A fence is to be built to enclose a rectangular area of 1250 square feet. The fence along three sides is to be made of material that costs $6 per foot. The material for the fourth side costs $18 per foot. Find the dimensions of the rectangle that will allow for the most economical fence to be built

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]

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

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.

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

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

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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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: 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: 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

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:

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 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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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

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: 0=9

Step-by-step explanation:

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 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:

More than likely no full answer key however there might be answers for each individual question.

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.

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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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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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.

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 required inequality is 4¹/₃ > -5¹/8.

Inequality shows relation between two expression which are not equal to each others.

The given numbers are 4¹/₃ and -5¹/8.

The numbers are plotted on the number lines below,

To determine the number which is greater,

The number which is greater than zero will be greater from the numbers 4¹/₃ and -5¹/8.

4¹/₃  is a greater number.

The inequality can be written as,

4¹/₃ > -5¹/8.

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Answer:

FINAL ANSWER: BODY B was moving at 1.35 m/s, 21 degrees above the x-axis.

Step-by-step explanation:

REFER TO THE IMAGES for the SOLUTIONS TO YOUR PROBLEM. Each step will be explained here.

When you solve for velocities before or after collision, you need to remember the law of conservation of moment which can be expressed through this formula:

 BEFORE                   AFTER

m1v1+m2v2      =     m1v1 + m2v2

This basically means, the sum of momentum of 2 objects BEFORE collision is equal to the same 2 objects AFTER collision.

The type of collision we have in your case is a 2D collision, where there is a gliding collision or they touch at an angle. So when you solve these type of problems, you have to consider the x and y components of motion. It makes things easier if you make a table like in the image to sort out your components.

STEP 1: COMPUTE FOR MOMENTUM BEFORE COLLISION for each OBJECT involved.

To solve for momentum, the formula is mass x velocity or mv:

STEP 1a: Body A: The problem states that before collision Body A is moving along the positive X-axis so the velocity will be +4.5 m/s. Notice that the velocity of the y component is 0 m/s. This is because BODY A is moving along the x-axis, with no mention that it deviated from it.

STEP 1b: Body B: Body B is at rest before collision, that is why it is not moving at all, which means both x and y components are equal to 0.

STEP 1c: Get the sum of all X components and the Sum of Y components.

STEP 2:   COMPUTE FOR MOMENTUM AFTER COLLISION for each OBJECT involved.

Step 2a: BODY A: Notice that we now have an angle. hence the cos and sin. We do this because we are breaking or decomposing the diagonal velocity into its x and y component. To get the x-component you get the cos of the angle and multiply it to the momentum of the diagonal or overall velocity. For y-component, instead of cos, you get the sin.

Step 2b: BODY B: Here we have unknowns, which we will derive later on. In this step, just plug in what you know into the formula.

Step 2c: We already know the x and y momentum of the objects BEFORE collision and the law of conversation of momentum states that the momentum AFTER is the same. With this total we can move onto the next step.

STEP 3: Solving for the X and y component of the velocity of BODY B AFTER collision.

Step 3a: Using the formula given in the image, we plug in what we know first. We know the momentum of the BODY A already, so we can put it into the equation. We also know the sum of both momenta and we put that into the equation too. Now all we do is derive the formula. DO NOT FORGET THAT WE ARE TO USE ONLY X COMPONENTS.

Step 3b: is the same as the previous step but instead, we use Y COMPONENTS only.

STEP 4: Combining X and Y components to get the resultant velocity:

For this step you need to remember the Pythagorean theorem. This is applied here because when you draw a free body diagram of the velocities, it creates a right triangle where :

the hypotenuse represents the final velocity

the opposite side represents the y-component and;

the adjacent represents the x-component.

Refer to the image for the solution.

STEP 5: Solving for the angle at which BODY B is moving:

For this step you need to remember SOH CAH TOA to find the angle at which BODY B is moving. You already have all the components you need, including the hypotheses. You can use any of the functions, and they should come up with the same approximation.

FINAL ANSWER: BODY B was moving at 1.35 m/s, 21 degrees above the x-axis.

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.)

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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