Find the equation of a line parallel to y = 3x - 6, passing through the point (-6, -7). options:
y = 3x + 11
y = 3x - 11
y = 3x - 7
y = -1/3x - 9

Answer:y =0.07272727273 x + 2.587272727

Step-by-step explanation:

Equation of regression line is: y=ax +b

Where, [tex]b=\frac{\sum y\sum x^2-\sum x\sum xy}{n\sum x^2-(\sum x)^2}[/tex]

[tex]a=\frac{n(\sum xy)-\sum x\sum y}{n(\sum x^2)-(\sumx)^2}[/tex]

Here [tex]n =11,\sum y=32.46,\sum x^2=385,\sum x=55,\sum xy=170.3,(\sum x)^2=3025[/tex]

On substituting the values in the formula above for a and b we get:

[tex]b=\frac{32.46\cdot 385-55\cdot 170.3}{11(385)-3025}[/tex]

On simplification we get: [tex]b=2.587[/tex]

[tex]a=\frac{11(170.3)-55\cdot 32.46}{11(385)-3025}[/tex]

On simplification we get: [tex]a=0.0727[/tex]

Answer:

Its option B -4

Step-by-step explanation:

Answer:

b) -4

Step-by-step explanation:

The roots are (1-sqrt5)  and (1+sqrt(5)

FOIL

first:1*1 =1

outer: 1 * sqrt(5) = sqrt(5)

inner -1*sqrt(5) = -sqrt(5)

last sqrt(5) * - sqrt(5) = -5

Add them together: 1+sqrt(5) - sqrt(5) -5  = -4

Answer:

864 calories came from fat. What I did was just subtract 2400 from 36% and got it.

Step-by-step explanation:

The calories that come out from fat will be 864 calories.

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

The percentage is also called the indicating hundredths. Thus, 2% is two-hundredth, which means 2%=2/100=0.02.

As per the given,

A person ate 2400 calories in a day. Of these, 36% came from fat.

36% of 2400 = (36/100)2400

⇒ 864 calories.

Hence "The calories that come out from fat will be 864 calories".

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Answer:

[tex]3\frac{13}{20}=3.65[/tex] kg.

Step-by-step explanation:        

Let S be amount of strawberries picked in the afternoon.

We have been given that Sheldon harvest the strawberries and tomatoes in his garden. He picks 1 2/5 kg less strawberries in the morning than in the afternoon and the strawberries picked in morning are [tex]2\frac{1}{4}[/tex] kg.

To find the amount of strawberries picked by Sheldon in the afternoon we will add [tex]2\frac{1}{4}[/tex] and [tex]1\frac{2}{5}[/tex]  :

[tex]S= 2\frac{1}{4}+1\frac{2}{5}[/tex]      

Upon converting our given mixed fractions into improper fraction we will get,

[tex]S= \frac{9}{4}+\frac{7}{5}[/tex]

Now let us have a common denominator.

[tex]S=\frac{9*5}{4*5}+\frac{7*4}{5*4}[/tex]

[tex]S=\frac{45}{20}+\frac{28}{20}[/tex]

[tex]S=\frac{45+28}{20}[/tex]

[tex]S=\frac{73}{20}[/tex]  

[tex]S=3\frac{13}{20}[/tex]  

[tex]S=3.65[/tex]

Therefore, Sheldon picked [tex]3\frac{13}{20}=3.65[/tex] kg of strawberries in the afternoon.  

Sheldon picks approximately 0.85 kg of strawberries in the afternoon.

To find out how many kilograms of strawberries Sheldon picks in the afternoon, we need to subtract 1 2/5 kg from the total he picks in the morning.

Given that Sheldon picks 2 1/4 kg of strawberries in the morning, we can subtract 1 2/5 kg from it:

2 1/4 kg - 1 2/5 kg = 9/4 kg - 7/5 kg = 45/20 kg - 28/20 kg = 17/20 kg.

Therefore, Sheldon picks 17/20 kg or approximately 0.85 kg of strawberries in the afternoon.

Answer:

4

Step-by-step explanation:

x = - 3

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

y - 4 = - 2.(- 3 + 3)

y - 4 = - 2.0

y - 4 = 0

y = 4

I hope I helped you.

(-3, ?)

To find the missing value, which is "y", since you know x = -3, you can plug it into the equation to find "y"

y - 4 = -2(x + 3)

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

y - 4 = -2(0)

y - 4 = 0  Add 4 on both sides

y = 4

Answer:

200 words are peter can be type in 5 minutes.

Step-by-step explanation:

As given

If peter can type 80 words in 2 minutes .

i.e

80 words = 2 minutes

Now words type in 1 minutes.

[tex]1\ minutes = \frac{80}{2}\ words[/tex]

1 minutes = 40 words

Now calculate number of words are type in 5 minutes.

Words are type in 5 minutes = Number of minutes × Number of words are type in 1 minutes.

Number of minutes = 5 minutes

Number of words are type in 1 minutes = 40 words

Words are type in 5 minutes = 5 × 40

                                                = 200 words

Therefore  200 words are peter can be type in 5 minutes.

Answer:

option A

Step-by-step explanation:

The following ordered pairs are solutions to a linear equation: (-20, 11.5), (-21, 12), and (-22, 12.5).

Frame the equation of line y=mx+b using ordered pairs

(-20, 11.5), (-21, 12)

[tex]slope m = \frac{y_2-y_1}{x_2-x_1} =\frac{12-11.5}{-21+20}=-0.5[/tex]

m= -0.5

Now plug in (-21,12)  and find out b

y=mx+b

12= -0.5(-21) + b

12= 10.5 +b

Subtract 10.5 on both sides

So b= 1.5

Equation of line is y=-0.5x + 1.5

Slope is negative so graph will be decreasing

Option A  and option C graphs are decreasing

y intercept is the b values = 1.5

y intercept is (0,1.5)

Lets find x intercept

Plug in 0 for y in the equation y=-0.5x+1.5

0 = -0.5x+1.5

subtract 1.5 on both sides

1.5 = -0.5x

Divide by -0.5

so x= 3

So x intercept is (3,0)

Option A graph has x intercept (3,0)  and y intercept (0,1.5)

The equation that represents the area of the doghouse base is 21 = x * (x + 4), where x is the width and x + 4 is the length.

Jason is building a doghouse with a rectangular base, where the area is known to be 21 square feet. If the width is x feet and given the length is 4 feet longer than the width, the length can be represented as x+4. As such, we can create an equation representing the area of the rectangular base as:

Area = Width * Length

By substituting the given values, we get the equation:

21 = x * (x + 4).

This algebraic equation can guide the solution to find the possible values of x, that is, the width of the doghouse.

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To determine the possible dimensions of the base of the doghouse, use the equation x^2 + 4x - 21 = 0.

To find the possible dimensions of the base of the doghouse, we can use the given information that the area of the base is 21 square feet and the length is 4 feet more than its width.

We can represent the width as x. So, the length would be x + 4.

The equation for the area of the rectangle is length x width.

Substituting the values, we get x(x + 4) = 21.

Simplifying the equation, we can rewrite it as x^2 + 4x - 21 = 0.

This equation can be used to determine the possible dimensions of the base of the doghouse.

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Hello.

The Answer: A. 300 ft^2

Step-by-step explanation: Find the area of two sides (Length*Height)*2 sides.

Find the area of adjacent sides (Width*Height)*2 sides.

Find the area of ends (Length*Width)*2 ends.

Add the three areas together to find the surface area.

Formula: A= 2( W l + H L + H W)

Have a nice day.

Answer:

A   300 ft2

Hope this help's!

Answer:

M= D) 6

Step-by-step explanation:

just do 30 divided by 5=M

Answer:

D) 6 is your answer

Step-by-step explanation: You have to substitute the #'s in for m then multiply it by 5, and if it equals 30, it's your answer... But it has to be a true statement...

A) 3:

m x 5 = 30

3 x 5 = 30

15 = 30

FALSE

B) 4:

m x 5 = 30

4 x 5 = 30

20 = 30

FALSE

C) 5:

m x 5 = 30

5 x 5 = 30

25 = 30

FALSE

D) 6:

m x 5 = 30

6 x 5 = 30

30 = 30

TRUE

Answer:

2, -2 and 1/2

Step-by-step explanation:

As the the first coefficient is 2 and the last number is 4  1/2, 2, -2 seem likely zeros ( By the rational roots theorem).

f(2) =  2*8 - 4 -16 + 4 = 0 so 2 is a zero.

f(-2) = -16 - 4 +16 + 4 = 0  so -2 is a zero

f(1/2) = 2*1/8 - 1/4 - 4 + 4 = 0 so 1/2 is the other zero.

Since the highest degree is 3  the maximum number of zeroes is 3.

Answer:

Try math

way if you need help on apex

Step-by-step explanation:

Two possible rectangular gardens with different side lengths and an area of 48 square yards are:

Square garden: 6 yards by 6 yards

Long and narrow garden: 8 yards by 6 yards

Given:

Total area of the garden = 48 square yards

Objective:

Find possible combinations of side lengths for rectangular gardens with the same area.

Step 1: Square Garden

Let the side length of the square garden be x.

Area of the square garden = x^2

Set the area equation: x^2 = 48

Solve for x:

Take the square root of both sides: x = √48

Approximate the value: x ≈ 6.928 yards

Therefore, a square garden with sides of approximately 6.93 yards will have an area of 48 square yards.

Step 2: Long and Narrow Garden

We know the total area is 48 square yards.

Try different values for the width (w) and calculate the corresponding length (l) using the area formula: l * w = 48

For example, if w = 6 yards:

Calculate the length: l = 48 / w = 48 / 6 = 8 yards

Verify that the area matches: l * w = 8 * 6 = 48 square yards

Therefore, a long and narrow garden with a length of 8 yards and a width of 6 yards will also have an area of 48 square yards.

Question

Kelly saved $150. That is 50% of the money she earned this summer. How much did Kelly earn this summer?

Answer:

Step-by-step explanation:

50% = 1/2 = 0.5

150 is the 50% of the money she earned this summer.

Solution

150 * 2 = 300$

Answer:

$300

Step-by-step explanation:

If 150 is 50% you multiply 150 by 2 to get 300 and that would make it 100% of what she got that summer.

Answer:

4

Step-by-step explanation:

due to the fact that this shape is a rhombus the point of intersection between two diagonals is perpendicular to each other.

Then notice that the sections are right triangles and x is the hypotenuse

using Pythagorean theorem

A*2+B*2=C*2

3*2+5*2=x*2

9+25=x*2

34=x*2

x=√34

Answer:

B) 3 radians

Step-by-step explanation:

The arc length is the product of the radius and angle. You have ...

... 3 radians = 1 × angle

so

... 3 radians = angle

_____

Comment on units

The formula is

... s = rθ . . . . . where s is the arc length, r is the radius, and θ is the central angle in radians.

The units of both s and r are units of length, so the units of angle are ...

... (length units)/(length units) = <no units>

That is, "radians" are fully equivalent to "no units."

The trouble with this problem statement is that it expresses "arc length" in units of "radians." This only works if the units of the radius of the unit circle are "no units". Ordinarily, that would not be the case. The length of the radius of the unit circle is usually "one length unit." If the central angle is 3 radians, then the arc length is "3 length units," not "3 radians."

Answer:

(a) what is the sample space for this chance process?

If we toss a coin three times then there are total [tex]2^{3}=8[/tex] outcomes

The sample space associated with the given chance process is:

[tex]S= \left \{ HHH,HHT,HTH,HTT,THH,THT,TTH,TTT\right \}[/tex]

(b) what is the assignment of probabilities to outcomes in this sample space?

Since the given sample space has eight outcomes and we know that a fair coin is tosses three times. Therefore, the probability of all the events mentioned in the given sample space is same. Hence we have:

[tex]Probability = \frac{1}{8}[/tex]

When tossing a fair coin three times, the sample space includes all combinations of heads (H) and tails (T). With a fair coin, the probability of each possible outcome (HHH, HHT, HTH, THH, TTH, THT, HTT, TTT) is equal, at 0.125.

When we're discussing the tossing of a fair coin three times, we're delving into the area of probability. (a) The sample space in this scenario is all the possible outcomes we could have. Those outcomes are: TTT, TTH, THT, THH, HTT, HTH, HHT, and HHH (Remember: H represents a head and T represents a tail).

(b) When we talk about the assignment of probabilities, we mean the likelihood of each potential outcome occurring. With a fair coin, it's equally likely to land on heads or tails - a 0.5 chance for each. Therefore, each of the eight possible outcomes has a 1/8 or 0.125 probability of occurring, granted that all outcomes are equally likely. So, for for instance, the probability of getting one head and two tails (HHT, HTH, THH) is 3/8 or 0.375, and similarly for all other cases.

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Answer:

$3.50

Step-by-step explanation:

Let x be the cost of per gallon gas.

We have been given that it costs Raquel 5$ in tolls to drive to work and back each day, plus she uses 3 gallons of gas. It costs her a total of 15.50$ to drive to work and back each day.

We can represent this information as:

[tex]3x+5=15.50[/tex]

[tex]3x+5-5=15.50-5[/tex]  

[tex]3x=10.50[/tex]    

[tex]x=\frac{10.50}{3}[/tex]

[tex]x=3.50[/tex]  

Therefore, Raquel is paying $3.50 for per gallon gas.

Answer:

18 years after 1996 which is 2014

Step-by-step explanation:

Town M had a population of 30,500 people. It grows by 2%. That means the next year will be 30,500+0.02(30,500)=31,110. The next year will be 31,110+0.02(31110)=31732.2 and so forth.

Town N had 32,500 and grows by 600 each year. That means the next year will be 32,500+600=33,100. The next year will be 33,100+600=33,700 and so forth.

Year      Town M       Town N

1            31,110            33,100

2           31,732.2       33,700

3           32366.8       34, 300

4           33014.2        34,900

5           33674.5       35,500

6           34348          36,100

7           35035          36,700

We can see the populations are getting closer but not very fast. Let's try higher numbers.

Year 20 gives 45,321 and 44,500.  We are close. Let's try year 18. We get 43,561.5 and 43,300.

To find the original quantity when given the percent it was reduced and the amount left, divide the amount left by the percentage that is left:

The bottle was reduced by 85%, which means there is 15% left left in the bottle ( 100% - 85% = 15%)

Now divide the amount left by the percentage left:

20 / 0.15 = 133.33

The original amount was 133.33 milliliters ( Round answer as needed)

Answer:

a) 4x + 20

b) y

c) 7x + 22

Step-by-step explanation:

Assuming these were originally 3 questions? Simply pack together the numbers and the numbers with letters.

Answer: 144x2y+11x+16

that is the correct answer.   144x2y+11x+16

Answer:

the domain is X so

Step-by-step explanation:

(-3,0,4,1) is the answer

Answer:

42 days.

Step-by-step explanation:

We have been given that Sherman goes golfing every 6th day and Brad goes golfing every 7th day.

To find the number of days after that both will go golfing on the same day we will find LCM of 6 and 7.

Multiples of 6 are: 6, 12, 18, 24, 30, 36, 42, 48,..

Multiples of 7 are: 7, 14, 21, 28, 35, 42, 49, 56,...

We can see that least common multiple of 6 and 7 is 42, therefore, both will go golfing on the same day again on 42nd day.

Answer:

11700

Step-by-step explanation:

The triangles are similar (presumably) because their ratios are the same for all three corresponding sides.

Equation

Givens

Solution

Answer:

11700

Step-by-step explanation:

Answer:

Approximately 11.99 years

Step-by-step explanation:

This is just a type of problem like finding how long it will take for you to get somewhere.  Like in finding how fast you need to go to go to a place that is 60 miles in one hour.  All you have to do is divide the distance of the star by the speed of light, and you get the amount of time it will take for the star's light to reach the Earth.

The time taken by the light to travel from a star to Earth is required.

It would take 12 years for the light to reach Earth.

Distance of star from Earth = [tex]1.135\times 10^{14}\ \text{km}[/tex]

Speed of light from star = [tex]9.4607\times 10^{12}\ \text{km/year}[/tex]

Time is given by

[tex]t=\dfrac{\text{Distance}}{\text{Speed}}\\\Rightarrow t=\dfrac{1.135\times 10^{14}}{9.4607\times 10^{12}}\\\Rightarrow t=11.996\approx 12\ \text{years}[/tex]

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Choice A is the answer which is the point (1,-1)

=========================================

How I got this answer:

Plug each point into the inequality. If you get a true statement after simplifying, then that point is in the solution set and therefore a solution. Otherwise, it's not a solution.

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

checking choice A

plug in (x,y) = (1,-1)

[tex]y - 2x \le -3[/tex]

[tex]-1 - 2(1) \le -3[/tex]

[tex]-3 \le -3[/tex]

This is true because -3 is equal to itself. So this is the answer.

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

checking choice B

plug in (x,y) = (2,4)

[tex]y - 2x \le -3[/tex]

[tex]4 - 2(2) \le -3[/tex]

[tex]0 \le -3[/tex]

This is false because 0 is not to the left of -3, nor is 0 equal to -3. We can cross this off the list.

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

checking choice C

plug in (x,y) = (-2,3)

[tex]y - 2x \le -3[/tex]

[tex]3 - 2(-2) \le -3[/tex]

[tex]7 \le -3[/tex]

This is false because 7 is not to the left of -3, nor is 7 equal to -3. We can cross this off the list.

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

checking choice D

plug in (x,y) = (3,4)

[tex]y - 2x \le -3[/tex]

[tex]4 - 2(3) \le -3[/tex]

[tex]-2 \le -3[/tex]

This is false because -2 is not to the left of -3, nor is -2 equal to -3. We can cross this off the list.

Answer:

(8, 85) Would make this relationship not a function because every time you count up 1 it goes up 10 and 8 would match to 80 not 85 making 8, 85 the ordered pair would not be on the graph.

Given Sue's speed of 10 miles per hour, we're looking for an ordered pair that does not fit the relationship y = 10x. While (2,20), (5,50), and (6,60) all fit this relationship, the pair (8,85) does not, hence it won't be on the graph.

Sue's speed on her bike is 10 miles per hour. This relationship can be graphed as a straight line in a coordinate plane because the speed remains constant - the distance covered increases uniformly over time. So, for each hour (x), she covers a distance of 10x miles (y). Therefore, we can identify the ordered pair that does not belong on the graph by determining which one does not fit the relationship y = 10x.

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Answer:

$16

Step-by-step explanation:

x*0.7=11.20

11.20/0.7=16