Solve

b = 3/4a
a + b = 21
​

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]

Answer: 50

Step-by-step explanation: First of all, you need to establish your rate of acceptance. This would be 10 out of 48 or 10/48. Next, you need to simplify this to 5/24. Okay now this is epic. Now you need to convert 5/24 to x/240. Simple. Just multiply both sides by ten in 5/24 and you get your answer of 50. Very cool.

Final answer:

Michelle can expect approximately 50 students to join her book club based on the proportion of surveyed students who expressed interest.

Explanation:

Michelle surveyed 48 students, and 10 said they would join the book club. To estimate how many out of the total 240 students might join, we use proportions. The first step is to set up a proportion with the numbers Michelle has provided and then solve for the unknown:

Number of students surveyed who would join / Total students surveyed = Expected number who would join / Total students in grade

10 / 48 = x / 240

To find x, multiply both sides by 240:

240 * (10 / 48) = x

Then solve for x:

x = 50

Thus, Michelle could expect about 50 students to join the book club.

To find the contribution of each man (this is a sexist problem as women could work as well, but that’s besides the point) take 5/2 and then multiply that value by 20 and you’ll find it takes 50 hours for two men to do it.

Answer: 50 hours

Answer:

50 hours.

Step-by-step explanation:

To solve these type of question we should always remember that man power is inversely proportionate to the work done.

That means if we double the manpower work done will be half. and when we reduce the manpower to the half time take to complete the work will be double.

It takes 5 men to brick a house = 20 hours

so 1 man will brick the house = 20 × 5

                                                = 100 hours

Therefore, 2 men will brick the house =  [tex]\frac{100}{2}[/tex]

                                                               = 50 hours.

We can convert the mixed fraction into simple fraction by following method

Multiply the whole number part by the fraction's denominator.

Add that to the numerator

Then write the result on top of the denominator.

For example  [tex]2\frac{3}{5}[/tex] can be written as [tex]\frac{13}{5}[/tex]

Answer:

5

Step-by-step explanation:

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]

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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8 x 2/3 = 16/3

8 - 16/3 = 8/3

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

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°

I think it’s 9.10 but I’m not really sure

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:

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

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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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.

♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫

➷ 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:

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:

[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

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

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°.

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:

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.

I am pretty sure that it is 8,12,16 and 20

if not plz forgive me

The common denominators for 1/4 and 1/2 are:

These denominators are found by identifying the multiples of the denominators of 1/4 and 1/2.

The question at hand involves finding four common denominators for the fractions 1/4 and 1/2. A common denominator is a shared multiple of the denominators of two or more fractions. This task is essential for operations like addition, subtraction, or comparison of fractions.

4: This is the most obvious choice since 4 is the denominator of one of the fractions, and 2 is a factor of 4. Hence, 1/2 can be expressed as 2/4.

8: Doubling the first common denominator gives us 8. In this case, 1/4 becomes 2/8 and 1/2 is 4/8.

12: Multiplying the denominators 4 and 2 gives us another common denominator, 12. Thus, 1/4 can be expressed as 3/12 and 1/2 as 6/12.

20: Choosing a higher number that is divisible by both 4 and 2. Here, 1/4 is 5/20 and 1/2 becomes 10/20.

These examples show how to scale the numerators accordingly to maintain the value of the original fractions while having the same denominator.

Answer:

C. 10z(x - 2y)

Step-by-step explanation:

10xz − 20y

Factor the terms

Factors of   10xz =          2 ×      5 × x ×        z

Factors of -20yz = (-1) × 2 × 2 × 5 ×       y × z

Identify their greatest common  factor

The common factors are 2, 5, and z. The greatest common  factor is 10z.

Rewrite them with the GCF as a factor

 10xz = 10z ×      x

-20yz = 10z × (-2y)

Replace the terms in the original expression with the factored terms

10xz − 20yz = 10z(x) + 10z(-2y)

Use the distributive property to isolate the greatest common factor

10z(x) + 10z(-2y) = 10z(x - 2y)

Answer:

C. 10z(x - 2y)

Step-by-step explanation:

Answer:

69

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:

36m^2

Step-by-step explanation:

Divide the figure into 2 rectangles with the dimensions : 6 x 3 and 2 x 9

Then, use the rectangle area formula A = b * h

18 + 18 = 36

Answer:

QP = 6

Step-by-step explanation:

We are given a line MP with a point on it Q and we are to find the length of the line segment QP.

We know that the length of MP is [tex] x + 17 [/tex], MQ is [tex]3[/tex] and QP is [tex] 2 x + 22 [/tex] so we can write it as:

[tex]MP=MQ+QP[/tex]

[tex]x+17=3+2x+22[/tex]

[tex]2x-x=17-22-3[/tex]

[tex]x=-8[/tex]

Substituting this value of x to find the length of QP:

QP = [tex] 2x +22 = 2(-8) +22 = [/tex] 6

Answer:

Step-by-step explanation:

its b trust me.

Answer:

b

Step-by-step explanation: