Graphing Geometry. Show work

The missing part of the attached proof:

a) definition of angle congruence

b) ∠CPA ≅ ∠CPB

c) CP ≅ CP

The complete paragraph proof would be,

Because CP is perpendicular bisector of AB, CP is perpendicular to AB and point P is the midpoint of AB.

By definition of midpoint,

AP = BP

and by the definition of perpendicuar lines,

m∠CPA = m∠CPB = 90°

Then by definition of segment congruence,

AP ≅ BP

and by definition of angle congruence,

∠CPA ≅ ∠CPB

By the reflexive property of segment congruene,

CP ≅ CP

So, ΔCPA ≅ ΔCPB         ........by SAS congruence theorem

and CA ≅ CB because corresponding parts of congruent triangles are congruent.

So, CA = CB by the definition of segment congruence.

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The length of the rectangle with the above information is calculated as: 7 feet.

Let the length of the rectangle be l and the width be w. Then, we know that:

Perimeter = 2(l + w) = 18 feet

Area = lw = 14 square feet

We can use the first equation to solve for one of the variables in terms of the other:

l + w = 9

l = 9 - w

Substituting l = 9 - w into the equation for the area, we get:

(9 - w)w = 14

w² - 9w + 14 = 0

Factorize

(w - 2)(w - 7) = 0

Therefore, w = 2 or w = 7. Since the length of the rectangle must be larger than its width, we choose w = 2 and l = 9 - w = 7.

Thus, the length of the rectangle is 7 feet.

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Answer:

<2  = 30°

Step-by-step explanation:

Let angle 1 = x

Let angle 2 = y

x + y = 95

x = 35 + y  Substitute 35 + y for x in x + y = 95

x + y = 95

35 + y + y = 95  Subtract 35 from both sides

y + y = 60    Combine like terms

2y = 60  Divide both sides by 2

y = 30

Helping in the name of Jesus.

The solution to the equation is x = 33/5.

We can start by simplifying both sides of the equation using the distributive property and combining like terms:

4/3 (x + 6) = 2x - 3 + x

4/3 x + 8 = 3x - 3

Next, we can isolate the variable x on one side of the equation by subtracting 4/3 x and adding 3 to both sides:

4/3 x - 3x = -8 - 3

-5/3 x = -11

Finally, we can solve for x by dividing both sides by -5/3:

x = -11 / (-5/3)

x = 33/5

Therefore, the solution to the equation is x = 33/5.

Answer: 16 pounds

Step-by-step explanation:

12/3=4 and 4x4=16

The solution to the inputs of the given function are:

a) f(0) = 13

b) f(2) = -1

c) f(-2) = 27

d) f(1) + f(-1) = 26

The set of input values of a function is referred to as the domain of the function. Then, the set of output values of the function is referred to as the range of the function. Thus, if we possess a set of ordered pairs, we can find the domain by listing all of the input values, which are the x-coordinates.

We are given the function:

f(x) = (-x)³ - x² - x + 13

a) f(0) = (-0)³ - (0)² - 0 + 13

f(0) = 13

b) f(2) = (-2)³ - (2)² - 2 + 13

f(2) = -1

c) f(-2) = (2)³ - (-2)² + 2 + 13

f(-2) = 27

d) f(1) = (-1)³ - (1)² - 1 + 13

f(1) = 10

f(-1) = (1)³ - (-1)² + 1 + 13

f(-1) = 16

f(1) + f(-1) = 10 + 16 = 26

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The vocabulary for a is called the apothem

The area of the regular polygon is [tex]2419.68 cm^2.[/tex]

a = 7√3 cm

s = 14 cm

The perimeter of the polygon is:

P = ns

where n is the number of sides of the polygon. We can find n using the formula:

[tex]n = 360 / (180 - (360 / 2n))[/tex]

where n is the number of sides. Substituting the given value for s, we get:

[tex]n = 360 / (180 - (360 / 2*7)) = 14[/tex]

Therefore, the polygon has 14 sides.

a = [tex]\sqrt{31.820 cm)^2 - (14 cm/2)^2}[/tex])

= 24.615 cm

A = (1/2) * apothem * perimeter

[tex](\frac{1}{2} ) * 24.615 cm * 196 cm \\=\\ 2419.68 cm^2[/tex]

Therefore, the area of the regular polygon is [tex]2419.68 cm^2.[/tex][tex]2419.68 cm^2.[/tex]

In summary,

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The measure of the side length x is 15.04.

The figure in the image is a right triangle.

Angle θ = 43 degrees

Adjacent to angle θ = 11

Hypotenuse = x

To determine the measure of the side length x, we use the trigonometric ratio.

Note that: cosine = adjacent / hypotenuse

Plug in the values:

cos( 43° ) = 11 / x

Solve for x

x = 11 / cos( 43° )

x = 15.04

Therefore, the value of x is 15.04 units.

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The probability that the population percentage would differ from the sample proportion of flops in a sample of 407 released films by less than 3% is roughly 0.8354, rounded to four decimal places.

For the trials we are looking at, the probability of receiving a success in a binomial distribution must stay constant. Since there are only two possible outcomes when tossing a coin, for instance, the probability of flipping a coin is 12 or 0.5 for each experiment we conduct.

To determine the likelihood that the sample proportion of flops is within 3% of the population proportion, we need to know the chance that |p - 0.09| 0.03.

We can suppose that the sample proportion's distribution is

approximately normal with mean μ = 0.09 and standard deviation σ = √((0.09)(0.91)/407)

≈ 0.017.

We may calculate the z-scores for the top and lower boundaries of the interval using the conventional normal distribution:

z1 = (0.06 - 0.09) / 0.017 ≈ -1.76

z2 = (0.12 - 0.09) / 0.017 ≈ 1.76

The probability between these two z-scores is represented by the region beneath the standard normal curve:

P(-1.76 < Z < 1.76)

= 0.9177 - 0.0823

= 0.8354

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Answer:

13.3333333333 or 13.3

Step-by-step explanation:

yeah :3

Answer:

[tex]y = -2(x - 1)^2 + 3[/tex]

Step-by-step explanation:

The given figure which is a quadratic is the shape of a parabola

The general vertex form equation of a parabola is
[tex]y = a(x - h)^2 + k[/tex]

where,
( h, k ) is the vertex and a is a constant

Looking at the figure we see the vertex is at [tex](1, 3)[/tex]

So the equation of the parabola is

[tex]y = a(x - 1)^2 + 3[/tex]

To compute the constant [tex]a[/tex] take a point (x, y) through which the parabola passes, plug in these x, y values into the above equation and solve

The parabola passes through point   [tex](3, -5)[/tex]

Plugging

[tex]x = 3, y = -5[/tex]

gives
[tex]- 5 = a(3-1)^2 + 3\\\\-5 = a\cdot 2^2 + 3\\\\-5 = 4a + 3\\\\-5-3=4a\\\\-8 = 4a\\\\a = -8/4 = -2\\\\[/tex]

Therefore the equation of the given quadratic(parabola) is

[tex]y = -2(x - 1)^2 + 3[/tex]

Answer:

1:8

Step-by-step explanation:

The original volume of the box can be calculated by multiplying the length, height, and width:

V = l x h x w = 40 x 8 x 20 = 6,400 cubic inches

If each of the dimensions is reduced by half, the new dimensions become:

Length = 20 inches

Height = 4 inches

Width = 10 inches

The volume of the new box can be calculated as follows:

V_new = l x h x w = 20 x 4 x 10 = 800 cubic inches

The ratio of the volume of the new box to the volume of the original box is:

V_new / V = 800 / 6,400 = 1/8

Therefore, the ratio of the volume of the new box to the volume of the original box is 1:8.

Answer:

I think it's 1 : 8

Step-by-step explanation:

if you don't understand, you can ask me

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Therefore, 4,000 centimeters are equivalent to 40 meters. Hence, the answer is A) 4,000 cm.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides, left-hand side (LHS) and right-hand side (RHS), connected by an equal sign (=). The LHS and RHS can contain numbers, variables, operators, and functions, and the equal sign indicates that the value of the expression on the LHS is equal to the value of the expression on the RHS.

Here,

Since there are 100 centimeters in one meter, we can convert meters to centimeters by multiplying the length in meters by 100.

So, to convert 40 meters to centimeters, we can multiply 40 by 100:

40 meters = 40 x 100

= 4,000 centimeters

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Answer:

symbols V

The symbols V L and D are not written to the left of a symbol that has greater value

Answer:

3. radius = 9.4

4. radius = 22.6

5. diameter = 13.3

Step-by-step explanation:

The diameter of a circle = 2 * radius

For problem 3 and 4,  you need to multiply the given radius by 2 to get the diameter.

For problem 5, you need to divide the diameter by 2 to get the radius.

a) We are given that f(x) = x^3 - 10x^2 + 19x + 30 and x - 6 is a factor of f(x). Using long division or synthetic division, we can divide f(x) by x - 6 to get the other factor(s):

 6 │ x^3 - 10x^2 + 19x + 30

     x^3 - 6x^2

     -------------

          -4x^2 + 19x

          -(-4x^2 + 24x)

          ---------------

                     5x + 30

                     5x - 30

                     -------

                            0

Therefore, we can write:

f(x) = (x - 6)(x^2 - 4x + 5)

The quadratic factor x^2 - 4x + 5 cannot be factored further using real numbers.

b) We are given that f(x) = x^3 + 6x^2 + 5x - 12 and x + 4 is a factor of f(x). Using long division or synthetic division, we can divide f(x) by x + 4 to get the other factor(s):

-4 │ x^3 + 6x^2 + 5x - 12

     -x^3 - 4x^2

     --------------

              2x^2 + 5x

              2x^2 + 8x

              ------------

                     -3x - 12

                     -3x - 12

                     --------

                            0

Therefore, we can write:

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

The quadratic factor x^2 + 2x - 3 can be factored further using the product-sum method:

x^2 + 2x - 3 = (x + 3)(x - 1)

Therefore, we have:

f(x) = (x + 4)(x + 3)(x - 1)

To find the mean time it takes for Diane and her friends to complete the obstacle course, we added up the time taken by each person and divided by the total number of people. The mean time is 13.0 minutes.

Add up the time taken by each person

Diane: 12

Friend 1: 14

Friend 2: 10

Friend 3: 16

Total time = 12 + 14 + 10 + 16 = 52 minutes

Count the total number of people:

Diane and three friends, so the total number of people = 4

Divide the total time by the total number of people to find the mean time

Mean time = Total time / Total number of people

Mean time = 52 / 4

Mean time = 13.0 minutes

Therefore, the mean time it takes for Diane and her three friends to complete the obstacle course is 13.0 minutes.

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--The given question is incomplete, the complete question is given

" Diane is a camp counselor she designs a new obstacle course in testicles with three friends. The plot data shows the time it takes them to complete the obstacle course. What is the mean of time

the plot data for the time taken by each person in minutes is as follows

Diane: 12

Friend 1: 14

Friend 2: 10

Friend 3: 16 "--

Answer:  The value of the test statistic to 2 d.p is z= 1.65

Step-by-step explanation:

P cap= 0.72

n= 170

P= 0.66

q= 1- p

q= 1- 0.66

q= 0.34

Z=( p cap - p)/√(p*q)/n

Z= (0.72- 0.66)/√(0.66*0.34)/170

Z= 0.06/0.036332

Z= 1.65

Answer:

Step-by-step explanation:

1/3 is greater.

Answer:

34

Step-by-step explanation:

This is sequnce has an easy pattern with adding 1 to the difference every time and goes +4, +5, +6 , so the next should be +7

Answer: think it’s a5=34

Step-by-step explanation:

Answer:5.25cm

Step-by-step explanation:

1)look back at your question

2)look after the 6th word

In 1973, the batting average of .350 of Rod Carew is more impressive as it has a higher z-score of 2.81

To establish which batting average was more spectacular, we must compare it to the mean and standard deviation of 1970s hitting averages. The case of Jackie Robinson,

z = (x - μ) / σ

z = (.342 - .261) / .0317

z = 2.56

For Rod Carew,

z = (x - μ) / σ

z = (.350 - .261) / .0317

z = 2.81

A higher z-score indicates a more impressive performance relative to the mean. As a result, Rod Carew's .350 batting average was more spectacular, as it had a higher z-score of 2.81 than Jackie Robinson's z-score of 2.56.

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The correct statement which is true about all perfect cubes is,

⇒ A perfect cube represents 3 times the area of a face of the cube.

We have to given that;

The model shown below is a perfect cube with a volume of 27 cubic units.

Now, We can formulate;

⇒ V = 27 cubic units.

⇒ V = 3 × 9 cubic units.

⇒ V = 3 × 3² cubic units.

Thus, The correct statement which is true about all perfect cubes is,

⇒ A perfect cube represents 3 times the area of a face of the cube.

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Answer:

Step-by-step explanation:

The sampling distribution of the sample mean for samples of size n is approximately normal with mean μ and standard deviation σ/sqrt(n), where μ is the mean of the population, σ is the standard deviation of the population, and sqrt(n) is the square root of the sample size.

In this case, the population mean is μ = 112 and the population standard deviation is σ = 22. We are interested in the sampling distribution of the sample mean for samples of size n = 16.

The mean of the sampling distribution of the sample mean is the same as the population mean, which is μ = 112.

The standard deviation of the sampling distribution of the sample mean is σ/sqrt(n) = 22/sqrt(16) = 5.5.

Therefore, the sampling distribution of the sample mean for samples of size 16 is approximately normal with mean 112 and standard deviation 5.5.

The probability of choosing a red marble is 6/17.

The probability of an event occurring is the number of favorable outcomes divided by the total number of possible outcomes.

To calculate this probability, we can use the formula:

P(red marble) = number of red marbles / total number of marbles

In this case, we substitute the numbers we know:

P(red marble) = 6 / 17

So the probability of choosing a red marble is 6/17 or approximately 0.35.

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Answer:

3rd choice:  when b>1

Step-by-step explanation:

For this function, a is the starting value (initial amount).  b is the decay or growth factor.  If b>1, then the function is a growth function.

FYI, if 0 < b < 1, then it is a decay function.

The number of acres pollinated by the bees in 18 beehives is 48 acres.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

The variables for this problem are given as follows:

x: number of beehives.

y: number of acres.

From the table, the constant is obtained as follows:

3k = 8

k = 8/3

Hence the equation is of:

y = 8x/3.

The number of acres that will be pollinated by 18 beehives is then given as follows:

y = 8(18)/3

y = 48 acres.

Therefore, the number of acres pollinated by the bees in 18 beehives is 48 acres.

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the equation for the curve C as n approaches infinity     is           y = x This is the equation of the diagonal line that passes through the points (0, 0) and (1, 1).

what is diagonal line ?

A diagonal line is a straight line that runs obliquely (at an angle) between two opposite corners of a geometric shape, such as a rectangle or a square. It is called "diagonal" because it connects two non-adjacent vertices of the shape, forming a diagonal across the interior of the shape.

In the given question,

As n increases, the process described in the question creates a set of line segments that connect the equally spaced points on the x-axis to the equally spaced points on the y-axis. The resulting curve is a piecewise linear function that converges to a continuous curve as n approaches infinity.

To derive an equation for this curve, we can start by considering the line segment connecting the first mark on the x-axis to the last mark on the y-axis. Let's call this point (0, 1) and the nth mark on the x-axis (1, 0). The slope of the line connecting these two points is given by:

m = (0 - 1) / (1 - nth mark) = (1 - nth mark)^(-1)

where the nth mark on the x-axis is given by:

nth mark = 1 - (1/n)

Substituting this expression for nth mark into the equation for m, we get:

m = (n/(n-1))

The y-intercept of the line is given by:

b = 1 - m = 1 - (n/(n-1)) = 1/(n-1)

Therefore, the equation for the line segment connecting the first mark on the x-axis to the last mark on the y-axis is:

y = (n/(n-1))x + 1/(n-1)

Similarly, the equation for the line segment connecting the second mark on the x-axis to the second last on the y-axis is:

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

Continuing this process for all n line segments, we get:

y = (n/(n-k))x + 1/(n-k)

where k = 1, 2, ..., n.

To get the equation for the curve C, we need to take the limit as n approaches infinity. As n goes to infinity, the value of k becomes insignificant compared to n, and we can approximate the equation for the curve as:

y = x

Therefore, the equation for the curve C as n approaches infinity is:

y = x

This is the equation of the diagonal line that passes through the points (0, 0) and (1, 1).

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