Hi I need help with question 3 :) . Directions: For each real world situation, write and solve a system of equations . Give the solution as either an ordered pair or list what each variable is worth . Then explain what the solution means in terms of the situation

Given:

The Radius of the circle: 2.5 inch

To find:

The area of the circle

Step-by-step solution:

We know that:

The Area of the circle = π(r)²

The Area of the circle = π(2.5)²

The Area of the circle = 3.14 × (2.5)²

The Area of the circle =

Given,

The speed of first train is 175km/h.

The speed of second train is 225 km/h.

Consider, the time taken by first train to meet is x h.

The time taken by the second train to meet is (x-2) h.

The distance is calculated as,

At the meeting point the distance covered by both train is same,

So, taking the distance equation of both trains in equal,

The first train meet to second train after distance,

The second train meet to first train after distance,

Hence, both train meet after 1575 km from the station.

SOLUTION

Let the total number of cards in Ketin's card collection be k

Let the number of baseball cards be b, and

the number of football cards be f

Now, the ratio of baseball cards to football cards is 6 to 7, that is

Also, he has 120 baseball cards.

This means

So, the total number of cards in Ketin's card collection is

Hence the answer is 260

The volume of a cylinder is given by

V = pi r^2 h where r is the radius and h is the height

We are given the diameter is 5

r = d/2 = 5/2 = 2.5 in

V = pi ( 2.5)^2 (7)

V =pi ( 6.25)*7

V = 43.75 pi

Assuming a value for pi of 3.14

V =137.375 in ^3

Rounding to the nearest hundredth

V = 137.38 in ^3

Assuming a value for pi by using the pi button

V = 137.44468

Rounding to the nearest hundredth

V = 137.44 in ^3

The linear equation parallel to y= 3x + 7 is:

y = 3x - 2

A general linear equation is of the form:

y = m*x + b

Where m is the slope and b is the y-intercept.

Two lines are parallel only if the lines have the same slope and different y-intercepts.

So a line parallel to y = 3x + 7 will be of the form:

y = 3x + c

To find the value of c we use the point (3, 7) which must belong to the line, replacing the values in the linear equation:

7 = 3*3 + c

7 = 9 + c

7 - 9 = c

-2 = c

The linear equation is y = 3x - 2

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Answer:

The answer is C.

Step-by-step explanation:

In order to solve this, you must use an inequality from one side of the equation.

Inequality is the growing inequality between rich and poor.

First thing you do is divide by 4 from both sides.

[tex]\sf{\dfrac{4x}{4} > \dfrac{-8}{4}}[/tex]

Solve.

Divide these numbers goes from left to right.

-8/4=-2

[tex]\boxed{\sf{x > -2}}[/tex]

Therefore, the graph represents the solution set of the inequality of 4x>-8 is C, which is our answer.

I hope this helps, let me know if you have any questions.

Pizza diameter D is given in mixed form:

Now, me must compare D with the lenght of the square box.

Since the lenght of the box is L=6.38 in. Hence, the box is big enough to

fit the pizza.

Answer:

25 feet

Step-by-step explanation:

we can set up the proportional relationship of the drawing vs the actual size

so 1 inch to 5 feet would be 1:5

so then if we scale up 1 inch to 5 inch

then we have 1:5=5:Actual length of the bus

so then we have 5*5=25 feet

The Quadratic format is

The answer to the question is that the factors must multiply to form c

The longest at an airport has the shape of a rectangle and an area of 2,181,600 this runaway is 180 feet wide how long is the runaway

Remember that

The area ofa rectangle is equal to

A=L*W

in this problem we have

A=2,181,600 ft2

W=180 ft

substitute given values

2,181,600=L*180

Solve for L

L=2,181,600/180

Answer:

Step-by-step explanation:

In math, a group is a set equipped with an operation that combines any two elements of the set to produce a third element of the set.

Therefore, for 4 groups of a number.

Let x be the missing number

So, 4 multiply x:

Given the equation

To solve this first pass all x-related terms to the left side of the equation and all other terms to the right side:

And solve

Answer:

• m∠1 =168 degrees

• m∠2 =12 degrees

Explanation:

From the diagram, Angles 1 and 2 are on a straight line.

We know that the sum of angles on a straight line is 180 degrees.

Therefore:

Substituting the given values, we have:

The measures of angles 1 and 2 are:

The measures of angles 1 and 2 are 168 degrees and 12 degrees respectively.

From the graph, the solution of the graph is given by the area of intersection of the two functions. The are under the area of the two functions are (-4, 1), (-5, 0), (-4, 4)

Inga should use the first option that is [tex]2(x^2+6x+9)=3+18[/tex] to solve the quadratic equation.

Given equation:-

[tex]2x^2+12x-3=0[/tex]

We have to find which one of the given options are needed to solve the quadratic equation.

The given quadratic equation can be rewritten as:-

[tex]2x^2+12x[/tex]-3+3=0+3

[tex]\\2x^2+12x[/tex]-3 + 3 + 18=0 +3 +18

[tex]2x^2[/tex] + 12x + 18 = 0 + 3 + 18

Hence, the answer is the first option.

Quadratic equation

Quadratic equations are the polynomial equations of degree 2 in one variable of type [tex]f(x) = ax^2 + bx + c = 0[/tex]where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where ‘a’ is called the leading coefficient and ‘c’ is called the absolute term of f (x). The values of x satisfying the quadratic equation are the roots of the quadratic equation (α, β).

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Answer:

(f o g) = 464

Step-by-step explanation:

f(x) = x² - 3x + 4; g(x) = -5x

(f o g)(4) = f(g(4))

f(g(4)) = -5(4) = -20

f(g(4)) = (-20)² - 3(-20) + 4

f(g(4)) = 464

I hope this helps!

-3(x + 1) - 5

(-3)(x) + (-3)(1) -5

-3x - 3 -5

-3x - 8

-2(u + 3) + 4u

-2u - 6 + 4u

2u - 6

Answer:

C. Infinite Solutions

Explanation:

Given the equation

First, open the bracket

Since the left-hand side equals the right-hand side, the system has Infinite Solutions.

Given point:

(2, 24)

To find the constant proportionality:

In general, the constant proportionality is

Hence, the constant proportionality is 12.

Use a rule of three to find the amount of rooms wire with 3/62 rolls:

Given:

The current week hour wage is 8579

Total payroll =14081.

The hourly wage will be increased 8 %.

The 8% of 8579 is

The hourly wage will be increased by 686 next week.

The total payroll also will be increased by 686.

So the total Payroll Variance from the current week to next week is 686.

Hence option D is correct.

Let the price of each ticket be represented by

The price of two tickets will be

The tax on the price of the tickets is 6% which be represented as

The price of the two tickets after tax will be

Therefore,

The price of the tickets after adding an additional booking fee of $20 will be given below as

Since,

We were asked to get the algebraic expression person, we would therefore divide the above expression by 2

Hence,

The algebraic expression to represent the price per person using variable t is

=0.53t + 10

Answer: y = x/5 + 12/5

Explanation:

The first step is to find the equation of line AC

The equation of a line in the slope intercept form is expressed as

y = mx + c

where

m represents slope

c represents y intercept.

The formula for calculating slope of a line is expressed as

m = (y2 - y1)/(x2 - x1)

Considering line AC with points, A(2, 1) and C(1, 6),

x1 = 2, y1 = 1

x2 = 1, y2 = 6

m = (6 - 1)/(1 - 2) = 5/- 1 = - 5

Recall, if two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line. Negative reciprocal of - 5 is 1/5

Thus, slope of the perpendicular line passing through B(3, 3) is m = 1/5

We would find the y intercept, c of the line by substituting m = 1/5, x = 3 and y = 3 into the slope intercept equation. We have

3 = 1/5 * 3 + c

3 = 3/5 + c

c = 3 - 3/5

c = 12/5

By substituting m = 1/5 and c = 12/5 into the slope intercept equation, the equation of the line is

y = x/5 + 12/5

The row echelon form of the matrix is presented as follows;

[tex]\begin{bmatrix}1 &-2 &-5 \\ 0& 1 & -7\\ 0&0 &1 \\\end{bmatrix}[/tex]

The row echelon form of a matrix has the rows consisting entirely of zeros at the bottom, and the first entry of a row that is not entirely zero is a one.

The given matrix is presented as follows;

[tex]\begin{bmatrix}-3 &6 &15 \\ 2& -6 & 4\\ 1&0 &-1 \\\end{bmatrix}[/tex]

The conditions of a matrix in the row echelon form are as follows;

Dividing Row 1 by -3 gives:

[tex]\begin{bmatrix}1 &-2 &-5 \\ 2& -6 & 4\\ 1&0 &-1 \\\end{bmatrix}[/tex]

Multiplying Row 1 by 2 and subtracting the result from Row 2 gives;

[tex]\begin{bmatrix}1 &-2 &-5 \\ 0& -2 & 14\\ 1&0 &-1 \\\end{bmatrix}[/tex]

Subtracting Row 1 from Row 3 gives;

[tex]\begin{bmatrix}1 &-2 &-5 \\ 0& -2 & 14\\ 0&2 &4 \\\end{bmatrix}[/tex]

Adding Row 2 to Row 3 gives;

[tex]\begin{bmatrix}1 &-2 &-5 \\ 0& -2 & 14\\ 0&0 &18 \\\end{bmatrix}[/tex]

Dividing Row 2 by -2, and Row 3 by 18 gives;

[tex]\begin{bmatrix}1 &-2 &-5 \\ 0& 1 & -7\\ 0&0 &1 \\\end{bmatrix}[/tex]

The above matrix is in the row echelon form

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Explanation:

The test contains 10 questions, each one can be answered either with 'true' or with 'false' which means that for each question there are only 2 options.

We need to find the number of ways in which the test can be completed.

To answer the question we use the fundamental counting principle:

In this case, there are 2 ways to complete each question, therefore, we multiply that by the 10 questions that we have:

This can be simplified to

which is equal to:

Answer:

1024

1 + c + 1.4 = c + 2.4

c + 2.4 = c + 2.4

c = c + 2.4 - 24

c = c

Step-by-step explanation:

what is the problem ?

first you need to put "1" in place of the x and calculate, and then you need to put "2" in place of the x and calculate.

just simple calculation !

(a)

R(1) = 1000×1² / (1² + 4) = 1000 / 5 = 200

$200 million

(b)

R(2) = 1000×2² / (2² + 4) = 4000 / 8 = 500

$500 million

there ! that's all that was needed.

Here are the steps in adding vector f and vector 2g.

1. First, multiply vector G by 2. To do this, simply multiply each component of g by 2.

2. Add the result in step 1 to vector f.

To add, simply add each component of vector f to its corresponding component of vector g.

The result is <0, -7>.

Hence, f + 2g = <0, -7>. (Option 3)

Hence, f + 2g = <0, -7>. (Option 3)

We have a sample that is:

a) We can find the median by first sorting the sample:

The median is the value that has 50% of the values below its values.

In this case, this value is in the third place of the sorted sample and has a value of 160.

b) We have to find the mean.

We can calculate it as:

c) We have to calculate the variance. To find its value we will use the mean value we have just calculated:

d) We have to calculate the standard deviation. As we have already calculated the variance, we can calculate it as:

e) We now have to find the coefficient of variation:

Answer:

a) 160

b) 146

c) 4468.4

d) 66.85

e) 46%

Jimmy is paid $14.50 per hour for a regular forty-hour work week and 5 point time and a half for any hour worked over 40. This pas week, Jimmy earned $754.00 in total pay. How many hours of overtime did Jimmy work? ​

Let

x -----> the total hours worked

we have that

$14.50 --------> 40 hours

5.5($14.50) -------> > 40 hours

so

754=14.50*40+5.5(14.50)x

solve for x

754=580+79.75x

79.75x=754-580

79.75x=174

x=2.2 hours