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Determine if the graph shows a proportional relationship.




Yes, it is proportional because the x-axis and y-axis are labeled correctly.

Yes, it is proportional because it is a line that intersects with the origin.

No, it is not proportional because the x-axis and y-axis are not labeled correctly.

No, it is not proportional because the line does not intersect with the origin.

Answer: Infinitely many

The answer is infinitely many

This is because if the sides are parallel, the other measurements must be the same. They can be any measurement

Using the angle and segment addition postulates, the measures are:

a. m<TSM = 95°

b. m<SIJ = 93°

c. SR = 12 units

d. PQ = 10 units

The angle addition postulate states that two smaller angles have a sum of measure that is equal to the larger angle they form.

Similarly, the segment addition postulate states that two smaller segments that make up a larger segment have a sum that equals the length of the larger segment.

a. m<TSM + m<MSR = m<TSR [angle addition postulate]

Substitute

32x - 1 + 48 = 48x - 1

Solve for x

32x + 47 = 48x - 1

32x - 48x = -47 - 1

-16x = -48

x = -48/-16

x = 3

m<TSM = 32x - 1 = 32(3) - 1

m<TSM = 95°

b. m<HIS + m<SIJ = m<HIJ [angle addition postulate]

Substitute

x + 40 + 2x + 93 = 133

3x + 133 = 133

3x = 133 - 133

3x = 0

x = 0/3

x = 0

m<SIJ = 2x + 93 = 2(0) + 93

m<SIJ = 93°

c. x + 14 + x + 15 = 23

2x + 29 = 23

2x = 23 - 29

2x = -6

x = -3

SR = x + 15 = -3 + 15

SR = 12 units

d. -6 + 2x + 2x - 4 = 22

-10 + 4x = 22

4x = 22 + 10

4x = 32

x = 32/4

x = 8

PQ = -6 + 2x = -6 + 2(8)

PQ = 10 units

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The two polygons are calculated to be similar and the correct statement to show the similarity is in option A

To show that the polygons are similar we show that

Comparing the angles

Comparing  the ratio of corresponding sides

10.5 / 7 = 12 / 8 = 6 / 4 = 9 / 6 = 3 / 2

This shows that option A is the correct choice

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Answer:

They all work at $13.5 an hour, so they all are payed $270 for 20 hours of work

Step-by-step explanation:

Answer:

good luck give other guy branilest

Step-by-step explanation:

The height of ∆EBA is 24cm in the given question where two triangles are similar.

Similar triangles are triangles that have the same shape but differ in size. Similar objects include all equilateral triangles and squares with any side length. In other words, if two triangles are similar, their corresponding angles and sides are congruent and in equal proportion. The " symbol here denotes the similarity of triangles.

We know that in two similar triangles, the ratio of corresponding sides are equal to ratio of their heights.

We have given that ∆DBC ≅ ∆EBA

So,

⇒ (36-h)/h = DC/AE

⇒ (36-h)/h = 10/20

Using cross multiplication

⇒ 20(36-h) = 10h

⇒ 720 - 20h = 10h

⇒ - 20h -10h = -720

⇒ -30h = -720

⇒ 30h = 720

⇒ h = 720/30

⇒ h = 24

Thus, the height of ∆EBA is 24cm in the given question where two triangles are similar.

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Full question

Use similar triangles to calculate the height, h cm, of triangle ABE.

10 cm

С

В.

36 cm

E

20 cm

The value of x will be 1.

What is Line segment?

A line segment is a part of line having two endpoints and it is bounded by two distinct end points and contain every point on the line that is between its endpoint.

Given that;

Point D is lie on the between C and E.

The value of CD = 4x

The value of DE = 19x - 12

The value of CE = 11

Now,

Since, D is lie is between C and E.

So, We can formulate;

CD + DE = CE

Substitute all the values, we get;

⇒ 4x + (19x - 12) = 11

Solve for x;

⇒ 4x + (19x - 12) = 11

Combine like term;

⇒ 23x - 12 = 11

Add 12 we get;

⇒ 23x = 11 + 12

⇒ 23x = 23

Divide by 23, we get;

⇒ x = 1

Therefore, The value of x will be 1.

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Let

x -----> number of liters of 10% acid solution

y ----> number of liters of 70% acid solution

so

we have that

x+y=90 ------> x=90-y -----> equation 1

Remember that

10%=10/100=0.10

70%=70/100=0.70

20%=20/100=0.20

so

0.10x+0.70y=0.20(90) ------> equation 2

Solve the system of equations

substitute equation 1 in equation 2

0.10(90-y)+0.70y=0.20(90)

solve for y

9-0.10y+0.70y=18

0.60y=18-9

0.60y=9

y=15

Find out the value of x

x=90-y

x=90-15=75

therefore

the answer is

Given expression

As given

Its solution will be,

For x=2, it will be,

This is the answer.

following a mixed number [tex]\frac{87}{8} + (\frac{75}{6} - \frac{21}{3} )[/tex] , we get  [tex]16 \frac{3}{8}[/tex]

According to the question, given that

Mixed numbers

[tex]\frac{87}{8} + (\frac{75}{6} - \frac{21}{3} )[/tex]

⇒ [tex]\frac{87}{8} + (\frac{25}{2} - 7 )[/tex]

⇒  [tex]\frac{87}{8} + \frac{25}{2} - 7[/tex]

⇒ [tex]\frac{87 + 100 - 56}{8}[/tex]

⇒ [tex]\frac{131}{8}[/tex]

⇒ [tex]16 \frac{3}{8}[/tex]

Therefore, after solving a mixed number [tex]\frac{87}{8} + (\frac{75}{6} - \frac{21}{3} )[/tex] ,  we get  [tex]16 \frac{3}{8}[/tex]

A whole number plus a proper fraction are combined to form a mixed number. Mixed numbers, commonly referred to as mixed fractions, make it easier for us to comprehend numbers.

A whole number and a legal fraction make up a mixed number. A mixed number like [tex]3\frac{1}{4}[/tex] is one where 1/4 is the correct fraction and 3 is the whole number portion. It should be emphasized that once mixed numbers are transformed into an incorrect fraction, they are simple to add, subtract, multiply, and divide.

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By using the formula for the slope of a line that passes through two points, we will get that the slopes are:

a)  3

b)  -2

c) -1.5

d)  -4

e) 1/4

For a line that passes through two points (x₁, y₁) and (x₂, y₂), the slope is given by the formula:

a = (y₂ - y₁)/(x₂ - x₁)

So we will use that for each of the given pairs.

a) The first pair is (3, 2) and (5, 8), so the slope is:

a = (8 - 2)/(5 - 3) = 6/2 = 3

b) The pair is: (-2, -7) and (-4, -3), so the slope is:

a = (-3 + 7)/(-4 + 2) = 4/-2 = -2

c) The pair is (1, -6) and (-2, -4) so the slope is:

a = (-4 + 6)/(-2 - 1) = 2/-3 = -3/2 = -1.5

d)  The pair is (4, -8) and (-2, 16) so the slope is:

a = (16 + 8)/(-2 - 4) = 24/-6 = -4

e) The pair is (-5, 10) and (7, 13) so the slope is:

a = (13 - 10)/(7 + 5) = 3/12 = 1/4

We found all the slopes for the lines that pass through the given pairs of numbers.

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Using the uniform distribution, it is discovered that there is a 0.625 = 62.5% chance that a randomly picked passenger will have to wait longer than 2.25 minutes.

The boundaries of a uniform distribution are a and b.

The likelihood of discovering a value greater than x is:

P(X > x) = (b - x)/(b - a)

In this problem, the time is equally distributed between 0 and 6 minutes, so.

a=0

b=6

P(X > 2.25) is the probability of a time larger than 2.25 minutes, so:

P(X > x) = (6 - 2.25)/(6 - 0) = 0.625

A randomly picked passenger has a 0.625 = 62.5% chance of waiting longer than 2.25 minutes.

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The slope between the scuba diver and fish would be; 0.5 .

The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.

Given that boat is located a sea level. A scuba diver is given as 80 feet along the surface of the water from the boat and 30 feet below the water surface.

A fish is given as 20 feet along the horizontal plane from the scuba diver and 10 feet.

We are asked to slope between the scuba diver and fish.

The Horizontal distance between diver and fish = 20 feet.

Fish below the scuba diver = 10 feet

Slope between scuba diver and fish is :

Tan Ф =10/20

Tan Ф = 0.5

Therefore, the slope between the scuba diver and fish would be; 0.5 .

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Answer:82

Step-by-step explanation:

Because you need to regroup the numbers, therefore leaving 4-4, which is just a 0, (don't include the 0 in a number).

The expression that represents the Volume , of the composite figure is (Four-thirds)π(10)³ + π(10)²(28) , the correct option is (a) .

In the question ,

it is given that

the composite figure has a cylinder and two hemisphere , one at top and other at bottom,

Formula for  Volume of Cylinder = πr²h ,where ,

r and h are radius and height of cylinder .

,

volume of Hemisphere = (2/3)πr³

where , r is the radius .

given the diameter of cylinder = 20

hence ,the radius of the cylinder = 10

and height of the cylinder = 28

So , the volume of cylinder = π(10)²(28)  ...(i)

since half sphere is stacked on the top and the bottom of the cylinder

the radius of sphere is also = 10

So, the volume of the one Hemisphere = (2/3)π(10)³    

the volume of the two Hemisphere = 2*(2/3)π(10)³

                                                          = (4/3)π(10)³     ....(ii)

The Volume of the composite figure = volume of cylinder + volume of the two Hemispheres

Substituting the values from (i) and (ii) , we get

Volume of the composite figure = π(10)²(28) + (4/3)π(10)³

Rewriting we get

= (4/3)π(10)³ + π(10)²(28)

in words , it is

= (Four-thirds)π(10)³ + π(10)²(28)

Therefore , the expression that represents the Volume , of the composite figure is (Four-thirds)π(10)³ + π(10)²(28) , the correct option is (a) .

The given question is incomplete , the complete question is

A cylinder is shown. A half-sphere is stacked on the top and the bottom of the cylinder. The diameter of the cylinder if 20 and the height of the cylinder is 28.

Which expression represents the volume, in cubic units, of the composite figure?

(a) (Four-thirds)π(10)³ + π(10)²(28)

(b) (Four-thirds)π(20)³ + π(20)²(28)

(c) 2(Four-thirds)π(10)³ + π(10)²(28)

(d) 2(Four-thirds)π(20)³ + π(20)²(28)

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Answer:

Option A

Step-by-step explanation:

EDGE

The linear equation representing the earnings of someone is y=$71.50x.

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.

It is given that x is the number of hours worked, and y is the total amount of money earned.

So, the rate of earning will be the ratio of total earnings to the total number of hours.

So, the rate of earning= y/x dollars per hour

It is given that someone earns $71.50 an hour.

So, the rate of earning= $71.50

Put the value of the earning rate in terms of x and y to obtain a linear equation.

y/x=$71.50

y=$71.50x

So, the linear equation representing the earnings of someone is y=$71.50x.

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Answer:

Step-by-step explanation:

What is the Product Rule of Exponents?When multiplying two numbers with the same base, their powers/exponents would be added.For example, .Given:(a²c)³Therefore:(a²c)³ = (a²c)(a²c)(a²c) (a²c)³ = (a²c)³ = Therefore, applying the product rule of exponents, (a²c)³ = .

The value of m that makes the expression a monomial is 10/3

From the question, the given parameters are

Monomial: -xy^3m

Degree = 10

The degree of a polynomial is the highest power of the polynomial

This means that

Degree = 10

Degree = 3m

Substitute the known values in the above equation

So, we have

3m = 10

Divide both sides of the equation by 3

m = 10/3

Hence, the value of m is 10/3

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The  values of the given numbers when it is rounded up to the nearest 10 thousands are:

Rounding up can be described as the process that is been used in the mathematics which is been used in the estimation of a particular number in a context.

It should be noted that in rounding the  a number up, it is required to look at the next digit at the right hand of the given figures in a case whereby the digit is less than 5,the digit can be rounded down, but in the case whereby the digit is more that 5 then it can be rounded up .

From the given values, we are given the 990,201 and 159,994  and if this were to rounded up to the nearest 10 thousand then we will start from the right hand sides and round down the values less than 5 and round up the values that is more that 5. and their values will be 990000

and 150000.

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Given:

The expression is,

Simplify the expression,

Answer: option G

Answer:

8 · (32 · x^5 / 9 x^3 y^4)

Answer: QR = 21 Units

P = 2(l) + 2(w)

[tex]88= 2(4z-1) + 2(3z+3)[/tex]

[tex]88 = 8z-2+6z+6[/tex]

[tex]88 +2-6= 8z+6z[/tex]

[tex]84=14z[/tex]

[tex]\frac{84}{14} =\frac{14z}{14}[/tex]

[tex]6 = z[/tex]

[tex]QR = 3z+3[/tex]

[tex]QR = 3(6) +3[/tex]

QR = 21 Units

The image point of the point (-1, 9) after the transformation R270° or y-axis as required in the task content is; (1, 9).

It follows from the task content that the image of the point under the rotation transformation; R270° be determined.

Since the pre-image point (-1, 9) exists in the 2nd quadrant, it follows that the transformation; R270° indicates a reflection over the y-axis.

Hence, only the x-coordinate of the pre-image changes sign and therefore, the image is; (1,9).

Ultimately, the image point is; (1, 9).

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The correct option: B. 5 cm, the image of DE will have the same length as DE, i.e. 5 cm.

For the given question;

DE segment length is 5 cm.

The transformation implemented to DE now is; Rx degrees R₀.-270 degrees.

That is, DE is the segment.

270° counter-clockwise rotation about the origin, then reflected across the x-axis

It is necessary to determine the length of a segment that is the image of DE.

Because, as we all know,

The only transformation that affects the figure's measurements is 'dilation.'

As a result, rotation and reflection have no effect on the shape and size of a segment DE.

Therefore, the image of DE will have the same length as DE, i.e. 5 cm.

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The complete question is-

DE has a length of 5 cm. What is the length of the image of DE after applying the composition Rx degrees R₀.-270 degrees?

A. 2.5 cm

B. 5 cm

C. 10 cm

D. 20 cm

Answer:

210 ways

Step-by-step explanation:

This is a combinatorics problem of the general nature of choosing r elements from a sample of n elements

It is indicated by the term
[tex]C(n,r) = $\displaystyle \binom{n}{r} = \dfrac{n!}{( r! (n - r)! )$}\\\\[/tex]

where n! represents the factorial of n = n x (n-1) x (n-2) x .... 3 x 2 x 1

With n = 10, r = 3 there are C(10, 3) ways of choosing the officers

[tex]C(n,r) = C(10,4)\\\\= \dfrac{10!}{4! (10 - 4)! }\\\\\\[/tex]

[tex]= \dfrac{10!}{4! \times 6! }[/tex]

[tex]$\displaystyle = 210[/tex]

The equation for g(x) =  -(x + 1)² - 4.

Where f(x) = x².

The given parent function is ,

f(x)= x²

f1(x) = -f(x)

So,

f1(x) = -x²

It has also been moved down 4 units.

f2(x) = f1(x) -4

f2(x) = -x² - 4

1 unit has also been shifted to the left.

g(x) = f2( x + 1)

g(x) = -(x + 1)² - 4

As a result, the required equation is.

g(x) = -(x + 1)² - 4.

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The values are, x = 287° and x = 82°

The external angle is the angle formed by any side of an object and a line that runs from another side.

An interior angle is the shape that results from joining the two rays at their terminal. An internal angle is the angle inside a shape. A polygon is a closed shape with sides and vertices.

If this angle is one, the total exterior angle is 360 degrees.

and if the angle is inside, enter 180 degrees.

I'm taking this given angles i.e, (7x+7)° and (2x+2)° as an exterior angle to solve for x.

Now, (7x+7)° + (2x+2)° = 360°

7x + 7 + 2x + 2 = 360°

9x + 9 = 360°

9(x + 1) = 360

x + 1 = 360 / 9

x + 1 = 40

x = 39

We get x = 39, now put these x value to find the angle

(7x+7)°               |           (2x+2)°            

(7 * 39 + 7)°       |           (2 * 39 + 2)°

280°                 |          80°

Hence, the  values are, x = 287° and x = 82°

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Sarah has taken 4/5 portion of the available water bottles.

How is a ratio determined?
Majority of the explanations for ratio and proportion use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers. A ratio is a comparison or condensed version of two quantities of the same type. We may determine how many times one quantity is equal to another using this relationship. The ratio can be defined as the number that can be used to represent one quantity as a percentage of another.

Given, Total number of water bottles bought = 4
Total number of people sharing the bottles = 5
Since each bottle is divided in equal portion, each portion of bottle = 1/5
Also, Sarah took one portion from each of the four bottles, thus
Sarah has portion of water = 4*(1/5) = 4/5
Sarah has taken 4/5 portion of the available water bottles.

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A recent survey on movies found that 1 out of 6 students likes comedy films. The probability that individuals will like comedies is equal to one in six.

This is further explained below.

Generally, If there are a total of 90 people, then the number of people who like comedic films is equal to 90 divided by 6, which is 15.

If there are a total of 180 people, then the number of people who like comedic films is equal to 180 divided by six, which is 30. If there are 270 people in total, then the number of people who like comedic films is equal to 270 divided by six, which is 45.

If there are a total of 360 individuals, then the number of persons who like comedic films is equal to 360 divided by six, which is 60.

Let the x-axis show the total number of persons, and let the y-axis show: The number of persons who like comedic motion pictures are shown along the y-axis.

In conclusion, The following will be the function: f(x) equals six times the total number of persons, where x is the total headcount.

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