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Answer:

(3, -5) or x=3, y=-5

Step-by-step explanation:

In a systems of equation, we're looking for what pair of (x, y) values make both equations true. When a pair of (x, y) makes an equation true, that just means it's on the line of the graph. So a pair of (x, y) values that makes both equations true, is simply when both lines intersect.

There are multiple methods to solve a systems of equation including: elimination, substitution, and graphing.

Each way has their advantages, and I'll show to to apply substitution and elimination

In this method we want to manipulate one of equations (or possibly both) so that they each have a variable with the "same coefficient" but different sign (one positive, one negative).

In the equations given, you may notice that the "y" variables each have the same coefficient, so we could multiply either of the equations by negative one, so one has positive y and another has negative y.

The reason we want the equations set up in this way, is so that we can add the equations which results in one of the variables being "eliminated" so that we can solve for a single value for the other variable.

So we start with:

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

let's multiply the top equation by -1 (remember to apply this to both sides so you don't actually change the equation)

[tex]-(x+y)=-(-2)\implies -x-y=2[/tex]

So now from here we have the two equations

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

If we add the two equations we get the following

[tex](-x+2x)+(-y+y)=(2+1)[/tex]

Notice how the -y and y cancel each other out? This is the entire point of the elimination method, so now we can solve for x

[tex]x=3[/tex]

This actually simplifies in our favor since -x + 2x = x, and the right side is just some constant, so we don't need to manipulate the equation anymore to solve for x.

Now that we know what the x-value is, we can plug this into either equation to solve for y. For simplicity I'll use the x + y = -2 equation.

[tex]3+y=-2\\y=-2-3\\y=-5[/tex]

So we know the solution is (3, -5) or [tex]x=3,\ y=-5[/tex]

The substitution method has the same goal as the elimination method, that is, get a one-variable equation so we can solve for one value. In this method, we want to define one variable in terms of the other variable, that way we can substitute this into the other equation, giving us a new equation with only one variable.

So let's just start with the top equation:

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

From here we can define "y" in terms of x, by subtracting x from both sides.

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

Now let's look at our other equation

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

Notice how it has a y variable, well we have one way of defining it: y = -2 - x. If we plug this into the bottom equation, now we only have x terms, giving us a one-variable equation.

[tex]2x+(-2-x)=1[/tex]

Now let's add 2 to both sides to cancel out the -2, and simplify 2x - x

[tex]x=3[/tex]

From here we essentially do the same thinkg we did in elimination method, except it may be a bit easier since we already have "y" solved for, we just need an x-value, which we now have!

[tex]y=-2-x\\\text{we know that x = 3}\\y=-2-(3)\\y=-5[/tex]

so now we have our solution: [tex](3, -5)\text{ or }x=-3, y=-5[/tex]

The simplified form of the given expression, 6 × 10⁻³ / 8 × 10⁻⁶, is 3/4  × 10³

From the question, we are to simplify the given expression

The given expression is

6 × 10⁻³ / 8 × 10⁻⁶

Simplifying the expression

6 × 10⁻³ / 8 × 10⁻⁶

This can be written as

6/8 × 10⁻³/10⁻⁶

Reduce the fraction

3/4  × 10⁻³/10⁻⁶

Apply the division law of indices

3/4  × 10⁻³ ⁻ ⁽⁻⁶⁾

3/4  × 10⁻³ ⁺ ⁶

3/4  × 10³

Hence, the value is 3/4  × 10³

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Answer:

4/11 is not a terminate

Because it is non- terminate,if we divide those non- terminating numbers than the divided answer is repeated.

Answer: y= 50x+ 100

Step-by-step explanation:the trend line starts below 200 hundred so you

can make an educated guess and say it is 100 then you got to 2 on the fat and it is at 200 but it is 2 so 100+100= 200 for one and 100+50+50= 200 which would give you your x

what I ended up with was each student needs to to collect about $17.87

Answer: 17 million

Step-by-step explanation: thank me later hehe

Answer: Teresa needs 27 logs to maintain the fire for 18 hours.

Step-by-step explanation:

We're dealing with a proportional relationship, so each ratio of logs to hours must be equivalent.

Hint #22 / 4

Here's one way to write the proportion:

18 hours = y logs

​

= 4 hours 6 logs

​

Hint #33 / 4

Now, solve the proportion for yyy:

18

y

yyy

=

4/6

​

=

2/3

​

=

2/3⋅18

=

2/3⋅18

​

=

1/2

3⋅18/9

=

1/3⋅9

​

= 1/27

​

=27

​

Answer: 20.65

Step-by-step explanation:

2.95 is the unit rate x 7 equals 20.65

Answer:

Step-by-step explanation:

We set up a proportion to find X, which in this case is the cost of seven packages.

Proportion: 5.90:2=x:7

Unit cost: 5.90/2=2.95

But we want to find the cost of seven cookies.

So, we multiply the unit cost by 7.

2.95*7= 20.65

Thus, seven packages of cookies costs $20.65.

Answer:

The probability of rolling a number less than 5 is 3/6 or 0.5.

Step-by-step explanation:

Step 1: List all the possible outcomes of rolling the die.

The set of equally likely outcomes is {1,2,3,4,5,6)

Step 2: Count the number of outcomes that fulfill the criteria.

Three outcomes fulfill the criteria (1,2,3)

Step 3: Calculate the probability by dividing the number of outcomes that fulfill the criteria by the total number of outcomes.

The probability of rolling a number less than 5 is 3/6 or 0.5

Step-by-step explanation:

5x³-6x³=-x³

5x²--3x²=8x²

-4x--5x= x

11--5=16

overall answer: -x³+8x²+x+16

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You planted the tomato seeds on the 10th of May

The complete question is added at the end of this solution

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

Number of days to ripe = 80 days

Date the tomato seed is eaten = July 29

The above parameters can be represented using the following subtraction equation:

The date you planted the seeds = Date the tomato seed is eaten - Number of days to ripe

Substitute the known values in the above equation, so, we have the following representation

The date you planted the seeds = July 29 - 80 days

Evaluate the difference

So, we have the following representation

The date you planted the seeds = May 10

Hence, the date you planted the seeds is May 10

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Complete question

It takes a tomato seed an average of 80 days to ripe. If you eat ripe tomatoes on July 29. When did you plant the tomato seeds?

Step-by-step explanation:

(X+3)/(x-2)=(x-4)/(X+5)

cross multiply

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

x(X+5)+3(X+5) = X(x-2)-4(x-2)

x²+5x+3x+15=x²-2x-4x+8

x²+8x+15=x²-6x+8

x²-x²+8x+6x=8-15

14x=-7

X=-7/14

X=-1/2

B)to verify substitute the answer in the equation given

that is RHS

X+3/x-2

=(-1/2+3)/(-1/2-2)

=5/2/-5/2

=-1

from LHS

x-4/(x+5)

=(-1/2-4)/(-1/2+5)

=-9/2/-9/2

=-1

the LHS= RHS

proved

Answer:6(a)+4(b)+9(c)

Step-by-step explanation:

Im pretty sure there was an equation that you did not put.

But the equal used to solve would be 6(a)+4(b)+9(c)

a= money earned pulling weeds

b=money earned raking leaves

c=money earned cutting grass.

Answer: c

Step-by-step explanation:

1) 2 2/5 + 5 2/10

2) 2 2/5 = 12/5 = 24/10

3) 5 2/10 = 52/10

4) 24 + 52 = 76

5) 76/10 = 38/5

6) convert to mixed number

Answer:

0.6

Step-by-step explanation:

3/5 is equal to 0.6

Answer:

3/5 could be equal to many things. I will just give a list of all the possibilities:

3/5 = 3/5

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

3/5 = 3:5

3/5 = 0.6

3/5 = 60%

Step-by-step explanation:

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Slope intercept form has the general form of y = mx + b, where m is the slope and b is the y-intercept.

You are given the y-intercept with the point (0, -10). Thus, the y-intercept is -10.

You are also given the slope of 1.

Next, just plug your numbers in!

y = 1x - 10

y = x - 10

Hope this helped!

The equation of the line can be written as y = -x - (7/12).

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is y-intercept.

Given that the line passes through  (5/12, −1) and (−3/4, 1/6). Therefore, the slope of the line can be written as,

Slope of the line = [(1/6) - (-1)] / [(-3/4) - (5/12)]

                            =  [(1/6) + 1] / [(-3/4) - (5/12)]

                            = (7/6) / [(-9-5)/12]

                            = (7/6) / (-14/12)

                            = -1

Now, the equation can be rewritten with slope and a point as,

y = mx + c

(1/6) = -1(-3/4) + C

(1/6) = (3/4) + C

C = (1/6) - (3/4)

C = (2/12) - (9/12)

C = (-7/12)

Therefore, the equation of the line can be written as,

y = mx + c

y = (-1)x + (-7/12)

y = -x - (7/12)

Hence, the equation of the line can be written as y = -x - (7/12).

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The value of angle RPQ in the circle is 115 degrees.

The intersecting chords theorem, also known as the chord theorem, is an elementary geometry statement that describes a relationship between the four line segments formed by two intersecting chords within a circle.

If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.

Therefore,

∠RPQ = 1  / 2 (arc angle RQ + arc angle SA)

arc angle RQ = 175 degrees

arc angle SA = 55 degrees

Hence,

∠RPQ  = 1 / 2 (175 + 55)

∠RPQ  = 1 / 2 (230)

∠RPQ  = 115 degrees.

The angle is 115°.

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Answer:

850

Step-by-step explanation:

Mackenzie has 3200 more red marbles than yellow,

(y + 3200 = r)

And she also has 3840 more blue marbles than the yellow marbles,

(y + 3840 = b)

Then let's assume that Mackenzie has 1 yellow marble.

1 + 3200 = 3201 red marbles

1 +3840 = 3841 blue marbles

If she gives away 1490 blue marbles away, then she is left with 2351 blue marbles.

(3841 - 1490 = 2351)

Now she's left with 2351 blue marbles, and 3201 red marbles.

r - b =?

3201 - 2351 = 850

Mackenzie has 850 more red marbles than blue marbles.

(If you want, you can change the number of yellow marbles, but it will be the same answer.)

If someone purchased 7 adult tickets and 3 kids tickets, they would get 10 total tickets.

If someone purchased a adult tickets and k kids tickets, they would get a+k total tickets.

Answer: 0=9

Step-by-step explanation:

At this rate, the number of tennis ball launched by the machine in 2 hours is 600.

The tennis ball machine can launch 60 tennis balls in 12 minutes. At the same rate the ball machine launched a particular amount of tennis ball in 2 hours.

The number of tennis ball the ball machine launched in two hours can be calculated as follows:

rate = number of tennis ball launched / time in minutes

rate = 60 / 12

rate = 5 tennis ball per minutes

Therefore, in 2 hours

5 = x / 120

x = 120 × 5

x = 600 tennis balls

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The number of variable terms in the given expression are 6g and 5h.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have the following expression -

6g − 11 + 5h

The number of variable terms in the given expression are -

6g and 5h.

Therefore, the number of variable terms in the given expression are 6g and 5h.

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Answer:

y = 3x + 1

Step-by-step explanation:

The general form of the slope intercept form is y = mx + b where m is the slope and b is the y-intercept.  

In perpendicular lines, we find the slope of the second equation (m2) using the formula:

[tex]m_{2}=-\frac{1}{m_{1} }[/tex]

Since -1/3 is m1 we have:

[tex]m_{2}=-\frac{1}{-(\frac{1}{3}) } \\ m_{2}=3[/tex]

Now that we've found the slope of the second line, we simply need to find b or its y-intercept by plugging in (-2, -5) and our slope:

[tex]-5=3(-2)+b\\-5=-6+b\\1=b[/tex]

Thus, the equation of the second line is y = 3x + 1

Answer:

1728

Step-by-step explanation:

Just multiply 108 by 16.

Answer:

384 ounces

Step-by-step explanation:

If it takes 4 1/2 pounds of grapes to make 1 pound of Rasins, then we need to figure out how many pounds of Rasins we can make with 108 pounds of grapes.

(Or you can do 108 divided by 4 1/2)

4 1/2 x 10 = 45

4 1/2 x 4 = 18

45 + 45 + 18 = 108

10 + 10 + 4 = 24

(Looking at the work you did above, we can take 54, and multiply that by 2 to get 108, therefore, we can just multiply 12 by two to get 24)

Now we need to convert the pounds to ounces.

If one pound is equal to 16 ounces, then we can use the equation,

24 x 16 = 384

108 pounds of grapes yields 384 ounces.

The zeros and the multiplicities of the polynomial are t = -7, t = -6 and t = -2 and 2, 3 and 6, respectively

The equation of the polynomial is given as

f(t) = -12(t+7)²(t+6)³(t+2)⁶

The multiplicities are the powers of the factors while the zeros are calculated by setting the factors to 0

So, we have

t + 7 = 0

t + 6 = 0

t + 2 = 0

Calculate the value of t

t = -7, t = -6 and t = -2

Hence the zeros are t = -7, t = -6 and t = -2

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The number of student that took neither chemistry nor biology is 17.

A study of 50 high school students showed that exactly 25 of them took biology, exactly 20 of them took chemistry, and exactly 12 of them took both subjects.

The number of student that took neither biology nor chemistry can be calculated as follows;

Hence,

U = 50

n(C) = 20

n(B) = 25

n(B n C) = 12

n(B n C)' = ?

Therefore,

U = n(C) + n(B) - n(B n C)  + n(B n C)'

Therefore,

50 = 20 + 25  - 12 + x

50 - 45 + 12 = x

x = 5 + 12

x = 17

Therefore, 17 student took neither chemistry nor biology.

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Could you elaborate a bit more on what the question is asking? Cuz it seems there is more to this then is shown. If you could, I'll see what else I can do to help. Tysm!

The equation would be (8 x b) + 10 or 8b + 10, hopefully this helped :))

Answer:

8b+10

Step-by-step explanation:

8b+10

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