A given line has the equation 10x - 2y=-2.
What is the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0, 12)?
y= -5x+12
5x+y=12
y- 12 = 5(x - 1)
5x+y=-1

[tex]8x=2^3\cdot x\\40y=2^3\cdot5\cdot y\\\\\text{gcf}(8x,40y)=2^3=8[/tex]

Answer:

[tex]\frac{\pi }{6}[/tex]

Step-by-step explanation:

[tex]\frac{7\pi }{6}[/tex] is in the third quadrant

To find the reference angle subtract π from it, that is

reference angle = [tex]\frac{7\pi }{6}[/tex] - π = [tex]\frac{\pi }{6}[/tex]

Answer:

[tex]\large\boxed{y=\dfrac{2}{5}x+\dfrac{24}{5}}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

We have the slope [tex]m=\dfrac{2}{5}[/tex] and the point (-2, 4).

Put them in the equation of a line:

[tex]4=\dfrac{2}{5}(-2)+b[/tex]

[tex]4=-\dfrac{4}{5}+b[/tex]       add 4/5 to both sides

[tex]4\dfrac{4}{5}=b\to b=\dfrac{24}{5}[/tex]

Answer:

I think that the answer is C

Answer:

Please see attached image.

Step-by-step explanation:

When you multiply a function by -1 you are basically reflecting the values of the function over the x-axis.

The values that were negative become positive and the positive values become negative.

Please, take a look at the attached graph below, where there are examples with two functions.

Answer:

352.8 feet

Step-by-step explanation:

The given triangle is drawn in the image attached with. Note that the image is not drawn to scale.

We can find the length of AB using the law of sines. According to which:

[tex]\frac{a}{sin(A)}=\frac{b}{sin(B)}=\frac{c}{sin(C)}[/tex]

Since sum of angles in a triangle is 180, we can write:

A + B + C = 180

A + 102.9 + 18.6 = 180

A = 58.5

Using the values, in the law of sines, we get:

[tex]\frac{943}{sin(58.5)} = \frac{c}{sin(18.6)}\\\\ c = \frac{943 \times sin(18.6)}{sin(58.5)}\\\\ c = 352.8[/tex]

Thus, the measure of side AB would be 352.8 feet

Answer:

The length of AB is 352.8 feet

Step-by-step explanation:

* Lets revise some facts to solve the problem

- The sine rule: [tex]\frac{sinA}{BC}=\frac{sinB}{AC}=\frac{sinC}{AB}[/tex]

- The sum of the measures of the interior angles of a triangle is 180°

* Lets solve the problem

- In Δ ABC

∵ m∠ B = 102.9°

∵ m∠ C = 18.6°

∵ m ∠A + m∠ B + m∠ C = 180° ⇒ interior angles of a Δ

∴ m ∠A + 102.9 + 18.6 = 180

∴ m ∠A + 121.5 = 180 ⇒ subtract 121.5 from both sides

∴ m∠A = 58.5°

* Lets use the sine rule to find AB

∵ BC = 943

∵ m∠A = 58.5°

∵ m∠ C = 18.6°

∴ [tex]\frac{sin(58.5)}{943}=\frac{sin(18.6)}{AB}[/tex]

- By using cross multiplication

∴ AB × sin(58.5) = 943 × sin(18.6)

- Divide both sides by sin(58.5)

∴ AB = [943 × sin(18.6)] ÷ sin(58.5) = 352.76 ≅ 352.8

* The length of AB is 352.8 feet

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}2x=-y+6&(1)\\-4x+3y=8&(2)\end{array}\right\\\\(1)\\-y+6=2x\qquad\text{subtract 6 from both sides}\\-y=2x-6\qquad\text{change the signs}\\y=6-2x\\\\\text{substitute it to (2):}\\\\(2)\\-4x+3(6-2x)=8\qquad\text{use the distributive property}\\-4x+(3)(6)+(3)(-2x)=8\\-4x+18-6x=8\qquad\text{subtract 18 from both sides}\\-10x=-10\qquad\text{divide both sides by (-10)}\\x=1\\\\\text{put the value of x to (1):}\\\\y=6-2(1)\\y=6-2\\y=4[/tex]

Answer:

(1,4)

Step-by-step explanation:

i just did the quiz and it was correct

Answer:

The side length is 7 yds

Step-by-step explanation:

We know the formula for area of a square is

A = s^2 where s is the side length

49 = s^2

Take the square root of each side

sqrt(49) = sqrt(s^2)

7 =s

The side length is 7 yds

Final answer:

To find the side length of a square given its area, calculate the square root of the area. In this case, the side length of the square is 7 yards.

Explanation:

A square has an area of 49yd². To find the side length of each side, you need to take the square root of the area. In this case, the side length of each side would be 7 yards.

Supplementary angles are 2 angles that have the sum of 180 degrees. Therefore, the requirement of supplementary angles is to have the 2 angles to equal 180 degrees.

Hope this helps!

Answer:

the sum of angles must be 180 degrees

Step-by-step explanation:

The definition of supplementary angles is

"Two angles are supplementary angles if their sum is 180 degrees".

For example, if x and y are supplementary angles then

x + y = 180

Therefore, we can conclude that the requirement of supplementary angles is " the sum of angles must be 180 degrees".

This was too long for me to write on the computer.

So I wrote it and took a picture.

If you have any questions, please don't hesitate to ask in the comments.

Answer:

L ≅ P

Step-by-step explanation:

To prove congruence through ASA, we need the measures of two angles that are adjacent to a given side. If we are given that two angles are congruent to other angles in another triangle respectively and both of those angles are adjacent to one side (in which each side of each triangle is congruent) then the triangles are congruent through ASA.

To prove congruence using the ASA congruence theorem, we need to show that the angle measures of the triangles are equal. The additional information needed is that angle NM is congruent.

To prove that the triangles are congruent using the ASA congruence theorem, we need to show that the angle measures of the triangles are equal.

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Answer:

The equation would be x²/a² - y²/b² =1 , x²/9 - y²/40 = 1 ....

Step-by-step explanation:

The standard equation of hyperbola with a horizontal transverse axis is:

(x-h)²/a² - (y-k)² /b²  = 1

Use Pythagorean theorem to find the value of b.

c² = a²+b²

c= 7

a = 3

Put the value in the equation:

(7)² = (3)² +b²

49= 9+b²

49-9 = b²

40 = b²

Square root both sides:

√40 = √b²

√40 = b

Assume that the center of hyperbola is(0,0)

Thus

(x-0)²/a²  - (y-0)²/b² = 1

x²/a² - y²/b² =1

x²/(3)² - y²/(√40)² = 1

x²/9 - y²/40 = 1

Therefore the equation would be x²/a² - y²/b² =1 , x²/9 - y²/40 = 1 ....

Answer:

[tex]\dfrac{x^{2}}{9} - \dfrac{y^{2}}{40}} = 1[/tex]

Step-by-step explanation:

The standard form of the equation of a hyperbola with center (0,0) and horizontal transverse axis is

[tex]\dfrac{x^{2}}{a^{2}} - \dfrac{y^{2}}{b^{2}} = 1[/tex]

and the distance c between the foci and the y-axis is given by

c² = a² + b²

1. Calculate b

7² = 3² + b²

49 = 9 + b²

40 = b²

b = √40

2. Write the equation

[tex]\dfrac{x^{2}}{3^{2}} - \dfrac{y^{2}}{(\sqrt{40})^{2}} = 1\\\\\mathbf{\dfrac{x^{2}}{9} - \dfrac{y^{2}}{40}}} = \mathbf{1}[/tex]

The figure shows your hyperbola with a horizontal transverse axis and c = 3.

Answer:

3 packages

Step-by-step explanation:

To find how many packages you can buy for $9, you have to divide 9 by 3.

Since each package costs $3.

So, 9/3 = 3

So you can buy 3 packages of blueberries.

Answer:

3 packages

Step-by-step explanation:

Since you can buy a package for $3, and you only have $9, how many $3 can you fit? Only 3. In conclusion, you can only buy 3 packages.

Answer:

Step-by-step explanation:

CPCTC: Corresponding Parts of Congruent Triangles are Congruent

If ΔLMN ≅ ΔXYZ, then:

B. LN ≅ XZ

C. ∠Y ≅ ∠M

E. MN ≅ YZ

Corresponding sides:

LN → XZ

LM → XY

MN → YZ

Corresponding angles:

∠L → ∠X

∠N → ∠Z

∠M → ∠Y

Answer:

C. MN=YZ; D. LN=XZ; and F. Y= M

Answer:

The equation is:

[tex]y=2500t+75000[/tex] where t is the number of years satisfying the inequality [tex]0\let\le5[/tex] and y is the population at that time.

Step-by-step explanation:

So it gives us the initial amount 75000; this is what happens at time 0.

So we have the point (0,75000) is on the function's graph.

(0,75000)

(1,77500)  -> It goes 2500 per year. So year 1 the population is 75000+2500.

So we have the y-intercept of the line which is (0,75000).

We just need the slope.

Our goal is to put into slope-intercept form: y=mt+b form where m is the slope and b is the y-intercept.

To find the slope, you line up the points vertically and subtract then put 2nd difference over 1st difference.

(  1   ,   77500 )

-( 0  ,    75000)

------------------------

 1           2500

So the slope is 2500/1=2500 which we should have known earlier since the y's are increasing by 2500 while the x's are increasing by 1.

So while t is between 0 and 5 inclusive we have the following equation:

y=2500t+75000

Answer:

[tex]y=\frac{3}{5} x+1[/tex] and [tex]5y=3x-2[/tex] are parallel.

[tex]10x-6y=-4[/tex] is neither parallel nor perpendicular.

Step-by-step explanation:

First, you have to simplify each equation in terms of y.

[tex]y=\frac{3}{5} x+1\\5y=3x-2\\10x-6y=-4[/tex]

Your first equation is already in terms of x, so simplify your second equation.

[tex]5y=3x-2\\y=\frac{3}{5} x-\frac{2}{5}[/tex]

Now you can simplify your third equation.

[tex]10x-6y=-4\\-6y=-10x-4\\y=\frac{5}{3} x+\frac{2}{3}[/tex]

These are your three equations in terms of y:

[tex]y=\frac{3}{5} x+1\\\\y=\frac{3}{5} x-\frac{2}{5} \\\\y=\frac{5}{3} x+\frac{2}{3}[/tex]

Now, all you have to know is how to tell using your slope if a line is parallel or perpendicular to another.

Two parallel lines will have the exact same slope.

Two perpendicular lines will have slopes which are opposite reciprocals. For example, a line with a slope of 2 is perpendicular to a line with a slope of [tex]-\frac{1}{2}[/tex], as they have opposite signs and are reciprocal (2/1 versus 1/2) to each other.

Your first two equations have the same slope and are therefore parallel.

Your third equation is a reciprocal, but it is not opposite, and is therefore not parallel nor perpendicular.

The first and the second lines are parallel as they both have a slope of 3/5. None of the lines is perpendicular to the others.

In geometry and algebra, lines can be either parallel, perpendicular, or neither. To determine this, we need to look at the slope of each line. The slope of a line is the value of 'm' in the equation of the line, y = mx + c.

The equations you have provided are:

When two lines have the same slope, they are parallel. When two lines have slopes that are negative reciprocals of each other (meaning their product is -1), they are perpendicular. In this case, the first and the second line are parallel (both have a slope of 3/5), and none of these lines is perpendicular to the others.

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Answer:

[tex]1.02 \times 10^{13}[/tex]

Step-by-step explanation:

Speed of the sound = [tex]3.4 \times 10^{2}[/tex] meters per second

Time to calculate the distance traveled = [tex]3 \times 10^{10}[/tex] seconds

Since,

Distance = Speed x Time

Using the values we get:

[tex]Distance=3.4 \times 10^{2} \times 3 \times 10^{10}\\\\ = 3.4 \times 3 \times 10^{(2+10)}\\\\ = 10.2 \times 10^{12}[/tex]

Since the calculators show the final answer is scientific notation, the above answer in scientific notation would be:

Distance = [tex]1.02 \times 10^{13}[/tex]

Answer:

1.02 E 13

Step-by-step explanation:

The Answer is 1.02 E 13 because E means "time 10 to the power of". So 1.02 E 13 is basically just 1.02 time 10 to the power of 13.

Answer:

35 games.

Step-by-step explanation:

5 out of 8 is 5/8 of their  games which they have won.

So they should win (5/8) * 56

= 5*56 / 8

= 5*7

= 35 games.

Given the Rangers' current win rate of 5 wins out of 8 games, we can predict they would win about 35 games out of 56 if they continue at this rate.

The question you've asked is related to

ratios

and

proportions

. You're given that the Rangers won 5 out of 8 games. If we extend this winning rate to 56 games, we need to find a proportion that equals the same win rate. The setup is: 5/8 = x/56, where 'x' is the number of games we expect the Rangers to win. To solve for x, we multiply across the diagonal (5*56) and divide by 8. That results in a value of

35

, so the Rangers should win 35 games out of 56 if they continue their current winning rate.

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Answer:

Part 1) The area of the structure is [tex]2,453.25\ ft^{2}[/tex]

Part 2) The slab will contain  [tex]1,226.625\ ft^{3}[/tex] of cement

Step-by-step explanation:

Part 1) Find the area of the structure

we know that

The area of the structure is equal to the area of rectangle plus the area of semicircle

Find the area of rectangle

The area of rectangle is equal to

[tex]A=LW[/tex]

we have

[tex]L=70\ ft[/tex]

[tex]W=30\ ft[/tex]

substitute

[tex]A=(70)(30)[/tex]

[tex]A=2,100\ ft^{2}[/tex]

Find the area of semicircle

The area of semicircle is

[tex]A=\frac{1}{2}\pi r^{2}[/tex]

we have

[tex]\pi =3.14[/tex]

[tex]r=15\ ft[/tex]

substitute

[tex]A=\frac{1}{2}(3.14)(15)^{2}[/tex]

[tex]A=353.25\ ft^{2}[/tex]

Find the area of the structure

Adds the areas

[tex]A=2,100+353.25=2,453.25\ ft^{2}[/tex]

Part 2) If the structure is 6 in thick, how many cubic feet of cement will the slab contain?

Remember that

[tex]1\ foot=12\ inches[/tex]

Convert inches to feet

[tex]6\ in=6/12=0.5\ ft[/tex]

Find the volume of the structure

To obtain the volume , multiply the area by 0.5 ft (thick)

so

[tex]V=2,453.25*0.5=1,226.625\ ft^{3}[/tex]

Answer:

-1/2

Step-by-step explanation:

The equation given is

[tex]f(x)=-\frac{3}{2} -x-1+2[/tex]

Write it in form of y=mx+c where m is the gradient and c is the y-intercept

[tex]f(x)=-\frac{3}{2} -x-1+2\\\\\\y=-\frac{3}{2} -x+1\\\\\\y=-x-\frac{3}{2} +1\\\\\\y=-x-\frac{1}{2}[/tex]

y-intercept is -1/2

Answer:

1) 32

2) 8 yards

Step-by-step explanation:

1. We must first subtract the base area of the pyramid from the total surface area to get the lateral surface area:

[tex]LA=2225-25^2=1600[/tex]

The lateral surface area is 4 times the area of one the congruent triangles.

[tex]LA=4\cdot \frac{1}{2}\cdot 25\cdot x[/tex]

[tex]\implies 1600=50x[/tex]

[tex]\implies \frac{1600}{50}=\frac{50x}{50}[/tex]

[tex]32=x[/tex]

Therefore the height of the slant surface is 32 yards

2) The surface area of a cone is [tex]S.A =\pi r^2+\pi r l[/tex], where l is the slant height.

We substitute the surface area S.A=151.58 and [tex]\pi=3.14,r=4[/tex] to obtain:

[tex]151.58=3.14\cdot 4^2+3.14\cdot 4 l[/tex]

[tex]151.58=50.24+12.56l[/tex]

[tex]101.34=12.56l[/tex]

[tex]\frac{101.34}{12.56}=l[/tex]

l=8.06

To the nearest whole number, the slant height is 8 yards

Step-by-step explanation:

Daquan's age = x

Juan's age = x

Phillipa's age = x + 3

x + x + x + 3 = 36

3x + 3 = 36

3x = 36 - 3

3x = 33

x = 33 ÷ 3

x = 11

the twins are 11 years old

Answer: The answer is A

Step-by-step explanation:

Its the only one that has the least amount of options and the highest probability chance

Answer:

y = 2½x - 14

Step-by-step explanation:

You simply do this:

-29 = 5⁄2[-6] + b; -14 = b

-15

Now remember, parallel rate of changes [slopes] have SIMILAR slopes, so they remain the same.

**2½ = 5⁄2 [Do not worry]

I am joyous to assist you anytime.

Answer:

y = [tex]\frac{30-3x}{5}[/tex]

Step-by-step explanation:

Given

3x + 5y = 30

Isolate the term in y by subtracting 3x from both sides

5y = 30 - 3x ( divide both sides by 5 )

y = [tex]\frac{30-3x}{5}[/tex]

Answer:

[tex]y=\frac{-3}{5}x+6[/tex]

Step-by-step explanation:

3x+5y=30 is the given equation.

We are asked to isolate y.

The term that contains y is 5y. I'm going to first isolate 5y.

To isolate 5y we see that we have +3x with it.  To undo addition of 3x we will need to subtract 3x on both sides.

3x+5y=30

-3x          -3x

     5y=-3x+30

We now have 5y by itself.  There is actually one step left to get the y by itself.

The last step is undo this multiplication between 5 and y.

To undo multiplication you divide.

So we will be dividing 5 on both sides. This gives us:

3x+5y=30

-3x        -3x

     5y=-3x+30

     --     ---------

     5          5

So the whole reason we did that is because 5y/5 is just y.  I'm going to separate that fraction on the right hand side.  This gives me:

     y=-3/5  x   +  30/5

I'm going to simplify the 30/5 to 6.

    y=-3/5   x          +6

Answer:

{f + c < 12

{7c + 4f < 100

-5⅓ < f

7⅓ > c

Step-by-step explanation:

The keyphrase is no more than, which tells you that the inequality symbol has to be less than.

I am joyous to assist you anytime.

Answer:

B. repeating

Step-by-step explanation:

An irrational number written in  decimal form will be nonterminating  and non-repeating  decimals.

For example we have √2 = 1.4142

This rational number is non-terminating and non-repeating.

Answer:

repeating

Step-by-step explanation:

Answer:

The answer is 3/5x^6y^6

Step-by-step explanation:

The given expression is:

-9x^-1 y^-9/-15x^5 y^-3

It can be written as:

= -9/-15 * x^-1/x^5 * y^-9/y^-3

As we know that [x^m/x^n = x^m-n]

= 3/5 * x^-1-5 * y^-9+3

= 3/5 * x^-6 * y^-6

= 3/5 * 1/x^6 * 1/y^6

= 3/5x^6y^6

The answer is  3/5x^6y^6....

The expression that is equivalent to the given expression is [tex]\frac{3}{5}x^{-6}y^{-6}[/tex]

From the question, we are to determine the expression that is equivalent to the given expression

The given expression is

(-9x^-1 y^-9)/(-15x^5 y^-3)

This can be written as

[tex](-9x^{-1}y^{-9} )\div (-15x^{5}y^{-3})[/tex]
[tex](-9\times \frac{1}{x} \times \frac{1}{y^{9} } )\div (-15 \times x^{5} \times \frac{1}{y^{3} } )[/tex]

[tex](\frac{-9}{xy^{9} } )\div (\frac{-15x^{5} }{y^{3} } )[/tex]

This becomes

[tex](\frac{-9}{xy^{9} } )\times (\frac{y^{3} }{-15x^{5} } )[/tex]

[tex]\frac{-9}{-15 } \times \frac{y^{3} }{xy^{9}\times x^{5} }[/tex]

[tex]\frac{3}{5 } \times \frac{1 }{y^{6}\times x^{6} }[/tex]

= [tex]\frac{3}{5x^{6}y^{6} }[/tex]

= [tex]\frac{3}{5}x^{-6}y^{-6}[/tex]

Hence, the expression that is equivalent to the given expression is [tex]\frac{3}{5}x^{-6}y^{-6}[/tex]

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Answer:

So the solution is -2<x<4 with it's graph is

       O~~~~~~O

------(-2)--------(4)-----------

Step-by-step explanation:

The intersection symbol means it has to be included in both sets.

We have that x<4 and x>-2.

If we graph this, where do we see both shadings:

~~~~~~~~~~~~~~~0                   x<4

         O~~~~~~~~~~~~~~~~~    x>-2

-------(-2)-------------(4)------------

Both shadings happen between -2 and 4 (and not outside that area).

So the solution is -2<x<4

It's graph is

       O~~~~~~O

------(-2)--------(4)-----------

Disclaimer:

I didn't see any equal signs in your problem.

You know the [tex]\ge[/tex] or the [tex]\le[/tex] so we didn't have any closed dots.

The graph is, °←--------------------→°

                   -2____0_________4

The intersection of two sets is the set of all those elements which are common to both of the sets.

Here, given that, {x | x < 4} ∩ {x | x > -2}

It indicates that, x is less than 4, i.e. x= 3,2,1,0,-1,-2,-3,......

Again, x is greater than -2, i.e. x = -1,0,1,2,3,4,....................

Now, as it is intersection of this two sets

So, we have, x= -1,0,1,2,3.

Hence, the required graph is,

       °←------------------------------------→°

_(-2)__________0____________4_____

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[tex]\bf \stackrel{\textit{number divided by 4}}{(x\div 4)}\qquad \stackrel{\textit{then added to 17}}{+17}\qquad \stackrel{\textit{the result is}}{=}\qquad 25\implies \cfrac{x}{4}+17=25 \\\\\\ \cfrac{x}{4}=25-17\implies \cfrac{x}{4}=8\implies x=(4)8\implies x=32[/tex]

Answer: 9 points

Step-by-step explanation:

The coefficient of determination is a number between 0 and 1 used to measure the level of precision with which the regression model  created fits the data. A measure of [tex]R ^ 2 = 1[/tex]   means that the model explains the entire variation between the two variables without error.

Therefore, in this case if [tex]R ^ 2 =1[/tex] means that the 9 points are on the line

Answer:

9 points

Step-by-step explanation: