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ICE Princess25 [194]
3 years ago
7

The area of a triangle is 12 in.^2 . The base of the triangle measures 2 in. more than twice the height of the triangle. Find th

e measures of the base and height.
Mathematics
1 answer:
Pani-rosa [81]3 years ago
6 0

Answer:

  base = 8 in; height = 3 in

Step-by-step explanation:

Let h stand for the height of the triangle. Then 2h+2 will be the base length, and the area is ...

  A = 1/2bh

  12 = 1/2(2h+2)(h) = (h+1)(h)

We know that factors of 12 that differ by 1 are 4 and 3, so we conclude ...

  h = 3

  2h+2 = 8

Both dimensions are in inches.

_____

<em>Comment on the solution</em>

If you work through the solution of the quadratic, you find solutions are ...

  h = -4, h = 3

That is, the pairs (-4, -3) and (3, 4) are both pairs of (h, h+1) that have a product of 12.

The negative solution is extraneous.

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The purchase price of a camera is $84. The carrying case is 12% of the purchase price. Tax 6% of the subtotal. What is the total
ICE Princess25 [194]
Hi there! So, we know that the price of the camera is $84, and the carrying case is 12% of that price. Let's find the cost of the case. To find the cost of the carrying case, all you have to do is multiply the price of the camera by the percentage. 84 * 12% (0.12) is 10.08. The price of the carrying case is $10.08. Let's add that price to the price of the camera. 84 + 10.08 is 94.08. $94.08 is the purchase price, but we're not done. We must add the tax in to find the total price. We can add 100% to the tax rate of 6% to get 106% Adding 100% to the amount of tax helps us get straight to the total price. Multiply that by 94.08. 94.08 * 106% (1.06) is 99.7248 or 99.72 when rounded to the nearest hundredth. There. The total price of the purchase is $99.72.
4 0
4 years ago
ALG TWO HELP ASAP?
Alexxx [7]

Answer:

Therefore the period of the sinusoidal wave = 3.14.

The amplitude of the function = 2.

Step-by-step explanation:

The period of a sinusiodal wave is given by the length of x axis which covers one full cycle of the wave, which one positive half-cycle and one negative half cycle.

From the graph we can see  that one of the cycles starts at -3.14 / 4 and ends at 3.14 \times 3/4.

Therefore we can sutract the start point value from the end point value to get the period

Therefore period  = (3.14 \times 3/4) - (-3.14 / 4) = (3.14 \times 3/4) + (3.14 / 4) = 3.14

Therefore the period of the sinusoidal wave = 3.14.

The amplitude of the function = 2.

6 0
3 years ago
Find the following expression by multiplying.<br><br> (a + b)^2
Hatshy [7]
You multiply it together like (a+b)(a+b)
the answer would be a^2 + 2ab + b^2
4 0
4 years ago
Read 2 more answers
Given that (-3,6) is on the graph of f(x), find the corresponding point for the function 1/3f(x)
Ierofanga [76]

Answer:

The corresponding point of (-3 , 6) is (-3 , 2)

Step-by-step explanation:

* Lets talk about some transformation to solve the problem

- A vertical stretching is the stretching of the graph away from

 the x-axis

- If k > 1, the graph of y = k•f(x) is the graph of f(x) vertically stretched

 by multiplying each of its y-coordinates by k.

- A vertical compression is the squeezing of the graph toward

 the x-axis.

- If 0 < k < 1 (a fraction), the graph is f(x) vertically compressed

 by multiplying each of its y-coordinates by k.

* Now lets solve the problem

∵ f(x) transformed to be 1/3 f(x)

∴ The graph of f(x) is stretched or compressed vertically

∵ k = 1/3

∴ 0 < k < 1

∴ The graph is compressed vertically

- The y-coordinate must be multiplying by k

∵ The y-coordinate of the point is 6

∵ 6 × 1/3 = 2

∴ The image of the point (-3 , 6) is (-3 , 2)

* The corresponding point of (-3 , 6) is (-3 , 2)

5 0
3 years ago
Read 2 more answers
The value of y when x=2
Igoryamba

Answer:

Step-by-step explanation:

Here,  

y

∝

x

⇒

y

=

k

x

where k is constant.

⇒

1

=

k

.2

[put y =1,x=2]

⇒

k

=

1

2

Again, y = kx

⇒

y

=

1

2

×

4

[put x = 4]

⇒

Y

=

2

Answer:

y

=

2

7 0
3 years ago
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