Factor and solve 121r^2-64t^2

Step-by-step explanation:

when defined like this, we remember that when the right-angled triangular is inscribed into a circle, sine of an angle is the length of the opposite side of the angle divided by the radius. while cosine of the same angle is the adjacent side divided by the radius.

so, sin(angle) = 12/13 makes us imagine a circle of radius 13, and the side (or leg) opposite of the angle is 12.

now, Pythagoras tells us

c² = a² + b²

c being the Hypotenuse (which is the radius in our scenario), a and b are the legs.

13² = 12² + second leg²

169 = 144 + second leg²

second leg² = 25

second leg = 5

so,

cos(theta) = 5/13

tan(theta) = sin(theta) / cos(theta) =

= 12/13 / 5/13 = (12×13)/(5×13) = 12/5

sin²(theta) + cos²(theta) = (12/13)² + (5/13)² =

= 144/169 + 25/169 =

= 169/169 = 1

sec²(theta) - tan²(theta) =

= (1/cos(theta))² - (12/5)² =

= (1 / 5/13)² - 144/25 = (13/5)² - 144/25 =

= 169/25 - 144/25 = 25/25 = 1

Answer:

------------------------------

The binomial coefficients can be found using Pascal's triangle.

Remember the rows are numbered starting from the second one on the top, and the first element is skipped in every row.

For the first one, follow the 11th row and 6th column, it is number 462, and for the second one follow the 4th row and 1st column, this is number 4, see the attached for both.

Calculation of the binomial coefficient is as follows:

The mean and standard deviation (in ) of the sampling distribution of the difference in sample means [tex]\sigma_1[/tex] -  [tex]\sigma_2[/tex] = (7)² ÷100+ 6² /150.

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

Given:

Level A:

S.D. = 7

Level B: Mean = 20

S.D. = 6

So, [tex]\nu_1[/tex] = 22

[tex]\nu_2[/tex] = 20

Then,  [tex]\nu_1[/tex] - [tex]\nu_2[/tex]   = 22-20=2

and, [tex]\sigma_1[/tex] -  [tex]\sigma_2[/tex]

= (7)² ÷100+ 6² /150

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Yes, there is a transformation that maps shape I onto shape IV. If the figure I is reflected over the x-axis, we get figure IV.

In mathematics, a transformation is a function or a mapping that takes a set of inputs and produces a new set of outputs.

Transformations can be applied to geometric shapes, functions, and other mathematical objects to change their properties or positions.

There are various types of transformations that can be performed in mathematics, including translation, rotation, reflection, dilation, and more. Each type of transformation has its own specific rules and properties that dictate how it affects the original object.

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Full Question:

See the attached Image

Answer:

not true:

3. AD = DC      

4. YZ = XW

explanation:

lower base is only congruent to upper base.

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

Also what you picked

The solution of the expression is ( 4 + √3 / x) ( 4 + √13 / x).

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The given expression is 4 + √(3x⁻²) and 4 + √(13⁻²). The expression will be solved as,

E = {[4 + √(3x⁻²)]} { {4 + √(13x⁻²).]}

E =  {4 + [√3 / √x²]  { [4 + √13 / √x²]}

E = ( 4 + √3 / x) ( 4 + √13 / x).

Therefore, the solution of the expression is ( 4 + √3 / x) ( 4 + √13 / x).

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Answer:

Square and Rectangle

Answer:

3/8

Step-by-step explanation:

75% of 1/2

3/4 of 1/2

3/4x1/2

3/8

Answer:

$52

Step-by-step explanation:

Sebastian spent $120 on the airline ticket and $55 * 4 = $<<55*4=220>>220 on the hotel.

So, he spent a total of $120 + $220 = $<<120+220=340>>340 on the airline ticket and hotel.

He has $600 - $340 = $<<600-340=260>>260 left to spend.

He plans to be on the trip for 5 days, so he can spend $260 / 5 = $<<260/5=52>>52 per day.

The volume of the cylinder is 180π cm³.

What is volume ?

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

Volume is a measurement of three-dimensional space that is occupied. Numerous imperial or US customary units, as well as SI-derived units (such the cubic meter and liter), are frequently used to quantify it numerically (such as the gallon, quart, cubic inch). Volume and length (cubed) have a symbiotic relationship.

As diameter = 6cm

We know that radius is half of diameter

∴ radius = 3 cm

height = 20 cm

Volume = π r² h

             = π (3)²×20  

             = π × 9 × 20

             = 180 π cm³

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The number of miles was each of Jerry’s flights travel is 240 miles.

A mile is characterized as the unit of length, which is precisely equivalent to 5280 feet, or 1760 yards, and normalized as precisely 1609.344 meters by the Peaceful accord in 1959. The biggest unit is generally used to quantify the distance between places that are not even close to one another.

Jerry flew 6 flights each month.

Total flights in 3 months = 3(6) = 18 flights

Let distance traveled in each flight be x

Then,

18x = 4320 miles

x = 4320/18

x = 240 miles

Thus, each flight flow 240 miles.

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6 shapes can be drawn by the given code.

Shapes in mathematics specify an object's boundaries or contour. Depending on their characteristics, the forms can be divided into many types. The shapes are typically enclosed by an outline or boundary that is composed of points, lines, curves, etc. Geometric figures and figures composed of fixed lines or curves are other names for forms. There are two types of shapes: closed shapes and open shapes. Examples of shapes in daily life are the Sun, Earth, Doors, Windows, Watches, Wall Clocks, and so forth.

Given

Codes are def draw shapes( centerx , centery, radius, points, color): star(centerx, centery, radius, points, fill.

6 shapes can be drawn by the given code.

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The required compatible number of the given two number are 500 and 200 and sum is 700.

In math, compatible numbers are the numbers that are not difficult to add, deduct, duplicate, or gap intellectually. compatible number  are close in worth to the real numbers that make assessing the response and figuring issues more straightforward. We can adjust the numbers to the closest ten, hundred, thousand or 10,000 to make them viable numbers. For example, in the event that we need to add 493 and 549, we can make the numbers viable by gathering them together to the closest tens or hundreds. 490 and 550 (adjusted to the closest tens) or 500 and 500 (adjusted to the closest hundreds) are a lot simpler to settle.

So, the compatible number of 455 is 500 and that of 225 is 200.

Then,

Compatible sum = 500 + 200 = 700.

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To have enough money to buy the radio, Jessica will have to babysit for 32 hours

From the question, we have the following parameters that can be used in our computation:

Earnings = $35 for 7 hours

This means that the hourly rate can be calculated as

Hourly rate = $35/7 hours

Using the above as a guide, we have the following:

Evaluate the quotients

Hourly rate = $5 per hour

The number of hours Jessica will have to babysit is calculated as

Number of hours = 160/Hourly rate

Substitute the known values in the above equation, so, we have the following representation

Number of hours = 160/5

Evaluate

Number of hours = 32

Hence, the number of hours is 32

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Therefore, the given  area of the slice which is covered with chocolate = 276.57 c[tex]m^{2}[/tex]

Area is a mathematical notion that describes the size of a region on a planar or curved surface. A surface area is the area of an open surface or the border of a three-dimensional object, whereas a plane region's or plane's area's refers to a shape's or planar lamina's area.

Here,

Given :

circular cake radius = 12 cm

circular cake height = 7 cm

thus,

the area of the slice which is covered with chocolate = θ/360 *π[tex]r^{2}[/tex]

=> 22/360 * 3.14 *12*12

=> 22/360 * 3.14 *144

=>69.08/360 * 144

=> 276.57 c[tex]m^{2}[/tex]

Therefore the given  area of the slice which is covered with chocolate = 276.57 c[tex]m^{2}[/tex]

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After solving the equation, the number of hours obtained is that after 2 hours, the cost ends up being the same for either artist.

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given information in the question,

Booking fee of Martha = $10

Additional hourly charge of Martha = $40

Then, the equation will be,

y = $10 + $40x            (i)

Here, y is the total cost and x is the number of hours.

Booking fee of Jackie = $20

Additional hourly charge of Jackie = $35

Then, the equation for this will be,

y = $20 + $35x           (ii)

Here, y is the total cost and x is the number of hours.

Then, depending on the length of the show, the cost could end up being the same for either artist.

So,

From equations (i) and (ii)

$20 + $35x =  $10 + $40x  

20 - 10 = 40x - 35x

5x = 10

x = 2 hours

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We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100. 0.5% of employees walk to work.

A % is a quantity or ratio that, in mathematics, represents a portion of one hundred.

A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.

The symbol "%" is frequently written after the number to indicate percentages.

We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.

Given,Employees who use;

Car: 758

Bus: 530

Walk: 7  

Other: 105

Total = 758+530+7+105 = 1400

Employees percentage who walk to work

=No of employees who walk /Total number*100

Percentage =700/1400 =0.5%

0.5% of employees walk to work.

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Answer:

(D) 52

Step-by-step explanation:

sum up correct answers from questions 1, 2 and both 1 and 2 incorrect this time therefore we have --> 18+23+11=52 students

You could also do a Venn diagram to understand this better with 8 being the intersection of students who goth both 1 and 2 correct and 11 being left out as the number of students who got both questions incorrectly.

Let y be the number of people that will attend the conference as a function of x. The given information tells us that when x = 0 (the admission price is $400), y = 1000. Additionally, for each $5 reduction in price, an additional 20 people will attend.

We can express this relationship as a function as follows:

This function tells us that the number of people that will attend the conference is equal to 1000, plus an additional 20 people for each $5 reduction in price (represented by the variable x).

For example, if the admission price is reduced by $10 (x = 2), the number of people that will attend the conference is given by:

y = 1000 + 20(2)

y = 1000 + 40

y = 1040

So, if the admission price is reduced by $10, 1040 people will attend the conference.

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The  shape of the sampling distribution of p hat is approximately Normal, because we would expect at least 10 success and 10 failures

The probability distribution of a statistic that is acquired by repeated sampling of a particular population is called the sampling distribution. It outlines a variety of potential possibilities for a statistic, such as the mean or mode of a population's mean or mode of some variable.

approximately Normal, because we would expect at least 10 success and 10 failures. because they are dividing three times a week

A typical probability distribution in the natural world is the normal distribution, sometimes known as the bell curve. When the sample size is high enough, scientists often assume that a sequence of measurements obtained from a population would be regularly distributed.

The complete question is : A large university with over 40,000 students recently took a survey in which 31% of the students claimed to exercise at least 3 times a week. A simple random sample of 250 students was selected. Let p hat = the proportion of students in the sample who claimed to work out at least 3 times a week. What is the shape of the sampling distribution of p hat and why?

A. approximately Normal, because all sampling distributions are approximately Normal

B. approximately Normal, because we would expect at least 10 success and 10 failures

C. skewed to the right, because 0.31 is lower than 0.5

D. skewed to the left, because 0.31 is lower than 0.5

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The equation of the regression line is y=-30.27+0.449x and predicted number of absences when the temperature is 910= 10.589

See table for sum of values.

The regression equation is:

y=α+βx

β = [tex]\frac{Sxx}{Syy}[/tex]=6995-97799779[tex]\frac{6995-9\times\frac{779}{9}\times\frac{77}{9}}{68613-9(\frac{779}{9} )2}[/tex]= 0.449

α=y-βx= 779-(0.449)7799 = =-30.27

The equation is y=-30.27+0.449x

Where y = predicted variable; x = independent variable = 0.449; - 30.27 = intercept/ slope

Constructing a 91% prediction interval for y:

x = 910

Inputting x = 91 into the regression equation : y = 0.449(91) - 30.27

y = 40.859 - 30.27 = 10.589

Prediction interval = y pm error margin

To save computing time, error margin (E) can be obtained using the online error margin calculator.

Obtained error margin (E) value = 2.3398

(10.589- 2.3398, 10.589+ 2.3398)

(8.2492, 12.9288)

(8, 13)

The equation of the regression line is y=-30.27+0.449x and predicted number of absences when the temperature is 910= 10.589

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Alona is using a quantitative approach to her studies.

The goal of quantitative research is to quantify the data collection and processing process.

It is based on a deductive method that emphasizes the validation of the hypothesis and is influenced by positivist and empiricist theories.

This research technique, which is related to the natural, applied, formal, and social sciences, encourages the unbiased empirical exploration of observable phenomena to test and comprehend correlations.

This is accomplished using a variety of quantification techniques and procedures, demonstrating the wide application of this approach as a research strategy across numerous academic fields.

So, in the given situation, Alona is using the quantitative research method.

Therefore, Alona is using a quantitative approach to her studies.

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Answer:

16

mark me brainliest

Step-by-step explanation:

The system of linear equations, that models the problem is represented  as x = 2 and 64x + 132y = 1040 while the cost of adult and student tickets is $8 and $4 respectively.

The system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1.

Let;

a)

x = 2y ...eq(i)

64x + 132y = 1040 ...eq(ii)

b)

From equation (i)

64(2y) + 132y = 1040

y = 4

Put y = 4 into equation (i)

x = 2(4)

x = 8

The cost of adult ticket is $8 and student ticket is $4

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Answer:

c.  g(x) = h(x)

Step-by-step explanation:

Given functions:

[tex]f(x) = 3^x+11[/tex]

[tex]g(x)=2^{3x+5}[/tex]

[tex]h(x)=32(8^x)[/tex]

Rewrite function g(x) using exponent rules.

[tex]\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c:[/tex]

[tex]\implies g(x)=2^{3x} \cdot 2^5[/tex]

[tex]\implies g(x)=2^{3x} \cdot 32[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c:[/tex]

[tex]\implies g(x)=(2^3)^{x} \cdot 32[/tex]

[tex]\implies g(x)=8^{x} \cdot 32[/tex]

[tex]\implies g(x)=32(8^{x})[/tex]

Therefore, g(x) = h(x).

Step-by-step explanation:

To solve an equation for a variable, you can isolate the variable by performing operations that eliminate all other terms.

In this case, the given equation is 2x^2/y = w + 2/4. To solve for w, you can first eliminate the 2/4 term on the right-hand side by multiplying both sides of the equation by 4/2:

4 * (2x^2/y) = 4 * (w + 2/4)

4 * 2x^2/y = 4w + 4 * 2/4

8x^2/y = 4w + 2

Then, you can subtract 2 from both sides to eliminate the 2 on the right-hand side:

8x^2/y - 2 = 4w + 2 - 2

8x^2/y - 2 = 4w

Finally, you can divide both sides of the equation by 4 to eliminate the 4 on the right-hand side:

(8x^2/y - 2) / 4 = (4w) / 4

w = 8x^2/7 - 2

Therefore, the correct answer is w = 8 x squared minus 2 y Over y. This is an equivalent equation to find w, as it gives the same value for w as the original equation when the same values are used for x and y.

The other equations given are not equivalent to the original equation for finding w.

We can solve the question using the concept Polynomial functions. The value of f(1) is 6 and f(2) is -7.

In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1. A function that can be expressed as a polynomial is referred to as a polynomial function. A polynomial equation's definition can be used to derive the definition. A polynomial is typically denoted by P. (x). The degree of the variable in P(x) is its maximum power. The degree of a polynomial function is crucial because it reveals how the function P(x) will behave when x is very large. Whole real numbers make up a polynomial function's domain (R).

Given f(x)=-5x2 + 2x + 9

      f(1)=-5(1)2+2(1)+9

      ∴f(1)=6

      f(2)=-5(2)2+2(2)+9

     ∴f(2)=-7

We can solve the question using the concept Polynomial functions. The value of f(1) is 6 and f(2) is -7.

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Answer:

2 : 18

Step-by-step explanation:

to find equivalent ratios , multiply or divide each part of the ratio by the same numeric value.

1 : 9 ( multiply both parts by 2 )

= 2 : 18

or

1 : 9 ( multiply both parts by 3 )

= 3 : 27

and so on...

Answer:

  48 m

Step-by-step explanation:

You want to know the distance XY between tangent points on a segment tangent to two circles that are externally tangent to each other. The circles have radii 18 m and 32 m.

As shown in the attachment, a segment parallel to XY joining segments PX and QY can form a right triangle whose hypotenuse is the sum of the radii, and whose short leg is the difference of the two radii. The length of XY is the unknown leg of the right triangle, and can be found using the Pythagorean theorem.

  a² +b² = c²

  14² +b² = 50²

  b² = 50² -14² = 2304

  b = √2304 = 48

The length of XY is 48 meters.

__

Additional comment

In this geometry, the length XY is twice the geometric mean of the two radii. XY = 2√(18·32) = 48.