10. How can you use similar triangles to solve real-world problems?​

Answer:

b

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange both equations into this form

x - 6y = - 30 (subtract x from both sides )

- 6y = - x - 30 ( divide all terms by - 6 )

y = [tex]\frac{1}{6}[/tex] x + 5 ← in slope- intercept form

with slope m = [tex]\frac{1}{6}[/tex]

y = - 6x + 5 ← in slope- intercept form

with slope m = - 6

Parallel lines have equal slopes.

Clearly the lines are not parallel.

The product of the slope of perpendicular lines equals - 1, thus

[tex]\frac{1}{6}[/tex] × - 6 = - 1

Hence the lines are perpendicular → b

Answer:

x = 1

Step-by-step explanation:

Well the first step is to apply the distributive property:

4(3x - 1) is equal to (12x - 4). You DISTRIBUTE a '4' to what is inside the parentheses.

And btw, to make it easier, you can make 9 - x so that x is first. For example, (-x + 9). They're both the same thing, just written differently.

Your new equation is 12x - 4 = -x + 9. You want to now solve the equation.

Add the (-x) to both sides. It cancels out on the right side and you add it to 12x on the left side.

[If there's no number in front of a variable, you can always just put 1 in order to make it easier]

12x + 1x = 13x. Your new equation is 13x - 4 = 9. This should look very familiar. You simply add 4 to both sides. 9 + 4 = 13

Finally, 13x = 13. Divide 13 ÷ 13 to get 1.

x = 1

Answer:

-m^5*x^10*y^15

Step-by-step explanation:

remember alphabetical order

The standard form of the monomial equation (–x²y³m)⁵ is -m⁵x¹⁰y¹⁵.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is (–x²y³m)⁵. The standard form of the number will be written as,

E = (–x²y³m)⁵

Solve the exponents and simplify.

E =  -m⁵x¹⁰y¹⁵

Therefore, the standard form of the monomial equation (–x²y³m)⁵ is -m⁵x¹⁰y¹⁵.

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The percent equation showing the fiction books is y = 0.65x showing that among the 4,000 books in the library, 2,600 are fiction.

An equation is a mathematical representation of the equality of two expressions.

The number of books in the town's library = 4,000

The number of fiction books = 2,600

The number of nonfiction books = 1,400 (4,000 - 2,600)

The percentage of fiction books to the total number of books = 65% (2,600/4,000 x 100)

Let the total number of books in the library = x

Let the number of fiction books = y

Equation:

y = 0.65x

y = 2,600 (0.65 x 4,000)

Answer: y= 2/3

Step-by-step explanation:

Divide 10 by 5 and you get the 2 so you keep the denominator and it makes 2/3

Answer:

8

Step-by-step explanation:

3u+4u=7u

7u=56

u=8 because you divide

Answer:

U=8

Step-by-step explanation:

3u+4u=56

7u=56

u=8

Answer:

d = 49

Step-by-step explanation:

Given that the expression is a perfect square of the form

(ay - b)² = a²y² - 2aby + b²

Then comparing like terms

a²y² = 25y², that is

a² = 25 ⇒ a = 5

and -2aby = - 70y, thus

2ab = 70, that is

2(5)b = 70

10b = 70 ⇒ b = 7

b² = 7² = 49

Hence

25y² - 70y + d = (5y - 7)² = 25y² - 70y + 49

Thus d = 49

Answer:

0.15

Step-by-step explanation:

Given expression

3 tenths- 3 twentieth

⇒

[tex]=\frac{3}{10} -\frac{3}{20} \\=\frac{6}{20} -\frac{3}{20}\\=\frac{6-3}{20} \\=\frac{3}{20} \\=0.15[/tex]

Therefore value of given expression is 0.15

Answer:

π/4

Step-by-step explanation:

The area of the circle is A = π(2x)^2 = 4πx².

The length of one side of the square is 2(2x), or 4x, so the area of the square is A = 16x².

The ratio of the area of the circle to the area of the square is

              4πx²

ratio = -------------   and this reduces to ratio = π/4.

              16x²

Answer:

The width of the base is 2.828 feet

Explanation:

Given the area of the table top is 4 square feet

The triangular table top is twice as high as it is wide at the base

Therefore, we can say that height = base

Area of a right angled triangle is calculated by, Area = ½ * base * height  

In this case, height = base

Therefore, area =[tex]\frac{1}{2}\times (base)^2[/tex]

Substituting the values,

4 = [tex]\frac{1}{2}\times (base)^2[/tex]

[tex](base)^2[/tex]  = 8

Base = 2√2 = 2 * 1.414 = 2.828 feet

Therefore, the width of the base is 2.828 feet  

More people are allergic to peanuts because the smaller the denominator, the bigger the fraction.

Answer:

The 3 examples are given below.

Step-by-step explanation:

1. While decorating my home the  amount of paint required ([tex]A_{m}[/tex]) for the wall is proportional to the area of the wall (A),

 or [tex]A_{m}[/tex] ∝ A .

2. The no. of tiles required(T)  to fill the floor of a house is proportional to the area of the floor(F) provided area of each tile(t) is constant here,

or  T ∝ F when t is constant

3.The tuition fee (M) taken by my sister's school for her studies is proportional to the no. of months(H) she is in that school,

or  M ∝ H

Final answer:

Examples of proportional relationships include electricity bills proportionate to usage, water in a tank related to tap flow time, and pay from a job based on the number of performed tasks.

Explanation:

Proportional relationships involve constants of proportionality which indicate a direct or inverse relationship between two quantities. For example, in a household setting, the electricity bill is directly proportional to the amount of electrical usage; the higher the usage, the higher the bill. Similarly, the amount of water in a tank can be seen as directly proportional to the time the tap runs if the flow rate is constant. Additionally, the pay for a college work-study job, such as making calls for donations, can be directly proportional to the number of calls made; if you're paid $2.50 per call, doubling the number of calls doubles your pay.

Answer:

No

Step-by-step explanation:

3(x+11/2)-3 = 3x + 33/2 -3 = 3x + (33-6)2 = 3x + 27/2

The expression 3(x+1 1/2)-3 is equivalent to 3x+1 1/2 once the distributive property is applied and the constants are combined.

The expression 3(x+1 1/2)-3 is not equivalent to 3x+1 1/2. To determine the equivalency, we need to apply the distributive property to the expression on the left-hand side. The distributive property states that we can multiply the outside term by each term inside the parentheses. Thus, the expression 3(x+1 1/2) becomes 3x + 4 1/2. When we subsequently subtract 3 from 4 1/2, we get 1 1/2, which results in the final expression of 3x + 1 1/2. This confirms the expressions are equivalent.

Answer:

72

Step-by-step explanation:

multiply

Answer:

72

Step-by-step explanation:

Answer:

1/3 or 0.33 feet

Step-by-step explanation:

This question can be easily answered by using simple proportions.

If 75 feet are represented by 45 inches on a scale, then the scaling factor from feet to inches is 45/75, or from inches to feet is 75/45

If we have 1/5 inch and want feet, just multiply by 75/45 to get

1/5*75/45=1/3=0.33 feet

Answer:

1/3 feet

Step-by-step explanation:

We are given that

On a scale drawing

45 inches represented =75 feet

We have to find a scale of 1/5 inch how many feet represents.

To find the value in feet represented by  a scale of 1/5 inch we will use unitary method.

Using unitary method

45 inches represents =75 feet

1 inch represents =[tex]\frac{75}{45}[/tex] feet

1/5 inch represents =[tex]\frac{75}{45}\times \frac{1}{5}[/tex] feet

1/5 inch represents=[tex]\frac{1}{3}[/tex] feet

Hence, a scale of 1/5 inch represents 1/3 feet

It takes 1 painter 24 hours to paint two class rooms

Step-by-step explanation:

When some worker do a job together, then

∵ It takes three painters 4 hours to paint 1 classroom

∵ It takes 1 painter x hours to paint 1 class room

- Equate 3 × 4 by 1 × x because they will do the same job

∴ 3 × 4 = 1 × x

∴ 12 = x

∴ It takes 1 painter 12 hours to paint 1 class room

We need to find it takes 1 painter to paint two class room

∵ The painter will paint 2 class rooms

∵ He takes 12 hours to paint 1 class room

- Multiply his time in one class room by 2

∵ 12 × 2 = 24

∴ It takes 1 painter 24 hours to paint 2 class rooms

It takes 1 painter 24 hours to paint two class rooms

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Answer:

6:32 is my answer to this question

so if it is three minutes to one that means it is

12:57

in 6 hours and 34 minutes will be

12:57 + 6= 6:57

if you add 34 (i didnt do it above to make it easier)  to 57 you get 91.

because minutes dont go past 60 you have to subtract..

91 - 60 = 31 and because you only subtracted 60 once you only add one hour..

so your answer is 7:31

i hope this helps you !!!

The correct answer is "behaviorally anchored rating scale."

Further Explanation:

This type of testing is used by employers to rate an employees patterns of behaviors or their performance. This testing is also known as BARS. They use a scale system from either 1-5 or 5-9. This helps to see how the employee or trainee will do in certain situations.

This is commonly used by Human Resource departments, supervisors, or other higher ups in a company. This is used to benefit the company in the long run in case the employee or trainee doesn't work out during the appraisal. This can also be done during a yearly review of a seasoned employee.

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Answer:

x = -8 , y = -2

Step-by-step explanation:

Solve the following system:

{3 x - 4 y = -16 | (equation 1)

2 x - 4 y = -8 | (equation 2)

Subtract 2/3 × (equation 1) from equation 2:

{3 x - 4 y = -16 | (equation 1)

0 x - (4 y)/3 = 8/3 | (equation 2)

Multiply equation 2 by 3/4:

{3 x - 4 y = -16 | (equation 1)

0 x - y = 2 | (equation 2)

Multiply equation 2 by -1:

{3 x - 4 y = -16 | (equation 1)

0 x+y = -2 | (equation 2)

Add 4 × (equation 2) to equation 1:

{3 x+0 y = -24 | (equation 1)

0 x+y = -2 | (equation 2)

Divide equation 1 by 3:

{x+0 y = -8 | (equation 1)

0 x+y = -2 | (equation 2)

Collect results:

Answer: {x = -8 , y = -2

the solution to the system of equations is [tex]\( x = -8 \) and \( y = -2 \).[/tex]

To solve this system of equations, we can use the method of substitution or elimination. Let's use the elimination method here.

Given equations:

1.[tex]\(3x - 4y = -16\)[/tex]

2.[tex]\(2x - 4y = -8\)[/tex]

We can see that both equations have the same term ( -4y), so we can eliminate ( y) by subtracting equation 2 from equation 1:

[tex]\[(3x - 4y) - (2x - 4y) = (-16) - (-8)\][/tex]

[tex]\[3x - 4y - 2x + 4y = -16 + 8\][/tex]

[tex]\[(3x - 2x) - 4y + 4y = -16 + 8\][/tex]

[tex]\[x = -8\][/tex]

Now that we have found ( x = -8 ), we can substitute this value into either of the original equations to find ( y ).

Let's substitute ( x = -8 ) into equation 1:

[tex]\[3(-8) - 4y = -16\][/tex]

[tex]\[-24 - 4y = -16\][/tex]

[tex]\[-4y = -16 + 24\][/tex]

[tex]\[-4y = 8\][/tex]

[tex]\[y = \frac{8}{-4}\][/tex]

[tex]\[y = -2\][/tex]

So, the solution to the system of equations is [tex]\( x = -8 \) and \( y = -2 \).[/tex]

Answer:

The coordinates of the original triangle are (2,4). (4,1) and (1,1)

Step-by-step explanation:

About the origin, I have to rotate a triangle 90° counterclockwise. Then I translate its image 1 unit left and 2 units down.

The vertices of the final image are (-5,0), (-2,2), and (-2,-1).

We need to get the vertices of the original triangle.

So, start from a triangle with vertices (-5,0), (-2,2), and (-2,-1) and do the reverse to get the original triangle.

So, we will translate the image triangle by 1 unit right and 2 units up and we will get the triangle with vertices (-5 + 1, 0 + 2), (- 2 + 1, 2 + 2) and (- 2 +1, - 1 + 2)  ≡ (-4,2), (-1, 4) and (-1,1).

Now, we have to rotate this intermediate triangle by 90° clockwise.

Therefore, the coordinates of the original triangle are (2,4). (4,1) and (1,1) (Answer)

{Since, for 90° rotation the coordinates of all the vertices will interchange their location (i.e. x-value to y-value and y-value to x-value) and a negative sign will be added to the y-coordinate of the interchanged coordinates}  

Answer:

(a) The cost of 1  model house A  = $24

(b) YES, with $200 Victor can purchase 3 A model &  4 B model houses.

Step-by-step explanation:

Let us assume the cost of  model house B = $ m

So, the cost of model house A  =$ ( m - 6)

So, the price of 5 A model house = 5 x ( Rate of 1 model house A)

                                                         = 5(m-6)

And, the price of 3 B model house = 3 x ( Rate of 1 model house B)

                                                         = 3 x (m) = 3 m

So, the cost of 3 B house +  5 A house =  5(m-6)  +  3 m

⇒5(m-6)  +  3 m  = $210

or, 5 m - 30 + 3 m = 210

or, 8 m = 240

or, m = 30

So, the cost of 1 B house = m = $30

And  the cost of 1 house A = (m -6) = (30 - 6) = $24

Now, The  cost of 3 A model + 4 B model

=  3( 24)  + 4(30)   = 72 + 120 =  192

So, The  cost of 3 A model + 4 B model  = $192 and $192 < $200

Hence, YES, with $200 Victor can purchase 3 A model + 4 B model houses.

Answer:

Theory

Step-by-step explanation:

A triangular number or triangle number counts objects arranged in an equilateral triangle. The nth triangular number is the number of dots in the triangular arrangement with n dots on a side, and is equal to the sum of the n natural numbers from 1 to n. The sequence of triangular numbers , starting at the 0th triangular number, is  0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666...

Answer: I think you answered your own question

Step-by-step explanation:

Answer: 3 Each hour × (difference in 10 am and 4 pm= 5) = 15.

Step-by-step explanation:

Answer:

18 tours are offered

Step-by-step explanation:

So 1/3 of a hour is 20 mins, so every 20 mins a tour is offered so we know 1 hour equals to 3 tours offered so

10:00 to 11:00 is 3, 11:00 to 12:00 is 3, 12:00 to 1:00 is 3, 1:00 to 2:00 is 3, 2:00 to 3:00 is 3, 3:00 to 4:00 is 3.

6 hours times 3 equals, 18 tours are offered

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

I'm assuming your teacher wants you to translate the given sentence into an algebraic expression.

y = some unknown number

4y = 4*y = four times a number y

4y+8 = four times a number, y, increased by 8

The ratio of quarters to dimes is not still 5 : 3

Solution:

Given that ratio of quarters to dimes in a coin collection is 5:3 .

You add same number of new quarters as dimes to the collection .  

Need to check if ratio of quarters to dimes is still 5 : 3

As ratio of dimes and quarters is 5 : 3

lets assume initially number of quarters = 5x and number of dimes = 3x.

Now add same number of new quarters as dimes to the collection

Let add "x" number of quarters and "x" number of dimes

So After adding,

Number of quarters = initially number of quarters + added number of quarters = 5x + x = 6x

Number of dimes = initially number of dimes + added number of dimes

= 3x + x = 4x

New ratio of quarters to dimes is 6x : 4x = 3 : 2

So we have seen here ratio get change when same number of new quarters and dimes is added to the collection

Ratio get change from 5 : 3 when same number of new quarters and dimes is added to the collection and new ratio will depend on number of quarters and dimes added to collection.

Answer:

The quantity of type A coffee is 73 pounds

The quantity of type B coffee is 94 pounds .

Step-by-step explanation:

Given as :

The price of Type A coffee costs = $ 5.70 per pound

The price of Type B coffee costs = $ 4.30 per pound

The total quantity of coffee does Reuben purchases = 167 pounds

The total cost of the coffee for 167 pounds = $ 820.30

Let The quantity for type A coffee = a pounds

And The quantity of type B coffee = b pounds

Now, According to question

a + b = 167 pounds      And

$ 5.70 × a + $ 4.30 × b = $ 820.30

Now solving equations

5.70 × ( a + b ) = 5.70 × 167

or, 5.70 a + 5.70 b = 951.9

Now ,

( 5.70 a + 5.70 b ) - (   5.70  a +  4.30  b ) = 951.9 - 820.30

or, ( 5.70 a - 5.70 a ) + ( 5.70 b - 4.30 b ) = 131.6

Or, 0 + 1.4 b = 131.6

∴ b = [tex]\frac{131.6}{1.4}[/tex]

I.e b = 94 pounds

Put the value of b to get a value

So, a = 167 pounds - b

Or, a = 167 - 94

∴   a = 73 pounds

Hence The quantity of type A coffee is 73 pounds

And The quantity of type B coffee is 94 pounds   .  Answer

One number is 7 less than a second number. Twice the second number is 1 less than 5 times the first. Then the two numbers are 5 and 7

Solution:

Given that one number is 7 less than a second number.

Twice the second number is 1 less than 5 times the first.

Need to determine two numbers.

Let assume first number be represented by variable x and second number be represented by variable y.

As first number is 7 less than a second number, adding 7 to first number will give us second number

=> x + 7 = y   ------ (1)

[tex]\begin{array}{l}{\text { Twice of second number }=2 \times \text { second number }=2 \times y=2 y} \\\\ {\text { 5 times the first number }=5 \times \text { first number }=5 \times x=5 x}\end{array}[/tex]

As given that Twice the second number is 1 less than 5 times the first , if we 1 to twice of second number we will get 5 times first number ,

=> 2y + 1 = 5x     ------ (2)

On substituting value of y as x + 7 from equation 1 into equation 2 , we get

2(x + 7) + 1 = 5x      

=> 2x + 14 + 1 = 5x

=> 2x – 5x = -15

=> -3x = -15

x = 5

Substituting x = 5 in equation (1) to get value of y  

=> y = 5 + 7 = 12

Hence first number is 5 and second number is 12

Answer:

P(The color of the car is red)  is 0.32 .

P(The color of the car is white) is 0.34 .

P(The color of the car is silver) is 0.19 .

P(The color of the car is blue) is 0.15 .

P(car color is not red or blue) is 0.53 .

Step-by-step explanation:

We know that total angle subtended at the center by a complete circle is

360° .

According to the question,

P(The color of the car is red)

= [tex]\frac {115.2}{360}[/tex]

= 0.32

P(The color of the car is white)

= [tex]\frac {122.4}{360}[/tex]

= 0.34

P(The color of the car is silver)

= [tex]\frac {68.4}{360}[/tex]

= 0.19

P(The color of the car is blue)

= [tex]\frac {54}{360}[/tex]

= 0.15

So

P(car color is not red or blue)

= 1 - (0.15 + 0.32)

= 0.53

Answer:

0.53 is the correct answer.

Step-by-step explanation: