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2 years ago

What is the midpoint of the segment shown below?

Mathematics

1 answer:

sashaice [31]2 years ago

3 0

Answer:

Step-by-step explanation:

average of x-coordinates = (-11+9)/2 = -1

average of y-coordinates = (0-1)/2 = -½

midpoint: (-1,-½)

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اسحب الإجابة الصحيحة إلى مكانها المناسب.

Inessa [10]

Mstwa do you know the meaning of this

4 0

3 years ago

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Verify that (cos²a) (2 + tan² a) = 2 - sin² a....<br>

Sveta_85 [38]

Trigonometric Formula's:

$\boxed{\sf \ \sf \sin^2 \theta + \cos^2 \theta = 1}$

$\boxed{ \sf tan\theta = \frac{sin\theta}{cos\theta} }$

Given to verify the following:

$\bf (cos^2a) (2 + tan^2 a) = 2 - sin^2 a$

$\texttt{\underline{rewrite the equation}:}$

$\rightarrow \sf (cos^2a) (2 + \dfrac{sin^2 a}{cos^2 a} )$

$\texttt{\underline{apply distributive method}:}$

$\rightarrow \sf 2 (cos^2a) + (\dfrac{sin^2 a}{cos^2 a} ) (cos^2a)$

$\texttt{\underline{simplify the following}:}$

$\rightarrow \sf 2cos^2 a + sin^2 a$

$\texttt{\underline{rewrite the equation}:}$

$\rightarrow \sf 2(1 - sin^2a ) + sin^2 a$

$\texttt{\underline{distribute inside the parenthesis}:}$

$\rightarrow \sf 2 - 2sin^2a + sin^2 a$

$\texttt{\underline{simplify the following}} :$

$\rightarrow \sf 2 - sin^2a$

Hence, verified the trigonometric identity.

7 0

2 years ago

Read 2 more answers

Students at three elementary schools collected a total of 29,294 cans of food to donate to a local food bank. Students at Johnso

amm1812

Answer:

6,845 cans

Step-by-step explanation:

Total of 29,294 cans of food to donate to a local food bank

Students at Johnson Elementary collected 9,987 cans of food

Students at Lincoln Elementary School collected 12,462 cans of food.

Total number of food can collected =

Food cans at Johnson Elementary + Food cans at Lincoln Elementary +

Food cans at Richardson Elementary

The Food cans collected at Richardson Elementary = Total food cans - (Food cans at Johnson Elementary + Food cans at Lincoln Elementary )

= 29,294 cans - (9,987 + 12,462) cans

= 29,294 cans - 22,449 cans

= 6,845 cans

Therefore, the cans of food that the students at Richardson Elementary School collected is 6,845 cans

4 0

3 years ago

A rectangular box is to have a square base and a volume of 20 ft3. If the material for the base costs $0.35 per square foot, the

denpristay [2]

Answer:

Length = 2 ft

Width = 2 ft

Height = 5 ft

Step-by-step explanation:

Let the square base of the box has one side = x ft

Therefore, area of the base = x² ft²

Cost of the material to prepare the base = $0.35 per square feet

Cost to prepare the base = $0.35x²

Let the height of the box = y ft

Then the volume of the box = x²y ft³ = 20

$y=\frac{20}{x^{3} }$ -----(1)

Cost of the material for the sides = $0.10 per square feet

Area of the sides = 4xy

Cost to prepare the sides of the box = $0.10 × 4xy

= $0.40xy

Cost of the material to prepare the top = $0.15 per square feet

Cost to prepare the top = $0.15x²

Total cost of the box = 0.35x² + 0.40xy + 0.15x²

From equation (1),

Total cost $C=0.35x^{2}+(0.40x)\times \frac{20}{x^{2} }+0.15x^{2}$

$C=0.35x^{2}+\frac{8}{x}+0.15x^{2}$

$C=0.5x^{2}+\frac{8}{x}$

Now we take the derivative of C with respect to x and equate it to zero,

$C'=0.5(2x)-\frac{8}{x^{2}}$ = 0

$x-\frac{8}{x^{2}}=0$

$x=\frac{8}{x^{2} }$

$x^{3}=8$

x = 2 ft.

From equation (1),

$(2)^{2}y=20$

4y = 20

y = 5 ft

Therefore, Length and width of the box should be 2 ft and height of the box should be 5 ft for the minimum cost to construct the rectangular box.

8 0

3 years ago

I need help with 2 questions please

Nookie1986 [14]

For the first one, the answer is yes.
2. A.-1.
i hope this helps.

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3 years ago

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