Every year 3% of university students drop out of their course at
a University. This year 12 people dropped out. How
many people started at the beginning of the year?

In thia problem we have that

m<1 and m< 2 are consecutive interior angles

that means

m<1+m<2=180 ------> supplementary angles

substitute the given values

4x+16+2x-22=180

solve for x

6x-6=180

6x=180+6

6x=186

x=31

Find the value of m<1

m<1=4(31)+16

m<1=140 degrees

Answer: 0.072 cm^3

Step-by-step explanation:

density=mass*volume

Volume=gensity/mass

5.4/75=0.72

Sandy hiked 13.6 miles on Sunday

The correct option is option c)

What is subtraction?

Subtraction is a basic arithmetic operation in which we remove a number from another number. the other arithmetic operations include addition ,multiplication and division

We are given that, Sandy hiked a total of 37.8 miles in 3 days.

Also that She hiked 12.3 miles on Friday and 11.9 miles on Saturday.

Let the miles hiked by her on Sunday be x

Hence the equation can be given as

37.8=12.3+11.9+x

x=37.8 - 24.2

x= 13.6 miles

Sandy hiked 13.6 miles on Sunday

Hence the correct option is option c)

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The distance from Jessica's school to her house is 7.48 miles.

Consider following diagram.

In right triangle ABC, vertex B is the Jessica's house vertex A be her school.

The route from her house to school consists of two straight legs.

She drives straight for 5 miles, and then she makes a right turn of 45 degrees and drives another 9 miles.

⇒ BC = 5 miles and AC = 9 miles

We need to find the distance from Jessica's school to her house in miles.

i.e., we need to find AB

Using Pythagoras theorem,

AC² = AB² + BC²

9² = AB² + 5²

AB = √(81 - 25)

AB = 7.48

Therefore, the distance from Jessica's school to her house is 7.48 miles.

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The correct point slope form is  y - 1 = 2 ( x - 9).

What is the point slope form?

The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form. Every point on a line must satisfy the equation for the line in order for it to exist. This implies that a line is represented by a linear equation in two variables. Depending on the facts at hand, there are different ways to find a line's equation.

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Using fractions, The faster one is : Robert

A fraction, which also symbolizes a piece of a whole, is a mathematical symbol for any number of equal parts. A fraction, such as one-half, eight-fifths, and three-quarters, denotes the number of components of a specific size when used in conversational English.

By converting the incorrect fraction, produce an appropriate fraction.

Jocab travels 5 miles in 1 1/2 hours; therefore, 1 1/2 hours is 3/2 hours in minutes, or 3/2 x 60 minutes.

Robert: Three miles in seventy-five minutes = forty-five minutes.

If Robert runs 3 miles in 45 minutes, he completes 6 miles, as opposed to Jocab's 5 miles in 90 minutes.

Robert thus moved more quickly than Jocab.

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Answer:C

Step-by-step explanation:

i believe it is C because at first i thought it was B then realized it was a negative but c is a positive and a grater number C=5.8

Answer:

e=32, f=79, d=69

Step-by-step explanation:

32 and e are vertical angles, so they share the same value. Same with 69 and d. 69+e+f=180, so process of elimination gives you your answer. Lmk if you need any more help or a better explanation, hope you get ungrounded !

Answer:

f = 79 , e = 32 , d = 69

Step-by-step explanation:

32 + 69 + f = 180

101 + f = 180

f = 79

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

69 + 79 + e = 180

148 + e = 180

e = 32

The equation of the given line in the diagram above is expressed as: b. y = 2/3x.

For a line that passes through the origin (0, 0) of a graph, the equation that represents the line can be written in slope-intercept form as y = mx, where the slope of the line is represented as m.

The y-intercept of this type of line is zero, that is why we have the equation expressed as y = mx. Where the y-intercept is not equal to zero, the equation of the line would be expressed as y = mx + b, where b is the y-intercept and m is the slope of the line.

Find the slope of the line using two points on the line, (0, 0) and (3, 2):

Slope of the line (m) = (2 - 0)/(3 - 0)

Slope of the line (m) = 2/3.

To write the equation of the line, substitute m = 2/3 into y = mx:

y = 2/3x.

The equation is: B. y = 2/3x.

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Answer:

second graph

Step-by-step explanation:

the graph of a proportional relationship is a straight line passing through the origin.

the only graph with points which lie on a straight line with a point at the origin is the second graph.

Answer:

E. [tex] a = 5-2b [/tex]

Step-by-step explanation:

how to find the value of a, we need to subtract 2b from both side to single out the variable

a + 2b = 5

subtract 2b from both sides

a + 2b - 2b = 5 - 2b

a = 5 - 2b

Therefore, Option E is the correct answer

Answer:

x = 5

Step-by-step explanation:

Take your starting equation:

5x - 6 = 2x + 9

Your first step should be to isolate the variable, X, by having it on only one side of the equation. This can be done by subtracting one of the X values (either 5x or 2x) from either side, but I recommend the side with 2x since it's a smaller value and won't result in a negative.

(This is the right side of the equation)

2x + 9

- 2x

= 9

We need to do the same thing on the other side of the equation too, to balance both sides:

(This is the left side of the equation)

5x - 6

- 2x

= 3x - 6

This is our equation now:

3x - 6 = 9

The next step is to isolate X further by removing any constants (regular numbers) from the side with X. Since the constant on that side is -6, we need to add 6 to that side so that it's cancelled out, and do the same on the other side to balance.

(This is the left side of the equation)

3x - 6

+ 6

= 3x

And now for the other side:

(This is the right side of the equation)

9

+ 6

= 15

This is our current equation:

3x = 15

The final step is to get X completely isolated. X is being multiplied by 3, so we need to divide both sides of the equation by 3 to finally get the value of X.

(This is the left side of the equation)

3x

÷ 3

= x

And now for the other side:

(This is the right side of the equation)

15

÷ 3

= 5

Our final equation:

x = 5

We can check our answer by taking the final X value, 5, and inserting it into our beginning equation.

This is the beginning equation, as a reminder:

5x - 6 = 2x + 9

Replace all instances of X with its value, 5:

(5 · 5) - 6 = (2 · 5) + 9

After simplifying, the result is:

19 = 19, which means the X value is correct.

To determine how much flour is required for 24 cups of sugar, assume that 12 cup of flour is required.

There are in total six types of fractions such as:

8 cup of flour is mixed with 16 cup of sugar

So for 8 cup of flour need 16 cup of sugar

Need to find how much flour is needed for 24 cups of sugar

Assume the amount of flour needed is x.

   [tex]\frac{8}{16}[/tex] = [tex]\frac{x}{24}[/tex]

cross multiply them :

 [tex]\frac{8}{16}[/tex] = [tex]\frac{x}{24}[/tex]

[tex]8 * 24 =16x[/tex]

[tex]x = \frac{8 * 24}{16}[/tex]

x = 12

12 cup flour is needed for 24 cups of sugar

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Answer:

1+1=2

Step-by-step explanation:

1111111111111111111111

Answer:

Your friends shadow would be 9 foot 3 inches

Answer:

Father: 24 Son: 8

Step-by-step explanation:

Adition and subtraction

Answer:

24 acres of corn, so the equivalent ratio is 18 acres of barley to 24 acres of corn.

Step-by-step explanation:

18 ÷ 3 = 6, so multiply 4 × 6 to obtain 24 acres of corn.

Alternately: Let c be the number of acres of corn. Set up and solve this proportion.

[tex] \frac{3}{4} = \frac{18}{c} [/tex]

[tex]3c = 72[/tex]

[tex]c = 24[/tex]

Step-by-step explanation:

4n

it is 4 times the price of 1 notebook "n".

so the expression actually represents the cost of buying 4 notebooks and 1 pen.

n represents the cost of one notebook.

4n is the cost of 4 notebooks.

The study and use of numbers, their connections, and mathematical observations are topics covered by the area of mathematics known as arithmetic. The fundamental ideas in number theory, measurement, and calculation are frequently referred to as "arithmetic" (which is derived from the Greek word "arithmos," "number") (that is, the processes of addition, subtraction, multiplication, division, raising to powers, and extraction of roots).

As per the given data in the question:

Cost of one pen = $2.50

The expression that represents the cost of buying 4 notebooks

and a pen = 4n+ 2.50

For finding the product in the expression:

The product is 4n {4 multiplied by n}

Here, n represents the cost of one notebook.

Hence, 4n is the cost of 4 notebooks.

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Answer:

Yes

Step-by-step explanation:

We can say this because monomial is term used when an algebraic expression consisting of one term.

The amount Bennet will have when he turns 18 will be equal to $3020.

Compound interest is the type of interest charged by banks or institutions on individuals in which the amount after 1 year becomes the principle for the next year. It can be calculated daily, monthly or yearly etc. The formula for compound interest compounded daily will be

A = P(1 + r/n) ^nt, where A is the amount, P is the principle, which is equal to $2000, r is rate of interest which is 3.2% or 0.032, n is compounding frequency which is equal to 365 and t is the time which is equal to 13 years. Now, the amount will be

A = 2000(1 + 0.032/365) ^365×13

A = 2000(1.51)

A = $3020 which is the required amount.

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Step-by-step explanation:

Please draw your graph on graph paper unlike me with a proper scale to get accurate results. for parts d and e, I simply substituted the known value back into the original equation s= 20+ 5(t) for each one to either find the s or t value. But the question said to use your graph so you must extrapolate your graph (find the corresponding value for the value they gave) and put that answer. your answer should be correct even if it's a point off from the accurate answer.

draw graph and curve in pencil. you can even shade the region between t=0 and t=10.

if you have any questions feel free to ask, and I apologize if the work is a bit messy :)

The length of BK in the triangle is 8 units

The given parameters are

As a general rule, the median of a triangle divides the triangle into the following ratio

Ratio of median = 2 : 1

This means that

Ratio of median, BK : KU = 2 : 1

Substitute 4 for KU

So, we have

BK : 4 = 2 : 1

Multiply the right ratio by 4

BK : 4 = 8 : 4

By comparison, we have

BK = 8

Hence, the value of BK is 8 units

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Answer:

It's A

Step-by-step explanation:

[tex]4x - 1 - 3(1) - 3( - x) = 10 \\ 4x - 1 - 3 + 3x = 10 \\ 4x + 3x - 1 - 3 = 10 \\ 7x - 4 = 10 \\ 7x = 10 + 4 \\ 7x = 14 \\ \frac{7x}{7} = \frac{14}{7} \\ x = 2[/tex]

ATTACHED IS THE SOLUTION

The term that best describe the quadrilateral formed by the points A(2, 3), B(4, 6), C(8, 9), and D(5, 5) is option D. Kite

Quadrilateral:

A quadrilateral is the closed shape and a type of polygon that has four sides, four vertices and four angles.

The distance of the tow points can be calculated by using the formula,

d = √(x₂ - x₁)² + (y₂ - y₁)²

Where

(x₁, y₁) and (x₂, y₂) represents the coordinates of the two endpoints on the side

Given,

Here we have the points  A(2, 3), B(4, 6), C(8, 9), and D(5, 5) that forms the quadrilateral.

And we need to find the shape of the quadrilateral.

Let us consider the coordinates of the vertices of the quadrilateral are A(2, 3), B(4, 6), C(8, 9), and D(5, 5),

To find its shape, we have to calculate the length of the sides of the quadrilateral can be found using the distance formula.

For side AB, we have the distance of

d1 = √(6 - 3)² + (4  - 2)²

d1 = √13

For side BC, we have the distance of

d2 = √(9 - 6)² + (8 - 4)²

d2 = √9 + 16

d2 = √25

d2 = 5

Now we have to take side CD,

d3 = √(5 - 9)² + (5 - 8)²

d3 = √16 + 9

d3 = √25

d3 = 5

Finally, side DA, we have;

d1 = √(3 - 5)² + (2  - 5)²

d1 = √13

Therefore, the given quadrilateral has two pairs of equal adjacent sides and the angles are equal at the meeting point of the two squares, it is best described as a kite.

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Answer:

Where is the question???