find the parametric equations for the line through the point p = (-4, 4, 3) that is perpendicular to the plane 2 1 0 = 1. at what point q does this line intersect the yz-plane?

The probability that the weight of a randomly selected steer is less than 1700lbs is 0.9772.

To solve this problem, we need to use the standard normal distribution with a mean of 0 and a standard deviation of 1. We can convert the given data into a standard normal distribution by using the formula:

z = (x - μ) / σ

where z is the z-score, x is the given value, μ is the mean, and σ is the standard deviation.

In this case, we want to find the probability that a randomly selected steer weighs less than 1700lbs. So we need to find the z-score for 1700lbs:

z = (1700 - 1400) / 200

z = 1.5

We can then use a standard normal distribution table or calculator to find the probability that a z-score is less than 1.5. This probability is 0.9332.

However, since we want to find the probability that a randomly selected steer weighs less than 1700lbs (not less than or equal to), we need to add half of the probability of the z-score being exactly 1.5 to this result:

0.9332 + 0.0228 = 0.956

Therefore, the probability that a randomly selected steer weighs less than 1700lbs is 0.9772 (rounded to four decimal places).

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Answer:

7083 KM/H

Step-by-step explanation:

17000 / 2.4 = 7083 (Plus some decimals, but rounded up its 7083.)

Answer:

no

Step-by-step explanation:

5(-4)+3(-7)+2= -20-21+2=-39

To determine the cost of production when the price is $9: Evaluate C(D(9))

The given function is h(x) = (x + 8)6, which can be represented as f(g(x)). Where, f(x) = x6 is given, and g(x) is to be found out. Therefore, we need to find g(x).

Let D(p) give the number of items demanded when the price is p and C(x) be the cost of producing x items. We can now express g(x) as follows:

g(x) = D-1(C(x))

where D-1(x) is the inverse of D(x).The cost of production when the price is $9 can be determined by evaluating C(D(9)).

This can be calculated as follows: C(D(9)) = C(2) = 24

Thus, the cost of production when the price is $9 is $24.

To solve D(C(x)) = 9, we need to find D(x) first and then solve for x.

In order to solve C(D(p)) = 9, we need to find D(p) first and then solve for p.

C(D(9)) = C(2) = 24D(C(x)) = 9 is equivalent to C(x) = 4, and its solution is D-1(4) = 5

Solve C(D(p)) = 9 is equivalent to D(p) = 2, and its solution is C(2) = 24.

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Answer:

6 hours

Step-by-step explanation:

Ella takes 1 3/5 hours to complete a painting. Holly takes 3/4 of the time that Ella takes. How long will Holly take to complete 5 paintings?

Ella =1 3/5 hours = 8/5 hours

Holly = 3/4 of 8/5 hours

= 3/4 × 8/5

= (3*8)/(4*5)

= 24/20

= 6/5 hours

Number of hours : number of painting = 6/5 hours : 1 painting

How long will Holly take to complete 5 paintings

Let x = number of hours

Number of hours : number of painting = x hours : 5 painting

6/5 hours : 1 painting = x hours : 5 painting

6/5 ÷ 1 = x ÷ 5

6/5 × 1/1 = x / 5

6/5 = x / 5

Cross product

6 * 5 = 5 * x

30 = 5x

x = 30/5

x = 6 hours

It will take Holly 6 hours to complete 5 paintings

The formula for finding the surface area of a sphere is given as;`Surface area of sphere = 4πr²`, where r is the radius of the sphere.We are given that the area of a great circle is 814.3.Therefore, the circumference of the great circle can be calculated as;`Circumference = πd`, where d is the diameter of the sphere.Since the great circle is a cross-section of the sphere, we can say that it is equal to the circumference of the sphere.`πd = 814.3`We can rearrange this formula to find the diameter;`d = 814.3/π`We can then use the diameter to find the radius of the sphere;`r = d/2`Now, we can substitute the value of r in the formula of the surface area of the sphere;`Surface area of sphere = 4πr²`= 4 x π x (d/2)²`= 4 x π x (814.3/2π)²`= 166271.2`Therefore, the surface area of the sphere is approximately equal to 166271.2 square units.

Answer:

3257.94 square units.

Step-by-step explanation:

To find the surface area of a sphere with the area of a great circle given, we can use the formula:

Surface Area = 4πr^2

Here, r represents the radius of the sphere.

Since the area of a great circle is equal to πr^2, we can determine the radius using the given area. Let's solve for r:

πr^2 = 814.3

Divide both sides of the equation by π:

r^2 = 814.3 / π

r^2 ≈ 259.65

Now, take the square root of both sides to find the radius:

r ≈ √259.65

r ≈ 16.10 (rounded to two decimal places)

Now that we have the radius, we can calculate the surface area of the sphere:

Surface Area = 4πr^2

Surface Area = 4π(16.10)^2

Surface Area ≈ 4π(259.21)

Surface Area ≈ 1036.84π

Given,x1 = 361n1 = 519x2 = 448n2 = 596And the level of confidence = 95%The confidence interval formula for the difference between two population proportions p1 - p2 is given as follows:p1 - p2 ± zα/2 * √((p1q1/n1) + (p2q2/n2))Whereq1 = 1 - p1, and q2 = 1 - p2zα/2 is the z-score obtained from .

The standard normal distribution table using the level of significance α/2.The formula for the standard error of the difference between two sample proportions is given by:SE = √[p1(1 - p1)/n1 + p2(1 - p2)/n2]Where,p1 = x1/n1, and p2 = x2/n2Now, we will substitute the given values in the above formulas.p1 = x1/n1 = 361/519 = 0.695p2 = x2/n2 = 448/596 = 0.751q1 = 1 - p1 = 1 - 0.695 = 0.305q2 = 1 - p2 = 1 - 0.751 = 0.249SE = √[p1(1 - p1)/n1 + p2(1 - p2)/n2] = √[(0.695 * 0.305/519) + (0.751 * 0.249/596)] ≈ 0.0365zα/2 at 95% .

Confidence level = 1.96Putting these values in the confidence interval formula:p1 - p2 ± zα/2 * √((p1q1/n1) + (p2q2/n2))= (0.695 - 0.751) ± 1.96 * √[(0.695 * 0.305/519) + (0.751 * 0.249/596)]= -0.056 ± 1.96 * 0.0365= -0.056 ± 0.071= [-0.127, 0.015].

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Answer:

Answer 1 is 4:2 or also write as 2:1.

The maximum rate of change of the function f(x,y) at the point (-2,5) is approximately 215.60.

To find the maximum rate of change of the function f(x,y) = 4x1x2y2 - 7y2 at the point (-2,5), we need to calculate the gradient vector and evaluate it at that point. The first paragraph provides a summary of the answer, and the second paragraph explains the details of the calculations.

The gradient vector of a function represents the direction of the steepest increase at any given point. To find the maximum rate of change, we need to calculate the magnitude of the gradient vector at the point (-2,5).

The gradient vector of f(x,y) = 4x1x2y2 - 7y2 is given by:

∇f = (∂f/∂x1, ∂f/∂x2, ∂f/∂y)

To calculate the partial derivatives, we differentiate each term of the function with respect to the corresponding variable:

∂f/∂x1 = 4x2y2

∂f/∂x2 = 4x1y2

∂f/∂y = -14y

Substituting the values x1 = -2, x2 = 5, and y = 5 into the partial derivatives, we can evaluate the gradient vector at the point (-2,5):

∇f(-2,5) = (4(-2)(5)^2, 4(-2)(5), -14(5))

         = (-200, -40, -70)

The magnitude of the gradient vector represents the maximum rate of change of the function at the given point:

Magnitude = |∇f(-2,5)| = √((-200)^2 + (-40)^2 + (-70)^2)

                       = √(40000 + 1600 + 4900)

                       ≈ √46500

                       ≈ 215.60

Therefore, the maximum rate of change of the function f(x,y) at the point (-2,5) is approximately 215.60.

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The second derivative, inflation point and slope of differential equation are explained below.

differential equation states how a pace of progress (a "differential") in one variable is connected with different factors. For example, when the position is zero (ie. the spring is neither extended nor compacted) then the  velocity isn't evolving.

We have,

dy/dx = 2x-y

Suppose f'(x) = 2x - y

d^2y/dx^2 = d(2x - y)/dx

⇒ 2

(b) To find the inflection points, equate f(x) to zero and solve for x.

f"(0) =0

f" (x)=2

So, the function defined on the interval (- ∞, 2) (2,  ∞)

In the interval (- ∞, 2), when x-1

f"(1)=2>0

So, the concave up wards on this interval.

In the interval (2,∞) when x=2

f"(2)=2>0

the concave up wards on this interval

Now, the slope of the function,

f(2)=3

here x-2y=3

Then, x = 2, y = 3

\(\frac{dy}{dx}|_{2, 3}\) = 2(2) - 3 = 1

Thus, the slope of the function is 1.

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The type of variable for,

a. The number of counties in California: Quantitative discrete.

b. The stages of childhood: Qualitative ordinal.

c. In the scenario above, 23 minutes is a statistic, because 28 students is a sample.

d. Between 6 minutes and 8 minutes: Approximately 68% of the athlete's mile times are expected to be between 6 and 8 minutes, according to the empirical rule.

e. Between 4 minutes and 7 minutes: Approximately 68% of the athlete's mile times are expected to be between 4 and 10 minutes, according to the empirical rule.

f. Less than 9 minutes: Approximately 84% of the athlete's mile times are expected to be less than 9 minutes, according to the empirical rule.

In statistics, variables can be categorized into two types: qualitative and quantitative.

Qualitative variables describe characteristics or qualities that cannot be measured numerically, such as gender or hair color.

Quantitative variables, on the other hand, represent numerical values that can be measured or counted.

There are two types of quantitative variables: continuous and discrete. Continuous variables can take any numerical value within a range, such as age or weight.

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Expected counts are calculated by the test of independence and also by using Homogeneity.

The main difference between a test of independence and a test of uniformity when analyzing voting results from a two-page table is how the expected count is calculated.

The test of independence calculates expected frequencies assuming no relationship between the two variables analyzed and is based on the marginal totals of the two-way table.

Independence tests are used to know whether there is a significant association between two variables or not.

Homogeneity tests, on the other hand, compute expected frequencies assuming that the two groups being compared have the same distribution for the variable being analyzed, based on the row sums of a two-way table.

Homogeneity tests are used to know whether there is a  difference in the distribution of a categorical variable between groups.

The number of columns and rows in the two-way table and the number of samples obtained are important factors to consider when performing both tests.

However, how the expected count is calculated is the main difference between the two tests. The degrees of freedom are also calculated differently for the two tests, but this is secondary. 

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The slope of the line perpendicular to the line through the points (-5,-4) and (3,0) is -7/5.

Slope of the line

The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line. The net change in y coordinate is Δy, while the net change in the x coordinate is Δx.

Slope of the line m = (y2-y1)/(x2-x1)

Given,

Point (-5,-4) and (3,0)

Here we need to find the slope of the line perpendicular to the line.

The slope of a perpendicular line will be equal to the negative inverse of the slope of the original line.

We have to begin by finding the slope of the original line. We can find this by taking the difference in y divided by the difference in x:

m = (0-(-5))/(3-(-4)

m = 5/3+4

m = 5/7

Now to find the slope of a perpendicular line, we just take the negative inverse of 5/7:

So,

m = -1/(5/7)

m = -7/5

This means that the slope of a line perpendicular to the original one is -7/5.

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Answer:

thee correct  answer is c not d

Step-by-step explanation:

i) Selling price of 20 lemons is ₹12.

ii) The profit is ₹2.

iii) The profit percentage is 20%.

i) Jaya bought 20 lemons for ₹10, which means the cost of one lemon is 10/20 = ₹0.50.

If she sells 5 lemons for ₹3, the selling price of one lemon is 3/5 = ₹0.60.

Therefore, the selling price of 20 lemons is 20 x ₹0.60 = ₹12.

ii) The cost price of 20 lemons is ₹10, and the selling price is ₹12.

So, the profit is ₹12 - ₹10 = ₹2.

iii) The profit percentage is calculated as (Profit/Cost price) x 100%.

In this case, the profit is ₹2 and the cost price is ₹10.

So, the profit percentage is (2/10) x 100% = 20%. Therefore, Jaya made a profit of 20% by selling lemons.

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Answer:

6 m

.006 km  

6,000 mm

Step-by-step explanation:

Let's look at some conversions real quick:

1 cm --> 10 mm (multiply cm by 10)

1 cm --> 0.00001 km (divide cm by 100000)

1cm --> 0.01 m (divide cm by 100)

Now that this is laid out, lets do these conversions for 600 cm.

Meters (m) = 600/100 = 6 meters

Kilometers (km) = 600/100000 = .006km

Millimeters (mm) = 600 * 10 = 6,000 mm

I hope this helps!!

- Kay :)

Answer:

18

Step-by-step explanation:

72% of 25 is 18.

Hope this helped! :)

Answer:

x=9

Step-by-step explanation:

3x-7=7+13

3x-7=20

3x=27

27/3

x=9

Answer:

X=9

Step-by-step explanation:

3x-7=7+20

3–7=20

3x=20+7

3x=27

x=9

Answer: The mean is 87

84+ 85 + 85+ 86 +90+ 92 = 522/6 = 87

Step-by-step explanation:

Answer:

87

Step-by-step explanation:

To find the mean of the a set of numbers, we first need to add all the numbers and divide by the number of terms in the set.

84 + 85 + 85 + 86 + 90 + 92 = 522

There are 6 terms so we divide by 6

522/6 = 87

The upper and lower bounds, we have shown that $T(n) = \Theta(n^3)$ for the given recurrence using the induction method and considering the base cases $T(1) = C_1$ and $T(2) = C_2$.

To determine whether the Master theorem applies to the given recurrence relation $T(n) = 2T(n/2) + f(n)$ and show that $f(n) = \Omega\left(n^{\log_b(a) + \epsilon}\right)$, we need to compare $f(n)$ with the lower bound function $n^{\log_b(a) + \epsilon}$, where $\epsilon > 0$.

In this case, we have $a = 2$, $b = 2$, and $f(n)$ defined as follows:

$$

f(n) = \begin{cases}

n^3 & \text{if } \lceil\log(n)\rceil \text{ is even} \\

n^2 & \text{otherwise}

\end{cases}

$$

To show that $f(n) = \Omega\left(n^{\log_b(a) + \epsilon}\right)$, we need to find a positive constant $c$ and an integer $n_0$ such that for all $n \geq n_0$, $f(n) \geq c \cdot n^{\log_b(a) + \epsilon}$.

Let's calculate $\log_b(a)$:

$$

\log_b(a) = \log_2(2) = 1

$$

Now, we need to consider two cases:

Case 1: When $\lceil\log(n)\rceil$ is even

In this case, $f(n) = n^3$. We need to show that $n^3 \geq c \cdot n^{1 + \epsilon}$ for some $c > 0$ and $n_0$.

Dividing both sides by $n$, we get $n^2 \geq c \cdot n^{\epsilon}$. By choosing $c = 1$ and $n_0 = 1$, the inequality holds true for all $n \geq 1$. Therefore, for this case, $f(n) = \Omega\left(n^{\log_b(a) + \epsilon}\right)$.

Case 2: When $\lceil\log(n)\rceil$ is odd

In this case, $f(n) = n^2$. We need to show that $n^2 \geq c \cdot n^{1 + \epsilon}$ for some $c > 0$ and $n_0$.

Again, dividing both sides by $n$, we get $n \geq c \cdot n^{\epsilon}$. By choosing $c = 1$ and $n_0 = 1$, the inequality holds true for all $n \geq 1$. Thus, for this case as well, $f(n) = \Omega\left(n^{\log_b(a) + \epsilon}\right)$.

Since $f(n) = \Omega\left(n^{\log_b(a) + \epsilon}\right)$ for both cases, we can conclude that $f(n) = \Omega\left(n^{\log_b(a) + \epsilon}\right)$.

Now, let's move on to explaining why the third case of the Master theorem does not apply to this recurrence. The third case states that if $f(n) = \Theta(n^{\log_b(a)})$, then $T(n) = \Theta(n^{\log_b(a)} \cdot \log(n))$. However, in our case, $f(n)$ does not satisfy the condition of being equal to $\Theta(n^{\log_b(a)})$.

To prove that $T(n) = \Theta(n^3)$ for this recurrence using the induction method, we

need to establish two things: (1) the upper bound and (2) the lower bound.

Base case:

For $n = 1$, we have $T(1) = C_1$, which satisfies the condition.

For $n = 2$, we have $T(2) = 2T(1) + f(2)$. Let's assume $T(1) = C_1$ and $T(2) = C_2$. By substituting these values, we can solve for $C_2$. Based on the given recurrence relation, we know that $f(2) = 2^2 = 4$. Therefore, $C_2 = 2C_1 + 4$.

Inductive hypothesis:

Assume that for all $k \leq n$, $T(k) = C_k$.

Inductive step:

We need to show that $T(n + 1) = C_{n+1}$.

Using the recurrence relation, we have:

$$

T(n + 1) = 2T\left(\frac{n+1}{2}\right) + f(n + 1)

$$

For simplicity, let's assume $n$ is a power of 2. The proof can be generalized to non-power-of-2 values as well.

By using the inductive hypothesis, we have:

$$

T(n + 1) = 2C_{(n+1)/2} + f(n + 1)

$$

Now, let's consider the two cases of $f(n + 1)$:

Case 1: When $\lceil\log(n+1)\rceil$ is even

In this case, $f(n + 1) = (n + 1)^3$. By substituting this into the equation, we get:

$$

T(n + 1) = 2C_{(n+1)/2} + (n + 1)^3

$$

Case 2: When $\lceil\log(n+1)\rceil$ is odd

In this case, $f(n + 1) = (n + 1)^2$. By substituting this into the equation, we get:

$$

T(n + 1) = 2C_{(n+1)/2} + (n + 1)^2

$$

In either case, we can see that the recurrence relation is a linear combination of the inductive hypothesis $C_{(n+1)/2}$ and a polynomial term.

Now, let's prove by induction that $T(n) = \Theta(n^3)$.

Base case: We have already established the base case.

Inductive hypothesis: Assume that for all $k \leq n$, $T(k) = C_k$, where $C_k = 2C_{k/2} + f(k)$.

Inductive step: We need to show that $T(n + 1) = C_{n+1}$. Based on the two cases above, we have:

$$

T(n + 1) = 2C_{(n+1)/2} + f(n + 1)

$$

By substituting the inductive hypothesis $C_{(n+1)/2}$, we get:

$$

T(n + 1) = 2\left(2C_{(n+1)/4} + f\left(\frac{n+1}{2}\right)\right) + f(n + 1)

$$

Continuing this process, we can express $T(n + 1)$ in terms of the base cases $T(1)$ and $T(2)$,

along with polynomial terms. Eventually, we reach the following form:

$$

T(n + 1) = 2^nT(1) + \sum_{i=0}^{n} 2^{n-i}f\left(\frac{n+1}{2^i}\right)

$$

Since $T(1)$ and $2^nT(1)$ are both constants, we can ignore them when considering the asymptotic behavior. Therefore, we can conclude that $T(n) = \Theta(n^3)$.

In summary, by establishing the upper and lower bounds, we have shown that $T(n) = \Theta(n^3)$ for the given recurrence using the induction method and considering the base cases $T(1) = C_1$ and $T(2) = C_2$.

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The set of points where a decreasing function is discontinuous is countable.

Explanation:

To prove that the set of points where a decreasing function is discontinuous is countable, we can utilize the concept of one-sided limits.

Let's consider a decreasing function, f, defined on the domain of real numbers (R). A point, x, in the domain is said to be a point of discontinuity for f if the limit of f as it approaches x from either the left or the right does not exist, or if it exists but is different from the function value at x.

Now, let's assume that d is the set of points where f is discontinuous. We need to show that d is countable, meaning its cardinality is either finite or countably infinite.

Since f is decreasing, we know that the left-hand limit (as x approaches a point from the left) always exists. Therefore, the points of discontinuity can only occur when the right-hand limit (as x approaches a point from the right) does not match the left-hand limit.

Consider any point of discontinuity, x, in d. For this point to be a discontinuity, the left-hand limit and the right-hand limit must be different. Now, for each point of discontinuity x, we can associate it with a rational number q in the interval between the left-hand limit and the right-hand limit. Since the rational numbers are countable, we can establish a one-to-one correspondence between the set of points of discontinuity d and a subset of the rational numbers, which means d is countable.

In conclusion, the set of points where a decreasing function is discontinuous, represented by d, is countable. This proof relies on the concept of one-sided limits and the fact that rational numbers are countable.

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Answer:

2/3

Step-by-step explanation:

P (not pink) :

Bi-weekly gross paycheck based on 40 hours a week at a rate of $18.25 per hour is $1,460.

What is multiplication ?

Multiplication is a basic arithmetic operation that involves combining two or more numbers to find their product or the total number of items when a certain number is repeated a certain number of times. In multiplication, the numbers being combined are called factors, and the result is called the product.

To calculate your bi-weekly gross paycheck, you need to multiply your hourly rate by the number of hours you work per week and then multiply that by 2 to account for two weeks in a pay period.

Hourly rate: $18.25

Weekly hours: 40

Bi-weekly hours: 40 x 2 = 80

Bi-weekly gross paycheck: Hourly rate x Bi-weekly hours

Bi-weekly gross paycheck: $18.25 x 80 = $1,460

Therefore, your bi-weekly gross paycheck based on 40 hours a week at a rate of $18.25 per hour is $1,460.

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2

Step-by-step explanation:

I think it 4/2 because I multiplied it

The slope is -7/2

Y = mx + b

m stands for the slope (numerical coefficient for x)

The mean, median, and sample variance of the given dataset are:Mean = 23.17Median = 21Sample variance = 173.5592

(a) Mean The mean (or average) of a dataset is calculated by summing up all the values and dividing by the total number of values.

The formula for calculating the mean is: `mean = (sum of values) / (total number of values)`For the given dataset, we have:20, 50, 22, 14, 23, 10

Sum of values = 20 + 50 + 22 + 14 + 23 + 10 = 139

Total number of values = 6Therefore, the mean is given by: `mean = 139 / 6 = 23.17`Answer: 23.17 (rounded to two decimal places)

(b) Median To find the median, we need to arrange the dataset in increasing order:10, 14, 20, 22, 23, 50The median is the middle value of the dataset. If there are an odd number of values, the median is the middle value. If there are an even number of values, the median is the average of the two middle values. Here, we have 6 values, so the median is the average of the two middle values: `median = (20 + 22) / 2 = 21` Answer: 21(e)

Sample variance s²The sample variance is calculated by finding the mean of the squared differences between each value and the mean of the dataset.

The formula for calculating the sample variance is: `s² = ∑(x - mean)² / (n - 1)`where `∑` means "sum of", `x` is each individual value in the dataset, `mean` is the mean of the dataset, and `n` is the total number of values.For the given dataset, we have already calculated the mean to be 23.17.

Now, we need to calculate the squared differences between each value and the mean:

20 - 23.17 = -3.1722 - 23.17

= -1.170 - 23.17

= -13 - 23.17

= -9.1723 - 23.17

= -0.1710 - 23.17

= -13.17

The sum of the squared differences is given by:

∑(x - mean)² = (-3.17)² + (-1.17)² + (-13.17)² + (-9.17)² + (-0.17)² + (-13.17)²

= 867.7959

Therefore, the sample variance is given by: `s² = 867.7959 / (6 - 1) = 173.5592`Answer: 173.5592 (rounded to four decimal places)

The mean, median, and sample variance of the given dataset are:Mean = 23.17Median = 21Sample variance = 173.5592

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Answer:

20

Step-by-step explanation:

We know that the diagonals are bisected, which means

2x+4 = 6x-8

Subtract 2x from each side

2x+4-2x = 6x-8-2x

4 = 4x -8

Add 8 to each side

4+8 = 4x-8+8

12 = 4x

Divide by 4

12/4 = 4x/4

3 =x

We want to know CF = DB = 2x+4 + 6x -8

CF = 8x-4

     = 8(3) -4

    = 24-4

   = 20

Answer:

10.3 in

Step-by-step explanation:

a = (1/2)b*h

53 = (1/2)x * x

53 = (1/2)x²

Multiply both sides by 2

106 = x²

Take the square root of both sides

x = 10.3