Elias completely covered a square canvas using 77.8 in.² of fabric without any overlap. Which measurement is closest to the side length of this canvas in inches? 8 in. 9 in. 19 in. 39 in.

Answer:

1) ASA

2) SSA

Step-by-step explanation:

The sine rule is used when we have; ASA, AAS or SSA cases. However, SSA is an ambiguous case which occurs when there are two sides and a given angle opposite one of these given sides. The triangles resulting from a situation like this requires a much closer look in comparison to SSS, ASA, and AAS cases. SSA may result in one triangle, two triangles, or even no triangle at all.

Answer:

64 degrees

Step-by-step explanation:

complementary-angle adds up to 90 degrees.

90-26 is 64 degrees.

168 ÷ 14 =12

ink

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Answer:

Let the cost the number of cartridges be x.

We have given that cost of one cartridge is 14 $/cartridge.

And we have 168 $ with us.

So, according to question we have an equation-

14x=168

x=168/14

x=12

Hence, we can buy 12 cartridges if we 168 $ and the cost of one cartridge is 14 $.

Answer:

B

Step-by-step explanation:

A tesselation uses 1 shape to create an image by translating it or reflecting it. The shape is translated in this scenario so they are congruent from a translation (they are in the sam orientation unlike reflections)

Answer:

1) V = 12 π  ㏑ 3

2) [tex]\mathbf{V = \dfrac{328 \pi}{9}}[/tex]

Step-by-step explanation:

Given that:

the graphs of the equations about each given line is:

[tex]y = \dfrac{6}{x^2}, y =0 , x=1 , x=3[/tex]

Using Shell method to determine the required volume,

where;

shell radius = x;   &

height of the shell = [tex]\dfrac{6}{x^2}[/tex]

∴

Volume V = [tex]\int ^b_{x-1} \ 2 \pi ( x) ( \dfrac{6}{x^2}) \ dx[/tex]

[tex]V = \int ^3_{x-1} \ 2 \pi ( x) ( \dfrac{6}{x^2}) \ dx[/tex]

[tex]V = 12 \pi \int ^3_{x-1} \dfrac{1}{x} \ dx[/tex]

[tex]V = 12 \pi ( In \ x ) ^3_{x-1}[/tex]

V = 12 π ( ㏑ 3 - ㏑ 1)

V = 12 π ( ㏑ 3 - 0)

V = 12 π  ㏑ 3

2) Find the line y=6

Using the disk method here;

where,

Inner radius [tex]r(x) = 6 - \dfrac{6}{x^2}[/tex]

outer radius R(x) = 6

Thus, the volume of the solid is as follows:

[tex]V = \int ^3_{x-1} \begin {bmatrix} \pi (6)^2 - \pi ( 6 - \dfrac{6}{x^2})^2 \end {bmatrix} \ dx[/tex]

[tex]V = \pi (6)^2 \int ^3_{x-1} \begin {bmatrix} 1 - \pi ( 1 - \dfrac{1}{x^2})^2 \end {bmatrix} \ dx[/tex]

[tex]V = 36 \pi \int ^3_{x-1} \begin {bmatrix} 1 - ( 1 + \dfrac{1}{x^4}- \dfrac{2}{x^2}) \end {bmatrix} \ dx[/tex]

[tex]V = 36 \pi \int ^3_{x-1} \begin {bmatrix} - \dfrac{1}{x^4}+ \dfrac{2}{x^2} \end {bmatrix} \ dx[/tex]

[tex]V = 36 \pi \int ^3_{x-1} \begin {bmatrix} {-x^{-4}}+ 2x^{-2} \end {bmatrix} \ dx[/tex]

Recall that:

[tex]\int x^n dx = \dfrac{x^n +1}{n+1}[/tex]

Then:

[tex]V = 36 \pi ( -\dfrac{x^{-3}}{-3}+ \dfrac{2x^{-1}}{-1})^3_{x-1}[/tex]

[tex]V = 36 \pi ( \dfrac{1}{3x^3}- \dfrac{2}{x})^3_{x-1}[/tex]

[tex]V = 36 \pi \begin {bmatrix} ( \dfrac{1}{3(3)^3}- \dfrac{2}{3}) - ( \dfrac{1}{3(1)^3}- \dfrac{2}{1}) \end {bmatrix}[/tex]

[tex]V = 36 \pi (\dfrac{82}{81})[/tex]

[tex]\mathbf{V = \dfrac{328 \pi}{9}}[/tex]

The graph of equation for 1 and 2 is also attached in the file below.

Answer:

38 minutes

Step-by-step explanation:

Volume of the first aquarium:

Volume of the second aquarium

The second aquarium is:

It will take

to fill this aquarium

Answer: 5/6

Step-by-step explanation:

p - 1/6 = 2/3

    +1/6   +1/6

p = 5/6

Answer:

p = 5/6

Step-by-step explanation:

For this problem, simply take the words of the problem and convert them into an equation as such:

The difference of p and one-sixth implies --> p - 1/6

is two-thirds implies --> 2/3

So, our equation:

p - 1/6 = 2/3

Now simply solve for p, and combine the fractions.

p - 1/6 = 2/3

p - 1/6 + 1/6 = 2/3 + 1/6

p = 2/3 + 1/6

p = 4/6 + 1/6

p = 5/6

Cheers.

Answer:

2 feet

Step-by-step explanation:

Given the question :

A 6 foot wide painting should be centered on a 10 foot wide wall. How many feet (x) should be on each side of the painting?

Width of painting = 6 foot

Width of wall = 10 foot

Since the painting is required to be centered on the wall, hence the space left on euth side of the wall after placing the painting should be equal.

Therefore,

Difference between painting width and wall width :

(10 - 6) foot = 4 foot

Hence, number of feet (x) on either side of the wall:

4 feet / 2 = 2 feet

Answer:

c

Step-by-step explanation:

its c

The cash received by the person who filled out this deposit is $88.79.

Option C is the correct answer.

Given,

Description                      Amount ($)

Cash, including coins.          15.00

Check 1                                 62.44

Check 2                                 27.83

Check 3                                 45.75

Subtotal                                  ??.??

Less cash received                ??.??

Total                                        62.23

We need to find the less cash received.

A deposit slip is a bank form where the customer fills in the required date such as the date, the depositor's name, the depositor's account number, and the deposit amounts.

Find the subtotal.

= Cash included coins + check 1 + check 2 + check 3

= 15.00 + 62.44 + 27.83 + 45.75

= 151.02

Find the less cash received.

We have,

Total = 62.23

Total = Subtotal - less cash received

62.23 = 151.02 - less cash received

less cash received:

= 151.02 - 62.23

= 88.79

Thus, the cash the person who filled this deposit slip received is $88.79.

Learn more about deposit slips here:

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The complete question:

Consider the following incomplete deposit slip:

Description - Amount ($)

Cash, including coins - 15.00

Check 1  - 62.44

Check 2 - 27.83

Check 3 - 45.75

Subtotal - ?? ??

Less cash received - ?? ??

Total - 62.23

How much cash did the person who filled out this deposit slip receive?

a. $381.23

b. $451.02

c. $88.79

d. $436.02

basically you wrote the answer

Answer is B

Answer:

Well since u know the answer (LOL) its B

Step-by-step explanation:

U already solved it so u know how!

Answer:

180

Step-by-step explanation:

-5= -a/36

-5*36= -a

-180= -a

180 = a

Answer:

Parallel

Step-by-step explanation:

2x+5 slope: 2

-6x+3y=30 slope: 2

Hence the answer is parallel

Answer:

The magnitude is  [tex]\Delta f(0,8)  =  72[/tex]

The  direction  is  [tex]i[/tex] i.e toward the x-axis

Step-by-step explanation:

From the question we are told that

   The function is  [tex]f(x, y) = 9sin(xy) \ \ \[/tex]

    The point considered is  [tex](0,8 )[/tex]

Generally the maximum rate of change of f at the given point and the direction is mathematically represented as

            [tex]\Delta f(x,y) =  [\frac{\delta  f(x,y)}{\delta x } i + \frac{\delta  f(x,y)}{\delta y } j  ][/tex]

             [tex]\Delta f(x,y) =  [\frac{\delta  (9sin(xy))}{\delta x} i  + \frac{\delta  (9sin(xy))}{\delta y} i   ][/tex]

            [tex]\Delta f(x,y) = [9y cos (x,y) i +  9xcos (x,y) j][/tex]

At  [tex](0,8 )[/tex]

            [tex]\Delta  f (0,8) =  [9(8) cos(0* 8)i  + 9(8) sin(0* 8)j  ][/tex]

            [tex]\Delta  f (0,8) = 72 i [/tex]

Answer:

792/7 is the correct answer

Step-by-step explanation:

V=4/3pi r^3

=4/3×22/7×3x×3x×3x

=88×9x÷7=792/7

Answer:

1 : 7

Step-by-step explanation:

Answer:

1:7

Step-by-step explanation:

5/5=1 35/5=7

Answer:

(x - 3)(x + 7)

Step-by-step explanation:

x^2 + 4x - 21

=> x^2 + 7x - 3x - 21

=> x(x + 7) -3(x + 7)

=> (x + 7)(x - 3)

Answer:

[tex](x+7)(x-3)[/tex]

Step-by-step explanation:

So we want to factor the expression:

[tex]x^2+4x-21[/tex]

When factoring, we want to find two numbers that equals (a)(c) and add up to b. We can then substitute it for b.

So, we want two numbers that when multiplied equals (1)(-21)=-21 and adds up to 4.

We can use 7 and -3.

So:

[tex]x^2+4x-21\\=x^2-3x+7x-21[/tex]

Factor out an x from the first two terms, and a 7 from the third and fourth terms:

[tex]=x(x+3)+7(x-3)[/tex]

Grouping:

[tex]=(x+7)(x-3)[/tex]

And we are done :)

Answer:

p = 2

Step-by-step explanation:

17 - 2p = 2p + 5 + 2p  

- 2p - 2p - 2p = 5 - 17

- 6p = - 12

p =  -12 / -6

p = 2

Answer:

(4x)¯² (4x)³ (4x)⁹ = (4x)¹⁰

Step-by-step explanation:

(4x)¯² (4x)³ (4x)⁹

The above expression can be simplified as follow:

Recall:

When we have two or more index number with same base and a multiplication sign in between them, we easily simply by adding the index number together while keeping the base constant. This is illustrated below:

a^m x a^n = a^(m + n)

Therefore,

(4x)¯² (4x)³ (4x)⁹ = (4x)^(-2 + 3 +9)

(4x)¯² (4x)³ (4x)⁹ = (4x)¹⁰

Answer:

B. Yes, they both mean the same thing. They can also both be represented by the expression y - 6.

Step-by-step explanation:

They are the same I think because 6 less than a number y means 6 less than y so y-6. 6 less a number y is the same.

Answer:

Jennifer should expect a number less than 3 23 times

Step-by-step explanation:

The probability of rolling a number less than 3 on a number cube is 2/6. .

The probability of rolling a number less than 3 on a number cube is 2/6

= 1/3

Jennifer rolls a number cube 69 times

Expectations= probability*total outcome

Expectations= 1/3 * 69

Expectations= 69/3

Expectations= 23 times

Answer:

30

Step-by-step explanation:

Answer:

8 miles

Step-by-step explanation:

Downhill

speed = s+2

time = 2 h

then distance d = (s+2)2....i

Uphill

speed = s

time = 4 h

then distance d= 4s...ii

According to question i = ii

⇒(s+2)2 =4s

s = 2 miles/h

then distance d = 2×4 = 8 miles [from eq. ii]

Answer:

15

Step-by-step explanation:

-3x = -5-10

-x=-15

therefore, x=15

Answer:

3kg = 3000 gm

Step-by-step explanation:

we use this formula

m1x (distance of m1 )= m2 x( distance of m2)

* the distance far from the triangle*

m1 =6 kg

d1 = 3m

m2 = ê (kg )

d2 = 600 cm = 6 m

m1 d1 = m2 d2

6 x 3 = ê 6

ê = 3 kg

mass = 3kg = 3000 gram

#

To make the scale balance, the weight must be added is 3000g.

"A balanced equation is an equation where both sides are equal to the same amount. The answer to the expression on the left side of the equals sign (=) should be equal to the value on the right side of the equals sign".

For the given situation,

From the diagram shown, the distance on both sides of the fulcrum (the triangle) must be the same to make the scale balance.

We know that

1 kg = 1000 g

1 m = 100 cm

Let the unknown quantity be 'x'

To write a balanced equation, units should be the same on both sides.

6 kg = 6000 g

3 m = 300 cm.

The equation is represented as

[tex]6000[/tex] × [tex]300 = x[/tex] × [tex]600[/tex]

⇒ [tex]x = \frac{(6000)(300)}{600}[/tex]

⇒ [tex]x=3000[/tex]

Hence we can conclude that to make the scale balance, the weight must be added is 3000g.

Learn more about the balance equation here

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Answer:

a) $675000

b) $289000 profit,3300 set, $190 per set

c) 3225 set, $272687.5 profit, $192.5 per set

Step-by-step explanation:

a) Revenue R(x) = xp(x) = x(300 - x/30) = 300x - x²/30

The maximum revenue is at R'(x) =0

R'(x) = 300 - 2x/30 = 300 - x/15

But we need to compute R'(x) = 0:

300 - x/15 = 0

x/15 = 300

x = 4500

Also the second derivative of R(x) is given as:

R"(x) = -1/15 < 0 This means that the maximum revenue is at x = 4500. Hence:

R(4500) = 300 (4500) - (4500)²/30 = $675000  

B) Profit P(x) = R(x) - C(x) = 300x - x²/30 - (74000 + 80x) = -x²/30 + 300x - 80x - 74000

P(x) = -x²/30 + 220x - 74000

The maximum revenue is at P'(x) =0

P'(x) = - 2x/30 + 220= -x/15 + 220

But we need to compute P'(x) = 0:

-x/15 + 220 = 0

x/15 = 220

x = 3300

Also the second derivative of P(x) is given as:

P"(x) = -1/15 < 0 This means that the maximum profit is at x = 3300. Hence:

P(3300) =  -(3300)²/30 + 220(3300) - 74000 = $289000  

The price for each set is:

p(3300) = 300 -3300/30 = $190 per set

c) The new cost is:

C(x) = 74000 + 80x + 5x = 74000 + 85x

Profit P(x) = R(x) - C(x) = 300x - x²/30 - (74000 + 85x) = -x²/30 + 300x - 85x - 74000

P(x) = -x²/30 + 215x - 74000

The maximum revenue is at P'(x) =0

P'(x) = - 2x/30 + 215= -x/15 + 215

But we need to compute P'(x) = 0:

-x/15 + 215 = 0

x/15 = 215

x = 3225

Also the second derivative of P(x) is given as:

P"(x) = -1/15 < 0 This means that the maximum profit is at x = 3225. Hence:

P(3225) =  -(3225)²/30 + 215(3225) - 74000 = $272687.5

The money to be charge for each set is:

p(x) = 300 - 3225/30 = $192.5 per set

When taxed $5, the maximum profit is $272687.5

Answer:

b) $289000 profit,3300 set, $190 per set

Answer:

0-3+5=2

Step-by-step explanation:

It starts in 0

The first line moves three spaces to the left so that's -3

the second line moves 5 spaces to the right so that's +5

add all up

0-3+5=2

Answer:

2

Step-by-step explanation:

1st line 0 → -3 = -3

2nd line -3  → 2 = 5

sum = 0 + (-3) + 5 = 2

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{18}}}}}[/tex]

Step-by-step explanation:

Given, y = 3 , z = 3

[tex] \sf{z(y + y)}[/tex]

Plug the value of y and z

⇒[tex] \sf{3(3 + 3)}[/tex]

Add the numbers : 3 and 3

⇒[tex] \sf{3 \times 6}[/tex]

Multiply the numbers : 3 and 6

⇒[tex] \sf{18}[/tex]

Hope I helped!

Best regards! :D

Answer: (a) y = 2.7394x - 118.1368

             (b) R² = 0.8215 or 82.15%

Step-by-step explanation: Regression line is the best line that relates the variables in the data.

To calculate the fitted regression equation:

1) Calculate average of x-values ([tex]x_{i}[/tex]) and average of y-values ([tex]y_{i}[/tex]);

2) Calculate the slope, b, by doing:

[tex]b=\frac{\Sigma (x-x_{i})(y-y_{i})}{\Sigma (x-x_{i})^{2}}[/tex]

3) Calculate y-intercept, a, by doing:

[tex]a=y_{i}-bx_{i}[/tex]

4) Then, it gives regression equation: y = bx + a

For the data on chemical reactions:

(a) [tex]b=\frac{ [(136.24-105.3955)+...+(86.18-105.3955)].[(234.5-170.58)+...+(106-170.58)]}{(136.24-105.3955)^{2}+...+(86.18-105.3955)^{2}}[/tex]

b = 2.7394

[tex]a=170.58-2.7394(105.3955)[/tex]

a = -118.1368

y = 2.7394x - 118.1368

The fittest regression equation is y = 2.7394x - 118.1368.

(b) R is correlation coefficient and measures the strength of the relationship between the variables. It is calculated as:

[tex]R=\frac{n\Sigma(xy)-(\Sigma x)(\Sigma y)}{\sqrt{[n\Sigma x^{2}-(\Sigma x^{2})][n\Sigma y^{2}-(\Sigmay^{2})]} }[/tex]

For this fit, R = 0.9064

The variable R² is the coefficient of determination, is the square of correlation coefficient and is usually stated as a percent.

What the variable represents is the percent of variation in the dependent variable (y) explained by the variation in the independent variable (x).

For this fit:

[tex]R^{2} = 0.9064^{2}[/tex]

[tex]R^{2} =[/tex] 0.8215

What it entails is that 82.15% of the variation of retention time is due to the molecular weight of each chemical compound.

Answer:

I think the scale factor is 2 because 12 divided by 6 is 2.

Answer:

x=9

Step-by-step explanation:

If the triangles are congruent, then the angles B and E are also congruent (because they lie in the same place). Set an equation where B is equal to E:

∠[tex]B=[/tex]∠[tex]E[/tex]

Substitute values:

[tex]5x=45[/tex]

Solve for x. Divide both sides by 5:

[tex]\frac{5x}{5}=\frac{45}{5}\\\\ x=9[/tex]

So, when ΔABC≅ΔDEC, and ∠B=5x and ∠E=45°, the value of x is 9.

:Done

Answer:

I agree with the first answer

Step-by-step explanation: