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2 years ago

7

(02.02)Angle X measures 110 degrees. If angle X is rotated 60 degrees, what is the measure of angle X'? 00 degree O 60 degrees 0

110 degrees O170 degrees

1 answer:

alisha [4.7K]2 years ago

3 0

Answer: 110 degrees

Step-by-step explanation:

Rotations are rigid motions and thus preserve angle measure.

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7. Which two equations are equivalent?

sineoko [7]

Answer:

C. $y=(x-3)^2$ and $y=x^2-6x+9$

Step-by-step explanation:

before answering the problem let us remind the formula for square of sum and differences

$(a+b)^2=a^2+2 \times a \times b + b^2$

$(a-b)^2=a^2-2 \times a \times b + b^2$

We are going to use the above two formulas to solve each part and come to an answer

A. $y = (x + 3)^2$

$(x + 3)^2=x^2+2 \times x \times 3 + 3^2$

$(x + 3)^2=x^2+6x+9$

Hence this option is not correct pair

B. $y = (x-5)^2$

$(x - 5)^2=x^2-2 \times x \times 5 + 5^2$

$(x -5)^2=x^2-10x+25$

Hence this option is also not correct pair

C. $y = (x -3)^2$

$(x - 3)^2=x^2-2 \times x \times 3 + 3^2$

$(x -3)^2=x^2-6x+9$

Hence this option is correct as it have equivalent pair

D. $y = (x + 5)^2$

$(x + 5)^2=x^2+2 \times x \times 5 + 5^2$

$(x + 5)^2=x^2+10x+25$

Hence this option is also not correct pair

6 0

3 years ago

Explain how to use Pascal's Triangle to expand the binomial (3x-4y)^11

Mars2501 [29]

The solution to the binomial expression by using Pascal's triangle is:

$\mathbf{=177147x^{11}-2598156x^{10}y +17321040x^9y^2-69284160x^8y^3+184757760x^7y^4}$

$\mathbf{-344881152x^6y^5+459841536x^5y^6-437944320x^4y^7+291962880x^3y^8}$

$\mathbf{-129761280x2y^9+34603008xy^{10}-4194304y^{11}}$

<h3>How can we use Pascal's triangle to expand a binomial expression?</h3>

Pascal's triangle can be used to calculate the coefficients of the expansion of (a+b)ⁿ by taking the exponent (n) and adding the value of 1 to it. The coefficients will correspond with the line (n+1) of the triangle.

We can have the Pascal tree triangle expressed as follows:

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

--- --- --- --- --- --- --- --- --- --- --- --- --- --- ---

From the given information:

The expansion of (3x-4y)^11 will correspond to line 11.

Using the general formula for the Pascal triangle:

$\mathbf{(a+b)^n = c_oa^nb^0 + c_1 a^{n-1}b^1+c_{n-1}a^1b^{n-1}+c_na^0b^n}$

The solution to the expansion of the binomial (3x-4y)^11 can be computed as:

$\mathbf{=177147x^{11}-2598156x^{10}y +17321040x^9y^2-69284160x^8y^3+184757760x^7y^4}$

$\mathbf{-344881152x^6y^5+459841536x^5y^6-437944320x^4y^7+291962880x^3y^8}$

$\mathbf{-129761280x2y^9+34603008xy^{10}-4194304y^{11}}$

Learn more about Pascal's triangle here:

brainly.com/question/16978014

#SPJ1

5 0

2 years ago

Can the sides of a triangle have lengths 1, 1, and 4?

qaws [65]

No, because the hypotenuse needs to be three. It would be true if the lengths were 2, 2, 4

8 0

3 years ago

calculate the volume of each cone. Use 3.14 for π. Round answers to the nearest hundredth if necessary.

coldgirl [10]

Answer:

2355 cm^2

Step-by-step explanation:

The volume of a cone is given by

V = 1/3 pi r^2 h

V = 1/3 (3.14) (15)^2 (10)

V =2355

8 0

2 years ago

Work out the area of this quarter circle of radius 8cm, Give you answer in terms of pi

oee [108]

Answer:

The area of the quarter circle is $16\pi\ cm^{2}$

Step-by-step explanation:

we know that

The area of a quarter circle is equal to

$A=\frac{1}{4}\pi r^{2}$

we have

$r=8\ cm$

substitute the value

$A=\frac{1}{4}\pi (8)^{2}$

$A=16\pi\ cm^{2}$

3 0

3 years ago