Cambridge has a job mowing lawns. He mowed 5 lawns last week and earned $82.50. The table shows his earnings for the week. Which coordinate pair represents the unit rate for this situation? A) (0, 0) B) (1, 16.5) C) (3, 49.5) D) (5, 82.5)

QUESTION POSTED AT 15/01/2020 - 03:10 AM

Related questions

The image of a point after a –90° rotation about the origin is (–4, 7). What are the coordinates of the preimage?

The point (-4, 7) is in the 2nd quadrant. The coordinate of the preimage of a -90 degrees rotation that resulted to point (-4, 7) will be in the third quadrant. (i.e. both x and y is negative). Hence, answer is (-7, -4).

ANSWERED AT 29/01/2020 - 05:41 PM


QUESTION POSTED AT 29/01/2020 - 05:41 PM

If y varies directly as x, and y is 12 when x is 1.2, what is the constant of variation for this relation? 1 10 10.8 14.4

Answer:

constant of variation is 10.

Second option is correct.

Step-by-step explanation:

We have been given that y varies directly as x. Thus, we have

y = kx.............(1)

k is the constant of variation

Now, it has been given that when y is 12 then x is 1.2.

Hence, substituting x = 1.2 and y = 12 in equation (1)

12 = 1.2 k

Divide both sides by 1.2

k = 12/1.2

k = 10

Therefore, constant of variation is 10.

Second option is correct.

ANSWERED AT 29/01/2020 - 05:40 PM


QUESTION POSTED AT 29/01/2020 - 05:40 PM

For every 10 fish you have, you need 5 gall how many gallons pf water do u have for 1 fish

10/5 = 1/x
cross multiply
10x = 5
x = 5/10
x = 1/2...u need 1/2 gallon per fish

ANSWERED AT 29/01/2020 - 05:40 PM


QUESTION POSTED AT 29/01/2020 - 05:40 PM

Which statement regarding the function y=cos(x) is true? A. The cosine function is odd, so it is symmetrical across the origin. B. cos(x)=cos(-x) C. -cos(x)=cos(x D. Since the cosine function is eevn, reflection across the x-axis does not change the graph.

Hints:
use the calculator to check if any of the options are correct.  Try x=pi/6 (or 30 degrees).

Odd functions satisfy the property
f(x)=-f(-x)
For this reason, odd functions are symmetrical about the origin.
Examples of odd functions: sin(x), x^3, x+3x^5, tan(x), sin(x)*cos(x), x*sin(x)
(use your calculator to check that the above are true).

Even functions satisfy the property
f(x)=f(-x)
Even functions are symmetrical about the y-axis.
Examples: x^2, cos(x), x^4+2, |x|, sin^2(x), x^2*cos(x)

There are functions that are neither odd nor even, 
examples:
x^2+4x+3, sin(x)+cos(x)

ANSWERED AT 29/01/2020 - 05:38 PM


QUESTION POSTED AT 29/01/2020 - 05:38 PM

The domain of the following relation R {(6, −2), (1, 2), (−3, −4), (−3, 2)} is

The domain is all the x values...so he domain is { 6,1,-3}

ANSWERED AT 29/01/2020 - 05:38 PM


QUESTION POSTED AT 29/01/2020 - 05:38 PM

If (f + g)(x) = 3x2 + 2x – 1 and g(x) = 2x – 2, what is f(x)? 3x2 + 1 3x2 – 1 3x2 + 4 3x2 – 4 x2 – 2

(f + g)(x) = 3x^2 + 2x – 1
g(x) = 2x – 2
f(x) = ? ; 3x^2 + 1

Check by Substituting:
3x^2 + 1 + 2x - 2

Simplify:
3x^2 + 2x - 1

ANSWERED AT 29/01/2020 - 05:38 PM


QUESTION POSTED AT 29/01/2020 - 05:38 PM

It takes Joaquin 1/5 hour to hike 1/4 mile. What is Joaquin's unit rate, in miles per hour?

(1/5) / (1/4) = x/1
cross multiply
1/4x = 1/5
x = 1/5 * 4
x = 4/5....he hikes 4/5 of a mile per hr

ANSWERED AT 29/01/2020 - 05:38 PM


QUESTION POSTED AT 29/01/2020 - 05:38 PM

A given line has the equation 10x 2y -2.What is the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0, 12)?)x 12O Submitted

10x + 2y = -2
2y = -10x - 2
y = (-10/2)x - 2/2
y = -5x - 1...the slope here is -5...a parallel line will have the same slope.

y = mx + b
slope(m) = -5
(0,12)...x = 0 and y = 12
now we sub...we r looking for b, the y intercept
12 = -5(0) + b
12 = b

so ur parallel line is : y = -5x + 12

ANSWERED AT 29/01/2020 - 05:36 PM


QUESTION POSTED AT 29/01/2020 - 05:36 PM

A given line has the equation 10x -2.2y What is the equation, in slope-intercept form, of the line that is parallel to given line passes through the point (0, 12)?the and )x 12submitted

10x + 2y = -2

2y = -10x - 2

y = -(10/2)x - 2/2

y = -5x  - 1    y = mx + c,   slope m = -5.

If it is parallel, then the slope of the second line ought to be -5 as well.

So you should fill -5 in the bracket.

ANSWERED AT 29/01/2020 - 05:36 PM


QUESTION POSTED AT 29/01/2020 - 05:36 PM

Hugh bought some magazines that cost $3.95 each and some books that cost $8.95 each. He spent a total of $47.65. Let m represent the number of magazines and b represent the number of books. Which equation models the situation?

Answer:

(3.95m) + (8.95b) = 47.65

Step-by-step explanation:

Hugh bought some magazines that cost = $3.95 each

the cost of each books = $8.95

He spent a total on purchase of books and magazines = $47.65

Let m represent the number of magazines and b represent the number of books.

Now the equation will be

(3.95m) + (8.95b) = 47.65

ANSWERED AT 29/01/2020 - 05:36 PM


QUESTION POSTED AT 29/01/2020 - 05:36 PM

Solve the following system of equations. Express your answer as an ordered pair in the format (a,b), with no spaces between the numbers or symbols. 2x+7y=4 -4x -3y=14

2x + 7y = 4.....multiply by 2
-4x - 3y = 14
------------------
4x + 14y = 8 (result of multiplying by 2)
-4x - 3y = 14
----------------add
11y = 22
y = 2

2x + 7y = 4
2x + 7(2) = 4
2x + 14 = 4
2x = 4 - 14
2x = - 10
x = -5

solution is : (-5,2)

ANSWERED AT 29/01/2020 - 05:36 PM


QUESTION POSTED AT 29/01/2020 - 05:36 PM

Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Check all that apply. a. 2.3p – 10.1 = 6.4p – 4 b. 2.3p – 10.1 = 6.49p – 4 c. 230p – 1010 = 650p – 400 – p d. 23p – 101 = 65p – 40 – p e. 2.3p – 14.1 = 6.4p – 4

Start with given equation  2.3p - 10.1 = 6.5p - 4 - 0.01p .

1. In the right side you have three terms, two of them include p, so you can rewrite right side as

 6.5p - 4 - 0.01p=(6.5p - 0.01p)-4=p(6.5-0.01)-4=6.49p-4.

Then the whole equation is

 2.3p - 10.1 = 6.49p - 4 as in option B. This means that option B is true and option A is false (because left sides are the same, but right sides differ).

2. Now multiply the equation  2.3p - 10.1 = 6.5p - 4 - 0.01p by 100:

 230p - 1010 = 650p - 400 - p, this equation is exactly as equation in option C. This gives you that option C is true.

3. Now multiply the equation  2.3p - 10.1 = 6.5p - 4 - 0.01p by 10:

 23p - 101 = 65p - 40 - 0.1p, this equation differs from the equation in option D (because left sides are the same, but right sides differ). This gives you that option D is false.

4. At last, subtract 4 from the equation  2.3p - 10.1 = 6.5p - 4 - 0.01p :

 2.3p - 14.1 = 6.5p - 8 - 0.01p,\\ 2.3p - 14.1 = 6.49p - 8,

this equation differs from the equation in option E (because left sides are the same, but right sides differ). This gives you that option E is false.

Answer: correct choices are B and C.

ANSWERED AT 29/01/2020 - 05:36 PM


QUESTION POSTED AT 29/01/2020 - 05:36 PM

Which of the following is an example of perpendicular lines? I'm thinking it's B, but not sure

Answer:

Second figure is an example of perpendicular lines.

Step-by-step explanation:

The perpendicular lines are those that forms 90^{\circ} at the base of the vertical line.

The straight lines denotes the  90^{\circ} angle

The first figure is not correct both are intersecting tilted lines.

The second figure is correct since they form right angle that is 90^{\circ} angle.

The third figure is again tilted lines hence, not correct.

The fourth figure is again tilted lines hence, not correct.

therefore, second figure is correct.

ANSWERED AT 29/01/2020 - 05:35 PM


QUESTION POSTED AT 29/01/2020 - 05:35 PM

What is the common ratio for the sequence 1, 4, 16, 64

Multiply the value by 4 for the next value.
1:4 ratio

ANSWERED AT 29/01/2020 - 05:34 PM


QUESTION POSTED AT 29/01/2020 - 05:34 PM

For what values of x is the rational expression below undefined? check all that apply x-4/3x^2-75 A.5 B.4 C.3 D.-3 E.-4 F.-5

Answer:

Rational expression is undefined for x = -5 and x=5

A and F are correct options.

Step-by-step explanation:

The ration function is \frac{x-4}{3x^2-75}

A rational function is undefined when the denominator is zero.

Hence, let us find the value where the expression is undefined by equating denominator equals zero.

3x^2-75=0\\\\3x^2=75\\\\x^2=25\\\\x=\pm5

Hence, the rational expression is undefined for x = -5 and x=5

Thus, A and F are correct options.

ANSWERED AT 29/01/2020 - 05:34 PM


QUESTION POSTED AT 29/01/2020 - 05:34 PM

A cylindrical container is packaged inside a prism-shaped box. The box has a volume of 96 cubic units. If the container has a diameter of 4 units and a height of 6 units, what is the volume of the empty space between the cylinder and the box? Round the answer to two decimal places.

Answer:

The volume of the empty space is 20.57 unit³.

Step-by-step explanation:

Given,

The volume of the box = 96 cubic units,

Also, the cylindrical container is packed inside the box.

We know that,

The volume of a cylinder is,

V=\pi (r)^2 h

Where r is the radius of cylinder,

h is its height,

Here, r = \frac{4}{2} = 2 unit   ( Radius = Diameter / 2 )

And, h = 6 units

Thus, the volume of the cylindrical container is,

V=\pi (2)^2(6)

=\frac{22}{7}\times 4\times 6 = \frac{528}{7}\text{ cubic unit}

Hence, the volume of the empty space between the cylinder and the box = Volume of the box - Volume of the container

= 96 - \frac{528}{7}

=\frac{672-528}{7}

=\frac{144}{7}=20.5714285714\approx 20.57\text{ cubic unit}

ANSWERED AT 29/01/2020 - 05:33 PM


QUESTION POSTED AT 29/01/2020 - 05:33 PM

What is the 1st term when 1 + 6x2 + 5x4 + 3x3 is arranged in descending order? 1 6x2 5x4 3x3

Answer:

the first term is 5x^4

Step-by-step explanation:

We have been given the polynomial 1+6x^2+5x^4+3x^3

Arrange this polynomial in descending order. In other words we arrange this polynomial having exponent from greatest to smallest.

Exponents from descending order is given by

4, 3, 2, 0

So, the polynomial when arranged in descending order is given by

5x^4+3x^3+6x^2+1

Therefore, the first term is 5x^4

ANSWERED AT 29/01/2020 - 05:33 PM


QUESTION POSTED AT 29/01/2020 - 05:33 PM

The coordinates on the coordinate grid is (-1,5) the point is reflected across the x-axis to obtain a new point . The coordinate of the reflected point is?

1,5 I think because the x is negative so it would become positive and the y would stay the same.

ANSWERED AT 29/01/2020 - 05:32 PM


QUESTION POSTED AT 29/01/2020 - 05:32 PM

Question 1 of 8Fill in the blank: Type your answer in the box and then click "submit."What is the value of y?114Answer:

The value of 'y' is 57.

ANSWERED AT 29/01/2020 - 05:32 PM


QUESTION POSTED AT 29/01/2020 - 05:32 PM

Find the zeros of the function. f(x)= 3x^3- 12x^2- 15x a. 0, 1, and -5 b. -1 and 5 c. 0, -1, and 5 d. 1 and -5

F(x) = 3x³ - 12x² - 15x

1) Factor Outside: 3x( x² - 4x - 5)

Factor Inside: 3x(x + 1)(x - 5)

2) Set Equal To 0:
3x = 0
x + 1 = 0
x - 5 = 0

3) Solve:
x = 0, -1, 5

ANSWERED AT 29/01/2020 - 05:31 PM


QUESTION POSTED AT 29/01/2020 - 05:31 PM

Evaluate 32 + (7 − 2) ⋅ 4 − 6 over 3.

Parenthesis statements are evaluated first such that 7-2 Is 5.
From left to right, multiplication and division are evaluated: 5×4=20 6/3 =2
Finally addition and subtraction equating finally to: 32 + 20 - 2 = 50

ANSWERED AT 29/01/2020 - 05:31 PM


QUESTION POSTED AT 29/01/2020 - 05:31 PM

What value of x makes this equation true? 6x/-4=6(-1/2) a) -2 b)2 c)3 d)-3

6x/-4 = 6(-1/2)
6x/-4 = - 3...multiply by -4
6x = -3 * -4
6x = 12
x = 2


ANSWERED AT 29/01/2020 - 05:30 PM


QUESTION POSTED AT 29/01/2020 - 05:30 PM

A square field has an area of 10 square miles. What is the approximate length, to the nearest thousandth, of one side of this field? A.) 2.5 miles B.) 3 miles C.) 3.162 miles D.) 3.612 miles

Area x² = 10

x = √10 ≈ 3.16227

x ≈ 3.162 mile to the nearest thousandth.    Option C.

ANSWERED AT 29/01/2020 - 05:30 PM


QUESTION POSTED AT 29/01/2020 - 05:30 PM

When a rate is simplified so that it has a denominator of 1 unit, it is called a(n)_________ rate

Unit rate is the only one that makes logic sense

ANSWERED AT 29/01/2020 - 05:29 PM


QUESTION POSTED AT 29/01/2020 - 05:29 PM

If g(x ) = 3x - 5, then g -1(x )=

G(x) = 3x - 5

let g(x) = y

y = 3x - 5

y + 5 = 3x

3x = y + 5

x = (y + 5)/3

From y = g(x),  x = g⁻¹(y) 

x = (y + 5)/3

 g⁻¹(y)  = (y + 5)/3

 g⁻¹(x)  = (x + 5)/3

ANSWERED AT 29/01/2020 - 05:29 PM


QUESTION POSTED AT 29/01/2020 - 05:29 PM