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WILL MARK BRAINLIEST

Answer:

Exact form: 121π

Decimal form: 380.1327111...

Step-by-step explanation:

The area of the circle is given by the formula A = πr², where A is the area of the circle and r is the radius.

Given the diameter of 22cm, we know that the radius is 11cm, as the radius is half the diameter.

We can then put this into the formula to find the area of the circle:

A = πr²

A = π * 11²

A = 121π

Note that the answer here is given in terms of π so it can be expressed in its exact form, as 121π is an irrational number roughly equivalent to 380.1327111... The answer you need to provide will depend on whether the question asks for the exact form, or to a certain number of decimal places / significant figures. If it the latter, you can round off the decimal answer as appropriate.

The diameter of the circle is 28 inches.

The formula for the area of a circle is:

[tex]A = \pi r^2[/tex]

Where A is the area and r is the radius.

Any straight line segment that travels through the centre of a circle and has endpoints that are on the circle is said to have a diameter.

To find the diameter of the circle, we first need to find the radius. We can rearrange the formula for the area to solve for the radius:

[tex]r = \sqrt{ (A/\pi )}[/tex]

Plugging in the given values:

[tex]r = \sqrt{(615.44/3.14)} = 14[/tex]

So the radius of the circle is 14 inches. The diameter is twice the radius, so:

d = 2r = 2(14) = 28

Therefore, the diameter of the circle is 28 inches.

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The zeros of the function [tex]f(t) = t^(2) + 7t + 12[/tex] are -3 and -4.

To find the zeros of a quadratic function, we can either factor the equation or use the quadratic formula. In this case, we can easily factor the equation to find the zeros.

First, we need to find two numbers that multiply to give us 12 and add to give us 7. These numbers are 3 and 4.

Next, we can rewrite the equation using these numbers:

[tex]f(t) = t^(2) + 7t + 12 = (t + 3)(t + 4)[/tex]

Now, we can set each factor equal to zero and solve for t:

[tex]t + 3 = 0  ->  t = -3[/tex]

[tex]t + 4 = 0  ->  t = -4[/tex]

So, the zeros of the function are -3 and -4.

In conclusion, the zeros of the function [tex]f(t) = t^(2) + 7t + 12[/tex] are -3 and -4.

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The value of y that satisfies the equation is y = -11.

An equation is a mathematical statement that expresses the equality of two expressions. It typically consists of two sides, separated by an equals sign (=), with each side containing one or more terms that may include variables, constants, and mathematical operators.

We can start by setting up the equation:

(y+1)/(y-5) + 10/(y+5) = (y+1)/(y-5) × 10/(y+5)

To solve for y, we need to simplify and manipulate the equation:

Multiply both sides by (y-5) × (y+5) to eliminate the denominators:

(y+1)(y+5) + 10(y-5) = 10 × (y+1)

Expand and simplify:

y² + 6y - 15 + 10y - 50 = 10y + 10

Combine like terms:

y² + 16y - 55 = 0

Factor the quadratic:

(y + 11)(y - 5) = 0

Solve for y:

y = -11 or y = 5

However, we need to check if either solution makes the denominators of the original equation equal to zero, since division by zero is undefined:

For y = -11, the denominators are -16 and -6, respectively, which are both nonzero. Therefore, y = -11 is a valid solution.

For y = 5, the denominator of the first fraction is 0, which is not allowed. Therefore, y = 5 is an extraneous solution and should be discarded.

Therefore, the value of y that satisfies the equation is y = -11.

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Using long division . The quotient of  (4x^3-6x^2-4x+8) divided by (2x-1) is: 2x^2 - 2x - 2 with a remainder of 7.

Let use long division to determine the quotient of (4x^3-6x^2-4x+8) divided by (2x-1).

Long division:

   2x^2  - 2x  - 2

    --------------------

2x - 1 | 4x^3  - 6x^2  - 4x  + 8

       - (4x^3  - 2x^2)

       --------------

            -4x^2  - 4x

            +  (4x^2  - 2x)

            --------------

                      -2x  + 8

                      -(-2x  + 1)

                      --------

                               7

Therefore, the quotient of (4x^3 - 6x^2 - 4x + 8) divided by (2x - 1) is:

2x^2 - 2x - 2 with a remainder of 7.

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The probability that a student surveyed was either a boy or had a bicycle is 0.62.

What is probability?

The mathematical concept of probability is used to estimate an event's likelihood. It merely allows us to calculate the probability that an event will occur. On a scale of 0 to 1, where 0 corresponds to impossibility and 1 to a particular occurrence.

We are given that of 1000 students surveyed, 490 were boys and 320 had bicycles. Of those who had bicycles, 130 were girls.

So, Total number of boys = 490

Total number of girls with bicycle = 130

Total number of students that was either a boy or had a bicycle is

490 + 130 = 620

The probability is

620 / 1000 = 0.62

Hence, the probability that a student surveyed was either a boy or had a bicycle is 0.62.

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angle = tan⁻¹(2,500 / 31,680)

angle ≈ 4.51 degrees

Therefore, the angle of descent is approximately 4.51 degrees.

When two rays collide at a given point, an angle is created. Indicated by the symbol is the "angle," also known as the "opening" between these two beams. Many angles, such as 60°, 90°, etc., are usually stated as numbers in degrees.

To find the angle of descent, we can use the tangent function, which relates the opposite and adjacent sides of a right triangle:

tan(angle) = opposite / adjacent

In this case, the opposite side is the change in elevation, which is 2,500 feet, and the adjacent side is the distance traveled, which is 6 miles or 31,680 feet (since 1 mile = 5,280 feet).

So we have:

tan(angle) = 2,500 / 31,680

To solve for the angle, we can take the inverse tangent (or arctangent) of both sides:

angle = tan⁻¹(2,500 / 31,680)

Using a calculator, we get:

angle ≈ 4.51 degrees

Therefore, the angle of descent is approximately 4.51 degrees.

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[tex]10^{32} \times 10^{36}[/tex] can be written as [tex]10^{68}[/tex] using a single exponent.

What is an exponents?

In mathematics, exponents are a way to indicate the repeated multiplication of a number or phrase.

Exponents are numbers that are superscripted above other numbers. In other words, it denotes that a certain level of power has been conferred upon the base. Index and power are other names for the exponent. If m is a positive number and n is its exponent, the expression Mn means that m has been multiplied by itself n times.

Exponents are required for a more comprehensible representation of numerical quantities. Repeated multiplication is simple to write down when using exponents. If both n and x are positive integers, the expression xn means that x has been multiplied by itself n times.

When multiplying two numbers with the same base, we can add their exponents. Therefore:

[tex]10^{32} \times 10^{36 }= 10^{(32+36) }= 10^{68}[/tex]

Hence, [tex]10^{32} \times 10^{36}[/tex]can be written as [tex]10^{68}[/tex] using a single exponent.

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Answer: $170

Step-by-step explanation:

6x + 18(6) = 1128.

6x + 108 = 1128

6x = 1020

x = 170

The price of one ticket is 170

if we take 32(origin amount) to be the 100%, what's 7.1 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 32 & 100\\ 7.1& x \end{array} \implies \cfrac{32}{7.1}~~=~~\cfrac{100}{x} \\\\\\ 32x=710\implies x=\cfrac{710}{32}\implies x\approx 22.19[/tex]

Answer:

Gina has 47 nickels

Step-by-step explanation:

Let's call the number of nickels that Gina has "n" and the number of dimes she has "d". We know that she has a total of 70 nickels and dimes, so:

n + d = 70 (equation 1)

We also know that the value of her nickels and dimes is $4.65, which is equal to 465 cents. Each nickel is worth 5 cents and each dime is worth 10 cents, so the value of n nickels is 5n cents and the value of d dimes is 10d cents. Therefore, we can write another equation based on the value of the coins:

5n + 10d = 465 (equation 2)

We can simplify equation 2 by dividing both sides by 5:

n + 2d = 93 (equation 3)

Now we have two equations with two variables. We can solve for one of the variables in terms of the other and substitute into the other equation to solve for the remaining variable. For example, we can solve equation 1 for d:

d = 70 - n

Substituting this expression for d into equation 3, we get:

n + 2(70 - n) = 93

Simplifying this equation, we get:

n + 140 - 2n = 93

-n + 140 = 93

-n = -47

n = 47

Therefore, Gina has 47 nickels and 23 dimes (since n + d = 70), and the total value of her coins is $4.65.

Answer:

47 nickels

Step-by-step explanation:

47 nickels

Answer:

Step-by-step explanation:

its is 192 ft2

Therefore, the original price of the shirts was $18.75 each.

An equality on both sides of the equal to sign signifies a mathematical equation, which is a relationship between two expressions. Here is an example of an equation: 3y = 16.

If the selling price of the shirts was 80% of their regular price, then we can use the following equation to find the original price:

Original price * 0.8 = Selling price

Let's substitute the given values into the equation:

Original price * 0.8 = 15

To solve for the original price, we need to isolate it on one side of the equation. We can do this by dividing both sides by 0.8:

Original price = 15 ÷ 0.8

Original price = 18.75

Therefore, the original price of the shirts was $18.75 each.

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(a) m∠BAC = 73°

(b) The value of y is 2.

A triangle that has two equal lengths of sides and two equal measures of angles is called an isosceles triangle.

(a) Given:

m∠BEA = 62°.

Assuming ABCD is a square.

The diagonal of the square divides the square into two isosceles right-angled triangles.

So, m∠BAD = 90° and m∠ABD = m∠ADB = m∠ABE = 45°.

So, the angle measure of ∠BAC,

m∠BAC = 180° - (45 + 62)

m∠BAC = 180° - 107°

m∠BAC = 73°

(b) Given:

BE = 6y + 2 and CE = 4y + 6.

Assuming ABCD is a square.

The diagonals of squares divide the diagonals into two equal parts.

So, BE = CE

6y + 2  = 4y + 6.

2y = 4

y = 2

Therefore, the value of y is 2.

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The value of the matrix is [[b+y-a,a+x-b,c+z+1-a],[a+x-b,b+y-a,c+z+1-b],[a+x-c-1,b+y-c-1,c+z]] when a+x=b+y=c+z+1, where a,b,c,x,y, z are non-zero distinct real numbers.

According to the given equation, a+x=b+y=c+z+1, where a,b,c,x,y, z are non-zero distinct real numbers, we can rearrange the equation to find the value of one of the variables in terms of the others. For example, we can rearrange the equation to find the value of x in terms of the other variables:

x = b+y-a = c+z+1-a

Similarly, we can rearrange the equation to find the value of y and z in terms of the other variables:

y = a+x-b = c+z+1-b

z = a+x-c-1 = b+y-c-1

Now, we can substitute these values into the given matrix to find the value of each element:

[[x,a+y,x+a],[y,b+y,y+b],[z,c+y,z+c]] = [[b+y-a,a+x-b,c+z+1-a],[a+x-b,b+y-a,c+z+1-b],[a+x-c-1,b+y-c-1,c+z+1-c-1]]

Simplifying the matrix, we get:

[[b+y-a,a+x-b,c+z+1-a],[a+x-b,b+y-a,c+z+1-b],[a+x-c-1,b+y-c-1,c+z]]

Therefore, the value of the matrix is [[b+y-a,a+x-b,c+z+1-a],[a+x-b,b+y-a,c+z+1-b],[a+x-c-1,b+y-c-1,c+z]] when a+x=b+y=c+z+1, where a,b,c,x,y, z are non-zero distinct real numbers.

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According to the Census Bureau, of the people 21 to 64 years old, 12.3% are not high school graduates, 27.8% have graduated high school, 30.6% have some college, 16.9% have a bachelor's degree, and 8.8% have an advanced degree. The words that look like different answers to one question are "not high school graduates," "graduated high school," "some college," "bachelor's degree," and "advanced degree."

These words all describe different levels of education and could be potential answers to a question about a person's education level. The paragraph describes the educational attainment of people between the ages of 21 and 64. The different percentages represent the proportion of individuals in each education category.

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The unknown side 'x' is found using pythagorean theorem as: x = 12.69.

The Pythagorean Theorem has a name for Pythagoras of Samos, a religious figure and mathematician who held the view that everything in the cosmos is made up of numbers.

Pythagorean Theorem is also known as:

a²+ b² = c²

Given sides are:

13, 3 and x.

Then,

3²+ x² = 13²

x² = 13² - 3²

x² = 169 - 9

x² = 160

x = √160

x = 12.69

Thus, the unknown side 'x' is found using pythagorean theorem as: x = 12.69.

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Answer:

squareroot(256)

16

Step-by-step explanation:

im genius

The expression can be written as a single logarithm using the laws of logarithms as: 2logx(y)+logx(z/y).

The exponent or power to which a base must be increased in accordance with the laws of logarithms to arrive at a certain number. If bx = n, then x is the logarithm of n to the base b, which is expressed mathematically as x = logb n

Using the laws of logarithms, we can combine the given expression as follows:

2 log(x) - log(y) + log(z)

Now, using the law of logarithmic addition, we can combine the second and third terms as follows:

2 log(x) + log(z/y)

Therefore, the given expression as a single logarithm is:

2 log(x) + log(z/y)

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Answer:

5/33

Step-by-step explanation:

5/6 divided by 11/2

Invert the divider

5/6 x 2/ 11

10/66

Reduce to smallest fraction

5/33

Answer:

5/33

Step-by-step explanation:

Apply the fraction rule: a/b ÷ c/d = (a × d) ÷ (b × c) for 5/6 ÷ 11/2

a = 5

b = 6

c = 11

d = 2

(5 × 2) ÷ (6 × 11)

For "(6 × 11)", break 6 down into "2 × 3", so that you can cancel out the common factor, because there is also a 2 in "5 × 2".

= (5 × 2) ÷ (2 × 3 × 11)         -- cancel out the 2's

= 5 ÷ (3 × 11)     *****3 × 11 = 33*****

= 5/33

After the transformation from f to g, g(x) = eˣ/3.

Vertical shrink refers to a transformation of a function that causes it to be compressed vertically. To perform a vertical shrink, you must multiply the output (y) values of the function by a constant value between 0 and 1.

The transformation of f(x) to g(x) involves a vertical shrink by a factor of 1/3. This means that the value of g(x) will be one third of the value of f(x). We can write this transformation as: g(x) = 1/3 · f(x).

Since f(x) = eˣ, we can substitute this into the equation for g(x) to find the final expression for g(x):

g(x) = (1/3)eˣ

Therefore, the function g(x) after the vertical shrink by a factor of 1/3 is g(x) = (1/3)eˣ or g(x) = eˣ/3.

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The graph of g(x) = 3x² + 6 is steeper and shifted upward compared to the graph of f(x) = x².

A graph can be defined as a pictorial representation or a diagram that represents data or values.

The graphs of g(x) = 3x² + 6 and f(x) = x² are both quadratic functions, which means that their graphs are parabolas.

However, they have different coefficients and constant terms, which means that they will have different shapes and positions.

Here, the graph of g(x) = 3x² + 6 is steeper and shifted upward compared to the graph of f(x) = x².

Both graphs have a vertex at the origin, but g(x) has a larger coefficient of x², which makes it steeper, and an added constant term, which shifts it upward.

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60Answer: it would be 60

Step-by-step explanation:

it’s going up and down by 10

The solution is, the triangle ABC and DBC are congruent, by the Side-Angle-Side Triangle Congruence Theorem.  

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

here, we have,

As we can seen from the given figure that two triangles are given.

The triangles ABC and BDC are :

AB = CD

AC = BD

BC = BC

Hence using the SSS theorem of the triangle, the triangle ABC and DBC are congruent, Thus the angle A  is equal to angle D.

Hence the option D and E are correct. i.e. congruent by the Side-Angle-Side Triangle Congruence Theorem.  

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The final answer is: \[ C = 40.32^{\circ} \]Therefore, the indicated angle is 40.32 degrees.

To determine the indicated angle, we can use the Law of Cosines, which states that: \[ c^2 = a^2 + b^2 - 2ab\cos(C) \]We can rearrange this equation to solve for the cosine of the indicated angle: \[ \cos(C) = \frac{a^2 + b^2 - c^2}{2ab} \]Plugging in the given values for a, b, and c, we get: \[ \cos(C) = \frac{69.01^2 + 39.28^2 - 42.65^2}{2(69.01)(39.28)} \]Simplifying the expression, we get: \[ \cos(C) = 0.7664 \]Now, we can use the inverse cosine function to find the indicated angle: \[ C = \cos^{-1}(0.7664) \]This gives us an angle of 40.32 degrees. However, the question asks us to round our answer to two decimal places, so the final answer is: \[ C = 40.32^{\circ} \]Therefore, the indicated angle is 40.32 degrees.

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The measurement of the angle F in the given circle is 41°

A circle is a round-shaped figure that has no corners or edges. In geometry, a circle can be defined as a closed, two-dimensional curved shape.

Given is a circle, with secants FX and FB, we need to find the measurement of the angle F in the given circle

Using the property of circle,

∠ F = 1/2(arc XB - arc VW)

∠ F = 1/2(126°-44°)

∠ F = 1/2 x 82

∠ F = 41°

Hence, the measurement of the angle F in the given circle is 41°

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The distance between Point A and Point B is 840 meters.

Let's start by using the formula:

distance = speed x time

Since Coco swam at a constant speed of 1.2 m/s, we can find his distance using:

distance(Coco) = speed(Coco) x time

where time is the same for both Coco and Azlinda. Let's call this common time "t".

distance(Coco) =[tex]1.2 m/s \times t[/tex]

Now, let's consider Azlinda's situation. After 5 minutes (or 5/60 = 1/12 hours), she had swum a distance of 420 m and was 37 m away from Coco. Let's call the distance between Point A and Point B "d".

Since Azlinda was swimming towards Point A, she must have covered a distance of (d - 37) m by the time she had swum 420 m. We can use the formula above to find her speed:

speed(Azlinda) = distance(Azlinda) / time

speed(Azlinda) = (d - 37) m / (1/12) h

speed(Azlinda) = 12(d - 37) m/h

Now, we know that Azlinda and Coco were swimming towards each other for a total of 5 minutes (or 1/12 hours), so their total distance apart at that time was:

distance apart = distance(Coco) + distance(Azlinda)

distance apart = [tex]1.2 m/s \times t + 12(d - 37) m/h \times (1/12) h[/tex]

distance apart =[tex]1.2t + d - 37[/tex]

We also know that when they were 37 m apart, Azlinda had swum a distance of 420 m, so we can write:

420 = d - 37 - distance(Coco)

Substituting the expression for distance(Coco) from above, we get:

420 = d - 37 - 1.2t

Now we have two equations with two unknowns (d and t). We can substitute into the other equation and solve for one variable in terms of the other. For example, we can solve the second equation for t:

[tex]1.2t = d - 37 - 420\\1.2t = d - 457\\t = (d - 457) / 1.2[/tex]

When we enter this into the initial equation, we obtain:

distance apart = [tex]1.2t + d - 37[/tex]

distance apart = [tex]1.2((d - 457) / 1.2) + d - 37[/tex]

distance apart = [tex]d - 380.6[/tex]

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

[tex]420 = d - 37 - 1.2t\\420 = d - 37 - 1.2(d - 457) / 1.2\\420 = d - 37 - (d - 457)\\420 = -d + 420\\d = 840[/tex]

Therefore, the distance between Point A and Point B is 840 meters.

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The measure m∠UTS is approximately 90 degrees.

Rhombus is a parallelogram whose all sides are of equal lengths.

Its diagonals are perpendicular to each other and they cut each other in half( thus, they're perpendicular bisector of each other).

Its vertex angles are bisected by its diagonals.

The triangles on either side of the diagonals are isosceles and congruent.

We are given that;

Angle VUR=(10x-23)degree

Angle TUV=(3x+19)degree

Now,

Since RSTU is a rhombus, its diagonals are perpendicular bisectors of each other, which means that angle VUT is a right angle. Therefore, we have:

m∠VUR + m∠TUV + m∠VUT = 180°

Substituting the given values, we get:

(10x - 23) + (3x + 19) + 90 = 180

13x + 86 = 180

13x = 94

x = 7.23 (rounded to two decimal places)

Now, we can find m∠UTS as follows:

m∠UTS = m∠VUR + m∠TUV

Substituting the value of x, we get:

m∠UTS = (10x - 23) + (3x + 19)

m∠UTS = (10 × 7.23 - 23) + (3 × 7.23 + 19)

m∠UTS = 72.3 - 23 + 21.69 + 19

m∠UTS = 89.99

Therefore, the answer of the given rhombus will be 90 degrees.

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The solution to the equation is z = 15.

To solve the equation 2(2z-3)=3(z+3), we first need to simplify each side of the equation by distributing the numbers outside of the parentheses to the terms inside the parentheses.

On the left side of the equation, we have 2(2z-3). Distributing the 2 to the terms inside the parentheses gives us:

2(2z) - 2(3) = 4z - 6

On the right side of the equation, we have 3(z+3). Distributing the 3 to the terms inside the parentheses gives us:

3(z) + 3(3) = 3z + 9

Now we can rewrite the equation as:

4z - 6 = 3z + 9

Next, we want to get all of the z terms on one side of the equation and all of the constant terms on the other side. We can do this by subtracting 3z from both sides of the equation and adding 6 to both sides of the equation:

4z - 3z = 9 + 6

Simplifying gives us:

z = 15

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Step-by-step explanation:

a) To form a committee of 8 with 3 prefects, we need to choose 3 prefects from the 5 available prefects, and 5 non-prefects from the remaining 7 boys. We can do this by using the combination formula:

Number of ways = (Number of ways to choose 3 prefects) × (Number of ways to choose 5 non-prefects)

Number of ways to choose 3 prefects from 5 = C(5, 3) = 10

Number of ways to choose 5 non-prefects from 7 = C(7, 5) = 21

Therefore, the total number of committees of 8 with 3 prefects that can be formed is:

Number of ways = 10 × 21 = 210

b) To form a committee of 8 with at least 3 prefects, we need to consider two cases: one where we choose exactly 3 prefects, and one where we choose all 5 prefects. We can calculate the number of ways for each case using the combination formula:

Number of ways to choose exactly 3 prefects and 5 non-prefects = C(5, 3) × C(7, 5) = 210

Number of ways to choose all 5 prefects and 3 non-prefects = C(5, 5) × C(7, 3) = 35

Therefore, the total number of committees of 8 with at least 3 prefects that can be formed is:

Number of ways = (Number of ways to choose exactly 3 prefects and 5 non-prefects) + (Number of ways to choose all 5 prefects and 3 non-prefects)

Number of ways = 210 + 35 = 245