Which other congruency statements are true?

Answer:

The width is 20 inches, the length is 32 inches and the height is 15 inches.

Step-by-step explanation:

Let x inches be the width of the box. If the length of the box is 12 inches greater than its width, then the length of the box is x+12 inches. If the height of the box is 5 inches less than its width, then the height of the box is x-5 inches.

The volume of box is

[tex]V=\text{length}\cdot \text{width}\cdot \text{height}\ in^3.[/tex]

Therefore,

[tex]9600=x\cdot (x+12)\cdot (x-5).[/tex]

Solve this equation:

[tex]x(x^2+12x-5x-60)=9600,\\ \\x^3+7x^2-60x-9600=0.[/tex]

The integer solutions of this equation can be among the divisors of -9600. The divisors of 9600 are:

[tex]\pm1, \pm2, \pm3, \pm4,\pm5,\pm6,\pm8,\pm10,\pm12,\pm15,\pm16,\pm20,\pm24,\pm25,\pm30,\pm32,....[/tex]

We can check all these divisors and see that x=20 is a solution, then using synthetic division

[tex]x^3+7x^2-60x-9600=(x-20)(x^2+27x+480).[/tex]

Since the quadratic factor has discriminant [tex]D=27^2-4\cdot 480=-1191<0,[/tex] we can state that the only solution is x=20 inches. The width is 20 inches, the length is 32 inches and the height is 15 inches.

Answer:

hmmmm lemme think

Step-by-step explanation:

Answer:

A. 63°

Step-by-step explanation:

Since line RU and line TU are tangent to the circle from a common point U, then RU = TU.

Therefore; Triangle RUT is an isosceles triangle.

Thus; m∠R = m∠T

Hence; m∠R = (180° -54°)/2

                     = 126°/2

                     = 63°

Answer:

4

Step-by-step explanation:

Using the rule of exponents

• [tex]a^{\frac{m}{n} }[/tex] ⇔ [tex]\sqrt[n]{a^{m} }[/tex], hence

[tex]16^{\frac{1}{2} }[/tex] = [tex]\sqrt[2]{16^{1} }[/tex] = 4

Answer:  4

Step-by-step explanation:

[tex]16^{\frac{1}{2}}=\sqrt{16}=\sqrt{4\cdot 4}=\boxed{4}[/tex]

Answer:

[tex]\large\boxed{B)\ y=(x-3)^2+9}[/tex]

Step-by-step explanation:

[tex]\text{The vertex form of equation}\ y=ax^2+bx+c:\\\\y=a(x-h)^2+k\\\\h=\dfrac{-b}{2a},\ k=f(h)\\\\\text{We have the equation:}\ y=x^2-6x+18\\\\a=1,\ b=-6,\ c=18\\\\\text{Substitute:}\\\\h=\dfrac{-(-6)}{2(1)}=\dfrac{6}{2}=3\\\\k=f(3)=3^2-6(3)+18=9-18+18=9[/tex]

Answer:

the answer is B

Step-by-step explanation:

i just did it on usa testprep trust me

Answer:

4.40 is that an option i did 17.60 divided by 4 it may be wrong

Step-by-step explanation:

This means it costs $17.60 for 4 pairs. Divide 17.60 by 4 to find the price per 1 unit. 17.60 / 4 = $4.40 per unit

Hope this helps!

The percent of decrease from 10 to 3 can be calculated by finding the difference between the two numbers, dividing this difference by the original number, and multiplying the result by 100. This method gives us a decrease of 70%.

The question is looking to find the percent of decrease between two numbers, specifically from 10 to 3. To calculate this, we first find the difference between the two numbers (which is 10 - 3 = 7), then divide this difference by the original number (7 divided by 10 equals 0.7) and finally multiply the result by 100 to convert it to percentage form. This gives us a 70% decrease.

Here are the step-by-step calculations:

So, the decrease from 10 to 3 is 70%.

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Answer:

36° or 101°

Step-by-step explanation:

Consider the figures given in the attachment.

Point C can be between A and B as shown in the left image of the attachment or outside AB chord as shown in the right image.

In both figures, ∠AOB = 115° and ∠AOC = 43°.

Both the triangles are isoceles triangle as OC and OA side is equal in ΔAOC and OA and OB is equal in ΔAOB.

In ΔAOC,

∠A + ∠O + ∠C = 180°

∠A = ∠C

∴ 2 ∠A =180-43=137°

∴∠A = 68.5

In ΔAOB,

∠A + ∠B + ∠O = 180°

∠A = ∠B

∴2 ∠A = 180-115=65°

∴∠A = 32.5°

For figure on the left side,

∠BAC = ∠OAC - ∠OAB = 68.5 - 32.5 =36°

For figure on right side,

∠BAC = ∠OAC + ∠OAB = 68.5 + 32.5 =101°

Answer:

(5, 9)

Step-by-step explanation:

Substitute the x- coordinate of the point into the equation to evaluate the y- coordinate, that is

x = 5 : y = (2 × 5 ) - 1 = 10 - 1 = 9 → B

Hence the coordinates of the point are (5, 9 )

Final answer:

Using the equation y = 2x - 1, the y-coordinate for the point (5, __) is calculated to be 9 by substituting x = 5 into the equation, resulting in the value that fits the identified pattern.

Explanation:

The question asks for the y-coordinate of the point (5, __) based on the pattern described by the equation y = 2x - 1. We see that the given points (3, 5) and (4, 7) fit this pattern, as plugging x = 3 into the equation gives y = 2(3) - 1 = 5, and plugging x = 4 into the equation gives y = 2(4) - 1 = 7. To find the y-coordinate for the point where x = 5, we can follow the same arithmetic pattern.

Using the equation, we plug in x = 5:

y = 2(5) - 1
= 10 - 1
= 9

Therefore, the y-coordinate for the point (5, __) is 9, which corresponds to option B.

Answer:84

Step-by-step explanation:

Set up a proportion

36/150 =x/350

Cross multiply then divide

Answer:

84 people wear blue jeans.

Step-by-step explanation:

This is the same out of questions that are multiples of each other, except we have to use decimals. 350/150 is 7/3, so we know in order to get 350 with 150, we need to multiply 7/3. Now, we multiply 36 by 7/3 to get 84 as our answer

Your ratio is 5:4.

We have 5 saxophone players & 4 trumpet players.

So if we have 4 trumpet players we have our first number in our ratio which would be: [tex]4:?[/tex]

Our second number is 5, that 5 represents the saxophone players.

That brings that to our equation 5:4.

Have an amazing day.

The ratio of trumpet players to saxophone players in the band is 4:5. This means there are 4 trumpet players for every 5 saxophone players.

To find the ratio of trumpet players to saxophone players in the band, we need to compare the numbers of each type of player.

So, the ratio of trumpet players to saxophone players in the band is 4:5.

This means that for every 4 trumpet players, there are 5 saxophone players.

ANSWER

[tex]y = 3x - 3[/tex]

EXPLANATION

Let

[tex]y = mx + c[/tex]

be the equation.

We can choose any two ordered pairs to determine the equation of the relation.

[tex](6,15) \: and \: (8,21)[/tex]

We find m using the formula;

[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]

[tex]m = \frac{21 - 15}{8 - 6} = \frac{6}{2} = 3[/tex]

The equation becomes

[tex]y = 3x + c[/tex]

When x=6, y=15.

This implies that,

[tex]15 = 3(6) + c[/tex]

[tex]15= 18 + c[/tex]

[tex]15 - 18= c[/tex]

[tex]c = -3[/tex]

The equation of the relation is therefore,

[tex]y = 3x -3[/tex]

2.7. Because of the CPCTC theorem, like CB is equal to 5.9 so if you add the lengths of CB, CD, and ED and subtract this by 17, you find the length of BE which is 2.7

Answer:

Option B, 2.7 is the answer.

Step-by-step explanation:

Perimeter of CBED = CD + ED + BC + BE

                         17   =  5.6 + 2.8 + 5.9 + BE

[Since ABEF ≅ CBED  so  AB = BC = 5.9]

Now      17   =  14.3 + BE

             BE =  17 - 14.3

                 = 2.7

Therefore, Length of BE = 2.7

Option B, 2.7 is the answer.

Answer:

The work shown here is correct.

It simplifies to 17x + 36y + 5.

Step-by-step explanation:

In this situation, there are four different items being purchased. This means their will be a sum of 4 terms. Each term will be the number of the item times its cost. When added together, the four terms will represent the total cost.

7 pens at $x is 7x

5 pens at $(2x+3) is 5(2x+3)

y pens at $6 is 6y

(3y-1) pens at $10 each is 10(3y-1)

All together the cost expression is 7x + 5(2x+3) + 6y + 10(3y -1).

Simplify by applying the distributive property and combine like terms.

7x + 10x + 15 + 6y + 30y - 10

17x + 36y + 5

Answer:

D) 68°

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the opposite interior angles

z = 39+29

z =68

Answer:

I believe that the answer is "D"

Step-by-step explanation:

Because the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.

Answer:

Step-by-step explanation:

its b trust me.

Answer:

b

Step-by-step explanation:

Answer:

[tex]<V=65\°[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

In the right triangle VWX

[tex]tan(V)=\frac{WX}{XV}[/tex] -----> opposite side angle V divided by the adjacent side angle V

substitute the values

[tex]tan(V)=\frac{57}{27}[/tex]

[tex]<V=arctan(\frac{57}{27})=65\°[/tex]

Final answer:

To find the measure of ∠V, we take the ratio of XV to WX (opposite to adjacent side) and use the tangent function. By calculating tan(∠V) = 27/57 and taking the inverse tangent, we get ∠V ≈ 25° to the nearest degree.

Explanation:

To find the measure of ∠V in ∆VWX, where ∠X=90°, XV = 27 feet, and WX = 57 feet, we use the trigonometric ratios, specifically the tangent function, since we are dealing with a right-angled triangle and we have the lengths of the opposite side (XV) and the adjacent side (WX) to ∠V.

Step by Step Solution:

Use the definition of the tangent function: tan(∠V) = opposite/adjacent.

Substitute the known values: tan(∠V) = XV/WX = 27/57.

Calculate tan(∠V) = 0.4737.

Find the angle whose tangent is 0.4737 using an inverse tangent function on a calculator: ∠V ≈ 25° (to the nearest degree).

Therefore, the measure of ∠V is approximately 25°.

6 x 6 = 36 x 3.14 = 113.04

Area = 113.04

Answer:

(-3, 0)

Step-by-step explanation:

The x-intercept is the value of x when y = 0.

                           2x +  5y   = -6

Set y = 0              2x + 5(0) = -6

                           2x            = -6

Divide each side by 2     x = -3

The x-intercept is at (-3, 0).

Let n represent the unknown number

n-10=9

+10 +10

—————

n=19

Brainliest??

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➷ At the top, the word is quadrilaterals

At the second one, the word is parallelograms

For the third layer on the left, the word is rectangles

For the third layer on the right, the word is rhombuses

Explanation:

a square is a rectangle too, and a rhombus is a shape with 4 equal sides.

Rhombuses and rectangles are parallelograms,

and a parallelogram is also a quadrilaterals.

In fact, all the shapes in the chart are all quadrilaterals.

✽

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

TROLLER

Answer:

At the top, the word is quadrilaterals

At the second one, the word is parallelograms

Step-by-step explanation:

➷ mean = n x p

mean = 185 x 0.712

mean = 131.72

Answer is option C

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

The mean of age is 131.72. Therefore, option C is the correct answer.

Given that, a binomial distribution the experiment consisted of 185 trials in the probability of success and age trial was 0.712.

The binomial distribution is a commonly used discrete distribution in statistics. The normal distribution as opposed to a binomial distribution is a continuous distribution. The binomial distribution represents the probability for 'x' successes of an experiment in 'n' trials, given a success probability 'p' for each trial at the experiment.

Here, mean= 185×0.712

= 131.72

The mean of age is 131.72. Therefore, option C is the correct answer.

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Answer:

[tex]-\frac{4m^{4}n^{2}}{9}[/tex]

Step-by-step explanation:

The given expression is

[tex]=\frac{(2m^3n^2)^3}{-18m^5n^4}[/tex]

Use the power rule of indices on the denominator;[tex](a^m)^n=a^{mn}[/tex]

[tex]=\frac{8m^9n^6}{-18m^5n^4}[/tex]

We apply the quotient rule of indices; [tex]\frac{a^m}{a^n} =a^{m-n}[/tex]

[tex]=\frac{8m^9n^6}{-18m^5n^4}[/tex]

[tex]=-\frac{4m^{9-5}n^{6-4}}{9}[/tex]

Simplify

[tex]=-\frac{4m^{4}n^{2}}{9}[/tex]

Answer:

The correct answer is

(2m³n²)³/(-18m⁵n⁴) = - m⁴n²/9

Step-by-step explanation:

It is given an expression,

(2m³n²)³/(-18m⁵n⁴)

Points to remember

Identities

1).  (xᵃ)ᵇ  =  xᵃᵇ

2).  xᵃ/xᵇ = xᵃ⁻ᵇ

To solve the expression

(2m³n²)³/(-18m⁵n⁴) = -2m⁹n⁶/18m⁵n⁴    (Using identity 1)

 = -2/18(m⁹⁻⁵n⁶⁻⁴)     (Using identity 2)

 = -1/9(m⁴n²)

 = - m⁴n²/9

Therefore the simplified form of given expression is given by,

(2m³n²)³/(-18m⁵n⁴) = - m⁴n²/9

8 x 2/3 = 16/3

8 - 16/3 = 8/3

There is 8/3 or 2 2/3 yards of fabric left.

The reciprocal of the fraction 1/11 is equal to 11/1.

To answer this question you need to know what the reciprocal of a number is.

The reciprocal of a number is the number that will multiply that number and give a product of 1.

To find the reciprocal of a fraction, simply invert it such that the denominator becomes the numerator and the numerator becomes the denominator.

In this scenario therefore, the reciprocal of 1/11 is:

= 11/1

In conclusion, the reciprocal of 1/11 is 11/1.

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Answer:

80000/0.0004 = 2'000'000'000 or 2 x 10^-9

8*10^4 = 80'000

4*10^-5 = 0.00004

Step-by-step explanation:

Answer:

0,2

Step-by-step explanation:

[8*10^4] / [4*10^5]

2*[10000/100000]

0,2

Best regards

Answer:

The answer is 65%

Step-by-step explanation:

q= 80-28

q= 52

52/80 = p/100

5200 = 80p

5200/80 = p

65 = p

Hope this helps! Have a great day!

(~‾ ▿ ‾)~

Answer: 65 %

Step-by-step explanation:

Answer:

5

Step-by-step explanation: