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4 years ago

Y - 2x + 4 y = 3x - 6 solve using substitution

Mathematics

1 answer:

dlinn [17]4 years ago

7 0

Answer:

(10,24)

Step-by-step explanation:

Well first we plug in y = 3x - 6 for y in y = 2x + 4

3x - 6 = 2x + 4

Then we combine like terms and seperate x.

x - 6 = 4

x = 10.

If x is 10 we plug that in

y = 3(10) - 6

y = 30 -6

y = 24

(10,24)

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Paula, linda and aaron make handmade cards

sergiy2304 [10]

Answer:

Linda makes 72 more handmade cards than Paula

Step-by-step explanation:

First you need to find out how many handmade cards Linda makes by making a proportion.

The first ratio is 3 to 2 and since we are trying to find out how many cards Linda makes, it will be represented by x.

3 to 2 represents how many Linda makes to how many Aaron makes so the second ratio will be x to 72 since that's how many cards Aaron made.

Now you can put it into a proportion:

3/2 = x/72

Next you have to do Cross Product Property to find x

So 3*72 = 216

2*x = 2x

2x = 216

Now divide 2 by itself and then by 216 to find what x equals.

2/2 = 1

216/2 = 108

So Linda makes 108 handmade cards.

Now we need to find how many cards Paula made.

The ratio for how many Paula makes to how many Linda makes is 1 to 3

Since we are trying to figure out how many Paula made we need to represent it with x.

The second ratio will be x to 108 since 108 is how many cards Linda made.

Now you can put it into a proportion:

1/3 = x/108

Then you need to do Cross Product Property to find x

So 1*108 = 108

3*x = 3x

3x = 108

Now we need to divide 3 by itself to isolate x and then divide 3 by 108 to find what it equals.

3/3 = 1

108/3 = 36

So Paula makes 36 handmade cards.

Since the question is asking for how many more does Linda make than Paula you need to subtract 108 and 36.

So 108 - 36 = 72

Linda makes 72 more handmade cards than Paula.

8 0

4 years ago

Read 2 more answers

Carissa also has a sink that is shaped like a half-sphere. The sink has a volume of 3000

defon

Answer:

a) 80
b) 56

Step-by-step explanation:

a) Calculate the volume of the the cup using volume of cylinder equation: $V = \pi r^{2} h$

Where V = Volume, r=radius, and h=height. Your answer should be in cubic inches ( $in^3$ ).
You're given diameter, so use equation $d/2 = r$ to find radius.
Substituting these equations will give you: $V = \pi (d/2)^2 h$
However, the given volume of the sink is 3000 $\pi$ , meaning that you should modify your results to match this value. Do not substitute $\pi$ for 3.14..., leave it as a symbolic value. Your final V of the cup should = 37.5 $\pi$
Divide the volume of the sink by the volume of the cup. This number will be the amount of cups needed to empty it. In equation form:
$Vsink / V cup =$ # of cups.
Note the the $\pi$ will cancel each other out, so there's not need to factor that in.
b) Repeat the steps above with the new d (diameter) value.

5 0

3 years ago

Place the indicated product in the proper location on the grid. (4x^3+7y^3 z^ 4) ^2

ella [17]

Answer:

$16x^{6} +56x^{3}y^{3} z^{4} +49y^{6} z^{8} \\$

Step-by-step explanation:

To solve this type of problems first need to review some laws of exponents:

When you are multiplying the same base, you need to add the exponents.

$x^{2} +x^{8} = x^{2+8} = x^{10}$

When you are raising a base with power to another power, you should keep the base and multiply the exponents:

$(x^{2} y^{5})^3 = x^{2*3} y^{5*3} = x^{6} y^{15}$

Now for the expression $(4x^{3} + 7y^{3} z^{4} )^2$

Write the multiplying factors:

$(4x^{3} + 7y^{3} z^{4} )(4x^{3} + 7y^{3} z^{4} )$

Multiply the term $4x^{3}$

$(4x^{3} + 7y^{3} z^{4} )(4x^{3} + 7y^{3} z^{4} ) = 16x^{3+3} + 28x^3y^{3} z^{4}$

Then multiply the term $7y^{3}z^{4}$

$(4x^{3} + 7y^{3} z^{4} )(4x^{3} + 7y^{3} z^{4} ) = 16x^{3+3} + 28x^3y^{3} z^{4}\\\\+ 28x^3y^{3} z^{4} + 49y^{3+3} z^{4+4}$

Simplify the exponents:

$(4x^{3} + 7y^{3} z^{4} )(4x^{3} + 7y^{3} z^{4} ) = 16x^{6} + 28x^3y^{3} z^{4}\\\\+ 28x^3y^{3} z^{4} + 49y^{6} z^{8}$

Add like terms:

$= 16x^{6} + 56x^3y^{3} z^{4} + 49y^{6} z^{8}$

5 0

3 years ago

From a train station, one train heads north, and another heads east. Some time later, the northbound train has traveled 12 miles

tigry1 [53]

9514 1404 393

Answer:

20 miles

Step-by-step explanation:

The north and east distances form the legs of a right triangle. The straight-line distance between the trains is the hypotenuse of that triangle. The Pythagorean theorem can be used to find the length of the hypotenuse (d).

d² = 12² +16²

d² = 144 +256 = 400

d = √400 = 20

The two trains are 20 miles apart.

<em>Additional comment</em>

You may recognize the given distances are in the ratio 3 : 4. You may recall that side ratios of 3 : 4 : 5 make a right triangle. If so, you recognize that the straight-line distance is (4 miles)×5 = 20 miles. (3:4:5 right triangles show up often in algebra and geometry problems, so might be something you want to look for.)

3 0

3 years ago

A researcher decides to split scores on an exam into quartiles. She determines that a score of 64 is at the 25th percentile, a s

wariber [46]

Answer: IQR = 16

Step-by-step explanation:

The given data is 25 th percentile is 64, 50th percentile is 74 and 75 th percentile is 80.

percentage : 25 50 75

score : 64 74 80

Median:- The median is obtained by first arranging the data in ascending or descending order and applying the following rule.

If the number of observations is odd, then the median is observation

term

If the number of observations is even, then the median is observation and observations.

given n=3, middle term is '74'

In this given data the median is (M) = 74

Interquartile range IQR = median of upper half-median of lower half

= 80-64

= 16

IQR = 16

8 0

2 years ago