Find the value of x

The cosine of angle B is: cos(B) = AC / AB = 20/29

The Pythagorean Theorem, a well-known geometric theorem that states that the sum of the squares of the legs of a right-angled triangle is equal to the square of the hypotenuse (the opposite side of the right angle) - that is, in familiar algebraic notation. , a2 + b2 = c2 .

In a right triangle, the cosine of an angle is defined as the ratio of the adjacent side to its hypotenuse. In this case, angle B is the angle we are interested in, and the adjacent side is side AC. Using the Pythagorean theorem, we find the length of side AC:

AC² = AB²+ BC²

AC² = 29² - 21²

AC² = 400

AC = 20

Therefore, the cosine of angle B is:

cos(B) = AC / AB = 20/29

Other trigonometric ratios of angle B can be found using the following formulas:

sin(B) = BC / AB = 21/29

tan(B) = BC / AC = 21/20

csc(B) = AB / BC = 29 / 21

sec(B) = AB / AC = 29/20

bed (B) = AC / BC = 20 / 21  

Thus, the trigonometric ratios of angle B are:

sin(B) = 21/29

cos(B) = 20/29

tan(B) = 21/20

csc(B) = 29/21

sec(B) = 29/20

crib(B) = 20/21

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Answer:

B

Step-by-step explanation:

Pretty sure this is B. The height of your parents is the clearest way to determine how tall someone you'll be, and usually, your shoe size depends on your height. You can see this in real life. Shaq has huge feet because he's a huge guy.

A makes no sense. C might, but this will only apply to really small children. And D makes no sense either. So B is the best choice.

Answer:

C. age of the student is likely to be the answer

A statistical question would be:  What is the average salary of teachers in this school district?

When a question can be answered statistically, it can be done so by gathering and analysing data, for example. This particular question aims to comprehend a population or a phenomenon by using numerical data. In contrast to non-statistical questions, which are more concerned with acquiring information or opinions, statistical questions are more concerned with getting and analysing data. Statistical procedures including sampling, data analysis, and inference are frequently used to answer statistical issues.

A statistical question would be:  What is the average salary of teachers in this school district?

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Answer:

b. parallelogram

Step-by-step explanation:

The figure cannot be square because a square has four congruent sides and four right angles, and this figure does not have either of those properties.

The figure cannot be a triangle because a triangle has only three vertices, and this figure has four vertices.

The figure cannot be a trapezoid because a trapezoid has at least one pair of parallel sides, and it is not clear from the given information whether any of the sides are parallel.

The figure could be a parallelogram, which is a quadrilateral with opposite sides parallel. To determine whether this is the case, we can check whether the slopes of opposite sides are equal. Here are the slopes of the sides:

AB: (4-1)/(1-(-4)) = 3/5

BC: (-1-4)/(6-1) = -5/5 = -1

CD: (-4-(-1))/(1-6) = 3/5

DA: (1-(-4))/(-4-1) = -5/5 = -1

We can see that the slopes of opposite sides AB and CD are equal, and the slopes of opposite sides BC and DA are equal. Therefore, the figure is a parallelogram.

The figure cannot be a kite because a kite is a quadrilateral with two pairs of adjacent congruent sides, and this figure does not have that property.

So the answer is: b. parallelogram.

The polynomial function with the given properties is:[tex]f(x) = x^3 - 7x^2 + 9x - 17[/tex]

A polynomial function is a function that contains only non-negative integer powers or only positive integer exponents in the equation, such as a  quadratic equation, a cubic equation, etc. For example, 2x + 5 is a polynomial whose exponent is 1.

Since the polynomial has real coefficients and one of its zeros is complex, the complex conjugate of 4+ i, which is 4-i, must also be  zero. So the three zeros of the polynomial are -1, 4+i and 4-i.  To form a polynomial with these zeros, we start by writing  the factors of the polynomial:

(x + 1) (x - 4 - i) (x - 4 + i)

We can simplify this expression by multiplying  the factors:

[tex](x + 1) (x^2 - 8x + 17)[/tex]

Expanding this, we get:

[tex]x^3 - 7x^2+ 9x - 17[/tex]

Thus, the polynomial function with the given properties is:  

[tex]f(x) = x^3 - 7x^2 + 9x - 17[/tex]

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The polynomial function is p(x) = (-17/5)x³ + (34/5)x² + (33/5)x - 16

A polynomial function is a function that contains only non-negative integer powers or only positive integer exponents in the equation, such as a  quadratic equation, a cubic equation, etc. For example, 2x + 5 is a polynomial whose exponent is 1.

If -1 is a zero of the polynomial function, then x+1 is a factor of the polynomial. Similarly, if 4+i is a zero, then 4-i is also a zero, because complex roots always occur in conjugate pairs. Therefore, (x+1) and (x - 4 - i)(x - 4 + i) = (x - 4)² + 1 are factors of the polynomial. We can then construct the polynomial function by multiplying these factors:

p(x) = A(x+1)(x - 4 - i)(x - 4 + i)

where A is a constant that we need to determine, and p(x) is the desired third-degree polynomial function.

To determine A, we can use the y-intercept given in the problem. The y-intercept is the value of p(0), so:

p(0) = A(0+1)(0 - 4 - i)(0 - 4 + i) = A(17+4i)

But we also know that p(0) = -17, so:

-17 = A(17+4i)

Solving for A:

A = -17/(17+4i) = (-17/5) + (68/5)i

Therefore, the polynomial function we seek is:

p(x) = [(-17/5) + (68/5)i](x+1)(x - 4 - i)(x - 4 + i)

Expanding the product and simplifying, we get:

p(x) = (-17/5)x³ + (34/5)x² + (33/5)x - 16

This is a third-degree polynomial with only real coefficients, -1 and 4+i are two of the zeros, and the y-intercept is -17.

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Answer:

PMT = $52,023.26

Step-by-step explanation:

To calculate how much Fiona must deposit into her retirement account each year, we can use the formula for annuity payments:

PMT = PV x (r / (1 - (1 + r)^(-n)))

Where:

PMT is the periodic payment

PV is the present value (or desired future value) of the annuity

r is the interest rate per period (in this case, the annual yield of 6% divided by the number of periods per year, which is 1)

n is the total number of periods (in this case, 20 years)

We know that Fiona wants to have a total of $600,000 in her retirement account by the time she retires, so PV = $600,000. We also know that the interest rate per period is 6% / 1 = 0.06, and the total number of periods is 20.

Plugging these values into the formula, we get:

PMT = $600,000 x (0.06 / (1 - (1 + 0.06)^(-20)))

PMT = $600,000 x (0.06 / (1 - 0.312))

PMT = $600,000 x (0.06 / 0.688)

PMT = $52,023.26

Therefore, Fiona would need to deposit approximately $52,023.26 into her retirement account each year for the next 20 years to have a total of $600,000 by the time she retires, assuming the annual yield remains constant at 6%.

Answer: The height of the cone is [tex]12 \text{ units}.[/tex]

Step-by-step explanation:

We are given that [tex]L = \pi r \sqrt{r^2+h^2}.[/tex] Plugging in the given values of [tex]L[/tex] and [tex]r[/tex] yields:

[tex]65 \pi = 5 \pi \sqrt{25+h^2} \implies 13 = \sqrt{25+h^2}.[/tex]

Now, squaring each side of the equation, and then isolating [tex]h^2[/tex] gives us [tex]h^2=144[/tex], so [tex]\boxed{h=12}.[/tex] Note that [tex]h[/tex] cannot take any negative values because it is a side length.

Answer:

3 (x + y) (x - y)

Step-by-step explanation:

3x²-3y²​

GCF is 3

3(x² - y²)

Since both terms are perfect squares, factor using the difference of squares formula, a² − b² = (a+b) (a−b) where a = x  and b = y.

So, the answer is 3 (x + y) (x - y)

Answer:

x = 16°

Step-by-step explanation:

What we know:

∠JML = 47°

∠JKL = (7x + 21)°

∠JML is an inscribed angle

∠JKL is an inscribed angle

Inscribed angles are half of the value of their intercepted arc

So if m∠JML = 47° then mArc JL is double that or 94°

And ∠JKL is intercepted by Arc JML which is the rest of the circle not intercepted by ∠JML so

mArc JL + Arc JML = 360°

94 + Arc JML = 360

Subtract 94 from both sides to isolate Arc JML

Arc JML = 266°

So if Arc JML = 266° then it's intercepted inscribed angle is half of that.

Arc JML ÷ 2 = ∠JKL

266 ÷ 2 = ∠JKL

133 °= ∠JKL

Now we can use this value and set it equal to the expression to find the value of x

(7x + 21) = 133

Subtract 21 from both sides to isolate the x

7x = 112

Divide both sides by 7

x = 16

The areas of the region between the curves is -40/3square units.

We must first graph the curves in order to identify which one is on top in order to calculate the area of the region bounded by the curves for x in [0, 3]. y = x²− 4x + 1 and y = −x²+ 4x − 5

The vertex of the graph of y = x²− 4x + 1is at (2, -3), and it opens upward. The vertex of the graph of y =−x²+ 4x − 5 is at (2, -1), and it opens downward.

Thus, the curve y = x²− 4x + 1 is on top for x in [0, 1], and the curve y = −x²+ 4x − 5 is on top for x in [1, 3].

To determine which curve is on top, we can set them equal to each other and solve for x:

x²− 4x + 1 = −x²+ 4x − 5

2x² - 8x + 6 = 0

x² - 4x + 3 = 0

(x - 3)(x - 1) = 0

x = 1 or x = 3

Thus, the curves cross at x = 1 and x = 3. To find which curve is on top between these two points, we can test a point in between, such as x = 2:

y = x²− 4x + 1 = 1

y = −x²+ 4x − 5 = -1

Using integration, we can find the area of the region:

∫[0,1] (x²− 4x + 1) dx + ∫[1,3] (−x²+ 4x − 5) dx

= [(1/3)x³ - 2x² + x] from 0 to 1 + [(-1/3)x³ + 2x² - 5x] from 1 to 3

=[1/3-2+1]+[{-9+8-15}-{-1/3+2-5}]

=-2/3+-38/3

=-40/3 square units.

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The value of y that makes the hanger balance is 3.

The value of y can be solved considering linear equation method.

A linear equation is an algebraic equation in which the highest power of the variable(s) is always 1. It represents a straight line when graphed on a Cartesian coordinate plane. A linear equation can have one or more variables.

To solve for y in the equation 5 + y = 8, you can follow these steps:

Step 1: Subtract 5 from both sides of the equation to isolate the term with y on one side.

5 + y - 5 = 8 - 5

This simplifies to:

y = 3

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Looking at the table, If Bridget has 10 animals in total with 30 legs, it only means she has 5 chicken.

Based on the information on the table,

For the number of chicken legs, we say

9 x 2 = 18       3 x 2 = 6          7 x 2= 14       14 x 2 = 28

If we sum these number to the total number of legs in each row, it would be;  4 + 18 = 22   8+6 = 14   12 + 14 = 26     16+28 = 44

This means that all the values provided so far does not give us the accurate number of legs of the animals.

If 5p = 20L the number of hen should be 30- 20 = 10/2 = 5

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 50000\\ P=\textit{original amount deposited}\dotfill &\$23000\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &7 \end{cases}[/tex]

[tex]50000 = 23000\left(1+\frac{ ~~ \frac{r}{100} ~~ }{4}\right)^{4\cdot 7} \implies \cfrac{50000}{23000}=\left( 1+\cfrac{r}{400} \right)^{28} \\\\\\ \cfrac{50}{23}=\left( \cfrac{400+r}{400} \right)^{28}\implies \sqrt[28]{\cfrac{50}{23}}=\cfrac{400+r}{400} \\\\\\ 400\sqrt[28]{\cfrac{50}{23}}=400+r\implies 400\sqrt[28]{\cfrac{50}{23}}-400=r\implies \stackrel{ \% }{11.25}\approx r[/tex]

The probability that a randomly selected point within the circle falls in the red-shaded circle is 0.25

We have,

The area of the whole circle.

= πr²

Where r = 8

So,

= 3.14 x 8 x 8

= 200.96

Now,

Area of the red shaded circle = πr²

Where r = 4

So,

= 3.14 x 4 x 4

= 50.24

Now,

The probability that a randomly selected point within the circle falls in the red-shaded circle.

= Area of the red shaded circle / Area of the whole circle

= 50.24 / 200.96

= 1/4

= 0.25

Thus,

The probability that a randomly selected point within the circle falls in the red-shaded circle is 0.25

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Answer:

y intercept when x is 0, so the answer is 3

Answer:

Part A:

To find the total length of the two sides of the triangle, we need to add Side 1 and Side 2:

Side 1: 3x² - 4x - 1

Side 2: 4x - x² + 5

Total length: (3x² - 4x - 1) + (4x - x² + 5)

Simplifying and combining like terms, we get:

Total length: -x² + 7x + 4

Therefore, the total length of the two sides of the triangle is -x² + 7x + 4.

Part B:

To find the length of the third side of the triangle, we need to subtract the sum of Side 1 and Side 2 from the perimeter of the triangle:

Length of Side 3 = Perimeter - (Side 1 + Side 2)

Length of Side 3 = (5x³ - 2x² + 3x - 8) - (3x² - 4x - 1 + 4x - x² + 5)

Simplifying and combining like terms, we get:

Length of Side 3 = 2x³ - 2x² + 7x - 12

Therefore, the length of the third side of the triangle is 2x³ - 2x² + 7x - 12.

Part C:

The answers for Part A and Part B show that the polynomials are closed under addition and subtraction. The sum of Side 1 and Side 2 is a polynomial (-x² + 7x + 4), and the difference between the perimeter of the triangle and the sum of Side 1 and Side 2 is also a polynomial (2x³ - 2x² + 7x - 12). In both cases, the result is a polynomial, which means that the set of polynomials is closed under addition and subtraction.

Answer:

4x + 2 > 10 and -3x-1 > 5 : No solution

| 3x | + 4< 10:  -2 < 2 x < 2

| x+2 | + 4< 3: No solution

|2x+4 | +2 > 4: x > -1 or x < -3

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

to check if (-1,-10) is a solution to the system of equations y = -8x + 7 and y = 6x + 5, we substitute x=-1 and y=-10 into both equations and check if both equations hold true.

y = -8x + 7 -10 = -8(-1) + 7 -10 = 8 + 7 -10 ≠ 15

y = 6x + 5 -10 = 6(-1) + 5 -10 = -1

Since (-1,-10) does not satisfy both equations simultaneously, it is not a solution to the system of equations.

The blanks when completed are

In a scale drawing, the scale factor represents the ratio of the size of an object in the drawing to the size of the corresponding object in real life.

In the given scale drawing, we have

Longest side in B = 12

So, the scale factor is

scale factor = size of object in drawing / size of corresponding object

This gives

scale factor = 12 / 4

scale factor = 3

This means that

Every side length in A grew by a factor of 3

Using the scale ratio formula, we have

A length in B/A corresponding length in A = 3

Lastly, the size of the angles remain unchanged

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Since 260 is close to 264, our answer of 264 is reasonable.

What is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas. It involves the study of variables, expressions, equations, and functions.

The sum of 401-137 can be found by subtracting 137 from 401:

401 - 137 = 264

Therefore, the sum of 401-137 is 264.

To estimate whether this answer is reasonable, we can use rounding. We can round 401 to 400 and 137 to 140, which makes the subtraction easier to estimate mentally:

400 - 140 ≈ 260

Since 260 is close to 264, our answer of 264 is reasonable.

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Using Integration,  Area of the curve is 16/3 unit² and the maximum height of the curve is 2 unit.

What exactly is integration?

Integration is a fundamental concept in calculus, which is a branch of mathematics that deals with rates of change and accumulated quantities. Integration is the process of finding the integral of a function, which is the inverse of differentiation.

Now,

For the maximum height that the curve has we have to

put dy/dx=0

d(4x-2x²)/dx=0

4-4x=0

x=4/4

x=1

and when x=1 then y=4*1-2*1²

=4-2

=2

So, the maximum height of the curve is 2 unit.

and for the area

we need to find y.dx for the curve

So,

y.dx=(4x-2x²).dx

=4x+2x²-2x³-2x³/3 for x=0 to x=2

=8+8-16-16/3

=16/3 unit²

Hence, Area of the curve is 16/3 unit².

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Answer:

5,500 ft²

Step-by-step explanation:

Easiest way is to find the area of the entire 100 x 80 square, then subtract the footprint of the house (50 x 50):

Backyard area = (100 x 80) - (50 x 50) = 8000 - 2500 = 5500 ft²

10 x 8 face as the base for prism 1

10 x 3 face as the base for prism 2

To find the area of the base, you simply multiply the length and width:

Base area = length x width = lw

Therefore, for rectangular prism 1 we get:

10 x 8

For rectangular prism 2 we get:

10 x 3

Similarly, if the base of the prism is a triangle, you would need to use the formula for the area of a triangle, which is:

Base area = 1/2 x base x height

where base and height are the base and height of the triangle respectively.

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The volume of the complete prism is  1625 cubic in

The volume of the figure is solved by dividing the figure into two sections and solving for each volume then adding the individual volume together.

The divisions are section 1 and section 2

section 1 has dimensions: 20 x 15 x 5

volume = 20 x 15 x 5 = 1500 cubic in

section 2 has dimensions: 5 x 5 x 5

volume = 5 x 5 x 5 = 125 cubic in

Volume of the complete figure

section 1  + section 2

= 1500 cubic in + 125 cubic in

= 1625 cubic in

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Answer:

the required answer are -8,0,4

according to the question the sample mean used to obtain the confidence interval was 173.

The arithmetic means (in contrast to the geometrical mean) of a dataset is the average of all values split by the total amount of values. The most popular way to measure central tendency is with the "mean," which is widely utilised. This is obtained by dividing the number of values in the dataset by the total number of all the values. Either raw information or information that has been included in frequency tables can be used for calculations. The average of a number is known as the average. Simple math can be used to determine: After summing up all the digits, divide by the number of digits. the sum divided by the number.

given,

The confidence interval's midpoint is determined by the sample mean. Therefore, to find the sample mean, we add the lower and upper bounds of the confidence interval and divide by 2:

Sample mean = (Lower bound + Upper bound)/2

Sample mean = (168.685 + 177.315)/2

Sample mean = 173

Therefore, the sample mean used to obtain the confidence interval was 173.

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