Directions: Find the missing angle in each of the following problems.

1. QR = 36 ; PR = 45 ; PQ = 21, Sin __?___ = 21 / 45

2. QR = 16 ; PR = 2 ; PQ = 8, tan __?__ = 8 / 16

3. QR = 15 ; PR = 28 ; PQ = 15, Cos __?__ = 15 / 28

4. QR = 47 ; PR = 64 ; PQ = 38, tan __?__ = 38 / 47

5. QR = 4 ; PR = 17 ; PQ = 12, Sin __?___ = 12 / 17

6. QR = 36 ; PR = 59 ; PQ = 20, Cos __?___ = 36 / 59

7. QR = 82 ; PR = 63 ; PQ = 29, tan __?__ = 29 / 82

8. QR = 10 ; PR = 28 ; PQ = 8, Sin __?___ = 8 / 28

9. QR = 51 ; PR = 42 ; PQ = 9, tan __?__ = 9 / 51

10. QR = 16 ; PR = 20 ; PQ = 17, Cos __?___ = 16 / 20

11. QR = 12 ; PR = 84 ; PQ = 60, Sin __?_ = 60 / 84

12. QR = 19 ; PR = 32 ; PQ = 45, Cos __? = 19 / 32

13. QR = 76 ; PR = 27 ; PQ = 64, tan __ ?_ = 64 / 76

14. QR = 26 ; PR = 48 ; PQ = 37, Cos __?_ = 37 / 48

15. QR = 19 ; PR = 66 ; PQ = 23, Cos __?__= 23 / 66

Step-by-step explanation:

if I understand you correctly, then the 3 sides are

a = 20 m

b = 34 m

c = 42 m

under this assumption the best is to use Heron's Formula to get the area :

s = (a + b + c)/2

area = sqrt(s(s - a)(s - b)(s - c))

in our case

s = (20 + 34 + 42)/2 = 96/2 = 48

area = sqrt(48(48-20)(48-34)(48-42)) =

= sqrt(48×28×14×6) = sqrt(112,896) =

= 336 m²

Answer:

sorry i didnt know this D: <3

Step-by-step explanation:

The potential zeros of f(x)=6x^4+ 2x^3 - 4x^2 +2 are ±(1, 1/2, 1/3, 1/6, 2, 2/3)

The function is given as:

f(x)=6x^4+ 2x^3 - 4x^2 +2

For a function P(x) such that

P(x) = ax^n +...... + b

The rational roots of the function p(x) are

Rational roots = ± Possible factors of b/Possible factors of a

In the function f(x), we have:

a = 6

b = 2

The factors of 6 and 2 are

a = 1, 2, 3 and 6

b = 1 and 2

So, we have:

Rational roots = ±(1, 2)/(1, 2, 3, 6)

Split the expression

Rational roots = ±1/(1, 2, 3, 6)/ and ±2/(1, 2, 3, 6)

Evaluate the quotient

Rational roots = ±(1, 1/2, 1/3, 1/6, 2, 1, 2/3, 1/3)

Remove the repetition

Rational roots = ±(1, 1/2, 1/3, 1/6, 2, 2/3)

Hence, the potential zeros of f(x)=6x^4+ 2x^3 - 4x^2 +2 are ±(1, 1/2, 1/3, 1/6, 2, 2/3)

The complete parameters are:

The function is given as:

f(x) = 3x^3 + 2x^2 + 3x + 6

The potential zeros of f(x)=6x^4+ 2x^3 - 4x^2 +2 are ±(1, 1/2, 1/3, 1/6, 2, 2/3)

Read more about rational roots at

brainly.com/question/17754398

#SPJ1

The area of the circle is 78.5 square yards and the circumference of the circle is 31.4  yards

The radius of the circle is given as:

r = 5 yard

The area is calculated using

A = pi r^2

Substitute the known values in the above equation

A =3.14 * 5^2

Evaluate the exponent

A =3.14 * 25

Evaluate the product

A =78.5

Hence, the area of the circle is 78.5 square yards

The radius of the circle is given as:

r = 5 yard

The circumference is calculated using

C = 2pi r

Substitute the known values in the above equation

C =2 * 3.14 * 5

Evaluate the product

C = 31.4

Hence, the circumference of the circle is 31.4  yards

Read more about area and circumference at:

https://brainly.com/question/15673093

#SPJ1

Step-by-step explanation:

The heaviest legal bowling ball weighs 16 pounds. The lightest weight you can usually find at most bowling alleys is six pounds.

PLEASE MARK ME AS BRAINLIST

The number of solutions to the system is 1

A linear equation is a equation that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

y = 4x + 8

4y = 4x - 8

Substitute y = 4x + 8 in 4y = 4x - 8

4(4x + 8) = 4x - 8

Expand the equation

16x + 32 = 4x - 8

Evaluate the like terms

12x = - 40

Divide by 12

x = -10/3

The above means that the number of solutions to the system is 1

Read more about system of linear equations at

https://brainly.com/question/14323743

#SPJ1

By the chain rule,

[tex]g(x) = f(4 - x^2) \\\\ \implies g'(x) = -2x f'(4 - x^2) \\\\ \implies g''(x) = -2 f'(4 - x^2) + 4x^2 f''(4 - x^2)[/tex]

Observe that

[tex]4 - x^2 = 1 \implies x^2 = 3 \implies x = \pm\sqrt3[/tex]

Then

[tex]g''(\sqrt3) = -2 f'(1) + 4\left(\sqrt3\right)^2 f''(1) = -2(-5) + 4(3)(-1) = \boxed{-2}[/tex]

The length of one of the remaining sides is 34.20 meters.

A trapezoid is a convex quadrilateral. A trapezoid has at least on pair of parallel sides. the parallel sides are called bases while the non parallel sides are called legs

Perimeter of an isosceles trapezoid =  sum of lengths of sides of a trapezoid

length of shorter base + length of longer base + (2 x legs)

108 = 11.5 + 28.1 + (2 x legs)

108 = 39.60 + (2 x legs)

108 - 39.60 =  (2 x legs)

68.40 =  (2 x legs)

leg = 68.40 / 2

= 34.20 meters

To learn more about trapezoids, please check: https://brainly.com/question/25748893

#SPJ1

Answer:

d - 7

Step-by-step explanation:

The word "difference" tells us that we will be using subtraction. Also, subtraction is not the same if you reverse the terms like, x - 2 and 2 - x are not the same. In your question it say "d and 7" so that's the order we use in the algebraic expression.

Using a linear function, it is found that it will take 13 hours for the candle to burn down to a height of .25 inches.

A linear function is modeled by:

y = mx + b

In which:

Considering the situation described, the y-intercept is of 10 while the slope is of -0.75, hence the height of the candle after t hours is given by:

h(t) = 10 - 0.75t

The height will be of 0.25 inches when h(t) = 0.25, hence:

0.25 = 10 - 0.75t

0.75t = 9.75

t = 9.75/0.75

t = 13 hours.

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

By analyzing the end behavior of the graphed function, we conclude that the graphed function is an exponential one.

On the graph, we can see that as the independent variable (the one in the horizontal axis) tends to large negative values, the dependent variable (the one in the vertical axis) tends to zero.

And, as the independent variable increases in the positive domain, also does the dependent variable. So we have an increasing function

Finally, we can see that the range (set of the outputs) of the function is the set of values larger than zero.

These 3 are characteristics of exponential functions, so we conclude that the graphed function is an exponential one, thus the correct option is the first one.

If you want to learn more about exponential functions:

https://brainly.com/question/2456547

#SPJ1

Answer:

Logarithmic

Step-by-step explanation:

HS Teacher

Answer:

2700 degrees

Step-by-step explanation:

The number of sides minus 2 times.

n = number of sides

(n-2)= 180

(17-2)(180)

(15)(180) = 2700

Answer:

the height would be around 19.2 cm

Step-by-step explanation:

hyp length = 63

base = 60

length = sqrt(63^2 - 60^2) = sqrt(369)

Step-by-step explanation:

1. Lower the confidence level.

2. Use a one-sided confidence interval. ...

3. Increase the sample size. Often, the most practical way to decrease the margin of error is to increase the sample size. ...

4. Reduce variability. The less that your data varies, the more precisely you can estimate a population parameter. ...

PLEASE MARK ME AS BRAINLIST

Answer:

Increase the sample size.

Usually, the more observations that you have, the narrower the interval around the sample statistic is.

The length of the transverse axis is 8.

Given the equation of hyperbola:[tex]\frac{(y-2)^{2} }{16}[/tex][tex]-\frac{(x+1)^{2} }{144 }[/tex][tex]=1[/tex]

Rewrite this equation as [tex]\frac{(y-2)^{2} }{4^{2} }[/tex][tex]-\frac{(x+1)^{2} }{12^{2} }[/tex][tex]=1[/tex]

When comparing this equation to the common hyperbola equation with a vertical transverse axis is [tex]\frac{(y-k)^{2} }{a^{2} }[/tex][tex]-\frac{(x+h)^{2} }{b^{2} }[/tex][tex]=1[/tex]

[tex]h = -1[/tex]

[tex]k= -2[/tex]

[tex]a = 4[/tex]

[tex]b = 12[/tex]

The length of the transverse axis is[tex]2a = 2*4[/tex]

                                                               [tex]=8.[/tex]

The length of the transverse axis is 8.

To learn more about length of the transverse axis, refer to:

https://brainly.com/question/2292250

#SPJ9

The option A is correct because the value of the statement is 6+3/n-8.

According to the statement

we have given that the statement and we have to write the statement in the numerical form.

So, For this purpose

we know that the given statement is

"Six more than the quotient of three and a number, decreased by eight".

In this statement "Six more than" indicates the sum between the quotient and 6.

And "The quotient of three and a number" indicates a fraction where the numerator is 3 and the denominator is , a number.

"Decreased by eight" indicates a subtraction between the quotient an 8 units".

If we unit all parts of the statements, we would have

6+3/n-8

So, From the given statement, The option A is correct because the value of the statement is 6+3/n-8.

Learn more about Numbers here

https://brainly.com/question/11408596

#SPJ1

Check the attached file.

Answer:

  34

Step-by-step explanation:

You want the value of |m² +n²| for m = -5 and n = 3.

Put the values where the variables are in the expression and do the arithmetic.

  |m² +n²| = |(-5)² +3²| = |25 +9| = |34| = 34

The value of the expression is 34.

__

Additional comment

Here, the absolute value bars don't do anything, because the value between them is positive. If it were negative, they would remove the minus sign.

<95141404393>

Answer:

[tex]\textsf{A)} \quad (x-40)^2=-100(y-16)[/tex]

B)  Focus = (40, -9)

    Directrix:  y = 41

    Axis of symmetry:  x = 40

Step-by-step explanation:

The x-intercepts of a parabola are the points at which the curve intercepts the x-axis (when y = 0).

The x-coordinate of the vertex of a parabola is halfway between the x-intercepts.

The y-coordinate of the vertex if the minimum or maximum height of the parabola.

A jumping spider's movement is modeled by a parabola.

Define the variables:

From the information given:

Standard form of a parabola with a vertical axis of symmetry:

[tex](x-h)^2=4p(y-k) \quad \textsf{where}\:p\neq 0[/tex]

If p > 0, the parabola opens upwards, and if p < 0, the parabola opens downwards.

Substitute the vertex (40, 16) and one of the x-intercept points (0, 0) into the formula and solve for p:

[tex]\implies (0-40)^2=4p(0-16)[/tex]

[tex]\implies 1600=-64p[/tex]

[tex]\implies p=-25[/tex]

Substitute the vertex and the found value of p into the formula:

[tex]\implies (x-40)^2=4(-25)(y-16)[/tex]

[tex]\implies (x-40)^2=-100(y-16)[/tex]

Given:

Substitute the given values into the formulas for focus, directrix and axis of symmetry:

Focus

⇒ (h, k+p)

⇒ (40, 16 + (-25)))

⇒ (40, -9)

Directrix

⇒ y = (k-p)

⇒ y = (16 - (-25))

⇒ y = 41

Axis of symmetry

⇒ x = h  

⇒ x = 40

The amount we should charge Tommy is $363.

How much should we charge Tommy:

The amount charged for 1000 words = $110

The amount charged per word = $110/1000

Amount to be charged for 3300 words = $(110/1000) × 3300

= $(0.11) × 3300

= $363

The amount we should charge Tommy is $363.

To learn more about the amount charged, refer to:

https://brainly.com/question/25922783

#SPJ9

Answer: d = 1/3

Step-by-step explanation: 48y = 48/4 = 12. So, 2d(18) is equal to 12. 12/18 is 2/3 so 2d has to equal 2/3. That means d = 1/3.

Answer:

Step-by-step explanation:

2^0 is less than or equal to 1!, because 1<= 1

if 2^n <= (n+1)!, we wish to show that 2^(n+1) <= (n+2)!, since

(n+2)! = (n+1)! * (n+2), and (n+1)!>= 2^n, then we want to prove that n+2<=2, which is always true for n>=0

Answer:

for normalian is a function of the form FX is equal to a and x n + a n - 1 x n - 1 + ax2 into X + A1 is equal to A2 is degree per normal highest power of X is

Part I: The correct formula is D. ((x₁ + x₂)/2, (y₁ + y₂)/2)

Part II: The midpoint of the segment with endpoints (-2, -1) and (0, 9) is (-1, 4)

From the question, we are to determine the formula for calculating the midpoint of a segment

The midpoint of a segment can be determined by using the formula,

Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)

The correct formula is D. ((x₁ + x₂)/2, (y₁ + y₂)/2)

II. To determine the midpoint of the segment with endpoints (-2, -1) and (0, 9)

x₁ = -2

y₁ = -1

x₂ = 0

y₂ = 9

Putting the parameters into the formula,

Midpoint of the segment = ((-2 + 0)/2, (-1 + 9)/2)

Midpoint of the segment = (-2/2, 8/2)

Midpoint of the segment = (-1, 4)

Hence, the midpoint of the segment with endpoints (-2, -1) and (0, 9) is (-1, 4)

Learn more on Midpoint of a segment here: https://brainly.com/question/896396

#SPJ1

A rigid motion is a type of motion in which all points on a given object move at the same time, in the same direction, and cover the same distance.

A rigid motion is a type of motion in which all points on a given object move at the same time, in the same direction, and cover the same distance. It is an essential type of motion used in geometry due to the rigid transformation of objects considered in the topic.

Rigid transformation is a method required to change the position, size, orientation, or dimensions of a given shape. This implies that the given shape (object) undergoes the appropriate transformation into its image. Types of rigid transformation are translation, rotation, dilation, and reflection.

Considering the given question, the quadrilateral performed a rigid motion. This was done by first reflecting it about the vertical axis, and now translating it 2 units downwards towards the horizontal axis.

for more clarifications on the rigid motion of objects, visit: https://brainly.com/question/11730139

#SPJ 1

The excluded values are x = 4 and x - 1

The complete question is added as an attachment

The function is given as:

(2x^2 - 7x - 4)/(x^2 - 5x + 4)

Set the denominator to 0

x^2 - 5x + 4 = 0

Expand

x^2 - x - 4x + 4 = 0

Factorize the equation

x(x -1) - 4(x - 1) = 0

This gives

(x - 4)(x - 1) = 0

Solve for x

x = 4 and x - 1

Hence, the excluded values are x = 4 and x - 1

Read more about excluded values at

https://brainly.com/question/1418453

#SPJ1

Answer: Its D 1 and 4

Step-by-step explanation:

I took the assignment

$3,717.14

Compound interest is the interest on the principal funding as well as the interest itself.

Compound Interest Formula

Compound interest can be solved by plugging known values into a formula.

In this formula, the variables stand for different values.

So, for this question, we can plug in the values we are given and solve for P.

Identifying Known Values

First, let's find the exact numbers we are going to plug in.

Solving For P

Now we can plug all of these values in.

First, simplify the values within the parentheses and in the exponent through arithmetic.

Next, divide both sides by [tex]1.005^{96}[/tex]

*Note that the answer has been rounded to the nearest hundredth.

This means that you would need to deposit $3,717.14 into the account to have $6,000 in 8 years.

The distance from the safe zone after t seconds is D(t) = 166 - 24t given that drove to get to the safe zone at 24 meters per second and after 4 seconds of driving, she was 70 meters away from the safe zone. This can be obtained by converting the conditions to equations.

A linear function containing one dependent and one independent variable.

It can be represented using the equation,

y = mx + c

where m is the slope

It is given in the question that,

Rachel is a stunt driver and one time during a gig where she escaped from a building about to explode she drove to get to the safe zone at 24 meters per second.

After 4 seconds of driving, she was 70 meters away from the safe zone.

Let, D(t) be the distance to the safe zone (measured in meters) and t be the  time (measured in seconds)

After 4 seconds of driving, she was 70 meters away from the safe zone.

⇒ This means that at t = 4 seconds, D(4) = 70 meters

Rachel's rate is the slope of the function D(t). Since the distance is decreasing when the time is increasing, the slope must be negative

⇒ m = - 24

y = mx + c

⇒ D(t) = (-24)t + c

Put t = 4,

D(4) = (-24)4 + c

70 = -96 + c ⇒ c = 166

⇒ D(t) = 166 - 24t

Hence the distance from the safe zone after t seconds is D(t) = 166 - 24t given that drove to get to the safe zone at 24 meters per second and after 4 seconds of driving, she was 70 meters away from the safe zone.

Learn more about linear function here:

brainly.com/question/13919345

#SPJ1

In calculating the factor A variation, there are two degrees of freedom. In determining the variation of factor B, there are two degrees of freedom.

A two-factor factorial design is an experiment that collects data for all potential values of the two factors of the study. The design is a balanced two-factor factorial design if equivalent sample sizes are used for every of the possible factor combinations.

Suppose we have two components, A and B, each of which has a high number of levels of interest. We will select a random level of component A and a random level of factor B, and n observations will be taken for each experimental combination.

From the data given:

a.

In calculating the factor A variation, there are two degrees of freedom.

In determining the variation of factor B, there are two degrees of freedom.

b.

Finding the degree of freedom using the interaction variation, there are four degrees of freedom.

c.

In finding the random variable, there are 9(4-1) = 27 degrees of freedom.

d.

In calculating the total variable, there are 9*4-1 =35 degrees of freedom.

Learn more about using a two-factor factorial design for determining the degree of freedom here:

https://brainly.com/question/14292694

#SPJ1

Answer: q = -2/3

Step-by-step explanation:

First, we need to apply the Distributive Law in order to proceed with the problem.

3(q + 4/3) = 2

3q + 3(4/3) = 2

We already know that 3(4/3) = 4, since the 3's cancel out. Or, 3(4/3) = 12/3 = 4.

Our new equation is,

3q + 4 = 2

Through transposition and isolation of variables, we get,

3q = -2

Dividing by 3 on both sides...

q = -2/3