Tuan is an artist. He is painting on a large canvas which is 40 inches wide. The height of the canvas is 6 inches less than the width. What is the area of Tuan's canvas?

Answer:

Lower bound for the length of the edge = 42.5 cm

Step-by-step explanation:

From the picture attached,

FH is the diagonal of square EFGH.

Therefore, length of diagonal FH = [tex]\sqrt{FG^2+HG^2}[/tex]

(By applying Pythagoras theorem)

In triangle AFH,

AH² = AF² + FH²

       = AF² + [tex](\sqrt{FG^2+HG^2})^2[/tex]

       = AF² + FG² + HG²

AH² = 3HG²

(11.3)² = 3(HG²)

HG = [tex]\sqrt{\frac{127.69}{3}}[/tex]

HG = 42.563 cm

For distance correct to the nearest mm, lower bound for the length of the edge = 42.5 cm

And upper bound for the length of the edge = 43.6 cm

The side lengths of a cu be are congruent, so the edge length of the cu be is 65 mm

The length of diagonal A H is given as:

[tex]\mathbf{AH = 11.3cm}[/tex]

Considering triangle A FH, we have:

[tex]\mathbf{AH^2 = A\ F^2 + FH^2}[/tex]

So, we have:

[tex]\mathbf{11.3^2 = A\ F^2 + FH^2}[/tex]

Considering triangle HE F, we have:

[tex]\mathbf{FH^2 = EF^2 + EH^2}[/tex]

Substitute [tex]\mathbf{FH^2 = EF^2 + EH^2}[/tex] in [tex]\mathbf{11.3^2 = A\ F^2 + FH^2}[/tex]

[tex]\mathbf{11.3^2 = A\ F^2 + EF^2 + EH^2}[/tex]

The side lengths of a cu be are congruent.

This means that: A F = EF = EH

So, we have:

[tex]\mathbf{11.3^2 = A\ F^2 + A\ F^2 + A\ F^2}[/tex]

Evaluate like terms

[tex]\mathbf{11.3^2 = 3A\ F^2}[/tex]

Evaluate squares

[tex]\mathbf{127.69 = 3A\ F^2}[/tex]

Divide both sides by 3

[tex]\mathbf{42.563= A\ F^2}[/tex]

Take square roots

[tex]\mathbf{6.52= A\ F}[/tex]

Rewrite as:

[tex]\mathbf{A\ F = 6.52cm}[/tex]

Convert to m m

[tex]\mathbf{A\ F = 6.52 \times 10mm}[/tex]

[tex]\mathbf{A\ F = 65.2\ mm}[/tex]

Approximate

[tex]\mathbf{A\ F = 65\ mm}[/tex]

Hence, the edge length is 65 mm

Read more about cu bes at:

https://brainly.com/question/23261883

Answer:

y does not vary directly with x

Step-by-step explanation:

The equation for direct variation is

y = kx ← k is the constant of variation

If k is constant for all ordered pairs in the table then direct variation.

k = [tex]\frac{y}{x}[/tex]

(2, 10 ) → k = [tex]\frac{10}{2}[/tex] = 5

(4, 24 ) → k = [tex]\frac{24}{4}[/tex] = 6

(6, 36 ) → k = [tex]\frac{36}{6}[/tex] = 6

Since k is not constant for all pairs then y does not vary directly with x

Answer:

geometry

Step-by-step explanation:

left side of paper

Answer:

Assuming the 2 at the ends are the exponents,

the answer is -x^2-5x+6 (x^2+5x-6)

from here, it cannot be simplified more

Explanation --

Just add everything by putting the terms in parentheses and adding them.

Keep simplifying by putting the like terms together and adding/subtracting them.

At the end, you come up with -x^2-5x+6, so multiply -1 on the whole thing (by putting parentheses on its sides. This makes x positive. But they are the same thing, but this step is just for simplifying the end product a little more.

Hope this helps!! Have a nice day!

Answer:

D) 180

Step-by-step explanation:

Formula for Surface area of Rectangular prism is

A = 2(lw+wh+lh)

A = 2(6*8 + 8*3 + 6*3)

A = 2(48 + 24 + 18)

A = 2 * 90

A = 180

Answer:

He needs 15 shirts

Step-by-step explanation:

We can use a ratio to solve

4 pants             6 pants

--------------- = -------------

10 shirts            x shirts

Using cross products

4x = 10 *6

4x = 60

Divide each side by 4

4x/4 = 60/4

x = 15

He needs 15 shirts

Answer:

[tex]x = 4[/tex]

Step-by-step explanation:

[tex]9x-13=23[/tex]

[tex]9x=23+13[/tex]

[tex]9x = 36[/tex]

[tex]x = \frac{36}{9} [/tex]

[tex]x = 4[/tex]

Answer:

X=4

Step-by-step explanation:

9x-13=23

9x=23+13

x=(23+13)/9

x=4

Answer:y=-4

Step-by-step explanation:

Answer:

20000000000000000000000000000

Answer:

e. a civil right infringement lawsuit

Step-by-step explanation:

A civil right infringement lawsuit is a lawsuit filed by an offender whose civil rights have been violated by others. Civil rights are those rights of the citizens that is guaranteed by the Constitution of the United States to its people. They are right to equality, right to freedom, right to employment and all those rights that is included in the Bill of Rights of the US constitution.

So, when Kirenna was terminated by her boss, Tanae on the grounds on the discrimination of gender, Kirenna can file a civil right infringement lawsuit against her boss, Tanae.

Answer:

kilo =1*10^3 grams

nano=one millionth

micro=0.01 litres

centi=0.0000000001 meters

Step-by-step explanation:

Answer:

89.38

Step-by-step explanation:

65 times 0.125 = 8.125

65 times 0.25 = 16.25

16.25 plus 8.125 plus 65 = 89.38 dollars

Answer:

0.5 = 2

0.75 = 2

1.0 = 3

1.25 = 4

1.5 = 5

2.0 = 2

2.25 = 1

2.5 = 1

Answer:

x = 11.85

Step-by-step explanation:

[tex]67 - 2x + \frac{89}{2} + 7 -8x = 0\\\\67 + \frac{89}{2}+7 = 8x + 2x\\\\\frac{134 + 89 +14}{2} = 10x\\\\10x = 118.5\\\\x = 11.85[/tex]

Answer:

[tex]x = 11 \frac{17}{20}[/tex] or [tex]\frac{237}{20}[/tex]

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

30

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

I took the quiz, I hope this helps!

Answer:

8.5

Step-by-step explanation:

slope of the line that contains KL

(y2 - y1)/(x2-x1)

(0-1)/(7-3)

m = -1/4

slope of the line that contains JK

(5-1)/(4-3)

m = 4

the linea are perpendicular so triangle is right

area = (leg1 x leg2)/2

KL = [tex]\sqrt{(7-3)^2 + (0-1)^2} = \sqrt{16 + 1} = \sqrt{17}[/tex]

KJ = [tex]\sqrt{(4-3)^2 + (5-1)^2}= \sqrt{1 + 16} = \sqrt{17}[/tex]

area = (√17)^2/2 = 17/2 = 8.5

Answer:

area=l*b

10*8

80#

Step-by-step explanation:

hope you like it

Answer:

Hi there! Subscribe to my animations Y0UTUBE channel! Channel name: Let Me Explain Studios. Have a nice day!

Step-by-step explanation:

Answer:

just use a calculator and add all the numbers-

Step-by-step explanation:

add

Answer:

It is increasing before x = -2 and from x = 0 to x = 2

Step-by-step explanation:

Option 1 - you can see the line going down starting at -2 and that means the line is decreasing but the choice says "It is increasing before x = 0". This contradicts the actual graph.

Option 2 - The line isn't increasing before x= -1, it's actually decreasing as seen in the graph.

Option 3 - The line doesn't even touch the point before x = -3 so this choice makes no sense.

Option 4 - Since all the other choices were eliminated this is the only choice standing. Looking at the line it is increasing before x = -2.

Answer:

B. Of the students who walk, the probability of choosing a female.

D. Of the females, the probability of choosing one who rides the bus.

Step-by-step explanation:

Conditional probability is the chance of something happening provided that something else has previously occured (think dependent events).

For example, the probability of getting into college P(college) is Event A.

The probability of receiving dormitory housing P(housing) is Event B.

First, the person must get into college before they are even able to receive dormitory housing. Therefore, this is a situation of conditional probability. The "condition" of being accepted into the college (Event A) is necessary before the individual can attempt Event B, housing.

The key word in the question is "Of all the students." This means that from the first instance, you are only calculating one probability.

However, in B, it first singles out "all the students who walk."

Therefore p(walk) must be met before p(gender) can happen.

Same with D, it singles out "of the females."

Therefore p(gender) must be met before p(transportation) can happen.

C does have two categories, but since it is still out of the general draw pool "of all students," it is not conditional. No condition needs to be met first to choose a male who walks out of ALL students.

Answer:

0

Step-by-step explanation:

Given that f(x) = 1/2x + 4

Let y = f(x)

y = 1/2 x + 4

Replace y with x

x = 1/2 y + 4

Make y the subject of the formula

1/2y = x - 4

y = 2(x-4)

If x = 3

y = 2(4-4)

y = 2(0)

y = 0

Hence ƒ -1(4) is 0

Answer:

Area of the figure is 88 square inches

Answer:

(1/2)z

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

Any number to the 0 power is equal to 1.

Hope that this helps!

Answer:

1 is correct

Any number that is raised to the power of 0 is 1, and any number that’s raised to the power of 1 is itself

Answer:

the perimeter is given in__in__, the height in_in___, and area of the base in_in²__.

so

none of the above.

Answer:

d

Step-by-step explanation:

none of the above