△ABC∼△DEF , △ABC has a height of 20 inches, and △DEF has a height of 24 inches. What is the ratio of the area of △ABC to the area of △DEF ? Enter your answer, in simplest form, in the boxes. :

Answer:

C. is the correct answer i took  the quiz

Step-by-step explanation:

The optimal level of production for Alonzo's Cycling is at the point where the profit reaches its peak before starting to decline with further increases in production. This is the level of production that Alonzo's Cycling should aim for to achieve the marginal profit.

To determine which levels of production provide Alonzo's Cycling with the maximum profit, one must consider both the fixed costs and the variable costs associated with production.

The profit for each level of production is calculated by subtracting the total costs (fixed costs plus variable costs) from the total revenue generated by sales. The level of production at which profit is maximized is where the difference between total revenue and total costs is the greatest.

This can be found by analyzing the marginal cost and marginal revenue of production. When marginal revenue equals marginal cost, and if the additional production leads to a decrease in profit, that is the point of maximum profit.

Beyond this point, producing more units would decrease the total profit due to the law of diminishing returns, where the cost of producing additional units exceeds the revenue they generate.

Therefore, the optimal level of production for Alonzo's Cycling is at the point where the profit reaches its peak before starting to decline with further increases in production. This is the level of production that Alonzo's Cycling should aim for to achieve the maximum profit.

Answer:

Given: Kite QRST has a short diagonal of QS and a long diagonal of RT. The diagonals intersect at point P. Side QR = 5m and diagonal QS = 6m.

Since, diagonals of kite bisect each other, thus QP=6m

Now, in ΔPQR, we have

(QR)²= (RP)²+(QP)²

(5)²= (3)²+(RP) ²

25=9+(RP)²

25-9= (RP)²16= (RP)²

RP= 4m

Therefore,  the length of segment RP is 4m.

Step-by-step explanation:

Answer:

Correct choice is A

Step-by-step explanation:

1 step. Multiply [tex]x-5[/tex] by [tex]2x^2[/tex] to get [tex]2x^3-10x^2[/tex] and subtract this polynomial from the polynomial [tex]2x^3-13x^2+16x-5:[/tex]

[tex]2x^3-13x^2+16x-5-(2x^3-10x^2)=2x^2-13x^2+16x-5-2x^3+10x^2=-3x^2+16x-5.[/tex]

2 step. Multiply [tex]x-5[/tex] by [tex]-3x[/tex] to get [tex]-3x^2+15x[/tex] and subtract this polynomial from the polynomial [tex]-3x^2+16x-5:[/tex]

[tex]-3x^2+16x-5-(-3x^2+15x)=-3x^2+16x-5+3x^2-15x=x-5.[/tex]

3 step.  Multiply [tex]x-5[/tex] by [tex]1[/tex] to get [tex]1[/tex] and subtract this polynomial from the polynomial [tex]x-5:[/tex]

[tex]x-5-(x-5)=x-5-x+5=0.[/tex]

Then

[tex]2x^3-13x^2+16x-5=(x-5)(2x^2-3x+1).[/tex]

Answer:

Correct answer is 2x2 − 3x + 1

Step-by-step explanation:

Answer:

its 14 in all actually

Step-by-step explanation:

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Answer:

THIS IS WRONG I TOOK THE TEST... DONT KNOW THE ANSWER STILL.

Step-by-step explanation:

Answer:

the answer is  (8x+9)

Step-by-step explanation:

The largest interior angle of the heptagon, given the angle measures as x, x, x-2, x-2, x+2, x+2, x+4, is 132 degrees after solving for x.

The problem is to determine the degree measure of the largest interior angle in a heptagon. The degree measures of the interior angles are given as x, x, x-2, x-2, x+2, x+2, and x+4 degrees. To solve this, we first use the fact that the sum of the interior angles of a heptagon (7-sided polygon) is given by the formula (n-2) 180 degrees, where n is the number of sides. So, for a heptagon, the sum is

We then set up the equation based on the given interior angles: 3x + (2x - 4) + (2x + 4) + (x + 4) = 900. Simplifying, we get 7x + 4 = 900. Solving for x, we find x = 896/7 = 128 degrees. The largest interior angle is x + 4, which equals

The units to measure the rate of water flow from a shower are smaller than cubic meters per second due to the typical small value of this rate. To determine the rate, you need to know the cross-sectional area of the outlet and the water speed, multiplying the area by the speed.

Part A: We do not measure the rate at which water flows out through a shower head in cubic meters per second because the typical rate of water flow from a shower is much smaller compared to one cubic meter per second. Using such a large unit for a typically small value would result in decimal figures that are often difficult to comprehend. For instance, a regular shower might output 0.01 cubic meters per minute, which convert to a very small number in cubic meters per second; hence cubic centimeters per second or liters per minute are more practical units.

Part B: To calculate the rate of flow from a showerhead, you need to know two quantities: the cross-sectional area of the outlet (which can be calculated if you know the diameter), and the speed at which the water is moving. The rate of flow (volume per unit time) can then be determined by multiplying the area by the speed of the water. Based on the given data from your textbook - a faucet with a 1.80-cm diameter and a speed of 0.500 m/s - the flow rate can be determined using the formula for the volume of a cylinder (Area of the base x Height), where in this case the 'height' would be the speed.

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Answer: $720.

Step-by-step explanation:

The formula to find the simple interest is given by :-

[tex]I=Prt[/tex], where P is the principal amount , r is the rate of interest in decimal and t is the time in years.

Given : Rate of interest : r= 0.025

Simple interest : I= $180

Time : t=10

Let P be the Natalie’s initial deposit when she opened the account, then we have:-

[tex]180=P(0.025)(10)\\\\\Rightarrow\ P(0.25)=180\\\\\Rightarrow\ P=\dfrac{180}{0.25}=\dfrac{18000}{25}=720[/tex]

Hence, the Natalie’s initial deposit when she opened the account was $720.

Answer:

No triangle is formed

Step-by-step explanation:

took test

The answer is defiantly D

The answer is $99! :)

Final answer:

To find the lengths of the sides of two isosceles triangles with equal bases and perimeters of 23 cm and 43 cm, we calculate based on the known relations. The smaller triangle has sides of 10 cm and 3 cm, while the larger triangle has sides of 20 cm and 3 cm.

Explanation:

The problem involves two isosceles triangles with the same base length, but the legs of one triangle are twice as long as the other. One triangle has a perimeter of 23 cm, and the other has a perimeter of 43 cm. To solve this, let's denote the common base of both triangles as b, the legs of the smaller triangle as l, and the legs of the larger triangle as 2l.

For the smaller triangle, the perimeter P is given by P = b + l + l or P = b + 2l. For the larger triangle, the perimeter P is P = b + 2l + 2l or P = b + 4l. Since the perimeters are 23 cm and 43 cm respectively, we can set up two equations: b + 2l = 23 and b + 4l = 43.

Solving these simultaneous equations, subtract the first from the second to find 2l = 20, so l = 10. Substituting l = 10 into the first equation gives us b + 20 = 23, thus b = 3.

Therefore, the sides of the smaller triangle are 10 cm (legs) and 3 cm (base), and the sides of the larger triangle are 20 cm (legs) and 3 cm (base).

Answer:

x = 4 and y = -3.

Step-by-step explanation:

Given  : 4x + 2y = 10  and 3x + 2y = 6.

To find : Solve the system algebraically. Check your work.

Solution : We have given that

4x + 2y = 10 ----(1)

3x + 2y = 6.------(2)

Subtracting equation 2 from 1

4x + 2y = 10

(-)3x + (-)2y =(-) 6.

_____________

x + 0 =  4

x =4

Plug x = 4 in equation 1

4 (4) + 2y = 10.

16 + 2y = 10.

2y  = 10 -16.

2y  = -6.

On dividing by 2 both sides

y = -3.

Check:

Plug the values x =4 , y =-3 in equation 1

4 (4) + 2 ( -3) = 10

16 -6 = 10

10 =10

Verify,

Therefore, x = 4 and y = -3.

The answer is [tex]\( 4.9 \times 10^{11} \)[/tex].

To solve the given mathematical problem, we will multiply the two numbers and then express the result in scientific notation.

First, let's multiply 1,400,000 by 3.5x10^5 without converting them to scientific notation:

[tex]\[ 1,400,000 \times 3.5 \times 10^5 \][/tex]

[tex]\[ = 1400000 \times 3.5 \times 10^5 \][/tex]

[tex]\[ = 4900000 \times 10^5 \][/tex]

Now, we have the product 4900000. To express this in scientific notation, we must write it as a number between 1 and 10 multiplied by a power of 10. The number 4900000 can be written as 4.9 followed by 11 zeros, which in scientific notation is [tex]\( 4.9 \times 10^{11} \)[/tex].

Therefore, the final answer, expressed in scientific notation, is:

[tex]\[ \boxed{4.9 \times 10^{11}} \][/tex]

Answer:

Triangles PQT and RQT are congruent (option D)

Step-by-step explanation:

The AAS or Angle- Angle- Side Theorem says that if two angles and any side of one triangle are congruent to two angles and any side of another triangle, then the triangles are congruent.

So, triangles PQT and RQT are congruent.

Both triangles have angle Q as right angle and angle P and R are also equal. And both have side QT common.

So, these are congruent via AAS.