Determine the number of terms in the arithmetic sequence below:-70, -69, -68, ..., 37, 38, 39, 40

Answer:

12

Step-by-step explanation:

The graph of a linear function is a straight line. The following is the form of a linear function. a + bx = y = f(x). One independent variable and one dependent variable make up a linear function. X and Y are the independent and dependent variables, respectively.

The equation y = mx + b, where y is the y-coordinate, denotes a linear function. m represents the line's slope, or how steep it is. The coordinate for x is x.

The equation y = mx + b, where y is the y-coordinate, denotes a linear function.

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The dimensions width and length are 11 cm and 13 cm, respectively .A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter.

A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter. There are numerous uses in real life for perimeter calculations.

Perimeter: 48 cm

The dimensions width and length are consecutive odd integers:

Width: x

Length: x+2

Equation:

2 [(x+2) + x] = 48

Find the width x:

2 [2x + 2) = 48

4x + 4 = 48

4x = 48 - 4

4x/4 = 44/4

x = 11   Width

Find the lenght x+2:

x+2  ⇒ 11+2 = 13   Length

The dimensions:

Width: 11 cm

Length : 13 cm

11 and 13 are consecutive odd integers.

Check:

2 (length + width) = 48

2 (13 + 11) = 48

2 (24) = 48

48 = 48  

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Answer: 6 [tex]\frac{17}{18}[/tex] gallons of gas left in the car

Step-by-step explanation:

   Upon further clarification, this question reads "3/8 of the gas" and not "38 of the gas."

     If Tom's car has 11 1/9 gallons of gas, and we want to know how much gas the car will have left if he uses 3/8 of that, we first need to find 3/8 of 11 1/9.

     "Of" can usually be written as multiplication.

3/8 of 11 1/9 = 3/8 * 11 1/9 = 4 1/6

     Next, we will use subtraction since he uses 4 1/6 gallons of gas.

11 1/9 - 4 1/6 = 6 17/18 gallons

Answer:

153

Step-by-step explanation:

x+27=180

x=180-27

x=153

We will investigate how to use ratios to determine the actual distance between cities as per defined scale.

We are given a scale conversion ( ratio ) at which distances are scaled down:

We will use the given scale ratio to determine the actual distance between two citites. The scale distance between Hawthorne and Doyelstown can be read.

Now utilize the scale conversion ratio to determine the actual distance:

Therefore, the distance between Hawthorne and Doylestown is:

The values of the angles for the two parallel lines will be ∠1 = 115°, ∠2=115°, ∠3=148°, and ∠4 = 148°.

Straight lines with little depth or width are present. You will learn about a number of lines, including transversal, intersecting, and perpendicular lines. A figure called an angle is one in which two rays originate from the same point.

Given that the lines s and t are parallel to each other. The values of the different angles will be:-

∠1  = 115° Exterior angle property

∠2 = 115° Vertically opposite angle

The value of angle ∠3 will be calculated by the supplementary angle property.

∠3 = 148°

The value of angle ∠4 is 148 by vertically opposite angle property.

∠4 = 148°

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The following table shows how the relation is a function when t is the independent variable and not a function when t is the dependent variable:

t   0   1   2   3   4   5

v   0   1   2   3   4   5

A vertical line drawn from the independent variable axis (x-axis) meets the function graph only once because a function is a relationship between an input and an output in which each input has just one output.

The independent variable is the input, while the dependent variable is the output.

Filling out the table in such a way that when t is the independent variable, the relationship is a function, and when t is the dependent variable, the relation is not a function, results in the following table:

t   0   1   2   3   4   5

v   0   1   2   3   4   5

Given that each value of the independent variable t has a corresponding value of the velocity v, the aforementioned is a function.

However, when t is the dependent variable, the independent variable value of 1 produces two outputs of 1 and 5, which results in the following table:

t   0   1   2   3   4   5

v   0   1   2   3   4   5

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Using the Pythagorean Theorem formula, the measurement of the unknown side (base) is 12 units.

According to the Pythagorean Theorem formula, c² = √a²+b², where c = hypotenuse, a = perpendicular, and b = base.

The hypotenuse is the longest side of a right triangle.

The shortest side is the perpendicular (adjacent side) while the other side is the base (opposite side).

Since the hypotenuse is given as equal to the square root of perpendicular squared and the base squared, we can compute the base, unknown side, using the following Pythagorean Theorem formula.

c² = √a²+b²

The perpendicular (shortest side) of a right triangle = 5

The hypotenuse (longest side) = 13

c² = √a²+b²

169 = √5²+b²

169 = √25 + b²

The base (unknown side):

b² = 169 - 25

b² = 144

The square root of √144 = 12

b = 12

Thus, the unknown side of the right triangle is the base, measuring 12 units.

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The length of the unknown side is 12 units, which is the base of the right triangle.

The right triangle's perpendicular (shortest side) = 5 units

The right triangle's hypotenuse (longest side) = 13 units

According to the Pythagorean Theorem,

H² = P² + B², Where H = hypotenuse, P = perpendicular, and B = base.

As per the given question, here H = 13 and P = 5

Substitute the values of H = 13 and P = 5 in the Pythagorean Theorem,

(13)² = (5)²+ B²

169 = 25 + B²

B² = 169 - 25

B² = 144

B = √144

B = 12 units

Therefore, the length of the unknown side is 12 units,

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Selena needs 4 more hours to prepare 264 more pancakes.

Unitary method is a process of finding the value of a single unit, and use this value to find the value of the required number of units.

Given is Selena made pancakes for an all-day breakfast fundraising event. She made 132 pancakes in 2 hours. Selena needs to make 264 more pancakes.

We have -

The rate at which Selena is making pancakes = 132 pancakes in 2 hours.

Number of pancakes left to be made = 264

Now, in 2 hrs she makes 132 pancakes

Then, in 1 hr she will make (132/2) or 66 pancakes.

Now, she makes 66 pancakes in 1 hour.

So, she will make 1 pancake in (1/66) hours

Therefore, she will make 264 pancakes in (264/66) or 4 hours.

Therefore, she will need 4 more hours to prepare 264 more pancakes.

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The correct answer for the given problem is option (D) .

growth rate in the initial population of 1.08.. So, the equation for solving this population growth problem is 10,000(1.08) ²⁰

Before twenty years, the actual population was 10,000.

Population growth per year = 8% = ((100+8)10,000)/100=10,800.

So, there will be an addition of 800 people to the population every year.

After a period of twenty years, the total population was 10,000 + 19×(800) = 25,200.

Population for t years = (Initial Population)× (Growth or Decay Rate)×time

Using the above population increment formula,

Time( in years) ----->Population

0------>10000

1------->10000 (1.08)

2------->10000(1.08)(1.08)

3------->10000(1.08)(1.08)(1.08)

------------------

n ----->10000(1.08)

Here, we are required to have a population after 20 years, i.e., n= 20. The required equation, which is used for solving population growth problem, is 10000(1.08)²⁰

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Answer:

7 # there were 7 people in the group

Step-by-step explanation:

C = 6.00 + 29.99x # the equation given

215.93 = 6.00 + 29.99x # 215.93 is the total so substitute it for C. Now we solve for x

209.93 = 29.99x # We subtracted 6 from both sides

7 = x # We divided 29.99 from both sides

7 is our answer

We want to find the places where the line

2x - 3y = 12

intercepts y-axis and x- axis

When the line intercepts y axis, we know that x=0, we replace it in the equation so we can find y value:

2x - 3y = 12

↓

2 · 0 - 3y = 12

↓

0 - 3y = 12

-3y = 12

y = 12 / -3

y = -4

In the same way, we find the interception with x- axis when y = 0. We find the value of x replacing y by 0 in the equation:

2x - 3y = 12

↓

2x - 3 · 0 = 12

↓

2x - 0 = 12

2x=12

x = 12 / 2

x = 6

We locate both points: y = -4 and x = 6:

Finally, we join the points with a straight line

The domain of the given function given range is {1.25, -0.25, 1.25, 4.75}

The range of values that we are permitted to enter into our function is known as the domain of a function.

The x values for a function like f(x) make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of value.

Given the range of the function as {-5, -3, 0, 7}

Determine the domain from the function 4x - 2y = 5

4x - 2y = 5

4x - 2(-5) =5

4x + 10 = 5

4x = 5

x = 5/4 = 1.25

If y = -3

4x - 2y = 5

4x - 2(-3) =5

4x + 6 = 5

4x = -1

x = -1/4 = -0.25

If y = 0

4x - 2(0) =5

4x - 0 = 5

4x = 5

x = 5/4 = 1.25

If x = 7;

4x - 2y = 5

4x - 2(7) =5

4x - 14 = 5

4x = 19

x = 19/4 = 4.75

Therefore the equivalent domain of the function is {1.25, -0.25, 1.25, 4.75}

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Answer:

3.75x + $119 = $400.25

x  = $75

Step-by-step explanation:

Lauren needed to get her computer fixed. She took it to the repair store. The technician at the store worked on the computer for 3.75 hours and charged her $119 for parts. The total was $400.25. Write and solve an equation which can be used to determine a, the cost of the labor per hour.

3.75x + parts = $400.25

so:

3.75x + $119 = $400.25

subtract $119 from both sides:

3.75x + $119 - $119 = $400.25 - $119

3.75x = $281.85

divide both sides by 3.75

3.75x/3.75 = $281.85/3.75

x = $75

so the tech charged $75 per hour.

Solution

For this case we have the following, the sum of the angles needs to be 360 since we have a circumference:

10a-4 +6a-2 +8a+6=360

Regrouping we have:

10a +6a +8a -4 -2 +6= 360

24a= 360

a= 360/24= 15

Step-by-step explanation:

You can add the two fractions by turning 1/2 and 5/6 to have the same denominator. Turn 1/2 into a fraction with a denominator of 6. That simplifies to 1 1/3. Hope this helps yo

Let's call x to an unknown even integer. The next (consecutive) even integer will be x + 2. For instance, if x = 6, then the next even integer will be 6 + 2 = 8.

In consequence, the sum of two consecutive even integers is:

x + (x + 2)

It would take 9 Teenagers to finish a very large pizza in $15$ minutes.

From the knowlegde of Propotional method/ subject formular in mathematics;

From the questions:

12 Teens finished a very large pizza in $20$ minutes.

The number of teens to finish a very large pizza in $ 15 minutes would calculate thus,

12 Teens=$20$ minutes.

x Teens=$15$ minutes.

then we cross multiply:

x Teens × $20$ minutes =$15$ minutes × 12 Teens

making  x Teens subject of the formula we have;

x Teens=$15$ minutes × 12 Teens/$20$ minutes

x Teens=9 Teens

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The angles are which alternate exterior angles include the following: A. ∠XWY and ∠STR.

Parallel lines can be defined as two (2) lines that are cut through by a transversal and they always have the same (equal) distance apart and never meet.

The alternate exterior angle theorem states that when two (2) parallel lines are cut through by a transversal, the alternate exterior angles that are formed lie outside the two (2) parallel lines, are located on opposite sides of the transversal, and are congruent angles.

In conclusion, we can logically deduce that both ∠XWY and ∠STR are alternate exterior angles because they lie outside the two (2) parallel lines and are located on opposite sides of the transversal.

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Answer:

A: $188.75

B: $566.25

Step-by-step explanation:

To find the amount of the discount you can either multiply the original price ($755) by 1/4 or you can divide by 4.

Either way will get you $188.75. This is a quarter of the original price and is what is subtracted from the original sale price ($755). To find the sale price after the discount you do:

755-188.75=$566.25.

To check this you can do 755 × 3/4.

Hope this helps.

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Answer:

What he said

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

There are 4.5 diamonds, which represent 9 hours in total.

This corresponds to 9/3 = 3 circles.

Answer:

3 circles

Step-by-step explanation:

For the pig, it's 4.5 squares. Each square is two hours, and 4.5*2 is 9. Each circle is 3 hours, and 9 divided by 3 is 3. Therefore, the answer is 3 circles.

The t-shirts she sell is 24.

What is profit and selling price?

Profit is considered as the gain amount from any business activity. Whenever a shopkeeper sells a product, his motive is to gain some benefit from the buyer in the name of profit.

The selling price is the price that the buyer pays to buy a product or goods. This is a price above cost and includes a profit ratio.

According to Question, Christine sold the t- shirts at $4 each and she earned a profit of $71 and his total expenses were $25

Let the total number of t- shirts sold by Christine be "x"

Profit = Selling price – Expenses

Selling price is given as:

selling price = total number to t-shirt sold ×price of each t shirt

selling price = n ×4

71 = (n×4) -24

71 + 25  = n×4

96/4 = n

n = 24

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The △ABE is congruent to △CDE (△ABE ≅ △CDE) under AAA, ASA, SSS, and SAS conditions.

So, △ABE ≅ △CDE:

Therefore, the △ABE is congruent to △CDE (△ABE ≅ △CDE) under AAA, ASA, SSS, and SAS conditions.

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Answer:

y-intercept= 12.99      slope= 15.00x+12.99

Step-by-step explanation:

P(A) = P(6) = 0.003

answer: 0.003

There are [tex]700[/tex] children and [tex]1300[/tex] adults.

What is system of linear equations?

A System of Linear Equations is when we have two or more linear equations working together.

Let [tex]x[/tex] be number of children and [tex]y[/tex] be number of adults.

Since [tex]2000[/tex] people enter the zoo then [tex]x+y=2000.[/tex]

The admission fee at a local zoo is $ [tex]1.50[/tex] for children and $ [tex]5.00[/tex] for adults and $[tex]7550.00[/tex] collected then [tex]1.5x+5y=7550[/tex].

Thus there are two linear equations to solve.

Substitute [tex]x=2000-y[/tex]  in  [tex]1.5x+5y=7550.[/tex]

[tex]1.5(2000-y)+5y=7550[/tex]

[tex]3000-1.5y+5y=7550[/tex]

[tex]3000+3.5y=7550[/tex]

[tex]3.5y=7550-3000[/tex]

[tex]3.5y=4550[/tex]

[tex]y=\frac{4550}{3.5}[/tex]

[tex]y=1300[/tex]

So [tex]x=2000-y=2000-1300=700.[/tex]

Therefore there are [tex]700[/tex] children and [tex]1300[/tex] adults.

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