Consider theta =239°.
a. State an angle coterminal to theta. _______
b. Sketch theta.
c. What is the reference angle?

The expression of the zeros is (4a - 3)(2a + 9) and the zeros are a = 3/4 and a = -9/2

From the question, we have the following parameters that can be used in our computation:

g(a) = 8a² + 30a - 27

Expand the expression

g(a) = 8a² + 36a - 6a - 27

Factorize

g(a) = 4a(2a + 9) - 3(2a + 9)

So, we have

g(a) = (4a - 3)(2a + 9)

To do this, we set g(a) to 0

So, we have

(4a - 3)(2a + 9) = 0

This gives

4a = 3 and 2a = -9

So, we have

a = 3/4 and a = -9/2

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Answer:

X(−64/3, 0); 8/3

Step-by-step explanation:

To find the coordinates of the point X, first find the scale factor for a dilation of two similar triangles in the coordinate plane

To determine the scale factor, set up a ratio of the lengths of two corresponding sides of the triangles.

Use the Distance Formula d=(x2−x1)2+(y2−y1)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√ to find the length of the sides JK and JW.

Point J is the origin. Thus, the coordinates of the point J are (0,0).

It is given in the figure that the coordinates of the point K are (0,6).

To find JK, substitute x1=0, x2=0, y1=0, and y2=6 into the distance formula.

JK=(0−0)2+(6−0)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√=62‾‾√=6

The length of JK is 6.

It is given in the figure that the coordinates of the point W are (0,16).

To find JW, substitute x1=0, x2=0, y1=0, and y2=16 into the distance formula.

JW=(0−0)2+(16−0)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√=162‾‾‾‾√=16

The length of JW is 16.

To determine the scale factor, set up a ratio of the lengths of two corresponding sides, JW and JK, of the triangles.

JWJK=166=83

The scale factor is 83.

To find the coordinates of the point X multiply the coordinates of the point L by the scale factor.

It is given in the figure that the coordinates of the point L are (−8,0).

X(−8⋅83,0⋅83)=X(−643,0)

The coordinates of the point X are (−643,0).

The figure shows the same triangles K J L and W J X as in the beginning of the task. Point X is at minus 64 thirds, zero.

Therefore, the coordinates of X is (−643,0) and the scale factor is 83.

With the stated cooling rate of k = 0.012, it follows that the puddle of water would ice in the arctic cold front in roughly 97.8 minutes

The oscillation of a substance's components is measured by its temperature. When something is hot, it indicates that its components move relatively quickly on average. Despite having a high temperature, a substance's heat capacity is very low because it has a small number of light elements.

We can use the Newton's law of cooling formula to solve this problem.

\(T = R + ( To - R ) \times e ^{(-kt )}\)

Let's assume that the initial temperature of the water is 55°F and the temperature of the surroundings is 5°F (due to the arctic cold front).

We are looking for the time it takes for the water to cool down to 32°F (the freezing point of water).

Therefore, we have:

T = 32°F

T0 = 55°F

R = 5°F

k = 0.012

Substituting these values into the formula, we get:

\(32 = 5 + (55 - 5) \times e^{(-0.012t)}\)

Simplifying the equation, we get:

\(27 = 50 \times e^{(-0.012t)}\)

Dividing both sides by 50, we get:

\(0.54 = e^{(-0.012t)}\)

Taking the natural logarithm of both sides, we get:

ln(0.54) = -0.012t

Solving for t, we get:

t = ln(0.54) / (-0.012)

t ≈ 97.8 minutes

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9514 1404 393

Answer:

  (2ac+1)/(abc+2c+1)

Step-by-step explanation:

It helps to understand the factoring of the numbers involved.

  63 = 3²·7

  140 = 2²·5·7

The "change of base" formula is also useful.

  \(\log_b{a}=\dfrac{\log{a}}{\log{b}}\)

__

Using this, we can write ...

  a = log(3)/log(2)   ⇒   log(3) = a·log(2)

  b = log(5)/log(3)   ⇒   log(5) = b·log(3) = ab·log(2)

  c = log(2)/log(7)   ⇒   log(2) = c·log(7)

This lets us write everything in terms of log(7):

  log(2) = c·log(7)

  log(3) = ac·log(7)

  log(5) = abc·log(7)

__

The desired logarithm is ...

  \(\log_{140}{}63=\dfrac{\log{63}}{\log{140}}=\dfrac{2\log{(3)}+\log{(7)}}{2\log{(2)}+\log{(5)}+\log{(7)}}\\\\=\dfrac{2ac\cdot\log{(7)}+\log{(7)}}{2c\cdot\log{(7)}+abc\cdot\log{(7)}+\log{(7)}}\\\\\boxed{\log_{140}{63}=\dfrac{2ac+1}{abc+2c+1}}\)

_____

The attachment is a numerical check of this result.

To find the equation of a parabola that satisfies the given conditions, we can use the slope-intercept form of a parabola, y = ax^2 + bx + c. We are given the slopes at x = 1 and x = -1, as well as a point on the parabola. By using these values, we can determine the coefficients a, b, and c and obtain the equation of the parabola.

Given that the parabola has a slope of 13 at x = 1, we can differentiate the equation y = ax^2 + bx + c with respect to x and set it equal to 13. This gives us the equation 2a + b = 13. Similarly, using the slope of -19 at x = -1, we obtain the equation -2a + b = -19.

Next, we use the point (1,14) that lies on the parabola to substitute the values of x and y into the equation. This gives us the equation a + b + c = 14.

Solving these three equations simultaneously will give us the values of a, b, and c, which can be used to form the equation of the parabola in the form y = ax^2 + bx + c.

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Answer:

B. One whole number one over two. 1½

To find -f(x) + 4g(x), we substitute the given functions f(x) = 2x + 5 and g(x) = x² - 3x + 2 into the expression. After performing the operation, we obtain a new function. The domain of the resulting function will depend on the domain of the original functions, which in this case is all real numbers.

First, we substitute f(x) = 2x + 5 and g(x) = x² - 3x + 2 into the expression -f(x) + 4g(x):

-f(x) + 4g(x) = -(2x + 5) + 4(x² - 3x + 2)

Expanding and simplifying the expression, we have:

-2x - 5 + 4x² - 12x + 8

Combining like terms, we get:

4x² - 14x + 3

The resulting function is 4x² - 14x + 3. The domain of this function will be the same as the domain of the original functions f(x) = 2x + 5 and g(x) = x² - 3x + 2. Since both f(x) and g(x) are defined for all real numbers, the domain of the resulting function, -f(x) + 4g(x), will also be all real numbers.

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Answer:

x=9.3

Step-by-step explanation:

use SohCahToa

in this case u use cos

cos(41°)=7/x

x=7/cos(41)

x=9.275090953

x=9.3

Students raised $225 in the first week and $90 in the second week.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, a student club has a goal to raise $750 to buy new books for a library.

In the first week, the club raised 30% of its goal.

Now, 30% of 750

= 30/100 ×750

= 3×75

= $225

In the second week, the club raised 12% of its goal.

Now, 12% of 750

= 12/100 ×750

= 0.12×750

= $90

Hence, students raised $225 in the first week and $90 in the second week.

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Answer:

1.) x = 5

2.) x = -5

Step-by-step explanation:

(22x2 -  15) -  85  = 0  

4x2 - 100  =   4 • (x2 - 25)  

(x + 5)  •  (x - 5)    

4 • (x + 5) • (x - 5)  = 0  

 x+5 = 0              

x = -5

x-5 = 0  

For the given function the zeroes will be 0,-11/2, and 11 while the degree of the function is 5.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

T(h)=h(2h+1)²(h-11)²

The function is simplified as,

T(h)=h((2h)²+1²+2(2h)(1))(h²+121-22h)

T(h)=h[4h²+1+4h](h²+121-22h)

T(h)=(h³+121h-22h²)(h²+121-22h)

From the above function, it is observed that the degree of the given function is 5.

The zeroes of the given function are obtained as,

T(h)=h(2h+1)²(h-11)²

T(h)=0

h = 0

(2h+1)²=0

2h+1=0

h= -1/2

(h-11)²=0

h=11

Thus, for the given function the zeroes will be 0,-11/2, and 11 while the degree of the function is 5.

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Lauren's accounting profit can be calculated by subtracting her total expenses (rent, labor costs, and overhead expenses) from her total revenue.

To determine Lauren's accounting profit, we need to subtract her total expenses from her total revenue. Her total revenue for the year was $145,000. Her total expenses include rent ($12,000), labor costs ($65,000), and overhead expenses ($15,000).

To calculate her accounting profit, we subtract the total expenses from the total revenue:

Accounting Profit = Total Revenue - Total Expenses

Accounting Profit = $145,000 - ($12,000 + $65,000 + $15,000)

Accounting Profit = $145,000 - $92,000

Accounting Profit = $53,000

Therefore, Lauren's accounting profit for the year is $53,000. This represents the amount of interests left after deducting all the expenses from the total revenue. It is important to note that accounting profit does not take into account other factors such as opportunity costs or non-cash expenses, but it provides a basic measure of the profitability of the business based on the given information.

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There are approximately 3.72 x 10⁴¹ ways that Anna can hand out 1 treat to each of the 36 children who come to her door.

Anna has 2 dozen Rollo bars, which is equivalent to 2 x 12 = 24 Rollo bars.

She also has 1 dozen apples, which is equivalent to 1 x 12 = 12 apples.

So, Anna has a total of 24 + 12 = 36 treats to hand out.

Now, she needs to hand out 1 treat to each of the 36 children who come to her door.

This can be thought of as selecting 1 treat from the total of 36 treats for each child, without replacement, as each child can only receive 1 treat.

The number of ways to do this is given by the concept of permutations, denoted by "nPr", which is calculated as;

nPr = n! / (n - r)!

where n is the total number of items (treats) to choose from, and r is the number of items (treats) to choose.

In this case, n = 36 (total number of treats) and r = 36 (number of children).

Plugging in the values, we get;

36P36 = 36! / (36 - 36)! = 36! / 0! = 36!

Since 0! (0 factorial) is equal to 1, we can simplify further:

36! / 1 = 36!

36! ≈ 3.72 x 10⁴¹

So, there are 3.72 x 10⁴¹ ways that Anna can hand out 1 treat to each of the 36 children who come to her door.

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Answer:

  z = 3√13

Step-by-step explanation:

The length of z is the geometric mean of the segments of the longest side that share a common point with z. The shorter of those is 9; the longer one is 4+9 = 13. Then ...

  z = √(9(13))

  z = 3√13

__

Additional comment

In like fashion, ...

__

These relations come about because all of these right triangles are similar. That means their side lengths are proportional.

  long side/hypotenuse = z/13 = 9/z   ⇒   z = √(9·13)

  short side/hypotenuse = x/13 = 4/x   ⇒   x = √(4·13)

  short side/long side = 4/y = y/9   ⇒   y = √(4·9)

Answer:

its 67...... ...........

Answer:

it's 67°

Step-by-step explanation:

48°+90°=(2x+4). reason is vertically opposite angles are equal

Answer: -10,30

Step-by-step explanation: I drew the graph, and it lined with 30 and interCepted -10

Step-by-step explanation:

1 with second

2 with third

3 with fourth

4 with first

Answer:

The order is 4,3,1,2

Step-by-step explanation:

The p-value of the test statistic is given as follows:

0.0072.

The test statistic is calculated as follows:

\(t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}\)

In which:

The parameters for this problem are givne as ofllows:

\(\overline{x} = 35400, \mu = 31400, s = 4700, n = 14\)

Hence the test statistic is given as follows:

\(t = \frac{35400 - 31400}{\frac{4700}{\sqrt{14}}}\)

t = 3.18.

We have a two-tailed test, as we are testing if the mean is different of a value, with t = 3.18 and 14 - 1 = 13 df, hence the p-value is given as follows:

0.0072.

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Answer:

500m/s

Step-by-step explanation:

speed= distance/time

= 100m/0.2s

=500m/s

Answer:

82°

Step-by-step explanation:

Answer:

The mistake Ivan made is that he did not follow the order of operations (PEMDAS) when evaluating the expression.

The correct order of operations is:

Parentheses

Exponents

Multiplication and Division (performed left to right)

Addition and Subtraction (performed left to right)

In this expression, there are no parentheses or exponents, so we move directly to multiplication and division.

The expression 2 x 3 should be evaluated first, which gives us 6.

So the expression becomes:

8 + 12 = 6

Adding 8 and 12, we get:

20 = 6

This is clearly not true, and we can see that Ivan made the mistake of not performing the multiplication before adding 8 and 12, which led to an incorrect answer of 10.

(PEMDAS)

2x3 = 6.

12 divided by 6 = 2

8+2= 10.

This above is what Ivan did.

2x3 = 6

equation so far: 8+12 = 6

8+12 = 20

equation after problem solved: 20 = 6

20 is not equal to 6, so therefore, Ivan made the mistake of interpreting the = sign as a division sign.

To solve the equation 15 + 2x = 36, we can start by subtracting 15 from both sides of the equation to get 2x = 21. Then, we can divide both sides by 2 to get x = 10.5. Rounded to the nearest ten-thousandth, the solution is x = 10.5000.

y = 5x + 35

When x = 0, we substitute x = 0 into the equation above and then solve for y

y = 5(0) + 35

y = 0+ 35

y = 35

when x =3, substitute into the equation and then solve for y

y = 5(3) + 35

y = 15 + 35

y = 50

when x=-7, substitute x=-7 into the equation above and then solve for y

y = 5(-7) + 35

y = -35+ 35

y=0

x y (x,y)

0 35 (0, 35)

3 50 (3, 50)

-7 0 (-7, 0)

Answer:

What is 12.5 percent of 350? = 43.75.

Answer:

The correct value for n is 2800.

Step-by-step explanation:

We need to find the value of n.  According to the given information, 12.5% of n is 350.  Here the percentagle 12.5% must be converted to the equivalent 0.125.  

Then the equation to be solved is 0.125n = 350, so that

       350

n = --------- = 2800

      0.125

The correct value for n is 2800.

The water capacity of the container, when completely full, is given by \(\(V_{\text{total}} = 5 \times 5 \times 12 + 6^3 = 985\)\) cubic inches.

To calculate the water capacity of the container, we need to find the total volume of the plastic rectangular prism and the plastic cube.

Let's denote the dimensions of the plastic rectangular prism as length \((\(L\)), width (\(W\)), and height (\(H\))\), and the side length of the plastic cube as \(S\).

The volume of the rectangular prism is given by \(\(V_1 = L \times W \times H\)\), and the volume of the cube is given by \(\(V_2 = S^3\).\)

Given the information provided, the dimensions are as follows: \(\(L = 5\) in, \(W = 5\) in, \(H = 12\) in, and \(S = 6\) in.\)

The total volume of the container is obtained by adding the volumes of the rectangular prism and the cube: \(\(V_{\text{total}} = V_1 + V_2\).\)

Substituting the values, we have: \(\(V_{\text{total}} = 5 \times 5 \times 12 + 6^3 = 985\)\) cubic in.

Therefore, the container will hold \(985\) cubic inches of water when completely full.

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The statement that , "The set Span{u,v} is always visualized as a plane through the origin" is False because if vectors are scalar multiples of each other, then set Span{u,v} is a line through origin .

The set Span{u,v} is defined as the set of all linear combinations of vectors "u" and "v" . This set can be visualized as a plane in three-dimensional space if the vectors are not scalar multiples of each other.

The plane may not necessarily pass through the origin, unless one of the vectors is the zero vector .

If the vectors are scalar multiples of each other, then the set Span{u,v} is a line through the origin, and if one of the vectors is the zero vector, then the set Span{u,v} is a plane through the origin.

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Answer:

Divide 3/4 by 3/5 to get 1 1/4.

Step-by-step explanation:

To find area, you multiply the length by the width. However, they gave you the area and the width. Therefore, you divide the width by the area (I think).

3/4 divided by 3/5 =  1 1/4

The length is 1 1/4.

Answer:

3x+38

Step-by-step explanation:

1. (10x2 +5x-3)+(7x2 -2x+7) : rewrite problem

2. (20+5x-3)+(14-2x+7) : PEMDAS (10x2=20 and 7x2=14)

3. (5x+17)+(-2x+21) : PEMDAS (20-3=17 and 14+7=21)

4. 3x+38 : Combine like terms