Find the value of x.

By solving a linear equation we will see that x = -8, and with that we will find that the measure of angle BDC is:

m∠BDC =  68°

On the diagram we can see that:

m∠BDC = (-7x + 12)°

m∠ADC = (-8x + 48)°

Notice that if we add these two angles we get a straight angle, then we can write the linear equation:

(-7x + 12)° + (-8x + 48)° = 180°

Now let's solve that linear equation for x.

-7x + 12 - 8x + 48 = 180

-7x - 8x + 12 + 48 = 180

-15x + 60 = 180

-15x = 180 - 60

-15x = 120

x = 120/-15 = -8

Now that we know the value of x we can replace it on the equation for the measure of BDC to get:

m∠BDC = (-7x + 12)° = (-7*-8 + 12)° = 68°

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Answer:

75/4 or 18¾ as a fraction and 18.75 as a decimal.

                                   Hope this helps!

Answer:

Step-by-step explanation:

For step explanation:

1. write the problem

2. distinguishing the neg sign

3. distributing 3

4. moving like terms next to each other through commutative property

5.  Combining like terms

6. getting rid of parentheses

Explanation

Step 1

we have a rigth triangle, then

let

to find the missing side we an use the Pythagorean theorem. it states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)

so

hence

b=505.66 km

Step 2

angles

a)A

and B

I hope this helps you

Answer:

Step-by-step explanation:

OK:

I won't be able to draw this but if I can I will

1. Find 2/3 of the 12 pieces

2/3*12=

24/3=

8

2. Answer: Shade 8 out of 12 pieces

Let x be the length of the third side.

Thus:

\(\mathsf{25^2=17^2+x^2}\\\\\mathsf{625=289+x^2}\\\\\mathsf{x^2=625-289}\\\\\mathsf{x^2=336}\\\\\mathsf{x=\sqrt{336}}\\\\\boxed{\mathsf{x=4\sqrt{21}}}\)

You have a box that contains g amount of cookies and you are given an additional 3 cookies. How many cookies are in the box (g) if you wanted to put all the cookies into 6 bags, with them all containing 15 each?

A study based on a population sample that includes 2000 respondents would be the most reliable out of the given options.

In statistical analysis, the reliability of a study depends on the representativeness and size of the sample.

A larger sample size generally provides more reliable results as it reduces the sampling error and increases the precision of the estimates.

Given that the population contains 20,000 people, we need to consider which number of respondents would yield the most reliable study.

Option A: 200 respondents

This represents only 1% of the population.

While it is better than having just 2 respondents, it may not be sufficient to accurately capture the characteristics of the entire population.

Option B: 20 respondents

This represents only 0.1% of the population.

With such a small sample size, the study would likely suffer from a high sampling error and may not provide reliable results.

Option C: 2000 respondents

This represents 10% of the population.

While it is a larger sample size compared to the previous options, it still only captures a fraction of the population.

The study may provide reasonably reliable results, but there is room for potential sampling error.

Option D: 2 respondents

This represents an extremely small sample size, accounting for only 0.01% of the population.

With such a small sample, the study would be highly susceptible to sampling bias and would likely yield unreliable results.

Based on the options provided, option C with 2000 respondents would be the most reliable study.

Although it does not include the entire population, a sample size of 2000 respondents provides a larger representation of the population and reduces the potential for sampling error.

However, it's important to note that the reliability of a study depends not only on sample size but also on the sampling method, data collection techniques, and other factors that ensure representativeness.

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Answer:

-5

Step-by-step explanation:

-2+(-3)

-2-3

-5

Answer: -5

Step-by-step explanation: We can use a number line to help us visualize what's going on.

-2 tells us to move 2 units to the left us 0.

Then from there, -3 tells s to move an

additional 3 units to the left and we end up at -5.

I have shown the number line below.

So -2 + -3 is -5.

Answer:

The polynomial function from number 2 is:

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

To write this in standard form, we need to arrange the terms in descending order of degree:

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

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

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

So the standard form of the polynomial function is:

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

Answer:

[0, infinity)

Step-by-step explanation:

Focus on f(x) = sqrt(x) first.  The domain of this function is [0, infinity), and the range is [0, infinity).

The product (f*g)(x) is sqrt(x)*(3x + 2).

This leads to the conclusion that the range of  (f.g) (x) is  identical to the range of sqrt(x), which is [0, infinity).

Answer:

[0, infinity)

Step-by-step explanation:

I just took the test; 100%.

The limit of the function as x approaches -2 is 20.To find the limit of the function (if it exists), we can substitute the given value into the function and simplify. Given function: f(x) = 4x² + 5x - 6x + 2

To find the limit as x approaches -2, we substitute -2 into the function:

f(-2) = 4(-2)² + 5(-2) - 6(-2) + 2
      = 4(4) - 10 + 12 + 2
      = 16 - 10 + 12 + 2
      = 20

Therefore, the limit of the function as x approaches -2 is 20.

To write a simpler function that agrees with the given function at all but one point, we can use a graphing utility. By plotting the given function and observing its behavior, we can create a simpler function that matches the original function except at one point.

However, without further information about the specific behavior of the given function, it is not possible to provide a more detailed explanation or a graph of the simpler function.

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Answer:

The measure of CD is 46

Step-by-step explanation:

From the midpoint theorem, we have,

FG = (1/2)CD

so,

\(13+5x=(1/2)(-3x+52)\\So,\\2(13+5x)=-3x+52\\26+10x=-3x+52\\13x=52-26\\13x=26\\x=26/13\\x=2\)

Now,

\(CD = -3x+52\\since \ x=2\\we \ get\\CD=-3(2) +52\\CD=-6+52\\CD=46\)

Answer:

A) 4

Step-by-step explanation:

Plug in the value for x and y.

(4 x 3) - 2(4)

12 - 8 = 4

Answer:

-19\(x^{2}\) + 8x + 6

Step-by-step explanation:

−12\(x^{2}\)−5x−7\(x^{2}\)+6+13x

= −12\(x^{2}\)−7\(x^{2}\)+13x-5x+6

= -19\(x^{2}\) + 8x + 6

The value of t₄ in the arithmetic sequence is 103/8.To determine the value of t₄ in an arithmetic sequence, we need to use the given information that t₁ = 11 (the first term of the sequence) and S₉ = 243 (the sum of the first 9 terms of the sequence).

We know that the formula for the sum of an arithmetic sequence is Sₙ = (n/2)(2a + (n-1)d), where Sₙ is the sum, a is the first term, n is the number of terms, and d is the common difference.

From the given information, we have S₉ = 243, a = 11, and n = 9. Plugging these values into the sum formula, we can solve for d:

243 = (9/2)(2(11) + (9-1)d)

243 = 9(22 + 8d)

243 = 198 + 72d

45 = 72d

d = 45/72 = 5/8

Now that we have the common difference, we can find t₄ using the formula for the nth term of an arithmetic sequence:

tₙ = a + (n-1)d

t₄ = 11 + (4-1)(5/8)

t₄ = 11 + 3(5/8)

t₄ = 11 + 15/8

t₄ = 88/8 + 15/8

t₄ = 103/8

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The complete question is

"Here is a table giving the number of US households (in thousands) in 2013 by tenure and insurance status:

Insurance status

Owns home

Rents home

Insured

71

13

Uninsured

5

27

Find the marginal distribution of tenure in counts.

Owns home:

Rents home:"

The marginal distribution of tenure in counts who owns a home is 76, while those who rent a home would be 40.

The addition is one of the mathematical operations. The addition of two numbers results in the total amount of the combined value.

For the given data. The marginal distribution of tenure in counts can be calculated as,

Owns home = 71 + 5 = 76

Rents home = 13 + 27 = 40

Hence, The marginal distribution of tenure in counts who owns a home is 76, while those who rent a home would be 40.

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Answer:

  x = 71

Step-by-step explanation:

The base angles of an isosceles triangle are congruent. The sum of angles in a triangle is 180°.

  x° +x° +38° = 180°

  2x = 142 . . . . . . . . divide by °, subtract 38

  x = 71 . . . . . . . . . divide by 2

\(\huge\bf\underline{\underline{\pink{A}\orange{N}\blue{S}\green{W}\red{E}\purple{R:-}}}\)

Let the given triangle be ∆ABC and let B and C be the base of triangle. As per the property we know that the bases of isosceles triangle are congruent or equal.

Also, sum of all angles in triangle is 180°.

By further simplification we get,

\(:\implies\tt{x + x + 38 = 180}\)

\(:\implies\tt{2x + 38 = 180}\)

\(:\implies\tt{2x = 180 - 38}\)

\(:\implies\tt{2x = 142}\)

\(:\implies\tt{x = \frac{142}{2} }\)

\(:\implies\tt{x = 71}\)

The ratio of the amount of money Alice has to the amount Bob has is approximately 3.36 : 1.

According to the problem, two equations can be set up:

If Alice receives n dollars from Bob, then she will have 7 times as much money as Bob. This gives us the equation:

A + n = 7(B - n)

If Alice gives n dollars to Bob, then she will have 2 times as much money as Bob. This gives us the second equation:

A - n = 2(B + n)

We can rearrange these equations to make them easier to solve:

8n = 7B - A

3n = A - 2B

Setting these equal to each other, since they are both equal to 24n, gives:

21B - 3A = 8A - 16B

37B = 11A

A / B = 37 / 11

= 3. 36

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Rate of change between 1 and 3: find the y values for 1 and 3:

Rate of change = (6-1) / (3-1) = 5/2

Rate of change from 2 and 4:

= (10-3) / (4-2) = 7/2

The rate from 2 to 4 is larger because 7/2 is larger than 5/2

Answer:

see below

Step-by-step explanation:

We need to find the slope

m = (y2-y1)/(x2-x1) for the points (1,1) and (3,6)

m = (6-1)/ (3-1)

   = 5/2

the average rate of change is 5/2

m = (y2-y1)/(x2-x1) for the points (2,3) and (4,10)

m= (10-3)/(4-2)

  = 7/2

the average rate of change is 7/2

Answer:

C. PO

Step-by-step explanation:

SURE PO AKO DYAN PA BRAINLEST PO

TAMA PO TALAGA YAN

The parts of the graph when labelled are :

There is the origin which is where the line starts from. The x-axis represents the independent variable, which is the variable that is being manipulated or changed in the experiment.

The y-axis represents the dependent variable, which is the variable that is being measured or observed. A trend line is a line drawn on the graph that shows the overall pattern or trend of the data. The x and y - intercepts are the points where the trend line crosses the x and y - axis.

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Step-by-step explanation:

Hi, there!!!

According to the question we must find the area of shaded region, but we must find area of circle and rectangle to find area of shaded region,

So, let's simply work with it,

Firstly, finding the area of rectangle,

length = 11cm.

breadth = 11cm.

now, area= length× breadth.

or, a = 11cm× 11cm.

a= 121cm^2

Now, let's work out the area of circle.

radius= 5cm

and pi. = 3.14 {using pi value as 3.14}

now,

area of a circle = pi× r^2

or, a= 3.14×5^2

or, a = 78.5 cm^2.

Therefore, The area of a circle is 78.5cm^2.

Now lastly finding the area of shadedregion,

area of shaded region = area of rectangle - area of circle.

or, area of shaded region = 121cm^2 - 78.5cm^2

Therefore, the area of shaded region is 42.5 cm^2.

Hope it helps...

9514 1404 393

Answer:

  supplement of ∠B = 180° -x°

Step-by-step explanation:

The supplement of an angle is the difference between 180° and that angle.

  supplement of ∠B = 180° - m∠B

  supplement of ∠B = 180° -x°

y = sqrt( x-4)

The domain is the value that x can take

sqrt( x-4) ≥ 0

Squaring each side

x-4≥ 0

x≥ 4

The domain is [4,∞)

The bracket means it included the value, parentheses does not include the value)

The range is the value that output can take

The smallest value a square root can be is 0

y ≥ 0

The range is [0,∞)

Answer:

Vale 95.

Me rebajan 27.

95-27=68

Me costará 68.

Step-by-step explanation:

The value of y for the right triangle is equal to 48, which makes the first option correct.

The perpendicular height of the right triangle divides the triangle in two triangles with the same proportions as the original triangle.

60/x = 36/60 {opposite/hypotenuse}

x = (60 × 60)/36 {cross multiplication}

x = 100

by Pythagoras rule the unlabeled side of the entire triangle is calculated as:

√(100² - 60²) = 80

so;

y/80 = 60/100 {opposite/hypotenuse}

y = (60 × 80)/100 {cross multiplication}

y = 48

Therefore, the value of y for the right triangle derived to be 48.

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