write an equation of the line through each pair of points in slope-intercept form.
1. (0,-1) (4,4)
2. (4,3) (1,-6)​

Final answer:

To solve probability questions, you need to understand the basic concepts and formulas.

Explanation:

To solve probability questions, you need to understand the basic concepts and formulas.

Answer:h= [tex]\frac{(p/0.7-b)}{r}[/tex]

Step-by-step explanation:

1) p/0.7=rh+b

2) (p/0.7)-b=rh

3) [tex]\frac{(p/0.7-b)}{r}[/tex] =h

h= [tex]\frac{(p/0.7-b)}{r}[/tex]

The equivalent equation for isolated variable h = [tex]\frac{p-0.7b}{r}[/tex] obtained from the equation p = 0.7(rh + b).

Isolating a variable is the re-arrangement of the equation for the required variable. Even though rewriting the terms, doesn't affect the logic of the equation. It forms an equivalent equation.

The given equation is p = 0.7(rh + b)

Where,

p - home pay

h - working hours

r - the rate of dollars per hour

b - bonus received

Re-writing the equation for the variable h:

p = 0.7(rh + b)

⇒ p/0.7 = rh + b

⇒ p/0.7 - b = rh

⇒ h = p/0.7r -b/r

∴ h = [tex]\frac{p-0.7b}{r}[/tex]

Therefore, variable h is isolated and obtained an equivalent equation.

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Answer:

42

Step-by-step explanation:

This means 0.84 divided by 0.02

which equals to 42

the points mean that there is a zero

if a number has been written in that format of  "point" then "number" without any number before the point, it means there is  a zero there

if you need anything else clarified please do so in the comment section i would like to help more

           Hope this helps and if it does mark as branliest answer thx

Answer:

One solution; x = -[tex]\frac{6}{7}[/tex]

Step-by-step explanation:

12x + 6 = 5x

12x - 5x = -6

7x = -6

x = -[tex]\frac{6}{7}[/tex]

[tex]8 - 4 \frac{2}{5} < 3 \frac{3}{4} \\ 3 \frac{3}{5} < 3 \frac{3}{4} [/tex]

Answer:

1. Number line 2

2. Number line 1

3. Number line 4

4. Number line 3

Step-by-step explanation:

1. x – 99 ≤ -104

Solving by adding +99 on both sides

x - 99 +99 ≤ -104 +99

x ≤ -5

Number line 2 represent x ≤ -5

2. x – 51 ≤ -43

Adding +51 on both sides

x -51 +51  ≤ -43 +51

x ≤ 8

Number line 1 represent x ≤ 8

3. 150 + x ≤ 144

Adding -150 on both sides

150 + x -150 ≤ 144 -150

x ≤ -6

Number line 4 represent x ≤ -6

4. 75 < 69 – x

Adding +x on both sides

75 + x < 69 -x +x

x < 69 -75

x < -6

Number line 3 represent x < -6

The correct matches are:

[tex]\(x - 99 \leq -104\)[/tex] with the number line showing [tex]\(x \leq -5\)[/tex].

[tex]\(x - 51 \leq -43\)[/tex] with the number line showing [tex]\(x \leq 8\)[/tex].

[tex]\(150 + x \leq 14475\)[/tex] with the number line showing [tex]\(x \leq 14325\)[/tex].

[tex]\(69 - x < 14475\)[/tex]  with the number line showing [tex]\(x > -14406\)[/tex].

To solve the given inequalities and match them to their corresponding number lines, we will first solve each inequality algebraically and then represent the solution on a number line.

1. For the inequality [tex]\(x - 99 \leq -104\)[/tex], we add 99 to both sides to isolate \[tex](x\)[/tex]:

[tex]\[x \leq -104 + 99\][/tex]

[tex]\[x \leq -5\][/tex]

This means that all values of [tex]\(x\)[/tex] less than or equal to -5 satisfy the inequality.

2. For the inequality[tex]\(x - 51 \leq -43\)[/tex], we add 51 to both sides:

[tex]\[x \leq -43 + 51\][/tex]

[tex]\[x \leq 8\][/tex]

This means that all values of [tex]\(x\)[/tex] less than or equal to 8 satisfy the inequality.

3. For the inequality [tex]\(150 + x \leq 14475\)[/tex], we subtract 150 from both sides:

[tex]\[x \leq 14475 - 150\][/tex]

[tex]\[x \leq 14325\][/tex]

This means that all values of [tex]\(x\)[/tex] less than or equal to 14325 satisfy the inequality.

4. For the inequality [tex]\(69 - x < 14475\)[/tex], we subtract 69 from both sides and reverse the inequality sign because we are dividing by a negative number (-1):

[tex]\[-x < 14406\][/tex]

[tex]\[x > -14406\][/tex]

This means that all values of [tex]\(x\)[/tex] greater than -14406 satisfy the inequality.

Now, let's represent these solutions on number lines:

- For [tex]\(x \leq -5\)[/tex], the number line will have a closed circle at -5 and shading to the left of -5.

- For [tex]\(x \leq 8\)[/tex], the number line will have a closed circle at 8 and shading to the left of 8.

- For[tex]\(x \leq 14325\)[/tex], the number line will have a closed circle at 14325 and shading to the left of 14325.

- For [tex]\(x > -14406\)[/tex], the number line will have an open circle at -14406 and shading to the right of -14406.

Matching the inequalities to the number lines:

- The inequality [tex]\(x - 99 \leq -104\)[/tex] corresponds to the number line with a closed circle at -5 and shading to the left.

- The inequality [tex]\(x - 51 \leq -43\)[/tex] corresponds to the number line with a closed circle at 8 and shading to the left.

- The inequality [tex]\(150 + x \leq 14475\)[/tex] corresponds to the number line with a closed circle at 14325 and shading to the left.

- The inequality [tex]\(69 - x < 14475\)[/tex] corresponds to the number line with an open circle at -14406 and shading to the right.

Therefore, the correct matches are:

[tex]\(x - 99 \leq -104\)[/tex] with the number line showing [tex]\(x \leq -5\)[/tex].

[tex]\(x - 51 \leq -43\)[/tex] with the number line showing [tex]\(x \leq 8\)[/tex].

[tex]\(150 + x \leq 14475\)[/tex] with the number line showing [tex]\(x \leq 14325\)[/tex].

[tex]\(69 - x < 14475\)[/tex]  with the number line showing [tex]\(x > -14406\)[/tex].

Answer:

reciprocals

Step-by-step explanation:

Let's actually find the slopes.  Then we can better compare them.

8x - 9y = 5 → - 9y = 5 - 8x → slope is m = (-8) / (-9), or 8/9.

9x - 8y = 1  →  - 8y = 1 - 9x  → slope is (-9) / (-8), or 9/8

These two slopes are reciprocals (but not negative reciprocals).

Answer:

reciprocals, but not negative reciprocals

Step-by-step explanation:

8x - 9y = 5

9y = 8x - 5

y = 8/9x - 5/9

m1 = 8/9

9x - 8y = 1

8y = 9x - 1

y = 9/8x - 1/8

m2 = 9/8

Answer:

Step-by-step explanation:

Answer:

The Answer IS: 2480 I just did the question

Step-by-step explanation:

Answer:

Yes there is GCF > 1 ⇒ (GCF = 4)

The completely factored form is 4(x - 2)(x² + 2x + 4)

Step-by-step explanation:

* Lets find the greatest common factor of the two terms

- The binomial is 4x³ - 32

- The terms of the binomial are 4x³ and 32

- The greatest common factor of 4 and 32 is 4 because both of them

  can divided by 4

∵ 4x³ ÷ 4 = x³

∵ 32 ÷ 4 = 8

∴ The greatest common factor GCF is 4

∴ 4x³ - 32 = 4(x³ - 8)

* Yes there is GCF > 1

# x³ - 8 is the difference of two cubs, it can factorize it into two

  brackets

- The first bracket has cube root of x³ and cube root of 8

- The second bracket comes from the first bracket it has three terms

# The 1st term is square the 1st term in the first bracket

# The 2nd term is the product of the 1st term and the 2nd term of the

  1st bracket with opposite sign of the 2nd term in the 1st bracket

# The 3rd term is the square of the 2nd term in the 1st bracket

* Lets do these steps with x³ - 8

∵ The first bracket = (∛x³ - ∛8)

∵ ∛x³ = x and ∛8 = 2

∴ The first bracket = (∛x³ - ∛8) = (x - 2)

- Lets make the 2nd bracket from the 1st bracket

∴ The second bracket = (x² + (x)(2) + 2²)

∴ The second bracket = (x² + 2x + 4)

∴ The factorization of x³ - 8 = (x - 2)(x² + 2x + 4)

* The completely factored form is 4(x - 2)(x² + 2x + 4)

Answer:

....Yes it is 4                                                                                                                       ....4(x-2)

Step-by-step explanation:

the screenshot shows proof :))

Answer:

Option C is correct.

Step-by-step explanation:

Slope of line JK

J (1,-6) K (0,4)

slope of JK = y₂ - y₁ / x₂ - x₁

Slope of JK = 4-1/0-(-6) = 3/6 = 1/2

so slope of JK = 1/2

Slope of line LM

L (-5,-3) and M(0,3)

slope of LM = y₂ - y₁ / x₂ - x₁

slope of LM = 3-(-5)/0-(-3) = 3+5/3 = 8/3

Slope of line NO

N(-6,-5) and 0 (0,0)

slope of NO = y₂ - y₁ / x₂ - x₁

slope of NO = 0-(-6)/0-(-5) = 6/5

So, slope of line NO = 6/5

Slope of PQ

P(-5,4) Q(0,-2)

slope of PQ = y₂ - y₁ / x₂ - x₁

slope of PQ = -2-4/0-(-5) = -2/5

so slope of line PQ = -2/5

the two lines are perpendicular if slope of one line is m then slope of other line is -1/m

The slope of given line =m= -5/6

The slope of line perpendicular to the given line = -1/m = 6/5

So, line NO is perpendicular to the given line as its slope is 6/5

Option C is correct.

Answer:

3. B. 128

4. B. 50.24

Step-by-step explanation:

3. The Books

The numbers of the problem make it quite easy.

We can easily figure out how many books will be stacked in each dimension of the trunk.

Length:

Books: 10 inches

Trunk: 40 iinches.

How may books can you fit lengthwise in the trunk?  40 / 10 = 4

We then to the same for the width:

Books: 6 inches

Trunk: 24 inches

How many books can you stack wide-wise in the trunk?  26/4 = 4

And then the height:

Books: 2.5 inches

Trunk: 20 inches

How many books stacked in height? 20 / 2.5 = 8

So, we can saw the trunk is 4 books long, by 4 books wide by 8 books thick... so, the number of books you can fit in that trunk is:

B = 4 * 4 * 8 = 128

4. Tomato juice

First, we have to find the volume of that big can...

Since it's a cylinder, its volume is calculated by:

V = π * r² * h and we have everything we need:

V = 3.14 * 4² * 12 = 192 * 3.14 = 602.88 cu in

We know a cup of tomato juice takes 12 cu inches...

So, how many cups of juice fit in that can?

C = 602.88 cu in / 12 cu in/cup = 50.24 cups

Answer:

The last choice.

Step-by-step explanation:

That would be the last one, with a minimum value of -4.

Answer:

IV graph

Step-by-step explanation:

Given is a picture consisting of 4 parabolas with first 3 open up and last one open down.

We are to find the minimum value vertex

Seeing the graph we can write coordinates of vertex as where they turn their direction.

Hence vertices are

Graph           Vertices        y value

I                      (0,5)               5

II                     (0,0)               0

III                    (1,2.5)             2.5

IV                   (0,-4)              -4

Of the 4 y values, IV graph has the minimum value vertex

The third angle would have to be either an obtuse angle or a right angle.

The third angle can either be an acute angle or obtuse angle

The sum of an interior angle of a triangle is 180 degrees

Acute angles are angles that are less than 90 degrees. If the two angles of a triangle are acute, the two angles can be 30 and 45 degrees

If the third angle is m<C

m<C = 180 - (30 + 45)

m<C = 180  - 75

m<C = 105 degrees

Since the angle is greater than 90 and less than 180, hence it is an Obtuse angle.

Similarly, if the two angles of a triangle are acute, the two angles can be 30 and 89 degrees

If the third angle is m<D

m<D = 180 - (30 + 90)

m<D = 180  - 119

m<D = 61 degrees

Since the angle is less than 90degrees, hence it is an acute angle.

This shows that the third angle can either be an acute angle or obtuse angle

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Answer:

10

Step-by-step explanation:

f(x) = 3x + 1

f(3)= 3 * 3 + 1 + 10

The value of larger and smaller angles are 135 and 45 degrees respectively.

Two angles are supplementary if their sum is 180 degrees.

Since, given that One angle measures three times the measure of a smaller angle.

Let us consider that one angle is 3x and other is x.

                   [tex]3x+x=180\\\\4x=180\\\\x=180/4=45[/tex]

Larger angle is, [tex]3x=3*45=135[/tex]

Smaller angle is, [tex]x=45[/tex]

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Answer: OPTION A.

Step-by-step explanation:

Find the length scale factor by dividing the known length of the larger triangle by the known length of the smaller triangle:

[tex]lenght\ scale\ factor=\frac{35}{25}=\frac{7}{5}[/tex]

Then, the  area scale factor is:

[tex]area\ scale\ factor=(\frac{7}{5})^2=\frac{49}{25}[/tex]

To find the area of the the larger triangle, multiply the area of the smaller triangle by the area scale factor. Then:

[tex]A_{(larger)}=(270ft^2)(\frac{49}{25})=529.2ft^2[/tex]

So, the option that shows an approximation of the area of the larger triangle is the option A:

[tex]A_{(larger)}[/tex]≈[tex]530ft^2[/tex]

Answer:

x=5

Step-by-step explanation:

3/2 = 3/2x - 6/5x

Get a common denominator of 10 for the fractions with x

3/2 = 3/2 *5/5 x - 6/5 *2/2 x

3/2 = 15/10x - 12/10x

3/2 = 3/10 x

Multiply each side by 10/3 to isolate x

10/3 * 3/2 = 10/3 * 3/10 x

10/2 = x

5 =x

Given - Length of the Rectangular Plot : 16 meters

Given - Width of the Rectangular Plot : 4 meters

We know that - Area of a Rectangle is given by : Length × Width

[tex]:\implies[/tex]  Area of the Rectangular plot = (16 × 4) m²

[tex]:\implies[/tex]  Area of the Rectangular plot = 64 m²

Given : Square plot and Rectangular plot have same Area

[tex]:\implies[/tex]  Area of Rectangular plot = Area of Square plot

[tex]:\implies[/tex]  Area of Square plot = 64 m²

We know that - Area of Square is given by : Side × Side

[tex]:\implies[/tex]  Side × Side = 64 m²

[tex]:\implies[/tex]  S² = 64 m²

[tex]:\implies[/tex]  S² = 8² m²

[tex]:\implies[/tex]  S = 8 m

Answer : One side of the Square Garden plot is 8 meter

Answer:

Side of the square plot = 8 m

Step-by-step explanation:

l = 16 m

b = 4 m

Area of the rectangular plot = l * b

                                                 = 16 * 4 = 64 m²

Area of square plot = Area of rectangular plot

          side  *  side    = 64 m²

                    side       =  √64 = 8 m

Answer:

D   sin 85         sin 31

    ---------- =     ----------

      b                  9.3

Step-by-step explanation:

We can use the law of sins

sin B        sin A         sin C

---------- = ----------- = ----------

b                   a            c

We do not know angle C, but we can calculate it

The angles of a triangle add to 180

A + B + C = 180

64+ 85 + C = 180

149 + C = 180

C = 180-149

C =31

sin B         sin C

---------- = ----------

b                  c

We know B =  85, C = 31, b = unknown and c = 9.3

sin 85         sin 31

---------- = ----------

b                  9.3

the correct answer would be D

Answer:

C - AC equals AD times AB over AE

Step-by-step explanation:

If Hiro is creating a larger scaled replica of a triangular canvas, then Hiro will get two similar triangles ABE (the small one) and ACD (the large one). Similar triangles have proportional corresponding sides, so

[tex]\dfrac{AC}{AB}=\dfrac{AD}{AE}[/tex]

From this proportion:

[tex]AC=\dfrac{AD\cdot AB}{AE}[/tex]

So, option C (AC equals AD times AB over AE) is correct option

Answer:

2 sets of possible solutions:

x=3, y = 5

and

x=-1, y = -3

Step-by-step explanation:

Using the graphical method, (see attached)

you can graph both equations and find their intersection points.

From the attached plot, you can see that the graphs intersect at (3,5) and (-1,-3)

Alternatively, you can solve this numerically by solving the following system of equations. You will get the same answer.

y = 2x + 1 ------------------- eq. (1)

y = x² - 4 ------------------- eq. (2)

[tex]\bf (\stackrel{x_1}{6}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{3}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{3-4}{-5-6}\implies \cfrac{-1}{-11}\implies \cfrac{1}{11}[/tex]

Answer:

1/11

Step-by-step explanation:

Answer:

x^3(2x+1)(2x-1)

Step-by-step explanation:

first take common then use formula of a^2-b^2

Answer:

The factor of the provided expression are: [tex]x^3(4x-1)(4x+1)[/tex]

Step-by-step explanation:

Consider the provided expression.

[tex]16x^5-x^3[/tex]

Here the Greatest common factor in the above expression is x³.

The above expression can be written as:

[tex]x^3(16x^2-1)[/tex]

[tex]x^3((4x)^2-1^2)[/tex]

Now use the difference of the square property: [tex]a^2-b^2=(a+b)(a-b)[/tex]

By using the above property we can rewrite the provided expression as shown:

[tex]x^3(4x-1)(4x+1)[/tex]

Hence, the factor of the provided expression are: [tex]x^3(4x-1)(4x+1)[/tex]

Answer:

D:Spring A is 3 m longer than spring B because 15 – 12 = 3.

Step-by-step explanation:

In this question, you should remember the Hooke's Law in physics.

The Hooke's Law simply explains that the extension that occurs on a spring is directly proportional to the load applied on it.

The mathematical expression for this law is

[tex]F=-kx[/tex]

where;

F= force applied on the spring

x = the extension on the spring

k= the spring constant which varies in spring.

The question will need you to calculate the extension on the springs A and B then compare the values obtained.

In spring A

Force, F=60N and spring constant ,k=4 N/m

To find the extension x apply the expression;

[tex]F=-kx\\\\60=-4*x\\\\60=-4x\\\\\frac{60}{-4} =\frac{-4x}{-4} \\\\\\-15=x[/tex]

Here the spring extension is 15 m

In spring B

Force, F=60N and spring constant , k=5N/m

To find the extension x apply the same expression

[tex]F=-kx\\\\60=-5*x\\\\60=-5x\\\\\\\frac{60}{-5} =\frac{-5x}{-5} \\\\\\-12=x[/tex]

Here the extension on the spring is 12 m

Compare

The extension on spring A is 3 m longer than that in spring B because when you subtract the value of spring B from that in spring A you get 3m

[tex]=15m-12m=3m[/tex]

Answer:

D)Spring A is 3 m longer than spring B because 15 – 12 = 3.

trust

The value of the rational expression when x is -2 or -1 is 0 and 3, respectively.

To find the value of the rational expression when x is -2 or -1, we substitute these values into the expression. Plugging in -2, we have (-2)^2 - 4/((-2)+2)((-2)+1) = 0.

Next, plugging in -1, we have (-1)^2 - 4/((-1)+2)((-1)+1) = 3.

Therefore, the value of the rational expression when x is -2 or -1 is 0 and 3, respectively.

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Answer:

Step-by-step explanation:89

Answer:

function

Step-by-step explanation:

hoped this helped;)

Answer:

Step-by-step explanation:

Not a function.  The number of people has little direct connection with the total number of watches owned.

Answer:

your answer would be just x

Step-by-step explanation:

you just subtract the exponents

The expression x^-8/x^-7 simplifies to 1/x. This is due to the rule for dividing exponential expressions with the same base, which involves subtracting the exponents.

To solve x^-8/x^-7, we need to understand the rule for division of expressions with exponents which is: x^a / x^b  = x^(a-b).

When you divide exponential expressions with the same base, you subtract the exponents.

In our case, x^-8 / x^-7 = x^(-8 - -7). This simplifies to x^-1 or x^-1 = 1/x. So, the result is 1/x.

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Answer:

the answer should be 1

Step-by-step explanation:

4[(-3+z)2-2(-3+z)]+1

4(-6+2z+6-2z)+1

-24+8z+24-8z+1

the 24's and 8's cancel out leaving 1

To find g(h(-3+z)), we first find h(-3+z) by substituting -3+z into h(a), it becomes z^2-8z+15. Then, substitute this into g(a) to get g(h(-3+z)), which results in 4z^2-32z+61.

In the field of Mathematics, to solve the problem g(h(-3+z)), we need to substitute h into g. It means that every 'a' in g(a) will be replaced by what h(-3+z) is equal to. To find h(-3+z), we substitute -3+z into h(a) in place of a. Therefore, h(-3+z) equals to (-3+z)^2-2(-3+z). After simplifying, it becomes z^2-6z+9+6-2z=z^2-8z+15. Next, we substitute this into g(a) to get g(h(-3+z))=4[z^2-8z+15]+1=4z^2-32z+61. Hence, the solution to the problem g(h(-3+z)) is 4z^2-32z+61.

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