Precalculus: Trigonometric Functions and Identities

Answer:

Using the cosines law

Step-by-step explanation:

So, we need to find the length of the other side, we will use the version of the Cosine Rule where a2 is the subject of the formula, which is given by, a2=b2+c2−2bccosA, Side a is the one we are trying to find. Sides band care the other two sides, and angle Ais the angle opposite side a. c2=a2+b2−2abcosC

Answer:

C 14

Step-by-step explanation:

Answer:

All angles that are either interior angles, exterior angles, alternate angles or corresponding angles are all considered congruent.

Hope this answered your question!

Answer:

exterior angles, interior angles, alternate angles , corresponding angles

Answer:

A. Zero points of intersection, Brainiest please

Step-by-step explanation:

Answer:

There is no solution.

Step-by-step explanation:

We have shown that the function f : Z × Z → Z × Z defined by f(m, n) = (2 − n, 3 + m) is both injective (one-to-one) and surjective (onto), satisfying the conditions of a bijective function.

a. To prove that the function f : Z × Z → Z × Z defined by f(m, n) = (2 − n, 3 + m) is injective (one-to-one), we need to show that for any two distinct inputs (m1, n1) and (m2, n2) in Z × Z, their corresponding outputs under f are also distinct.

Let (m1, n1) and (m2, n2) be two arbitrary distinct inputs in Z × Z. We assume that f(m1, n1) = f(m2, n2) and aim to prove that (m1, n1) = (m2, n2).

By the definition of f, we have (2 − n1, 3 + m1) = (2 − n2, 3 + m2). From this, we can deduce two separate equations:

1. 2 − n1 = 2 − n2 (equation 1)

2. 3 + m1 = 3 + m2 (equation 2)

From equation 1, we can see that n1 = n2, and from equation 2, we can observe that m1 = m2. Therefore, we conclude that (m1, n1) = (m2, n2), which confirms the injectivity of the function.

b. To prove that the function f : Z × Z → Z × Z defined by f(m, n) = (2 − n, 3 + m) is surjective (onto), we need to show that for every element (a, b) in the codomain Z × Z, there exists an element (m, n) in the domain Z × Z such that f(m, n) = (a, b).

Let (a, b) be an arbitrary element in Z × Z. We need to find values for m and n such that f(m, n) = (2 − n, 3 + m) = (a, b).

From the first component of f(m, n), we have 2 − n = a, which implies n = 2 − a.

From the second component of f(m, n), we have 3 + m = b, which implies m = b − 3.

Therefore, by setting m = b − 3 and n = 2 − a, we have f(m, n) = (2 − n, 3 + m) = (2 − (2 − a), 3 + (b − 3)) = (a, b).

Hence, for every element (a, b) in the codomain Z × Z, we can find an element (m, n) in the domain Z × Z such that f(m, n) = (a, b), demonstrating the surjectivity of the function.

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Given:

Area and altitude PS of ∆PQR are ar(∆PQR) = 180cm² and PS = 15​.

To find:

The measure of side QR.

Solution:

According to the given information, PS is an altitude of ∆PQR. It means QR is the base of ∆PQR.

We know that, the area of a triangle is

\(Area=\dfrac{1}{2}\times Base\times Height\)

\(ar(\Delta PQR)=\dfrac{1}{2}\times QR\times PS\)

Substituting the given values, we get

\(180=\dfrac{1}{2}\times QR\times 15\)

\(180\times 2=QR\times 15\)

\(360=QR\times 15\)

Divide both sides by 15.

\(\dfrac{360}{15}=QR\)

\(24=QR\)

Therefore, the measure of side QR is 24 cm.

The expression in the scientific notation will be 7.79 × \(10^{7}\) .

Simplifying 8.2 × \(10^{7}\) - 4.1 × \(10^{6}\)

To simplify the equation power should be same

To convert to decrease power the decimal will move to the right

It can be written as

8.2 × \(10^{7}\) = 82.0 × \(10^{6}\)

Now solving the equation

82.0 × \(10^{6}\) - 4.1 × \(10^{6}\)

= 77.9 × \(10^{6}\)

To convert the equation into scientific notation

The decimal should be after one significant figure

To convert to increase power the decimal will move to the left

It can be written as

7.79  × \(10^{7}\)

Simplifying the equation will give 7.79 × \(10^{7}\) .

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it would help if we were given the equations to choose from ^^'

Answer:

y = 3x - 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 1, - 8 ) and (x₂, y₂ ) = (3, 4 )

m = \(\frac{4-(-8)}{3-(-1)}\) = \(\frac{4+8}{3+1}\) = \(\frac{12}{4}\) = 3 , then

y = 3x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (3, 4 ) , then

4 = 9 + c ⇒ c = 4 - 9 = - 5

y = 3x - 5 ← equation containing the 2 points

The total number of samples will be 1109 .

Given ,

Margin of error 0.02

Here,

According to the formula,

\(Z_{\alpha /2} \sqrt{pq/n}\)

Here,

p = proportions of scientist that are left handed

p = 0.09

n = number of sample to be taken

Substitute the values,

\(Z_{0.01} \sqrt{0.09 * 0.91/n} = 0.02\\ 2.33 \sqrt{0.09 * 0.91/n} = 0.02\\\\\\\)

n ≈1109

Thus the number of samples to be taken will be approximately 1109 .

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Answer: here my answer IIn The picture .

Step-by-step explanation:

Answer:

I'll need a picture of it, and/or the options to help you out.

Step-by-step explanation:

Answer:

-1.4

Step-by-step explanation:

rise over run y2-y1 (top) and x2-x1 (bottom)

Becca made a total of 24 rolls and 12 biscuits.

Multiplication is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division. The result of a multiplication operation is called a product.

Becca made 2 trays of rolls and biscuits, with 12 rolls and 6 biscuits in each tray. To find the total number of rolls and biscuits, we need to multiply the number of rolls and biscuits per tray by the number of trays, and then add them together:

Total rolls = 2 trays × 12 rolls per tray = 24 rolls

Total biscuits = 2 trays × 6 biscuits per tray = 12 biscuits

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Answer:

210

Step-by-step explanation:

6 times 3.5=210

The 90% confidence interval for the difference in the population means is -2.51 to 0.31

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

xˉ₁ = −17.1

s₁² = 8.4

n₁ = 22

​xˉ₂ = −16.0

s₂² = 8.7

n₂ = 24

Calculate the pooled variance using

P = (df₁ * s₁² + df₂ * s₂²)/df

Where

df₁ = 22 - 1 = 21

df₂ = 24 - 1 = 23

df = 22 + 24 - 2 = 44

So, we have

P = (21 * 8.4 + 23 * 8.7)/44

P = 8.56

Also, we have the standard error to be

SE = √(P/n₁ + P/n₂)

So, we have

SE = √(8.56/22 + 8.56/24)

SE = 0.86

The z score at 90% CI is 1.645, and the CI is calculated as

CI =  (x₁ - x₂) ± z * SE

So, we have

CI = (-17.1 + 16.0) ± 1.645 * 0.86

This gives

CI = -1.1 ± 1.41

Expand and evaluate

CI = (-2.51, 0.31)

Hence, the confidence interval is -2.51 to 0.31

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Answer:

3/6

Step-by-step explanation:

Well 3 is half of 6 and if you were to turn that into a fraction it would either be 3/6 or 1/2.

The probability that you will see even numbers on both dice will be 0.25.

Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences. Then the probability is given as,

P = (Favorable event) / (Total event)

Two dice are tossed. Then the total number of events will be

Total events = 6 × 6

Total events = 36

The probability that you will see even numbers on both dice will be

The number of the favorable event will be given as,

Favorable events = 9

Then the probability is given as,

P = 9 / 36

P = 1/4

P = 0.25

The probability that you will see even numbers on both dice will be 0.25.

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Answer:

£4.20

Step-by-step explanation:

Let :

Equations formed :

Multiply Equation 1 by 5 and Equation 2 by 3 :

Subtract the newly formed equations :

Finding y :

Then :

Cost of 2 kg bananas and 2 kg of apples :

Answer:

I fairly sure the answer is 12 days

It would 12 days to take to produce 4,512 phones.

A ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.

/ Division operation: Divides left-hand operand by right-hand operand

For example 4/2 = 2

We have been given that machine that makes cellphones can produce 47 cellphones per hour when running. The machine can only run for 8 hours per day.

We have to determine the number of days will it take to produce 4,512 phones.

Here machine produces (47×8) i.e 376 cellphones per day

Let x days would it take to produce 4,512 phones.

We can write this as a ratio as:

376 phones : 1 day = 4,512 phones : x days

⇒ 376/1= 4,512 /x    

⇒ (376)(x) = 4,512

Divide each side by 376

⇒ x = 4,512/376

⇒ x = 12

Therefore, it would 12 days to take to produce 4,512 phones.

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The inferential statistics would employ the probability to predict how many miles one should be able to drive a 2000 Toyota Celica during its lifetime.

The inferential statistics are calculated by using analytical tools such as test-statistic values, degree of freedom, sample size, and the rejection criteria(assumption or hypothesis).

Thus, the given information is about predicting the miles. So, according to the probability theory, it needs a sample of data about 2000 Toyota Celica.

Hence, it falls under the inferential branch of statistics. So, option C is correct.

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Disclaimer: The given question on the portal was incomplete. Here is the complete question.

Question: Which branch of statistics would employ probability to predict how many miles one should be able to drive a 2000 Toyota Celica during its lifetime?

A. Predictive statistics

B. Descriptive statistics

C. Inferential statistics

D. Differential statistics

The value of x in the two congruent triangles is 3.9 and length CB is 53.9.

The value of x can be determined by applying the principle of congruent theorem.

The congruent theorem states that, if all the three sides of one triangle are equal to all the three sides of another triangle, then both the triangles are congruent to each other.

( 11x + 11 ) / 77 = 21 / 30

11x + 11 = 53.9

11x = 53.9 - 11

11x = 42.9

x = 42.9 / 11

x = 3.9 units

The length of CB = ( 11 x 3.9 ) + 11 = 53.9

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Answer:

the answer is b 4-n. Hope this helps

Answer:

the second one (4-n).

Step-by-step explanation:

lol

Answer:

The coordinates of the original point would be (-9,4). This is because, by reflecting over the way y-axis, the point is moving across the x-axis and therefore, makes the x-coordinate negative.

Answer:

2/3 cup

Step-by-step explanation:

first you need to convert the fractions so that they have the same denominator (1/3 turns into 2/6)

then you just add up the numerators (2+2=4..... 4/6)

you can stop there or you can simplify it (4/6 turns into 2/3)

\(\\ \rm\rightarrowtail x^2-3x-10=0\)

\(\\ \rm\rightarrowtail x^2-5x+2x-10=0\)

\(\\ \rm\rightarrowtail x(x-5)+2(x-5)=0\)

\(\\ \rm\rightarrowtail (x+2)(x-5)=0\)

\(\\ \rm\rightarrowtail x=-2\;or\:5\)

Given,

\(\small\bold{x² – 3x – 10 =0}\)

Taking LHS,

\(\small\bold\red{ → }\small\bold{x^2 – 5x + 2x – 10}\)

\(\small\bold\red{ → }\small\bold{ x(x – 5) + 2(x – 5)}\)

\(\small\bold\red{ → }\small\bold{ (x – 5)(x + 2)}\)

The roots of this equation, x² – 3x – 10 = 0 are the values of x for which (x – 5)(x + 2) = 0

Therefore,\( \small\bold{x – 5 = 0 \: or \: x + 2 = 0}\)

\(\small\bold\red{ → }\small\bold{x = 5 \: or \: x = -2 }\)

Ionization energy generally increases as you move left to right in Period 4 from potassium through iron on the periodic table.

Ionization energy refers to the amount of energy required to remove an electron from an atom or ion in the gaseous state. As you move from left to right in Period 4, the number of protons in the nucleus increases, resulting in a stronger attraction between the nucleus and the electrons. This increased attraction makes it more difficult to remove an electron, hence requiring more energy. Therefore, ionization energy generally increases as you move from potassium to iron in Period 4 on the periodic table.

This trend can be observed by looking at the atomic numbers of the elements in Period 4. Potassium has a lower ionization energy compared to iron because it has fewer protons and a larger atomic radius. As you move towards iron, the increasing number of protons leads to a stronger nuclear charge, resulting in higher ionization energy. However, it's important to note that there may be some irregularities or exceptions within this trend due to factors such as electron configuration and shielding effects.

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Answer:

60

Step-by-step explanation:

b = the hypotenuse of a right angle triangle

a = the adjacent side.

R is being defined by the cosine

cos(R) = adjacent /  hypotenuse

adjacent = 16* sqrt(2)

hypotenuse = 32*sqrt(2)

Cos(R) = 16*sqrt(2) / 32*sqrt(2)      sqrt(2) cancels.

cos(R) = 1/2

R = cos-1(1/2)

R = 60 degrees.

Answer:

w=4

Step-by-step explanation:

The surface area of a prism is SA= 2lw+2lh+2hw

We are trying to find out the width if the SA is 240 square inches, length is 12 inches, and the height is 5 inches. Let's plug these numbers into the equation.

240=(2*12*w)+(2*12*5)+(2*5*w)

          24w+120+10w

240= 34w+120

-120           -120

120= 34w

120/34 = 34w/34

w is approximately equal to 3.5 which can be rounded to 4

w=4

Hope this is right! It was confusing at first but I understood it!

By using the functions we have found the value of x and it is found out to be as x = -20/3.

What is a function?

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

Given data:

f(x) = -4x + 1, g(x) = x2 - 8x + 21, and h(x) = 19 - 3x and h(x) = 39.

By using the h(x) function, we can write

               h(x) = 19 - 3x

                39 = 19 - 3x

                3x = 19 - 39

                3x = -20

                  x = -20/3

Hence, by using the functions we have found the value of x and it is found out to be as x = -20/3.

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Answer:

80%

Step-by-step explanation:

If it's 20 out of 100 than it's 80 because
100 - 20 = 80

Step-by-step explanation:

x = -2

y = -3

= x² - y²

= (-2)² - (-3)²

= 4 - 9

= -5