The ratio table shows the numbet of miles karen can drive for 1,2,3 and 4 gallons of gasoline.Based on the table, How far would she be able to drive on 8 gallons of gasoline

Answer:

g(x) = x^2+4

Step-by-step explanation:

The graph of f(x) = x^2 is translated up 4 units to become g(x) = x^2+4

Answer:

44 pears and 52 apples

Step-by-step explanation:

pears are 8 more than apple so 52-8 = 44

Number of apples and pears in a box is equals to [tex]30[/tex] and [tex]22[/tex] respectively.

" Number is defined as the count of any given quantity as per given condition."

According to the question,

Given,

Total number of apples [tex]= 52[/tex]

[tex]'x'[/tex] represents the number of pears

[tex]'x+ 8'[/tex] represents the number of apples

As per the given condition required equation we get,

[tex]x + x + 8 = 52\\\\\implies 2x = 52-8\\\\\implies x = \frac{44}{2} \\\\\implies x = 22[/tex]

number of pears [tex]= 22[/tex]

number of apples [tex]= 22+8[/tex]

                              [tex]=30[/tex]

Hence, number of apples and pears in a box is equals to [tex]30[/tex] and [tex]22[/tex] respectively.

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Answer:

Step-by-step explanation:

how many triangles are in a 18 sided polygon

An 18 sided polygon, sometimes also called an octakaidecagon, it has 18 sides and therefore is made up of 18 triangles and has 18 vertices.

(look at the picture)

The rule represents the translation from the pre-image, ΔABC, to the image, ΔA'B'C' is (x, y) → (x + 7, y - 6).

When a line is translated, it means the line is moved from one position to another. The coordinate for triangle ABC are A(-3 ,4) , B(-4,1) and C(-2,1).

The coordinate of triangle A'B'C' is A'(4,-2), B'(3,-5), and C'(5,-5).

From above, it can be seen that the image A'B'C' is obtained from the pre-image ABC by translating the vertices of the image by 7 units to the right and 6 units down.

Therefore, the rule represents the translation from the pre-image, ΔABC, to the image, ΔA'B'C' is (x, y) → (x + 7, y - 6)

Hence, the rule represents the translation from the pre-image, ΔABC, to the image, ΔA'B'C' is (x, y) → (x + 7, y - 6).

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Let's take this problem step by step:

What we know:

 [tex]x+y=4\\xy=-2[/tex]

Before we solve, let's do one thing that will help us out greatly later down the road:

 [tex]x+y=4\\(x+y)^2=4^2\\x^2+2xy+y^2=16\\x^2+2(xy)+y^2=16\\x^2+2(-2)+y^2=16\\x^2+4+y^2=16\\x^2+y^2=20[/tex]<--- useful equation

Let's rearrange the problem a little bit:

 [tex]x+\frac{x^3}{y^2}+\frac{y^3}{x^2} +y=\frac{x^3}{x^2} +\frac{x^3}{y^2}+\frac{y^3}{x^2}+\frac{y^3}{y^2}[/tex]

Combine fractions of common denominators:

[tex]\frac{x^3+y^3}{x^2} +\frac{x^3+y^3}{y^2} =(x^3+y^3)*(\frac{1}{x^2}+\frac{1}{y^2} )[/tex]

Now's let factor everything apart:

 [tex](x^3+y^3)=(x+y)(x^2-xy+y^2)\\\\\frac{1}{x^2}+\frac{1}{y^2} =\frac{x^2+y^2}{x^2y^2}[/tex]

Let's use what we know and our useful equation:

 [tex](x+y)*(x^2-xy+y^2)*(\frac{x^2+y^2}{x^2y^2} )\\=4*(x^2+y^2-xy)*(\frac{20}{(xy)^2} )\\=4*(20-(-2))*\frac{20}{(-2)^2} \\=4*22*5\\=440[/tex]

The value is 440

Answer: 440

Hope that helps!

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Answer:

hope this is helpful.

putting values of X and y in the equation

Answer is 12

Answer:

answer is 39

Step-by-step explanation:

So, we start with the original problem:

3

x

2

−

4

y

2

Then we substitute the given

x

and

y

values into the expression:

3

(

5

)

2

−

4

(

3

)

2

Now, according to the order of operations, we simplify the exponential powers first, thus, reducing the expression to this:

3

(

25

)

−

4

(

9

)

Then, we use the order of operations again and do the multiplication next:

75

−

36

We then use the order of operations a final time and finish off the expression with subtraction:

39

Answer:

s = 17units

Step-by-step explanation:

For this problem, we are trying to find a specific unknown side length.

We're actually given some extraneous information (information that is not needed to solve the problem):  It isn't necessary to know that BC is 5.

If the side AD with the unknown length is part of a right triangle (the triangle in red in the attached diagram), we can use the Pythagorean Theorem to solve for AD.

It isn't clear if the diagram you were provided gives ∠ABD as a right angle,  if it only gives ∠CBD as a right angle, or if it gives both as a right angle.  Below, we prove that it doesn't matter, because regardless, both must be right angles.

Is Triangle ABD a "right triangle"?

Since B is between A and C, then the two angles ∠ABD & ∠CBD form a linear pair, and by the linear pair postulate are supplementary.  Since they are supplementary, their measures add to 180°.  Using the fact that all right angles are 90°, substitution, the subtraction property of equality, arithmetic, the measure of ∠ABD is also 90°, and thus must be a right angle.  Thus, based on the given information, both ∠ABD & ∠CBD must be right angles.

Consequently, triangle ABD is a right triangle, by definition (it is a triangle that has a right angle).

Pythagorean Theorem

Since triangle ABD is a right triangle, the Pythagorean Theorem can be applied.

The Pythagorean Theorem states that [tex]a^{2} +b^{2} =c^{2}[/tex] where "c" is the hypotenuse (the side across from the right angle) and "a" and "b" the the lengths of the two other sides (called legs) of the right triangle.  (Aside: Because of the commutative property of addition, it doesn't matter which of the two legs' lengths is used for a, and which is used for b.  The only thing that is required is that "c" be the length of the hypotenuse)

In our triangle, side AD, with unknown length "s" is the length of our hypotenuse, and sides AB and BD are the two legs.  Substituting values into the Pythagorean Theorem equation, we can solve for the unknown "s":

[tex]a^{2} +b^{2} =c^{2}[/tex]

[tex](8)^{2} +(15)^{2} =(s)^{2}[/tex]

[tex]64 +225 =s^{2}[/tex]

[tex]289 =s^{2}[/tex]

Applying the square root property...

[tex]\pm \sqrt{289} =\sqrt{s^{2}}[/tex]

[tex]s=17 \text{ or } s=-17[/tex]

Final Solution

We discard the negative solution we obtained, since s represents the length of the side of a triangle.

s = 17units

Answer:

17

Step-by-step explanation:

Answer:

from the image above

Triangle ABE = Triangle ADE

AE = AE ( common).

angle AEB = angle AEO ( each 90°)

AB = AD ( given).

by side angle side criteria

so area of ABE = area of ADE

similarly,

BC = DC ( given)

BEC = DEC ( 90°)

EC = EC ( 9m each)

so area of BEC = Area of DEC

answer:

x=74 y=27

steps:

triangle in the middle is

180-126 = 54

180-85 = 95

180-149 = 31

126=2x+1+31

126=2x+32

2x=94

x=74

126+2y=180

2y=54

y=27

As angles opposite congruent sides in a triangle are congruent, and also since the interior angles of a triangle add to 180 degrees, if we let angle EFG have a measure of x, then angle GEF also measures x, and thus:

82+x+x=180

2x=98

x=49

Thus, angle EFG is 49 degrees.

So, by the exterior angle theorem, angle DEG measures 82+49=131 degrees

The difference quotient of the expression will be 4.

f(x) = 5 + 5x + 4x²

f(3) = 5 + 5(3) + 4(3)³

= 56

Now [f(x) - f(3)]/(x - 3) will be:

= (4x² + 5x + 5 - 56)/(x - 3)

= (4x² + 5x - 51)/(x - 3)

= (4x² + 17x - 12x - 5)/(x - 3)

= (4x + 17)(x - 3)/(x - 3)

= 4x + 17

The difference quotient will be:

g(x + h) = 4(x + h) + 17

= [g(x + h) - g(x)]/h

= (4x + 4h + 17 - 4x - 17)/h

= 4h/h

= 4

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The statement that is most likely true is , The mean is less than the median because the data is skewed to the left.

Option  E is the correct answer.

The method of representing the variation in a data set is called a Box and Whisker Plot .

A data distribution in which the data is skewed to the left

the mean is less than the median.

A data distribution in which the data is skewed to the right

the mean of the data is greater than the median.

It is given in the question that

The distance from the minimum value to the first quartile is greater than the distance between the third quartile and the maximum value.

this means data is skewed to the left,

Therefore, the statement that is most likely true is , The mean is less than the median because the data is skewed to the left.

Option  E is the correct answer.

The complete question is

Indira makes a box-and-whisker plot of her data. She finds that the distance from the minimum value to the first

quartile is greater than the distance between the third quartile and the maximum value. Which is most likely true?

The mean is greater than the median because the data is skewed to the right.

The mean is greater than the median because the data is skewed to the left.

The mean is less than the median because the data is skewed to the right

The mean is less than the median because the data is skewed to the left.

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Answer:

There are no solutions

Step-by-step explanation:

If y is greater or equal to 3x+1 it can not be less than 3x-3 since 3x-3 is 4 less than 3x+1. Therefore, there can not be any solutions for the system of inequalities.

Answer:

B. [tex]\mathsf {\frac{1}{13}(26x-169)=\frac{1}{12}(-156+24x) }[/tex]

Step-by-step explanation:

[tex]\mathsf {\frac{1}{13}(26x-169)=\frac{1}{12}(-156+24x) }[/tex]

2x - 13 = -13 + 2x

2x - 13 = 2x - 13

As both sides are equal, any value can be substituted for x, and hence it has infinitely many solutions.

Answer:

B. 1/13(26x - 169) = 1/12(-156 + 24x)

Step-by-step explanation:

When looking for an equation with infinetly many solutions, we are looking for an equation that is true when simplified

such as: 3c = 3c

or x - 10 = - 10 + x

this is because any value that we put in for x will simplify to a true equation (will be a solution)

so, let's examine the options:

A. if we combine like-terms on both sides, we will end up with                                23 + 32x = 32x + 26

which is false, for any value that we put in for x

B. this statement is true--regardless of the value for x.

1/13 · 26 is the same as 1/12 · 24 (both equal 2; so both sides would distribute to 2x)

1/13th of -169 is -13; and 1/12th of -156 is -13

so, for all values of x, option B is true

(all values of x are a solution; and "x" could be any value)

C. by distributing the 2 (6 - 4x = -5x + 7), we find an equation that is not true for all values of x [we don't even have to find the solution, we just know that there will only be a/a few solution ]

D) because the variable, x, is only on one side (and when distributed, is not cancelled by any other x), we know that it cannot be true for infinetly many solutions

(the only true solution will be when the equation is simplified to 4/18 = 4/18)

hope this helps!!

Answer:

D. (90, 60)

Step-by-step explanation:

A proportional relationship is a relationship in which the ratios of two variables are equivalent.

If we take two points on the graph such as (45, 30) and (30, 20), we can see that they can both be simplified to the ratio 3:2. Using this we can find the correct answer. From looking at all the points we can see that only (90,60) would also form a ratio of 3:2, thus d would be the correct answer.

Answer: −x2+

5

x

=

7

Move

7

to the left side of the equation by subtracting it from both sides.

−

x

2

+

5

x

−

7

=

0

Once the quadratic is in standard form, the values of

a

,

b

, and

c

can be found.

a

x

2

+

b

x

+

c

Use the standard form of the equation to find

a

,

b

, and

c

for this quadratic.

a

=

−

1

,

b

=

5

,

c

=

−

7

Step-by-step explanation:

Answer:

f^-1(x)=8x/5

Step-by-step explanation:

The inverse of f(x)=5x/3+5 is 8x/5

The inverse function of f(x)=5x/3+5 is f-1(x) = 3x/5 - 15

We have:

f(x)=5x/3+5

Rewrite as:

y=5x/3+5

Swap x and y

x = 5y/3 + 5

Subtract 5 from both sides

5y/3 = x - 5

Multiply through by 3

5y = 3x - 15

Divide through by 5

y = 3x/5 - 15

Rewrite as:

f-1(x) = 3x/5 - 15

Hence, the inverse function of f(x)=5x/3+5 is f-1(x) = 3x/5 - 15

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Answer:

Step by step explanation:

The problem tells us that at the end of the day, there are only 5 workers left, which we must find how many days it takes to finish said work.

We start by finding the type of proportionality we have.

In this case, we have that the more workers there are, they will finish that work in less time, and the fewer workers there are, the longer it will take to finish the work. This is the inverse proportionality, to more less, to less more.

We have only 5 workers left.

In the first case there are 10 workers, and in the second case there are 5 workers left. We find the relationship between the workers in the second case among the workers in the first case.

We see that the time is found by dividing the number of days in which the 10 workers finish the work, by 1/2.

As we know, dividing two fractions is the SAME as multiplying by the inverse fraction.

[tex]\rm 30 * 2/1 \: = 60 \: days[/tex]

By so

Answer:

i think B i don't know but i only guess

Step-by-step explanation:

I don't know on my mommy that Is the answer

Answer:

There were 920 children and 830 adults.

Step-by-step explanation:

Let C be the number of children and A be the number of adults. Set up equations. Using the attendance of 1750 people, we can write:

c+a=1750

Using the total money collected of 9860, we can write:

3.50c+8.00a = 9860

Solve by substitution. Using (1), we solve for a to obtain (3): a=1750—c

Substutute (3) to (2) and solve for c:

3.50c + 8.00(1750 — c) = 9860

3.50e+ 14000 — 8.00c = 9860

—4.50e= —4140

c=920

Solve for a using (3):

a=1750 — 920

a=830

So, there were 920 children and 830 adults. (They better have been 6 ft apart)

Answer:

You are right...........

Answer:

Simplifying -16t2 + 48t + 160 = 0

Reorder the terms: 160 + 48t + -16t2 = 0

Solving 160 + 48t + -16t2 = 0 Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '16'. 16(10 + 3t + -1t2) = 0

Factor a trinomial. 16((5 + -1t)(2 + t)) = 0 Ignore the factor 16.

hope it helps.

Answer:

1.5

Step-by-step explanation:

The average rate of change is 1.5

when x=0 , the value of y =1

when x=2 the value of y = 4

average rate of change formula = [tex]\frac{f(b)-f(a)}{b-a}[/tex]

a= 0 , f(a)=1

b=2, f(b)= 4

4 - 1 / 2 - 0 = 3/2 = 1.5

ответ: д
-1/2 * 16 = -8
или 16/(-2) = -8

Answer: by rewriting equation in the form, / 1\2 16 X 4X 4 f=~1_~) (Do-2)2=g=~

Step-by-step explanation: hope this helps

The sum of the angle 5 and angle 6 is 180 degrees. Then the correct option is C.

When two angles are said to be supplementary angles if their sum is 180 degrees.

A triangle is shown with its exterior angles.

The interior angles of the triangle are angles 2, 3, 5.

The exterior angle at angle 2 is angle 1.

The exterior angle at angle 3 is angle 4.

The exterior angle at angle 5 is angle 6.

We know that the sum of interior and exterior angle of the triangle is 180 degrees.

∠1 + ∠2 = 180°

∠3 + ∠4 = 180°

∠5 + ∠6 = 180°

Then the correct option is C.

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Answer:

5 ,6,8,8,9,18

Step-by-step explanation:

5 ,6,8,8,9,18

Range:

18-5=13

Median:

8

Mean:

5+6+8+8+9+18=54

54÷6=9

Answer:

x=1/5

Step-by-step explanation:

You have to isolate x. First, add the one to the sider to give you 5x=1. In order to get the x by itself, you have to divide the 5 into both sides. In the end, this gives you x=1/5.

The length of the diagonal LN would be 8.60 units.

To find the distance between the two coordinates, We use distance formula ;

[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]
Lets put the values of L and N,
d= [tex]\sqrt{(0 - -5)^2 + (-3-4)^2}[/tex]

d =[tex]\sqrt{25+49}[/tex]

d= [tex]\sqrt{74}[/tex]

d= 8.60 units

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Answer:

16.6

Step-by-step explanation:

Add the numbers together.

13.2+20=33.2

Now divide the number by 2.

33.2/2=16.6

Hope this helps!

If not, I am sorry.