From the diagram below, if AD = 5, and DB = 10, what is the length of CD? ​

[tex] - 4 = \frac{ - 9 + x}{2} \\ - 8 = - 9 + x \\ x = 1[/tex]

[tex]1 = \frac{5 + y}{2} \\ 2 = 5 + y \\ y = - 3[/tex]

1) The equation of the parallel line in Slope Intercept Form is; y = -x - 1

2) The equation of the perpendicular line in Slope Intercept Form is;

y = ³/₂x - 4

1) When two lines are parallel, it means their slopes are the same.

Formula for equation in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Thus, slope of y = -x + 1 is m = -1.

Equation of parallel line is;

(y - (-5))/(x - 4) = -1

y + 5 = -x + 4

y = -x - 1

2) When two lines are perpendicular, it means their slopes are the negative inverse of each other. Thus;

Slope of line = -2/3 and so slope of perpendicular line = 3/2. Thus, equation of new line is;

(y + 1)/(x - 2) = 3/2

2y + 2 = 3x - 6

2y = 3x - 8

y = ³/₂x - 4

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From the given output the regression equation is

StopDist = ₋89.99 ₊5.7053(speed)

The slope of the regression equation is 5.7053

from the Excel output the 95% confidence interval for the slope of the regression line is (5.0809, 6.3296)

By the rejection rule ,reject the null hypothesis.

Given,

from the given output the regression equation is

StopDist = ₋89.99 ₊ 5.7053(speed)

Interpreting the slope of the regression line.

from the given output the regression equation the slope is 5.7053.

To find a 95% confidence interval for the slope of the regression line follow the excel procedure:

From the excel output the 95% confidence interval for the slope of the regression line is (50809, 6.3296).

State the hypothesis

Null hypothesis:

H₀ : β₁ ≠ 0

Alternative hypothesis:

Hₓ : β₁ ≠ 0

Reject rule:

If p value≤ α(=0.05), then reject the null hypothesis.

By the rejection rule, reject the null hypothesis (H₀)

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Polynomials are algebraic expressions whose standard form is defined below:

[tex]p(x) = \sum \limit_{i=0}^{n} c_{i}\cdot x^{i}[/tex]

The expression p(x) = - 13 represents a zeroeth polynomial.

Herein we must present what the form of polynomials are. Polynomials are algebraic expressions whose standard form is defined below:

[tex]p(x) = \sum \limit_{i=0}^{n} c_{i}\cdot x^{i}[/tex]     (1)

Where:

An example is the expression p(x) = - 13, real numbers can be define as zeroeth polynomials. In this regard, the example can be seen as:

p(x) = 0 · xⁿ + 0 · xⁿ⁻¹ + ... + 0 · x² + 0 · x - 13

The statement is incomplete. We decided to re-define the statement to what polynomials are.

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Answer:

FEJ and JED

Step-by-step explanation:

Supplementary means that the pair of angles add up to 180° or a straight angle. FEJ and JED are both 90° and so they add up to 180° But there are many pairs of angles that are NOT 90° that add up to 180° (but they just weren't in the answer choices)

The probability of getting a total less than 4 is 1/12

In a roll of two dice, we have

Outcomes = 36

Sum less than 4 = 3

The probability is then calculated as:

P  = Sum less than 4/Outcomes

This gives

P = 3/36

Simplify

P = 1/12

Hence, the probability of getting a total less than 4 is 1/12

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Answer:

27

Step-by-step explanation:

Answer:

12km

Step-by-step explanation:

Let unknown= x

40 km = 3 2/3 hrs

xkm = 1 hr

cross multiplying

x =44÷ 3 2/3

=12 km

I believe the it would be 2x^2 + 6x + 20 = 0.

Answer:

[tex]\frac{7^{36}}{9^{24}}[/tex]

Step-by-step explanation:

Check the picture

The permutation shows that when one has been cast yet, the different ways that are there to cast Fantine from the 28 women is 28.

The different ways that are there to cast Fantine from the 28 women will be:

= 28!/(28 - 1)!

= 28!/27!

= 28

When Fantine has already been cast, the number of ways that are there to cast adult Cosette from the remaining women will be:

= 27!(27 - 1)!

= 27!/26!

= 26

When Fantine and adult Cosette have already been cast, the different ways that are there to cast Éponine from the remaining women is:

= (28 - 2)!/(28 - 2 - 1)!

= 26!/25!

= 25

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Answer:

28%

Step-by-step explanation:

250÷ .28 = 180

.28 = 28%

Answer:

8x + 16

Step-by-step explanation:

(f - g)(x) = f(x) - g(x)

g(x) = -(x+4)(x+4)

= -(x² + 4x + 4x + 16)

= -(x² + 8x + 16)

= -x² - 8x - 16

1) Subtract the two functions.

= (-x²) - (-x² - 8x - 16)

= -x² + x² + 8x + 16

= 8x + 16

The inverse function will be g(x) = (x + 3) / 5. Then the value of the function f(5) and g(3) will be 22 and 6/5.

Let the function will be

f: X → Y

Then the inverse function will be

f⁻¹: Y → X

The function is given below.

f(x) = 5x – 3

Then the value of the function f(x) at x = 5, will be

f(5) = 5 × 5 – 3

f(5) = 22

The g(x) is the inverse function of f(x).

Then the function g(x) will be

5g(x) – 3 = x

        g(x) = (x + 3) / 5

Then the value of function g(x) at x = 3, will be

g(3) = (3 + 3) / 5

g(3) = 6 / 5

The complete question is given below.

The function f(x) = 5x – 3. And the function g(x) is the inverse of f(x). Find the value of the function f(5) and g(3).

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Step-by-step explanation:

length = 2 × width

the perimeter of a rectangle is

2×length + 2×width

and it is 360 yards in our case

2×length + 2×width = 360

and then we use the first equation (2×width = length) in this second equation :

2×length + length = 360

3×length = 360

length = 360/3 = 120 yards

The solution to the inequality is (7/6, ∝) and (-∝, 7/6)

The inequality expression is given as:

2−5|6x−4|<−13

Subtract 2 from both sides

|6x−4|<−15

Divide through by -5

|6x−4| > 3

Remove the inequality sign

6x - 4 > 3 or 6x - 4 < 3

Add 4 to both sides

6x > 7 or 6x < 7

Divide by 6

x > 7/6 or x < 7/6

In interval notation, we have:

(7/6, ∝) and (-∝, 7/6)

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1(2x^9y^n) (4x²y^10)-8x^11 y^20

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Answer:

C: 10

Step-by-step explanation:

Edge 2022

The radioactive isotope of phosphorus P-32 is used as a tracer in the liver. If 3.5 mg is left in a sample after 288 hrs then the initial amount of P-32 administered was 7 mg.

A radioactive isotope is a form of an element that has an unstable nucleus and undergoes radioactive decay, emitting radiation in the form of particles and/or energy.

These isotopes can be used for various purposes in medicine, industry, and research.

We can use the radioactive decay formula to solve this problem:

N = N0 * (1/2)^(t/T)

where:

- N is the final amount of P-32 remaining after 288 hours (3.5 mg)

- N0 is the initial amount of P-32

- t is the time elapsed (288 hours)

- T is the half-life of P-32 (14.3 days converted to hours is approximately 343.2 hours)

Substituting the given values into the formula, we get:

3.5 mg = N0 * (1/2)^(288/343.2)

Simplifying and solving for N0:

N0 = 3.5 mg / (1/2)^(288/343.2) = 7 mg

Therefore, the initial amount of P-32 administered was 7 mg.

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Answer:

za

Step-by-step explanation:

Answer:

x=8 and y=3 (So, yes!)

Step-by-step explanation:

I will solve your system by substitution.

(You can also solve this system by elimination.)

−x+4y=4;−x+3y=1

Step: Solve −x+4y=4 for x:

−x+4y+−4y=4+−4y(Add -4y to both sides)

−x=−4y+4

-x/-1 = -4y+4/-1 (Divide both sides by -1)

x=4y−4

Step: Substitute 4y−4 for x in −x+3y=1:

−x+3y=1

−(4y−4)+3y=1

−y+4=1(Simplify both sides of the equation)

−y+4+−4=1+−4(Add -4 to both sides)

−y=−3

-y/-1 = -3/-1 (Divide both sides by -1)

y=3

Step: Substitute 3 for y in x=4y−4:

=4y−4

x=(4)(3)−4

x=8(Simplify both sides of the equation)

Answer:

x=8 and y=3

The answer to this question is y = 847728300000/1366991599

Given 4y/1.025⁴ ₊ y ₋ 2y × 1.05² = 1500

1. covert decimal to fraction

= 4y/(1025/1000)⁴ ₊ y ₋ 2y × (105/100)² = 1500

2. Calculate the power

4y/2825761/2560000 ₊ y ₋ 2y × 441/400 = 1500

3. Divide the fraction by multiplying its reciprocal

4y × 2560000/2825761 ₊ y ₋ 2y × 441/400 = 1500

4. Multiply the monomials

10240000/2825761 y ₊ y ₋ 2y × 441/400 =1500

5. Combine like terms

10240000/2825761 y ₊ y ₋ 441/200 y = 1500

1366991599/565152200 y = 1500

6. Divide both sides of the equation by the coefficient of variable.

y = 1366991599/565152200 × 1500

y = 847728300000/1366991599

Hence we get the final value as  y = 847728300000/1366991599

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Answer:

12

Step-by-step explanation:

The Surface Area of the cone 12π cm².

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. The theorem can be used to determine how steep mountains or slopes are. To calculate the distance between an observer and a location on the ground when the observer is looking down from a tower or structure. It is mostly utilized in the construction industry.

Given,  A cone with the height of 2√3 and the radius of base is 2 cm.

Since, Surface are of Cone = rlπ + B

Where l= slant height, and B = area of the base

In our case,

r = 2

B = π * r*r = π* 4

for slant height,

Slant makes a perfect right angle triangle with the center line thus,

from Pythagorean theorem,

l² = (2√3)² + 2²

l² = 12 + 4

l = 4 cm

Thus,

Surface area for the Cone = π * 2 *4 + π * 4

Surface area for the Cone = 12π

therefore, Surface Area of the cone 12π cm².

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Answer:

4/5

Step-by-step explanation:

one and one third times as much sugar as chocolate chips

=> S + 1/3(S) = C

one and two thirds cups of sugar is used

=> S + 2/3(S) = ?

now criss cross the two:

S + 1/3(S) = C

S + 2/3(S) = ?

C×(S+2/3(S)) = S + 1/3(S)....find C

C = (S + 1/3(S)) / (S + 2/3(S))

= (3S + S / 3) / (3S + 2S/ 3)

= 3S + S / 3S + 2S

= 4S / 5S

= 4/5.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation for table 3 is y=(5/2)x-4.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is y-intercept.

The slope for the tables,

Table 1.

m₁ = (3-1)/(5-2) = 2/3

m₂ = (43-31)/(20-17) = 12/3 = 4

Since the slope is different the relationship is not linear.

Table 2.

m₁ = (13-10)/(2-1) = 3/1

m₂ = (34-29)/(7-6) = 5/1

Since the slope is different the relationship is not linear.

Table 2.

m₁ = (6-1)/(4-2) = 5/2

m₂ = (31-26)/(14-12) = 5/2

Since the slope is the same the relationship is linear.

The equation for table 3 will,

y = (5/2)x + c

1 = (5/2)2 + c

1 = 5 + c

c = -4

Hence, the equation for table 3 is y=(5/2)x-4.

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Answer:

Step-by-step explanation:

d = r/t

d = 40/40

d = 1 hour

Step-by-step explanation:

just think : what does 40 mph mean ?

it stands for

40 miles per hour

it means with that speed you will drive 40 miles in 1 hour.

20 miles in 1/2 hour.

80 miles in 2 hours and so on.

you always have to multiply both sides of the ratio with the same factor to keep the ratio itself unchanged.

so, as per the definition, it takes 1 hour to drive 40 miles when going 40 mph.

Using the continuity concept, it is found that the function is continuous at x = -3.

A function f(x) is continuous at x = a if it is defined at x = a, and:

[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]

These three values are equal for x = -3, hence the function is continuous at x = -3.

For the other options, the function is not continuous for the reasons given as follows:

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Answer:

D. Opposite angles in a parallelogram are supplementary.

Answer:

Minimum

Step-by-step explanation:

The equation is a quadratic function meaning the the shape is a parabola. The sign of x^2 is + so the graph open upward. Thus the vertex is the minimum point on the graph.

Answer:  -1/9  which is choice B

Explanation:

The term "zeros" refers to the x intercepts.

Plug in y = 0 and solve for x.

y = -9x-1

0 = -9x - 1

9x = -1

x = -1/9

For the given cost equation we have:

a) Fixed cost is $900.

b) For making 25 items the cost is $1150.

c) D: x ∈ [0, 150]

   R: c ∈ [900, 2400]

Here we know that the cost equation is:

c(x) = 10*x + 900.

First, we want to get the fixed cost, it is given by evaluating the function in x = 0.

c(0) = 10*0 + 900 = 900

The fixed cost is 900.

b) Now we want to get the cost for making 25 items, to get this, we just evaluate in x = 25.

c(25) = 10*25 + 900 = 250 + 900 = 1150

c) Now, if the maximum cost is 2400, then the maximum number of items that we can make is x₀, such that:

c( x₀) = 2400 = 10*x₀ + 900

Solving for x₀ we get:

x₀ = (2400 - 900)/10 = 150

Now we want to get the range and domain.

We know that we can make between 0 and 150 items, so the domain is:

D: x ∈ [0, 150]

For the range, we know that the fixed cost for 0 items is 900, and the maximum cost is 2400, then the range is:

R: c ∈ [900, 2400]

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