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9966 [12]
4 years ago
11

Which two values of X are roots of the polynomial below 4x^2-6x+1

Mathematics
1 answer:
PtichkaEL [24]4 years ago
5 0

4x^2-6x+1=0\\\\a=4,\ b=-6,\ c=1\\\\\Delta=b^2-4ac\\\\\Delta=(-6)^2-4(4)(1)=36-16=20\\\\\sqrt\Delta=\sqrt{20}=\sqrt{4\cdot5}=\sqrt4\cdot\sqrt5=2\sqrt5\\\\x_1=\dfrac{-b-\sqrt\Delta}{2a},\ x_2=\dfrac{-b+\sqrt\Delta}{2a}\\\\x_1=\dfrac{-(-6)-2\sqrt5}{2\cdot4}=\dfrac{3-\sqrt5}{4}\\\\x_2=\dfrac{-(-6)+2\sqrt5}{2\cdot4}=\dfrac{3+\sqrt5}{4}

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What is x?????????????
Mekhanik [1.2K]

Answer:

BGC=180-90

=90

BGC=BGE+EGC

BGC=BGE+15

90=BGE+15

BGE=90-15

BGE=75

BGE=AGF

AGF=X,

X =75

8 0
3 years ago
A 2x2 square is centered on the origin. It is dilated by a factor of 3. What are the coordinated of the vertices of the square?
Alexxx [7]

<u>Answer</u>:

The vertices are:

A' = (-3, -3)

B' = (3, -3)

C' = (3, 3)

D' = (-3, 3)

The ratio of area of  larger square to smaller square is 9:1

<u>Step-by-step explanation:</u>

Given:

A 2 x 2 square is centered at the origin.

So, the center of the square is (0, 0)

Since it is 2 x 2 square, the side of the square is 2 units.

So, the vertices of the 2 x 2 square are A (-1, -1),  B(1, -1), C(1. 1), D(-1, 1)

The above square is dilated by a factor of 3.

Let's name the dilated square A'B'C'D'

To find the coordinates of the vertices of dilated square, we need to multiply each vertices of ABCD by 3.

A(-1, -1) = 3(-1, -1) = A'(-3, -3)

B(1, -1) = 3(1, -1) = B'(3, -3)

C(1, 1) = 3(1, 1) = C'(3, 3)

D(-1, 1) = 3(-1, 1) = D'(-3, 3)

To find the area of the small square

the side  of the small square is 2 units

so the are of the small square is 2^2 = 4 square units

To find the area of the larger square

lets find the side AB of the square using distance formula

=>\sqrt{(x_2 -x_1)^2 +(y_2-y_1)^2}

=>\sqrt{(3 - (-3))^2 +(-3 - (-3))^2}

=>\sqrt{(3 +3)^2 +(-3 +3)^2}

=>\sqrt{(6)^2 +(0)^2}

=>\sqrt{36}

=>6

AB =6 units

In a square all the sides will be equal

Now the area of the larger square will be

6^2

36 square units

The ratio of larger square to smaller square is

=>36 : 4

=>9 : 1

5 0
3 years ago
You have a pet hamster and a pet mouse. The hamster weighs 416 of a pound. The mouse weighs 116 of a pound. How much more does t
Harrizon [31]

How much more does the hamster weighs than the mouse is 300 pounds.

Since we have a pet hamster and a pet mouse. We know that the hamster weighs 416 of a pound and the mouse weighs 116 of a pound.

To know how much more the hamster weighs more than the mouse, we take the difference between the weight of the hamster and the weight of the mouse.

Since the weight of the hamster = 416 pounds and the weight of the mouse equals 116 pounds.

<h3>The difference in weight</h3>

The difference in the weight d = weight of hamster - weight of mouse

= 416 pounds - 116 pounds

= 300 pounds.

So, how much more does the hamster weighs than the mouse is 300 pounds.

Learn more about difference here:

brainly.com/question/751620

4 0
3 years ago
The probability that a child will learn to swim before age 6 is 0.312. If you take a group of 12 children, what is the probabili
vagabundo [1.1K]

Answer:

The probability of 1 or less children from that group to learn how to swim before 6 years of age is 0.072

Step-by-step explanation:

In this case we need to compute the probability of none of these 12 children learns to swim before 6 years of age. This is given by:

p(0) = (1 - 0.312)^(12) = 0.688^(12) = 0.01124

We now need to calculate the probability that one child learns to swim before 6 years of age.

p(1) = 12*0.312*(1 - 0.312)^(11) = 3.744*(0.688)^(11)

p(1) = 3.744*0.01634

p(1) = 0.0612

The probability of 1 or less children from that group to learn how to swim before 6 years of age is:

p = p(0) + p(1) = 0.01124 + 0.0612 = 0.07244

6 0
3 years ago
Find a polynomial that describes the area of the lawn which kevin has to mow in his front yard 6x+5,4x-9
Likurg_2 [28]

Answer:

Area=24x^2-34x-45

Step-by-step explanation:

Length and width of the yard are (6x+5) and (4x-9).

Area=length\times width\\\\Area=(6x+5)\times (4x-9)\\\\Area=24x^2+20x-54x-45\\\\Area=24x^2-34x-45

7 0
3 years ago
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