Triangle ABC ~ triangle DEF. Use the image to answer the question.
Determine the measurement of DF.
DF = 1.58
DF = 1.52
DF = 1.1
DF = 5.5

(Use Image Added)

[tex]\cos^{-1}(\tan(-\pi/4)) = \pi[/tex]

[tex]\tan(-\pi/4)[/tex]

[tex]= -\tan(\pi/4)[/tex]

[tex]= -1[/tex]

So [tex]\cos^{-1}(\tan(-\pi/4))[/tex]

[tex]= \cos^{-1}(-1)[/tex]

[tex]=\pi[/tex]

These functions are called the inverse trigonometric functions. The function [tex]\cos^{-1}(x)[/tex] called arc cosine of x is a function whose domain is [-1,1] and which for a given value of x, gives the angle in the interval [tex](0,\pi)[/tex], whose cosine is x. Similarly the function [tex]\sin^{-1}(x)[/tex] called arc sine of x is a function whose domain is [-1,1] and which for a given value of x, gives the angle in the interval [tex][-\pi/2,\pi/2][/tex], whose sine is x, and the function [tex]\tan^{-1}(x)[/tex] called arc cosine of x is a function whose domain is [tex](-\infty,\infty)[/tex] and which for a given value of x, gives the angle in the interval [tex][-\pi/2,\pi/2][/tex], whose tangent is x.

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The value of [tex] {cos}^{ - 1} ( tan (- \frac{\pi}{4} ))[/tex] is π.

What are the functions?

The function cos(x) called arc cosine of x is a function whose domain is [-1,1] and which for a given value of x, gives the angle in the interval (0, T), whose cosine is x. Similarly the function sin ¹(x) called arc sine of x is a function whose domain is [-1,1] and which for a given value of x, gives the angle in the interval [-π/2, π/2] whose sine is x, and the function tan 1(x) called arc cosine of x is a function whose domain is (-∞, ∞) and which for a given value of x, gives the angle in the interval [-π/2, π/2], whose tangent is x.

Here given expression is [tex] {cos}^{ - 1} ( tan (- \frac{\pi}{4} ))[/tex]

Now, [tex]tan( - \frac{\pi}{4} ) \\ = - tan \frac{\pi}{4} \\ = - 1[/tex]

So,

[tex] {cos}^{ - 1} ( tan (- \frac{\pi}{4} )) = {cos}^{ - 1}( - 1) \\ = {cos}^{ - 1}(cos\pi) \\ = \pi[/tex]

Therefore, required value of [tex] {cos}^{ - 1} ( tan (- \frac{\pi}{4} )) [/tex] is π

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The equation of the circle is (x + 9)² + (y + 8)² = 36 with a center (-9, -8) and a point (-9, -2).

The standard form of the equation of a circle:

(x - h)² + (y - k)² = r²

Here (h, k) is the center of the circle and r is the radius.

Given that the center of the circle is (-9, -8), so h = -9 and k = -8.

The distance between the center and the point on the circle:

r  = √[(-9 - (-9))² + (-2 - (-8))²]

r  = √[0² + 6²]

r  = 6

So, the equation of the circle is:

(x - (-9))² + (y - (-8))² = 6²

(x + 9)² + (y + 8)² = 36

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The complete question is follows as:

Center: (−9, −8)

Point on Circle: (−9, −2)

Find the equation of the circle.

Answer:

55.0

Step-by-step explanation:

To find the length of the ladder, we can use the Pythagorean theorem, which states that for any right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs¹.

In this case, the ladder forms a right triangle with the ground and the wall, where the ladder is the hypotenuse and the distance from the house and the height of the ladder are the legs. We can label these lengths as follows:

- c = length of ladder (hypotenuse)

- a = distance from house (leg)

- b = height of ladder (leg)

Using the Pythagorean theorem, we can write:

$$c^2 = a^2 + b^2$$

We are given that a = 33 feet and b = 44 feet, so we can plug in these values and solve for c:

$$c^2 = 33^2 + 44^2$$

$$c^2 = 1089 + 1936$$

$$c^2 = 3025$$

$$c = \sqrt{3025}$$

$$c \approx 55.0$$

Therefore, the length of the ladder should be about **55.0 feet**.

S

The unit conversion of liters to milliliters indicates that the volume that the 3.4 liters pail Juanita has is 3,400 liters

Unit conversion is the change of the measurement of a quantity to use a different scale of measurement for the same property.

The volume capacity of the pail Juanita has = 3.4 l

The unit conversion for volume indicates

The volume equivalent in ml contained in 1 liter volume = 1000 ml

1 l is the volume equivalent of 1000 ml

Therefore;

The volume equivalent of 3.4 liter capacity of the pail Juanita has is 3,400 milliliters

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y = -1x - 6

Slope (m) = 1-

You would need approximately 381.51 cubic inches of air to fill up the basketball. The correct option is 381.51.

To calculate the volume of a sphere (which a basketball is approximately shaped like), you use the formula V = (4/3)πr³, where r is the radius (half the diameter) of the sphere.

So, the radius of the basketball would be 4.5 inches (half of 9 inches), and plugging that into the formula we get:

V = (4/3)π(4.5)³
V = (4/3)π(91.125)
V = 381.51 cubic inches

Therefore, the correct option is 381.51.

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1. The value of

x = -8

y = 100

z = 80

2. x = 5

y = 135°

Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.

x+ 88 = 180-(108+x)

x + 88 = 180-108 -x

2x = 180-88-108

2x = -16

x = -16/2

x = -8

y = 108+(-8)

= 108-8 = 100

z = x+88

= -8+88

= 88-8 = 80

2. 26x+5 = (27x)

26x-27x = -5

-x = -5

x = 5

y = 27 × 5

= 135°

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30 percent of the 10 cars in the parking lot, or 3 cars, were blue.

If 40% of the cars were silver, then the remaining percentage of cars must be split between red and blue cars. Since there were 10 cars in total, we can set up the following equation:

40% + R% + B% = 100%

where R% and B% represent the percentage of red and blue cars, respectively.

Simplifying this equation, we get:

60% = R% + B%

Since we know that there were 3 red cars, we can use this information to find the percentage of red cars:

3 cars = R% of 10 cars

R% = (3/10) x 100% = 30%

Substituting this into our equation, we get:

60% = 30% + B%

B% = 30%

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The length of WZ if XW is the angle bisector of YXZ  is 4 units

The statements from the question cam be listed as:

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

WZ = 1/2 * YZ

From the question, we have

YZ = 8

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

WZ = 1/2 * 8

Evaluate

WZ = 4

Hence, the length is 4

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Answer:

Part A:

[tex]2 {x}^{3} y = 2(x)(x)(x)(y)[/tex]

[tex]18xy = 2(3)(3)(x)(y)[/tex]

[tex]10 {x}^{2} y = 2(5)(x)(x)(y)[/tex]

[tex]90y = 2(3)(3)(5)(y)[/tex]

So the greatest common factor is 2y.

Part B:

[tex]2 {x}^{3} y - 18xy - 10 {x}^{2}y + 90y [/tex]

[tex]2xy( {x}^{2} - 9) - 10y( {x}^{2} - 9)[/tex]

[tex]2y(x - 5)( {x}^{2} - 9)[/tex]

[tex]2y(x - 5)(x - 3)(x + 3)[/tex]

Answer:

the answer should be 16, if you're looking for X that is

The Stapel scale is a type of interval scale used in survey research to measure attitudes and opinions. It is a unipolar scale with a range of numerical values, typically from -5 to +5 or -10 to +10, with a neutral point of zero in the center.

The Stapel scale is a type of interval scale that is commonly used in market research. It is a unipolar rating scale that measures attitudes and opinions towards a particular object or concept.

The scale consists of a single horizontal line, with a numerical scale ranging from -5 to +5, and a single adjective or phrase representing the concept being measured placed at one end of the line.

Respondents are asked to rate the concept by placing a mark on the line, with higher values indicating more positive attitudes or opinions and lower values indicating more negative attitudes or opinions.

The Stapel scale is often used in situations where a traditional bipolar scale (such as the Likert scale) may not be appropriate.By using the Stapel scale, researchers can gather precise and nuanced data about people's attitudes and opinions, making it a valuable tool in survey research.

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Emma would have approximately $4,723 more than Juan.

To solve given problem, we will use the formula for compound interest:

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

A = amount

P = principal investment

r = interest rate

t = number of years.

For Emma's account, we have:

P = $90,000

r = 3.375% = 0.03375 (since 3 (3/8) % is equivalent to 0.03375 as a decimal)

n = 365

t = 17 years

So, we can calculate the amount of money in Emma's account after 17 years as:

A = $90,000(1 + 0.03375/365)⁽³⁶⁵⁾⁽¹⁷⁾

A = $ 159,737.70

For Juan's account, we have:

P = $90,000

r = 3.25% = 0.0325 (since 3 (1/4) % is equivalent to 0.0325 as a decimal)

n = 1

t = 17 years

So, we can calculate the amount of money in Juan's account after 17 years as:

A = $90,000(1 + 0.0325)¹⁷

A = $155,014.93

Therefore, Emma would have more money in her account than Juan after 17 years by:

$ 159,737.70 - $155,014.93 = $4,722.77

Rounding to the nearest dollar, Emma would have approximately $4,723 more than Juan.

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Answer: First one: 1/3 Second one: 1/4 Third One: 1/4

Step-by-step explanation:

First one:

1/2 Blue marble 2/3 green marble

1/2 * 2/3 = 1/3

Second One:

1/2 odd number roll 1/2 even-numbered card

1/2 * 1/2 = 1/4

Third one:

1/2 even 1/2 odd

1/2 * 1/2 = 1/4

The area swept clean by the wiper blade is 221.128 square inches.

To find the area swept clean by the wiper blade, we can calculate the area of the sector of a circle that the blade moves through.

The radius of the circle that the blade moves through is the length of the arm, which is 19 inches.

The angle that the blade moves through is 105 degrees.

To calculate the area of the sector, we need to convert the angle to radians:

105 degrees * (π/180) = 1.8326 radians (rounded to 4 decimal places)

The area of the sector is then:

(1/2) * r^2 * θ = (1/2) * (19^2) * 1.8326 = 325.628 square inches (rounded to 3 decimal places)

However, the area swept clean by the wiper blade is not the full area of the sector, as the blade itself has a width of 11 inches. Therefore, we need to subtract the area of the triangle formed by the blade and the two radii of the sector that intersect at the blade's pivot point.

The length of one of the radii is the length of the arm, which is 19 inches. The length of the other radius is 19 - 8 = 11 inches since the blade is mounted 8 inches from the pivot point.

Using the formula for the area of a triangle:

(1/2) * base * height = (1/2) * 11 * 19 = 104.5 square inches

Therefore, the area swept clean by the wiper blade is:

325.628 - 104.5 = 221.128 square inches (rounded to 3 decimal places)

So the area swept clean by the wiper blade is approximately 221.128 square inches.

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Answer: 75

Step-by-step explanation:

The method that does not represent 6 + 6 + 6 + 6 using multiplication is 6 ÷ 4 since it represents division, not multiplication or repeated addition.

The question is asking which method does not represent 6 + 6 + 6 + 6 in terms of multiplication. The equivalent multiplication expression for 6 + 6 + 6 + 6 is 6 x 4 which is also represented as 6(4). This is because multiplication is repeated addition. The expression 6.4 is a decimal multiplication, not an integer multiplication. Therefore, it is not a correct representation of 6 + 6 + 6 + 6. However, the method that clearly does not represent 6 + 6 + 6 + 6 in terms of multiplication is 6 ÷ 4 as it expresses division, not multiplication or repeated addition as requested.

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Answer: D

Step-by-step explanation:

SSS Similarity is when all the corresponding sides are proportion or scaled.  Each of the sides have been divided by 3 (scaled by 1/3)

So yes

D.    Yes, by the SSS rule

For bought four pairs of earrings by annu and price of each being $25.00, then the average price of each pair of earrings is equals to the $20.00.

The average of a group of numbers is also known as mean of numbers. It is calculated by summing up all the numbers together and then dividing the resultant by the total number of numbers in the group. Annu bought four pairs of earrings. The price of one pair of earrings = $25.00

Also, she will get one pair free at buying four pairs of earrings. We have to determine the average price each pair of earrings. Number of pairs of earrings = 5

Total price paid by annu for earings = 4 × $25.00 = $ 100.00

That sum of prices of earings pairs = $100.00

Using the average formula, the average price = ( sum of each pair of earings prices )/total pairs of earrings she bought

[tex]= \frac{100}{5}[/tex]

= 20

Hence required value is $20.

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Complete question:

Ann bought four pairs of earrings for 25.00 each by buying 4 pairs. Received a free pair. What was the average price of each pair of earrings?

Answer:

  a) 15.75 minutes

  b) 3.54 km

Step-by-step explanation:

Given speeds to school and back of 13.5 km/h and 10.5 km/h, respectively, and a total travel time of 36 minutes, you want to know the time to ride to school, and the distance.

The ratio of times is the inverse of the ratio of speeds over the same distance. The ratio of times is ...

  time to school : time to home = 10.5 : 13.5 = 7 : 9

Then the fraction of total time it takes to get to school is ...

  (7/(7+9))·(36 min) = 15.75 min = 0.2625 hour . . . . . . . 1 min = 1/60 hour

The distance can be found from the relation ...

  distance = speed · time

  distance = (13.5 km/h)(0.2625 h) = 3.54375 km ≈ 3.54 km

It takes Torrin 15.75 minutes to ride the 3.54 km to school.

FALSE, f(x) have a greater y-intercept than g(x)  

TRUE, f(x) have a greater x-intercept than g(x)

FALSE, f(x) have a greater slope than g(x)

The equation of the line in the table is written

To find the equation of the line passing through two points, we can use the point-slope form of the equation of a line:

y - y1 = m(x - x1)

where

(x1, y1) are the coordinates of one point on the line,

m is the slope of the line, and

(x, y) are the coordinates of any other point on the line.

Let's use the points (-5, -22) and (1, 14) to find the equation of the line:

First, we need to find the slope of the line:

m = (y2 - y1) / (x2 - x1)

m = (14 - (-22)) / (1 - (-5))

m = 36 / 6

m = 6

Now we can use one of the points and the slope to write the equation of the line:

y - y1 = m(x - x1)

y - (-22) = 6(x - (-5))

y + 22 = 6(x + 5)

y + 22 = 6x + 30

y = 6x + 8

Therefore, the equation of the line passing through (-5, -22) and (1, 14) is y = 6x + 8.

comparing f(x) = 2x - 5 with g(x) = 6x + 8

f(x) have a greater y-intercept than g(x) FALSE since -5 < 8

f(x) have a greater x-intercept than g(x) TRUE since 5/2 > -8/6

f(x) have a greater slope than g(x) FALSE since 2 < 8

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The number of minutes it would take Steve to weed the entire backyard by himself is 26.67 minutes.

Let's start by finding out how much of the backyard Hillary can weed in one minute by dividing the total time she takes by the amount of work she does in that time

Hillary's rate = 1 backyard / 80 minutes = 1/80 backyard per minute

Now, we know that Hillary worked alone for 32 minutes, so she weeded:

Hillary's work = Hillary's rate x Hillary's time = (1/80 backyard per minute) x (32 minutes) = 0.4 backyards

We also know that Hillary and Steve weeded together for 16 minutes, so they weeded

Combined work = Combined rate x Combined time

We can set up an equation to solve for the combined rate

Combined rate = Combined work / Combined time

Combined rate = (Hillary's work + Steve's work) / 16 minutes

We know that Hillary and Steve weeded the entire backyard together, so

Combined work = 1 backyard

Substituting the values we know into the equation for the combined rate, we get

1/16 = (0.4 + Steve's work) / 16

0.4 + Steve's work = 1

Steve's work = 0.6

So Steve can weed 0.6 of a backyard in 16 minutes.

Now, we can use Hillary's rate to find out how long it would take Steve to weed the entire backyard by himself

Steve's time = Steve's work / Steve's rate

Steve's time = 1 backyard / (0.6 backyard per 16 minutes)

Steve's time = 26.67 minutes

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The given question is incomplete, the complete question is:

by herself, it takes hillary 80 minutes to weed her backyard. one saturday, after hillary has been weeding for 32 minutes, her brother steve helps and they finish after weeding together for 16 minutes. how long would it have taken if steve weeded the yard by himself?

Answer:  

Figure out your monthly interest due by dividing your interest rate by 12. For example, an 8% interest rate loan would be . 007 (. 08 divided by 12).    

Principle amount is $600 (P), rate of interest is 8\% per annum (R), and the number of years is 5 (N). Hence, here, the interest the man would be paying is $240 and the total money he'd be collecting at the end of 5-year tenure is $840.

The margin of error of the 99% confidence interval is given as follows:

0.0549 = 5.49%.

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.

The margin of error is given as follows:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The parameters for this problem are given as follows:

[tex]n = 143, \pi = \frac{10}{143} = 0.0699[/tex]

Hence the margin of error is of:

M = 2.575 x sqrt(0.0699 x 0.9301/143)

M = 0.0549 = 5.49%.

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The correct option stating number of roses and carnation to be bought are 4 roses and 7 carnations.

The equation to be formed here is -

Cost of each Rose × number of roses + cost of each carnation × number of carnations = total amount.

We will keep each option in the formula to find the correct choice.

Option 1

5×4 + 1.75×7

20 + 12.25

32.25 which is less than $35

Option 2

5×8 + 1.75×4

40 + 7

47 which is greater than total amount

Option 3

5×6 + 1.75×6

30 + 10.5

40.5 which is greater than total amount

Option 4

5×7 + 1.75×4

35 + 7

42 which is greater than total amount

Since only option 1 is less than total amount, it is the feasible and correct option.

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The complete question is -

Myra wants to buy flowers for her mom. Roses cost $5 each and carnations cost $1.75 each. If Myra has $35, how many roses and how many carnations can she buy?

4 roses and 7 carnations

8 roses and 4 carnations

6 roses and 6 carnations

7 roses and 4 carnations

the answer to 8 ÷ 8 (2+2) is indeed 1.

What is BODMAS?

BODMAS is an acronym used to help remember the order of operations in arithmetic expressions. It stands for: Brackets, Orders (exponents and roots), Division, Multiplication, Addition,Subtraction. The order in which these operations are performed can greatly affect the result of a mathematical expression, so following the BODMAS rule ensures that the calculation is done in the correct order.

You are correct! The order of operations requires that we perform the multiplication and division operations before addition and subtraction, and within each group, we should perform the operations from left to right. So, using PEMDAS or BODMAS, we get:

8 ÷ 8 (2 + 2)

= 8 ÷ 2(2 + 2)

= 8 ÷ 2(4)

= 8 ÷ 8 = 1

So the answer to 8 ÷ 8 (2+2) is indeed 1.

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If the result of (294 * y%) is greater than or equivalent to x, then the quantity of approaches taken is satisfactory; however, if the sum is less than x, more efforts must be made in order to meet the specified scope.

In order to answer the question of whether it is enough to reach out to 294 people and acquire the desired number of volunteers, two critical things must be recognized:

the specified amount of volunteers for the project, as well as the predicted rate of conversion (the percentage of those contacted that will volunteer).

Assume a necessity for 'x' volunteers, and a ratio of 'y%'.

The following formula can be used to calculate how many volunteers can be obtained from reaching out to 294 people:

Number of Volunteers = (Number of People Reached) * (Conversion Rate). In this particular case: Number of Volunteers = 294 * (y%).

Finally, so as to determine if the outreach is sufficient in regards to achieving the target number of volunteers ('x'), one must compare the attained number with the given goal.

If the result of (294 * y%) is greater than or equivalent to x, then the quantity of approaches taken is satisfactory; however, if the sum is less than x, more efforts must be made in order to meet the specified scope.

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The vertical intercept of the graph is (0, 4).

The slope of the graph is -2/3.

The equation of the line graph is y = -2x/3 + 4.

The vertical intercept of the table is (0, -1).

The slope of the table is 4.

The equation of the table is y = 4x - 1.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

First of all, we would find the slope of the graph;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (0 - 4)/(6 - 0)

Slope (m) = -4/6

Slope (m) = -2/3

At point (0, 4) and a slope of -2/3, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 4 = -2/3(x - 0)  

y = -2x/3 + 4

For the table, we have:

Slope (m) = (7 - 3)/(2 - 1)

Slope (m) = 4/1

Slope (m) = 4

At point (1, 3) and a slope of 4, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 3 = 4(x - 1)  

y = 4x - 1

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