Write an equation of the line passing through point
P(-8, 0) that is perpendicular to the line y=-3

Answer:

f(x) = - x² + 2x - 2 :

x → - ∞

f(x) → - ∞

f(x) = x⁴ + 3x² + x - 3 :

x → ∞

f(x) → ∞

23/25 is greater than 9/10

23/25=92/100

9/10=90/10

92>90

Answer:

f(-5) = -16

Step-by-step explanation:

f(-5) =  -  [tex](-5)^{2}[/tex] + 9

-(25) + 9

-25+9

-16

As per the concept of counting problem, the reason that the answers in part (a) and part (b) are not the same is because Q1 and Q2 are treated as two different coins in part (a) whereas they are effectively treated as the same coin in part (b). And the reason they are treated as one coin is because they both contribute the same amount to the sum of money.

Counting Problems

Basically, counting refers the process of finding the number of elements of a finite set of objects.

Given,

Suppose you have a nickel, two dimes, and a quarter. One of the dimes was minted in 1976, and the other one was minted in 1992.

While we looking into the given problem,

For A) states that,  If you choose at least one coin, this means you could choose 1, 2, 3 or 4 coins. Let us label the dime as D, the penny as P, the quarter minted in 1976 as Q1 and the quarter minted in 1992 as Q2.

Here in this process if you choose one coin, you could choose either D, P, Q1, or Q2. This gives us 4 possible sets.

And If you choose two coins, you choose the following sets of coins: DP, DQ1, DQ2, PQ1, PQ2, Q1Q2. This gives us 6 possible sets.

Then If you choose three coins, you could the following sets of coins: DPQ1, DPQ2, DQ1Q2, PQ1Q2. This gives us 4 possible sets.

So, If you choose four coins, you can only choose DPQ1Q2. This gives us 1 possible set.

So, the total number of different sets of coins you can form is 4 + 6 + 4 + 1 = 15 different sets of coins can be formed.

Similarly, for b) If you choose at least one coin, this means you could choose 1, 2, 3 or 4 coins.

Then If you choose one coin you could choose either D, P, Q1, or Q2. However, since Q1 and Q2 give us the same sum, they are effectively the same set. This gives us 3 possible sums.

So, If you choose two coins, you could choose the following sets of coins : DP, DQ, PQ, Q1Q2.And this gives us 4 possible sums

Then If you choose three coins, you could choose the following sets of coins: DPQ, DQ1Q2, PQ1Q2. And this gives us 3 possible sums

Then If you choose four coins, you can only choose DPQ1Q2. This gives us 1 possible sum.

So, the total number of different sums of coins you can form is 3 + 4 + 3 + 1 = 11 different sums of money can be produced.

Finally, c) The reason that the answers in part (a) and part (b) are not the same is because Q1 and Q2 are treated as two different coins in part (a) whereas they are effectively treated as the same coin in part (b). And the reason they are treated as one coin is because they both contribute the same amount to the sum of money.

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Answer: The answer is 81m + 27t

Step-by-step explanation:

Answer: (3t)^t+3 and 3^t^2 x 27^t are both equivalent to the expression while 9^t x 27^t is not equivalent.

Step-by-step explanation:

Answer: 60%

Step-by-step explanation:

(5 × p) / 100 = 3

((5 × p) / 100) × 100 = 3 × 100

5p = 300

5p / 5 = 300 / 5

p = 60

Percent Increase = 60

[tex]y = 4x -8\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

The value is 13/20

We do simplification here

2/5+1/4

=(8+5)/20

=13/20

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Answer:6x

Step-by-step explanation: Put the x's on one side and other on the other side

Answer:

The equation has a solution,

Step-by-step explanation:

Given equation,

→ 8x + 16 = 2x + 16

Now the value of x will be,

→ 8x + 16 = 2x + 16

→ 8x - 2x = 16 - 16

→ 6x = 0

→ x = 0/6

→ [ x = 0 ]

Hence, the value of x is 0.

The order from least to greatest is "forty percent, 0.5, eight-ninths, six-fifths".

A fraction is a part of the whole represented by a/b, where a and b are any integers.

The given numbers are,

six fifths = 6/5 = 1.2

eight ninths = 8/9 = 0.9

0.5

40% = 0.4

Therefore, the order from least to greatest is "forty percent, 0.5, eight-ninths, six-fifths".

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The amount of pure antifreeze that needs to be added = 1.429 quarts

What is antifreeze ?

A colored liquid called antifreeze, often known as engine coolant, is combined with water to assist regulate your engine in extremely hot weather.

Let x be the amount of pure antifreeze that needs to be added

The amount of pure antifreeze added (x) plus the amount of pure antifreeze in the 5 quart of 10% antifreeze solution [ 0.1*5] should be equal to the amount of pure antifreeze in the final mixture [ 0.3*(5+x) ]

The equation obtained is:

x+[0.10*5]=0.30(5+x)

x+0.5=1.5+0.30x

x-0.30x =1.5-0.5 = 1

0.70x=1

divide each side by 0.70

x=1.429 quarts

So, the amount of pure antifreeze that needs to be added = 1.429 quarts

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Answer:

B. 1 over 3 x 12 hours

Step-by-step explanation:

The oil company fills 1/12 of a tank in 1/3 an hour. So, you multiply 1/3 times 12, since 12 is a full tank. It'll take 4 hours to fill the tank at this rate.

1/12 tank: 1/3 hour

2/12 tank: 2/3 hour

3/12 tank: Full hour

3/12 is equivalent to 1/4, meaning 1/4 of the tank is filled after 1 hour. Thus, it'll take 4 hours.

Marcia has written the expression 0. 75p to represent the sale price. The best description for her expression is she multiplied p by 0.25 then subtracted that from p.

How to express the sale price?

The sale price is the price after discount. Discount is the amount by which the origin price of an item is reduced. In this case, Marcia wants to buy a television with the origin prices is p dollars. The store is offering 25% discount.

p = the origin price

25% discount = 0.75p

The sale price = p - (0.25p)

So, the best description for Marcia's expression is  multiplied p by 0.25 then subtracted that from p.

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The volume of the solid bounded above by the parabolic cylinder is 191π/64.

Given:

the Parabolic cylinder z=1−y^2 and below the plane 3x+3y+z+10=0 and on the sides of circular cylinder x^2+y^2−x=0.

[tex]x^2+y^2-x=(x-\frac12)^2 +y^2-\frac14=0[/tex]

Recenter the circle with x−1/2=u and integrate the volume over the disk

u^2+y^2 = 1/4.

[tex]\int_{u^2+y^2 < \frac14} [(1-y^2)-( -2x-3y-10)][/tex]

[tex]=\int_{u^2+y^2 < \frac14} (2u+3y-y^2 +12)[/tex]

[tex]=\int_{u^2+y^2 < \frac14} (12-y^2)[/tex]

[tex]=\int_0^{2\pi}\int_0^{1/2} (12-r^2 \sin^2\theta)rdr d\theta =\frac{191\pi}{64}\\[/tex]

Therefore The volume of the solid bounded above by the parabolic cylinder is 191π/64.

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The given expression 7x - y = -9 in the slope intercept form can be represented as y = 7x + 9.

The expression given to us is -

7x - y = -9

We have to represent this in the slope intercept form.

The slope intercept form can be represented as -

y = mx + c

where, y = y coordinate of the line

           m = slope of the line

            x = x coordinate of the line

            c = y intercept of the line

Thus, representing the given expression in the slope intercept form, we have

7x - y = -9

=> -y = -7x - 9

=> y = 7x + 9

Thus, the given expression in the slope intercept form can be represented as y = 7x + 9.

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The inequality represents the situation group of parents who would like to earn at least $600, after paying for the cost of renting the space $40 an hour, and charging $8 per person for entry into the event is 8x - 4y ≥ 600, and x > 0, Y > 0.

We are given the following;

They charge $8 per person for entry into the event.

The group would like to earn at least $600, after paying for the cost of renting the space, which is $40 an hour.

Let the number of people be x and the number of hours they are present in the space be y.

Per person entry cost is $8.

Donations by all the people entering the space are 8x.

The per hour cost of rent is $40.

The total cost of renting the space is 40y which will be subtracted from the total amount of donations.

They plan to earn a minimum of $600.

So, the inequality will be given by;

8x - 4y ≥ 600 and x > 0, Y > 0.

Thus, the inequality represents the situation group of parents who would like to earn at least $600, after paying for the cost of renting the space $40 an hour, and charging $8 per person for entry into the event is 8x - 4y ≥ 600, and x > 0, Y > 0.

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The rotational symmetry of the above attached figure is 4 ...

What is the rotational symmetry ?

= Rotational symmetry is the number of times a shape can “fit into itself” , when it is rotated 360° about its centre....

Example: Rotational Symmetry of Equilateral Triangle..

Equal sides and angles define an equilateral triangle.

• How can u find rotational symmetry ?

= An object has rotational symmetry if that figure is itself after you rotate it less than 180 degrees. If it is itself after exactly 180 degrees no more no less then that figure has point symmetry.

The rotational symmetry of the above attached figure is 4 ...

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The answer of the given question is $6.4, this is the money that need to be added onto the bill for the tip.

How to calculate a 20% tip?

To calculate tip, we need to multiply the total bill by 1 plus the decimal percentage tip we'd like to leave. If we wanted to leave a 20% tip, we would add 1 to 0.20 to get 1.20. Then, multiply the bill by 1.20 to get the total amount we'd leave including tip.

In this case, we have a $32 bill and we would like to add on an 20% tip. So, it will be as follows:

20% = 0.20

1 + 0.20 = 1.20

Total bill will be 1.20 x $32 = $38.4

Hence, the tip amount is $38.4 - $32 = $6.4

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The smallest number of people when one could have been at the party is 211 people.

This is a least common multiple question, also known as an LCM. We know this because all groups would have formed evenly if the one extra person had not arrived at the party. This means that there are 1 more people at the party than a number 2, 3, 5, or 7.

In this case, the number will be:

= (2 × 3 × 5 × 7) + 1

= 210 + 1

= 211

Applicable multiples of 7

(7 × 10) = 70 → 70 + 1 = 71 → 71/3 = 23 R2 → not possible

(7 × 20) = 140 → 140 + 1 = 141 → 141/3 = 47 → not possible

(7 × 30) = 210 → 210 +1 = 211 → 211/3 = 70 R1 → possible.

Therefore, the number of people is 211.

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Considering the data in the table, it is found that:

a) The scatter plot is given by the image at the end of the answer.

b) The correlation of the scatter plot is negative, as when the input increases the output decreases.

c) The estimate for the depth at 15 seconds is of 50.37 cm.

The scatter plot is built inserting all the points in the table, which are in the following format:

(Time, Depth).

Hence the points are given as follows:

(2, 47), (4, 41), (6, 38), (8, 37), (10, 32), (12, 24), (14, 20), (16, 19).

From both the table and the scatter plot given by the image at the end of the answer, as the input increases, the output decreases, hence the scatter plot has a negative correlation.

To make a prediction for a given input, the line of best fit has to be constructed using these points.

Inserting these points into a linear regression calculator, the line of best fit is:

y = -2.07x + 50.89.

At a time of 15 seconds = 0.25 minutes, the depth will be of:

y = -2.07 x 0.25 + 50.89 = 50.37 cm.

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Answer:The answer is:

k

=

2

.

Given two point,

A

(

x

a

,

y

a

)

and

B

(

x

b

,

y

b

)

the slope of the line that passes from them is:

m

=

y

b

−

y

a

x

b

−

x

a

.

So:

−

2

=

6

−

2

k

−

4

⇒

−

2

(

k

−

4

)

=

4

⇒

−

2

k

+

8

=

4

⇒

−

2

k

=

−

4

⇒

k

=

2

.

Step-by-step explanation:The answer is:

k

=

2

.

Given two point,

A

(

x

a

,

y

a

)

and

B

(

x

b

,

y

b

)

the slope of the line that passes from them is:

m

=

y

b

−

y

a

x

b

−

x

a

.

So:

−

2

=

6

−

2

k

−

4

⇒

−

2

(

k

−

4

)

=

4

⇒

−

2

k

+

8

=

4

⇒

−

2

k

=

−

4

⇒

k

=

2

.

The side length, x, of the right triangle will be 26 units.

According to the question,

We have the following information:

In a right triangle, two of the sides are 24 units and 10 units.

The complete question is that 24 units is the perpendicular and 10 units is the base of the given right triangle.

Let's denote hypotenuse with h, perpendicular with p and base with b.

We will find the hypotenuse of the triangle using the Pythagoras theorem:

[tex]h^{2} = b^{2} +p^{2}[/tex]

[tex]h^{2}= (24)^{2}+ (10)^{2}[/tex]

[tex]h^{2} = 476+100\\h^{2} = 576[/tex]

h = √576

h = 26 units

Hence, the side length, x, of the right triangle will be 26 units.

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In the expression 5x + 5 = 95,  the value of x is 18

What is an angle ?

An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

The given angle 5x + 5 is equal to 95

We need to calculate the value of x

5x + 5 = 95

5x = 95 - 5

5x = 90

x = 90/5

x = 18

Therefore, the expression 5x + 5 = 95 is solve and the value of x is 18

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Answer:

x = 8

Step-by-step explanation:

since the triangle is isosceles then the 2 legs are congruent, that is both 4x - 3

the perimeter is the sum of the 3 sides , that is

x + 4x - 3 + 4x - 3 = 66

9x - 6 = 66 ( add 6 to both sides )

9x = 72 ( divide both sides by 9 )

x = 8

Answer:

$65.14

Step-by-step explanation:

You will line up the numbers according to the decimal points.

You add as you normally would, ignoring the decimal point.

When you get your answer you will bring the decimal point down.

(How your problem should look:)

  $41.25

+ $23.89

  $65.14

Answer:  only one solution

Step-by-step explanation:

9x + 2/3 = 3x + 3 is a linear equation.

Linear equations only have one solution as the lowest power in numbers is 1.

9x + 2/3 = 3x + 3

9x - 3x = 3 - 2/3

3x = 7/3

x = (7/3)/3

x = 7/9

The value of x in the isosceles triangle is 9.25.

An isosceles triangle is a polygon that has three sides. The opposite length have the same length and equal angles.  has two opposite sides. If the two angles are equal , it means the triangle is an isosceles.

Th perimeter of an isosceles triangle is the sum of the length of the three sides of the triangle.

Perimeter = (2 x length of leg) + base

43 = (2x x) + 2x - 6

43 = 2x + 2x - 6

43 = 4x - 6

43 - 6 = 4x

37 = 4x

x = 37 / 4

x = 9.25

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