someone please help asap.. what even is this. ill give brainliest
Given: line AC is perpendicular to line BC
Prove: the slopes of lines AC and BC is -1
Complete the Proof.
first blank: angle addition; definition of perpendicular lines; definition of congruent angles; definition of a straight angle.
second blank: addition property of equality; subtraction property of equality; transitive property of equality; substitution property of equality.
third blank: transitive property of equality; substitution property of equality; definition of slope; corresponding sides of similar triangles are proportional.
fourth blank: multiplication property of equality; substitution property of equality; addition property of equality; transitive property of equality.

Answer:

48

Step-by-step explanation:

So I attached an image explaining how I solved the problem, but essentially you use the Pythagorean Theorem to define the two other sides, which I named "a" and "b", and then defined them in terms of x, using the Pythagorean Theorem. I finally defined the hypotenuse of the entire triangle which is 36+64 in terms of these two equations. Once that entire thing was set up it was a matter of solving for x, to get 48

One landscaper's hourly rate is $15 lower than the other landscaper's. Casey is deciding which of two landscapers to hire. Each landscaper charges an hourly rate plus a fee for each job.

What is system of linear equations?

A set of two linear equations with two variables is a system of linear equations. Casey is deciding between hiring one of two landscapers. Each landscaper bills a fee for each job in addition to an hourly rate. A set of linear equations was appropriately written and solved by Casey using substitution. He solved for the other variable and substituted an expression for one in his work. The intersection of the lines that represent the linear equations is where a system of linear equations finds its solution. Each landscaper bills a fee for each job in addition to an hourly cost. Casey produced a system of linear equations that was correctly written and solved. The hourly rates for both landscapers are the same, however their rates for individual jobs vary.

Casey is deciding between hiring one of two landscapers. Each landscaper bills a fee for each job in addition to an hourly cost. By using substitution, Casey created and properly figured out a set of linear equations. He solved for the other variable and replaced an expression for one in his work, producing the equation 5 = 20.

equation 5=20

20-5 = 15

Therefore, One landscaper's hourly rate is $15 lower than the other landscaper's.

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The simplified form of R(x) is [tex]R(x) =\frac{x^{2} -13x+42}{x^{2} -10x+25}[/tex]

From the question, we are to simplify the expression

From the given information,

[tex]f(x) =\frac{x^{2}-11x+28 }{x^{2}-11x+30}[/tex]

and

[tex]g(x) =\frac{x^{2}-9x+20 }{x^{2}-12x+36}[/tex]

Also,

[tex]R(x) = f(x) \div g(x)[/tex]

∴ [tex]R(x) =\frac{x^{2}-11x+28 }{x^{2}-11x+30} \div \frac{x^{2}-9x+20 }{x^{2}-12x+36}[/tex]

[tex]R(x) =\frac{x^{2}-11x+28 }{x^{2}-11x+30} \times \frac{x^{2}-12x+36 }{x^{2}-9x+20}[/tex]

Factoring each of the quadratics

[tex]R(x) =\frac{x^{2}-7x-4x+28 }{x^{2}-6x-5x+30} \times \frac{x^{2}-6x-6x+36 }{x^{2}-4x-5x+20}[/tex]

[tex]R(x) =\frac{x(x-7)-4(x-7) }{x(x-6)-5(x-6)} \times \frac{x(x-6)-6(x-6) }{x(x-4)-5(x-4)}[/tex]

[tex]R(x) =\frac{(x-4)(x-7)}{(x-5)(x-6)} \times \frac{(x-6)(x-6)}{(x-5)(x-4)}[/tex]

Simplifying

[tex]R(x) =\frac{(x-7)}{(x-5)} \times \frac{(x-6)}{(x-5)}[/tex]

[tex]R(x) =\frac{(x-7)(x-6)}{(x-5)(x-5)}[/tex]

[tex]R(x) =\frac{x^{2} -6x-7x+42}{x^{2} -5x-5x+25}[/tex]

[tex]R(x) =\frac{x^{2} -13x+42}{x^{2} -10x+25}[/tex]

Hence, the simplified form of R(x) is [tex]R(x) =\frac{x^{2} -13x+42}{x^{2} -10x+25}[/tex]

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the PERT weighted average is 9 days

PERT can be defined as an estimating technique that uses a weighted average of three numbers to get a final estimate.

The formula for finding the PERT weighted average is given as;

PERT weighted average = (Optimistic + (4 X Most Likely) + Pessimistic)/6

We have;

Substitute the values into the formula

PERT weighted average  = [tex]\frac{6 + 4(8) + 16 }{6}[/tex]

PERT weighted average  = [tex]\frac{54}{6}[/tex]

PERT weighted average  = 9 days

Thus, the PERT weighted average is 9 days

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Answer:

36 in.

Step-by-step explanation:

find the area of the rectangle and triangle first

area of rectangle = length x height

aR = (6 + 6) x 5

aR = 12 x 5

aR = 60

area of triangle = base x height x 1/2

aT = (6 + 6) x 4 x 1/2

aT = 12 x 4 x 1/2

aT = 24

now, to find the area of the shaded area subtract the triangle from the rectangle

area = rectangle - triangle

a = 60 - 24

a = 36

Answer:

Step-by-step explanation:

hello :

1)

the equation is : f(x)= a(x+1)(x-2)  because : x- ints of -1 and 2  means :

f(-1)=0 and f(2)=0

calculate : a   given f(4)=10

so :  a(4+1)(4-2)=10

10a =10   so : a = 1

the equation is : f(x)= (x+1)(x-2)

2) and 3) same method but   * y int of -3* meanes : f(0)= - 3

Answer:

f(0)=g(0)

Step-by-step explanation:

The problem is asking for where the output (y value) of one function, f(x), matches the output of another function, g(x), otherwise called an intersection. You can see that the two lines intersect at 0 on the x axis in the graph, therefore f(0)=g(0) meaning the outputs of f(x) are the same as g(x) at x value 0.

The average change in the temperature of the city is 0.87°C.

The average quantity is the sum of all quantities divided by the number of quantities.

In the question, we are informed that a newspaper reports the changes in the temperature of the city over 4 days to be 3.24°C, - 3/8 °C, - 0.15 °C, and 7/9 °C.

We are asked to write an expression to show the daily average change in the temperature of the city.

As we know, the average quantity is the sum of all quantities divided by the number of quantities.

Thus, average = {(3.24 - 3/8 -0.15 +7/9)/4} °C,

or, average = {{324/100 - 3/8 - 15/100 + 7/9}/4} °C,

or, average = [{(23328 - 2700 - 1080 + 5600)/7200}/4] °C,

or, average = 25148/28800 °C,

or, average = 6287/7200 °C = 0.8732 °C ≈ 0.87 °C.

Thus, the average change in the temperature of the city is 0.87°C.

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Answer:

I think that this answer is 22

Answer:

Step-by-step explanation:

Each intercept is found by solving for the variable after the other variable is set to zero.

Set y = 0 and solve for x:

  -3x = 66

  x = 66/(-3) = -22 . . . . . divide by the coefficient of x

The x-intercept is (-22, 0).

Set x = 0 and solve for y:

  11y = 66

  y = 66/11 = 6 . . . . . . . . divide by the coefficien tof y

The y-intercept is (0, 6).

__

Additional comment

The given equation is in standard form (almost). This form makes it easy to find the intercepts by dividing the constant by the variable's coefficient, as we did above.

(We say "almost" standard form because the leading coefficient is negative. It would be positive in standard form: 3x -11y = -66.)

Answer: (-22,0) and (0,6) in order

Step-by-step explanation:

x-intercept means point of graph that intersects the x-axis and y=0

y-intercept means point of graph that intersects the y-axis and x=0

So the x-intercept is -3x + 0 = 66 as y = 0

x = -22 so the coordinate is (-22,0)

The y-intercept is 0 + 11y = 66 as x = 0

y = 6 so the y-intercept is (0,6)

Answer:

2625 different numbers

Step-by-step explanation:

This type of problem is classified as a "Combinatorics" problem:  Counting up the number of ways something can happen.

Many times when attempting to count a large number of items, patterns are recognized and shortcuts to count are developed so that one doesn't need to physically count all of the items.  Perhaps the trickiest part of counting with these shortcuts is to ensure that one does not over-count (counting a scenario more than once), although it is equally important that we don't under-count (fail to count a situation that applies).

It should be noted that for a number to be a 4 digit number, it must have 4 digits, and thus the first digit must not be zero (despite that that would be an even digit, the number itself would not be a 4 digit number).

There are 2 main scenarios:

1.  All 4 digits are even

2. Exactly 3 digits are even (meaning that exactly one digit is odd).

There are two sub-cases to Scenario 2:

2.1. The first digit is odd, and all three of the other digits are even.

2.2. The first digit is even, and exactly two of the other digits are even (meaning that exactly one of the last three digits is odd).

None of scenarios 1, 2.1, and 2.2 overlap, so we're not over-counting:  

Further, this is all of the possibilities for a 4 digit number with least three even digits, so we're not under-counting.

Scenario 1 -- All 4 digits are even.

If all 4 digits are even, then the first digit has fours choices (2,4,6,8), and the next 3 digits each have 5 choices (2,4,6,8,0).

[tex]4*5*5*5=500\text{ choices}[/tex]

Scenario 2.1 -- The first digit is odd, and all three of the other digits are even

If the first digit is odd, there are 5 choices for the first digit (1,3,5,7,9), and the next 3 digits each have 5 choices (2,4,6,8,0).

[tex]5*5*5*5=625\text{ choices}[/tex]

Scenario 2.2 -- The first digit is even, and exactly two of the other digits are even

If the first digit is even, there are 4 choices for the first digit (2,4,6,8), and if exactly two of the next 3 digits are even, then there are 5 choices for each of the two even digits (2,4,6,8,0), and 5 choices for the odd digit (1,3,5,7,9), and there are "3 permuted by 2" ways of ordering those three digits.

[tex]4* \left [(5*5*5) * {}_3 \! P_2 \right ]=\\\\=4*\left [5*5*5 * \dfrac{3!}{2!} \right ]\\\\=4*\left [ 5*5*5 * \dfrac{3*2*1}{2*1} \right ] \\\\=4*\left [5*5*5 * 3 \right ] \\\\=1500\text{ choices}[/tex]

Scenario 2.2 broken down (calculated without using the permutation operation) -- The first digit is even, and exactly two of the other digits are even

Then either the second digit is odd (scenario 2.2.1), the third digit is odd (scenario 2.2.2), or the fourth digit is odd (scenario 2.2.3).

Scenario 2.2.1.  The second digit is odd.

The first digit is even: 4 choices for the first digit (2,4,6,8)

The second digit is odd:  5 choices for the odd digit (1,3,5,7,9)

The third and fourth digits are even: 5 choices for each even digit (2,4,6,8,0).

[tex]4*5*5*5=500\text{ choices}[/tex]

Scenario 2.2.2.  The third digit is odd.

The first digit is even: 4 choices for the first digit (2,4,6,8)

The second and fourth digits are even:  5 choices for each even digit (2,4,6,8,0).

The third digit is odd:  5 choices for the odd digit (1,3,5,7,9)

[tex]4*5*5*5=500\text{ choices}[/tex]

Scenario 2.2.3.  The last digit is odd.

The first digit is even: 4 choices for the first digit (2,4,6,8)

The second and third digits are even:  5 choices for each even digit (2,4,6,8,0).

The last digit is odd:  5 choices for the odd digit (1,3,5,7,9)

[tex]4*5*5*5=500\text{ choices}[/tex]

Scenarios 2.2.1, 2.2.2, and 2.2.3 comprise all of Scenario 2.2, so [tex]500+500+500=1500\text{ choices}[/tex]

How many ways can a 4 digit number be formed where at least 4 of the digits are even?

This is the sum of the choices from Scenario 1, Scenario 2.1, and Scenario 2.2, so    [tex]500+625+1500=2625\text{ choices}[/tex].

Answer:

3x³ + 3x² - 30x - 48

Step-by-step explanation:

3(x + 2)(x² - x - 8) ← distribute (x + 2) by 3

= (3x + 6)(x² - x - 8)

each term in the second factor is multiplied by each term in the first factor

= 3x(x² - x - 8) + 6(x² - x - 8) ← distribute both parenthesis

= 3x³ - 3x² - 24x + 6x² - 6x - 48 ← collect like terms

= 3x³ + 3x² - 30x - 48

Answer:

x-intercept is 6 [(6, 0) is the point]

y-intercept is 4 [(0, 4) is the point]

Step-by-step explanation:

To find the x-intercept, we can set y equal to 0 and solve for x. This works because the x-intercept is the point of the graph where the line crosses the x-axis (meaning y is equal to 0 at this point. So, if we set y=0 and solve, we get this:

[tex]2x+3(0)=12\\2x=12\\x=6[/tex]

So, the x-intercept is 6; if it is written as a point, it is (6, 0) since y is 0

To find the y-intercept, we can set x equal to 0 and solve for y. This works the same way - x is equal to 0 at the point where the line crosses the y-axis. If we set x=0 and solve, we get this:

[tex]2(0)+3y=12\\3y=12\\y=4[/tex]

So, the y-intercept is 4; if it is written as a point, it is (0, 4) since x is 0

Answer:

sin a = -3/5

Step-by-step explanation:

sin^2(a)+cos^2(a)=1

sin^2(a)+ (4/5)^2 = 1

sin^2(a) = 1 - 16/25 = 9/25

sin a = 3/5 ( in Quadrant 1)

In quadrat IV the sine is negative

so sin a = -3/5

Answer:

t = -35/8

Step-by-step explanation:

Divide both sides by 2/5.

Answer:

a. 25 seniors are randomly selected; 14 plan to go to a 4 year college

b. 420 students

Step-by-step explanation:

a. the less they have in common, the better

b. 14/25 is only between 25 students. make the denominator the same (750) and multiply the same to the numerator

750/25 = 30

14/25 x 30 = 420/750

The values which could be the slope of the line are numbers > 0.

According to the task content, it follows that the given line originates from the lower left quadrant and continues through the upper right quadrant.

It therefore follows that the line is ascending from left to right in which case, the slope of the line is positive.

Hence, the possible values of the slope include the set of numbers greater than 0.

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Answer: C and D

Step-by-step explanation: Trust me bro

The volume of the space filled with tissue paper in the packaging box is 198.264 cubic centimeters

Let l,b,h be the dimensions of small gift box V1 = Volume = l*b*h

= 24cm^3

Dimension of Large box are 2.1l , 2.1b,2.1h

Volume of large box = 2.1 l*2.1b*2.1h

= (2.1)^3*lbh

= (2.1)^3*24

V2 =222.264

Volume filled with tissue paper is V2-V1

222.264 - 24

= 198.264cm^3

Hence The volume of the space filled with tissue paper in the packaging box is 198.264 cubic centimeters

The complete question is shown below

Zoe is packaging a gift to send in the mail. A smaller gift box is placed inside a similar yet larger packaging box. The empty space inside the packaging box is filled with tissue paper to keep the gift box from moving. The dimensions of the larger box are each 2.1 times longer than the corresponding dimensions of the smaller box. The volume of the smaller box is 24 cubic centimeters.What is the volume of the tissue paper in the packaging box?

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Answer:

(4)(2)(1)=

4+2+1=

explanation:

The time taken for Jenny to run the same distance at 10% faster is 13.05 seconds

Time taken by Jenny = 14.5 - (10% × 14.5)

= 14.5 - (0.1 × 14.5)

= 14.5 - (1.45)

= 13.05 seconds

Therefore, the time taken for Jenny to run the same distance is 13.05 seconds

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The number of students with heights less than 163 cm should be expected is 12.

According to the statement

The mean of height is 175 cm

and  the standard deviation of height is 6 cm.

We use normal distribution here with formula

Z= X - μ /σ

Here X is 167.5 and μ is 175 and σ is 6 cm.

Substitute the values in it then

Z = 167.5 - 175 / 6

Z = -1.25

-1.25 have a p value 0.012

Out of 1000 students:

0.012 x 1000 = 12.

So, The number of students with heights less than 163 cm should be expected is 12.

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Answer:

Ok nice! Have Fun! Don't be scared it will be ok just face your fear and it will be fun. I never seen or been here. What is this amusement park called and where is it?

Answer:

D.  d = √(V/5)

E.  A = √(b/c).

Step-by-step explanation:

V = 5d^2

Divide both sides by 5:

V/5 = d^2

Now take the square root of both sides:

d = √(V/5)

Note - it's the square root of the whole term (V/5).

b = cA^2

A^2 = b/c

A = √(b/c).

There are two methods of solving systems of equations:

Substitution is where we substitute one equation into the other by isolating a certain variable, or a group of terms.

Elimination is where we subtract the two equations. Before doing this, we may have to multiply one equation by a certain number to make sure one variable cancels out.

We're given the following equations:

Because they are organized in the same manner (i.e. x [operation] y [equals] number), it is easier for us to use elimination.

First, multiply the first equation by 2:

[tex]x + 3y = 7\\2(x + 3y) = 2(7)\\2x + 6y = 14[/tex]

Now, subtract the second equation from the one we just created:

[tex]\hspace{10}2x + 6y = 14\\-2x + 4y = 11\\\rule{67}{0.3}\\2y=3[/tex]

Solve for y:

[tex]y=\dfrac{3}{2}[/tex]

To solve for x, we can use substitution in the first equation:

[tex]x + 3y = 7\\\\x + 3(\dfrac{3}{2}) = 7\\\\x + \dfrac{9}{2} = 7\\\\x = 7- \dfrac{9}{2}\\\\x = 7- 4.5\\\\x = 2.5\\\\x=\dfrac{5}{2}[/tex]

[tex]x=\dfrac{5}{2}[/tex]

[tex]y=\dfrac{3}{2}[/tex]

The probability of randomly getting first a red marble and then a blue marble is:

P = 0.083

There are:

For a total of 9 marbles.

The probability of getting a red marble is equal to the quotient between the number of red marbles and the total, so:

P(red) = 2/9

Then the probability of getting a blue marble is equal to the quotient between the number of blue marbles and the total, but because we already took one marble, now the total is 8.

P(blue) = 3/8

The joint probability is given by the product:

P = (2/9)*(3/8) = 0.083

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Answer:

Original equation:

y = a sin(b(θ -c)) + d

a = vertical dilation (stretch) of the amplitude

b = horizontal compression (shrink) of the period

c = horizontal shift (left/right)

d = vertical shift (up/down)

Your function is:

y = 3 sin(3θ + π) - 2

First, put it into the general from by factoring out the three in the argument of the sine:

y = 3 sin(3(θ + π/3)) - 2

a = vertical (amplitude) dilation = 3

b = horizontal (period) compression = 2π/period = 3

c = horizontal shift = π/3 to the left

d = vertical shift = -2

Answer:

r = -1.5

Step-by-step explanation:

recall that ,the recursive formula for a geometric sequence [tex]a_n[/tex] is :

[tex]a_{n} = r \times a_{n-1} \ \ \text{where r is the common ratio }[/tex]

therefore

The common ratio of the sequence:

[tex]a_{n} = -1.5 \times a_{n-1}[/tex]

is r = -1.5

Answer:

the third : x + x + x + 2 = 10

Step-by-step explanation:

x = the length of the first 2 pieces.

the third piece will be x+2 ft long.

so, the total length of the original board is the sum of all 3 pieces and must be all in all 10 ft.

10 = x + x + (x + 2) = x + x + x + 2

so, it is the third answer option.

Answer:

n^3 + 1.

Step-by-step explanation:

Each term is 1 more than a perfect cube.

2 = 1^3 + 1

9 = 2^3 + 1

28 = 3^3 + 1

65 =  4^3 + 1

126 = 5^3 + 1

So the explicit formula is n^3 + 1.

The explicit formula that generates the given sequence is indeed aₙ = n³+1.

Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

The nth term of the sequence can be obtained by substituting n = 1, 2, 3, ... into the expression n³+1:

a₁ = 1³+1 = 2

a₂ = 2³+1 = 9

a₃ = 3³+1 = 28

a₄ = 4³+1 = 65

a₅ = 5³+1 = 126

Hence, the explicit formula that generates the given sequence is indeed aₙ = n³+1.

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