erved.
6
What is the reason for step 3 of this proof?
OA
Alternate Interior Angles Theorem
OB.
Corresponding angles in congruent triangles are congruent.
OC. For parallel lines cut by a transversal, corresponding angles are congruent.
OD.
Vertical Angles Theorem
OE.
SAS criterion for congruence

Answer:

[tex]\textsf{D.} \quad x=4 \pm \sqrt{17}[/tex]

Step-by-step explanation:

Rearrange the equation so it equals zero:

[tex]\begin{aligned} x^2+4 & =8x+5 \\ \implies x^2+4-8x-5 & = 0\\x^2-8x-1&=0\end{aligned}[/tex]

Now use the quadratic formula to solve for x:

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]

[tex]a=1, \quad b=-8, \quad c=-1[/tex]

[tex]\implies x=\dfrac{-(-8) \pm \sqrt{(-8)^2-4(1)(-1)}}{2(1)}[/tex]

[tex]\implies x=\dfrac{8 \pm \sqrt{68}}{2}[/tex]

[tex]\implies x=\dfrac{8 \pm \sqrt{4\cdot 17}}{2}[/tex]

[tex]\implies x=\dfrac{8 \pm \sqrt{4}\sqrt{17}}{2}[/tex]

[tex]\implies x=\dfrac{8 \pm 2\sqrt{17}}{2}[/tex]

[tex]\implies x=4 \pm \sqrt{17}[/tex]

The equation x = 7 - 4√3 is a radical expression, and the value of the radical expression is [tex](x + \frac 1x)^2 = 3650401 -2107560\sqrt 3[/tex]

The equation is given as:

x = 7 - 4√3

So, we have:

[tex](x + \frac 1x)^2 = (7 - 4\sqrt 3 + \frac{1}{7 - 4\sqrt 3})^2[/tex]

Take the LCM

[tex](x + \frac 1x)^2 = (\frac{49 -56\sqrt3 + 48}{7 - 4\sqrt 3})^2[/tex]

Evaluate the like terms

[tex](x + \frac 1x)^2 = (\frac{97 -56\sqrt3 }{7 - 4\sqrt 3})^2[/tex]

Rationalize

[tex](x + \frac 1x)^2 = (\frac{(97 -56\sqrt3)(7 - 4\sqrt 3) }{49 -48})^2[/tex]

Evaluate the difference

[tex](x + \frac 1x)^2 = ((97 -56\sqrt3)(7 - 4\sqrt 3))^2[/tex]

Expand

[tex](x + \frac 1x)^2 = (679 -388\sqrt 3 -392\sqrt 3 + 672)^2[/tex]

Evaluate the like terms

[tex](x + \frac 1x)^2 = (1351 -780\sqrt 3 )^2[/tex]

Expand

[tex](x + \frac 1x)^2 = 1825201 +1825200 -2107560\sqrt 3[/tex]

[tex](x + \frac 1x)^2 = 3650401 -2107560\sqrt 3[/tex]

Hence, the value of the radical expression is [tex](x + \frac 1x)^2 = 3650401 -2107560\sqrt 3[/tex]

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Answer:

113.1 inches

Step-by-step explanation:

The area of a circle can be calculated using the formula [tex]\pi r^{2}[/tex], with r being the radius of the circle.

On this circle, the radius is 12 inches, making the area of the entire circle [tex]\pi 12^{2} =\pi 144[/tex], which is about 452.39.

The shaded area of the circle is 1/4 of the circle, so we use the equation [tex]\frac{452.39}{4}[/tex] to get an area of 113.1 inches.

Hope this helps! :)

Answer:

YES

Step-by-step explanation:

A rational number is a number that can be expressed as the quotient or fraction p/q of two integers

- 23 and 100 are both integers

- 23 / 100 = 0.23 which is not a continious decimal

Answer:

Yes,it is.

Step-by-step explanation:

Rational numbers are usually expressed in fractions with both the numerator and denominator greater than zero

The employee that has the larger pay increase is Jane. Her income is larger by £65.

Percentage is the fraction out of an amount that is usually expressed as a number out of hundred.

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The expression is rewritten in standard form and they are not the same due to the negative.

Usually, simplification involves proceeding with the pending operations in the expression.

Simplification usually involves making the expression simple and easy to use later.

Both (x−3)(x+3) and (3−x)(3+x) contain a sum and a difference and have only 3 and x in each factor.

Let see the equation formed by the factor;

(x−3)(x+3)

= x^2 + 3x - 3x - 9

= x^2 - 9

(3−x)(3+x)

= 9 + 3x - 3x - x^2

= 9 - x^2

The expression is rewritten in standard form and they are not the same due to the negative.

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Answer:

Step-by-step explanation:

The correct option is option B.

The common difference between given data is -3/4.

A sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

Here, given points;

                            x₁ = 1 , x₂ = 2 and y₁ = -3.75 , y₂ = -4.5

Now,

    d = (y₂ - y₁)/(x₂-x₁)

    d = (-4.5 - (-3.75))/(2 - 1)

     d = -0.75 / 1

     d = - 75/100

      d = -3/4

Thus, The correct option is option B.  The common difference between given data is -3/4.

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Answer:

Radius = 3

Circumference = 18.84

Step-by-step explanation:

A = πr²

28.26 = 3.14r²

√9 = √r²

3 = r

C = 2πr

C = (2)(3.14)(3)

C = 18.84

Using proportions, considering the amount she received from each person, it is found that Annie had 30 sweets originally.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, we have that:

The final amount was of 63, hence:

1.4 x 1.5 x n = 63

n = 63/(1.4 x 1.5)

n = 30.

Annie had 30 sweets originally.

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Answer:

0

Step-by-step explanation:

simplfy: 4.5(6.2) = 0

Multiply 4.5 * 6.2

27.9 = 0

and solve

27.9 = 0

I  hope this helps ^^

Answer:

= -27.9

If you mean multiplication,  [tex]4.5\times(-6.2)=-27.9[/tex].

The product is negative because the (-)6.2 is negative.

Step-by-step explanation:

Answer:

Area = 63ft

Step-by-step explanation:

7*9=63

multiply the base and height

157.5 square feet is the area of the roof.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Given that the roof of a clock tower is a pentagonal pyramid.

a pentagonal pyramid is a pyramid with a pentagonal base upon which are erected five triangular faces that meet at a point

Each side of the base is 7 ft long.

The slant height is 9 ft.

We need to find the  area of the roof.

Area=1/2×7×9×5

=315/2

=157.5

Hence, 157.5 square feet is the area of the roof.

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Answer:

1st triangle: missing angle is 100

2nd triangle: missing angles are 50

3rd triangle: missing angle is 90, this is also a right triangle. The hypotenuse on this is the side length that reaches from angle 70 to 20. the other sides are legs

Step-by-step explanation:

Answer:

1. Center: (-4,3) Radius: 4

2. C

3. C (x^2 + (y+4)^2 = 16)

4. 50 miles

Step-by-step explanation:

1. Look up how to read equations of circles

2.Soh Cah Toa

3. equations of circles again

4. Pythagorean Theorem

Answer:

C

Step-by-step explanation:

M is less than n because it comes before it in the number line

Answer:

15, 2

Step-by-step explanation:

Number one: 15

Number two: 2

Well 15 is 13 more than two meaning this is correct.

By eliminating numbers, I was able to find a range of possible numbers which eliminated all the others. Then using that range I found out the number.

The first number is 2 and the second number will be 15.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

There are two numbers that add up to 17.

If one number is 13 more than the other.

Then the two numbers will be

Let the first number be x. Then the second number will be x + 13

x + x + 13 = 17

  2x + 13 = 17

         2x = 4

           x = 2

The first number is 2 and the second number will be 15.

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Answer:

12:11

Step-by-step explanation

Answer:

I think it would be 12:11

Step-by-step explanation:

This is because you can't down size the 11

It is TRUE, so shade on the SAME side as (0,0)

Answer: x=11

Step-by-step explanation:

Set the two equations equal to each other

5x+9 = 6x-2

9=x-2

11=x

x=11

X will need to be 11 in order to make the two equations equal to each other

Step-by-step explanation:

We know that,

[tex]\boxed{\sf \sin θ = \dfrac{Opposite \: side}{Hypotenuse}}[/tex]

[tex]\longmapsto \sf \sin 30^{\circ} = \dfrac{x}{12}[/tex]

[tex]\longmapsto \sf \dfrac{1}{2}= \dfrac{x}{12}[/tex]

[tex]\longmapsto \sf \dfrac{1}{2}×12= \dfrac{x}{12}×12[/tex]

[tex]\longmapsto \sf x = 6[/tex]

Answer:

x = 6

Step-by-step explanation:

Hello!

The missing angle is 60°, and is found by subtracting 90° and 30° from 180°.

Using basic triangle theorems of a 30° - 60° - 90° triangle, we know that the leg opposite to 30°, x, is one-half of the hypotenuse.

The value of x is 6.

The leg opposite to 60° is √3 times the leg opposite to 30°.

Step-by-step explanation:

please mark me as brainlest

Answer:

[tex]x < - 5[/tex]

Step-by-step explanation:

[tex] - 2x - 6 > x + 9[/tex]

[tex] - 2x - x > 9 + 6[/tex]

[tex] - 3x > 15[/tex]

[tex] \frac{ - 3x}{ - 3} > \frac{15}{ - 3} [/tex]

[tex]x < - 5[/tex]

Step-by-step explanation:

here,

principal (p)=£6000

Rate (R)=. 3.4%

time (t)=3 yrs

now,

total investment is compound amount i.e CA

here,

[tex]CA = p(1 + \frac{r}{100} ) ^{t} [/tex]

=£6000(1+3.4/100)^3

=£6633.044

here he will get his total investment as £6633.044 in compound interest of 3.4%

Step-by-step explanation:

I hope this will help you

Answer:

198

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

▪︎ ADE and ABC are similar triangles (AAA)

▪︎ DA = DB + BA = 30 + 12 = 42

▪︎ k = DA / BA = 42 / 12 = 3.5

▪︎ DE = BC * k = 8 * 3.5 = 28

Answer:

B. (2, 4)

Explanation:

Given equations:

a) y = x + 2

b) y = 3x – 2

Solve them simultaneously:

x + 2 = 3x – 2

x - 3x = -2 - 2

-2x = -4

x = 2

Then find y = x + 2 = 2 + 2 = 4

Solution: (x, y) = (2, 4)

Answer:

(2,4)

Step-by-step explanation:

substitute the value of y x+2 = 3x-2

solve the value of x  x = 2

substitue the value of x into one of the equations y = 2+2

solve for y value y = 4