Proportions in similar triangles

Answer:

The number of boys are 18 and the number of girls are 30.

Step-by-step explanation:

The ratio of number of girls to the boys = 3 : 5

Let the number of girls is g and boys is b initially.

b : g = 3 : 5

5 b = 3 g ..... (1)

Now, girls are 6 + g and boys are b - 9

So, the ratio is

(b - 9) : (6 + g) = 1 : 4

4 b - 36 = 6 + g

4 b - g = 42 .... (2)

From ( 1 ) and ( 2 )

[tex]4 b - \frac {5 b}{3}= 42\\\\\frac{7 b }{3} = 42\\\\b = 18[/tex]

And , g = 5 x 18/3 = 30

So, the number of boys are 18 and the number of girls are 30.  

Answer:

1) f(x) = 500·(1.1)ˣ

2) f(x) = 500·(0.9)ˣ

Step-by-step explanation:

1) The given values in the table are;

x; 0, 1, 2, 3

f(x); 500, 550, 605, 665.5

By observation, we have that each two subsequent term of f(x) have a common ratio, given as follows;

550/500 = 11/10 = 1.1 = 605/550 = 665.5/605

From which we have;

The values of f(x) are in a geometric progression

The nth of a geometric progression = a·rⁿ

The common ratio, r = 1.1

The first term, a = 500

The number of terms, n = x

Therefore, xth term, f(x) = a×(r)ˣ

Substituting the values gives;

The equation for the data shown in the table is f(x) = 500·(1.1)ˣ

2) The given table of values is presented as follows;

x; 0, 1, 2, 3

f(x); 500, 450, 405, 364.5

The common ratio, f(xₙ)/f(xₙ₋₁) = 450/500 = 9/10 = 0.9 = 405/450 = 364.5/405

The terms of f(x) are in a geometric progression

The first term. a = 500

The common ratio, r = 9/10 = 0.9

The nth term of a geometric progression, G.P. = a·rⁿ

By plugging in the values of 'a', 'r', and 'n', the value of the xth term, f(x), therefore;

The equation for the data shown in the table is f(x) = 500·(0.9)ˣ.

Answer:

Try to glue it back together

Step-by-step explanation:

I heard gorilla glue works, but be careful and don't get the glue on your body. If that happens it can cause irritation and call posion control immediately.

Step-by-step explanation:

a)50°

b)75°

c)125°

d)d=40°

Answer:

Step-by-step explanation:

A)180-(60+70)=50

C)180-30=150 150/2=75

B)180-(35+20)=125

D)2d+d+60=180

3d+60=180

3d=120 ; d=40 ; 2d=40×2=80

Answer:

Step-by-step explanation:

[tex]carry\: on \: learning[/tex]

Answer:

x = 35

Step-by-step explanation:

-6/5x-4=-46​

Add 4 to each side

-6/5x-4+4=-46+4

-6/5x=-42​​

Multiply each side by -5/6 to isolate x

-5/6 * -6/5x=-42 * -5/6​

x = 35

Answer:

x = 35

Step-by-step explanation:

-6 / 5x - 4 = - 46

Add 4 to each side

- 6 / 5 x - 4 + 4 = - 46 + 4

- 6 / 5 x = - 42

To find x, multiply 42 by 5 and then divide by 6.

x = 42 × 5 / 6

x = 7 × 5

x = 35

Answer:

2 + y > 16

Step-by-step explanation:

the sum of 2 and y is greater than 16

                   2 + y           >                   16

2 + y > 16

Answer:

x≈95,6

Step-by-step explanation:

x= cos 15⁰ x 99 ≈95,6

Answer:

After the distribution of the 5 and the addition of x to both sides, the x variable is cancelled out leaving 1 = - 20.

This statement is false. Hence, no solution

Step-by-step explanation:

1 - x = 5(x - 4) - 6x (Distribute 5)

1 - x = 5x - 20 - 6x (Combine like terms)

1 - x = -x - 20  add x to both sides

1 = - 20 False

Answer:

72

Step-by-step explanation:

all you had to do was divide by 2

Answer:

second option: product is irrational because both are irrational

Step-by-step explanation:

The second option which is the product is irrational because both are irrational numbers.

These are those numbers which are impossible to  be written in the form of p/q.

We have been the given the following numbers.

[tex]\sqrt{2 } and \sqrt{7}[/tex] and we have been asked to find the description of the product of both. We know that these are irrational numbers because it cannot be written in the form of p/q. When we multiply this we can get root 14 which is also a irrational number.

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Answer: 4

2x2+3(2)−6

lets make sure we do OOO (order of operations correctly)

2x2+3(2)−6

4+3(2)−6

4+6−6

10−6

4

Step-by-step explanation:

Answer: x = 34

Step-by-step explanation:

2x+3+3x+7=180

5x+10=180

5x=170

x = 34

Answer:

21 x 3.1 / 2 = 32.55

Step-by-step explanation:

Answer:

B: The retiree has a pension savings of $51,000

Step-by-step explanation:

Step-by-step explanation:

Finding the (maximum) respective prime powers would yield the answer. Also we need not ... Is perfectly divisible by 720^n? ... So we can say that for any positive value of n it not divisible.

Answer:

its 55 not 60

Step-by-step explanation:

just divide 260 by 5 and 3

The required number of large and small popcorn boxes sold are 40 and 20 respectively.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,
Let the number of the large box be x and the small box is y.
According to the question,
5x + 3y = 260   - - - - - -  -(1)
x + y = 60
x = 60 - y - - - - - - - - (2)
Put the value of equation, (2) in equation 1
5 (60 - y) + 3y = 260
300 - 5y + 3y = 260
2y = 40
y = 20
Now,
x = 60 - 20
x = 40

Thus, the required number of large and small popcorn boxes sold are 40 and 20 respectively.

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Answer:

25 in and 9 cm

Step-by-step explanation:

Using Pythagoras' identity

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

let x be the missing side

A

x² = 7² + 24² = 49 + 576 = 625 ( take square root of both sides )

x = [tex]\sqrt{625}[/tex] = 25

B

x² + 12² = 15²

x² + 144 = 225 ( subtract 144 from both sides )

x² = 81 ( take square root of both sides )

x = [tex]\sqrt{81}[/tex] = 9

Answer:

A) [tex]\sqrt{7^{2} +24^{2} }[/tex] = 25

B) [tex]15^{2} -12^{2} = B^{2}[/tex]

   [tex]B^{2} =81\\[/tex]

B = 9

Step-by-step explanation:

Answer:

sorry only doing the ones i know how to do

b) for the histogram, just write all the numbers on the table on the bottom, theres 13 lines but 2 repeats so it should be even. on the side write a range of minutes

c) mean = 7.8 ; standard deviation = 3.13

d)

min = 2

max = 13

range = 11

q1 = 5.5

q3 = 10.75

iqr = 5.25

median = 8

what does iqr represent? it represents the middle 50% of all the values

e) write the numbers from the table without repeats and mark them how many times theyre written

Answer:

y=1/2x+6

Step-by-step explanation:

Answer:

-10

-7

-4

-1

2

Step-by-step explanation:

Substitute  in the x value

Remember a negative minus a negative is a negative.

Answer:

(-2,-10),(-1,-7),(0,-4),(1,-1),(2,2)

Step-by-step explanation:

f(x)=3x-4

f(x)=y

y=3x-4 ; x(-2)

y=3(-2)-4

y= -6-4

y= -10

y=3x-4

y = -1(3)-4

y= -7

y= 3x-4

y = 3(0) -4

y= -4

y= 3x-4

y = 3(1)-4

y= -1

y=3x-4

y=3(2)-4

y= 6-4

y =2

Answer:

Step-by-step explanation:

[tex]\frac{3*4}{2*4}=\frac{12}{8}\\\\\frac{5*4}{2*4}=\frac{20}{8}[/tex]

Three rational numbers:

[tex]\frac{13}{8};\frac{14}{8};\frac{15}{8}[/tex]

Answer:B

Step-by-step explanation:

simple, there is one point of intersection or where the lines meet

Answer:

B:  One solution

Step-by-step explanation:

The graphs show that the two lines intersect at one point.  This point represents the ONE solution of this system of equations.

If the lines did not intersect, the system would have no solution.

If the lines coincide, the system would have infinitely many solutions.

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {x\:=\:33}}}}}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex]x = 42 - 9[/tex]

➼[tex]\:x = 33[/tex]

Therefore, the value of [tex]x[/tex] is 33.

[tex]\sf\pink{Thank\:you. \:ヅ}[/tex]

Answer:

x =33

Step-by-step explanation:

x = 42-9

We are solving for x, which is already isolated

42-9 = 33

x = 33

Check 33+9 = 42

Answer:

35/87

Step-by-step explanation:

To find the probability, we must find (total number of favorable outcomes)/ (total number of outcomes). We thus need to find the total number of outcomes. As people have only answered "yes" or "no", the total number of outcomes is 208+140 = 348.

The total number of favorable outcomes, or what we're looking for, is 140 (140 people responded that they had run a red light). Thus, our fraction is 140/348, or 35/87

Answer:

[tex]13x=39[/tex]

Step-by-step explanation:

Given

[tex]2x - y = -4 \to 10x - 5y =-20[/tex]

[tex]3x +5y =59 \to 3x +5y = 59[/tex]

Required

What can replace [tex]3x +5y = 59[/tex] ?

We have:

[tex]10x - 5y =-20[/tex]

and

[tex]3x +5y = 59[/tex]

Add up both equations:

[tex]10x +3x-5y+5y=-20+59[/tex]

[tex]10x +3x=39[/tex]

[tex]13x=39[/tex]

Since [tex]13x=39[/tex] is a result of [tex]10x - 5y =-20[/tex] and [tex]3x +5y = 59[/tex],

[tex]13x=39[/tex] can replace [tex]10x +3x=39[/tex]

Answer:

C. 12x² + 8x + 25

Step-by-step explanation:

A. 12x² + 15

B. 20x² + 25

C. 12x² + 8x + 25

D. 24x² + 16x + 50

Hypotenuse = 8x²

Height = 4x² + 15

Base = 8x + 10

Perimeter of the triangle = hypotenuse + height + base

= 8x² + (4x² + 15) + (8x + 10)

= 8x² + 4x² + 15 + 8x + 10

Perimeter of the triangle = 12x² + 8x + 25

C. 12x² + 8x + 25

Answer:The answer is C

Answer:

5

Step-by-step explanation: