Frank can build a fence in twice the time it would take Sandy. Working together, they can build it in 7 hours. How long will it take each of them to do it alone?
Answer
If Frank and Sandy can build the fence in 7 hours, they must be building
1
7
of the fence every hour.
Now, let the amount of time it takes Sandy be
x
hours so that Frank takes
2
x
hours. Sandy can build
1
x
of the fence every hour and Frank can build
1
2
x
of the fence every hour.
We now have the following equation to solve.
1
x
+
1
2
x
=
1
7
2
+
1
2
x
=
1
7
21
=
2
x
x
=
21
2
=
10.50
Thus, Sandy takes
10.50
hours and Frank takes
21
hours.
SOLVE THIS EXTREMELY IMPORTANT EQUATION
Answer:
Option B; EF = ( About ) 4.47 units, Perimeter of Δ EFG = ( About ) 12.94 units
Step-by-step explanation:
If we were to consider the height of this triangle EFG, it would be 4 units of length, supposedly splitting base GF into two ≅ parts, each 2 units of length. First let us name the point drawn to base GF ⇒ point H, so that the height of Δ EFG ⇒ EH. Now as EH splits GF into two ≅ parts, by Converse to Coincidence Theorem, Δ EFG ⇒ Isosceles Δ;
EH and FH are legs of a right triangle EFH, so that Pythagorean Theorem can be applied to solve for the length of EF and EG, knowing that as Δ EFG ⇒ Isosceles Δ, EF ≅ EG;
( EH )^2 + ( FH )^2 = ( EF )^2,
( 4 )^2 + ( 2 )^2 = ( EF )^2 ⇒ take square of 4 & 2,
16 + 4 = ( EF )^2 ⇒ combine like terms,
( EF )^2 = 20 ⇒ take square root on either side to solve for EF,
EF = √ 20 = ( About ) 4.47 units = EG,
Perimeter of Δ EFG = EF + GF + EG = 4.47 + 4 + 4.47 = ( About ) 12.94 units,
Solution; Option B
What is the midpoint of Line segment A B ?
point F
point G
point H
point I
Answer:
the answer is Point G
The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.917 g and a standard deviation of 0.303 g. The company that produces these cigarettes claims that it has now reduced the amount of nicotine. The supporting evidence consists of a sample of 37 cigarettes with a mean nicotine amount of 0.872 g. Assuming that the given mean and standard deviation have NOT changed, find the probability of randomly seleting 37 cigarettes with a mean of 0.872 g or less.
Answer:
[tex] z = \frac{0.872-0.917}{\frac{0.303}{\sqrt{37}}}= -0.903[/tex]
And we can find this probability to find the answer:
[tex] P(z<-0.903)[/tex]
And using the normal standar table or excel we got:
[tex] P(z<-0.903)=0.1833 [/tex]
Step-by-step explanation:
Let X the random variable that represent the amounts of nocatine of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(0.917,0.303)[/tex]
Where [tex]\mu=0.917[/tex] and [tex]\sigma=0.303[/tex]
We have the following info from a sample of n =37:
[tex] \bar X= 0.872[/tex] the sample mean
And we want to find the following probability:
[tex] P(\bar X \leq 0.872)[/tex]
And we can use the z score formula given by;
[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And if we find the z score for the value of 0.872 we got:
[tex] z = \frac{0.872-0.917}{\frac{0.303}{\sqrt{37}}}= -0.903[/tex]
And we can find this probability to find the answer:
[tex] P(z<-0.903)[/tex]
And using the normal standar table or excel we got:
[tex] P(z<-0.903)=0.1833 [/tex]
94 cities were surveyed to determine sports teams. 26 had baseball, 23 had football, 22 had basketball, 12 baseball and football, 13 had baseball and basketball, 14 had football and basketball, and 7 had all three.A) How many had only a basketball team?B) How many had baseball or football?C) How may had baseball or football, but not basketball?
Answer:
A) 2
B) 33
C) 13
Step-by-step explanation:
Baseball =26
Football = 23
Basketball = 22
Baseball and Football (BF) = 12
Baseball and basketball (BK) = 13
Football and basketball (FK) = 14
All three (BFK) = 7
A) The total number of cities that have basketball teams is given by the cities with basketball only, added to the cities with basketball and football and cities with basketball and baseball, minus the cities with all three sports:
[tex]22=K+BK+FK-BFK\\22=K+13+14-7\\K=2[/tex]
B) The total number of cities with baseball of football is given by sum of the cities with either sport, minus the number of cities with both sports:
[tex]B\ or\ F = 23+22-12\\B\ or\ F =33[/tex]
C) If 22 cities have basketball and only 2 have basketball only, 20 cities have basketball and either baseball, football or all three sports. The number of cities with baseball or football, but not basketball is:
[tex](B\ or\ F)\cap (not\ K) = 33-20=13[/tex]
a number,x, rounded to 1 significant figure is 40 write down the error interval for x
Answer:
Error interval is [tex]35\leq x< 45[/tex]
Step-by-step explanation:
Given: A number x becomes 40 if it is rounded to 1 significant figure
To find: error interval for x
Solution:
In the given question, an error interval is the range of values that a number x can be equal to before it is rounded to 1 significant figure.
As a number x becomes 40 if it is rounded to 1 significant figure, error interval is [tex]35\leq x< 45[/tex].
A number x in this interval becomes equal to 40 if it is rounded to 1 significant figure.
Mary is building a sandcastle with rectangular prism molds. One mold is 4 inches long, 6 inches wide, and 2 inches tall. The other mold is 3 inches long, 5 inches wide, and 1 inch tall. If she creates a castle by stacking these molds on top of each other, what volume of sand will be contained in her castle?
Answer:
63 cubic inches
Step-by-step explanation:
You have to first find the volume of each mold:
6 × 4 × 2= 48 cubic inches
3 × 5 × 1= 15 cubic inches
Add these two volumes together to find the overall volume of the whole sand castle.
48+15= 63 cubic inches
Answer:
The whole castle can hold 63 in² of sand.
Step-by-step explanation:
First, find the volume of the first mold.
V = whl Substitute
V = (6)(2)(4) Multiply
V = 48 in²
Now, find the volume of the second mold.
V = whl Substitute
V = (5)(1)(3) Multiply
V = 15 in²
Add together both volumes to find the volume of the whole castle.
48 + 15 = 63 in²
Lucy obtains a 1-year payday loan for $5000.00 at 12% interest compounded monthly. To get the loan, she
also pays an origination fee of $125.00. What is the total cost of the loan to Lucy? Enter your answer as a
dollar amount, such as: 1400.68.
Answer:
$5759.12
Step-by-step explanation:
$5759.12
At the end of the year, the compound interest on her loan is: $5000(1+0.1212)12=$5000(1.01)12≈$5634.12. To pay off the loan at the end of the year, she pays 5634.12+125=$5759.12.
A chemist has 20% and 50% solutions of acid available. How many liters of each solution should be mixed to obtain 75 liters of 28% acid solution?
Answer:
we will mix 55 liters of 20% solution and 20 Liters of 50% solutions.
Step-by-step explanation:
let the 20% solution = x liters
let the 50% solution = y liters
total solution of the mixture of the two solutions in % = 28%
total solution of the mixture of the two solutions in liters = 75 liters
considering the total solutions given, we will have the following equations if we mix the solutions in equal proportion;
20x + 50y = 28 (75)
0.2x + 0.5y = 0.28(75)
0.2x + 0.5y = 21 -------equation 1
Also,
x + y = 75 ------equation 2
y = 75 - x
(substitute this into equation 1)
0.2x + 0.5(75 - x) = 21
0.2x + 37.5 - 0.5x = 21
0.2x - 0.5x = 21 - 37.5
-0.3x = -16.5
x = -16.5 / -0.3
x = 55 liters
Recall, y = 75 - x
y = 75 -55
y = 20 Liters
Thus, we will mix 55 liters of 20% solution and 20 Liters of 50% solutions.
For each problem clearly describe the conditional distribution of each coordinate given the others. Then describe the procedure for running Gibbs sampling to sample from the joint distribution. Assume that Gibbs sampling works for continuous densities as well as discrete distributions. Guess the conditional from the structure of the joint distribution. Avoid doing integration as much as possible. Use your knowledge of the all the named one dimensional distributions/ densities.
a. Sample from the mixed joint pmf/pdf:
f(p, n) = p(1 - p)^-1, 0
Answer:
Step-by-step explanation:
Write a matrix equation for the given systems of equations.
2x-6y-2z = 1
3y - 2z = -5
2y + 2z = -3
Answer:
[tex]\left[\begin{array}{ccc}2&-6&2\\0&3&-2\\0&2&2\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right]= \left[\begin{array}{ccc}1\\-5\\-3\end{array}\right][/tex]
Step-by-step explanation:
Given system of equations are
2x-6y-2z = 1
3y - 2z = -5
2y + 2z = -3
given
2 x - 6 y - 2 z = 1
0 x + 3 y - 2z = -5
0 x +2y + 2 z = - 3
The Matrix form of the given system of equations
A X = B
[tex]\left[\begin{array}{ccc}2&-6&2\\0&3&-2\\0&2&2\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right]= \left[\begin{array}{ccc}1\\-5\\-3\end{array}\right][/tex]
Identify the like terms in the algebraic expression 2x/5-5.2y+2.2+x/3
Question:
Identify the like terms in the algebraic expression
[tex]\frac{2x}{5} -5.2y +2.2 + \frac{x}{3}[/tex]
Answer:
The like terms in the given expression are [tex]\frac{2x}{5}[/tex] and [tex]\frac{x}{3}[/tex]
Step-by-step explanation:
Given:
[tex]\frac{2x}{5} -5.2y +2.2 + \frac{x}{3}[/tex]
Required:
Identify the like terms
To solve this, we need to understand what like term is all about.
Like term simply refer to terms or entities that have the same variable and exponents (power)
From the expression above, there are two variables;
x and y.
To get the like terms of x and/or y;
we simply look for another occurrence of x and/or y in the expression; and this occurrence must have the same exponent as x and/or y.
For x
[tex]\frac{2x}{5}[/tex] and [tex]\frac{x}{3}[/tex] have the same variable and exponent; Hence, they are like terms
There's only one occurrence of variable y;
Conclusively, the like terms in the given expression are [tex]\frac{2x}{5}[/tex] and [tex]\frac{x}{3}[/tex]
2x/5 and -5.2y
hope this helps
A local hamburger shop sold a combined total of 621 hamburgers and cheeseburgers on Friday there were 71 more cheeseburgers old and hamburgers how many hamburgers were sold on Friday
plifying a Radical
Find the values for a, b, and c that complete the simplificatio
12.95
Y Z
12
y8 .y . z. z = x y z Syz
a =
I
b =
Answer: answer is D
Step-by-step explanation:
Answer: The correct answer is 6,4,2
Step-by-step explanation: Doing a 100 point giveaway stay tuned!
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
A. [tex]F(x) = (\frac{3}{4}x )^2-1[/tex]
Step-by-step explanation:
The correct answer is "A," because the function F(x), shifted downwards 1 unit. This means that the function has to have a -1 being subtracted. Note that when the number in front of x is less than one, the function widens. In this case, [tex]\frac{3}{4}[/tex] is less than one, making it grow bigger as shown on the graph above.
Bisi leaves 5km from school. She walks 1km at 4km/h and travels the rest of the way by bus at 16km/h . what is the average speed for the whole distance
Answer:
1/2 hour
Step-by-step explanation:
I am assuming you meant "lives 5km"
The first km would take 1/4 an hour because she is going 4km/h for one hour. One hour she would go 4km but we only need 1 mile so it would be cut to a fraction.
The same fraction goes for the bus. 4 is 1/4 of 16 so you would have to add them together and have 1/2 and hour to get home.
I need help with this please.
The Thomas Supply Company Inc. is a distributor of gas-powered generators. As with any business, the length of time customers take to pay their invoices is important. Listed below, arranged from smallest to largest, is the time, in days, for a sample of the Thomas Supply Company Inc. invoices.13 13 13 20 26 28 30 34 34 34 35 35 36 37 38
41 41 41 45 46 47 47 49 52 54 54 56 62 67 82(Round your answer to 2 decimal places.)a. Determine the first and third quartiles.
b. Determine the second decile and the eight decile.c. Determine the 67th percentile.
Answer:
Q1 = 33
Q3 = 49.75
D2 = 28.4
D8 = 29.6
67th percentile = 46.10
Step-by-step explanation:
Given the data:
13 13 13 20 26 28 30 34 34 34 35 35 36 37 38
41 41 41 45 46 47 47 49 52 54 54 56 62 67 82
The first quartile (Q1) ;
1/4(n + 1)
Where n = number of observations
n = 30
Q1 = 0.25(30 + 1) = 0.25 × 31 = 7.75
7 : corresponds to 30
0.75 : (34 - 30) × 0.75 = 4 × 0.75 = 3
30 + 3 = 33
Third quartile (Q3) :
3/4(n + 1)
Where n = number of observations
n = 30
Q3 = 0.75(30 + 1) = 0.75 × 31 = 23.25
23 : corresponds to 49
0.25 : (52 - 49) × 0.25 = 3 × 0.25 = 0.75
49 + 0.75 = 49.75
Determine the second decile and the eighth decile.
Second decile (D2)
((n+1) × (2)) / 10
= (30 + 1)(2)/10 = 6.2
6 : corresponds to 28 +
0.2 : (30 - 28 )× 0.20 = 0.4
28 + 0.4 = 28.4
Eight decile (D8)
((n+1) × (8)) / 10
= (30 + 1)(8)/10 = 24.8
24 : corresponds to 52 +
0.8 : (54 - 52 )× 0.80 = 1.6
28 + 1.6 = 29.6
67th percentile :
67% × n = 0.67 × 30 = 20.10
20: corresponds to 46
0.1 : (47 - 46) × (0.1) = 0.1
46 + 0.1 = 46.10
The first quartiles is 33 and third quartiles is 23.25.
The second decile is 24.8 and the eight decile is 29.6
The 67th percentile is 46.10.
Given that,
Sample of the Thomas Supply Company Inc. invoices.13 13 13 20 26 28 30 34 34 34 35 35 36 37 38.
41 41 41 45 46 47 47 49 52 54 54 56 62 67 82
We have to determine,
Determine the first and third quartiles.
Determine the second decile and the eight decile.
Determine the 67th percentile.
According to the question,
The first quartile (Q1) ; [tex]\dfrac{1(n+1)}{4}[/tex]Where n = number of observations
n = 30
Then,
[tex]= \dfrac{1(30+1)}{4}\\\\= 0.2 \times 31\\\\= 6.2[/tex]
Then, 7 : corresponds to 30,
[tex](34 - 30) \times 0.75 = 4 \times 0.75 = 3\\\\30 + 3 = 33[/tex]
And Third quartile (Q3) is; [tex]\dfrac{3(n+1)}{4}[/tex]
Where n = number of observations
n = 30
Then,
[tex]= \dfrac{3(30+1)}{4}\\\\= 0.75 \times 31\\\\= 23.25[/tex]
23 : corresponds to 49
[tex]0.25 : (52 - 49) \times 0.25 = 3 \times 0.25 = 0.75\\\\49 + 0.75 = 49.75[/tex]
To determine the second decile and the eighth decile.
Second decile (D2) ; [tex]\dfrac{2(n+1)}{10}[/tex]
Where n = 30
Then,
[tex]= \dfrac{2(30+1)}{10}\\\\= 0.2 \times 31\\\\= 6.1[/tex]
6 : corresponds to 28,
[tex](30 - 28 ) \times 0.20 = 0.4\\\\28 + 0.4 = 28.4[/tex]
And the Eight decile (D8); [tex]\dfrac{8(n+1)}{10}[/tex]
Where n = 30,
Then,
[tex]\dfrac{(30 + 1)(8)}{10} = 24.8[/tex]
24 : corresponds to 52,
[tex](54 - 52 ) \times 0.80 = 1.6\\\\28 + 1.6 = 29.6[/tex]
To determine the 67th percentile :
67% × n = 0.67 × 30 = 20.10
20: corresponds to 46
0.1 : (47 - 46) × (0.1) = 0.1
46 + 0.1 = 46.10
The 67th percentile is 46.10
To know more about Percentile click the link given below.
https://brainly.com/question/16842626
A piece of wire is 290 cm long.
Dawid cuts three 25 cm lengths off the wire.
He then cuts the rest of the wire into as many 30 cm lengths as possible.
Work out how many 30 cm lengths of wire Dawid cuts.
Answer:
8
Step-by-step explanation:
(290-25)/30
265/30
8 and 5/6
so how many full 30 cm lengths?
8
Answer:
7
Step-by-step explanation:
3 × 25 = 75cm
He cuts 75cm of 290cm so the remaining length is 290 - 75 = 215 cm
→ He then cuts the rest of the wire into as many 30 cm lengths as possible.
215 ÷ 30 = 7.17
What is the area of an rectangle with sides lengths of 5/12 foot and 2/3 foot
Answer:
Area = 5/18 square feet
Step-by-step explanation:
To find the area of a rectangle, you need to multiply 5/12 and 2/3. You multiply the numerators and then multiply the denominators. Then you should get 10/36. This fraction can be simplified into 5/18. To do this find the greatest common factor of 10 and 36 (you'll get 2 as the GCF). Then divide 2 to both the numerator and denominator.
Find the length of the portion of the line y = 4 that lies inside a circle of radius 7
centered at the origin
Answer: 2sqrt(33)
Step-by-step explanation:
We want to find the length of the line y = 4 in the circle x^2+y^2=49.
Substitute y = 4 to get x^2 = 33, so x = sqrt(33) or -sqrt(33).
That means the total length is sqrt(33) * 2 = 2sqrt(33).
Hope that helped,
-sirswagger21
The approximate length of the portion of the line is 11.49.
Circle centered at (h,k) with radius r is [tex](x-h)^{2} + (y-k)^{2}=r^{2}[/tex]
A circle of a radius 7 centered at the origin:
[tex]x^{2} +y^{2}=49[/tex] ......... (i)
[tex]y=4[/tex] ..........(ii)
We have a circle and a line. We need to find the points of
intersection and find the distance between those two points.
Replace y with 4 in the 1st equation and solve for x.
[tex]x^{2} +4^{2} =49\\x^{2} =49-16\\x^{2} =33\\[/tex]
[tex]x=[/tex] ±[tex]\sqrt{33}[/tex]
We have the 2 values of x where the line intersects the circle.
Plug those into one of the original equations to find the associated
y values.
[tex]\sqrt{33} ^{2} +y^{2} =49\\y^{2}=49-33\\y=4[/tex]
Two points on the circle are [tex](\sqrt{33} , 4)[/tex] and [tex](-\sqrt{33} , 4)[/tex]
Using the distance formula:-
[tex]=\sqrt{(4-4)^{2}+(-\sqrt{33}-\sqrt{33)} ^{2} } \\=\sqrt{(2\sqrt{33}) ^{2} } \\=2\sqrt{33}\\[/tex]
≈ 11.49
Therefore, the length of the portion of the line is approximately 11.49.
For more information:
https://brainly.com/question/24214108
What is the square root of -1?
–i
i
–1
1
Answer:
[tex]i[/tex]
Step-by-step explanation:
[tex]\sqrt{-1} =i[/tex]
[tex]i[/tex] is an imaginary number that represents the square root of -1.
(3x+12)+x=180 Find the value of x.
Answer:
x =42
Step-by-step explanation:
(3x+12)+x=180
Combine like terms
4x +12 = 180
Subtract 12 from each side
4x +12-12=180-12
4x = 168
Divide by 4
4x/4 =168/4
x =42
Answer:
x=42
Step-by-step explanation:
180-12=168
168 divided by 4 = 42
x=42
What is imaginary 34
Answer:
raising a number to the 34th power
Step-by-step explanation:
A teacher needs to cut pieces of yarn, each 3/4 yards in length. How many
pieces can he cut from a string of yarn that is 6 yards long?
Answer:
8 pieces
Step-by-step explanation:
Take 6 yds and divide by the length of each piece
6 ÷ 3/4
Copy dot flip
6 * 4/3
24/3
8
We can get 8 peices
What is the vertex of the graph of f(x) = |x-13[ + 11?
оооо
о(-11, 13)
о(-13, 11)
О(11, 13)
О (13, 11)
Answer:
(13, 11)
Step-by-step explanation:
The vertex of g(x) = |x| is (0, 0).
When the function is transformed to ...
f(x) = g(x -h) +k
the vertex is moved to (h, k).
Here, we have (h, k) = (13, 11), translating the function to ...
f(x) = |x -13| +11
and moving the vertex to (13, 11).
Answer:
D. (13, 11)
Step-by-step explanation:
EDGE 2020 :)
Suppose that you are testing the hypotheses Upper H 0: pequals0.16 vs. Upper H Subscript Upper A: pnot equals0.16. A sample of size 350 results in a sample proportion of 0.21. a) Construct a 90% confidence interval for p. b) Based on the confidence interval, can you reject Upper H 0 at alphaequals0.10? Explain. c) What is the difference between the standard error and standard deviation of the sample proportion? d) Which is used in computing the confidence interval?
Answer:
Given:
Sample size, n = 350
Sample proportion, P' = 0.21
H0 : p = 0.16
Ha : p ≠ 0.16
a) A 90% confidence interval for P.
Significance level = 1 - confidence interval = 1 - 0.90 = 0.10
For Z critical, we have:
Z critical = [tex] Z_0_._1_/_2 = Z_0_._0_5 = 1.645 [/tex] (using z table)
Standard error, S.E = [tex] \sqrt{\frac{P'(1 - P')}{n}} = \sqrt{\frac{0.21(1 - 0.21)}{350}} = 0.02177 [/tex]
Margin of error, E = 1.645 * 0.02177 =0.03581
The 90% confidence interval =
0.21 ± 0.03581
The lower limit: 0.21 - 0.03581 = 0.17419
The upper limit: 0.21+0.03581 =0.24581
b) Based on the confidence interval at significance level = 0.10,
We reject null hypothesis, H0, since 0.16 is not cointained in the confidence interval. We conclude that p ≠ 0.16.
c) Standard error is based on sample proportion p^ while standard deviation is based on hypothesized proportion Po.
d) Standard error is used to compute the confidence interval.
The radius of a circle is 1 meter. What is the area of a sector bounded by a 135º arc?
Answer:
d=2
Step-by-step explanation:
Shape: Circle
Solved for diameter
Radius: 1
Formula: d=2r
Formula: Radius
Answer: 2
Hope this helps.
simplify without using the table log 6 - log 16 + log 4 - log 3 + log 20 equals to
Answer:
[tex]1[/tex]
Step-by-step explanation:
[tex]log(6)-log(16)+log(4)-log(3)+log(20)[/tex]
[tex]0.77815125038-1.20411998266+0.60205999132-0.47712125472+1.30102999566[/tex]
[tex]=0.99999999998[/tex]
A Florida neighborhood is comprised of a total of 250 houses of which 12% are in foreclosure. A random sample of 91 homes from this neighborhood was selected. The standard error of the proportion is ________.
Answer:
the standard error of the proportion is 0.0272
Step-by-step explanation:
We have that if the sample size is greater than 5% of the entire population, a finite population correction factor (fpc) is multiplied with the standard error :
fpc = [tex]\sqrt{\frac{N -n}{N -1} }[/tex]
We know that N = 250 n = 91, replacing:
fpc = [tex]\sqrt{\frac{250 - 91}{250 -1} }[/tex]
fpc = 0.799
Now, the formula would then be:
SE = [tex]\sqrt{\frac{p * (1 -p)}{n} }[/tex]*fpc
Now replacing, knowing that p = 0.12
SE= [tex]\sqrt{\frac{0.12 * (1 - 0.12)}{91} }[/tex]*0.799
SE = 0.0272
So the standard error of the proportion is 0.0272
Please help ;-; what is the answer?
Answer:
5.7
Step-by-step explanation:
The altitude divides right triangle ABC into similar right triangles ADB and BDC. The ratios of short leg to long leg will be proportional in these similar triangles, so you have ...
AD/BD = BD/CD
Cross multiplying gives ...
AD·CD = BD²
(x+3)(2x+3) = 5²
2x² +9x = 16 . . . . . perform the multiplication, subtract 9
2(x² +4.5x) = 16
2(x² +4.5x +2.25²) = 16 +2(2.25²) . . . . . add 2(2.25²) to complete the square
2(x +2.25)² = 26.125 . . . . . write as a square
x +2.25 = √13.0625 . . . . . .divide by 2, take the positive square root
x = -2.25 +√13.0625 . . . . subtract 2.25 to find x
We want the value of CD, so ...
CD = 2x +3 = 2(-2.25 +√13.0625) +3
CD = -1.5 +2√13.0625 ≈ 5.7284
The length of CD is about 5.7 units.
