the length of a rectangle is 6 units shorter than 1/4 of the width x. Write an expression for the perimeter of the rectangle.

Yes, the equation defines y as a function of x.

Yes, the equation defines y as a function of x.

A function is a relation where each input x corresponds to exactly one output y. In this equation, y is defined as 8 over x. For any given value of x, the equation will give us a unique value for y. For example, if we plug in x = 2, y = 8/2 = 4. If we plug in x = 4, y = 8/4 = 2.

Thus, this equation defines y as a function of x.

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Where B₁ and B₂ are the areas of the bases, the volume of the frustum is given by

... V = (1/3)(B₁ +B₂ +√(B₁B₂))h

For your dimensions, the volume is

... V = (1/3)(100 + 25 + √(100·25))·12 = (1/3)·175·12 = 700

The appropriate choice for the volume of the frustum is

... B. 700 in³

Answer:

a

Step-by-step explanation:

Who prescribed the most medicine?

It would be Dr. Hong. This is because Dr. Hong has prescribed more than Dr.Tannenbaum and Dr.Evans.

Who prescribed the least?

It would be Dr.Evans. Because he has prescribed 0.02 less than Dr.Hong and 0.01 less than Dr.Tannenbaum.

Dr. Hong prescribed most medicine and Dr. Evan prescribed less medicine among all other doctors.

Further explanation:

Given:

Dr. Hong prescribed 0.019 liter more medicine than Dr. Tannenbaum.

Dr. Evans prescribed 0.02 liter less than Dr. Hong.

Calculation:

Consider Dr. Tannenbaum prescribed x liter medicine.

It is given that the Dr. Hong prescribed 0.019 liter more than the Dr. Tannenbaum.

Therefore Dr. Hong prescribed [tex]x+0.019{\text{liter}}[/tex] medicine.

It is also given that the Dr. Evans prescribed 0.02 liter less than Dr. Hong.

Therefore, Dr. Evans prescribed [tex]\left({x+0.019-0.02}\right){\text{liter}}[/tex] medicine.

So the Dr. Evans prescribed exactly [tex]\left({x-0.001}\right){\text{liter}}[/tex].

Therefore the medicine prescribed by Dr. Hong is [tex]\left({x+0.019}\right){\text{liter}}\\[/tex].

The medicine prescribed by Dr. Tannenbaum is x liters.

The medicine prescribed by Dr. Evans is [tex]\left({x-0.001}\right){\text{liter}}[/tex].

Arrange all doctors in ascending order with their prescribed medicine.

Dr. Hong > Dr. Tannenbaum > Dr. Evans

So it is obtained from the above expression that the Dr. Evans prescribed less medicine and Dr. Hong prescribed most medicine than other doctor.

Thus, Dr. Hong prescribed most medicine and Dr. Evans prescribed less medicine among all other doctors.

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Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Algebraic expression

Keywords:

Dr. Hong, Dr. Tannenbaum, Dr. Evans, medicine, Doctor, prescribed, less, more, liter.

The reasonable estimate for multiplying 94 by 689 is found by rounding the numbers to the nearest convenient figures, which gives an estimated result of 70,000.

To estimate the product of 94 and 689, you can round each number to its nearest simple form and then multiply. Round 94 to 100 because it is close to that multiple of ten. Round 689 to 700, as it is close to this hundred mark. When you multiply 100 by 700, you get 70,000.

This process of rounding to the nearest convenient number simplifies the multiplication and gives us an answer that is easy to calculate and understand. Hence, by rounding the numbers before multiplying, the reasonable estimate for the problem 94 · 689 is 70,000.

Final answer:

By rounding the numbers and multiplying, a reasonable estimate for the product of 94 and 689 is 70,000.

Explanation:

To estimate the product of 94 · 689, we can round the numbers to the nearest ten or hundred and then multiply. For estimation purposes, we can approximate 94 to 100 (since it's closer to 100 than 90) and 689 to 700 (since it's closer to 700 than 600).

Multiplying these rounded figures: 100 × 700 equals 70,000. Therefore, 70,000 is a reasonable estimate for the product of 94 and 689.

The dimension of the rectangle will be 15 meters (width) and 75 meters (length).

The sum of all the sides of the rectangle will be known as the perimeter of the rectangle. Let L be the length and W be the width of the rectangle.

Then the perimeter of the rectangle will be

Perimeter of the rectangle = 2(L + W) units

The length is M and the width is m. A rectangle's width is one-fifth its length, and its perimeter is 180 metes. Then the equation will be

m = (1/5)M

m = M/5

M = 5m

Then the perimeter of the rectangle will be

P = 2(m + M)

180 = 2(m + 5m)

90 = 6m

m = 15 meters

Then the length of the rectangle will be

M = 5m

M = 15 x 5

M = 75 meters

The dimension of the rectangle will be 15 meters (width) and 75 meters (length).

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Answer: 3 × 5

Step-by-step explanation: To find the prime factorization of 15, first create a factor tree with two branches.

Since 15 divided by 3 gives us 5, we know that  and 5 are factors of 15. This means that we can write 3 and 5 at the bottom of our branches.

While 1 and 15 are also factors of 15, we don't use them in our factor tree. This because when finding a prime factorization, we only want factors other than 1 and the number itself.

Next, we circle any prime numbers in our factor tree. Since 3 and 5 are both prime numbers, we circle both 3 and 5. Since we have circles at the bottom of our branches, we are finished.

Therefore, the prime factorization of 15 is 3 × 5.

Answer:

Hence, the monthly payment to the nearest cent is 510.31

Step-by-step explanation:

Consider the provided information,

A college student borrow ​$1,500 for 3 months to pay for a semester of school.

Let us consider the monthly payment is $x.

If he pay $x for next 3 months, then the total amount student paid in 3 month is: 3x

The interest is ​$30.94 for 3 months.

Student pay all the borrowed money and interest in 3 months.

That means he pay $1,500 + $30.94 in 3 months while the monthly payment was 3x.

This can be written as:

[tex]3x = 1500+30.94[/tex]

[tex]3x = 1530.94[/tex]

[tex]x = \frac{1530.94}{3}[/tex]

[tex]x = 510.31[/tex]

Hence, the monthly payment to the nearest cent is 510.31

First calculate the time it takes to reach the building using the x-component of the velocity.

t = 57.6 m / (42.7 m/s * cos35.2) = 1.65 s

Then we calculate the height y using the y-component of the velocity:

y = (42.7 m/s * sin35.2) * 1.65 s – 0.5 (9.81 m/s^2) (1.65 s)^2

y = 11.26 m

Final answer:

Using principles of projectile motion and given the initial speed, angle of projection, and horizontal distance, the stream of water from the fire hose will strike the building at a height of approximately 20.3 meters.

Explanation:

To determine at what height the stream of water will strike the building, we need to apply the principles of projectile motion. We are given the initial speed of the water stream (42.7 m/s), the angle of projection (35.2 degrees), and the horizontal distance from the fireman to the building (57.6 meters).

First, we separate the initial velocity into horizontal (ux) and vertical (uy) components:

ux = u * cos(θ) = 42.7 m/s * cos(35.2°) = 42.7 m/s * 0.8192 ≈ 35.0 m/s

uy = u * sin(θ) = 42.7 m/s * sin(35.2°) = 42.7 m/s * 0.5759 ≈ 24.6 m/s

Next, we use the formula for the horizontal motion to find the time (t) it takes for the water to reach the building:

x = ux* t => 57.6 m = 35.0 m/s * t => t ≈ 1.65 s

Finally, we can calculate the vertical distance (y) using the time and the vertical component of the velocity:

y = uy*t - (1/2) * g * t2 = 24.6 m/s * 1.65 s - (0.5 * 9.81 m/s2 * (1.65 s)2) ≈ 20.3 m

Therefore, the stream of water will strike the building at a height of approximately 20.3 meters above the ground.

Answer:

B

Step-by-step explanation:

To write the equation of the line, use the slope formula to find the slope. Then substitute the slope and a point into the point slope form. Simplify using the distributive property to write in slope intercept form.

[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{25 - 17}{7-3} = \frac{8}{4} = 2[/tex]

Using the point slope form of a line equation, substitute m = 2 and the point (3,17).

[tex]y - y_1 = m(x-x_1)\\y -17 = 2(x - 3)\\y - 17 = 2x - 6 \\ y = 2x - 6 + 17 \\ y = 2x + 11 [/tex]

The temperature at 4:00 pm will be 66° F.

What are Integers?

An integer is a number with no decimal number or fractional part.

Given that;

At 4:00 am the outside temperature was 28*F. By 4:00 pm that same day it rose to 38 degrees.

Now, The temperature at 4:00 pm is calculated as;

= 28° F + 38° F

= 66° F.

Thus, The temperature at 4:00 pm will be 66° F.

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The complete question is this;

At 4:00 am, the outside temperature was 28*F. By 4:00 P.M. it rose 38 degrees. What was the temperature at 4:00 P.M. ?

Answer:

Prime factorization: 56 = 2 x 2 x 2 x 7.

Step-by-step explanation:

Given  : 56

To find : Write the prime factorization.

Solution : We have given number 56.

Prime factorization : Factors of 56 as prime number

56 = 56 = 1 x 56, 2 x 28, 4 x 14, or 7 x 8.

Prime factorization: 56 = 2 x 2 x 2 x 7

Therefore, Prime factorization: 56 = 2 x 2 x 2 x 7.

Two consecutive integers are - 7 and - 8.

Here,

We have to find the two consecutive integers.

What are Integers?

An integer is a number which includes negative and positive numbers, including zero.

Now,

Let the smaller number is x.

Then, the larger is nine more than twice the smaller.

So, Larger number = 2x + 9

Since, The difference of two consecutive number are always 1.

So,

2x + 9 - x = 1

x + 9 = 1

x = -8

Therefore, The larger number = 2x + 9 = 2*-8 + 9 = -16 + 9 = -7

Hence,

Two consecutive integers are - 7 and - 8.

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Answer:

Expression representing the measure of the two angles of the given regular polygon is 16x² - 26x + 20.

Step-by-step explanation:

Given Expression of the Sum of the all interior angles of a regular polygon

40x² - 65x + 50

We need to find expression representing the measure of the two angles.

We know that regular polygons have all side and all angles equal.

Number of side or angles in regular polygon = 5

So, when we divide given expression by 5 we get expression for an angle of the regular polygon.

[tex]\frac{40x^2-65x+50}{5}=\frac{5(8x^2-13x+10)}{5}=8x^2-13x+10[/tex]

Expression for an angle of regular pentagon = 8x² - 13x + 10

Now, For 2 angles  = 2( 8x² - 13x + 10 ) = 16x² - 26x + 20

Therefore, Expression representing the measure of the two angles of the given regular polygon is 16x² - 26x + 20.

Final answer:

The baker's revenue R can be expressed as R = x * 6.50, and the cost C can be expressed as C = 45 + 25 + (x * 1.75). To find the number of cakes he needs to sell before making a profit, we set the revenue equal to the cost and solve for x. The baker will need to sell at least 15 cakes before making a profit.

Explanation:

To express the revenue R as a function of x, we can use the equation R = x * 6.50. This is because the revenue is the number of cakes sold multiplied by the price per cake. So, every cake sold contributes $6.50 to the revenue.

To express the cost C as a function of x, we can use the equation C = 45 + 25 + (x * 1.75). The initial fixed costs of $45 for reserving a booth and $25 for traveling expenses are added to the variable costs of $1.75 per cake multiplied by the number of cakes sold.

To find the number of cakes he needs to sell before making a profit, we need to set the revenue equal to the cost and solve for x:

R = C => x * 6.50 = 45 + 25 + (x * 1.75)

Combining like terms, we get:

4.75x = 70

x = 70 / 4.75

x ≈ 14.74

Since you cannot sell a fraction of a cake, the baker will need to sell at least 15 cakes before making a profit.