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3 years ago

Please help me asap!!

Mathematics

1 answer:

dem82 [27]3 years ago

4 0

Answer:

28/3

Step-by-step explanation:

We see that the triangles are simalar to eachother, so we can set up this ratio:

x/(8+x) = 7/13

x = 56/13 + 7x/13

13x = 56 + 7x

6x = 56

x=56/6=28/3

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What are the solutions to the quadratic equation (5y + 6)2 = 24?

Ivenika [448]

Answer:

y = $\frac{2\sqrt{6} }{5} -\frac{6}{5}$ OR y = $\frac{-2\sqrt{6} }{5} -\frac{6}{5}$

Step-by-step explanation:

Our quadratic equation is: (5y + 6)² = 24.

The first step is to square root both sides:

5y + 6 = ±√24 = ±2√6

Now subtract 6 from both sides:

5y = ±2√6 - 6

Finally divide by 5 from both sides:

y = $\frac{2\sqrt{6} }{5} -\frac{6}{5}$ OR y = $\frac{-2\sqrt{6} }{5} -\frac{6}{5}$

And, those are the solutions to the equation.

7 0

3 years ago

Read 2 more answers

Find the derivative of ln(cosx²).

RoseWind [281]

Answer:

$\displaystyle \frac{dy}{dx} = -2x \tan (x^2)$

General Formulas and Concepts:

Calculus

Differentiation

Derivatives
Derivative Notation

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]: $\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle y = \ln (\cos x^2)$

Step 2: Differentiate

Logarithmic Differentiation [Derivative Rule - Chain Rule]: $\displaystyle y' = \frac{(\cos x^2)'}{\cos x^2}$
Trigonometric Differentiation [Derivative Rule - Chain Rule]: $\displaystyle y' = \frac{-\sin x^2 (x^2)'}{\cos x^2}$
Basic Power Rule: $\displaystyle y' = \frac{-2x \sin x^2}{\cos x^2}$
Rewrite [Trigonometric Identities]: $\displaystyle y' = -2x \tan (x^2)$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

8 0

3 years ago

6. Find average of the following expressions (4-2x), (-7-3x), and (11x+6)

svetoff [14.1K]

Answer:

2x+1

Step-by-step explanation:

(4-2x), (-7-3x),(11x+6)

Add the three expressions

(4-2x)+ (-7-3x)+(11x+6)

Combine like terms

-2x-3x+11x+4-7+6

6x+3

Divide by the number of expressions which was 3

(6x+3)/3

2x+1

The average is 2x+1

7 0

3 years ago

Read 2 more answers

Find the distance CD rounded to the nearest tenth

motikmotik

Answer:

CD ≈ 15.0

Step-by-step explanation:

calculate CD using the distance formula

d = $\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }$

with (x₁, y₁ ) = C (7, - 4) and (x₂, y₂ ) = D (- 8, - 5)

CD = $\sqrt{(-8-7)^2+(-5-(-4))^2}$

= $\sqrt{-15)^2+(-5+4)^2}$

= $\sqrt{225+(-1)^2}$

= $\sqrt{225+1}$

= $\sqrt{226}$

≈ 15.0 ( to the nearest tenth )

3 0

2 years ago

Uncle percy sold t-shirts at the show. Now he only have 10% of the t-shirts he started with. If he has 25 t-shirts now, how many

Nikitich [7]

Percy used to have 100% of the shirts (before he started selling them). Since then, he has given away 90% of the shirts and is now left with only 10% of what he used to have. He currently has 25 shirts, meaning that 25 is 10% of what he had.

Lets set up a proportion:

25 shirts : 10%
x shirts : 100%

x = 25*100 / 10
x = 2500 / 10
x = 250 shirts
Percy started off with 250 shirts.

8 0

3 years ago