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3 years ago

Based on the picture below (note that it is not drawn to scale), Maggie says that . Is she correct? Explain why or why not.

Mathematics

1 answer:

valentinak56 [21]3 years ago

6 0

Answer:

Step-by-step explanation:

By using the property of similar triangles,

"Corresponding sides of two similar triangles are proportional"

If ΔSMA ~ ΔPOD

$\frac{SM}{PO}=\frac{MA}{OD}=\frac{SA}{PD}$

$\frac{6}{10}=\frac{5}{10}=\frac{5}{12}$

$\frac{3}{5}=\frac{1}{2}=\frac{5}{12}$

Since, ratios of corresponding sides are not equal,

Therefore, the given triangles are not similar.

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A rectangular box with a volume of 272ft^3 is to be constructed with a square base and top. The cost per square foot for the bot

ASHA 777 [7]

Answer:

The dimensions of the box is 3 ft by 3 ft by 30.22 ft.

The length of one side of the base of the given box is 3 ft.

The height of the box is 30.22 ft.

Step-by-step explanation:

Given that, a rectangular box with volume of 272 cubic ft.

Assume height of the box be h and the length of one side of the square base of the box is x.

Area of the base is = $(x\times x)$

$=x^2$

The volume of the box is = area of the base × height

$=x^2h$

Therefore,

$x^2h=272$

$\Rightarrow h=\frac{272}{x^2}$

The cost per square foot for bottom is 20 cent.

The cost to construct of the bottom of the box is

=area of the bottom ×20

$=20x^2$ cents

The cost per square foot for top is 10 cent.

The cost to construct of the top of the box is

=area of the top ×10

$=10x^2$ cents

The cost per square foot for side is 1.5 cent.

The cost to construct of the sides of the box is

=area of the side ×1.5

$=4xh\times 1.5$ cents

$=6xh$ cents

Total cost = $(20x^2+10x^2+6xh)$

$=30x^2+6xh$

Let

C $=30x^2+6xh$

Putting the value of h

$C=30x^2+6x\times \frac{272}{x^2}$

$\Rightarrow C=30x^2+\frac{1632}{x}$

Differentiating with respect to x

$C'=60x-\frac{1632}{x^2}$

Again differentiating with respect to x

$C''=60+\frac{3264}{x^3}$

Now set C'=0

$60x-\frac{1632}{x^2}=0$

$\Rightarrow 60x=\frac{1632}{x^2}$

$\Rightarrow x^3=\frac{1632}{60}$

$\Rightarrow x\approx 3$

Now $C''|_{x=3}=60+\frac{3264}{3^3}>0$

Since at x=3 , C''>0. So at x=3, C has a minimum value.

The length of one side of the base of the box is 3 ft.

The height of the box is $=\frac{272}{3^2}$

=30.22 ft.

The dimensions of the box is 3 ft by 3 ft by 30.22 ft.

7 0

3 years ago

If the output number y is -52 (y=5x-2) what is the input number? SHOW WORK

nordsb [41]

Answer:

the input number is -10

Step-by-step explanation:

output is always y

input is always x

so instead of y, put -52

-52=5x-2 add 2 to each side to ger 5x by itself

-50=5x divide both sides by 5 to get x by itself

-10=x

x is the input so the input is -10

8 0

3 years ago

Elizabeth works for Picasso paint supplies. Her annual salary is $72,580. What is Elizabeth’s annual social security deduction?

Nikolay [14]

Social Security's Old-Age, Survivors, and Disability Insurance (OASDI) tax rate for wages paid in 2018 is set by the state at 6.2 % for employees and employers, each. An individual with wages equal to or larger than $128,400 would contribute $7,960.80 to the OASDI program. Since Elizabeth receives a salary of $72,580 from Picasso paint supplies, a lot lower than <span>$128,400, there will be no deduction. </span>

8 0

4 years ago

Y = 1000x = _____???

Georgia [21]

Answer:

Simplifying

y = 1000X

Solving

y = 1000X

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Simplifying

y = 1000X

Step-by-step explanation:

5 0

3 years ago

Can someone plz help? I do not understand

Slav-nsk [51]

Answer:

y=x no

y=12x yes

y=1.6x yes

y=3/(4x) no

y=2x+1 no

y=3+x no

Step-by-step explanation:

4 0

4 years ago