Solve the inequality and graph the solution. |x + 7| − 15 < 8

Answer:

Step-by-step explanation:

We know that [tex]\angle OEB = 90\°[/tex], by given, so it's a right angle, by definition.

[tex]\angle OEA[/tex] and [tex]\angle OEB[/tex] are adjacent angles on a straight angles. That means they are sumplementary angles by definition.

[tex]\angle OEA + \angle OEB = 180\°\\ \angle OEA = 180\° -90\°\\\angle OEA = 90\°[/tex]

Therefore, [tex]\angle OEA = \angle OEB[/tex].

Sides AE and BE are congruent, because the congruence between those right angles, and the congruence between the other corresponding sides justify the congruence between sides AE and BE.

Notice that the hypothenuses of each right triangle are congruent, because they are also radius of the circle, which means they are congruent by definition.

Additionally, side OE is a common leg for both right triangles.

Therefore, sides AE and BE are congruent.

We know that [tex]d=20[/tex] and [tex]CE=4[/tex], that means the radius is

[tex]r=\frac{d}{2}=\frac{20}{2}=10[/tex]

Notice that the chord AB is formed by AE and BE by sum of segments.

We know the hypothenuses are equal to 10 units of length, because they are radius.

Additionally,

[tex]OC=OE+EC[/tex], by sum of segments.

[tex]10=OE+4\\OE=10-4\\OE=6[/tex]

Which means the common leg is 6 units long.

Now, we use the Pythagorean's theorem to find the missing leg

[tex]OB^{2}=EB^{2}+OE^{2}\\ 10^{2}=EB^{2}+6^{2}\\100-36=EB^{2}\\EB=\sqrt{64}\\ EB=8[/tex]

But, [tex]AB=AE+EB[/tex], by sum of segments.

[tex]AB=8+8=16[/tex], because [tex]AE=EB[/tex] we said before.

Therefore, the length of AB is 16 units.

Answer:

0, 0, 1/4, 1/2, 1/2, 1, 1, 1, 5/4, 2, 2

Step-by-step explanation:

Answer:

Option D

Step-by-step explanation:

Hope this helps! :)

The coordinates of the preimage will be at A(-2.5, 5.5), B(-2.5, 2.5) and C (-6.5, 2.5)

Translation is a transformation technique for changing the size and position of an object on the x-y plane.

From the given diagram, the coordinate A'B'C' is given as:

A' = (-1, 2)

B' = (-1, -1)

C' = (-5, -1)

If the triangle ABC was translated according to the rule (x, y) = (x + 1.5, y-3.5) to create the image A'B'C'

A (x + 1.5, y-3.5) = (-1, 2)

x + 1.5 = -1

x = -2.5

y - 3.5 = 2

y = 5.5

Hence A = (-2.5, 5.5)

B = (x + 1.5, y-3.5) = (-1, -1)

x + 1.5 = -1

x = -2.5

y - 3.5 = -1

y = 2.5

Hence B = (-2.5, 2.5)

C (x + 1.5, y-3.5) = (-5, -1)

x + 1.5 = -5

x = -6.5

y - 3.5 = -1

y = 2.5

Hence C = (-6.5, 2.5)

Hence the graph that shows the pre image ABC is attached below

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John's speed is 6.67 miles per hour. Therefore, it would take him approximately 0.15 hours or 9 minutes to run 1 mile at the same pace.

The subject of this problem is rate. We can calculate John's speed by dividing the distance he covers by the time it takes. In this case, John ran 5 miles in 3/4 of an hour. So, his speed is 5 miles divided by 3/4 hour, which equates to 6.67 miles per hour. This means he runs 6.67 miles in 1 hour.

Given that speed is constant, if John wants to run only 1 mile, we simply divide this distance by his speed. So, 1 mile divided by 6.67 miles per hour gives 0.15 hours, or approximately 9 minutes. So, it would take John about 0.15 hours or 9 minutes to run 1 mile at the same pace.

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Answer:

16 weeks

Step-by-step explanation:

400/25 =16

Answer: 3/32

Do Keep Change Flip (KCF)

Keep: 3/8

Change: ÷ into ×

Flip: 4/1 into 1/4

Your New Problem: 3/8×1/4

Multiply

3/8×1/4=3/32

Final Answer: 3/32

Answer:

[tex] \frac{3}{32} [/tex]

Step-by-step explanation:

[tex] \frac{3}{8} \div \frac{4}{1} \\ \frac{3}{8} \times \frac{1}{4} \\ = \frac{3}{32} [/tex]

Answer:

they all equal 15

Step-by-step explanation:

Answer: The answer is 1.

Step-by-step explanation:

The correlation coefficient is “r” on the regression calculator. When you put the data into the calculator r=1.

Answer:

The radius is 14 with a circumference of 28

The radius of the circle with circumference 28π is given by r = 14 inches

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

The equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r² be equation (1)

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

Given data ,

Let the radius of the circle be represented as r

Now , the equation will be

The circumference of the circle C = 28π inches

And , circumference of circle = 2πr

On simplifying , we get

2πr = 28π

Divide by π on both sides , we get

2r = 28

Divide by 2 on both sides , we get

r = 14 inches

Hence , the radius of the circle is 14 inches

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Answer:

48 batches of muffins

Step-by-step explanation:

There are 4 cups in 1 quart

4 quarts in 1 gallon

there are 3 gallons

3 gallons = 3(4 quarts)

3 gallons = 12 quarts

12 quarts = 12(4 cups)

12 quarts = 48 cups

48 cups per batch = 48 batches of muffins

Answer:

18

Step-by-step explanation:

Answer:18 bo 20*7=140 140-104=36 36:2=18

Step-by-step explanation:

Answer:

Analyze then add

Step-by-step explanation:

Basically, just analyze the lengths of the sides, and then add them together for the perimeter

Thank me later :)

Answer:

s+s+s=p

Step-by-step explanation:

Just add the three side measurements. Answer will contain a unit most of the time. Remember to convert units if its asking for different units.

Answer:

Step-by-step explanation:

finding financing in any economic climate can be challenging, whether you're looking for start-up funds, capital to expand or money to hold on through the tough times. ...

Step-by-step explanation: the primary ways to finance your business are through savings, credit cards, friends and family, loans from lending networks or programs, angel investors, business loans and lines of credit, factoring, and purchase order funding.

Answer:

SAS POSTULATE

Step-by-step explanation:

ON SIDE IS COMMON

TWO SIDES ARE CONGRUENT TO EACHOTHER

WHILE SAME WITH THE TWO ANGLES

Answer:

They are not congruent

Step-by-step explanation:

Answer:

negative - $9.50

Step-by-step explanation:

The expected value of a ticket of the local fire company given the price and the expected values is $-9.50.

The expected value is the sum of the prizes added to the cost.

Expected value = value of the prizes - cost

(300 + 150 + 50 + 0) - (10 x 1000)

500 - 10,000

- 9500

Expected value of a ticket = - 9500 / 1000 = -9.50

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Answer:

19, 300 i think thats correct im sorry if not

Step-by-step explanation:

Answer:

the answer is 1.4 inches taller

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The exponent is negative so you put the number under 1 with the exponent positive

Answer:

I think the correct answer should be C

Step-by-step explanation:

2-4= -2

Answer:

[tex]m=\frac{2KE}{y^{2} }[/tex]

Answer:

It is 6 (six)

Step-by-step explanation:

The length of PQ of the triangle PQJ is [tex]5\frac{1}{3}[/tex] units.

A triangle is a two-dimensional geometrical figure that has three sides, three vertices and three interior angles.

Given, m∠B = m∠P, m∠T = m∠J.

Therefore, ΔBLT and ΔPQJ are similar triangles.

Let, the length of PQ is 'x'.

Therefore, [tex]\frac{BL}{PQ} = \frac{BT}{PJ}[/tex]

⇒ [tex]\frac{4}{x} = \frac{6}{8}[/tex]

⇒ [tex]x = \frac{(4)(8)}{6}[/tex]

⇒ [tex]x = \frac{32}{6} = 5\frac{1}{3}[/tex]

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Answer:

1120 square inches or OPTION D

Step-by-step explanation:

40 × 50 = 2000

(50 - 10) × (40 - 18) =

40 × 22 = 880

2000 - 880 = 1120

Answer:

5 and 12

Step-by-step explanation:

Answer:

218 boxes of cereal

Step-by-step explanation:

To get the explicit rule, find the difference between each week:

53-20 = 33

86-53 = 33

The explicit rule is:

aₓ = 33x - 13  

or

f(x) = 33x - 13

If you use this rule, you can plug in 7 for x and you get:

218 boxes of cereal

Answer:

x=-5                   x=3

Step-by-step explanation:

−x2 = 2x − 15

Add x^2 to each side

x^2−x2 =x^2+ 2x − 15

0 = x^2+ 2x − 15

Factor

What two numbers multiply to -15 and add to 2

5*-3 = -15

5-3 =2

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

Using the zero product property

x+5 =0        x-3=0

x+5-5=0-5    x-3+3=0+3

x=-5                   x=3

Answer:

x = 30°

Step-by-step explanation:

The complete circle is 360°, thus

arc AB = 360° - 300° = 60°

The tangent- secant angle ABT is half the measure of the intercepted arc AB, that is

x = 0.5 × 60° = 30°

Answer:

Its x = 30°

Step-by-step explanation:

Answer:

t = - [tex]\frac{1}{8}[/tex]

Step-by-step explanation:

Given

[tex]\frac{t}{\frac{5}{12} }[/tex] = - [tex]\frac{3}{10}[/tex]

Multiply both sides by [tex]\frac{5}{12}[/tex]

t = [tex]\frac{5}{12}[/tex] × - [tex]\frac{3}{10}[/tex] ← cancel 5 and 10 by 5 and 3 and 12 by 3, leaving

t = [tex]\frac{1}{4}[/tex] × - [tex]\frac{1}{2}[/tex] = - [tex]\frac{1}{8}[/tex]

Answer:

y= -2x +5

Step-by-step explanation:

Answer:

y=-2x+5

Step-by-step explanation:

ok an easy way to tell is on the y axis when x=0 the lnumber that y is,is the regualar number.  Then if you go down and over till you get another point is you x. down is like 2x but if you went over 3 it would be 2/3x but since you only going over once it is just 2x. and the minus is because your going down