find the measures of angles of triangle DEF

Let's prove that (sec x)(csc x) is equal to cot x + tan x

[tex]\Longrightarrow \sf (sec(x) )(csc(x))[/tex]

[tex]\Longrightarrow \sf \dfrac{1}{\cos \left(x\right)\sin \left(x\right)}[/tex]

[tex]\Longrightarrow \sf \dfrac{\cos ^2\left(x\right)+\sin ^2\left(x\right)}{\cos \left(x\right)\sin \left(x\right)}[/tex]

[tex]\Longrightarrow \sf \dfrac{\cos ^2\left(x\right)}{\cos \left(x\right)\sin \left(x\right)} + \dfrac{\sin ^2\left(x\right)}{\cos \left(x\right)\sin \left(x\right)}[/tex]

[tex]\Longrightarrow \sf \dfrac{\cos\left(x\right)}{\sin \left(x\right)} + \dfrac{\sin \left(x\right)}{\cos \left(x\right)}[/tex]

[tex]\Longrightarrow \sf cot(x) + tan(x)[/tex]

Hence student A did correctly prove the identity properly.

Also Looking at student B's work, he verified the identity properly.

So, Both are correct in their own way.

Identities used:

[tex]\rightarrow \sf sin^2 (x) + cos^2 (x) = 1[/tex]       (appeared in step 3)

[tex]\sf \rightarrow \dfrac{cos(x) }{sin(x) } = cot(x)[/tex]               (appeared in step 6)

[tex]\rightarrow \sf \dfrac{sin(x )}{cos(x) } = tan(x)[/tex]               (appeared in step 6)

Answer:

[tex]2x^{2}[/tex] - 16x + 14

Step-by-step explanation:

(2x - 4)(x - 6)

= (2x + −4)(x + −6)

= (2x)(x) + (2x)(−6) + (−4)(x) + (−4)(−6)

= [tex]2x^{2}[/tex] − 12x − 4x + 24

= [tex]2x^{2}[/tex] - 16x + 14

The multiplication of the expression will be 1215 cubic yd 2295 cubic inches.

It is also known as the product. If the object n is given to m times, then we just simply multiply them.

The expression is given below.

(9 cubic yd and 17 cubic in) × 135

On multiplication, we have

135 × 9 cubic yd and 135 ×  17 cubic in

1215 cubic yd and 2295 cubic inches

1215 cubic yd 2295 cubic inches

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The multiplication is 56,689,335 cu in

A number system is defined as a system of writing to express numbers. It is the mathematical notation for representing numbers of a given set by using digits or other symbols in a consistent manner.

9 cu yd 17cu in

1 cu yard = 46656 cu inches

9 cu yard = 9*46656 = 419904 cu inches

Now, total inches

= 419904 cu inches + 17 cu in

= 419,921 cu inches.

and, the multiplication is

=56689335

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Answer:

[tex]\displaystyle\frac{dy}{dx} \ = \ 3x^{2} \ + \ \displaystyle\frac{1}{2\sqrt{x^{3}}} \ - \ \displaystyle\frac{12}{x^{5}}[/tex]

Step-by-step explanation:

                      [tex]y \ = \ x^{3} \ - \ \displaystyle\frac{1}{\sqrt{x}} \ + \ \displaystyle\frac{3}{x^{4}} \\ \\ y \ = \ x^{3} \ - \ x^{-\frac{1}{2}} \ + \ 3x^{-4} \\ \\ \displaystyle\frac{dy}{dx} \ = \ 3x^{3 \ - \ 1} \ - \ \left(-\displaystyle\frac{1}{2}\right)x^{-\frac{1}{2} \ - \ 1} \ + \ \left(-4 \ \times \ 3\right)x^{-4-1}[/tex]

                       [tex]\displaystyle\frac{dy}{dx} \ = \ 3x^{2} \ + \ \displaystyle\frac{1}{2}x^{-\frac{3}{2}} \ - \ 12x^{-5} \\ \\ \displaystyle\frac{dy}{dx} \ = \ 3x^{2} \ + \ \displaystyle\frac{1}{2\sqrt{x^{3}}} \ - \ \displaystyle\frac{12}{x^{5}}[/tex]

The probabilities for various binomial distribution have been determined.

The complete question is

About 5% of hourly paid workers in a region earn the prevailing minimum wage or less. A grocery chain offers discount rates to companies that have at least 30 employees who earn the prevailing minimum wage or less. Complete parts (a) through (c) below.

(a) Company A has 285 employees. What is the probability that Company A will get the discount? (Round to four decimal places as needed.)

(b) Company B has 502 employees. What is the probability that Company B will get the discount? (Round to four decimal places as needed.)

(c) Company C has 1033 employees. What is the probability that Company C will get the discount? (Round to four decimal places as needed.)

Probability is a stream in mathematics that study the likeliness of an event to happen .

On the basis of the given data

(a) Let X is a random variable that denotes the number of employees that earn less than prevailing average.

Here X has binomial distribution with

n=285 and p=0.05.

As np and n(1-p) are greater than 5 so using normal approximation X has normal distribution with parameters

μ=  np-285 * 0.05

= 14.25

standard deviation is given by

[tex]\sigma=\sqrt{np(1-p)}=\sqrt{285* 0.05* 0.95}\\\\=3.6793[/tex]

Applying continuity correction.

The z-score for X = 30-0.5 = 29.5 is

[tex]z=\dfrac{29.5-14.25}{3.6793}\\\\=4.14[/tex]

The probability that Company A will get the discount is given by

[tex]P(X\geq 30)=P(z > 4.14)=0.0000[/tex]

(b) Let X is a random variable that denotes the number of employees that earn less than prevailing average.Here X has binomial distribution with

n=502 and p=0.05.

[tex]\rm \mu=np=502* 0.05=25.1[/tex]

standard deviation

[tex]\rm \sigma=\sqrt{np(1-p)}=\sqrt{502\cdot 0.05\cdot 0.95}=4.8831[/tex]

Applying continuity correction.

The z-score for X = 30-0.5 = 29.5 is

[tex]\rm z=\dfrac{29.5-25.1}{4.8831}=0.90[/tex]

The probability that Company B will get the discount is

[tex]P(X\geq 30)=P(z > 0.90)=0.1841[/tex]

(c)Let X is a random variable that denotes the number of employees that earn less than prevailing average.Here X has binomial distribution with

n=1033 and p=0.05.

[tex]\mu=np=1033\cdot 0.05=51.65[/tex]

standard deviation

[tex]\rm \sigma=\sqrt{np(1-p)}=\sqrt{1033*0.05* 0.95}=7.0048[/tex]

Applying continuity correction.

The z-score for X = 30-0.5 = 29.5 is

[tex]\rm z=\dfrac{29.5-51.65}{7.0048}=-3.16[/tex]

The probability that Company C will get the discount is

[tex]\rm P(X\geq 30)=P(z > -3.16)=0.9992[/tex]

Therefore the probabilities for various binomial distribution have been determined.

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Using it's concept, it is found that the domain of the function is given as follows:

d. 0 < c ≤ 15

The domain is the set that contains all possible input values for the function.

He is losing weight consistently, hence c > 0, and the maximum amount is of 15 calories, hence c ≤ 15 and the domain is given by:

d. 0 < c ≤ 15

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Answer:

The solution is 4 - 9/(2x + 1)

No, the divisor does not evenly divide into the dividend

Step-by-step explanation:

Please see the attached image

The length of the diagonal of the state of Wyoming is 457 miles.

The length of the diagonal of the diagonal can be determined using Pythagoras theorem.

The Pythagoras theorem: a² + b² = c²

where:

√365² + 275² = 457 miles

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Answer:

78.7

Step-by-step explanation:

To find the mean, we can do the sum of all scores divided by the total amount of scores.

We see that there are 7 scores of 70, and 70*7=490.

We see that there are 5 scores of 75, and 75*5=375.

We see that there are 4 scores of 80, and 80*4=320.

We see that there is 1 score of 85, and 85*1=85.

We see that there are 6 scores of 90, and 90*6=540.

Now we can do [tex]\frac{490+375+320+85+540}{7+5+4+1+6} =\frac{1810}{23} =78.7[/tex]

the answer should be 5 inches I guess

The interest rate is 36% per year if the value of a savings account can be found using the equation 300(1.03)²⁴ option (c) is correct.

It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.

We can calculate the compound interest using the below formula:

[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]

Where A = Final amount

          P = Principal amount

          r  = annual rate of interest

          n = how many times interest is compounded per year

          t = How long the money is deposited or borrowed (in years)

We have:

The value of a savings account can be found using the equation =

= 300(1.03)²⁴

From the function:

F(x) = a(1+r)ˣ

On compare:

1 + r = 1.03

r = 0.03

or

r = 3% monthly

r = 3×12 = 36% yearly

Thus, the interest rate is 36% per year if the value of a savings account can be found using the equation 300(1.03)²⁴ option (c) is correct.

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[tex] {8x}^{0} \\( {8 \times 0})^{0} \\ {0}^{0} \\ it \: is \: undefined[/tex]

PLEASE GIVE BRAINLIEST

Answer:

[tex]sec(\theta)=\frac{2}{\sqrt3}[/tex]

Step-by-step explanation:

Given [tex]sin(\theta)=\frac{1}{2}[/tex] , to find [tex]sec(\theta)[/tex], it will be helpful to visualize a right triangle (triangle with a 90 degree angle) associated with that particular θ.  There are a few ways to go about this:

All of the basic trigonometric functions, applied to an angle) are a ratio of two specific sides of any right triangle that holds that angle.

Remember that the Sine of an angle is defined specifically, the ratio of the opposite side (the side across from the angle in the Sine function), and the hypotenuse (the side across from the right angle).  You might remember this through SohCahToa

[tex]sin(\theta)=\frac{opp}{hyp}[/tex]

In our case, since [tex]sin(\theta)=\frac{1}{2}[/tex] , so  [tex]\frac{opp}{hyp}=\frac{1}{2}[/tex] .  While there are an infinite number of triangles that have that ratio of those sides, they are all "similar" triangles (corresponding angles congruent, and corresponding sides are proportional, yielding common ratios of sides), and for ease, we can consider simply the triangle where the value of the numerator is the length of the opposite side, and the value of the denominator is equal to the hypotenuse.  So, [tex]opp=1[/tex], and [tex]hyp=2[/tex].

While we haven't actually talked about θ yet, we can still set up the triangle that has these sides so that we can visualize what the triangle looks like. (see image)

This triangle represents the triangle for the unknown θ in the original sine function.  We're tasked with finding the secant of that particular unknown θ.

Working toward Secant

Here, it will be helpful to remember either the reciprocal identities for[tex]sec(\theta)=\frac{1}{cos(\theta)}[/tex], or the definition of the secant function [tex]sec(\theta)=\frac{hyp}{adj}[/tex].

I find that most people remember the reciprocal identities more easily than keeping track of the definitions, so, since secant is related to cosine, it will be important to remember that [tex]cos(\theta)=\frac{adj}{hyp}[/tex].  From there, take the reciprocal of the cosine-value to get the secant-value (which matches the definition of the secant function).

Either way, it comes down to knowing the lengths of the side adjacent to theta, and the hypotenuse.  We already know the length of the hypotenuse, so we just need the length of the adjacent side.

Applying the Pythagorean Theorem

Fortunately, because it is a right triangle, the Pythagorean Theorem applies: [tex]a^{2} +b^{2} =c^{2}[/tex]  (where c is the length of the hypotenuse, and a & b are the lengths of the legs)

Substituting the known values for the sides we do know...[tex](adj)^{2} +(1)^{2} =(2)^{2}\\(adj)^{2} +1 =4[/tex]

...isolating "adj" by subtraction...

[tex](adj)^2=4-1\\(adj)^2=3[/tex]

...applying the square root property...

[tex]adj=\sqrt{3}[/tex]  or  [tex]adj=-\sqrt{3}[/tex]

Identifying which Quadrant the triangle is in

Since we were given that [tex]0^o < \theta < 90^o[/tex], our triangle is an acute triangle (as drawn in the diagram), and is in quadrant I (indicating that both legs will be measured with a positive value.

Thus, we discard the negative solution and conclude that [tex]adj=\sqrt{3}[/tex].

Finding the final solution

From there, [tex]cos(\theta)=\frac{adj}{hyp}[/tex] implies [tex]cos(\theta)=\frac{\sqrt3}{2}[/tex], and through the reciprocal relationship (or simply the definition of secant, whichever is easier for you to remember), [tex]sec(\theta)=\frac{2}{\sqrt3}[/tex]

Note:  This method did not require knowing what the angle θ was.

If you know well the values of special triangles in the unit circle, you may have identified that [tex]sin(\theta)=\frac{1}{2}[/tex]  is associated with [tex]\theta=30^o[/tex].  If so, if you also recall that the ordered pair associated with that point on the unit circle is [tex](\frac{\sqrt3}{2} ,\frac{1}{2} )[/tex], and that the [tex]cos(\theta)=x\text{-coordinate on the unit circle}[/tex], then you can quickly identify that  [tex]cos(\theta)=\frac{\sqrt3}{2}[/tex].

This method still ends the same: recalling the reciprocal relationship between cosine and secant, giving [tex]sec(\theta)=\frac{2}{\sqrt3}[/tex].

Answer: (6, -5)

Step-by-step explanation: I used the midpoint formula and this is what I got. I hope this helps!

The formula:

(xm, xy) = (x1 + x2/2, y1 + y2/2)

D. 12.5

The equation to find the average rate of change is

[tex] \frac{y2 - y1 }{x2 - x1} [/tex]

To find the average rate of change between points (0,20) and (8,120) you need to plug it into the equation so it'll be

[tex] \frac{120 - 20}{8 - 0} [/tex]

this simplifies to

[tex] \frac{100}{8} [/tex]

which is 12.5

The irrational number in the given options is √11

Irrational numbers are set of all real numbers in mathematics that are not rational numbers in nature. By the word rational, we mean that they cannot be expressed or represented in a fraction of a/b.

where;

In other words, it is impossible to describe an irrational number as the ratio of two integers.

From the given options, the square root of 11 is the only number that cannot be expressed as a fraction, therefore, we can conclude that it is considered the only irrational number in the given options.

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Answer:

1 cup

Step-by-step explanation:

1/3 cup of chocolate chips : 2 cup of flours

So 1/3:2 = x:3

Because we want to find x, the number of how many cups of chocolate chips he needs.
you can cross multiply where you get 1/3·3=2x
which is 1=2x and x=1

Answer:

B

Step-by-step explanation:

4, 16, 64 should be the correct order

An arithmetic sequence is a sequence in which the difference between any two consecutive terms of the sequence is equal. The number of term 107 is 17th.

What is Arithmetic Sequence?

An arithmetic sequence is a sequence in which the difference between any two consecutive terms of the sequence is equal.

a_n = a₁ + (n-1)r

where,

a_n is the nth term of the sequence,

a₁ is the first term of the sequence,

r is a common difference between every two terms.

Given the formula for the nth term of the arithmetic sequence is,

[tex]a_n = 11+6(n-1)[/tex]

Now, the number of term that 107 will be,

107 = 11 + 6(n-1)

96 = 6(n-1)

16 = n- 1

n =17

Hence, the number of term that 107 is 17.

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Answer: (I am copying and pasting my answer from the same question you did before in case you are waiting for an answer on this instead.)

1/2

Step-by-step explanation:

To find the x-int of any equation, you will need to replace the y with a 0 since when the x-int is when y is 0.

8x+2y = 4 ➨ 8x+2*0 = 4

Now I will do 2*0 which anything times 0 is equal to 0. And we are left with the equation of:

8x = 4

Now I will divide both sides by 8, which isolates our x.

x = 1/2

The x-int is 1/2.

Answer:

(0.5 , 0) or (1/2 , 0)

Step-by-step explanation:

Any x-intercept must be at (x,0), so we substitute y=0 into the equation.

8x + 2(0) = 4

8x = 4

x = 1/2 = 0.5

Therefore, the x-intercept is at (0.5 , 0) or (1/2 , 0)

If the geometric series has first term [tex]a[/tex] and common ratio [tex]r[/tex], then its [tex]N[/tex]-th partial sum is

[tex]\displaystyle S_N = \sum_{n=1}^N ar^{n-1} = a + ar + ar^2 + \cdots + ar^{N-1}[/tex]

Multiply both sides by [tex]r[/tex], then subtract [tex]rS_N[/tex] from [tex]S_N[/tex] to eliminate all the middle terms and solve for [tex]S_N[/tex] :

[tex]rS_N = ar + ar^2 + ar^3 + \cdots + ar^N[/tex]

[tex]\implies (1 - r) S_N = a - ar^N[/tex]

[tex]\implies S_N = \dfrac{a(1-r^N)}{1-r}[/tex]

The [tex]N[/tex]-th partial sum for the series of reciprocal terms (denoted by [tex]S'_N[/tex]) can be computed similarly:

[tex]\displaystyle S'_N = \sum_{n=1}^N \frac1{ar^{N-1}} = \frac1a + \frac1{ar} + \frac1{ar^2} + \cdots + \frac1{ar^{N-1}}[/tex]

[tex]\dfrac{S'_N}r = \dfrac1{ar} + \dfrac1{ar^2} + \dfrac1{ar^3} + \cdots + \dfrac1{ar^N}[/tex]

[tex]\implies \left(1 - \dfrac1r\right) S'_N = \dfrac1a - \dfrac1{ar^N}[/tex]

[tex]\implies S'_N = \dfrac{1 - \frac1{r^N}}{a\left(1 - \frac1r\right)} = \dfrac{r^N - 1}{a(r^N - r^{N-1})} = \dfrac{1 - r^N}{a r^{N-1} (1 - r)}[/tex]

We're given that [tex]a=1[/tex], and the sum of the first [tex]n[/tex] terms of the series is

[tex]S_n = \dfrac{1-r^n}{1-r} = 364[/tex]

and the sum of their reciprocals is

[tex]S'_n = \dfrac{1 - r^n}{r^{n-1}(1 - r)} = \dfrac{364}{243}[/tex]

By substitution,

[tex]\dfrac{1 - r^n}{r^{n-1}(1-r)} = \dfrac{364}{r^{n-1}} = \dfrac{364}{243} \implies r^{n-1} = 243[/tex]

Manipulating the [tex]S_n[/tex] equation gives

[tex]\dfrac{1 - r^n}{1-r} = 364 \implies r (364 - r^{n-1}) = 363[/tex]

so that substituting again yields

[tex]r (364 - 243) = 363 \implies 121r = 363 \implies \boxed{r=3}[/tex]

and it follows that

[tex]r^{n-1} = 243 \implies 3^{n-1} = 3^5 \implies n-1 = 5 \implies \boxed{n=6}[/tex]

The formula for the surface area N(t) of the balloon after t seconds is [tex]N(t) = \frac {64}9\pi t^2[/tex]

We have:

[tex]S(r) = 4\pi r^2[/tex]

Also, we have:

[tex]P(t) = \frac 43t[/tex]

The above can be rewritten as:

[tex]r = \frac 43t[/tex]

Substitute [tex]r = \frac 43t[/tex] in S(r) to determine the function N(t)

[tex]S(r) = 4\pi (\frac 43t)^2[/tex]

Express as N(t)

[tex]N(t) = 4\pi (\frac 43t)^2[/tex]

Expand the exponent

[tex]N(t) = 4\pi *\frac {16}9t^2[/tex]

Evaluate the product

[tex]N(t) = \frac {64}9\pi t^2[/tex]

Hence, the formula for the surface area N(t) of the balloon after t seconds is [tex]N(t) = \frac {64}9\pi t^2[/tex]

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Answer:

x=1

Step-by-step explanation:

20(3x-3/5) = 20(2x-2/4)

12x-12= 10x-10

12x-10x =12-10

x= 1

Answer:

Step-by-step explanation:

Solution

3x - 3       2x - 2

=====  =  ======                       Cross Multiply

5              4

4(3x - 3) = 5(2x - 2)                   Remove the brackets. Distributive Property

12x - 12 = 10x - 10                     Subtract 10 x from both sides

12x-10x - 12 = 10x-10x - 10       Combine

2x - 12 = - 10                             Add 12  to both sides

2x-12+12 = -10 + 12                   Combine  

2x = 2                                       Divide by 2

2x/2 = 2/2                                

Answer

x = 1

The total price of the truck =$x + $ 0.13x

We have given that,

Camacho is buying a monster truck. The price of the truck is x dollars, and he also has to pay a 13%, percent monster truck tax.

We have to determine the expressions that could represent how much Camacho pays in total for the truck.

We will consider the price of the truck to be $x

And the amount of tax in the percentage would be 13%

13/100 = $ 0.13x (this is the actual amount of the tax)

Now we will calculate the total price of the truck =$x + $ 0.13x

= $ x(1 + 0.13)

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Step-by-step explanation:

1) the required equation in common form is:

(x-x₀)²+(y-y₀)²=r², where (x₀;y₀) - coordinates, where Michael is standing; r - the social distance;

According to the common form and given coordinates (x₀=-5; y₀=2; r=6) it is possible to make up the required equation:

(x+5)²+(y-2)²=6².

2) if the distance between two friends is:

[tex]d=\sqrt{(-5-1)^2+(2-1)^2}=\sqrt{37}, \ then[/tex]

this distance is longer than social (6 ft). For more info see the attachment.

Answer:

The value of x is 200 in the equation 1/5x - 2/3y = 30, when y = 15

Step-by-step explanation:

Given

equation: x - 2/3y = 30

when y = 15

Plug in y:

1/5x - 2/3(15) = 30

1/5x - 10 = 30

add 10 to both sides,

1/5x - 10 + 10 = 30 + 10

1/5x = 40

multiply both sides by 5

1/5x * 5= 40 * 5

x = 200

Answer:

x = 200

Step-by-step explanation:

[tex]\frac{1x}{5} -\frac{2y}{3} =30[/tex]

Given that, y = 15.

So, to find the value of x you have to replace y with 15 and make the x the subject.

Let us do that now.

[tex]\frac{1x}{5} -\frac{2*15}{3} =30\\[/tex]

[tex]\frac{1x}{5} -\frac{30}{3} =30\\[/tex]

[tex]\frac{1x}{5} =30+ \frac{30}{3}\\[/tex]

[tex]\frac{1x}{5} =\frac{30}{1} + \frac{30}{3}\\[/tex]

[tex]\frac{1x}{5} =\frac{30*3}{1*3} + \frac{30}{3}\\[/tex]

[tex]\frac{1x}{5} =\frac{90}{3} + \frac{30}{3}\\[/tex]

[tex]\frac{1x}{5} =\frac{120}{3}[/tex]

Use cross multiplication.

[tex]1x*3=120*5\\3x=600[/tex]

Divide both sides by 3.

x = 200

Answer: 1

Step-by-step explanation:

[tex]f(8+h)=8+h+10=18+h\\\\f(8)=8+10=18[/tex]

So, the average rate of change is:

[tex]\frac{(18+h)-18}{(8+h)-8}=\frac{h}{h}=\boxed{1}[/tex]

The question is wrong, the expression will not be in terms of h since it is a linear function.

The recurrence relation is dn = 0.4d(n-1) where d1 = 75

The given parameters are:

Since, the medication is eliminated from the blood; then it means that the function is an exponential decay function.

This is represented as:

d(n) = d(n - 1) * (1 - r)

Substitute r = 60%

d(n) = d(n - 1) * (1 - 60%)

Evaluate the difference

d(n) = d(n - 1) * 0.4

Evaluate the product

dn = 0.4d(n-1)

Hence, the recurrence relation is dn = 0.4d(n-1) where d1 = 75

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Answer:

if angle 2 is congruent to 6 them the slope of line o and q is equal

that is line o is parallel to q