7. An antique dealer has a fund of $1,160 for investments. She spends 50%of the fund on a 1911 rocking chair. She then sells the chair for $710, all ofwhich she returns to the fund.a) What was the percent gain on the investment?b) What percent of the original value of the fund is the new value of the fund?

Answers

Answer 1

Given:

Total amount dealer has is $1160.

Spend 50% of the fund to buy a 1911 rocking chair and sells it for $710.

[tex]Fund\text{ she spends on chair=}1160\times\frac{50}{100}[/tex][tex]Fund\text{ she spends on chair= \$580}[/tex]

a)

[tex]\text{Fund gain on selling the chair= 710-580}[/tex][tex]\text{Fund gain on selling the chair= \$}130[/tex][tex]\text{Percent gain on the investment=}\frac{130}{580}\times100[/tex][tex]\text{Percent gain on the investment=}22.41\text{ \%}[/tex]

b)

[tex]\text{New value of the fund=1160+130}[/tex][tex]\text{New value of the fund= \$}1290[/tex][tex]\text{Percentage of original to the new value = }\frac{1290}{1160}\times100[/tex][tex]\text{Percentage of original to the new value =111.21 \%}[/tex]

111.21% of the original value of the fund is the new value of the fund.


Related Questions

19. Translate the following statement into an algebraic statement: "Two more than seven times a number is fifteen" I

Answers

2+7x=15

Explanation

Step 1

Let

x represents the number

seven times a number = 7x

two more = +2 or 2+, you need to add 2

is = "="

Step 2

replace,

"Two more than seven times a number is fifteen"

[tex]2+7x=15[/tex]

I hope this helps you

The previous tutor helped me with solution but we got cut off before we could graph I need help with graphing please

Answers

We want to graph the following inequality system

[tex]\begin{gathered} x+8\ge9 \\ \text{and} \\ \frac{x}{7}\le1 \end{gathered}[/tex]

First, we need to solve both inequalities. To solve the first one, we subtract 8 from both sides

[tex]\begin{gathered} x+8-8\ge9-8 \\ x\ge1 \end{gathered}[/tex]

To solve the second one, we multiply both sides by 7.

[tex]\begin{gathered} 7\cdot\frac{x}{7}\le1\cdot7 \\ x\le7 \end{gathered}[/tex]

Now, our system is

[tex]\begin{gathered} x\ge1 \\ \text{and} \\ x\le7 \end{gathered}[/tex]

We can combine those inequalities into one.

[tex]1\le x\le7[/tex]

The number x is inside the interval between 1 and 7. Graphically, this is the region between those numbers(including them).

A local real estate company has 5 real estate agents. The number of houses that each agent sold last year is shown in the bar graph below. Use this bar graph to answer the questions.

Answers

Given:

Rachel sold 4 houses.

Heather sold 4 houses.

Kaitlin sold 12 houses.

Lena sold 11 houses.

Deshaun sold 3 houses.

Required:

a) We need to find which agent sold the most houses.

b) We need to find the number of houses Lna soldemore than Heather.

c) We need to find the number of agents who sold fewer than 4 houses.

Explanation:

a)

The greatest number of houses sold =12 houses.

Kaitlin sold 12 houses.

Answer:

The agent Kaitlin sold the most houses.

The agent sold 12 houses.

b)

Lena sold 11 houses.

Heather sold 4 houses.

The difference between 11 and 4 is 11-4 =7.

Answer:

Lena sold 7 housmore than Heather

I need help to find the indicated operation:g(x)= -x^2 +4xh(x)= -4x-1Find (3g-h)(-3)

Answers

We have the following functions:

[tex]\begin{gathered} g\mleft(x\mright)=-x^2+4x \\ h\mleft(x\mright)=-4x-1 \end{gathered}[/tex]

And we need to find:

[tex](3g-h)(-3)[/tex]

Step 1. Find 3g by multiplying g(x) by 3:

[tex]\begin{gathered} g(x)=-x^2+4x \\ 3g=3(-x^2+4x) \end{gathered}[/tex]

Use the distributive property to multiply 3 by the two terms inside the parentheses:

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

Step 2. Once we have 3g, we subtract h(x) to it:

[tex]3g-h=-3x^2+12x-(-4x-1)[/tex]

Here we have 3g and to that, we are subtracting h which in parentheses.

Simplifying the expression by again using the distributive property and multiply the - sign by the two terms inside the parentheses:

[tex]3g-h=-3x^2+12x+4x+1[/tex]

Step 4. Combine like terms:

[tex]3g-h=-3x^2+16x+1[/tex]

What we just found is (3g-h)(x):

[tex](3g-h)(x)=-3x^2+16x+1[/tex]

Step 5. To find what we are asked for

[tex]\mleft(3g-h\mright)\mleft(-3\mright)​[/tex]

We need to evaluate the result from step 4, when x is equal to -3:

[tex](3g-h)(-3)=-3(-3)^2+16(-3)+1[/tex]

Solving the operations:

[tex](3g-h)(-3)=-3(9)^{}-48+1[/tex][tex](3g-h)(-3)=-27^{}-48+1[/tex][tex](3g-h)(-3)=-74[/tex]

Answer:

[tex](3g-h)(-3)=-74[/tex]

Sobczak,€8(.8((8.8(.;77;.;&

Answers

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Instructions: Find the value of that completes the square and creates a perfect square trinomial.

Answers

Solution:

Given the expression;

[tex]x^2+18x+c[/tex]

c is the half of square of coefficient of x. That is;

[tex]\begin{gathered} x^2+18x+c=x^2+18x+(\frac{1}{2}(18))^2 \\ \\ x^2+18x+c=x^2+18x+9^2 \\ \\ x^2+18x+c=x^2+18x+81 \\ \\ x^2+18x+81=(x+9)(x+9) \end{gathered}[/tex]

Hence, the value of c is;

[tex]c=81[/tex]

I have a question about how to solve graphing a system of inequalities and about how to do the (0,0)

Answers

The given system of inequality is

[tex]\begin{gathered} 2x-3y>-12 \\ x+y\ge-2 \end{gathered}[/tex]

At first, we must draw the lines to represent these inequalities

[tex]2x-3y=-12[/tex]

Let x = 0, then find y

[tex]\begin{gathered} 2(0)-3(y)=-12 \\ 0-3y=-12 \\ -3y=-12 \\ \frac{-3y}{-3}=\frac{-12}{-3} \\ y=4 \end{gathered}[/tex]

The first point is (0, 4)

Let y = 0

[tex]\begin{gathered} 2x-3(0)=-12 \\ 2x-0=-12 \\ 2x=-12 \\ \frac{2x}{2}=\frac{-12}{2} \\ x=-6 \end{gathered}[/tex]

The second point is (-6, 0)

We will do the same with the second line

Let x = 0

[tex]\begin{gathered} 0+y=-2 \\ y=-2 \end{gathered}[/tex]

The first point is (0, -2)

Let y = 0

[tex]\begin{gathered} x+0=-2 \\ x=-2 \end{gathered}[/tex]

The second point is (-2, 0)

Since the sign of the first inequality is >, then the line will be dashed

Since the sign of the second inequality is >=, then the line will be solid

Let us substitute x, y by the origin point (0,0) in both inequalities to find the shaded part of each one

[tex]\begin{gathered} 2(0)-3(0)>-12 \\ 0-0>-12 \\ 0>-12 \end{gathered}[/tex]

Since the inequality is true then the point (0, 0) lies on the shaded area

[tex]\begin{gathered} 0+0\ge-2 \\ 0\ge-2 \end{gathered}[/tex]

Since the inequality is true, then point (0, 0) lies in the shaded area

Let us draw the graph

The red line represents the first inequality

The blue line represents the second inequality

The area of two colors is the area of the solution

Point (0, 0) lies in this area, then it is a solution for the given system of inequalities

Given these points please solve this problme.

Answers

The point that belongs to the solution set is A( 4, 4)

What are inequalities?

Inequalities are defined as mathematical relations involving an unequal comparison between two numbers, elements or other arithmetic expressions.

They are mostly used to compare two numbers on the number line on the basis of their sizes.

Given the inequalities;

x + y > 63x - 5y ≤ 2

Make 'x' the subject from equation 1, we have;

x > 6 - y

substitute the value into equation 2, we have;

3( 6 - y) - 5y  ≤ 2

expand the bracket

18 - 3y - 5y ≤ 2

collect like terms

- 8y ≤ 2 - 18

- 8y ≤ -16

Make 'y' the subject of formula

y ≤ 2

Substitute the value in equation 3

x > 6 - 2

x > 4

Hence, the point is A( 4, 4)

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Given f <-2, 3> and g <1, -5> find f + 2g

Answers

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.

[tex]<2(1),2(-5)>\Rightarrow<2,-10>[/tex]

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.

[tex]\begin{gathered} <-2,3>+<2,-10> \\ <-2+2,3+(-10)> \\ <0,-7> \end{gathered}[/tex]

The result is <0, -7>.

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

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

helppppppppppppppppppppppppppppppppppp

Answers

For (fog)(x) all you do is substitute the value of x for the value of (g)(x) because (fog)(x)=(f(g(x))), and vice versa for (gof)(x)!!

In December, 64 teams qualify for a basketball tournament. After each round, half of the teams are eliminated.
Which exponential function can be used to find the number of teams left after a rounds, where is a whole number?
O f(x) = (64)
O f(x) =
(x)64
O f(x) = 64 (¹)
○ f(x) = x(¹)

Answers

The exponential function is f(x) = 64·(1/2)ˣ which can be used to find the number of teams left after a round.

What is an exponential function?

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

Given that 64 teams qualify for a basketball tournament. After each round, half of the teams are eliminated.

Because it is an exponential function, f(x) will reach 0 as x increases, allowing us to construct the following table of values:

x    f(x)

0    64

1     32

2    16

3     8

4     4

5     2

6     1

At that point, 64 teams are in the tournament, and the total number of teams (from this point forward)

Therefore, half of the teams are eliminated after each round and the exponential function is:

f(x) = 64·(1/2)ˣ

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Which of the following ordered pairs is a solution to the equation 2x+y=2? Select all that apply.(11,0)(−4,10)(−13,4)(−11,−1)(0,2)

Answers

You have the following equation:

2x + y = 2

In order to determine which of the given pairs is a solution, replace the values of x and y of such pairs and verify the equation, as follow:

(11,0)

2(11) + 0 = 22 ≠ 2 it's not a solution

(-4,10)

2(-4) + 10 = -8 + 10 = 2 it's a solution

(-13,4)

2(-13) + 4 = -26 + 4 ≠ 2 it's not a solution

(-11,-1)

2(-11) + (-1) = -22 - 1 ≠ 2 it's not a solution

(0,2)

2(0) + 2 = 2 it's a solution

If 6 is subtracted from the third of three consecutive odd integers and the result is multiplied by 2, the answer is 23 less then the sun if the first and twice the second of the integers

Answers

[tex]\begin{gathered} \text{Let }x\text{ be the first odd integer, then it goes that} \\ x+2\rightarrow\text{second odd integer} \\ x+4\rightarrow\text{third odd integer} \\ \text{If 6 is subtracted from the third of three consecutive odd integer, translates to} \\ (x+4)-6\Rightarrow x+4-6\Rightarrow x-2 \\ \text{and the result is multiplied by 2, which translates to} \\ (x-2)\cdot2\Rightarrow2x-4 \\ \text{the answer is 23 less than the sum of the first and twice of the second integers} \\ (x)+2(x+2)\rightarrow x+2x+4\rightarrow3x+4 \\ (3x+4)-23 \\ 3x-19 \\ \text{equate them both sides and we have} \\ 2x-4=3x-19,\text{ left hand is the first part, right hand is the second part} \\ \text{solve for }x \\ 2x-4=3x-19 \\ -4+19=3x-2x \\ 15=x \\ x=15 \\ \text{so the three odd integers are, } \\ x=15 \\ x+2=17 \\ x+4=19 \\ 15,17,19 \end{gathered}[/tex]

Which equation could be represented by the number line? A. 3 OB.-4 5=1 OC. 1+ -5)= OD. -3+4 -1

Answers

According to the given number line, we have to go back from the second point to the first point 4 spots. In other words, the equation has to include a sum with -4.

Therefore, the answer is A since it's expressing an initial number 3, then the sum with -4.

Santa worked 3.5 hours, 6.9 hours, & 4.3 hours in the last three days. If he earns $7.1 an hour, how much did he earn in the last three days?

Answers

ANSWER:

$104.37

STEP-BY-STEP EXPLANATION:

To calculate the total profit, we must add the amount he earned each day, multiplying the salary by the number of hours, like this:

[tex]\begin{gathered} e=3.5\cdot7.1+6.9\cdot7.1+4.3\cdot7.1 \\ e=24.85+48.99+30.53 \\ e=104.37 \end{gathered}[/tex]

Therefore, he earned in the last three days a total of $104.37

An integer is chosen at random from 1 to 50. find the probability that the chosen integer is not divisible by 2, 7 or 9a)13/50b)16/25c)9/25

Answers

There are a total of 50 numbers that are between 1 and 50. Halft of these numbers are even (divisible by 2 ) and half of then odd.

There are 25 integers that are not even and in total there are 50 integers; thereofre, the probablity of finding an even integer is

25/50 = 1/2

Find the distance between the pair of points. (16,0) and (1, -7) The distance is. (Round to the nearest thousandth as needed.)

Answers

Solution

For this case we can use the formula for the distance between two points:

[tex]d=\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]

and replacing we got:

[tex]d=\sqrt[]{(-7-0)^2+(1-16)^2}=\sqrt[]{274}[/tex]

And the correct answer after round would be:

16.553

Solve the equation for y.1/3 x + y = 4

Answers

In order to solve the equation for y, we just need to isolate the variable y in one side of the equation. So we have:

[tex]\begin{gathered} \frac{1}{3}x+y=4 \\ y=4-\frac{1}{3}x \end{gathered}[/tex]

So the answer is y = 4 - 1/3 x

in the inequality 6a+4b>10, what could be the possible value of a if b=2?

Answers

We are given the following inequality:

[tex]6a+4b>10[/tex]

If we replace b = 2, we get:

[tex]\begin{gathered} 6a+4(2)>10 \\ 6a+8>10 \end{gathered}[/tex]

Now we solve for "a" first by subtracting 8 on both sides:

[tex]\begin{gathered} 6a+8-8>10-8 \\ 6a>2 \end{gathered}[/tex]

Now we divide both sides by 6

[tex]\frac{6a}{6}>\frac{2}{6}[/tex]

Simplifying:

[tex]a>\frac{1}{3}[/tex]

Therefore, for b = 2, the possible values of "a" are those that are greater than 1/3

Find all the factors of 99.

Answers

The factors of 99 are: 1, 3, 9, 11, 33 and 99.

Which is the image of vertex K after the parallelogram is rotated 180degrees about the origin?

Answers

Answer:

The image of vertex K is (3,-2)

Step-by-step explanation:

Rotated 180 degrees about the origin means that the value of x will not change, while y will have the same distance from the origin, but in a different direction.

Vertex K:

Value of x: x = 3

Value of y: y = 2

Distance from the origin: 2 - 0 = 2

Rotated, new coordinate: 0 - 2 = -2

The image of vertex K is (3,-2)

Benjamin & Associates, a real estate developer, recently built 194 condominiums in McCall, Idaho. The condos were either two-bedroom units or three-bedroom units. If the total number of rooms in the entire complex is 494, how many two-bedroom units are there? How many three-bedroom units are there

Answers

x = number of 2 bedrooms units

y= number of 3 bedroom units

194 condominiums

x+y = 194 (a)

the total number of rooms in the entire complex is 494

2x + 3y = 494 (b)

We have the system of equations:

x+y = 194 (a)

2x + 3y = 494 (b)

Solve (a) for x

x = 194-y

Replace x on (b) and solve for y

2 (194-y ) + 3 y = 494

388 - 2y +3 y = 494

-2y+3y = 494-388

y= 106

Replace y on (a) and solve for x

x + 106 = 194

x = 194-106

x= 88

2-bedroom units = 88

3- bedrooms units = 106

-Quadratic Equations- Solve each by factoring, write each equation in standard form first.

Answers

Answer

The solutions to the quadratic equations are

[tex]\begin{gathered} a^2-4a-45 \\ \text{Solution: }a=-5\text{ or }9 \\ \\ 5y^2+4y=0 \\ \text{Solution: }y=0\text{ or }-\frac{4}{5} \end{gathered}[/tex]

SOLUTION

Problem Statement

The question gives us 2 quadratic equations and we are required to solve them by factoring, first writing them in their standard forms.

The quadratic equations given are:

[tex]\begin{gathered} a^2-4a-45=0 \\ 5y^2+4y=0 \end{gathered}[/tex]

Method

To solve the questions, we need to follow these steps:

(We will represent the independent variable as x for this explanation. We know they are "a" and "y" in the questions given)

The steps outlined below are known as the method of Completing the Square.

Step 1: Find the square of the half of the coefficient of x.

Step 2: Add and subtract the result from step 1.

Step 3: Re-write the Equation. This will be the standard form of the equation

Step 4. Solve for x

We will apply these steps to solve both questions.

Implementation

Question 1:

[tex]\begin{gathered} a^2-4a-45=0 \\ \text{Step 1: Find the square of the half of the coefficient of }a \\ (-\frac{4}{2})^2=(-2)^2=4 \\ \\ \text{Step 2: Add and subtract 4 to the equation} \\ a^2-4a-45+4-4=0 \\ \\ \text{Step 3: Rewrite the Equation} \\ a^2-4a+4-45-4=0 \\ (a^2-4a+4)-49=0 \\ (a^2-4a+4)=(a-2)^2 \\ \therefore(a-2)^2-49=0 \\ \text{ In standard form, we have:} \\ (a-2)^2=49 \\ \\ \text{Step 4: Solve for }a \\ (a-2)^2=49 \\ \text{ Find the square root of both sides} \\ \sqrt[]{(a-2)^2}=\pm\sqrt[]{49} \\ a-2=\pm7 \\ \text{Add 2 to both sides} \\ \therefore a=2\pm7 \\ \\ \therefore a=-5\text{ or }9 \end{gathered}[/tex]

Question 2:

[tex]\begin{gathered} 5y^2+4y=0 \\ \text{ Before we begin solving, we should factorize out 5} \\ 5(y^2+\frac{4}{5}y)=0 \\ \\ \text{Step 1: Find the square of the coefficient of the half of y} \\ (\frac{4}{5}\times\frac{1}{2})^2=(\frac{2}{5})^2=\frac{4}{25} \\ \\ \text{Step 2: Add and subtract }\frac{4}{25}\text{ to the equation} \\ \\ 5(y^2+\frac{4}{5}y+\frac{4}{25}-\frac{4}{25})=0 \\ \\ \\ \text{Step 3: Rewrite the Equation} \\ 5((y^2+\frac{4}{5}y+\frac{4}{25})-\frac{4}{25})=0 \\ 5(y^2+\frac{4}{5}y+\frac{4}{25})-5(\frac{4}{25})=0 \\ 5(y^2+\frac{4}{5}y+\frac{4}{25})-\frac{4}{5}=0 \\ \\ (y^2+\frac{4}{5}y+\frac{4}{25})=(y+\frac{2}{5})^2 \\ \\ \therefore5(y+\frac{2}{5})^2-\frac{4}{5}=0 \\ \\ \text{ In standard form, the Equation becomes} \\ 5(y+\frac{2}{5})^2=\frac{4}{5} \\ \\ \\ \text{Step 4: Solve for }y \\ 5(y+\frac{2}{5})^2=\frac{4}{5} \\ \text{ Divide both sides by 5} \\ \frac{5}{5}(y+\frac{2}{5})^2=\frac{4}{5}\times\frac{1}{5} \\ (y+\frac{2}{5})^2=\frac{4}{25} \\ \\ \text{ Find the square root of both sides} \\ \sqrt[]{(y+\frac{2}{5})^2}=\pm\sqrt[]{\frac{4}{25}} \\ \\ y+\frac{2}{5}=\pm\frac{2}{5} \\ \\ \text{Subtract }\frac{2}{5}\text{ from both sides} \\ \\ y=-\frac{2}{5}\pm\frac{2}{5} \\ \\ \therefore y=0\text{ or }-\frac{4}{5} \end{gathered}[/tex]

Final Answer

The solutions to the quadratic equations are

[tex]\begin{gathered} a^2-4a-45 \\ \text{Solution: }a=-5\text{ or }9 \\ \\ 5y^2+4y=0 \\ \text{Solution: }y=0\text{ or }-\frac{4}{5} \end{gathered}[/tex]

The number of chaperones on a field trip must include 1 teacher for every 4 students, plus 2 parents total. The function describing the number of chaperones for a trip of x students is f(x) = 1/4x + 2.

a. How will the graph change if the number of parents is reduced to 0?

b. How will the graph change if the number of teachers is raised to 1 for every 3 students?

Answers

Number of chaperones for a trip defined by function f(x) = (1/4)x+2 then,

a. If the parents is reduced to 0 then the graph passes through origin (0,0).

b. If the number of teachers is raised to 1 for every 3 students then line cut x-axis at (-6,0) .

As given in the question,

Given conditions:

Field trip must include 1 teacher for every 4 students and add 2 parents in total.

Number of chaperones for a trip defined by function f(x) = (1/4)x+2

a. If the parents is reduced to 0 then the changes seen in the graph are as follow:

f(x) =  (1/4)x+2 passes through the point (0,2)

when parents changes to 0 then graph passes through (0,0).

b.  If the number of teachers is raised to 1 for every 3 students then the changes seen in the graph are as follow:

For f(x) = (1/4)x+2 the graph cut axis at (-8,0)

When for every 1 teacher there are 3 students then graph cut x-axis at (-6,0).

Therefore, number of chaperones for a trip defined by function f(x) = (1/4)x+2 then,

a. If the parents is reduced to 0 then the graph passes through origin (0,0).

b. If the number of teachers is raised to 1 for every 3 students then line cut x-axis at (-6,0) .

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Graph the inequality and give interval notation for the solution. Use two o's (as in octopus) forinifinity and a U for union as needed.-- 5x + 4 >I 19 OR – 22 - 15 – 3-8 -7 -6 -5-4-3-2-] 022345678Clear All Draw:Interval notation for the above inequality and graph is

Answers

- 5x + 4 > 19

1st step let us move 4 to the other side by subtracting both sides by 4

- 5x + 4 - 4 > 19 - 4

- 5x > 15

2nd step is move - 5 to the other side by dividing both sides by -5, BUT when we divide the sides of an inequality by a negative number we must reverse the sign of inequality

[tex]\frac{-5x}{-5}<\frac{15}{-5}[/tex]

x < -3

The solution is all values smaller than -3

On the number, line draw an empty circle at -3 then draw from it an arrow pointing to the left ( - ve infinity)

The solution is {x : x < -3} or (-00, -3)

I need help with this question

Answers

A person who watches TV 11.5 hours can do 36 sit-ups.

Define Regression Analysis

Regression analysis is a mathematical measure of the average relationship between two or more variables in terms of the original units of the data

Given,

y = ax +b

a = -1.073

b = 27.069

r² = 0.434281

r = -0.659

No. of hours TV watched = 11.5 hours

we have , y = ax + b

where, a = 1.073 , b = 27.069 and x = 11.5 hours

put this value in given equation,

y = 1.073 * 11.5 + 27.069

After calculating, we get

y = 39.4085 or 39

Therefore, a person who watches TV 11.5 hours can do 36 sit-ups.

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9) solve using substitution method and check your answer:4x - 3y + 2z = 16- 4y - Z = 7= 146x - y

Answers

Given the system of equations, solve the third equation for y, as shown below

[tex]\begin{gathered} 6x-y=14 \\ \Rightarrow y=6x-14 \end{gathered}[/tex]

And, solve for z in the second equation,

[tex]\begin{gathered} -4y-z=7 \\ \Rightarrow z=-4y-7 \\ \Rightarrow z=-4(6x-14)-7=-24x+49 \end{gathered}[/tex]

Thus, substitute the values of y and z in terms of x into the first equation, as shown below

[tex]\begin{gathered} \Rightarrow4x-3y+2z=4x-3(6x-14)+2(-24x+49)=4x-18x+42-48x+98 \\ \Rightarrow-62x+140=16 \\ \Rightarrow-62x=-124 \\ \Rightarrow x=2 \end{gathered}[/tex]

Then, solving for y and z given x=2,

[tex]\begin{gathered} x=2 \\ \Rightarrow y=6*2-14=-2 \\ and \\ z=-24*2+49=-48+49=1 \end{gathered}[/tex]Therefore, the solution to the system of equations is x=2, y=-2, z=1

To verify the solutions, substitute the values we found into the three equations of the system, as shown below

[tex]\begin{gathered} x=2,y=-2,z=1 \\ \Rightarrow4x-3y+2z=4*2-3*(-2)+2*1=8+6+2=16\rightarrow correct \\ \Rightarrow-4y-z=-4*(-2)-1(1)=8-1=7\rightarrow correct \\ \Rightarrow6x-y=6*2-1(-2)=12+2=14\rightarrow correct \end{gathered}[/tex]

A triangle has vertices on a coordinate grid at D(-10, -1), E(-10,6), and F(2,6). What is the length, in units, of DE?

Answers

A triangle has vertices on a coordinate grid at D(-10, -1), E(-10,6), and F(2,6). What is the length, in units, of DE?​

we know that

The formula to calculate the distance between two points is equal to

[tex]d=\sqrt[]{(y2-y1)^2+(x2-x1)^2}[/tex]

we have

D(-10, -1), E(-10,6)

substitute the given values in the formula

[tex]\begin{gathered} d=\sqrt[]{(6+1)^2+(-10+10)^2} \\ d=\sqrt[]{(7)^2+(0)^2} \\ d=\sqrt[]{49} \\ d=7\text{ units} \end{gathered}[/tex]

therefore

the distance DE is 7 units

if you run 5/6 of a mile in 1/12 of how hour how much is that

Answers

The entire miles that the person runs in 1 hour is 10 miles

What is a fraction?

A fraction simply means the numbers that's expressed as a/b where a = numerator and b = denominator.

In this case, the person runs 5/6 of a mile in 1/12 of an hour.

The number of miles for the entire run will be the division of the fractions given. This will be illustrated as:

= 5/6 ÷ 1/12

= 5/6 × 12

= 5 × 2

= 10 miles

The entire race is 10 miles.

Learn more about fractions on:.

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A student is trying to solve the set of two equations given below:Equation A: x + z = 6Equation B: 3x + 2z = 1Which of the following is a possible step used in eliminating the z-term

Answers

[tex]\begin{gathered} Let\colon \\ x+z=6_{\text{ }}(A) \\ 3x+2z=1_{\text{ }}(B) \end{gathered}[/tex][tex]\begin{gathered} Multiply_{\text{ }}A_{\text{ }}by_{\text{ }}-2\colon \\ -2(x+z)=-2(6) \\ -2x-2z=-12 \\ Add_{\text{ }}A_{\text{ }}and_{\text{ }}B\colon \\ -2x+3x-2z+2z=-12+1 \\ x=-11 \end{gathered}[/tex]

Answer:

multiply equation A by -2

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