"John is 3 years older than Mary. Five years ago he was four times as old as Mary was then. How old is John?"

Answer:

$105 per hour

Step-by-step explanation:

$648.50 - $71 = $577.50

$577.50 / 5.5 = $105 per hour

105 x 5.5 = 575.50

+ 71.00

648.50

The per hour charge of the technician is given as $15.

A ratio is the relation between two numbers as a / b. A proportion is the equality of two ratios as a / b = c / d.

Ratio and proportion can be applied to solve Mathematical problems dealing with unit values of the quantities.

The given problem can be solved by ratio method as follows,

The remaining cost charged by the technician is $648.50 - $71 = $577.50

Now, the per hour charge is remaining cost divided by total number of hours as given below,

577.50/5.5

= 57750/550

= 15

Hence, the cost of labor per hour is given as $15.

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Answer:

4

Step-by-step explanation:

f(-3) simply means finding -3 for on the x axis and location its y coordinate. Hope it helps!

Answer:

[tex]\frac{1331x-6\times \:121^x}{5\times \:121^x}[/tex]

Step-by-step explanation:

[tex]\frac{11^2x\times \:11^1-6\times \:121^x}{5\times \:121^x}[/tex]

[tex]\mathrm{Apply\:exponent\:rule}:\quad \:a^b\times \:a^c=a^{b+c}[/tex]

[tex]11^2\times \:11^1=11^{2+1}[/tex]

[tex]=\frac{11^{2+1}x-6\times \:121^x}{5\times \:121^x}[/tex]

[tex]\mathrm{Add\:the\:numbers:}\:2+1=3[/tex]

[tex]=\frac{11^3x-6\times \:121^x}{5\times \:121^x}[/tex]

[tex]11^3=1331[/tex]

[tex]=\frac{1331x-6\times \:121^x}{5\times \:121^x}[/tex]

[RevyBreeze]

Answer:

1

Step-by-step explanation:

[tex] \dfrac{11^{2x} \times 11^1 - 6 \times 121^x}{5 \times 121^x} = [/tex]

​[tex] = \dfrac{11 \times 11^{2x} - 6 \times 11^{2x}}{5 \times 11^{2x}} [/tex]

​[tex] = \dfrac{5 \times 11^{2x}}{5 \times 11^{2x}} [/tex]

​[tex] = 1 [/tex]

Answer:

4

Step-by-step explanation:

Answer:

1.The total cost is $520.47

2New Blance is $3,054.53

A) 80

B)-60

C) 2

D) -54

Step-by-step explanation:

Answer:

132cm2

Step-by-step explanation:

1. Split the figure into a trapezoid and a rectangle.

2. Find the area of the trapezoid, which is 104cm2.

3. Find the area of the rectangle, which is 28cm2.

4. Add the areas to get 132cm2.

Answer:

Step-by-step explanation:

The expression (1+0.0325)^t represents amount in account after t years for 1 dollar. So multiplying the expression by 500 which is the initial deposit amount means it represents the amount of money in the account after t years.

Answer:

C D F

Step-by-step explanation:

Taking -40/2, we know our answer must be -20.

Testing each answer choice proves this.

A= 40*1/2, which is equal to 40/2, which is 20.

B= -40*-1/2, again, equaling 20.

C= 40/-2. Since one of our terms is negative, this one is -20.

D= 40*-1/2, again, -20.

E= -1/40*2. This would equal -2/40, using fraction multiplication.

F= -40*1/2, Which is the exact same thing the original question asks.

Thus, our final answer is C, D, and F.

Answer:

Please refer to the image

Step-by-step explanation:

Answer:

9=n-3

Step-by-step explanation:

Answer:

90 I think

Sorry if its wrong!

The equation of the line passing through the points (–3, 11) and (1, –3) is 7x +2y = 1. Then the correct option is B.

A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.

The line JK passes through points J(–3, 11) and K(1, –3).

We know that the equation of a line passing through two points is given as

[tex]\rm (y - y_1) = \dfrac{y_2-y_1}{x_2-x_1} (x - x_1)[/tex]

Then we have

[tex]\rm (y - 11) = \dfrac{-3-11}{1 + 3} (x + 3)\\\\\\(y - 11) = \dfrac{-14}{4} (x +3)\\\\\\(y - 11) = \dfrac{-7}{2}(x +3)\\\\\\2y - 22 \ = -7x -21\\\\\\7x + 2y \ = 1[/tex]

The equation of the line passing through the points (–3, 11) and (1, –3) is 7x +2y = 1. Then the correct option is B.

More about the linear system link is given below.

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Answer:

7.1

Step-by-step explanation:

Use SOH-CAH-TOA

With repsect to the angle, the adjacent and the hypotenuse was given. This calls for cosine:

cos(27) = 6.3/x

x = 6.3/cos(27)

x = 7.1

Answer: 7.07

Step-by-step explanation:

[tex]\cos = \frac{opposite}{hypotenuse}[/tex]

[tex]\begin{aligned}\cos 27^{\circ} &=\frac{K L}{K M} \\K M &=\frac{K L}{\cos 27^{\circ}} \\K M &=\frac{6.3}{\cos 27^{\circ}} \\K M &=7.07\end{aligned}[/tex]

The amount of paint required by Madeline will be 0.8325 gallons

Given that

[tex]1cm=1.5ft[/tex]

We will first find the area of the wall

Area of the wall = Area of trapezoidal shape+ Area of triangular shape

Area of trapezoid = [tex]\dfrac{a+b}{2} \times h[/tex]

a= 4cm

b=14cm

h=10cm

putting this values

[tex]A=\dfrac{4+14}{2} \times 10[/tex]

[tex]A=90cm^{2}[/tex]

Area of triangular shape=  [tex]\dfrac{1}{2} \times width\times height[/tex]

width=14cm

height=8cm

putting the values

[tex]A=\dfrac{1}{2} \times 14\times 8=58cm^{2}[/tex]

[tex]Total area of the wall= 90+58=148cm^{2}[/tex]

since we have

[tex]1cm=1.5ft[/tex]

[tex]148cm^{2} = 148\times (1.5)^{2} =333 ft^{2}[/tex]

Now

[tex]1gallon = 400ft^{2}[/tex]

so for  [tex]333 ft^{2}[/tex]  amount of paint in gallons required will be

[tex]1ft^{2} =\dfrac{1}{400} gallons[/tex]

[tex]333ft^{2} =\dfrac{333}{400} gallons=0.8325gallons[/tex]

Thus the amount of paint required by Madeline will be 0.8325 gallons

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Answer:

9

Step-by-step explanation:

[tex] \sqrt{3 {}^{4} } =( 3 {}^{4} ) {}^{ \frac{1}{2} } = {3}^{2} = 9[/tex]

Answer:

200 because i trust a calculator

Step-by-step explanation:

The point (2,50) means that the Cost of renting a generator for 2 hours is $50..

Answer:

Its A :))

Step-by-step explanation:

Answer:

Option A

Step-by-step explanation:

Since its an exponential of a decimal number, as x goes on increasing the graph will start going to y=0.

You can plot the graph on any online graphing tool and see for yourself :)

Answer:

Option A

EXPLANATION

[tex]{{{\colorbox{teal}{{\huge \boxed{\bold{\color{red}{T}\color{bluee}{H}\color{pink}{A}\color{yellow}{NKS}\:\color{brown}{P}\color{purple}{o}\color{black}{i}\color{green}{n}\color{orange}{t}\color{gray}{s}}}}}}}}[/tex]

Answer:  49.0 square meters

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

Explanation:

We'll first need to find the radius of the rug using the circumference.

C = 2*pi*r

r = C/(2pi)

r = (24.8)/(2*3.14)

r = 3.949045 which is approximate.

Now we can find the area

A = pi*r^2

A = 3.14*(3.949045)^2

A = 48.968163 this is also approximate

Rounding to the nearest tenth gets to 49.0

Answer:

0.5 ft

Step-by-step explanation:

Base = 8 ft and Height = 6 ft

Area of Triangle = 0.5*b*h

Area of Triangle = 0.5*8*6 = 24 sq.ft

To increase the Area by 2 sq.ft  so the New Area will be 26 sq.ft

New Area = 0.5*b*(New Height)

26=0.5*8*(New Height)

New Height = 6.5 ft

The Increase in Height = New Height - Old Height =  6.5 - 6 = 0.5 ft

The increase in the height of the triangle which has a base of 8 feet and a height of 6 feet, to increase its area by 2 square feet is 0.5 feet.

The area of a triangle is half the product of its base and its height, that is,

Area = (1/2)*base*height.

We have been asked to find the increase in the height of a triangle with base(b) = 8 feet and height(h) = 6 feet, such that its area increases by 2 square feet.

First, we find the initial area of the triangle,

Area = (1/2)*b*h (1/2)*8*6 = 24 square feet.

New area = initial area + 2 square feet = 24 + 2 = 26 square feet

Let the increase in height be x feet,

∴ New height(h1) = 6+x feet

∴ New area = (1/2)*8*(6+x),

But we know that the new area is 26 square feet, so we equate them to get:

(1/2)*8*(6+x) = 26

or, 4(6+x) = 26

or, 24 + 4x = 26

or, 4x = 26 - 24 = 2

or, x = 2/4 = 0.5

∴ The increase in the height of the triangle which has a base of 8 feet and a height of 6 feet, to increase its area by 2 square feet is 0.5 feet.

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- - - - - - - - - - - - - - - - - -

Let's try to divide 1,772 and see how much math we need to do...

1,772 / 90 = 19.6888888889

Well, clearly we need more than 1,772!

- - - - - - - - - - - - - - - - - -

Now, play around with adding numbers.

(I'm gonna skip all the experimenting, here's the closest # available for easy division!)

⇣

1,800 / 90 = 20

1,800

hope this helps

Answer:

B

Step-by-step explanation:

Line B best fits the data because some of the points fall on line B.

Hope this helps!