Find m∠1 and m∠2. Tell which theorem can be used.

Step-by-step explanation:

1.First work out the equation of the line.

1.1 work out gradient

[tex]y = ( \frac{ - 1 - 8}{3 - ( - 2)} )x + c[/tex]

[tex]y = - \frac{9}{5} x + c[/tex]

1.2 substitute in x and y value of one of the two given point. ill use (3;-1).

[tex] - 1 = - \frac{9}{5} (3) + c[/tex]

[tex]c = \frac{22}{5} [/tex]

therefore equation is

[tex]y = - \frac{9}{5} x + \frac{22}{5} [/tex]

2. Now sub in x value of the point you want to test and see if y value correlates.

[tex]y = - \frac{9}{5} (1) + \frac{22}{5} [/tex]

[tex]y = \frac{13}{5} [/tex]

3. We can conclude that point (3;1) does not fall on the graph

Answer:

y=-3x+7

Step-by-step explanation:

:]

Answer:

Y=-3x+7

Step-by-step explanation:

Use rise/run

You will need to use at least 267 minutes in a month in order for the second plan to be preferable.

Given the following:

First plan=23 cent per minute

Second plan=$34.95 plus 10 cents per minute

Calculate the number of mins to use in a month to make second plan preferable:

We first change $34.95 to cents:

1 usd=100 cents

$34.95=($34.95*100 cents)/$1

           =3495 cents

Second plan will now be 3495 plus 10 cents per minute

Now, calculate the number of mins to use:

Let x represents the number of mins, now 23 cent per minute will be:

23(x)>3495 plus 10 cents per minute

23x>3495+10x

23x-10x>3495

13x=3495

x=3495/13

x>268.85 mins

Therefore, one will need to use at least 267 minutes in a month in order for the second plan to be preferable.

The question is incomplete, complete question is given below:

You are choosing between two different cell phone plans. The first plan charges a rate of 23 cents per minute. The second plan charges a monthly fee of $34.95 plus 10 cents per minute. How many minutes would you have to use in a month in order for the second plan to be preferable?

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Answer:

-4 + -10

Step-by-step explanation:

Even with an addition sign, it still adds up to the same amount.

Hope this helps!

(Btw, if u get this right, pls do brainliest, I really need it! Thanks!)

Three pepper plants are present per population density.

You must divide the population by the area's size to determine the population density. Population Density is therefore equal to the number of people divided by the land area.

Since we are working with plants here, the formula is as follows:

Population Density = Plants Per Unit Area

Given,

There are 120 plants.

Area of Land = 5 x 8

= 40 m^2

Just enter the values into the formula now.

Number of People = 120/40

= 3

Consequently, the number of pepper plants per square foot is 3.

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Answer: 2.7 kg

1 kilogram (kg) = 2.204623 pounds (lb)

[tex]\frac{6 lb}{1}[/tex] × [tex]\frac{1 kg }{2.204623 lb}[/tex] = 2.721553753 kg

You place 1 kg over 2.204623 lb since they are equal. In the above equation, the pounds (lb) cancel out since one is in the numerator (the number on top of the fraction) and one is in the denominator (the number on the bottom of the fraction). You multiply 6 by the 1 in the numerator and multiply the 1 in the denominator by 2.204623. This turns the equation into:

[tex]\frac{6 kg}{2.204623}[/tex] =2.721553753 kg

You divide 6 by 2.204623 to get 2.721553753

To round to the tenths place, you include only the first number to the right of the decimal, which is 7. Since the number to the right of the 7 is less than five, it stays 7. If it were five or bigger, 7 would turn into 8.

The answer: 2.7 kg

[tex] \frac{4}{5} (w + z) \\ = \frac{4}{5} (12 + 43) \\ = \frac{4}{5} (55) \\ = 4(11) \\ = 44[/tex]

ATTACHED IS THE SOLUTION

Answer:

x= 19

Step-by-step explanation:

I believe you would put both expressions equal to each other. So,

3x-11= x+27

3x-x=27+11

2x=38

x= 38/2

x=19

Given:

The lengths of time spent in the store are normally distributed and are represented by the variable X

The survey indicates that for each trip to a supermarket, a shopper spends an average of 43 minutes with a standard deviation of 12 minutes in the store.

so, the mean = μ = 43

And the standard deviation = σ = 12 minutes

We will find the probability that supermarkets between 31 and 58 minutes

We will use the following formula to convert to the z-scores

So, we will find Z when x = 31 and When x = 58

So, we will find the probability of P (-1 < z < 1.25)

From the tables of the z-score:

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

Work Shown:

[tex]\frac{n^2+n-6}{n-2}\\\\\frac{(n+3)(n-2)}{n-2}\\\\n+3[/tex]

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

Explanation:

Often when simplifying, it's a good idea to factor and see what cancels (if anything does cancel).

To factor the numerator, think of two numbers that

Through trial and error, you should find the two numbers to be 3 and -2

So that's how [tex]n^2+n-6[/tex] factors to [tex](n+3)(n-2)[/tex].

After this point, the (n-2) terms cancel leaving n+3 behind

We can say [tex]\frac{n^2+n-6}{n-2}=n+3 \ \ \text{when } n \ne 2[/tex]

The [tex]n \ne 2[/tex] is to avoid a division by zero error.

Answer: Option (D) property of distribution

Step-by-step explanation:

got it right on test

Answer:

b

Step-by-step explanation:

because you need ti 2x +

The perfect match leading coefficient for the given polynomial will be as below:-

A. P(x) = (x + 2)(2x - 3)(4x + 7) => 2. 8

B. P(x) = (x-2)(2x - 3)(4x + 7)  => 3. 4

C. P(x) = 5(x-2)(2x - 3)(4x + 7) => 1. 40

D. P(x) = -(x-2)(2x - 3)(4x + 7) => 5. - 8

E. P(x) = (x + 2)(2x - 3)(4x + 7) => 4.  2

Leading Coefficient:

The leading coefficient of the polynomial is means the coefficient of the variable having the highest power in the polynomial.

Given,

Here we have the following list of polynomials,

A. P(x) = (x + 2)(2x - 3)(4x + 7)

B. P(x) = (x-2)(2x - 3)(4x + 7)

C. P(x) = 5(x-2)(2x - 3)(4x + 7)

D. P(x) = -(x-2)(2x - 3)(4x + 7)

E. P(x) = (x + 2)(2x - 3)(4x + 7)

Now, we need to find the matching leading coefficients for this polynomials.

In the given polynomials, we have to calculate the highest power variable in each polynomial with the coefficient. That coefficient is known as the leading coefficients.

First, we have to take the expression A, then we get,

A. P(x) = (x + 2) (2x - 3) (4x +7)

Here we have to multiply the x term alone to get the leading coefficient,

P(x) = (x)(2x) (4x)

Thus will results the leading coefficient as P(x) = 8x³

Similarly, for expression B,

P(x) = 1/2(x - 2) (2x - 3) (4x + 7)

P(x) = 1/2(x) (2x)(4x)

P(x) = 1/2 8x³

P(x) = 4x³

For expression C,

P(x)= 5(x - 2) (2x - 3) (4x + 7):

P(x) = 5(x)(2x)(4x)

P(x)= 40x³

For expression D,

P(x) = -(x - 2) (2x - 3) (4x + 7):

P(x) = -(x)(2x)(4x)

P(x) = -8x³

Finally, for the expression E,

P(x) = 1/4(X + 2) (2x - 3) (4x + 7):

P(x) = 1/4(x)(2x(4x)

P(x) = 2x³

Therefore, the corresponding leading coefficients are 8, 4, 40, -8, and 2 respectively.

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By identifying the y and x-intercepts of the linear equation, we conclude that the correct graph is the third one

We know that the relation between altitude and time is given by the linear equation:

1,500x + y = 35,000

If we isolate y, we get:

y  = -1,500x + 35,000

Notice that when x = 0, we have:

y = -1,500*0 + 35,000

y = 35,000

So the y-intercept is 35,000

And the plane reaches the ground when:

0 = -1,500*x + 35,000

1,500*x = 35,000

x = 35,000/1,500 = 23.3

So it intercepts the x-axis at x  = 23.3

With that in mind, we can see that the correct graph is the third one.

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When the result of one function is utilized as the input for another, this is known as a composite function. If f(x) = (6x³ - 7)³ and g(x) = 6x³ - 7 then the value of h(x) = x³.

A function is composed in mathematics when two functions, f and g, are used to create a new function, h, such that h(x) = g(f(x)). The function of g is being applied to the function of x, in this case. Therefore, a function exists essentially applied to the output of another function.

Function composition is an operation used in mathematics that takes two functions, f and g, and creates a function, h = g ° f, such that h(x) = g. The function g is applied in this operation on the outcome of applying the function f to x.

Let the two functions be f(x) = (6x³ - 7)³ and g(x) = 6x³ - 7.

f(x) = (h° g)(x)

⇒ f(x) = (h(g(x))

If f(x) = (h° g)(x) (6x³ - 7)³ = (h(g(x)) then h(x) = x³.

The complete question is:

Let f(x) = (6x³ - 7)³ and g(x) = 6x³ - 7. Given that f(x) = (h° g)(x), find h(x).

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Answer:

h(x) = x³

Step-by-step explanation:

Given:

  [tex]f(x)=(6x^3-7)^3[/tex]

  [tex]g(x)=6x^3-7[/tex]

  [tex]f(x)=(h \circ g)(x)[/tex]

The relationship between f(x) and g(x) is that function f is function g cubed:

[tex]f(x)=(g(x))^3[/tex]

(h o g)(x) means we replace the x-variable of function h(x) with function g(x). So:

[tex](h \circ g)(x)=h(g(x))[/tex]

If (h o g)(x) equals f(x), then h(x) must be h(x) = x³.

Check by replacing the x-variable of function h(x) with the function g(x) and comparing it to f(x):

[tex]\begin{aligned}(h \circ g)(x)&=h(g(x))\\&=(g(x))^3\\&=(6x^3-7)^3\\&=f(x)\end{aligned}[/tex]

Hence proving that h(x) = x³.

Answer: C

Step-by-step explanation:

This is the definition of a negative exponent.

To maximize the number of circular tables, he must thus employ 9 circular tables and 3 square tables.

Combinatorics is a branch of math focused on the arrangements of objects.

Estimates of the number of operations needed by a computer algorithm can be created using combinatorial approaches.

It is given that the number of persons in each circular table and the square table will be 10 and 4 respectively.

We now need to determine the largest multiple of 10 in order to maximize the number of circular tables.

Now, if we take 100, there will only be 2 seats left. However, 4 people are needed for square tables. Therefore, 100 is incorrect.

The circular tables utilized would be if we choose 90 as a multiple of 10 is,

= 90 / 9

= 10

Number of guests left,

=102 - 90

= 12

12 is a multiple of 4 as a result 3 square tables may therefore fit 12 people,

=4 × 3

=12

Thus, to maximize the number of circular tables, he must thus employ 9 circular tables and 3 square tables.

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Answer: x=3

Step-by-step explanation:

[tex]\displaystyle\\4x-\frac{2}{3}=\frac{34}{3}\\[/tex]

Multiply both parts of the equation by 3:

[tex]4x(3)-2=34\\12x-2=34\\12x-2+2=34+2\\12x=36[/tex]

Divide both parts of the equation by 12:

[tex]x=3[/tex]

The unknown number from the equation is 3.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, the difference of the product of 4 times a number and 2/3 is 34/3.

Let the unknown number be x.

4x-2/3 =34/3

(12x-2)/3=34/3

12x-2=34

12x=36

x=3

Therefore, the unknown number is 3.

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.The inequality is given by:

Subtract 2.75 from both sides of the inequality:

Therefore, the maximum time of additional hour is 4

Answer:

4 hours

Step-by-step explanation:

→ Write inequality

2.75 + 1.25x < 8

→ Minus 2.75 from both sides

1.25x < 5.25

→ Divide both sides by 1.25

x < 4

The percentage is that indicating the hundredth total number of students surveyed such that 20% of them are 25 will be 125.

What is the percentage?

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 %.

Let's suppose the total number of students that are surveyed was x.

It is known that x% of y is given as, (x/100)y.

Therefore,20% of x is (20/100)x = 0.2x

The 20% of the total students is 25.

So, 0.2x = 25

x = 25/0.2 = 125

Hence "The percentage is that indicating the hundredth total number of students surveyed such that 20% of them are 25 will be 125".

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Answer: [tex]y=\frac{1}{9}x[/tex]

Step-by-step explanation:

Perpendicular lines have negative reciprocal slopes, so the slope of the line we want to find is 1/9.

Since the y-intercept is 0, the equation is [tex]y=\frac{1}{9}x[/tex].

You can graph the lines on a website like Desmos.

Step-by-step explanation:

it is a rectangle.

the area is a rectangle is

length × width

in our case

length × width = 55 ft²

length = 3×width + 4

we use that in the first equation :

(3×width + 4)×width = 55

3×width² + 4×width - 55 = 0

the general solution to a quadratic equation like

ax² + bx + c = 0

is

x = (-b ± sqrt(b² - 4ac))/(2a)

so,

width = (-4 ± sqrt(4² - 4×3×-55))/(2×3) =

= (-4 ± sqrt(16 + 660))/6 = (-4 ± sqrt(676))/6 =

= (-4 ± 26))/6

width1 = (-4 + 26)/6 = 22/6 = 11/3 = 3 2/3 ft

width2 = (-4 - 26)/6 = -30/6 = -5

negative numbers for the size of a physical object don't make sense, so

11/3 = 3 2/3 ft is our solution.

length = 3×width + 4 = 3×11/3 + 4 = 11 + 4 = 15 ft

so,

the length = 15 ft

the width = 3 2/3 ft (or 11/3 ft)

The equation that Sasha can use to determine the minimum and maximum distance her city is from her vacation destination is 450 + 30 and 450 - 30.

It should be noted that an equation is simply used to illustrate the relationship between the variables that are illustrated or given in the data.

It should be noted that for the minimum distance, she has to subtract 30 miles from the vacation destination.

The minimum value will be:

= 450 - 30

= 420. miles.

For the maximum distance, she has to add 30 miles from the vacation destination.

The maximum distance will be:

= 450 + 30

= 480 miles.

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Answer:

Step-by-step explanation:

52 + b = 52b or 52(b = 52b         ( means x

The equation will be y = -15x + 40

Equations help us to understand a particular problem better, they give us possible insights into the situation. Equation Formation is an important aspect of Mathematics. We can form equations on the basis of the information given and then analyze it.

Given:

The biker, Dudley wants to travel 40 miles.

It is given that he travels 30 miles every 2 hours.

Obtaining Equation,

Distance traveled in 2 hours = 30 miles

Then, distance traveled in x hours = [tex]\frac{30}{2}*x = 15x[/tex]

So, the remaining distance to cover = 40 - 15x

or  y = 15x - 40

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Answer:

y=30 x=22.5 =25 = 55

Step-by-step explanation:

Answer:

Step-by-step explanation:

y=30x

Answer:

B, 28.

Step-by-step explanation:

728 divided by 208, which is 3.5. then you multiply 3.5 & 8 to get 28.

The answer above me has the answer.

Step-by-step explanation: He is 101% confident its it and I back it up because got it right (he should've been 102% confident tho)