Determine whether the graph represents a function. Explain

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! :)

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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Answer: rational

Step-by-step explanation:

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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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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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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Step-by-step explanation:

let this number is x

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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Answer:

7.2

Step-by-step explanation:

7.4-0.2=7.2

80 thousand and 8 thousand.

Using place value diagrams, we can check that the digits are in the right positions. Writing the digits in the place value chart first, followed by writing the numbers in their customary and standard form, can help you precisely determine the positional values of numbers.

Given that: we have given 88,000.

The number 88000 has two 8s, as can be seen.

One of them is located at 10,000 places, while the other is at 1,000 places.

Value of first 8 from right is

8 thousand

Values of second 8 from right is

80 thousand.

Therefore, 80 thousand and 8 thousand

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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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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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Here are some steps in the photo.

Mark me Brainliest. :)

Source of the photo: Calculator Soup

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

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:

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

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

Answer:

bStep-by-step explanation:

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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By elimination, the solution of the system of equations, x - 2y + 3z = 12, 2x - y - 2z = 5 and 2x + 2y - z = 4, is (4 , -1 , 2).

A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.

There are three methods that can be used to solve system of equations.

1. Elimination

2. Substitution

3. Graphing

Given:

x - 2y + 3z = 12     (equation 1)

2x - y - 2z = 5     (equation 2)

2x + 2y - z = 4     (equation 3)

Using the elimination method, given the equations in x, y, and z, a variable should be eliminated by adding/subtracting the equations.

Adding equations 1 and 3 will eliminate the variable y.

x - 2y + 3z = 12     (equation 1)

2x + 2y - z = 4     (equation 3)

3x       + 2z = 16     (equation 4)

Multiply equation 2 by 2 and add with equation 3.

2x - y - 2z = 5     (equation 2)

⇒ 4x - 2y - 4z = 10

+  2x + 2y -   z = 4     (equation 3)

   6x        - 5z = 14     (equation 5)

Multiply equation 4 by 2 and subtract with equation 5.

3x + 2z = 16     (equation 4)

⇒ 6x + 4z = 32

-   (6x - 5z = 14)    (equation 5)

9z = 18

z = 2

Substitute the value of z to either equation 4 or 5 and solve for x.

3x + 2z = 16     (equation 4)

3x + 2(2) = 16

3x = 16 - 4

3x = 12

x = 4

Finally, substitute the value of x and z to any of the first three equations, and solve for y.

x - 2y + 3z = 12     (equation 1)

4 - 2y + 3(2) = 12

-2y = 12 - 4 - 6

-2y = 2

y = -1

Hence, the solution of the system of equations is (4 , -1 , 2).

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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:(-∞,∞)

Answer:

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

Step-by-step explanation:

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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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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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:

Step-by-step explanation:

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

~~

Answer:

B. 4/5

Glad to help :)

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: 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

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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