solve the system by substitution 2x+y=10 x-3y=-2 state whether the system had one solution infinite solutions or no solution

Let's go:

[tex]x^2 = [- 6 - (- 10)]^2 + [- 1 - (- 3)]^2 \\\ x^2 = 16^2 + 4^2 \\\ x^2 = 256 + 16 \\\ x^2 = 272 \\\ x = \sqrt{272} \\\ x = 16,5[/tex]

I hope I helped you.

Use the distance formula

d= square root of [(x-x)^2+(y-y)^2]

Step-by-step explanation:

d= sq. root of [(10-(-6))^2+(-1-3)^2]

= sq. root of [16^2 + (-4)^2]

= sq root of (256+16)

= sq root of 272 or 4.7

Answer:

a

Step-by-step explanation:

the mean = [tex]\frac{total score}{count}[/tex]

let the fifth score be x and count = 5, hence

[tex]\frac{86+82+72+69+x}{5}[/tex] = 79 ( multiply both sides by 5 )

309 + x = 395 ( subtract 309 from both sides )

x = 86

the student requires a score of 86% → a

Answer:

Step-by-step explanation:

1) 144 x $12 = $1728.00

2) $10 x 2 = $20       $20 x 3 = $60      $30 x 2 = 60;   $20+$60+$60 = $140

3)  $350 - $234 = $116.00

4) $225 ÷ $15 = 15 lawns will need to be cut

5) 2/4 = 1/2 = .50 = 50%  B

6) 0.99 + 1.19 + 1.50 + 0.99 =  $4.67

7)  B  90 seconds is = 1 minutes and 30 seconds  (1 minute = 60 seconds)

8) 4 weeks x 5 nights = 20 nights of studying

   20 nights x 30 minutes = 600 minutes

   600 minutes ÷ 60 (minutes in an hour) = 10 hours of studying  D

Answer:

503.7 is the best estimate when rounding each number to the nearest tenth.

Step-by-step explanation:

Round 552.17 and 48.35 to the nearest tenth. That gives us 552.1 and 48.4 (because 5 makes the number round up). Subtract that, and it gives us 503.7.

Answer:

The most money she can borrow is $48478.7

Step-by-step explanation:

We are given

Kylie can afford a $1310-per-month house loan payment

so,

PMI=1310

t=25 years

n=12

APR=8.4%=0.084

So,

total money =(PMI)*t*n

[tex]A=1310\times 12\times 25[/tex]

[tex]A=393000[/tex]

now, we can use formula

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

we can plug values

[tex]393000=P(1+\frac{0.084}{12})^{12\times 25}[/tex]

now, we can solve for P

so, we get

[tex]P=\frac{393000\times \:12^{300}}{12.084^{300}}[/tex]

[tex]P=48478.7[/tex]

So,

The most money she can borrow is $48478.7

Answer:

The is ($1310)((1+0.007)^300-1)/(0.007)(1+0.007)^300

Step-by-step explanation:

Put the value of slope to the equation of the function:

[tex]y=-\dfrac{1}{6}x+b[/tex]

Put the coordinates of the point B(12, 3) to the equation:

[tex]3=-\dfrac{1}{6}(12)+b[/tex]

[tex]3=-2+b[/tex]            add 2 to both sides

[tex]5=b[/tex]

Answer:

The value of b is 5.

Step-by-step explanation:

Consider the provided information.

It is given that the slope intercept form is, y = mx + b

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

Also, it is given that the slope of the line is -1/6.

Line AB passes through points A(–6, 6) and B(12, 3).

That means Point A and B must satisfy the equation of line.

Substitute [tex]m=\frac{-1}{6}, x=-6\ \text{and}\ y = 6[/tex] in slope intercept form:

[tex]6=\frac{-1}{6}\times(-6)+b[/tex]

[tex]6=1+b[/tex]

[tex]5=b[/tex]

Thus, the value of b is 5.

Answer:

-3

Step-by-step explanation:

-3-16=-19

-19+16=-3

Answer:

-3

Step-by-step explanation:

Answers:

Rent = 750

Savings = 750

Groceries = 625 (you are correct)

Other = 375

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

Explanation:

Convert each percent to decimal form. You do this by moving the decimal point 2 spots to the left.

Rent has 30% turn into 0.30, which multiplies with 2500 to get 0.30*2500 = 750

For savings, the same multiplier is used because we also have 30% here as well. So the same amount is devoted to savings.

You have the correct answer for groceries. Multiply 0.25 with 2500 to get 625. Nice work on getting the correct answer here.

Finally, we have 15% devoted to other, so we multiply 0.15 by 2500 and we get 0.15*2500 = 375

As a check, we can add up the subtotals 750, 750, 625, 375 to get 750+750+625+375 = 2500 which helps us confirm our answers.

Answer:

Rent: $750

Savings: $750

Groceries: $625

Other: $375

Step-by-step explanation:

I used the formula:   Part/Whole  =  Percent/100

So for the first two, since they are the same, I did x for the part, 2,500 for the whole, 30 for the percent, and 100. Then I did 30 times 2,500 and I got 75,000. Next I did 75,000 divided by 100 and got 750.

For "Groceries", I did the same thing except used x for the part, 2,500 for the whole, 25 for the percent, and 100.

For "Other", I did the same thing except used x for the part, 2,500 for the whole, 15 for the percent, and 100.

HOPE THIS HELPS!    :)

Answer:

? = 113

Step-by-step explanation:

The angles are alternate interior angles.  Alternate interior angles are equal if the lines are parallel.  Since the lines are parallel, the angles are equal.

? = 113

Answer:

x < [tex]\frac{3}{2}[/tex]

Step-by-step explanation:

distribute the parenthesis on the right side

5x + 3 < 3x + 6 ( subtract 3x from both sides )

2x + 3 < 6 ( subtract 3 from both sides )

2x < 3 ( divide both sides by 2 )

x < [tex]\frac{3}{2}[/tex]

Answer:

x <  [tex]\frac{3}{2} \\[/tex]

Answer:

I believe it is 2 / h = the amount she blew in 1 minute. Hope this helps

Answer:

h / 120

Step-by-step explanation:

2 hours equals 120 minutes.

So h bubbles in 120 minutes is h/120 per minute.

Verification: suppose she blew 240 bubbles in two hours; this would be 240/120 = 2 per minute. That makes 120 per hour and, as expected, 240 in two hours.

Answer:

see explanation

Step-by-step explanation:

∠RHC = 145° ( given )

∠JHK = 145° ( vertical to ∠RHC )

∠RHJ = 180° - 145° = 35° ( straight angle )

∠CHK = 35° ( vertical or straight )

∠HKS = 35° ( alternate to ∠CHK )

∠SKU = 145° ( straight angle )

∠OKU = 35° ( vertical or straight )

∠HKO = 145° (vertical to ∠SKU )

Answer:

Area of the figure is 304 sq. units

Step-by-step explanation:

The area is divided into two identical trapezoids of height 8 units and bases 14 and 24 units.

Area of a trapezoid = (1/2) * (Sum of base lengths) * height

So, area of 1 one trapezoid = (1/2)*(14+24)*8=152

The area of the figure is twice the area of the trapezoid.

So, area of figure = 2 * 152 = 304 sq. units

∴ Area of the figure is 304 sq. units

Part A: x=2

This would make both perimeters equal to 24.

Part B: No solution.

You cannot make x equivalent to anything but 2, or the square would not be real. All four sides of the square must equal 6. This would make the area 36 units squared. If x was 2 for the rectangle, the area would be 20. It is impossible to make them equal. Tell me if I'm wrong, though.

The correct substitution of the values a, b, and c from the given equation into the quadratic formula is a = 1, b = -1, and c = -2, resulting in the formula x = [1 ± √(1 - 4(1)(-2))] / 2.

For the equation –2 = –x + x² – 4, we need to rewrite it in the standard quadratic equation form ax² + bx + c = 0.

First, rearrange the terms to get x² – x – 4 – (–2) = 0, which simplifies to x² – x – 2 = 0. Here, a = 1, b = -1, and c = -2.

Using the quadratic formula, x = [-b ± √(b2 - 4ac)] / 2a, we substitute a, b, and c:

Answer:

5.91%

Step-by-step explanation:

We are given an investment deposited fro 1 year compounded daily at an annual interest rate of 5.75%.

Compounding period per year, n: 365

The effective annual yield can be calculated by the following formula:

Effective Annual Yield = [tex] (1+\frac{r}{n})^{n}-1[/tex]

where n = 365

Interest rate, r= 5.75% = 0.0575

[tex]=(1+\frac{0.0575 }{365})^{365}-1[/tex]

= 0.059

The annual effective yield is 5.91%

Answer:

a1 = 8

a2 =10

a3 = 13

a4 = 17

Step-by-step explanation:

The first term is a1 = 8

The second term is a2 = a1 + n

                                       = 8+2

                                       = 10

The third term is a3 = a2 + n

                                       = 10+3

                                       = 13

The fourth term is a4 = a3 + n

                                       = 13+4

                                       = 17

Answer:

if the x-axis and y-axis is keeping the same numbers of its value , then it should be crossing the x then to the y axis . if the x-axis and y-axis is not kept in the same number , for instance , (-8 , 4 ) (8 , 6 ) then , It should be crossing the y- axis .

Step-by-step explanation:

Answer:

[tex]a=1,\ 2,\ 3,\ 6.[/tex]

Step-by-step explanation:

A whole number is any number of a set [tex]\{0,\ 1,\ 2,\ 3,...\}[/tex]

The equation [tex]ax=6[/tex] has a solution [tex]x=\dfrac{6}{a},\ a\neq 0.[/tex]

If [tex]a=1,[/tex] then [tex]x=\dfrac{6}{1}=6[/tex] is a whole number.

If [tex]a=2,[/tex] then [tex]x=\dfrac{6}{2}=3[/tex] is a whole number.

If [tex]a=3,[/tex] then [tex]x=\dfrac{6}{3}=2[/tex] is a whole number.

If [tex]a=6,[/tex] then [tex]x=\dfrac{6}{6}=1[/tex] is a whole number.

For all other values of [tex]a[/tex] equation  [tex]ax=6[/tex]  will have solution that is not a whole number.

Put the coordinates of the points to the inequality and check.

y > 2x + 1

for (1, 4):

4 > 2(1) + 1

4 > 2 + 1

4 > 3   CORRECT

for (1, 6):

6 > 2(1) + 1

6 > 2 + 1

6 > 3   CORRECT

for (3, 8):

8 > 2(3) + 1

8 > 6 + 1

8 > 7   CORRECT

for (2, 5):

5 > 2(2) + 1

5 > 4 + 1

5 > 5   FALSE

You move figure 5 to figure 7. You move 4 units right and 8 units up.

Describing the transformation in the figure

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

The figure

From the figure, we have:

Figures 5 and 7 have the same size, orientation and the same shape

This means that both figures can be translated

In this case, it is:

You move figure 5 to figure 7. You move 4 units right and 8 units up.

Answer: 164.4 or 165

Step-by-step explanation: So, you do 226 x 3 and you get $678. So now that you know that you have $678 worth of student tickets, you want to find how much more you need for the adult tickets, so you do $1500-$678, and you get $822. Divide it by 5 and you get 164.4, so you wanna sell about 165 tickets. Check your work by multiplying 5 by 165 and you get $825, which meets your $1500 minimum

After calculating the revenue already obtained from the student tickets sold, the remaining revenue needed to reach $1500 is found. This amount is divided by $5 (the cost of an adult ticket) to find the minimum number of adult tickets needed. Since you can't sell fractions of tickets, we round up to the next whole number, which is 165 adult tickets.

The first step to solve this problem is to calculate how much revenue has already been raised from the student tickets sold, which is $3 x 226 = $678. Then subtract this amount from the total revenue target of $1500, which gives $1500 - $678 = $822.

The choir director now needs to raise $822 from selling adult tickets. As each adult ticket costs $5, we can calculate the minimum number of adult tickets that need to be sold by dividing the amount of revenue needed by the price of an adult ticket. This is $822 / $5 = 164.4.

Since you can't sell .4 of a ticket, we'll need to round up to the next whole number, giving a minimum of 165 adult tickets that need to sell in order to reach the revenue target.

https://brainly.com/question/31539865

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Answer:

10:45

Step-by-step explanation:

v...speed = 40 mph

s...distance = 60

t...time

if he was 15 min late he arrived at 12:15

v=s/t => t=s/v

t = 60/40 = 1.5 h = 1h and 30 min

if he arrived at 12:15 and he was driving for an hour and a half just substract

12:15 - 1:30 = 11:15 - 0:30 = 10:45

he left at 10 45

Answer:

The coordinates of image are X'(-3,4), Y'(-5,0) and Z'(-1,1).

Step-by-step explanation:

The vertices of triangle XYZ are X(-2,1), Y(-4,-3) and Z(0,-2).

It is given that the triangle translated by rule

[tex](x,y)\rightarrow (x-1,y+3)[/tex]

The coordinates of image of XYZ are

[tex]X(-2,1)\rightarrow X'(-2-1,1+3)[/tex]

[tex]X(-2,1)\rightarrow X'(-3,4)[/tex]

[tex]Y(-4,-3)\rightarrow Y'(-4-1,-3+3)[/tex]

[tex]Y(-4,-3)\rightarrow Y'(-5,0)[/tex]

[tex]Z(0,-2)\rightarrow Z'(0-1,-2+3)[/tex]

[tex]Z(0,-2)\rightarrow Z'(-1,1)[/tex]

Therefore coordinates of image are X'(-3,4), Y'(-5,0) and Z'(-1,1).

The Answer: V=216cm³

Answer:

The volume of a cube shaped box with edges 6 centimeters in length is 216

Step-by-step explanation:

volume is

Width • Length • Height

The cube's width is 6 centimeters, it's length is 6 centimeters, and it's height is 6 centimeters.

6 • 6 • 6 = 216

Answer:

$100

Step-by-step explanation:

We can see from the graph that the rate of change is $20.  This is because for every increase in x, the value of y increases by $20.

Going from this, the value at x=4 is $80; this will make the value at x=5

80+20 = 100.

Answer:

The answer is C 100

Step-by-step explanation: