Lisa solved 40 math fact problems in 2 1/2 minutes.
And then she solved 80 math fact problems in 5
minutes. Which best represents her unit rate?

Answer:

D. The possible degrees are 0, 1, and 2 because it cannot be higher than the degree of either P or Q but it can be less depending on which terms cancel.

Step-by-step explanation:

The possible degrees are 0, 1, and 2. Let's explain why by assuming the following is given:

P = 6x² - 3x - 2

Q = 3x² + 2x - 6

Let R = P - Q

Thus:

(6x² - 3x - 2) - (3x² + 2x - 6)

Open parentheses by distributing the factor of -1

6x² - 3x - 2 - 3x² - 2x + 6

Add like terms together

6x² - 3x² - 3x - 2x - 2 + 6

R = 3x² - 5x + 4

The leading term of R has a degree of 2. Therefore, the difference of two degree-2 polynomial functions P and Q can give us a a polynomial function of R with a degree of 2.

Also, let us assume the following:

P = 4x² + 4x - 3

Q = 4x² + x - 8

Let R = P - Q

R = (4x² + 4x - 3) - (4x² + x - 8)

R = 4x² + 4x - 3 - 4x² - x + 8

Collect like terms

R = 4x² - 4x² + 4x - x - 3 + 8

R = 4x + 5 (4x² cancels 4x²)

The leading term of R has a degree of 1. Therefore, the difference of two degree-2 polynomial functions P and Q can give us a a polynomial function of R with a degree of 1.

Also, let us assume the following:

P = x² + 2x - 3

Q = x² + 2x - 8

Let R = P - Q

R = (x² + 2x - 3) - (x² + 2x - 8)

R = x² + 2x - 3 - x² - 2x + 8

Collect like terms

R = x² - x² + 2x - 2x - 3 + 8

R = 5 (x² cancels x², and 2x cancels 2x)

The polynomial R has a degree of 0. Therefore, the difference of two degree-2 polynomial functions P and Q can give us a a polynomial function of R with a degree of 0.

Therefore we can conclude that:

D. The possible degrees are 0, 1, and 2 because it cannot be higher than the degree of either P or Q but it can be less depending on which terms cancel.

Answer:

x[tex]\leq[/tex]30

Step-by-step explanation:

X can be many possiblities

So we can write it out with a smaller than sign and an equal sign

So now it means that x has to be smaller than 30 or equal to 30

Answer:

D

Step-by-step explanation:

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Answer:

-8 degrees

Step-by-step explanation

Half of negative 16 would be negative 8.

Answer:

-8

Step-by-step explanation:

-16 ÷ 2 = -8

You could also do:

16 ÷ 2 = 8

and then put a negative in front of 8

And to prove it's true,

8 x 2 = 16

-8 x 2 = -16

Answer: A) 52 ft  B) $134.68

Step-by-step explanation:

First find the surface area by multiplying the dimensions together.

2 x 4 = 8

2 x 3 = 6

4 x 3 = 12

Then add them up and multiply by two because there are two of each side.

26 x 2 = 52

To find the cost, multiply 52 by $2.59 to get the price.

52 x $2.59 = $34.68

Part A:

The y-intercept is $1,500

The x-intercept is 20 days

Part B:

Equation of the line in point-slope form is  y - 1350 = -75×(x - 2)

Equation of the line in slope-intercept form is y = -75·x + 1500

Equation of the line in standard form  is y + 75·x = 1500

Part C:

f(x) = -75·x + 1500

Part D:

$1,125

Step-by-step explanation:

The information given are;

x,                 g(x)

0,                 $1,500

2,                 $1,350

4,                 $1,200

The equation of a straight line relation between the x, and y, coordinates in slope and intercept form is  y = m·x + c

Where;

m = The slope

c = The y-intercept

From the data, we have two points, (x₁, y₁), (x₂, y₂) given as (0, 1,500), (2, 1350);

The y-intercept = y at x = 0 = 1,500

y = -75·x + 1500

x = 1500/75 = 20

Part B:

The equation in point-slope form is y - y₁ = m×(x - x₁)

Which gives;

Equation of the line in point-slope form is  y - 1350 = -75×(x - 2)

Equation of the line in slope-intercept form is y = -75·x + 1500

Equation of the line in standard form  is y + 75·x = 1500

Part C:

The equation of the line using function notation is f(x) = -75·x + 1500

Part D:

The balance in the bank after 5 days is f(5) = -75 × 5  + 1500 = $1,125

Answer:

y = -1/4x - 1

Step-by-step explanation:

First, put the equation in slope intercept form:

4x - y = 2

4x - 2 - y = 0

4x - 2 = y

y = 4x - 2

Perpendicular lines have opposite reciprocal slopes. Since the original slope is 4, the other line's slope will be -1/4

Plug in the given point and the slope into y = mx + b, then solve for b:

y = mx + b

-2 = -1/4(4) + b

-2 = -1 + b

-1 = b

Plug in the slope and b into the equation:

y = -1/4x - 1 is the equation

Answer:

252

Step-by-step explanation:

252-

Who ever is reading this:

I love u.

U matter.

The world needs u

hang in there ik it may be bad but u deserve the world <3

ur beautiful for who u r, not wht u look like. no matter ur shape, size, color, gender.. anything

don't give up bby i need u to live.

i wish i could take everyones problems so yall wouldn't have to have em but i cant so just know ily and if anyone needs to talk u can talk to me

Pls pass this on. Everyone deserves to know this. ♥️♥️

just copy and paste its not hard pls this could save someones life

Answer:

2/21

Step-by-step explanation:

10 1/2=21/2 and then flip it

Answer:

20 cookies and 15 cupcakes (20:15)

Explanation:

First you need to multiply 4 by 5 which equals 20. Then 3 by 5 which equals 15. Then you need to add them together to get 35!

Ratio Table!

   4    |    3   x4

  16    |   12  + 4:3

 20   |   15   = 35!

I Hope This Helps!

Answer:

The lab technician must screen 5 slides per hour

Step-by-step explanation:

If the lab technician works 5 days a week, and 7 hours per day, then she works 5*7 = 35 hours a week.

Given she must screen 175 slides each week, we can calculate on average, the number of slides per hour needed to complete the work.

The average is calculated as:

[tex]\displaystyle average=\frac{\text{total slides}}{\text{total hours}}[/tex]

[tex]\displaystyle average=\frac{175}{35}=5\ slides/hour[/tex]

The lab technician must screen 5 slides per hour

Answer:

28 inches

Step-by-step explanation:

Answer:

512 ounces

Step-by-step explanation:

Answer:

512

Step-by-step explanation:

multiply the volume value by 128

Answer:

382

Step-by-step explanation:

540 - 158

Given:

4 groups of ___ tenths is 1.6.

To find:

The value for the blank.

Solution:

Let the unknown value be x.

4 groups of x tenths is 1.6.

[tex]4x=1.6[/tex]

Divide both sides by 4.

[tex]\dfrac{4x}{4}=\dfrac{1.6}{4}[/tex]

[tex]x=0.4[/tex]

So, 4 groups of 0.4 tenths is 1.6.

Therefore, the required answer for the blank is 0.4.

Answer:

I counted 32 squares in and out

Answer:

A=a^2, so A=4^2=16 , or 4*4=16

Step-by-step explanation:

All sides of a square are equal, so the length of the sides are all 4. Put 4 in for a in the formula A=a^2 or Area = side length squared.

A = 4^2

A = 4 * 4

A = 16

Answer:

the square root of -1 is i

Step-by-step explanation:

Well, actually, the square root of -1 (or any negative number at that) is not a real number. What I mean by that is that there is no way to square a real number to get a negative number (ie [tex]2^{2} = 4, -2^{2} =4[/tex], there is no way to square a real number to get -4).

To solve this, mathematicians came up with the "imaginary number" i which, when squared, equals to -1. This allows us to get the square root of negative numbers ([tex]\sqrt{-4} = 2i[/tex]) or get negative numbers through squaring ([tex]2i^{2} = -4[/tex]).

The required value of the square root of -1 is i. The correct answer is option B.

As we know that complex number is made up of real and imaginary values. It is represented by the equation z = a + ib, where a, b, and i are real values and i is an imaginary number.

The square root of -1 is denoted as "i" in mathematics, where "i" represents the imaginary unit.

The imaginary unit is defined as the square root of -1. It is important to note that the square root of a negative number is not a real number, but an imaginary number.

⇒ √(-1)

⇒ √(i²)

⇒ i

So, the correct answer is "i."

Learn more about complex numbers here:

brainly.com/question/19007885

#SPJ6

Answer:

d) 3

Step-by-step explanation:

4t^2 +5t -1

in this equation there are 3 terms:

4t^2,      5t,        and  -1

Answer:

1 2. 3

Answer:

Week 1 = 80

Week 2 =88

Week 3 = 96.8

Week 4 = 106.48

Week 5 = 117.128

Step-by-step explanation:

Given

Week 1 = 80

Growth = 10%

Required

Fill week 1 to 5

We have week 1 already.

Week 2 is calculated as thus:

Week 2 = Week 1 + 10% * Week 1

Week 2 = 80 + 10% * 80

Week 2 = 80 + 8

Week 2 = 88

Week 3 is calculated as thus:

Week 3 = Week 2 + 10% *Week 2

Week 3 = 88 + 10% * 88

Week 3 = 88 + 8.8

Week 3 = 96.8

Week 4 is calculated as thus:

Week 4 = Week 3 + 10% * Week 3

Week 4 = 96.8 * 10% *96.8

Week 4 = 96.8 + 9.68

Week 4 = 106.48

Lastly, week 5 is calculated as thus:

Week 5 = Week 4 + 10% * Week 4

Week 5 = 106.48 + 10% * 106.48

Week 5 = 106.48 + 10.648

Week 5 = 117.128

Answer:2182

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

Answer:

Below are the steps to take

Answer:

a

Step-by-step explanation:

Answer:

the answer is 5

Step-by-step explanation:

f(4) = 3(4) -2

7 - 2 = 5