What does the fundamental theorem of algebra state about the equation 2x^2-4x+16=0?

Problem 1

Answer: Choice A

Vertically stretching it by a factor of 2 is the same as compressing it horizontally by a factor of 2

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Problem 2

Answer: choice B

Add up the functions to get

M(s) + L(s) = (225+0.65s) + (54 + 1.15s)

M(s) + L(s) = (225+54) + (0.65s+1.15s)

M(s) + L(s) = 279 + 1.80s

Answer:

A

Step-by-step explanation:

The equations are ...

... s + p = 15

... 3s + 10p = 94

Matrix equation A is equivalent.

Answer:

A quadrilateral has 4 right angles

Step-by-step explanation:

In a conditional statement

If hypothesis, then conclusion

OR

Conclusion, if hypothesis.

The hypothesis goes with the if part.

Parallel lines have the same slopes (but different y intercepts). Parallel lines never cross. Parallel lines are the same distance from each other no matter where you are on either line. Think of it like a pair of perfectly straight railroad tracks.

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Perpendicular lines cross at one point. The two lines form a 90 degree angle. The two slopes multiply to -1, which is another way of saying that the slopes are negative reciprocals of one another. For example, a line with a slope of 2/3 and another line with a slope of -3/2 has these two values multiply to -1; therefore showing they are perpendicular lines.

To provide a short definition,

Parallel lines are lines as the word suggests "parallel" which means they will stay side by side and never cross.

Perpendicular lines are lines that cross, usually to determine perpendicular lines you would take a slope and negatively reciprocate it.

Perpendicular:

1/2 -> -2

Parallel:

1x + 3

1x

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:

The answer is D

Step-by-step explanation:

Answer:

d. -5/8

Step-by-step explanation:

To find slope, use the following equation

slope (m) = (y₂ - y₁)/(x₂ - x₁)

First, set each coordinate. Let:

(x₁ , y₁) = (-6 , 8)

(x₂ , y₂) = (2 , 3)

Plug in the corresponding numbers for the corresponding variables.

m = (y₂ - y₁)/(x₂ - x₁)

m = (3 - 8)/(2 - (-6))

Simplify. Note that two negative signs would result in a positive sign.

m = (3 - 8)/(2 + 6)

m = -5/8

d. -5/8 is your answer

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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:

-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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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:

f(t)=35,400(1.02)t

Exponential Growth Function:

y=b(1+r)^t

where:

f(t) = 35,400(1 + 0.02)^t

f(t)=35,400(1.02)^t

Answer:

f(t)=35,400(1.02)t

Step-by-step explanation:

im taking the test i gotchu i just finished it and this was the correct answer

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 ;)

11/12 - 7/9

=>taking L.C.M of the denominator

=>11/36 - 7/36

=>4/36

=>2/18=>1/9

Answer:

it is 5 36

heres why

Step-by-step explanation:

Here's how to subtract 7/9 from 11/12:

11

12

−  

7

9

Step 1

We can't subtract two fractions with different denominators. So you need to get a common denominator. To do this, you'll multiply the denominators times each other... but the numerators have to change, too. They get multiplied by the other term's denominator.

So we multiply 11 by 9, and get 99.

Then we multiply 7 by 12, and get 84.

Next we give both terms new denominators -- 12 × 9 = 108.

So now our fractions look like this:

99

108

−  

84

108

Step 2

Since our denominators match, we can subtract the numerators.

99 − 84 = 15

So the answer is:

15

108

Step 3

Last of all, we need to simplify the fraction, if possible. Can it be reduced to a simpler fraction?

To find out, we try dividing it by 2...

Nope! So now we try the next greatest prime number, 3...

Are both the numerator and the denominator evenly divisible by 3? Yes! So we reduce it:

15

108

÷ 3 =  

5

36

Let's try dividing by 3 again...

Nope! So now we try the next greatest prime number, 5...

Nope! So now we try the next greatest prime number, 7...

No good. 7 is larger than 5. So we're done reducing.

There you have it! The final answer is:

11

12

−  

7

9

=  

5

36

Answer:

We are given the following information:

The number of apples Jim has [tex]=15[/tex]

The number of oranges Susie has [tex]=7[/tex]

The number of strawberries Greg has [tex]=3[/tex]

The number of banana Michelle has [tex]=1[/tex]

The number of limes Carrie has [tex]=5[/tex]

The number of pineapples Tim has [tex]=9[/tex]

Therefore, the total would be the sum of the above numbers. Therefore, we have:

[tex]Total=15+7+3+1+5+9=40[/tex]

Hence, the total would be 40.

Answer:

80

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Option a:

a=79

b=1.002

r=0.2%

Step-by-step explanation:

Q = 79 (1.002)^t

Q = a b^t = a (1+r)^t

Comparing with the formulas:

a=79

b=1.002

1+r=1.002

Solving for r: Subtrating 1 both sides of the equation:

1+r-1 = 1.002 - 1

r = 0.002

Writting r as percent:

r = (0.002) 100%

r = 0.2%

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:

Step-by-step explanation:9÷3=3 +6÷3=2 for a total of 5 baskets

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: p = $100,  R = $25,000

Step-by-step explanation:

The maximum is the y-value of the Vertex.

Step 1: Use the Axis-Of-Symmetry (AOS) formula to find x: [tex]x=\dfrac{-b}{2a}[/tex]

R(p) = -2.5p² + 500p

        a=-2.5  b=500

[tex]p=\dfrac{-(500)}{2(-2.5)}[/tex]

   [tex]=\dfrac{-500}{-5}[/tex]

   [tex]=100[/tex]

Step 2: Find the maximum by plugging the p-value (above) into the given equation.

R(100) = -2.5(100)² + 500(100)

          = -25,000 + 50,000

          = 25,000

The price that maximizes revenue for the software package is $100, and the maximum revenue attainable is $25,000 based on the given revenue function R(p).

To find the price that maximizes revenue and the maximum revenue itself, we can use the given revenue function R(p) = -2.5p² + 500p.

To find the price that maximizes revenue, we need to find the vertex of the quadratic function, as the vertex represents the maximum point. The formula for the x-coordinate (price in this case) of the vertex of a quadratic function in the form of ax² + bx + c is given by:

x_vertex = -b / (2a)

In our case, a = -2.5 and b = 500:

x_vertex = -500 / (2 * (-2.5))

x_vertex = -500 / (-5)

x_vertex = 100

So, the price that maximizes revenue is $100.

To find the maximum revenue, we need to substitute this price back into the revenue function:

R(100) = -2.5(100)² + 500(100)

R(100) = -2.5 * 10000 + 50000

R(100) = -25000 + 50000

R(100) = 25000

Therefore, the maximum revenue is $25,000.

So, the price that maximizes revenue is $100, and the maximum revenue is $25,000.

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Look at the picture.

common part, then "and"

Answer: w = 7cm

Step-by-step explanation:

Perimeter = 2 x length + 2 x width  = 2L  + 2w

 Width is 4 cm less than the length, so w = L-4

  36 = 2L + 2(L-4)

 36 = 2L + 2L - 8

 36 = 4L - 8

44 = 4L

 L = 11

w = 7

2(11) + 2(7) = 22 + 14 = 36

Length is 11, width is 7

Answer:

7cm

Step-by-step explanation:

36x2= 72

86-72= 14

14/2= 7

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:

-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.

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:

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

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: (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:

C. 20 seconds

Step-by-step explanation:

We want to know when y=0.

We are finding the x intercepts.

The first y is when it started and the second y=0 is when it stops.

Looking at the graph y=0 at x=0 and  y=0 at x=20

The fan started at time 0 and stopped at 20 seconds.

The difference is the length of the test.

20-0 = 20

20 seconds

Answer:

20 seconds

Step-by-step explanation:

Given :

[tex]y=-5x^2+100x[/tex]

Where x  represents time in seconds and y represents the speed in rotations per minute.

To Find : Assuming that the test was complete when the fan stopped spinning completely, how long was the test?

Solution:

Since we are supposed to find how long will it take to stop the fan completely

We assumed that  test was complete when the fan stopped spinning completely

i.e. y = Speed = 0

So, Substitute y = 0 in the equation    [tex]y=-5x^2+100x[/tex]

⇒[tex]0=-5x^2+100x[/tex]

⇒[tex]5x^2=100x[/tex]

⇒[tex]5x=100[/tex]

⇒[tex]x=\frac{100}{5}[/tex]

⇒[tex]x=20[/tex]

Thus it took 20 seconds to stop the fan

Hence the test was 20 seconds long.

Answer:

A: x+5

B: 4x-1

Step-by-step explanation:

4x^2+19x-5

(4x     )  ( x     )

We know that 1 will be positive and 1 will be negative.

Our choices for the numbers are 5 and 1

4*5 -1 = 19

(4 x - 1) (x + 5)