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The length of the diagonal of the Triangle is 14.86 units

What is Diagonal?

When two polygonal vertices are not on the same edge, a diagonal is a line segment connecting them. Any sloping line is known as a diagonal informally.

Given,

Area of Rectangle = 110square units

Length = 11units

Breadth = ?

Area of Rectangle = length x breadth

Breadth = Area of Rectangle / length

Breadth = 110 / 11

Breadth = 10units

Length of diagonal (Pythagoras Theorem)

H^2 = P^2 + B^2

H^2 = (11)^2 + (10)^2

H^2 = 121 + 100

H^2 = 221

H = [tex]\sqrt{221}[/tex]

H = 14.86 units

Hence, The length of its diagonal is 14.86 units

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a) (2, -2)

answer: the ordered pair is not a solution of the given system

b) ( -1, 5)

answer: the ordered pair is a solution of the given system

Answer:

2[tex]\sqrt{3}[/tex]

Step-by-step explanation:

[tex]\frac{6}{\sqrt{3} }[/tex]  They do not want a radical in the denominator.  So you need to multiple the numerators and the denominator by [tex]\sqrt{3}[/tex]

[tex]\frac{6}{\sqrt{3} }[/tex]  x  [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex]  = [tex]\frac{6\sqrt{3} }{3}[/tex] = 2[tex]\sqrt{3}[/tex]

[tex] \frac{6}{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } = \frac{6 \sqrt{3} }{3} = 2 \sqrt{3} [/tex]

hope it will work

The slope of the line represented by the equation; 4/5x - 3 is; 4/5.

It follows from the task content that the slope of the line represented by the equation; (4/5)x - 3 is to be determined.

Recall, from line geometry and equation of lines;

The slope-intercept form of the equation of a line, y is given as; y = mx + c.

Where, m is the slope and c is the y-intercept.

Therefore, by comparison of the equation defined as; 4/5x - 3; it follows that the slope of the equation is; 4/5.

Ultimately, the required slope is; 4/5.

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Answer: 4 gallons

Step-by-step explanation:

The boat can travel 228 miles on 19 gallons of gasoline. We can divide 228 by 19 to find out how many miles the boat can travel on 1 gallon of gasoline, which is 12. For the boat to go 48 miles, we can divide 48 by 12 to get the answer, which is 4. The boat can travel 48 miles with 4 gallons of gasoline.

1. There will be $102, 826 in the account in 25 years.

2. The total amount of money you will put into the account is $60, 000

3. The total interest that you would have earned is $42,826.

For us to calculate the future value of the account in 25 years, we shoud use the formula; FV = P x (((1 + r)^nt - 1) / r)

When we insert the values, it will be

FV = 200 x (((1 + 0.04/12)^(12 x 25) - 1) / (0.04/12))

= 102, 825. 9. If we round this up, we should get

$102, 826

For us to calculate the total amount of money you put into the account, we should us the formula;

Total Deposits = Monthly Deposit x Number of Months

If we insert the values it wil be

200 x (25 x 12)

60,000

Lasty, if we are to find the total interest earned:

Total Interest = Future Value - Total Deposits

$102, 826 - 60,000

=  $42,826

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Answer:

A: A unique triangle

B: A unique triangle

C: More than a triangle

The restaurant salesman will pay a commission of $1,052

Commission is the amount of money that is paid to a worker when a work is completed.

The commission rate of the total sales is 4%

= 4/100

= 0.04

The total sales for the week is $26,300

The commission that will be paid can be calculated as follows

= 26,300 × 0.04

= 1.052

Hence the amount of commission that will be paid is $1,052

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Take into account that the slope of a line is given by the following formula:

where (x1,y1) and (x2,y2) are two points on the line.

In this case:

(x1,y1) = (p,3)

(x2,y2) = (6,p)

By replacing the previous values into the formula for m, we get:

Now, by making m = 2 and solving for p, we obtain:

Hence, the value of p is p = 5

Given that April has 30 days, Luke used, on average, 20.05 kilowatt-hours of electricity per day during April.

The average is the mean value obtained by dividing the total value of a data set by the number of items.

In this situation, we can divide the total electric bill for April by 30 to obtain the average daily charge.

In addition, we can divide the average charge per day by the cost per kilowatt-hour to obtain the number of kilowatt-hours used per day.

The total electric bill for April = $84.21

The charge per kilowatt-hour (kWh) = $0.14

The number of days in April = 30

The bill per day = $2.807 ($84.21/30)

The kilowatt-hours per day = 20.05 kWh ($2.807/$0.14)

Thus, Luke used an average of 20.05 kilowatt-hours per day in April.

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Answer:

[tex]\boxed{\sf{t=24}}[/tex]

Step-by-step explanation:

Find the value of t, to isolate on one side of the equation.

t-18=6

First, add by 18 from both sides.

[tex]\rightarrow \sf{t-18+18=6+18}[/tex]

Solve.

Add the numbers from left to right.

6+18=24

[tex]\Rightarrow \boxed{\sf{t=24}}[/tex]

Therefore, the final answer is t=24.

The answer should have a positive sign.

I hope this helps, let me know if you have any questions.

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{t - 18 = 6}[/tex]

[tex]\large\text{ADD \boxed{\textsf{18}} to BOTH SIDES:}[/tex]

[tex]\mathsf{t - 18 + 18 = 6 + 18}[/tex]

[tex]\large\text{CANCEL out: \boxed{\mathsf{-18 + 18}} because it gives you 0.}[/tex]

[tex]\large\text{KEEP: \boxed{\mathsf{6 + 18}} because it gives you the answer of the t-value.}[/tex]

[tex]\large\text{New equation: }\mathsf{t = 6 + 18}[/tex]

[tex]\mathsf{t = 6 + 18}[/tex]

[tex]\mathsf{t = 24}[/tex]

[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{t = 24}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:B

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

x=172°

Step-by-step explanation:

5x-11=3x-5

2x-11=5

2x=16

x=8

180-8=172

Answer:

Step-by-step explanation:

Find the number that makes the ratio equivalent to 3:5

6:10

9:15

12:20

The unknown value from the given linear expression is 1/4

Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5.

When an equation is given in this format, finding both intercepts is rather simple (x and y).

Given the equation below;

6 = 12k * 2

6 = 24k

Divide both sides by 24

24k = 6

k = 6/24

k = 1/4

Hence the value of k from the given expression is 1/4

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The equation of the line is y = x - 8 which passes through the point  (13,5) with slope 1.

We have to determine the equation of a line that passes through the point (13,5) with slope 1.

The slope of a line is defined as the angle of the line. It is denoted by m

Slope m = (y₂ - y₁)/(x₂ -x₁ )

Let the required line would be as

⇒ y - y₁ = m (x - x₁ )

The required line passes through the point (13, 5)

Here x₁ = 13 and y₁ = 5 and m = 1

Substituting these inputs into the above equation obtains the line equation.

⇒ y - 5 = (1)(x - 13)

⇒ y - 5 = (x - 13)

⇒ y = x - 13 + 5

⇒ y = x - 8

Thus, the equation of the line is y = x - 8 which passes through the point (13,5) with slope 1.

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Paige's profit for the three-month period given the information provided in the question is $569.84.

Profit is the difference between total revenue and total cost. Revenue is the product of total units sold and the price per output.

Profit = revenue - cost

Revenue from selling the $15 bracelet = total bracelets sold for the 3 months x price of the bracelet

(8 + 11 + 22) x 15

41 x $15 = $615

Revenue from selling the $20 bracelet =  total bracelets sold for the 3 months x price of the bracelet

(7 + 6 + 14) x $20

27 x $20 = $540

Total revenue = $615 + $540 = $1,155

Total cost =  $292.58  x 2  = $585.16

Profit = $1,155 - $585.16 = $569.84

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Answer: y = -4 + x/2

Step-by-step explanation:

Answer:

I think it's 4 on the left and 5 on the right side

Step-by-step explanation:

4*4*4=64

and

5*5*5=125

In linear equation, If the person doesn't attend any events, n = 0, and the price stays at 10, therefore f(n) = 10 + 2n.

What in mathematics is a linear equation?

To describe the cost of attending n events, create an equation using function notation.

A 10 dollar entrance fee is required each time, and a further 2 dollars must be paid for each unique exhibit that a visitor chooses to visit.

The function, which would depend on n events, is

If the person doesn't attend any events, n = 0, and the price stays at 10, therefore f(n) = 10 + 2n.

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Answer:x-intercepts (5,0)

y-intercepts (0,-5)

Step-by-step explanation: To find the x-intercept substitute in 0 for y and solve for x. to find the y-intercept subsitute 0 for x and solve for y

The pre-tax subtotal was $171.00.

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that:

After-tax total = $1,656.99

Tax rate in the area = 8.396%

The pre-tax price would be 100% and this tax rate is an addition.

Total percent = (100+8.396)% = 108.3%

Consider x be the pre-tax amount.

The total bill=  (after-tax total) = (pre-tax subtotal) + 8.3% · (pre-tax subtotal)

 (after-tax total) = (pre-tax subtotal) 108.3

Divide by the coefficient on the right;

 (pre-tax subtotal) = (after-tax total)/108.3

= $1,656.99/108.3

= $171.00

Therefore, The pre-tax subtotal was $171.00.

The pre-tax amount was $130.

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Answer:

7.3units

Step-by-step explanation:

[tex] \sqrt{(x2 - x1) {}^{2} + (y2 -y1) {}^{2} } [/tex]

[tex] \sqrt{ (- 1 - 6) { \\ }^{2} + (14 - 16) {}^{2} } [/tex]

[tex] = 7.3[/tex]

The amount of water left in the bathroom is 0.93 gallons

From the question, the given parameters are:

The amount of water left is the difference between the total amount of water in the bathroom  and the amount of eater drained out

This is represenetd as

Amount left = Total amount of water in the bathroom - Amount of eater drained out

Substitute the known values in the above equation

Amount left = 7.2 - 6.27

Evaluate

Amount left = 0.93

Hence, the amount left is 0.93 gallons

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The required measure of the volume of water left in the bathtub is 0.93 gallons.

As per the given data, There were 7.2 gallons of water in Sandra's bathtub. Then 6.27 gallons drained out. How much water is left in the bathtub is to be determined.

Here,
According to the question, the water left after the 6.27 gallons of draining out can be evaluated by the arithmetic subtraction of the initial volume to the volume that drained out, that is,
The volume of water left in the tub  = 7.2 - 6.27 = 0.93.

Thus, the required measure of the volume of water left in the bathtub is 0.93 gallons.

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The solution for the system of equations of three variables is:

x = 4

y = -1

z = -3

Or (4, -1, -3) written as a point.

Here we have a system of equations on 3 variables, the system is:

3x + 2y + z = 7

5x + 5y +4z = 3

3x + 2y + 3z = 1

Notice that the "x" and "y" coefficients in the first and last equation are the same ones, so we can take the difference between these to get:

(3x + 2y + 3z ) - (3x + 2y + z ) = 1 - 7

2z = -6

z = -6/2 = -3

So the value of z is -3.

Replacing that in the first and second equation we get:

3x + 2y - 3 = 7

5x + 5y + 4*(-3) = 3

Now we can simplify these:

3x + 2y = 10

5x + 5y = 15

We can divide the second one by 5 to get:

(5x + 5y)/5 = 15/5

x + y = 3

Isolating x, we get:

x = 3 - y

Now we replace that in the other equation:

3*(3 - y) + 2y = 10

9 - y = 10

9 - 10 = y

-1 = y

Now we know the value of y, finally with:

x = 3 - y

We can get the value of x:

x = 3 - (-1) = 4

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The solution to the simultaneous equation is y = 5.5 and x = 1.5

Simultaneous equations are the types of equations in mathematics that is made up of two equations where the equations would have to share variables.

we have

y = 3x + 1 - - - - 1

x + y = 7 - - - - 2

we have to put the value of y in equation 1 into equation 2

we would have

x + 3x + 1 = 7

4x + 1 = 7

4x = 7 - 1

4x = 6

x = 6 / 4

x = 1.5

put the value of x in equation 2 to get y

1. 5 + y = 7

y = 7 - 1.5

y = 5.5

Therefore the values of y is 5.5 while the value of x is 1.5

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The required solution of the given simultaneous equation is x = 1.5 and y = 5.5.

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

Here,
y = 3x + 1    _ _ _ _ _ _ (1)
x + y = 7      _ _ _ _ _ _ (2)
From equation 2
y = 7  - x substitute this in equation 1
7 - x = 3x + 1
4x = 6
x = 6 / 4
x = 3 / 2
Now put this x in equation 2
3/2 + y = 7
y = 7 - 3/2
y = 11 / 2

Thus, the required solution of the given simultaneous equation is x = 1.5 and y = 5.5.

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The total distance of the trip is 50 miles

From the question, we have the following parameters

Distance completed = 40%

Distance travelled = 20 miles

Represent the total distance with x

So, we have the following equation

Distance travelled = Distance completed  *Total distance

This gives

Distance travelled = Distance completed  * x

So, we have

20 miles = 40% * x

Divide both sides by 40%

x = 50 miles

Hence. the length of the trip is 50 miles

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