what are the coordinates of P​?

In ΔRST, the measure of angle R is  73.1°

Let us assume that r represents the opposite side of ∠R, and 't' represents the opposite side of ∠T

i.e., r = side ST and t = side RS

We know that the law of sine for triangle states that the ratio of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides.

i.e., for triangle ABC,

[tex]\frac{sin~A}{a} =\frac{sin~B}{b} =\frac{sin~C}{c}[/tex]

Using sine law for ΔRST,

[tex]\frac{sin~R}{r} = \frac{sin~S}{s} =\frac{sin~T}{t}[/tex]

Consider equation,

[tex]\frac{sin~R}{r} =\frac{sin~T}{t} \\\\\frac{sin~R}{79} = \frac{sin~(58)}{70}[/tex]

79 × 0.8481 = sin(R) × 70

sin(R) = 66.99 / 70

sin(R) = 0.9571

∠R = arcsin(0.9571)

∠R = 73.1°

Thus, measure of angle R = 73.1°

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The logarithmic form of the exponential expressions are;

1) log2 5 = x

2) log3 10 = y

3) logk 6 = 5

4) log2 32 = 5

5) log3 81 = 4

6) log 3 27 = 3

7) log10 100 = 2

8) logx y = 2

9) log10 x = 20

10) logp q = 10

11) logx y = 1/2

12) log9 3 = 1/2

We have to note that we can be able to write an exponential equation in the logarithmic form or in the exponential form. In the exponential form we we would have something like;

a^x = P

While in the logarithmic form we can be able to have something like;

logaP =x

These are the two forms that we can be able to write the equations that we have in the question.

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Answer: The answer is 5 units

Step-by-step explanation:

If you plot it on a graph and what not it comes out to 5 units, going diagonally.

In a city, the distance between the library and the post office is three units. This may be calculated by counting the gaps between the two points on the grid illustrated above. The Library is in position 1 and the Post Office is in position 4, therefore the distance between them is three units.

The amount of space between two locations is defined as distance. It is commonly measured in meters, kilometers, miles, or feet. Distance is used to compute the length of a journey, the time required to go a specific distance, and the speed of an item moving a specific distance. It may also be used to determine the dimensions of an item. In trigonometry, distance is also used to measure angles, such as the angle between two points on a circle. Distance may be present in practically every facet of our daily lives, from city distances to item sizes. Distance is an important term to grasp in both physics and mathematics.

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So, the height of the tower is approximately 363.6 feet.

You can use trigonometry to solve this problem.

If we call the height of the tower "h" and the distance between the man and the base of the tower "d", then the angle of elevation is defined as the angle between the line of sight from the observer to the top of the tower and the horizontal line.

We can use the tangent function to relate the angle of elevation to the height and distance.

tan(67) = h/d

We know that the distance between the man and the tower is 200 feet. We can use this information to find the height of the tower.

h = d * tan(67)

h = 200 * tan(67)

The height of the tower is approximately 363.6 feet.

Please note that due to the approximation of the trigonometric functions, the answer may not be exactly as calculated.

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Answer:The factors of 28 and 49 are 1, 2, 4, 7, 14, 28 and 1, 7, 49 respectively

Step-by-step explanation:Some numbers have 28 and 49 as answers

Inter-Item Reliability is a measure of how consistently different items within a measure are related to each other. It is used to assess the internal consistency of a measure.

An indicator of reliability based on the correlations of each item in a measure with every other item is called: Inter-Item Reliability.

Inter-Item Reliability is a measure of how consistently different items within a measure are related to each other. This is assessed by calculating the correlations between each item and every other item in the measure.

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The probability of passing the practical test is 0.25. This is calculated by subtracting the probability of passing the theory test (0.75) from the probability of passing at least one of the two parts (0.36).

0.25

The probability of passing the practical test can be calculated by subtracting the probability of passing the theory test (0.75) from the probability of passing one of the two parts (0.36).

0.36 - 0.75 = 0.25

The probability of passing the practical test is 0.25. This is calculated by subtracting the probability of passing the theory test (0.75) from the probability of passing at least one of the two parts (0.36). The two events of passing the theory test and passing the practical test are independent, so their probabilities can be calculated separately.

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Answer:

11+x

Step-by-step explanation:

6 + (5 + x)

because you have a + between 6 and the parentheses then you can just add everything up without warring about them. so:

6+5+x which equals to 11+x

The ASA and AAS theorems are used in the proof as explained below for each given statements.

A proof is a logical argument that demonstrates the truth of a mathematical statement.

The proof that can be used to prove each given statements are demonstrated below.

14. Proof for ∆UVY ≅ ∆XVW:

Statement Reason

1. V is the midpoint of YW. 1. Given

2. UY || XW 2. Given

3. YV ≅ WV. 3. Def. of midpoint

4. <UYV ≅ <XWV. 4. Alternate <s theorem

5. <UVY ≅ <XVW 5. Vertical<s theorem

6. ∆UVY ≅ ∆XVW 6. ASA

15. Proof for ∆MSP ≅ ∆RQP:

Statement Reason

1. MS ≅ RQ 1. Given

2. MS || RQ 2. Given

3. <MSP ≅ <RQP. 3. Alternate <s theorem

5. <MPS ≅ <QPR 4. Vertical<s theorem

6. ∆MSP ≅ ∆RQP 6. AAS

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The answer to the inequality system is y > 2 – x, y < -1

Step 1: Formulate each inequality as y = x + b.

(1) x + y > 2

(2) 2x – y > 1

(3) y > 2 - x Each side of the equation had x subtracted (1)

-y > 1 - 2x 2x were taken out of either side of 2.

(4) y < 2x – 1 -1 multiplied each side, then the inequality was turned around.

Graphing the functions as equalities in step two

(5) y = 2 – x

(6) y = 2x - 1

The borders of the inequalities will be formed by the lines. On one side of a line, the condition will be true, but not on the other (see the diagram below).

Step 3: Highlight the graphs' areas where the inequalities exist.

The graph of y > 2 - x is shown by the red line.

Shade the area above the line because y exceeds a value on the high side of the line (red).

The graph of y = 2x - 1 is shown by the blue line.

Shade the area below the line because y is less than a value on the line's low side (blue).

Any location where the colored regions overlap constitutes the solution set for both inequality problems (purple).

4. Check the outcome.

Input a point in the shaded region, such as (2, 2), and confirm that each inequality is true.

(1) x + y > 2 (2) 2x – y >1

2 + 2 > 2 2(2) – 2 > 1

4 > 2 4 – 2 > 1

2 > 1

It verifies.

The answer to the inequality system is

y > 2 – x, y < -1.

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Correct option is A, (1,2) is the correct option for the given system of equations.

Equations occurring simultaneously, system of equations Algebraic equations involving two or more must be solved cooperatively (i.e., the solution must satisfy all the equations in the system).

For a system to have a single solution, the number of equations must equal the number of unknowns.

A set of simultaneous equations, often known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

A system of equations is a collection of equations with one or more variables. Systems of equations have solutions that are either the variable mappings that satisfy each component equation or the intersections of all of these equations.

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Answer:

$327.73

Step-by-step explanation:

$25,800 - $8,000 = $17,800

The car loan is a total of 60 months (so at 60 her payment will be $0) and the interest rate is 3.99%

Growth formula: A = P(1+r)^t

We're asking for what value at x = 60 would make P(1+r)^60 = 0?

As such, $327.73

The radius of the circle is approximately =71.96 units

Circles can be defined by their radii and all points on the circumference of a circle are equidistant from the center. Circles are widely used in mathematics, science and engineering for various applications, including modeling and solving problems in geometry.

The formula for the circumference of a circle is 2 * pi * r, where r is the radius.

Given the circumference, we can solve for the radius:

452.16 = 2 * pi * r

r = 452.16 / (2 * pi)

The radius of the circle is approximately 71.96 units.

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the value of x, y, and z are 2√14, √74, and √252.

A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.

Given, the right triangle that has two other right triangles inside it:

From the Pythagorean theorem:

Hyppotaneus ² = height ² + base²

from the Bigger triangle:

H = 14 + 4 = 18

b = y

h  = x

Thus,

y² + z² = 18*18

y² + z² = 324.....(1)

from the triangle with a height of 14,

z² = x² + 14²

z² = x² +  196....(2)

From the triangle with the base of 4:

y² = x² +  16...(3)

For equations 2 and 3 substitute the value in equation 1

2x² + 212 = 324

2x² = 112

x² = 56; x = 2√14

Thus,

y² = 56 +16

y² = 74; y = √74

z² = 56 + 196

z² = 252; z = √252

Therefore, the value of x, y, and z are 2√14, √74, and √252.

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Answer:

F(x)=-x^2

Step-by-step explanation:

The one example of function with range of only negative number is:

F(x)=-x^2

Why this? We know for every x, x^2 is positive. So -x^2 will be negative.

Answer:

  $340

Step-by-step explanation:

You want to know the original price of a desk priced such that $272 is 80% of its original price.

We can write the relation as an equation. If p represents the original price, then we have ...

  $272 = 80% × p

  p = $272/0.80 = $340 . . . . . . . divide by the coefficient of p

The original price is $340.

<95141404393>

The rental cost for each movie and each video game are  $1.25 and $5.25 respectively

An algebraic expression can be defined as an expression that is usually composed of terms, variables, constants, factors and coefficients.

These expressions are also made up of some mathematical operations, such as;

From the information given;

Let movies be x

Let the video games be y

We have that;

3x + 5y = 30

6x + 2y = 18

Make 'x' the subject from equation 1

x = 30-5y/3

Substitute the value

6(30-5y/3) + 2y = 18

expand the bracket

180 - 30y/3 + 2y = 18

-24y + 180/3 = 18

-24y + 180 = 54

y = $5.25

Then, x = $1.25

Hence, the values are $1.25 and $5.25

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Answer: 100

Step-by-step explanation:

x/2 = 50

Multiply both sides by 2:

x = 100

Answer:

Easy Peasy, MULTIPLY 2 by 50

Just type 100

Answer:

input, output

Step-by-step explanation:

A function is a rule that assigns each input exactly one output.

Some questions that have you check a list of points, a table of values, a graph or an equation, to figure out if its a function... you check to see if every x only has one y to go with it. This is what the vertical line test does also.

The number of customers are not exactly same in two cases.

In mathematics →

Given is the -

Number of customers this month -

{x} = 250 - {12% of 250}

{x} = 250 - {12/100 x 250}

{x} = 250 - 12 x 2.5

{x} = 250 - 30

{x} = 220

Number of customers last month -

250 = {x} + {12% of x}

250 = {x} + (12/100){x}

250 = {x} (1 + 3/25)

250 = {x} (28/25)

{x} = (250 x 25/28)

{x} = 223 {approx.}

Therefore, the number of customers are not exactly same in two cases.

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Rotate 90 clockwise around E, then reflected over the vertical line K

Answer: 16

Step-by-step explanation:

1/5 x 70 = 14
70 - 14 = 56
5/7 x 56 = 40
56 - 40 = 16

Answer:

16

Step-by-step explanation:

Yesterday, the bookstore sold 1/5 of the 70 copies, which is 70 * 1/5 = 14 copies.

After selling 14 copies, the bookstore was left with 70 - 14 = 56 copies.

Today, the bookstore sold 5/7 of what remained, which is 5/7 * 56 = 40 copies.

So, the bookstore has 56 - 40 = 16 copies left.

1. The function for this problem is given as follows: f(x) = x - 3.

2. The numeric value of the function at x = 2 is of f(2) = -1.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

We define the function in this problem as follows:

f(x) = x - 3.

The numeric value at x = 2 is found replacing the lone instance of 2 by 2, hence:

f(2) = 2 - 3

f(2) = -1.

We attribute the function in this problem as f(x) = x - 3.

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The graph is a step function with a horizontal jump at x=7, where the cost changes from $350 to $10 per day.

What is the Graph?

The graph of the step function that represents the cost of renting a dumpster for x days is a graph that shows how the cost of the rental changes based on the number of days. The x-axis represents the number of days, and the y-axis represents the cost in dollars.

To write the step function that represents the cost of renting a dumpster for x days, we can use the information provided in the problem statement. The cost for the first week is $350, and the cost for each additional day is $10.

We can write the step function as:

y = 350, if x <= 7

y = 350 + 10(x-7), if x > 7

In the first case, if x is less than or equal to 7 (i.e. within the first week), the cost is $350. In the second case, if x is greater than 7 (i.e. more than one week), the cost is $350 for the first week plus $10 for each additional day.

To graph the step function, we can start by plotting the two points on the graph:

(7,350) represents the point at which the cost changes from $350 to $10 per day

(x,y) = (7,350) + (x-7,10x-70)

The graph is a step function with a horizontal jump at x=7, where the cost changes from $350 to $10 per day.

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The slope and y intercept for y-5=2(x-5) is 2 and -5 respectively.

What is Linear equation ?

Linear equation can be defined as the equation in which the highest degree is one.

Given

expression

y- 5 = 2(x-5)

y - 5 = 2x - 10

y = 2x+5-10

y = 2x-5

Its in the form of y = mx+c

where m is slope

and c is y intercept.

So,

From the equation ,

we can say that  m = 2 that is slope = 2 and y intercept is -5.

Therefore, The slope and y intercept for y-5=2(x-5) is 2 and -5 respectively.

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A plot of the two points, where x is the time in minutes and y is the number of pages is shown in the graph attached below.

First of all, we would convert the value of time in hours to minutes as follows;

Conversion:

60 minutes = 1 hour.

x minutes = 2 hours.

Cross-multiplying, we have:

x minutes = 60 minutes × 2 hours

x minutes = 120 minutes.

In this scenario, the time in minutes would be plotted on the x-axis (x-coordinate) of the graph while the number of pages would be plotted on the y-axis (y-coordinate) of the graph.

Next, we would use an online graphing calculator to plot the points representing the time in minutes and the number of pages on a coordinate axes as shown in the image attached below.

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For the quadratic equation -2x²+12x-13, the range is option D: All real numbers less than or equal to 5.

What is a quadratic function?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.

The values for x and h(x) are given in the table.

Real numbers can be said to be all continuous values of quantity, which can be negative or positive values.

The range of h, h(x), in the table given are all real numbers.

The quadratic equation from the points in the table can be deduced as -2x²+12x-13.

The maximum of the graph is at (3,5).

For a parabola ax²+bx+c with Vertex (xv,yv) -

If a<0, then the range is f(x) ≤ yv.

If a>0, then the range is f(x) ≥ yv.

Since, a = -2, then f(x)≤ 5.

Therefore, the range values of h is f(x)≤ 5.

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According to 43% of eighth graders, they spend more than an hour a day on social media.

A ratio stated as a fraction of 100 is what is meant by the term %. Students were asked in a poll if they thought they spent more or less time per day on social media.more less , 7th 12 14 , 8th 20 ,26 . The number of students who responded "more" must be divided by the total number of 8th graders polled in order to arrive at the %, which must then be multiplied by 100.

This percentage is the proportion of 8th graders who believe they spend more than an hour each day on social media.Twenty of the forty-six students (20+26) responded "more," or roughly 43.48 percent. As a result, 43% of eighth graders claim to spend more than an hour every day on social media.

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Yes, it is worth the extra drive to going the far store for buying the chicken. The difference between the both store worth is about $1.24.

We have to buy some chicken for dinner tonight. We found an ad showing that the store across town has it on sale for $3.09 a pound, which is cheaper than our usual neighborhood store, which sells it for $3.19 a pound.

$3.09 ×3 = $19.14 (far store)

$3.19 × 3 = $20.34 (near store)

For the neighbourhood store :

Distance = 2.3 mile

Multiply by 2 because we not only have to drive there, but also back home for the round trip: so, total distance = 2.3 miles × 2 = 4.6 miles

As car average is 19 miles per gallon

= 4.6 mile/ 19 miles per gallon

= 0.24 gallon < 13 gallons

Now, costs to travel to each store from the gas used. Cost of gas is $3.62/gallon,

total cost = 0.2421 gallons×$3.62 /gallons = $0.88

Similarly for far store : distance from home to store = 8.7 miles but take double of it we get, 8.7 miles × 2 = 17.4 miles

As car average is 19 miles per gallon

= 17.4 miles /19 miles per gallons

= 0.915 gallons < 13 gallons

The cost of gas for the respective trip = 0.915 gallons × $3.62 /gallons = $3.32

Now, let's add the gas and chicken costs together to get total worth

$19.14 + $3.32 = $22.46 to the far store

$20.34+ $0.88 = $21.22 to the near store

Hence, the worth in travelling far store is greater than neighbourhoid store.

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Complete question:

You need to buy some chicken for dinner tonight. You found an ad showing that the store across town has it on sale for $3.09 a pound, which is cheaper than your usual neighborhood store, which sells it for $3.19 a pound. Is it worth the extra drive? First, determine what information you need to answer this question, then click here to display that info (along with other info).

How much chicken will you be buying? 3 pounds

How far apart are the two stores? My neighborhood store is 2.3 miles away, and takes about 8 minutes. The store across town is 8.7 miles away, and takes about 25 minutes.

How kind of mileage does your car get? It averages about 19 miles per gallon in the city.

How many gallons does your car hold? About 13 gallons

How much is gas? About $3.62/gallon right now.

Yes, it is worth the extra drive to the far store to get the chicken. The value of the two stores varied by around $1.24.

To make chicken for dinner tonight, we must purchase some. We discovered an advertisement indicating that the supermarket across town is selling it for $3.09 per pound, which is less expensive than our typical neighborhood grocery, which charges $3.19 per pound.

Compare the prices of chicken: We would pay for the 3 pounds of chicken that we require.

$3.09 ×3 = $19.14 (far store)

$3.19 × 3 = $20.34 (near store)

Let's look at the expense of driving in our car:

For the local retailer: = 2.3 miles away

Because we need to travel both ways, we must double the distance by two, making the total distance 2.3 miles x 2 = 4.6 miles.

Since the average automobile gets 19 mpg

19 miles per gallon/4.6 miles = 13 gallons x 0.24 gallons

Now, add the cost of gas used to drive to each store. Gas costs $3.62 per gallon.

Total cost = 0.2421 gallons at a cost of $0.88 per gallon.

The same goes for a far store:

the distance from home to the store is 8.7 miles, but if we double that by two, we get 17.4 miles.

Since the average automobile gets 19 mpg = 17.4 miles per gallon /19 miles per mile

13 gallons equals 0.915 gallons.

The gas price for the relevant journey is 0.915 gallons times $3.62 a gallon, or $3.32.

To determine the overall cost,

let's now combine the costs of the chicken and petrol.

$22.46 to the far store from $19.14 plus $3.32

$20.34 plus $0.88 equals $21.22 for the nearby retailer.

Therefore, a far store is more valuable than a nearby store. The difference is $1.24

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