The equation of line c is y = 5* - . Line d is parallel to line c and passes through (2, 6).
What is the equation of line d?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified
proper fractions, improper fractions, or integers.

Answer:

f(x) = x^3 + 7x^2 + 7x -15

Step-by-step explanation:

f(x) = (x+5)(x+3)(x-1)

f(x) = (x^2 + 3x + 5x + 15)(x-1)

f(x) = (x^2 + 8x + 15)(x-1)

f(x) = x^3 + 8x^2 + 15x -x^2 -8x -15

simplify

f(x) = x^3 + 7x^2 + 7x -15

Answer:

[tex]f(x) = (x + 5)\, (x + 3)\, (x - 1)[/tex].

Step-by-step explanation:

By the factor theorem, if a constant [tex]a[/tex] is zero of the polynomial [tex]f(x)[/tex], [tex](x - a)[/tex] would be a factor of this polynomial. (Notice how [tex]x = a[/tex] would indeed set the value of [tex](x - a)\![/tex] to [tex]0[/tex].)

For instance, since [tex](-5)[/tex] is a zero of the polynomial [tex]f(x)[/tex], [tex](x - (-5))[/tex] would be a factor of [tex]f(x)\![/tex]. Simplify this expression to get [tex](x + 5)[/tex].

Likewise, the zero [tex](-3)[/tex] would correspond to the factor [tex](x + 3)[/tex], while the zero [tex]1[/tex] would correspond to the factor [tex](x - 1)[/tex].

All three of these factors above are linear, and the degree of the variable [tex]x[/tex] in each factor is [tex]1[/tex]. Multiplying three such linear factors would give a polynomial of degree [tex]3[/tex].

Given the three factors, the expression of [tex]f(x)[/tex] in factored form would be:

[tex]f(x) = m\, (x + 5)\, (x + 3)\, (x - 1)[/tex] for some constant [tex]m[/tex].

When this expression is expanded, the constant [tex]m[/tex] would be the coefficient of the [tex]x^{3}[/tex] term (the leading term.) In other words, [tex]m\![/tex] is the leading coefficient of [tex]f(x)[/tex]. This question has required this coefficient to be [tex]1[/tex]. Thus, [tex]m = 1[/tex]. The expression of [tex]f(x)\![/tex] in factored form would be:

[tex]f(x) = (x + 5)\, (x + 3)\, (x - 1)[/tex].

Answer:

16:20??

Lol I think it's wrong sorry.

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Divide 6 3/4 by 1 1/2

Convert into improper fractions, 27/4 and 3/2

[tex]\frac{27}{4} / \frac{3}{2}[/tex]

[tex]\frac{27}{4} * \frac{2}{3}[/tex]

[tex]\frac{9}{2} = 4.5[/tex]

The question asks for the number of whole cakes, so the answer would be 4.

Answer : 4

Step - by - step explanation :

In - order to find out how many cakes Hannah can make we need to find out how many 1 1/2 cups of sugar she has . . .

what is 6 3/4 divided by 1 1/2 --> 6 3/4 divided by 1 2/4 ?  4 1/2

SO ! Hannah can make 4 complete cakes

The correct relation between the triangles if the triangles are similar is, [tex]\dfrac{RY}{RS} = \dfrac{RX}{RT} = \dfrac{XY}{TS}[/tex].

Given that,

Consider [tex]\rm \triangle RST[/tex] and [tex]\rm \triangle RYX[/tex].

Triangle RST is shown.

Line XY is drawn parallel to side ST within triangle RST to form a triangle [tex]\rm \triangle RYX[/tex].

We have to determine,

If the triangles are similar, which must be true?

According to the question,

Consider [tex]\rm \triangle RST[/tex] and [tex]\rm \triangle RYX[/tex].

Triangle RST is shown.

The relationship between the triangles is line XY is drawn parallel to side ST within triangle RST to form [tex]\rm \triangle RYX[/tex].

The point X on side RT and point Y on side RS in [tex]\rm \triangle RYX[/tex].

Then,

The [tex]\rm \triangle RST[/tex] is similar to [tex]\rm \triangle RYX[/tex], the corresponding ratio of their sides are equal,

[tex]\dfrac{RY}{RS} = \dfrac{RX}{RT} = \dfrac{XY}{TS}[/tex]

Hence, The correct relation between the triangles if the triangles are similar is, [tex]\dfrac{RY}{RS} = \dfrac{RX}{RT} = \dfrac{XY}{TS}[/tex].

For more details about Triangle refer to the link given below.

https://brainly.com/question/13858149

Answer:

B.

Step-by-step explanation:

Edge 2022

Based on the amount of gasoline Mario bought in gallons, the amount in liters would be 5.8 liters.

A single gallon is equivalent to 3.875 liters.

If Mario bought 1.5 gallons of gasoline, the amount he bought in liters would be:

= Gasoline in gallons x Number of liters per gallon

= 1.5 x 3.875

= 5.8125

= 5.8 liters

In conclusion, Mario bought 5.8 liters of gasoline.

Find out more at https://brainly.com/question/237650.

Answer:

$100-5(15) aka $25 still owed

Answer: 8v+24

Step-by-step explanation:

[tex]4(2v+6)=4(2v)+4(6)=8v+24[/tex]

The fare without tip for the Metro Taxi is of 1 passenger and 9.5 miles is $27.83.

The given parameters:

The fare without tip for the Metro Taxi is calculated as follows;

[tex]cost \ of \ distance = \$ 0.75 \ \ + \ \ \frac{\$ 0.55}{0.2 \ mile} \times 9.3 \ miles\\\\cost \ of \ distance = \$ 26.325[/tex]

Cost of 1 passenger = $1.50

The total cost is calculated as follows;

total cost = $1.50 + $26.325

total cost = $27.83

Thus, the fare without tip for the Metro Taxi is of 1 passenger and 9.5 miles is $27.83.

The complete question is below:

Compute the fare without tip: 1 passenger, 9.5 miles. Round to nearest fifth of a mile when dividing.

Metro Taxi: first 1/5 mi= $0.75, each additional 1/5 mi= $0.55, each additional passenger= $1.50.

Learn more about cost per miles here: https://brainly.com/question/2513267

Answer: Factoring is essentially the reverse of the distributive property. You are basically trying to simplify the polynomial by taking out common factors. You also may try reducing the power (or the highest exponent) of the polynomial with factoring. I would say that factoring is the breaking down of a bigger polynomial into a product of two expressions that are usually multiplied by each other. One specific use of factoring we see a lot is the quadratic formula.

1. Quadratic Factoring --> [tex]x^2+2x-15[/tex] --> we have an [tex]x^2[/tex] but we want there to only be "[tex]x[/tex]"s. Here we need to constant numbers (integers), that multiply together to get [tex]-15[/tex], and add up to [tex]+2[/tex]. (5 and -3)

    - [tex]x^2+2x-15[/tex] ==> [tex]x^2+5x-3x-15[/tex] ==> [tex]x(x+5)-3(x+5)[/tex] ==> [tex](x-3)(x+5)[/tex]

Above: We can see that we factor out [tex]x[/tex] from [tex]x^2+5x[/tex] (This shows that we are aiming to break it down to make it easier to evaluate).

Remember: Factoring does not always mean that the polynomial is in a simpler form. There are many situations where factoring is totally unnecessary and complicates the polynomial even more.

--------------------------------------------------------------------------------------------------------------On a separate note: Distributive Property, if you are unsure or not fully sure on what that means, is when you multiply two expressions together to create one expression. Multiple expressions are combining into one.

Let potatoes be a and tomatoes be b

[tex]\\ \sf\longmapsto a+b=12---(1)[/tex]

[tex]\\ \sf\longmapsto 0.24a+0.76b=6.52[/tex]

Simplify 2nd one

[tex]\\ \sf\longmapsto 0.06a+0.19b=1.63[/tex]--(2)

Solving both equations

Step-by-step explanation:

Angle c + angle d = 180° ( linear pair)

given,

angle c = 5x + 9

angle d = 5x - 6

now,

5x + 9 + 5x - 6 = 180

10x + 3 = 180

10x = 180 - 3 = 177

10x = 177

x = 177/10 = 17.7

so,

angle C = 5x + 9 = 5(17.7) + 9 = 97.50°

angle D = 5x - 6 = 5(17.7) - 6 = 82.50°

Hope this answer helps you dear! take care!.

Answer: 1/4

Step-by-step explanation:

There are three even numbers and three odd numbers on a 6 sided dice

The probability of rolling an even number on the red die is: p(red with even) = 3 / 6, or 1 / 2, since there are six numbers on a die.

The probability of rolling an even number on the green die is the same as the probability of rolling an even number on the red die, or 3 / 6, or 1 / 2.

Since rolling the red die and rolling the green die are independent events, to find the probability of both occurring, you need to multiply the individual probabilities.

P(of both red and green even) = 1/2 * 1/2, or 1/4.

Answer:

3/4

Step-by-step explanation:

This is what I got for Acellus

Answer:

d? Kerana ianya tidak sama kaki

Answer:

The answer is  $22.79. Hope this helped! If the answer is wrong i'm super sorry!

Step-by-step explanation:

$13.50 + $8 = $21.50

0.06 x 21.50 = $1.29

$1.29 + $21.50 = $22.79

Answer:

ililil

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

To solve this question we will be using BIDMAS.

This stands for, Brackets, indices, division, multiplication, addition and subtraction.

As brackets is first, we need to do 5+4, to get 9.

This gives us 26-9-20 divide 4

Next is division so we do 20 divide by 4, to get 5.

This gives us 29-9-5

So now we subtract 9 from 29 to get 20, and 5 from 20 to get 15, which is our final answer.

Answer:

(0, 1) and (1, 2)

Step-by-step explanation:

[tex]{ \rm{f(x) = {3}^{x} }}[/tex]

• Assume f(x) is one

[tex]{ \rm{ {3}^{x} = 1}}[/tex]

• Apply logarithms:

[tex]{ \rm{x log(3) = log(1) }} \\ \\ { \rm{x = 0 }}[/tex]

• Assume f(x) is 2

[tex]{ \rm{x = \frac{ log(2) }{ log(3) } }} \\ \\ { \rm{x = 1}}[/tex]

The value of the angle subtended by the distance of the buoy from the

port is given by sine and cosine rule.

Reasons:

Location from which the ship sails = Port

The speed of the ship = 10 mph

Direction of the ship = N35°W

Location of the warning buoy = 5 miles north of the port

Required: The bearing of the warning buoy from the ship after 7.5 hours.

Solution:

The distance travelled by the ship = 7.5 hours × 10 mph = 75 miles

By cosine rule, we have;

a² = b² + c² - 2·b·c·cos(A)

Where;

a = The distance between the ship and the buoy

b = The distance between the ship and the port = 75 miles

c = The distance between the buoy and the port = 5 miles

Angle ∠A = The angle between the ship and the buoy = The bearing of the ship = 35°

Which gives;

a = √(75² + 5² - 2 × 75 × 5 × cos(35°))

By sine rule, we have;

[tex]\displaystyle \frac{a}{sin(A)} = \mathbf{ \frac{b}{sin(B)}}[/tex]

Therefore;

[tex]\displaystyle sin(B)= \frac{b \cdot sin(A)}{a}[/tex]

Which gives;

[tex]\displaystyle sin(B) = \mathbf{\frac{75 \cdot sin(35^{\circ})}{\sqrt{75^2 + 5^2 - 2 \times 75\times5\times cos(35^{\circ}) } }}[/tex]

[tex]\displaystyle B = arcsin\left( \frac{75 \cdot sin(35^{\circ})}{\sqrt{75^2 + 5^2 - 2 \times 75\times5\times cos(35^{\circ}) } }\right) \approx 37.32^{\circ}[/tex]

Similarly, we can get;

[tex]\displaystyle B = arcsin\left( \frac{75 \cdot sin(35^{\circ})}{\sqrt{75^2 + 5^2 - 2 \times 75\times5\times cos(35^{\circ}) } }\right) \approx \mathbf{ 142.68^{\circ}}[/tex]

The angle subtended by the distance of the buoy from the port, C is therefore;

C ≈ 180° - 142.68° - 35° ≈ 2.32°

By alternate interior angles, we have;

The bearing of the warning buoy as seen from the ship is therefore;

Bearing of buoy ≈ 270° + 35° + 2.32° ≈ 307.35°

Learn more about bearing in mathematics here:

https://brainly.com/question/23427938

Answer

64.8

Step-by-step explanation:

brainliest pls

Answer:

64.8 cm.

Step-by-step explanation:

Add up the sides:

Perimeter = 2(8.7) + 2(5.5) + 2(5.5) + 2(10.8) + 2(1.9)

= 17.4 + 11 + 11 + 21.6 + 3.8

= 64.8 cm.

Answer:

21 day

Step-by-step explanation:

EASY MArk as brainliest

Answer:

January 1 is new years day! can I get branliest:>

Using Venn probabilities, it is found that:

In this problem, the events are:

In this problem:

The probability of either is:

[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]

Hence:

[tex]P(A \cup B) = 0.62 + 0.73 - 0.48 = 0.87[/tex]

You can learn more about Venn probabilities at https://brainly.com/question/25698611

Answer:

87%.

Step-by-step explanation:

The probability that a resident chosen at random shops at either Comet Mall or at Star Mall is 87%.

Answer:

sorry I didnt get you. whats the mean of ^ symbole.

618 hope this helps you have an amazing week

Answer:

A:B::2:3

123:x

set up as fractions:

[tex]\frac{2}{3}[/tex]   [tex]\frac{120}{x}[/tex]   120*3=360

360/2=180

Betty Received $180

Answer:

I can't write the equation but getting the answer is easy.

The difference in volume of the 2 aquariums is .2 cubic feet.

The difference in weight is 12.48 pounds.

Therefore, .2 cubic feet of water weighs 12.48 pounds.  Therefore the

weight of 1 cubic foot of water = 12.48 / .2 = 62.4 pounds.

Step-by-step explanation:

The inverse of a function may or may not be a function

The function g(x) is given as:

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

(a) Inverse function g^-1(x)

We have:

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

Replace g(x) with y

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

Swap the positions of x and y

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

Add 3 to both sides

[tex]x + 3 = 2(y - 1)^2[/tex]

Divide both sides by 2

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

Take square roots of both sides

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

Add 1 to both sides

[tex]1 + \sqrt{\frac{x + 3}2} = y[/tex]

Rewrite as:

[tex]y = 1 + \sqrt{\frac{x + 3}2}[/tex]

Express as inverse function of g

[tex]g^{-1}(x) = 1 + \sqrt{\frac{x + 3}2}[/tex]

Hence, the inverse function of g is [tex]g^{-1}(x) = 1 + \sqrt{\frac{x + 3}2}[/tex]

(b) The domain, and the range of g(x) and g^-1(x)

Function g(x)

The function g(x) is a quadratic function.

So, the domain is:

The range is:

Function g^-1(x)

The function g^-1(x) is a square root function.

So, the domain is:

The range is:

The domain of g(x) is the range of g^-1(x), while the range of g(x) is the domain of g^-1(x).

(c) The graph

See attachment for the graph

Read more about inverse functions at:

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Answer:

72/4=18 with remainder of 3 peices given to her mom

Step-by-step explanation: