(3.07A MC)

The graph shows two lines, A and B:

A graph is shown with x and y axes labeled from 0 to 6 at increments of 1. A straight line labeled A joins the ordered pair 2, 6 with the ordered pair 5, 0. Another straight line labeled B joins the ordered pair 0, 2 with the ordered pair 6, 6.

Based on the graph, which statement is correct about the solution to the system of equations for lines A and B?

(3, 4) is the solution to both lines A and B.
(3, 4) is the solution to line A but not to line B.
(0, 2) is the solution to both lines A and B.
(0, 2) is the solution to line A but not to line B.

Answer:

Kindly check explanation

Step-by-step explanation:

Given :

Lewis :

y = 17x

x = number of hours worked

y = amount of money earned

Carl:

Carl’s Earnings Time (h) 3 5 8 10

Money earned ($) 45 75 120 150

(a) How much money does Carl earn per hour? Show your work on how you found the constant of proportionality for both.

Money earned = pay per hour * hours worked

$45 = pay per hour * 3

Pay per hour = $45 / 3 = $15

Hence, Carl's earning per hour = $15

(b) Who earns more per hour? Justify your answer by comparing the two. Please use complete sentences.

Lewis : y = 17x

Carl : y = 15x

Where $17 and $15, represents Lewis and Carl's hourly pay respectively.

Hence, Carl earns more.

(c) Draw a graph that represents Carl’s earnings over time in hours. Remember to label the axes with the real world quantities that x

The simplified expressions are:

a) 36

b) 28

c) 13

d) 4

f) 4

b) 54

d) 256

f) 28

h) 185

j) -30

Let's simplify the given mathematical expressions step by step:

a) 4 times the sum of 7 and 2:

4 * (7 + 2)

= 4 * 9

= 36

b) 7 times the difference of 12 and 8:

7 * (12 - 8)

= 7 * 4

= 28

c) 9 is subtracted from 2 times the sum of 7 and 4:

2 * (7 + 4) - 9

= 2 * 11 - 9

= 22 - 9

= 13

d) 48 is divided by 3 times the difference of 15 and 11:

48 / (3 * (15 - 11))

= 48 / (3 * 4)

= 48 / 12

= 4

f) The sum of 60 and 30 is divided by 10 and the difference of quotient 5:

((60 + 30) / 10) - 5

= (90 / 10) - 5

= 9 - 5

= 4

b) 6 times the sum of 5 and 4:

6 * (5 + 4)

= 6 * 9

= 54

d) 32 times the difference of 14 and 6:

32 * (14 - 6)

= 32 * 8

= 256

f) 35 minus the quantity of (15 minus the quotient of (19 + 5) divided by 3):

35 - (15 - ((19 + 5) / 3))

= 35 - (15 - (24 / 3))

= 35 - (15 - 8)

= 35 - 7

= 28

h) 5 times the quantity of (13 + 12 + 3 times (2 times 2) minus 4):

5 * (13 + 12 + 3 * (2 * 2) - 4)

= 5 * (13 + 12 + 3 * 4 - 4)

= 5 * (13 + 12 + 12 - 4)

= 5 * (37)

= 185

j) 25 minus the quantity of (90 minus 5 times the quantity of (9 minus (14 minus 12))):

25 - (90 - 5 * (9 - (14 - 12)))

= 25 - (90 - 5 * (9 - 2))

= 25 - (90 - 5 * 7)

= 25 - (90 - 35)

= 25 - 55

= -30

So, the simplified expressions are:

a) 36

b) 28

c) 13

d) 4

f) 4

b) 54

d) 256

f) 28

h) 185

j) -30

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Answer:

OC

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

Answer:

What is this????

Answer:

24 by 4

Step-by-step explanation:

Answer:

y= 5x -9

Step-by-step explanation:

Slope-intercept form:

y= mx +c, where m is the gradient and c is the y-intercept.

y= 5x -15

Gradient of given line= 5

Since parallel lines have the same gradient, gradient of the line is 5. Thus, m=5.

Substitute m=5 into the equation:

y= 5x +c

To find the value of c, substitute a pair of coordinates.

When x =1, y= -4,

-4= 5(1) +c

-4= 5 +c

c= -4 -5

c= -9

Thus, the equation of the line is y= 5x -9.

Answer:

x=26.68 inches

Step-by-step explanation:

The attached figure shows a triangular ramp. Height of the ramp is 6 inches and the base of the ramp is 26 inches.

We can use Pythagoras theorem to find the value of x as follows :

Hypotenuse²=base²+height²

So,

[tex]x^2=26^2+6^2\\\\x^2=712\\\\x=26.68\ \text{inches}[/tex]

Hence, the value of x is 26.68 inches

Step-by-step explanation:

Given expression is :

[tex]9x^2-4[/tex]

We can write it as :

[tex](3x)^2-2^2[/tex]

Now using identity : [tex]a^2-b^2=(a-b)(a+b)[/tex]

Here, a = 3x and b = 2

So,

[tex](3x)^2-2^2=(3x-2)(3x+2)[/tex]

Hence, the given expression is equivalent to (3x - 2)(3x + 2) .

The solution to the equation A = 9x² - 4 is given by A = ( 3x + 2 ) ( 3x - 2 )

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

A = 9x² - 4   be equation (1)

On simplifying the equation , we get

a)

Let the equation be A = ( 3x + 2 ) ( 3x - 2 )

A = 3x ( 3x ) - 3x ( 2 ) + 2 ( 3x ) - 2 ( 2 )

On simplifying the equation , we get

A = 9x² - 6x + 6x - 4

A = 9x² - 4

Therefore , the value of A is 9x² - 4

Hence , the equation is A = ( 3x + 2 ) ( 3x - 2 )

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Answer:

2.4 and round by the nearest ones place value

Answer:

B. Graph B Only

Step-by-step explanation:

Answer:

63,800,000,000 square metres equals 63,800 square kilometres

Step-by-step explanation:

The rule of three or is a way of solving problems of proportionality between three known values and an unknown value, establishing a relationship of proportionality between all of them. That is, what is intended with it is to find the fourth term of a proportion knowing the other three.

If the relationship between the magnitudes is direct, that is, when one magnitude increases, so does the other (or when one magnitude decreases, so does the other), the direct rule of three must be applied. To solve a direct rule of three, the following formula must be followed:

a ⇒ b

c ⇒ x

Being a, b and c the known numbers and x the unknown variable to be calculated you have:

[tex]x=\frac{c*b}{a}[/tex]

In this case, knowing that 1 square meter equals 1*10⁻⁶ square kilometers, the rule of three applies as follows: if 1 square meter equals 1.0 * 10-6 square kilometers, 63,800,000,000 square meters to how many square kilometers is it?

[tex]Area=\frac{63,800,000,000 square meters*1*10^{-6}square kilometers }{1square meter}[/tex]

Area= 63,800 square kilometres

63,800,000,000 square metres equals 63,800 square kilometres

Answer:

f(g(3) = 1

Step-by-step explanation:

f(g(3)

Step one: Plug in 3 for X

g(x)= 2x - 5  ->  g(3) = 2 * 3 - 5

Step two : Solve ( By Using PEMDAS)

g(3) = 6 -5

g(3) = 1

Answer:

Since the pendulum moves from side to side in 1 sec, the length of the arc covered by the pendulum in an oscillation will be the length travelled in 1 sec

From trigonometry, we know the relation:

Θ(in radians) = l / r (where r is the length of the pendulum and l is the length of arc travelled)

But first, we need to convert 20 degrees to radians

20 degrees = π/9 radians

r = 7 feet

Now, plugging these values in the equation:

π / 9 = l / 7

l = 7π / 9 feet

l = 2.44 feet (approx)

Step-by-step explanation:

We humans are social beings; we share mirror neurons that allow us to match each other’s emotions unconsciously and immediately. We leak emotions to each other. We anticipate and mirror each other’s movements when we’re in sympathy or agreement with one another—when we’re on the same side. And we can mirror each other’s brain activity when we’re engaged in storytelling and listening – both halves of the communication conundrum.

This view of the human state is directly contrary to the way most people think about communications. The old model has a sender, a message, a receiver, feedback and noise. It’s far too mechanistic and simple to describe adequately what’s really going on. It leaves out the communal nature of communications.

Answer:

It is

Step-by-step explanation:

If a is positive and b is greater than 1 , then it is exponential growth. If a is positive and b is less than 1 but greater than 0 , then it is exponential decay.

Answer:

77% decrease

Step-by-step explanation:

Answer:

The x intercept is -9

Step-by-step explanation:

−2x+12y=18

To find the x intercept, let y=0

-2x + 12(0) = 18

-2x = 18

Divide each side by -2

-2x/-2 = 18/-2

x = -9

The x intercept is -9

Answer:

x-intercept of the given line is, (-9, 0)

Step-by-step explanation:

Substitute y = 0 and solve for x:

⇒-2x = 18

Divide both sides by -2 we get;

x = -9

Therefore, the x-intercept of the line is, (-9, 0)

Answer:

Every time Jill loses a match in a video game, she loses 4 points. She loses 5 matches, and sits at -20 points

Step-by-step explanation:

Answer:

Amount of space in a 3 dimensional object

Figure1: 36.5625ft^3

Figure2: .015625ft^3

Figure one is 2340 times larger than the second figure

Step-by-step explanation:

Answer:

The second one

Step-by-step explanation:

Y=11/4x+3/2

Answer:

Can you send me a picture or reformat this, It is unintelligible

a) The ratio of the median weekly earnings of the holder of a high school diploma only to the median weekly earnings of the holder of a bachelor's degree is 3:5.

b) The ratio of the area of the red rectangle to the area of the blue rectangle in graph A is 3:5.

c) The ratio of the area of the red square to the area of the blue square in graph B is 9:25.

d) The ratio of the volume of the red cube to the volume of the blue cube in graph C is 27:125.

e) The most misleading graph is graph C.

In Mathematics and Geometry, a scale factor can be calculated or determined through the division of the dimension of the image (new figure) by the dimension of the original figure (pre-image).

Part a.

The ratio of the median weekly earnings of a high school diploma only to the median weekly earnings of a bachelor's degree is given by;

Median ratio = 750/1250

Median ratio = 3:5.

Part b.

The ratio of the area of the rectangles is given by:

Ratio of rectangle areas = (3 × 1)/(5 × 1)

Ratio of rectangle areas = 3:5.

Part c.

The ratio of the area of the squares is given by;

Ratio of square areas = (3 × 1)²/(5 × 1)²

Ratio of square areas = 9:25.

Part d.

The ratio of the volume of the cubes is given by:

Ratio of cube volumes = (3 × 1)³/(5 × 1)³

Ratio of cube volumes = 27:125.

Part e.

The most misleading graph is graph C because the distribution of depth, values, and shapes differ.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

Y = 2(x - 5/4)^2 + 71/8

Answer:

A. There is a pivot position in each row of the coefficient matrix. The augmented matrix will have columns and will not have a row of the form ​, so the system is consistent.

Step-by-step explanation:

Based on Godel's second incompleteness theorem, a system is considered consistent only when the far-right column of the augmented matrix is not a pivot column.

However, given that every column of the coefficient matrix is a pivot column, then there are no top coefficients in the far-right column of the augmented matrix.

Hence, there is a pivot position in each row of the coefficient matrix. The augmented matrix will have columns and will not have a row of the form ​, so the system is consistent.

Answer:

  -1

Step-by-step explanation:

The slope is given by ...

  (y2 -y1)/(x2 -x1)

We want this equal to A, so we have ...

  (-3 -A)/(2 -0) = A

  -3-A = 2A . . . . . multiply by 2

  -3 = 3A . . . . . . . add A

  A = -1 . . . . . . . . . divide by 3

The value of A is -1.

Answer:

<A= right

<B= acute

<C= obtuse

<D= acute

Step-by-step explanation: