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3 years ago

What is the factorization of 3x^2 – 8x + 5?

Mathematics

1 answer:

I am Lyosha [343]3 years ago

5 0

Answer:

Step-by-step explanation

Step 1: multiply the coefficient a and the constant c. Given that the general expression of a parabolic equation is ax^2+bx+c

3*5=15

Step 2: examine the coefficient b and try to find 2 numbers which you can multiply to get 15, add or subtract and get - 8

In this Case: - 3*-5=15 and - 3+(-5)= - 8

Step3:

You separate the equation in terms of the two factors you have found

3x^2-3x-5x+5=0

Step 4:Factorise

3x(x-1)-5(x-1)=0

(3x-5)(x-1)=0

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At a point on the ground 80 ft from the base of a tree, the distance to the top of the tree is 11 ft more than 2 times the heigh

Sergio039 [100]

Let h be the height of the tree and d the distance to the top of the tree from the point on the ground. Draw a diagram to visualize the situation:

Since the distance to the top of the tree is 11 ft more than two times the height, then:

$d=2h+11$

Use the Pythagorean Theorem to relate the length of the sides of the right triangle:

$\begin{gathered} h^2+80^2=d^2 \\ \Rightarrow h^2+6400=(2h+11)^2 \\ \operatorname{\Rightarrow}h^2+6400=(2h)^2+2(11)(2h)+11^2 \\ \operatorname{\Rightarrow}h^2+6400=4h^2+44h+121 \end{gathered}$

Notice that we have obtained a quadratic equation in terms of h. Write it in standard form and use the quadratic formula to solve for h:

$\begin{gathered} \Rightarrow0=4h^2+44h+121-h^2-6400 \\ \Rightarrow0=4h^2-h^2+44h+121-6400 \\ \Rightarrow0=3h^2+44h-6279 \\ \Rightarrow3h^2+44h-6279=0 \\ \\ \Rightarrow h=\frac{-44\pm\sqrt{(44)^2-4(3)(-6279)}}{2(3)} \\ \\ \therefore h_1=39 \\ h_2=-53.666.. \end{gathered}$

Since the height of the tree must be positive, the only solution is h=39ft. To the nearest foot, the height of the tree is 39.

Therefore, the height of the tree is 39 ft.

4 0

1 year ago

Solve the following inequality for s. Write your answer in simplest form.<br> 7s - 9 < 6s – 10

kirza4 [7]

Answer:

2<-1

Step-by-step explanation:

7s-9<6s-10

-6s. -6s.

S-9<-10

+9. +9

S<-1

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3 years ago

A birthday cake in the shape of a circle needs to be decorated with icing. If the diameter of the cake is 5 inches, how much ici

Dmitry [639]

<h2>19.63495408 inches²</h2>

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Diameter = 5

The radius is half the diameter.

Radius = 2.5

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3 years ago

1. 7x(9+2) = (7x) + (7x)

hram777 [196]

Answer:

7x11=14x

77=14x

77/14=x

11/2=x

2.3x5=4x

15=4x

15/4=x

3 )35+15=

the question is wrong

Step-by-step explanation:

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3 years ago

I’m so confused on how to find the answer to this

nalin [4]

Step-by-step explanation:

download an app called algebrator its way easier than asking brainly

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