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3 years ago

Use the quadratic formula to find the complex solutions to the equation 10x2 – x + 9 = 0.

Mathematics

1 answer:

melomori [17]3 years ago

7 0

Quadratic formula: (-b +/- sqrt(b^2 - 4ac)) / 2a

a = 10

b = -1

c = 9

1 +/- sqrt((-1)^2 - 4(10)(9)) / 2(10)

1 +/- sqrt(1 - 360) / 20

x = 1 +/- sqrt(359i) / 20

Hope this helps!

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PQR has two known interior angles of 34°, and 80°. △RST has two known interior angles of 24°, and 90°. What can be determined ab

Shalnov [3]

Answer:

△PQR and △RST are not similar.

Step-by-step explanation:

In triangle △PQR, two known interior angles are 34° and 80°. So the measure of third angle is

$180-34-80=66$

In triangle △RST, two known interior angles are 24° and 90°.

$180-24-90=66$

Two triangles are similar if their corresponding angles are same and the corresponding sides are proportional.

Since the angles of △PQR and △RST are not same, therefore we can say that the △PQR and △RST are not similar.

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Answer:

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2 years ago

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3 years ago

A right triangular prism is shown. Find (A) the total surface area and (B) the volume. You must show formulas and your work.

enyata [817]

Hello!

We are going to use the rectangular prism of the image as a guide:

First of all, the AC segment is calculated using the Pythagoras' theorem:

$AC= \sqrt{ AB^{2}+ BC^{2} } =\sqrt{ 10^{2}+ 8^{2} }=12,81 m$

(A) The surface area of a prism is the sum of the surface areas of each face.

For the 2 triangles ABC and DEF

$A=2*(1/2*b*h)=2*(1/2*8m*10m)=80m$

For the ABEF Rectangle

$A=w*l=10,77m*10m=107,7m^{2}$

For the ACDE Rectangle

$A=w*l=10,77m*12,81m=137,96 m^{2}$

For the BCDF Rectangle

$A=w*l=10,77m*8m=86,16 m^{2}$

To finish you need to sum up the areas of each face:

$SA=2A_{ABC}+ A_{ABEF}+A_{ACDE}+A_{BCDF}= \\ 80 m^{2} +107,7m^{2} +137,96m^{2} +86,16m^{2} =411,82m^{2}$

(B) The volume of a prism is the product of the area of its base and the height of the prism. In this case, the base is a triangle so the formula and the calculations for the volume are as follows

$V= \frac{1}{2} *w*h*l= \frac{1}{2}* 8m*10m*10,77m=430,8m^{3}$

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You deposit $70 in a savings account that pays an annual interest rate of 30%. How much simple interest would you earn in 2.5 ye

blagie [28]

The formula is
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I interest earned?
P principle 70
R interest rate 0.3
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