Find the x and y intercepts of the function

3x + 2y + z = 7   ⇒   z = 7 - 3x - 2y

*****************************************

  5x + 5y + 4z = 3  

= 5x + 5y + 4(7 - 3x - 2y) = 3

= 5x + 5y + 28 - 12x - 8y = 3

= -7x -3y + 28 = 3

= -7x - 3y = -25

*****************************************

  3x + 2y + 3z = 1

= 3x + 2y + 3(7 - 3x - 2y) = 1

= 3x + 2y + 21 - 9x - 6y = 1

= -6x - 4y + 21 = 1

= -6x - 4y = -20

*****************************************

-7x - 3y = -25   ⇒  4(-7x - 3y = -25)   ⇒   -28x - 12y = -100

-6x - 4y = -20   ⇒ -3(-6x - 4y = -20)   ⇒    18x + 12y =  60

                                                                  -10x         =   -40

                                                                       x         =     4

-7x - 3y = -25

-7(4) - 3y = -25

-28  - 3y = -25

        -3y  = 3

           y  = -1

z = 7 - 3x - 2y

  = 7 - 3(4) - 2(-1)

  = 7 - 12 + 2

  = -3

Answer: x = 4, y = -1, z = -3

Answer:

Both trains are traveling at 90 miles per hour.

Step-by-step explanation:

We are told that the rate is the same for both trains, and we know that the distance traveled by train a plus the distance traveled by train b equals 585 miles.

We will use [tex]Distance=Rate* Time[/tex] formula to solve this problem.

Train A: [tex]D_a=R*2.5[/tex] (Using 2.5 instead of 2 and 1/2)

Train B: [tex]D_b=R*4[/tex]

We can set an equation to solve for rate R of trains as:

[tex]D_a+D_b=585[/tex]

[tex]2.5R+4R=585[/tex]

[tex]6.5 R=585[/tex]

[tex]R=\frac{585}{6.5}[/tex]

[tex]R=90[/tex]

Therefore, rate of both train a and train b is 90 miles per hour.

The total distance between the two stations is

[tex]585 miles[/tex]

Let the distance between the Central Station and station b be x

This implies that the distance between the Central Station and station a is

[tex](585 - x) \: miles[/tex]

[tex]speed=\frac{distance}{time}[/tex]

so, let us write equations in terms of speed for the two trains and solve

 For train a,

[tex]speed=\frac{585 - x}{4 } ....eqn \: 1[/tex]

For train b,

[tex]speed=\frac{x}{2  \frac{1}{2} } .....eqn \: 2[/tex]

We were told that both trains traveled with the same speed

This means that eqn 1 = eqn 2

[tex]\frac{585 - x}{4 }=\frac{x}{2.5} [/tex]

Cross multiplying

[tex]2.5(585 - x)=4(x) [/tex]

Expanding the brackets

[tex]1462.5  - 2.5x =4x[/tex]

Grouping like terms

[tex]1462.5= 4x + 2.5x[/tex]

[tex]6.5x = 1462.5 \\ x = \frac{1462.5}{6.5 } =225 \: miles[/tex]

The speed at which the trains were travelling is

[tex] \frac{225}{2.5}= 90 \: miles /hour[/tex]

Hence the rate of the trains is  

[tex]=90\: miles /hour[/tex]

1. The cost of items are= $2.50, $8.75, $3.00, $10.25

Total cost = $ 24.50

Tax rate = 6%

Hence tax amount is = [tex]\frac{6}{100} *24.50[/tex] = $ 1.47

2. Time involved in exercise in 1 month = 24 hours

Hence, total time involved in exercising for a year = [tex]24*12=288[/tex]  hours

3. find the value of this integer expression: -2( 3+ -4 +-8+ 7)

Value is obtained by [tex]-2(3+(-4-8)+7)[/tex]

= [tex]-2(3-12+7)=-2(-2)=4[/tex]

4. find the value of this fraction computation: 6( 1/2 + 2/3 + 3/4)

[tex]6(\frac{1}{2}+\frac{2}{3}+\frac{3}{4})[/tex]

=[tex]6(\frac{6+8+9}{12})[/tex]

=[tex]6(\frac{23}{12}) = \frac{23}{2}[/tex]

5. find the perimeter of a rectangular area with a length of 13 inches and width of 7 inches.

Perimeter of a rectangle = 2(length + width)

perimeter = [tex]2(13+7)[/tex]

=[tex]2(20)=40[/tex] inches

6. a situation in which the distributive property could be used is the perimeter of a rectangle.

2(length + width) = 2length + 2width

example- suppose the length of the rectangle is 10 cm and width is 4 cm

so, perimeter is 2(10+4)

= 2(10) + 2(4) = 20+8 =28cm  ..... with distributive property

or

2(10+4) = 2(14) =28cm  ........ without distributive property

Take the breadth as x,as its the smallest value--(1)

Length is 2 more than 5 times the breadth--(2)

perimeter=160m

l=2+5x

b=x

Perimeter=2(l+b)

2(2+5x+x)

=2(2+6x)

Opening the brackets

=4+12x

4+12x=160

12x=160-4

x=156/12

=13

Therefore , by substituting the value of x

l=2+5*13=67m

b=13m

Answer:67.8 is the answer

Step-by-step explanation:

i hope it helps

Simplify both sides of the inequality.

−5.3≥q+11

Flip the equation.

q+11≤−5.3

Subtract 11 from both sides.

q+11−11≤−5.3−11

ANSWER: q≤−16.3

(10m – 6) – (7m – 4)

= 10m - 6 - 7m + 4

= 3m - 2

So

[10m + (–7m)] + [(–6) + 4]

= 3m + (-2)

= 3m - 2 ..............matching answer.

Answer

[10m + (–7m)] + [(–6) + 4]

To add or subtract any algebraic expression,  variables add or subtract with variables and constant term add or subtract with constant terms in the expression.

To solve given expression, we use [10m + (–7m)] + [(–6) + 4] expression.

Given expression is,

                               (10m – 6) – (7m – 4)

Now, variables add or subtract with variables and constant term add or subtract with constant terms in the above expression.

                        10m - 6 - 7m + 4

                      (10m - 7m) + (-6 + 4)

                    [10m + (–7m)] + [(–6) + 4]

So, first option is correct.

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$56 a week

earnings = $12 × 28 = $336

saved = [tex]\frac{1}{6}[/tex] x $336 = [tex]\frac{336}{6}[/tex] = $56

width = 7cm

Length= 41cm

width=x

length=3x+20

96=3x+20+3x+20+x+x

96=8x+40

56=8x

x=8

Rectangle has 4 sides

You have the 2 side lengths (l) and the 2 side widths (w)

"The length is 20 centimeters more than triple the width" in math terms is

l = 20 + 3w

The perimeter is 96 centimeters, which is all the sides added up

2l + 2w = 96

2(20 + 3w) + 2w = 96

40 + 6w + 2w = 96

40 + 8w = 96

8w = 56

w = 7

now plug in w = 7 to get length in

l = 20 + 3w

For this case we have:

Part A:

Since d is the variable that represents the number of days, we can represent an inequality for the gains given by:

[tex]680d + 52000 <960d\\[/tex]

Part B:

We want to know the moment from which Julianne obtains earnings, for that we clear d of the previous inequality:

[tex]52000 <960d-680d\\\\52000 <280d\\\\\frac{52000}{280}<d\\[/tex]

[tex]185.7 <d\\\\d> 186 days\\[/tex]

To start making a profit, Julianne must work more than 186 days.

Answer:

[tex]680d + 52000 <960d\\\\d> 186 days\\\\[/tex]

Final answer:

To calculate the sale price of the Game Boy with an original price of $50.00 and a discount of 2/5, you multiply the original price by the discount to find the amount reduced ($20), then subtract that from the original price to find the sale price ($30).

Explanation:

The question involves calculating the sale price of an item after a discount. Initially, the original price of the Game Boy is $50.00. The discount is given as 2/5 of the original price. To find the amount of discount, we multiply the original price by 2/5:

Discount = Original Price × Fraction of discount
Discount = $50 × 2/5
Discount = $20

Now, we subtract this discount from the original price to find the sale price:

Sale Price = Original Price - Discount
Sale Price = $50 - $20
Sale Price = $30

Therefore, the sale price of the Game Boy after the discount is $30.

Answer:

Average speed = 65 miles per hour

Step-by-step explanation:

Mike drove 100 miles in 2hrs

He stopped to take lunch then;

drove  420 miles in 6hrs

Total distance covered = 100 + 420 miles = 520 miles

Total time taken = 2 + 6 hrs = 8hrs

Average speed = Total distance ÷ total time = 520/8 = 65 miles per hour

Answer:

A 75-year-old person can expect to live 11.7 more years.

Step-by-step explanation:

edmentum/plato

All you have to do is just add 26.7 with 12.8, with the result being 39.5

Answer: The mean of the data is 433.75, variance of the data is 99667.19 and the standard deviation of the data is 315.7011.

Explanation:

The given data is 900, 35, 500 and 300.

The number of observation is 4.

Formula of mean is,

[tex]\text{Mean}=\frac{\text{Sum of observations}}{\text{Number of observations}}[/tex]

[tex]\bar{X}=\frac{900+35+50+300}{4} =433.75[/tex]

The formula of variance is given below,

[tex]\sigma^2=\frac{1}{n}\sum{(X-\bar{X})^2}[/tex]

[tex]\sigma^2=\frac{398668.75}{4}[/tex]

[tex]\sigma^2=99667.19[/tex]

The variance of the data is 99667.19

[tex]\sigma=\sqrt{99667.19}[/tex]

[tex]\sigma=315.7011[/tex]

The standard deviation of the data is 315.7011.

The other information or values of given chart is shown in the attached table.

Answer:

i.  mean of the data is 402.5

ii.  variance of the data is 77556.25

iii.  standard deviation of the data is 278.49

Step-by-step explanation: (x - ⁻x)²

from the chart given to me, the observation are:  45, 340, 400, 825

i.  mean is the summation of the observation divided by number of observation. ∈x÷n =( 45 + 340 + 400 + 825)÷ 4 = 402.5

ii.  variance is the square of the difference between the observation and mean divided by the number of observation.

variance = (45-402.5)²+(340-402.5)²+(400-402.5)²+(825-402.5)²÷4=77556.5

357+421 = 778

Hope this helps :)

The student needs 78 more pounds of coffee to reach the total of 112 pounds required.

The student's question:
The total amount of coffee needed is 112 pounds. You have already put 34 pounds into your cart. To find out how many more pounds you need, you subtract the amount you have from the total needed.

I believe the radius would be 3.39

Hope this helps! Good luck! :)

144(π)cm² = 4(π)r²             Divide by π on both sides

144cm² = 4r²                      Divide by 4 on both sides

36 = r²                               Find the square root of both sides

√36 = √r²

To find the cost of admission to the fair, subtract the cost of the ride tickets from the total spent. The linear equation 2.50x + y = 55.50 can be used to calculate the cost for anyone. The coefficient on x represents the cost per ride ticket, while the constant represents the total amount spent on ride tickets and admission.

(A) To find the cost of admission to the fair, we need to subtract the cost of the ride tickets from the total spent. Since Henry bought 15 tickets and spent a total of $55.50, we can use the equation 2.50x + y = 55.50, where x represents the number of ride tickets. Substituting x = 15, we can solve for y to find the cost of admission.

(B) The linear equation that can be used to determine the cost for anyone who pays for ride tickets and fair admission is 2.50x + y = 55.50, where x represents the number of ride tickets and y represents the cost of admission.

(C) In the linear equation, the coefficient on x (2.50) represents the cost per ride ticket. The constant (55.50) represents the total amount spent on ride tickets and admission.

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A reasonable estimate for 697 times 82 would be 56,000

Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility. Rounding to some place keeps it accurate on the left side of that place but rounded or sort of like trimmed from the right in terms of exact digits.

We could round both numbers to make estimation easier to find.

So let's consider that 82 is 80 and 697 is 700.

As we know that 8 x 7 is 56, then the product of them will be;

80 x 700 =  56,000.

Therefore, This is a great way to estimate of big numbers easily.

Hence, A reasonable estimate for 697 times 82 would be 56,000

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Given: [tex]x^2 + 6x + 2x + 12 = 0.[/tex]

1. Combining like terms (here terms 6x and 2x both contain x, then we can combine them):

[tex]x^2+(6x+2x)+12=0,\\\\x^2+8x+12=0.[/tex]

2. Distributive postulate:

[tex]x^2+8x+12=(x+6)(x+2).[/tex]

The equation is

[tex](x+6)(x+2)=0.[/tex]

3. Zero product postulate (zero product postulate state that if a product of two factors is equal to zero, then first factor is equal to zero or second factor is equal to zero):

[tex]x+6=0 \text{ or } x+2=0.[/tex]

4. Subtraction property of equality:

a) subtract 6 from the first equation:

[tex]x+6=0\Rightarrow x+6-6=-6, \ x=-6.[/tex]

b) subtract 2 from the second equation:

[tex]x+2=0\Rightarrow x+2-2=-2, \ x=-2.[/tex]

Answer:

1. x2 + 6x + 2x + 12 = 0 1. Given

2. x2 + 8x + 12 = 0        2. Combining like terms

3. (x + 6)(x + 2) = 0       3. Distributive Postulate

4. x + 6 = 0 or x + 2 = 0 4. Zero product postulate

5. x = -6 or x = -2         5 Subtraction property of equality

To solve this problem you must apply the proccedure shown below:

1. You have the following system of equation:

[tex]\left \{ {{-4x-2y=-12} \atop {4x+8y=-24}} \right.[/tex]

2. As you can see, you can cancel out the variable [tex]x[/tex], because it has equal coefficient with different signs at both equations. Then, if you add both equations, you obtain:

[tex]6y=-36\\y=-6[/tex]

3. Let's substitute the value obtained into the second equation to calculate the other variable:

[tex]4x+8(-6)=-24\\4x-48=-24\\x=6[/tex]

The answer is: (6,-6).

The value of x in the isosceles right triangle is 52.5.

The measure of the acute angle in an isosceles right triangle can be determined by setting the expression equal to 90 degrees:

(2x - 15) = 90

Simplifying the equation, we get:

2x = 90 + 15

2x = 105

x = 105/2

x = 52.5

Therefore, the value of x is 52.5.

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Answer:

Option C

Step-by-step explanation:

Given a quadratic equation

x^2+10x+24 =0

We can use either formula or factorization method to solve this equation.

The last term is 24, it is a product of 6 and 4. Sum =6+4 =10

Hence factoring can be done easier

Split the middle term as 6x +4x

x^2+6x+4x+24 =0

x(x+6)+4(x+6)=0

(x+4)(x+6)=0

Either x+4 =0 or x+6 =0

x=-6 or x =-4

I took it last time it D. YOu welcome

The point that represents a viable solution is (4, 3)

From the question, we have the following parameters that can be used in our computation:

The graph

This is given as an attachment

From the graph, we have solution to the system to be the shaded region

This means that all coordinates in the shaded region are the solutions to the system

One of the coordinates in the solution to the systems of inequalities graphically is (4, 3)

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Answer:

The probability of my name being chosen is 1/6. As a decimal, that's 0.16666...

Step-by-step explanation:

As a decimal, that's 0.16666...

Answer:  Cole and his sister Chloe will take 81 minutes to clean the whole house.

Step-by-step explanation:

Total rooms in the house = 9

Total persons to clean the house = 2 (Cole and his sister Chloe)

Time taken by 1 person to clean one=18 minutes

Time taken by 2 persons to clean one room together=18 divided by 2 = 9 minutes

Time taken by 2 persons to clean 9 rooms (which is the total number of rooms in the house)=9 multiply 9 = 81 minutes

therefore, they will take 81 minutes to clean the whole house.

Answer:

C

Step-by-step explanation:

I would say not enough information. You cannot tell from the givens how A,B and m<2 are related to each other.

Answer C

Answer:

c

Step-by-step explanation: