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Misha Larkins [42]

3 years ago

14

A custom rectangular tabletop has a length that is twice it’s width, and the tabletop measures 76 inches on its diagonal. What a

re the dimensions of the tabletop? What is it’s perimeter?

1 answer:

Sunny_sXe [5.5K]3 years ago

5 0

Answer:

<em>The dimensions of the tabletop: Length= 67.976... inches and Width= 33.988... inches and the perimeter will be 203.929... inches.</em>

Step-by-step explanation:

Suppose, the width of the rectangular tabletop is $x$ inch.

As the tabletop has a length that is twice it’s width, so the length will be: $2x$ inch.

The tabletop measures 76 inches on its diagonal.

<u>Formula for length of diagonal of rectangle</u>: $d=\sqrt{l^2+w^2}$

So, the equation will be..........

$76=\sqrt{(2x)^2+ x^2}\\ \\ 76=\sqrt{4x^2+x^2} \\ \\ 76=\sqrt{5x^2} \\ \\ 5x^2= 76^2= 5776\\ \\ x^2= \frac{5776}{5}=1155.2 \\ \\ x= \sqrt{1155.2} =33.988...$

Thus, the width of the tabletop is 33.988... inches and the length will be: (2×33.988...) = 67.976... inches.

The perimeter will be: 2(33.988...+ 67.976...) inches = 203.929... inches.

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2. Ashley had a summer lemonade stand where she sold small cups of lemonade for $1.25 and large

Drupady [299]

Answer:

$\boxed {\boxed {\sf 98 \ Small \ Cups}}\\\\\boxed {\boxed {\sf 57 \ Large \ Cups}}$

Step-by-step explanation:

Let's make a system of equations.

First, define the variables.

Let s= small cups and g= large cups

Next, make 2 equations. 1 for the money and 1 for the number of cups.

<u>Money</u>

A small cup costs 1.25 and a large cup costs 2.50. The total money made is 265.
1.25s+2.50g=265

<u>Number</u>

A total of 155 cups of lemonade were sold. The sum of small cups and large cups sold will equal 155.
s+g=155

Here is our system of equations:

$1.25s+2.50g=265 \\s+g=155$

Now, solve. Let's isolate a variable in the 2nd equation, so we can plug it in after.

Subtract g from both sides of the equation.
s+g=155
s+g-g=155-g
s=155-g

Now we know that s is equal to 155-g. We can substitute (155-g) in for s in the first equation.

$1.25s +2.50g=265$

$1.25(155-g)+2.50g=265$

Distribute the 1.25

1.25(155-g)= (1.25*155)+ (1.25*-g)= 193.75-1.25g

$193.75-1.25g+2.50g=265$

Work to isolate the variable. Subtract 193.75 from both sides of the equation and combine like terms on the left.

$193.75-1.25g+2.50g=265-193.75$ (Subtract 193.75)

$-1.25g+2.50g=265-193.75$

$1.25g=71.25$ (Combine like terms).

1.25 and g are being multiplied. The inverse of multiplication is division. Divide both sides by 1.25

$1.25g/1.25=71.25/1.25\\g=71.25/1.25\\g=57$

Now we know that 57 large cups were sold. Plug 57 back into the original second equation to find the small cups.

$s+g=155$

$s+57=155$

Subtract 57 from both sides of the equation to isolate the variable, s.

$s+57-57=155-57\\s=155-57\\s=98$

Ashley sold 57 large cups and 98 small cups.

5 0

3 years ago

Read 2 more answers

How many solutions are there to the system of equations graphed below if the lines are parallel

mash [69]

If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line<span>. If a system has no solution, it is said to be </span>inconsistent<span> . The graphs of the </span>lines<span> do not intersect, so the graphs </span>are parallel<span> and there is no solution.

Sorry, this is a general answer. I could not view the graph below...</span>

3 0

3 years ago

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Lines x and y are parallel and are cut by the transversal b. If the measure of angle 1 is 57°, what is the measure of angle 6? E

lana [24]

Answer:

$\angle6=123$

Step-by-step explanation:

Given

Lines x and y

Transversal b

$\angle 1 = 57$

Required

Find $\angle 6$

From the attachment, $\angle1$ and $\angle7$ are vertically opposite.

This means that

$\angle 1 =\angle 7 = 57$

Similarly

$\angle 7$ and $\angle 6$ are supplementary angles

So:

$\angle7 + \angle6=180$

Make $\angle6$ the subject

$\angle6=180-\angle7$

$\angle6=180-57$

$\angle6=123$

The relationship between $\angle1$ and $\angle6$ is that they are supplementary angles because:

$\angle6+ \angle1=180$

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bixtya [17]

Answer:

i would say about $1.85

Step-by-step explanation:

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