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The equation of the line in​ point-slope form is y = -1/3 x + 20/3 and 3y + x = 20

The equation of line perpendicular to another line in point slope form is expressed as;

y-y₁ = -1/m(x-x₁)

Given the equation of a line x -3y - 8 = 0

x - 3y = 8

-3y = -x + 8

y = 1/3x - 8/3

Slope m = 1/3

Substitute the point (-7, 9) and slope 1/3 into the equation

y-9 = -1/3(x-(-7))

y-9 = -1/3(x+7)

3(y-9) = -(x+7)

3y-27 = -x -7

3y = -x + 20

y = -1/3 x + 20/3

Write in general form.

3y = -x + 20

3y + x = 20

Hence the equation of the line in​ point-slope form is y = -1/3 x + 20/3 and 3y + x = 20

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Answer: I got my answer by dividing 14 by 35, then multiplying by 100.

Answer: 250 minutes.

Step-by-step explanation: You make a fraction.

Actual time / Percentage

Then you multiply that by 100.

The equivalent expression of the given expression is (x^3y + 5xy^2)/6

The expression is given as:

(1)/(6)x^(3)y+(5)/(6)xy^(2)

Rewrite properly as

1/6x^3y + 5/6xy^2

Take the LCM

So, we have

(x^3y + 5xy^2)/6

Hence, the equivalent expression of the given expression is (x^3y + 5xy^2)/6

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f (5) =  -7  is the output for the given input .

How can you tell whether a function is linear or not?

f(x)= -4 x+1

Put x = -2    ⇒   - 4 × -2  + 1

                ⇒   - 8 + 1

                ⇒   - 7

Therefore f (5) =  - 7

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Main Answer:

c. The value of x = 5 and y = 5.

d. The value of x = 1and y = 2.

e. The value of x = 10 and y = 2.

f. The value of x = 2 and y = 1.

g. The value of x=2 and y = 4.

Explanation for all parts:

c.  Given: 3y = x + 10

               [tex]x^{2} +y^{2}=100[/tex]

    To find: Solve the simultaneous equations.

    [tex]x^{2} +y^{2}=100[/tex]

    On taking square root from both sides of the equations, we get,

     x + y = 10

     3y = x + 10

     x = 3y - 10

     x - 3y = -10

     By elimination method,

     x - 3y = -10

     x + y  = 10

     -----------------

         -4y = -20

            y = 5

    On substituting the value of y = 5 in the equation x + y = 10 , we get,

    x + y =10

    x + 5 = 10

    x = 5

   Therefore, the required value of x = 5 and y = 5.

d.  Given: y = 3x - 1

               8[tex]x^{2}[/tex] - 2xy = 4

     To find: Solve the simultaneous equations.

     By substitution method,

     We will substitute the value of y in equation 8[tex]x^{2}[/tex] - 2xy = 4 to get,

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

      8[tex]x^{2}[/tex] - 6[tex]x^{2}[/tex] +2x = 4

      2[tex]x^{2}[/tex] + 2x = 4

      By dividing the equation by 2 on both sides, we get,

       [tex]x^{2}[/tex] + x = 2

       [tex]x^{2}[/tex] + x - 2 = 0

       [tex]x^{2}[/tex] + 2x - x - 2 = 0

       x(x+2) -1(x+2) = 0

       (x+2)(x-1) = 0

       x+2 = 0 or x - 1= 0

       x = -2 or x = 1

       We will not consider the negative values of x.

       So, x = 1.

       y= 3x - 1

       y = 3 × 1- 1

       y = 3 - 1

       y = 2  

       The value of x = 1and y = 2..

e. Given: x - 2y = 6

              [tex]x^{2}[/tex] - 4xy = 20

  To find: Solve the simultaneous equations

     x - 2y = 6

     x= 6 + 2y

     By substitution method,

     We will substitute the value of x= 6 + 2y in the equation  

      [tex]x^{2}[/tex] - 4xy = 20 to get,

     [tex](6+2y)^{2}[/tex] - 4(6+2y)y = 20

      36 + 4[tex]y^{2}[/tex] +24y - 24y - 8[tex]y^{2}[/tex] = 20

      -4[tex]y^{2}[/tex] = 20 - 36

       -4[tex]y^{2}[/tex]  = -16

       By dividing the equation by -4 on both sides, we get,

        [tex]y^{2}[/tex] = 4

        y = 2

       So, x = 6 +2y

             x = 6 + 2×2

             x = 6+4

             x=10

       Therefore, the value of x = 10and y = 2.

f. Given: 4x - 3y = 5

              [tex]x^{2} +3xy = 10[/tex]

  To find: Solve the simultaneous equations.

  4x - 3y = 5

   4x= 5 + 3y

   x = [tex]\frac{5+3y}{4}[/tex]

  By substitution method,

  We will substitute the value of x = [tex]\frac{5+3y}{4}[/tex] in the equation

        [tex]x^{2} +3xy = 10[/tex] to get,

   [tex](\frac{5+3y}{4} )^{2}[/tex] + 3[tex](\frac{5+3y}{4} )[/tex]y =10

    [tex]\frac{25+9y^{2}+30y }{16}+ \frac{15y+9y^{2} }{4}[/tex] = 10

    [tex]\frac{25+9y^{2}+30y+60y+36y^{2} }{16}[/tex]=10

    25 + 45[tex]y^{2}[/tex] + 90y=160

  By dividing the equation by 5 on both sides, we get,

    5 + 9[tex]y^{2}[/tex] +18y= 32

     [tex]9y^{2}[/tex] +18y - 27 = 0

   By dividing the equation by 3 into both sides, we get,

    [tex]y^{2}[/tex] +2y - 3 = 0

    [tex]y^{2}[/tex] +3y -y - 3 = 0

    y(y+3) - 1(y+3) = 0

     (y+3)(y-1) = 0

     y =-3 or y =1

     We will not consider the negative values of x.

     So, y=1.

     x= [tex]\frac{5+3y}{4}[/tex]

     x = [tex]\frac{5+3(1)}{4}[/tex]

    x= [tex]\frac{5+3}{4}[/tex]

    x= [tex]\frac{8}{4}[/tex]

    x = 2

Therefore, the value of x=2 and y= 1.

g. Given: 2x+ y= 8

               xy= 8

   To find: Solve the simultaneous equations.

According to the equation,

    2x+ y= 8

    y = 8 - 2x

By substitution method,

  We will substitute the value of y = 8 - 2x in the equation xy = 8 to get,

x(8-2x) = 8

8x - 2[tex]x^{2}[/tex] = 8

8x - 8 = 2[tex]x^{2}[/tex]

2[tex]x^{2}[/tex] - 8x + 8 = 0

2[tex]x^{2}[/tex] - 4x - 4x + 8 =0

2x(x - 2) - 4(x - 2) = 0

(x - 2)(2x - 4) = 0

x = 2 or 2x = 4

x= 2 or x =2

So, y = 8 - 2x

     y = 8 - 2(2)

     y = 8 - 4

    y = 4

Therefore, the value of x = 2 and y= 4.

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The numbers from least to greatest is 72%, 5/4. 1 3/4. 3.48

To order a number from least to greatest, the numbers would be arranged in ascending order. The farther a positive number is from zero on the number line, the greater the number is. For example, 100 is greater than 1.

The numbers are not written in equivalent forms. Some are written as improper fractions, percentages, decimals and mixed fractions.

An improper fraction is a fraction where the numerator is greater than the denominator. A mixed fraction is a non-integer that is made up of a whole number and a proper fraction. Percentages are numbers written as a quantity out of 100. A decimal is a number that is made up of integers and non-integers.

To order the numbers, all the numbers would be converted to decimals:

5/4 = 1.25

1 3/4 = 1.75

72% = 72/100 = 0.72

The numbers from least to greatest is: 72%, 5/4. 1 3/4. 3.48

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The set of numbers that are written in order from least to greatest is: 15.75, √250, 4², 50/3, 16.7 x 10³.

You need to solve for the quantities given to see which numbers are the smallest and which are the largest.

15.75 = 15.75

√250 = 15.8

4² = 16

50 / 3 = 16.7

16.7 x 10³ = 16,700

The order from least to greatest is therefore:
15.75, √250, 4², 50/3, 16.7 x 10³.

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Answer:

The solution h < 5.5 means that Melanie can rent the bike for no more than 5.5 hours.

Hope this helps :)

Explanation and Check part below.

Step-by-step explanation:

1. Isolate the variable by doing the inverse operation which is in this case subtracting 6 on bothsides of the equation.

8h + 6 < 50

- 6 - 6

8h < 44

2. Dive both sides of the equation by 8.

8h < 44

--- ----- <--------- fraction bar, divide

8 8

h < 5.5

The equation of the line in point-slope form, which passes through the pair of points located at (-4 , 2) and (-3 , 5), is y - 2 = 3(x + 4).

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).

Getting the slope of the two points: (-4 , 2) and (-3 , 5).

m = (y2 - y1)/(x2 - x1)

m = (5 - 2)/(-3 - -4)

m = 3

Using the point slope form, plug in the values of the slope and Point A to set up the equation.

(y - y1) = m(x - x1)

where m = 3 and (x1 , y1) = (-4 , 2)

(y - 2) = 3(x - -4)

y - 2 = 3(x + 4)

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Answer:that is already in slope intercept form

Step-by-step explanation:

Answer:

y = x + 17

Step-by-step explanation:

Given equation,

→ y = x + 17

Now we have to,

→ write it in slope-intercept form.

The slope-intercept form,

→ y = mx + b

Let's solve the given problem,

→ y = mx + b

→ y = x + 17

(It's already in slope-intercept form)

Hence, the answer is y = x + 17.

The solution of the given equation 3/b+2 = 6/b-1 is found to be (y = -5).

The numerator of the 1st fraction is multiplied by denominator of the 2nd fraction, and the numerator of the 2nd fraction is multiplied by denominator of the 1st fraction in cross-multiplication.

Now, for the given equation in the question;

3/b+2 = 6/b-1

Cross multiplying the terms;

3(b - 1) = 6(b + 2)

Opening the brackets;

3b - 3 = 6b + 12

Bring the variables and constants on the different sides.

6b - 3b  = -3 - 12

3b = -15

b = -5

Therefore, the solution of the stated equation 3/b+2 = 6/b-1 is found to be (b = -5).

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Answer:

4 / -2 / 3

Step-by-step explanation:

The relationship between 5 tablespoons of cocoa per 2 cups of milk is proportional(multiplicative). Let's represent the amount of tablespoons of cocoa we need for 1 cup of milk with x.

We can divide 5 by 2 in order to get x tablespoons for 1 cup of milk.

5 / 2 = 2.5

So, you need 2.5 tablespoons of cocoa for 1 cup of milk :)

Answer:

Only A

Step-by-step explanation:

[tex]b) \: \frac{1}{ {n}^{ - 5} } = {n}^{5} \\ \\ c) \: {n}^{6} \times {n}^{ - 8} = {n}^{ - 2} \\ \\ d) \: {n}^{7} \times {n}^{8} = {n}^{15} \\ \\ e) \: \frac{1}{ {n}^{3} } = {n}^{ - 3} [/tex]

Answer:

23 cm, 25 cm

Step-by-step explanation:

Let the Width be W cm.

Since the Length and Width are consecutive odd integers we know that the length:

Length = (W + 2) cm

Perimeter of Rectangle = Sum of all sides = 2 x Length + 2 x Width

So rewriting the perimeter , we have:

2W + 2(W+2) = 96 cm

Now lets solve for W to get the width.

2W + 2W + 4 = 96 cm

4W + 4 - 4 = 96 - 4

4W = 92 cm

W = 23 cm

Next, we know that the length = (W + 2) cm

Therefore the length = 23 + 2 = 25 cm

Answer:

Again the answer is D

Step-by-step explanation:

x = 345.54545454 is  the value of x to the nearest tenth. 1086/π = x

What is π ?

Why is pi so important?

1086/π = x

Put value of π = 22/7

1086/22/7 = x

x = 49.363636 × 7

x = 345.54545454

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We have the expression to be written as 2 × 10 =  2 x 10^ 1  = 20

The index form of a number  can be defined as that number written as an exponential expression.

It is also said to be a single number that is  raised to another number.

Given the expression;

2x _____ = 2 x 10^ 1 = ______

It is important to note that a number raised to the power 1 is that same number, so we have;

2 × 10

2 x 10^1 = 2 × 10

2 × 10  = 20

Thus, we have the expression to be written as 2 × 10 =  2 x 10^ 1  = 20

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Answer:8.75

Step-by-step explanation:

3/4=0.75

0.75+8=8.75

The equation that models the cost x in dollars of a single phone is given by 293.75 ≤ x ≤ 306.25.

What are inequalities ?

When two values are compared , an inequality represents whether one is greater than, less than, or not equal to the other.

It is given that total cost of phone is $25 above or below $1200.

This is a case of inequality.

Let's assume the cost of one phone is $x.

So cost of 4 phones will be given by 4x.

and this will be equal to total cost which is given as $25 above or below $1200.

So , the inequality is given by ;

1200 - 25 ≤ 4x ≤ 1200 + 25

1175 ≤ 4x ≤ 1225

If we divide by 4 through this inequality then ;

(1175/4) ≤ (4x/ 4) ≤ (1225/ 4)

or

293.75 ≤ x ≤ 306.25

The cost of one phone will lie between $293.75 and $306.25.

Therefore , the equation that models the cost x in dollars of a single phone is given by 293.75 ≤ x ≤ 306.25.

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The function rule for the direct variation in the table is [tex]y = 24/x[/tex] , indirect variation ; x = 2.4.

Direct variation is the change in one quantity as a result of the change in another. This suggests that if one quantity rises or falls, the other must rise or fall correspondingly as well.

The formula y = kx is used to answer direct variation questions. If finding the proportionality constant is necessary, the answer is obtained by dividing y by x.

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The following set of numbers, 44, 46, and 91, cannot be the measures of the sides of a triangle.

A triangle is a polygon with three sides and three vertices.

To know if a set of number is a valid measure of the sides of a triangle, it must follow the Triangle Inequality Theorem which states that the sum of any two sides must be greater than the third side, such that a + b > c, a + c > b, and b + c > a.

let a = 44, b = 46, and c = 91

a + b > c     44 + 46 > 91     90 > 91     False

a + c > b     44 + 91 > 46     135 > 46     True

b + c > a     46 + 91 > 44     137 > 44     True

If at least one of these three statements is not true, then the set of numbers is not a valid measure of the sides of a triangle.

Hence, the set of numbers 44, 46, and 91 can not be the measure of the sides of a triangle.

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The missing measure to the nearest hundredth is  r = 2.25 in, C = 14.13 in.

A circle's outside boundary is called the circumference and can be measured, or calculated, by using

Circumference = 2πr

where r is the radius of circle.

Now it is given that,

Diameter of circle, d = 8 1/2 in = 9/2 in

So, radius of circle, r = d/2 = 9/4 in

⇒ r = 2.25 in

Therefore,

∵ Circumference of circle, C = 2πr

∴ Circumference of circle, C = 2π*9/4

⇒ Circumference of circle, C = 14.130 in

Thus, the missing measure to the nearest hundredth is r = 2.25 in, C = 14.13 in.

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(i) 6 litres = 6000 cm³

(ii) The rate at which the water is now flowing from the tap is 50cm³/second

From the question, we are to convert the given value in litres to cm³

(i) We are to determine the value of 6 litres in cm³

NOTE: 1 litre = 1000 cm³

Thus,

6 litres = 6 × 1000cm³

= 6000 cm³

(ii)

From the given information,

It takes 60 seconds to fill a 6 litre watering can from the tap

That is,

At a rate of 6000 cm³ per 60 seconds

Now,

The rate at which water flows from the tap is halved

Then,

The new rate will be

6000/2 cm³ per 60 seconds

= 3000 cm³ per 60 seconds

Thus,

The new rate is 3000/60 cm³/second

= 50 cm³/second

= 50cm³/second

Hence, the rate at which the water is now flowing from the tap is 50cm³/second

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[tex]\textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &\stackrel{grams}{0.67}\\ t=\textit{elapsed time}\dotfill &\stackrel{years}{460}\\ h=\textit{half-life}\dotfill &\stackrel{years}{92} \end{cases} \\\\\\ A=0.67\left( \frac{1}{2} \right)^{\frac{460}{92}}\implies A=0.67\left( \frac{1}{2} \right)^5\implies A\approx 0.021~grams[/tex]

The final coordinates of the triangle are A''(x, y) = (3, 2), B''(x, y) = (- 1, 4) and C''(x, y) = (2, 0), respectively.

In this question we know the coordinates of the three vertices of the triangle, whose image must be generated by combining reflection across y-axis and translation, two kinds of rigid transformations, whose formulas are summarized below:

Reflection across y-axis

P'(x, y) = P(x, y) + (- 2 · p, 0)                (1)

Translation

P'(x, y) = P(x, y) + T(x, y)                      (2)

Where:

If we know that A(x, y) = (1, - 3), B(x, y) = (5, - 1) and C(x, y) = (2, - 5), then the final coordinates are:

Reflection across y-axis

A'(x, y) = (1, - 3) + (- 2, 0)

A'(x, y) = (- 1, - 3)

B'(x, y) = (5, - 1) + (- 10, 0)

B'(x, y) = (- 5, - 1)

C'(x, y) = (2, - 5) + (- 4, 0)

C'(x, y) = (- 2, - 5)

Translation

A''(x, y) = (- 1, - 3) + (4, 5)

A''(x, y) = (3, 2)

B''(x, y) = (- 5, - 1) + (4, 5)

B''(x, y) = (- 1, 4)

C''(x, y) = (- 2, - 5) + (4, 5)

C''(x, y) = (2, 0)

The final coordinates of the triangle are A''(x, y) = (3, 2), B''(x, y) = (- 1, 4) and C''(x, y) = (2, 0), respectively.

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Answer:

See the attached photos for help!

Step-by-step explanation:

I also recommend looking up desmos graphing calculator to actually see the graphs!

If you need more in depth assistance on this, feel free to let me know :]

It will take 0.006 seconds for bat's cry to reach its prey and echo back.

Sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid.

Given is the speed of sound which is 330 m/s. The prey is 1 meter away from the bat.

The time it takes a bat's cry to reach its prey and echo back can be calculated using the formula -

time = distance / speed

The distance covered by the sound as it reaches the prey and echo back is equal to 2 x 1 = 2 meters.

Speed of sound → 330 m/s.

So, the time taken will be -

t = 3/330

t = 0.006 s

Therefore, it will take 0.006 seconds for bat's cry to reach its prey and echo back.

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Answer:

GCF of numbers 24, 40, 60 is 4

GCF(24, 40, 60) = 4