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vagabundo [1.1K]
3 years ago
9

5162x40 please sir i don´t feel like doing this sh/ it

Mathematics
1 answer:
ExtremeBDS [4]3 years ago
3 0

Answer:

206480

Step-by-step explanation:

Don't even bother with this part ever.

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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
On a scale drawing with a scale of 1/20, the height of the building is 8 inches. How tall is the actual building in feet?
Alecsey [184]
That means its downgraded to 1/20 of actual height, let actual height is x. Then 
(1/20) * x = 8, x = 20 * 8 = 160, actual height = 160 inch
160 inch = 160/12 feet = 13 1/3 feet or 13.333 feet.
3 0
3 years ago
Similar Triangles
NeTakaya

Answer:

5.3 ft

Step-by-step explanation:

Because CD corresponds to BC, the scale factor from triangle ABC to triangle CDE, is 7/8. Now, DE corresponds to AB, so to get DE, we must multiply the value of AB by 7/8. 6 times 7/8 is 5.25, and rounding to the nearest tenth of a foot, the value of DE is 5.3.

3 0
2 years ago
Solve the system of linear equations by substitution.
Anastasy [175]

Answer: The solution is the ordered pair (1/2,  -3/4) so x = 1/2 and y = -3/4 pair up together. The two lines, when graphed, cross at this location.

note: 1/2 = 0.5 and -3/4 = -0.75; so the intersection point can be written as (0.5, -0.75)

===================================================

Explanation:

The second equation has y isolated. We can replace the y in the first equation with the expression 1/2x - 1

3x + 2y = 0

3x + 2( y ) = 0

3x + 2( 1/2x - 1) = 0 ... y is replaced with 1/2x-1

3x + 2(1/2x) + 2(-1) = 0 .... distribute

3x + x - 2 = 0 .... note how 2 times 1/2 is 1

4x - 2 = 0

4x = 2

x = 2/4

x = 1/2

Use this x value to find the y value it pairs with

y = (1/2)*x - 1

y = (1/2)*(1/2) - 1 ... replace x with 1/2

y = 1/4 - 1

y = 1/4 - 4/4

y = (1-4)/4

y = -3/4

8 0
3 years ago
Evaluate each expression.<br> 3√9 ∙ 3√3
statuscvo [17]

Answer:

27

Step-by-step explanation:

6 0
3 years ago
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