Simplify
sin (7x)−sin(3x)cos(7x)−cos(3x) to an expression involving a single trigonometric function.

Slope of line is 578.5, point-slope equation is y-24658491600 = 578.5(x-0)  slope-intercept equation is y=578.5 x+24658491600, (0, 24658491600) is y-intercept, number of customers can be predicted by equation.

A line is a geometric entity marked as a zero width entity extending on both sides. A straight line is line without curves. A line that extends to infinity on both sides and has no curves is called a straight line.

Given,

table of the points of the graph

from the table

(x₁ , y₁) = (0 ,  24658491600)

(x₂ , y₂) = (10 ,  24658497385)

Slope of the line

m = (y₂ - y₁)/(x₂ - x₁)

m = (24658497385 - 24658491600)/(10 - 0)

m = 5785/10

m = 578.5

Point-slope equation of the line

y - y₁ = m(x - x₁)

y - 24658491600 = 578.5(x - 0)

slope-intercept equation of the line

y  = 578.5 x + 24658491600

Comparing with general slope intercept equation of line y = mx + c

slope m = 578.5

y-intercept = (0, 24658491600)

By the equation, we can predict number of customers on counter.

Hence, 578.5 is slope of line, y - 24658491600 = 578.5(x - 0) and y  = 578.5 x + 24658491600 are point-slope and slope-intercept equations respectively, y-intercept is (0, 24658491600), with the equation, number of customers on counter can be predicted.

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Answer:

X is greater than or equal to 2 or X > 1

Jim did not buy any tickets (n_Jim = 0).

Larry bought 7 more tickets than Jim.

To determine the number of tickets Larry bought more than Jim, we need to find the values of n for Larry and Jim's ticket purchases.

For Larry:

Let's substitute C = $170 into the equation C = 24n + 2 and solve for n:

$170 = 24n + 2

Subtracting 2 from both sides:

$168 = 24n

Dividing both sides by 24:

n = 7

For Jim:

We can calculate the number of tickets Jim bought by subtracting 12 from Larry's number of tickets:

n_Jim = n_Larry - 12

n_Jim = 7 - 12

n_Jim = -5

Since we cannot have a negative number of tickets, we can conclude that Jim did not buy any tickets (n_Jim = 0).

To find the difference in the number of tickets bought, we subtract the number of tickets Jim bought from the number of tickets Larry bought:

n_difference = n_Larry - n_Jim

n_difference = 7 - 0

n_difference = 7

Therefore, Larry bought 7 more tickets than Jim.

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Question

The equation C=24n+2 represents the cost, C, in dollars, of buying n tickets to a play. J $170. How many more tickets did Larry buy than Jim? 12

Answer 10d + .25q = $16.95

Step-by-step explanation:

d = number of dimes

q = 2d + 3 number of quarters

We can sub 2d + 3 in for q, in the first equation.

We get:

.10d + .25(2d + 3) = $16.95

Once we solve this equation we get d = 27. We can plug 27 back into the original equation to get how many quarters.

hope it helps:)!

Answer:  $4,000

Step-by-step explanation:

If the total earnings were $40,000 and the base pay was $10,000, then the commission earned would be $40,000 - $10,000 = $30,000.

Since the commission rate is 40%, we can set up the equation:

40% x Total Sales = Commission Earned

We know that the commission earned is $30,000, and we also know that 15 cars were sold. Therefore, we can solve for the average price of each car:

40% x Total Sales = Commission Earned

40% x (15 x Price per Car) = $30,000

6 x Price per Car = $30,000

Price per Car = $5,000

However, this is just the average price per car. Since the commission is based on the total sales, we need to calculate the actual commission earned on each car:

Commission per Car = 40% x Price per Car

Commission per Car = 40% x $5,000

Commission per Car = $2,000

Therefore, the total earnings of $40,000 divided by the number of cars sold (15) gives the amount earned per car:

Amount earned per Car = Total Earnings / Number of Cars Sold

Amount earned per Car = $40,000 / 15

Amount earned per Car = $4,000

Using the percentage, Rapunzel participated in 9581/100 matches.

In the given question we have to find the fraction of the wrestling matches did Rapunzel participate in.

Rapunzel's team participated in a total of 143 wrestling matches.

Rapunzel participated in 67 percent of the wrestling matches.

Total matches = 143

Participated in = 67%

Total number of matches in which Rapunzel participated is

= 143*67%

= 143* 67/100

= 9581/100

Rapunzel participated in 9581/100 matches.

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Answer:

?⋅3=4.5 or 3⋅?=4.5

The percentage error in the density of metal will be 3.4%.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that the density of the metal in the handbook is 4.018 g/mL and the measured value of the density is 4.16 g/mL.

The percentage error will be calculated as:-

Percentage = [ ( 4.16 - 4.018 ) / 4.16 ] x 100

Percentage = 0.034x 100

Percentage = 3.4%

Hence, the percentage error will be 3.4% for the densities.

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Answer: 20/10

Step-by-step explanation:

Take (calculate) 4/5 of 2/5 mile:

4x5= 20

---- * ---- = 20/10

2x5= 10

The section that needs to be repaved is 1/2 of a mile.

Fractions represent the parts of a whole or collection of objects.

A fraction has two parts. The number on the top of the line is called the numerator and the number on the top of the line is called the denominator.

Now it is given that,

Length of road = 4/5 of a mile

Road needs to repave = 2/5 of the road

Thus, road needs to repave = 2/5 of 4/5

⇒ road needs to repave = (2*4)/(5*5)

⇒ road needs to repave = 10/20

or, road needs to repave = 1/2

Thus, the section that needs to be repaved is 1/2 of a mile.

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is a problem where the Pythagorean theroem must be used

we have two sides

both sides are the legs of the triangle where the hypotenuse will be the minimum distance

so

the formula of the theorem is

where h is the distance

and a and b are t

the distance is 8.02 m

you have to square both 20 and 18

h=8.04

Answer:

Therefore, the correct statements are A, B, and E.

Explanation:

Based on my knowledge, a vector is a quantity that has both magnitude and direction. A scalar is a quantity that has only magnitude. When a vector is multiplied by a scalar, the magnitude of the vector is multiplied by the absolute value of the scalar, and the direction of the vector is either preserved or reversed depending on the sign of the scalar.

To answer your question, we need to find the component form, magnitude, and direction of the scalar product –4⇀

.

- The component form of −4⇀

is obtained by multiplying each component of ⇀

by –4. Therefore, −4⇀

= ⟨–8, –12⟩. This means that statement A is true.

- The magnitude of −4⇀

is obtained by multiplying the magnitude of ⇀

by 4. The magnitude of ⇀

is √(2^2 + 3^2) = √13. Therefore, the magnitude of −4⇀

is 4√13. This means that statement B is true.

- The direction of −4⇀

is opposite to the direction of ⇀

because the scalar –4 is negative. This means that statement C is false.

- The vector −4⇀

is in the third quadrant because its components are both negative. This means that statement D is false.

- The direction of −4⇀

is 180° greater than the inverse tangent of its components because it is opposite to ⇀

. The inverse tangent of its components is tan^(-1)(–12/–8) = tan^(-1)(3/2). Therefore, the direction of −4⇀

is 180° + tan^(-1)(3/2). This means that statement E is true.

Therefore, the correct statements are A, B, and E.

Answer:

130° and 310°

Step-by-step explanation:

the bearing of A from B is the measure of the clockwise angle from a north line at B to A

the angle at B and A are same- side interior angles and sum to 180°

angle at B = 180° - 50° = 130°

the bearing of A from B is then 130°

the bearing of B from A is the measure of the clockwise angle from the north line at A to B

the complete angle about A = 360° then clockwise angle from north line at A to B is

360° - 50° = 310°

the bearing of B from A is 310°

A. The following are sets A and B:

A = {2, 3, 5, 7, 11}

B = {1, 2, 3, 4, 6, 12}

C. Elements not in A or A' = ∅

B. The Venn diagram is attached

A universal set is a set which consists of all elements related to the given sets. It is denoted by U.

A. Set A:

A = {2, 3, 5, 7, 11}

Set B:

B = {1, 2, 3, 4, 6, 12}

U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

A' = {1, 4, 6, 8, 9, 10, 12}

C. Elements not in A or A' = ∅

Complement of set A is refers to a set that contains the elements present in the universal set but not in set A.

Hence, the Venn diagram of sets A, B and U has been attached.

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Answer:

Therefore, the angle ∠CDA is 58°.

Step-by-step explanation:

∠CDA = 58°

In the given figure, let's consider the angle ∠CDA as x.

Since AB is the diameter of the circle, we know that the angle subtended by any diameter at any point on the circumference is always 90°. Therefore, ∠CAB = 90°.

In triangle CAD, the sum of angles is 180°. So, we have:

∠CAD + ∠CDA + ∠CAB = 180°

Substituting the known values:

32° + x + 90° = 180°

Combining like terms:

x + 122° = 180°

Subtracting 122° from both sides:

x = 180° - 122°

x = 58°

Answer:

a

Step-by-step explanation:

The equation of a proportional relationship is

y = kx ← k is the constant of proportionality

Divide both sides by x

\(\frac{y}{x}\) = k

To find k use any ordered pair from the table

Using (2, \(\frac{5}{2}\) ) , then

k = \(\frac{2}{\frac{5}{2} }\) = 2 × \(\frac{2}{5}\) = \(\frac{4}{5}\)

Answer:

\(5^{15} * 5^{5}\)

= \(25^{20\\}\)

Answer:

\(5n+10d=455\)

Step-by-step explanation:

Multiply both sides of the equation by 100.

Step-by-step explanation:

to be honest I'm not sure how to do

Comment

ANSWER:

A: (4, 9)

B: (-1, -3)

STEP-BY-STEP EXPLANATION:

We have the following function:

We determine the two points when x = 4 and when x = -1, like this:

Therefore point A is (4, 9) and point B is (-1, -3)

It will take Sarah approximately 15.9 years to pay off the loan.

To determine how long it will take Sarah to pay off the loan, we can use the formula for the number of periods required to pay off a loan:

\(\(n = \frac{{\log\left(\frac{{P \cdot r}}{{P - M \cdot r}}\right)}}{{\log(1 + r)}}\)\)

Where:

n is the number of periods (in this case, the number of months)

P is the principal amount (loan amount), which is $300,000

r is the monthly interest rate, which is 0.525% or 0.00525 (expressed as a decimal)

M is the monthly payment, which is $1,925

Substituting the values into the formula, we have:

\(\(n = \frac{{\log\left(\frac{{300,000 \cdot 0.00525}}{{300,000 - 1,925 \cdot 0.00525}}\right)}}{{\log(1 + 0.00525)}}\)\)

Using a calculator to evaluate the logarithms and perform the division, we find that \(\(n \approx 190.6\)\) months.

Since we are asked to determine the time to the nearest tenth of a year, we divide 190.6 by 12 to convert it into years:

\(\(\frac{{190.6}}{{12}} \approx 15.9\) years\)

Therefore, it will take Sarah approximately 15.9 years to pay off the loan.

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Answer:

B.

Step-by-step explanation:

Answer:

85% = 29.75 or 30 add-on sales (rounded)

Step-by-step explanation:

Answer:

85% = 29.8or 30 add-on sales (rounded)

Answer:

As baby porcupine is backed into cactus, so the spines of cactus will feel like spines of mother porcupine. So the baby porcupine will give  call to its mother.

Step-by-step explanation

He said hi Ma.

Answer:

-60

Step-by-step explanation:

-6 √100

We know the square root of 100 is 10 ( 10x10=100), so replace √100 with 10, and then multiply:

-6(10) = -60

Answer:

Step-by-step explanation:

Simplify the inequalities:

Or

The system becomes:

The intersection is:

or

The graph is attached

#1

\(\\ \sf\longmapsto 2+3x>8\)

\(\\ \sf\longmapsto 3x>6\)

\(\\ \sf\longmapsto x>2\)

#2

\(\\ \sf\longmapsto 4-7x\leqslant -17\)

\(\\ \sf\longmapsto -7x\leqslant -21\)

\(\\ \sf\longmapsto x\geqslant 3\)

Graphs attached

Answer:

(-infinity,+infinity)

Step-by-step explanation:

Any real value of x can be defined with a unique output in this function.

Answer:

y = -3x + 7

Step-by-step explanation:

\(y = mx + b\)

m = slope

b = y intercept

eq:

\(y = - 3x + 7\)