For f(x) = 2x + 1 and g(x) = x2 – 7, find (f + g)(x).

x^2 + 2x + 8
2x ^2– 15
2x^3 – 6
x^2 + 2x – 6

Karl must cycle for seven hours and stroll for three hours each week in order to burn precisely 3000 calories.

Given:

No. of calories to burn by Karl = 3000

No. of calories burnt per hour by walking = 200

No. of calories burnt per hour by cycling = 350

No. of hours per week for Karl = 10

To find: No. of hours required to exercise through walking and cycling for burning 3000 calories.

Let W be the no. of hours required to burn calories in one hour by walking.

Let C be the no. of hours required to burn calories in one hour by cycling.

Formulating the given information

W+C = 10    ⇒ (1)

200W + 350C = 3000

Multiplying equation (1) by 200

200W + 200C = 2000

Subtracting equation (3) from equation (2)

150C = 1000

C ≈ 7

Substituting in equation (1)

W + C = 10

W + 7 = 10

W = 3

Therefore W = 3 and C = 7

Karl must cycle for seven hours and stroll for three hours each week in order to burn precisely three thousand calories.

To learn more about combination , refer

https://brainly.com/question/11732255

#SPJ13

Answer:

y = -6x + 2

Step-by-step explanation:

(1, -4)     m = -6

(x₁, y₁)

y - y₁ = m (x - x₁)

y - (-4)= -6 (x - 1)

y + 4 = -6x + 6

  -4             -4

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

y = -6x + 2

I hope this helps!

Answer:

I do not think that you can write √2 as a fraction. (4/3)² is  16/9.

Step-by-step explanation:

For √2 it cannot be written as a fraction because it has an infinite amount of decimals. For (4/3)² that equals 16/9 so you would place it on the second number line two ninths before 2.

Hope this helps!

As given by the question

There are given that a expression

Now,

Simplify the above expression

Hence, the value of the given expression is shown below:

If the scale used is 3cm to 100mi, the distances will be larger, because 100 miles is a lot more than 3 centimeters.

A change of scale is what we use to represent large objects (or smaller objects) in diagrams.

They allow us for example to have a big drawing of a cell, or put an area of the size of a country in a A4 piece of paper.

In this case, the change of scale is:

3cm to 100mi

This means that each 3 centimeters in the real object will measure 100 miles in the scale diagram, so the distances in the diagram will be larger, as 100 miles is a lot more than 3 centimeters.

Learn more about changes of scale.

https://brainly.com/question/15891755

#SPJ1

( 5x + 3 )( 4x - 5 ) is the factorized form of the polynomial 20x² - 13x - 15 using the AC method.

AC Method is simply a method of factoring trinomials in the form ax² + bx + c.

Given the polynomial in the question;

20x² - 13x - 15

Compare to the form ax² + bx + c

To factor, compare to the form ax² + bx + c and rewrite the middle term as a sum of two terms whose product is;

a × c = 20 × -15 = -300

and whose sum is;

b = -13

Now, factor -13 and of -13x

20x² - 13(x) - 15

We know that -13 is the same as 12 - 25

20x² + (12 - 25)(x) - 15

20x² + (12 - 25)x - 15

Apply distributive property

20x² + 12x - 25x - 15

Group the terms

(20x² + 12x) - 25x - 15

Now, factor out the greatest common factor from each group

4x( 5x + 3 ) - 5( 5x + 3 )

( 5x + 3 )( 4x - 5 )

Therefore, the factorized form of the polynomial is ( 5x + 3 )( 4x - 5 ).

Learn more about the AC method of factorizing here: https://brainly.com/question/15386738

#SPJ1

x  = { 0, 3, 2}

The input of relation ((3,5), (3,2), (0, 6), (2, 7)} is x=  { 0, 3, 2}.

Here given a relation ,

((3,5), (3,2), (0, 6), (2, 7)}

We know that input x and output y together form a relation ,

Here x is the input.

so in this relation , Input = x  = { 0, 3, 2}

                             Output  y = { 2, 5,6,7}

∴ Input of the given relation ((3,5), (3,2), (0, 6), (2, 7)} is x =  {0, 3, 2}.

To learn more about relations refer to :

https://brainly.com/question/26098895

#SPJ13

For the given equation 2(x-0.1x-2.70)=56.70, the value of x is 7.76

The equals sign is used in mathematical formulas to show that two expressions are equal. The first stage in resolving a variable equation is determining the values of the variables that lead to equality. The variables for which the equation must be solved are known as the unknown variables, while the values of the unknown variables that satisfy the equality are referred to as the equation's solutions. Identity equations and conditional equations are the two types of equations.

Given equation, 2(x-0.1x-2.70) = 56.70

or, 2(0.9x-2.70) = 56.70

or, 1.8x - 5.40 = 56.70

or, 1.8x = 56.70+5.40

or, x = 62.10/1.8 = 7.76

To know more about an equation, click on the link

https://brainly.com/question/27893282

#SPJ13

The value of t is $12.

Solution:

3 x 50 = 150

18 x 20 = 360

The sum is 360 + 150 = 510. Then subtract the value 510 from 630.

$630 - 510

$120

120 / 10 = 12

Subtract the null hypothesis mean from the sample mean. Divide the difference by the sample standard deviation. Multiply the result by the square root of the sample size. The t value measures the magnitude of the difference relative to the variability of the sample data. In other words, T is simply the calculated difference expressed in units of standard error.

The larger the size of T the more evidence against the null hypothesis. The important t-value is the limit of the t-distribution. The t distribution is a probability distribution used to compute population parameters when the sample size is small and the population variance is unknown. The T-score is used to analyze whether to support or reject the null hypothesis.

Learn more about The value of t here:-https://brainly.com/question/25071687

#SPJ1

It is discovered that:

a) 45 percent using the exponential function.

b) 950.

c)9013 bacterium

n(t)= n(0) e square( kt )

n(5) = 950 e square 0.45(5)

9013 microbes then.

The number of bacteria in a culture is increasing according to the law of exponential growth. There are 125 bacteria in the culture after 2 hours and 350 bacteria in the culture after 4 hours

A model for an exponential function is?

n(t)= n(0) e square( kt )

In which

The model in this quandary is:

So,

n(t)=950 e square( 0.45t)

also

k=0.45 n(0) = 950 ,and:

(A) 45 percent.

b) 950.

Item c:

We have that at t = 5:

n(5) = 950 e square 0.45(5)

9013 microbes then.

to learn more about the problem refer to:

https://brainly.com/question/15398250

#SPJ13

Answer:

[tex]image = (0 \: \: 2)[/tex]

Answer: v = 92

Step-by-step explanation:

8.81. (v – 89) – 10 = 16.43

8.810 +8.81. -89 – 10 = 16.43

8.81v – 784.09 – 10 = 16.43

8.81v – 794.09 = 16.43

8.81v – 794.09 = 16.43

(8.810 – 794.09) + 794.09 = 16.43 + 794.09

8.81v = 16.43 + 794.09

8.81v = 810.52

8.81v = 810.52

810.52

(8.81) 8.81

8.81

810.52 / 8.81

v = 92

Answer:

72 jars per minute

Hope this helps!

Step-by-step explanation:

432/6 is 72.

Answer:

15kg of oranges.

Step-by-step explanation:

cost of 3kg of apples = cost of 5kg of oranges

cost of 9kg of apples which is (3 x 3) = cost of (5 x 3) kg of oranges

= cost of 15kg of oranges.

Answer:

y = 4x - 14

Step-by-step explanation:

The equation of a straight line is y=mx+b, where m is the slope and b is the y-intercept (the value of y when x=0).

We can calculate the slope with the two given points.  Slope is the Rise/Run between these 2 points:

(4,2) and (6,10)

Rise:  10 - 2 = 8

Run:    6 - 4 = 2

Slope = Rise/Run = 8/2 = 4

m is 4, so we can write:  y = 4x + b

We can find b by entering either of the given points and solving for b.  I'll use (4,2):

y = 4x + b

2 = 4*(4) + b

2 = 16 + b

b = -14

The equation becomes y = 4x - 14

See the attached graph.

Answer:

Equation of line is given as y = mx + c, where m is the gradient and c is the y-intercept.

Parallel lines have the same gradient so gradient of line is -3.

Equation of line is y = -3x + c.

Substitute C(2,7) into the equation to find c.

7 = -3(2) + c

c = 13

Hence, equation of line is y = -3x + 13.

Answer:

f(x) = a·(x + 1)·(x - 3)

f(2) = a·(2 + 1)·(2 - 3) = a·3·(-1) = -3·a = -6 --> a = 2

f(x) = 2·(x + 1)·(x - 3)

f(x) = 2·(x^2 - 3·x + x - 3)

f(x) = 2·(x^2 - 2·x - 3)

f(x) = 2·x^2 - 4·x - 6

Answer: 0 & -7

Step-by-step explanation:

Answer:

12. 0

13. -7

Hope this helps :)

If you need an explanation just comment!

We will have the following:

Firs, we can see that once we find one side we will have both, since they are equal.

Now, using the law of sines:

So, the length of side Z is 2sqrt(2).

The position of the trout now relative to the surface is -17 feet. Therefore, Denis is wrong.

It should be noted that a expression shows the relationship between the variables.

From the information, a trout was swimming 9 feet below the surface of a lake and it drove down 8 more feet to search for food.

The position will be the addition of the feets. This will be:

= -9 + (-8)

= -9 - 8

= -17 feet

The position is -17 feet.

Learn more about expressions on:

brainly.com/question/723406

#SPJ1

we can write x = 10/p to represent the number of toy cars x, in each package.

Expression: An expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.) Expressions can be thought of as similar to phrases. In language, a phrase on its own may include an action, but it doesn't make a complete sentence

The management purchased n cars, which equals 10.

There were p packages altogether, and each box contained one car. Per bundle, there should be x cars

Since there are x cars in each box, p packages would contain x*p cars

The equation can be written as 10 = x*p because we know there were p packages with 10 cars in them.

The multiplication of x and p is indicated by an asterisk (*).

You can write x = 10/p to represent the number of cars x, in each package.

The division symbol is denoted by a slash (/).

Because the number of cars and parcels can only be whole numbers, the values of x and p must also be whole numbers. Since the result of x and p is 10, both x and p must be factors of 10.

The factors of 10 are: 1,2,5 and 10

So, we get the following scenarios:

1 package with 10 cars inside it

2 packages each with 5 cars

5 packages each with 2 cars

10 packages each with 1 car

If the number of cars/packages must be greater than 1, then we have the following two cases:

2 packages each with 5 cars

5 packages each with 2 cars

we can write x = 10/p to represent the number of toy cars x, in each package.

To learn more about Expressions visit:

brainly.com/question/14083225

#SPJ1

Answer: If two students solved the problems below one of the students made an error.  Mary is wrong while Nico is correct.

Error in calculation

Mary =66÷3 = 6. 33 (Wrong)

Nico= 62.4÷13=4.8 (Correct)

Hence.

Mary:

Using calculator 66/3 will gives us 22 and not 6.33.

66÷3=22

Nico

Using calculator 62.4/12 will give us 4.8 which means that Nico was correct.

Therefore If two students solved the problems below one of the students made an error.  Mary is wrong while Nico is correct.

Answer:

Part A-Well, Miranda is going 4mph, so the answer would be t=m/4, because it's how many miles she's traveled divided by 4 to get how long she's been skiing. With the info we have, we could also write 0.5=2/4

Part B-So, we have that m=5.2, so we do t=5.2/4 5.2/4=1.3, so we have 1.3=5.3/4. So, she's been skiing for 1.3 hours.

Answer:

33

Step-by-step explanation:

because 18 divided by 6 is 3

and 11 times 3 is 33

Answer: 1. 33

Step-by-step explanation:

I say 33 because the short side on the one is 6 and is 18 on the other so they multiply by 3. That being said 11 times 3 is 33. I hope this helps! :)

The ratio of coins to notes in a bag is 3 to 8.

The total number of coins is 24.

Let there be y number of notes in the bag. Then we can write,

On solving we get,

Thus there are 64 notes in the bag.

Answer:

x^{2} +8x+15

Step-by-step explanation:

Use Distributive Property:

(x+3)(x+5)

[tex]x^{2}+5x+3x+15[/tex]

[tex]x^{2} +8x+15[/tex]  Answer

Answer: x ^ 2 + 8x + 15

Step-by-step explanation: You can use the FOIL method to multiply. F - first two variables, so the two x.

x • x = x^2

O - outside, the outermost variables in the parenthesis, which would be x and 5.
x • 5 = 5x

I - inside, the innermost variables in the parenthesis, which would be x and 3.

x • 3 = 3x

L - last two variables, so 3 and 5.

3 • 5 = 15

Altogether:
x^2 + 5x + 3x + 15, which simplifies to x^2 + 8x + 15.

Image & example for clarity! Hope this helped!

To convert miles per hour to feet per second the conversion factor that wouldn't be used is option d: 1 mi/5280 ft  and 5 miles per hour will be equal to 7.34 feet per seconds.

As per the question statement, we are asked that which of the given conversion factors, will not be used for converting miles per hour to feet per second.

We should be knowing the following values for conversion:

we know, 1 mile = 1.6 km = 5280 feet

and 1 hour = 60 minutes = 3600 seconds.

Now, mi/hr * 1hr/60min * 1min/60sec * 5280ft/mi

Note that units all cancel out leaving only ft/sec

Hence option d : 1 mi/5280 ft is not appropriate for converting mi/hr to ft/sec.

For e.g., 5 miles per hour = 5*5280/3600

5 mil/hr = 7.34 ft/sec

Hence, to convert miles per hour to feet per second the conversion factor that wouldn't be used is option d: 1 mi/5280 ft  and 5 miles per hour will be equal to 7.34 feet per seconds.

To learn more about conversion factor, click on the link given below:

https://brainly.com/question/16964835

#SPJ1

The answer to the given statement is FALSE. This is the commutative property of multiplication and not of addition.

To "commute" is to move about or travel. According to the commutative property of addition, the sum is unaffected by changes in the order of the numbers being added.

The formula for the commutative property of numbers is A + B = B + A if two numbers A and B are supplied.

A + B = B + A

A × B = B × A

A - B ≠ B - A

A ÷ B ≠ B ÷ A

According to the commutative property formula, the result is unaffected by the sequence in which two numbers are added or multiplied. However, the order of the integers matters for subtracting and dividing any two real numbers, so it cannot be changed.

To know more about commutative property visit:

https://brainly.com/question/778086

#SPJ13

Answer:

There are 15 boys.

Step-by-step explanation:

Let x represent the answer!

it would be 4x+3x=35

add 4x+3x

7x=35

divide 35 by 7

x=5

multiply 5 x 4 then you get 20 girls

then multiply 5 x 3 to get 15 boys.

your welcome <3