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3 years ago

99 POINTS

Mathematics

2 answers:

Alik [6]3 years ago

6 0

Answer:

-a^2 - a + 12

Step-by-step explanation:

You only need to find the products of the first and last terms to determine the correct answer:

(-a)(a) = -a^2

(3)(4) = 12

You're looking for an expression with -1 as the leading coefficient and +12 as the constant. There is only one choice like that:

-a^2 - a + 12

Viktor [21]3 years ago

4 0

Answer: -a^2 - a + 12

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The running trail in the local park is 2.826 miles long. If the park board were planning to extend the trail by 1.46 miles, what

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The problem consists in finding the new length of a running trail knowing the original length and the extension required. So the new length will be equal to original length + extension. New length = 2.826 miles + 1.46 miles = 2.826 miles + 1. 460 miles (I added a 0 in the place of the thousandths for the second summand to make clear the sumation) = 4.286 miles. Then<span> the answer is 4.286 miles.</span>

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3 years ago

What function is graphed below?

lidiya [134]

Answer: y = 2x^4

The graph represents a parabolic-looking shape so it's either a quadratic or some even degree polynomial. This rules out y = -2x^3 and y = 2x^3 as they are cubics with odd degrees

The degree of a polynomial is the largest exponent. It determines the end behavior. In this case, both ends are rising upward together. Because they are rising up in the positive y direction, this means that we cannot have y = -2x^4 as the answer. For example, if x = 2 then y = -2*x^4 = -2*2^4 = -32, but the point (x,y) = (2,-32) isn't on the blue curve. So we can rule y = -2x^4 out.

The fact that y = 2x^4 has a positive leading coefficient tells us that the endpoints point upward.

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2 years ago

in 2 h, kelly laid new floor tile over 1/5 of the room. when she was joined by annette, the rest of the work was completed in 3h

jeyben [28]

Answer: Annette will take 6 hours to do the entire job alone.

Step-by-step explanation:

Given: Time taken by Kelly to do $\dfrac{1}{5}$ of job = 2 hours

i.e. Time for complete job done alone by Kelly = $5\times2=10\ hours$

Rest of work = $1-\dfrac{1}{5}=\dfrac{4}{5}$ of the job

$\dfrac{4}{5}$ of the complete job done by both Kelly and Annette in 3 hours

Time would be taken by then to do entire job together = $3\times\dfrac{5}{4}=3.75\ hours$

Let t be the time taken by Annette to do job alone.

Then, as per situation

$\dfrac{1}{3.75}=\dfrac{1}{10}+\dfrac{1}{t}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{1}{3.75}-\dfrac{1}{10}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{4}{15}-\dfrac{1}{10}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{1}{6}\\\\\Rightarrow\ t=6$

hence, Annette will take 6 hours to do the entire job alone.

7 0

3 years ago

Write f(x)=8x^2-4x+11 in vertex form

Vlad [161]

Answer:

$f(x)=8(x-\frac{1}{4})^{2}+\frac{21}{2}$

$f(x)=8(x-0.25)^{2}+10.5$

Step-by-step explanation:

we have

$f(x)=8x^{2}-4x+11$

This is a vertical parabola open upward (because the leading coefficient is positive)

The vertex is a minimum

Convert to vertex form

Factor the leading coefficient

$f(x)=8(x^{2}-\frac{1}{2}x)+11$

Complete the square. Remember to balance the equation by adding the same constants to each side.

$f(x)=8(x^{2}-\frac{1}{2}x+\frac{1}{16})+11-\frac{1}{2}$

$f(x)=8(x^{2}-\frac{1}{2}x+\frac{1}{16})+\frac{21}{2}$

Rewrite as perfect squares

$f(x)=8(x-\frac{1}{4})^{2}+\frac{21}{2}$ ----> equation in vertex form

$f(x)=8(x-0.25)^{2}+10.5$

The vertex is the point (0.25,10.5)

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3 years ago

The regular octagon shown is divided into 8 congruent triangles. Each triangle has an area of 21.7 square centimeters. The

neonofarm [45]

I believe the formula to find the height would be h= 2a/b and if you use that formula and plug in the area (21.7) of each triangle as well as the base (6) then you would get a height of 7.2 cm. I hope this is correct! :)

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2 years ago