Triangle EFG is congruent to triangle JKL.
What is KL, in units?

Answer:

65 + 5[tex]\sqrt{2}[/tex]

Step-by-step explanation:

5(13 + [tex]\sqrt{2}[/tex]) ← multiply each term in the parenthesis by 5

= 65 + 5[tex]\sqrt{2}[/tex]

The height of the escalator is as calculated using trigonometric ratios.

We know that in a right angled triangle the trigonometric ratios are

tan θ = perpendicular ÷ base

For a right angled triangle the tanθ is defined as the ratio of the perpendicular to the base of the triangle . The side opposite the angle θ is the perpendicular and the side adjacent to the θ is the base .

Now it is given that for every 2 feet vertically moved the horizontal distance moved is 3 feet.

Now using the trigonometric ratio of tanθ

tan θ = 2 / 3

Now we will use this ratio to calculate the vertical height for horizontal movement of 90 feet .

Now, the height is given as h .

∴ tan θ = h / 90

or, 2 / 3 = h / 90

or, h = 60 feet

Therefore the height of the escalator is 60 feet.

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Answer:

5

Step-by-step explanation:

Answer:

5 centimeters

Step-by-step explanation:

leaf is 11cm, catepillar is 6.... 11-6=5

Answer:

(ii) 1 dollar

Step-by-step explanation:

each pencil costs 17 cents

- thus 3 pencils x 17c is 51c

1.00 dollars minus 0.51 is 49

- 5 pencils x 17c is equal to 85

1.00 dollars minus 0.85 is 15 c

Answer:

A

Step-by-step explanation:

The graph below could be the graph of A) F(x) = 2*[tex](0.7)^x[/tex] exponential function.

The graph of the function F(x) = 2 * [tex](0.7)^x[/tex] is a decreasing exponential function. This is because the base of the exponent, 0.7, is between 0 and 1. As x increases, the value of [tex](0.7)^x[/tex] decreases, so the value of F(x) decreases.

The graphs of the other functions are all increasing exponential functions. This is because the bases of the exponents, 2, 5, and 1.4, are all greater than 1. As x increases, the value of [tex]2^x[/tex], [tex]5^x[/tex], and [tex]1.4^x[/tex] increases, so the value of the functions F(x) = 2 * [tex]2^x[/tex], F(x) = 2 * [tex]5^x[/tex], and F(x) = 2 * [tex]1.4^x[/tex] increases.

Therefore, the graph of the function F(x) = 2 * [tex](0.7)^x[/tex] is the only graph that is decreasing. So the answer is A.

Here is a table that summarizes the properties of the graphs of the four functions:

Function Base of the exponent Graph

F(x) = 2 * [tex](0.7)^x[/tex] 0.7 (between 0 and 1) Decreasing

F(x) = [tex]2^x[/tex] 2 (greater than 1) Increasing

F(x) = 2 * [tex]5^x[/tex] 5 (greater than 1) Increasing

F(x) = 2 * [tex]1.4^x[/tex]  1.4 (greater than 1) Increasing

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Answer:

Let P(t) = population t years after 2010

           = 45230e0.02t

Population in 2030 = P(20)

                           = 45230e0.4≈ 6747

Answer:

506.093

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The answer is A

The roots of the given quadratic equation are -

x = 2   and   x = 1.

A function is a relation between a dependent and independent variable. We can write the examples of functions as -

y = f(x) = ax + b

y = f(x, y, z) = ax + by + cz

Given is a quadratic function f(x) defined as -

f(x) = x³ - 3x² + 2

The given quadratic function f(x) is -

f(x) = x³ - 3x² + 2

We can write the roots of the equation as -

x = {3 ± √(9 - 8)}/2

x = {3 + √(9 - 8)}/2    and    {3 - √(9 - 8)}/2

x = (3 + 1)/2   and    x = (3 - 1)/2

x = 2   and   x = 1

Therefore, the roots of the given quadratic equation are -

x = 2   and   x = 1.

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Answer:

He would make $49.40

Step-by-step explanation:

28.60 divided by 3 2/3 is 7.80

Multiply that by 6 1/3 to get 49.40

Answer:

1. 4 1/2 can be converted into 4.30 / 20 = 0.125f per minute

2. it would descend 4.64 or 5f rounded in 8 minutes (8/0.125)

Answer:

4.45 feet p/m

35.56 feet per 8 minutes

Step-by-step explanation:

20 / (60x4.5) = 60 seconds  = ( 1 x 4.5 minutes)

20/270=0.0740740741 1 = multiplier of feet/seconds

60 x 0.0740740741 1 =4.44444445 feet in one minute = 4.45feet

60 x 8 = 480 seconds   (1 x 8 minutes)

480 x 0.0740740741 1 =35.5555556 feet

= 35.56feet in 8 minutes

Answer:3.8

Step-by-step explanation:

Answer: I would say 4

Step-by-step explanation:

Answer:

There are more factories in the city than in the country.

Step-by-step explanation:

Hope this helps!

Answer:

4/3

Step-by-step explanation:

Answer:

The answer is 4/3.

Answer:

lol

Step-by-step explanation:

to get x in quadratic equations, factor it

Answer:

its x

Step-by-step explanation:

Answer:

X = 14

Step-by-step explanation:

In pic

(Credits: Symbolab)

(Hope this helps can I pls have brainlist (crown)☺️)

Answer:

0 is the answer on 16 x 64y

Answer:

1  x = 4      y= 2/3  = 1. 66667   see attached and join the lines to create shaded area.

Step-by-step explanation:

2x -3y = 3

16x (64y) = ?

we can multiply the 2x by 8 to find x = 16 and -3y = -24y and 3 = 24

as shown 2nd one.

16x + (64y) =  c

16x -24y = 24    =   64y - 24y = c

40y = c - 24

40y/24 = y

1.66667 = y

y = 1.6667 or  1  2/3

2x -3 (  1 2/3 ) = 3

2x - 5 = 3

2x = 8

x = 4

y = 1. 66657

Answer:

y=-2x+1

Step-by-step explanation:

Just look at photo dap

Answer:

9

Step-by-step explanation:

.9*10=10

it's basically simple multiplication with a decimal

Answer:

161 donuts

Step-by-step explanation:

(231+89)/2 then add one more donut as the question asked for at least $231

320/2 = 160 + one more donut = 161 donuts have to sold to make at least $231.

You have add the machine price as he wouldn't be making a profit off it if he didn't surpass what he spent for it.

Check your work by doing 161 times 2 minus 89 minus the 1 donut added and you'll get the $231. Not subtracting the one shows the profit of a dollar aka at least $231

Answer:

Step-1 : Multiply the coefficient of the first term by the constant   1 • 7 = 7  

Step-2 : Find two factors of  7  whose sum equals the coefficient of the middle term, which is   -8 .

     -7    +    -1    =    -8    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -7  and  -1  

                    x2 - 7x - 1x - 7

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-7)

             Add up the last 2 terms, pulling out common factors :

                    1 • (x-7)

Step-5 : Add up the four terms of step 4 :

                   (x-1)  •  (x-7)

            Which is the desired factorization

Step-by-step explanation:

x = 7 or 1

In the United States, the Interstate Highway standards for the Interstate Highway System use a 12 ft (3.7 m) standard lane width, while narrower lanes are used on lower classification roads. In Europe, laws and road widths vary by country; the minimum widths of lanes are generally between 2.5 to 3.25 m (98 to 128 in).

Answer:

Progression in increments of value 12

Step-by-step explanation:

13 25 37 49 61 73 85 97 .....

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Miss Hawaii

Answer:

-1/10

Step-by-step explanation:

-7/24 by the reciprocal of 35/12

The reciproical of 35/12 is 12/35

-7/24 * 12/35

Rewriting

-7/35 * 12/24

-1/5 * 1/2

-1/10

Answer:

hope you like my answer its 2/7

The expected value of n is 1.152

The question states that ratio of 2n+2 and 2n-2 = 99:7. This means that

2n+2:2n-2 = 99:7, this also means that

[tex]\frac{2n+2}{2n-2}[/tex] = [tex]\frac{99}{7}[/tex]

If that is so, we can cross multiply so that

99 * (2n - 2) = 7 * (2n + 2), on expanding the bracket, we have

198n - 198 = 14n + 14

198n - 14n = 14 + 198

184n = 212, dividing both sides by 184, we have

n = 212/184

n = 1.152

Therefore, the value of n is 1.152

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Answer:

x=1

Step-by-step explanation: