Find a common solution for the system of equations given below:
-1/4x+y=-2
-x+4y=-8

V=480cm³ . 10 and 12

11-7=4

7*4=28

28is your answer

0.4 feet per second is the answer.

Answer:

B.y=−3x−1

Step-by-step explanation:

given that the line is parallel to y = -3x+4

Hence required line will be of the form

y =-3x+k for some k.

(Reason: slopes will be equal for parallel lines)

Since the line passes through (-2,5)

Substitute x =-2 and y =5 in the equation.

5=-3(-2)+k

Simplify

5 = 6+k

Subtract 6

Or k =-1

Hence required line has equation y =-3x-1

The function represented by the graph is (b) the reciprocal, y = 1/x

From the question, we have the following parameters that can be used in our computation:

The graph

From the graph, we can see that

The function has horizontal and vertical asymptotes

Only rational functions have this property

This means that the function represented by the graph is (b) the reciprocal, y = 1/x

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we are given two system of equations

First equation is

[tex]y=2x-1[/tex]

we can write as

[tex]-2x+y=-1[/tex]

Second equation is

[tex]6x-y=13[/tex]

now, we can find augmented matrix

[tex]A=\begin{pmatrix}-2&1&-1\\ 6&-1&13\end{pmatrix}[/tex]

now, we can change it into reduced row echelon form

step-1: multiply the 1st row by -1/2

[tex]A=\begin{pmatrix}-1&-1/2&1/2\\ 6&-1&13\end{pmatrix}[/tex]

step-2: add -6 times the 1st row to the 2nd row

[tex]A=\begin{pmatrix}-1&-1/2&1/2\\ 0&2&10\end{pmatrix}[/tex]

step-3:multiply the 2nd row by 1/2

[tex]A=\begin{pmatrix}-1&-1/2&1/2\\ 0&1&5\end{pmatrix}[/tex]

step-4:add 1/2 times the 2nd row to the 1st row

[tex]A=\begin{pmatrix}1&0&3\\ 0&1&5\end{pmatrix}[/tex]

so, we will get

[tex]x=3,y=5[/tex]

Answer is (3,5)

the value of x for which L is parallel to M :28 done

Answer:

[tex]\text{The equation of line is }x=-4[/tex]      

Step-by-step explanation:

Given that line is passing through the point (-4, 0) and parallel to the y-axis.

we have to find the equation of the line.

[tex]\text{As the slope of y-axis is }\infty\text{ i.e }\frac{1}{0}[/tex]

Since the slope of parallel lines are equal therefore we have to find the equation of line with slope infinity and passing through the point (-4, 0).

The equation of line pass through the point (x',y') with slope m is

[tex]y-y'=m(x-x')[/tex]

The equation of line with slope infinity and passing through the point (-4, 0) is

[tex]y-0=\frac{1}{0}(x-(-4))[/tex]

[tex]x+4=0[/tex]

[tex]x=-4[/tex]

which is required equation.

Hence, option 1 is correct.

Answer:

200 CD's.

Step-by-step explanation:

Jake recorded a special album in honor of mother's day. His mom was so excited that she purchased 40% of the copies in the store.

we have tell the total number of CD's in the store.

Let total number of CD's available in the store was = A

Then 40% of the total numbers of CD's = A×40% = 0.04 A

Since 0.04A = 80

A = 80/0.04 = 200

Therefore there were 200 CD's in the store for the sale.

The non real roots 1+4i and -4i will also have their complements as roots:- 1 - 4i and 4i

So the least number of roots = 5 and this will also be the least possible degree of the polynomial.

answer 5

Answer:

D

Step-by-step explanation:

The requried simplified value of the given function at x = 1/2 is 5/8.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

here,
Given function f(x) = -3/4x + 1
For f(1/2), put x = 1/2 in the above expression,

f(1/2) = -3/4(1/2) + 1
f(1/2) = -3/8 + 1
f(1/2) = [-3 + 1×8]/8
f(1/2) = [5]/8
f(1/2) = 5/8

Thus, the requried simplified value of the given function at x = 1/2 is 5/8.

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Answer: Two consecutive square numbers be 16 and 9.

Step-by-step explanation:

Let first consecutive square number be x²

Let second consecutive square number be (x+1)²

According to question,

[tex]x^2\times (x+1)^2=144[/tex]

Now we'll do this by factorisation,

[tex]144=2\times2\times2\times2\times3\times3\\\\144=16\times 9[/tex]

So, two consecutive square numbers are 16 and 9

Consecutive numbers are numbers that follow one another.

The consecutive squares are: 9 and 16

Let the bigger square be x^2

So, we have:

[tex]\mathbf{(x - 1)^2 \times x^2 = 144}[/tex]

Express 144 as 12^2

[tex]\mathbf{(x - 1)^2 \times x^2 = 12^2}[/tex]

Take square roots of both sides

[tex]\mathbf{(x - 1)\times x = 12}[/tex]

Expand

[tex]\mathbf{x^2 - x = 12}[/tex]

Rewrite as:

[tex]\mathbf{x^2 - x - 12 = 0}[/tex]

Expand

[tex]\mathbf{x^2 - 4x +3x- 12 = 0}[/tex]

Factorize

[tex]\mathbf{x(x - 4) +3(x- 4) = 0}[/tex]

Factor out x - 4

[tex]\mathbf{(x +3) (x- 4) = 0}[/tex]

Solve for x

x= -3 or x = 4

x cannot be negative.

So: x = 4

Square both sides

[tex]\mathbf{x^2 = 4^2}[/tex]

[tex]\mathbf{x^2 = 16}[/tex]

Calculate the smaller square

[tex]\mathbf{(x - 1)^2 = (4-1)^2}[/tex]

[tex]\mathbf{(x - 1)^2 = 9}[/tex]

Hence, the consecutive squares are: 9 and 16

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3(3x - 8) + 4x = -2(12 - 7x) - x

9x - 24 + 4x = -24 + 14x - x    distributed 3 on the left and -2 on the right

   - 24 + 13x = -24 + 13x        added like terms on the left and the right

            -13x            -13x

   -24          =   -24

           TRUE

A true statement means infinitely many solutions (aka All Real Numbers)

Answer: C

Answer: the first choice, |x − 18.25| > 0.36; x < 17.89 or x > 18.61

Explanation:

1. Target weight: 18.25 oz

2. Variability accepted: 0.36 oz

3. Range of accepted masses: 18.25 oz - 0.36 oz ≤ x ≤ 18.25 oz + 0.36 oz

4. Addition property of the inequalities (subtract 18.25 oz to the three parts of the inequality):

- 0.36 oz ≤ x - 18.25 oz ≤ 0.36 oz

5. Definition of absolute value inequality: | x - a | ≤ c equals - c ≤ x - a ≤ c

   ∴ - 0.36 ≤ x - 18.25 ≤ 0.36  equals | x - 18.25 | ≤ 0.36, which is the range of accepted masses.

6. The range of rejected masses is the complement, so it is:

          |x - 18.25 | > 0.36

7. Solve the inequality to find the range of rejected masses:

    a) x - 18.25 > 0.36 ⇒ x > 18.25 + 0.36 ⇒ x > 18.61

    b) x - 18.25 < 0.36 ⇒ x < 18.25 - 0.36 ⇒ x < 17.89

Answer:

A) 30 cubes.

B) 30 units³.

Step-by-step explanation:

A) 1. Calculate the volume of the rectangular prism, as following:

[tex]Vr=(lenght)(width)(height)[/tex]

2. You have that:

- The length is: [tex]1^{\frac{1}{2}}ft=1.5ft[/tex]

- The width is: [tex]1ft[/tex]

- The heigth is: [tex]2^{\frac{1}{2}}ft=2.5ft[/tex]

3. Substitute these values into the formula:

[tex]Vr=(1.5ft)(1ft)(2.5ft)=3.75ft^{3}[/tex]

4. The volume of one cube is:

[tex]Vc=side^{3}[/tex]

5. The length of one side is: [tex]\frac{1}{2}ft=0.5ft[/tex]

6. Substitute this value into the formula:

[tex]Vc=(0.5ft)^{3}=0.125ft^{3}[/tex]

7. The number of small cubes that can be packed in the rectangular prism is:

[tex]cubes=\frac{Vr}{Vc}\\cubes=\frac{3.75ft^{3}}{0.125ft^{3}}\\cubes=30[/tex]

B) 1. The length, the width and the height of the rectangular prism in term of units cubes is:

[tex]Length=\frac{1.5ft}{0.5ft}=3units[/tex]

[tex]Width=\frac{1ft}{0.5ft}=2units[/tex]

[tex]Heigth=\frac{2.5ft}{0.5ft}=5units[/tex]

2. Therefore, the volume of the rectagular prism in terms of the small cube and a unit cube is:

[tex]Vr=(3units)(2units)(5units)=30units^{3}[/tex]

Answer:

30 cubes.

Step-by-step explanation:

the first few bars are the people who walked fewer than 4,000, so add up the numbers on the side (2 and 5) and you get 7, so a

7 people have averaged fewer than 4,000 steps.

Option A is the correct answer.

Given,

The bar graph of the number of steps on the horizontal line and the number of people on the vertical line.

We need to find how many people averaged fewer than 4,000 steps each day.

Read the bar graph.

Steps - 0 - 1,999

= 2 people

Steps - 2,000 - 3,999

= 5 people

Steps - 4,000 - 5,999

= 12 people

Steps - 6,000 - 7,999

= 7 people

Steps - 8,000 - 9,999

= 3 people

Find the number of people who have fewer than 4,000 steps.

We have,

Steps - 0 - 1,999

= 2 people

Steps - 2,000 - 3,999

= 5 people

So,

2 + 5 = 7

= 7 people

Thus 7 people have averaged fewer than 4,000 steps.

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The ball hits the ground at unknown time (t) when the height (h) = 0

h(t) = -16t² + vt + h    ⇒ v = 64, h = 0, h(t) = 0, find t

 0  = -16t² + 64t

 0  = -16t(t - 4)

0 = -16t       or    0 = t - 4

  t = 0         or        t = 4

It starts at t = 0 seconds and ends at t = 4 seconds

Answer: B

Final answer:

Using the kinematic equation for vertical motion, we find that the golf ball will hit the ground after 4 seconds. We factor the kinematic equation to solve for the time given initial velocity and gravity's acceleration, ignoring the 0 time solution. TΔherefore, the correct option is b.

Explanation:

The question asks after how many seconds a golf ball hit from ground level with an initial vertical velocity of 64 ft/s will hit the ground. This problem involves kinematic equations of motion under the influence of gravity. We can use the equation for vertical motion: distance = initial velocity × time + 0.5 × acceleration × time². Since the ball returns to ground level, the distance covered is 0. Taking downward as positive, gravity's acceleration is +32 ft/s² (the usual acceleration due to gravity in units of ft/s²). We can rearrange the equation to solve for time (t): 0 = 64t + 0.5 × 32t². Factoring out t gives us t(64 + 16t) = 0, and solving for t gives us t = 0 or t = -64/16 = -4 seconds. Since time cannot be negative in this context, the positive solution reflects the time after launch, thus the answer is 4 seconds, which is option b.

$0.07. use the formula provided and just substitute.

Cost per gallon= Price per gallon/miles per gallon.

cost=$2.56/35

That led to 0.0731428571 and the nearest cent would be $0.07

3,744 inches. You would multiply 312 and 12, since there is 12 inches in a foot, to get 3,744 inches.

Hope this helped! :)

Let's have time in minutes as x.

Now we will make the next equation

3x+126 = 2x+151  First we will add number (-126) to the both sides and get

3x+126-126=2x+151-126 => 3x= 2x + 25

3x=2x+25 Now we will add monom (-2x) to the both sides and get

3x-2x=2x-2x+25 => x=25 minutes

They spent the same time 25 minutes and earned the same amount of money

Wilson earned  3*25+126= 75+126= $201

Jonathan earned 2*25+151=50+151= $201

Good luck!!!

If the points P, Q and R are collinear, then a slope of line PQ and a slope of line QR are equal.

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

PQ → (0, 3), (2, 0).

Substitute:

[tex]m=\dfrac{0-3}{2-0}=\dfrac{-3}{2}=-1.5[/tex]

QR → (2, 0), (4, -3).

Substitute:

[tex]m=\dfrac{-3-0}{4-2}=\dfrac{-3}{2}=-1.5[/tex]

CORRECT :)

Answer:

-3/2

Step-by-step explanation:

I just did this lesson.

The line has a slope of -3/2

Replace x and Y in the answers and see which one works:

A) 4(4) -3 = 16-3 = 13, not -3 FALSE.

B) 1/2(4) - 5 = 2-5 = -3 TRUE

The correct answer is B

-58.82% is the percent increase

Leila's gross earnings are calculated by adding her base pay of $290 to her commission of $13.80, which is 3% of her sales over $500. For the week, her total gross earnings are $303.80.

The question involves calculating Leila's gross earnings for a week where she sold $960 worth of merchandise while working at Famous Footwear. To find her earnings, we need to calculate her base pay plus the commission on sales over $500.

Leila's base pay is $290 per week. Since she sold $960, the amount over $500 that is eligible for commission is $960 - $500 = $460. Her commission is 3% of this amount, which is 0.03 * $460 = $13.80.

Therefore, Leila's total gross earnings for the week are her base pay plus her commission: $290 + $13.80 = $303.80.

Answer:

It's false, only if the situation gets worse.

Step-by-step explanation:

On the off chance that a debate over a contract emerges and casual endeavors at determination fall flat, the foremost common next step may be a claim. On the off chance that the sum at issue is underneath a certain dollar figure (ordinarily $3,000 to $7,500 depending on the state), the parties may be able to resolve the issue in small claims court.

Please correct any mistakes in my answer :) Glad to help ya!

Answer:

1/4 = 3/12 and 1/6 = 2/12

Step-by-step explanation:

We are given two fractions with denominator 4 and 6.

To find the least common denominator, of 4 and 6.

Factorise 4 and 6.

4 = 2x2

6=2x3

Hence Least common denominator = 2x2x3 =12

Make the given fractions to equivalent fractions with common denominator 12.

1/4 = 1(3)/4(3) = 3/12 and

1/6 = 1(2)/6(2)= 2/12

Hence answer would be

3/12 and 2/12

To rewrite the fractions 1/4 and 5/6 with a least common denominator, find the least common multiple (LCM) of the denominators, which is 12. Multiply the numerators and denominators of each fraction by the appropriate factor to obtain the rewritten fractions.

To rewrite the fractions 1/4 and 5/6 with a least common denominator, we need to find the least common multiple (LCM) of the denominators, which in this case are 4 and 6.

To find the LCM, we can list the multiples of each denominator until we find a common multiple. For 4, the multiples are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, ... And for 6, the multiples are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ... The first common multiple we find is 12, so that is the least common denominator (LCD).

To rewrite 1/4 with the LCD of 12, we need to multiply both the numerator and the denominator by 3: (1 * 3) / (4 * 3) = 3/12.

To rewrite 5/6 with the LCD of 12, we need to multiply both the numerator and the denominator by 2: (5 * 2) / (6 * 2) = 10/12.

Answer:

The correct answer is option D, the approximate population density of the bacteria in the dish is 4,246 bacteria / square inch

Step-by-step explanation:

They give us the diameter of the plate, then the first step is to calculate their area.

The area of a circle according to the diameter is:

[tex]A = \frac{\pi}{4}(d) ^ 2[/tex]

Where d is the diameter.

So:

[tex]A = \frac{\pi}{4}36\\ A = 9\pi\\ A = 28.274.inches ^ 2[/tex]

Now, to find the number of bacteria in per square inch, we divide [tex]\frac{120000}{28.274} = 4244.132.[/tex]

So, the correct answer is option D, the approximate population density of the bacteria in the dish is 4,246 bacteria / square inch