An isosceles trapezoid has perimeter of 70. Each of the congruent nonparallel sides has length 13, and the height of the trapezoid is 12. How long is the longest side?

She sold 125 sandwiches and 175 viands as per the equation using substitution method as the definition of substitution method says, "The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable from one equation is substituted in the other equation in this method, as the name implies".

A mathematical formula is an equation that uses algebraic operations like add, subtract, multiply, divide, raise to a power, take the natural logarithm, take the cosine, or some combination of operations to express one variable as a combination of other variable(s). One-step equations can be solved in four different ways: by adding, subtracting, multiplying, and dividing. In an equation, both sides will remain equal if we add the same amount to each side. The "scale" (or equation) must ALWAYS be balanced when solving math equations so that both sides are ALWAYS equal.

Here,

Let x be the sandwiches she sold and y be the viands she sold.

x+y=300

y=50+x

x+50+x=300

2x+50=300

2x=250

x=125

y=50+125

y=175

In accordance with the equation and applying the substitution method, she sold 125 sandwiches and 175 appetizers "The substitution method is an algebraic strategy for resolving simultaneous linear equations. This method, as the name suggests, involves substituting the value of a variable from one equation into the other equation ".

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To find the price per ounce for each grocery store we have to divide the price by the size of the bottle:

Hawkin's Grocery:

$0.25 per ounce

MItchell's Store:

$0.32 per ounce

Selena's Market:

$0.30 per ounce

Teresa's Store:

$0.20 per ounce

We can see that Teresa's Store has the lowest price per ounce

The measures of the numbered angles in the rhombus ABCD if m∠ABC = 49° are m∠1 = 24.5°, m∠2 = 90°, m∠3 = 24.5° and m∠4 = 65.5°.

We are given:

A rhombus ABCD and m∠ABC = 49°.

The diagonal of the rhombus divides the angles into 2 equal parts. Therefore,

m∠1 = m∠ABC / 2 = 49 / 2 = 24.5°

The diagonal AC is perpendicular to the diagonal DB.

And we know that diagonals bisect each at right angles.

So, m∠2 = 90°.

Opposite angles of the rhombus are equal.

Therefore,

∠B = ∠D

multiply both sides by 1/2, we will get;

1/2 ∠B = 1/2 ∠D

m∠1 = m∠3 = 24.5°

Sum of angles in a quadrilateral = 360°

360 -  98 = 262°

∠A = ∠C = 262 / 2 = 131

Therefore,

m∠4 = 1 / 2 ∠C

m∠4 = 1 /2 * 131

m∠4 = 65.5°

Thus, the measures of the numbered angles in the rhombus ABCD if m∠ABC = 49° are m∠1 = 24.5°, m∠2 = 90°, m∠3 = 24.5° and m∠4 = 65.5°.

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True about translations is they can help you see if two figures are congruent

What are translations?

In mathematics, a translation is an up, down, left, or right movement of a shape. Because the translated shapes appear to be exactly the same size as the original ones, they are consistent with one another. Just one or more directions have been altered. There is no change in the shape because it is simply being moved from one location to another.

Each point in a figure is moved the same distance in the same direction using a type of transformation known as translation.

Hence, they can help you see if two figures are congruent.

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Using conditional probability, it is found that there is a 0.83 = 83% almost 0.8403  probability that this student does spend more than $25 a week on gas, given that he/she does commute to school each day.

Probability: -

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%).

Conditional Probability :

Using conditional probability, it is found that there is a 0.83 = 83% = P( A∩ B) / P(A)

In which

In this problem:

Event A: Commute to school each day.

Event B: Spends more than $25 a week.

80% indicated that they commute to school each day. of those that commute to school each day, hence , P(A) = 0.8

Of those, 83% spend more than $25 a week on gasoline, hence .

                     P(B|A) = 0.83

Thus, 0.83 = 83% probability that this student does spend more than $25 a week on gas, given that he/she does commute to school each day.

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The answer to the inequality is P> 5

What is Inequality?

Inequality in mathematics, the relationship between two values that are not equal

To solve the inequality we follow the steps;

P+5 > 10

Subtract 5 from both sides

P + 5-5 > 10-5

P>5

Therefore, the answer to the inequality is P> 5

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There are 31 perfect square numbers that are less than 1000.

Among them there are 5 numbers which are 3 times an odd integer those are 9,81, 225, 441, 729

Answer: I believe it is A.

Step-by-step explanation:let me start by saying that D and B aren't true because u is greater than 3 to the square root of 3, which is roughly 5.2. So were left with A and C. Then we realize that 3 to the square root of 3 is the same as 3 to the square root of 3, so it can't be C, so were left with A. (I could be wrong, I'm not the smartest in math, but I hope this helped and wish you luck)

Answer:

====================

Given is 30° × 60° × 90° triangle.

The matching choice is A

The side opposite to 30 degree angle is 1/2. So,

The measure of side opposite to angle 60 degree is,

The measure of side x is,

The measure of hypotenuse is 2a. So,

So answers are,

and

1.

What do you know?

the troposphere extends 8 to 20 km above the Earth's surface. The surface temperature is 15°C and decreases at a rate of 6.5°C per kilometer away.

What do you want to find out?

The temperature at any point of the troposphere

What kind of answer do you expect?

Any value below 15°C

2. Define variables,

T is for temperature, and

d is the distance away from the surface

3. What is the b -value

b = 15

which is the Earth's surface temperature or the initial temperature for our problem

4. What is the slope

the slope 'm' equals -6.5

which means that the temperature decreases 6.5°C per km

5. write the equation

the general form for this equations is y = b + mx

thus, for our problem, the equation is: T = 15 - 6.5*d

6.

a) the slope represents the rate of change of temperature with respect to distance, since m = -6.5 °C/km , this means the troposphere is getting 6.5 °C colder per km away from Earth's surface

b) the y-intercept represents the Earth's surface temperature

Graph:

7. identify 3 points

when d = 0 then T = 15, so our first point is (0,15)

when d = 1 then T = 15 - 6.5 = 8.5 , so our second point is (1,8.5)

when d = 2 then T = 15 - 13 = 2 so our third point is (2,2)

8. calculate the slope

let's use this equation and this set of points,

let's replace and solve

We can see that it does match the slope from our model, which is -6.5

9. graph the line and the points,

10. Complete the sentence

... ends between 8 km and 20 km above Earth.

11. temperature at the farthest point

when d = 20 then,

... the temperature is -115°C

12. Temperature range,

from... 15 °C to -115 °C

Answer:

B

Step-by-step explanation:

Answer:

Step-by-step explanation:

i think its B

By using the concept of percentage, the equation which is equivalent to  60% of 25 is [tex]0.6 \times 25 = x[/tex]

What is percentage?

Suppose there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage.

For example 2% means [tex]\frac{2}{100}[/tex]. Here 2 is expressed as a fraction of 100.

Here,

Using concept of percentage.

Let 60% of 25

[tex]\frac{60}{100}\times 25 = x\\0.6 \times 25 = x[/tex]

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The relation is a function because (a) Yes, because every x-value corresponds with a single y-value.

From the question, we have the graph to represent the given parameters that can be used in our computation

We are to find out if the graph represents a function

For a graph to represent a function, the graph must pass the vertical line test

This means that a line drawn from the x-axis must touch the points at most once

In this case, the graph would pass the vertical line test because no two points have the same y coordinate

Hence, it is a function

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The fraction of 2 hrs 15 minutes to 1/4 of an hour is 1/9.

What is fraction?

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Since,

1 hour = 60 minutes.

2 hours = 120 minutes.

2 hours 15 minutes = 120 + 15 = 135 minutes.

1/4 of an hour = 60/4 = 15 minutes.

So, the fraction is,

[tex]\frac{15}{135} = \frac{1}{9}[/tex]

Therefore, the fraction of 2 hrs 15 minutes to 1/4 of an hour is 1/9.

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Let 'x' be the number of pounds of Yurly's package and let 'y' be the number of pounds of Anduray's package. Since the combined weight of both packages is 9 pounds, then:

now, we have that Yurly's package weights three pounds more than two times the weight of Anduray's, we can write this as:

thus, we have the following system of equations to represent this situation:

Given:-

7th term is 77 and 8th term is 231.

To find:-

The common ratio.

Now to find the common ratio we divide both the numbers. we get,

So the common difference is 3.

So the common ratio is 1/3.

Answer:

3

Step-by-step explanation:

Geometric sequence:

        [tex]\sf Common \ ratio = \dfrac{(n+1)^{th} \ term}{n^{th}}[/tex]

                              [tex]\sf = \dfrac{8^{th} \ term}{7^{th} \ term}\\\\\\ =\dfrac{213}{77}\\\\\\=3[/tex]

Given

Arielle plans to purchase hanging baskets for her front porch. There are three businesses in her area that sell hanging baskets and she plans to purchase the baskets from one of these business.

To find: Which answer best describes the sample and population?

Explanation:

It is given that,

Arielle plans to purchase hanging baskets for her front porch. There are three businesses in her area that sell hanging baskets and she plans to purchase the baskets from one of these business.

That implies,

Sample: all available hanging baskets at one of the businesses in town that sells them.

And,

Population: all available hanging baskets at the three businesses in town that sell them.

Answer:

∡BCA = 29

∡BOC = 58

Explanation:

The angles BDC and BAC form the same arc on the circle, the arc BC. Then, these angles have the same measure, so

∡BCA = ∡BDC

∡BCA = 29

Then, we can use the inscribed angle theorem to find the arc BC as follows

Therefore, arc BC has a measure of 58 degrees, which means that ∡BOC is equal to

∡BOC = Arc BC

∡BOC = 58

So, the answers are

∡BCA = 29

∡BOC = 58

Answer:

Rides cost $4

Games cost $2.50

Step-by-step explanation:

Let g = cost of games

Let r = cost of rides

6g + 3r = 27

2g + 9r = 41  Multiple this through by -3 and then add to the equation above.

-3(2g + 9r) = (41) -3

-6g - 27r = - 123

6g + 3r = 27

       -24r = -96  Divide both sides by -24

r = 4  This is the cost of the rides.

Plug is 4 for r in either of the two original equations to solve for g

6g + 3r = 27

6g + 3(4) = 27

6g + 12 = 27  Subtract 12 from both sides

6g = 15  Divide both sides by 6

g = 2.5  This is the cost of the games.

The rate of change of the company Water's Edge rafts is greater than Ryan’s Rafts.

The slope is the ratio of rising or falling and running. The difference between the ordinate is called rise or fall and the difference between the abscissa is called run.

From the graph, the two points are taken as (0, 0) and (1, 6). Then the slope of the Water's edge rafts will be given as,

⇒ (6 - 0) / (1 - 0)

⇒ $6 per hour

From the table, the two points are taken as (1, 15) and (5, 24). Then the slope of Ryan's rafts will be given as,

⇒ (24 - 15) / (5 - 1)

⇒ 9 / 4

⇒ $2.25 per hour

The rate of change of the company Water's Edge rafts is greater than Ryan’s Rafts.

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Let base = x

Height = 2x + 3

The height is 2x + 3 and the base is just x.

The number of heavy equipment operators employed=16

The number of laborers employed=14

Assume

x=number of heavy equipment operators employed

30-x=number of laborers employed

From the question, we have

135x+97(30-x)=3518

135x+2910-97x=3518

38x=608

x=16

number of heavy equipment operators employed=16

number of laborers employed=14

Multiplication:

Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.

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Answer:

The number of heavy equipment operators employed=16

The number of laborers employed=14

Assume

x=number of heavy equipment operators employed

30-x=number of laborers employed

From the question, we have

135x+97(30-x)=3518

135x+2910-97x=3518

38x=608

x=16

Step-by-step explanation:

Answer:

Reflection over y-axis.

Step-by-step explanation:

The transformation being described is a reflection across the y-axis since we would have to flip the signs of the x-values to transform the function.  See pictures below.

Hope this helps.

Answer:

Step-by-step explanation:

window*

The compound inequality for the graph shown above is :

Answer:

b

Step-by-step explanation:

just took the test yyyyyyyyyyyyyyyyyyyyyyyyy

Answer: 2.5, 5.4

Step-by-step explanation:

[tex]-16t^2 +126t=213\\ \\ 16t^2 -126t+213=0\\\\t=\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(213)}}{2(16)}\\\\t \approx 2.5, 5.4[/tex]

To answer this question, we need to find the unit rate for the steady speed. Then, we can proceed as follows:

Then, we have that the unit rate, in this case, is 2/3 miles per minute.

Hence, the car will travel in 34 minutes:

Thus, the car will travel 222/3 miles in 34 minutes.

The car will travel in one hour or 60 minutes:

Then, the car will travel 40 miles in one hour or 60 minutes.

The equation is modelled as [tex]y\ = \frac{kx}{z^2}[/tex].

Given,

y varies directly with x

y varies inversely with square of z

According to given data the equation can be modelled as follows:

y varies directly with x, it can be written as [tex]y \ \alpha \ x[/tex]

and also y varies inversely with square of z, it can be written as [tex]y\ \alpha \ \frac{1}{z^2}[/tex]

Combining both, then we get,

[tex]y\ \alpha \ \frac{x}{z^2}\\\\y\ = \frac{kx}{z^2}[/tex]

Where, k is proportionality constant.

Thus, the combined equation is modelled as [tex]y\ = \frac{kx}{z^2}[/tex].

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Answer:

D. 2200 ft.lb/s

Explanation:

First, recall the standard conversion between horsepower and foot-pounds per second.

Therefore:

The correct choice is D.