Find three consecutive even numbers such that the difference
between the square of the third and twice the square of the first is 32

Answer:

Step-by-step explanation:

It is assumed the triangles in the picture are similar.

As per similarity, the ratio of corresponding sides is same.

Compare the ratios and find the value of x:

Find the length of MN:

[tex]\\ \sf\longmapsto \dfrac{12}{5}=\dfrac{2x-4}{15}[/tex]

[tex]\\ \sf\longmapsto 15(12)=5(2x-4)[/tex]

[tex]\\ \sf\longmapsto 180=10x-20[/tex]

[tex]\\ \sf\longmapsto 10x=200[/tex]

[tex]\\ \sf\longmapsto x=20[/tex]

Answer:

[tex]x=-8[/tex] if [tex]f(x)=-1[/tex]

Step-by-step explanation:

Given --> [tex]f(x)=-\frac{3}{4}x-7[/tex]

Substitute [tex]f(x)=-1[/tex] into the equation and solve for [tex]x[/tex]:

[tex]-1=-\frac{3}{4}x-7[/tex]

[tex]6=-\frac{3}{4}x[/tex]

[tex]24=-3x[/tex]

[tex]-8=x[/tex]

So, when [tex]f(x)=-1,x=-8[/tex]

Answer: B

Step-by-step explanation: 6x represents the positive because it represents the amount being made from each ornament. The -30 represents the one-time cost of the table. And the -2.50x represents the cost of each ornament.

Answer:

  g(x) = 24(2^(x-1)) +16

Step-by-step explanation:

A function is stretched vertically by a factor of 'a' by multiplying by 'a'.

  g(x) = 4·f(x) = 4(6(2^(x-1) +4)

  g(x) = 24(2^(x-1)) +16

Answer:

The equation of the line is- y = x + 13

Answer:

A: 97/30x + 23

so percentage is always out of 100

so 57%is upon 100 then it is 200 upon 1 cuz it is a whole

Hey there!

57% of 200

= 57% * 200

= 57/100 * 200/1

= 0.57 * 200

= 57(200)/100(1)

= 11,400/100

= 114

Therefore, your answer is: 114

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

21 = 10 + 5.5h

Step-by-step explanation:

Total cost = initial cost + hourly cost

21 = 10 + hourly cost

hourly cost = 5.5 per hour, or 5.5 * h as we add 5.5 for each hour

21 = 10 + 5.5h

Answer:

Step-by-step explanation:

$10 + $5.50h ≤ $21

Let h stand for the hours the canoe is rented.

Fixed cost = $10, regardless of h.

$5.50h for the cost of n hours of rental.

Total cost = $10 + $5.50h

The total cannot exceed $21, legally.  

So we should write:

$10 + $5.50h ≤ $21  

If $10 + $5.50h ≥ $21  then ║║║║║║║

Answer:

Well to solve this I’m gonna use substitution

So

2x-3y=-14

5x+9y=14

I‘m gonna isolate ”x” on the first equation

So it’ll be

2x-3y=-14

2x=-14+3y

x=-7+1.5y

X is -7+1.5y

Now you can subsitute into other equations to find what Y is worth

So lets use the second equation

5(-1+1.5y) + 9y = 14

Now solve for y which is -2

If you subsitute Y back in an equation you’d get -4 for x

So y = -2

and X= -4

Answer:

y = -2/5x - 2

Step-by-step explanation:

Answer:

y = 2/5x -2 or y = 0.4x -2

Explanation:

Step 1: Calculating Slope (m).

m =   [tex]\frac{y2-y1}{x2-x1}[/tex]

m =    [tex]\frac{0-(-2)}{5-0}[/tex]

m =  [tex]\frac{2}{5}[/tex]  

m = 0.4

Now putting value of m in equation (i)

y = 0.4x + b -----(ii)

Step 2: Calculating Y-intercept (b).

Lets choose the first point, (0,-2) for calculating y-intercept:

y = mx + b

-2 = 0.4(0) + b

-2 = 0 + b

-2 = b

b = -2

Now put the value of b in equation (ii)

y = 0.4x + -2

Answer:

-4

Step-by-step explanation:

xy-y = ?

(5)(-1)-(-1) = ?

-5 + 1 = -4

Hope that helps

Answer:

y-1=-4(x+5)

Step-by-step explanation:

y-y1=m(x-x1)

y-1=-4(x-(-5))

y-1=-4(x+5)

Answer: y - 1 = -4(x + 5)

Step-by-step explanation:

      The point-slope formula is y - [tex]y_1[/tex] = m(x - [tex]x_1[/tex]) where m is the slope and ( [tex]x_1[/tex], [tex]y_1[/tex]) is a point on the graph.

      Using the formula, we will plug in our known values to write our equation.

y - [tex]y_1[/tex] = m(x - [tex]x_1[/tex])

y - (1) = (-4)(x - (-5))

y - 1 = -4(x + 5)

        However, in the picture the slope is [tex]\frac{1}{4}[/tex], so we would write it as;

                      y - 1 = [tex]\frac{1}{4}[/tex](x + 5)

The average speed of the airplane which travels the given distance and time is 400mph.

Speed is simply defined as distance traveled per unit of time. It is the change of position of a moving object per unit of time.

It is expressed as;

s = distance / time = d / t

Given the data in the question;

To determine the average speed of the airplane, we substitute our given values into the expression above.

s = d / t

s = 1000mi / 2.5hrs

s = 400mph

Therefore, the average speed of the airplane which travels the given distance and time is 400mph.

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There are 3 right triangles in this picture, and they are all mutually similar.

• the smallest triangle has legs 4 and y, and hypotenuse z

• the middle one has legs y and 16, and hypotenuse x

• the largest one has legs z and x, and hypotenuse 16 + 4 = 20

Note the order in which I've listed the sides (shortest to longest). Because these triangles are similar, the corresponding sides occur in a fixed ratio. In particular, we have

4/y = y/16 = z/x … (ratios of each side of the smallest and middle triangles)

4/z = y/x = z/20 … (ratios of the sides of the smallest and largest triangles)

y/z = 16/x = x/20 … (ratios of the sides of the middle and largest triangles)

We just want to find x, which we can do easily with the last equality,

16/x = x/20

Solve for x :

20 • 16/x = 20 • x/20

320/x = x

x • 320/x = x • x

320 = x²

⇒   x = √320 = √(64 • 5) = 8√5

Answer:

[tex]{ \rm{perimeter = side + side + side}} \\ \\ { \rm{perimeter = 3 \frac{1}{2} + 4 \frac{2}{3} + 5 \frac{1}{4} }} \\ \\ { \rm{perimeter = 13 \frac{5}{12} \: cm}}[/tex]

The solution is Option C.

The height of the wall to the top of the ladder is 15 feet

What is a Triangle?

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Given data ,

Let the triangle be represented as ABC

Let the height of the wall be represented as h = AB

Now , Larry liens a 16 foot ladder against a wall

So , the hypotenuse of the triangle AC = 16 feet

And , the base is 5 feet away from the wall

So , the base of the triangle BC = 5 feet

The height of the wall h is given by the Pythagoras theorem ,

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Substituting the values in the equation , we get

AC² = AB² + BC²

16² = AB² + 5²

On simplifying the equation , we get

Subtracting 5² on both sides of the equation , we get

AB² = 16² - 5²

AB² = 256 - 25

AB² = 231

Taking square root on both sides of the equation , we get

AB = 15.19

AB ≈ 15 feet

Therefore , the value of h is 15 feet

Hence , the height of the wall is 15 feet

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Answer:

11. 10

12. -9v + 7

13. 1-10b

14. 5n+10

15. 12v

16. 0

17. 0

18. -4n+10

19. 9b - 9

20. 5v-8

Hope it help.

Answer: 13: 1-10b

14: 5n +10

15: 12v

16: nothing

17 0

18: 10 -4n

19: 11 + 5b

20: 5x + -8

Step-by-step explanation:

13: 6b + 4b = 10b

1-0=1

1-10b

14: n+4n = 5n

5n+10

15: 10v + 2v = 12v

16: 6v - 6v = 0

17: -2 +2 =0

18: 9 + 1 = 10

5n + n = 4n

10 - 4n

19: 10 + 1 = 11

7b-2b = 5b

11 + 5b

20: 1 -9 = -8

5x + -8

Answer:

30%

Step-by-step explanation:

[tex]\frac{1020}{3400} =\frac{30}{100}[/tex]

Answer:

30%

Step-by-step explanation:

given

Total:3400

satisfied people:1020

we know that,

percent of satisfied:3400/1020x100%

=30%

Answer: No, this relation is not a function.

Step-by-step explanation:

Two of the points with the same Y axis have different X values (as stated in answer A)

Answer:

$26.32

Step-by-step explanation:

0.94x28 = 26.32

(Meeting character limit)

6(4a-3b)

if you draw a factor tree that goes like:

    24

1         24

2        12

...       ...  (and so on, you'll find 6 is the highest)

The missing number in the table is 1296

The y-values of the table form a geometric sequence as shown:

6, 36, 216,......

The nth term of a geometric progression is expressed using the formula;

[tex]T_n=ar^{n-1}[/tex]

Substitute the given parameters into the formula:

[tex]T_5=6(6)^{4-1}\\T_5=6(6)^3\\T_5=1296[/tex]

Hence the missing number in the table is 1296

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Answer:

1296

Step-by-step explanation:

Answer:

option A is the answer 2x-3

Answer:

2x-3

Step-by-step explanation:

(6x-9)/3

This can be simplified to

6x/3  - 9/3

2x -3

Answer:

ASA

Step-by-step explanation:

two angles are the same and one side is the same

Here's some required measures !

Let's calculate its surface area ~

Answer:

idek not gonna lie

Step-by-step explanation:

Answer:

The first one is A) 4 The second on is D) 65

Step-by-step explanation:

You divide the first number by the second number eg. 12 divided by 3=4. so 4.

You repeat the process for the second one, which is 32.5 divided by 5=6.5 so then you multiply that times 100 so 65.

Answer:

The area of the large rectangle = the sum of the areas of the three smaller rectangles

areas of the smaller rectangles are : 2a, 3a, and 4a respectively

Therefore the area of the lage rectangle = 2a + 3a + 4a

The sum of the area of all the rectangles will be 2a + 3a + 4a.

Let W be the rectangle's width and L its length.

The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be

Area of the rectangle = L×W square units

The dimensions of the rectangle are 2 by a, 3 by a, and 4 by a.

The area first rectangle is given as,

⇒ 2 × a

⇒ 2a

The area second rectangle is given as,

⇒ 3 × a

⇒ 3a

The area third rectangle is given as,

⇒ 4 × a

⇒ 4a

The total area of the rectangle will be given as,

A = 2a + 3a + 4a

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Answer:

207

Step-by-step explanation:

Answer:

1.7m

Step-by-step explanation:

Given that 'm' was the waiting time before the outbreak

After the outbreak, waiting time increased by 70%.

This implies that :

70% of m increase

m + 70% of m

m + 70/100 of m

m + ( 70÷100 ) × m

m + 0.7m

= 1.7m

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. 15/50 = 3/10

2. 8/24 = 1/3

3. 14/49 = 2/7

4. 6/63 = 2/21

5. 18/81 = 2/9