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2 years ago

I RLLY NEED HELP PLS!!

Mathematics

1 answer:

lara [203]2 years ago

5 0

Answer: $(x+2)^2+3\\\\$

a = 2 and b = 3

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Explanation:

Let's expand out $(x+a)^2+b$ to get the following:

$(x+a)^2+b\\\\(x+a)(x+a)+b\\\\x(x+a)+a(x+a)+b\\\\x^2+ax+ax+a^2+b\\\\x^2+2ax+a^2+b\\\\$

The x term here is 2ax

Compare this to the x term of $x^2+4x+7$ and we see that

$2ax = 4x\\\\2a = 4\\\\a = 4/2\\\\a = 2\\\\$

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The constant term of $x^2+2ax+a^2+b\\\\$ is the $a^2+b$ portion since it doesn't have the variable x attached to it.

Compare this with the 7 of $x^2+4x+7$ which is also the constant.

Equate the two items, plug in a = 2 and solve for b.

$a^2+b = 7\\\\2^2+b = 7\\\\4+b = 7\\\\b = 7-4\\\\b = 3\\\\$

Therefore,

$x^2+4x+7 = (x+a)^2+b\\\\x^2+4x+7 = (x+2)^2+3\\\\$

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Suppose that you are to make a rectangular box with a square base from two different materials. The material for the top and fou

saw5 [17]

Answer:

height = 14.5 ft

width = length = 3.2 ft

Step-by-step explanation:

Let the side of the square base is a and the height of the box is h.

The material required to make the box is equal to the total surface area of the box.

Area of base = a²

Cost of square base is $ 2 per ft²

So, the cost of making base = 2a²

Area of four walls + area of top = 2 (a² + ah + ah) + a² = 3a² + 2ah

Cost of making walls and the top is $ 1 per ft²

So, the cost of making walls and the top = 1 x ( 3a² + 2ah)

Total cost of making the box = 2a² + 3a² + 2ah = 5a² + 2ah

According to the question

144 = 5a² + 2ah

$h = \frac{144-5a^{2}}{2a}$ .... (1)

The volume of the box is V = length x width x height

V = a x a x h

V = 72 a - 2.5 a³ from equation (1)

Differentiate both sides with respect to a.

dV/da = 72 - 7.5 a²

Put, it equal to zero for maxima and minima

7.5 a² = 72

a = 3.2 ft

Put in equation (1)

$h = \frac{144-5\times 3.2\times 3.2}{2\times 3.2}$

h = 14.5 ft

So, the dimensions of the box are

height = 14.5 ft

width = length = 3.2 ft

6 0

3 years ago

Figure ABCD is reflected across the x-axis. What are the coordinates of A' , B' , C' , and D' ? Enter your answer by filling in

sp2606 [1]

Answer:

Step-by-step explanation:

A' (2,-3)

B' (5,-5)

C' (7,-3)

D' (5,-2)

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3 years ago

Read 2 more answers

Jon bought a printer for $189 and a set of printer cartridges for $192. Sales tax on these items was 6.5%. What is Jon's total b

julia-pushkina [17]

So first we need to find the total before tax. Let's add up the two prices:

$189+192=381$

So we know that the total before tax is $381. Now we are told that the sales tax on these items is 6.5%. It would be easier for us to convert 6.5% to a decimal in order to multiply. Let's convert 6.5% to a decimal by dividing by 100:

$\frac{6.5}{100}=0.065$

Now that we have the sales tax in decimal form, let's multiply this sales tax by the total amount of the items before tax ($381):

$381*0.065=24.77$

This means that $24.77 is the tax for this purchase. To find the total amount that Jon paid for these items after tax, you must add the tax to the total amount before tax to give you:

$381+24.77=405.77$

So now we know that Jon's total bill for these items is $405.77.

4 0

3 years ago

Please tell me !!!!!!

vlada-n [284]

Answer:

Step-by-step explanation:

Its H because a square has 4 sides and 58 divided by 4 is 14.5

8 0

3 years ago

How would I figure out a linear equation with two plot points with fractions? (1/3(6),3) and (1/2(19),-2) are my two plot points

murzikaleks [220]

Answer: $m=\frac{-30}{79},\ y=5.40$

Step-by-step explanation:

Given

Points are $\left(6\frac{1}{3},3\right),\ \left(19\frac{1}{2},-2\right)$

Convert mixed numeral to fraction

$\left(6\frac{1}{3},3\right)\Rightarrow \left(\dfrac{19}{3},3\right)\\\\\left(19\frac{1}{2},-2\right)\Rightarrow \left(\dfrac{39}{2},-2\right)$

Slope of the line is

$\Rightarrow m=\dfrac{3-(-2)}{\dfrac{19}{3}-\dfrac{39}{2}}\\\\\Rightarrow m=\dfrac{5}{\dfrac{38-117}{6}}\\\\\Rightarrow m=\dfrac{-30}{79}$

Equation of line

$\Rightarrow \dfrac{y-3}{x-\dfrac{19}{3}}=\dfrac{-30}{79}\\\\\text{for y-intercept, put x=0}\\\\\Rightarrow \dfrac{y-3}{0-\dfrac{19}{3}}=\dfrac{-30}{79}\\\\\Rightarrow y-3=\dfrac{190}{79}\\\\\Rightarrow y=3+2.40\\\Rightarrow y=5.40$

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3 years ago