2x+3y=15
x+y=6
work out the value of x and y

Answer:

14. [tex]y = -2x -1[/tex]

15. [tex]y = -\frac{3}{4}x +3[/tex]

16. [tex]y= 4x + 9[/tex]

17. [tex]y = -\frac{5}{3}x -2[/tex]

18. [tex]y= -\frac{2}{3}x -5[/tex]

19. [tex]y = 4x -3[/tex]

20. [tex]y = -3x -7[/tex]

Step-by-step explanation:

Solving (14):

Given

[tex](x_1,y_1) = (-7,13)[/tex]

[tex]Slope (m) = -2[/tex]

Equation in [tex]slope- intercept[/tex] form is:

[tex]y - y_1 = m(x-x_1)[/tex]

Substitute values for y1, m and x1

[tex]y - 13 = -2(x -(-7))[/tex]

[tex]y - 13 = -2(x +7)[/tex]

[tex]y - 13 = -2x -14[/tex]

Collect Like Terms

[tex]y = -2x -14 + 13[/tex]

[tex]y = -2x -1[/tex]

Solving (15):

Given

[tex](x_1,y_1) = (-4,6)[/tex]

[tex]Slope (m) = -\frac{3}{4}[/tex]

Equation in [tex]slope- intercept[/tex] form is:

[tex]y - y_1 = m(x-x_1)[/tex]

Substitute values for y1, m and x1

[tex]y - 6 = -\frac{3}{4}(x - (-4))[/tex]

[tex]y - 6 = -\frac{3}{4}(x +4)[/tex]

[tex]y - 6 = -\frac{3}{4}x -3[/tex]

Collect Like Terms

[tex]y = -\frac{3}{4}x -3 + 6[/tex]

[tex]y = -\frac{3}{4}x +3[/tex]

Solving (16):

Given

[tex](x_1,y_1) = (-5,-11)[/tex]

[tex](x_2,y_2) = (-2,1)[/tex]

First, we need to calculate the [tex]slope\ (m)[/tex]

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

[tex]m = \frac{1 - (-11)}{-2 - (-5)}[/tex]

[tex]m = \frac{1 +11}{-2 +5}[/tex]

[tex]m = \frac{12}{3}[/tex]

[tex]m = 4[/tex]

Equation in [tex]slope- intercept[/tex] form is:

[tex]y - y_1 = m(x-x_1)[/tex]

Substitute values for y1, m and x1

[tex]y - (-11) = 4(x -(-5))[/tex]

[tex]y +11 = 4(x+5)[/tex]

[tex]y +11 = 4x+20[/tex]

Collect Like Terms

[tex]y= 4x + 20 - 11[/tex]

[tex]y= 4x + 9[/tex]

Solving (17):

Given

[tex](x_1,y_1) = (-6,8)[/tex]

[tex](x_2,y_2) = (3,-7)[/tex]

First, we need to calculate the [tex]slope\ (m)[/tex]

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

[tex]m = \frac{-7 - 8}{3- (-6)}[/tex]

[tex]m = \frac{-7 - 8}{3+6}[/tex]

[tex]m = \frac{-15}{9}[/tex]

[tex]m = -\frac{5}{3}[/tex]

Equation in [tex]slope- intercept[/tex] form is:

[tex]y - y_1 = m(x-x_1)[/tex]

Substitute values for y1, m and x1

[tex]y - 8 = -\frac{5}{3}(x -(-6))[/tex]

[tex]y - 8 = -\frac{5}{3}(x +6)[/tex]

[tex]y - 8 = -\frac{5}{3}x -10[/tex]

Collect Like Terms

[tex]y = -\frac{5}{3}x -10 + 8[/tex]

[tex]y = -\frac{5}{3}x -2[/tex]

18.

Given

[tex](x_1,y_1) = (-6,-1)[/tex]

[tex]y = -\frac{2}{3}x+1[/tex]

Since the given point is parallel to the line equation, then the slope of the point is calculated as:

[tex]m_1 = m_2[/tex]

Where [tex]m_2[/tex] represents the slope

Going by the format of an equation, [tex]y = mx + b[/tex]; by comparison

[tex]m = -\frac{2}{3}[/tex]

and

[tex]m_1 = m_2 = -\frac{2}{3}[/tex]

Equation in [tex]slope\ intercept\ form[/tex] is:

[tex]y - y_1 = m(x-x_1)[/tex]

Substitute values for y1, m and x1

[tex]y - (-1) = -\frac{2}{3}(x - (-6))[/tex]

[tex]y +1 = -\frac{2}{3}(x +6)[/tex]

[tex]y +1 = -\frac{2}{3}x -4[/tex]

[tex]y= -\frac{2}{3}x -4 - 1[/tex]

[tex]y= -\frac{2}{3}x -5[/tex]

19.

Given

[tex](x_1,y_1) = (-2,-11)[/tex]

[tex]y = -\frac{1}{4}x+2[/tex]

Since the given point is parallel to the line equation, then the slope of the point is calculated as:

[tex]m_1 = -\frac{1}{m_2}[/tex]

Where [tex]m_2[/tex] represents the slope

Going by the format of an equation, [tex]y = mx + b[/tex]; by comparison

[tex]m_2 = -\frac{1}{4}[/tex]

and

[tex]m_1 = -\frac{1}{m_2}[/tex]

[tex]m_1 = -1/\frac{-1}{4}[/tex]

[tex]m_1 = -1*\frac{-4}{1}[/tex]

[tex]m_1 = 4[/tex]

Equation in [tex]slope\ intercept\ form[/tex] is:

[tex]y - y_1 = m(x-x_1)[/tex]

[tex](x_1,y_1) = (-2,-11)[/tex]

Substitute values for y1, m and x1

[tex]y - (-11) = 4(x - (-2))[/tex]

[tex]y +11 = 4(x +2)[/tex]

[tex]y +11 = 4x +8[/tex]

Collect Like Terms

[tex]y = 4x + 8 - 11[/tex]

[tex]y = 4x -3[/tex]

20.

Given

[tex](x_1,y_1) = (-10,3)[/tex]

[tex](x_2,y_2) = (2,7)[/tex]

First, we need to calculate the slope of the given points

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

[tex]m = \frac{7 - 3}{2 - (-10)}[/tex]

[tex]m = \frac{7 - 3}{2 +10}[/tex]

[tex]m = \frac{4}{12}[/tex]

[tex]m = \frac{1}{3}[/tex]

Next, we determine the slope of the perpendicular bisector using:

[tex]m_1 = -\frac{1}{m_2}[/tex]

[tex]m_1 = -1/\frac{1}{3}[/tex]

[tex]m_1 = -3[/tex]

Next, is to determine the coordinates of the bisector.

To bisect means to divide into equal parts.

So the coordinates of the bisector is the midpoint of the given points;

[tex]Midpoint = [\frac{1}{2}(x_1+x_2),\frac{1}{2}(y_1+y_2)][/tex]

[tex]Midpoint = [\frac{1}{2}(-10+2),\frac{1}{2}(3+7)][/tex]

[tex]Midpoint = [\frac{1}{2}(-8),\frac{1}{2}(10)][/tex]

[tex]Midpoint = (-4,5)[/tex]

So, the coordinates of the midpoint is:

[tex](x_1,y_1) = (-4,5)[/tex]

Equation in [tex]slope- intercept[/tex] form is:

[tex]y - y_1 = m(x-x_1)[/tex]

Substitute values for y1, m and x1: [tex]m_1 = -3[/tex] & [tex](x_1,y_1) = (-4,5)[/tex]

[tex]y - 5 = -3(x - (-4))[/tex]

[tex]y - 5 = -3(x +4)[/tex]

[tex]y - 5 = -3x-12[/tex]

Collect Like Terms

[tex]y = -3x - 12 +5[/tex]

[tex]y = -3x -7[/tex]

Answer:

5/6x+4 1/6=y

Step-by-step explanation:

The equation to find a slope-intercept is mx+b=y

m=slope

x=x coordinates

y=y coordinates

b= y intercept

m=5/6

x=-1

y=-5

b=4 1/6

Y intercept:

5/6(-1)+b=-5

-5/6+b=-5

b=4 1/6

However, it asks for an equation of the line, not (-1,-5), so we only need to write m and b, but not x and y.

So: 5/6x+4 1/6=y

Hope this helps!

Answer:

1 5555/10000

Step-by-step explanation:

One plus five thousand, five hundred and fifty-five all over 10000.

Answer:

[tex]\frac{311}{200}[/tex]

Step-by-step explanation:

1.5555

=[tex]\frac{15555}{10000}[/tex]

=[tex]\frac{311}{200}[/tex] (dividing numerator and denominator by 5)

Answer:k=5b/4 - 3/4

Step-by-step explanation:

Answer:

[tex]k=\frac{5}{4}b - \frac{3}{4}[/tex]

Step-by-step explanation:

-3k + 7k = 5b - 3

4k = 5b - 3

[tex]k=\frac{5}{4}b - \frac{3}{4}[/tex]

Answer:

a) 323 kph with a directional bearing of S 22° E

Step-by-step explanation:

to find the ground speed:

just do the pythagorean theorem.

c²=300²+120²

c²=104400

c=323

to find the directional bearing:

use the law of sines!

sin(90)/323 = sin(θ)/120

(*explanation: since the plane is heading due south and the wind is from due west, it makes a 90 degree angle; and the side opposite of the 90 degree angle is 323. set it equal to sin theta over 120; theta is the angle u r trying to find, and the side opposite of it is 120)

cross multiply:

120sin90=323sin(θ)

divide 323 on both sides:

sin(θ)=0.3715

use inverse sin to find out degree measure:

sin⁻¹(0.3715)=21.8

rounds up to 22.

The ground speed and direction of the plane is 323 kph with a directional bearing of S 22° E. Therefore, option A is the correct answer.

To find the ground speed of the plane, we need to know what a vector is

What is a vector?

A vector is a variable that has both magnitude and direction.

Since the airplane is headed due south with an airspeed of 300 kph, its vector is V = (-300 kph)j.

Also, the wind is blowing from the west at 120 kph. Its vector is v = (-120 kph)i

Now, the ground speed of the plane V' is the resultant vector of the airspeed and wind speed.

A resultant vector is the sum of two or more vectors.

So, V' = v + V

V' = (-120 kph)i + (-300 kph)j

So, its magnitude V' = √(x² + y²) where

x = -120 kph and

y = -300 kph.

So, V' = √[(-120 kph)² + (-300 kph)²]

= √[14400 kph² + 90000 kph²]

= √(104400 kph²)

= 323.11 kph

≅ 323 kph

The direction of the plane

Its direction, Ф = tan⁻¹(y/x)

Ф = tan⁻¹(-300 kph/-120 kph)

Ф = tan⁻¹(2.5)

Ф = 68.2°

From the South-line we have α = 90° - Ф = 90° - 68.2° = 21.8° ≅ 22°

So, the directional bearing of the plane is S22°E.

So, the ground speed and direction of the plane is 323 kph with a directional bearing of S 22° E.

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Answer:

It will be $85,  34÷ 4

will give you 8.5 then you multiply it by 10,× 10=85

Answer:

272

Step-by-step explanation:

56:7=8 (she earns 8$ in 1 hour)

8×34=272

Answer: (x-5)^2

Step-by-step explanation:

-5 and -5 multiply to 25 and add to -10

The expression for the inequality is written as a > 200.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that each day, the cafeteria serves more than 200 apples with lunch.

The inequality will be written as,

a > 200

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c = k(r + 1)

8 = k(3 + 1)

8 = 4k

8/4 = k

2 = k

c=2(r + 1)

When c = 20, then

20 = 2(r + 1)

20 = 2r + 2

20 - 2 = 2r

18 = 2r

18/2 = r

9 = r

Therefore, the value of r is 9 when c is 20.

Answer:

53

Step-by-step explanation:

5 choices × 5 choices × 5 choices = 53 possible 3 digit codes including repeats

 [tex]\boldsymbol{125}[/tex] unique [tex]3[/tex] digit codes can be created from the [tex]5[/tex] digits.

Given that digits are [tex]=\boldsymbol{\{1,2,3,4,5 \}}[/tex].

Number of digits [tex]=\boldsymbol{5}[/tex]

With repetition" means that repetition is allowed. Thus, in each of the three places, we have five choices.

Therefore,

Number of unique three digit codes can be created from the five digits [tex]=5\times 5\times 5[/tex]

[tex]=\boldsymbol{125}[/tex]

So, [tex]\boldsymbol{125}[/tex] unique [tex]3[/tex] digit codes can be created from the [tex]5[/tex] digits.

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59.9%

Sorry I don’t have time to explain in the middle of an exam

The rate of growth needs to be 59.9%.

The formula used to determine the future value of an investment when interest is compounded continuously is:

FV =  A x [tex]e^{r}[/tex] x N

$320,000 = $16,000 x [tex]e^{r}[/tex] x 5

Divide both sides by $16,000

20 = 5[tex]e^{r}[/tex]

Take the In of both sides

In(20) = 5r

Divide both sides by 5

r = 59.9%

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Answer:

36

Step-by-step explanation:

40 * .10 = 4

40-4 = 36

Answer:

im willing to bet that there is 3 in each carton

(just a guess for the points also theres no multiple choice?)

The quantity of trays that were in each of the cartons the manager unloaded was 12 trays.

To determine the quantity of trays in each carton, we need to analyze the given information step by step:

From these points, we can deduce the following:

Now, let's solve for the number of trays in each carton.

Let's assume that the number of trays in each carton is "x."

We know that 24 trays were taken initially, and each serving line ended up with 12 trays. So, we can set up the equation:

24 + 12 + 12 + 12 = 4x

48 = 4x

Dividing both sides of the equation by 4:

12 = x

Therefore, there were 12 trays in each of the cartons that were unloaded.

To summarize, each carton that Elvira unloaded contained 12 trays.

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Answer:

-4

Step-by-step explanation:

Slope intercept form is

-y = Mx + b

Answer:

= -32a+64b

Step-by-step explanation:

thats the answer

Answer:

????

Step-by-step explanation:

Answer:

where's the shape

Step-by-step explanation:

what's the length and width, maybe I can help

Answer:

B

a proportional relationship in a graph needs to go through the 0.0, and also needs to be a stright line.

Answer:

hil how are you doing

Step-by-step explanation:

Answer:

100000

Step-by-step explanation:

 The given expression is;

       Log x = 5

Find x;

 Solution:

The log is to the base of 10;

   Log₁₀x  = 5

     if Logₓ t  = n;

                 t = xₙ

So;

      Log₁₀x  = 5

               x  = 10⁵

               x  = 100000

Answer:

B and $684

Step-by-step explanation:

B, because wednesday is three days after sunday so 4 times 3 because she walks 4 more laps each day until saturday. Add the 24 laps she already walks 4(3)=12+24=36

By saturday she would've walked 48 laps, so 48 times 3 for the 3 dollars each lap. 48(3)=144 now u have to find the other days so the equation you would use is 3(24 + 4x), x for the day until saturday. 3(24+4(1))=3(28)=84,just do that for each day and then add all them together because the question asked by the end of the week, saturday, how much money so yea. 84+96+108+120+132+144=684

(honestly u could just keep adding 12 to the previous number as that's what it's increasing by.) haha rlly hope I'm not wrong on the second one. Have a nice day!

Answer:

Step-by-step explanation:

an hour, or 60 minutes

Answer:

60 minutes

Step-by-step explanation:

i d 1 0 t

Answer:

So you need to compute all the rates to see which is the best deal.

$1.79/12.5ft^2=$0.1432 per ft^2

$5.29/40ft^2=$0.13225 per ft^2

$8.49/50ft^2=$0.1698 per ft^2

$6/60ft^2=$0.10 per ft^2

So the last option is the cheapes per square foot and thus is the best deal.  Ordered from least to greatest.

Sherbert, blue, red, and green

Step-by-step explanation:

hope this helps

Answer:

The order goes Orange, Blue, Red, and Green

Step-by-step explanation:

By dividing the total cost by the amount of square feet, you get the unit value for the wrapping paper per square foot.