Write an equation to represent the relationship "the product of a number and-2.5 is 60." Then solve the equation

The sum of the first n consecutive even numbers can be found using S = n2 + n, where n ≥ 2.

viktelen [127]

The following are the choices on this question:
A.6
B. 39
C. 26
D. 12
The answer is option D. 12.

Check this out:
S=n² + n
S= 12² + 12
(you can get the square of 12 by multiplying 12 by itself: 12 × 12)
S=144 +12
S=156

3 0

3 years ago

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A solid silver paperweight in the form of a square pyramid is shown below. If silver costs $0.12 per cubic centimeter, how much

Rufina [12.5K]

Answer:

It would cost $232.32, this answer is rounded.

Step-by-step explanation:

The formula for the volume of a square pyramid is:

$V=a^2\frac{h}{3}$

So its just:

$8.8^2\frac{12.5}{3} = 322.67 cm^3$

Then you just multiply the volume by the cost per cubic centimetre:

$322.67cm^3*$0.12=$38.704$

After just multiply the cost of one by how many you want, which is 6:

$38/704*6=232.32$

4 0

3 years ago

Find the expected value of the winnings

Bas_tet [7]

Answer:

2.65

Step-by-step explanation:

Multiply each payout by its probability, then add those products.

See the attached image.

The first column has the payouts. The second column has the probabilities. The third column has the results of multiplying a payout by its probability.

The sum of the entries in the third column is 2.65

6 0

2 years ago

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David and his friends are making lasagna for a school dinner. There will be 400 people at dinner. The recipe for 100 people uses

blagie [28]

134.4$ will be spent on hamburgers

3 0

3 years ago

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The area of the triangle formed by x− and y− intercepts of the parabola y=0.5(x−3)(x+k) is equal to 1.5 square units. Find all p

Juliette [100K]

Check the picture below.

based on the equation, if we set y = 0, we'd end up with 0 = 0.5(x-3)(x-k).

and that will give us two x-intercepts, at x = 3 and x = k.

since the triangle is made by the x-intercepts and y-intercepts, then the parabola most likely has another x-intercept on the negative side of the x-axis, as you see in the picture, so chances are "k" is a negative value.

now, notice the picture, those intercepts make a triangle with a base = 3 + k, and height = y, where "y" is on the negative side.

let's find the y-intercept by setting x = 0 now,

$\bf y=0.5(x-3)(x+k)\implies y=\cfrac{1}{2}(x-3)(x+k)\implies \stackrel{\textit{setting x = 0}}{y=\cfrac{1}{2}(0-3)(0+k)} \\\\\\ y=\cfrac{1}{2}(-3)(k)\implies \boxed{y=-\cfrac{3k}{2}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{area of a triangle}}{A=\cfrac{1}{2}bh}~~ \begin{cases} b=3+k\\ h=y\\ \quad -\frac{3k}{2}\\ A=1.5\\ \qquad \frac{3}{2} \end{cases}\implies \cfrac{3}{2}=\cfrac{1}{2}(3+k)\left(-\cfrac{3k}{2} \right)$

$\bf \cfrac{3}{2}=\cfrac{3+k}{2}\left( -\cfrac{3k}{2} \right)\implies \stackrel{\textit{multiplying by }\stackrel{LCD}{2}}{3=\cfrac{(3+k)(-3k)}{2}}\implies 6=-9k-3k^2 \\\\\\ 6=-3(3k+k^2)\implies \cfrac{6}{-3}=3k+k^2\implies -2=3k+k^2 \\\\\\ 0=k^2+3k+2\implies 0=(k+2)(k+1)\implies k= \begin{cases} -2\\ -1 \end{cases}$

now, we can plug those values on A = (1/2)bh,

$\bf \stackrel{\textit{using k = -2}}{A=\cfrac{1}{2}(3+k)\left(-\cfrac{3k}{2} \right)}\implies A=\cfrac{1}{2}(3-2)\left(-\cfrac{3(-2)}{2} \right)\implies A=\cfrac{1}{2}(1)(3) \\\\\\ A=\cfrac{3}{2}\implies A=1.5 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\textit{using k = -1}}{A=\cfrac{1}{2}(3+k)\left(-\cfrac{3k}{2} \right)}\implies A=\cfrac{1}{2}(3-1)\left(-\cfrac{3(-1)}{2} \right) \\\\\\ A=\cfrac{1}{2}(2)\left( \cfrac{3}{2} \right)\implies A=\cfrac{3}{2}\implies A=1.5$

7 0

3 years ago