What is the common difference between the elements of the arithmetic sequence below?
–18, –22.5, –27, –31.5, –36

Answer:

A) For line l = (2x + 8°) + (5x - 10°) = 180° ....... (i)

For line k = (3x + 42°) + (x + 34°) = 180° ....... (ii)

B) In line l, two angles are = 60° and 120°

In line k, two angles are =  120° and 60°

Step-by-step explanation:

Requirement A

To find the measure of each angle, we have to use equation.

According to the graph, line l and k are parallel, therefore, both are straight angle. We know that a straight angle is equal to 180°. Therefore, line l and k are 180°. As both the line are intersected by line j, the lines are separated by two angles. So, the equation for line l is -

(2x + 8°) + (5x - 10°) = 180° ....... (i)

the equation for line k is -

(3x + 42°) + (x + 34°) = 180° ....... (ii)

Requirement B

For line "l "

By solving the equations, we can measure the angles

(2x + 8°) + (5x - 10°) = 180°

or, 2x + 8° + 5x - 10° = 180°

or, 7x - 2° = 180°

or, 7x = 180° + 2°

or, 7x = 182°

or, x = 182° ÷ 7 [Dividing both the sides by 7]

or, x = 26°

Therefore, 2x + 8° = 2 × 26° + 8° = 52° + 8° = 60°

the other angle is = 5x - 10° = 5 × 26° - 10° = 130° - 10° = 120°

For line "k "

(3x + 42°) + (x + 34°) = 180°

or, 3x + 42° + x + 34° = 180°

or, 4x + 76° = 180°

or, 4x = 180° - 76° [Deducting 76° from the both the sides]

or, 4x = 104°

or, x = 104° ÷ 4

Hence, x = 26°

Therefore, 3x + 42° = 3 × 26° + 42° = 78° + 42° = 120°

The other angle is = x + 34° = 26° + 34° = 60°

Solution:

Distance between two points is given by:

[tex]d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}[/tex]

We have to find the distance in the standard (x, y) coordinate  plane between the points (2,3) and (5,5)

From given,

[tex](x_1, y_1) = (2, 3)\\\\(x_2, y_2) = (5, 5)[/tex]

Substituting the values we get,

[tex]d = \sqrt{(5-2)^2 + (5-3)^2}\\\\Simplify\\\\d = \sqrt{3^2 + 2^2}\\\\d = \sqrt{9+4}\\\\d = \sqrt{13}\\\\In\ decimal\ form\\\\d = 3.605 \approx 3.6[/tex]

Thus distance between the points (2,3) and (5,5) is 3.6 units

The distance between the points (2,3) and (5,5) on the standard (x, y) coordinate plane is determined using the distance formula. After substituting the given coordinate points into the formula, we find that the distance is √13 units.

In Mathematics, the distance between two points in the (x, y) coordinate plane is given by the distance formula, which is √[(x₂-x₁)² + (y₂-y₁)²]. This formula is acquired from the Pythagorean theorem. Here, the points are (2,3) and (5,5). So, substituting these values in the distance formula, we get:

Distance = √[(5-2)² + (5-3)²] = √[3² + 2²] = √[9+4] = √13.

Therefore, the distance between the two points (2,3) and (5,5) on the standard (x, y) coordinate plane is √13 units.

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Answer:

Step-by-step explanation:

(4x^2-2x+8)+(x^2+3x-2)

Collect like terms

5x^2+x+6

5x^2+x+6 dont know if you need to siplify it any more

Answer:

D) 50ft

Step-by-step explanation:

(18×x) + (32×18) + [(48-18-18)×(32-11)]

= 1728

18x + 576 + (12×21) = 1728

18x = 1728 - 828

18x = 900

x = 50

Answer(s): 1/2, 1, 1/3, 1/4

Any of these could work. Any number beyond 1 could work. The fraction 1/12 is pretty small, and the bigger the number in fractions, the smaller they get.

Example: 1/24 is bigger than 1/64

Because 64 is a bigger number, you'd have to cut it up more and more, getting smaller pieces.

So,  any number smaller than 12 in a fraction could work- EXCEPT negatives. All whole numbers work as well.

yes is an equilateral triangle also a rhombus

Answer:

ues it is   a equilateral triangle

Step-by-step explanation:

from the meaning of equilateral, equilateral means all sides are equal in length.

a rrhombus has all its side equal.and therefore it s an  equilateral triangle

Answer: Amount of change : $30

percent increase : 200%

Step-by-step explanation:

Hi, to answer this question we have to analyze the information given:

To obtain the amount of change we have to subtract the wholesale price to the retail price:

Mathematically speaking:

45 -15 = $30

For the percent increase, the amount of change (30) is some percent of the original price (15). So:

30 / 15 =2 (decimal form)

If we multiply it by 100, the percentage is:

200%

Answer:

8:36

Step-by-step explanation:

Answer:

Step-by-step explanation:

2/8

Answer:

11+(2×4)

11+8

$19....

Answer:

Cost for 2 hours=19, Cost for 2 hours=11+4t

Answer:

1. 6100

2. 1150

3. 60

4. 50

Step-by-step explanation:

Answer:

The penny has a circuferance of  2.356194

Step-by-step explanation:

To get this I used the formula for circumference c = πd or c = 2π x r²

And you just plug in 0.75 for d and multiply it by 5 to get you answer

The circumference of the penny is approximately 2.36 inches.

A circle is simply a closed 2-dimensional curved shape with no corners or edges.

The circumference of a circle is expressed mathematically as;

Circumference = 2πr or dπ

Where r is the radius, d is the diameter, and π is constant pi.

Given the parameter:

Diameter of the penny d = 0.75 inches

Circumference =?

To find the circumference of the penny, we can use the formula for the circumference of a circle.

Circumference = dπ

Plug in the diameter values:

Circumference = 0.75 × π

Circumference = 0.75π in or 2.36 in.

Therefore, the circumference is approximately 2.36 inches.

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The resulting coordinate of X is (0, -2)

Given the coordinate point X (-3, -2). If the coordinate is translated using the rule (x, y) = (x+3, y + 4), the resulting coordinate will be (-3+3, -2+4) = (0, 2)

In conclusion, the resulting coordinate of X is (0, -2)

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After translation and reflection, the coordinate of X" is (0, -2).

To find the coordinate of X" after a translation and reflection, we need to first apply the translation rule to point X (-3, -2). Using the rule (x, y) = (x+3, y + 4), we add 3 to the x-coordinate and add 4 to the y-coordinate:

x' = -3 + 3 = 0

y' = -2 + 4 = 2

After the translation, the new coordinates are (0, 2). To reflect over the x-axis, we change the sign of the y-coordinate, giving us the final coordinate of X" as (0, -2).

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Answer:

7/8

Step-by-step explanation:

Simplify the following:

(1 + 3/4)/2

Put 1 + 3/4 over the common denominator 4. 1 + 3/4 = 4/4 + 3/4:

(4/4 + 3/4)/2

4/4 + 3/4 = (4 + 3)/4:

((4 + 3)/4)/2

4 + 3 = 7:

(7/4)/2

7/4×1/2 = 7/(4×2):

7/(4×2)

4×2 = 8:

Answer:  7/8

Answer:

2h+3 Because they bought 2 hot dogs and h represents the amount they cost. And the 3 represents the drink he purchased

Answer:

n = 3

Step-by-step explanation:

Equation:  17.1 = 5.7 * n

Divide both sides by 5.7 to get n by itself.

Step 1:  Divide both sides by 5.7

17.1 = 5.7 * n

17.1 / 5.7 = 5.7 * n / 5.7

    divide            divide

3 = n

Answer:  n = 3

We are given the following equation and want to solve for the unknown variable, n:

[tex]17.1=5.7 \times n[/tex]

To solve for an unknown variable, we want to isolate the variable by doing operations to both sides of the equation:

For this equation, we'll divide both sides by 5.7 to isolate the unknown variable n

[tex]17.1 \boxed{\div 5.7} = 5.7 \times n \boxed{\div 5.7}[/tex]

After dividing both sides by 5.7 and simplifying, we get:

[tex]3=n[/tex]

The next step is a bit tedious, but in math, you usually want to have the variable on the LEFT side of the equation after isolation.

After reversing the equation accordingly, we have:

[tex]\boxed{n=3}[/tex]

We have a value for n, which is 3.

Let me know if you need any clarifications, thanks!

~ Padoru

The graph of g(x) = f(–2x) will be a horizontally stretched and reflected version of the graph of the parent function f(x) = x^3. The reflection occurs over the y-axis, and the stretch is by a factor of 1/2.

The student's question involves a transformation of a cubic parent function. The original function, f(x) = x3, represents a standard cubic graph, which is symmetric about the origin and increases from negative infinity to positive infinity as x does the same. The transformation g(x) = f(–2x) modifies the parent function in two notable ways. First, the multiplication by –2 reflects the graph over the y-axis (because of the negative sign) and also stretches it horizontally by a factor of 1/2 (because the absolute value of the number is greater than 1).

To visualize this, if we consider specific points on the graph of f(x) such as (1,1), (2,8), and (3,27), you would find their corresponding points on g(x) at (-0.5,1), (-1,8), and (-1.5,27), respectively. This indicates that every point on g(x) is twice as far from the y-axis as it is on f(x), and on the opposite side due to the reflection.

The effect of this transformation demonstrates the result of horizontal stretching and reflection when contrasts with the original function f(x), providing insight into how linear transformations affect the shape and position of graphs.

Answer:74

Step-by-step explanation:

Since RP is 72, you would divide 72 by 2. The quotient you would get is 36. So then Q=38, you would add 36+38 and get 74.

Answer:

116.9FT

Step-by-step explanation:

Height of the trapezoid is 14.4 meter.

Solution:

Given data:

One base [tex](b_1)[/tex] = 12 meter

Other base [tex](b_2)[/tex] = 8 meter

Area = 144 square meter

Area of the trapezoid = [tex]\frac{1}{2} \times(b_1+ b_2)\times h[/tex]

[tex]$144=\frac{1}{2} \times(12+8)\times h[/tex]

[tex]$144=\frac{1}{2} \times 20 \times h[/tex]

[tex]$144= 10 \times h[/tex]

Divide by 10 on both sides, we get

14.4  =  h

Switch the sides of the equation.

h = 14.4

Height of the trapezoid is 14.4 meter.

Answer:

1

Step-by-step explanation:

Only 1 right angle can be in any triangle.

Answer:

D

Step-by-step explanation:

Answer: 1 1/40.

Step-by-step explanation:

Answer:

The answer is:

No, they are not independent because P(student)≈ 0.82 and P(student|pirate) ≈0.94

Step-by-step explanation:

so the answer is B

No, they are not independent because P(student) = 0.82 and P(Student|pirate) = 0.94

The probability of being student P(student) = 0.82

The probability of perferring pirate P(pirate) = 0.94

These two events are not independent events.

Hence, they are not independent because P(student) = 0.82 and P(Student|pirate) = 0.94

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Answer:

C. $5.55

Step-by-step explanation:

Total cost of installing 60 square feet of flooring

= $253.00 + $80

= $333

Total number of square feet for flooring = 60

Now cost per square foot of the flooring

= total cost/total number of square feet

That’s

$333/60 = $5.55

Each square foot cost $5.55

72 = l . w . h

72 = x . (x - 1) . (x + 9)

72 = (x² - x) . (x + 9)

72 = x³ + 9x² - x² - 9x

72 = x³ + 8x² - 9x

0 = x³ + 8x² - 9x - 72

0 = x² (x + 8) - 9 (x + 8)

0 = (x² - 9)(x + 8)

0 = (x - 3)(x + 3)(x + 8)

x = 3 or x = -3 or x = -8

so, x = 3

length = x = 3

width = x - 1 = 2

height = x + 9 = 12

Final answer:

To find the dimensions of the rectangular prism, set up an equation using the volume formula and solve for x. The dimensions of the box are 3 feet, 2 feet, and 12 feet.

Explanation:

To find the dimensions of the box, we need to set up an equation using the volume formula for a rectangular prism. The volume of a rectangular prism is given by V = length x width x height.

So, we have the equation x(x - 1)(x + 9) = 72.

Simplifying this equation, we get x³ + 8x² - 9x - 72 = 0.

Using factoring or synthetic division, we find that x = 3 is a solution to the equation. Therefore, the length of the box is 3 feet, the width is 2 feet, and the height is 12 feet.

Hello, remember you need to write complete questions in order to get good and exact answers. Here you haven't provided any fractions, so I'll give you my own fractions.

The first fraction is:

[tex]\frac{1}{2}[/tex]

The second fraction is:

[tex]\frac{1}{4}[/tex]

So let's say that difference is:

[tex]\frac{1}{2}-\frac{1}{4}[/tex]

Therefore, the result is:

[tex]\frac{1}{2}-\frac{1}{4}=\frac{1}{4}[/tex]

The representation of this problem is shown using the number line below. As you can see, we have written both 1/2 and 1/4 and the difference is also indicated giving the result 1/4. That is, if we walk from 1/4 to 1/2 we'll walk 1/4 units.

Answer:

-7/10

Step-by-step explanation:

Bruh trust me

Answer:

151 trays, 1 left over

Step-by-step explanation:

907/6 = 151 remainder 1

The Bake Stars could sell 151 trays of caramel apples with 1 apple left over.

The Bake Stars picked 907 apples and sold them in trays of 6.

To determine how many trays they can sell, divide the total number of apples by the number of apples in each tray:

907 apples / 6 apples per tray = 151 trays with 1 apple remaining (since 907 = 151 * 6 + 1).

Answer:

The scale factor of the dilation is 3

Step-by-step explanation:

we know that

A dilation is a non rigid transformation that produce similar figures

so

Rectangle ABCD and rectangle A'B'C'D' are similar

Remember that

If two figures are similar, then the ratio of its corresponding sides is proportional

Let

z ----> the scale factor

[tex]z=\frac{D'C'}{DC}[/tex]

we have

[tex]D'C'=12-3=9\ units[/tex] ----> difference of x-coordinates

[tex]DC=4-1=3\ units[/tex]  ---> difference of x-coordinates

substitute

[tex]z=\frac{9}{3}=3[/tex]

The scale factor is greater than 1

so

The dilation is a enlargement

Answer:

4/7

Step-by-step explanation:

you just flip the numbers across the division/fraction sign

Heya.

First, let us learn about reciprocals.

Basically, it's the fraction flipped. Easy as 1, 2, 3!

Let's do an example:

We have an equation that says Find the reciprocal of 5/2.

1. Flip the fraction.

2. We then have 2/5 as a final answer.

Now onto the question:

1. We need to flip the equation.

2. This results as 4/7.

Therefore, our answer is "4/7".

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Answer:

Step-by-step explanation:

[tex]15a\geq 75\\15(5)\geq75\\75\geq75\\True[/tex]

If we substituted 1 for a then:

[tex]15a\geq75\\15(1)\geq75\\15\geq75\\False[/tex]