If four times a number plus 3 is 11, what is the number? A. 16 B. 5 C. 2 D. 4

After converting mixed numbers to improper fractions and completing the multiplication, options B, C, and E yield products that are greater than 2 5/6. Options A and D are less than 2 5/6.

The question asks to evaluate which of the given products are greater than 2 5/6.

We will convert the mixed numbers to improper fractions to make the multiplication easier and then compare the products with 2 5/6 (= 17/6).

Therefore, the correct answers are options B, C, and E.

Answer:

[tex]\frac{8}{9}[/tex]

Step-by-step explanation:

perform the indicated operation 1/3 divide 3/8

divide the fraction 1/3  and 3/8

When we divide the fractions, we flip the second fraction and multiply with first fraction.

[tex]\frac{\frac{1}{3} }{\frac{3}{8} }[/tex]

When we flip 3/8 it becomes 8/3

[tex]\frac{1}{3} \cdot \frac{8}{3}[/tex]

Multiply numerator with numerator and denominator with denominator

1 times 8 is 8

3 times 3 is 9

So final answer is [tex]\frac{8}{9}[/tex]

Answer:

(x - 7)² + (y - 3)² = 4

Step-by-step explanation:

The equation formula of a circle is (x - h)² + (y - k)² = r², where the center is at ordered pair (h, k) and r represents the radius in units.

With the information given in the question itself, we plug and play, simplifying if need be:
center (7, 3), h = 7, k = 3
radius = 2

(x - 7)² + (y - 3)² = (2)²
(x - 7)² + (y - 3)² = 4

The equation of this circle is (x - 7)² + (y - 3)² = 4

The exponential function is f(x) = 3(2)× which is passes throgh the two points (1,6) and (3,24).

It is defined as the function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a^x

where a is a constant and a>1

We have:

An exponential function:

f(x) = c(a)×

The two points are given:

(1,6) and (3,24)

Plug x = 1

f(x) = 6

6 = c(a) ...(I)

Plug x = 3

f(x) = 24

24 = c(a)³  ...(II)

Divide equations (1) and (II)

24/6 = c(a)³/c(a)  

4 = a²

a = 2

Plug a = 2 in equation I

6 = c(2)

c = 6/2

c = 3

The exponential function:

f(x) = 3(2)×

Thus, the exponential function is f(x) = 3(2)× which is passes throgh the two points (1,6) and (3,24).

Learn more about the exponential function here:

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Answer: 12 inches

Step-by-step explanation: In this problem, since we're asked to find the length of the median, let's use our formula for the area of a trapezoid that involves the median which is shown below.

Area = median · height

We know that the area is 144 and the height is 9 so we can set up the equation 144 = M · 12. Now to solve for m, we divide both sides of the equation by 12 and we find that 12 = M.

So the length of the median of the trapezoid is 12 inches.

Given an area of 144 square inches and a height of 12 inches, the median is found to be 24 inches.

To find the length of the median of a trapezoid, we can use the formula for the area of a trapezoid, which is:

Area = 0.5 × (Base1 + Base2) × Height

We are given that the area is 144 square inches and the height is 12 inches. The formula can be rearranged to solve for the average of the two bases or the median (M):

144 = 0.5 × M × 12

Simplifying this equation, we get:

M = (144 × 2) / 12

M = 288 / 12

M = 24 inches

Thus, the length of the median is 24 inches.

The scale factor between two similar cones with surface areas of 20 ft² and 125 ft² is found by taking the square root of the ratio of the surface areas, which is [tex]\frac{1}{6.25}[/tex], resulting in a scale factor of B. [tex]\frac{2}{5}[/tex].

The question is asking about the scale factor between two similar cones with given surface areas. In the case of similar figures, the ratio of their surface areas is equal to the square of the scale factor. To find the scale factor, we take the square root of the ratio of the surface areas.

First, find the ratio of the surface areas: surface area of smaller cone : surface area of larger cone = [tex]\frac{20 ft^2}{125 ft^2}[/tex] = [tex]\frac{1}{6.25}[/tex].

Then, we take the square root of the ratio to find the scale factor: [tex]\sqrt{ (\frac{1}{6.25})}[/tex] = [tex]\frac{1}{2.5}[/tex], which simplifies to [tex]\frac{2}{5}[/tex]. Therefore, the scale factor is [tex]\frac{2}{5}[/tex], making option B the correct answer.

To find the scale factor between two similar cones, you can use the ratio of their corresponding lengths.

The surface area of a cone is proportional to the square of its height.

Let's denote the scale factor as kk. If A1A1​ and A2A2​ are the surface areas of the first and second cone respectively, then:

A1/A2=(k/1)^2

Given A1=20 ft^2 and A2​=125 ft^2, we have:

20/125=(k/1)^2

Solving for k:

k= √ 20/125=√ 4/25=2/5​=52

So, the correct answer is B. 2/5

complete question;

The surface areas of two similar cones are 20 ft^2 and 125 ft^2. What is the scale factor?

A. 1/5

B. 2/5

C. 3/5

D. 4/5

Observe the given figure, we have to determine the segments which is a radius of K.

1. RT is a diameter of a circle K as it is a straight line passing from side to side through the center of a circle.

2. MT is a chord of a circle K as it is the line segment connecting two points on a circle's circumference.

3. KM is a segment which is a radius of circle K as it is the length of the line from the center to any point on its edge.

4. MR is a chord of a circle K as it is the line segment connecting two points on a circle's circumference.

So, KM segment is a radius of circle K.

Therefore, option 3 is the correct answer.

Answer: KM

Step-by-step explanation:

The equation without fractions is 8x - 36 = 9.

To eliminate fractions from the equation 2/3x - 3 = 3/4, you can multiply both sides of the equation by the least common multiple (LCM) of the denominators, which is 12:

(12) * (2/3x - 3) = (12) * (3/4)

This will clear the fractions:

2(4x) - 3(12) = 3(3)

Now, simplify each term:

8x - 36 = 9

So, the equation without fractions is:

8x - 36 = 9

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9514 1404 393

Answer:

  x = 39

Step-by-step explanation:

The usual approach is ...

  12x -48 = 10x +30 . . . . use the distributive property to eliminate parentheses

  2x -48 = 30 . . . . . . . . . subtract 10x from both sides [1]

  2x = 78 . . . . . . . . . . . . add 48 to both sides [2]

  x = 39 . . . . . . . . . . . . divide both sides by the coefficient of x

The solution is x = 39.

__

Check

4(3x -12) = 5(2x +6) . . . . given

4(3·39 -12 = 5(2·39 +6) . . . . substitute for x

4(117 -12) = 5(78 +6) . . . . . . . multiply

4(105) = 5(84) . . . . . . . . . . . . add

420 = 420 . . . . . . . . . . . . . . multiply

The found value of x makes the equation true, so is the solution.

_____

Additional Notes

[1] The point of the solution process is to put the variable on one side of the equal sign and a constant on the other side. To that end, we subtract the smallest variable term from both sides of the equation. The net result is a variable term on one side of the equal sign that has a positive coefficient.

We could have subtracted either of the constant terms first, and subtracted the variable term second. In this latter approach, the variable term subtracted is the one on the same side of the equation as the remaining constant term. Unless care is taken to select the constant on the side of the largest variable term (for subtraction), the net result may be a negative variable term. Technically, that works just as well, but can tend to increase the probability of an error being made.

__

[2] We notice that all of the terms in the equation after the last step have the x-coefficient as a common factor. This gives us the opportunity to divide by that coefficient at this stage. Doing this would give x-24=15. Then adding 24 would give the same final solution. Sometimes I like to work equations this way so the variable is "bare" (has a coefficient of 1) sooner, and the numbers are smaller.

__

In this discussion, when we talk about subtracting or dividing, we mean the entire equation is involved. The properties of equality tell us the equal sign remains valid if the same operation is performed on both sides of the equation. Our discussion here takes for granted that understanding. We have occasionally said "[do such and such] to both sides". Even where it isn't stated, the "to both sides" always applies.

Answer:

No real solutions, or 0

Explanation:

We can determine how many real solutions a quadratic function has, we can use the quadratic formula.

The quadratic formula for expressions written in ax² + bx + c form is:

[tex]x = \frac{-b +/- \sqrt{b^{2}-4ac}}{2a}[/tex]

In the equation x² + 5x + 7, a = 1, b = 5 and c = 7

When we plug them in, we get:

[tex]x = \frac{-5 +/-\sqrt{5^2 - 4(1)(7)}}{2(1)}\\ \\= \frac{-5+/-\sqrt{25 - 28}}{2}\\ \\=\frac{-5+/-\sqrt{-3}}{2}}[/tex]

We cannot find the square root of a negative number without diving into the realm of imaginary numbers in which √-3 becomes i√3. Therefore, the equation has no real solutions. This is because the equation x² + 5x + 7 is an upward-facing parabola translated up 7 units and, as such, does not cross the x-axis. If the equation yields a graph that does not cross the x-axis, then there will be zero answers for what variable x equals.

Answer:

16 cm

Step-by-step explanation:

Given : The area of triangle ABC is 24 square centimeters.

To Find: If B = 30° and a = 6 cm, what is the measure of side c?

Solution:

Formula : [tex]Area = \frac{1}{2} \times a \times c \times sin B[/tex]

a = 6

Area = 24

B = 30°

Substitute the values in the formula

[tex]24 = \frac{1}{2} \times 6 \times c \times sin 30[/tex]

[tex]24 = \frac{1}{2} \times 6 \times c \times \frac{1}{2}[/tex]

[tex]24 =3 \times c \times \frac{1}{2}[/tex]

[tex]\frac{24 \times 2}{3} =c[/tex]

[tex]16=c[/tex]

Hence the measure of side c is 16 cm

So, Option c is correct.

Answer:

It helps distinguish it from other means, such as the geometric mean and the harmonic mean. When someone asks for the average of a group of numbers, they’re most likely asking for the arithmetic mean. An arithmetic mean is calculated by adding several quantities together and dividing the sum by the number of quantities.

Step-by-step explanation:

I got a 100% for this answer :)

There are 2730 different ways for a club with 15 members to choose a president, vice president, and treasurer, with each office being held by a different person.

To determine the number of ways the club can choose a president, vice president, and treasurer, we can use the concept of permutations since the order of selection matters here, and no person can hold more than one office.

The first office to be filled is the president's.

There are 15 potential members to fill this role.

Once the president has been chosen, there are 14 remaining members who could be the vice president.

Finally, for the treasurer, there are 13 members left to choose from.

To find the total number of ways to choose these officers, we multiply the number of choices for each office together.

Number of ways = 15 (for president) × 14 (for vice president) × 13 (for treasurer) = 2730 ways.

So, there are 2730 different ways in which the club can select a president, vice president, and treasurer.

The inequality representing the weight of the freezer when the stove weighs 170 pounds and the combined weight of both is at least 370 pounds is 170 + F ≥ 370.

To find the correct inequality for the weight of the freezer, given that the stove weighs 170 pounds and the combined weight of the stove and freezer is at least 370 pounds, you can represent this as an inequality.

170 + F ≥ 370

In this inequality, 170 represents the weight of the stove and F represents the weight of the freezer.

Therefore, the correct inequality is 170 + F ≥ 370.

yepAnswer:

Step-by-step explanation: