In triangle ABC, segment AD is perpendicular to segment BC, and segment AC, is perpendicular to segment BA.

Based on the information in the diagram, what is the length of segment DC?

Answer: The correct answer would be 71.

step-by-step explanation:

9^2 - 10 =

Calculate the exponents: 9^2 : 81

Then subtract 81 by 10

81 - 10 = 71

Answer:  Choice B

[tex]2k^5\sqrt[3]{25}[/tex]

================================================

Work Shown:

[tex]\sqrt[3]{200k^{15}}\\\\\sqrt[3]{8*25k^{5*3}}\\\\\sqrt[3]{8*25(k^5)^3}\\\\\sqrt[3]{8(k^5)^3*25}\\\\\sqrt[3]{8(k^5)^3}*\sqrt[3]{25}\\\\2k^5\sqrt[3]{25}[/tex]

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

Explanation:

The goal is to factor the radicand in such a way that we pull out perfect cube factors.

Notice that 200 = 8*25 and 8 is a perfect cube (since 2^3 = 8). It is the largest perfect cube factor of 200.

We can rewrite the k^15 as k^(5*3) which is equivalent to (k^5)^3

Once these perfect cube factors are pulled out, they cancel with the cube root to get what you see above.

A polynomial function of least degree with rational coefficients so that P(x) = 0 has the given roots is P(x)=x²-5x-14

A function is said to as polynomial when a variable in an equation, such as a quadratic equation or cubic equation, etc., has only positive integer exponents or non-negative integer powers. One polynomial with an exponent of 1 is 2x+5, for instance. One that has more than two algebraic terms is referred to as a polynomial expression. Polynomial is a monomial or binomial that is repeatedly added, as the name suggests.

A mathematical expression containing one or more algebraic terms, where each algebraic term is made up of a constant multiplied by one or more variables raised to a nonnegative integral power.

x= -2, x=7

Given,

P(x) = 0

This polynomial function has the roots,

x= -2, x=7

So,

(x+2)(x-7)

We have to multiply both of them we get,

P(x)=(x+2)(x-7)

0=x²-5x-14

x²-5x-14=0

Therefore, P(x)=x²-5x-14 is the polynomial function.

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Using the distance formula, [tex]AP=\sqrt{(-1-2)^2+(-1-7)^2} \approx \boxed{8.54}[/tex]

(a) 794g of the initial sample will be left in the sample after 25 years. (b) Time taken to decay to half of its original amount is 3.39 years.

Isotopes(200g) are atoms that have the same number of protons in their nucleus, but a different number of neutrons. This means that they have the same atomic number, but a different atomic mass. Because of this, isotopes have different physical and chemical properties. Isotopes can be stable, meaning that they do not undergo radioactive decay, or they can be unstable, meaning that they will undergo radioactive decay over time.

(a) Substituting 25 for t in the expression, we get:

[tex]A(25) = 200e^{0.0541 \times 25}[/tex]

         [tex]= 200e^{1.3525}[/tex]

Thus, after 25 years, there will be

[tex]200e^{1.3525} = 2003.97[/tex]

794 g of the initial sample left in the sample.

(b) We want to find t such that

[tex]A(t) = 200e^{0.0541}[/tex]                                          

       = 100.

Solving for t, we get:

[tex]= 200e^{0.0541} \times t=100[/tex]

Dividing both sides by 200 and applying the natural logarithm to both sides, we get:

0.0541 × t = ln(0.5)

Therefore,

[tex]t = \frac{ln(0.5)}{0.0541}[/tex]

  = 3.39 years.

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Answer:

from the options given it seems that it can only be divided by 3 or –3 which will give you 147 or – 147

Step-by-step explanation:

i hope this helps

Answer:3/c

i am doing this for extra characters

Answer:

-65

Step-by-step explanation:

Substitute: g (1) =_50-15

Calculate the sum or difference:

Answer=-65

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27

The x- and y-coordinates of point C, which partitions the directed line segment from A to B into the ratio 3:10 are (-2.6,5.2).

A line segment in geometry has two different points on it that define its boundaries. A line segment is sometimes referred to as a section of a line that links two places. The difference between a line and a line segment is that a line has no endpoints and can go on forever in either direction. A ray has only one endpoint and an endlessly long another end, as opposed to a line segment that has two ends.

If a point (x,y) divides the line segment joining the points A(x1,y1) and B (x2,y2) is in the ratio m:n, then

[tex]x=\frac{mx2+nx1}{m+n} \\y=\frac{my2+ny1}{m+n} \\[/tex]

Here,

m:n = 3:10

The endpoint of line AB are at: A(-4,8) and B(2,-4)

We substitute the given values to obtain:

x= 3*2+10*(-4)/3+10

x= -34/13

x= -2.6

and

y= 3*(-4)+10*(8)/3+10

y= 68/13

y= 5.2

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The equation of line r, in slope-intercept form, is: y = -1/9x - 9.

The equation that represents a line, in slope-intercept form, is expressed or written as:

y = mx + b, where the slope is m, and the y-intercept is b.

The slope of line q, with the equation y + 7 = 9(x + 4) is 9. The negative reciprocal of 9 is -1/9. This means line r that is perpendicular to line q and passes through (9, -10) has a slope, m = -1/9.

To write the equation of the line in slope-intercept form, first, substitute m = -1/9 and (a, b) = (9, -10) into y - b = m(x - a):

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

y + 10 = -1/9(x - 9)

Rewrite in slope-intercept form:

y + 10 = -1/9x + 1

y = -1/9x + 1 - 10

y = -1/9x - 9

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The required fraction that makes the equation true is 3/15.

What is a fraction?

Fractions represent parts of a whole or group of objects. A fraction is made up of two parts. The number at the top of the line is referred to as the numerator. It specifies the number of equal parts of the whole or collection that are taken. The denominator is the number below the line. It displays the total number of equal parts into which the whole is divided or the total number of identical objects in a collection.

Let x be the required fraction.

Blank divided by 3/7 = 7/15

Then, [tex]\frac{x}{3/7} = \frac{7}{15}[/tex]

or, [tex]\frac{7x}{3} = \frac{7}{15}[/tex]

or, 7x = 21/15

or, x = 3/15

Hence the required fraction that makes the equation true is 3/15.

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Answer: The coefficient of the term with the power of 3 is (D. 1)

Step-by-step explanation:

The power of 3 is x^3. When there's no number besides x, we can think of it as an imaginary 1. So, therefore, it's D-1.

The values of a and b for the exponential function are given as follows:

The standard definition of an exponential is given as follows:

y = ab^x.

In which the meaning of the parameters a and b is given as follows:

The function passes through the points (0,10000), hence the value of the parameter a is given as follows:

a = 10000.

The function also passes through the point (3,3430), hence the value of the parameter b is obtained as follows:

10000b³ = 3430

b = cubic root of (3430/10000)

b = (3430/10000)^1/3

b = 0.1143.

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Hello,

I hope you and your family are doing well!

The answer is y = 5 (See below for the explanation).

To find a linear equation representing a line passing through two points, you can use the slope-intercept form of the equation, which is written as y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis).

To find the slope of the line, you can use the formula:

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

Substituting the coordinates of the two given points, we get:

m = (5 - 5) / (-8 - 3) = 0 / -11 = 0

Since the slope of the line is 0, the line is horizontal and passes through both points at the same y-value (5). The x-intercept (the point at which the line crosses the x-axis) is not relevant in this case.

Therefore, the linear equation representing this line is y = 5.

Happy Holiday & New Year!

Please give this answer 5 stars and brainliest if you find it helpful.

Best,

Answer:

y=5

Step-by-step explanation:

y=mx+b

if you put your two point on a graft, they are on same line for the y-intersept. So if that is true then your answer has to y=5

The coordinate on which the residual values are shown on a residual plot is: A) on the y-axis.

A residual value can be defined as a difference between the measured (given or observed) value from a residual plot (scatter plot) and the predicted value from a residual plot (scatter plot).

Mathematically, the residual value of a data set can be calculated by using this formula:

Residual value = given value - predicted value

In Mathematics, the independent variable (fitted values) are generally plotted on the x-axis of a residual plot (scatter plot) while the residual value is plotted on y-axis of a residual plot (scatter plot).

In conclusion, a line of best fit simply refers to a trend line on a residual plot (scatter plot).

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Step-by-step explanation:

44r + 43g = 217

45r + 18g = 144

r = a pound of raspeberries

g = a pound of grapes

Answer: 12.5%

Explain:

There are two main ways to express a fraction as a percentage:

-Divide 100 by the numerator, and then multiply both numerator and denominator by the answer.

-Convert the fraction to a decimal first, then multiply the answer by 100.

Answer:32

Step-by-step explanation:

Assuming this is a triangle, there are three sides.

All sides of a triangle must add up to 180 degrees

180-108-40 = 32

Step-by-step explanation:

Exponential Function, example y=e×;

Cubic Function, example y=x³;

Quadratic Function, example y=x²;

Linear Function, example y=x-1;

Absolute Function, example y=|x|;

Cube Root Function, example y=∛x;

Constant Function, example y=2.

The ratio of the volume of the second cylinder to the volume of the first cylinder is 25.

To find the ratio of the volume of the second cylinder to the volume of the first cylinder, we need to calculate the volumes of both cylinders and then compare them.

The formula to calculate the volume of a right circular cylinder is given by V = πr^2h, where V represents the volume, r is the radius, and h is the height.

For the first cylinder:

Radius (r₁) = 3 centimeters

Height (h₁) = 5 centimeters

Volume of the first cylinder (V₁) = π * (3 cm)^2 * 5 cm

                             = 45π cm³

For the second cylinder:

Radius (r₂) = 15 centimeters

Height (h₂) = 5 centimeters

Volume of the second cylinder (V₂) = π * (15 cm)^2 * 5 cm

                              = 1125π cm³

To find the ratio of the volumes, we divide the volume of the second cylinder by the volume of the first cylinder:

Ratio = V₂ / V₁

     = (1125π cm³) / (45π cm³)

     = 25

Therefore, the ratio of the volume of the second cylinder to the volume of the first cylinder is 25.

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(f . g)(x) is multiplication of f(x) and g(x). So,

(f. g)(x) = [tex]49x^{4}-70x^{3}+319x^{2} -420x+150[/tex] . Option (c) is correct answer.

A new function that is the product of the original two functions is created when two independent functions are multiplied together.

To multiply two functions together, perform these steps:

In given question we have two functions

f(x) = 7x³-5x²+42x-30

g(x) = 7x - 5

we need to find (f.g)(x) that is nothing but multiplication of f(x) and g(x).

So multiplying both the functions, we get

(f.g)(x) = f(x). g(x)

=( 7x³-5x²+42x-30)*(7x - 5)

=(49[tex]x^{4}[/tex]-35x³-35x³+25x²+294x²-210x-210x+150)

= [tex]49x^{4}-70x^{3}+319x^{2} -420x+150[/tex]

So, option (c) is correct answer.

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A rectangular prism with 10 inches in height and 2 inches in base length and height. The sides are labeled A and the base is labeled B. the total area of all the copies of Rectangle A is 80 square inches.

b) 8 square inches.

c) 88 square inches.

Generally, To find the area of the Face A rectangles, you need to multiply the length and the height of one rectangle.

In this case, the length is 10 inches and the height is 2 inches, so the area of one rectangle is 10*2=20 square inches.

There are four copies of Rectangle A in the prism, so the total area of all the copies of Rectangle A is

20*4=80 square inches.

b) To find the area of the Face B squares, you need to multiply the length and the height of one square. In this case, both the length and the height are 2 inches, so the area of one square is

2*2=4 square inches.

There are two copies of Square B in the prism, so the total area of all the copies of Square B is

4*2=8 square inches.

To find the total surface area of the prism, you need to add the areas of all the faces. In this case, the total surface area is

80+8=88 square inches.

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THE COMPLETE QUESTION WAS NOT FOUND

the height of the flag pole should be 108 inches.

Answer:

To earn $65 in interest in 16 months at a simple interest rate of 3%, you would need to invest $2,166.67. The formula for calculating simple interest is I = P * R * T, where I is the interest earned, P is the principal amount invested, R is the interest rate, and T is the time in years. In this case, we are given that the interest rate is 3%, the time is 16 months, and the interest earned is $65, so we can plug these values into the formula to solve for the principal amount invested:I = P * R * T

$65 = P * 0.03 * (16/12)

$65 = P * 0.03 * (4/3)

$65 = P * 0.01

P = $2,166.67Therefore, to earn $65 in interest in 16 months at a simple interest rate of 3%, you would need to invest $2,166.67.

The Mann-Whitney U test is not appropriate for a comparison of two means in a causal comparative study.

To determine if two samples are likely to come from the same population, researchers employ the Mann Whitney U test, also known as the Mann Whitney Wilcoxon Test or the Wilcoxon Rank Sum Test (i.e., that the two populations have the same shape). When a continuous level variable is measured across all observations in two groups and we wish to test if the distribution of this variable differs between the two groups but we are unable to assume normality in both groups, we use the Mann-Whitney test.

Here,

Mann-Whitney test In a causal comparative investigation, comparing two means is not acceptable using the U test.

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The population of Greene country in 2015 was 51408 which is greater than the population of Orange country in 2015.

What is an exponential function?

The definition of an exponential function is given by the equation

y = aeᵇˣ, where a and b are constants.

The given function is f(x) = 87000(0.9)ˣ.

Given that x = 0 represents the year 2010.

Therefore, x= 5 represents the year 2015.

Substitute x = 5 into the given function:

f(5) = 87000(0.9)⁵

    ≈ 51373

Hence, the population of Orange country is about 51373 in 2015.

Now, the population of Greene country was 78000 in 2010 and has decreased exponentially at a rate of 8% each year.

The population of Greene city after 5 years is given by:

78000(1-8%)⁵

= 78000(1 - 0.08)⁵

= 78000(0.92)⁵

= 51408

Therefore, the population of Greene country in 2015 was 51408 which is greater than the population of Orange country in 2015.

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[tex]2x^4 - 5x^3 + 6x^2 - 15x \\ \\ =x(2x^3 - 5x^2 + 6x-15) \\ \\ =x(x^2(2x-5)+3(2x-5)) \\ \\ =\boxed{x(2x-5)(x^2+3)}[/tex]

Answer:

x=-1

Step-by-step explanation:

we 2 minus 1 and plus 3 (i forgot)

After 25 years, about 52g of the sample will be left and the sample never reaches half of its original amount

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

A(t)= 200е⁻⁰⁰⁵⁴⁺

Also from the question, we have

The variable t represents the number of years

This means that

t = 25, in this case

So, we have

A(25)= 200е⁻⁰⁰⁵⁴ ˣ ²⁵

Evaluate the above equation

A(25)= 51.848052128

Approximate

A(25) = 52

This means that the remaining sample is 52 grams

Here, we have

A(t) = 0.5 * 200

A(t) = 100

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

200е⁻⁰⁰⁵⁴⁺ = 100

Divide both sides by 100

е⁻⁰⁰⁵⁴⁺ = 0.5

Take the natural logarithm of both sides

0.054t = -0.69314718056

So, we have

t = -0.69314718056/0.054

Evaluate

t = -13

Time cannot be negative

This means that it never reaches half of its original amount

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Answer:

(0,3)

Step-by-step explanation:

(0,3) is not on the graph