MATHEMATICS HIGH SCHOOL

Mike recently increased the size of his Jeep tires from the original 29 inch diameter to the larger 33.73 inch diameter. If Mike didn't recalibrate his speedometer, how fast is he really going on the new tires when his speedometer shows he is traveling 60 mph?a. 54.5 mph
b. 62.1 mph
c. 66.1 mph
d. 69.8 mph

Answers

Answer 1

Answer:

Answer:

d. 69.8 mph

Step-by-step explanation:

Since, the ratio of the diameter of the tyre of a vehicle and its speed must be constant,

Given,

The original diameter of the tyre = 29 inch,

Original speed = 60 mph,

Thus, the ratio of diameter and the speed of the vehicle = $(29)/(60)$

New diameter of the tyre = 33.73 inch,

Let x be the new speed of the vehicle = $(33.73)/(x)$

$\implies (29)/(60)=(33.73)/(x)$

$\implies x=(33.73* 60)/(29)=69.79\approx 69.8\text{ mph}$

Hence, the actual speed of the vehicle would be 69.8 mph.

OPTION D is correct.

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Solve by elimination8x+9y=-55-8x+y=65

Find the value of 4x^2– 2y when x = 3 and y = 2.

Answers

Answer:

The answer is 32.

Step-by-step explanation:

Remember that order of operation is very important in this problem.

Substitute x for 3 and y for 2 in the equation.

When solving the first term, we must note that we have to square the 3 first before we multiply it by 4. So, 4(3)^2 is basically 36. To simplify the second term you just have to do 2*2, which is 4. 36-4=32, which is the answer.

you began membership in a new health and fitness club which has access to a dietician and personal trainer. They help you develop a special eight-week diet and exercise program. The data in the following table represents your weight, w, as a function of time, t, over an eight-week period. Time (weeks) 0 1 2 3 4 5 6 7 8 Weight (lb) 150 144 143 141 140 137 137 132 129. If you lost 13 pounds in the first five weeks, what is the average rate of change of weight with respect to time over the first five weeks of the program?

Answers

Time (weeks) 0 1 2 3 4 5 6 7 8
Weight (lb) 150 144 143 141 140 137 137 132 129

Change in time (weeks) = 5 - 0 = 5 = -0.3846
Change in weight (lbs) 137 -150 -13

The average rate of change of weight with respect to time over the first five weeks of the program is -0.3846. It is a negative sign because the weight is decreasing.

Answer:

On e2020 the correct answer is D -2.6 pounds per week

Step-by-step explanation:

I just took the test.

If cot(theta)= 4/3, find csc(theta) (Picture provided)

Answers

Answer:

Step-by-step explanation:

If $\cot \theta=(4)/(3),$ then we can consider right triangle with adjacent leg 4 un. and opposite leg 3 un.. By the Pythagorean theorem,

$\text{hypotenuse}^2=\text{adjacent leg}^2+\text{opposite leg}^2,\n \n\text{hypotenuse}^2=4^2+3^2,\n \n\text{hypotenuse}^2=16+9,\n \n\text{hypotenuse}^2=25,\n \n\text{hypotenuse}=5\ un.$

So,

$\csc \theta=\frac{\text{hypotenuse}}{\text{opposite leg}}=(5)/(3).$

Answer:

The correct answer is option d

Step-by-step explanation:

Trigonometric ratio

Cot θ = Adjacent side/Opposite side

It is given that,

Cot θ = 4/3

Adjacent side = 4

Opposite side = 3

Csc θ = Hypotenuse/Opposite side

To find the Hypotenuse

Hypotenuse² = Opposite side² + Adjacent side ² = 3²+ 4²

Hypotenuse = √(3²+ 4²) = 5

To find Csc θ

Csc θ = Hypotenuse/Opposite side = 5/3

The correct answer is option d

Csc θ = 5/3

Quadrilateral QRST is a square. If the measure of QR 3x-6 and TS is 6-x. Find the value of x.

Answers

Answer:

x = 3

Step-by-step explanation:

Since the quadrilateral QRST is a square, all sides are equal

Therefore QR must be equal to TS

3x - 6 = 6 - x

4x = 12

x = 3

Evaluate the expression, -1 x (-0.1 x -5 + 0.5)

Answers

Answer:

-1

Step-by-step explanation:

-1 x (-0.1 x -5 + 0.5)

= -1 x 1

= -1

Y − x = -13 -4x + 3y = -51

Answers

y - x = -13
-4x + 3y = -51

Use any of the equation to find the value of x or y. In this case, I'll use the 1st equation to find the value of y.

y - x = -13
y = x - 13

Substitute the value of y in the 2nd equation to find the value of x.

-14x + 3y = -51
-14x + 3(x-13) = -51
-14x + 3x - 39 = -51
-11x = -51 + 39
-11x = -12
x = 12/11 or 1 1/11

Substitute the value of x in any equation to find the value of y.

y = x - 13
y = 12/11 - 13
y = 12/11 - (13*11/11) *to get the common denominator
y = (12 - 143)/11 = -131/11 = 11 10/11

to check: x = 12/11 or 1 1/11 ; y = -131/11 or 11 10/11

y - x = -13
-131/11 - 12/11 = -13
(-131 - 12)/11 = -13
-143/11 = -13
-13 = -13

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