Mary is also a civil engineer, and she is building a triangular community garden. She knows two angles in the triangular garden, diagramed below. A triangle has angle measures 92 degrees, 27 degrees, and a degrees. The exterior angle to a degrees is b degrees. What are the measures of interior angle a and exterior angle b? a = ° b = °

Answer:

C

Step-by-step explanation:

Answer:

" Expected Payoff " ⇒ $ 1.80 ; Type in 1.80

Step-by-step explanation:

Take the probability of winning into consideration;

[tex]Total Number of Tickets - 500,\\Tickets 1 Person Can Enter - 1 Ticket,\\\\Probability of Winning - 1 / 500,\\Money Won - 900 Dollars,\\\\Proportionality - 1 / 500 = x / 900 - where, x = " Expected Payoff "\\1 / 500 = x / 900 - CrossMultiplication,\\\\500 * x = 900,\\x = 900 / 500,\\x = 1.80 Dollars Won!\\\\Conclusion ; x = 1.80 Dollars[/tex]

Solution ; " Expected Payoff " ⇒ $ 1.80

Answer:

x=S/4

Or

x=S(1/4)

Step-by-step explanation:

Surface Area(S)=4x

Where

x=length

Inverse by solving for x without switching the variables

S=4x

Divide both sides by 4

S/4=4x/4

S/4=x

x=S/4

Or can also be written as

x=S(1/4)

Answer:

The equation for the following graph:

[tex]y = -\frac{1}{5}x[/tex]

Step-by-step explanation:

- You first need to find the slope by using the slope formula:

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

(where [tex](x_{1},y_{1})[/tex] is the first point and [tex](x_{2}, y_{2})[/tex] is the second point)

-Use the given points [tex](0,0)[/tex] and [tex](10, -2)[/tex] from the graph for the formula:

[tex]m = \frac{-2 - 0}{10 - 0}[/tex]

Then, you solve:

[tex]m = \frac{-2 - 0}{10 - 0}[/tex]

[tex]m = -\frac{1}{5}[/tex]

After you have found the slope, use the slope [tex]-\frac{1}{5}[/tex] and the first point [tex](0,0)[/tex] for the point-slope formula:

[tex]y - y_{1} = m ( x - x_{1})[/tex]

(where [tex]m[/tex] is the slope and [tex](x_{1}, y_{1})[/tex] is the first point)

[tex]y - 0 = -\frac{1}{5} ( x - 0)[/tex]

Then, you solve:

[tex]y - 0 = -\frac{1}{5} ( x - 0)[/tex]

[tex]y - 0 = -\frac{1}{5}x - 0[/tex]

[tex]y - 0 + 0 = -\frac{1}{5} - 0 + 0[/tex]

[tex]y = -\frac{1}{5}x[/tex]

So, the equation for the following graph is [tex]y = -\frac{1}{5}x[/tex] .

Answer:d

Step-by-step explanation:(2√7 +3√6) (5√2 +4√3)

To open the bracket, multiply the first rational number (2√7 ) with the two numbers in the other bracket and 3√6 with the other numbers in the other brackets.

2√7(5√2+4√3) + 3√6(5√2+4√3)

Multiply number with number and root with root

10√14 +8√21+15√12+12√18

Then look for the roots which have a perfect number and can be broken down. There is 12 and 18 which have perfect numbers.

10√14 +8√21+(15√4 x√3) +(12√9 x √2)

10√14 +8√21 +15 x 2 x√3 +12 x 3 x √2

10√14+8√21+30√3 +36√2 ans

Answer:

If the triangular prism is bigger than the rectangular prism, it will have a greater volume. There are also many other reasons listed below:

Possible reasons:

Please mark Brainliest if correct.

Sorry if it is not correct.

Answer:

600

Step-by-step explanation:

the value of 6 in 6000 is thousands

600x10=6000

Answer:

Step-by-step explanation:

Answer:

x = -7

Step-by-step explanation:

4(2x + 14) = 0

Divide each side by 4

2x+14 = 0

Subtract 14 from each side

2x+14-14 = 0-14

2x= -14

Divide each side by 2

2x/2 = -14/2

x = -7

Answer:

C, -7

Step-by-step explanation:

Use distributive property to get: 8x +56 = 0

Isolate x to get: 8x = -56

Then divide each side by 8: x= -7

The answer is C

Answer:

D

Step-by-step explanation:

The mean is the average summing all values together and dividing by the number of values been investigated.

Hence since no values exist between 201-350 that means the mean can not be there.

Answer:

The relative frequency of the class 201 - 350 is 0.

Step-by-step explanation:

Answer:

69.08

Step-by-step explanation:

Area equals pi r times 2

A equals 3.14 times 11 times 2

Step-by-step explanation:

area of circle = pi r^2

area = 22/7 × 11yd× 11yd

area = (2662yd^2)/7

area = 380.3 yd^2

Answer:

I think the commission amount is $210

Answer:

d=-2 c=-3

Step-by-step explanation:

3c-8d=7

4(c+2d=-7)

3c-8d=7

4c+8d=-28

4c+3c-8d+8d=7-28

7c=-21

c=-3

c+2d=-7

-3+2d=-7

2d=-4

d=-2

Given.

[tex](3c-8d=7)=(c+2d=-7)[/tex]

Multiply 4 to the second equation.

[tex]4(c+2d=-7)[/tex]

[tex]3c+8d=-28[/tex]

Compare the like terms.

[tex]4c+3c-8d+8d=7-28[/tex]

Solve.

[tex]7c=-21[/tex]

Divide 7 to both sides

[tex]\frac{7c}{7}=\frac{-21}{7}[/tex]

[tex]c=-3[/tex]

Substitute (-3) for c into the original second equation.

[tex]c+2d=-7[/tex]

[tex]-3+2d=-7[/tex]

Add (3) to both sides.

[tex](-3+2d=-7)+3[/tex]

[tex]2d=-4[/tex]

Divide (2) to both sides.

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

[tex]d=-2[/tex]

Check your work.

[tex]3(-3)-8(-2)=7[/tex]

[tex]-9+16=7[/tex]

[tex]7=7[/tex]

[tex]c+2d=-7[/tex]

[tex]-3+2(-2)=-7[/tex]

[tex]-3-4=-7[/tex]

[tex]-7=-7[/tex]

Therefore your answer is.

[tex]c=-3\\d=-2[/tex]

Answer:

Step-by-step explanation:

Given the first step in determining the solution to the system of equations,

y = –x2 – 4x – 3 and y = 2x + 5, algebraically as setting the two equations equal as shown:  –x2 – 4x – 3 = 2x + 5, the next step will be to combine like terms onto one side of the equation. The like terms are the terms containing the variable x as shown;

-x²-4x-2x = 5+3

As we can see, the term containing x in the right hand side of the equation (i.e 2x) are being brought to the left side of the equation. This will be the next step in the calculation

Answer:

D. Combine like terms onto one side of the equation.

Step-by-step explanation:

Answer:

x= 5t - a

Step-by-step explanation:

6x + a = 5(x+t)

If you expand 5(x+t), you will get 5x + 5t

i.e. 6x + a = 5x + 5t

Add the additive inverse of 5x to both sides (The additive inverse of 5x is -5x)

i.e. 6x + a - 5x = 5x + 5t - 5x

     x + a = 5t

Then, add the additive inverse of "a" to both sides (The additive inverse of a is -a)

i.e. x + a - a = 5t - a

x = 5t - a

Hope this helps!!!

Answer:

165

Step-by-step explanation:

First, m<UTS=m<UTV+m<VTS by Angle Addition Postulate.  Then, you substitute all the values that you provided for the angles.  15x+15=x+15+140.  You then solve for x.

15x+15=x+155

14x=140

x=10

You then plug back in 10 for X in the value of m<UTS.  15(10)+15=165

Answer:

(x+6)² = 13

Step-by-step explanation:

Answer:

a) (5, 7, 9, 11, 13, 15, 17, 19, ...) Recursivo

b) (1, 4, 9, 16, 25, 36, 49, 64, ...) Recursivo

c) (1, 8, 27, 64, ...) Recursivo

d) (2, 5, 8, 11, 14, 17, ...) Recursivo

Step-by-step explanation:

Uma função recursiva é aquela em que os termos subsequentes da função são calculados com base nos termos anteriores

O comportamento recursivo é exibido pelos objetos quando consiste em seguir as partes;

1) Uma base que é predefinida

2) Um processo ou etapa recursiva que produz termos subsequentes pela aplicação de certos processos

Para a série;

a) (5, 7, 9, 11, 13, 15, 17, 19, ...)

Aqui 5 é a base e os termos subsequentes são encontrados adicionando 2 ao termo anterior, portanto, é uma função recursiva

aₙ = aₙ₋₁ + 2

b) (1, 4, 9, 16, 25, 36, 49, 64, ...)

Aqui 1 é a base e os termos subsequentes são encontrados ao quadrado da soma da raiz do termo anterior e 1, portanto, é uma função recursiva

aₙ = (√ (aₙ₋₁) + 1) ²

c) (1, 8, 27, 64, ...)

Aqui 1 é a base e os termos subsequentes são encontrados elevando à potência de três a soma da raiz cúbica do termo anterior e 1, portanto, é uma função recursiva

aₙ = (∛ (aₙ₋₁) + 1) ³

d) (2, 5, 8, 11, 14, 17, ...)

Aqui 2 é a base e os termos subsequentes são encontrados adicionando 3 ao termo anterior, portanto, é uma função recursiva.

Answer:

length times width so.... 24

Answer:

12.73

Step-by-step explanation:

The diagonal of the square forms the shape of a right angle with two adjacent sides of the square.

The diagonal is the hypotenuse.

Pythagoras theorem states that the square of the hypotenuse is equal to the sum of the square of the other two sides of the triangle:

[tex]d^2 = a^2 + b^2[/tex]

where d = hypotenuse = diagonal.

Since the other two sides are equal, then:

[tex]d^2 = a^2 + a^2\\\\d^2 = 2a^2[/tex]

The length of the side of the square is 9:

[tex]d^2 = 2 * 9^2 \\\\d^2 = 2 * 81\\\\d^2 = 162\\\\d = \sqrt{162}\\ \\d = 12.73[/tex]

The length of the diagonal is 12.73

Answer:

12.73

Step-by-step explanation:

Answer:

scale factor = 3

Step-by-step explanation:

The scale factor is the ratio of corresponding sides, larger to smaller.

scale factor = [tex]\frac{BC}{TB}[/tex] = [tex]\frac{12}{4}[/tex] = 3

Answer:

10

Step-by-step explanation:

Since each ornament takes 1/4 of a piece of Bristol board we divide 2 1/2 by 1/4

2 1/2 = 5/2

(5/2)/(1/4) = 20/2 = 10

Answer:

'''A ray has one endpoint and extends indefinitely in one direction. A pair of opposite rays are two rays that have the same endpoint and extend in opposite directions. Rays are always named with two points and the first point in the name must be the endpoint.'''

Answer:

[tex]25:35[/tex]

Step-by-step explanation:

[tex]\frac{60}{5+7}[/tex]

[tex]\frac{60}{12}[/tex]

[tex]=5[/tex]

[tex]5:7[/tex]

[tex]5 \times 5 :7 \times 5[/tex]

[tex]25:35[/tex]

Answer:

The correct option is;

The expressions are equivalent because Negative 3 (2) (5 minus 4) + 3 (2 - 6) = negative 18 and Negative 12 (1) minus 6 = negative 18

Step-by-step explanation:

The parameters given are;

First expression 3 × X × (5 - 4) + 3 ×(X - 6)

Second expression -12 × X - 6

Therefore;

For the first expression, for all X, e have;

3 × X × 1 + 3 ×(X - 6) = -3·X  + 3·X -18 = -18

The second expression gives -12·X - 6

When both expressions are equal, we have;

-12·X - 6 = -18

∴ X = (-18 + 6)/(-12) = 1

Hence the correct option is that the expressions are equivalent because Negative 3 (2) (5 minus 4) + 3 (2 - 6) = negative 18 and Negative 12 (1) minus 6 = negative 18.

Answer:

The expressions are not equivalent because Negative 3 (2) (5 minus 4) + 3 (2 minus 6) = negative 18 and Negative 12 (2) minus 6 = negative 30

Or

Answer A

Step-by-step explanation:

Apparently, we're trying to see if ...

 -3(x)(5 -4) + 3(x -6) = -12(x) -6

by evaluating the expressions for x=2:

 -3(2)(5-4) +3(2 -6) ?= -12(2) -6

 -6 -12 ?= -24 -6

 -18 ≠ -30 . . . . . . . . . shows expressions are not equivalent

Answer:

Federal tax amount = $18,425

Step-by-step explanation:

Given:

Total sales amount = $335,000

Federal tax rate = 5.5%

Find:

Federal tax amount = ?

Computation:

⇒ Federal tax amount = Total sales amount × Federal tax rate

⇒ Federal tax amount = $335,000 × 5.5%

⇒ Federal tax amount = $335,000 × 0.055

⇒ Federal tax amount = $18,425

Therefore, total amount of federal tax owed is $18,425

Answer: B) -8/9

Step-by-step explanation:

I would start by looking inside the parenthesis to see if anything could be simplified. We see the terms -5 and -3x, and upon realizing that there is no way to simplify, we can go ahead and just simplify the left side of the equation as much as we can before worrying about breaking the equation down. Distribute the -9 to the -5 and the -3x (multiply -9 by -5 and -9 by -3x). Multiplying two negative numbers will result in a positive value, so the left side of your equation should end up looking like this: 45+27x=21. Now, we can start working to get the variable on its own. Subtract 45 from both sides of the equation. On the left side this cancels out and leaves you with 27x. On the right side you have more of the negative value than positive value, so you end up with -24. The equation now looks like this: 27x=24. The only thing left to do is divide the equation by 27. On the left side of the equation, this leaves you with just x. On the right side, you get -24/27. Normally at this point I would divide out to get the decimal form (I prefer working with decimals) but bc the answer choices are all fractions there's not really a good use to, so instead let's just find the greatest common denominator (GCD) which would be 8. (Just as a clarification the GCD is the largest number you can divide both numbers by evenly.) Divide both the numerator and denominator by eight leaves you with -8/9. Therefore, x= -8/9.

________________________________

Hey!!

Solution,

(x-2)(X+5)=0

Either,

x-2=0

X=0+2

X=2

or,

X+5=0

X=0-5

X=-5

Hope it helps

Good luck on your assignment

____________________________

Answer:

Average speed of boat = 3.67 km/h

Average speed of stream = 0.63 km/h

Step-by-step explanation:

30 km upstream in 10 hours gives a speed of 30/10 = 3 km/h relative speed of boat and stream

Same way, 44 km in 10 hrs = 4.4 km/h relative speed of boat and stream.

Let the speed of the stream be y

Let the speed of both be x, then

x - y = 3.... (1)

x + y = 4.4.... (2)

Subtract 1 from 2

2y = 1.4

y = 1.4/2 = 0.7 km/h

substitute value of y in 1

x - 0.7 = 3

x = 3.7 km/h

Also, 40 km upstream in 13 hrs gives speed of 3.08 km/h

55 km in 13 hrs gives 4.2 km/h

Let speed of boat be x and that of stream be y

x - y = 3.08.... (1)

x + y = 4.2..... (2)

Subtract 1 from 2

2y = 1. 12

y = 0.56 km/h

Substitute value of y in 1

x - 0.56 = 3.08

x = 3.64 km/h

Average speed of boat = (3.7 + 3.64)/2

= 3.67 km/h.

Average speed of stream = (0.7 + 0.56)/2 = 0.63 km/h

Answer:

As we know that,

[tex]\bigstar \: \: \sf Time = \dfrac{Distance}{Speed} \\ \\ [/tex]

[tex]\bigstar\:\underline{\boldsymbol{According\: to \:the\: Question\:now :}} \\[tex]

[tex]:\implies \sf \dfrac{30}{x - y} + \dfrac{44}{x + y} = 10 \\ \\ \\ [/tex]

[tex]:\implies \sf \dfrac{40}{x - y} + \dfrac{55}{x + y} = 13 \\ \\ \\[/tex]

[tex]\sf Let \: \dfrac{1}{x - y} = \textsf{\textbf{m}} \sf \: \: and \: \: \sf{\dfrac{1}{x + y} = \textsf{\textbf{n} }}\\ \\ \\[/tex]

[tex]:\implies \sf 30m + 44n = 10\: \: \: \: \Bigg\lgroup \textsf{\textbf{Equation (i)}}\Bigg\rgroup \\ \\ \\[/tex]

[tex]:\implies \sf 40m + 55n = 13\: \: \: \: \Bigg\lgroup \textsf{\textbf{Equation (ii)}}\Bigg\rgroup \\ \\ \\[/tex]

[tex]\qquad\tiny \underline{\frak{ Multiply \: equation \: (ii) \: by \: 3 \: and \: equation \: (i) \: by \: 4 :}} \\[/tex]

[tex]:\implies \sf 120m + 176n = 40\: \: \: \: \Bigg\lgroup \textsf{\textbf{Equation (iii)}}\Bigg\rgroup \\ \\ \\[/tex]

[tex]:\implies \sf 120m + 165n = 39\: \: \: \: \Bigg\lgroup \textsf{\textbf{Equation (iv)}}\Bigg\rgroup \\ \\ \\[/tex]

[tex]\qquad\tiny \underline{\frak{ Substracting \: equation \: (iii) \: from \: equation \: (iv) \: we \: get :}} \\[/tex]

[tex]\sf 120m + 176n = 40 \\ \\

\sf 120m + 165n = 39 \\ \\ [/tex]

[tex]\sf \: \: ( - ) \:\:\: \: \: ( - ) \: \: \: \: \: \: \: ( - ) [/tex]

_____________________

[tex]\: \: \: \: \qquad\sf 11n= 1 \\[/tex]

[tex]\: \: \: \: \: \qquad\sf n= \dfrac{1}{11} \\ \\ [/tex]

[tex]\qquad\tiny {\frak{ Put\: n = \dfrac{1}{11}\:in\:equation \: (i) \: we \: get :}} \\[/tex]

[tex]\dashrightarrow\:\:\sf 30m + 44 \times \dfrac{1}{11} = 10 \\ \\ \\[/tex]

[tex]\dashrightarrow\:\:\sf 30m= 10 - 4 \\ \\ \\[/tex]

[tex]\dashrightarrow\:\:\sf 30m= 6 \\ \\ \\[/tex]

[tex]\dashrightarrow\:\:\sf m= \dfrac{6}{30} \\ \\ \\ [/tex]

[tex]\dashrightarrow\:\:\sf m= \dfrac{1}{5} \\ \\ \\[/tex]

[tex]\dashrightarrow\:\:\sf \dfrac{1}{x - y} = m\\ \\ \\[/tex]

[tex]\dashrightarrow\:\:\sf x - y= 5\: \: \: \: \Bigg\lgroup \textsf{\textbf{Equation (v)}}\Bigg\rgroup \\ \\ \\[/tex]

[tex]\dashrightarrow\:\:\sf \dfrac{1}{x + y} = n\\ \\ \\[/tex]

[tex]\dashrightarrow\:\:\sf x + y= 11\: \: \: \: \Bigg\lgroup \textsf{\textbf{Equation (vi)}}\Bigg\rgroup \\ \\ \\[/tex]

[tex]\qquad\tiny {\frak{Adding\:equation \: (v) \: and \: equation \: (vi) \: we \: get :}} \\[/tex]

[tex]:\implies \sf 2x = 16 \\ \\ \\[/tex]

[tex]:\implies \underline{ \boxed{ \textsf {\textbf{x = 8 km/hr}}}} \\ \\[/tex]

[tex]\qquad\tiny {\frak{Putting\:x = 8\: in \: equation \: (v) \: we \: get :}} \\[/tex]

[tex]:\implies \sf 8 - y = 5 \\ \\ \\ [/tex]

[tex]:\implies \sf y = 8 - 5 \\ \\ \\[/tex]

[tex]:\implies \underline{ \boxed{ \textsf {\textbf{y = 3 km/hr}}}} \\ \\[/tex]

[tex]\bigstar\:\underline{\sf{Therefore\: speed\: of \:boat\: in\: still \:water\: and\: speed\: of\: stream:}} \\[/tex]

[tex]\bullet\:\:\textsf{Speed of boat in stream = \textbf{8 km/hr}}\\[/tex]

[tex]\bullet\:\:\textsf{Speed of boat in still water = \textbf{3 km/hr}}\\[/tex]