What is the slope and y-intercept of the equation 3(y − 2) + 6(x + 1) − 2 = 0? A. slope = -2, y-intercept = B. slope = 2, y-intercept = C. slope = -2, y-intercept = D. slope = 2, y-intercept = E. slope = -2, y-intercept = Reset Next

[tex]\bf \qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ \stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+6}x\stackrel{\stackrel{c}{\downarrow }}{+9}=0 ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{\underline{one solution}}~~\textit{\Large \checkmark}\\ positive&\textit{two solutions}\\ negative&\textit{no solution} \end{cases} \\\\\\ 6^2-4(1)(9)\implies 36-36\implies 0[/tex]

Answer:

0

Step-by-step explanation:

Descriminator is calculated by the following formula:

b*b - 4 * a * c, where a,b,c are the numbers in equitation.

For this case we have that by definition, the equation of the line of the slope-intersection form is given by:

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

Where:

m: It's the slope

b: It is the cut point with the y axis.

By definition, if two straight lines are parallel then their slopes are equal. Thus, the slope of the line sought will be [tex]m = 2.[/tex]

[tex]y = 2x + b[/tex]

We substitute the given point to find b:

[tex]2 = 2 (-1) + b\\2 = -2 + b\\2 + 2 = b\\b = 4[/tex]

Finally the line is:

[tex]y = 2x + 4[/tex]

Answer:

[tex]y = 2x + 4[/tex]

Answer:

y = 2x + 4.

Step-by-step explanation:

The slope = the slope of y = 2x - 3 which is 2.

Using the point-slope form:

y - y1 = 2(x - x1)

Using the point (-1, 2):

y - 2 = 2(x - -1)

y =  2x + 2 + 2

y = 2x + 4  is the answer.

Answer: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225.

Step-by-step explanation:

1 x 1 = 1

2 x 2 = 4

3 x 3 = 9

4 x 4 = 16

5 x 5 = 25

6 x 6 = 36

7 x 7 =49

8 x 8 = 64

9 x 9 = 81

10 x 10 = 100

11 x 11 = 121

12 x 12 = 144

13 x 13 = 169

14 x 14 = 196

15 x 15 = 225

Answer:

13

Step-by-step explanation:

Using pythag the. , we see the rule a2+b2=c2 (Square)

so, a2=25, b2= 144,

25+144=c2

c2=169

sqrt=13

Answer:

a = 44 degrees

Step-by-step explanation:

angle 0 + angle a + angle b = 180 degrees

angle b = angle a

92 + a + b = 180 degrees

92 + 2a = 180 degrees

a = 44 degrees

!!

Answer:

The exact distance is √(29) or 29^(1/2)

Step-by-step explanation:

Find the answer using the distance formula (aka the Pythagorean theorem)

d=√(x1+x2)^2+(y1+y2)^2)

d=√(-1+6)^2+(4+-2)^2), Solve for d:

d= √((25)+(4))

d=√(29)

Answer:

[tex]\sqrt{35}[/tex]

Step-by-step explanation:

To calculate the distance (d) use the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 1, 4) and (x₂, y₂ ) = (6, - 2)

d = [tex]\sqrt{(6+1)^2+(-2-4)^2}[/tex]

  = [tex]\sqrt{7^2+(-6)^2}[/tex]

  = [tex]\sqrt{49+36}[/tex] = [tex]\sqrt{85}[/tex] ← exact value

Answer:

{1,-1}

Step-by-step explanation:

Let's do both!

Factoring!

x^2-1 is a difference of squares.

The formula for factoring a difference of squares is: u^2-v^2=(u-v)(u+v).

So the factored form of x^2-1 is (x-1)(x+1).

So we want to solve the equation x^2-1=0 which is equivalent to solving

(x-1)(x+1)=0.

If you have A*B=0 then either A=0 or B=0.

So in our case we have x-1=0 or x+1=0.

Now we just solve the equations.

x-1=0 can be solved by adding 1 on both sides giving us x=1.

x+1=0 can be solved by subtracting 1 on both sides giving us x=-1.

Square root!

When you want to use square roots, you have to have a perfect square containing the variables and a constant.  We have that here.

We have x^2-1=0 which is equivalent to x^2=1.  You could get this last equation by adding one on both sides of x^2-1=0.

Anyway, once you have the square part equals the constant, all you have to do is square root both sides to get rid of the square on the variable part.

[tex]x^2-1=0[/tex]

[tex]x^2=1[/tex]

[tex]\sqrt{x^2}=\sqrt{1}[/tex]

[tex]x=\pm \sqrt{1}[/tex]  It leads to two answers because [tex]\sqrt{x^2}=|x|[/tex].

[tex]x=\pm 1[/tex]

The solution to the equation x^2-1=0 is x = 1 or x = -1.

To solve the equation x^2-1=0 by factoring or finding square roots, we can start by rearranging the equation to get x^2=1. This means that the square of x is equal to 1. To find the square root of both sides, we take the square root of 1, which gives us x=±1. So the solution to the equation is x = 1 or x = -1.

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Answer:

True options: 1, 2 and 5

Step-by-step explanation:

From the given diagram, you can see that the center of the hyperbola is placed at the origin, so first option is true (see attached diagram for definition of center, vertices, foci, i.e.)

There are two vertices of the hyperbola, they are placed at (-6,0) and (6,0), so second option is true.

The transverse axis is the segment connecting vertices, this segment is horizontal, so option 3 is false.

The foci are not placed within the rectangular reference box, so this option is false.

The directrices are vertical lines with equations [tex]x=\pm \dfrac{a}{e}[/tex], so this option is true.

Answer:1 2 5

Step-by-step explanation:

The answer is 12 points

I have the table so I added the numbers to get 108, and there are 9 numbers, so yu do 108/9 equaling to 12

Answer:

[tex]2 {x}^{2} + 8x + 6 \\ 2( {x}^{2} + 4x + 3) \\ = 2( {x}^{2} + x + 3x + 3) \\ = 2(x + 1)(x + 3)[/tex]

Answer:

the answer is correct, just backwards. thanks for your help!

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

let's recall that

1² = 1

1⁴ = 1

1¹⁰⁰⁰⁰⁰⁰⁰⁰⁰ = 1

[tex]\bf \textit{difference and sum of cubes} \\\\ a^3+b^3 = (a+b)(a^2-ab+b^2) \\\\ a^3-b^3 = (a-b)(a^2+ab+b^2) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ x^{12}y^{18}+1\implies x^{4\cdot 3}y^{6\cdot 3}+1^3\implies (x^4)^3(y^6)^3+1^3\implies (x^4y^6)^3+1^3 \\[2em] [x^4y^6+1][(x^4y^6)^2-(x^4y^6)(1)+1^2]\implies (x^4y^6+1)(x^8y^{12}-x^4y^6+1)[/tex]

Answer:

Choice C:

slope = -18x

y-intercept = 850

Step-by-step explanation:

Drew uses 18 ounces of flour

-18x represents the amount of flour used

850 ounces of flour

or (0,850) is the y-intercept and represents the total number of flour

Answer

slope = -18x

y-intercept = 850

Answer:

C

Step-by-step explanation:

C

A. [tex]\sqrt{3}[/tex]

In the  Geometry, the triangle is a 3-sided polygon that consists of 3 edges and 3 vertices. The most important property of the triangle is that the sum of the internal angles of the triangle is = to 180 degrees. its property is known as angle sum property of triangle.

We have been given the image of the right triangle and we are asked to find the value of the tan(60) for our given triangle

from we know that tangent represents the relation between opposite or adjacent of the right triangle.

[tex]tan = \frac{opposite}{adjacent}[/tex]

We can see that our adjacent side is not given, but corresponding angle to adjacent side is given that is 30 degrees. So we could conclude that our given triangle is 30-60-90 triangle.

from the sides corresponding to 30-60-90 triangle equals to[tex]x,x\sqrt{3}[/tex] and [tex]2x[/tex] , so the adjacent side for our given triangle will be,

[tex]x\sqrt{3} =8 \sqrt{3\\\\\\[/tex]

[tex]\frac{x \sqrt{3} }{\sqrt{3} } =\frac{8\sqrt{3} }{\sqrt{3} }[/tex]

[tex]x=8[/tex]

Upon substituting these values on above formula we will get,

[tex]tan( 60^{0} ) = \frac{8\sqrt{3} }{8} \\tan( 60^{0})=\sqrt{3}[/tex]

hence, the value of tan(60) is  [tex]\sqrt{3}[/tex]and option B is the correct choice.

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Answer:

This is the zero product rule.

Step-by-step explanation:

a: b = 0, then a = 0, b = 0, or both a = 0 and b = 0.

This is the zero product rule.

It shows that for the product to be zero,  at least  one factor must be zero

If a*b= 0: It shows that one of the factor is zero or may be both the factors are zero that is why their resultant product is 0....

Answer:

4x^5\sqrt[3]{3x}

Step-by-step explanation:

Given

[tex]\sqrt[3]{16x^7}\left(\sqrt[3]{12x^9}\right)\\\sqrt[3]{4^{2} x^7}\sqrt[3]{4(3)x^9}\\  4^\frac{2}{3} . x^\frac{7}{3} . 4^\frac{1}{3} . 3^\frac{1}{3} . x^\frac{9}{3}\\  4^\frac{2+1}{3} .  3^\frac{1}{3}. x^\frac{9+7}{3} \\4^\frac{3}{3} . 3^\frac{1}{3}. x^\frac{16}{3}\\ 4\sqrt[3]{3x^16}[/tex]

[tex]4\sqrt[3]{3} . x^\frac{16}{3} \\4\sqrt[3]{3} . x^\frac{15}{3} .x^\frac{1}{3} \\4\sqrt[3]{3} . x^5 .x^\frac{1}{3} \\4x^5\sqrt[3]{3x}[/tex] !

Answer:

The expression [tex]\sqrt[3]{16x^{7} } * \sqrt[3]{12x^{9} }[/tex] = [tex]4x^{5}} (\sqrt[3]{3x})[/tex]

Step-by-step explanation:

Given

[tex]\sqrt[3]{16x^{7} } * \sqrt[3]{12x^{9} }[/tex]

Required

Products of both

To do this, we have to apply the laws of indices,

Follow the highlighted steps

Step 1: Multiply both parameters directly

Since they both have the same roots, they can be multiplied directly according to the law of indices

[tex]\sqrt[3]{16x^{7} } * \sqrt[3]{12x^{9} }[/tex] becomes

[tex]\sqrt[3]{16x^{7} * 12x^{9} }[/tex]

Step 2: Apply the 1st law of indices

First law of indices states that

[tex]x^{a} * x^{b} = x^{a + b}[/tex]

So, [tex]\sqrt[3]{16x^{7} * 12x^{9} }[/tex] becomes

[tex]\sqrt[3]{16x^{7} * 12x^{9} }[/tex] = [tex]\sqrt[3]{16 * 12 * x^{7} * x^{9} }[/tex]

[tex]\sqrt[3]{16x^{7} * 12x^{9} }[/tex] = [tex]\sqrt[3]{16 * 12 * x^{7+9} }[/tex]

[tex]\sqrt[3]{16x^{7} * 12x^{9} }[/tex] = [tex]\sqrt[3]{16 * 12 * x^{16} }[/tex]

[tex]\sqrt[3]{16x^{7} * 12x^{9} }[/tex] = [tex]\sqrt[3]{192 * x^{16} }[/tex]

Step 3: Rewrite the expression

[tex]\sqrt[3]{192 * x^{16} }[/tex] = [tex]({192 * x^{16} })^{\frac{1}{3} }[/tex]

Step 4: Expand the Expression in bracket

[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex]({64 * 3* x^{15} * x^{1} })^{\frac{1}{3} }[/tex]

Break down into bits

[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex]64^\frac{1}{3} * 3^\frac{1}{3} * (x^{15})^\frac{1}{3} * (x^{1})\frac{1}{3}[/tex]

[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex](4^{3}) ^\frac{1}{3} * 3^\frac{1}{3} * (x^{15})^\frac{1}{3} * (x^{1})\frac{1}{3}[/tex]

[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex](4^{3*\frac{1}{3}}) * 3^\frac{1}{3} * (x^{15}*^\frac{1}{3}) * (x^{\frac{1}{3}})[/tex]

[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex]4 * 3^\frac{1}{3} * (x^{5}}) * (x^{\frac{1}{3}})[/tex]

[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex]4 (x^{5}})* 3^\frac{1}{3} * (x^{\frac{1}{3}})[/tex]

[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex]4x^{5}} * (3^\frac{1}{3} * x^{\frac{1}{3}})[/tex]

[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex]4x^{5}} * (3x)^\frac{1}{3}[/tex]

[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex]4x^{5}} * \sqrt[3]{3x}[/tex]

[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex]4x^{5}} (\sqrt[3]{3x})[/tex]

Hence, the expression [tex]\sqrt[3]{16x^{7} } * \sqrt[3]{12x^{9} }[/tex] = [tex]4x^{5}} (\sqrt[3]{3x})[/tex]

Answer:

The ratio of their volumes is 27/64

Step-by-step explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

In this problem

The scale factor is 3/4

step 2

Find the ratio of their volumes

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

so

[tex](\frac{3}{4})^{3}=\frac{27}{64}[/tex]

Answer:

g(2) = 3

Step-by-step explanation:

g(x) = x² - 1.

Substituting 2 for x in this formula, we get:

g(2) = 2² - 1, or g(2) = 3

Answer:

g(2) =3

Step-by-step explanation:

g(x) = x^2 -1

Let x=2

g(2) = 2^2 -1

       =4-1

        =3

Answer:

(1, 3).

Step-by-step explanation:

The tree tiles coordinates are x = 5-3 = 2 and the y coordinate = 4 - 2 = 2

- that is (2, 2).

So the coordinates of the second sun are (2-1, 2 + 1)

= (1. 3).

Answer:

hello : answer: A

Step-by-step explanation:

a(1) = –10 and a(n) = 4a(n– 1) + 7, if n ≥ 2.

n=2 : a(2)=4a(1)+7        a(2) =4(-10)+7 = -33

n=3 : a(2)=4a(2)+7        a(3) =4(-33)+7 = -125

n=4 : a(2)=4a(3)+7        a(4) =4(-125)+7 = -493

n=5 : a(2)=4a(4)+7        a(5) =4(-493)+7 = -1965

n=6 : a(2)=4a(5)+7        a(6) =4(-1965)+7 = -7853

Answer:

Step-by-step explanation:

A Mutual Fund is invested by Managers in a diversity of stocks bonds and other securities.

A mutual fund is a type of investment in which investors pool their money together to buy a portfolio of stocks, bonds or other securities in order to take advantage of diversification and professional portfolio management at a reasonable cost. It is operated by money managers, who invest the fund capital on the investors behalf. Investing in mutual funds enables those investing a modest amount of money to benefit from the same advantages enjoyed by large institutional investors....

Answer:

7.5 ft

Step-by-step explanation:

Volume of a prism is V = L*W*H.

In this case, the volume is V = 300 ft^3 (not 300 ft).  Therefore,

300 ft^3 = L*W*H = (8 ft)(5 ft)(height)

Solving for the height, H, we get:

       300 ft^3

H = --------------- = 7.5 ft

         40 ft^2

Answer:

7.5 ft

Step-by-step explanation:

Vole is the length time the width times the height

V = l*w*h

Substituting what we know

300 = 5*8*h

300 = 40h

Divide each side by 40

300/40 =40h/40

7.5 =h

Angle 6, an acute angle, measures below 90 degrees, reflecting a sharp inclination. Angle 4, a right angle at precisely 90 degrees.

In the geometric configuration, Angle 6 is characterized as an acute angle, signifying that its measure falls between 0 and 90 degrees. Acute angles are typically associated with sharp inclinations, emphasizing a compact angular span. On the other hand, Angle 4 is identified as a right angle, precisely measuring 90 degrees.

Right angles are distinctive for their perpendicular alignment, forming the cornerstone of rectangular shapes and providing structural stability. The significance of Angle 4 lies in its pivotal role in defining perpendicularity within geometric constructs.

This geometric interplay showcases the diversity of angles, with acute angles like Angle 6 emphasizing sharpness and right angles like Angle 4 embodying orthogonality, contributing to the intricacies and precision inherent in geometric relationships.

Answer:

False

Step-by-step explanation:

This statement states that If opposite angles of a quadrilateral are supplementary, then the quadrilateral is a parallelogram.

This is a false statement.

Lets recall the properties of a parallelogram to understand the concept. The definition says that a quadrilateral is said to be a parallelogram if its opposite angles are congruent and two consecutive angles are supplementary.

Therefore the statement is false....

Answer:

12

Step-by-step explanation:

  Mass of apples = number of containers × mass in each container

                     6 lb = No of containers × ½ lb

No of containers = 6/½  

To divide a whole number by a fraction, invert the fraction and change divide to multiply.

6/½ = 6 × 2/1

Multiply the numerator by the whole number.

6 × 2/1 = 12/1

Simplify the fraction.

12/1 = 12

Elise can make 12 containers of applesauce.

Answer:

3

Step-by-step explanation:

12 times table= 12,24,36..

if we have 24 books then not everyone can get a book.

it's best to get the 3 boxes of 36 as everyone can get one. As my teacher always said, the more the better.

Answer:

4.21 and 4.22 (answers will vary)

Step-by-step explanation:

There are a lot of different numbers you can pick. It just has to be between 4.2 and 4.3. This means that 4.200000000000000000000000000001 can be an answer and 4.29999999999999999999999999 can be an answer.

This image is being reflected over the y-axis.  When reflecting over the y-axis the y-coordinate will stay the same, but the x-coordinate will have the opposite sign. Here is the rule for this reflection:

(-x, y)

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Correct answer is figure D.

Step-by-step explanation:

According to the attached image Figure  D is correct option.

In a reflection transformation, all the points of an object are reflected or flipped. It is a type of transformation where the new image is the mirror image of the original and x-coordinates and y-coordinates changes the place.

Figure A is rotation and translation and Figure B and C are translation

Thus the correct option is Figure D....

Answer:

Step-by-step explanation:

The absolute value of number a:

|a| = a for a ≥ 0

|a| = -a for a < 0

|9| = 9

|-3| = -(-3) = 3

Answer:

[tex]\frac{3}{4}[/tex]

Step-by-step explanation:

There are 4 steps to complete to go from 0 to 1. Hence each step is:

1 out of 4, or simply  [tex]\frac{1}{4}[/tex]

F is located at the 3rd mark, which will be  [tex]\frac{1}{4}+\frac{1}{4}+\frac{1}{4}=\frac{3}{4}[/tex]

Hence, F is located at  [tex]\frac{3}{4}[/tex]

Answer:

F is on [tex]\frac{3}{4}[/tex] on the number line

Step-by-step explanation:

Notice in the image that between 0 and 1 there are 4 subdivisions.

Then divide.

[tex]\frac{1}{4} = 0.25[/tex].

Each subdivision is equal to 0.25 units.

Point F is in the third subdivision.

This means that the distance between 0 and F is:

[tex]\frac{1}{4}*3 = \frac{3}{4} = 0.75[/tex].

Finally F is on [tex]\frac{3}{4}[/tex] on the number line