answer all ........................................................................................................................................................................................................................................................................................................................................1

Answer:

[tex]\textsf{Point-slope form}: \quad y-1=\dfrac{1}{5}(x-3)[/tex]

Step-by-step explanation:

Define the given points:

Substitute the defined points into the slope formula to find the slope of the line:

[tex]\implies \textsf{Slope $(m)$}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-1-1}{-7-3}-\dfrac{-2}{-10}=\dfrac{1}{5}[/tex]

Substitute the found slope and one of the points into the point-slope formula:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-1=\dfrac{1}{5}(x-3)[/tex]

Simplify to slope-intercept form, if necessary:

[tex]\implies y-1=\dfrac{1}{5}x-\dfrac{3}{5}[/tex]

[tex]\implies y=\dfrac{1}{5}x+\dfrac{2}{5}[/tex]

Linear pair angles are the ones that form a straight line, in other words they will form a 180º angle. Therefore if the angle 2 measures 44 degrees we can find the angle 1 by doing as follows:

The angle one is equal to 128 degrees.

2x+32+x = 17

Combine 2x and X to get 3x.

3x+32 = 17

Subtract 32 on both sides.

3x = 17−32

Remains 32 of 17 to obtain −15.

3x = −15

Divide both sides by 3.

x = -15/3

Divide −15 by 3 to get −5.

x = −5

The value of x after solving the given equation 2x + 32 + x = 17, is x = -5, which is the last option.

Given an equation:

2x + 32 + x = 17

It is required to find the value of x after solving or simplifying the equation.

In order to get the value of x, the equation has to be solved in such a way that the terms with the variable have to be placed on one side and the constant terms on the other side.

Consider:

2x + 32 + x = 17

Add x and 2x since they are like terms in variables.

3x + 32 = 17

Subtract 32 from both sides of the equation.

3x = 17 - 32

3x = -15

Divide both sides of the equation by 3.

x = -5

Hence, the value of x is -5.

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The percent of the people surveyed were completely satisfied with the car is 55%.

Number of people completely satisfied = 1155

Number of people somewhat satisfied = 755

Number of people not satisfied = 190

Total number of people = 1155 + 755 + 190 = 2100

Therefore, the percent of the people surveyed were completely satisfied with the car will be:

= Number of people completely satisfied / Total number of people × 100

= 1155 / 2100 × 100

= 55%

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Answer:

Step-by-step explanation:

4 and 2/5 inches by 8 and 3/5 inches.

60 and 6 feet by 120 and 9 feet.

66 by 129 feet

8514 feet squared

Answer:

Step-by-step explanation:

Step 1: Simplify both sides of the inequality.

12x+36>4x−8

Step 2: Subtract 4x from both sides.

12x+36−4x>4x−8−4x

8x+36>−8

Step 3: Subtract 36 from both sides.

8x+36−36>−8−36

8x>−44

Step 4: Divide both sides by 8.

8x/8 > -44/8

Therefore your answer will now equal  [tex]x > \frac{-11}{2}[/tex]

[tex]{ \boxed{ \pink{ \sf{x > - \frac{11}{2}}}}}[/tex]

Step-by-step explanation:

The given inequality is, [tex]{ \green{ \sf{12(x + 3) > 4x - 8}}}[/tex]

[tex]{ \star}[/tex]Step 1: Simplify both the sides of inequality.

[tex]{ \green{ \sf{12x + 36 > 4x - 8}}}[/tex]

[tex]{ \star}[/tex]Step 2: Now Subtract 4x from both sides.

[tex]{ \purple{ \sf{12x+36−4x> { \cancel{4x}−8{ \cancel{−4x}}}}}}[/tex]

[tex]{ \purple{ \sf{8x+36>−8}}}[/tex]

[tex]{ \star}[/tex]Step 3: Subtract 36 from both sides.

[tex]{ \blue{ \sf{8x+{ \cancel{36}{ \cancel{−36}}}>−8−36}}}[/tex]

[tex]{ \blue{ \sf{8x>−44}}}[/tex]

[tex]{ \star}[/tex]Step 4: Divide both sides by 8.

[tex]{ \orange{ \sf{ \frac{ \cancel8}{ \cancel8} x > - \frac{ \cancel{44^{ \blue{ \tt{11}}}} }{ \cancel8_{ \blue{ \tt{2}}} }}}} [/tex]

[tex]{ \boxed{ \red{ \sf{x > - \frac{11}{2}}}}} [/tex]

The probability of a less-than-ideal day (no free pizza and no sun) is 0.25

Let us define the events from the example.

Let event A: Sunny day for any given day

event B: Getting free pizza for any given day.

Now, we will translate the word problem into our symbols.

The probability of a sunny day is 80% i.e P(A)=0.8

The probability of free getting pizza is 30% i.e. P(B) = 0.3

The probability of free pizza and a sunny day is 35% .i.e P(A∩B) = 0.35

a)Complement means not happening an event i.e. event A’ : No sunny day for any given day event B’: Not getting day free pizza for any given.

Here dash ( ‘ ) complement.

The probability of a less-than-ideal day

(no free pizza and no sun) is

P(A'∩B') = P(A∪B)'... (De Morgan's Jaw)

De Morgan's law: (A∩B)'= A'∪B'

                             (A∪B)’ = A'∩B'

P(A'∩B') = 1-P(A∪B)    (P(A) = 1-P(A)).

= 1-[P(A) + P(B)-P(A∩B)]

= 1-[0.8+0.3-0.35]

P(A'∩B') = 0·25

The probability of a less-than-ideal day (no free pizza and no sun) is 0.25.

b)To check whether free pizza and sun are independent events or not, let us see when two events are said to be independent.

Two events (A & b) are said to be independent if P(A∩B) = P(A)· P(B)

Let us check whether this property satisfies our case or not.

LHS = P(A∩B)=0.35

RHS= P(A) P(B)

= 0.8 x 0.3

RHS = 0.24.

LHS ≠ RHS

P(ANB) ≠ P(A). P(B) in our case.

Two events A and B are not independent in our case

Sun and free pizza are not independent events.

c)Probability of no free pizza on a sunny day is P(A∩B').

P(A∩B') = P(A) - P(A∩B) = 0.8 0.35

P(A∩B') = 0·45

The probability of no free pizza on a sunny day is 0.45

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1) The general form of a cosine function is:

2) Let's pick from the graph, the amplitude, the period, the horizontal and the vertical shift.

We can tell that half of the distance between the maximum point and the minimum point is 2

Let's find the period

3) Let's resort to the picture. The only cosine function that has an amplitude of 2 and a period of 3 is C and y=2cos(3x) has a vertical shift =0

There are 264 red marbles in a bag.

What is Marbles?

A marble is a tiny, sphere-shaped object that is frequently fashioned of agate, glass, clay, steel, or plastic. They come in a variety of sizes, but the most have a diameter of about 13 mm (12 in). These toys can be made into works of art or utilized in a variety of marble-based activities. They can also be used in races or runs. They are frequently collected for their pleasing colors and nostalgic appeal.

Let x = Number of red marbles

y = Number of black marbles.

A bag contains 275 marbles.

So, x + y = 275             ..(1)

There are 24 red marbles for every black marble.

x = 24y       ..(2)

Plug value of x in equation (1).

24y + y = 275

25y = 275

y = 11

Put y = 11 in equation (2),

x = 24(11)

x = 264

Hence, there are 264 red marbles in the bag.

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Answer:

The equation in slope-intercept form is:

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

So the second option is the correct one.

Step-by-step explanation:

Step 1: Identify the gradient

The perpendicular line's equation is given as:

[tex]y=-3x+4[/tex]

This equation is in the form of:

[tex]y=mx+b[/tex]

Upon comparing the [tex]x[/tex] components of both equations, we get[tex]-3x=mx\\\text{Remove the}~ x~ \text{from both sides:}\\-3=m\\m=-3[/tex]

So, the gradient of this 'reference' equation is -3.

The equation we need to find is perpendicular to this 'reference' equation.

So, its gradient should be the negative reciprocal of the gradient of the 'reference' equation.

The negative reciprocal of -3 is:

[tex]-\frac{1}{(-3)}\\=\frac{1}{3}[/tex]

So, the gradient of our equation is [tex]\frac{1}{3}[/tex].

Step 2: Create the equation:

The equation crosses the x-axis at -9, which means its y-coordinate is 0 (at x-axis, y=0) ,so its coordinate is [tex](-9,0)[/tex].

The formula for an equation is:

[tex]y-y_{1}=m(x-x_{1})[/tex]

The coordinate [tex](x_{1},y_{1})[/tex] is [tex](-9,0)[/tex], and the gradient ([tex]m[/tex]) is [tex]\frac{1}{3}[/tex].

Substitute the values into the equation:

[tex]y-y_{1}=m(x-x_{1})\\y-0=\frac{1}{3}(x-(-9))\\\\\text{Simplify}\\y=\frac{1}{3}(x+9)[/tex]

[tex]\text{Simplify further}\\y=\frac{1}{3}x+3[/tex]

Since, the slope-intercept form is:

[tex]y=mx+b[/tex]

We already have our equation in the slope-intercept form.

Working 32 hours a week will fetch you $818

From the question, the given parameters are:

Number of hours = 160

Earnings in a month = $4090

Start by calculating the unit rate

This is calculated using the following unit rate formula

So, we have

Unit rate = Earnings in a month/Number of hours

Substitute the known values in the above equation

So, we have

Unit rate =  4090/160

Evaluate the quotient

Unit rate =  25.5625

For 32 hours, the total earnings is

Total = Unit rate x Number of houts

So, we have

Total = 25.5625 x 32

Evaluate

Total = 818

Hence, you will earn $818 weekly

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Two yellow marbles are added to the bag to make the probability of choosing a yellow marble 1/3 .

There is a bag containing five green marbles, three red marbles, and four blue marbles and four yellow marbles.

The probability that a given event will happen is expressed as a number between 0 and 1 where 0 means there is no chance of the event occurring and 1 means that the outcome is certain.

There are a total of 16 marbles in the bag (5 + 3+ 4+4 = 16). This means that the probability of drawing a marble of a particular color is the number of marbles of that color divided by the total number of marbles in the bag.

Let ‘x’ number of additional yellow marbles be added to the bag.

Then, the required probability will be

(4 + x )/ (16+x ) = 1/3

=> 3(4+x) =16 +x

=> 12+3x = 16+x

=> 2x =4

=> x= 2

Hence, the required number of marbles is 2.

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20 shares purchased at $30, means that the initial inversion is 20 times 30 = $600

they are sold for $710, so the difference is 710 - 600 = 110

the commision is 6, so the final gain is 110 -6 =104

profit divided by the inversion:

104/600 = 0.1733

the answer is 17.33 %

Explanation

Step 1

the sum of the internal angles in a triangle equals 180, then

for triangle CDE

Step 2

as we can see, in poitn c, we have a 180 degrees angle(ACD)

so

I hope this helps you

Answer:

994

Step-by-step explanation:

work inside the parenthesis first. 8+2 = 10 then raise 10 to the power of 3 which is 1000. subtract 6 from 1000 & you get 994

Answer:

994

Step-by-step explanation:

PEDMAS

Do the math inside the parentheses first

8+2 = 10         Now do the exponent    10^3 = 1000   Now subtract 6  = 994

Answer:

Step-by-step explanation:

Find the amount of increase:

Find the percent value of the increase over the initial price:

Answer:

They are equal

Step-by-step explanation:

5+3=8 and 3+5=8

If you are seeking the answer in terms of evaluation, then the answer would be 8 = 8. Both sides of the equation are equal, so in addition to this, the given equation is true.

5 + 3 = 8

3 + 5 = 8

So, if you were to attempt breaking down the equation, you could easily write it as 8 = 8.

Hope this helps!

The sum of  -1  and 3/4 and 2 and 1/2 is the same as the difference between 2 and 1/2 and 1 and 3/4.

First we will convert the mixed fractions into improper fractions.

-1 and 3/4 = -7/4

2 and 1/2 = 5/2

Sum of -1 and 3/4 and 2 and 1/2 = -7/4 + 5/2 = -7/4 + 10/4 = 3/4

Difference between  2 and 1/2 and 1 and 3/4 = 5/2 - 7/4 = 10/4 - 7/4 = 3/4

As both the values equal to 3/4 , we can say that the sum of  -1  and 3/4 and 2 and 1/2 is the same as the difference between 2 and 1/2 and 1 and 3/4.

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Real numbers are numbers that are continous on the number line. They include positive and negative numbers. They can be integers, natural numbers, rational or irrational numbers.

In this exercise the number 1.030030003 is a real number because it can be found on the real number line

It is also a rational number because it is a repeating decimal

Answer:

B C and D

Step-by-step explanation:

Answer:

2π=6.2831853071795864769252867

An integer number is a number that can be written without using a rational component. In other words, if a number can be written without using a fraction, then that number is considered an integer.

For example, let's take the first number:

This number is written as a fraction. But, this is also equivalent to:

Since it can also be written without making use of a fraction then this number is an integer.

Also, there are numbers that are written in decimal form. For example:

These types of numbers are not integers.

Answer:

the answer is 2 and one fourth

Step-by-step explanation:

because the 3s cancel out

Answer:

i hope it was good for you

Answer: [tex]n=12i[/tex]

Step-by-step explanation:

Combine like terms.

Answer:

a. 11

Step-by-step explanation:

What is the mode of the following numbers?

12, 11, 14, 10, 8, 13, 11, 9

a. 11

b. 10

C. 14

d. 8

the mode is 11 because it is the most frequent number in the list.

Answer:the answer is a

Step-by-step explanation:

Answer:

3-[1]

3-1

2

Step-by-step explanation:

=//7777/))_+++++++4

The coordinates of the rotated triangle will be (2, - 2) , (3, -8) , (7, 0)

Function translation takes a function (and its graph) and, by adding and subtraction, moves the graph around the plane without changing its shape.

Given is a triangle coordinate on x - y plane.

The rule (x, y) → (- x, - y) represents the rotation of a figure by 180 °.

Now, initially the coordinates of the triangle are -

(-2, 2) , (-3, 8) , (-7, 0)

After transforming the graph by the rotation of 180°, the new coordinates will be -

(2, - 2) , (3, -8) , (7, 0)

Plot the coordinates on the graph and you will get the rotated image.

Therefore, the coordinates of the rotated triangle will be (2, - 2) , (3, -8) , (7, 0).

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