Your teacher draws a line segment on the board that connects points A and B in the coordinate plane. Using what you know about midpoints, explain how can you find the point that is 1/4 of the distance from A to B?

If this figure was a parallelogram, then the opposite angles would be congruent. This would make angles B and D the same measure

angle B = angle D

x^2+20 = 7x+50

x^2+20-7x-50 = 0 .... get everything to one side

x^2-7x-30 = 0

(x-10)(x+3) = 0 ... see note below

x-10 = 0 or x+3 = 0

x = 10 or x = -3

Note: In this step is where the factoring occurs. To factor, we need to find two numbers that multiply to -30 which is the last term, and also add to -7 which is the middle coefficient. This is a trial and error process. You should find that -10 and 3 both multiply to -30 and add to -7. I suggest making a table as shown below (attached image) to list out all the possible choices.

Perhaps a much more efficient route is to use the quadratic formula.

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

We found two possible solutions for x. If x = 10, then 7x+50 is 7(10)+50 = 120 which is an obtuse angle. If x = -3, then 7x+50 = 7(-3)+50 = 29 which is acute.

Assuming the diagram is drawn to scale, this means angle D is obtuse and we'll go with x = 10 and 7x+50 = 120

Angles A and D add to 180 degrees. This is true for any pair of adjacent angles in a parallelogram.

A+D = 180

A+120 = 180

A = 180-120

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

This answer is based on the assumption that the diagram is drawn to scale and that this quadrilateral is a parallelogram.

Answer:

[tex]\angle A=60\textdegree[/tex]

Step-by-step explanation:

So we have the following parallelogram and we wish to solve for ∠A.

To do so, we will need to solve for x first. Look carefully at the parallelogram...

Notice that ∠A and ∠D are consecutive angles. In other words:

[tex]\angle A+\angle D=180[/tex]

Since we have an equation for ∠D, substitute:

[tex]\angle A+7x+50=180[/tex]

Notice that ∠A and ∠B are also consecutive angles. So:

[tex]\angle A+\angle B=180[/tex]

We know the equation for ∠B. Substitute:

[tex]\angle A+x^2+20=180[/tex]

Since both equations equal 180, we can set them equal to each other:

[tex]\angle A+7x+50=x^2+20+\angle A[/tex]

Let's subtract ∠A from both sides. This gives us:

[tex]7x+50=x^2+20[/tex]

Now, we can solve for x. This is a quadratic, so let's move all the terms to one side. To start off, let's subtract 50 from both sides:

[tex]7x=x^2-30[/tex]

Now, let's subtract 7x from both sides:

[tex]0=x^2-7x-30[/tex]

Solve for x. We can factor.

Here's the trick to factoring. If we have the following:

[tex]0=ax^2+bx+c[/tex]

The we will need to find two numbers, p and q, such that:

[tex]p+q=b\text{ and } pq=ac[/tex]

In our equation, a is 1, b is -7, and c is -30.

So, we want two numbers that sum to -7 and multiply to (1)(-30)=-30.

We can use -10 and 3. -10+3 is -7 and -10(3) is -30. So, let's substitute our b term for -10x and 3x. In other words, we have:

[tex]0=x^2-7x-30[/tex]

Substitute -7x for 3x-10x. This gives us:

[tex]0=x^2+3x-10x-30[/tex]

This is equivalent to our old equation.

Now, we can factor. Factor out a x from the first two terms:

[tex]0=x(x+3)-10x-30[/tex]

And factor out a -10 from the two last terms:

[tex]0=x(x+3)-10(x+3)[/tex]

Since the expressions within the parentheses are the same, we can use grouping to acquire:

[tex]0=(x-10)(x+3)[/tex]

Note that this is essentially the distribute property. If we distribute, we will get the same as above.

Zero Product Property:

[tex]x-10=0\text{ or }x+3=0[/tex]

Solve for x:

[tex]x=10\text{ or } x=-3[/tex]

So, we have two cases for x. Each case will yield a different answer for ∠A.

Case I: x=10

Use our original equation of:

[tex]\angle A+7x+50=180[/tex]

Substitue 10 for x:

[tex]\angle A+7(10)+50=180[/tex]

Multiply:

[tex]\angle A+70+50=180[/tex]

Add:

[tex]\angle A+120=180[/tex]

Subtract 120 from both sides:

[tex]\angle A=60\textdegree[/tex]

So, in our first case, ∠A is 60°

Case II: x=-3

Again, same equation:

[tex]\angle A+7x+50=180[/tex]

This time, substitute -3 for x. This yields:

[tex]\angle A+7(-3)+50=180[/tex]

Multiply:

[tex]\angle A-21+50=180[/tex]

Add:

[tex]\angle A+29=180[/tex]

Subtract 29 from both sides:

[tex]\angle A=151\textdegree[/tex]

So, in our second case, ∠A is 151°

However, 151° doesn't seem likely with how the figure is drawn.

Therefore, our final answer is 60°.

And we're done!

Edit: Fixed Incorrect Answer

Answer:

-1

Step-by-step explanation:

Answer:

D. 96 degrees

Step-by-step explanation:

In a parallelogram, opposite angles must add up to 180

3x + x + 52 = 180

4x = 128

x = 32

∠B = 3x

∠B = 3(32)

∠B = 96

Answer:

96

Step-by-step explanation:

3x + x + 52 = 180

4x = 128

x = 32

∠B = 3x

∠B = 3(32)

∠B = 96

Answer:

EG = 18

Step-by-step explanation:

Answer:

how everany they want to choose abviously

Answer:

12 people!

Step-by-step explanation:

each pizza is cut into 4 pieces, and there are 3 whole pizzas. 4 times 3= 12!

Answer:

12

Step-by-step explanation:

Since we have 3 pizzas, and we know that the pizzas are cut 1/4, We can multiply 3 to 4. We should get 12!

Deeper explanation:

We have 3 pizzas and they're cut 1/4. Draw 3 pizzas cut by fourths. Now count the pizza slices. We have 12 slices!

Answer:

1. MO=14 units

2. M=3

3.X=5

Step-by-step explanation:

1. The length is just how many units between each point

2. Find the average of the two points (use absolute value)

(|-4|+10)÷2=(4+10)÷2=14÷2=7, the midpoint is 7 units from each endpoint. so 10-7=3

3. the length of the line ac=10x, the parts are 12 and 8x-2 set up an equation

10x=12+8x-2 combine like terms

2x=10 divide both sides by 2

x=5

Step-by-step explanation:

1. 10-(-4)

10+4=14

3. AB+BC=AC

12+8X-2=10x

10+8x=10x

10= 10x-8x

10=2x

5=x

therefore x=5

i am sorry i do not know number 2

Answer:

Result for Inequality expression 1:

[tex]x < 5[/tex]

Result for Inequality expression 2:

[tex]x \geq -3[/tex]

Step-by-step explanation:

-Inequality expression 1:

[tex]2x - 3 < 7[/tex]

-Inequality expression 2:

[tex]5 - x \leq 8[/tex]

-Solve inequality expression 1:

[tex]2x - 3 < 7[/tex]

[tex]2x - 3 + 3 < 7 + 3[/tex]

[tex]2x < 10[/tex]

[tex]\frac{2x}{2} < \frac{10}{2}[/tex]

[tex]\boxed {x < 5}[/tex]

-Solve inequality expression 2:

[tex]5 - x \leq 8[/tex]

[tex]5 - 5 - x \leq 8 - 5[/tex]

[tex]- x \leq 3[/tex]

[tex]\frac{-x}{-1} \leq \frac{3}{-1}[/tex]

[tex]\boxed {x \geq -3}[/tex] (inequality sin changed by divide by a negative integer or variable)

The following inequality represents the solution set -

-3 ≤ x < 5.

We have the following compound inequality -

2x – 3 < 7

5 – x ≤ 8

We have to solve for x.

A compound inequality (or combined inequality ) is two or more inequalities joined together with OR or AND. There are two types of compound inequalities in the form of conjunction problems and disjunction problems.

According to the question, we have -

2x – 3 < 7

Add 3 on both sides -

2x - 3 + 3 < 7 + 3

2x < 10

Divide both sides by 2, we get -

x < 5

5 – x ≤ 8

Subtract 5 on both sides -

5 - x - 5 ≤ 8 - 5

- x ≤ 3

Multiply both sides by '-1' -

x ≥ -3

Combining both solutions, we can write it as -

-3 ≤ x < 5

Hence, the following inequality represents the solution set -

-3 ≤ x < 5

To solve more questions on Compound inequalities, visit the link below-

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Answer: Lily is Correct.

Step-by-step explanation:

Lily is correct because the product of 15x52 is 15 times bigger than 15, therefore making a product (way larger) than 15. Lily is correct. Tell me if this helped or didn't help, but I hope it did (: !

Answer:

400

Step-by-step explanation:

The least common multiple (LCM) of two or more non-zero whole numbers is the smallest whole number that is divisible by each of those numbers. In other words, the LCM is the smallest number that all of the numbers divide into evenly.

Answer:

400

Step-by-step explanation:

I used the cake/ladder method. The screen shot below shows the cake/ladder method for this problem.

The last part not shown in the photo, is that you have to multiply the highlighted part: 2 × 2 × 5 × 4 × 1 × 5 = 400

I hope this helps!

Answer:

x≤ 50

Step-by-step explanation:

Answer: x = 8

Step-by-step explanation: 4x + 7 ≤ 39, first subtract 7 to get 4x ≤ 32, then divide on both sides by 4 to get x ≤ 8.

Hope this helps!

Please Mark Brainliest!

(I play FN too and I am Champs)

Answer:

23

Step-by-step explanation:

You must first do 4(3)+11 to equal 23

Answer:

23

Step-by-step explanation:

If x = 3, then that means you must replace x with 3.

But it doesn't mean that the number will be 43, it will become into 4x3+11.

4x3= 12

12+11 = 23

Answer:

52 stickers

Step-by-step explanation:

I hope that this helps you. :)

Answer:

2*26=52

Step-by-step explanation: you can just use a calculator to find 2*26 and you will find that the answer to your question is 52.

Answer:

52

because you can add 26+26=52

Answer:

I'm a sophomore in highschool.

Step-by-step explanation:

uhhhh uh yeah :)

Answer:

Both Anoki and David are correct. Both expressions are equivalent to the difference between the measurements and are always positive because they give the absolute value of the difference.

Sorry for answering so late.

Step-by-step explanation:

Both of their absolute value expression is correct because the final height will always be same.

Given,

At a theme park, a person must be a certain height to ride a rollercoaster.

A person must be h inches tall, plus or minus 1.5 inches.

Anoki says the absolute value expression | 1.5 - h | represents an acceptable height.

David says the absolute value expression I h - 1.5 | represents an acceptable height.

We have to find who is correct in expressing the absolute value.

It is expressed in | x |.

Where x is any number.

The value of x can be negative or positive.

The absolute value will always be a positive value.

|m| =  and |-m| = m.

We have,

Anoki absolute value expression: | 1.5 - h |

David absolute value expression: | h - 1.5 |

Suppose let us consider h = 72.

Now,

| 1.5 - h | = | 1.5 - 72 | = | -70.5 | = 70.5

| h - 1.5 | = | 72 - 1.5 | = | 70.5 | = 70.5

We see that both have the same value.

Thus both of their absolute value expression is correct.

Learn more about absolute value here:

https://brainly.com/question/1301718

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Answer:

x=9

Step-by-step explanation:

2(x-3)=12

First you use the distributive property

so you do 2 times x then 2 times -3

rewrite it as 2x-6=12

add 6 on both sides

2x=18

divide 2 from both sides and you get x=9

Answer:

X=3

Step-by-step explanation:

FOIL

2X-6=12

    -6=-6

2X=6

_=_

2   2

Answer:

Depending on what type of math class you are in, or how your teacher taught it, it could be either 12 R:4 or 12 + 1/370.

Step-by-step explanation:

Remainders can be written in two ways, R: [remainder] or the whole number quotient + [remainder number]/[dividend]. For this problem you would have to simplify 4/1480 to 1/370 because 1480/4 equals 370. So, your final answer would be 12 + 1/370 or 12 R:4.

Answer:

The second option with the ordered pairs.

Step-by-step explanation:

A function is basically when there is one and only one output for every input. Basically meaning there is only one x for every y. If you really want to learn more about functions, go to khan academy, they can explain it better than I can.

Answer:

Answer would be $366.70

Step-by-step explanation:

220/60%=366.70

Hope it helps

The best subset that describes the dimension of a rectangle is the set of all rational numbers.

We have,

The dimension of a rectangle refers to its length and width, which are usually measured in units such as feet or meters.

These measurements can be any real number, including irrational numbers such as √2 or π.

Now,

The only subset of the rational numbers listed in the answer choices is the positive rational numbers, which are the set of all numbers that can be expressed as a ratio of two integers where the denominator is not zero and the numerator and denominator are both positive.

While the dimensions of a rectangle can be positive rational numbers, they can also be negative rational numbers or zero, as long as they satisfy the properties of a rectangle (e.g., length and width are both positive, and the angles are right angles).

Therefore, the answer is not D.

Also, whole numbers and integers are not sufficiently precise to describe the dimensions of a rectangle, as they do not include fractions or decimals.

The only subset of rational numbers that include all possible values for the dimensions of a rectangle is the set of all rational numbers, which includes positive, negative, and zero rational numbers, as well as fractions and decimals.

Therefore,

The best answer is "the set of all rational numbers".

Learn more about rectangles here:

https://brainly.com/question/15019502

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Answer:

d

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Answer:

just subtract 8 and 3 ---> 3 + 5 = 8

Answer:

p=5

Step-by-step explanation:

3 + p = 8

Subtract 3 from both sides

3 - 3 and 8 -3

p = 5

Answer: 16.8

Hope this helps!

Answer:

[tex]\boxed {x = 7}[/tex]

Step-by-step explanation:

[tex]FJ[/tex] and [tex]JH[/tex] is half of the whole measurement of [tex]FH[/tex]. So, to find the value of  [tex]x[/tex], you need to write an expression by using those measurements of both [tex]FJ[/tex] and [tex]JH[/tex]. Then, solve for [tex]x[/tex]:

[tex]FJ = 24[/tex]

[tex]JH = 3x - 3[/tex]

[tex]3x - 3 = 24[/tex]

-Solve:

[tex]3x - 3 = 24[/tex]

[tex]3x - 3 + 3 = 24 + 3[/tex]

[tex]3x = 27[/tex]

[tex]\frac{3x}{3} = \frac{27}{3}[/tex]

[tex]\boxed {x = 7}[/tex]

So, the value of [tex]x[/tex] is [tex]7[/tex].

Answer:

x=45

Step-by-step explanation:

90+2x=4x

2x=4x-90

2x-4x=-90

-2x=-90

x= -90/-2

x=45

Answer:

1 12

4 48

5 60

Step-by-step explanation:

1x12=12

4x12=48

5x12=60