What is the value of x in the figure below? In this diagram, AABD - ACAD.АXB5 D9CA. 126O B. 45C. 45O D.914E. 170F. 14
Answers
We are given a right angled triangle that also houses two other right angles and are asked to find the length of the line opposite to acute angles in the two inner right angled triangles.
Our approach is to create a relationship for one of the lengths and in two instances and equate the length to allow us get our variable.
We will employ the Pythagoras Theorem that states that the square of the length of the hypothenuse is a sum of the length of the square of the opposite and the square of the adjacent.
\(\begin{gathered} \text{Length AC = }\sqrt[]{9^2+x^2} \\ \text{Length AB = }\sqrt[]{5^2+x^2} \\ \text{Length AC = }\sqrt{\text{14}^2-(\sqrt[]{5^2+x^2})^2} \end{gathered}\)We can equate the 2 lengths of the square of AC.
\(\begin{gathered} AC^2=\text{ (}\sqrt[]{9^2+x^2})^2=(\text{ }\sqrt[]{\text{14}^2-(\sqrt[]{5^2+x^2})^2})^2 \\ AC^2=9^2+x^2=14^2-5^2-x^2 \\ \text{Add x}^2\text{ to both sides to get:} \\ 2x^2+9^2=14^2-5^2 \\ Subtract9^2\text{ from both sides to get:} \\ 2x^2=14^2-5^2-9^2 \\ 2x^2=90 \\ \text{Divide both sides by 2 to get:} \\ x^2=45 \\ \text{Getting the square root of both sides gives:} \\ \sqrt{x^2}=\sqrt{45} \\ x=\sqrt[]{45} \end{gathered}\)OPTION C
Related Questions
identify which equations have one solution, infinitely many solutions, or no solution 3u+40+2u=6u-30-u
Answers
Answer:
I did the math there is no answer
If you know the answer please put the answer and the explanation thank you.
Answers
In the class, Lucy's score is 6.
How to work out Lucy's score?In statistics, the median is the middle value in a sorted, ascending or descending list of numbers. Thus, it represents the midpoint of the data.
The median is often compared with other descriptive statistics such as the mean (average), mode, and standard deviation.
Since Lucy is one of the 29 students in the class and her score was the same as the median score for her class.
Thus, the median score will be 15th score (i.e. the midpoint of 29). Using the frequency in of each score from the figure, let's keep adding the frequency until we reach 15 and we will then check the corresponding score at the 15th position:
2 + 2 + 4 + 7 = 15
Thus, the the corresponding score at the 15th position is 6.
Therefore, the median score is 6 and consequently Lucy's score is 6.
Learn more about median on:
https://brainly.com/question/14532771
#SPJ1
Factor 36+21. Write your answer in the form a(b+c) where a is the GCF of 36 and 21.
Answers
Answer:
3(12 + 7)
Step-by-step explanation:
To find the GCF of 36 and 21, list out their factors.
36: 1, 2, 3, 4, 6, 9, 12, 18, 36
21: 1, 3, 7, 21
The greatest factor which both numbers share is 3.
Therefore, you can factor 36 + 21 as 3(12 + 7)
QUESTION 16. 1 POINTA sample of bacteria is growing at an hourly rate of 5% according to the continuous exponential growth function. Thesample began with 10 bacteria.How many bacteria will be in the sample after 28 hours? Round your answer down to the nearest whole number.Provide your answer below
Answers
We can express the exercise in terms of a function
\(n(t)=n_0\cdot e^{rt}\)Where
n is the number of bacterias
t is the time
r is the relative rate of growth
From the problem we have
\(n(t)=10\cdot e^{0.05t}\)if t=28
\(\begin{gathered} n(28)=10\cdot e^{0.05(28)} \\ n(28)=10\cdot e^{1.4} \\ n(28)=40.552 \end{gathered}\)After 28 hours will be 40 bacteriasHow many solutions are there to the equation
8x - 7 = 2 (2x + 7) - 5
Answers
Answer:
x=4
Step-by-step explanation:
8x - 7 =2(2x +7) - 5
8x - 7 =4x +14 - 5
8x - 7 =4x +9
8x - 4x =9 +7
4x =16
x=16 :4
x=4
How many Mg's are there
Answers
Answer:
2
Step-by-step explanation:
the amount of things in the formula is told by the number that comes after it
(for example H2O would have 2 hydrogens)
Jesse bought 3 tennis balls for $6. How much did each
tennis ball cost?
Answers
Answer:
The answer is 2$
Step-by-step explanation:
To get each price of the ball divide the total cost of the purchase divide by the quantity of items.
Every weekday, Mr. Jones bikes from his home to his job. Sometimes he rides along two roads, the long route that is shown by the solid lines. Other times, he takes the shortcut shown by the dashed line.
A right triangle. The distance from the angle with measure 90 degrees to Job is 15 kilometers. From the angle to Home is a. They hypotenuse is 17 kilometers.
How many fewer kilometers does Mr. Jones bike when he takes the shortcut instead of the long route?
6 kilometers
8 kilometers
23 kilometers
32 kilometers
Mark this and return
Answers
Answer:
(A)6 kilometers
Step-by-step explanation:
First, we determine the value of a using Pythagoras Theorem.
\(Hypotenuse^2=Opposite^2+Adjacent^2\\17^2=a^2+15^2\\a^2=17^2-15^2\\a^2=289-225\\a^2=64\\a^2=8^2\\a=8$ km\)
Therefore:
Distance along the long route = 8 + 15 =23 km
Distance along the shortcut =17 km
Difference =23-17 =6km
Therefore, Mr. Jones bikes 6km less when he takes the shortcut instead of the long route.
Answer:
a
Step-by-step explanation:
on edge
What is the correct answer please I’m stumped
Answers
Answer:
The choose C. 2
\(( \frac{4 ^{ \frac{5}{4} } \times 4^{ \frac{1}{4} } }{4 ^{ \frac{1}{2} } } )^{ \frac{1}{2} } = 2\)
Answer:
2
Step-by-step explanation:
inside the parenthesis is equivalent to 4^(5/4 + 1/4 - 1/2) = 4¹ = 4
√4 = 2
Help pleaseeeeee
A car was valued at $26,000 in the year 1990. The value depreciated to 13,000 by the year 2003.
A) What was the annual rate of change between 1990 and 2003?
r= ---------- Round the rate of decrease to 4 decimal places.
B) What is the correct answer to part A written in percentage form?
r= ------------%
C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2006 ?
value = $ ------------- Round to the nearest 50 dollars.
Answers
The rate of depreciation is 5.19% and the value of the car in the year 2006 is $11,078.35.
A car was valued at $26,000 in the year 1990. The value depreciated to 13,000 by the year 2003.
The exponent is given as,
$13,000 = $26,000 (1 - r)ⁿ
Here, n represents the number of years from 1990.
Then the rate is calculated as,
$13,000 = $26,000 (1 - r)¹³
1/2 = (1 - r)¹³
0.94807 = 1 - r
r = 0.0519 or 5.19%
The value of the car in the year 2006 is calculated as,
A = $26,000 (1 - 0.0519)¹⁶
A = $26,000 (0.94807)¹⁶
A = $26,000 x 0.426
A = $11,078.35
More about the exponent link is given below.
https://brainly.com/question/5497425
#SPJ1
What’s -4 1/2 divided by (-1 3/8) Diving Mixed Numbers with negatives?
Answers
Answer:
3 3/11
Step-by-step explanation:
The best way to divide fractions is to not divide them at all.
Convert both mixed numbers into improper fractions.
4 times 2 is 8
8 + 1 is 9
I have 9/2 halves. Don't forget to put the negative back in.
1 times 8 is 8
8 + 3 is 11
I have 11/8 eighths. Dont forget to put the negative back in.
You will end up with
-9/2 ÷ -11/8
Flip the second fraction and change the division sign to a multiply sign
-9/2 × 8/-11
Multiply the numerators together and the denominators together
-9 x 8 and 2 x -11
-72 / -22
Dividing a negative by a negative will give us a positive
72 / 22
Simplify by dividing the top and bottom by 2
36/11
We cannot simplify further. You can answer like this or convert back into a mixed number.
There are 3 sets of 11 in 36, with 3 left over
3 3/11
Answer:
\( = - (5 \frac{3}{5} )\)
Step-by-step explanation:
\( - 4 \frac{1}{2} \div ( -1 \frac{3}{8} )\)
\( = - 4 \frac{1}{2} \div -1 \frac{3}{8} \)
\( = \frac{(2 \times ( - 4) + 1)}{2} \div \frac{(8 \times ( - 1) + 3}{8} \)
\( = \frac{ - 7}{2} \div \frac{ - 5}{8} \)
\(= \frac{ - 7}{2} \times \frac{8}{ - 5} \)
\( = \frac{ (- 7 )\times 8}{2 \times ( - 5)} \)
\( = \frac{ - 56}{( - 10)} \)
\( = - (5 \frac{6}{10} )\)
\( = - (5 \frac{3}{5} )\)
You pick a card at random. 5 6 7 What is P(odd or greater than 6)?
Answers
The answer to the question is 1/3.
There are three possible outcomes: 5, 6, or 7.
Out of these three outcomes, only two satisfy the condition of being odd or greater than 6: 7.
Therefore, the probability of picking a card that is odd or greater than 6 is 1/3, or approximately 0.333 or 33.3%.
To solve more on probability :
https://brainly.com/question/12594357?referrer=searchResults
The following probability distribution represents the number of books read over asummer vacation. What is the probability for reading 4 books? Represent the value as aproportion (decimal form) as the other values are.Outcome23456P(x).23.27?.18.07
Answers
In order to determine which is the probability for reading 4 books, you consider that the sum of all probabilities must be equal to 1.0. In that sense, you know that the unknow value of the probability distribution for x = 4 can be calculate as follow:
- Add up all known values of the probability distribution
0.23 + 0.27 + 0.18 + 0.07 = 0.75
- Next, you subtract the previous result to 1.0:
1.0 - 0.75 =0.25
The previous result is the value of the probability distribution for x = 4.
Hence, the probability of reading 4 books is 0.25, which is equivalent to 25.0%.
4(x-1)+2x=-3(x-1) find x
Answers
Answer:
the answer is \(x=\frac{7}{9}\)
Step-by-step explanation:
Try using Symbolab, I use it all the time it gives the correct answer and it gives good explanations (I use it all the time).
PLEASE ANSWER ASAP !!!!!!!!!!!!!!!!!!! WILL GET BRAINLEST IF CORRECT!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
Only Felpie is right because it asks the function of 24, 16, 8, 0
Not 32, 24, 16, 8, 0
Step-by-step explanation:
If you have a statistical calculator or computer, use it to find the actual sample mean and sample standard deviation. Otherwise, use the values Σx = 2769 and Σx2 = 132,179 to compute the sample mean and sample standard deviation. (Round s to four decimal places.)
Answers
By using a statistical calculator, the actual sample mean and sample standard deviation are:
Actual sample mean = 46.1500.
Actual ample standard deviation = 8.6256.
How to calculate the sample mean for the set of data?In Mathematics and Geometry, the sample mean for any set of data can be calculated by using the following formula:
Mean = ∑x/(n - 1)
∑x represents the sum of all data values.(n - 1) represents the number of data contained in a sample.In Mathematics and Geometry, the sample standard deviation for any set of data can be calculated by using the following formula:
Standard deviation, δx = √(1/N × ∑(x - \(\bar{x}\))²)
x represents the observed values of a sample.\(\bar{x}\) is the mean value of the observations.N represents the total number of of observations.By using a statistical calculator, the actual sample mean and sample standard deviation are as follows;
Actual sample mean = 46.1500.
Actual ample standard deviation = 8.6256.
Read more on standard deviation here: brainly.com/question/14467769
#SPJ1
Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Hey! Can you please help me? Please answer each question and show work!! I’d appreciate it so much and mark you brainliest!!!!
17. The hourly temperature at Portland, Oregon, on a particular day is recorded below.
Answers
Answer:
Please type the question down
Step-by-step explanation:
Hard too see
Find two positive numbers whose difference is 9 and whose product is 2950.
Answers
Answer: 50 and 59
I divided 2950 by 25 because I knew it would somehow factor into that since it ends in 50. Then, I got 25 and 118. From there, I just divided 118 by 2 since I knew that it would end in a 9 and I multiplied 25 by 2. Not sure if this is really helpful, but you also try using a GCF calculator and look up all the factors of that number next time!
Parametric Functions
Answers
Answer:
Step-by-step explanation:
it think it 23 becasue u add
1 divide it by 2
(45 POINTS!!!) Which is the equation of a parabola with a directrix at y = −3 and a focus at (−2, 3).
y = one twelfth(x − 2)
2 y = one twelfth(x + 2)
2 y = −one twelfth(x + 2)
2 y = −one twelfth(x − 2)2
Answers
Answer:
y = −one twelfth(x − 2)2
Step-by-step explanation:
y = −one twelfth(x − 2)2
Answer:
y = −one twelfth(x − 2)2
Step-by-step explanation:
James wants to have earned $6,180 amount of interest in 28 years. Currently he finds
that his annual interest rate is 6.12%. Calculate how much money James needs to invest
as his principal in order to achieve this goal.
Answers
Answer:
$3606.44
Step-by-step explanation:
The question asks us to calculate the principal amount that needs to be invested in order to earn an interest of $6180 in 28 years at an annual interest rate of 6.12%.
To do this, we need to use the formula for simple interest:
\(\boxed{I = \frac{P \times R \times T}{100}}\),
where:
I = interest earned
P = principal invested
R = annual interest rate
T = time
By substituting the known values into the formula above and then solving for P, we can calculate the amount that James needs to invest:
\(6180 = \frac{P \times 6.12 \times 28}{100}\)
⇒ \(6180 \times 100 = P \times 171.36\) [Multiplying both sides by 100]
⇒ \(P = \frac{6180 \times 100}{171.36}\) [Dividing both sides of the equation by 171.36]
⇒ \(P = \bf 3606.44\)
Therefore, James needs to invest $3606.44.
Determine whether the two expressions are equivalent. If so, tell what property is applied.
7 × (6 × t) and (7×6)×t
a. Associative
b. Commutative
c. Identity
d. Inverse
e. Distributive
f. Not a property
Answers
Answer:
I think its associative property but I am not sure.
Step-by-step explanation:
Solve the equation.
x^2 − 4x + 4 = 3
Answers
why is 2 × 3/4 less than 2
Answers
Answer:
becuase 2*3 is 6, and 2*4 is 8, and when you simplfy it is 1 and 1/2, which in decimal form is 1.5, making it less than 2
Answer:
Is 2/4 smaller than 2/3? These are the same questions with one answer.
To get the answer, we first convert each fraction into decimal numbers. We do this by dividing the numerator by the denominator for each fraction as illustrated below:
2/4 = 0.5
2/3 = 0.667
Then, we compare the two decimal numbers to get the answer.
0.5 is less than 0.667.
Therefore, 2/4 is less than 2/3 and the answer to the question "Is 2/4 less than 2/3?" is yes.
i think this will help
13 X 1/2 in simplest form
Answers
Answer:
6
Step-by-step explanation:
13 × 1/2 = 6
anything multiplied by 1/2 is just half that number.
using d=rt , where d=distance r=rate and t=time how fast is a jogger moving if she travels 5.7 miles in 1.3 hours? to the nearest tenth
Answers
Answer:
\(r=4.38\)
Step-by-step explanation:
Step 1: Arrange the equation so that you are calculating rate (divide both sides by t)
\(\frac{d}{t} = \frac{rt}{t}\)
\(t\) cancels out on the right side.
Step 2: Substitute in the numerals
\(r=\frac{d}{t}\)
\(r=\frac{5.7}{1.3}\)
Step 3: Divide
\(r=4.38\) \(mph\)
There's your answer!
Hope this helps you!
What is the difference of (Three-fourths x minus two-thirds) minus (Negative StartFraction 5 over 6 EndFraction + 2 x)? Negative StartFraction 5 over 4 EndFraction x + StartFraction 1 over 6 EndFraction Negative StartFraction 5 over 4 EndFraction x minus StartFraction 1 over 6 EndFraction StartFraction 11 over 4 EndFraction x + StartFraction 1 over 6 EndFraction StartFraction 11 over 4 EndFraction x minus StartFraction 1 over 6 EndFraction
Answers
Answer:
-5/4x + 1/6
Step-by-step explanation:
Got it correct on edge
Answer:
a
Step-by-step explanation:
Find the value of each variable.
Answers
Answer: x = 15, y = 10
Step-by-step explanation:
1. Start by looking at the equation on the left side of the diagram, which is 3x = y + 15.
2. To find the value of x, we can use algebra to isolate it on one side of the equation: x = (y + 15) / 3.
3. Now look at the equation on the right side of the diagram, which is y + 2x = 25.
4. To find the value of y, we can use algebra to isolate it on one side of the equation: y = 25 - 2x.
5. Now we have two equations with two unknowns, x and y. We can substitute our first equation into the second equation in order to solve for x: y = 25 - 2x => y = 25 - 2(y + 15) / 3 => y = 25 - (2y + 30) / 3.
6. Now we have an equation with only the variable y, so we can solve for y by using algebra: 25 - (2y + 30) / 3 => 3y + 90 = 75 => 3y = -15 => y = -5.
7. Now that we know the value of y, we can substitute it into our first equation to find the value of x: x = (y + 15) / 3 => x = (-5 + 15) / 3 => x = 15.
8. Therefore, the values of x and y are x = 15 and y = -5.
List all the vertices, edges, and faces in the figure below.
Answers
The vertices are A, B, C, D, E, F. The edges are AB, BC, CA, ED, DF, FE, BD, CF, and AE and the faces are DBCF, DEAB, EFCA, EDF, and ABC.
What are vertices, edges, and faces?The three-dimensional shape's vertices are the points at which the edges converge. Edges are the lines where two faces converge, while faces are flat surfaces.
Vertices are the locations where the sides of a polyhedron constructed of line segments connect.
According to the definition given above, the vertices are A, B, C, D, E, and F.
Line segments from which the formation of a polyhedron takes place are known as edges.
Hence in the given figure, AB, BC, CA, ED, DF, FE, BD, CF, and AE are the edges.
Two-dimensional surfaces in a three-dimensional figure are known as faces.
In the given prism, DBCF, DEAB, EFCA, EDF, and ABC are the faces of the prism.
To know more about vertices, edges and faces, visit:
https://brainly.com/question/23347978
#SPJ1
solve the inequality-2+4x<14
Answers
Answer: x<4
Step-by-step explanation:
If we break this down as
-2+4x<14 and we add 2 to both sides
4x+<16 and divide by 4
and you get x<4