A set of two or more equations with the same variables is called a system of equations. When you set the
two expressions that are equal to the same variable equal to each other, like you did in the previous lesson,
you are using the Equal Values Method of solving a system of equations. Use the Equal Values Method to
solve the following problem.
It is time to cool off on a hot summer day! Team Sunshine is filling an inflatable kiddie pool from a garden
hose. The pool has 30 gallons in it and Team Sunshine is adding 8 gallons per minute with a garden hose.
Next door, Team Breeze's pool is already filled with 180 gallons of water. They are emptying the pool at 5
gallons per minute with buckets.
Write two equations to represent the situation. Use the equations to find how long it takes until both pools
have the same amount of water. Check your calculations.

Answer: 4x^2

Step-by-step explanation: Multiply that by -1 to get -4x^2 and multiply by 7x to get 28x^3

Answer:

2x-7

Step-by-step explanation:

Answer:

They are all correct.

Step-by-step explanation:

1.

1/2(b)(h)

1/2(4)(6)

1/2(24)

12

2. l x w

7 x 5

35

3. (b)(h)

(8)(4)

32

Step-by-step explanation:

side length(a)=5yd

slant height(l)=7yd

vertical height(h)=?

Now,

h2=(l)2+(a/2)2

h=find it

Then,

T.S.A.=a2+2al

Surface area of square pyramid is 95 square yard.

The word "surface" means " the exterior or outside part of an object or body". So, the total surface area of a square pyramid is the sum of the areas of its lateral faces and its base.

So, the surface area of a square pyramid is the sum of the areas of four of its triangular side faces and the base area which is square.

Given

Length = 5 yd

Slant height = 7 yd

Surface area of square pyramid = 4 (Area of triangle) +  area of square

S = [tex]4\frac{1}{2}bh+side^{2}[/tex]

S = [tex]4 . \frac{1}{2} (5)(7)+5.5[/tex]

S = 70 + 25

S = 95 square yard.

Hence, Surface area of square pyramid is 95 square yard.

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Answer:

See explanations below

Step-by-step explanation:

Using the coordinate points in the table (0, 4) and (2, 9)

Slope m = y2-y1/x2-x1

m = 9-4/2-0

m = 5/2

slope = 5/2

Get the y-intercept

Substitute m = 5/2 and (0,4) into y = mx+c

4 = 5/2(0) + c

4 = 0+c

c = 4

y-intercept is 4

Get the equation

Recall that y = mx+c

y = 5/2x + 4

Using another 2 points (2,9) and (4, 14)

Slope = 14-9/4-2

Slope = 5/2

Since the slope is the same for the coordinates, hence the the equation is correct

Answer:

A. 107 kg

B. 49 kg

Step-by-step explanation:

Answer:

I dont know I am sorry I really had to ask a question and i don't have enough points so sorry you can report me if you want but I really need some

Answer:

Step-by-step explanation:

Let's start with function (x, y)

Transformations in the given order result in following

A dilation by a factor of 4 with the origin as the center of dilation

A reflection across the y-axis

A 90° counterclockwise rotation about the origin

A translation 3 units down

The final function is:

Answer:

l(x) = (-4y, -4x - 3)

I got the same answer as Mhanifa and if you want the explanation check his, because mine sucks :(

Answer:

e. A matched pairs t-test for a mean difference

Step-by-step explanation:

When the observations from two samples are paired either naturally or by design we find the differences between the two observations of each pair.Treating the differences as a random sample from a normal population with mean ud= u1-u2 and unknwn standard deviation σd we perform one sample t- test on them. This is called the paired difference t- test or a paired t- test.

Suppose 10 young recruits are given a physical training by the Army . Their weights are recorded before and after the training. These observations constitutes natural pairing .

When we eliminate the undesireable sources of variation to take observations in pairs , this is called pairing by design.

Answer:

53

Step-by-step explanation:

106 miles per hour would get him home in 1 hour but it takes 2 hours so you can divide 106 by 2 to 53 miles per hour.

Answer:

It can't be simplified or added together because one is multiplied by x and the other is not

Step-by-step explanation:

Answer:

The number of milk chocolate pieces is between 115 and 120 pieces.

Step-by-step explanation:

Answer:

If the goal is to break the vases: 3/20 = 15.0% or 0.15

If the goal is to not break the vases: 17/20 = 85.0% or 0.85

Answer:

Angle C

Step-by-step explanation:

By applying sine rule in the given triangle,

[tex]\frac{\text{sinB}}{CD}=\frac{\text{sinC}}{BD}=\frac{\text{sinD}}{BC}[/tex]

[tex]\frac{\text{sinB}}{\text{sinC}}=\frac{\text{CD}}{\text{BD}}[/tex]

Therefore, sides of the given triangle will be in the same ratio as the sine of the angles.

Since, BD > BC > CD

Therefore, Opposite angles of these sides will be in the same ratio.

∠C > ∠D > ∠B

Largest angle of the triangle is angle C.

Answer:

x-30

Step-by-step explanation:

Answer: 5(x-2)=40     5x-10 = 40      5x=50    x=10  

Step-by-step explanation:

^

Answer:

1.86/2 = 0.93/2 = 0.465/2 = 0.2325

Step-by-step explanation:

Answer:

No, there is not sufficient evidence to support the claim that the bags are underfilled

Step-by-step explanation:

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 434 gram setting.

This means that the null hypothesis is:

[tex]H_{0}: \mu = 434[/tex]

It is believed that the machine is underfilling the bags.

This means that the alternate hypothesis is:

[tex]H_{a}: \mu < 434[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

434 is tested at the null hypothesis:

This means that [tex]\mu = 434[/tex]

A 9 bag sample had a mean of 431 grams with a variance of 144.

This means that [tex]X = 431, n = 9, \sigma = \sqrt{144} = 12[/tex]

Value of the test-statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{431 - 434}{\frac{12}{\sqrt{9}}}[/tex]

[tex]z = -0.75[/tex]

P-value of the test:

The pvalue of the test is the pvalue of z = -0.75, which is 0.2266

0.2266 > 0.01, which means that there is not sufficient evidence to support the claim that the bags are underfilled.

Answer:

1568

Step-by-step explanation:

The computation of the minimum sample size is shown below:

Given that

Error E = 11

The population standard deviation [tex]\sigma[/tex] =217

Confidence level 1-α = 95%

Now following formula should be used

n > (Zalpha ÷ 2 × sigma ÷ E)^2

As we know that

Zalpha ÷ 2= 1.96

Now the sample size is

n> (1.96 × 202  ÷ 10)^2

= 1568

Answer:

345 - 40% = 207$

Step-by-step explanation:

(345 - 30%) - 15% = 205.3 (Better deal)

Answer:

30% off and additional 15% at the register

Step-by-step explanation:

Deal 1

$345 × 40% = $138

$345 - $138 = $207

Deal 2

$205.30

Answer:

Semiconductors are somewhere in-between conductors and insulators. This means that they are specific when it comes to conducting electricity meaning that their conduction of electricity varies based on their condition at the time.

For instance, they can conduct electricity when heated.

Properties:

    1. Perfect insulator at Absolute Zero.

As mentioned above, semi conductors are better at conducting electricity when they are heated. At Absolute zero - the lowest temperature possible -  therefore, these materials would conduct absolutely no electricity thereby making them perfect insulators.

   2. More resistance than Conductors but less than Insulators

As mentioned above, they have properties in-between those of insulators and conductors. One of those is their resistance. They can resist more than conductors but less than insulators.

Answer:I think 3 years

Step-by-step explanation:

sorry if im wrong

Answer:

Step-by-step explanation:

There are several sort of "obvious" properties of equality/congruence. Keeping them sorted out can be a bit of a trick.

  A = A . . . . reflexive property

  A = B ⇔ B = A . . . . symmetric property (erroneously cited in the proof)

  A = B, B = C ⇒ A = C . . . . transitive property (the one needed in the proof)

__

Not to confuse the issue, but there is also the "substitution property of equality" that says if X = Y, then X can be substituted for Y or vice versa. In the end, the transitive property is an application of this, where we're substituting for B in the second equation, or for A in the first equation.

The A=B=C form of Statement 1) in the proof is what gives you the clue it is the transitive property that is wanted here.

9514 1404 393

Answer:

  143 in²

Step-by-step explanation:

The figure is dimensioned in such a way that it can be divided easily into three rectangular areas. The top rectangle is 10 in wide and 7 in high. The vertical rectangle below that is 4 in wide and 12 in high, and the square appendage on the right is 5 in square.

Then the total area is the sum of products of length and width:

  A = (10 in)(7 in) + (4 in)(12 in) + (5 in)(5 in) = (70 +48 +25) in²

  A = 143 in²

The area of the irregular figure is 143 in².

Answer:

54= 15 + J

Step-by-step explanation:

j= 39

Answer: Area of the shape is 168 ft.

Step-by-step explanation: Split the shape into 2 shapes: A rectangle and a triangle.

Area of the rectangle shape is 144 and the area of the triangle is 24. Add them and you get 168.

Answer:

B)  x = 12

Step-by-step explanation:

m∡EOU = m∡TQE

m∡EOU =180 - (39+45) = 96°

m∡TQE:  7x + 12 = 96

7x = 84

x = 12

Answer:

The number of required shelves is 5

You have to find the HCF of 45, 105, and 75.