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Lelu [443]
2 years ago
13

After triangle ace is dilated by a factor of 5, it has an area of 100 square inches. What was its area before dilation?

Mathematics
1 answer:
NISA [10]2 years ago
5 0

Answer:

20in^2

Step-by-step explanation:

Since you multiply the original area of the triangle by the scale factor to get the new area, you can find the original area (before dilation) by dividing the dilated triangle's area by the scale factor. Since 100 is the area of the dilated triangle, and 5 is your scale factor, you do 100/5 to get the area of the triangle before it was dilated.

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The square of a number decreased by 3 times the number 28 find all possible values for the number
stealth61 [152]

Question:

The square of a number decreased by 3 times the number is 28 find all possible values for the number  

Answer:

The possible values of number are 7 and -4

Solution:

Given that the square of a number decreased by 3 times the number is 28

To find: all possible values of number

Let "a" be the unknown number

From given information,

square of a number decreased by 3 times the number = 28

a^2 - 3a = 28

a^2 - 3a - 28 = 0

Let us solve the above quadratic equation

\text {For a quadratic equation } a x^{2}+b x+c=0, \text { where } a \neq 0

x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}

Using the above formula,

\text { For } a^{2}-3 a-28=0 \text { we have } a=1, b=-3, c=-28

\begin{aligned}&a=\frac{-(-3) \pm \sqrt{(-3)^{2}-4(1)(-28)}}{2 \times 1}\\\\&a=\frac{3 \pm \sqrt{9+112}}{2}\\\\&a=\frac{3 \pm \sqrt{121}}{2}=\frac{3 \pm 11}{2}\\\\&a=\frac{3+11}{2} \text { or } a=\frac{3-11}{2}\\\\&a=7 \text { or } a=-4\end{aligned}

Thus the possible values of number are 7 and -4

5 0
2 years ago
. Cara is playing a game. For each dart she can toss onto a board, she
Kaylis [27]
She will need 12 seconds because -20•12=-240
6 0
2 years ago
A waterbed filled with water has the dimensions 8ft by 7 ft by .75 ft taking the density of water to be 1.00/gm cubed how many k
monitta

By definition, the density is given by:

D = \frac{m}{V}

Where,

m: mass

V: volume

Clearing the mass we have:

m = DV

The volume is given by:

V = (8) * (7) * (0.75)

V = 42ft ^ 3

Then, we have the following conversion:

1foot = 0.3048m

Applying the conversion we have:

V = 42 * (0.3048) ^ 3

V = 1.19m ^ 3

On the other hand we have the following conversions:

1m = 100cm

1Kg = 1000g

Applying the conversions for the density we have:

D = (1\frac{g}{cm^3})((\frac{100}{1})^3\frac{cm^3}{1m^3})(\frac{1}{1000}\frac{Kg}{g})=1000\frac{Kg}{m^3}

Then, the mass of the water is:

m = (1000) * (1.19)

m = 1190

Answer:

1190 kilgrams of water are required to fill the waterbed

7 0
2 years ago
George saves 18% of his total gross weekly earnings from his 2 part-time jobs. He earns $6.25 per hour from one part-time job an
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What do u mean man i don't get it ether sorry brah <span />
7 0
2 years ago
Which function in vertex form is equivalent to f(x) = 4 + x2 – 2x?
viktelen [127]
To express a function of the form f(x)= x^{2} +bx+c in vertex form f(x)=a(x-h)^2+k where (h,k) is the vertex of the parabola, we need to find the vertex first.
To find the vertex we are going to use the vertex formula: h= \frac{-b}{2a}, and k will be the function evaluated at h.
We can infer from our function that a=1 and b=-2. So lets find h:
h= \frac{-b}{2a}
h= \frac{-(-2)}{2(1)}
h= \frac{2}{2}
h=1
Now that we have h, we can evaluate the function at 1 to find k:
f(x)=4+ x^{2} -2x
f(1)=4+(1)^2-2(1)
f(1)=4+1-2
f(1)=3

We have the vertex (1,3) of our parabola, so we can use its vertex form:
f(x)=a(x-h)^2+k
f(x)=1(x-1)^2+3
f(x)=(x-1)^2+3

We can conclude that the vertex for of our parabola is <span>f(x) = (x + 1)2 + 3.</span>
8 0
2 years ago
Read 2 more answers
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