Triangle proofs level 2 please help!!!

As a result, the hotel has 208 single rooms and 112 double rooms. We can now use these two equations to find the values of x and y.

An equation in mathematics is a claim that two mathematical expressions are equivalent. In an equation, the two expressions on either side are separated by the equals sign (=). As in the following equation: 3x + 2 = 11 declares that the formula 11 is identical to the formula 3x + 2. Finding the value of x that causes the equation to be true is the first step towards solving this equation. By first removing 2 from both sides of the equation and then dividing by 3, we may find x in this situation: 3x + 2 - 2 = 11 - 2 (subtracting 2 from both sides) (subtracting 2 from both sides) .3x = 9 (simplifying the right side) (simplifying the right side) .

given

Assume that there are x single rooms and y double rooms at the hotel.

We may create an equation since we are aware that there are 320 rooms in the hotel overall:

x + y = 320 (Equation 1) (Equation 1)

We can create another equation based on sales since we also know the prices for each type of accommodation and the overall sales:

40x + 65y = 15,600 (Equation 2) (Equation 2)

We can now solve for x and y using these two equations. To accomplish this, one method is to solve for x in Equation 1 and replace it in Equation 2:

x + y = 320

x = 320 - y

Equation 2 using x = 320 - y as a replacement:

12,800 - 40y + 65y = 15,600

25y = 2,800 y = 112

40x + 65y = 15,600

40(320 - y) + 65y

= 15,600

There are 112 double rooms in the hotel. In order to determine the number of single rooms, we can reenter this value into Equation 1 as follows:

x + y = 320

x + 112 = 320

x = 208

As a result, the hotel has 208 single rooms and 112 double rooms. We can now use these two equations to find the values of x and y.

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Therefore, the length of the perpendicular side x is approximately 12.64 feet, rounded to two decimal places.

A trigonometric ratio is a mathematical function that relates the sides of a right triangle to its angles. There are three basic trigonometric ratios: sine, cosine, and tangent. Each of these ratios is defined as the ratio of two sides of the triangle. Sine (abbreviated as sin) is the ratio of the length of the side opposite an acute angle to the length of the hypotenuse. That is, sin(theta) = opposite/hypotenuse. Cosine (abbreviated as cos) is the ratio of the length of the adjacent side to the length of the hypotenuse. That is, cos(theta) = adjacent/hypotenuse. Tangent (abbreviated as tan) is the ratio of the length of the opposite side to the length of the adjacent side. That is, tan(theta) = opposite/adjacent.

Here,

We can use the trigonometric ratio of sine to solve for x in this problem.

Sine is defined as the ratio of the length of the opposite side (in this case, x) to the length of the hypotenuse (21 feet):

sin(37°) = x/21

We can solve for x by multiplying both sides of the equation by 21:

x = 21 sin(37°)

Using a calculator to evaluate sin(37°), we get:

sin(37°) ≈ 0.6018

Substituting this value into the equation, we get:

x ≈ 21(0.6018)

x ≈ 12.64

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Check the picture below.

so if we cut the pyramid like a pie with a knife from the top and open it up, it'd look more or less like that picture, so its area is just the area of four triangles with a base of 4 and a height of 3 and a 4x4 square.

[tex]\stackrel{ \textit{\LARGE Areas} }{\stackrel{\textit{four triangles}}{4\left[ \cfrac{1}{2}(4)(3) \right]}~~ + ~~\stackrel{square}{(4)(4)}}\implies 24+16\implies \text{\LARGE 40}~yd^2[/tex]

Answer:

c=(a+d)÷b

Step-by-step explanation:

a=bc-d

a+d=bc-d+d

bc÷b=(a+d)÷b

c=(a+d)÷b

Answer:

D. -3, -7

Step-by-step explanation:

Answer: There isn't an answer because there's an negative.

Answer:

x = - 1, 6

Step-by-step explanation:

the denominator of h(x) cannot be zero as this would make h(x) undefined

equating the denominator to zero and solving gives the values of x that cannot be in the domain of h(x)

x² - 5x - 6 = 0

(x + 1)(x - 6) = 0

equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

x - 6 = 0 ⇒ x = 6

then x = - 1, 6 are values not in the domain of h(x)

Answer: There are 7 marbles in the bag and in the first attempt, all 7 marbles are there. After one marble is taken away, then we have 6 marbles to choose from. Therefore we will multiply 7*6 = 42.

Hence, there are 42 possible outcomes.

Answer:

A) 0

Step-by-step explanation:

1.5+(-1 x (.5 + .25)) / .5

1.5+(-1 x .75) / .5

1.5 + -0.75 / .5    Because of order of operations division comes first

1.5 + (-1.5)

1.5 - 1.5

0

Answer:

Step-by-step explanation:

There Are 450 students in a school & 74% of them are boys.

1)Find the number of boys

2)Find the numver of girls​

first we find 74% of 450 and we have the number of boys, we subtract the result from the total number and we have the number of girls

450 : 100 x 74 =

4.5 x 74 =

333

450 - 333 =

117

Step-by-step explanation:

To find F^-1(x), we need to solve for x in terms of f(x) using the given equation for f(x):

f(x) = 4(3x+2)

First, we can simplify the expression inside the parentheses:

f(x) = 12x + 8

Next, we can solve for x by isolating it on one side of the equation:

f(x) - 8 = 12x

(x is isolated)

x = (f(x) - 8) / 12

Therefore, F^-1(x) = (x - 8) / 12.

Answer: The area of the rectangular prism would be S.A. = 66m²

Step-by-step explanation: :)

What is the surface area of this rectangular prism?

A rectangular prism is a three-dimensional shape that has two at the top and bottom and four are lateral faces. The surface area of this rectangular prism = l x b

We have given

4 rectangles with area

A₁ = 3m × 4m  = 12 m²

2 rectangles with area

A₂ = 3m × 3m = 9 m²

Therefore the Surface Area of the rectangular prism is:

S.A. = 4A₁ + 2A₂

S.A. = 4(12) + 2(9)

= 48 + 18

= 66

Hence, the net surface area of the rectangular prism would be 66 meters sq.

a.  The elasticity of demand is E = -1.607.

b. Total revenue is maximized at q ≈ 1354.00.

The demand function is: q = 40,600 - 9p^2

a. To find the elasticity of demand, we need to differentiate the demand function with respect to p and then multiply by p/q:

dq/dp = -18p

(p/q) * (dq/dp) = (-18p/q)

Then, we can substitute p = 2000 and q = 22,400 (the values given in a previous question) into this expression:

E = (-18(2000)/22400) = -1.607

b. Total revenue is maximized where the demand is unit elastic (E = -1). We can set the expression for E equal to -1 and solve for p to find the corresponding value of q:

-1 = (-18p/q)

q = 18p

Substituting the demand function into this expression and simplifying, we get:

q = 40,600 - 9p² = 18p

Rearranging and solving for p, we get:

9p² + 18p - 40,600 = 0

Using the quadratic formula, we get:

p = (-18 ± √(18² - 4(9)(-40,600)))/(2(9)) ≈ 75.22 or -227.22

Since the price must be positive, the only valid solution is p ≈ 75.22. Substituting this back into the demand function, we get:

q ≈ 18(75.22) ≈ 1354.00

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If you know your turning point form (vertex form) of a quadratic (y = a(x - h)2 + k), k is the y value, so k = -2

A production process that is in control has a mean of 80 and a standard deviation of 10. The upper and the lower control limits for sample sizes of 25 is 124 and 36 respectively.

The production process that is in control has a mean of 80 and a standard deviation of 10.

To find the upper and lower control limits for a sample size of 25, we need to calculate the following formulas:
Upper Control Limit (UCL) = mean + 3*standard deviation
Lower Control Limit (LCL) = mean - 3*standard deviation
Therefore, for this process with a mean of 80 and standard deviation of 10, the UCL is 130 and the LCL is 30.
For sample sizes of 200, the formulas will be slightly different as the control limits are adjusted for larger samples:
UCL = mean + 2.66 x standard deviation
LCL = mean - 2.66 x standard deviation
Therefore, the UCL is 124 and the LCL is 36.
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We may conclude after answering the provided question that angles NM = 10 + 6 = 16 (as seen in the figure) m JML = 60 - x m KML = 120 m

An angle is a form in Euclidean geometry that is made up of two rays that meet at a point in the centre known as the angle's vertex. Two rays may combine to form an angle in the plane where they are situated. When two planes intersect, an angle is generated. They are referred to as dihedral angles. An angle in plane geometry is a potential configuration of two radiations or lines that represent a termination. The word "angle" comes from the Latin word "angulus," which meaning "horn." The vertex is the place where the two rays, also known as the angle's sides, meet.

Let x be the angle JML measurement. Next, using the angle connections we discovered earlier:

m LKN = x m KML = m LMN = 180 minus x (since they form a linear pair with angle JML)

180 - x - (180 - m LKN) m JML

JML m = LKN m - x

JML = 60 - x KML = m LMN = 180 - 60 = 120 F

JMN = JML (alternative interior angles) KMN = KML (alternate interior angles) m JMN + KMN + m N = 180 (angles in a triangle)

m JMN = 60 x m KMN = 120 60 x + 120 + m N = 180 m N = x

As a result, we have:

LK + KL = NM (segment addition postulate)

NM = 10 + 6 = 16 (as seen in the figure) m JML = 60 - x m KML = 120 m

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Answer:

2550

Step-by-step explanation:

Step-by-step explanation:

To multiply decimals, we can simply multiply the numbers as if they were whole numbers and then count the total number of decimal places in the factors. In this case, we have:

25.5 x 10 x 10 = 255 x 10

Now, we multiply 255 by 10 as if they were whole numbers:

255 x 10 = 2550

Finally, we count the total number of decimal places in the factors, which is two (one in 25.5 and one in 10). Therefore, the answer should have two decimal places, so we can add a decimal point to the result and place two zeros after it:

25.5 x 10 x 10 = 2550.00

Therefore, 25.5 x 10 x 10 = 2550.00.

Answer:

( a + 2 ) ( a - 15 )

Step-by-step explanation:

a² - 13a - 30

a² + 2a - 15a - 30

( a² + 2a ) - ( 15a - 30 )

a ( a + 2 ) - 15( a + 2 )

( a + 2 ) ( a - 15 )

The solution to the system of equations is x = 31/7 and y = 1/7.

An equation is a mathematical statement that shows the equality between two expressions. It consists of two parts, the left-hand side and the right-hand side, separated by an equal sign (=). The left-hand side and right-hand side may contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.

Here,

We can solve this system of equations using the elimination method. We will eliminate one of the variables by adding or subtracting the equations to get an equation with just one variable.

Multiply the first equation by 4 and the second equation by 3 to get:

16x + 12y = 76

9x + 12y = 45

Subtract the second equation from the first to eliminate y:

16x + 12y - (9x + 12y) = 76 - 45

7x = 31

Solve for x by dividing both sides by 7:

x = 31/7

Substitute the value of x into either equation to solve for y. Let's use the first equation:

4x + 3y = 19

4(31/7) + 3y = 19

3y = 19 - 124/7

3y = 3/7

y = 1/7

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Complete question:

Solve the equation for x and y:

4x+3y=19

3x+4y=15

Answer:

answer is 2 into 2 into twenty three

Step-by-step explanation:

2×2×23

√2^2×23

2√23

Answer: The square root of 92 is approximately 9.59166304663. Rounding this to the nearest tenth gives 9.6. Therefore, the square root of 92 rounded to the nearest tenth is 9.6.

Step-by-step explanation:

Using the net below, find thesurface area of the triangular prism.Start by finding thearea of each piece.6 cm9 cm[?]576 cmcm6 cm9 cmTo find the surface area of the triangular prism, we need to find the area of each face and add them up. First, let's find the area of the triangular base: Area of triangle = (1/2) x base x height The base of the triangle is 6 cm and the height is 9 cm, so: Area of triangle = (1/2) x 6 cm x 9 cm = 27 cm^2 Next, let's find the area of each rectangular face: Area of rectangle = length x width One rectangular face has a length of 9 cm and a width of 6 cm: Area of rectangular face = 9 cm x 6 cm = 54 cm^2 The other rectangular face also has a length of 9 cm and a width of 6 cm: Area of rectangular face

The value of x that will make ∆ABC similar to ∆ RST is 12

Similar triangles are triangles with similar shapes but their sizes are not necessarily thesame. The ratio of the corresponding sides of similar triangles are equal.

This means ,

2x+6/36 = 40/48 = 25/x+18

therefore, 2x+6/36 = 40/48

48( 2x+6) = 36× 40

96x + 288 = 1140

96x = 1140-288

96x = 1152

divide both sides by 96

x = 1152/96

x = 12

therefore the value of x that will make the two triangles similar is 12

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Answer:

We need to find the number of points of intersection between the line with equation y = -3/4x + 25/4 and the circle. The equation of the circle is not given, so we cannot directly solve for the intersection points. However, we can use the fact that the intersection points must satisfy both the equation of the line and the equation of the circle.

Let (x, y) be a point on the circle. Then the coordinates satisfy the equation of the circle, which we will assume is (x - a)^2 + (y - b)^2 = r^2, where (a, b) is the center of the circle and r is the radius. Substituting y = -3/4x + 25/4, we get:

(x - a)^2 + (-3/4x + 25/4 - b)^2 = r^2

This is a quadratic equation in x, which we can expand and simplify:

(x^2 - 2ax + a^2) + (-3/2)x^2 + (15/2)x - 3bx + (625/16) + b^2 - (25/2)b + (625/16) - r^2 = 0

Simplifying further, we get:

(-5/2)x^2 + (-2a - 3b + 15/2)x + (2a^2 - 25/2b + 125/8 - r^2) = 0

This is a quadratic equation in x, with coefficients that depend on the center and radius of the circle. We can use the quadratic formula to solve for x, and then substitute into y = -3/4x + 25/4 to get the corresponding value of y.

The discriminant of the quadratic equation is:

(-2a - 3b + 15/2)^2 - 4(-5/2)(2a^2 - 25/2b + 125/8 - r^2)

Simplifying and factoring, we get:

(4a + 6b - 15)^2 - 25(4a^2 - 50b + 250/8 - 2r^2)

This is a quadratic expression in b, which tells us whether the equation has real solutions (i.e., whether the line intersects the circle). If the discriminant is positive, then the equation has two real solutions, which means the line intersects the circle at two points. If the discriminant is zero, then the equation has one real solution, which means the line is tangent to the circle. If the discriminant is negative, then the equation has no real solutions, which means the line does not intersect the circle.

Without knowing the equation of the circle, we cannot determine the discriminant and therefore the number of intersection points. Therefore, the answer is D: "There is not enough information to determine the number of points of intersection."

Step-by-step explanation:

Answer:

One expression equivalent to B + B + B + B + B that is a product of a coefficient and a variable is 5B, where 5 is the coefficient and B is the variable

Step-by-step explanation:

Answer:

The zeroes are -2 and 4.

Step-by-step explanation:

x^2 - 2x - 8 = 0

(x + 2)(x - 4) = 0

x + 2 = 0 or x - 4 = 0

x = -2, 4

The general form of the equation is ax^2 + bx + c = 0.

The sum of the zeroes should be equal to -b/a:-

-2 + 4 = 2

and -(-2)/1 = 2

Verified

The product of the zeroes should be c/a = -8:-

-2 * 4 = -8.

Verified.

Answer:

answer: 7

Step-by-step explanation:

u have to find the median by finding the middle of all of those numbers which will me seven

The value of 2 (x²+2/x²) is D) 1/4.the calculation is given below.

Value in math is a measure of the amount of a quantity, such as size, cost, or weight. It is used to compare different quantities or compare different elements in a set. Value can be measured in a variety of ways, such as absolute value, relative value, or fractional value. Ultimately, value helps to explain how different elements interact and relate to one another.

Solution:
The given equation is:
sin θ = 2x
cos θ = 2
0°< θ < 90°

Now we can solve for x using the first equation to get
x = sinθ/2

Now we can substitute this value of x in the second equation and solve for θ
2 = cosθ
θ = cos-1 (2)
θ = 60°

Thus, x = sin60°/2
x = √3/2

Now we can substitute this value of x in the given equation and solve for the value of 2 (x²+2/x²)
2 (x²+2/x²) = 2 ((√3/2)²+ 2/ (√3/2)²)
2 (x²+2/x²) = 2 (3/2 + 2/3)
2 (x²+2/x²) = 2 (5/3)
2 (x²+2/x²) = 10/3

Therefore, the value of 2 (x²+2/x²) is D) 1/4.

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