what is the digital index of 23475

Answer:

x-9

Step-by-step explanation:

1/10×1 =1/10

1/10×9=9/10

so 1/10(1x-9) = 1/10x-9/10

The range of the function g(x) is given as follows:

[0, ∞).

From the graph of the function given in this problem, y assumes all real non-negative values, hence the interval notation representing the range of the function is given as follows:

[0, ∞).

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Answer:

Step-by-step explanation:

AFR = VFN (opposite angle rule)

7x + 33 = 9x + 7

33 - 7 = 9x - 7x

26 = 2x

x = 26 : 2

x = 13°

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

check

7 * 13 + 33 = 9 * 13 + 7   (remember PEMDAS)

91 + 33 = 117 + 7

124 = 124

the answer is good

Answer:

x<7

Step-by-step explanation:

x+4>2x-3

Add 3 to both sides: x+7>2x

Subtract x from both sides: 7>x or x<7

Answer:

Area = 24.75 sqr units

Step-by-step explanation:

You will need these formulas:

\(d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}\)

Midpoint = \((\frac{x_{1} + y_{1} }{2} , \frac{x_{2} + y_{2} }{2})\)

Area = b x h

Let us treat CD as the base. Find the length of the base with the distance formula. Use the coordinates for points C & D.

\(d = \sqrt{(-2 - (-8))^2 + (-8-(-7))^2}\)

\(d = \sqrt{37}\)

The base is \(\sqrt{37}\).

The height is the distance between point E and the midpoint of line CD.

Midpoint of CD = \((\frac{-8 + (-7) }{2} , \frac{-2 + (-8) }{2})\) = (\(-\frac{15}{2}\), \(-5\))

Use the distance formula to find the height.

\(d = \sqrt{(-5 - (-\frac{15}{2} ))^2 + (-2-(-5))^2}\)

\(d = \frac{\sqrt{61} }{2}\)

Find the area with the two distances that were found.

Area = \((\sqrt{37}) (\frac{\sqrt{61} }{2})\)

Area = \(\frac{\sqrt{2257} }{2}\)

Area = 24.75 sqr units

Both options a. A = 129.9° and b. A = 53.1° are correct.

To find the possible values for angle A in triangle ABC, we can use the Law of Sines, which states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant.

Using the Law of Sines, we have sin(A)/a = sin(B)/b. Plugging in the given values, we get sin(A)/36 = sin(51°)/35.

To find the two possible values for angle A, we can solve the equation sin(A)/36 = sin(51°)/35. Taking the arcsine of both sides, we have A = arcsin((sin(51°)/35)*36).

Calculating this expression, we find two possible values for angle A:

A ≈ 53.1° (rounded to the nearest tenth)

A ≈ 129.9° (rounded to the nearest tenth)

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The rectangle's dimensions are 9 yards in width and 14 yards in length.

Let's assume the width of the rectangle is "x" yards. According to the given information, the length of the rectangle is more than twice the width. Thus, the length can be expressed as 2x + y, where y represents the additional length.

The area of a rectangle is calculated by multiplying its length and width. In this case, we have the equation: (2x + y) * x = 63 yd².

Expanding the equation, we get: 2x² + xy = 63.

Since we know the area is 63 yd², we can find two factors that multiply to give 63 and solve for x. The factors of 63 are 1 and 63, 3 and 21, and 7 and 9. Since the length is more than twice the width, the factor pair that satisfies this condition is 7 and 9.

Therefore, x = 7 and 2x + y = 9. Solving for y, we find that y = 2.

Thus, the dimensions of the rectangle are 7 yards in width and 9 yards in length.

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The statement that best proves that <XWY ≅ <ZYW is that two parallel lines are cut by a transversal, then the alternate interior angles are congruent

To determine the correct statement, we need to know the properties of a parallelogram.

These properties includes;

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Answer:

f(-3)= -60

Step-by-step explanation:

f(x)=20(2)

f(-3)=20(-3)

=-60

Answer:

b

Step-by-step explanation:

just got it right

Markus scored 82 on his fifth test.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

We know that Markus' score on the fifth test is 5 points lower than the average of all five tests. Let x be the score Markus got on his fifth test. Then the average score of all five tests is:

(85 + 92 + 82 + 94 + x)/5

So the equation to determine Markus' score on the fifth test is:

x = (85 + 92 + 82 + 94 + x)/5 - 5

Simplifying this equation, we can first add the numbers in the numerator:

x = (353 + x)/5 - 5

Next, we can multiply both sides by 5 to eliminate the denominator:

5x = 353 + x - 25

Simplifying further, we can combine like terms:

4x = 328

Finally, we can solve for x by dividing both sides by 4:

x = 82

Therefore, the correct equation for Markus to determine his score on the fifth test is:

4(x - 5) = 353 + x.

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The equation 2x + cos(x) = 0 has exactly one real root. This can be shown by considering the behavior of the function f(x) = 2x + cos(x) and using the intermediate value theorem.

To prove that the equation 2x + cos(x) = 0 has exactly one real root, we need to demonstrate the existence and uniqueness of the root.

Existence of a real root: By considering the behavior of the function f(x) = 2x + cos(x), we can observe that f(x) is continuous for all real numbers. As x approaches negative infinity, the value of f(x) becomes more negative, and as x approaches positive infinity, the value of f(x) becomes more positive. Since f(x) is continuous and changes sign as x varies, the intermediate value theorem guarantees the existence of at least one real root.

Uniqueness of the real root: To prove uniqueness, we consider the derivative of f(x), which is f'(x) = 2 - sin(x). Since the derivative f'(x) is always positive, it indicates that the function f(x) is strictly increasing. As a result, f(x) = 0 can have at most one real root since there are no significant changes in f(x) after the initial root.

Therefore, the equation 2x + cos(x) = 0 has exactly one real root.

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Answer:

Q1:

\(-5\sqrt{27c^2}\)

\(-5\sqrt{27}\sqrt{c^2}\)

\(-5\times\sqrt{9} \sqrt{3} \sqrt{c^2}\)

\(-5\times3\sqrt{3}\sqrt{c^2}\)

\(-5\times3\sqrt{3}c\)

\(-15\sqrt{3}c\)

Q2:

\(5\sqrt{72}-3\sqrt{32}\)

\(5\sqrt{36} \sqrt{2} -3\sqrt{16} \sqrt{2}\)

\(5\times6\sqrt{2}-3\times4\sqrt{2}\)

\(30\sqrt{2}-12\sqrt{2}\)

\(18\sqrt{2}\)

Q3:

\(\sqrt{108yz}+3\sqrt{98yz}+2\sqrt{75yz}\)

\(\sqrt{36} \sqrt{3} \sqrt{yz} +3\sqrt{49} \sqrt{2} \sqrt{yz} +2\sqrt{25} \sqrt{3} \sqrt{yz}\)

\(6\sqrt{3}\sqrt{yz}+21\sqrt{2}\sqrt{yz}+10\sqrt{3}\sqrt{yz}\)

\(16\sqrt{3}\sqrt{yz}+21\sqrt{2}\sqrt{yz}\)

Q4:

\(\sqrt{15n^2}\sqrt{10n^3}\)

\(\sqrt{15}n\sqrt{10n^3}\)

\(\sqrt{15}n\sqrt{10}\sqrt{n^2}\sqrt{n}\)

\(\sqrt{15}\sqrt{10}n^2\sqrt{n}\)

\(\sqrt{5}\sqrt{3}\sqrt{5}\sqrt{2}n^2\sqrt{n}\)

\(5\sqrt{3}\sqrt{2}n^2\sqrt{n}\)

\(5\sqrt{6}n^2\sqrt{n}\)

Q5:

\(\frac{\sqrt{3x^2y^3}}{4\sqrt{5xy^3}}\)

\(\frac{\sqrt{3}xy\sqrt{y}}{4\sqrt{5}y\sqrt{x}\sqrt{y}}\)

Cancel off \(\sqrt{x}\):

\(\frac{\sqrt{3}y\sqrt{x}\sqrt{y}}{4\sqrt{5}y\sqrt{y}}\)

Cancel off \(y:\)

\(\frac{\sqrt{3}\sqrt{x}\sqrt{y}}{4\sqrt{5}\sqrt{y}}\)

Cancel off \(\sqrt{y} :\)

\(\frac{\sqrt{3}\sqrt{x}}{4\sqrt{5}}\)

Multiply \(\sqrt{5}\) on the numerator and denominator:

\(\frac{\sqrt{3}\sqrt{x}\sqrt{5}}{4\sqrt{5}\sqrt{5}}\)

\(\frac{\sqrt{15}\sqrt{x}}{20}\)

sorry i pushed add answer

Answer:

2,795,173,960 miles

Step-by-step explanation:

Metric: 4,498,396,441 km English: 2,795,173,960 miles Scientific Notation: 4.4983964 x 109 km (3.0069923 x 101 A.U.) By Comparison: 30.070 x Earth

The correct answer is D. Both A and B are correct, to make predictions about values of y for given x value and to determine the strength of linear association between variables.

The regression line is a statistical tool that allows us to model the relationship between two variables, usually called X (the independent variable) and Y (the dependent variable), assuming a linear relationship between them. Once the regression line has been fitted to the data, it can be used for two main purposes:

A. To make predictions about the values of Y for a given X-value: Once the regression line has been fitted, we can use it to predict the value of Y for any given X-value. This is done by plugging in the X-value into the equation of the regression line, which will give us an estimated value of Y.

B. To determine the strength of a linear association between two variables: The regression line is also a measure of the strength of the linear relationship between X and Y. Specifically, the slope of the regression line (which represents the change in Y for a unit change in X) is a measure of how much Y changes for a given change in X. The closer the slope is to zero, the weaker the linear relationship between X and Y; the farther the slope is from zero, the stronger the linear relationship between X and Y.

Therefore, both A and B are correct uses of the regression line.

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Question:

Look at the picture of a scaffold used to support construction workers. The height of the scaffold can be changed by adjusting two slanting rods, one of which, labeled PR, is shown: Part A: What is the approximate length of rod PR? Round your answer to the nearest hundredth. Explain how you found your answer stating the theorem you used. Show all your work. (5 points)

B) The length of rod PR is adjusted to 16 feet. If width PQ remains the same, what is the approximate new height QR of the scaffold? Round your answer to the nearest hundredth.

Answer:

A) 16.64 Feets

B) 7.65 feets

Step-by-step explanation:

Given the following :

The question above can be solved by applying Pythagoras rule :

A^2 = B^2 + C^2

PR² = PQ² + QR²

PR² = 14² + 9²

PR² = 196 + 81

PR = √277

PR = 16.64feet

Now if PR is adjusted to 16 Feets, the New height of the scaffold will be:

QR² = PR² - PQ²

QR² = 16² - 14²

QR² = 256 - 196

QR² = 60

Take the Square root of both sides

QR = √60

QR = 7.7459666 Feets

The Annual Percentage Yield (APY) in this situation is approximately 2.454%.

To find the Annual Percentage Yield (APY) in this situation, use the formula:

\(APY = (1 + r/n)^n - 1\)

where:

- r is the annual interest rate (APR) expressed as a decimal,

- n is the number of compounding periods per year.

In this case, the APR is 2.42% or 0.0242 (expressed as a decimal), and the interest is compounded monthly, so there are 12 compounding periods per year (n = 12).

Substituting these values into the formula,

\(APY = (1 + 0.0242/12)^{12} - 1\)

Calculating this expression:

\(APY = (1 + 0.002017)^{12} - 1\)

  \(= (1.002017)^{12} - 1\)

   ≈ 0.02454 or 2.454%

Therefore, the Annual Percentage Yield (APY) in this situation is approximately 2.454%.

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Step-by-step explanation:

5.

just look at the table. what logic do you see in the change of the numbers ?

x changes by +1 from one point to the next.

y changes by +6 from one point to the next.

and we have the point with x=0 in the table, where y = 12. this is the y-intercept (where the line function crosses the y-axis, which means the point where x=0).

the changes line function is

y = ax + b

a is the slope. this is the ratio of y change / x change when going from one point to another.

in our case here this is 6/1 = 6.

b is the y-intercept. in our case 12.

so, the first equation is

y = 6x + 12

now, look at the second table.

x changes again by +1 from one point to the next.

y changes now by -3 from one point to the next.

so, our slope (a) here is -3/1 = -3.

we don't have the x=0 point in the table, so we get b by using the coordinates of one of the points (e.g. 2, 12) in the half finished equation and solve for b :

12 = -3×2 + b = -6 + b

18 = b

so, the full second equation is

y = -3x + 18

6.

this is totally simple. we put -3 in place of all x we find in the function definition and calculate the result :

f(-3) = (-3)³ + 27 = -27 + 27 = 0

remember that the exponent says how often the base number (here -3) is multiplied by itself. so, (-3)³ = -3×-3×-3.

-3×-3 = +9.

but then 9×-3 = -27.

7.

the domain of a function is the interval or set of valid values of x (the input variable).

remember, an empty dot means excluding, a filled dot means including.

I see the graph is drawn to go from x = -4 to x = +4.

-4 is included, +4 is excluded.

so, the domain is then the interval of the real numbers

[‐4, +4)

or

-4 <= x < +4

please consider that a round bracket means excluding.

Answer: it’s 8y-20

Step-by-step explanation:

The estimated market value of Citrus County's assets, with an average duration of 8 and a market value of $1 million, would be approximately $1,055,284 if the interest rate changes to 4%.

In this case, the assets have an average duration of 8. When the interest rate changes from 5% to 4%, the change in interest rates is 1%. By applying the duration formula, the estimated percentage change in the market value of the assets would be approximately -8% (negative duration multiplied by the change in interest rates).

To calculate the estimated market value, we need to multiply the estimated percentage change (-8%) by the current market value ($1 million) and add it to the current market value. Thus, the estimated market value would be approximately $1,055,284 (1,000,000 + (1,000,000 * -8%)).

Duration is a measure of the sensitivity of an asset's price to changes in interest rates. It provides an estimate of the percentage change in the market value of an asset for a given change in interest rates. The duration formula states that the percentage change in the market value of an asset is approximately equal to the negative duration multiplied by the change in interest rates.

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Coordinates of point B are (5x₂+6x₁)/11 and (5y₂+6y₁)/11

What is the section formula in coordinate geometry?

When the line segment is divided internally in the ratio m:n, we use this formula.  That is when point C lies somewhere between points A and B. p= (mx₂+nx₁)/(m+n) & q= (my₂+ny₁)/(m+n)

Given here,  point B on AC such that the ratio of AB to AC is 5:6

Let the point B(p,q) internally divide the line joining points A(x₁, y₁) and C(x₂, y₂) in the ratio m : n , then,

p= (mx₂+nx₁)/(m+n)

q= (my₂+ny₁)/(m+n)

Here. m=5 and n=6

p=(5x₂+6x₁)/11 , q=(5y₂+6y₁)/11

Hence, the Coordinates of point B are (5x₂+6x₁)/11 and (5y₂+6y₁)/11

I hope this helps <3

Answer:

$82.50 is the discount.

Step-by-step explanation:

550 x .15 = $82.50

Hope that helps!

The slope (m) will be "279.33". A further solution to the question is provided below.

At one moment this same instantaneous modification rate would be the same with the functionality derivative assessed somewhere at the time. In certain other terms, the pitch of such tangent line towards the curvature is somewhere at a level equivalent to that as well.

According to the question,

As we know,

⇒  \(Slope (m) = \frac{y_2-y_1}{x_2-x_1}\)

By substituting the values, we get

⇒                  \(=\frac{838-0}{6-3}\)

⇒                  \(=\frac{838}{3}\)

⇒                  \(=279.33\)

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The instantaneous rate of change is the rate of change at a particular point or instant in the graph. The instantaneous rate of change of P at \(t=4\) is 250

I've added as an attachment, the graph that represents the population of the fish.

To determine the instantaneous rate of change at \(t=4\), we simply calculate the slope (m) of the tangent line using:

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

Because of the scale of the graph, I will use the following estimated points from the tangent line

\((x_1,y_1) = (3,0)\)

\((x_2,y_2) = (4,250)\)

So, the slope is:

\(m = \frac{250 - 0}{4 - 3}\)

\(m = \frac{250}{1}\)

\(m = 250\)

Hence, the instantaneous rate of change of P at \(t=4\) is 250

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Answer: yes

Step-by-step explanation:

Answer:

10:15:12

Step-by-step explanation:

c:g:t

2:3:3

5:5:4

10:15:12