0).
D. The functions are approximately equal on the interval 0.5 smaller than or equal to x larger than or equal 1.0.
E. The graphs intersect at the point (2,1).
F. The slope of the line equals g'(2).
G. None of the above are true.

Answers

Using function concepts, it is found that the correct options are:

A. The functions are approximately equal on the interval 1.9 smaller than or equal to x larger than or equal to 2.1.
E. The graphs intersect at the point (2,1).
F. The slope of the line equals g'(2).

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The value of x we are interested is x = 2, thus, considering a margin, the functions are approximately equal between x = 1.9 and x = 2.1, which means that option A is correct, while option D is not.
The y-interceptof g is $g(0) = 0^3 - 4(0) + 1 = 1$ , while the y-intercept of L is $L(0) = 8(0 - 2) + 1 = -16 + 1 = - 15$ . Not the same, thus, option B is not correct.
The slope of the tangent line to g at x = 2 is the derivative of g at x = 2, that is, g'(2), thus option F is correct while option C is not.
At (2,1), the g(x) and L(x) intersect, thus, option E is correct.

A similar problem is given at brainly.com/question/22426360

well, about A and D, I just plugged the values on the slope formula of

$\bf \begin{array}{llll} g(x)=x^3-4x+1\n L(x) = 8(x-2)+1 \end{array} \qquad \begin{cases} x_1=1.9\n x_2=2.1 \end{cases}\implies \cfrac{f(b)-f(a)}{b-a}$

for A the values are 8.01 and 8.0, so indeed those "slopes" are close. $\textit{\huge \checkmark}$

for D the values are -2.25 and 8.0, so no dice on that one.

for B, let's check the y-intercept for g(x), by setting x = 0, we end up g(0) = 0³-4(0)+1, which gives us g(0) = 1.

checking L(x) y-intercept, well, L(x) is in slope-intercept form, thus the +1 sticking out on the far right is the y-intercept, so, dice. $\textit{\huge \checkmark}$

for C, well, the slope if L(x) is 8, since it's in slope-intercept form, the derivative of g(x) is g'(x) = 3x² - 4, and thus g'(0) = -4, so no dice.

for E, do they intercept at (2,1)? well, come on now, L(x) is a tangent line to g(x), so that's a must for a tangent. $\textit{\huge \checkmark}$

for F, we know the slope of the line L(x) is 8, is g'(2) = 8? let's check

recall that g'(x) = 3x² - 4, so g'(2) = 3(2)² - 4, meaning g'(2) = 8, so, dice. $\textit{\huge \checkmark}$

A rectangle is 5 units long. The rectangle is also 3 units wide. What is its perimeter?

Answers

5+5+3+3= 16
(5x2)+(3x2)=16

you add 5+3 (=8)and multiply your by two (8*2=16 units)

Laticia randomly selected 25% of the seventh-grade students in her school an asked them their favorite season.Of the students surveyed,51 chose summer as their favorite season. Based on the data, what is the most reasonable prediction of the number of seventh-grade students in her school who would choose summer as their favorite season.

Answers

if 25% is 51 students an easy way of finding it would be adding 51 4 times. so the answer should be 204. unless im wrong then im sorry.

25% is equal to 1/4. If 51 is 25% of the students, that means it is 1/4. To find the total amount of students who would choose summer, you multiply 51 x 4 and you get 204 students, give some/take some. Hope this helps!

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Answers

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