Please help me. Thank you!

I WILL USE THE LAWS OF EXPONENTS WHEN WE MULTIPLY POWERS OF THW SAME BASES WE KEEP ONE POWER AND ADD THE EXPONENTS.

[tex] = 7^{ - 5} \times 7^{2} \\ = {7}^{ - 5 + 2} \\ = {7}^{ - 3} \\ = \frac{1}{ {7}^{3} } \\ = \frac{1}{343} [/tex]

ATTACHED IS THE SOLUTION

Answer:

0

Step-by-step explanation:

7 is not in the sample space, meaning it is impossible. Therefore, the probability is 0.

Answer:

207/4 some other forms are 51 3/4 or 51.75

Step-by-step explanation:

Answer:

24  3/4 gal

Step-by-step explanation:

2 3/4 gal / bucket    *   9 bucket   = 24 3/4 gal

Answer:

Green

Verde = green

Answer:

2.5

Step-by-step explanation:

if it is divison then the answer would be 2.5

if its additin is  35

if subtraction it is 15

if multipcation  250

Answer:

45

Step-by-step explanation:

In this picture we can see that they gave us 2 angles.

Angle V has an angle of x+83

Angle S has an angle of 4x - 53

As one of the circle thermoses in mathematics said when there is an angle in the center of the circle, the angle at the circumference is half the angle at the center, which means we could create and equation such that:

angle of angle V = 2 times the angle of angle S

x + 83 = 2(4x - 53)

x + 83 = 8x - 106

189 = 7x

27 = x

Since we know x = 27, we can substitute into the equation angle of S to find what is the angle of TSU:

4x - 53

= 4(27) - 53

= 108 - 53

= 45

Answer:

<TSU = 55°

Step-by-step explanation:

We know that,

Angle at the circumference of a circle is twice the angle at the centre.

Therefore,

2 × <UST = <UVT

Given that,

< UVT = x + 83

< TSU = 4x - 53

Accordingly, we can make an expression like this.

[tex] \sf2 × <UST = <UVT[/tex]

[tex] \sf2(4x - 53) = x + 83 \\ [/tex]

And now solve the above expression and find the value of x.

Let us solve it now.

[tex] \sf8x - 106 = x + 83 \\ \sf8x - x = 106 + 83 \\ \sf7x = 189 \\ \sf \: x = 27[/tex]

And now, according to the question they've asked us to find the value of <TSU.

As we mentioned earlier, they've given that, <TSU = 4x - 53.

So, to find the value of Angle TSU, we have to replace x with 27 and find the value of angle TSU.

Let us solve it now

[tex] \sf \: <TSU = 4x - 53 \\ \sf \: <TSU = 4 \times 27 - 53 \\ \sf \: <TSU = 108 - 53 \\ \sf \: <TSU = 55 \degree[/tex]

Applying the slope formula, we have:

16. Slope = -9/4; Parallel slope = -9/4; Perpendicular slope = 4/9.

17. Slope = -4; Parallel slope = -4; Perpendicular slope = 1/4.

See explanation below for the rest answers.

Slope of a line = change in y / change in x.

The slope of parallel lines are the same, while the slopes of two lines that are perpendicular to each other are negative reciprocals of each other, i.e. 1/a and -a can be the slopes of two lines that are perpendicular to each other.

In an equation given in slope-intercept form, y = mx + b, the slope is represented as "m".

16. Given, (3, 7) and (7, -2):

Slope (m) = (-2 - 7)/(7 - 3)

Slope = -9/4

Parallel slope = -9/4

Perpendicular slope = 4/9.

17. Given, y = -4x + 2,

Slope = -4

Parallel slope = -4

Perpendicular slope = 1/4.

18. Rewrite 5x - 2y = 8 in slope-intercept form:

-2y = -5x + 8

y = 5/2x - 4

Slope = 5/2

Parallel slope =  5/2

Perpendicular slope = -2/5.

19. Rewrite  4x + 3y = 2 in slope-intercept form:

3y = -4x + 2

y = -4/3x + 2/3

Slope (m) = -4/3

Substitute (a, b) = (2, -5), and m = -4/3 into y - b = m(x - a):

y - (-5)) = -4/3(x - 2)

y + 5 = -4/3(x - 2) [point-slope form]

20. Given, y = -5x + 2

Slope (m) = -5

Substitute (a, b) = (-4, -6), and m = -5 into y - b = m(x - a):

y - (-6) = -5(x - (-4))

y + 6 = -5(x + 4) [point-slope form]

21. Rewrite 9x - 3y = 6 in slope-intercept form:

-3y = -9x + 6

y = 3x - 2

The slope of y = 3x - 2 (9x - 3y = 6) is 3.

The slope of -3x - 5 is -3.

Therefore, the lines are neither parallel nor perpendicular.

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Answer:

D

Step-by-step explanation:

[tex]2x-12y=24 \\ \\ x-6y=12 \\ \\ 6y-x=-12 \\ \\ 6y=x-12 \\ \\ y=\frac{1}{6}x-2[/tex]

The slopes of the lines are neither the same nor are they negative reciprocals, so the answer is D.

The angle whose supplement is 12 degrees less than twice its measure is 64 degrees.

supplementary angles are angles that add up 180 degrees.

Given the data in the question;

Let x represent the first angle.

Since the angle are supplementary, sum of angles = 180°

First angle + second angle = 180

x + ( 2x - 12 ) = 180

Solve for x

x + 2x - 12 = 180

3x - 12 = 180

3x = 180 + 12

3x = 192

x = 192/3

x = 64

Therefore, the measure of the angle 64 degrees.

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The most appropriate choice for exponent will be given by-

Keiko is not correct because the exponent [tex](-1)^n[/tex] does not always give -1

What is exponent?

Exponent denotes how many times a number is multiplied by itself.

For example in [tex]2^4[/tex] = [tex]2 \times 2 \times 2 \times 2[/tex], here 2 is multiplied 4 times.

Suppose [tex]a^m = a \times a \times a \times a[/tex][tex].....[/tex] (m times), here a is the base and m is the power.

Here,

The given exponents are[tex](1)^n[/tex] and [tex](-1)^n[/tex]

[tex](1)^n = 1 \times 1 \times 1\times.....\times 1[/tex] (n times)

      = 1

For [tex](-1)^n[/tex]

If n is even,  [tex](-1)^n[/tex] = 1

If n is odd ,  [tex](-1)^n[/tex] = -1

But Keiko told that [tex](-1)^n[/tex] always results in -1

So, Keiko is not correct.

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The two solutions of the quadratic function are 0.58 and -1.1.

The solution of a quadratic equation can be obtained using the substitution method or formula method.

The solution of the given quadratic function is determined as follows;

f(x) = 8x² + 4x - 5

0 =  8x² + 4x - 5

The formula method of a quadratic function is given as;

[tex]x = \frac{-b \ \ \pm \ \sqrt{b^2 - 4ac} }{2a}[/tex]

from the above equation, a = 8, b = 4, c = -5

[tex]x = \frac{-4 \ \ \pm \ \sqrt{4^2 - 4(8\times -5)} }{2a}\\\\x = \frac{-4 \ \ \pm \ \sqrt{16 + 160} }{2(8)}\\\\[/tex]

x = 0.58 or -1.1

Thus, the function has two solutions, a negative and positive solution.

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The solution for the inequality is x < 11/130.

The problem we dealing with is related to inequality which is referred to as An inequality in mathematics could be a relationship that produces a non-equal comparison between two integers or other numerical expressions.

Since we are provided with inequality which is 81 - 11/5x < 55

Now multiplying both by 5x we get

81 × 5x - (11/5x) × 5x < 55 × 5x

=> 405x - 11 < 275x

=> 405x - 275x < 11

=> 130x < 11

=> x < 11/130

so it is the solution for the inequality 81 - 11/5x < 55

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The graph of the inequality 7< f has been plotted.

The given inequality is 7 < f

The inequality states that the the relationship between two numbers. The relationships are greater than, greater than or equal to , less than, less than or equal to, equal to. These are the commonly used relationship between the two number in the inequality.

Here the inequality is 7 < f

The value of f is greater than 7

Plot the inequality in the graph

At the point 7 we use a small circle to represents the term greater than, if it was greater than or equal to we use a dot at that point

Hence, the graph of the inequality 7< f has been plotted

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Answer:

I see a right angle, so the transversal is perpendicular to the parallel lines. Therefore, x and y are supplementary and congruent, and so we have x = 90 and

y = 90.

By using the Unitary method, $468 was spent on newspapers in 52 weeks.

Unitary method is a method used for finding the unit cost in which we divide the total cost by the total number of articles and to find the cost of more than one article, we multiply the unit cost by the number of articles required.

Cost of newspapers in a week from monday to saturday = $(1 x 6) = $6

Cost of newspaper only on sunday of a week = $3

Cost of newspapers in a week = $(6 + 3) = $9

Therefore, the cost of newspapers in 52 weeks = $(52 x 9) = $468.

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Answer:

205

Step-by-step explanation:

we first enter the desired number equaling the equation, so 21. then we enter the first term and find the common difference, in this case it's going up by 9. then we take the desired term, subtract 1 and we end up with 205 as the 21st term.

21 = 25 + 9 (21 - 1)

If A is in the interior of NFL. If m/NFA = 5x+10, m/AFL = 30-2x, and m/NFL = 58°, the value of x would be 6

It is important to note that the formula for determining the sum of interior angles of a shape is expressed as;

(n-2) 180

Where 'n' is the number of sides

From the information given, we have that the shape has 3 sides, so we have

(3 -2)180

180°

Give the angles as;

Equate the angles to m/NFL, we have

5x+10 + 30-2x = 58

Now, collect like terms

5x - 2x = 58 - 40

Subtract like terms

3x = 18

Make 'x' the subject by dividing both sides by 3, we have

x = 18/3

x = 6

Thus, the value of 'x' is 3

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The rate/speed at which one must travel to cover 227.5 miles in 3.5 hours is 65 miles per hours.

Speed or rate is simply referred to as distance traveled per unit time.

It is expressed as;

r = d / t

Where r is the speed/rate, d is the distance and t is time elapsed.

Given the data in the question;

To determine the rate at which one must travel to cover 227.5 miles in 3.5 hours, plug the given values into the equation above and solve for r.

r = d / t

r = 227.5 miles / 3.5 hours

r = 65m/h

r = 65mph

Therefore, the speed/rate one must travel is 65mph.

Option A)65mph is the correct answer.

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The multiplication of the mixed fractions as 4²/₇ * 2¹/₅ gives; 9³/₇

A mixed fraction is one that has a part that is a whole number and a part that is a proper fraction.

Now, a proper fraction has its' numerator lesser than its' denominator while an improper fraction has it's numerator greater than its' denominator.

Let us convert each fraction into an improper fraction before multiplication.

4²/₇ = 30/7

2¹/₅ = 11/5

Thus, we have;

30/7 * 11/5

This can be reduced to;

66/7 which can be converted back to a mixed fraction to get 9³/₇

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Answer:

Option 4: a reflection over the y-axis and a translation 4 units down

Step-by-step explanation:

f(x) = 3x + 1 ---> g(x) = -3x - 5

to go from 3x to -3x is a reflection across the y axis

to go from 1 to -5 is a shift 4 units down

Answer:

No solution.

Step-by-step explanation:

 Solving using elimination method:

           3a = - 5b - 2

    3a + 5b = -2 ------------------(I)

            10b = 1 - 6a

   6a + 10b = 1 --------------------(II)

[tex]\sf \dfrac{a_1}{a_2}= \dfrac{3}{6}=\dfrac{1}{2}\\\\\dfrac{b_1}{b_2}=\dfrac{5}{10}=\dfrac{1}{2}\\\\\dfrac{c_1}{c_2} = \dfrac{-2}{1}[/tex]

[tex]\sf \dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq \dfrac{c_1}{c_2}[/tex]

So, this system of linear equations are two parallel lines and has no solution.

Let the original amount be n.

(n) (percentage) = (final amount)

We're given:

Organize this information into an equation:

n(13.5%) = 27

⇒ Convert 13.5% into a decimal:

0.135n = 27

⇒ Divide both sides by 0.135:

n = 27 ÷ 0.135

n = 200

Therefore, the original amount is 200.

200

The percentage of the tip that Serena's father paid was 20%.

Mathematically, a percentage is a numerical ratio, usually expressed as a fraction of 100 and denoted by the percent sign (%).

Percentages show the proportional relationship between two fractions, like proportions and ratios.

The amount of the tip = $5

The cost of the ride = $25

The total amount paid by Serena's father = $30 ($5 + $25)

The percentage of tip to the ride's cost = The amount of the tip divided by the cost of the ride.

= 20% ($5/$25 x 100)

Thus, in percentage terms, the amount that Serena's father tipped the taxi driver is 20% of the ride's actual cost.

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The saved amount after selling the tank and by using the code is $21.24.

What is selling price?

The selling price is the amount in the form of extra charges which was decided by the shopkeepers for the different commodities. The cost spent by the shopkeeper for the purchase is the cost price. And for profit selling price should be more than the cost price.

According to the question, the given parameter is as written below:

The selling price of the Jellyfish tank is: $24.99

And the discount with special code is: 15 percent

The calculated money saved by using the special code is:

Discount Amount = (24.99 x 15)/100 = 3.7485

Saved money = $24.99 - $ 3.7485 = $ 21.2415 ≅ $ 21.24

Hence, the saved amount after selling the tank and by using the code is $21.24.

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In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

Scale factor: 1 : 8

Scale drawing:

A = 2 cm²

Object:

A = ?

Step 02:

A = 2 cm² * (8 / 1) = 16cm²

The answer is C:38

explanation: you multiply 8x4=32, so then you add 6 to 32

Hope this helped!

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices.

10. In the given figure,

l ║m

(3x - 29)° + (8y + 17)° = 180° [Because they are linear pairs]

⇒ 3x -29 + 8y + 17 = 180

⇒ 3x + 8y - 12 = 180

⇒ 3x + 8y = 192 ............ (1)

Now,

8y + 17 = 6x -7 [Alternate interior angles]

⇒ 6x - 8y = 24 ..............(2)

On adding (1) and (2),

(3x + 8y) + (6x - 8y) = 192 + 24

simplifying the above equation, we get

⇒9x = 216

⇒ x = 216/9 = 24

⇒ x = 24

Now, 6x - 8y = 24

⇒ 8y = 6(24) - 24

⇒ y = (144 - 24)/8

⇒ y = 120/8 = 15

So, x = 24 and y = 15

11. In this given figure,

l ║m

7x - 23 = 49 + 3x ...... (Alternate interior angles)

⇒ 7x - 3x = 49+23

⇒ 4x = 72

⇒ x = 18

11y -1 = 3x [Alternate exterior angles]

⇒ 11y - 1 = 3 x 18

⇒ 11y = 54 + 1

⇒ 11y = 55

⇒ y = 5

Therefore, the value of x = 18 and y = 5

12. 11. In this given figure,

l ║m

3x - 4 = 5x - 38 [Alternate interior angles]

⇒ 5x - 3x = 38 - 4

⇒ 2x = 34

⇒ x = 17

7y - 20 + 5x - 38 + 90° = 180° [Angle sum property of a triangle]

⇒ 7y - 20 + 85 - 38 + 90 = 180

⇒ 7y + 117 = 180

simplifying the above equation, we get

⇒ 7y = 180 - 117

⇒ 7y = 63

⇒ y = 63/7 = 9

Therefore, the value of x = 17 and y = 9

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Answer:

y=12x+40

Step-by-step explanation:

The earnings are the initial payment per month plus the pay per hour times the number of hours.