Find the smallest angle of ASTU. Assume that b is a
positive number.

Were the above figure is given, the complete sentence with regard to the triangles are

ΔAGC ~  ΔCDF

ΔCDE ~ ΔCAB

And, the length of BC is, 51

The length of DE is, 132.7

We have to given that;

⇒ CF = 32

Hence, We get;

tan 24 = CF / DF

0.44 = 32 / DF

DF = 72.7

Thus, ΔAGC ≈ ΔCDF

Here, We have;

⇒ ΔCDE ≈ ΔCAB

In triangle BCG;

BC² = 24² + 45²

BC² = 576 + 2025

BC² = 2601

BC = 51

In triangle CEF;

⇒ EC² = CF² + EF²

⇒ 68² = 32² + EF²

⇒ 4624 = 1024 + EF²

⇒ EF² = 4624 - 1024

⇒ EF² = 3600

⇒ EF = 60

Thus, We get;

DE = DF + EF

DE = 72.7 + 60

DE = 132.7

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To solve for x in the equation −1.5x−2.7=20.1+4.5x, we need to isolate x on one side of the equation. We can do this by adding 1.5x to both sides of the equation and adding 2.7 to both sides of the equation, which gives us:

-1.5x - 2.7 + 1.5x = 20.1 + 4.5x + 1.5x

Simplifying the left side of the equation and combining like terms on the right side of the equation gives us:

-2.7 = 6x + 20.1

Subtracting 20.1 from both sides of the equation gives us:

-22.8 = 6x

Dividing both sides of the equation by 6 gives us:

x = -3.8

Therefore, the value of x that satisfies the equation is -3.8.

Answer: $0.0195

Step-by-step explanation: To find the price per ounce of apple juice, we need to divide the total cost by the number of ounces.

Price per ounce = Total cost / Number of ounces

Here, the total cost is $2.50 and the number of ounces is 128.

Price per ounce = $2.50 / 128 ounces

Price per ounce = $0.0195

Therefore, the price per ounce of apple juice is $0.0195, which is approximately 2 cents per ounce.

Answer: $0.0195 per ounce

Step-by-step explanation:

We will create a proportion to help us solve this question.

➜ To do this, we will set two fractions equal to each other with the dollar amount in the numerator and the ounce amount in the denominator.

[tex]\displaystyle \frac{\$2.50}{128\;ounces} =\frac{\$x}{1\;ounce}[/tex]

Cross-multiply:

      128x = $2.50

Divide both sides of the equation by x:

      x = $0.0195 per ounce

Step-by-step explanation:

To determine the constant of proportionality (k) in a proportional relationship, we need to compare corresponding values of x and y and calculate the ratio between them.

Let's examine the given values:

2. UX: x 6 15 9 y 42 200

To find the constant of proportionality (k), we can take any pair of corresponding values and calculate their ratio. Let's choose the first pair: (6, 42).

k = y / x

k = 42 / 6

k = 7

So, the constant of proportionality (k) is 7.

Now, let's find the missing values for the second set of values:

d. X: 14 y: 21 6 15 3 7 8

Since we know the constant of proportionality is 7, we can calculate the missing values of y by multiplying each corresponding x value by 7.

Missing values for y:

- For x = 21, y = 21 * 7 = 147

- For x = 6, y = 6 * 7 = 42

- For x = 15, y = 15 * 7 = 105

- For x = 3, y = 3 * 7 = 21

- For x = 7, y = 7 * 7 = 49

- For x = 8, y = 8 * 7 = 56

Therefore, the missing values of y are: 147, 42, 105, 21, 49, and 56.

The compound interest is solved and the amount in her account in 2047 is given by A = $ 1315.46

Given data ,

To determine how much money Carly has in her account after 37 years, we need to substitute the value of t as 37 into the equation:

P = 600(1.0375)^t

P = 600(1.0375)^37

P ≈ 600(1.0375)^37 ≈ 600(2.19243) ≈ $ 1315.46

Therefore , Carly has approximately $1315.46 in her account after 37 years.

To calculate the growth rate, we need to find the rate of change between the initial and final amounts over the given time period.

Regarding how long it takes for Carly's account to reach $750, we'll assume you mean when the account reaches or exceeds $750. Let's set up the equation and solve for t:

750 = 600(1.0375)^t

Dividing both sides by 600, we get:

1.25 = 1.0375^t

Taking the logarithm of both sides (base 1.0375):

log(1.25) = t * log(1.0375)

t ≈ log(1.25) / log(1.0375) ≈ 8.5 years

Hence , it takes approximately 8.5 years for Carly's account to reach or exceed $750

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Answer:

C. Through a given point not on a given line, there is exactly one line parallel to the given line.

Step-by-step explanation:

hope i helped

Answer:

Look down

Step-by-step explanation:

Thanks for reaching out for assistance! Based on the context you provided, it seems like the correct answer is C. Playfair's axiom states that there is exactly one line parallel to a given line that can be drawn through a point not on it. I hope this helps! Let me know if there's anything else I can do for you.

Answer:

$223,787

Step-by-step explanation:

r = 0.02

C = 191,000

t = 8

S = 191,000 (1 + 0.02)⁸

Follow order of operations (PEMDAS).

S = 191,000 (1.02)⁸

S = 191,000 (1.171659381)

S = 223,786.9

(We want to round to the nearest dollar, which is the ones place, so ignore all digits after the tenths place.)

Rounding, S = 223,787

"The correct option is (C) $25w < $168." This means that Joe needs to save for at least 7 weeks (since he can't save for a fraction of a week) to afford the hoverboard.

The hoverboard costs $168 and Joe earns $25 each week. To determine if Joe can afford the hoverboard, we need to determine how many weeks he needs to save to reach the cost of the hoverboard.

Let's represent the number of weeks Joe needs to save as "x". Each week, he earns $25, so the total amount he will have after "x" weeks is 25x. In order to buy the hoverboard, he needs to have saved $168. Thus, we can write the inequality:

25x ≥ 168

This inequality represents the fact that the amount of money Joe earns after "x" weeks must be greater than or equal to $168, the cost of the hoverboard, for him to be able to afford it. Simplifying this inequality, we get:

x ≥ 6.72.

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The solution of the function is as follows:

f(3) = 16

h(0) = -4

h(g(x)) = 3x + 5

g(y) = y + 3

f(x) - h(x) =  x² - x + 5

A function relates input and output. In other words, a function is an expression that defines a relationship between one variable (the independent variable) and another variable(dependent variable).

Therefore, let's solve the function as follows:

f(x) = x² + 2x + 1

g(x) = x + 3

h(x) = 3x - 4

Therefore,

f(3) =  (3)² + 2(3) + 1 = 9 + 6 + 1 = 16

h(0) = 3(0) - 4 = -4

h(g(x)) = 3(x + 3) - 4 = 3x + 9 - 4 = 3x + 5

g(y) = y + 3

f(x) - h(x) =  x² + 2x + 1  - (3x - 4) =  x² + 2x + 1  - 3x + 4 = x² - x + 5

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Answer:

$2.48 and $2.15, respectively

Step-by-step explanation:

2.30 * 1.08 = 2.48

1.99 * 1.08 = 2.15

__________________________________

__________________________________

The Parallelogram area is 96 square meters.

We have,

The area of a parallelogram is given by the formula A = bh, where b is the length of the base and h is the height.

In this case,

The base of the parallelogram is the length of one of its parallel sides, which is 12 m.

The height of the parallelogram is given as 8 m.

Therefore, the area of the parallelogram is:

A = bh

A = 12 m x 8 m

A = 96 square meters

Thus,

The Parallelogram area is 96 square meters.

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Answer: -3 to -infinity

Step-by-step explanation:

A higher credit score reduces your fixed costs because you will pay lower interest rates. That is option A.

A higher credit score is one of the factors that are being considered by banks or lenders before one is being viewed as being legible to borrow money.

This is soo because a higher credit score will reduce the lending interest rates of the individual because it shows such will pay back the borrowed money as soon as possible.

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Answer:

8 am

Step-by-step explanation:

First train has a 50 m/hr x 3 hr = 150 mile head start

Second train is going 60 - 50 = 10 m/hr faster and will close this 150 mile distance

 in 15 hours to catch the first train

2pm + 3 hours + 15 hours = 8 am

The first term of GP is  a₁ = -4.

Given that,

Sum of five terms of GP = s₅ = -16.3804

Common ratio = 9/10  which is less than 1

Number of terms = n = 5

We know that,

Sum of nth term of GP when common ration is less than 1,

s₅ = a₁(1-[tex]r^{n}[/tex])/(1-r)

Substituting the values,

⇒ -16.3804 = a₁(1-0.9⁵)/(1-0.9)

⇒             a₁ = -16.3804/4.0951

⇒             a₁ = -4

Hence, the value of  a₁ is -4.

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The scale factor used to create the image is given as follows:

k = 1/4.

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

The equivalent segment lengths for the original figure and the image are given as follows:

Hence the scale factor used to create the image is given as follows:

k = 2/8

k = 1/4.

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The symmetric equations for the line are:

(36x + 40y - 28z - 100) / 0 = (x-5) / -6 = (y-8) / -5 = (z+2) / 7

To find the parametric equations for the line passing through A(5, 8, -2) and B(-1, 3, 5), we can use the vector equation:

r = A + t(B-A)

where r is the position vector of any point on the line, t is a scalar parameter, and A and B are the given points. Substituting the values, we get:

r = (5, 8, -2) + t((-1)-5, 3-8, 5-(-2))

r = (5, 8, -2) + t(-6, -5, 7)

The parametric equations for the line are:

x = 5 - 6t
y = 8 - 5t
z = -2 + 7t

To find the symmetric equations, we can use the fact that any point on the line is equidistant from points A and B. Thus, the distance from a point (x, y, z) to A must be the same as the distance from the same point to B. Using the distance formula, we get:

√[(x-5)² + (y-8)² + (z+2)²] = √[(x+1)² + (y-3)² + (z-5)²]

Squaring both sides and simplifying, we get:

36x + 40y - 28z - 100 = 0

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The inequality in slope - intercept form is,

⇒ y ≤ x + 5

We have to given that;

The graph of the inequality is shown in image.

Let two points on the line is,

⇒ (- 5, 0) and (0, 5)

Hence, The equation of line is,

⇒ y - 0 = (5 - 0) / (0 + 5) (x + 5)

⇒ y = x + 5

Thus, The inequality in slope - intercept form is,

⇒ y ≤ x + 5

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In the graph, differential is 4 or (p+k)-p = k as well as difference is -2 when y = 7 or y = 5, respectively.

A graph comprises a visual representation and diagram that displays facts or values in an organised manner in mathematics. The points of a graph are widely used to depict the connections between various objects. A. The difference between y = 7 or y = 5 is 4 and -2, respectively B. 4 is the difference, so (p+k)-p = k C. It differs by -2 D. Part C depends on 'k' rather than 'p,' not 'p'.

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Step-by-step explanation:

do it yourself what do you do while teacher is teaching

do it yourself what do you do while teacher is teaching

Answer:

If it can be exactly 150, then 50.

there’s not exactly enough info for me to solve.

The method of bar chart is appropriate for representation.

According to the given data,

The most effective way to present the data is in a bar chart.

An effective visual representation of categorical data that shows the frequency or count of each category is a bar chart.

The length of each bar would reflect the frequency or count of each score, and the categories would be the test results in this instance.

It would be a simple and unambiguous approach to compare the various test results.

These are the three key characteristics of bar graphs:

The bar graph makes it simple to compare various sets of data among various groups.

The relationship is depicted using two axes, with the discrete values on one axis and the categories on the other.

The graph displays the key alterations in the data over time.

Hence,

Bar chart method should be used.

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The equations are solved to get

2/5 * (1 1/4 * x - 3 1/3) - 1 1/3 x here x = 1 3/5

2 1/8 x + 3/4 x + 1/6 - 7/12 x + 5 2/3 here x = 2 6/11

0.5(x + 1.6) + 1.4(3x + 2.4) = 9.8 here x = 1.2

1.

2/5 * (1 1/4 * x - 3 1/3) - 1 1/3 * x

opening the parenthesis and converting to improper fraction

1/2 x - 4/3 - 4/3 x

-5/6 x - 4/3

-5/6 x = 4/3

x = 8/5

x = 1 3/5

2.

2 1/8 x + 3/4 x + 1/6 - 7/12 x + 5 2/3

adding like terms

55/24 x + 35/6 = 0

55/24 x = - 35/6

x = 28/11

x = 2 6/11

3.

0.5(x + 1.6) + 1.4(3x + 2.4) = 9.8

removing the parentheses:

0.5x + 0.8 + 4.2x + 3.36 = 9.8

4.7x + 4.16 = 9.8

4.7x = 5.64

x = 1.2

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Answer:

2.

Step-by-step explanation:

The data is skewed towards 1-25. From this we can conclude that patients only call the doctor once or twice when they are sick.

The number of terms n of the geometric progression is n = 12

Given data ,

Let the geometric progression be represented as A

Now , the value of A is

10 + 30 + 90 + .... = 2657200

And , let the number of terms be n

common ratio r = 30 / 10 = 3

where sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )

On simplifying , we get

2657200 = 10 ( 3ⁿ - 1 ) / ( 2 )

Divide by 5 on both sides , we get

3ⁿ - 1 = 5,31,440

Adding 1 on both sides , we get

3ⁿ = 5,31,441

Taking log on both sides , we get

n = 12

Hence , the number of terms of GP is n = 12

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