If 8x−4y=20 and 4x−8y=4, what is the value of x−y?
(A) 1 (B) 2 (C) 3 (D) 4 (E) 6

Step-by-step explanation:

We know any line that is parallel to other line has same slope.

Here, m1=m2

So, slope will be -1/2.

For this case we have by definition, that if two lines are parallel then their slopes are equal. That is to say:

[tex]m_ {1} = m_ {2}[/tex]

If we have a line of the form:

[tex]y_ {1} = - \frac {1} {2} x_ {1} + b_ {1}[/tex]

Then a parallel line will be given by:

[tex]y_ {2} = - \frac {1} {2} x_ {2} + b_ {2}[/tex]

That is, the slopes are the same!

Answer:

Option C

Answer:

the y-intercept is -6

Step-by-step explanation:

3x+5y=30

    -5y -5y

(30-)3x=30-5y(-30)

3x-30=5y/y

3/5x-6=y

Answer:

Step-by-step explanation:

y=5/2x+2

2y=5x+4

y=5/2x+2

y=5/2x+2

they are the same line/equation so infinite number of solutions

Answer:

Option c. 30,000

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]

Let

y ----> safe load in pounds

x ----> length in feet of a horizontal beam

we have

For [tex]x=15\ feet, y=2,000\ pounds[/tex]

Remember that

[tex]k=y*x[/tex]

substitute

[tex]k=2,000*15=30,000[/tex]

Hello There!

X=2

To solve this, we first need to understand that when we see an X in parentheses, we multiply the number before it in this case 4 by X.

The answer is 2 because we multiply 4 by 2 which is the x value so 4*2 is equal to 8 and they we add 9 to it because the sum of 6 and 3 is 9.

Finally, our answer we get is 17 so our X value is 2.

Have A Great Day!

Answer:

I believe it's 22/15

Step-by-step explanation:

17x -6 + 3x - 5 = 1x + 11 + 4x first you add the 17x and 3x and 1x and the 4x

which it would be: 20x - 6 -5 = 5x + 11;

20x - 11 = 5x + 11,

 -5            -5

15x - 11 = 11

      +11   +11

15x = 22

15       15     Divide

x = 22/15

Hope my answer has helped you if not i'm sorry.

Area of a triangle is 1/2 x base x height.

The base is 6 units long and the height is 4 units.

Area = 1/2 x 6 x 4 = 12 square units.

Answer:

Sample Response: The goal is to get x alone on one side of the equals sign. First, isolate the variable by applying the subtraction property of equality to subtract 1/2x from both sides. Next, find a common denominator to combine like terms. Then use inverse operations to multiply both sides by the reciprocal of the fraction coefficient. The result will be x = 16. Finally, check the solution by substituting 16 for x in the original equation.

Step-by-step explanation:

58x = 12x + 2

58x -12x = 2

46x = 2

x = 2/46 = 0.434

There are many situations in which equations can be used. Whenever an unknown quantity has to be found, an equation can be formed and solved.

An equality relationship between two expressions written on both sides of the equal to sign.

Learn more about Equation here

brainly.com/question/13763238

#SPJ2

0.001, 0.014, 0.1, 9.41

Answer:

d) Isoceles triangle

Step-by-step explanation:

you can only split it down the middle

Answer:

D. Isosceles Triangle

Step-by-step explanation:

Answer: 2(10y+3x)(10y-3x)

Step-by-step explanation:

2(100y²- 9x²)

2[ (10y+3x)(10y-3x) ]

Answer:

199

Step-by-step explanation:

For this problem, you have to write an formula.

a(n)=a(1)+(n-1)d

n is the term you are trying to find (in this case it's 50).

a(1) is the first term in the sequence (in this case it's 3).

d is the common difference (in this case it's 4).

Plug those in, and you get:

a(50)=3+(50-1)4

And you can easily solve that and get a(50)=199.

Answer:

199

Step-by-step explanation:

Answer:

Minimum = 50

First Quartile = 80

Median = 135

Third Quartile = 165

Maximum = 200

Step-by-step explanation:

First, it is important to reorder our values into ascending order:

50, 60, 100, 130, 140, 150, 180, 200

You've correctly identified the minimum, median and maximum values, however the quartiles are where the mistakes lie.

1. In order to calculate the first quartile, you need to look at where the median of the first half of the values is, ie. 50, 60, 100, 130

The median will be the value between (or the average of) 60 and 100:

(60 + 100)/2 = 80

Thus, the first quartile is 80.

2. In order to calculate the third quartile, we must find the median of the second half of the data set, ie. 140, 150, 180, 200

The median will be the value between (or the average of) 150 and 180:

(150 + 180)/2 = 165

Thus the third quartile is 165.

I find it's always a good idea to just draw this out and label the different values on paper to make it a bit easier.

Hope that helped! If you find anything confusing just ask :)

The minimum, first quartile, median, third quartile, and maximum of the data set are:

Minimum = 50

First quartile = 115

Median = 145

Third quartile = 190

Maximum = 200

It is the middle value of the given set of numbers after arranging the given set of numbers in order.

We have,

To find the minimum, first quartile, median, third quartile, and maximum of the given data set, we need to arrange the data in order from smallest to largest:

50, 60, 100, 130, 140, 150, 180, 200

The minimum is the smallest number in the set, which is 50.

To find the first quartile, we need to find the median of the lower half of the data set.

Since there are 8 numbers in the set, the median is the average of the 4th and 5th numbers in the set:

First quartile = (100 + 130)/2 = 115

The median is the middle number in the set.

Since there are 8 numbers in the set, the median is the average of the 4th and 5th numbers in the set:

Median = (140 + 150)/2 = 145

To find the third quartile, we need to find the median of the upper half of the data set.

Since there are 8 numbers in the set, the median is the average of the 6th and 7th numbers in the set:

Third quartile = (180 + 200)/2 = 190

The maximum is the largest number in the set, which is 200.

Therefore,

The minimum, first quartile, median, third quartile, and the maximum of the data set are:

Minimum = 50

First quartile = 115

Median = 145

Third quartile = 190

Maximum = 200

Learn more about the median here:

https://brainly.com/question/28060453

#SPJ3

Hello There!

To find out if these lengths make a triangle, you have to add up any two sizes and they must be greater than the third side for it to form a triangle.

Let's Test It!

"9+12=21" 21 is greater than 15

"9+15=24" 24 is greater than 12

Yes This Does Form A Triangle!

Answer:

Yes, the triangle lengths 9, 12, and 15 are lengths of the sides of a right triangle.

Step-by-step explanation:

There are multiple different ways to prove that this answer is correct.

To begin, we could recognize that these side lengths are a Pythagorean triple, or multiples of side lengths that satisfy the Pythagorean theorem, and thus prove that the lengths constitute a right triangle. In this case, 9, 12, and 15 represent the 3, 4, 5 Pythagorean triple where each side length is multiplied by a factor of three.

3x3=9

4x3=12

5x3=15

Therefore, these side lengths do make a right triangle because they represent a multiple of a Pythagorean triple.

If we didn’t recognize this, we could always plug the side lengths into the Pythagorean theorem, a^2 + b^2 = c^2.

In this case, we get

9^2 + 12*2 = 15^2

If we simplify, we get:

81+144 = 225

And if simplified further, we get:

225=225,

Which is a true statement, proving that these side lengths do make up a right triangle.

Hope this helps!

Answer: The general equation for the lateral area of a pyramid is LSA=(1/2)pl

P is the perimeter

L is the slant

Answer:

"It is translated 1 unit left and stretched vertically by a factor of 3"

Step-by-step explanation:

The parent function here is y = x^2

Let's give out some general rules of transformation:

If y = f(x) is a parent function, then

1. If we have y = a * f(x)

| a | > 1 is a stretch;  

0 < | a | <1 is a compression, vertically for both

and

2. If we have y = f(x-c), this means horizontal translation to right c units and y = f(x+c) means horizontal translation c units left

Looking at y = 3(x+1)^2, we can say that "it is vertical stretch by a factor 3 and horizontal translation 1 units left"

Answer:

60

Step-by-step explanation:

There are 5 different ways to choose the first class.

There are 4 classes left to choose from.

There are 4 different ways to choose the second class.

There are 3 classes left to choose from.

There are 3 different ways to chooses the third class.

5*4*3 = 60

Answer:

2x10 + 8x6 + 4x2 - x + 3

Step-by-step explanation:

it has the same numbers and variables. it is descending because it's starting from the the highest value or biggest variable then goes from greatest to least from there.

Answer:

[tex]2x^{10}+8 x^{6} +4x^{2} -x+3[/tex]

Step-by-step explanation:

The given polynomial is

[tex]4x^{2} -x+8x^{6}+3+2x^{10}[/tex]

A descending order refers to the position of terms, where the "higher term" has the greatest exponent (greatest grade), and we order from greatest to least to have a descending order, as follows

[tex]2x^{10}+8 x^{6} +4x^{2} -x+3[/tex]

Notice that the temrs are placed from greatest expoenent to least.

Therefore, the answer is [tex]2x^{10}+8 x^{6} +4x^{2} -x+3[/tex]

[tex]\dfrac{x-3}{x}[/tex] - initial fraction

[tex]\dfrac{x-3+1}{x+1}=\dfrac{2}{3}\\\\\dfrac{x-2}{x+1}=\dfrac{2}{3}\\\\2(x+1)=3(x-2)\\2x+2=3x-6\\x=8\\\\\dfrac{8-3}{8}=\dfrac{5}{8}[/tex]

It's [tex]\dfrac{5}{8}[/tex]

Answer:

20 , 20 , 30 will produce a triangle

Step-by-step explanation:

* Lets study how to know if the lengths of the three segments

 can formed a triangle

- It is a fact that in any triangle the sum of the smallest two sides

 must be greater than the largest side

- Lets study some examples

# If the lengths of the three segments are 5 , 6 , 7

∵ 5 and 6 are the smallest

∴ 5 + 6 = 11

∵ 11 > 7 ⇒ the sum greater than the 3rd side

∴ 5 , 6 , 7 can formed a triangle

# If the lengths of the three segments are 5 , 7 , 12

∵ 5 and 7 are the smallest

∴ 5 + 7 = 12

∵ 12 = 12 ⇒ the sum equal the 3rd side

∴ 5 , 7 , 12 can not formed a triangle

# If the lengths of the three segments are 10 , 12 , 24

∵ 10 and 12 are the smallest

∴ 10 + 12 = 22

∵ 22 < 24 ⇒ the sum less than the 3rd side

∴ 10 , 12 , 24 can not formed a triangle

* Now lets solve the problem

∵ The length of the three segments are 20 , 20 , 30

∵ 20 and 20 are the smallest

∴ 20 + 20 = 40

∵ 40 > 30 ⇒ the sum greater than the 3rd side

∴ 20 , 20 , 30 will produce a triangle

Answer:

Δ = 60

Step-by-step explanation:

Given a quadratic in standard form : ax² + bx + c = 0 : a ≠ 0

Then the discriminant

Δ = b² - 4ac

Given

3x² + 6x = 2 ( subtract 2 from both sides )

3x² + 6x - 2 = 0 ← in standard form

with a = 3, b = 6 and c = - 2

b² - 4ac = 6² - (4 × 3 × - 2) = 36 - (- 24) = 36 + 24 = 60

Answer:

Green: 5/9 Red:2/9

Step-by-step explanation:

Answer:

Step-by-step explanation:

Look at the picture.

If polygons ABCD and EFGH are similar, then corresponding sides are in proportion.

[tex]\dfrac{GH}{CD}=\dfrac{FG}{BC}[/tex]

We have

[tex]GH=z,\ CD=10,\ FG=6,\ BC=8[/tex]

Substitute:

[tex]\dfrac{z}{10}=\dfrac{6}{8}[/tex]          croaa multiply

[tex]8z=(10)(6)[/tex]

[tex]8z=60[/tex]           divide both sides by 8

[tex]z=\dfrac{60}{8}\\\\z=7.5[/tex]

The value of  [tex]f(g(x))=-6x-5[/tex]

Given functions are, [tex]f(x)=-2x-3,g(x)=3x+1[/tex]

We have to find composite function [tex]f(g(x))[/tex].

         [tex]f(g(x))=f(3x+1)\\\\f(g(x))=-2(3x+1)-3\\\\f(g(x))=-6x-2-3\\\\f(g(x))=-6x-5[/tex]

Learn more about the composite function here:

https://brainly.com/question/10687170

To find (fxg)(X), you need to multiply the two given functions, apply the distributive property, and then combine like terms. The result for (fxg)(X) is -6x² - 11x - 3.

Step-by-step Explanation:

Therefore, (fxg)(X) = -6x² - 11x - 3.

Answer:

The correct answer option is D. [tex]10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}[/tex].

Step-by-step explanation:

We are given the following expression:

[tex] \left ( \sqrt { 10 x ^ 4 } -x \sqrt { 5 x ^ 2 } \right ) \left ( 2 \sqrt { 15 x ^ 4 } + \sqrt { 3 x ^ 3 } \right ) [/tex]

Assuming that [tex]x\geq 0[/tex], we are to find its simplified product.

[tex] \left ( \sqrt { 10 x ^ 4 } -x \sqrt { 5 x ^ 2 } \right ) \left ( 2 \sqrt { 15 x ^ 4 } + \sqrt { 3 x ^ 3 } \right ) [/tex]

[tex]\\\\ = 2 \sqrt { 150 x ^ 8 } + \sqrt { 3 0 x ^ 7 }-2x\sqrt{75x^6}-x\sqrt{15x^5} \\\\ =2\sqrt{25\times6x^8}+x^3\sqrt{30x}-2x\sqrt{25\times3x^6}-x^3\sqrt{15x} \\\\ =10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}[/tex]

The simplified product is:

       [tex]10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}[/tex]

The expression is given by:

[tex](\sqrt{10x^4}-x\sqrt{5x^2})(2\sqrt{15x^4}+\sqrt{3x^3})[/tex]

Now we know that:

[tex]\sqrt{x^2}=x\\\\and\\\\\sqrt{x^4}=\sqrt{(x^2)^2}=x^2[/tex]

Hence, we get the expression as follows:

[tex](\sqrt{10x^4}-x\sqrt{5x^2})(2\sqrt{15x^4}+\sqrt{3x^3})=(x^2\sqrt{10}-x\cdot x\sqrt{5})(2x^2\sqrt{15}+x\sqrt{3x})[/tex]

Now, we will use the property that:

[tex](a+b)(c+d)=a(c+d)+b(c+d)[/tex]

Hence, we have the expression as:

[tex]=x^2\sqrt{10}(2x^2\sqrt{15}+x\sqrt{3x})-x^2\sqrt{5}(2x^2\sqrt{15}+x\sqrt{3x})[/tex]

[tex]=2x^4\sqrt{10}\sqrt{15}+x^3\sqrt{10}\sqrt{3x}-2x^4\sqrt{5}\sqrt{15}-x^3\sqrt{5}\sqrt{3x}[/tex]

Now we know that:

[tex]\sqrt{a}\sqrt{b}=\sqrt{ab}[/tex]

i.e. we have:

[tex]=2x^4\sqrt{150}+x^3\sqrt{30x}-2x^4\sqrt{75}-x^3\sqrt{15x}\\\\=2x^4\sqrt{5^2\cdot 6}+x^3\sqrt{30x}-2x^4\sqrt{5^2\cdot 3}-x^3\sqrt{15x}\\\\=10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}[/tex]

Answer:

D for both

Step-by-step explanation:

Exercise is the condition and healthier is the outcome. So if you exercise then you will be healthier.

All cardinals are red. But not all red birds are cardinals. So d is the only one that is always true

1. if you exercise, then you will be healthier.

2. if a bird is a cardinal, it is red

A conditional statement is a statement that can be written in the form “If P then Q,” where P and Q are sentences.

Given:

Exercise makes you healthier.

So, we have to write in the form of if- then statement

Thus, the statement is if you exercise, then you will be healthier..

Now, for the second statement "Cardinals are red birds."

The conditional statement is  if a bird is a cardinal, it is red.

Learn more about Conditional Statement here:

https://brainly.com/question/18152035

#SPJ6

Answer:

(-2,0.2)

Step-by-step explanation:  

we have

[tex]f(x)=2(3)^{x}[/tex]

[tex]g(x)=10log(x+3)[/tex]  

Solve the system of equations by graphing

Remember that the solution of the system of equations is the intersection point both graphs

The intersection points are (-1.9,0.2) and (1,6)

see the attached figure

therefore

The solution of the system of equations are the points (-1.9,0.2) and (1,6)

Answer:

Girls: 9; Boys: 11

Step-by-step explanation:

16-7=9

14-3=11

Answer:

n=+ -0.0321563225311

Answer:

The coordinates of vertex A" is (3 , 1)

Step-by-step explanation:

* Lets revise The translation of a point

- If the point (x , y) translated horizontally to the right by h units

 then the new point = (x + h , y)

- If the point (x , y) translated horizontally to the left by h units

 then the new point = (x - h , y)

- If the point (x , y) translated vertically up by k units

 then the new point = (x , y + k)

- If the point (x , y) translated vertically down by k units

 then the new point = (x , y - k)

* Now lets solve the problem

∵ Δ ABC has a vertex A = (-4 , 2)

∵ The Δ ABC is translated 2 units right and 5 units down to form

   triangle A′B′C′

- From the rule above the x coordinate id added by 2 and the

 y-coordinate is subtracted by 5

∴ A' = (-4 + 2 , 2 - 5) = (-2 , -3)

∴ The image of vertex A is A' = (-2 , -3)

∵ Δ A'B'C' is then translated 5 units right and 4 units up to form

   triangle A″B″C″

- From the rule above the x coordinate is added by 5 and the

 y-coordinate is add by 4

∴ A" = (-2 + 5 , -3 + 4) = (3 , 1)

* The coordinates of vertex A" is (3 , 1)

Answer:

it is a

Step-by-step explanation: