Find the slope of the line: 6x – 3y + 6 = 0

Answer:

2 gallons

Step-by-step explanation:

If you use one whole gallon, you will have covered 2/4.

When you simplify this fraction, you get 1/2. This means you have another half to cover.

So, 1 gallon plus another gallon is 2.

Answer:

2 gallons of paint.

Step-by-step explanation:

Since [tex]\frac{1}{2}[/tex] gallon of paint covered = [tex]\frac{1}{4}[/tex] of the wall.

Therefore, 1 gallon of paint covered = 1 × [tex]\frac{1}{4}[/tex] = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex] of the wall.

To paint 1 wall we need the paint = [tex]\frac{1}{\frac{1}{2} }[/tex] = [tex]1\times\frac{2}{1}[/tex] gallon of paints

                                                      = 2 gallons of paint.

2 gallons of paint covers the whole wall.

Answer:

y=x

Step-by-step explanation:

We want a line parallel to y =x+42

The slope of y =x+42 is 1

Parallel lines have the same slope

We have the slope m=1 and a point (2,2)

We can use point slope form to write a line

y-y1 = m(x-x1)

y-2 = 1(x-2) point slope form

Changing to slope intercept form

y-2 = x-2

Add 2 to each side

y-2+2 = x-2+2

y=x

The line parallel to y = x + 42 travels through (2,2) can be represented by the equation y = x. This conclusion is based on the principles of line equations in a two-dimensional space, with slopes determining the parallelism of lines.

The subject of the question pertains to the formula of a line in a two-dimensional space. Specifically, you're asked to find a line that passes through the point (2,2) and is parallel to the line described by the equation y = x + 42.

In a standard equation of a line, y = mx + b, 'm' represents the slope of the line and 'b' indicates the y-intercept. Two lines are parallel if they have the same slope. Bearing this in mind, as the line y = x + 42 has a slope of 1 (since 1 is the coefficient of 'x'), the required line would also possess a slope of 1.

Substituting the point coordinates (2,2) into the equation y = mx + b (replacing 'm' with 1), gives us 2 = 2 + b. Solving for 'b', we find that it equals zero. Hence, the equation of a line parallel to y = x + 42 passing through the point (2,2) is y = x.

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Answer:

The x intercept = -3

Step-by-step explanation:

The x intercept is where it crosses the x axis.

Looking at the graph, it crosses at x =-3

Using the equation, we set y=0 and solve for x

2x-y =-6

2x -0 =-6

2x = -6

Divide by 2

2x/2 =-6/2

x=-3

Answer: A

Step-by-step explanation:

Edgen 2023

Answer:

q = -2

Step-by-step explanation:

-2x²-8x = 10 (divide both sides by -2)

x² + 4x = -5 (Apply completing the square method)

x² + 4x + (4/2)²= -5 + (4/2)²

x² + 4x + 2²= -5 + 2²    (reduce left hand side using a²+2ab+b² =  (a+b)² )

(x+2)² = -5 +4

(x+2)² = -1

(x+2)² + 1 = 0   (multiply both sides by -2)

(-2)(x+2)² + 1 (-2) = 0

-2[x - (-2)]² + (-2) = 0  ---> compare this with -2(x-p)² + q = 0

We can see that p = 2 and q = -2

The value of 'q' in the rearranged form of the given quadratic equation -2(x-p)²+q = 0 is -6. This is obtained by completing the square and comparing the equations.

Given the quadratic equation -2x² -8x = 10, it's rearranged to the form -2(x-p)²+q = 0. The objective is to find the value of 'q'.

To achieve this, you first need to rewrite the given equation -2x² -8x - 10 = 0 in the form -2(x-h)²+k = 0. This is called completing the square. The 'h' value here is equal to -b/2a, where 'b' is the coefficient of 'x' and 'a' is the coefficient of x². In this equation, a is -2 and b is -8 so h=(-(-8)/(2×(-2))=8/4=2.

Substituting h into the equation, you have -2(x-2)²+k=0. Now expand and simplify to get -2x²+8x-4+k=0. Comparing this with the original equation -2x² -8x -10 = 0, you can see that 'k' is equal to -10+4=-6, which is the 'q' value in the form -2(x-p)²+q = 0. So, the value of 'q' is -6.

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Answer:

There are are 30 possible ways for the 6 students to be ranked 1st and 2nd

Step-by-step explanation:

There are 6 students, and any of them could receive first place. Therefore, there are 6 possibilities for first place.

A student cannot receive first and second place, so the student who won first place cannot also win second place. Therefore, there are only 5 students who could win second place.

We can multiply these two possibilities to find the number of possible rankings of 1st and 2nd

6*5=30

There are are 30 possible ways for the 6 students to be ranked 1st and 2nd....

Answer:

8/100.   Eight hundredths  or we can write it as 8 * 10^-2.

Step-by-step explanation:

The first digits after the decimal point is  tenths ( 7 tenths) and the second is hundredths, the third is thousandths.

[tex]0.0\overline{3}=\dfrac{1}{30}\\0.\overline{03}=\dfrac{1}{33}\\\\\dfrac{0.0\overline{3}}{0.\overline{03}}=\dfrac{\dfrac{1}{30}}{\dfrac{1}{33}}=\dfrac{1}{30}\cdot33=\dfrac{11}{10}=1\dfrac{1}{10}[/tex]

Answer:

42

Step-by-step explanation:

all I did was multiply 6 by 7 and i got 42

Step-by-step explanation:

We arrange numbers in ascending order

Range - numbers appearing (without repetition)

Median - middle value

Mean - the sum of the numbers divided by the number of items

Mode - the value that appears most often.

[tex]\bold{Q4.}\\\\22,\ 36,\ 39,\ 39,\ 40,\ 40,\ 41,\ 42,\ 45,\ 46,\ 46,\ 49\\\\\bold{Range:}\ 22,\ 36,\ 39,\ 40,\ 41,\ 42,\ 45,\ 46,\ 49\\\\\bold{Median:}\ 40,\ 41\to\dfrac{40+41}{2}=40.5\\\\\bold{Mean:}\ \dfrac{22+36+39+39+40+40+41+42+45+46+46+49}{12}=40\dfrac{5}{12}\\\\\bold{Mode:}\ 39,\ 40\ and\ 46[/tex]

[tex]\bold{Q5.}\\\\79,\ 83,\ 84,\ 86,\ 86,\ 90,\ 94\\\\\bold{Range:}\ 79,\ 83,\ 84,\ 86,\ 90,\ 94\\\\\bold{Median}:\ 86\\\\\bold{Mean:}\ \dfrac{79+83+84+86+86+90+94}{7}=86\\\\\bold{Mode:}\ 86[/tex]

Answer:

x = 2

y = 0

Step-by-step explanation:

We can solve using substitution, substitute y in the first equation with the second equation:

-(-6x + 12) + 3x = 6

Distribute the negative sign:

6x - 12 + 3x = 6

Combine like terms:

9x - 12 = 6

Isolate the variable and solve for x by adding 12 in both sides:

9x = 18

x = 2

Substitute 2 with x in any equation to find the value of y:

-y + 3(2) = 6

-y + 6 = 6

Subtract 6 in both sides to isolate the variable:

-y = 0

0/-1 = 0

y = 0

Our answer would be x = 2 and y = 0

Answer:

(2,0)

Step-by-step explanation:

I'm going to use substitution since one of the variables in one of the equation is already solved for.

-y+3x=6

y=-6x+12

I'm going to replace the first y with the second y which is (-6x+12).

This gives me:

-(-6x+12)+3x=6

Distribute:

6x-12+3x=6

Combine like terms:

9x-12=6

Add 12 on both sides:

9x=18

Divide both sides by 9:

x=2

If x=2 and y=-6x+12, then y=-6(2)+12=-12+12=0.

The solution (the intersection) is (2,0).

any other details you could give me ?

It is proved that f and g are inverses by showing that f(g(x)) = x and     g(f(x)) = x.

An inverse function is a function that returns the original value for which a function has given the output.

According to the problem,

Now,   f(g(x)) =  [tex](\sqrt[3]{x-4})^{3} + 4[/tex] = x

           g(f(x)) = [tex]\sqrt[3]{x^{3}+4 -4}[/tex] = x

Thus it is proved that f and g are inverse functions.

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Hey there! :)

1/2(n - 1) - 3 = 3 - (2n + 3)

Simplify.

1/2n - 1/2 - 3 = 3 - 2n - 3

Add like terms.

1/2n - 3 1/2 = -2n

Add 3 1/2 to both sides.

1/2n = -2n + 3 1/2

Then, add 2n to both sides.

1/2n + 2n = 3 1/2

Simplify!

2 1/2n = 3 1/2

Make everything into improper fractions!

5/2n = 7/2

Multiply everything by 2 to get rid of the denominators.

5/2n × 2 = 7/2 × 2

Simplify!

5n = 7

Divide both sides by 5.

n = 7/5

Hope this helped! :)

Answer:

[tex]\frac{7}{5} = n[/tex]

Step-by-step explanation:

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

Solve the brackets.

[tex] \frac{n}{2} - \frac{1}{2} - 3 = 3 - 2n - 3 \\ [/tex]

Make the denominator the same to solve the fractions.

[tex] \frac{n}{2} - \frac{1}{2} - \frac{3 \times 2}{1 \times 2} = 3 - 2n - 3 \\ [/tex]

Combine like terms.

[tex] \frac{n}{2} - \frac{1}{2} - \frac{6}{2} = - 2n \\ \\ \frac{n - 7}{2} = - 2n \: \: \: \: \: \: \: \: [/tex]

Use cross multiplication to solve for n.

[tex]n - 7 = - 4n \\ \\ - 7 = - 4n - n \\ \\ - 7 = - 5n \: \: \: \: \: \: \\ \\ \frac{ - 7}{ - 5} = \frac{ - 5n}{ - 5} \: \: \: \: \\ \\ \frac{7}{5} = n \: \: \: \: \: \: \: [/tex]

Answer:

auditory nerve

Step-by-step explanation:

the auditory nerve carries sound signals to the brain. The cochlea picks up sound waves and makes nerve signals.

Answer:

The auditory nerve

Step-by-step explanation:

Answer:

=20.0

Step-by-step explanation:

We can first find the angle B using the sine rule as follows:

a/Sin A=b/Sin B

9/Sin 15=12/ Sin B

Sin B= (12 Sin 15)/9

=0.345

B=Sin⁻¹ 0.345

=20.18°

We then find C by using the summation of the interior angles of a triangle.

C=180-(20.18+15)

=144.82

Finding the length of c:

a/Sin A= c/ Sin C

9/Sin 15=c/Sin 144.82

c=(9 Sin 144.82)Sin 15

=20.0

Answer:

20.0 unit ( approx )

Step-by-step explanation:

Here,

ABC is a triangle in which,

m∠A=15°, a=9, and b=12,

By the law of sine,

[tex]\frac{sin A}{a}=\frac{sin B}{b}=\frac{sin C}{c}----(1)[/tex]

[tex]\frac{sin A}{a}=\frac{sin B}{b}[/tex]

[tex]\implies sin B=\frac{b sin A}{a}[/tex]

By substituting the values,

[tex]\implies sin B=\frac{12\times sin 15^{\circ}}{9}\approx 0.3451[/tex]

[tex]\implies B \approx 20.19^{\circ}[/tex]

Now, by the property of triangle,

m∠A + m∠B+ m∠C = 180°

⇒ m∠C = 180° - 15° - 20.19° = 144.81°,

By the equation (1),

[tex]c=\frac{b sin C}{sin B}=\frac{12\times sin 144.81^{\circ}}{sin 20.19^{\circ}}=20.0370532419\approx 20.0[/tex]

Answer:

Option 2) 20°

Step-by-step explanation:

Step 1: Write relevant properties of triangle.

All 3 sides of a triangle are equal to 180 degrees.

In an isosceles triangle, 2 sides and 2 angles are same.

Step 2: Calculate another angles

Since it is an isosceles triangle, two sides will be same therefore, 2 angles will be same.

Angle 1 = Angle 2 = 20 degrees (because isosceles triangle)

Therefore, 20° is the measure of one of the other angles.

Option 2

!!

Answer: FIRST OPTION.

Step-by-step explanation:

It is important to remember that an Acute Isosceles triangle has two congruent sides and all its angles measure less than 90 degrees. Then, the third option and the the fourth option are not one of the other angles.

You know that the sum of the interior angles of a triangle is 180 degrees.

Then, let be "x" one the other angles, let's check the first option:

[tex]80\°+20\°+x=180\°\\x=80\°[/tex]

Since [tex]80\°<90\°[/tex], the angle provided in the first option is one of the other angles.

 Let's check the second option:

[tex]20\°+20\°+x=180\°\\x=140\°[/tex]

Since [tex]140\°>90\°[/tex], the angle provided in the second option is not one of the other angles.

Answer:

a) 3

b) 364

Step-by-step explanation:

A geometric sequence in explicit form is [tex]a_n=a_1 \cdot r^{n-1}[/tex] where [tex]a_1[/tex] is the first term and [tex]r[/tex] is the common ratio.

We are given:

[tex]a_5=9 \cdot a_3[/tex]

[tex]a_6+a_7=972[/tex].

What is a) r?

What is b) the sum of the first 6 terms?

So I'm going to use my first equation and use my explicit form to find those terms in terms of r:

[tex]a_1 \cdot r^4=9 \cdot a_1 \cdot r^{2}[/tex]

Divide both sides by [tex]a_1r^2[/tex]:

[tex]r^2=9[/tex]

[tex]r=\sqrt{9}[/tex]

[tex]r=3[/tex].

So part a is 3.

Now for part b).

We want to find [tex]a_1+a_2+a_3+a_4+a_5+a_6[/tex].

So far we have:

[tex]a_1=a_1[/tex]

[tex]a_2=3a_1[/tex]

[tex]a_3=3^2a_1[/tex]

[tex]a_4=3^3a_1[/tex]

[tex]a_5=3^4a_1[/tex]

[tex]a_6=3^5a_1[/tex].

We also haven't used:

[tex]a_6+a_7=972[/tex].

I'm going to find these terms in terms of r (r=3).

[tex]3^5a_1+3^6a_1=972[/tex]

[tex]243a_1+729a_1=972[/tex]

You have like terms to add:

[tex]972a_1=972[/tex]

Divide both sides by 972:

[tex]a_1=1[/tex]

The first term is 1 and the common ratio is 3.

The terms we wrote can be simplify using a substitution for the first term as 1:

[tex]a_1=a_1=1[/tex]

[tex]a_2=3a_1=3(1)=3[/tex]

[tex]a_3=3^2a_1=9(1)=9[/tex]

[tex]a_4=3^3a_1=27(1)=27[/tex]

[tex]a_5=3^4a_1=81(1)=81[/tex]

[tex]a_6=3^5a_1=243(1)=243[/tex].

Now we just need to find the sum of those six terms:

1+3+9+27+81+243=364.

Answer:

So the x-intercept is (9,0) and the y-intercept is (0,-3).

So I'm going to graph both points and connect them with a straight-edge.

Step-by-step explanation:

I would graph this using it's x- and y-intercepts.

To find the x-intercept, set y=0.

-3x+9(0)=-27

-3x+0=-27

-3x=-27

Divide both sides by -3:

x=9

To find the y-intercept, set x=0:

-3(0)+9y=-27

 0  +9y=-27

       9y=-27

Divide both sides by 9:  

        y=-3

So the x-intercept is (9,0) and the y-intercept is (0,-3).

So I'm going to graph both points and connect them with a straight-edge.

well, so we know the ratio of compost to soil is 2 : 10, or namely 2/10 which simplifies to 1/5 or namely the ratio of 1 : 5.

the mix will be 6 kgs total, so we'll simply divide the whole amount by (1 + 5), the sum of the ratios, and then distribute accordingly.

[tex]\bf 2:10\implies 1:5\qquad \qquad \cfrac{compost}{soil}\qquad \cfrac{1\cdot ~~\frac{6}{1+5}~~}{5\cdot \frac{6}{1+5}}\implies \cfrac{1\cdot 1}{5\cdot 1}\implies \cfrac{\stackrel{compost}{\boxed{1~kg}}}{5~kg}[/tex]

Answer:

Gabriel Is making a mixture of compost and soil to use for a special plant. He wants his Final mix to be two parts compost to 10 parts potting soil. he wants to end up with 6 kg of mix. How many kg of compost should Gabriel use?

Step-by-step explanation:

We have a total of 12 parts, where 2 are compost, and on the other hand 6 kg which is the total of the whole mixture, divided by 12; 6/12 = 0.5 would be each of the parts, we multiply it by 2; 0.5 x 2 = 1 kg would be the part of compost, and 0.5 x 10 = 5 kg would be the part of potting soil which added, gives us the total 6 kg.

Answer:

The price decreased by 16 1/3%, or approximately 16.3%

Step-by-step explanation:

Use the formula for percent change. If the answer is negative, it is a percent decrease. if the answer is positive, it is a percent increase.

percent change = (new price - old price)/(old price) * 100%

In this case, use:

new price = 50

old price = 60

percent change = (new price - old price)/(old price) * 100%

percent change = (50 - 60)/60 * 100%

percent change = -10/60 * 100%

percent change = -1/6 * 100%

percent change = -100/6% = -50/3% = -16 1/3%

The price decreased by 16 1/3%, or approximately 16.3%

Answer:

-1.5

Step-by-step explanation:

So your set of points I believe is:

(1,4)

(2,2.5)

(3,1)

(4,-0.5)

You are asked to find the average rate of change. This just means find the slope.

So you can make sure the slope is the same per pair of points.

So I like to find the slope by lining two points up vertically and subtracting vertically then put 2nd difference over 1st difference.

(2 , 2.5)

-( 1 ,  4)

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

 1,  -1.5

So the slope is -1.5/1 or just -1.5.

Check another pair:

 (3  , 1  )

- (2  ,2.5)

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

 1 ,  -1.5

So the slope is -1.5/1 or just -1.5.

Check one more:

 (4 , -.5)

-(3  , 1)

-----------

1, -1.5

So the slope is -1.5 or just -1.5

So the average rate of change is -1.5.

Answer:

[tex]f^{-1}(x)=\frac{x+4}{3}[/tex]

C is the correct option.

Step-by-step explanation:

The given function is [tex]f(x)=3x-4[/tex]

Replace f(x) with y

[tex]y=3x-4[/tex]

Interchange x and y as shown below

[tex]x=3y-4[/tex]

Solve the equation for y

[tex]x+4=3y\\\\y=\frac{x+4}{3}[/tex]

Therefore, the inverse of f(x) is given by

[tex]f^{-1}(x)=\frac{x+4}{3}[/tex]

C is the correct option.

Answer:

Absolute value means the distance between a number and 0.

Examples:

The absolute value of -7 is 7.

The absolute value of 5 is 5.

Key Concepts:

The absolute value sign is |x|, where x is any real number.

The absolute value removes any negative sign in front of a number.

Absolute value is an important math concept to understand. To represent the absolute value of a number, we use a vertical bar on either side of the number. Absolute value means "distance from zero" on a number line. Let's try an example to understand how absolute value works.

What is the absolute value of 4 and -4?

To find the absolute value of 4, we know that 4 is 4 units from zero on a number line. Therefore, the absolute value of 4 is 4.

For the absolute value of -4, we know that -4 is also 4 units from zero on the number line. Therefore, the absolute value of -4 is also 4.

Another way that I like to think about absolute value is no matter what number you have inside the absolute value, the result will always be positive. In other words, the absolute value of any number is the positive version of that number.

Answer:

56√10.

Step-by-step explanation:

7√8 * 4√5

= 28 √40

= 28 √4√10

= 28 * 2√10

= 56√10.

Answer:

56[tex]\sqrt{10}[/tex]

Step-by-step explanation:

Using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]

Given

7[tex]\sqrt{8}[/tex] × 4[tex]\sqrt{5}[/tex]

= 7 × 4 × [tex]\sqrt{8(5)}[/tex]

= 28 × [tex]\sqrt{40}[/tex]

= 28 × [tex]\sqrt{4(10)}[/tex]

= 28 × [tex]\sqrt{4}[/tex] × [tex]\sqrt{10}[/tex]

= 28 × 2 × [tex]\sqrt{10}[/tex]

= 56[tex]\sqrt{10}[/tex]

Answer:

[tex]\large\boxed{A)\ 5x^2(2y+5)}[/tex]

Step-by-step explanation:

[tex]10x^2y+25x^2=(5x^2)(2y)+(5x^2)(5)\qquad\text{distributive}\\\\=5x^2(2y+5)[/tex]

The value of equivalent expression is,

⇒ 5x² (2y + 5)

We know that;

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Here, Given that;

The expression is,

⇒ 10x²y + 25x²

Now, We can simplify the expression as;

⇒ 10x²y + 25x²

⇒ 2×5x²y + 5×5x²

⇒ 5x² (2y + 5)

Thus, The value of equivalent expression is,

⇒ 5x² (2y + 5)

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Answer:

true.

Step-by-step explanation:

(x - y)z = xz - yz

Apply the distributive property of multiplication over addition to the left side:

(x - y)z =

= z(x - y)

= xz - yz

This is the same as the right side, so the statement is true.

Answer:

6 oz

Step-by-step explanation:

If he spilled 1/4 of the juice, then he has 3/4 of the original volume left.

(3/4)(8 oz) = 6 oz.

He has 6 oz left to enjoy.

Answer:

See below.

Step-by-step explanation:

To multiply a monomil by a polynomial, multiply the monomial by each term of the polynomial.

Example: Multiply 3x^2 by 4x^2 + 5x - 2

3x^2(4x^2 + 5x - 2) =

= 3x^2 * 4x^2 + 3x^2 * 5x + 3x^2 * (-2)

= 12x^4 + 15x^3 - 6x^2

To multiply a monomial and a polynomial that is not monomial, distribute the monomial term to each term of the polynomial, and then simplify the resulting expression by combining like terms.

To multiply a monomial and a polynomial that is not monomial, distribute the monomial term to each term of the polynomial, and then simplify the resulting expression by combining like terms.

For example, let's multiply the monomial 3x^2 by the polynomial 4x^3 + 2x - 1:

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Answer:

C

Step-by-step explanation:

Parallel and opposite sides of a parallelogram are equal. Hence, we can say:

x + 30 = 2x - 10

and

2y-10 = y +10

Solving first one, we get:

x + 30 = 2x - 10

30+10 = x

x = 40

Also

2y - 10 = y + 10

y = 10 + 10

y = 20

Now, z = x - y, so

z = 40 - 20 = 20

Answer C is right.

I can confirm that the answer is right.

Parallelograms have equal opposite sides. Do the math:

x - y = z

40 - 20 = 20

z = 20