which pair of angles is a pair of corresponding angles?

Answer:

(<1 and <3) (<2 and <4) (<3 and <6)

Step-by-step explanation:

1 and 3 are corresponding equal angles

If one and three are equal, so are 2 and 4 since they are supplementary to equal angles.

6 and 7 are supplementary but not equal.

3 and 6 are equal angles because they are alternate interior angles.

Answer:

see below

Step-by-step explanation:

The odd degree (7) tells you the end behaviors are in opposite directions. The negative leading coefficient (-4) tells you the sign of y will be opposite the sign of x.

For x going toward negative infinity, y goes toward positive infinity.

For x going toward positive infinity, y goes toward negative infinity.

Answer: Corey substituted the number of swimmers into the variable (x) representing the temperature. Then he didn't wonder if the polar bear club really has 80 members.

Step-by-step explanation:

Answer:

A. He substituted 80 for x instead of y.

Step-by-step explanation:

Answer: Length of each of rope will be 9.93 feet.

Step-by-step explanation:

Since we have given that

Length of rope that Emma brandy and Damien will cut = 29.8

Number of jumps = 3

According to question, each of the three jumps ropes will be the same length l.

Length of rope can be attained by dividing the length of rope with number of jumps.

so, length of each rope will be

[tex]l=\frac{\text{Length of rope}}{\text{Number of jumps cut into }}\\\\=\frac{29.8}{3}\\\\=9.93\ feet[/tex]

Hence, Length of each of rope will be 9.93 feet.

Answer:

Surface Area = 150

Step-by-step explanation:

The surface area of this triangular prism is the sum of area of all the sides.

Surface Area = triangle 1 (with base 8 and height 3) + triangle 2 (same as triangle 1) + lateral surface 1 (with length 7 and width 5 (calculation shown below)) + lateral surface 2 (same as lateral surface 1) + bottom (side not shown with length 7 and width 8)

Summing all these gives us the total surface area.

Total surface area = [tex]12+12+35+35+56=150[/tex]

**** The triangle shown is divided into half by the perpendicular line (3cm) to the base. So the base is divided in half (4 cm and 4 cm).

Now, we have a right triangle with one leg 4 cm and another leg 3 cm. How do we get the hypotenuse? We use Pythagorean Theorem. Which is:

[tex]leg^2+leg^2=hypotenuse^2\\3^2+4^2=hypotenuse^2\\25=hypotenuse^2\\hypotenuse=5[/tex]

Hence, the side length of the hypotenuse is 5 [used above in the calculation]

Answer:

8 and 14

Step-by-step explanation:

let the 2 numbers be x and y with x > y

We can model the situation using the following 2 equations

x + y = 22 → (1)

3x - y = 34 → (2)

adding the equations term by term will eliminate the term in y

(x + 3x) + (y - y) = (22 + 34)

4x = 56 ( divide both sides by 4 )

x = 14

substitute x = 14 into (1)

14 + y = 22 ⇒ y = 22 - 14 = 8

Answer:

d. The bonds will earn $26.40 more than the stocks.

Step-by-step explanation:

Assuming, the rates are uniform for 6 years.

Stock in Ombor Medical Supplies earns a return of 5.3% annually, so $1000 will yield annually;

[tex]0.053\times1000=53[/tex] dollars

Total amount in 6 years will become = [tex]53\times6=318[/tex] dollars

Bonds issued by Ombor Medical Supplies earns a return of 4.1% annually, so $1400 will yield annually;

[tex]0.041\times1400=57.40[/tex] dollars

Total amount in 6 years will become = [tex]57.40\times6=344.40[/tex] dollars

We can see that bonds have high yield than stocks.

So, difference amount is = [tex]344.40-318=26.40[/tex] dollars.

Therefore, The bonds will earn $26.40 more than the stocks.

Answer:

it is d

Step-by-step explanation:

i took the edu test :)

Answer:

Margo is incorrect.She is selling tea in loss.

Step-by-step explanation:

Let the cost price of teas when purchased from the warehouse = $ x

Then Margo marks retail price of teas a = x + 0.40 x

                                       a = x (1 +0.40)

                                       a = 1.4 x

After 2 months she marks down the retail price by 40% then retail price becomes b = 1.4 x - 40% of 1.4 x

               b = 1.4 x - 0.4 x 1.4 x

               b = 1.4 x - 0.56 x

               b = 0.84 x

Difference between cost price and selling price b is = x - .84 x

                                                                                      = 0.16 x

which shows now Margo is selling under the cost price so Margo is incorrect.

Margo is not correct in saying that she is breaking even by marking down the retail price by 40% when teas go unsold for more than two months. In fact, she is losing money on those teas.

Margo is not correct in saying that she is breaking even by marking down the retail price by 40% when teas go unsold for more than two months. In fact, she is losing money on those teas. Let's break it down:

Therefore, Margo is not breaking even, she is actually making a loss by marking down the price of unsold teas.

Answer:

The amount of the earth’s surface covered by water is 2.12*10^8 greater than the amount of the earth’s surface covered by land.

Step-by-step explanation:

(Subtraction of scientific notation)

Earth’s surface covered by water- 3.61*10^8

Earth’s surface covered by land- 1.49*10^8

(3.61*10^8) - (1.49*10^8)

(3.61-1.49) *10^8

2.12*10^8

Hope this helps you out

Answer:

4 adult dinosaurs and 12 baby dinosaurs.

Step-by-step explanation:

Let the number of adult dinosaurs be x.

Number of baby dinosaurs = 3x

Number of paintings made by each baby dinosaur = 15

Number of paintings made by each adult dinosaur = 7

Total number of paintings made by 3x baby dinosaurs = Number of baby dinosaurs * Number of paintings made by each baby dinosaur

= 3x * 15

= 45x

Total number of paintings made by x adult dinosaurs = Number of adult dinosaurs * Number of paintings made by each adult dinosaur

= x * 7

= 7x

Total number of paintings made by both baby and adult dinosaurs = 45x + 7x

= 52 x

Again the problem says that the total number of paintings made  = 208

So, 52x = 208

Dividing both sides by 52

[tex]\frac{52x}{52}[/tex]  = [tex]\frac{208}{52}[/tex]

Cancelling out the 52's from the top and bottom on the left

x = 4

So, number of adult dinosaurs = 4

Number of baby dinosaurs = 3x = 3*4 = 12

A system of equations based on the information given can be used to find the number of baby and adult dinosaurs. The two equations are 1515b + 77a = 208208 and b = 33a. Solve these to find the number of each type of dinosaur.

This problem can be solved by setting up a system of equations. Let's denote the number of baby dinosaurs as 'b' and the number of adult dinosaurs as 'a'. Then, from the statement, we know two things:

By substituting the second equation into the first, we can determine the number of adult dinosaurs, and subsequently, the number of baby dinosaurs. Solving this would give us the solution needed.

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The new ticket price after a 25% increase from the original price of $4.80 will be $6.00.

The question asks about the new cost of a ticket if its current price is $4.80 and a 25% (or 1.25 times) increase is applied, so we perform a simple multiplication. To find out the new ticket price, we need to calculate 1.25 times the original price. Therefore, the new ticket price will be 1.25 times $4.80, which can be calculated as follows:

1.25 * $4.80 = $6.00

Hence, the new ticket price after the 25% increase will be $6.00.

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Answer:

A

Step-by-step explanation:

The equations are ...

... s + p = 15

... 3s + 10p = 94

Matrix equation A is equivalent.

Answer: (b) x = -7, x = 2, x = 4

Step-by-step explanation:

Remainder Theorem is used to determine if a given value is a root.

It is stated that (x + 7) is a root ⇒ x + 7 = 0  ⇒ x = -7

We can confirm this by plugging in x = -7 and getting a value of 0.

f(x) = 5x³ + 5x² - 170x + 280

f(-7) = 5(-7)³ + 5(-7)² - 170(-7) + 280

      = -1715 + 245 + 1190 + 280

     = 0

CONFIRMED that x = -7 is a zero!

Next, let's try x = 2

f(2) = 5(2)³ + 5(2)² - 170(2) + 280

      = 40 + 20 - 340 + 280

     = 0

CONFIRMED that x = 2 is a zero!

Lastly, let's try x = 4

f(4) = 5(4)³ + 5(4)² - 170(4) + 280

      = 320 + 80 - 680 + 280

     = 0

CONFIRMED that x = 4 is a zero!

Answer:

C. [tex]x\geq 55000[/tex]

Step-by-step explanation:  

Let x be the total monthly sales.

We have been given that a salesperson earns a salary of $700 per month plus 2% of the sales. The salesperson want to have a monthly income of at least $1800.  

This means that 700 plus 2% of total monthly sales should be greater than or equal to 1800. We can represent this information in an equation as:

[tex]700+(\frac{2}{100})x\geq 1800[/tex]

[tex]700+0.02x\geq 1800[/tex]

Let us solve our inequality to find the monthly sales (x).

Subtract 700 from both sides of our inequality.

[tex]700-700+0.02x\geq 1800-700[/tex]

[tex]0.02x\geq 1100[/tex]

Divide both sides of inequality by 0.02.

[tex]\frac{0.02x}{0.02}\geq \frac{1100}{0.02}[/tex]

[tex]x\geq \frac{1100}{0.02}[/tex]

[tex]x\geq 55000[/tex]

Therefore, the total monthly sales must be greater than or equal to 55,000 and option C is the correct choice.

To solve a system of equations by elimination, make the coefficients of one variable equal. Subtract one equation from the other to solve for one variable, then substitute this solution into one of the original equations to solve for the other variable. In this case, the solution to the given system of equations is x = 3, y = 6.

In mathematics, specifically in algebra, the method of elimination is used to solve a system of simultaneous equations. Your equations are:

To solve this system by elimination, we need to make the coefficients of y in both equations equal by multiplying if necessary. We can obtain this by multiplying the first equation by 2:

4x - 2y = 0
3x - 2y = -3

Next, we subtract one equation from the other to eliminate y:

4x - 3x = 0 - (-3) => x = 3

To find y, substitute x = 3 into the first equation:

2*3 - y = 0 => y = 2*3 = 6

So, the solution to the system of equations is x = 3, y = 6.

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Answer:

-11 is real and 3i is

Step-by-step explanation:

i is a imaginary number is equals to rad(-1) which doesn't exist

The real part of the complex expression is - 11 and the imaginary part of the complex number will be 3i.

The complex number is the combination of the real part and the imaginary part. Then the complex number is given as a+bi where the value of i is √(-1) and the value of i² is -1.

The complex number is given below.

⇒ - 11 + 3i

The term that has iota is known as imaginary part and the term that does not have iota is known as real part.

The real part of the complex expression is - 11 and the imaginary part of the complex number will be 3i.

More about the complex number link is given below.

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Answer:

-1%

Step-by-step explanation:

The population will not be the same unless the starting value is the same. Percent is a portion of the total 100%. If the total in 2011 and 2012 was different, then the change in population will be different.

To find the percent change,

To calculate the percent increase or decrease, we:

The population originally in 2011 was 1500. In 12013, the population is 1485.

1485-1500=-15

-15/1500=-0.01

100(-0.01)=-1%

0.75(100)=75%

The towns population increase by 75%

Andy's reasoning is flawed because the percentage increase and percentage decrease do not result in the same net change in population. The percent change in the number of students from 2011 to 2013 is a 1% decrease.

Andy's reasoning is flawed because the percentage increase and percentage decrease do not result in the same net change in population. Let's calculate the population in 2012 after a 10% increase. 10% of 1500 students is 150 students. So the population in 2012 would be 1500 + 150 = 1650 students.

Now, let's calculate the population in 2013 after a 10% decrease from 1650 students. 10% of 1650 students is 165 students. So the population in 2013 would be 1650 - 165 = 1485 students.

To determine the percent change in the number of students from 2011 to 2013, we calculate the difference between the initial population (1500 students) and the final population (1485 students) and divide it by the initial population. (1500 - 1485) / 1500 = 15 / 1500 = 0.01 or 1%. Therefore, there was a 1% decrease in the number of students from 2011 to 2013.

The inverse function of f(x) = (x - 5)² for x greater or equal to 5 is g(x) = sqrt(x) + 5.

The function f(x) = (x - 5)² for x greater or equal to 5 has a specific inverse function denoted as g(x). To find the inverse of a function, one typical solution is to replace f(x) with y, swap x and y, and solve for y. Here, it means writing y = (x - 5)², changing it to x = (y - 5)², and solving for y.

The solved y function is g(x) = √(x) + 5 (where sqrt indicates a square root), ensuring the range for x is greater than or equal to 5 to adhere to the original function constraints.

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Answer:

97.8%

Step-by-step explanation:

110 is 2 standard deviations above the mean (6+6 = 12)

12+98 = 110

Looking at the standard deviation curve

P(x< or = to 110)  = 1 - P(x>110)

We can find the probability that x>100 by adding  anything above 2 standard deviations above the curve.

P(x>110) = 2.1+.1 = 2.2%

P(x< or = to 110)  = 1 - P(x>110)

                                = 1- 2.2%

                                = 1- .022

                                  = .978

                               = 97.8 %

Answer:

0.975

Step-by-step explanation:

A P E X

Answer:

Each individual investment changed by $2250 due to the loss.

Step-by-step explanation:

It is given that Brian Steve and Rita invested a total of $24,000 in a business.

Each person invested the same amount. So amount invested by each person is

[tex]\frac{24000}{2}=12000[/tex]

Therefore invested by each person is $12000.

They suffered a loss of $4500, which they shared equally. Each individual  suffered a loss of

[tex]\frac{4500}{2}=2250[/tex]

Therefore Brian Steve and Rita suffered a loss of $2250 each. So, each individual investment changed by $2250 due to the loss.

Answer:

1500

Step-by-step explanation:

Answer:$80.00

Step-by-step explanation:

APEX

Answer:   [tex]| x - \frac{15}{3} | = 120[/tex]  or [tex]\frac{1}{3}| 3 x - 15|= 120[/tex] or  [tex]| 3x - 15| = 360[/tex] or  [tex]| x - 5 | = 120[/tex]

Step-by-step explanation:

Since, According to the question,

For each pound the operator’s guess differs from the contestant’s weight, the contestant will receive $3.

And, If a contestant weighing x pounds received $15

Then the guessed weight of contestant = [tex]| x - \frac{15}{3} |[/tex]

But,  Again according to the question,

The guessed weight is 120 pounds,

Thus, [tex]| x - \frac{15}{3}|= 120[/tex]

⇒ [tex]\frac{1}{3}| 3 x - 15|= 120[/tex]

⇒  [tex]| 3x - 15|= 3\times 120[/tex] (by multiplying 3 on both sides)

⇒  [tex]| 3x - 15|= 360[/tex]

⇒  [tex]3| x - 5|= 360[/tex]

⇒  [tex]| x - 5|= 120[/tex]  ( On dividing both sides by 3 )

Answer:

3|x-120|=15

Step-by-step explanation:

what's that?

your welcome ;)

Answer: (A) 1.18 North, 0.92 East

Step-by-step explanation:

The vertical component is sin 52° times the Force of 1.5 newtons

⇒ 1.5 sin 52° = 1.18

The horizontal component is cos 52° times the Force of 1.5 newtons

⇒ 1.5 cos 52° = 0.92

Answer:

a. ≈ 1.18N; ≈ 0.92 E

Answer:

D

Step-by-step explanation:

Answer:

I and II

Step-by-step explanation:

Statement I: The perpendicular bisectors of ABC intersect at the same point as those of ABE.

Statement 1 is true because the perpendicular bisectors intersect at the center of the circumcircle.

Since the two triangles have the same circumcircle, therefore, their perpendicular bisectors intersect at the same point. So statement I is true.

Statement II: The distance from C to D is the same as the distance from D to E.

Since they both, that is distance from C to D and the distance from D to E represent the radius of the circle therefore, they both are equal in length.

Therefore, only I and II are correct.

pErIoD

Answer:

1/16 x^4 - 1/2x^3y +3/2 x^2y ^ - 2 xy^3 + y^4

The relationship between the year and the number of cinema sites can be expressed with the linear equation y = -300x + 608300, where y is the number of cinema sites and x is the year. This equation was derived by calculating the slope and y-intercept using the points provided.

The subject of the question falls into the domain of mathematics, specifically algebra. We are given two points on a line where the x-axis is the year and the y-axis represents the number of cinema sites. The two points are (2000, 8300) and (2004, 7100).

First, we need to calculate the slope, m: m = (y2 - y1) / (x2 - x1) = (7100 - 8300) / (2004 - 2000) = -1200 / 4 = -300.

The slope, -300, is the rate of change suggesting the number of cinemas decreases by 300 each year.

The equation of the line, or the linear equation, will be in the form y = mx + b. We now need to find the y-intercept (b) by substituting one of our points into the equation and solving for b.

If we use the point (2000, 8300): 8300 = -300*2000 + b. Solving for b gives b = 8300 + 600000 = 608300.

Therefore, the equation describing the relationship between the year and the number of cinema sites is y = -300x + 608300.

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Answer:

option B

Step-by-step explanation:

the correct answer is option B

A Line, segment, or ray that bisects a segment at a right angle is Perpendicular bisector.

The slope of the is the rate of change of y-axis w r t to x-axis.

Midpoint is the center of any line segment.                    

An angle bisector is a line which bisects angle in equal proportion