Angle Terminology with Equations
Aug 03, 8:18:32 AM
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ZA and ZB are complementary angles. If m2A = (2x – 10)° and m
B = (x - 2), then find the measure of ZA.
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Answer:

2^4 x 6^4

Step-by-step explanation:

The length of the rectangular delivery box must be equal to 4 inches.

Let the length of the box be L.

Let the width of the box be W.

Let the height of the box be H.

Given the following data:

Translating the word problem into an algebraic expression;

[tex]W = 3 + L[/tex]  ......equation 1

[tex]H = 4 + L[/tex]  ......equation 2.

Mathematically, the volume of a rectangular solid is given by the formula;

[tex]Volume = length * width * height[/tex]  .....equation 3.

Substituting the values into equation, we have;

[tex]224 = L * (3 + L) * (4 + L)\\\\224 = (3L + L^{2})* (4 + L)\\\\224 = 12L + 3L^{2} + 4L^{2} + L^{3} \\\\224 = 12L + 7L^{2} + L^{3}[/tex]

Rearranging the polynomial, we have;

[tex]L^{3} + 7L^{2} + 12L - 224 = 0[/tex]

We would apply the remainder theorem to solve the polynomial.

According to the remainder theorem, if a polynomial P(x) is divided by (x - r) and there is a remainder R; then P(r) = R.

When x = 3

[tex](x - 3) = 0\\x = 3[/tex]

[tex]P(3) = 3^{3} + 7(3^{2}) + 12(3) - 224\\\\P(3) = 27 + 7(9) + 36 - 224\\\\P(3) = 27 + 63 + 36 - 224 = -98 \neq 0[/tex]

We would try with 4;

[tex]P(4) = 4^{3} + 7(4^{2}) + 12(4) - 224\\\\P(4) = 64 + 7(16) + 48 - 224\\\\P(4) = 64 + 112 + 48 - 224\\\\P(4) = 224 - 224 = 0[/tex]

Therefore, 4 is one of its roots.

Hence, the length of the rectangular delivery box must be equal to 4 inches.

Find more information on polynomial here: https://brainly.com/question/10689855

Answer:

15. 6444.44445

14. 484

Step-by-step explanation:

Answer:

-1/100

Step-by-step explanation:

Answer:-1/100

Step-by-step explanation:

Answer:

Step-by-step explanation:

If the function is f(x), then shift 8 units left and 3 units down will result in:

Apply to the given function to get:

Correct choice is A

Answer:

V = 1/32 yd^3

Step-by-step explanation:

To find the volume

V= l*w*h  where l is length, w is width, and h is height

V = 1/4 * 1/4 * 1/2

V = 1/32 yd^3

Answer:

First, we apply the Distributive property and then we combine like terms,

To combine like terms, we add or subtract.

[tex]-(2x +y) - 2 ( -x - y)[/tex]

[tex]=-2x-y+2x+2y[/tex]

[tex]=(-2x+2x)+(-y+2y)[/tex]

[tex]=0+y[/tex]

[tex]=y[/tex]

OAmalOHopeO

Answer:

y is the simplest result here.

Step-by-step explanation:

Perform the indicated multiplication as a first step towards simplifying this expression:

-2x - y + 2x + 2y

-2x and 2x cancel each other out, leaving 2y - y, or just y

Answer:

hope this helps

Step-by-step explanation:

Adjacent angles are two angles that have a common side and a common vertex (corner point) but do not overlap in any way.

Answer:

the two angles that have a common sides and a common vertex but do not overlap in any way is called adjacent angles.

Step-by-step explanation:

a)-5x+6=y

b)2x-1=y

c) -3/6x+2=y

Step-by-step explanation:

5x = -y + 6

y = 6-5x

-5y +10x = 5

5y = 10x -5

y = 10x-5/5

y = 2x -1

6y = -3x+12

y = -3x+12/6 = -1/4x +2

Step-by-step explanation:

it was helpful to you

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[tex] {x}^{2} + 7x \\ x(x + 7) \\ \\ \\ 6 + 9x \\ 3(2 + 3x) \\ \\ 6 {y}^{2} - 9xy \\ 3x(2y - 3x)[/tex]

Answer:

A. (Pay as you go) $120 B. (Regular deal) $90 C. (All-in-one price!) $100 D. The "Regular deal" option would be the least expensive for Carl.

Step-by-step explanation:

If Carl does the "Pay as you go" option he would be charged $6 each time. If he works out 20 times a month, we can multiply 20 by 6 to get a total of $120 for that option.

If Carl does the "Regular deal" option he would be charged $50 + an additional $2 for each time he works out. From there, we can get the equation 2x + 50 where x is the amount of time he works out. If we plug in 20 for x (as he works out 20 times a month), we get 2(20) + 50 which equals a total of $90 for that option.

If Carl does the "All-in-one Price!" option he would be charged $100 for the whole month meaning he has unlimited use of the gym with no extra charge besides the $100.

The cheapest option is the "Regular deal" option as it charges $90 compared to the $100 for the "All-in-one Price!" option & the $120 for the "Pay as you go" option.

Answer:

2.)4n>(n/2)^2

3. (The problem isn't clear)

4.)n^2+2n-3=129

5.)n-5=171

Step-by-step explanation:

2.)

4n(four times the number) >(larger than) (n/2)^2 (half the number squared)

4.)

Sum=addition

n^2 (number squared) +2n (twice the number)-3=129

5.)

N(unknown number of pages) -5(amount of pages already read)= 171(the number of pages it took her to finish)

Answer:

X+y=7

Step-by-step explanation:

i  remember  doing something like this but mines had the word onion rings .

Answer:

1g - 50 = p(g)

Step-by-step explanation:

The profit function is,

⇒ p(g) = g - 50

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Betty sets up a lemonade stand and charges $1 per glass.

It cost her $50 to set up the stand.

And, We have to find the function gives the profit, p, she makes by selling g glasses of lemonade.

Now, The number of glasses of lemonade sold = g,  

And, A profit, p by function p(g)

Setup cost = $50

Since, Charges for 1 glass  = 1 $

Hence, Charges for g glasses = 1.g  = $g

Here, The cost = $50  

Hence, Profit  = $g - 50

⇒ p(g)  =  g - 50  

Therefore, The profit function is,

⇒ p(g) = g - 50

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Answer:

D) 12.2

Step-by-step explanation:

EH is median

FH = HG

6x - 1.1 = 4x + 1.3

Add 1.1 to both sides

6x = 4x + 1.3 + 1.1

6x = 4x + 2.4

Subtract 4x from both sides

6x - 4x = 2.4

2x = 2.4

Divide both sides by 2

x = 2.4/2

x = 1.2

FH = 6x - 1.1

    = 6*1.2 - 1.1

    = 7.2 - 1.1

    = 6.1

FG = 6.1 + 6.1 = 12.2

Answer:

Step-by-step explanation:

Subtract 3x from both sides

3x - 3x - 2y = -3x + y

Combine

-2y = - 3x + 7  

Divide by - 2

-2y/-2 = -3x/-2 + 7/-2

y = 3x/2 - 7/2

Answer:

(0.5,3)

Hope this helps..Have a good day!!

Answer:

[tex]{ \underline{ \bf{ \frac{dy}{dx} = - \frac{30m}{ {(1 + {m}^{2}) }^{2} } }}}[/tex]

Step-by-step explanation:

[tex]{ \bf{m = 3x + 1}} \\ { \sf{ \frac{dm}{dx} = 3 }} \\ \\ { \bf{y = \frac{5}{1 + {m}^{2} } }} \\ \\ { \tt{ \frac{dy}{dm} = \frac{ - 10m}{ {(1 + {m}^{2} )}^{2} } }}[/tex]

Using chain rule:

[tex]{ \boxed{ \bf{ \frac{dy}{dx} = \frac{dy}{dm}. \frac{dm}{dx} }}}[/tex]

[tex]{ \sf{ \frac{dy}{dx} = - \frac{10m}{ {(1 + {m}^{2}) }^{2} } \times 3}} \\ \\ { \sf{ \frac{dy}{dx} = - \frac{30m}{ {(1 + {m}^{2}) }^{2} } }}[/tex]

[tex]{ \underline{ \sf{ \blue{christ \:† \: alone }}}}[/tex]

Answer:

Step-by-step explanation:

Never saw a problem presented in this way in all my years of teaching calculus. But I'm thinking that we need to sub that given expression for m into the equation for y and get everything into y in terms of x in order to find the derivative. I see no other way that makes sense. Can't find the derivative of y in terms of x if there's an m in there. Making that substitution:

[tex]y=\frac{5}{1+(3x+1)^2}[/tex] which simplifies to

[tex]y=\frac{5}{1+9x^2+6x+1}[/tex] and a bit more to

[tex]y=\frac{5}{9x^2+6x+2}[/tex] and now we're ready to find the derivative. Using the quotient rule:

[tex]y'=\frac{(9x^2+6x+2)(0)-[5(18x+6)]}{(9x^2+6x+2)^2}[/tex] which simplifies to

[tex]y'=\frac{-90x-30}{(9x^2+6x+2)^2}[/tex] or, equally:

[tex]y'=-\frac{90x+30}{(9x^2+6x+2)^2}[/tex]

Answer:

D) 9

Step-by-step explanation:

These angles are equal to each other because they’re alternate interior angles so:

9x + 8 = 15x - 46

9x - 15x = -46 - 8

-6x = -54

x = 9

For large enough x, exponential functions like 2ˣ will always dominate a polynomial of any degree. This is to say the denominator will always be larger than the numerator (again, for sufficiently large x). So the limit in this case would be 0. (I'll leave a link in comments to a variety of answers regarding this detail.)

But if you've been introduced to L'Hopital's rule: we have

[tex]\displaystyle \lim_{x\to\infty}\frac{5x^3+10}{6\times2^x-1} = \lim_{x\to\infty}\frac{15x^2}{6\ln(2)\times2^x} = \lim_{x\to\infty}\frac{30x}{6\ln^2(2)\times2^x} = \lim_{x\to\infty}\frac{30}{6\ln^3(2)\times2^x} = \frac1\infty = 0[/tex]

Answer:

AB is not a tangent to the circle

Step-by-step explanation:

The angle between a tangent and the radius at the point of contact = 90°

Using Pythagoras' identity to determine if the triangle is right at A

If the square of the longest side is equal to the sum of the squares on the other 2 sides then A is right.

longest side = 15 , then 15² = 225

8² + 9² = 64 + 81 = 145 ≠ 225

Then AB is not a tangent to the circle

Answer:

6 1/6  or 6 2/12

Step-by-step explanation:

2 4/6 + 3 1/2

Get a common denominator

2 4/6 + 3 1/2 * 3/3

2 4/6 + 3 3/6

5 7/6

Rewriting

5 6/6 + 1/6

6 1/6

To obtain an estimate of a parameter of a population, we use confidence intervals.

Confidence intervals:

The larger the sample size, the closest the parameter estimate is to the value of the population, as the margin of error of confidence intervals is inversely proportional to the sample size, that is, a greater sample leads to a smaller margin of error.

Thus, you should select the highest sample size in the options.

For more on confidence interval/margin of error, you can check https://brainly.com/question/22718960

Answer: 1/6

Step-by-step explanation:

Probability of getting heads = 50/100

= 1/2

Probability of tossing a 3 or 5 = 2/6

= 1/3

Now probability of getting both = 1/2×1/3

= 1/6

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Answer:

1/6

Step-by-step explanation:

There are two possible outcomes for tossing a coin

heads and tails

P(heads)= heads/ total = 1/2

Rolling a die has 6 possible outcomes 1,2,3,4,5,6

P*3 or 5) = 3 or 5 /total = 2/6 = 1/3

Multiply the probability of independent events together

1/2 * 1/3 = 1/6

Answer:

the answer is 10 or 6^2+8^2=100

√100=10

Step-by-step explanation:

Looking at the graph, if you plot the point (-1,-4) you'll see that the point is on the area(red one, in the graph I attached) the graph covers, you can also put x=-1 and y=-1 to check if it's true or not

Answer:

(-1, -6)

Step-by-step explanation:

1. Identify the coefficients

a = 1/4 b = 1/2

2. Substitute the coefficients in the equation.

x = -b/2a

3. Solve the equation.

x = -1

4. Evaluate the function for x = -1 (to find y).

5. Calculate the function value.

6. y = -6

2x+5

x+1

2+3.......

x+1

Answer:

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Answer: option A the amount of gasoline larry uses

Step-by-step explanation:

This is because a independent variable is not changed by other variables.

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