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astra-53 [7]
3 years ago
6

Solve for x. (17x - 23) (&r - 4)* -(3x + 17)

Mathematics
1 answer:
Finger [1]3 years ago
6 0

Answer:

17rx2−23rx−71x+75

Step-by-step explanation:

(17x−23)(xr−4)−(3x+17)

=(17x−23)(xr−4)+−1(3x+17)

=(17x−23)(xr−4)+−1(3x)+(−1)(17)

=(17x−23)(xr−4)+−3x+−17

=(17x)(xr)+(17x)(−4)+(−23)(xr)+(−23)(−4)+−3x+−17

=17rx2+−68x+−23rx+92+−3x+−17

=17rx2+−68x+−23rx+92+−3x+−17

=(17rx2)+(−23rx)+(−68x+−3x)+(92+−17)

=17rx2+−23rx+−71x+75

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In a triangle the first angle is 10 degrees more than the second angle. The third angle is equal to the sum of first 2 angles .
timurjin [86]
First angle= x+10
Second angle = x
Third angle = x+x+10 or 2x+10

X+10+x+2x +10=180
4x+20=180
Subtract 20 from both sides
4x=160
Divide both sides by 4
X=40
First angle =50
Second angle=40
Third angle =90
8 0
2 years ago
A circle passes through points A(7,4), B(10,6), C(12,3). Show that AC must be the diameter of the circle.
Artist 52 [7]

so we have three points, A, B and C, if indeed AC is the diameter of the circle, then half the distance of AC is its radius, and the midpoint of AC is the center of the circle, morever, since B is also on the circle, the distance from B to the center must be the same radius distance.

in short, half the distance of AC must be equals to the distance of B to the midpoint of AC, if indeed AC is the diameter.

\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{7}~,~\stackrel{y_1}{4})\qquad C(\stackrel{x_2}{12}~,~\stackrel{y_2}{3}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{12+7}{2}~~,~~\cfrac{3+4}{2} \right)\implies \left( \cfrac{19}{2}~~,~~\cfrac{7}{2} \right)=M\impliedby \textit{center of the circle}

now, let's check the distance from say A to the center, and check the distance of B to the center, if it's indeed the center, they'll be the same and thus AC its diameter.

\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{7}~,~\stackrel{y_1}{4})\qquad M(\stackrel{x_2}{\frac{19}{2}}~,~\stackrel{y_2}{\frac{7}{2}})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AM=\sqrt{\left( \frac{19}{2}-7 \right)^2+\left( \frac{7}{2}-4 \right)^2} \\\\\\ AM=\sqrt{\left( \frac{5}{2}\right)^2+\left( -\frac{1}{2} \right)^2}\implies \boxed{AM\approx 2.549509756796392} \\\\[-0.35em] ~\dotfill

\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ B(\stackrel{x_1}{10}~,~\stackrel{y_1}{6})\qquad M(\stackrel{x_2}{\frac{19}{2}}~,~\stackrel{y_2}{\frac{7}{2}}) \\\\\\ BM=\sqrt{\left( \frac{19}{2}-10 \right)^2+\left( \frac{7}{2}-6 \right)^2} \\\\\\ BM=\sqrt{\left( -\frac{1}{2}\right)^2+\left( -\frac{5}{2} \right)^2}\implies \boxed{BM\approx 2.549509756796392}

6 0
2 years ago
Which table represents a linear function that has a slope of 5 and a y-intercept of 20?
erastovalidia [21]

Answer:

The first image.

x |  y

-4 | 0

0 | 20  <--- When x = 0, the y value is the y-intercept.

4 | 40

8 | 60

Step-by-step explanation:

To check the slope, we can use the equation (y₂ - y₁) ÷ (x₂ - x₁) using any two pairs given. For this example, I'll use (-4, 0) and (4, 40).

                                                              x₂  y₂         x₁   y₁

(0 - 40) ÷ (-4 - 4)

(-40) ÷ (-8)

<u>Slope = 5</u>

<u></u>

~Hope this helps!~

8 0
2 years ago
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A box is in the shape of an equilateral triangular prism. if the box is to be covered with paper on its lateral sides, how many
Zarrin [17]

The total surface area of the triangular prism that has a height of h and the side length of a is given below.

\rm a(\dfrac{\sqrt3}{2} \ a + 3h)

<h3>What is a triangular prism?</h3>

A triangular prism is a closed solid that has two parallel triangular bases connected by a rectangle surface.

A box is in the shape of an equilateral triangular prism.

If the box is to be covered with paper on its lateral sides.

Let a be the side length of the equilateral triangle and h be the height of the prism.

Then the surface area of the triangular prism will be

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The area of the triangle will be

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The area of the rectangle will be

\rm Area \ of \ rectangle = a \ h

Then the total surface area will be

\rm Surface\ area =  2 \times \dfrac{\sqrt3 a^2 }{4} + 3 ah\\\\\\Surface\ area =  a(\dfrac{\sqrt3}{2} \ a + 3h)

More about the triangular prism link is given below.

brainly.com/question/21308574

7 0
2 years ago
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leonid [27]
The answer would be 3
8 0
3 years ago
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