Given: See the diagram.
Prove: DC = DB






Statement

Reason

1. given
2. AG = GC given
3. is the perpendicular
bisector of . deduced from steps 1 and 2
4. DA = DC
5. given
6. AH = HB given
7. is the perpendicular
bisector of . definition of perpendicular bisector
8. DA = DB deduced from steps 6 and 7
9. DC = DB Transitive Property of Equality

What is the reason for the fourth and eighth steps in the proof?

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]f(x)=2^{x}[/tex]

This is a exponential function of the form

[tex]y=a(b)^{x}[/tex]

where

a is the initial value

b is the base

In this problem

[tex]a=1[/tex]

[tex]b=2[/tex]

[tex]b=1+r[/tex]

[tex]r=2-1=1=100\%[/tex]

using a graphing tool

The graph in the attached figure

Answer:

C

Step-by-step explanation:

x² + 6x = 18

To complete the square, take the coefficient of the x term, halve it, square the result, then add to both sides.

(6/2)² = 3² = 9

x² + 6x + 9 = 18 + 9

(x + 3)² = 27

x + 3 = ±√27

x = -3 ± √27

Answer:

=204.13 inches.

Step-by-step explanation:

Using the side x, we can use sine to find the hypotenuse of the triangle with the angle marked 30°.

Sin 30 =x/hypotenuse.

sin 30 = 27/hyp

hyp= 27/sin 30

=54 inches

We can also find the adjacent as follows.

Cos 30 = adjacent/ 54

Adjacent= 54 cos 30

=46.77 inches

Using the angles marked 45 we can find the hypotenuse of the isosceles triangle.

sin 45= x/hypotenuse

sin 45 =27/hypotenuse

hypotenuse = 27/sin 45

=38.18 inches

The hypotenuse of both the triangles making the isosceles triangle are 38.18 inches long.

Perimeter = 54+ 46.77+27+ 38.18+38.18

=204.13 inches.

The total perimeter of the given figure is 204.13 inches

Let's break down the solution step by step:

1. Triangle with 30° Angle:

  - We have a right triangle with one angle measuring 30°.

  - The side opposite the 30° angle (labelled as "x") is 27 inches.

  - We want to find the hypotenuse (the longest side).

  - Using the sine function:

   [tex]\[ \sin(30°) = \frac{x}{\text{hypotenuse}} \] - Solving for the hypotenuse: \[ \text{hypotenuse} = \frac{27}{\sin(30°)} = 54 \text{ inches} \][/tex]

2. Adjacent Side of the 30° Triangle:

  - We can also find the adjacent side (labelled as "adjacent") using the cosine function:

   [tex]\[ \cos(30°) = \frac{\text{adjacent}}{54} \] - Solving for the adjacent: \[ \text{adjacent} = 54 \cos(30°) = 46.77 \text{ inches} \][/tex]

3. Isosceles Triangle with 45° Angles:

  - We have an isosceles triangle with two angles measuring 45° each.

  - The side opposite each 45° angle is also 27 inches (since it's an isosceles triangle).

  - We want to find the hypotenuse of this triangle.

  - Again using the sine function:

  [tex]\[ \sin(45°) = \frac{x}{\text{hypotenuse}} \] - Solving for the hypotenuse: \[ \text{hypotenuse} = \frac{27}{\sin(45°)} = 38.18 \text{ inches} \][/tex]

4. Total Perimeter:

  - The perimeter of the entire figure is the sum of all sides:

   [tex]\[ \text{Perimeter} = 54 + 46.77 + 27 + 38.18 + 38.18 = 204.13 \text{ inches} \][/tex]

Therefore, the total perimeter of the given figure is 204.13 inches.

To find sin 75°, use the half-angle identity for sine: sin(2θ) = 2sinθcosθ. Since sin 150° = 1/2, find cos 150° using the Pythagorean identity. Then, use the half-angle identity for sine to find sin 75°.

To find sin 75°, we can use the half-angle identity for sine: sin(2θ) = 2sinθcosθ.

Given that sin 150° = 1/2, we can find cos 150° using the Pythagorean identity: sin²θ + cos²θ = 1.

sin²150° + cos²150° = 1, (1/2)² + cos²150° = 1, cos²150° = 1 - (1/4), cos²150° = 3/4.

Since 150° falls in the second quadrant, it has a negative value: cos 150° = -√(3/4) = -√3/2.

Now, we can use the half-angle identity for sine: sin 75° = 2sin(150°/2)cos(150°/2).

sin 75° = 2(sin 150°/2)(cos 150°/2) = 2(√(1/4))(√3/2) = √3/2.

Final answer:

To find sin 75°, we can use the double angle formula for sine and substitute the given value of sin 150°. The result is sin 75° = cos 75°.

Explanation:

To find sin 75°, we can use the double angle formula for sine.

The formula is sin 2θ = 2sin θcos θ. We know that sin 150° = 1/2, so we can substitute θ = 75° into the formula:

sin 2(75°) = 2sin 75°cos 75°

Using the double angle formula, we get:

2sin 75°cos 75° = 2(1/2)cos 75° = cos 75°

Therefore, sin 75° = cos 75°

Answer:

(x + 3)² = 15

Step-by-step explanation:

Given

x² + 6x - 6 = 0 ( add 6 to both sides )

x² + 6x = 6

To complete the square

add (half the coefficient of the x- term )² to both sides

x² + 2(3)x + 9 = 6 + 9

(x + 3)² = 15

Follow below steps:

The question asks about rewriting the quadratic equation x^2+6x-6=0 by completing the square. To complete the square for an equation of the form ax^2+bx+c=0, we need to add and subtract the square of half the coefficient of x, which is (b/2)^2, to make it a perfect square trinomial.

Here are the steps for completing the square for the given equation:

Divide all terms by the coefficient of x^2 if it is not 1 (in this case, it is already 1).

Move the constant term to the other side of the equation: x^2 + 6x = 6.

Find (b/2)^2, where b is the coefficient of x, which is 6 in this case. So, (6/2)^2 = 9.

Add and subtract this value inside the equation: x^2 + 6x + 9 - 9 = 6.

Write the left-hand side as a perfect square and simplify the right-hand side: (x+3)^2 - 9 = 6.Finish by repositioning: (x+3)^2 = 15.

The equation x^2+6x-6=0 rewritten by completing the square is (x+3)^2 = 15.

Answer:

1000 times

Step-by-step explanation:

The Richter scale is a logarithmic scale, so we can say an earthquake of magnitude 8 on the Richter scale shows an intensity of 10^8.

In the same way, an earthquake of magnitude 5 on Richter scale will have an intensity of 10^5.

To evaluate the difference, we divide one by the other.

10^8 / 10^5 = 10^3 = 1,000

An earthquake of intensity of 8 is 1,000 times more powerful than one of intensity 5.

Answer:

on edge

A magnitude 8 earthquake is 1,000 times more intense than a magnitude 5 earthquake. A magnitude 8 earthquake is 108 times more intense than a standard earthquake, while a magnitude 5 earthquake is 105 times more intense than a standard earthquake, and 108 ÷ 105 = 103. Each unit increase on the Richter scale corresponds to an intensity increase by a factor of 10. So from 5 to 8 on the Richter scale, the intensity increases by 103 = 1,000.

Answer:

The answer should be: A.

An equation which describes the same line as [tex]y-5=-2(x+4)[/tex] is [tex]y=-2x-3[/tex].

Given the following data:

[tex]y-5=-2(x+4)[/tex]

To find an equation which describes the same line as the one given:

In Mathematics, the standard form of an equation of line is given by the following formula;

[tex]y = mx+b[/tex]

Where:

Simplifying the given equation, we have:

[tex]y-5=-2(x+4)\\\\y-5 =-2x -8\\\\y = -2x-8+5\\\\y=-2x-3[/tex]

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The midpoint between AB is at point G

Data;

The midpoint of AB can be found as the middle between point A and point B.

Point A starts from -6 and point B is at 8.

If we look through this, the midpoint between A and B is 1 which falls at point G

The midpoint between AB is at point G

Learn more on midpoint of a line here;

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Answer:

Reflection

Step-by-step explanation:

reflect it over the y axis it will be congruent

Answer:

reflection

Step-by-step explanation:

if the triangle is reflected it will keep its exact shape and only be flipped over.

(pls mark brainliest)

Answer:

-3/7

Step-by-step explanation:

If the lines are parallel, they have the same slope.

The green line has a slope of -3/7, so the red line must have a slope of -3/7

Answer:

y^3 + 27

Step-by-step explanation:

(y+3)(y2 – 3y+9)

distribute y

y^3 - 3y^2 + 9y

distribute 3

3y^2 - 9y + 27

add/combine like terms and order correctly

y^3 + (3y^2 - 3y^2) + (9y - 9y) + 27

answer

y^3 + 27

Answer:

40%

Step-by-step explanation:

We are given that last month, Joe's puppy weight 5.4 pounds while this month, the puppy weighed 7.56 pounds.

We are to find the percentage increase of the weight of the puppy

We know that the formula of percentage increase if given by:

Percentage increase = (new value - initial value)/initial value × 100

So substituting the given values to get:

Percentage increase in puppy's weight = [tex]\frac{7.56-5.4}{5.4} \times 100[/tex] = 40%

Answer:

Choice B), [tex]f(x) = -3|x|[/tex].

Step-by-step explanation:

Each point on the graph of [tex]g(x)[/tex] can be represented as [tex](x, g(x))[/tex].

When the graph of [tex]g(x)[/tex] is reflected over the x-axis, each point on the graph is also reflected over the x-axis. The x-coordinate of each point will not change but the sign in front of the y-coordinate will flip. For example, [tex]1[/tex] (same as [tex]+1[/tex]) will become [tex]-1[/tex], and vice versa. In general, [tex](x, g(x))[/tex] will become [tex](x, -g(x))[/tex].

On the other hand, points on the graph of [tex]f(x)[/tex] can be represented as [tex](x, f(x))[/tex]. [tex]f(x)[/tex] is the reflection of [tex]g(x)[/tex], so [tex](x, -g(x))[/tex] and [tex](x, f(x))[/tex] shall be equivalent. In other words,

[tex]f(x) = -g(x) = - 3|x|[/tex].

Answer:

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

Step-by-step explanation:

we have

[tex]2(x-2)^{2}=8(7+y)[/tex]

step 1

Exchange x for y and y for x

[tex]2(y-2)^{2}=8(7+x)[/tex]

step 2

isolate the variable y

[tex](y-2)^{2}=4(7+x)[/tex]

take the square root both sides

[tex]y-2=(+/-)\sqrt{4(7+x)}[/tex]

[tex]y=2(+/-)\sqrt{4(7+x)}[/tex]

step 3

Let

[tex]f^{-1}(x)=y[/tex]

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

[tex]f^{-1}(x)=2(+/-)2\sqrt{(7+x)}[/tex]  ----> equation of the inverse

Answer:

y=2+√28+4x

Step-by-step explanation:

Answer:

[tex]\large\boxed{-\sqrt{12}+3\sqrt3=\sqrt3}[/tex]

Step-by-step explanation:

[tex]-\sqrt{12}+3\sqrt3=-\sqrt{4\cdot3}+3\sqrt3\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=-\sqrt4\cdot\sqrt3+3\sqrt3=-2\sqrt3+3\sqrt3=(-2+3)\sqrt3=1\sqrt3=\sqrt3[/tex]

Answer:

Because he could only cover 50% of the price 25 by the coupon and 25 which he had.

How many minutes are in 9 hrs

1 hr = 60 min

You must apply dimensional analysis (aka setting up fractions where the units you want will cancel out and the ones you want stay)

[tex]\frac{9 hr}{1} *\frac{60 min}{1hr}[/tex]

9 hrs is 540 min

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

so since there is 60 minutes in 1 hour and 60 is divisible by 10 all you have to do is multiply 6 by 9 and you get 54 but since it's 60 than that changes the answer to 540 since it's divisible by 10

Answer: the slope is 4 and the y intercept is 3. Hope this helps!

Answer:

slope = 4

y-intercept = 3

Step-by-step explanation:

Note the slope-intercept form: y = mx + b

x & y is found inside the point (x , y).

m is the variable for the slope.

b is the variable for the y-intercept.

Find the corresponding number for the corresponding variable.

slope = m = 4

y-intercept = b = 3

~

Answer:

A segment has exactly one endpoint- false

Answer:

A segment do not have only one endpoint. A line segment is part of a line that is bounded by two points and contains every point on the line between the two endpoints.

Answer:

First option.

Step-by-step explanation:

In this case you need to remember that an angle formed by two intersecting chords is equal to the sum of the intercepted arcs divided by 2. This is:

[tex]Angle\ formed\ by\ two\ intersecting\ chords=\frac{1}{2}(Sum\ of\ intercepted\ arcs)[/tex]

You can identify in the figure that the angle ∠1 is an angle formed by two intersecting chords. Therefore, since the intercepted arcs are SP and QR, you can say the following:

[tex]m\angle 1=\frac{1}2}(mSP+mQR)[/tex]

You can observe that this matches with the first option.

Answer: 500 as 49 is closer to 500 by 1, if it was 550 then it would have been 600. It's basically just estimation or rounding it off to the nearest hundred

Answer:

Option B is correct.

Step-by-step explanation:

Solving using synthetic division

-8 | 2 14 9

The synthetic division is shown in image attached.

The remainder is: 25

The quotient is : 2x-2

So, Option B is correct.

Answer:

1 / y^7

Step-by-step explanation:

Y^-9•y^-8•y^10

= y^10 / y^9•y^8

= y^10 / y^17

= 1 / y^7

Answer: The answer is y^-7

Answer:

C

Step-by-step explanation:

The volume (V) of the cylinder is calculated as

V = πr²h

where r is the radius of the base and h the perpendicular height

here r = 5 and h = 8.5

V = π × 5² × 8.5

   = 25π × 8.5 ≈ 667.59 in³ ( to the nearest hundredth )

C. 667.59in^3

The procedure to use the volume of the cylinder calculator is follows:

The volume (V) of the cylinder is calculated as

V = πr²h

where r is the radius of the base and h the perpendicular height

here r = 5 and h = 8.5

V = π × 5² × 8.5

  = 25π × 8.5 ≈ 667.59 in³ ( to the nearest hundredth )

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Answer:

The answer is c

Answer:

Sqrt [ 6 ] * 2

Step-by-step explanation:

Sqrt[3]*2 Sqrt[2]

Sqrt [ 3 ] Sqrt [ 2 ] = Sqrt [ 3 * 2 ]:

Sqrt[ 3 * 2 ] 2

Answer:

Sqrt [ 6 ] * 2

ANSWER

[tex]2 \sqrt{6} [/tex]

EXPLANATION

[tex] \sqrt{3} \times 2 \sqrt{2} [/tex]

This is the same as:

[tex]2 \times \sqrt{3} \times \sqrt{2} [/tex]

Recall that:

[tex] \sqrt{a} \times \sqrt{b} = \sqrt{ab} [/tex]

We apply this property of radicals to obtain;

[tex]2 \times \sqrt{3} \times \sqrt{2} = 2 \sqrt{3 \times 2} [/tex]

We simplify to get;

[tex]2 \times \sqrt{3} \times \sqrt{2} = 2 \sqrt{6} [/tex]

Therefore the simplified form of the given expression is

[tex]2 \sqrt{6} [/tex]

Answer:

1 cubed 1

2 cubed 8

3 cubed 27

4 cubed 64

5 cubed 125

6 cubed 216

10 cubed 1,000

Cube Root of 1 is 1

Cube Root of 8 is 2

Cube Root of 27 is 3

Cube Root of 64 is 4

Cube Root of 125 is 5

Cube Root of 216 is 6

Cube Root of 1,000 is 10

Step-by-step explanation:

To find the cube of a number multiply that number by itself three times and to find the cube root of a number find one perfect cube less than the original number and then find one greater than the original number and then round if you need to.

To find the cubes of numbers without a calculator, multiply each number by itself twice. To find the cube root, determine which number, when multiplied by itself twice, equals the given cube.

In order to list the cubes of the numbers from 1-6 and 10 without a calculator, we need to multiply each number by itself twice. Here are the cubes:

To find the cube root of each cube, we need to determine which number, when multiplied by itself twice, equals the given cube. Here are the cube roots:

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Answer:

(-2, 6) on edge

Step-by-step explanation:

Answer:

A: Natasha should have multiplied 100 by 2.

Step-by-step explanation:

i got it right in e2021

and mark me Brainliest

Answer:

14 numbers.

Step-by-step explanation:

Since -4 is in the negatives, we would go up on the number line until we reached positive 10. Which would therefore equal, 14.

Answer:

14 units

Step-by-step explanation:

We have to take the absolute value of the measure in both directions, that is

| 10 - (- 4) | = | 10 + 4 | = | 14 | = 14

| - 4 - 10 | = | - 14 | = 14