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3 years ago

What is the value of x? Enter your answer in the box13 is top 12 is bottem and the left is X

Mathematics

1 answer:

alukav5142 [94]3 years ago

3 0

Answer: x = 5

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Explanation:

We have a right triangle as indicated by the square angle marker. Two of the sides are known: specifically the hypotenuse (13) and one of the legs (12). The other leg (x) is unknown.

We can use the Pythagorean Theorem to find x

a = 12 is one of the known legs
b = x is the unknown leg
c = 13 is the hypotenuse

Pythagorean Theorem:
a^2 + b^2 = c^2
12^2 + x^2 = 13^2
144 + x^2 = 169
144 + x^2-144 = 169-144 ... subtract 144 from both sides
x^2 = 25
sqrt(x^2) = sqrt(25) ... apply square root to both sides
x = 5

Side Note: Keep in mind that x can't be negative so it doesn't make sense to use the plus/minus here. We'll only stick with the positive version.

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Which expression has a value of 23?

DaniilM [7]

A) $7 - (-16) = \fbox {23}$

B) $-3 - 20 = \fbox {-23}$

C) $10 - 13 = \fbox {-3}$

D) $-18 - (-5) = \fbox {-13}$

You were correct, the exact answer is A. The others do not equal 23 besides that one. Good job!

6 0

3 years ago

Read 2 more answers

Match each function with the corresponding function formula when h(x)=5-3x and g(x)=-3+5

Grace [21]

Answer:

k(x) = (3g + 5h)(x) ⇒ (1)

k(x) = (5h - 3g)(x) ⇒ (3)

k(x) = (h - g)(x) ⇒ (2)

k(x) = (g + h)(x) ⇒ (4)

k(x) = (5g + 3h)(x) ⇒ (5)

k(x) = (3h - 5g)(x) ⇒ (6)

Step-by-step explanation:

* To solve this problem we will substitute h(x) and g(x) in k(x) in the

right column to find the corresponding function formula in the

left column

∵ h(x) = 5 - 3x

∵ g(x) = -3^x + 5

- Lets start with the right column

# k(x) = (3g + 5h)(x)

∵ g(x) = -3^x + 5

∵ 3g(x) = 3[-3^x + 5] = [3 × -3^x + 3 × 5]

- Lets simplify 3 × -3^x

take the negative out -(3 × 3^x), and use the rule a^n × a^m = a^(n+m)

∴ -3(3 × 3^x) = -(3^x+1)

∴ 3g(x) = -3^x+1 + 15

∵ h(x) = 5 - 3x

∵ 5h(x) = 5[5 - 3x] = [5 × 5 - 5 × 3x] = 25 - 15x

- Now substitute 3g(x) and 5h(x) in k(x)

∵ k(x) = (3g + 5h)(x)

∴ k(x) = -3^x+1 + 15 + 25 - 15x ⇒ simplify

∴ k(x) = 40 - 3^x+1 - 15x

∴ k(x) = 40 - 3^x+1 - 15x ⇒ k(x) = (3g + 5h)(x)

* k(x) = (3g + 5h)(x) ⇒ (1)

# k(x) = (5h - 3g)(x)

∵ 5h(x) = 25 - 15x

∵ 3g(x) = -3^x+1 + 15

∵ k(x) = (5h - 3g)(x)

∴ k(x) = 25 - 15x - (-3^x+1 + 15) = 25 -15x + 3^x+1 - 15 ⇒ simplify

∴ k(x) = 10 + 3^x+1 - 15x

∴ k(x) = 10 + 3^x+1 - 15x ⇒ k(x) = (5h - 3g)(x)

* k(x) = (5h - 3g)(x) ⇒ (3)

# k(x) = (h - g)(x)

∵ h(x) = 5 - 3x

∵ g(x) = -3^x + 5

∵ k(x) = (h - g)(x)

∴ k(x) = 5 - 3x - (-3^x + 5) = 5 - 3x + 3^x - 5 ⇒ simplify

∴ k(x) = 3^x - 3x

∴ k(x)= 3^x - 3x ⇒ k(x) = (h - g)(x)

* k(x) = (h - g)(x) ⇒ (2)

# k(x) = (g + h)(x)

∵ h(x) = 5 - 3x

∵ g(x) = -3^x + 5

∵ k(x) = (g + h)(x)

∴ k(x) = -3^x + 5 + 5 - 3x ⇒ simplify

∴ k(x) = 10 - 3^x - 3x

∴ k(x)= 10 - 3^x - 3x ⇒ k(x) = (g + h)(x)

* k(x) = (g + h)(x) ⇒ (4)

# k(x) = (5g + 3h)(x)

∵ g(x) = -3^x + 5

∵ 5g(x) = 5[-3^x + 5] = [5 × -3^x + 5 × 5] = 5(-3^x) + 25

∴ 5g(x) = -5(3^x) + 25

∵ h(x) = 5 - 3x

∵ 3h(x) = 3[5 - 3x] = [3 × 5 - 3 × 3x] = 15 - 9x

- Now substitute 5g(x) and 3h(x) in k(x)

∵ k(x) = (5g + 3h)(x)

∴ k(x) = -5(3^x) + 25 + 15 - 9x ⇒ simplify

∴ k(x) = 40 - 5(3^x) - 9x

∴ k(x) = 40 - 5(3^x) - 9x ⇒ k(x) = (5g + 3h)(x)

* k(x) = (5g + 3h)(x) ⇒ (5)

# k(x) = (3h - 5g)(x)

∵ 3h(x) = 15 - 9x

∵ 5g(x) = -5(3^x) + 25

∵ k(x) = (3h - 5g)(x)

∴ k(x) = 15 - 9x - [-5(3^x) + 25] = 15 - 9x + 5(3^x) - 25 ⇒ simplify

∴ k(x) = 5(3^x) - 9x - 10

∴ k(x) = 5(3^x) - 9x - 10 ⇒ k(x) = (3h - 5g)(x)

* k(x) = (3h - 5g)(x) ⇒ (6)

4 0

3 years ago

Una carretera recta tiene un ángulo de elevación de 3 grados respecto al plano horizontal. ¿Qué distancia hay que recorrer para

geniusboy [140]

Answer:

572.4 m

Step-by-step explanation:

Fórmula del ángulo de elevación =

tan θ = Opuesto / Adyacente

θ = 3 °

Opuesto = 30 m

Adyacente =?

Por eso

bronceado 3 = 30 m / x

Multiplicar cruzada

bronceado 3 × x = 30 m

x = 30 m / bronceado 3

x = 572.43410063m

Aproximadamente = 572.4 m

5 0

3 years ago

I need help please please

Westkost [7]

The answer is four .......

6 0

3 years ago

The Westside Bakery uses 310 pounds of flour to make 1,000 loaves of bread. Each loaf

DanielleElmas [232]

Answer:

310 / 1000 = 0.31 pounds

Step-by-step explanation:

When dividing by a number that is 1 less 0 than how many digits the number has, we can move the decimal point the number of times zero is repeated at the end of the number.

1000 has 3 zeroes, so we move the decimal point 3 moves to the left.

So, we do this:

After 0 moves: 310

After 1 move: 31.0

After 2 moves: 3.10

After 3 moves = 0.310

0.310 is the same as 0.31

Therefore, 0.31 pounds of flour are in each loaf.

7 0

3 years ago