If f(x)=x-5, then match each of the following.

1.-5
2.0
3.-6
4.-3
5.3
6.-4
f(1)
f(-1)
f(2)
f(0)
f(5)
f(8)

15 is the number of possible outcomes.

To find the possible outcomes:

Given: 5 flavors and ice cream of 3 different toppings.

Therefore, the number of possible outcomes is 15.

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Answer:

x=-15 and x=-15

Step-by-step explanation:

We try to move everything from the left to the right starting with the number that is further away from x, so 4. We subtract it from both sides.

1/3|x-3|+4-4=10-4

1/3|x-3|=6

Next, we have the fraction so basically, 1 is being divided by 3 so we are going to multiply both sides by three.

1/3|x-3|×3=6×3

|x-3|=18

We get rid of the absolute value signs to get

x-3=18

But we are not sure if 18 is negative so we put it like this.

x-3=-18

x-3=18

Then we add 3 from both sides.

x-3+3=-18+3

x-3+3=18+3

Which equals:

x=-15

x=21

Hope this helped! :)

Considering the definition of an equation and the way to solve it, the cost of 2 pounds(lb) of the first type of candy is $4 per pound.

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.

The solution of a equation means determining the value that satisfies it (this is, the equality must be true).To solve an equation, keep in mind:

Knowing that:

the equation in this case is:

2x + 3×1.50 = 2.50×(2 + 3)

Solving:

2x + 4.5= 12.5

2x= 12.5 - 4.5

2x= 8

x= 8÷ 2

x=4

Finally, the cost of 2 pounds(lb) of the first type of candy is $4 per pound.

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The formula to find the sum of an arithmetic sequence: Sn = n/2[2a + (n - 1)d], where a is the first term, n is the number of terms and d is the common difference.

1) Let's substitute the values into the formula.

S17 = 17/2[2(11) + (17 - 1)6]

S17 = 17/2[22 + (16)6]

S17 = 17/2[22 + 96]

S17 = 17/2[118]

S17 = 17/2 × 118

S17 = 1003

Therefore, the sum of the first 17 terms of this arithmetic sequence is 1003.

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Answer:

Step-by-step explanation:

In all three pictures, the data are correctly matching except this one..

~~

The given sequence 100,117,134,151,168, ........... is in AP. The next three terms are 185, 202, 219..

The difference between two numerical orders is a constant value in Arithmetic Progression (AP). Another name for it is Arithmetic Sequence.

We'd emerge across a few fundamental words in AP that have been labeled as:

The AP can also be described in terms of common differences, as shown below.

Now, the given sequence is; 100,117,134,151,168, ...........

The series comprises of five given terms.

Let the initial term be 'a₁' = 100.

The second term be 'a₂' = 117.

The third term be 'a₃' = 134.

And, the fourth term is 'a₄' = 151.

The AP must have the equal common difference. So,

d = a₃ - a₂

Substitute the values.

d = 134 - 117

d = 17

Thus, the computed common difference is 17.

or d = a₄ - a₃ (Substitute the values)

d = 151 - 134

d = 17

Since, a₃ - a₂ = a₄ - a₃

Thus, we can get to know that the given sequence is in AP.

Now, the 6th term is estimated as; a₆ = a₅ + d = 168 + 17

a₆ = 185

Similarly, the 7th term will be; a₇ = a₆ + d = 185 + 17

a₇ = 202

And, the 8th term will be calculated as; a₈ = a₈ + d = 202 + 17

a₈ = 219.

Therefore, it can be said that the given sequence is in AP next three terms be 185, 202, 219.

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Answer:

B. 4/5

Glad to help :)

The value of fraction is 6 1/4 inches are equal to 19+6/425mm.

Given that the precipitation in March was 4 3/4 inches below average and the precipitation in April was 1 1/2 inches below average.

We must determine how many inches the precipitation in March and April fell short of typical.

Add 4 3/4 inches and 1 1/2 inches to get the answer. So,

4 3/4 + 1 1/2

19+6 / 4

= + 4 312

6 1/4 inches are equal to 19+6/425mm.

six inches Therefore, the precipitation was 4 less than usual for both March and April.

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The equation that we need to solve and the solution is:

A = 11.7mi/3 = 3.9 mi

We conclude that he needs to ride an average of 3.9 miles per day.

Here we know that Carter wants to ride his bicycle 28.7 miles this week, and he has already ridden 17 miles, so the distance left is:

D = 28.7 mi - 17mi = 11.7mi

Now, if he has 3 days to complete that distance, then the average distance that he needs to travel each day is given by the quotient:

A = 11.7mi/3 = 3.9 mi

So that is the equation that we need to solve and the solution, we conclude that he needs to ride an average of 3.9 miles per day.

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Answer:

7.2

Step-by-step explanation:

7.4-0.2=7.2

Answer:

6 is the y intercept and 1 is the slope, so it goes up 1 unit right 1 unit

Step-by-step explanation:

Answer: In geometry, when you translate an object, it means that you have turned that object in a different direction. Hence a translated angle is an angle that has been turned in a different direction.

From the first option in part A, it is clear from the image that the angle didn't change. It moves 7 units from the positive to the negative part of the x-axis.

From Part B, the angles also do not change. Note that when an angle is rotated or translated, it does not modify the angles.

From Part C, what we have is the reflection of the angles. This means that both angles are equal because they are a reflection of each other.

From Part D, the two sets of parallel lines will remain parallel to each other also long as they are both translated as the same time.

From part E, although in each set of parallel lines, the two sets of lines remain equidistant to each other, the parallel line that is at an angle to the Y-axis will not intersect that which is at an angle to the x-axis if they are extended infinitely.

Step-by-step explanation: hope this helps alittle

Binary relation  is a function .

Functions are relationships where each input has a single output. There is one output for each input in a relation that passes the vertical line test.

How can I tell if a relationship serves a purpose?

A relation is considered to be a function if each element in the domain is mapped to a distinct element in the codomain.

What are the characteristics of a binary relation?

Binary relationship A subset of P x Q from the set P to Q is defined as R. If (a, b) R and R P x Q, then a and b are connected by R, or aRb. When sets P and Q are equal, we say that R is a relation on P, for example.

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The advanced trail is 4.32 times as long as the beginner's trail.

A decimal is a number that is made up of integers and non-integers. The whole numbers are separated from numbers that are not whole number by a decimal point. An example of a decimal is 1.2.

Let:

The equation that represents the length of the medium trail: 1.2 x b = 1.2b

The equation that represents the length of the advanced trail: 3.6 x 1.2b = 4.32b

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The company profit approximately increased by E) 70%.

An approximation is an equivalent value or number obtained by rounding off to the required significant figure.

The result obtained through approximation is not an exact value but is the nearest rounded value.

For instance, 71.4% can be approximated to 71% or 70%.  58 minutes can be rounded off or approximated to 1 hour.

Profit in 3 months = $3,500

Profit in 6 months = $6,000

Increase in profit = $2,500 ($6,000 - $3,500)

Percentage increase in profit = 71.43% ($2,500/$3,500 x 100)

71.43% ≈ 70%

Thus, the company profit approximately increased by E) 70%.

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In mathematics, the logarithm is the reciprocal of a power. This means that the logarithm of a given number x is the exponent by which another fixed number (the base b) must be increased to get that number x. The simplest logarithm counts the number of times the same element occurs when multiplying repeatedly. The logarithm of x to base b is denoted by log b (x), or log b x without parentheses. Also, if confusion is impossible or the base doesn't matter, log x shows that even without an explicit base: B. In big O notation.

Logarithm base 100 of 100 is 1.

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Answer: rational

Step-by-step explanation:

The ninth and tenth term of the given arithmetic sequence are: -18 and -21.

A series of numbers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.

Now,

Given: 6, 3, 0, -3, ....; it is a decreasing AP.

Here, a = 6 (initial term) and d = -3 (common difference)

Thus, in the formula: [tex]a_n[/tex] = a + (n - 1) d, substituting these values:

=>  [tex]a_n[/tex] = 6 + (n - 1)(-3)

For ninth term, n = 9

Thus,  [tex]a_n[/tex] = [tex]a_9[/tex] = 6 + (9 - 1)(-3)

=> [tex]a_9[/tex] = 6 + (8)(-3)

=> [tex]a_9[/tex] = 6 -24

=> [tex]a_9[/tex] = -18

Similarly, for the tenth term, n = 10

Thus, [tex]a_n=a_{10}[/tex] = 6 + (10 -1) (-3)

=> [tex]a_{10}[/tex] = 6 + (9) (-3)

=> [tex]a_{10}[/tex] = 6 - 27

=> [tex]a_{10}[/tex] = -21

Hence, The ninth and tenth term of the given arithmetic sequence are: -18 and -21.

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Answer: the length of the 1st side is 4 m

Step-by-step explanation:

P=a+b+c

b=a+3

c=4a

Hence,

27=a+(a+3)+4a

27=a+a+3+4a

27=6a+3

27-3=6a+3-3

24=6a

Divide both parts of the equation by 6:

4=a

Thus,

a=4 m

It can be seen that QPN and JKL have: JK = QN; JL = QP; KL = NP

They are congruent triangles.

What do you mean by congruent?

In the triangle JKL, the sides can be calculated as following:

J(2;5); K(1;1)

            => JK = [tex]\sqrt{( ( 1 - 2 )^{2} + ( 1 - 5 )^{2} } = \sqrt{( -1 )^{2} + ( -4)^{2} } \\= \sqrt{ 1 + 16 } = \sqrt{17}[/tex]

J(2;5); L(5;2)

            JL = [tex]\sqrt{( 5 - 2 )^{2} + ( 2 - 5 )^{2} } = \sqrt{3^{2} + ( -3)^{2} } \\[/tex]

                 = [tex]\sqrt{ 9 + 9 } = \sqrt{18} = 3\sqrt{2}[/tex]

K(1;1); L(5;2)

            =>  KL = [tex]\sqrt{ ( 5 - 1 )^{2} + ( 2 - 1 )^{2} } = \sqrt{4^{2} + 1^{2} } = \sqrt{ 1 + 16} = \sqrt{17}[/tex]

In the triangle QNP, the sides can be calculate as following:

Q(-4;4); N(-3;0)

            => QN  = [tex]\sqrt{[ -3 - ( -4)^{2} ] + ( 0-4)^{2} } = \sqrt{1^{2} + 16 } = \sqrt{17}[/tex]

Q (-4;4); P(-7;1)

  => QP =  [tex]\sqrt{ [ -7 - ( -4 )^{2} + ( 1 - 4 )^{2} } = \sqrt{( -3)^{2} + ( -3)^{2} } = \sqrt{9 + 9} = \sqrt{18} = 3\sqrt{2}[/tex]

N(-3;0); P(-7;1)

      =>  NP = [tex]\sqrt{[-7 -( -3)]^{2} + ( 1 - 0 )^{2} } = \sqrt{ - 4^{2} + 1 } = \sqrt{ 16 + 1} = \sqrt{ 17}[/tex]

It can be seen that QPN and JKL have: JK = QN; JL = QP; KL = NP

=> They are congruent triangles

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Answer:

See proof below

Step-by-step explanation:

[tex]4cos^2(x) +4sin(x) = 5\\\\\sf Divide\; both \; sides\; by\; 4\\== > cos^2(x) + sin(x) = \dfrac{5}{4} .................(1)\\\\cos^2(x) + sin^2(x) = 1\\\\cos^2(x) = 1- sin^2(x) \\\\\textsf {Substituting into equation (1) }\\1-sin^2(x) + sin(x) = \dfrac{5}{4}\\\\\\sf Subtract\; 1\; from\; both \; sides\\\mathsf{-\sin^2(x) + \sin(x) = \dfrac{5}{4} - 1}\\\\ \dfrac{5}{4} - 1 = \dfrac{5}{4} - \dfrac{4}{4} = \dfrac{1}{4}\\[/tex]

[tex]\sf {-\sin^2(x) + \sin(x) = \dfrac{1}{4}\\[/tex]

[tex]\sf Subtract\; \dfrac{1}{4}\;from\;both\;sides\\[/tex]
[tex]{-\sin^2(x) + \sin(x) - \dfrac{1}{4} = 0\\\\[/tex]

Multiply throughout by -1
[tex]\sf \sin^2(x) - \sin(x) + \dfrac{1}{4} = 0\\\\[/tex]

Let u = sin(x). Substituting we get
[tex]\sf u^2 - u + \dfrac{1}{4} = 0[/tex]

This is a quadratic equation which can be solved using sum of squars

Note that

[tex]\sf (u - \dfrac{1}{2})^2 = u^2 -2\cdot \dfrac{1}{4}u + (\dfrac{1}{2})^2 \\= \sf u^2 - u + \dfrac{1}{4} = 0[/tex]

So
[tex]\sf (u - \dfrac{1}{2})^2 = 0\\Solution\; is \;u = \dfrac{1}{2}\\\\Substituting\sin(x) \;for\;u \;gives\\sin(x) = \dfrac{1}{2}[/tex]

PROVED

Here are some steps in the photo.

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Source of the photo: Calculator Soup

Answer:

Antibiotic

Step-by-step explanation:

Alexander Fleming discovered penicillin, the most important drug that destroys bacteria within the human body. This discovery has led to the prevention of many diseases and untimely deaths in society. He was a pharmacologist, botanist, and biologist that won a Nobel Prize in Physiology for his major contributions in developing antibiotic substances.

Answer:

The first one would be -11x + 3

The second on would be 29x + 3

Step-by-step explanation:

For the first equation you add -2 to 5 so you have 9x+3-20x. Then you add the 9x to -20x which will leave you with -11x+3.

For the second equation you add the -2 to 5 and have 9x+3+20x. You add 9x to 20x which will leave you with. 29x+3

Answer: Large Box: 18.75 kilograms

Small Box: 15.75 kilograms

Step-by-step explanation:

l=large box. s=small box

5l+3s=141

7l+9s=273

(5l+3s=141)*3

15l+9s=423    ==> subtract this equation

7l+9s=273   ==> subtract this equation

8l=150 ==> subtract the two above equations

l=150/8

l=18.75

5(18.75)+3s=141

93.75+3s=141

93.75+3s=141.00

3s=47.25

s=15.75

Large Box: 18.75 kilograms

Small Box: 15.75 kilograms

1)The neighborhood park is 60m by 50 m. The park is reduced in size by 321m2 as a portion of it is ripped up to create a uniform-width sidewalk around it. What quadratic equation best captures the circumstances?

2)A rectangle's length is 1 m less than twice its width. The rectangle has a 120 m2 area. What quadratic equation best describes the circumstances?

Answer for the first question is the quadratic equation is [tex]4x^{2} -220x+321=0\\[/tex].

Answer for the second question is The quadratic equation is [tex]x^{2} -x-120=0[/tex].

1)Let 'x' stand in for the sidewalk's width.

The area of the park is: [tex]A_{1} =60\times50[/tex]

The reduced area of the park measures

60-2x by 50-2x with area of [tex]A_{2} =(60-2x)(50-2x)[/tex]

[tex]A_{1} -A_{2} =321[/tex]

[tex]60\times50-(60-2x)(50-2x)=321[/tex]

[tex]3000-(60-2x)(50-2x)=321\\3000-(3000-120x-100x+4x^{2} )=321\\220x-4x^{2} =321\\4x^{2} -220x+321=0\\[/tex]

Therefore, the quadratic equation is [tex]4x^{2} -220x+321=0\\[/tex].

2) Given that,

Width=x.

length=2x-1

Area=120[tex]m^{2}[/tex]

We know area=length[tex]\times[/tex]width

120=x(x-1)

[tex]x^{2} -x=120\\x^{2} -x-120=0[/tex]

Therefore, The quadratic equation is [tex]x^{2} -x-120=0[/tex].

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Step-by-step explanation:

let this number is x

Answer:

Step-by-step explanation:

Answer: x=-3/4

Step-by-step explanation:

12-x=15+3x

12-x+x=15+3x+x

12=15+4x

12-15=15-15+4x          ==> isolate the variable x.

-3=4x

4x/4=-3/4

x=-3/4

Number of songs that will be downloaded in 2020 = 2600 million

Given that in 2004, 200 million songs were downloaded and in 2006, 500 million songs were downloaded from the internet.

When we graph this trend, these data corresponds to the points (4,200) and (6, 500).

Also it will be a straight line. So its slope can be found.

Slope = [tex]\frac{y_2-y_1}{x_2-x_1} = \frac{500-200}{6-4}[/tex] = 300/2 = 150

This means that there is an increase of 150 million songs downloads pe year.

Also 2020-2006 = 14 years

So the number of songs downloaded in 2020 = Number of songs downloaded in 2006 + 14 x 150 = 500 + 14 x 150

                                                     = 500 +2100

                                                     = 2600 million

So 2600 million songs will be downloaded legally from the internet by 2020.

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Answer:

Step-by-step explanation:

Answer:

A: D:(-6,6)

B: D:(-7,5]

C: Not a function D: -5

D: Not a function D:(-4,4)

E: Not a function D:(0,∞)

F:  D:[0,∞)

G: D:[-3,5)

H: D:(-4,2)

I: D:[-3,4]

J: Not a function D:(-3.-4)

K: D:(-∞,∞)

L: D:(-∞,∞)