Solve the system of equations. y = -6x + 9 y = -3x + 3 a. ( 3, -2) c. ( 2, -3) b. ( -2, -3) d. No solution

Answer:

D

Step-by-step explanation:

The difference in the x-coordinates is Δx = 6 - 3 = 3.

The difference in the y-coordinates is Δy = 8 - 2 = 6.

One third the difference is Δx/3 = 3/3 = 1 and Δy/3 = 6/3 = 2.

So the one-third point is at (3 + 1, 2 + 2) = (4, 4).

In general the segment from A to B has parametric equation

X = (1-t)A + tB

t=0 gives point A, t=1 gives point B, and in between we move linearly with t from A to B.

So if we want AX:BX=1:3, that's 1/(1+3)=1/4 of the way along from A to B, so corresponds to t=1/4.  So the point we seek is

X = (1 - 1/4)(3, 2) + (1/4)(6,8) = ((9+6)/4, (6+8)/4)=(15/4, 7/2)

Answer: Choice C

[tex]\bf \qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{\textit{\underline{v}olume varies inversely with \underline{p}ressure}}{V=\cfrac{k}{p}}~\hfill[/tex]

[tex]\bf \qquad \qquad \textit{sum of a finite arithmetic sequence} \\\\ S_n=\cfrac{n}{2}(a_1+a_n)\quad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\[-0.5em] \hrulefill\\ n=12\\ S_{12}=156 \end{cases}\implies 156=\cfrac{12}{2}(a_1+a_{12}) \\\\\\ 156=6(a_1+a_{12})\implies \cfrac{156}{6}=a_1+a_{12}\implies 26=a_1+a_{12}[/tex]

Final answer:

The sum of the first and twelfth terms of an arithmetic progression, whose first 12 terms sum to 156, is 26. This is determined by using the arithmetic progression sum formula and understanding that the sum of equidistant terms from the beginning and end of the series is constant.

Explanation:

To determine the sum of the first and twelfth terms of an arithmetic progression (AP) given the sum of the first 12 terms, we can use the properties of AP. The sum of an arithmetic progression can be expressed using the formula Sn = n/2(2a + (n-1)d), where Sn is the sum of the first n terms, a is the first term, n is the number of terms, and d is the common difference.

For this question, the sum of the first 12 terms (S12) is given as 156, and we want to find the sum of the first and twelfth terms. By properties of AP, the sum of equidistant terms from the beginning and end (first and last terms in this case) is the same. So the sum of the first and twelfth terms is equal to the sum of the second and eleventh terms, and so on. This sum is consistent and equals a + a + 11d, which simplifies to 2a + 11d.

Since S12 = 12/2(2a + 11d) and we know S12 = 156, we can simplify the formula to get 156 = 6(2a + 11d). However, to solve for 2a + 11d directly, we do not need the value of d; we only need the fact that the sum of the first and last terms will be constant and equal to the sum of 2a + 11d. Therefore, the sum of the first and twelfth terms is 156/6, which equals 26.

Answer:

She had more correct answers on the first quiz

Explanation:

1- For the first quiz:

We know that the quiz had a total of 15 questions and that Kelly had [tex]\frac{4}{5}[/tex] of those correct

This means that:

Number of correct answers = [tex]\frac{4}{5}*15 = 12[/tex] answers

2- For the second quiz:

We know that the quiz had a total of 12 questions and that Kelly had [tex]\frac{5}{6}[/tex] of those correct

This means that:

Number of correct answers = [tex]\frac{5}{6}*12=10[/tex] answers

3- Comparing the number of correct answers:

From the above calculations, we know that she had 12 correct answers on the first quiz and 10 on the second

This means that she had more correct answers on the first quiz

Hope this helps :)

Kelly got more questions correct on the first quiz with 12 correct answers compared to 10 correct answers on the second quiz.

To figure out on which quiz Kelly got more questions correct, we need to calculate the number of correct answers for each quiz.

First Quiz (Decimals): Kelly answered 4/5 of 15 questions correctly.

To find the number of correct answers, multiply:

(4/5) × 15 = 12

So, Kelly got 12 questions correct in the first quiz.

Second Quiz (Fractions): Kelly answered 5/6 of 12 questions correctly.

To find the number of correct answers, multiply:

(5/6) × 12 = 10

So, Kelly got 10 questions correct in the second quiz.

Therefore, Kelly got more questions correct on the first quiz with 12 correct answers compared to 10 on the second quiz.

Answer:

B

Hope this helps!

Answer:

B

Step-by-step explanation:

The rate of change is the slope.  Function 1 has a slope of 4.  Function 2 has a slope of:

m = Δy / Δx

m = (10 - 6) / (3 - 1)

m = 4 / 2

m = 2

So function 1 has the greater rate of change.  Answer B.

Answer:

Step-by-step explanation:

2*pi - sqrt(3)

pi = 3.14159

2pi = 6.283184

sqrt(3) = 1.73205

Answer

6.283184 - 1.73205

4.51133

Answer:

Sorry about being so late, but the answer is

4.55

OR

4.55113449961

Step-by-step explanation:

Answer:

346 trucks are needed

Step-by-step explanation:

We know that one acre equals 43560 feet ^ 2

In this case the area is 3 acres. So:

[tex]3\ acres * \frac{43,560\ ft^2}{1\ acre} = 130,680\ ft^2[/tex]

We know that 1 foot equals 12 inches. So:

[tex]24\ in * \frac{1\ ft}{12\ in} = 2\ ft[/tex]

So the volume of the contaminated area is:

[tex]V = 2* 130,680\ ft^3\\\\V = 261,360\ ft^3[/tex]

In a cubic yard there are 27 cubic feet. So:

[tex]28\ yard^2 * \frac{27\ ft^3}{1\ yard^3} = 756\ ft^3[/tex]

Finally if we have a volume of [tex]261,360\ ft ^ 3[/tex] and each truck can transport [tex]756\ ft ^ 3[/tex] then the amount of trucks x we need is:

[tex]x = \frac{261,360\ ft ^ 3}{756\ ft ^ 3} = 346\ trucks[/tex]

Answer:

Part A) The system has one solution

Part B) The solution is the point (4,4)

Step-by-step explanation:

step 1

Find the equation of the line A

we have

(0,6) and (6,3)

Find the slope

m=(3-6)/(6-0)

m=-0.5

Find the equation of the line into slope intercept form

y=mx+b

we have

m=-0.5

b=6 -----> the point (0,6) is the y-intercept

substitute

y=-0.5x+6 ------> equation A

step 2

Find the equation of the line B

we have

(0,0) and (6,6)

Find the slope

m=(6-0)/(6-0)

m=1

Find the equation of the line into slope intercept form

y=mx+b

we have

m=1

b=0 -----> the line represent a direct variation

substitute

y=x ------> equation B

step 3

Find how  many solutions does the pair of equations for lines A and B have

we have

y=-0.5x+6 ------> equation A

y=x ------> equation B

Solve the system of equations by graphing

Remember that the solution of the system of equations is the intersection point both lines

using a graphing tool

There is one point of intersection

therefore

The system has one solution

see the attached figure

step 4

What is the solution to the equations of lines A and B?

we know that

The solution of the system of equations is the intersection point both lines

The intersection point is (4,4)

therefore

The solution is the point (4,4)

so

x=4,y=4

Answer:

I think it would be true

The provided statement "When researchers incorrectly interpret the responses to a survey question, this is poor analysis" is true.

The practice of assessing client insights is known as survey analysis. It could be customer satisfaction scores or other customer experience measures.

We have a statement:

When researchers incorrectly interpret the responses to a survey question,

this is a poor analysis.

The above statement is true because when we have survey data that is incorrectly interpreted, it will create a problem in the final phase or implementation phase.

Thus, the provided statement "When researchers incorrectly interpret the responses to a survey question, this is poor analysis" is true.

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Answer:

  500

Step-by-step explanation:

A sequential search starts with the first item on the list, making a comparison with every item until the desired one is found. It takes 500 comparisons to find the 500th item.

This function starts at 30 where x=0, and then gains 15 units each time x is increased by 1.

So, we deduce that renting the storage has a fixed price of 30, and then you have to pay 15 each month.

It will add 15 dollar for each month.

The domain is the X values and the range is the y values.

The blue line starts at X 0 and Y 0 and moves up and to the right.

This means the range and domain are equal to or greater than 0.

The 3rd choice is the correct one.

Answer:

[tex]x^{1/4} y^{1/2}[/tex]

Step-by-step explanation:

When you have a power then a root like that, you have to divide the power by the root.

So, in this case, you have (x^2y^4) and a 8th root (8√).

So, you take your exponents from (x^2y^4) and divide them by the root (8), to get new powers of 2/8, or 1/4, and 4/8 or 1/2

As I already explained you in other questions, that leaves a fractional exponent that is equivalent to the regular exponent then rooted.

Answer is then: [tex]x^{1/4} y^{1/2}[/tex]

Answer:

Step-by-step explanation:

Let's say the numbers are x and y, and y is larger than x.

x + y = 27

y = 6 + 2x

Substitute:

x + (6 + 2x) = 27

3x + 6 = 27

3x = 21

x = 7

So x = 7 and y = 20.

Answer:

x=6,-4

Step-by-step explanation:

Use the formula (b/2)^2 in order to create a new term.  Solve for x by using this term to complete the square.

x=6,-4

Each pack costs 5 dollars so you take 5 times 8 to get 45 dollars. Then you take to 8 and times it by 10 to get a total of 80 pens

Answer:

8

Step-by-step explanation:

First Step

Convert meters to centimeters

For every meter there are 100 (centi)meters

6 meters ×100=600 cm

Second Step

Find how many scarves can be made

We have 600 cm of fringe

It takes 70 cm to make 1 scarf

Divide 70 into 600

600÷70=8.571

Rounding down we get 8

a. On Graph B, at 0 minutes, the height of the graph will be 12 miles.

b. Then, the graph will decrease linearly until 15 minutes, when Adalyn reaches the school.

Certainly, let's delve a bit deeper into each part of Graph B in relation to Adalyn's journey from home to school and back:

a. Initial Point at 0 Minutes:

On Graph B, the vertical axis represents the distance from the school, while the horizontal axis represents time. At the start of her journey (0 minutes), Adalyn is at her home, which is 12 miles from the school. This is the farthest point from the school she will be during her trip. Therefore, the height of Graph B at 0 minutes must be the full distance to the school, which is 12 miles. This is the starting point for the graph on the vertical axis.

b. Graph Behavior from 0 to 15 Minutes:

As time progresses from 0 to 15 minutes, Adalyn is driving towards the school, getting closer every minute. On the graph, this is represented by a decreasing line, since the vertical distance from any point on the line to the horizontal axis represents her distance from the school, which is getting smaller. The rate of decrease is constant because we're assuming she's driving at a steady pace.

At exactly 15 minutes, Adalyn reaches the school. Since she is now at the school, her distance from it is 0 miles. On Graph B, this is represented by the graph touching the horizontal axis. At this point, the height of the graph is 0 miles, indicating that there is no distance between Adalyn and the school.

After 15 minutes, the graph would stay at 0 miles (the line would run along the horizontal axis) until she begins her journey back home. Once she starts the return trip, the graph would begin to increase linearly from 0, reflecting her increasing distance from the school as she drives back home.

If we were to continue completing Graph B based on Graph A, after the 15-minute mark, we'd see a flat line at 0 miles until 60 minutes when Adalyn starts her journey back home, at which point the line would ascend back to 12 miles by 75 minutes, mirroring the initial descent but in the opposite direction.

The word which completes the statement are,

12 miles,

Steady,

Decrease

Complete each statement about Graph B.

On graph B, at 0 minutes, the height of the graph will be 12 miles.

Then, the graph will remain steady until 15 minutes, the height of graph B will be decreased.

Therefore, graph B is the reverse of graph A which is the distance from the school to her home.

Answer:  B) 115

Step-by-step explanation:

S₅ means the sum of the first 5 numbers in the sequence.

3 + 13 + 23 + 33 + 43 = 115

Answer:

9

Step-by-step explanation:

coefficients = numbers in front of variables (x, x^2 etc)

so 5 + 3 + 1 = 9

In the expression 3x^4 + 5x^2 + x, the coefficients are 3, 5, and 1. Adding these values together gives a sum of 9.

In the expression 3x^4 + 5x^2 + x, the coefficients are 3, 5, and 1 respectively. The term x is implied to have a coefficient of 1 though it is not written explicitly. We find the sum of the coefficients by simply adding all these values together. So the sum would be 3 + 5 + 1 = 9.

The term x is implied to have a coefficient of 1 though it is not written explicitly. We find the sum of the coefficients by simply adding all these values together.

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The ratio of areas of similar triangles is the square of the ratio of their linear dimensions. If the smaller triangle is 1/2 the area of the larger, then its linear dimensions are √(1/2) those of the larger triangle.

  smaller side length = √(1/2) × larger side length

  = (√2)/2×36 = 18√2 ≈ 25.4558

Answer:

  Hari is 20; Harry is 28

Step-by-step explanation:

The ratio in 4 years is equivalent to the ratio 6:8, which has each of the original ratio unit numbers increased by 1. That means each of those ratio units stands for 4 years, and the present ages are ...

  Hari: 5·4 = 20

  Harry: 7·4 = 28

_____

Conventional method of solution

If you like, you can write equations for the ages of Hari (x) and Harry (y):

  x/y = 5/7

  (x+4)/(y+4) = 3/4

These can be solved a variety of ways. For some methods, it may be useful to write them in standard form:

These have solution (x, y) = (20, 28).

Answer:

  36

Step-by-step explanation:

The total number of options is the product of the numbers of independent options: 3×3×4 = 36.

__

For each of the bedroom options, she can choose any parking option, so can have ...

  1 br, street parking

  2 br, street parking

  3 br, street parking

  1 br, assigned parking

  2 br, assigned parking

  3 br, assigned parking

  1 br, garage spots

  2 br, garage spots

  3 br, garage spots

That is, 3×3 = 9 options. Any of these can be put with any of the four lease options, for a total of 9×4 = 36 options altogether.

The answer would be 36

Answer:

x = 48.37

Step-by-step explanation:

x^2 = 58^2 - 32^2

x^2 = 3364 - 1024

x^2 = 2340

x = 48.37

Answer:

48.37

Step-by-step explanation:

Answer:

120

Step-by-step explanation:

5x4x3x2x1 =120

The number of ways to arrange the trophies is 120. The correct answer is option A.

The arrangement of the different things or numbers in a number of ways is called the combination.

Given that:-

The number of the ways will be calculated as:-

N  =  5!

N  =  5  x 4  x 3  x 2 x 1

N  =  120 ways

Therefore the number of ways to arrange the trophies is 120.

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Explanation:

___

Similar relationships pertain to the diagonal BD and segments EH and FG. You can also conclude that area EFGH is half of area ABCD by considering the various triangles you get by connecting midpoints different ways.

Answer:

Step-by-step explanation:

The factors of each term are ...

So, the greatest common factor is 3a. Factoring that out gives ...

  3a(16a^2 -25) . . . . . . matches answer 2

The factor in parentheses is the difference of squares, so it can be factored. You have memorized the form for the difference of squares ...

  p^2 -q^2 = (p -q)(p +q)

so you know the factoring of this with p=4a and q=5 will be ...

  3a(4a -5)(4a +5) . . . . . . matches answer 4

__

Any pair of factors can be multiplied by -1 without changing the value of the expression. So, two more answers are equivalent:

   (-3a)(-(16a^2 -25) = -3a(25 -16a^2) . . . . . . matches answer 5

  (-3a)(-(4a -5)(4a +5) = -3a(5 -4a)(5 +4a) . . . . . . matches answer 6

Answer:

2 4 5 6

Step-by-step explanation:

The highest common factor is 3a That means that 48a^3 must be divided by 3a which means 48a^3 / 3a = 16a^2. Notice what happened. 48/3 = 16. a^3/a = a^2.

Now you have to pull out 3a from 75a. That wasn't done to Answer 1. So answer one is incorrect.

75a/3a = 25

So far what you answer looks like is

3a(16a^2 - 25) which is answer 2

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

Answer 3 is wrong because one of the factor has to be - 5. Neither one is.

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

Answer 4 is correct

16a^2 - 25 factors into (4a - 5)(4a + 5)

So what is written reflects those factors + the 3a

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

Now we come to the brutal ones.

If you take out a minus sign from the brackets, it has the effect of turning the two terms inside the brackets around.

-3a(25 - 16a^2) is what the above sentence means. so 5 is correct

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

The two terms inside the brackets still factor

-3a ( 5 - 4a)(5 + 4a) It is just that they are turned around.

6 is correct.

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

Answer:

No.

Step-by-step explanation:

Because x²-5x+7, as x = 9 is 9²-5·9+7 = 81-45+7 ≠ 0

f(x) = x²-5x+7 is divisible by x-9 only if f(9) = 0.

Answer:

2.3 and 3.6

Step-by-step explanation:

Final answer:

To solve the equation x^2 - 9|||-3 = log3 x, simplify both sides of the equation and then find the values of x that satisfy the equation.

Explanation:

To find the values of x that satisfy the equation, we can start by simplifying both sides of the equation.

On the left side, we have x^2 - 9|||-3. To simplify this, we first evaluate the absolute value of -3, which is 3. Then we have x^2 - 9(3), which simplifies to x^2 - 27.

On the right side, we have log3 x.

Setting the two sides equal to each other, we have x^2 - 27 = log3 x.

To solve this equation, we can graph both sides and find the intersection points, or we can use numerical methods like iteration or Newton's method to find the approximate solutions.