Find the volume of composite solid.

An example of two fraction whose product is an integer due to common factors is [tex]\frac{6}{3}[/tex].

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

What is a common factor?

The largest positive integer that divides each of the integers is known as the greatest common divisor of two or more non-zero integers. The greatest common divisor of two integers x and y is indicated by the display style "gcd"

Given that,

Two fraction whose product is an integer due to common factor.

The fraction is

[tex]\frac{6}{3}[/tex].

Since,

2 x 3 = 6

1 x 3 = 3

Here, 3 is the common factor.

[tex]\frac{6}{3}[/tex] = 2

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Answer:5in

Step-by-step explanation:

1. Identify the triangle

you are given a right triangle with the hypotonus missing and are given the side lengths 3 and 4 you know the hypotonus is 5 by the 3,4,5 Pythagorean tripe, if you do not notice this it can be solved with the Pythagorean theorem a^2+b^2=c^2

2. solve (if not done with 3,4,5 triple)

3^2+4^2=c^2

9+16=c^2

25=c^2

5=c | square root both sides to cancel the square

Answer:

Step-by-step explanation:

The total number of terms in the given expression 2x + 7 is equal to two.

As given in the question,

Expression is given by:

2x + 7

Number of terms in the given expression 2x + 7  are as follow:

7 is the constant term of the given expression 2x + 7

x is the variable which is multiply by two written as 2x in the given expression 2x + 7.

Both the terms 7 and 2x in the given expression are related with the operation addition'+'

Therefore, the total number of terms in the given expression 2x + 7 is equal to two.

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1220 km apart

rates

320 km/ hr

290 km/hr

___________________________________

x= t* rate

t = time in hours

x = distance in km

__________________

total distance = t1 * 320 Km/h + t2* 290 km/h

because they started at the same time

Total distance = 1220 km = t * 320 Km/h + t* 290 km/h

1220 = (320 + 290 ) t

1220 = 610 t

t = 1200/ 610

t = 2 hours

_______________________--

Answer

2 hours

Answer:

1. x = 18

2. x = 154

Step-by-step explanation:

 2          12

------- = -------

  3          x

 3 × 12 = 36

2 × x = 2x

36 = 2x

÷2    ÷2

---------------

x = 18

----------------------------------------------------------------------------------------------------------

  6         84

------- = -------

  11           x

6 × x = 6x

84 × 11 = 924

6x = 924

÷6     ÷6

-----------------

x = 154

I hope this helps!

The new amount as a percentage of the price before the increase is =[tex]\frac{118.2x}{100}[/tex]

The Latin word "per centum," which means "by the hundred," is where the word "percentage" originally came from. With 100 as the denominator, percentages are fractions. To put it another way, it's the relationship between a component and a whole in which the value of the whole is always assumed to be 100.

Let, the odd price be x then

we can write the new amount as a percentage of the price before increasing as

x ×[tex]\frac{(100+18.2)}{100}[/tex]

=[tex]\frac{118.2x}{100}[/tex]

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If Peyton needs to order some new supplies for the restaurant where she works. The restaurant needs at least 732 forks. the number of sets of forks Peyton could buy for the restaurant to have enough forks is 44.5.

Let x represent the number of sets of forks

Formulate the inequality

287 + 10 × x = 732

Hence,

10x = 732 -287

10x = 445

Divide both side by 10x

x = 445/10

x = 44.5

Therefore we can conclude that 44.5 represent the number of the set of forks that could be bought.

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We can try to write the expression 36+26 taking a common factor, so:

The option B is the correct answer.

Answer:

5 + 2x

Since 2 times a number is multiplication we make it 2x

Answer:

A) 32 is 4 times as many as 8

C) 32 is 8 times as many as 4

Step-by-step explanation:

8x4=32

4×8=32

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Define a quadratic equation that does not passes through the x-axis

When a quadratic function never crosses the x-axis, then it has no real roots or solutions. Hence, the discriminant must be negative. meaning the solutions are imaginary/complex.

Hence, the answer will be:

The function has two imaginary roots

The constant of proportionality for the equation y = 2x is k = 2.

The number of pieces of fruit the monkey can eat is two times the amount of time the monkey takes.

The equation y = 2x can be used to represent a monkey eating 24 pieces of fruit in 12 hours.

The constant of proportionality, which is a fixed value that represents the rate at which two or more ratios rise or decrease, is used to compare them. The result of dividing the denominator by the numerator when a ratio is expressed as a fraction is the constant of proportionality.

When a ratio is expressed as a fraction, the constant of proportionality is found by dividing the denominator by the numerator. The constant of proportionality, k, can be calculated from the equation if x is the ratio's numerator and y is its denominator.

k = y/x

Therefore, the constant of proportionality in this case is:

y = 2x

k = y/x = 2

The constant of proportionality in this case represents that the number of pieces of fruit a monkey eats is two times the amount of time the monkey takes.

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Answer:

D

Step-by-step explanation:

...................

The solutions to the quadratic equation x² + 10x - 13 = 17 are x = -5 + √55 and x = -5 - √55. The correct answer is option D.

The quadratic equation is given as:

x²+10x-13 =17

Move the constant term to the right side of the equation:

x² + 10x - 13 - 17 = 0

x² + 10x - 30 = 0

Take half of the coefficient of the x-term (10) and square it: (10/2)² = 25.

Add the squared value to both sides of the equation:

x² + 10x + 25 - 30 = 25

(x + 5)² - 30 = 25

Simplify the equation:

(x + 5)² = 25 + 30

(x + 5)² = 55

Take the square root of both sides of the equation:

√((x + 5)²) = ±√55

x + 5 = ±√55

Solve for x by subtracting 5 from both sides:

x = -5 ± √55

Therefore, the solutions to the equation x² + 10x - 13 = 17 are:

x = -5 + √55 and x = -5 - √55.

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The amount of Muskco's work force that he has in  his business is; 138 people

We are told that Muskco gave 88 people a bonus. Now, we are further told that if he had given 4 more people bonuses, then it means he would have rewarded two thirds of his workforce.

Thus we can begin too solve this problem to find the size of Muskco's work force by;

Let the total number of his workforce be denoted as x. Then the algebraic equation for this problem would be expressed as;

88 + 4 = (2/3)x

Simplify by adding up the left hand side values to get;

(2/3)x = 92

Use multiplication property of equality to Multiply both sides by 3 to get;

2x = (92 * 3)

2x = 276

Now, use division property of equality to divide both sides by 2 to get;

2x/2 = 276/2

x = 138

Thus, we would conclude from the calculations as seen in the above that the size of Muskco's workforce is 138 people.

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Explanation

we have a linear function, to graph a linear function you need 2 points

Step 1

find 2 coordinates of the line

a) when x= 0

then

b)when x=2

Step 2

now, draw a line that passes through the points

I hope this helps you

Answer:

I believe it is -123

Step-by-step explanation:

you have to replace all the x's with -4 so you would do the equation -6(-4)^2+8(-4)+5

-6(-4)^2 is -96

-96+8(-4) is -128

-128+5 is -123

The elements in the set A'∩B is { z } .

Set theory is a branch of mathematical logic that studies sets, which are essentially collections of objects.

Given universal set U = {q, r, s, t, u, v, w, x, y, z}

set A = {q, s, u, w, y}

∴A' = {r, t, v, x, z}

set B =  {q, s, y, z}

Now A'∩B = { z }

Hence the elements in the set A'∩B is { z } .

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The given numbers are :

Simplify each term into decimal form :

- 2.5 = - 2.5

Now simplify the second term : -1 1/2

So, the numbers are :

Thus, we get :

The greater is the number with the neagtive sign least is the number,

So, the greatest number - 2.9 < - 2.5 < - 0.75 < - 0.5 < -0.3

Arrange of these number from least to greatest :

No comapre :

-2.9 < - 2.5 < - 0.75 < - 0.5 < -0.3

Answer : d)

The inches of wire that he will have left on a spoop after he makes the repair is 4 2/3 feet.

From the information, the electrician has a 16 foot spool of wire and he needs to cut an 11 foot, 4 inch piece from the spool to make a repair.

Therefore, the inches of wire that he will have left will be:

Note that 1 feet = 12 inches

11 foot 4 inches = 11 4/12 = 11 1/3

The amount left will be:

= 16 - 11 1/3

= 4 2/3 feet.

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Answer:

90 degrees

Step-by-step explanation:

We can take a look at that each these triangles are in truth right triangles, seeing that the two angles of and both have measures of 90 degrees.

Answer:

x = 15

Step-by-step explanation:

[tex]4 + \frac{x}{3} = 9[/tex]

[tex] \frac{x}{3} = 5[/tex]

[tex]x = 15[/tex]

Answer:

x = 15

Step-by-step explanation:

Subtract 3 from each side: 12 + x = 27

Subtract 12 from both sides: x =27 − 12

Subtract 12 from 27 to get 15: x = 15

For Pizza 1, Adam multiplies 6 by 6 slices

For Pizza 2, he multiplies 6 by 7 slices

For Pizza 3, he multiplies 4 by 7 slices, while

for Pizza 4, he multiplies 4 by 8 slices.

A product is the outcome of multiplication or an expression that indicates factors to be multiplied in mathematics.

To put it another way, we may deduce that in math, multiplying implies adding equal groups.

The number of items in the group grows as we multiply. A multiplication issue includes the two elements and the product. The factors in the multiplication problem, 4 7 = 28, are the numbers 4 and 7, while the result (product) is the number 28.

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Is valid proportion here

(10 + 5 )/ 18 = 10/d

then find d

d= 18• 10/ (10+5)

d= 180/15 =

d= 12

Then answer is

d = 12 mm

The non-real solutions of the polynomial expression are x = (2 + i√26)/3 and  x = (2 - i√26)/3

The equation of the polynomial expression is given as:

3x^3 + 14x^2 - 14x + 60 = 0

From the question, we have

Real solution = -6

Rewrite the above equation as

x = -6

Add 6 to both sides of the equation

So, we have

x + 6 = 0

The next step is to divide the polynomial equation 3x^3 + 14x^2 - 14x + 60 = 0 by x + 6 = 0

This is represented as

3x^3 + 14x^2 - 14x + 60/x + 6

Using a graphing calculator, we have

3x^3 + 14x^2 - 14x + 60/x + 6 = 3x^2 - 4x + 10

Next, we determine the solution of the quadratic expression 3x^2 - 4x + 10 using a quadratic formula

So, we have

x = (-b ± √(b² - 4ac))/2a

This gives

x = (4 ± √((-4)² - 4 * 3 * 10))/2 * 3

So, we have

x = (4 ± √-104)/6

This gives

x = (4 ± 2√-26)/6

Divide

x = (2 ± √-26)/3

Rewrite as

x = (2 ± i√26)/3

Split

x = (2 + i√26)/3 and  x = (2 - i√26)/3

So, the conclusion is that

Using the polynomial expression, the non-real solutions are x = (2 + i√26)/3 and  x = (2 - i√26)/3

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For Quadrilateral A B C D as shown the remaining angle measures if the figure is to be a parallelogram ∠B=∠D=101°  ∠C = 79

This is further explained below.

A parallelogram is a basic quadrilateral in Euclidean geometry that has two pairs of sides that are parallel to one another.

The sides that are perpendicular to one another, also known as facing sides, of a parallelogram, have the same length, and the angles that are perpendicular to one another have the same measure.

In most cases, a parallelogram will have two sets of parallel opposing sides. The angles that are diagonal to it are likewise equal.

When angle A is given as 79 degrees and the parallelogram ABCD is used, the remaining angles may be obtained as follows:

Angle A is diametrically opposed to angle C.

[tex]\angle A$ is opposite to $\angle C \\\\\angle A=\angle C \\\\\angle C=79^{\circ}[/tex]

Hence ∠C=79°

Because it is a parallelogram, the two remaining angles are complementary to one another and have the same degree:

[tex]\angle B=\angle D\\\\=0.5\left(360^{\circ}-2 \times 79^{\circ}\right)[/tex]

<B=101

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