The formula for the surface area S of a rectangular prism is S=2hl+2hw+2lw, where l is the length,w is the width, and h is the height. Solve the formula for height h.

Let the angles are x, y and z.

Let the smallest angle is x

one angle is 78 degrees more than the smallest angle.⇒ y = x + 78 → (1)

the third angle is 4 times as large as the smallest angle. ⇒ z = 4 x → (2)

we should know that the sum of the angles of the triangle = 180°

∴ x + y + z = 180 →(3)

substitute from (1) and (2) at (3)

∴ x + ( x +78) + (4x) = 180

∴ 6x = 180 - 78 = 102

∴ x = 102 ÷ 6 = 17°

∴ y = 17 + 78 = 95°

∴ z = 4x = 68°

So, the measures of all three angles are 17°, 95° and 68°

The answer would be 0.002

The answer to 0.45 / 225 = 0.002

Hope this helps you..

Answer:

- The equation is: [tex]\frac{249}{2}=2(x+\frac{17}{4})+2x[/tex]

- The width of the postage stamp is 29 milimeters.

- The length is 33.25 milimeters.

Step-by-step explanation:

1. The length ([tex]y[/tex]) is [tex]4^{\frac{1}{4} }mm=\frac{17}{4}mm[/tex] longer than the width ([tex]x[/tex]):

[tex]y=x+\frac{17}{4}[/tex]

2. The perimeter is [tex]124^{\frac{1}{2}}mm=\frac{249}{2}mm[/tex].

3. The perimeter of a rectangle is:

[tex]Perimeter=2Length+2Width[/tex]

4. Substitute values:

[tex]\frac{249}{2}=2(x+\frac{17}{4})+2x[/tex]

5. Solve for the width [tex]x[/tex]:

[tex]\frac{249}{2}=2x+\frac{34}{4}+2x\\x=\frac{116}{4}\\x=29[/tex]

6. Calculate the length:

[tex]y=x+\frac{17}{4}\\y=29+\frac{17}{4}\\y=33.25[/tex]

The width and length of the postage stamp are calculated by formulating and solving an equation based on the given perimeter and the relationship between the length and width. The width is found to be 29 mm, and the length is 33.25 mm.

The subject of this question is Mathematics and it's related to the concept of the perimeter of a rectangle. If we denote the width of the postage stamp as 'W' (in millimeters), then it's length will be 'W + 4.25' millimeters because it's stated in the problem that the length is 4.25 mm longer than the width.

The perimeter of a rectangle (which is the shape we can assume for a postage stamp) is calculated as follows: Perimeter = 2(Length + Width). Substituting the value for length that we've assigned, we get this equation:

124.5 = 2[(W + 4.25) + W]

Solving this equation step-by-step will lead you to the answer. First, distribute the 2 into the parentheses which gives: 124.5 = 2W + 8.5 + 2W. Combine like terms to simplify: 124.5 = 4W + 8.5. Then, subtract 8.5 from both sides of the equation: 116 = 4W. Lastly, divide by 4 to find 'W': W = 29 mm. Therefore, the width of the postage stamp is 29 mm, and the length is 29 mm + 4.25 mm = 33.25 mm.

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m = 4, n = 4

Plug in 4 for m and n

10(4) + (4)^2

Simplify. Multiply

4^2 = 4(4) = 16

10(4) = 40

40 + 16 = 56

56 is your answer

hope this helps

The Answer to this is: True.

a. The independent variable is r. The dependent variable is m.

b. The domain is the set of numbers used in the independent variable. You can rent 0 videos, or 1 video, or 2 videos, etc., up to the amount of money you have. If you rent 0 videos, you are left with m = 30 - 3r = 30 - 3(0) = 30 - 0 = 30 dollars. If you rent 10 videos, you will have m = 30 - 3(10) = 30 - 30 = 0 dollars left. The domain is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. The range is {0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30}. Both the domain and range are discrete.

c. I can't do it online.

The length of pine street would be; 7.

When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get. Division can be interpreted as equally dividing the number that is being divided into total x parts, where x is the number of parts the given number is divided.

We have been given that maple street is 3 times as long as pine street.

We need to find the length of pine street.

Therefore,

We have to divide 21 divided by 3 which is;

21/3 = 7

Hence, A pine street would be; 7.

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The answer to your question is  

d.

78.5 m^2

78.54 m² is your answer. So to recap, a goat tethered to a stake in the ground with a 5 m rope has 78.54 meters to graze.

We get this answer by putting the information into an equation. We know that a circle has 360° (360 degrees) and so when we see the problem say that the goat can graze 360 degrees around the stake, we instantly know it's talking about a circle. Look at the question, it's asking about the area of the circle. Now we can make an equation to find the area of this circle.

The area of a circle is A = πr²

That's Area = Pi times Radius squared.

We'll use 3.14 as substitute for Pi. The radius was given to us, it is 5 m. Put the information into the formula.

A = 3.14 * 5²

Now we do the order of operations. In the order of operations, we have no parenthesis to work with, but we do have an exponent. So we take 5 to the second power, (5² = 5 * 5) and we update our problem.

A = 3.14 * 25

Now we finish the problem by multiplying 3.14 and 25.

A = 78.54

We're not entirely done. Now we include our units of measurement. In this case, we were using m for meters. When solving for area, the unit is always squared in the final answered. So this would be our final answer:

A = 78.54 m²

Answer:

a-bi

Step-by-step explanation:

If a quadratic equation lx^2+mx+n=0 has one imaginary root as a+bi then the other root is the conjugate of a+bi = a-bi

Because we have l, m and n are real numbers and they are the coefficients.

Sum of roots = a+bi + second root = -m/l

When -m/l is real because the ratio of two real numbers, left side also has to be real.

Since bi is one imaginary term already there other root should have -bi in it so that the sum becomes real.

i.e. other root will be of the form c-bi for some real c.

Now product of roots = (a+bi)(c-bi) = n/l

Since right side is real, left side also must be real.

i.e.imaginary part =0

bi(a-c) =0

Or a =c

i.e. other root c-bi = a-bi

Hence proved.

The number of girls who work there are:

                              92

It is given that:

The number of girls who work at Super shopper is 2 more than 3 times the number of boys.

This means that:

If the number of boys= x

Then the number of girls= 3x+2

If 30 boys work at super shopper.

i.e. x=30

Then 3x+2=92

Hence, the number of girls who work there are: 92

Answer:

The rate of change is of 0.25 lbs / person

Step-by-step explanation:

According to my research the formula for the Rate of Change is the following

[tex]\frac{y2 - y1}{x2 - x1}[/tex]

In this situation we can use y for lbs and x for people. Since all the information was given to us in the question we can just plug the values into the formula above and solve for the rate of change.

[tex]\frac{17lbs-9lbs}{68-36} = \frac{8lbs}{32people} = 0.25lbs/person[/tex]

So we can see that the rate of change is of 0.25 lbs / person

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

(1) y = 7x , (2) y = 11x , (3) y = 9x , (4) y = 28x

given y varies directly as x then y = kx ( k is the constant of variation )

(1) find k using the given conditions k = [tex]\frac{y}{x}[/tex] = [tex]\frac{63}{9}[/tex] = 7

equation is y = 7x

(2) k = [tex]\frac{121}{11}[/tex] = 11

equation is y = 11x

(3) k = [tex]\frac{36}{4}[/tex] = 9

equation is y = 9x

(4) k = [tex]\frac{224}{8}[/tex] = 28

equation is y = 28x

negative

Let's find the slope of our line using the slope formula:

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

where

[tex]m[/tex] is the slope of the line

[tex](x_{1},y_{1})[/tex] are the coordinates of the first point on the line

[tex](x_{2},y_{2})[/tex] are the coordinates of the second point

From the graph we can get the points (-2, 1) and (2, -1), so [tex]x_{1}=-2[/tex], [tex]y_{1}=1[/tex], [tex]x_{2}=2[/tex], and [tex]y_{2}=-1[/tex]. Let's replace the values in our formula to find [tex]m[/tex]:

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m=\frac{-1-1}{2-(-2)}[/tex]

[tex]m=\frac{-2}{2+2}[/tex]

[tex]m=\frac{-2}{4}[/tex]

[tex]m=-\frac{2}{4}[/tex]

[tex]m=-\frac{1}{2}[/tex]

The slope of the graph of the linear function is [tex]-\frac{1}{2}[/tex]; since [tex]-\frac{1}{2}[/tex] is a negative number, the slope of the graph is negative.

-3x = -15      divide both sides by (-3)

-3x:(-3)=-15:(-3)

x = 5

Answer:

The answer is b, 5

Step-by-step explanation:

-3x = -15

(it sometimes helps to flip it, so that's what I'm going to do here to help it to make more sense)

x(-3) = -15

x(-3) devided by (-3) = -15 devided by (-3)

when you devide a negitive by a negative the answer will be positive

the absolute value of 15 devided by three is 5

your answer is a positive five, or just 5

Answer:

Number sentences.

Addition-Addend-Sum.

Subtraction-Difference.

Step-by-step explanation:

1. By definition Number sentences contains number and common symbols.

2. They can be: "Addition" (which has "Addend" that form the "Sum") and "Subtraction" (whose result is known as "Difference").

3. You can see the answer of the tree map in the figure attached.

C=2 πr which is the formula for circumference

The quotient and remainder of the given division operations are:

4)76 = 19

3)92 = 30 remainder 2

6)53 = 8 remainder 5

From the question, we are to evaluate the given divisions

The divisions can be evaluated as follows:

  19    

4)76

-  4      

   36

-   36  

 = 19

  30    

3)92

-  9      

   02

-     0  

     2

= 30 R 2

  08    

6) 53

-  0      

    53

-   48    

      5

= 8 R 5

It is true in this case, because you are trying to find the distance between two points. That also means you are trying to find the difference between two points, and to find the difference, you subtract. That is why what Brittany says is true.

Absolute value is always positive because absolute value represent distance and distance can not be negative.

Yes it is true, To determine the distance between 180 and 34, you can just subtract 180 - 34.

Since, absolute value is represent distance between two points

and absolute value is always greater or equal to zero.

Now, To  determine the distance between 180 and 34,  just subtract 180 - 34.

and then take absolute value.

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Answer:

b and c

Step-by-step explanation:

Jack popped some popcorn, but 3 of the 150 did not pop.

the ratio of the jack's popcorn = [tex]\frac{3}{150}[/tex]

                                                   = [tex]\frac{1}{50}[/tex]

                                                  = 1 : 50

We will go through all the other given ratio to find whether they are same ratio of Jack's or not.

a. 2 unpopped out of 75 kernels  = [tex]\frac{2}{75}[/tex]

                                                       = 2 : 75  This is not a match

b. 2 unpopped out of 200 kernels = [tex]\frac{4}{200}[/tex]

                                                         = [tex]\frac{1}{50}[/tex]

                                                         = 1 : 50   This is same

c. 1 unpopped out of 50 kernels = [tex]\frac{1}{50}[/tex]

                                                     = 1 : 50 This is also same

So b and c has the same ratio of unpopped to total kernels as Jack's popcorn.

The solution of expresison is, r = - 38

We have to give that,

An expression to simplify,

12r - 18 = 13r + 18

Now, We can simplify the expression as,

12r - 18 = 13r + 18

Subtract 12r on both sides,

12r - 18 - 12r = 13r - 12r + 18

- 18 = r + 18

Subtract 18 on both sides,

- 18 - 18 = r

r = - 36

Therefore, The solution is, r = - 36

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Hello!

Explanation:

↓↓↓↓↓↓↓↓↓↓

First, rewrite 10 as 2*5

[tex]2k+2*5[/tex]

Then, factor out common term 2.

[tex]=2(k+5)[/tex]

Answer⇒⇒⇒⇒2(k+5)

Hope this helps!

Thank you for posting your question at here on Brainly.

-Charlie

ANSWER

[tex]x>2[/tex]

EXPLANATION

We have the inequality

[tex]8(\frac{x}{4})>4[/tex]

We can cancel directly to get;

[tex]2(\frac{x}{1})>4[/tex]

[tex]\Rightarrow 2x>4[/tex]

We now divide both sides by 2,

[tex]\Rightarrow x>\frac{4}{2}[/tex]

[tex]x>2[/tex]

See graph in attachment

PEMDAS:

20 + [tex]4^{3}[/tex] ÷ -8

Exponent

20 + 64 ÷ -8

Divide

20 +  -8

Add

20 + -8 = 12

hope this helps :)

The value of [tex]20+4^{3} /(-8)[/tex] is 12.

Given:

[tex]20+4^{3} /(-8)[/tex]

Simplifying the equation by the PEMDAS rule

We can remember the order using PEMDAS: Parentheses, Exponents, Multiplication, and Division (from left to right), Addition, and Subtraction (from left to right).

[tex]$\quad 4=2^{2}$[/tex]

[tex]$(4)^{3}=\left(2^{2}\right)^{3}=2^{6}$[/tex]

Substituting the values in the given equation,

[tex]$20+\frac{2^{6}}{-8}$$[/tex]

Dividing exponents as

[tex]$2^{6}$[/tex] divided by [tex]$2^{3}=2^{(6-3)}=2^{3}$[/tex]

[tex]$20+-8$$[/tex]

Simplify,

[tex]$20+-8$$[/tex]

Therefore, the value of [tex]20+4^{3} /(-8)[/tex] is 12.

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Answer:

The least value of n is, 9.

Step-by-step explanation:

Let n be the number of sheep in Integer.

Mary(M) owned the number of sheep is n i.e, M = n sheep

Sam(S) had exactly four times as many sheep as Mary , i.e, S = 4 n sheep

As per the given condition Mary buys 17 extra sheep

Now, Mary has total number of sheep, M = n +17 sheep

And Sam sells 8 of his sheep that means he has now,

[tex]S = 4n -8[/tex]

But, Sam still has more sheep than Mary i.e,  [tex]4n-8 > n+17[/tex]

Solve an inequality: [tex]4n-8 > n+17[/tex]

Add 8 both sides we get;

[tex]4n-8+8>n+17+8[/tex]

Simplify:

[tex]4n>n+25[/tex]

Now, subtract n from both the side, we get;

[tex]4n -n>n+25-n[/tex]

Simplify:

[tex]3n>25[/tex] or [tex]n>\frac{25}{3}=8.33333333[/tex]

Since n is the number of sheep in integer,

then the least value of n is, 9.  

Answer:

990 pounds

Step-by-step explanation:

If one troop eats 11 pounds and there are 90 troops, you only need to multiply 90 by 11.

(2,3)

(x,y)

x=2

y=3

This is because both lines meet at this direct point on the graph.

Answer:

Yes, the lines will intersect because the slopes are different. Also, both lines have a y-intercept of -7, so they both include the point (0, –7).

Step-by-step explanation: