You want to borrow three rock CDs from your friend. She loves math puzzles and she always makes you solve one before you can borrow her stuff. Here's the puzzle: Before you borrow three CDs, she will have 39 CDs. She will have half as many country CDs as rock CDs, and one-fourth as many soundtracks as country CDs. How many of each type of CD does she have after you borrow three rock CDs?

Problem 1.

Yes it is true that vertical angles are congruent, but that's not what your teacher is asking. Instead, your teacher is asking basically how the term "congruent" is defined.

Two segments are congruent if they are the same length. Two angles are congruent if they are the same measure. Two triangles are congruent if they have the same angles and sides.

So in short, "congruent" just means "same". You can think of having mirror copies.

==========================================

Problem 2.

Angles 2 and 4 are one pair of vertical angles. They are opposite one another in this X shape formed by the two lines. The other pair of vertical angles are angle 1 and angle 3.

Angle 2 is given to be 76 degrees, so this means angle 4 is this measure as well.

Angle 1 = 180 - (angle 2) = 180 - 76 = 104, which is also the measure of angle 3 as well. I'm using the idea that the adjacent angles form a straight angle. This is known as a linear pair (ie the angles form a straight line).

==========================================

Problem 3.

If all three angles are the same (all 60 degrees), then we have an equilateral triangle. We could say it's equiangular, but it's also equilateral as well meaning all 3 sides are the same length. "equi" means "equal", "angular" means what you'd expect, and "lateral" means "side".

If only two angles are equal with the third one different, then we have an isosceles triangle. An isosceles triangle is one where only two sides are the same length.

If none of the angles are the same, then we have a scalene triangle. As you probably expect, none of the sides are the same length with a scalene triangle.

----

If all three angles are less than 90 degrees, then the triangle is acute

If one angle is 90 degrees, then we have a right triangle

If one angle is over 90 degrees (but less than 180), then the triangle is obtuse

---

Often you'll see the terms of the previous two sections combined. For instance, we could have an isosceles right triangle. Or we might have an obtuse scalene triangle. Any equilateral triangle is acute (as all three angles are less than 90).

To solve this problem we have to understand what congruent angles are and then find the angles that are congruent to one other in this given question.

Congruent angles are angles that are equal to one another and in the given question, we were given m<2 = 76 degrees.

Data;

If we look critically at the angles, we can use opposite angle theorem here to predict angles that are congruent to another here.

angles 2 and angle 4 are congruent to one another while angle 1 and angle 3 are congruent to one another.

This implies that

Let's solve for other angles.

But the some of angles at a point is equal to 360°

Applying that theorem here,

[tex]m > 1=x\\m > 2 = 72^0\\m > 3 = x\\m > 4 = 72^0[/tex]

Let's substitute the values and solve.

[tex]x+ x + 72+72 = 360\\2x + 144 = 360\\2x = 360 - 144\\2x = 216\\x = \frac{216}{2} \\x = 108^0[/tex]

This can be further summarized as

Learn more on corresponding angles here;

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Answer:

Hey There. ☆~<___`£《》£`____>~☆ The correct answer is: 33% okay if you don't understand this. Just tell me Okay. k=11 And, let me know if you don't understand how I got this. So, I'm gonna write it out

U V total

S 26 42 68

T 21 k 32

Total 47 53 100

So, you want to look at the column and row labeled total, this is the key. for the row total, it sums up everything in the column above it. so for the u column, the total value is 47 while the two values above it are 26 and 21. These two values sum to 47. This is the same for all other columns, and you can use the same reasoning with the total column as well summing rows.

This gives you two ways to solve for k. either 21 + k = 32 or 42 + k = 53. Either way gets you the answer k = 11

Hope It Helps!~ ♡

ItsNobody~

Answer:

The answer is B

Step-by-step explanation:

/////////////nvm///////////

Answer:

[tex]\huge\boxed{2k-13}[/tex]

Step-by-step explanation:

[tex]\sf -3(2+4k)+7(2k-1)\\Expanding \ brackets\\-6-12k+14k-7\\Combining \ like \ terms\\-12k+14k-6-7\\2k -13[/tex]

Standard form is written Ax + By = C where A, B, and C are all integers.

In other words, no fractions.

Also, the A or the coefficient of the x term must be positive.

The only thing we need to do is add 7x to both sides to get 7x + y = -1.

So 7x + y = -1 is our answer.

Answer: 7x+y=-1

Step-by-step explanation:

Add 7x to both sides

Answer:

Positive

Step-by-step explanation:

negative times negative is postive positive times negative is negative

Answer:

A positive.

Step-by-step explanation:

Let's replace these with numbers.

-1 · 2  · (-3)

A negative times a positive will always equal a negative. So, we have:

-2 · (-3)

Any numbers with the same sign (positive or negative)  multiplied by each other will equal a positive. Since we have two negatives and we're multiplying them, our result will be a positive number.

6

Hope this helps!! <3 :)

Answer:

t=3.5 seconds

Step-by-step explanation:

Given

h(t) = −16t^2 + 111t + 0

h'(t)= -32t + 111

Maximum height occurs when h(t) = 0 and the ball begins to fall

h(t)= -32t + 111=0

-32t + 111=0

-32t=-111

Divide both sides by -32

t=3.46872

Approximately, t=3.5 seconds

Recall,

Maximum height occurs when h(t) = 0

h(t)= -32t + 111=0

= -32(3.46872)+111

= -110.99904+111

= 0.00096 ft

Answer:

x = 3 and y = 0

Step-by-step explanation:

3y+x=3

-2y+5x=15

Isolate y in 3y + x = 3 :

[tex]y=[/tex] [tex]\frac{3-x}{3}[/tex]

Substitute [tex]y = \frac{3-x}{3}[/tex]  in -2y + 5x = 15 :

[tex]-2 * \frac{3-x}{3} + 5x = 15[/tex]

Simplify the equation :

[tex]\frac{-6+17x}{3} =15[/tex]

Isolate x in [tex]\frac{-6 + 17x}{3} = 15[/tex] :

Proving x = 3

Isolate y in [tex]y = \frac{3-3}{3}[/tex] :

Proving y = 0

Your solved system of equations are x being 3, and y being 0.

Answer:

[tex]\boxed{\sf 200 \ feet^2}[/tex]

Step-by-step explanation:

The 3D shape is a square-based pyramid.

The surface area of a square-based pyramid is given as:

[tex]\sf SA=2 \times (base \ length) \times (slant \ height) + (base \ length)^2[/tex]

Plug in the values.

[tex]\sf SA=2 \times 10 \times 5 + 10^2[/tex]

[tex]\sf SA=100 + 100[/tex]

[tex]\sf SA=200[/tex]

Answer:

See explanation

Step-by-step explanation:

Atlantic area = πr² = (3.14)(2.5)² = 19.63 ft²

Circumference = 2πr = 2(3.14)(2.5) = 15.7 ft

Pacifica A = (3.14)(6)² = 113.04 ft²

C = 2(3.14)(6) = 37.68 ft

Mediterranean A = (3.14)(1.75)² = 9.62 ft²

C = 2(3.14)(1.75) = 10.99 ft

Baltica A = (3.14)(1)² = 3.14 ft²

C = 2(3.14)(1) = 6.28 ft

Japanesque A = (3.14)(2.25)² = 15.90 ft²

C = 2(3.14)(2.25) = 14.13 ft

Floridian A = (3.14)(3.25)² = 33.17 ft²

C = 2(3.14)(3.25) = 20.41 ft

Answer:

1.3

Step-by-step explanation:

5.2/4 = 1.3

To check, 1.3 multiplied by four is 5.2.

Answer:

It’s 1.3

Step-by-step explanation:

Make meeee brainliest

Answer:

216,004

Step-by-step explanation:

so 5(14-2)third power + 8/2,

that would be

5(12)third power + 8/2

(60) third power + 4

216,000 + 4

Answer:

y = 6x - 2

Step-by-step explanation:

slope-intercept form: y = mx + b

Note that:

m = slope = 6

b = y-intercept = -2

x = (x , y)

y = (x , y)

Plug in the corresponding numbers to the corresponding variables:

y = 6x + (-2)

y  = 6x - 2

y = 6x - 2 is your answer.

~

Answer:

y = 6x-2

Step-by-step explanation:

The slope intercept equation  form of a line is

y = mx+b where m is the slope and b is the y intercept

y = 6x-2

Answer:

x=20

<B=150°

Step-by-step explanation:

Opposite Interior Angles

8x-10=3x+90

8x-3x=90+10

5x=100

x=20

<B=3x+90

=3(20)+90

=60+90=150

Answer:

x=20

<B = 150

Step-by-step explanation:

The angles are alternate interior angles and when the lines are parallel, alternate interior angles are equal

8x-10 = 3x+90

Subtract 3x from each side

8x-10 -3x = 3x+90-3x

5x-10 = 90

Add 10 to each side

5x-10 +10 = 90+10

5x = 100

Divide by 5

5x/5 = 100/5

x = 20

<B = 3x+90

    = 3*20 +90

    = 60+90

    = 150

Answer:

1) 0.3 ; 0.7

Step-by-step explanation:

Given the following :

Probability that product A launch : P(A) = 0.45

Probability that product B launch : P(B) = 0.60

Probability that both product launch : P(AnB) = 0.35

P(A alone) = p(A) - p(AnB)

P(A alone) = 0.45 - 0.35 = 0.1

P(B alone) = p(B) - p(AnB)

P(B alone) = 0.60 - 0.35 = 0.25

Probability that neither product will launch :

1 - [p(A alone) + p(B alone) + p(AnB)]

1 - [0.1 + 0.25 + 0.35]

1 - 0.7 = 0.3

Probability that at least one product will launch :

P(A alone) + p(B alone) + p(AnB)

0.1 + 0.25 + 0.35 = 0.7

Answer:

  1/4

Step-by-step explanation:

There are 12 inches in a foot, so 3 inches is 3/12 of a foot. As a reduced fraction, that is 1/4 of a foot.

Answer: 1/4 of a foot.

Step-by-step explanation: If you ever see this, I'm guessing you're in Elementary. But all3 of your questions have gotten me weak.

Answer:

110 feet per second

Step-by-step explanation:

You would mutiply your speed in miles per hour by 5,280. That's the number of feet in a mile and your result is your speed in feet per hour.

75 x 5,280 = 396,000 feet per hour

Then you would divide your speed by 60 and that result is your speed in feet per minute.

396,000 / 60 = 6,600 feet per minute

Lastly, you would divide that speed by 60 and the result is your speed in feet per second.

6,600 / 60 = 110 feet per second

The conversion of 75 miles per hour to feet per second is approximately 110 feet per second.

We can do this by using conversion factors that relate the two units. Specifically, we can use the fact that 1 mile equals 5,280 feet and 1 hour equals 3,600 seconds.

To convert miles per hour to feet per second, we need to multiply the value in miles per hour by a conversion factor that will cancel out the "miles" unit and replace it with "feet," and another conversion factor that will cancel out the "hours" unit and replace it with "seconds."

So, first we convert miles per hour to feet per hour by multiplying 75 miles/hour by 5,280 feet/mile.

This gives us:

= 75 miles/hour x 5,280 feet/mile

= 396,000 feet/hour

Next, we convert feet per hour to feet per second by dividing by 3,600 seconds/hour.

This gives us:

=396,000 feet/hour ÷ 3,600 seconds/hour

= 110 feet/second

Therefore, 75 miles per hour is approximately equal to 110 feet per second.

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Answer: B. down

Step-by-step explanation:

Translation rules:

For a function h(x):

Here, the graph of f(x) becomes the graph of g(x) =f(x)-4 which is similar to "h(x)-c".

That means , f(x) is shifted 4 units down to become g(x).

So, correct option : B. down

Answer:

x = -7

Step-by-step explanation:

DE + EF + FG = DG

2x+17 + 8+2 = x+20

Combine like terms

2x+ 27 = x+20

Subtract x from each side

2x+27-x = x+20-x

x+27 = 20

Subtract 27 from each side

x+27-27 = 20-27

x = -7

Answer:

The properties and characteristics of the sum of two cubes

1) In the sum of two cubes, the middle sign of the binomial factor on the right hand side of the equation is positive

2) The trinomial factor has a middle sign that is opposite to the middle sign in the question on the sum of two cubes

The properties and characteristics of the difference of two cubes

1) In the difference of two cubes, the middle sign of the binomial factor on the right hand side of the equation is always negative

2) The trinomial factor has a middle sign that is opposite to the middle sign in the question on the difference of two cubes

Step-by-step explanation:

The sum and difference of two cubes are;

a³ + b³, and a³ - b³

Factorizing the expressions for the sum and difference of two cubes can be shown as follows;

Sum of two cubes; a³ + b³ = (a + b) × (a² - a·b + b²)

Difference of two cubes; a³ - b³ = (a - b) × (a² + a·b + b²).

Answer:

[tex]\frac{x^{3} }{4y^{5} }[/tex]

Step-by-step explanation:

Simplifica la expresión

See the diagram, and tell me if it's clear

Answer:

$ 175

Step-by-step explanation:

cost to make the shirt = the price of cloth+stitching expenses

C=800+200

C=1000 dollars

Profit that Derek made : selling price-expenses

P=1175-1000

p=175 dollars

Answer:

1306.24 cm².

Step-by-step explanation:

From the diagram given above, we obtained the following information:

Radius (r) = 13 cm

Pi (π) = 3.14

Slant height (l) = 19 cm

Surface Area (SA) =.?

The surface area of the cone can be obtained as follow:

SA = πr² + πrl

SA = πr ( r + l)

SA = 3.14 × 13 ( 13 + 19)

SA = 40.82 (32)

SA= 1306.24 cm²

Therefore, the surface area of the cone is 1306.24 cm².

Answer:

I may be wrong but I think 8 is your answer.

Step-by-step explanation:

(-1)^(3/7)  x 128^(3/7)

-1 x 128^3/7

128^(3/7) = 8

= 8

Answer:

[tex]p = \frac{25}{4}[/tex]

Step-by-step explanation:

Given

[tex]x\² - 5x + p[/tex]

Required

Find p, such that the expression is a perfect square

Write out the coefficient of x

Coefficient = -5

Next step is to divide the coefficient of x by 2

[tex]Result = \½(-5)[/tex]

Take the square of the above expression to give p

[tex]p = (\½(-5))\²[/tex]

[tex]p = (\½(-5) * (\½(-5)[/tex]

[tex]p = \½ * \½ * (-5) * (-5)[/tex]

[tex]p = \¼(25)[/tex]

[tex]p = \frac{25}{4}[/tex]

Substitute 25/4 for p in the given expression

[tex]x\² - 5x + p[/tex] becomes

[tex]x\² -5x + \frac{25}{4}[/tex]

Expand the above expression

[tex]x\² - \frac{5x}{2} - \frac{5x}{2} + \frac{25}{4}[/tex]

Factorize

[tex]x(x - \frac{5}{2}) - \frac{5}{2}(x - \frac{5}{2})[/tex]

[tex](x - \frac{5}{2})(x - \frac{5}{2})[/tex]

[tex](x - \frac{5}{2})\²[/tex]

Hence, the value of p is [tex]p = \frac{25}{4}[/tex]

40 pigs.

p=pigs c=chickens.

4p=pigs have 4 legs.

2c=chickens have 2 legs.

4p+2c=200

p+c=60

4p+2c=200

(-4)p+c=60

4p+2c=200

-4p-4c=-240

-2c=-40

c=20

p+20=60

p=60-20

p=40

Hope this helps!

BRAINLIEST would help me a lot:)

Answer:

3.5 hours

Step-by-step explanation:

Paul:

Mary:

Since the distance is same, we have:

Answer: Paul's travel took 3.5 hours

Answer:

[tex]\boxed{\frac{1}{25} \text { OR } 0.04}}[/tex]

Step-by-step explanation:

[tex]5^{-2}\\\\\text {Apply Negative Exponent Rule: } a^{-b}=\frac{1}{a^b}\\\\5^{-2}=\frac{1}{5^2}=\boxed{{\frac{1}{25}} \text { OR } 0.04}[/tex]

Answer:

[tex]x\geq 22[/tex]

Step-by-step explanation:

If someone wants to practice for at least 22 minutes a day, they want to practice 22 minutes or more. This is the same as greater than or equal to, and  we want the minutes practices to be greater than or equal to 22. We can assume minutes practiced is x, and create the inequality [tex]x\geq 22[/tex].

Hope this helped!