I checked the answer for this question and its. Angle PSR = ⁴⁄₇x = ⁴⁄₇ x 105 = 60°


What I don't understand is how they find the 105°. Could someone write down a step by step explanation answer to this question please?

Answer: Given the two equations x + y = 8 and x^2 + y^2 = 80, we can use the first equation to solve for x or y and substitute that expression into the second equation.

Let's solve for y:

y = 8 - x

Now we can substitute this expression for y into the second equation:

x^2 + (8 - x)^2 = 80

Expanding the square and collecting terms gives:

x^2 + 64 - 16x + x^2 = 80

Combining like terms:

2x^2 - 16x + 16 = 80

Moving all terms to the left side:

2x^2 - 16x - 64 = 0

Using the quadratic formula, we can solve for x:

x = (-b ± √(b^2 - 4ac)) / (2a)

where a = 2, b = -16, and c = -64

x = (-(-16) ± √((-16)^2 - 4 * 2 * -64)) / (2 * 2)

x = (16 ± √(256 + 512)) / 4

x = (16 ± √768) / 4

x = (16 ± 8√6) / 4

Since x and y must be real numbers, we reject the negative square root. Therefore, x = (16 + 8√6) / 4.

Finally, substituting x into the first equation to find y:

y = 8 - x = 8 - (16 + 8√6) / 4 = (8 - 16) / 4 - 8√6 / 4 = -8 / 4 - 8√6 / 4 = -2 - 2√6.

Therefore, xy = x * y = (16 + 8√6) / 4 * (-2 - 2√6) = -16 - 16√6.

The answer is d. -16.

Step-by-step explanation:

Answer:

10 degrees

Step-by-step explanation:

In a triangle, the interior angles of a triangle (the angles in the inside) will always add up to 180 degrees.

We're given that the triangle is a right triangle which immediately gives us one angle, of 90 degrees, since that's a right angle. We're also given another angle of 80, and adding up these two angles plus the last angle, should give us 180.

Let's represent the unknown angle as "A", giving us the equation: [tex]90 + 80+ A= 180[/tex]

Now from here we can combine the 90 and 80 to get:

[tex]170+A=180[/tex]

Now from here we subtract 170 from both sides (to maintain equality and get rid of the 170):

[tex]170-170+A=180-170[/tex]

We simplify 170-170 to 0, which we don't need to put in the equation as 0 + A is just A. We also simplify 180 - 170 to 10:

[tex]A=10[/tex]

So the other acute angle is 10 degrees.

The sentence regarding how many books must be sold to make a profit is given as follows:

Anna must sell at least 2 books to make a profit.

The profit function is given by the subtraction of the revenue function by the cost function, as follows:

P(x) = R(x) - C(x).

The revenue function and the cost function for this problem are given as follows:

Hence the profit function is given as follows:

P(x) = 6.56x - 1.09x - 10.063.

P(x) = 5.47x - 10.063.

A profit is made when:

P(x) > 0.

Hence:

5.47x - 10.063 > 0

5.47x > 10.063

x > 10.063/5.47

x > 1.84.

As the number of books is a countable amount, we have that:

Anna must sell at least 2 books to make a profit.

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The first mechanic worked for 5 hours and the second mechanic worked for 15 hours.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given:

Two mechanics worked on a car.

The first mechanic charged $55 per hour,

and the second mechanic charged $65 per hour.

The mechanics worked for a combined total of 20 hours,

and together they charged a total of $1250.

Let x be the number of working hours of the First mechanic and y be the

number of working hours of the second mechanic.

So

x + y = 20  {equation 1}

55x + 65y = 1250 {equation 2}

Substituting the value of y from the equation 1 to the equation 2,

55x + 65(20 - x) = 1250

55x + 1300 - 65x = 1250

-10x = -50

x = 5

And y = 15

Therefore, x = 5 and y = 15.

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If the population of a town increased from 3200 in 2008 to 5700 in 2009, the absolute and relative (percent) increases are:

What is the difference between absolute and relative increases?

Absolute increase refers to a numerical addition to the quantity of an item.  

The absolute increase is the difference between the current value and the initial value.

On the other hand, the relative increase is expressed in percentage terms.

To compute the relative increase, divide the absolute increase by the initial value.

The population of the town in 2008 = 3,200

The population in 2009 = 5,700

The absolute increase in population = 2,500 (5,700 - 3,200)

The relative increase in population = 78.125% (2,500/3,200 x 100)

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A linear equation indicating the number of grades students will receive in Mr. Perez's class is as follows;

Slope: 2.

Y-Intercept: 7.

Equation: y = 2x + 7.

In Mathematics, the slope-intercept form of a line can be calculated by using this mathematical expression:

y = mx + b

Where:

From the information provided above, we have the following slope and y-intercept on the line:

Y-intercept = 7

Slope, m = 2

Therefore, the required equation of line is given by:

y = mx + c

y = 2x + 7

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If the Time taken by object is 2 hour then the height will be 80.4 feet.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

We have Given the function as

h(t) = 50t - 4.9t²

If time = 2 hours then put the value of t=2 in the above Equation we get

h(t) = 50t - 4.9t²

h(t) = 50(2) - 4.9(2)²

h(t) = 100 - 4.9 x 4

h(2) = 100 - 19.6

h(2)= 80.4

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The triangle's missing angle, according to the provided assertion, is (a) 62° (b) 57° (c) 59° (d) sin0

Trigonometry is typically included in math courses for sophomores or juniors. Trigonometry is frequently included as a unit or term emphasis in other math classes in adding to being given as a separate course.

(a) sin(28°) = cos(90° - 28°) = cos(62°)

      62° is right answer.

(b) cos (33°) = sin (90° – 33°) = sin (57°)

      57° is correct answer.

(c) cos (31°) = sin(90° - 31°) = sin (59°)

      59° is correct answer

(d) cos(90° - 0) = sin0

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A. The displacement is the change in position, which is given by the change in the height, so:

i. [1,2] = -5.46 m/s

ii. [1,1.1) = -1.39 m/s

iii. [1,1.01) = -0.138 m/s

iv. [1,1.001) = -0.0138 m/s

(a) To find the average velocity over a time interval, we need to calculate the displacement during that time interval and divide it by the length of the interval. The displacement is the change in position, which is given by the change in the height, so:

i. [1,2]: Δs = y(2) - y(1) = [20(2) - 1.87(2)²] - [20(1) - 1.87(1)²] ≈ -5.46

Average velocity = Δs / Δt = -5.46 / (2 - 1) = -5.46 m/s

ii. [1,1.1): Δs = y(1.1) - y(1) = [20(1.1) - 1.87(1.1)²] - [20(1) - 1.87(1)²] ≈ -1.39

Average velocity = Δs / Δt = -1.39 / (1.1 - 1) = -1.39 m/s

iii. [1,1.01): Δs = y(1.01) - y(1) = [20(1.01) - 1.87(1.01)²] - [20(1) - 1.87(1)²] ≈ -0.138

Average velocity = Δs / Δt = -0.138 / (1.01 - 1) = -0.138 m/s

iv. [1,1.001): Δs = y(1.001) - y(1) = [20(1.001) - 1.87(1.001)²] - [20(1) - 1.87(1)²] ≈ -0.0138

Average velocity = Δs / Δt = -0.0138 / (1.001 - 1) = -0.0138 m/s

(b) The instantaneous velocity at t=1 is given by the derivative of the height function with respect to time, which is:

dy/dt = 20 - 3.74t

So the instantaneous velocity at t=1 is:

dy/dt(1) = 20 - 3.74(1) = 16.26 m/s (approximately)

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The solution is, c. Sarah rounded the area of the floor to 100 square feet., is statement BEST explains why Sarah’s prediction is incorrect.

Area of a rectangle (A) is the product of its length (l) and width (w).

A= l. w

here, we have,

rectangular dining room floor, which has a length of 12 feet and a width of 9 feet.

The cost to install the carpet is $5 per square foot.

so, area of the floor = A= l. w

                                     = 108 ft^2

so, total cost = 108* 5

                     =$ 540

i.e. Sarah rounded the area of the floor to 100 square feet.

because, 100*5 = $500

Hence, The solution is, c. Sarah rounded the area of the floor to 100 square feet., is statement BEST explains why Sarah’s prediction is incorrect.

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Answer:

Below

Step-by-step explanation:

From 11:57 to 12:00 is 3 min    then add 49 min to get to 12:49 then add the 15 min late =   3 + 49 + 15 = 67 MIN    or    1hr 7 min

Answer: divide $39857

Step-by-step explanation:

The equation of the line is y=-2x/5 -10

The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.

Given here: A line that passes through (5,-12) and m=-2/5

Thus using the slope intercept form constructing it we get

y=mx+c

Putting (5,-12) and m=-2/5

-12=-2/5×5+c

c=-12+2

c=-10

The equation of the line is y=-2x/5 -10

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Kerys should substitute the values of k from 0 to 4 (inclusive) in the binomial theorem expression to expand the binomial (2x + y)⁴.

The binomial theorem states the principle for expanding the algebraic expression (x + y)ⁿ and describes it as the total of the phrases involving the unique exponents of the x and y variables. Each word in a binomial expansion has a coefficient, which is a numerical value.

here, we have,

The binomial theorem states that the expansion of the binomial (x+y)^n is given by the formula:

(x+y)n = ∑nk=0nCk xn-kyk = ∑nk=0nCk xkyn-k

The variable n represents the power to which the binomial is raised, in this case n = 4.

The variable k is the exponent of the second term in the binomial (b), in this case y.

So, with k = 0, the term will be aⁿ = (2x)⁴, with k = 1, the term will be

a^(n-1) *b = (2x)³y , and so on.

Therefore, he should substitute the values of k from 0 to 4 (inclusive) in the binomial theorem expression to expand the binomial (2x + y)⁴.

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Answer:

To find out how many packs of cardinal flower seeds you bought, you need to divide the total amount you spent ($36) by the cost per pack ($4).

$36 ÷ $4 = 9

Therefore, you bought 9 packs of cardinal flower seeds.

A pack of cardinal flower seeds costs $4. You spend $36 on seeds. The correct answer is 9.

Cardinals love sunflower seeds, particularly black oil sunflower seeds. Their thin shells are quite easy for cardinals to break. These songbirds can also eat hulled and heavier-shelled striped sunflower seeds due to their sturdy beaks.

So, if we spend $36 on seeds. we are going to use 36 and 4 to find are answer:

→ 36/4

→ = 9

Therefore, A pack of cardinal flower seeds costs $4. You spend $36 on seeds. The correct answer is 9.

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Answer:

23 to 42

23:42

[tex]\frac{23}{42}[/tex]

The expected number of times the sequence "proof" appears in a randomly generated string of 1,000,004 letters is approximately 36.

The expected number of times the sequence "proof" appears in a randomly generated string of n = 1,000,004 letters can be calculated using the formula:

expected_occurrences = (n - 4) / 26^4

where 26^4 is the number of possible 4-letter sequences that can be formed using a 26-letter keyboard. Plugging in n = 1,000,004, we get:

expected_occurrences = (1,000,004 - 4) / 26^4

                 ≈ 36.08

So, the expected number of times the sequence "proof" appears in a randomly generated string of 1,000,004 letters is approximately 36.

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Check the picture below.

[tex]\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ A=900\\ b=2a\\ h=40 \end{cases}\implies 900=\cfrac{40(a+2a)}{2} \\\\\\ 1800=40(3a)\implies 1800=120a\implies \cfrac{1800}{120}=a\implies \boxed{15=a}~\hfill \boxed{b=30}[/tex]

Answer:

2

Step-by-step explanation:

the degree of polynomial is 2

The depreciable cost,

$1,800,000

The straight-line rate,

5%

The annual straight-line depreciation,

90,000

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

If a building acquired the beginning of the year at a cost of 2,200,000 has an estimated residual value of 400,000 and an estimated useful life of 20 years.

The depreciable cost,

= cost - residual value

= 2,200,000 - 400,000

= $1,800,000

The straight-line rate,

=100/20

= 5%

The annual straight-line depreciation,

= 1,800,000 x 5/100

= 90,000

Therefore, all the required values are given above.

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From the data that teacher described, the following information could be determined:

1. The distribution of midterm and final exam scores for the students. This would allow you to see the range of scores and the overall performance of the students.

2. The average midterm and final exam scores for the students. This would give you an idea of the average performance of the students on each exam.

3. The correlation between final exam and midterm scores. This would indicate if there were a relationship between performance on the midterm and final exams.

4. The distribution of total points calculated for each student. This would allow you to see the range of total scores and the overall performance of the students.

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Answer:

48 minutes

Step-by-step explanation:

Why did the ant cross the road?

Speed of ant = 7 inches per minute
Width of road = 28 feet

28 feet = 28 x 12 inches = 336 inches

At 7 inches per minute, to cross 336 inches , it would take 336/7 or 48 minutes

The amount of solar radiation available is 415.4 W/m² and the albedo was higher during the last glacial maximum than it is today because there was more ice and snow on the planet.

Radiation refers to the emission and transmission of energy through space or a material medium in the form of electromagnetic waves or energetic particles. Radiation can take many forms, including light, X-rays, and radio waves, and can be either ionizing (having enough energy to remove electrons from atoms and molecules) or non-ionizing (having insufficient energy to cause ionization). Radiation is a fundamental aspect of physics and plays a crucial role in many natural processes, such as nuclear reactions and the warming of the Earth by the sun.

a) The amount of solar radiation available to warm the average square meter on Earth during the last glacial maximum can be found by multiplying the solar constant by the average albedo:

En = 1363 W/m² * 0.305 = 415.4 W/m²

b) The albedo was higher during the last glacial maximum than it is today because there was more ice and snow on the planet. Ice and snow are very reflective and therefore have a high albedo, which means that they reflect more of the incoming solar radiation back into space, making the planet cooler. During the last glacial maximum, there was more ice and snow, which led to a higher average albedo and a cooler planet.

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Answer:

Check the image for the answer!

Step-by-step explanation:

Please mark me Brainliest!

However, we can't determine the exact number of participants with this information alone.

an individual who engages in or becomes engaged in a specific action. Examples. Over three thousand people will be competing in the games, a worldwide athletic event. She has contributed significantly to the conversation.

Let's use logic to determine the possible rankings of the participants:

A placed seventh, so at least 6 people ranked higher than A.

B placed sixth, so at least 5 people ranked higher than B.

C ranked above A and B, so C must have ranked at least fifth. This means there are at least four people who ranked higher than C.

D does worse than E and ranks penultimate, which means D ranked second to last. Therefore, there must be at least two people who ranked worse than D. Also, E must have ranked higher than D, so there is at least one person who ranked higher than D.

Putting this information together, we know that there are at least 6 + 5 + 4 + 2 + 1 = 18 people who participated in the contest.

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In the triangle where G is the incenter of AABC, GT = 7, m>BAG = 120.

An incenter is a position within a triangle where the triangle's three angle bisectors connect. The lines that divide the angles in a triangle into two equal pieces are known as angle bisectors. The incenter is equidistant from the triangle's three sides, which means that the distance from the incenter to each side is the same. The incenter is also the core of the inscribed circle of the triangle, which is the greatest circle that can fit within the triangle. The incenter is a crucial point in trigonometry and geometry because it may be used to compute angles, sides, and other triangle features.

Given:

AABC, AC; GR = 7, and m<BAC = 60

Step 1: Since the angle bisector of any angle in a triangle divides that angle into two equal parts, m<BAC = 60 implies m<BAG = 120.

Step 2: Since the incenter of a triangle is equidistant from the three sides, GR = 7 implies GT = 7.

Therefore, GT = 7 and m>BAG = 120.

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The rate of inflation for potatoes was 21%, for oranges it was 40%, and for ground beef it was 67%.

The idea of rate is used in mathematics to describe how one quantity changes in relation to another. It is frequently expressed as a fraction or ratio and is a measurement of how quickly one thing is changing in relation to another.

For instance, velocity is the measure of how quickly a position changes in relation to time. Acceleration is the measure of how quickly a velocity changes with relation to time. The derivative of a function, which denotes the instantaneous rate of change at a specific location, is the rate of change of any function with regard to its independent variable.

The rate of inflation for each item can be calculated using the formula:

r = (P2/P1)¹/ⁿ - 1

where P1 is the price per pound in 2009 and P2 is the price per pound in the given year, and n is the number of years between the two prices (in this case, n = 1 year).

For Potatoes:

P1 = $0.620

P2 = $0.749

n = 1

r = (0.749/0.620)¹/¹ - 1 = 0.21 or 21%

For Oranges:

P1 = $0.910

P2 = $1.280

n = 1

r = (1.280/0.910)¹/¹ - 1 = 0.40 or 40%

For Ground beef:

P1 = $2.251

P2 = $3.775

n = 1

r = (3.775/2.251)¹/¹ - 1 = 0.67 or 67%

So, the rate of inflation for potatoes was 21%, for oranges it was 40%, and for ground beef it was 67%.

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Answer:

Step-by-step explanation:

This graph goes up to 2 and down to -2, which tells us that the amplitude of the waves is 2. In the equation for the parent graph, y = sinx, we will throw the 2 out front which is where the amplitude goes in sin and cos curves:

y = 2sinx