Use the zero product property to find the solutions to the equation (x 2) (x 3) = 12.

Answer:

Step-by-step explanation:

       [tex]\sf \boxed{\bf y = mx +b}[/tex]

Here, m is the slope and b is the y-intercept

  Find the slope with the given two points.

   [tex]\sf \boxed{slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]

             [tex]\sf =\dfrac{4-6}{8-5}\\\\=\dfrac{-2}{3}[/tex]

Slope = -2/3 and choose any one the given points.

Substitute m = -2/3  and (5,6)  in the above equation and find 'b'

      [tex]\sf 6 =\dfrac{-2}{3}*5+b\\\\6 =\dfrac{-10}{3}+b\\\\6+\dfrac{10}{3}=b\\\\\dfrac{6*3}{1*3}+\dfrac{10}{3}=b\\\\\dfrac{18}{3}+\dfrac{10}{3}=b\\\\\boxed{b=\dfrac{28}{3}}[/tex]

Equation of the line:

            [tex]y = \dfrac{-2}{3}x + \dfrac{28}{3}[/tex]

The value of y if x is equal to 5 is 75 and the value of y when x = 7 is 8/7

Variations shows the relationship between variables.

4) If y varies directly as x², hence;

y = kx²

27 = 9k
k = 3

In order to determine y if x = 5

y = 3(5*5)
Y = 75

Hence the value of y if x is equal to 5 is 75

5) If y varies inversely as x, hence;

y = k/x
k = xy
k = 16(1/2)

k = 8

If x = 7, the value of y will be;

y = 8/7

Hence the value of y when x = 7 is 8/7

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The probability that the auditor will select a week in which you paid overtime wages and hired is 0.28

In 2010, your company paid overtime wages or hired temporary help during 32 weeks of the year. Overtime was paid for 26 weeks and temporary help was hired for 15 weeks.

Probability, can be define as the ratio of favorable outcomes to the n number of total events.

Here, p(a) = Overtime was paid for 26 weeks = 26/32= 0.81
       p(b) =  temporary help was hired for 15 weeks = 0.46
Required probability = P(a) + P(b) - 1
                                  =   0.81 + 0.46 -1
                                  =   0.28

The the required probability that the auditor will select a week in which you paid overtime wages and hired is 0.28

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The scientific notation of the product of the given numbers is [tex]5.291 \times 10^{12}[/tex].

Given, [tex](4.81 \times 10^{16} ) (1.1 \times 10^{-4} )[/tex].

We need to write the scientific notation of the product.

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form.

Now, [tex](4.81 \times 10^{16} ) (1.1 \times 10^{-4} )=4.81 \times 1.1 \times 10^{16} \times10^{-4}[/tex]

[tex]=5.291 \times 10^{16-4} =5.291 \times 10^{12}[/tex]

Hence, the scientific notation of the product of the given numbers is [tex]5.291 \times 10^{12}[/tex].

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Answer:C

Step-by-step explanation:

5.291 times 10 Superscript 12

Answer:

34800

Step-by-step explanation:

As, the nearest hundred to 766 is 800.

[tex] {a}^{4} \: - \: {a}^{3} \: + \: {2a}^{2} [/tex]

[tex] \boxed{ \bold{ {a}^{2} \: \times \: ( {a}^{2} \: - \: a \: + \: 2)}}[/tex]

Answer:

a²​(a²​-a+2)

Step-by-step explanation:

Solution Given:

a⁴-a³+2a²​

first taking common a²​

we get

a²​(a²​-a+2) which is a required answer.

The inequality 25b ≤ 375 describes the price she can afford for each individual box of supplies.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

We have:

Ms. Jerome wants to buy identical boxes of art supplies for her 25 students. If she can spend no more than $375 on art supplies

Let's suppose b is the price of each box of supplies.

Total cost for a 25 number of boxes = $25b

25b ≤ 375

Thus, the inequality 25b ≤ 375 describes the price she can afford for each individual box of supplies.

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Answer:

B - fixed rental for the book.

Since for everyday the book is late the fee is 0.25 multiplied by X, X is the days the book is not returned.

Thus, the constant would be 2, 2 is the constant whereby the rental for the book regardless of other variables.

Answer:

  (x, y) = (0, -3)

Step-by-step explanation:

On a graph, the solution to a system of equations is the set of points where the graphs of the equations intersect.

__

The graphs for this system of equations intersect at the point (0, -3). That point is the only solution for this system of equations.

The solution is (x, y) = (0, -3).

Answer:

C

Step-by-step explanation:

supplementary because it adds to 180

Answer:C

Step-by-step explanation:

khan

Answer:

Step-by-step explanation:

Your question was incomplete. Please check below the full content.

There are 8 ounces in 1 cup and 16 cups in 1 gallon.

(a) Diane brought 4.5 gallons of water to a campout. How many ounces of water did she bring? Show your work.

(b) Diane started a hike with 24 ounces of water in her backpack. What fraction of a gallon of water did she start the hike with? Show your work.

a) 576 ounces of water Diane brought.

b) 3/16 of a gallon of water did she start the hike with.

Given that there are 8 ounces in 1 cup and 16 cups in 1 gallon. 

a) Amount of water diana brought for campout = 4.5 gallons Ounce of water she brought = 4.5×16×8

= 576ounces

b) Diane started a hike with 24 ounces of water in her backpack.

The fraction of gallons in 24 ounces is calculated as follows:

The fraction of gallons in 24 ounces = 24 / (8×16)

= 3/16

Hence, a) 576 ounces of water Diane brought.

b) 3/16 of a gallon of water did she start the hike with.

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1. 6 km ≈ 3.73 mi

2. 2.5 L ≈ .66 gal

3. 90 lb ≈ 40.82 kg

Step-by-step explanation:

(X1,Y1) = (-2,2)

(X2,Y2) = (0,1)

• Find slope.

m = (Y2 - Y1)/(X2 - X1)

m = (1 - 2)/(0 - (-2))

m = -1/2

The answer is C.

Answer:

radius = 8

Step-by-step explanation:

the equation of a circle centred at the origin is

x² + y² = r² ( r is the radius )

x² + y² = 64 ← is in this form

with r = [tex]\sqrt{64}[/tex] = 8

Answer:

[tex] \sqrt[2]{3} + \sqrt{5} = \sqrt[2]{8} [/tex]

[tex] \sqrt{3 } - \sqrt[3]{5} = \sqrt[3]{2} [/tex]

Answer:

x = 0 y = -5

x = 3 y = 4

Step-by-step explanation:

x² + y² = 25

y - 3x = -5

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

y = 3x-5

x² + y² = 25

x² + (3x-5)² = 25

(3x-5)(3x-5) = 9x² -15x -15x + 25

x² + 9x² -15x -15x + 25 = 25

x² + 9x² -15x -15x = 0

x² + 9x² - 30x = 0

10x² - 30x = 0

x(10x-30)=0

x = 0

10x-30=0

x = 3

y - 3x = -5

y - 3(0) = -5

y = -5

y - 3(3) = -5

y - 9 = -5

y = 4

Answer:

(4,3) and (0,-5) are both solutions where we have (x,y).

Step-by-step explanation:

Here are simplified steps:

https://www.symbolab.com/solver/matrix-calculator/x%5E%7B2%7D%2By%5E%7B2%7D%3D25%3B%20y-3x%3D-5?or=input

Symbolab is an excellent tool for just most math.

Median: 6

Range: 9

Mode: 7, appeared 3 times

Total Earned Saturday: $45

Total Earned Sunday: $63

Total: $108

Time and a quarter means that you divide his normal rate by 4 and add that to his normal rate.

9/4 = 2.25     2.25 + 9 = 11.25

Jarvis makes $11.25 an hour on Saturdays.

Since he worked 4 hours, you multiply,

11.25 x 4 = 45.

Time and three quarters mean that you multiply his normal rate by 3/4 and add that to his normal rate

9x0.75 = 6.75     6.75 + 9 = 15.75

Jarvis makes $15.75 an hour on Sundays. Since he worked 4 hours, you multiply 15.75 x 4 = 63.

To get the total, you add his earnings on Saturday and earnings on Sunday

45 + 63 = 108.

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1. The value of x is 40

m ∠2x + 10 = 90

m ∠3x = 120

m ∠2x +5 = 85

m ∠2x -15 = 65

2. The value of x is 15

m ∠5x = 75

From the question, we are to determine the value of x and the given angles

Since sum of angles is 360°

3x + 2x + 10 + 2x + 5 + 2x -15 = 360°

Collect like terms

3x + 2x + 2x + 2x  = 360° - 10° - 5° + 15°

9x = 360

x = 360 / 9

x = 40

∴ x = 40

Then,

m ∠2x + 10 = 2(40) + 10

m ∠2x + 10 = 80 + 10

m ∠2x + 10 = 90

m ∠3x = 3(40)

m ∠3x = 120

m ∠2x +5 = 2(40) + 5

m ∠2x +5 = 80 + 5

m ∠2x +5 = 85

m ∠2x -15 = 2(40) - 15

m ∠2x -15 = 80 - 15

m ∠2x -15 = 65

Hence, the measure of angle 2x-15 is 65

2.

Since sum of angles is 180°

Then,

5x° + x° + 90° = 180°

6x° = 180° - 90°

6x° = 90°

x = 90/6

x = 15

m ∠5x = 5(15)

m ∠5x = 75

Hence, the measure of angle 5x is 75

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The slant height of the given cone will be 12.06 inches.

The measurement from the base to the peak along the "center" of a lateral face of an object, such as a cone, is its slant height.

Given that:-

The slant height will be calculated as:-

Surface area = π r l

151.58 = π x 4 x l

l = 151.58 / ( π x 4 )

l = 12.06 inches.

Therefore slant height of the given cone will be 12.06 inches.

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Answer:

Last choice

Step-by-step explanation:

The basic definition of inverse function is both domain and range are swapped.

The domain is defined as set of all x-values while range is defined as set of all y-values.

If we have set of function h = {(1,2), (3,4), (5,6)} then the inverse will be {(2,1), (4,3), (6,5)}. Thus, if set of (x,y) is original function then set of (y,x) will be inverse of set of (x,y).

Henceforth, the inverse of f(x) will be g(x) = {(3,8), (1,4), (-1,0), (-3,-4)}.

Answer:

D. g(x) = {(3, 8), (1, 4), (–1, 0), (–3, –4)}

Step-by-step explanation:

hope this helps:)

The equation [tex](\frac18)^{-3a} = 512^{3a}[/tex] as no solution

The equation is given as:

[tex](\frac18)^{-3a} = 512^{3a}[/tex]

Express the equation as a base of 2

[tex](2^{-3})^{-3a} = 2^{9*3a}[/tex]

Evaluate the products

[tex]2^{9a} = 2^{27a}[/tex]

Cancel out the common base

9a = 27a

The above equation is not true because [tex]9a \ne 27a[/tex]

Hence, the equation [tex](\frac18)^{-3a} = 512^{3a}[/tex] as no solution

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Step-by-step explanation:

0.000672, 6.72×10⁵, 67.2×10‐⁴, 672×10⁴

Scientific notation is a way of writing numbers that looks like the following:

[tex]a\times10^n[/tex]

For instance, we can write 2930 in scientific notation.

First, write all the given values in scientific notation:

Now, let's compare the values of n, and organize the numbers from least to greatest:

[tex]6.72\times10^{-4}[/tex]

[tex]6.72\times 10^{-3}[/tex]

[tex]6.72\times10^5[/tex]

[tex]6.72\times 10^6[/tex]

Finally, rewrite all the numbers as their given format:

[tex]0.000672[/tex]

[tex]67.2\times 10^{-4}[/tex]

[tex]6.72\times10^5[/tex]

[tex]672\times 10^4[/tex]

[tex]0.000672[/tex]

[tex]67.2\times 10^{-4}[/tex]

[tex]6.72\times10^5[/tex]

[tex]672\times 10^4[/tex]

Answer:

false

Step-by-step explanation:

if the 2 shorter segments dont add up to be equal or greater to the longest segment, then its impossible for a triangle to be formed :)

Answer:

True

Step-by-step explanation:

General formulas and concepts:
Subject: Geometry

Unit: Triangular Line Segments

Definitions:

Triangle Inequality Theorem

Steps:

Use the triangle inequality theorem:

9 + 4 > 11

13 >  11 ⇒  True

9 + 11 > 4

20 > 4 ⇒ True

4 + 11 > 9

15 > 9 ⇒ True

Conclusion:

Because the 3 segments that are given satisfy the statements of the triangle inequality theorem, they can therefore form a triangle.

Answer:

For 60 gallons of fuel, the airplane would weigh 2430 gallons.

Step-by-step explanation:

Concept: Use the values and conditions to make a linear equation of a straight line. Let the y-axis be fuel and x-axis be airplane weight. The given points are (2210, 20) and (2397, 54). Use these points to make an equation of line.

[tex]\frac{y-20}{x-2210} =\frac{54-20}{2397-2210} \\\frac{y-20}{x-2210} = \frac{34}{187}[/tex]

Let this be the equation of straight line.

We have to find the airplane weight at 60 gallons of fuel. This means y = 60 and we have to find the x.

[tex]\frac{60-20}{x-2210} =\frac{34}{187} \\x-2210=\frac{(187)(40)}{34} \\x-2210=220\\x=2430[/tex]

So, the airplane weight is 2430 gallons.

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Answer:

  (a)  x = 12

Step-by-step explanation:

The radicals in this equation can be eliminated simply by squaring both sides. Then the resulting linear equation is solved in two steps.

__

  [tex]\left(\sqrt{2x-8}\right)^2=\left(\sqrt{x+4}\right)^2\\\\2x-8=x+4\qquad\text{simplify}\\\\x-8=4\qquad\text{subtract $x$}\\\\\boxed{x=12}\qquad\text{add 8}[/tex]

_____

Additional comment

You know the contents of each radical must not be negative. That means 2x-8 ≥ 0, or x≥4. We know x=4 doesn't work in the equation (0≠√8), so we only need to check the answers x=12 and x=7. Of those, only x=12 satisfies the equation.

Answer: [tex]\left(\frac{4}{3}, -\frac{5}{3} \right)[/tex]

Step-by-step explanation:

Setting the equations equal to each other.

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

Answer:

y = 5z

Step-by-step explanation:

added in the picture

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[ let the point at which line segments SV and RT intersects be O ]

[tex]\qquad \tt \rightarrow \: \angle ROV + \angle ROS = 180° [/tex]

[ linear pair ]

[tex]\qquad \tt \rightarrow \: \angle ROV = 180 - \angle ROS[/tex]

[tex]\qquad \tt \rightarrow \: \angle ROV = 180 -2y[/tex]

____________________________________

[tex]\qquad \tt \rightarrow \: \angle SVU = \angle ROV + \angle TRV[/tex]

[ Exterior angle = sum of opposite interior angles ]

[tex]\qquad \tt \rightarrow \: \angle SVU = 180 - 2y + y[/tex]

[tex]\qquad \tt \rightarrow \: \angle SVU = 180 - y [/tex]

( let it be equation 1 )

____________________________________

[tex]\qquad \tt \rightarrow \: \angle SVU + \angle SUV + \angle VSU = 180°[/tex]

[ Sum of angles of Triangle ]

[tex]\qquad \tt \rightarrow \: \angle SVU + 4z + z = 180°[/tex]

[tex]\qquad \tt \rightarrow \: \angle SVU + 5z = 180°[/tex]

[tex]\qquad \tt \rightarrow \: \angle SVU = 180° - 5z[/tex]

( let it be equation 2 )

____________________________________

By comparing both equations :

[tex]\qquad \tt \rightarrow \: \angle SVU = 180 - y = 180 - 5z[/tex]

[tex]\qquad \tt \rightarrow \: 180 - y = 180 - 5z[/tex]

( Add 180° on both sides )

[tex]\qquad \tt \rightarrow \: 180 - y + 180 = 180 - 5z + 180[/tex]

[tex]\qquad \tt \rightarrow \: - y = - 5z[/tex]

[tex]\qquad \tt \rightarrow \: y = 5z[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞