What is the equation of the line that passes through (0, 3) and (7,0)?
A.y =3/7x-3
B.y=3/7x+3
C.y=-3/7x+3
D.y=-3/7x-3

Answer:

Question 1. (2.2, -1.4)

Question 2. (1.33, 1)

Step-by-step explanation:

Equations for the given lines are

-----(1)

It is given that this line passes through two points (0, 2.5) and (2.2, 1.4).

------(2)

This equation passes through (0, -3) and (2.2, -1.4).

Now we have to find a common point through which these lines pass or solution of these equations.

From equations (1) and (2),

x =

x = 2.2

From equation (2),

y = -1.4

Therefore, solution of these equations is (2.2, -1.4).

Question 2.

The given equations are y = 1.5x - 1 and y = 1

From these equations,

1 = 1.5x - 1

1.5x = 2

x =

Therefore, the solution of the system of linear equations is (1.33, 1).

The correct approximate solution of the system of linear equations[tex]\( y = 1.5x - 1 \) and \( y = 1 \) is \( (1.33, 1) \).[/tex]

To find the solution, we need to set the two equations equal to each other since they both equal \( y \). This gives us the equation:

[tex]\[ 1.5x - 1 = 1 \][/tex]

Now, we solve for [tex]\( x \)[/tex]:

[tex]\[ 1.5x = 1 + 1 \][/tex]

[tex]\[ 1.5x = 2 \][/tex]

[tex]\[ x = \frac{2}{1.5} \][/tex]

[tex]\[ x = 1.\overline{3} \][/tex]

[tex]\[ x \approx 1.33 \][/tex]

Having found [tex]\( x \)[/tex], we can now find the corresponding [tex]\( y \)[/tex] value by substituting [tex]\( x \)[/tex] into either of the original equations. Since [tex]\( y = 1 \)[/tex] is given, we already know that [tex]\( y \)[/tex] is exactly 1. Therefore, the solution to the system is approximately [tex]\( (1.33, 1) \)[/tex].

Without additional information about the height or area of the base of the prism, it is impossible to determine the base length from the volume alone.

To determine the base length of a prism when the volume is known, one must have additional information about the prism, such as the area of the base or other dimensions. Since the question does not provide any information about the height or the area of the base, we cannot calculate the base length solely from the volume. Typically, the volume of a prism is calculated using the formula V = base area × height. Without knowing either the base area or the height of the prism in this question, we cannot find the base length. Thus, we cannot choose from the provided options (10 inches, 12 inches, 13 inches, 15 inches) without additional information about the prism.

Answer:

0.53333333333

Step-by-step explanation:

The fraction of the class that is boys is 16/30.Therefore, the decimal equivalent the fraction of boys in Daniel's class is 0.53.

The fraction of the class that is boys is obtained by dividing the number of boys by the total number of students. In this case, there are 16 boys and 30 students in total. The fraction is therefore 16/30.

To write this fraction as a decimal, divide the numerator (16) by the denominator (30). The decimal equivalent of 16/30 is approximately 0.5333.

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Answer:

C. The vertex of the function doesn't change.

Answer:

1) x/8+ x/16= 3/4    2) 4 miles

Step-by-step explanation:

The table is an illustration of distance, rates (speed) and time.

From the question, we have:

[tex]t =45\ mins[/tex] --- total time spent

Convert to hours

[tex]t =\frac{45}{60}hr[/tex]

Reduce fraction

[tex]t =\frac{3}{4}hr[/tex]

The times spent to school and back home are given as:

[tex]t_1 = \frac x8[/tex]

[tex]t_2 = \frac x{16}[/tex]

So, we have:

[tex]t_1 + t_2 = t[/tex]

This gives:

[tex]\frac x8 + \frac x{16} = \frac 34[/tex]

Hence, the equation that can be used to solve for x is: [tex]\frac x8 + \frac x{16} = \frac 34[/tex]

Take LCM

[tex]\frac{2x + x}{16} = \frac 34[/tex]

[tex]\frac{3x}{16} = \frac 34[/tex]

Multiply through by 16

[tex]\frac{3x}{16}\times 16 = \frac 34 \times 16[/tex]

[tex]3x = 12[/tex]

Divide both sides by 3

[tex]x = 4[/tex]

The distance to school and back home are given as:

[tex]d_1 = d_2 = x[/tex]

So, we have:

[tex]d_1 = d_2 = 4[/tex]

This means that Gerry lives 4 miles from school

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Answer:

856.4

Step-by-step explanation:

10% of 8564 =856.4

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

Explanation:

The rule is that if [tex]|a| \le k[/tex] for some positive number k, then it can be written as the compound inequality [tex]-k \le a \le k[/tex]. This is a shorthand way of writing the two inequalities [tex]a \ge -k \ \text{ and } \ a \le k[/tex] combined together.

note: [tex]-k \le a[/tex] is the same as [tex]a \ge -k[/tex]

From here, we replace k with 3

Therefore, [tex]|a| \le 3[/tex] turns into [tex]-3 \le a \le 3[/tex] which breaks down further to [tex]a \ge -3 \ \text{ and } \ a \le 3[/tex]

The keyword "and" is important as we can't pick one or the other. We must pick both [tex]a \ge -3[/tex] and also [tex]a \le 3[/tex]

Answer:

Choice 2.  

Step-by-step explanation:

Answer:

B. 5,200

Step-by-step explanation:

Sarah's essential (fixed) expenses = $750 per month

Her essential (flexible) expenses = $500 per month

Her non-essential expenses = $250 per month

Her total monthly living expenses = 750 + 500 + 250 = $1,500

Sarah wants an emergency fund of 5 times monthly living expenses.

1500 × 5 = $7,500

Currently she is having her emergency fund savings account is = $2,300

She needs to save more = 7,500 - 2,300 = $5,200

Sarah need to save more $5,200.

Sarah need to save $5,200 to have an adequate emergency fund.

An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.

Now it is given that,

Sarah's essential (fixed) expenses = $750 per month

Her essential (flexible) expenses = $500 per month

Her non-essential expenses = $250 per month

⇒ total monthly living expenses = 750 + 500 + 250 = $1,500

∵ Sarah wants an emergency fund of 5 times monthly living expenses.

∴ emergency fund = 1500 × 5 = $7,500

Currently she is having her emergency fund savings account = $2,300

Thus, Amount needs to be save = 7,500 - 2,300 = $5,200

Thus, Sarah need to save $5,200 to have an adequate emergency fund.

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Answer: 397.39 cm2

Step-by-step explanation:

Hi, first we have to calculate the area of the circle:

Area of a circle = π x r^2

Replacing with the values:

A(C) =π x 12^2 = 452.39cm2

Now, we have to calculate the rectangle area:

Rectangle area = width x length = 5 x11 = 55cm2

Finally, since the shaded region is the circle and the rectangle is inside of it, we have to subtract the area of the rectangle to the area of the circle:

452.39 -55 = 397.39 cm2

Feel free to ask for more if needed or if you did not understand something.

Answer:

397.39

Step-by-step explanation:

extras...

Answer:

Volume of the completes tower = 160 units³

Step-by-step explanation:

Martin is using unit cubes to build a tower in the shape of rectangular prism.

Bottom layer of the prism is in the square shape.

Since number of unit cubes used in the bottom layer = 16

So, one side of the square base will measure = √16 = 4 units

Therefore, Length = width = 4 units

On this base, additional layers added on the top = 9

Therefore, height of the tower = (9 + 1) = 10 units (each layer having 16 cubes)

Volume of the tower = Volume of the rectangular prism

                                  = Length × width × height

                                  = 4×4×10

                                  = 160 cubic units.

Volume of the completed tower will be 160 cubic units.

The total volume  in cubic units of the completed tower is 160 units³.

Since number of unit cubes used in the bottom layer = 16

So, one side of the square base should be

= √16 = 4 units

Now

Length = width = 4 units

The additional layers added on the top = 9

So, height of the tower = (9 + 1)

= 10 units

Now

Volume of the tower = Volume of the rectangular prism

                                = Length × width × height

                                 = 4×4×10

                                 = 160 cubic units.

hence, The total volume in cubic units of the completed tower is 160 units³.

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Answer:

Step-by-step explanation:

Recognize that the (1/2) in  4n=1/2(2n-12)  is a coefficient, the coefficient of the (2n - 12) term.

Thus, multiply both sides of this equation 4n=1/2(2n-12) by 2, to obtain:

8n = 2n - 12

Combining like terms, we get 6n = -12, so that n = -2.  

Multiplying both sides of the equation by a constant does not in any way affect your ability to find a solution and does not change the solution.

Answer:

= 3

Step-by-step explanation:

4 − 5 + 9 = 5 − 9

− + 9 = 5 − 9

i hope this helps<3

:)

The value of solution of expression is,

⇒ x = 3

We have to given that;

Mathematical expression is,

⇒ 4x - 5x + 9 = 5x - 9

Now, We can simplify as;

⇒ 4x - 5x + 9 = 5x - 9

⇒ - x + 9 = 5x - 9

⇒ 9 + 9 = 5x + x

⇒ 18 = 6x

⇒ 6x = 18

⇒ x = 18 / 6

⇒ x = 3

Thus, The value of solution of expression is,

⇒ x = 3

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Answer:

This does make a right triangle

Step-by-step explanation:

Because when you square 8 you get 64 and when you square 15 you get 225. Then you add those together and you should get 289 so when you find the square root of 289 is 17 which makes those number true

Yes, a triangle with side lengths a = 8, b = 15, and c = 17 is a right triangle.

Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We can apply this theorem only in a right triangle.

Example:

The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.

Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm

We have,

Yes, a triangle with side lengths a = 8, b = 15, and c = 17 is a right triangle. This is because these side lengths satisfy the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, we have:

a² + b² = 8² + 15² = 64 + 225 = 289

c² = 17² = 289

Since a² + b² = c², these side lengths satisfy the Pythagorean theorem, and the triangle is a right triangle.

Thus,

Yes, a triangle with side lengths a = 8, b = 15, and c = 17 is a right triangle.

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Answer:

2.9

Step-by-step explanation:

The mean is the average of the date It is surprisingly easy to calculate: add up all the data, then divide by how many data points there are.

Becker's data added up is 28. Kayla's data added up is 30. The total amount is 58.

The amount of data points are 20.

58/20 = 2.9

Hope this helps!

The mean number of games chess team members play per day is 2.9

Becker = 5,2,4,1,1,4,5,3,2,1

= (5 + 2 + 4 + 1 + 1 + 4 + 5 + 3 + 2 + 1) / 10

Mean average = 28 / 10

= 2.8

Kayla = 2,3,1,1,4,1,5,3,5,5

= (2 + 3 + 1 + 1 + 4 + 1 + 5 + 3 + 5 + 5) / 10

= 30 / 10

= 3

Total = Becker + Kayla

= 2.8 + 3

= 5.8

Mean average = 5.8 / 2

= 2.9

Therefore, the mean number of games chess team members play per day is 2.9

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Answer:22.5

Step-by-step explanation: just saying that is no the actual answer you still have to estimate it

The equation n² =45 is solved step by step. The nearest perfect squares, 36 and 49, are identified. Using a calculator, the square root of 45 is found to be approximately 6.708, satisfying the equation.

let's go through the steps to solve n² = 45 in detail:

Step 1: Find the Perfect Squares

The closest perfect squares to 45 are 6² = 36 and

7² = 49.

Since 45 is between 6² and 7², we'll use these values as reference.

Calculate the Square Root

We'll use a calculator to find the square root of 45.

√45 ≈ 6.708203932499369

So, the square root of 45 is approximately 6.708203932499369.

Step 3: Solve for n

Since we're looking for n² = 45, we have √n = 45.

Plugging in the calculated square root:

√n = 45

n ≈ 6.708203932499369

Thus, the approximate value of n that satisfies the equation n² = 45 is n ≈ 6.708.

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Answer:

10/20=1/2

Step-by-step explanation:

Answer:

You are drawing a right triangle. So draw the two lines off of the right angle. Then write 5 along one line. That line is now BC, so you can start naming points and putting in lengths. Then, draw the hypotenuse (AB) going from the end of the line you were writing next to, to the other line. Make sure it is at least twice as long, because it is 13 long. Then, to find the length of the last line,  square 13, and subtract 25 from it. Take that number and find it's square root. You should get 12, which is your answer.

Step-by-step explanation:

Answer:

P(2 or fewer left-handed) = 9/25 = 0.36

Step-by-step explanation:

From Chayton simulations, we can see that in 9 simulations there are 2 or fewer left-handed students in a class of 20 students. He simulated 25 classes of 20 students, then the probability to find 2 or fewer left-handed is: 9/25 = 0.36

Answer:

C.Lines r and s and lines t and u must be parallel.

Step-by-step explanation:

Line r s and t must be parallel and c is closest to that lol

The lines r and s and lines t and u must be parallel option third "Lines r and s and lines t and u must be parallel" is correct.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have:

If Angle 2 is congruent to angle 4 and Angle 5 is congruent to angle 7.

From the information given we can draw lines r, s, t, and u(please attached picture)

From the picture, we can clearly see: lines r and s and lines t and u must be parallel.

Thus, the lines r and s and lines t and u must be parallel option third "Lines r and s and lines t and u must be parallel" is correct.

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Answer: The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola. The vertex of the parabola is (2,1) . So, the axis of symmetry is the line x=2.

Step-by-step explanation:

Answer:

What shapes can be cross sections of the rectangular pyramid?

A slice parallel to the base will take the shape of a

✔ rectangle

.

A slice perpendicular to the base and through the top vertex will take the shape of a

✔ triangle

.

A slice perpendicular to the base and not through the top vertex will take the shape of a

✔ trapezoid

.

A slice parallel to the base will take the shape of the rectangle. A slice perpendicular to the base and through the top vertex will take the shape of a "triangle".A slice perpendicular to the base and not through the top vertex will take the shape of a "trapezoid".

A slice perpendicular to the base and through the top vertex will take the shape of a .

A slice perpendicular to the base and not through the top vertex will take the shape of a .

Take a rectangle and the base. Now take four triangles such that each of them is connected to one-one side of the base rectangle and when they are taken together, they form a closed object.

That shape is called a rectangular pyramid.

A slice parallel to the base will take the shape of a "rectangle"

A slice perpendicular to the base and through the top vertex will take the shape of a "triangle".

A slice perpendicular to the base and not through the top vertex will take the shape of a "trapezoid".

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Answer: C(t) = -475.5*cos(t*pi/6) + 475.5

Step-by-step explanation:

We know that we have a sinusoidal relation, with a minimum at 9:00 am and at 9:00 pm.

If we define the 9:00 am as our t = 0, we have that the maximum, at 3:00pm, is at t = 6 hours.

and the other minimum, at 9:00pm, is at t = 12 hours.

Then we need to find a trigonometric function that has the minimum at t = 0, we can do this as:

-Cos(c*t)

when t = 0

-cos(0) = - 1

then we have a function:

C(t) = -A*cos(c*t) + B

where A, c and B are constants.

We know that at t = 0 we have 0 customers, and that at t = 6h we have 875 customers, that is the maximum.

then:

C(0) = 0 = -A + B

this means that A  = B, then our function is:

C(0) = -A*cos(c*t) + A.

now, at t = 6h we have a maximum, this means that -A*cos(c*6h) = A

then:

C(6h) = A + A = 875

2A = 875

A = 875/2 = 437.5

and we also have that, if -cos(c*6) = 1

then cos(c*6) = -1

and we know that cos(pi) = -1

then c*6 = pi

c = pi/6

Then our function is

C(t) = -475.5*cos(t*pi/6) + 475.5

Final answer:

On average, one customer arrives every two minutes at Somerset Mall on a Saturday, which means it takes six minutes on average for three customers to arrive. This question applies trigonometry, algebra, and statistical concepts.

Explanation:

A research firm finds that the average number of customers in Somerset Mall on a Saturday varies sinusoidally with time. The question involves understanding sinusoidal functions, their applications, and basic statistical concepts related to customer arrival rates. The sinusoidal nature of customer arrivals is a practical application of trigonometry and algebra in solving real-world problems.

Part a: Average Minutes Between Arrivals

Given that 30 customers arrive per hour, to find the average time between successive arrivals, we divide the number of minutes in an hour by the number of arrivals: 60 minutes / 30 customers = 2 minutes. Therefore, on average, one customer arrives every two minutes.

Part b: Time for Three Customers to Arrive

Since one customer arrives every two minutes on average, for three customers to arrive, it would take 3 * 2 minutes = 6 minutes on average.

The model's assumption that customers arrive one at a time and at a constant rate throughout the day simplifies the real-life complexity of customer behavior and peak shopping times. This is a critical consideration in the practical application of mathematical models in business.

Answer:

The vertex is (6, -4)

Step-by-step explanation:

f(x) =(х – 8)(х – 4)

First find the zeros

0 = (х – 8)(х – 4)

0 = x-8      0 =x-4

x=8          x=4

The zeros are x=8 and x=4

The vertex is 1/2 way between the zeros

(8+4)/2 = 12/2 =6

To find the y value, substitute 6 into the function

f(6) = (6-8) (6-4)

     =  -2 (2) = -4

The vertex is (6, -4)

Answer:

B. distribution skewed to the right, mean pulled to the right, median not effected

Step-by-step explanation:

When a distribution is skewed to the right, it means that the data is positively skewed or has more positive numbers than negative numbers.

An outlier can affect the mean of a distribution since a high value outlier will make the mean be much higher than the median. In this case, since the distribution is positively skewed, a high outlier will pull the mean to the right (to higher positive values).

The high outlier  in a data set affects the mean and median is

B. distribution skewed to the right, mean pulled to the right, median not effected

At the time When a distribution is skewed to the right, so it represents the data is positively skewed or it contains more positive numbers as compared to the negative numbers. An outlier can impact the mean of the distribution.

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Answer:  C) 297 in2

Step-by-step explanation:

Hi, to answer this question we have to apply the next formula:

Surface area of a square pyramid (S) = 2 (length of the base) slant + length of the base ^2

S = 2bs + b^2

Replacing with the values given:

S = 2 (9) 12 + 9^2

S = 216 +81 = 297 square inches

Feel free to ask for more if needed or if you did not understand something.

Answer:

あなたがこれを翻訳するなら私はあなたを愛しています

Step-by-step explanation:

私は英語がわかりませんが、答えは4倍になります

Step-by-step explanation:

2X alla seconda meno 3