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5. Determine whether each pair of triangles is similar. Justify your answer.

Simplified expression for total amount spent is 10(2.05 + m)

Step-by-step explanation:

Expense = 8.50 + 6.25 × m

Expense = 12 + 3.75 × m

Total Amount = 8.50 + 6.25m + 12 + 3.75m = 20.5 + 10m = 10(2.05 + m)

Sabra spends a total amount represented by the simplified expression 20.50 + 10m after m months on both the cooking and movie clubs.

To find the total amount of money Sabra spends on both clubs after m months, we need to consider the costs of joining each club and the ongoing monthly fees.

Sabra's cooking club costs $8.50 to join and $6.25 per month. This can be represented by the expression:

Sabra's movie club costs $12 to join and $3.75 per month. This can be represented by the expression:

To find the total amount spent on both clubs, we sum these expressions:

So, the total amount of money Sabra spends on both clubs after m months can be expressed as 20.50 + 10m

Therefore possible committees are [tex]^5C_3[/tex] =10

Step-by-step explanation:

Given , from a group of 5 candidates , an environmental committee of 3 people is selected.

Therefore possible committees are [tex]^5C_3[/tex] =10

Answer:

6/7 and 1 5/7

Step-by-step explanation:

Answer:

6/7 and 1 5/7

5/6 and 10/12= 5/6

Answer: The Fund last year was 19,860

Step-by-step explanation:

Just set up a ratio using 70 over 13902 and set it equal to 100 over x and cross multiply to get x = 19,860

Answer:

(x + 7) (x + 5)

Step-by-step explanation:

Factor the following:

x^2 + 12 x + 35

The factors of 35 that sum to 12 are 7 and 5. So, x^2 + 12 x + 35 = (x + 7) (x + 5):

Answer: (x + 7) (x + 5)

The constant of proportionality for this relationship is  [tex]\frac{5}{3}[/tex]

Step-by-step explanation:

Proportional relationship is the relation between two variables that vary directly with each other

∵ The equation is 3 y = 5 x

∵ x and y are proportional

- That means y = k x, where k is the constant of proportionality

∴ Put the equation in the form y = k x

- Divide both side by the coefficient of y

∵ The coefficient of y is 3

∴ Divide both sides of the equation by 3

∴ y = [tex]\frac{5}{3}[/tex] x

-  The value [tex]\frac{5}{3}[/tex]  is constant

∴ k =  [tex]\frac{5}{3}[/tex]

∵ k represents the constant of proportionality

∴ The constant of proportionality =  [tex]\frac{5}{3}[/tex]

The constant of proportionality for this relationship is  [tex]\frac{5}{3}[/tex]

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Answer:

31.94 miles

Step-by-step explanation:

we know that

The circumference of a tire represents the distance traveled by the vehicle in one revolution

so

by proportion

Find out the distance traveled by the vehicle in 23,000 revolutions

[tex]\frac{88}{1}\ \frac{in}{rev}=\frac{x}{23,000}\ \frac{in}{rev}\\\\x=88(23,000)\\\\x=2,024,000\ in[/tex]

Convert inches to miles

Remember that

[tex]1\ mile=63,360\ inches[/tex]

To convert inches to miles divided by 63,360

therefore

[tex]2,024,000\ in=2,024,000/63,360=31.94\ miles[/tex]

Answer:

It took Albert 2 1/2 hours to ride to the park

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Speed of Albert to the park = 12 mph

Speed of Albert back home = 20 mph

Total time of the round trip = 4 hours

Distance each way = 30 miles

2. How long did the ride to the park take?

Let's recall that the formula of speed is:

Speed = Distance/Time, therefore Time = Distance/Speed

Time it took Albert to ride to the park = 30/12

Time it took Albert to ride to the park = 5/2 = 2 1/2 hours

Time it took Albert to ride back home = 30/20

Time it took Albert to ride back home = 3/2 = 1 1/2 hours

It took Albert 2 1/2 hours to ride to the park

Step-by-step explanation:

The complete question:

What is the value of y in the formula shown when x = [tex]\dfrac{4}{5}[/tex] ?

[tex]y=\dfrac{4}{x}+\sqrt{x+0.2}-5x[/tex]

We have,

[tex]\dfrac{4}{x}+\sqrt{x+0.2}-5x[/tex]       ...... (1)

To find, the value of y = ?

Put x = [tex]\dfrac{4}{5}[/tex] in equation (1), we get

[tex]y=\dfrac{4}{\dfrac{4}{5}}+\sqrt{\dfrac{4}{5}+0.2}-5(\dfrac{4}{5})[/tex]

[tex]=5+\sqrt{0.8+0.2}-4[/tex]

[tex]=1+\sqrt{1}[/tex]

= 1 + 1

= 2

Thus, the value of y is equal to 2.

It will need 864 meters³ of water to fill it completely

Step-by-step explanation:

The formula of the volume of a prism is V = B h, where

The swimming pool is shaped a prism

∵ The length of each side of the four sides is 12 meters

- That means its base is shaped a square with side length 12 meters

∵ Area of a square = (side)²

∴ The area of the base of the swimming pool = (12)² = 144 meters²

∴ B = 144

∵ The pool is 6 meters deep

- That means its height is 6 meters

∴ h = 6

The volume of the water in the swimming pool is equal to the volume of the swimming pool because it will be needed to fill completely

∴ The volume of the water = B h

∴ The volume of the water = 144(6)

∴ The volume of the water = 864 meters³

It will need 864 meters³ of water to fill it completely

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Answer:

160-153=7 dogs

you will need 1 more truck to hold 160 dogs

Step-by-step explanation:

1 truck=9 dogs

9x17=153 dogs

160-153=7 dogs

you will need 1 more truck to hold 160 dogs

Answer:

  m = StartFraction 9 minus 0 Over 0 minus 3 EndFraction; y = –3x + 9

Step-by-step explanation:

The given points are the y-intercept and the x-intercept, so they can be used directly in the intercept form of the equation of a line.

  x/(x-intercept) +y/(y-intercept) = 1

  x/3 +y/9 = 1

Multiplying by 9 gives ...

  3x +y = 9

This can be rearranged to the slope-intercept form ...

  y = -3x +9

_____

The answer selection shown above is the only one that matches the slope and y-intercept of the line through the given points.

Answer:

because m = StartFraction 9 minus 0 Over 0 minus 3 EndFraction; y = –3x + 9

Step-by-step explanation:

Answer:

46

Step-by-step explanation:

47.84 / 1.04, which is 46

The opening price of Company A's stock before the 4% increase to the closing price of $47.84 was $46.00.

To calculate the opening price of Company A's stock at the beginning of the day, before the 4% gain, we need to work backwards from the closing price. Since the stock closed at $47.84 after gaining 4%, we can represent the closing price as 104% of the opening price. Thus, the equation to find the opening price (OP) is:

OP x1.04 = $47.84

Now we solve for OP:

OP = $47.84 / 1.04

OP = $46.00

The opening price of Company A's stock at the beginning of the day was $46.00.

Answer:

Senior citizen tickets = 9

Student tickets = 10

Step-by-step explanation:

We begin by converting the question into simultaneous linear equations;

Senior citizen tickets = a

Student tickets = b

4a + 6b = 96

8a + 13b = 202

to find a,

if 4a +6b = 96

a = 96/4 - 6b/4

a = 24 - 1.5b

We now substitute this into the second equation

8(24 - 1.5b) + 13b = 202

192 - 12b + 13b = 202

b = 202 - 192

b = 10

We now put the value of b in either equation

4a + 6b = 96

4a + 6(10) = 96

4a + 60 = 96

4a = 96 - 60

4a = 36

a = 9

Answer:66

Step-by-step explanation:

27.5x4.8/2

Answer:

66 meters squared

Step-by-step explanation:

You multiply 27.5 and 4.8. Which gets you 132. And because your finding the area of a triangle you have to divide 132 by 2 which gets you 66.

Answer:

The cost for one pound of birdseed is $0.67

Step-by-step explanation:

Use Mariela's example first

To find the cost per pound, get the pounds to 1.

15 pounds = $10.00       Divide both sides by 15 to get 1 pound

1 pound = $0.67  

Use Mark's example to see if it is the same rate

12 pounds = $8.00   Divide both sides by 12 pounds to get one pound

1 pound = $0.67

Use Daryl's example to prove the other answers

18 pounds = $12.00    Divide both sides by 8 pounds to get one pound

1 pound = $0.67

Answer:

i) $500 at 5% simple interest for two years.

   Interest = 550 - 500 = $50

ii) $500 at 3% compounded monthly for 2 years.

   Interest = 530.88 - 500 = $30.88

I would take the first option i)$500 at 5% simple interest for two years.

Step-by-step explanation:

i) $500 at 5% simple interest for two years.

  Initial amount, P = $ 500

  Rate of interest, r = 0.05

  Time in years, t = 2

 Therefore Final amount A = P(1 + rt) = 500(1 + (0.05  2) ) = $550

  Therefore Interest = 550 - 500 = $50

ii) $500 at 3% compounded monthly for 2 years

   Initial or Principal Amount, P  = $500

   Rate of interest, r =0.03

   number of conversions, m = 12

    Time in years, t = 3

 Therefore final amount,   = $530.88

Therefore Interest = 530.88 - 500 = $30.88

I would take the first option i) $500 at 5% simple interest for two years.

Answer:

16 fluid ounces=2 cups

Hope this helps!

Step-by-step explanation:

Answer:

16 fluid ounces

Step-by-step explanation:

1 cup is equal to 8 fluid ounces, so 2 cups is 16 fluid ounces.

Answer:

s = 32

Step-by-step explanation:

-5(s - 30) = -10

-5s + 150 = -10

-5s = -10 - 150

-5s = -160

s = -160/-5

s = 32

Answer:

480 tons

Step-by-step explanation: You have to figure out how many minutes are in 24 hours. (1440 min) Then, you multiply 1440 x 1/3.

Answer:

the answer is 480

Step-by-step explanation:

it is common sense but in your case it is uncommon sense

Answer:

The statement is true.

Step-by-step explanation:

Given : Reflecting the graph of y = sin x across the y-axis is the same as reflecting it across the x-axis.

To find : Is this statement true or false?

Solution:

Rules of reflection :

Along across y-axis if we have a point

So, y=sinx

The reflection across y-axis→ .......[1]

Along across x-axis if we have a point

so, y=sinx

The reflection across x-axis →  .....[2]

Hence, [1] and [2] both of them are equal

Therefore, the statement is true.

Answer:

The answer is true for A P E X

Step-by-step explanation:

Answer:

7 10/9 - 6 7/9

1 4/9

Step-by-step explanation:

the denominator stays the same

Change the FIRST fraction to an improper mixed fraction

then keep the denominators the same and subtract the numerators

subtract the whole numbers

Answer:

Five times nine plus twenty

Step-by-step explanation:

Just remember the order of operations... multiplication and division are done first before adding and subtracting.

Answer:

45 metres

Step-by-step explanation:

You have to get the base to answer the question.

Do this by dividing 315 by 15 then timesing by 2

You get 42.

Do 42^2 = 1764

Do 15 ^2 = 225

Because you want the hypotenuse you add them

1764 + 225 =1989

Do the square root of 1989 which is 45 to the nearest metre

Answer:

25.80

Step-by-step explanation:

Area = 315 [tex]m^{2}[/tex]

Area = l*b

315 = 15 *b

b= 315/15

b = 21

From Right angled Triangle ,

Hypotenuse square = side square + side square

[tex]x^{2}[/tex] = [tex]21^{2}[/tex] + [tex]15^{2}[/tex]

[tex]x^{2}[/tex] = 441 + 225

[tex]x^{2}[/tex] = 666

apply sq root on both sides, the we get

[tex]\sqrt{x^{2}} = \sqrt{666}[/tex]

x= 25.80

Answer:

NO

Step-by-step explanation:

The equation y = 15/x is not a linear function. A linear process follows the form y = a + bx and graph as a straight line. The given equation doesn't track that form or behavior; hence, it is not linear.

No, the equation y = 15/x is not a linear function. In Mathematics, a linear function is defined by the equation y = a + bx, where a is the y-intercept, b is the slope, x is the independent variable, and y is the dependent variable. In this equation, the relationship between x and y is direct, meaning if x increases or decreases, y will also increase or decrease at a constant rate.

However, in the equation y = 15/x, the relationship between x and y is inverse. If x increases, y decreases, and vice versa. Furthermore, the form of the equation doesn't follow the standard form of a linear equation (y = a + bx) because the x variable is in the denominator. Therefore, it is not linear because it will not graph as a straight line.

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Answer:

The complement of 33 is the angle that when added to 33 forms a right angle

Step-by-step explanation:

it is un needed for a explanation

Answer: 5 + 25n

Explanation: Let's simplify this problem using the distributive property.

In this problem, the 5 "distributes" through the parentheses which means that it multiplies by each of the terms inside.

So we have 5(1) + 5(5n) which simplifies to 5 + 25n.

Answer:

the degree for the polynomial is 2

We can conclude that, if two pairs of corresponding sides and the corresponding included angles are congruent, the two triangles will be congruent.

Given that, two pairs of corresponding sides and the corresponding included angles are congruent.

Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.

If two pairs of corresponding sides are equal and corresponding included angles are equal.

By SAS congruence theorem, two triangles are congruent.

Therefore, we can conclude that, if two pairs of corresponding sides and the corresponding included angles are congruent, the two triangles will be congruent.

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Answer:

The answer A) b=-8

Step-by-step explanation:

Answer:

b = -8

Step-by-step explanation: