Solve this system of equations using the SUBSTITUTION method, then answer the questions below.

x + 2y = 4
3x + 6y = 18

What did you get for the (x, y) solution to this system? If you were to graph these equations, would their lines cross? Explain why or why not.

Bob is walking at the rate of 6 kilometer per hours

Jack and Bob leave their houses at 10:00 am walking toward each other and they meet at 10.30 am.

The distance between two houses = 7 kilometer

The speed of the Jack = 8 kilometer per hour

The distance traveled by Jack in 30 minutes = 8 / 2

= 4 kilometer

The remaining distance = 7 - 4

= 3 kilometer

Bob traveled 3 kilometers in 30 minutes

Then the speed of the Bob = 3 × 2

= 6 kilometer per hour

Hence, the Bob is walking at the rate of 6 kilometer per hours

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Answer:

Step-by-step explanation:

As described in the hint:

The product is:

This is a quadratic expression ax² + bx + c with the leading coefficient of a = - 1, b = 20 and c = 0.

It has a maximum and no minimum value since a < 0.

The x-coordinate of the maximum is the vertex which is x = - b/2a.

The x- coordinate of the vertex is:

The maximum value itself is:

Answer:

10 and 10.

[tex]f(x)=-x^2+20x[/tex]

Maximum value of the function is 100.

Step-by-step explanation:

Two numbers whose sum is a positive integer, and whose product is the maximum possible value have to be two positive integers.

Pairs of positive integers whose sum is 20:

The pair of numbers whose product is the maximum possible value is the pair of numbers that are closest to each other.  

Therefore the pair of numbers is 10 and 10:

[tex]\implies x = 10[/tex]

[tex]\implies 20 - x = 10[/tex]

Form a quadratic function by multiplying:

[tex]\implies f(x)=x(20-x)[/tex]

[tex]\implies f(x)=20x-x^2[/tex]

[tex]\implies f(x)=-x^2+20x[/tex]

The maximum value of the function is the y-value of its vertex.

[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]

To convert the function to vertex form, complete the square.

Factor out negative 1:

[tex]\implies f(x)=-(x^2-20x)[/tex]

Add and subtract the square of half the coefficient of the term in x:

[tex]\implies f(x)=-\left(x^2-20x+\left(\dfrac{-20}{2}\right)^2-\left(\dfrac{-20}{2}\right)^2\right)[/tex]

[tex]\implies f(x)=-(x^2-20x+100-100)[/tex]

[tex]\implies f(x)=-(x^2-20x+100)+100[/tex]

Factor the perfect square trinomial:

[tex]\implies f(x)=-(x-10)^2+100[/tex]

Therefore, the vertex of the function is (10, 100), and so the maximum value of the function is 100.

The function f(x)=(1-x)^2-4 is decreasing only throughout the interval is

-∞ < x < 1.

Given function:

f(x)=(1-x)^2-4

= 1 + x^2 - 2x - 4

= x^2 - 2x - 3

for decreasing:

f'(x) ≤ 0

2x - 2 - 0 ≤ 0

2x -2 ≤ 0

2x ≤ 2

x ≤ 1

-∞ < x < 1.

Therefore The function f(x)=(1-x)^2-4 is decreasing only throughout the interval is -∞ < x < 1.

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Quotient is 2x³ +x² -4x+3 for (2x⁴ – 3x³ – 6x² + 11x + 8) ÷ (x – 2)

A division is a process of splitting a specific amount into equal parts.

(2x⁴ – 3x³ – 6x² + 11x + 8) ÷ (x – 2)

Let f(x)=2x⁴ – 3x³ – 6x² + 11x + 8

and g(x)=x-2

We need to divide the f(x) by g(x),

f(x)=g(x)× (2x³ +x² -4x+3)+16

If we equate the above equation with division algorithm which says,

a=bq+r

f(x)=g(x)q(x)+r(x)

so quotient is 2x³ +x² -4x+3

Hence quotient is 2x³ +x² -4x+3 for (2x⁴ – 3x³ – 6x² + 11x + 8) ÷ (x – 2)

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Answer:Older workers are staying in the workforce longer.

Step-by-step explanation: I had the same question as you it should be right.

The percent decrease in the number of people who went to the pool over these four weeks is 15.2%.

The change regarding the people at the swimming pool for the number of weeks will be:

= 1020 - 125 + 145 - 175

= 865

The initial number of people is 1020.

Therefore, the percentage decrease will be:

= Decrease in number / Initial number × 100

= (1020 - 865) / 1020 × 100

= 155/1020 × 100

= 15.2%

The Percentage is 15.2%.

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The sum using the distributive property is 75

From the question, we have the following expression

30 + 45

Rewrite the given expression as follows

This is represented using

(30 + 45)

Factor out 5 from the expression

So, we have the following representation

30 + 45 = 5(6 + 9)

The above means that 5 is the GCF of the sum expression 30 + 45

This represents the GCF

Solving further, we have

30 + 45 = 5 * 15

Evaluate

30 + 45 = 75

Hence, the sum is 75

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Answer:Anything between the square root of 8.36 and 8.99

Step-by-step explanation:

Any of the square roots of the number above are between 2.8 repeating and 2.9 repeating.

Answer:

-243, 729

Step-by-step explanation:

[tex]f(x) = {( - 3)}^{x} [/tex]

x = 0, 1, 2, 3, .....

[tex]f(5) = {( - 3)}^{5} = - 243[/tex]

[tex]f(6) = {( - 3)}^{6} = 729[/tex]

The number of integers between 1 and 2022 inclusive that are multiples of 11 but not multiples of 3, using arithmetic sequences, is of:

122.

An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.

The nth term of an arithmetic sequence is given by the rule presented as follows:

[tex]a_n = a_1 + (n - 1)d[/tex]

In which [tex]a_1[/tex] is the first term of the arithmetic sequence.

The sequence composed by the integer multiples of 11 between 1 and 2022 are given as follows:

(11, 22, ..., 2013)

The first term and the common ratio of the sequence are given as follows:

[tex]a_1 = 11, d = 11[/tex]

The number of terms is obtained as follows:

2013 = 11 + 11(n - 1)

11n = 2013

n = 2013/11

n = 183.

The sequence composed by terms that are multiples of 11 and of 3 is given by:

(33, 66, ..., 2013).

The first term and the common ratio of the sequence are given as follows:

[tex]a_1 = 33, d = 33[/tex]

The number of terms is obtained as follows:

2013 = 33 + 33(n - 1)

33n = 2013

n = 2013/33

n = 61.

Hence the number of integers that are multiples of 11 but not 3 is given by:

183 - 61 = 122.

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The specification as an absolute value inequality is l w - 18 l ≤ 0.1.

Given:

A furniture maker uses the specification 17.9≤w≤18.1 for the width w in inches of a desk drawer.

m = 17.9 + 18.1 / 2

= 36/2

= 18

t = 18.1 - 17.9

= 0.2/2

= 0.1

l w - 18 l ≤ 0.1

Therefore The specification as an absolute value inequality is l w - 18 l ≤ 0.1.

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Answer:

15% and 40%

Step-by-step explanation:

22500/150000 is 15/100 or 15%

60000/150000 is 40/100 or 40%

Answer:

2nd one

Step-by-step explanation:

You can see that at the end, it is +5. That means it is to the left, NOT the right. So the second one is correct.

The relation represented by the ordered pair is not a function

The given parameter is represented as

{(-2, 4), (-1, 3), (0, 2), (-2, 0), (1, 1)}

As a general rule;

For a relation to be considered a function, the following must be true:

One x value must not point to several y values

Using the above as a guide, the ordered pair in the relation are not functions

This is because one x value must not point to several y values

Hence, (d) the ordered pair is not a function

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6 liters of brand A fruit punch must be mixed with 9 L of brand b fruit punch.

Let x=liters of Brand A fruit punch to be mixed with 9 liters of Brand B fruit punch.

x + 9 = liters of mixture.

20%(x) + 9*40% = 32%(x+9)

20/100 x + 9*40/100 = 32/100 (x+9)

0.2x + 360/100 = 0.32x + 9*0.32

0.2x + 3.6 = 0.32x + 2.88

0.12x = 3.6 - 2.88

0.12x = 0.72

divide by 0.12 on both sides

x = 0.72/0.12

= 72/100/12/100

= 72/12

= 6 liters.

Therefore 6 liters of brand A fruit punch must be mixed with 9 L of brand b fruit punch.

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Answer:

1.8291

Step-by-step explanation:

Answer: -9

Step-by-step explanation:

I will have to reject the offer of the rival company since it's lesser than $40560.

From the information, the person works a basic week of 40 hours and the basic rate is $19.50 per hour. It should be noted that there are 52 weeks in a year. The total amount will be:

= 40 × 19.50 × 52

= $40560

The rival company offers you an annual salary is $36000.

I'll reject the rival company's offer since it's lower.

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Complete question

You work a basic week of 40 hours and your basic rate is $19.50 per hour. A rival company offers you an annual salary is $36.000. Except for the pay, everything is identical between the conpanies. Do you accept or reject the rival company's offer, and why?

answer:

0.25 (or 1/4) x 20 = 5

step-by-step explanation:

math. 0.25x20 = 5

Answer: 5

Step-by-step explanation:

Answer:

150 plates

Step-by-step explanation:

if 1 stack = 10 plates then

15 stacks =?

15×10 =150

Answer:

150

Step-by-step explanation:

If 1 stack = 10 plates all you have to do is figure out how 1 changes to 15 ( in this case multiply). You tyen multiply 10 by 15 which equals to 150.

Answer:

then he has 6 marbl3s total.

Answer:

  19%

Step-by-step explanation:

You want the probability a student is a senior, given that they are female.

The table indicates that 3 +4 +6 +3 = 16 students are female. Of those, 3 are seniors. The desired probability is ...

  P(senior | female) = N(senior & female)/N(senior) = 3/16 = 0.1875

The probability that a female student is a senior is about 19%.

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The number of marigold in the garden of Paula is 24.

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Let the number of marigold be m.

In this case, the number of tulips in Paula's garden is 8 less than the number of marigolds. The number of marigold will be:

m - 8 = 16

m = 16 + 8.

m = 24

The number of marigold is 24.

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The will be A'(0, 20),  B'(20, 10) and  '(-10, 0). Transformation is the  of a point from its to a. Types of transformation are reflection, translation, rotation and dilation.

What is transformation?
When a function is transformed, the graph's curve either "moves to the left/right/up/down," "expands or compresses," or "reflects." For instance, by simply moving the graph of the function g(x) = x2 up by 3 units, the graph of the function f(x) = x2 + 3 is obtained. Function transformations are very useful for graphing functions without having to start from scratch because they allow you to move, expand, compress, or reflect the curve. In this article, we will examine the guidelines for function transformations as well as examples of how to transform various function types.

Let ABC be a   with coordinates A(0, 2), B(2, 1), C(-1, 0).

The coordinate of points A, B, C will change by below rule

(x, y)↔(10x, 10y)        

where 10 is the scale factor.

∴A(0, 2) ↔A'(0, 20)

B(2, 1) ↔B'(20, 10)

C(-1,0) ↔C'(-10, 0)

Hence,   will be A'(0, 20) ,B'(20, 10)  and C'(-10, 0)

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Answer:

dilation (sorry if i got it wrong im trying my best)

Answer:

Rotation

Step-by-step explanation:

It is rotated 180° at a point (which u could draw line of each object with its respective image to find the rotation point)

Answer:

10i

Step-by-step explanation:

using the fact that [tex]\sqrt{-1}[/tex] = i , then

[tex]\sqrt{-100}[/tex]

= [tex]\sqrt{100(-1)}[/tex]

= [tex]\sqrt{100}[/tex] × [tex]\sqrt{-1}[/tex]

= 10 × i

= 10i

= 0 + 10i ← in standard form

Answer:

w to the power of 3 or w^3

Step-by-step explanation:

For example, plug in a number for the variable given, and in this case, I used the number 2. When using the number 2, the question would become 2 * 2 * 2. It would be simplified as 2 to the power of 2 to the power of 3. That's how I got the answer of w to the power of 3.

The 42nd term of the sequence is 248

What is Arithmetic Progression?

Arithmetic Progression (AP) is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value.

The furmula is [tex]a_{n}[/tex]=a + (n - 1 )d

where a = The first form of A.P

n = Number of terms given to find

d = Common difference between each terms

Given,

a = 2

n = 42

d = 6

Now,

[tex]a_{42\\[/tex] = 2 + (42 - 1)6

[tex]a_{42}[/tex] = 2 + (41)6

[tex]a_{42}[/tex] = 2+ 246

Therefore, for 42nd term

[tex]a_{42}[/tex] = 248

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