What is the value of x in trapezoid ABCD? x=15 x=20 x=45 x=60

Answer:

In words, Cosine theta equals plus or minus square root of seven over 4,tangent theta equals plus or minus  three over root seven

Step-by-step explanation:

Given that sin ∅ =3/4 It means the ratio of the opposite side to the hypotenuse side is 3:4.

Using the Pythagoras theorem we can calculate the hypotenuse adjacent as follows.

a²+b²=c²

a²=c²-b²

a²=4²-3²

a²=16-9

a²=7

a=√7

Then Cos ∅= opposite/ adjacent

=√7/4

Then Tan ∅ = opposite/adjacent

=3/√7

In words, Cosine theta equals plus or minus square root of seven over 4,tangent theta equals plus or minus  three over root seven.

Answer:

  x = -0.5 or x = 2

Step-by-step explanation:

Finding solutions graphically is often easier if the equation can be put in the form f(x) = 0. Here, we can do that by subtracting the right-side expression to give ...

  (-2x^2 +2) -(-3x) = 0

This could be put in standard form, but there is no need. A graphing calculator can deal with this directly.

The solutions are x = -0.5 and x = 2.

Answer:

Cyclical unemployment.

Step-by-step explanation: It is not part of the natural unemployment rate.

It's caused by the contraction phase of the business cycle. That's when demand for goods and services generated by the company fall dramatically, forcing businesses to lay off large numbers of workers to cut or reduce costs.

Answer:

Step-by-step explanation:

You know that ...

Using what you know about the relationships of these trig functions, you can find ...

  cos(θ)² = 1 - ((-√3)/2)² = 1 - 3/4 = 1/4

  cos(θ) = -1/2 . . . . . negative square root of 1/4

__

  tan(θ) = sin(θ)/cos(θ) = ((-√3)/2)/(-1/2)

  tan(θ) = √3

Answer:

0

Step-by-step explanation:

if you added anything else you would be higher than 24

Answer: The following statements are correct :

Data are typically collected from a sample because it is too difficult and expensive to collect data from an entire population.

When the results from a sample are extended to the​ population, it is called inference.

If data are not collected​ properly, the conclusions that are drawn will be meaningless.

The following statement is false: The first step in the process of statistics is to collect the data.

The first step in the process of statistics is to Plan: develop a statistical inquiry that can be answered with aggregation of data.

Answer:

21 ways

Step-by-step explanation:

number = 7 digit

5 digit no = 52115

to find out

How many different seven-digit numbers

solution

first we need to place the two missing 3s in the number 52115

we consider here two cases

case 1  the two 3's appear separated (like 532135 or 3521135)  

case 2 the two 3's appear together (like 5332115 or 5211533)  

Case 1 we can see  that number type as _5_2_1_1_5_  

place 3's placeholders show potential locations

( type a ) for  3's  separated we will select 2 of  6 place and place 3 in every location so we do this 6C2  = (15) ways  

and (type b): again use same step as  _5_2_1_1_5_  

here 3s together for criterion and we will select 1 of the 6 place and place both 3s here and there are 6 ways.  

so that here will be 15+6=21 ways

If 3 and 3 are separate so 6C2 = 15  ways

If 3 and 3 are together so there = 6  ways

= 15 + 6 = 21 ways

Answer:

5 seconds

Step-by-step explanation:

This follows the pattern

[tex]h(t)=-4.9t^2+v_{0}t+h_{0}[/tex]

It is parabolic and it is used to model projectile motion.  This is the model you would use.  Now for the math of it.

The v₀ is the initial velocity and the h₀ is the initial height.  The whole thing is negative because it is an upside down parabola.  Our initial velocity is 12 and the initial height is 62.5.  That means that our particular model is

[tex]h(t)=-4.9t^2+12t+62.5[/tex]

h(t) is the height of the projectile after a certain length of time, t, has gone by.  We want to know how long, t, it takes the projectile to hit the ground.  When something is laying on the ground, its height is 0.  Therefore, in order to find how long it takes for the height to be 0, we replace h(t) with 0 and then factor to find the values of t:

[tex]0=-4.9t^2+12t+62.5[/tex]

If you plug this into the quadratic formula you will get that the values of t are

t = -2.55 and t = 5

We all know that the 2 things in math that will never EVER be negative are time and distance/measures, so we can disregard the negative value of time and say that the length of time it takes for the object to hit the ground from its initial height of 62.5 m is 5 seconds.

Answer:

8

Step-by-step explanation:

167.39 is right but it can be simplified.

1.61 was replaced by (161/100).

3 more similar replacement(s)

  839          2      161

 (——— +  (0 -  —)) +

  100          1      100

639 + 161     8

—————————  

   100        1

Sorry if it looks confusing

Answer:

(x - 1)²/4² - (y - 2)²/2² = 1 ⇒ The bold labels are the choices

Step-by-step explanation:

* Lets explain how to solve this problem

- The equation of the hyperbola is x² - 4y² - 2x + 16y - 31 = 0

- The standard form of the equation of hyperbola is

  (x - h)²/a² - (y - k)²/b² = 1 where a > b

- So lets collect x in a bracket and make it a completing square and

  also collect y in a bracket and make it a completing square

∵ x² - 4y² - 2x + 16y - 31 = 0

∴ (x² - 2x) + (-4y² + 16y) - 31 = 0

- Take from the second bracket -4 as a common factor

∴ (x² - 2x) + -4(y² - 4y) - 31 = 0

∴ (x² - 2x) - 4(y² - 4y) - 31 = 0

- Lets make (x² - 2x) completing square

∵ √x² = x

∴ The 1st term in the bracket is x

∵ 2x ÷ 2 = x

∴ The product of the 1st term and the 2nd term is x

∵ The 1st term is x

∴ the second term = x ÷ x = 1

∴ The bracket is (x - 1)²

∵  (x - 1)² = (x² - 2x + 1)

∴ To complete the square add 1 to the bracket and subtract 1 out

   the bracket to keep the equation as it

∴ (x² - 2x + 1) - 1

- We will do the same withe bracket of y

- Lets make 4(y² - 4y) completing square

∵ √y² = y

∴ The 1st term in the bracket is x

∵ 4y ÷ 2 = 2y

∴ The product of the 1st term and the 2nd term is 2y

∵ The 1st term is y

∴ the second term = 2y ÷ y = 2

∴ The bracket is 4(y - 2)²

∵ 4(y - 2)² = 4(y² - 4y + 4)

∴ To complete the square add 4 to the bracket and subtract 4 out

   the bracket to keep the equation as it

∴ 4[y² - 4y + 4) - 4]

- Lets put the equation after making the completing square

∴ (x - 1)² - 1 - 4[(y - 2)² - 4] - 31 = 0 ⇒ simplify

∴ (x - 1)² - 1 - 4(y - 2)² + 16 - 31 = 0 ⇒ add the numerical terms

∴ (x - 1)² - 4(y - 2)² - 16 = 0 ⇒ add 14 to both sides

∴ (x - 1)² - 4(y - 2)² = 16 ⇒ divide both sides by 16

∴ (x - 1)²/16 - (y - 2)²/4 = 1

∵ 16 = (4)² and 4 = (2)²

∴ The standard form of the equation of the hyperbola is

   (x - 1)²/4² - (y - 2)²/2² = 1

Answer:

Refer to attachment below.

Answer:

Step-by-step explanation:

To maximize profit, the greatest possible number of the most profitable item should be manufactured. Remaining capacity should be used for the less-profitable item.

Up to 30 of model B, which has the highest profit, can be made each day. The remaining amount (20 sets) of the daily capacity of 50 sets should be used to make model A sets.

Answer: [tex]\dfrac{3}{4389}[/tex]

Step-by-step explanation:

Given : Number of math books = 5

Total number of books = 5+6+8+3=22

Number of books except math = 17

Number of ways to arrange 22 books in bookshelf = [tex]22![/tex]

When all math books are together , then we count whole set as one

Now, the number of objects in bookshelf = 17+1=18

Number of ways to arrange books such that all math books are together = [tex]18!5![/tex]

Now, the probability that all the math books are together :-

[tex]\dfrac{5!18!}{22!}=\dfrac{3}{4389}[/tex]

Hence, the probability that all the math books are together [tex]=\dfrac{3}{4389}[/tex]

The answer is:

[tex]WatchCost=StartingBalance-EndingBalance\\\\WatchCost=515.50-496.11=19.39[/tex]

The cost of the watch is $19.39.

To solve the problem, we can create a linear equation using the given information about the starting balance and the ending balance.

We know that the starting balance was $515.50, and then, after writing a check to buy the watch, the balance was $496.11, so, writing the function we have:

[tex]WatchCost=StartingBalance-EndingBalance\\\\WatchCost=515.50-496.11=19.39[/tex]

Hence, we have that the cost of the watch is $19.39.

Have a nice day!

Answer:

Reflects over the x-axis, then translate (x + 3, y + 1).

Step-by-step explanation:

Your have to flip is over the X-axis to get the short side on the bottom.

Then move is 3 places to the right, so X+3. After which it is move 1 place up, Y+1

Reflects over the x-axis, then translate (x + 3, y + 1).

Answer:

D

Step-by-step explanation:

Consider the inequality

[tex]\dfrac{x^2+4x-12}{x}>0[/tex]

First, factor the numerator:

[tex]x^2+4x-12=x^2+6x-2x-12=x(x+6)-2(x+6)=(x+6)(x-2)[/tex]

Now, the inequality is

[tex]\dfrac{(x+6)(x-2)}{x}>0[/tex]

The equivalent inequality is

[tex]x(x+6)(x-2)>0[/tex]

On the number line plot doted points -6, 0 and 2 and put signs +, -, +, - from the right to the left. Intervals with + signs are the solution of the inequality:

[tex]x\in(-6,0)\cup(2,\infty)[/tex]

that is represented by D number line.

Answer:

D

Step-by-step explanation:

Answer:

  B.  sin35/9=sin40/b

Step-by-step explanation:

The law of sines tells you ...

  sin(A)/a = sin(B)/b

Filling in the given values, you get ...

  sin(35°)/9 = sin(40°)/b

Answer:

B.[tex]\frac{sin 35}{9}=\frac{sin 40 }{b}[/tex]

Step-by-step explanation:

We are given that in a triangle ABC. [tex]m\angle =35^{\circ}[/tex]

[tex]m\angle B=40^{\circ}[/tex]

a=9

We have to find an equation  which solve for b

We know that a sine law

[tex]\frac{a}{sine A}=\frac{b}{sinB}=\frac{c}{sinC}[/tex]

Using above formula of sine law

Substituting all given values in the above formula of sine law

Then we get

[tex]\frac{9}{sin 35}=\frac{b}{sin 40}[/tex]

By cross multiply then we get

[tex]sin 40\times 9=sin35 \times b[/tex]

[tex] \frac{sin 40 \times 9}{b}= sin 35[/tex]

Using division property of equality

[tex]\frac{ sin 40}{b}=\frac{sin 35}{9}[/tex]

Using division property of equality

Hence, option B is true option for solving b.

Answer:B.[tex]\frac{sin 35}{9}=\frac{sin 40 }{b}[/tex]

Answer:

The answer is 27 on edge as well!

Step-by-step explanation:

The answer is 27

This is because 15x15 is 225 plus 8x8 is 64 which is 289 and the square root of that is 17 and that is the diameter of the circle and the hypotenuse of the triangle and since the kite has two congruent sides which are both radii or half of a diameter times two would be the same as the length of the diameter which is 17 plus the two bottom sides which are both 5 and 5 plus 5 is 10 and 10 plus 17 is 27 or the perimeter of the kite.

Your Welcome!

Answer:

27

Step-by-step explanation:

im taking the test right now on edg. 2020

Answer:

Step-by-step explanation:

Wherever you see an x in g(x) you are supposed to put f(x).

If g(x) = x

then

g(f(x)) = f(x)

g(x) = f(x)

Since g(x) has no xs, then g(f(x)) = - 2

g(x) = -2 no matter what x is in g(x)

g(2x - 1) = - 2

Answer:

[g ◦ f](x)=-2

Step-by-step explanation:

f(x) = 2x – 1

g(x) = – 2

[g ◦ f](x)

This is a composite function.  It means we take f(x) and substitute it in for x in the function g(x)

g(x) = -2

There is no x in the function, so g(x) remains the same

[g ◦ f](x)= -2

Answer:

Step-by-step explanation:

[tex]4^0=1\\2^2=2\cdot2=4\\3^3=3\cdot3\cdot3=27\\\\4^0\cdot2^2\cdot3^3=1\cdot4\cdot27=108[/tex]

Answer:

108

Step-by-step explanation:

4 to the power of 0 is always 1. multiply to 2 to the power of 2 gives you 4. multiplying 4 to 3 to the power of 3 gives you 108 because 3^3 is 27 but if you multiply that by 4, you get 108

Answer:

  nothing

Step-by-step explanation:

Loan payments are linear in the loan amount for a given rate and period, so the payments for loans of $2000 and $1000 sum to the amount of payments for a loan of $3000.

The only possible savings (or cost) might come from rounding to the nearest cent. (In any event, the final payment on each loan should make up for any differences due to rounding.)

Answer:

 nothing

Step-by-step explanation:

Loan payments are linear in the loan amount for a given rate and period, so the payments for loans of $2000 and $1000 sum to the amount of payments for a loan of $3000.

The only possible savings (or cost) might come from rounding to the nearest cent. (In any event, the final payment on each loan should make up for any differences due to rounding.)

Answer:

V=8.5

Step-by-step explanation:

o=oil. vinegar=v. furniture polish=f

O=3v

34= 3v + v

Using a system of guessing and checking if that number fits equation you can tell that 8 causes the equation to be unequal and also 9. You can learn V must be between 8 and 9 so 8.5 might fit the equation. 8.5=V

Final answer:

To make 34 oz of furniture polish, 8.5 oz of vinegar and 25.5 oz of olive oil are needed, with the olive oil being three times the amount of vinegar.

Explanation:

To create 34 oz of nontoxic furniture polish, where the amount of olive oil should be three times the amount of vinegar, we need to solve a simple algebraic equation. Let's denote the amount of vinegar as v ounces. According to the conditions, the amount of olive oil will then be 3v ounces.

The total amount of furniture polish equals the amount of vinegar plus the amount of olive oil:

v + 3v = 34 oz

This simplifies to:

4v = 34 oz

Dividing both sides by 4 gives us:

v = 8.5 oz

Therefore, the amount of olive oil needed is:

3v = 3 Times 8.5 oz = 25.5 oz

To conclude, we need 8.5 oz of vinegar and 25.5 oz of olive oil to make 34 oz of furniture polish.

Answer:

∠4

Step-by-step explanation:

The angle of elevation is the measure of the angle from the horizontal upwards.

The angle of elevation from C to B is ∠4

Angle of elevation from C to B will be ∠4. Option (1) will be the answer.

Angle of elevation of an object from a point on the ground is defined by,

   "Angle between the horizontal line and line of site (line joining the observer and the object above the horizontal line)"

Following the definition,

Angle of elevation of an object at B from C will be → ∠4

   Therefore, Option (1) will be the answer.

Learn more about angle of elevation here,

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Answer:

  a) r(x) = 28x

  b) p(x) = -x^2 +30x +9

  c) 15

Step-by-step explanation:

a) Let x represent the number of items sold. Each sale results in $28 of revenue, so the revenue function r(x) is ...

  r(x) = 28x

__

b) p(x) = r(x) - c(x) = 28x -(x^2 -2x -9)

  p(x) = -x^2 +30x +9

__

c) The axis of symmetry of ax^2 +bx +c is -b/(2a). Here, the axis of symmetry of the profit function is ...

  x = -30/(2(-1)) = 15

15 is the quantity of sales that maximizes profit.

Answer:

Step-by-step explanation:

Let X be the pulse rates of females

X is N(72,12.5)

a) P(66<x<78) = P(|Z|<6/12.5)

= P(|Z|<0.48) = 2*.1844=0.3688

b) Each person is independent of the other

Hence P(4*66<4x<4*78) = P(|Z|<24/50) =0.3688^4

c) Because parent distribution is normal

Answer:

segment EG over segment LN equals segment FG over segment MN

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem

The corresponding sides are

EF and LM

EG and LN

FG and MN

The corresponding angles are

∠E≅∠L

∠F≅∠M

∠G≅∠N

therefore

EF/LM=EG/LN=FG/MN=3/1

Answer:

C: Segment EG over segment LN equals segment FG over MN.

Step-by-step explanation:

We are given that [tex]\triangle EFG \sim\traingle LMN[/tex] with ratio 3:1

We have to find the true statement about two similar triangles in given options

When two triangle are similar

Then ratios of all sides of one triangle to its  corresponding  all sides of another triangle are equal.

Therefore, Corresponding side of EF is LM

Corresponding side of FG is MN

Corresponding side of EG is LN

Ratio

[tex]\frac{EF}{LM}=\frac{FG}{MN}=\frac{EG}{LN}=\frac{3}{1}[/tex]

Hence, segment FG over segment MN equals to segment EG over segment LN.

Therefore, option C is true.

Answer : C: Segment EG over segment LN equals segment FG over MN.

Answer:

interest rate is 38.68 %

Step-by-step explanation:

Given data

installment = $60

time = 36 months = 36/12 = 3 years

principal = $1000

to find out

interest rate

Solution

we know student pay $60 for 36 months

so he pay total = 60 × 36 = 2160

total amount pay by student = $ 2160

so we can find interest rate by given formula

rate = (1/time)(amount/Principal - 1)

put the value time amount and principal here

rate = (1/3)(2160/1000 - 1)

rate = 0.386667

interest rate is 38.68 %

Answer:

the probability that their minimum is larger than 5 is 0.2373

Step-by-step explanation:

For calculate the probability we need to make a división between the total ways to selected the 5 numbers and the ways to select the five numbers in which every number is larger than 5.

So the number of possibilities to select 5 numbers from 20 is:

20                 *      20         *          20     *        20         *       20

First number  2nd number   3rd number  4th number   5th number

Taking into account that a number can be chosen more than once, and the order in which you select the numbers matters, for every position we have 20 options so, there are  [tex]20^{5}[/tex] ways to select 5 numbers.

Then the number of possibilities in which their minimum number is larger than 5 is calculate as:

15                 *      15         *             15     *        15          *       15

First number  2nd number   3rd number  4th number   5th number

This time for every option we can choose number from 6 to 20, so we have 15 numbers for every option and the total ways that satisfy the condition are  [tex]15^{5}[/tex]

So the probability P can be calculate as:

[tex]P=\frac{15^{5} }{20^{5} } \\P=0.2373[/tex]

Then the probability that their minimum is larger than 5 is 0.2373

Answer:

accounting profit =$ 51,000

Economic profit = $ 7000

Step-by-step explanation:

In economic profit we consider opportunity cost opportunity cost is next best alternative for gone.

Economic profit =140,000 - 50,000 - 50,000 - 15,000 - 4000 - 20,000 + 6000            

                           = $ 7000

In accounting profit we do not consider opportunity cost.

hence,

accounting profit = 140,000 - 50,000 - 15,000 - 4000 - 20,000

                            = $ 51,000

Answer:

C.

Step-by-step explanation:

p(x)=sin(x) is an odd function since sin(-x)=-sin(x).

q(x)=cos(x) is an even function since cos(-x)=cos(x).

r(x)=tan(x) is an odd function since tan(-x)=-tan(x).

s(x)=csc(x) is an odd function since csc(-x)=-csc(x).

So the only contender seems to be C.

Let's check.  To check we have to plug in (-x) in place of (x) and see if we get the same function back since we are looking for an even function.

[tex]f(x)=\cos(\frac{5\pi}{4}x)[/tex]

Replace (x) with (-x):

[tex]f(-x)=\cos(\frac{5\pi}{4}(-x)[/tex]

[tex]f(-x)=\cos(\frac{-5\pi}{4}x)[/tex]

[tex]f(x)=\cos(\frac{5\pi}{4}x)[/tex] since cosine is even; that is cos(-u)=cos(u) where u in this case is [tex]\frac{5\pi}{4}x[/tex].

So f is even.

C. f(x) = cos(x) The cosine function is an even function. So, the correct answer is C. f(x) = cos(x).

An even function is a function that satisfies the following property:

f(x) = f(-x)

Let's examine the provided functions:

A. f(x) = sin(-31)

This is not an even function because the sine function is an odd function, and negating the angle in a sine function doesn't produce an even function.

B. f(x) = tan(3x)

The tangent function is an odd function, so this function is not even.

C. f(x) = cos(x)

The cosine function is an even function. This is the correct answer.

D. f(x) = csc(-1)

The cosecant function (csc) is the reciprocal of the sine function, and as mentioned earlier, the sine function is an odd function. So, the cosecant function is also odd, and this function is not even.

for such more question on even function

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Answer:

[tex]F_{k^{th}}=F_{(k-2)^{th}}+F_{(k-1)^{th}}[/tex]

Step-by-step explanation:

Since each number is the sum of it's 2 preceding numbers thus mathematically it can be written as

[tex]F_{k^{th}}=F_{(k-2)^{th}}+F_{(k-1)^{th}}[/tex]

Fibonacci Series can be written as

1,1,2,3,5,8,13...