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2 years ago

Calculate the area of the shape below.

Mathematics

1 answer:

Vsevolod [243]2 years ago

3 0

Answer:

24ft²

Step-by-step explanation:

divide up the shape:

big triangle:

(looking for base)

9.8²= 4² + b²

b = 8.95ft

(finding area)

0.5*8.95*4 = 17.9ft²

small triangle:

(looking for base)

12-8.95=3.05ft

(finding area)

0.5*3.05*4 = 6.1ft²

Whole Shape:

17.9+6.1 = 24ft²

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Which is the constant term of the algebraic expression -2x2 + 17 -15x + 7xy?

Over [174]

17 is the constant term because it does not have any variables.

5 0

2 years ago

I NEED HELP!! please show all work

PtichkaEL [24]

Take the logarithm of both sides. The base of the logarithm doesn't matter.

$4^{5x} = 3^{x-2}$

$\implies \log 4^{5x} = \log 3^{x-2}$

Drop the exponents:

$\implies 5x \log 4 = (x-2) \log 3$

Expand the right side:

$\implies 5x \log 4 = x \log 3 - 2 \log 3$

Move the terms containing x to the left side and factor out x :

$\implies 5x \log 4 - x \log 3 = - 2 \log 3$

$\implies x (5 \log 4 - \log 3) = - 2 \log 3$

Solve for x by dividing boths ides by 5 log(4) - log(3) :

$\implies \boxed{x = -\dfrac{ 2 \log 3 }{ 5 \log 4 - \log 3 }}$

You can stop there, or continue simplifying the solution by using properties of logarithms:

$\implies x = -\dfrac{ \log 3^2 }{ \log 4^5 - \log 3 }$

$\implies x = -\dfrac{ \log 9 }{ \log 1024 - \log 3 }$

$\implies \boxed{x = -\dfrac{ \log 9 }{ \log \frac{1024}3 }}$

You can condense the solution further using the change-of-base identity,

$\implies \boxed{x = -\log_{\frac{1024}3}9}$

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2 years ago

Determine whether the given statement is true or false. 27 €(14, 16, 18,..., 32)

Vera_Pavlovna [14]

Answer:

answer is true because 27 is belong between 14 to 32 so, it true

8 0

2 years ago

Is -3.45 closer to -3 or -4 on a number line please i really need help

oksano4ka [1.4K]

Answer:

-3.45 is closer to -3

Step-by-step explanation:

because, since it's negative the closer the negative number is closer to 0 its number is lower (-) like -4 is farther away from the 0 than -3.

5 0

2 years ago

Select the correct answer from each drop-down menu.

vazorg [7]

Answer:

Step 1: Distribute $-2$ to $5x$ and $8$

Step 2: Subtract from both sides of the equation $6x$

Step 3: Add to both sides of the equation $16$

Step 4: Divide both sides of the equation by $-16$

Step-by-step explanation:

Step 1: Apply the Distributive Property. Then you must distribute $-2$ to $5x$ and $8$

Then:

$-2(5x+8)=14+6x\\\\-10x-16=14+6x$

Step 2: You must apply the Subtraction property of Equality and subtract $6x$ from both sides of the equation. Then:

$-10x-16-6x=14+6x-6x\\\\-16x-16=14$

Step 3: You must apply the Addition property of Equality and add $16$ to both sides of the equation. Then:

$-16x-16+16=14+16\\\\-16x=30$

Step 4: You must apply the Division property of Equality and divide both sides by $-16$ . Then:

$\frac{-16x}{-16}=\frac{30}{-16}\\\\x=\frac{30}{-16}\\\\x=-\frac{15}{8}$

6 0

2 years ago