Solve the right triangle. Round decimal answers to the nearest tenth.

The perimeter of triangle QST is 32.

option D.

The perimeter of triangle QST is calculated by determining the value of x as shown below.

If length SQ = length ST, then angle STQ must be equal to angle SQT,  so we will have the following equation.

Cos T = ( 3x - 1 ) / ( 5x + 1 )

Cos Q = ( 2x + 1 ) / (5x + 1 )

Cost T = Cos Q

( 3x - 1 ) / ( 5x + 1 ) = ( 2x +1 ) / ( 5x + 1 )

3x - 1 = 2x + 1

x = 2

The perimeter of triangle QST is calculated as;

= 5x + 1  + (3x -1  + 2x + 1 ) + 5x + 1

= 15x + 2

= 15 (2)  + 2

= 32

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Answer:

You didn't give the answers

Answer:

A

Step-by-step explanation:

step by step you will learn

The volume of the sphere is,

⇒ The volume of sphere = 14,130 cm³

The multiplication means to add a number to itself with a particular number of times. And, Multiplication can be viewed as a process of repeated addition.

Given that;

Radius of sphere = 15 cm

Now, We know that;

⇒ The volume of sphere = 4/3πr³

Substitute value of Radius = 15 cm

⇒ The volume of sphere = 4/3 × 3.14 × 15³

⇒ The volume of sphere = 14,130 cm³

Thus, The volume of the sphere is,

⇒ The volume of sphere = 14,130 cm³

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Answer:Let's convert hours to minutes:

Now we have:

44 minutes to 300 minutes

We write the ratio as a fraction:

We can reduce both the numerator and denominator by 4, to get:

The correct answer is:

Step-by-step explanation:

[tex]x^{5/6}[/tex]  is value of x in expression .

What is a mathematical expression?

A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself.

                           This mathematical operation may be addition, subtraction, multiplication, or division. An expression's basic components are as follows: The formula is (Number/Variable, Math Operator, Number/Variable).

expression  = [tex]x^{1/2} . x^{1/3}[/tex]            

                     = [tex]x^{1/2 + 1/3}[/tex]    

                    =  [tex]x^{5/6}[/tex]

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a. Journal entries for the issue of debentures:

Issues 4000, 12% debentures of Rs. 100 each at Rs 100 and redeemable at Rs 100.

Debit: Cash/Bank Account (4000 x 100) = 400,000

Credit: Debentures Account (4000 x 100) = 400,000

Issued 4000, 12% debentures of Rs. 100 each at Rs 100 and redeemable at Rs 90.

Debit: Cash/Bank Account (4000 x 100) = 400,000

Credit: Debentures Account (4000 x 90) = 360,000

Credit: Discount on Issue of Debentures Account (4000 x 10) = 40,000

Issued 4000, 12% debentures of Rs. 100 each at Rs 100 and redeemable at Rs 110.

Debit: Cash/Bank Account (4000 x 100) = 400,000

Credit: Debentures Account (4000 x 110) = 440,000

Credit: Premium on Issue of Debentures Account (4000 x 10) = 40,000

Issued 4000, 12% debentures of 100 each at Rs 110 and redeemable at Rs 100.

Debit: Cash/Bank Account (4000 x 110) = 440,000

Credit: Debentures Account (4000 x 100) = 400,000

Credit: Loss on Issue of Debentures Account (4000 x 10) = 40,000

Issued 4000, 12% debentures of 100 each at Rs 110 and redeemable at Rs 90.

Debit: Cash/Bank Account (4000 x 110) = 440,000

Credit: Debentures Account (4000 x 90) = 360,000

Credit: Discount on Issue of Debentures Account (4000 x 20) = 80,000

Issued 4000, 12% debentures of 100 each at Rs 110 and redeemable at Rs 110.

Debit: Cash/Bank Account (4000 x 110) = 440,000

Credit: Debentures Account (4000 x 110) = 440,000

Issued 4000, 12% debentures of Rs.100 each at Rs 90 and redeemable at Rs 100.

Debit: Cash/Bank Account (4000 x 90) = 360,000

Credit: Debentures Account (4000 x 100) = 400,000

Credit: Discount on Issue of Debentures Account (4000 x 10) = 40,000

Issued 4000, 12% debentures of Rs.100 each at Rs 90 redeemable at Rs 105.

Debit: Cash/Bank Account (4000 x 90) = 360,000

Credit: Debentures Account (4000 x 105) = 420,000

Credit: Premium on Issue of Debentures Account (4000 x 15) = 60,000

b. for the redemption of debentures:

Redemption of debentures issued at Rs. 100 and redeemable at Rs. 100:

Debenture Redemption A/C Dr. 400,000

To Debentureholders A/C 400,000

(Being the debentures of Rs. 100 each redeemed at par)

Redemption of debentures issued at Rs. 100 and redeemable at Rs. 90:

Debenture Redemption A/C Dr. 360,000

Loss on Redemption A/C Dr. 40,000

To Debentureholders A/C 400,000

(Being the debentures of Rs. 100 each redeemed at a discount of Rs. 10)

Redemption of debentures issued at Rs. 100 and redeemable at Rs. 110:

Debenture Redemption A/C Dr. 440,000

Gain on Redemption A/C Dr. 40,000

To Debentureholders A/C 400,000

(Being the debentures of Rs. 100 each redeemed at a premium of Rs. 10)

Redemption of debentures issued at Rs. 110 and redeemable at Rs. 100:

Debenture Redemption A/C Dr. 400,000

To Debentureholders A/C 400,000

(Being the debentures of Rs. 110 each redeemed at par)

Redemption of debentures issued at Rs. 110 and redeemable at Rs. 90:

Debenture Redemption A/C Dr. 360,000

Loss on Redemption A/C Dr. 40,000

To Debentureholders A/C 400,000

(Being the debentures of Rs. 110 each redeemed at a discount of Rs. 20)

Redemption of debentures issued at Rs. 110 and redeemable at Rs. 110:

Debenture Redemption A/C Dr. 440,000

To Debentureholders A/C 400,000

Gain on Redemption A/C Cr. 40,000

(Being the debentures of Rs. 110 each redeemed at par with a premium of Rs. 10)

Redemption of debentures issued at Rs. 90 and redeemable at Rs. 100:

Debenture Redemption A/C Dr. 400,000

Loss on Redemption A/C Dr. 10,000

To Debentureholders A/C 390,000

To Securities Premium Reserve A/C 20,000

(Being the debentures of Rs. 90 each redeemed at a discount of Rs. 10 and Securities Premium Reserve credited with Rs. 2.50 per debenture redeemed)

Redemption of debentures issued at Rs. 90 and redeemable at Rs. 105:

Debenture Redemption A/C Dr. 420,000

Loss on Redemption A/C Dr. 30,000

To Debentureholders A/C 390,000

To Securities Premium Reserve A/C 30,000

(Being the debentures of Rs. 90 each redeemed at a discount of Rs. 15 and Securities Premium Reserve credited with Rs. 7.50 per debent

The quadratic equation whose roots are (2α-β) and (2β-α) is given as follows:

y = x² - 5x - 23.02.

The quadratic equation for this problem is defined as follows:

x²-5x+3=0.

The coefficients of the equation are given as follows:

a = 1, b = -5, c = 3.

Hence the discriminant of the equation is of:

D = (-5)² - 4 x 1 x 3

D = 13.

Then the roots are given as follows:

Then the roots of the second equation are given as follows:

Applying the Factor Theorem, the quadratic function is defined as a product of it's linear factors, as follows:

y = (x + 2.91)(x - 7.91)

y = x² - 5x - 23.02.

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The translatiοn directiοn is 4 units tο the left.

A triangle is a clοsed, twο-dimensiοnal geοmetric figure with three straight sides and three angles. It is οne οf the basic shapes in geοmetry.

A pοlygοn with three edges and three vertices is called a triangle. It is οne οf the fundamental geοmetric shapes. Triangle ABC is a triangle with vertices A, B, and C. In Euclidean geοmetry, any three nοn-cοllinear pοints give rise tο a distinct triangle and a distinct plane.

The translatiοn directiοn is 4 units tο the left because Z' has mοved frοm (3,4) tο (-1,4), and the x-cοοrdinate has decreased by 4.

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After finding the difference, we found that the amount of rice left after lunch, written in mixed fraction form, is 9 11/12 lbs.

What are fractions?

Every number of equal parts is represented by a fraction, which also represents a portion of a whole. A single object or a collection of objects might be whole. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object. The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves. The number of parts into which the whole has been divided is shown by the denominator. How many sections of the fraction are displayed or chosen is shown in the numerator.

Given,

 The amount of rice the restaurant had when they opened = 13 lbs

The amount of rice that was cooked and served = 3 1/12lbs

We are asked to find the amount of rice left.

This can be found by subtracting the amount of rice served from the total amount of rice.

Note that the amount of rice served is in fractions.

So we use fraction subtraction to solve this.

Then,

amount of rice left = 13 - 3 1/12

3 1/12 is a mixed fraction.

We should convert it into an improper fraction.

3 1/12 = (3*12 + 1 ) /12 = 37/12

Now solving,

amount of rice left = 13 - 3 1/12 = 13 - 37/12

Taking LCM to make a common denominator.

LCM = 12

amount of rice left = 13 - 37/12 = (13*12 - 37)/12 = 119/12 = 9 11/12 lbs.

Therefore after finding the difference, we found that the amount of rice left after lunch, written in mixed fraction form, is 9 11/12 lbs.

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Answer: 112 business cards

Step-by-step explanation:

    We will divide the number of business cards by the number of days cards were handed out to see how many cards were handed out per day.

5,376 cards / 48 days = 112 business cards

Some numeric values of the exponential function y = 9(3)^x are given as follows:

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

The function for this problem is given as follows:

y = 9(3)^x.

Hence some numeric values of the function are given as follows:

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Making linear equations for given scores, Grace scored 51 marks, John scored 47 marks, and Julius scored 52 marks in the examination.

What is a linear equation, exactly?

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a variable, with the degree of each variable being 1. In other words, a linear equation is an equation of a straight line, which can be expressed in the form of y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept of the line. Linear equations are used to model relationships between variables that have a constant rate of change, such as distance traveled over time or cost per item.

Now,

Let's assume that Grace's score is x.

Then, John's score will be x-4.

And, Julius's score will be x-4+5 = x+1.

The sum of their scores is given as 150. So, we can write an equation as:

x + (x-4) + (x+1) = 150

Simplifying the equation, we get:

3x - 3 = 150

Adding 3 to both sides, we get:

3x = 153

Dividing by 3 on both sides, we get:

x = 51

So, Grace's score is x = 51.

John's score is x-4 = 47.

And, Julius's score is x+1 = 52.

Therefore,

                      Grace scored 51 marks, John scored 47 marks, and Julius scored 52 marks in the examination.

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Answer: We will start by using the identity cos² A + sin² A = 1 to replace sin² A with cos² A - 1 in the expression 1 - 2sin A sin B sin C:

1 - 2sin A sin B sin C = 1 - 2sin A (cos B cos C - sin B sin C) [Using the product-to-sum formula for sin (B + C)]

= 1 - 2sin A cos B cos C + 2sin A sin B sin C

Now, we will use the identity cos (180° - x) = -cos x to replace cos C with -cos (A + B):

cos² A + cos² B - cos² C = cos² A + cos² B - cos² (A + B)

= cos² A + cos² B - (cos² A cos² B - 2cos A cos B sin A sin B)

= cos² A + cos² B - cos² A cos² B + 2cos A cos B sin A sin B

= (cos² A)(1 - cos² B) + (cos² B)(1 - cos² A) + 2cos A cos B sin A sin B

= cos² A + cos² B - cos² A cos² B + 2cos A cos B sin A sin B

Now, we will use the identity sin (A + B) = sin A cos B + cos A sin B to rewrite the last term:

cos² A + cos² B - cos² A cos² B + 2cos A cos B sin A sin B

= cos² A + cos² B - cos² A cos² B + 2sin A sin B cos A cos B

= (cos² A)(1 - cos² B) + (cos² B)(1 - cos² A) + 2sin A sin B cos A cos B

= (cos² A + cos² B - 1) + (1 - cos² A)(1 - cos² B) + 2sin A sin B cos A cos B

= 2sin² A sin² B + 2sin A sin B cos A cos B

= 2sin A sin B (sin A cos B + cos A sin B)

= 2sin A sin B sin (A + B)

= 2sin A sin B sin (180° - C) [Using A + B + C = 180°]

= -2sin A sin B sin C

Substituting this expression back into the original equation, we get:

cos² A + cos² B - cos² C = 1 - 2sin A sin B sin C

Therefore, the expression is proved.

Step-by-step explanation:

Answer:

X+15 is the answer..................

5/18 counter-clockwise is equivalent to 100 degrees counter-clockwise.

What is Fraction ?

A fraction is a number that represents a part of a whole or a ratio between two quantities. It is expressed as a ratio of two integers, with the numerator (top number) representing the part or quantity being considered and the denominator (bottom number) representing the total or whole.

To convert a fraction of a full rotation to degrees, we can use the fact that a full rotation is equivalent to 360 degrees.

In this case, 5/18 represents a fraction of the full rotation, where the numerator (5) represents the number of counter-clockwise rotations and the denominator (18) represents the total number of rotations in a full circle.

To find the number of degrees, we can multiply the fraction by 360 degrees:

(5/18) * 360 = 100 degrees

Therefore, 5/18 counter-clockwise is equivalent to 100 degrees counter-clockwise.

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To determine whether the function f(x) = (x^2-2x-3)/(x^2+3x+2) has any holes, we can factor the numerator and denominator and simplify the expression. The numerator can be factored as:

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

And the denominator can be factored as:

x^2 + 3x + 2 = (x + 1)(x + 2)

Therefore, we can simplify the function as:

f(x) = [(x - 3)(x + 1)]/[(x + 1)(x + 2)]

The factor of (x + 1) appears in both the numerator and denominator, so we can simplify further by canceling it out:

f(x) = (x - 3)/(x + 2)

Since (x + 1) was canceled out, we have a hole in the graph of the original function at x = -1. To find the coordinates of the hole, we can evaluate the simplified function at x = -1:

f(-1) = (-1 - 3)/(-1 + 2) = -4

Therefore, the hole in the graph of the original function is located at the point (-1, -4).

Using the scale factor of 5:2, the volume of the larger cylinder is (C) 70m³.

When a shape is magnified and each side is multiplied by the same number, this is known as a scale factor.

The scaling factor is this figure. Scale factors are used on maps to accurately depict distances between locations.

With a scale factor of 2, the new shape that results from scaling the old shape is twice as large.

So, get the volume of the larger cylinder as follows:

x/5 = 28/2

2x = 28*5

2x = 140

x = 70m³

Therefore, using the scale factor of 5:2, the volume of the larger cylinder is (C) 70m³.

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Complete question:

The scale factor of two similar cylinders is 5:2. The volume of the smaller cylinder is 28 m3. What is the volume of the larger cylinder?

Question 8 options:

A. 700 m3

B. 350 m3

C. 70 m3

D, 437.5 m3

E. 175 m3

Equations that correctly expresses the system of equations in standard form are x + y = 22 and 3x + 4y = 76.

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given,

Cost of blue sea shells = $3

Cost of pink sea shells = $4

Cost of 22 sea shells = $76

Let number of blue sea shells is x and number of pink sea shells is y

then number of total shells

x + y = 22

Cost of shells

3x + 4y = 76

Hence, x + y = 22 and 3x + 4y = 76 are the equations that correctly expresses the system of equations in standard form

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Answer:

$ 1,937.50.

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 3.875%/100 = 0.03875 per year,

then, solving our equation

I = 10000 × 0.03875 × 5 = 1937.5

I = $ 1,937.50

The simple interest accumulated

on a principal of $ 10,000.00

at a rate of 3.875% per year

for 5 years is $ 1,937.50.

Answer:ILL GIVE BRAINLIEST!! Pls answer A

Find the mÁB

104°

126°

B

D

Step-by-step explanation:ILL GIVE BRAINLIEST!! Pls answer A

Find the mÁB

104°

126°

B

D

Using  Remainder Theorem and synthetic division, f(-10) = 191, f(2) = 1, f(3) = 34

What is synthetic division?

A polynomial's coefficients are split one by one in synthetic division.

The split polynomial's zero, which belongs in the box on the far left, has this value.

To use the Remainder Theorem and synthetic division to evaluate f(-10), f(2), and f(3) for the function[tex]f(x)=2x^2+x^2-10x+1[/tex], we can proceed as follows:

First, we need to perform synthetic division using -10, 2, and 3 as the divisors.

1) For f(-10):

The result of the division is 191, so f(-10) = 191.

2) For f(2):

The result of the division is 1, so f(2) = 1.

3) For f(3):

The result of the division is 34, so f(3) = 34.

Therefore, we have:

f(-10) = 191

f(2) = 1

f(3) = 34

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The inverse of function is (x + 3)^(1/3) + 2 and the graph is attached below

a) To find the inverse of the function f(x) = (x - 2)^3 - 3, we can follow these steps:

1. Replace f(x) with y: y = (x - 2)^3 - 3

Solve for x in terms of y:

a. Add 3 to both sides: y + 3 = (x - 2)^3

b. Take the cube root of both sides: (y + 3)^(1/3) = x - 2

c. Add 2 to both sides: x = (y + 3)^(1/3) + 2

Replace x with f^-1(x): f^-1(x) = (x + 3)^(1/3) + 2

b) To graph the inverse function f^-1(x), we can use the equation we found in part a) and plot some points:

So we have three points: (0, 3^(1/3) + 2), (1, 2^(1/3) + 2), and (3, 4).

To sketch the graph, we can also note that the function f(x) = (x - 2)^3 - 3 has a vertical asymptote at x = 2 and a local minimum at (2, -3). Therefore, the inverse function f^-1(x) will have a horizontal asymptote at y = 2 and a local maximum at (4, 2).

Combining all of this information, we can sketch the graph of f^-1(x) as shown below:

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As the temperature of the pan increases, the heat transfer from the butter to the pan increases, causing the butter to melt faster. Ultimately, this heat transfer is necessary for Luke to prepare his food. Without it, the butter would stay solid and would not cook properly.

Heat transfer is the transfer of energy from one place to another due to a difference in temperature. Heat transfer can occur through conduction, convection, and radiation. Heat is always transferred from hotter to colder objects and the rate of transfer depends on the temperature difference between the two and the material it is passing through. Heat transfer is essential in many natural and man-made processes.

The energy is moving in two directions. Cold is moving from the pan and into the butter, while the heat is moving from the butter and into the pan. This is known as a heat transfer. Heat transfers occur when two objects at different temperatures come into contact with each other. In this case, the cold pan is coming into contact with the warm butter, causing the heat to move from the butter and into the pan. This heat transfer causes the butter to melt. As the temperature of the pan increases, the heat transfer from the butter to the pan increases, causing the butter to melt faster. Ultimately, this heat transfer is necessary for Luke to prepare his food. Without it, the butter would stay solid and would not cook properly.

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Answer: x = 100

Step-by-step explanation:

The angles of a triangle add up to 180, meaning that (x-35)+(x-25)+(1/2 x - 10) = 180. Now you can solve for x

Answer:

Step-by-step explanation:

To rewrite the equation x² + 18x + 7 = 4 in the form (x - p)² = q, we need to complete the square by adding and subtracting a constant term.

First, we subtract 4 from both sides of the equation:

x² + 18x + 7 - 4 = 0

Simplifying, we get:

x² + 18x + 3 = 0

To complete the square, we need to add and subtract the square of half the coefficient of x, which is (18/2)^2 = 81:

x² + 18x + 81 - 81 + 3 = 0

Simplifying, we get:

(x + 9)² - 78 = 0

Now, we can rewrite the equation in the desired form by adding 78 to both sides:

(x + 9)² = 78

Therefore, the values to be entered in the boxes are:

1: (x + 9)

2: 78

The correct statement regarding the histogram is given as follows:

The data is bimodal, with a maximum range of 24. This means that the tide was frequently between 6 to 10 or 16 and 20 feet.

An histogram is a graph that shows the number of times each element of x was observed.

Hence the number of observations of each interval is:

Here are two similarly high bins, hence the distribution can be said to be bimodal, with maximum range given as follows:

25 - 5 = 21 - 1 = 20.

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Answer: its d

Step-by-step explanation: