Answers
Answer:
x = -8 + √114 ≈ 2.7 [nearest tenth]
y = 7
Step-by-step explanation:
Given that ∆CAB ≅ ∆CDB, you can use CPCTC [corresponding parts of congruent triangles are congruent] to evaluate the given lengths and angle measures, to show that the corresponding measures are the same for both triangles. Using the triangle sum theorem which states that all angles in a triangle must add up to 180°, you can find ∠ACB.
If ∠CAB = 70°, and ∠ABC = 60°,
∠ACB = 50° because ∠CAB + ∠ABC + ∠ACB = 180°.
∠CAB + ∠ABC + ∠ACB = 180° →
∠ACB = 180° – ∠CAB – ∠ABC
∠ACB = 180° – 70° – 60°
∠ACB = 50°
70° + 60° + 50° = 180°.
Remember, the order of the letters in the angle are very important because it corresponds to the parts of the angle that make up the vertex which is the middle letter, along with the first and last letters which are the endpoints.
Because ∆CAB ≅ ∆CDB,
∠ACB ≅ ∠DCB [CPCTC].
As indicated in the problem, ∠DCB = (x² + 16x)°.
Because ∠DCB ≅ ∠ACB = 50°,
(x² + 16x)° = 50°.
So this can be completed as a square by converting this into vertex form.
x² + 16x = (x + 8)² – 64.
Then, (x + 8)² – 64 = 50.
(x + 8)² – 64 + 64 = 50 + 64 →
(x + 8)² = 114 →
(x + 8) = ±√114 →
x = -8 ± √114 [one more step]
[The measure must be positive so the expression must be added]
x = -8 + √114.
______________
Related Questions
Pls I need help ASAP
Answers
Answer:
2x+12=22
Step-by-step explanation:
the side we don't know is x and there are 2 and there are 2 lengths the same in a rectangle. we know one of them and it is 6 so we do 6 x 2 which is 12.
PLEASE HELPPPPPPPPPPPPP!!!!!!!! 10 POINTS
Answers
answer: 58% ?? if I'm wrong I am sorry
If 18,20,26 are the side lengths of a triangle would the triangle be acute , obtuse or right?
Answers
Answer: It would be acute
Step-by-step explanation:
what is 3x+3(x+y). I need help answering this algebra I question
Answers
Answer:
6x + 3y
Step-by-step explanation:
3x + 3x + 3y (use the distributive property)
6x + 3y
= 6x + 3
A city has a population of 330,000 people. Suppose that each year the population grows by 3.75%. What will the population be after 7 years?
Use the calculator provided and round your answer to the nearest whole number.
people
5
?
Answers
Answer:
429 058 people
Step-by-step explanation:
We will use the population growth formula.
Initial population * e ^ (rate * time)
With the information given, the equation will look like this:
[tex]330000 * e^(0.0375*7)[/tex]
(The numbers in the parantheses are exponents.)
Plug this into the calculator and you will get:
429 058 people.
Let me know if you have anymore questions.
Which number line shows the solution set of the inequality 162 – 15 > 9?
Answers
Answer:
147 > 9
Step-by-step explanation:
162 - 15 > 9
147 > 9
you dont have any number lines, but if you add it to your question, i will edit my answer to tell you what one it is...
Hope this Helps!!
what is the perimeter?
Answers
Answer:
24
Step-by-step explanation:
Count the outer boxes.
Shelter A has a capacity of 300 beds and is 60% occupied. Shelter B is 30% occupied. The ratio of the occupancy of Shelter A to Shelter B is 1 : 2. How many beds are in Shelter B?
Answers
Answer:
1200 beds
Step-by-step explanation:
Shelter A has a capacity of 300 beds and is 60% occupied.
The amount of beds occupied =
60% × 300 beds
= 60/100 × 300
= 180 beds
Shelter B is 30% occupied.
Let the number of beds in Shelter B = x
30% × x = 0.30x beds
Hence:
180 beds + 0.30x beds
The ratio of the occupancy of Shelter A to Shelter B is 1 : 2.
Let the sum of the proportion = 1 + 2 = 3
Hence:
Number of beds in Shelter B =
2/3(180 beds + 0.30x beds) = 0.3x
2/3(180 + 0.30x) = 0.3x
Cross Multiply
2(180 + 0.30x) = 0.3x × 3
360 + 0.6x = 0.9x
Collect like terms
360 = 0.9x - 0.6x
360 = 0.3x
x = 360/0.3
x = 1200 beds
Therefore, the number of beds that are in Shelter B is 1200 beds
15 POINTS!! What is 58% of 18? SHOW YOUR WORK!
Answers
Answer:
10.44
this is the answer of this question
Answer:
58 ×18
100
10.44
hope it helps..
solve the system of equations
-3y+4x=13
-5y-6x=-67
Answers
Answer:
{x,y} = {67/16,-15/4}
Step-by-step explanation:
// Solve equation [2] for the variable y
[2] 2y = -8x + 26
[2] y = -4x + 13
// Plug this in for variable y in equation [1]
[1] 4x + 5•(-4x+13) = -2
[1] -16x = -67
// Solve equation [1] for the variable x
[1] 16x = 67
[1] x = 67/16
// By now we know this much :
x = 67/16
y = -4x+13
// Use the x value to solve for y
y = -4(67/16)+13 = -15/4
You are trying to decide whether to use Uber or Lyft during a vacation. Uber charges $3 to pick up plus an additional $0.25 for each mile driven. Lyft does not charge to pick up but they have a rate of $0.75 for each mile driven.
Let x = the number of miles traveled and y = the total cost for the trip.
Answers
Answer:
Uber: y = .25x + 3
Lyft: y = .75x
Step-by-step explanation:
A quadrilateral has two angles that measure 10° and 70°. The other two angles are in a ratio of 3:11. What are the measures of those two angles?
Answers
Answer:
The measures of those two angles are 60° and 220°
Step-by-step explanation:
The sum of the measures of the angles of any quadrilateral is 360°Let us solve the question
∵ A quadrilateral has two angles that measure 10° and 70°
→ By using the rule above, subtract their measure from 360
∴ The sum of the other two angles = 360° - 10° - 70°
∴ The sum of the other two angles = 280°
∵ The other two angles are in a ratio of 3: 11
→ Find the sum of the parts of the ratio
∵ The sum of the parts of the ratio = 3 + 11 = 14
∵ The sum of the measures of these 2 angles is 280°
→ By using the ratio method
→ m∠1 : m∠2 : their sum
→ 3 : 11 : 14
→ x : y : 280°
→ By using cross multiplication
∵ x × 14 = 3 × 280
∴ 14x = 840
→ Divide both sides by 14
∴ x = 60
∴ m∠1 = 60°
∵ y x 14 = 11 x 280
∴ 14y = 3080
→ Divide both sides by 14
∴ y = 220
∴ m∠2 = 220°
∴ The measures of those two angles are 60° and 220°
4. Solve the following equation: 9x - 6 +7x = 16x - 6
Answers
Answer: the answer is 0=0
Step-by-step explanation:
Ratios as Ordered Pairs
PLS HELP I WILL GIVE YOU BRAINLIST AND 50 POINTS
Which ordered pairs represent the equivalent ratios in the table? Check all that apply.
(1, 2)
(1, 4)
(2, 8)
(4, 1)
(3, 12)
Answers
Answer:
1,4, 2,8, and 3,12 are all equivalent
Plzzzzz give me Brainliest!!!!!
Subtract 23.4 − 8.78 = Haven't been taught how to do this
Answers
Answer:
14.62
Step-by-step explanation:
23.4-8.78
so align it like if you were going to subtract it like this:
23.4
- 8.78
You have to add a zero behind the four just so it can be easier for you,
23.40
- 8.78
--------
Now subtract it
I will give you the answer so you know if you are correct or wrong
Please help!! What is RS?
Answers
Answer:
RS = 47Step-by-step explanation:
RV=VU and SW=WT means [tex]VW=\frac{RS+UT}{2}[/tex]
So:
[tex]3x+5=\dfrac{2x+15+6x-37}{2} \\^{\qquad\times2\qquad\qquad\qquad\qquad\times2} \\6x+10=8x-22\\^{\qquad-10\qquad-10}\\6x=8x-32\\^{-8x\qquad-8x}\\-2x=-32\\^{\div(-2)\quad\div(-2)}\\x=16\\\\RS=2x+15=2\times16+15=32+15=47[/tex]
what is the slope of the line (-3,-6) and (9,-2)
Answers
Steps: y2-y1/x2-x1
-6+2/-3-9 = -4/-12
-4/-12 = 1/3
Answer:
the slope is 1/3
please correct me if I am wrong, as I have not done this in a while.
Step-by-step explanation:
I used the formula (y2-y1)/ (x2-x1)
floor. How many tooth picks will it take to
build 12 stories? How many marshmallows
will it take to build 12 stories?
Answers
would love to help but I need the size of tooth picks and marshmallows and how tall each story needs to be
According to the U.S.
Census, 76% of U.S. workers commute
to work by driving alone. Write 75% as
a decimal
Answers
.75. Simply have to move the decimal place from where the % sign is to the left two times.
Solve the following equation:
x2 = 64
x = 32
X = 8
x = -8
x = 8 or x = -8
Answers
Answer:
X=±8
Step-by-step explanation:
x²=64
x²=8²
X=±✓8²
X=±8
Ten gallons of a 25% salt solution are to be obtained by mixing solutions that are 13% salt and 33% salt
respectively. How many gallons of each are needed?
Answers
Answer:
salt + salt = salt
0.13x +3.3-0.33x =2.5
-0.20x=-0.8
x= 4 gallons (amt of 13% solution to be mixed)
10-x= 6 gallons (amt of 33% solution to be mixed)
-----------
Cheers,
Stan H.
Step-by-step explanation:
Write an algebraic expression that models the given situation.
24 more than the product of 2 and a number.
Enter the correct answer in the box.
Answers
Answer:
2x + 24
Step-by-step explanation:
The product of 2 and a number is: 2x
because product means multiply. 2 and a number means 2 times an unspecified number represented as x. 24 more than that product just means to add 24 to the product of 2x.
Answer:2x + 24
Sorry I was gonna do it when it was posted but I was grounded that time sorry. Have a great day!
33 1/3% of 27
I have no clue how to solve this
Answers
Answer:
9
Step-by-step explanation:
Answer:
9
Step-by-step explanation:
33⅓ % = 1/3
1/3 x 27 = 9
The graph of a linear function passess through the points (3, 19) and (5, 23). Write an equation for the function. Show your work
Answers
Answer:
y = 2x +13
Step-by-step explanation:
1. find the slope by using the formula y2-y1
--------
x2-x1
which is
23 - 19 4
------------ = --- = 2
5-3 2
2. finding the y intercept
so to find the y intercept you plug in the numbers to this formula
y-y1 = m (x-x1)
y - 19 = 2 (x -3)
y - 19 = 2x -6
+19 +19
y = 2x +13
help me plzzz!?!?? true or false
Answers
Answer:
false, true, false
Step-by-step explanation:
A. False - She has 15 plants
B. True - She has 4 plants that are 7-9 and 4 plants that are 10-12
C. True - Medain means middle, and since it is an even number, and it's between 9 and 10, there's a good chance it's around 11
The library holds 200 books on 5 shelves. The unit rate is the number of books
per shelf. Explain how you find the answer to the number of books that are
held on each shelf.
Answers
Answer:
40 books are held on each shelf
Step-by-step explanation:
To find the unit rate you would divide the 200 books by the 5 shelves. this would give you 40 books per shelf.
Select the correct answer.
What is the product of -3 1/3 and -8 7/10?
A. 9/5
B. 2
C. 175/30
D.
29
Answers
Answer:
awser 29
Step-by-step explanation:
`22
Answer:29
Step-by-step explanation:
what is the first step when solving this equation: 2(x-4)+6=3x+19
Answers
Answer: The first step is to follow order of operations so parenthesis goes first e potential next multiplication and division and finally adding and subtracting.
Step-by-step explanation:
f(x) = 3x for x = –4
Answers
Answer:
Step-by-step explanation:
f(x)=3x+x^4. f(x)=3x+x4 f ( x ) = 3 x + x 4.
The average cost of a gallon of gasoline increased to $2.99 per gallon from $2.85. Find the percent change.
Answers
Answer:
There was a 4.9% increase in gasoline prices.
Step-by-step explanation: