Given the function defined in the table below, find the average rate of change, in
simplest form, of the function over the interval 1 < x < 5.
2
f(x)
1
77
2
68
3
59
4
50
5
5
41
-

Given data:

The given table is shown.

Draw the points on the graph paper as shown below.

The unit rate for each situation is $5.00 for 1 pound, $8 for 1 pound, $65 for 1 pound, $2 for 1 pound, $18 for 1 pound, $108 for 1 pound

What is unit rate and how to compute it?

Unit rate is the rate for 1 unit and to compute the unit rate we divide the total price by the total number of elements

We are given certain price we have to find there unit rate

a) $45 for 9 pound

Divide both sides by 9 to find the unit rate

we get $5 for 1 pound

a) $24 for 3 pound

Divide both sides by 3 to find the unit rate

we get $8 for 1 pound

a) $390 for 6 pound

Divide both sides by 6 to find the unit rate

we get $65 for 1 pound

a) $42 for 21 pound

Divide both sides by 21 to find the unit rate

we get $2 for 1 pound

a) $180 for 10 pound

Divide both sides by 10 to find the unit rate

we get $18 for 1 pound

a) $864 for 8 pound

Divide both sides by 8 to find the unit rate

we get $108 for 1 pound

Hence the unit rates are for each situation is $5.00 for 1 pound, $8 for 1 pound, $65 for 1 pound, $2 for 1 pound, $18 for 1 pound, $108 for 1 pound

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The equation for the given summation is:

   [tex]\sum_{n=1}^4 u_n = u_1 + u_2 + u_3 + u_4[/tex]

Here we have a summation of unknown terms of the form:

uₙ

That summation goes between n = 1 and n = 4, this means that we will have a sum of 4 terms, such that:

[tex]\sum_{n=1}^4 u_n[/tex]

Means that we need to sum the terms u₁, u₂, u₃, and u₄, then we can write the equation:

[tex]\sum_{n=1}^4 u_n = u_1 + u_2 + u_3 + u_4[/tex]

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∠GJI ≅ ∠LKF is proved below.

If two shapes are similar in size and shape, they are congruent. We can also state that if two shapes are congruent, then their mirror images are identical. If it is possible to superimpose one geometric figure on the other so that their entire surface coincides, that geometric figure is said to be congruent, or to be in the relation of congruence.

Given Data

EF║GH

AB║CD

In given figure,

AB║CD,

While line segment GH is the transversal line.

So,

∠GJI ≅ ∠JLK (because it is corresponding angle) ..(1)

Also,

EF ║GH

Line segment DL  is the transversal line.

So,

∠JLK ≅ ∠LKF (because it is interior alternate angle)..(2)

From (1) and (2)

∠GJI ≅ ∠LKF

Hence, proved.

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Given:

solve for y:

Value of y is zero and

Answer:

3x^5y^8

Step-by-step explanation:

so the cube root of 27 is 3

to find the cube root of x^15 divide the exponent by 3 which gets you x^5

do the same thing for y^24 and that gets you y^8

mhm and i think thats right

Answer:

1018.3

Step-by-step explanation:

The volume of a cylinder=πr2h

=22\7*6*6*9

=1018.3

therefore, the of the cylinder is 1018.3

Given the area of a rhombus is 208 cm square and the perimeter of rhombus is 64 cm.

Recall that all the sides of the rhombus are equal.

Hence,

Area of rhombus is :

Hence the altitude of the Rhombus is 13 cm.

Answer:

47/68

Step-by-step explanation:

total candies=136

not red candies=94

94/136=47/68

Given data:

The given graph.

The equation of the line when x is less than or equal to 1 is,

x+1

he equation of the linne when x is greater than 1 is,

-x+2.

Thus, the correct option is (c).

Given the word problem, we can deduce the following information:

Principal amount = $4739

Future amount = $5336

Interest = 5.1 % =0.051

To determine the time to accumulate the $5336, we use the compound interest formula:

A=Future amount=$5336

P=Present amount=$4739

r=interest rate = 0.051

n=number of compounding periods =12

t=time in years

We also note that the number of compounding periods must be 12 since the investment is compounded monthly.

We plug in what we know:

Therefore, the answer is 2.33 years.

Isosceles triangle have 2 equal lengths

Square or Rectangle have 4 equal teiangles

Isosceles trapezoid also divides

Then answer is

Isosceles trapezoid. Option A)

The correct option C: y = (x + 2)(x -3)²(x - 1)² is function which correctly represents the given graph.

For the given graph;

Select one coordinate of the curve from the graph.

Point (0, 18); in which y is 18 for x = 0.

Now, go by option and put the value of x = 0 and find the correct value of y.

Option C:   y = (x + 2)(x -3)²(x - 1)²

Put x = 0

y = (0 + 2)(0 -3)²(0 - 1)²

y = (2)(-3)²(- 1)²

y = 18

We, get the correct coordinates (0, 18).

Thus, the correct option is C, which satisfies the given graph.

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The number of children's tickets sold is 13750.

Let the number of children be x and the number of adults be y.

The total number of attendance at the amusement park is 25,000.

So we have an equation

x + y = 25000 ......(i)

The cost for children is $15 and the cost for adults is $35, and the total money earned by the park is $600,000.

So we have another equation,

15x + 35y = 600,000

3x + 7y = 120,000 ......(ii)

Multiplying equation (i) with 3 we get

3x + 3y = 75000

3x + 7y = 120,000

Now subtract both the equation we have,

4y = 45000

y = 11250

Now put the value of y in equation (i) we get

x + 11250 = 25000

x = 13750

Where x is the number of children's tickets sold.

Therefore the number of children's tickets sold is 13750.

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Answer:

7/8

Step-by-step explanation:

3 per thousand?

10000 ------------------------- 1000

x ------------------------ 3

x = (3 x 10000)/1000

x = 30000/1000

x = 30

The answer is 30

The first equation is increasing at highest rate.

Which function has highest increasing rate?

We can know which function has the highest rate of increase by looking at its slope. The function with the highest slope will have the highest rate.

In equation first m = 2 and is highest among every slope.

12x - 6y = -24

-6y = -12x -24

y = 2x +4

m = 2 (increasing)

In second equation m = 1

m = (-4 + 5)/(2-1) = 1

for a straight line function , the slope is given by

m = ( y₂ -y₁)/(x₂-x₁)

m = ( -3 -3)/(2- (-1)) = -6 /3 = -2

Therefore the function is decreasing

8,0) (0,-4)

m = (-4 -0) /(0-8) = 4/8 = 1/2

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We can conclude that Jeffry will reach his home in the time of 9 hours.

So, the time taken by Jeffrey to get home:

Now calculate time as follows:

Rounding off: 9 hours

Therefore, we can conclude that Jeffry will reach his home in the time of 9 hours.

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Answer:

3 is missing in there numbers,the last pair

The absolute number of an integer is the distance that separates the number from position zero "0" so, if it is a distance it cannot be a negative value.

Then the absolute value of these numbers is:

Part A: The vertex, domain, and range of the function g(x) = |x-5|  is

( 5, 0 ), ( - ∞ , ∞ ) and [0, ∞ ).

Part B: The function f(x) = |x| is vertically shifted by 3 units to get the function h(x) = |x| + 3. The y - coordinate of the vertex is shifted by 3 units.

In Part A:

The given function is;

g(x) = | x - 5 |.

Now, The x - coordinate of the vertex will be:

x - 5 = 0

x = 5

Therefore, the y- coordinate of the vertex will be:

y = g(x) = | x - 5 |

y = g(7) = | 5 - 5|

y = 0

So, The vertex of the absolute function is ( 5, 0 ).

Since, All real numbers fall under the expression's domain, with the exception of cases where it is undefined. In this case, the phrase is defined even if there is no real number.

Hence, In Interval Notation the domain is;

⇒ ( - ∞ , ∞ )

And, The set of all legitimate y values is the range.

Hence, In Interval Notation the range is:

⇒ [0, ∞ )

Now, In Part B:

Function h(x) = |x| + 3 is the transformed version of the parent function

f(x) = |x|.

For the parent function f(x) = |x|, the vertex is ( 0, 0).

Since, The range of an absolute function in the form c( | ax + b | ) + k is

f(x) ≥ k.

Therefore, The range of the function f(x) = |x| is f(x) ≥ 0 and in interval notation is [ 0, ∞ ).

For the transformed function h(x) = |x| + 3.

The vertex of the function is ( 0, 3 ).

The range of function is h(x) ≥ 3 and in interval notation is [3, ∞ ).

Hence, the y coordinate of the vertex is transformed by 3 from f (x) to h(x).

So, Part A: The vertex, domain, and range of the function g(x) = |x-7|  is  

( 5, 0 ), ( - ∞ , ∞ ) and [0, ∞ ).

Part B: The function f(x) = |x| is vertically shifted by 2 units to get the function h(x) = |x| + 3. The y coordinate of the vertex is shifted by 3 units.

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Answer:

D) 10

Step-by-step explanation:

2x - 2 < 8 + x

add 2 to both sides:

2x - 2 + 2 < 8 + x + 2

2x < 10 + x

subtract x from both sides:

2x - x < 10 + x - x

x < 10

Lin says that about 6.2 x 10^5 more people live in San Jose than in Atlanta. To find if she is right you substract the population of Atlanta from the population in San Jose:

Substraction of numbers in scientific notation:

1. Turn the numbers to get the same power of base 10.

You move to the left the decimal to increase the power of base 10 and move to the right to g

6 bracelets Eva can make with the yarn she has left with .

The equation is [tex]\frac{3n}{2}=9[/tex]

Algebra is a branch of mathematics that helps translate real-world situations or problems into mathematical truths. Mathematical operations like addition, subtraction, multiplication, and division are needed in addition to variables like x, y, and z to construct a meaningful mathematical expression. All branches of mathematics, such as calculus, trigonometry, and coordinate geometry, employ algebra. A fundamental algebraic expression is 2x + 4 = 8, which results from operations like addition, subtraction, multiplication, and division on variables and constants. Algebraic expressions are obtained as the mathematical statement.

Eva has 11 meters of yarn and she gives 2 meters of the yarn to her friend

Now she left with 11 -2 = 9

As Each bracelet uses [tex]\frac{3}{2}[/tex] meters of yarn

n braclet = [tex]\frac{3n}{2}[/tex]

9= [tex]\frac{3n}{2}[/tex]

n = [tex]\frac{18}{3}[/tex]

=6

6 bracelets Eva can make with the yarn she has left with .

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1) In this question, we can solve it in two different ways. Either algebraically, or by mental Math.

2) Algebraically we have:

By mental math, we just need to ask ourselves how much can I add to 4 and get 10,? The answer will be six.

3) Thus, the answer is 6

GROUP THE LIKE TERMS FIRST.

[tex]9x - 3x = 7 + 9[/tex]

WHEN TERMS CROSS THE EQUAL SIGN THEY CHANGE SIGN.

[tex]6x = 16 \\ \frac{6x}{6} = \frac{16}{6} \\ x = \frac{16}{6} [/tex]

x can be simplified further

[tex]x = \frac{8}{3} [/tex]

HOPE THIS HELPS.

Answer:

The answer should be x=2.6

Step-by-step explanation:

9x-9=3x+7

-first you should move the numbers so you can get all your x values on one side and all your regular numbers on the other like this

9x-3x=7+9

-What i basically did was i passed the 3x from the right side to the left side of the equation, since in adding the 3x originaly, when i pass it to the left side itll be subtracting. then i passed my -9 to the right side of my equation, since i was subtracting originaly ill have to now switch it to adding

-after you do this you are going to want to want to combine like terms

6x=16

-then you are going to want to devide on both sides so you can get x alone

x=2.6

The test statistic for the anova is an F test and it is said to be positively skewed which would be to the right of the F test statistic.

This is the term that is used to refer to the short form of the term that says analysis of variance.

The ANOVA is used to show the variation that would be in existence of a group of observations.

The F test is known to be positively skewed at all times. So we would have it that the P value would have to be to the right and not to the left in the ANOVA hypothesis.

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Answer:

-2, 6 or -2/6 is what im seeing i could be wrong though

Step-by-step explanation:

sub to imaginefn

line 1 = y = 5/3 x - 6

Find the slope of the line by comaring it with y = mx+ b

m= 5/3

Line 2

Write the equation in the form y =mx +b and find the slope m

10x - 6y = 8

6y = 10x - 8

Divide through by 6

y = 10/6 x - 8/6

y = 5/3 x - 4/3

m= 5/3

Line 3

3y = 5x + 7

Also write in the form y =mx + b and find the slope m

y = 5/3 x + 7/3

m = 5/3

Line 1 and line 2 are parallel since they have the same slope

Line 1 and 3 are parallel (they have the same slope)

Line 2 and 3 are parallel, they have the same slope