In △ABC,a=14 , b=17 , and c=22 . Find m∠A . law of sines 4 A. 49.4 B. 39.5 C. 55.2 D. 50.45

In slope intercept form, the line's equation is y = 2x + 1. We must apply the formula y = mx + b to formulate an equation in slope intercept form. The slope of the line is represented by m, while the y-intercept is represented by b.

We need two locations on the line to find the slope. Assume we have points (2,5) and (4,9). We may calculate the slope using the following formula:

m = (9 - 5) / (4 - 2) m = (9 - 5) / (4 - 2)

m = 2

As a result, the slope of the line is 2.

We must now identify the y-intercept, which is the point at where the line crosses the y-axis.

We can utilise one of the points we already have to discover this. Let's start with (2,5).

y = mx + b

5 = 2(2) + b

5 = 4 + b

b = 1

As a result, the y-intercept is 1.

Now we can enter the numbers we discovered for m and b into the formula:

y = mx + b

y = 2x + 1

As a result, the slope intercept form equation of the line is y = 2x + 1.

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Answer:

Los Angeles, 479,689.21, 46.9

Step-by-step explanation:

A: 1,356,000/372.4 v.s. 3,884,000/503 = Los Angeles

B: 479,689.21 or 4,729.1 * 100.1
C: 837,442/17,855=46.9

The value of length of EF is,

⇒ EF = 6.25

We have to given that,

Here, lines 1, m, and n are parallel,

And, AB = 8, BC = 5, and DE = 10,

Now, By using proportionality theorem we get;

⇒ AB / AC = DE / DF

Substitute all the values, we get;

⇒ 8 / (8 + 5) = 10 / (10 +EF)

⇒ 8 / 13 = 10 / (10 + EF)

⇒ 8 (10 + EF) = 10 × 13

⇒ 80 + 8EF = 130

⇒ 8 EF = 130 - 80

⇒ 8 EF = 50

⇒ EF = 50 / 8

⇒ EF = 6.25

Therefore, The value of length of EF is,

⇒ EF = 6.25

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The nurse needs to prepare 0.8 ml of medication R to administer the correct dose of 4,000 units subcutaneously every 6 hours.

To calculate the correct dose of medication R, the nurse needs to use the formula:

dose (in units) = concentration (in units/ml) x volume (in ml)

In this case, the nurse received an order for 4,000 units of medication R and the medication label stated that the concentration of the medication is 5,000 units/ml.

To calculate the volume of medication that the nurse needs to prepare, the nurse can rearrange the formula:

volume (in ml) = dose (in units) / concentration (in units/ml)

Plugging in the values, we get:

volume (in ml) = 4,000 units / 5,000 units/ml = 0.8 ml
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Certainly! Here are the steps to prove the trigonometric identity :

Step 1: Start with the left-hand side of the equation:

[tex]\qquad\sf\:\frac{{\tan \theta}}{{\cos \theta}} \\[/tex]

Step 2: Use the identity $$\sf\:\tan \theta = \frac{{\sin \theta}}{{\cos \theta}}\\$$ to rewrite the numerator:

$$\sf\:\frac{{\frac{{\sin \theta}}{{\cos \theta}}}}{{\cos \theta}}\\$$

Step 3: Simplify the fraction by multiplying the numerator and denominator by $$\sf\:\cos \theta\\$$:

$$\large\sf\:\frac{{\sin \theta}}{{\cos \theta}} \cdot \frac{{\cos \theta}}{{\cos \theta}}\\$$

Step 4: Cancel out the $$\sf\:\cos \theta\\$$ terms in the numerator and denominator:

$$\sf\:\sin \theta\\$$

Step 5: Rewrite the right-hand side of the equation:

$$\sf\:\frac{{\sin \theta}}{{1 - \sin^2 \theta}}\\$$

Step 6: Replace $$\sf\:\theta with \delta\\$$ to represent delta:

$$\sf\:\frac{{\sin \delta}}{{1 - \sin^2 \delta}}\\$$

Therefore, the equation $$\sf\:\frac{{\tan \theta}}{{\cos \theta}} = \frac{{\sin \theta}}{{1 - \sin^2 \theta}} {\text{can be represented as}} \frac{{\tan \delta}}{{\cos \delta}} = \frac{{\sin \delta}}{{1 - \sin^2 \delta}}\\$$ when using delta $$\sf\:(\delta)\\$$ to represent the angle.

[tex]\huge{\mathcal{\colorbox{black}{\textcolor{lime}{\textsf{I hope this helps !}}}}}[/tex]

♥️ [tex]\large{\textcolor{red}{\underline{\texttt{SUMIT ROY (:}}}}[/tex]

To determine the function that models the data, we need to analyze the relationship between the cost per photo and the number of photos a customer buys. From the given information, we can observe that the cost per photo varies inversely with the number of photos. This implies that as the number of photos increases, the cost per photo decreases, and vice versa.

To model this relationship, we can use the inverse variation equation, which can be expressed as:

y = k/x

Here, y represents the cost per photo, x represents the number of photos, and k is the constant of variation.

Let's examine the data given in the table to find the value of k:

Number of Photos (x) Cost per Photo (y)

10 10

25 4

50 2

100 1

We can see that as the number of photos increases, the cost per photo decreases. We can use any pair of values from the table to solve for k. Let's choose the pair (50, 2):

2 = k/50

Solving for k:

k = 2 * 50 = 100

Now that we have the value of k, we can write the function that models the data:

y = 100/x

Therefore, the function that models the data is y = 100/x, where y represents the cost per photo and x represents the number of photos a customer buys.

Answer:

  C:  y = -(x +3)² -1

Step-by-step explanation:

You want the vertex-form equation of the parabola with vertex (-3, -1) and opening downward.

For vertex (h, k), the vertex form equation of a parabola is ...

  y = a(x -h)² +k

Given that (h, k) = (-3, -1), the equation will have the form ...

  y = a(x -(-3))² + (-1)

  y = a(x +3)² -1 . . . . . . . . . . matches choice C

The value of 'a' will be negative when the parabola opens downward. Here, its value is -1.

  y = -(x +3)² -1

__

Additional comment

Once you identify the left-shift of 3 units as resulting in an equation with (x +3)² as a component, you can make the appropriate answer choice without considering anything else. Of course, the fact that the curve opens downward immediately eliminates choices A and B.

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The domain of the function is (-∝, 6/7) U (6/7, 1) U (1, 6/5) U (6/5, ∝)

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

f(x) = x/(x - 1)

g(x) = 13/(x² - 36)

The composite function (f o g)(x) is calculated as

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

Using the above as a guide, we have the following:

(f o g)(x) = 13/((x/(x - 1))² - 36)

Evaluate

(f o g)(x) = 13(x - 1)²/(-35x² + 72x - 36)

Set the denominator not equal to 0

So, we have

-35x² + 72x - 36 ≠ 0

Evaluate

[tex]x < \frac{6}{7}\quad \mathrm{or}\quad \frac{6}{7} < x < 1\quad \mathrm{or}\quad \:1 < x < \frac{6}{5}\quad \mathrm{or}\quad \:x > \frac{6}{5}[/tex]

Express as interval notation

(-∝, 6/7) U (6/7, 1) U (1, 6/5) U (6/5, ∝)

Hence, the domain of the function is (-∝, 6/7) U (6/7, 1) U (1, 6/5) U (6/5, ∝)

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The equation P10i=1(xi − 2) = 30 represents the sum of the differences between each observation xi and 2, summed over 10 observations.

To find the arithmetic mean of these 10 observations, we need more information. The given equation only represents the sum of differences, but it doesn't provide the individual values or the actual arithmetic mean.

The arithmetic mean, also known as the average, is calculated by summing all the observations and dividing by the total number of observations. However, since we don't have the individual observations, we cannot directly calculate the arithmetic mean.

To determine the arithmetic mean, we would need the actual values of the observations, rather than just the sum of differences. Without further information, we cannot determine the arithmetic mean based solely on the given equation.

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The value of x that satisfies the equation x = 12 log₆ (8x) is x = 0.

We have,

To find the value of x in equation x = 12 log₆ (8x), we can solve it algebraically.

Here's how:

Start by isolating the logarithm term by dividing both sides of the equation by 12:

x/12 = log₆ (8x)

Now, rewrite the logarithmic equation in exponential form:

6^(x/12) = 8x

Apply the properties of exponents to simplify the equation further:

(2^3)^(x/12) = (2^3)^x

2^(3x/12) = 2^(3x)

Since the bases are equal, we can equate the exponents:

3x/12 = 3x

Next, cross-multiply to get rid of the fraction:

3x = 12 * 3x

Simplify:

3x = 36x

Subtract 36x from both sides:

3x - 36x = 0

Simplify:

-33x = 0

Divide both sides by -33:

x = 0

Therefore,

The value of x that satisfies the equation x = 12 log₆ (8x) is x = 0.

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The time it will take for the account balance to reach $42,125.54 is 20 years.

The time it will take for the account balance to reach $42,125.54 is calculated by applying the following formula.

[tex]A = Pe^{rt}[/tex]

where;

The time it will take for the account balance to reach $42,125.54 is calculated as;

42,125.54 = 8,505 e^(0.08t)

42,125.54 / 8,505 = e^(0.08t)

4.953 = e^(0.08t)

Take ln of both sides;

ln(4.953) = 0.08t

1.6 = 0.08t

t = 1.6 / 0.08

t = 20 years

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Answer:

D. 9 in

Step-by-step explanation:

The volume of a sphere is given by the formula[tex]\bold{ V = \frac{4}{3} \pi r^3}[/tex] where r is the radius of the sphere.

In this case, we know that the volume is[tex] 972\pi[/tex] cubic inches.

Substituting this into the formula, we get:

[tex]972\pi = \frac{4}{3} \pi r^3[/tex]

Dividing both sides by π, we get:

[tex]972 = \frac{4}{3} r^3[/tex]

Multiplying both sides by [tex]\frac{3}{4}[/tex], we get:

[tex]729 = r^3[/tex]

Taking the cube root of both sides, we get:

r = 9

Therefore, the radius of the sphere is 9 inches.

The amount of tax that is added to the cost of the computer is 159.72

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

Computer cost = 968

Tax percentage = 16.5%

Using the above as a guide, we have the following:

Tax amount = Computer cost * Tax percentage

substitute the known values in the above equation, so, we have the following representation

Tax amount = 968 * 16.5%

Evaluate

Tax amount = 159.72

Hence, the amount of tax that is added to the cost of the computer is 159.72

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Answer:

Step-by-step explanation:

The polynomial in descending order is:-6x^4 - 7x^3 + 5x + 3

Answer:

Step-by-step explanation:

follow the exponents little numbers

Answer:

C. 16/20

Step-by-step explanation:

Given:

To find:

Sine Theta

Sine of Theta is defined as the ratio of the perpendicular to the hypotenuse.

In this case, the perpendicular is 16 and the hypotenuse is 20.

Sin theta : Perpendicular/Hypotenuse

Therefore, Sin Theta = 16/20

a. The function will have 4 zeros

b. There are 2 negative zeroes, 2 positive zeros and no complex zero.

c. The possible zeros are ±1, ±2, ±3, ±6

d. The zeros are -1, 1, -2 and 3

Given that

-x⁴ + x³ + 7x² - x - 6

The degree of the above polynomial is 4

This means that it will have 4 zeros

Here, we have

-x⁴ + x³ + 7x² - x - 6

There are two sign changes from negative to positive, and vice versa.

So, there are 2 negative zeroes, 2 positive zeros and no complex zero.

Here, we have

-x⁴ + x³ + 7x² - x - 6

In the above, we have

p = -1

q = -6

The possible zeros are calculated as

Zeros = ±Factor of q/Factor of p

This gives

Zeros = ±(1, 2, 3, 6)/1

This gives

Zeros = ±1, ±2, ±3, ±6

Here, we have

-x⁴ + x³ + 7x² - x - 6

Set x = 1

-(1)⁴ + (1)³ + 7(1)² - (1) - 6 = 0

This means that, we x - 1 is a factor

So, we have the following synthetic setup

1   |  -1  1   7   -1  -6

           -1   0   7  6

      -1   0   7   6  0

So, we have

(x - 1)(-x³ + 7x + 6)

When factored, we have

-(x - 1)(x + 1)(x + 2)(x - 3)

This means that the zeros are -1, 1, -2 and 3

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Sally drank 1 cup more than Tammy did.

To compare the amount of water Sally and Tammy drank, we need to convert the units of measurement so that they are both in the same units. There are 4 cups in a quart, so we can use this conversion factor to convert Tammy's 1.5 quarts to cups:

[tex]1.5 quarts \times 4 cups/quart[/tex]= 6 cups

Therefore, Tammy drank 6 cups of water.

To compare who drank more, we can see that Sally drank 7 cups of water, which is more than what Tammy drank (6 cups). Therefore, Sally drank more water than Tammy.

To find out how much more Sally drank than Tammy, we can subtract the amount Tammy drank from the amount Sally drank:

7 cups - 6 cups = 1 cup

In summary, while Tammy drank 1.5 quarts of water, Sally consumed 7 cups of water. We know that Sally drank more water because 7 is more than 6 (the number of cups Tammy drank). Sally drank 1 cup more than Tammy did.

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Answer:

(2x + 21)/24

Step-by-step explanation:

To add or subtract functions, a common denominator must be achieved. We can do this by multiplying the numerator and denominator of the first term by 2 and the numerator/denominator of the second term by 3 so the denominator for both terms is 24.
(4x + 3)2/24 - (2x + 5)3/24

Now, simplify the expression

(8x + 6 - 6x + 15)/24

(2x + 21)/24

The population mean weight of the packages is 6.74 pounds and the population proportion of packages that weigh less than 5 pounds is approximately 0.301.

To calculate the population mean, we need to multiply each weight value by its corresponding frequency (number of packages), sum up these products, and divide by the total number of packages.

Population mean = Sum of (Weight × Packages) / Total number of packages

Population mean = 1967.5 / 292

Population mean = 6.74 pounds

To find the population proportion of packages that weigh less than 5 pounds, we need to sum up the frequencies (packages) of weights less than 5 pounds and divide it by the total number of packages.

Packages with weight less than 5 pounds: 5 + 16 + 28 + 22 + 17 = 88

Population proportion = Packages with weight less than 5 pounds / Total number of packages

Population proportion = 88 / 292

Population proportion = 0.301

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One could afford to borrow $34,892.

To calculate the loan amount one could afford, we will use formula for the present value of an annuity. The formula is [tex]PV = PMT * [(1 - (1 + r)^{-n}) / r][/tex]

Plugging values:

PV = $250 × [(1 - (1 + 0.625%)^(-240)) / 0.625%]

PV ≈ $250 × [1 - (1 + 0.00625)^(-240)] / 0.00625]

PV ≈ $250 × [1 - 0.1277] / 0.00625]

PV ≈ $250 × 0.8723 / 0.00625]

PV ≈ $34,892.

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Answer: a) To find out how many dollars Mr Anil got with Rs 540,000, we'll divide the amount in Nepali rupees by the exchange rate.

Therefore, Mr Anil got 4,500 dollars with Rs 540,000.

b) After the devaluation of the Nepali rupee by 5%, the new exchange rate would be 5% less than the previous rate.

New exchange rate = Previous exchange rate - (Previous exchange rate * 5%)

The new exchange rate after the devaluation is 1$ = Rs 114.

c) To calculate how much Mr Anil gained or lost, we need to compare the initial exchange rate with the new exchange rate.

Gained or lost = Number of dollars * (New exchange rate - Initial exchange rate)

Mr Anil lost 27,000 rupees due to the devaluation of the Nepali rupee.

d) If the bank took a 2% commission on the transaction, we need to calculate the commission amount and adjust the gain or loss accordingly.

After the devaluation of the Nepali rupee and considering the 2% commission, Mr Anil would lose 27,090 rupees.

Then x = -3.5, correct step to find x and y is to add the equations to eliminate x.

To find the values of x and y from the given equations, we need to use a method to eliminate one of the variables. In this case, we can use the method of adding the equations to eliminate x. Adding the two equations gives us:

y + y = x + 15 - x + 8

Simplifying the above equation gives us:

2y = 23

Therefore, y = 11.5

Substituting the value of y in any of the given equations, we can find the value of x. Using the equation y = x + 15, we have:

11.5 = x + 15

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3 pounds 32 ounces < 14 pounds 40 ounces

1,000 pounds = 1 ton

1 pound and 5 ounces < 1.5 pounds

2 tons = 4,000 pounds

28 ounces > 25 ounces

The comparison of the values of the given weights is as follows:

3 pounds 32 ounces < 14 pounds 40 ounces

This is because there are fewer pounds and ounces in 3 pounds 32 ounces compared to 14 pounds 40 ounces.

1,000 pounds = 1 ton

This is because 1,000 pounds is equal to 1 ton.

1 pound and 5 ounces < 1.5 pounds

This is because 1 pound and 5 ounces is less than 1.5 pounds.

2 tons = 4,000 pounds

This is because 2 tons is equal to 4,000 pounds.

28 ounces > 25 ounces

This is because 28 ounces is greater than 25 ounces.

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Complete question:

Write the comparison using <, >, or =.

3 pounds 32 ounces vs  14 pounds 40 ounces

1,000 pounds vs 1 ton

1 pound and 5 ounces vs 1.5 pounds

2 tons vs 4,000 pounds

28 ounces vs 25 ounces

Answer:

C

Step-by-step explanation:

I hope this helps!

Answer:

C.) a great circle

Step-by-step explanation:

The probability of both coins landing on heads when two coins are tossed is 1/4, or 0.25, or 25%.

When two coins are tossed, there are four possible outcomes: both coins can land on heads (HH), both coins can land on tails (TT), the first coin can land on heads and the second coin on tails (HT), or the first coin can land on tails and the second coin on heads (TH).

Since we are interested in the probability of both coins landing on heads, we need to determine the number of favorable outcomes (HH) out of the total number of possible outcomes.

Out of the four possible outcomes, only one outcome is favorable (HH). Therefore, the probability of both coins landing on heads is 1 out of 4.

In fraction form, this can be written as 1/4. The probability can also be expressed as a decimal, which is 0.25, or as a percentage, which is 25%.

It's important to note that in this case, we assume that the coins are fair and unbiased, meaning that the probability of landing on heads is equal to the probability of landing on tails, which is 1/2 or 0.5 for each coin individually.

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The equation that models the relationship between the amount of time Rita spends on the treadmill (t) and the distance she walks (d) is: d = 2t

To determine the equation that models the relationship between the amount of time Rita spends on the treadmill (t) and the distance she walks (d), let's analyze the given table.

Since the table displays the relationship between time and distance, we can observe the pattern and infer the equation. Let's assume that Rita walks at a constant speed.

Table:

Time (t) Distance (d)

10 2

20 4

30 6

40 8

50 10

From the table, we can see that the distance Rita walks is always twice the amount of time she spends on the treadmill. This implies that for every 10 units of time, Rita walks 2 units of distance. Therefore, we can conclude that the relationship between time and distance can be represented by a linear equation.

Let's define the equation:

d = m * t

In this equation, 'd' represents the distance, 't' represents the time, and 'm' represents the slope or rate at which Rita walks.

From the given table, we can observe that for every 10 units of time (t), the distance (d) increases by 2 units. This indicates that the slope (m) of the equation is 2.

Therefore, the equation that models the relationship between the amount of time Rita spends on the treadmill (t) and the distance she walks (d) is:

d = 2t

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Kenneth's speed given that he was able to walk 2 miles in 40 minutes was 0. 05 miles per minute.

To calculate Kenneth's speed, there is a need to divide the distance he walked by the time it took. This would show how fast he was walking such that he could cover the distance in that time.

Kenneth walked 2 miles in 40 minutes.

His speed was therefore:

Speed = Distance / Time

Speed = 2 miles / 40 minutes

Speed = 0. 05 miles per minute

In conclusion, Kenneth's speed is 0. 05 miles per minute.

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The probability of choosing a ball numbered 30 is determined as 0.

The probability of an event is a number that indicates how likely the event is to occur.

Also we can defined probability as  the ratio of the number of favorable outcomes to the total number of outcomes of an event.

Mathematically, the formula for probability is given as;

Probability =  number of favorable outcomes / total number of outcomes of an event.

In the given question;

There are zero 30 between 1 to 29.

Probability = 0 / 29

Probability = 0

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The domain of (s - t)(x) in interval notation is (-∞, -8) U (-8, 5) U (5, 8) U (8,

∞).

To find (s - t)(x), we subtract the function t(x) from s(x).

s(x) =[tex](x - 5)/(x^2 - 64)[/tex]

t(x) = (x - 8)/(5 - x)

To subtract the functions, we need a common denominator. In this case, we can use (x^2 - 64) as the common denominator.

(s - t)(x) =[tex][(x - 5)/(x^2 - 64)] - [(x - 8)/(5 - x)][/tex]

To simplify the expression, we need to factor the denominators and simplify further:

[tex](x^2 - 64) = (x - 8)(x + 8)[/tex]

(5 - x) = -(x - 5)

Substituting these into the expression, we get:

(s - t)(x) = [(x - 5)/(x - 8)(x + 8)] - [(x - 8)/-(x - 5)]

Next, we need to find a common denominator for the two fractions. The common denominator will be (x - 8)(x + 8)(x - 5).

(s - t)(x) = [(x - 5)(-(x - 5))/((x - 8)(x + 8)(x - 5))] - [(x - 8)(x + 8)/((x - 8)(x + 8)(x - 5))]

Simplifying further:

(s - t)(x) = [tex][-(x - 5)^2 - (x - 8)(x + 8)]/[(x - 8)(x + 8)(x - 5)][/tex]

The domain of the function (s - t)(x) is the set of values for which the denominator is non-zero, since division by zero is undefined.

The denominator (x - 8)(x + 8)(x - 5) will be non-zero as long as x is not equal to 8, -8, or 5.

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