Find X and Y.
TEACHING TEXTBOOKS GEOMETRY

7.21

The Pythagoras theorem allows us to solve for unknown sides of right triangles.

Right Triangles

Right triangles are triangles that have one 90-degree angle (aka a right angle). The side directly across from the right angle is called the hypotenuse. The hypotenuse is always the longest side of a triangle. The other 2 sides of a right triangle are called the legs of the triangle.

Pythagorean Theorem

The Pythagorean theorem states that a² + b² = c², where a and b are the legs of the triangle and c is the hypotenuse. To find the missing side we can plug in the values we know and solve for b.

Then, subtract 12² from both sides.

Finally, take the square root of both sides. When you square root a number, the resulting value is plus or minus, but since we are finding a distance, we will only take the positive answer.

The verification of the given trig identity is shown in below.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

⇒ (1 - sin x) / (1 + sin x) = (sec x - tan x)²

Now, We can simplify as;

⇒ (1 - sin x) / (1 + sin x) = (sec x - tan x)²

LHS;

⇒ (1 - sin x) / (1 + sin x)

⇒ (1 - sin x) (1 - sin x) / (1 + sin x) (1 - sin x)

⇒ (1 - sin x)² / (1 - sin²x)

⇒ (1 - sin x)² / cos²x

⇒ ( (1 - sin x )/ cos x )²

RHS;

⇒ (sec x - tan x)²

⇒ ( 1/cos x - sin x / cos x)²

⇒ ( (1 - sin x) / cos x )²

Hence, We get;

⇒ (1 - sin x) / (1 + sin x) = (sec x - tan x)²

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The mean for the low income group is the average of all the values in the group.

It is calculated by adding up all the values and then dividing by the total number of values. In the low income group, the mean is calculated by adding up all the incomes, and then dividing by the total number of people.

The median for the low income group is the middle value when all the values are arranged in order. To calculate the median, first arrange the incomes in order from lowest to highest, and then find the middle value.

The standard deviation for the low income group is a measure of how spread out the values are. It is calculated by taking the square root of the variance, which is calculated by taking the average of the squared difference between each value and the mean, and then dividing by the number of values.

The mean for the high income group is the average of all the values in the group. It is calculated by adding up all the values and then dividing by the total number of values. In the high income group, the mean is calculated by adding up all the incomes, and then dividing by the total number of people.

The median for the high income group is the middle value when all the values are arranged in order. To calculate the median, first arrange the incomes in order from lowest to highest, and then find the middle value.

The standard deviation for the high income group is a measure of how spread out the values are. It is calculated by taking the square root of the variance, which is calculated by taking the average of the squared difference between each value and the mean, and then dividing by the number of values.

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If the  height of the football could be described by the model: f(x) = -16x² + 64x , then the time at which the ball at its highest point after being kicked is t = 2 seconds .

In order to find time at which ball is at its highest point,

we have to find the time at which the derivative of height function is = 0.

the height function is ⇒ f(x) = -16x² + 64x ;

So , the derivative of the height function will be :

⇒  f'(x) = -32x + 64 ;

equating the derivative of height function to 0 , and solving for x ,

we get ;

⇒ -32x + 64 = 0

⇒ -32x = -64

⇒ x = 2

Therefore , the time at which the ball is at its highest point is 2 seconds .

The given question is incomplete , the complete question is

Justin punts a football. The height of the football could be described by the model: f(x) = -16x² + 64x. h describes the height of the ball in feet and the time in seconds after the ball was kicked.

At what time in seconds is the ball at its highest point after being kicked ?

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Answer:

A ≈ 34.91 m²

Step-by-step explanation:

the area (A) of the sector is calculated as

A = area of circle × fraction of circle

  = πr² × [tex]\frac{40}{360}[/tex] ( r is the radius )

  = π × 10² × [tex]\frac{1}{9}[/tex]

  = [tex]\frac{100\pi }{9}[/tex]

  ≈ 34.91 m² ( to 2 decimal places )

Answer:

(round 35m²)

Step-by-step explanation:

360° : 40° = 9  

Area of Circle Formulas · Area = π × r2, where 'r' is the radius

Area = π × r2

Area = π × 10²

Area = π × 100

Area = 3.14 × 100

Area = 314 m²

314 : 9 = 34.88m² (round 35m²)

well, let's first find out how many cups was that in 24 hours anyhow.

so in 1hr the hose leaks 0.25 cups, so in 24 hrs that'd be (24)(0.25) = 6 cups.

Since a gallon has 16 cups, that'd be 6/16 gallons or 3/8 = 0.375 of a gallon.

Please find attached the image of the enlargement of the shape X by a scale factor of -1 created using MS Word, which is a drawing equivalent to option B. The correct option is therefore;

B.

An enlargement transformation is one in which the pri-image object size is scaled about a center of enlargement, using a scale factor, with the sign of the scale factor indicating the direction of the enlargement, which for a +ve sign is on the same side, and for a -ve sign is on the other side of the center of enlargement.

An enlargement by a scale factor of -1, can be obtained by producing the image on the alternate side of the center of enlargement, which with a scale factor of -1, is the same size as the size of the image.

Therefore, the dilation by a scale factor of -1, with the center at the origin, produces an image which is equivalent to a reflection of the original object (pre-image), across the y-axis followed by a reflection across the y-axis.

The image of the object following the dilation will therefore be the mirror image of the mirror image of the object reflected across the y-axis, which takes the shape of a vertically flipped, left flipped F, which is option B

Please find attached a drawing of the shape of the image of the enlargement of shape X by a scale factor of -1, created with MS Word

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The number of hours that Jenny drove in her new car is 3.2 hours

The speed is 62 miles

The distance is 198.4 miles

The number of hours can be calculated as follows

speed= distance/time

62= 198.4/x

cross multiply both sides

62x= 198.4

x= 198.4/62

x= 3.2

Hence the number of hours that Jenny drove is 3.2 hours

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Answer:

opposite angles are equal and parallel

Answer:

Yes, the friend is correct in finding the sum of -3.7 + (-0.25) = 3.95.

To find the sum, the friend first takes the absolute value of each number (ignoring the negative sign) to find that the absolute value of -3.7 is 3.7 and the absolute value of -0.25 is 0.25.

Then, the friend adds the absolute values of the numbers (3.7 + 0.25) to get 3.95 which is the final answer.

The order of operation is correct and the arithmetic is also correct, so the final result is the correct sum of the two given numbers.

The information shows that Larry is incorrect as a composite number is a positive integer that has at least one positive divisor.

It should be noted that composite numbers are those numbers that have more than two factors. Composite numbers have factors other than 1 and itself

Larry is incorrect. A composite number is a positive integer that has at least one positive divisor other than one and itself. For example, 4 is composite because it can be divided by 2 (and 1). However, a number's ones place simply refers to the digit in the units place and has no bearing on whether a number is prime or composite.

For example, the number 22 is composite because it is divisible by 2 and 11, but the number 12 is composite because it is divisible by 2,3,4 and 6.

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Due to the lack of a common ratio, the above sequence is not geometric.

A series of integers with a common ratio is referred to as a geometric sequence. A geometric sequence has a next number that is a multiple of the one before it.

if the sequence is geometric.the common ratio of the number's

-1, 1, 4, 8, are

-1/1 = -1 ratios of the numbers in the sequence

4/1 = 4

8/4 = 2

There isn't a ratio that unites the numbers.

The lack of a common ratio leads us to the conclusion that the presented sequence is not geometric.

Due to the lack of a common ratio, the above sequence is not geometric.

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The factored expression to the expression is (4y + 1)(y + 6)

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

4 y2 + 25 y + 6

Express properly

So, we have the following representation

4y² + 25 y + 6

Expand the expression

This gives

4y² + 24y + y + 6

Next, we factor the expression

4y(y + 6) + 1(y + 6)

Factor out y + 6

(4y + 1)(y + 6)

Hence, the solution is (4y + 1)(y + 6)

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a. The angular velocity of the ball is 1.57rad/sec

b. The angular acceleration of the bicycle is 0.23 rad/sec²

angular is the rate of change of angular distance . it is measured in rad/sec. it is represented by w. Angular acceleration is the rate of change in angular velocity with time.

angular velocity = change in angle/ time

w = 2π/t

w = 2× 3.14/4

w = 6.28/4

w = 1.57 rad/sec

angular acceleration =( final angular velocity - initial angular velocity )/time

= (4.2 - 3.5)/3

= 0.7/3

= 0.23 rad/s²

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The breaking of number using addition is discussed above.

Given is the breaking apart of numbers with addition.

We can breaking apart the numbers with addition as follows. Assume the number to be 50. We can break the number 50 as follows -

50 = 25 + 25

50 = 15 + 10 + 15 + 10

50 = 10 + 10 + 10 + 10 + 10

50 = 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5

Therefore, the breaking of number using addition is discussed above.

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Answer:

The machine makes 45 bottles per minute.

Step-by-step explanation:

We can first find the slope through this equation: [tex]\frac{y2-y1}{x2-x1}[/tex]

Since we are given two points, (2,90) and (7,315), we can plug those two points into the formula given above:

[tex]\frac{315-90}{7-2}[/tex]

= 45

Therefore, m = 45.

Now, we can pick one of the two points given--in this case, I'll use (2,90)--to find the equation of the line: [tex]y-y1 = m(x-x1)[/tex]

For (2,90), y1 will be 90, and x1 will be 2. Let's also plug in m:

y - (90) = 45(x - 2)

We can solve for y now to find what y=mx+b is:

y = 45(x-2) + 90

y = 45x

Since the problem asks how many bottles the machine can make per minute, we can plug x = 1: 45(1) = 45

The machine makes 45 bottles per minute.

Answer:

Hi, I'm Za'Riah! I will gladly assist you with your problem. (see explanation)

Step-by-step explanation:

The answer is C

Hope this helped!

Answer:

14 dollars

Step-by-step explanation:

They vary in direct proportion

Thus; If 15 copies = 6dollars

35 copies = (35 × 6) ÷ 15

= 210 ÷ 15

= 14

It would cost 18$

Every fifteen copies you have to pay 6$, and since 35 is 3 times 15, it would also be 3 times the price, or 6 * 3$ which equals 18$

The volume of solid generated when region s is revolved about the horizontal line y is 93.04919.

We have to find the volume of the solid generated when region s is revolved about the horizontal line y.

As shaded region is revolved around y = -3.

Outer radius = f(x) + 3

Inner radius = g(x) + 3

Width = dx

Thus small volume "dv" formed when shaded region in above diagram is revolved around y = -3.

dv = π[tex](f(x) + 3)^3[/tex]dx - π[tex](g(x) + 3)^2[/tex]dx

dv = π([tex]f^2[/tex](x) + 6f(x) + 9)dx - π([tex]g^2[/tex](x) + 6g(x) + 9)dx

dv = π([tex]f^2[/tex](x) + 6f(x))dx - π([tex]g^2[/tex](x) + 6g(x))dx

Now integrating on both side:

[tex]\int dv=\pi\int^{3}_{0}9(1+x)\cos(\pi x/6) + 6\int^{3}_{0}f(x)dx-\pi\times 5.32021-6\times3.24125[/tex]

Using the provided result or a scientific calculator, the entire definite integral was discovered.

v = π × 25.54298 + 6 × 8.16083 - π × 5.32021 - 6 × 3.24125

v = 93.04919

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The complete question is given below:

The total distance of the trip Ella's family took is 700 miles.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, Ella slept through the last 14% of the trip.

So, Before Ella fell to asleep they covered (100 - 14)% = 86% of the trip.

Let The total distance be 'x'.

Therefore, 602 miles is 86% of 'x' which can be numerically expressed as,

(86/100)×x = 602.

0.86x = 602.

x = 602/0.86.

x = 700 miles.

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Answer:

.................................................................................

Step-by-step explanation:

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Applying proportion, 2520 ounces of solution Z will contain 44040 ounces of ingredient a.

To determine the number of ounces of ingredient a in 2520 ounces of solution Z, we need to first calculate the proportion of ingredient a in solutions X and Y, and then use that information to determine the proportion of ingredient a in solution Z.

Solution X contains 2 ounces of ingredient a and 3 ounces of ingredient b in one ounce of solution, so the proportion of ingredient a is 2/(2+3) = 2/5.

Solution Y contains 1 ounce of ingredient a and 2 ounces of ingredient b in one ounce of solution, so the proportion of ingredient a is 1/(1+2) = 1/3.

Solution Z is created by mixing solutions X and Y in a ratio of 3:11, so 3 ounces of solution X are mixed with 11 ounces of solution Y.

Thus, the proportion of ingredient a in solution Z = (32/5) + (111/3) = 6/5 + 11/3.

To find out the number of ounces of ingredient a in 2520 ounces of solution Z, we need to multiply the proportion of ingredient a with the number of ounces of solution Z

2520 * (6/5 + 11/3) = 2520 * (6/5 + 11/3) = 2520 * (252/15 + 11/3) = 2520 * (16+11/3) = 2520 * (16+11/3) = 2520 * (16+11/3) = 2520 * (16+37/3) = 2520 * (16+37/3) = 2520 * (53/3) = 252053/3 = 252017.66666 = 44040 ounces of ingredient a.

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The range of values of x which satisifies both of the inequalities is:

(-3, 2)

Here we have two inequalities:

3 + x < 5

8 + x > 5

And we want to see which range of values of x satisfie both of these inequalities.

If we isolate x on both inequalities, we will get:

3 + x < 5

x < 5 - 3

x < 2

And the other one is:

8 + x > 5

x > 5 - 8

x > -3

Then we havethe compound inequality:

x < 2

x > -3

Then the range of values that satisfies both inequalities is (-3, 2)

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Answer:

Step-by-step explanation:

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis).

Given that the slope of the line is m = 4/6, we can substitute it into the equation.

We know that the line passes through the point (1, -1), so we can use that point to find the value of b.

Plugging in the point (1, -1) into the equation, we get:

-1 = (4/6)(1) + b

Solving for b, we get:

b = -1 - (4/6) = -1 - 2/3 = -5/3

So the equation of the line is:

y = (4/6)x - (5/3)

which can be rewritten as

y = (2/3)x - (5/3)

this line is the equation of the line you are looking for.

Answer:

Y--1=m(x-1) this is the rule of the equation of straight line

The measure of the angle m∠GEH  = 33° for the given Quadrilateral EFGH which is a rectangle.

Examples:

For this stated question:

In the rectangle EFGH.

m∠FEG=57°

Then,

m∠FEG + m∠GEH  = 90 (complimentary angles)

57° + m∠GEH  = 90

m∠GEH  = 90 - 57

m∠GEH  = 33°

Thus, the measure of the angle m∠GEH  = 33° for the given Quadrilateral EFGH which is a rectangle.

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The tenth term of the given arithmetic sequence is; -49

The formula for the nth term of an arithmetic sequence is;

aₙ = a + (n - 1)d

where;

a is first term

d is common difference

From the given sequence, we see that;

a = -13

d = -17 - (-13)

d = -17 + 13

d = -4

Thus, the tenth term of the arithmetic sequence is;

a₁₀ = -13 + (10 - 1)-4

a₁₀ = -13 -36

a₁₀ = -49

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The length of the segment PS is 100 units.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.

From the given image we can see that the segments PT, PQ, and TQ form a right- angled triangle PQT.

Applying Pythagorean theorem to this triangle we have:

PQ^2 + TQ^2 = PT^2

(45)^2 + (TQ)^2 = (53)^2

2025 +  (TQ)^2 = 2809

(TQ)^2 = 2809 - 2025

(TQ)^2 = 784

TQ = 28

Similarly, segments PR, PS, and SR form a right-angled triangle PRS, where TQ = SR = 28 and PR = 96.

Applying Pythagorean theorem to this triangle we have:

PR^2 + SR^2 = PS^2

(96)^2 + (28)^2 = (PS)^2

(PS)^2 = 9216 + 784

(PS)^2 = 10000

PS = 100

Hence, the length of the segment PS is 100 units.

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The function is  y = 1500[tex](0.985)^t[/tex].

What is function?

A mathematical function , rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Here initial population is 1500 .

Rate of decrease = 1.5%

Number of years = 10

After 10 years , the end population = 1290.

Now using formula,

=> P = [tex]P_0[/tex][tex](1-\frac{r}{100})^n[/tex]

Here number of deer, y, in this population at the end of t years then

=> y = 1500[tex](1-\frac{1.5}{100})^t[/tex]

=> y = 1500[tex](1-0.015)^t[/tex]

=> y = 1500[tex](0.985)^t[/tex]

Hence the function is y = 1500[tex](0.985)^t[/tex].

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Answer:

x = 60.4

Step-by-step explanation:

First, let's remember the three different trigonometric functions: sine, cosine, and tangent. In this case, we would use cosine because the adjacent side to the angle and hypothenuse are used/given.

[tex]cos(22) = \frac{56}{x}[/tex]

We need to set up a proportion because there is not much else you could do here.

[tex]\frac{cos(22)}{1} =\frac{56}{x}[/tex]

Then, cross-multiply.

[tex]cos(22) * x = 56[/tex]

Finally, divide both sides by cos(22). You'll probably need your calculator and make sure it's in degrees mode and not radians!

[tex]\frac{cos(22) * x}{cos(22)} = \frac{56}{cos(22)}[/tex]

[tex]x = 60.4[/tex]

Rounded to the nearest tenth, x = 60.4.

From the inequalities 30x + 20y ≤ 200 and x + y ≥ 6, Roger can buy 3 pants and 3 shirts.

An equation is an expression that shows the relationship between numbers and variables.

Inequalities is used for the non equal comparison of these numbers and variables.

Let x represent the number of pants that Roger buys and y represent the number of shirts he buys.

He can buy pants for $30 and shirts for $20. Roger received $200 for his birthday, therefore:

30x + 20y ≤ 200    (1)

Also:

He wants at least 6 new items. hence:

x + y ≥ 6    (2)

From both equations, the solution to these equalities is (3, 3)

Roger can buy 3 pants and 3 shirts.

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