Answers
so
AB = BC
x + 4 = 3x - 8
3x - x = 4 + 8
2x = 12
x = 6
AC = x = 6
The length of [tex]AC[/tex] is [tex]6[/tex].
Given:
In triangle [tex]ABC, \angle A\cong \angle C,AB=x+4,BC=3x-8,AC=x[/tex].
To find:
The length of [tex]AC[/tex].
Explanation:
In the given triangle, two angles are congruent and we know that the base angles of an isosceles triangle are congruent. It means the triangle [tex]ABC[/tex] is an isosceles triangle with [tex]AB=BC[/tex].
[tex]x+4=3x-8[/tex]
[tex]x-3x=-4-8[/tex]
[tex]-2x=-12[/tex]
Divide both sides by [tex]-2[/tex].
[tex]x=6[/tex]
Now,
[tex]AC=x[/tex]
[tex]AC=6[/tex]
Therefore, the length of [tex]AC[/tex] is [tex]6[/tex].
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Related Questions
Which expression is equivalent to (^4√5^3)^(1/2)
5^6
5^3/8
5^16/3
5^2/3
Answers
To solve this, we must solve the equation..
(^4√5³)^(1/2) = 1.82...
It can't be A because 5^6 = 15625
It can't be C because 5^16/3 = 5343.67...
It can't be D because 5^2/3 = 2.92...
It can be B because 5^3/8 also equals 1.82...
So, (^4√5³)^1/2 = 5^3/8.
Hope this helps! ☺♥
4ab over c divided by 3a over 2c
Answers
[tex]\frac{\frac{4ab}{c} }{\frac{3a}{2c} }[/tex] simplifies to (8b)/3.
To simplify the expression[tex]\frac{\frac{4ab}{c} }{\frac{3a}{2c} }[/tex]
1. Rewrite the expression using the rule that dividing by a fraction is the same as multiplying by its reciprocal:
[tex]\frac{\frac{4ab}{c} }{\frac{3a}{2c} }[/tex]=[tex]\frac{4ab}{c} *\frac{2c}{3a}[/tex]
2. Cancel out common factors:
- 'c' in the numerator and denominator cancels out.
- 'a' in the numerator and denominator cancels out.
3. After canceling, we're left with:
4b * ([tex]\frac{2}{3}[/tex])
4. Multiply 4b by [tex]\frac{2}{3}[/tex]:
4b * [tex]\frac{2}{3}[/tex] = [tex]\frac{8b}{3}[/tex]
So, [tex]\frac{\frac{4ab}{c} }{\frac{3a}{2c} }[/tex] simplifies to (8b)/3.
The probable question maybe:
simplify the expression[tex]\frac{\frac{4ab}{c} }{\frac{3a}{2c} }[/tex].
Which statements include two quantities in the real world that are additive inverses? Select each correct answer.
A. A diver descends 18 feet and then ascends 5 feet.
B. A person pours 6 ounces of water out of a glass and then pours 6 ounces of water back in to the glass.
C. The outside temperature increases 15 degrees from the morning to the afternoon, and then decreases 6 degrees from the afternoon in to the evening.
D. A person loses 12 points playing a game and then earns 12 points.
Answers
Did the test B and D are correct
what is a close but easier numbers to estimate the answer to the problem
Answers
Simon tosses a coin 20 times. The coin lands heads up 7 times. Based on these results, how many times can Simon expect the coin land heads up in the next 100 tosses?
Answer choices:
28
21
14
35
Answers
NEED HELP ASAP 12+ PTS WILL MARK BRAINLIEST A remote controlled toy truck is traveling at a constant rate of 15 feet per second. What is the distance traveled when time = 3 seconds? Table with column 1 heading Seconds and values 0, 1, 2, 3 and column 2 heading Feet and no values showing. A. 5 ft B. 15 ft C. 30 ft D. 45 ft
Answers
15:1 =45:3
D is the answer
The function graphed is f(x). What is the function rule? Write the rule in function notation, using the slope-intercept form of a line. Enter your answer in the box.
Answers
Answer: i did it
Step-by-step explanation:
Elio Makes candles that are 14 cm tall. Each candle burns eight hours before going out. He is wondering how many hours a 21 cm tall candle can burn for.
Answers
Final answer:
A 21 cm tall candle should burn for 12 hours, as it is 1.5 times taller than a 14 cm candle which burns for 8 hours.
Explanation:
The problem is one of direct proportion where the height of the candles is directly proportional to the burning time. If a 14 cm tall candle burns for 8 hours, then a 21 cm tall candle, which is 1.5 times taller, should burn for 1.5 times longer. Hence, to calculate the burning time for the 21 cm candle, we multiply 8 hours by 1.5.
Calculation:
21 cm / 14 cm = 1.5
8 hours × 1.5 = 12 hours
Therefore, a 21 cm tall candle should burn for 12 hours.
Hi!
Which of the following is closest to 0.0432
A) 4 times 10 to the power of negative 2
B) 4 times 10 to the power of negative 1
C) 4 times 10 to the power of positive 1
D) 4 times 10 to the power of positive 2
Answers
______________________________________
Note: The number provided is:
__________________________
"0.0432" ; which equals: "4.32 * 10⁻² " .
______________________________________
Final answer:
The exponential form closest to the number 0.0432 is 4 times 10 to the power of negative 2, because it gives us 0.04 which is very close to 0.0432. So the correct option is A.
Explanation:
The student is asking which exponential form is closest to the number 0.0432. To express a number in scientific notation, we move the decimal point to the right or left to create a new number from 1 up to 10, and then we multiply this number by 10 raised to a power that corresponds to the number of places the decimal point was moved.
If we look at the options given:
A) 4 times 10 to the power of negative 2 would be equivalent to 0.04, which is very close to 0.0432.B) 4 times 10 to the power of negative 1 is 0.4, which is much larger than 0.0432.C) 4 times 10 to the power of positive 1 is 40, andD) 4 times 10 to the power of positive 2 is 400, both of which are drastically larger than 0.0432.Therefore, the correct answer is A) 4 times 10 to the power of negative 2, because it is the option closest to 0.0432.
Is this question impossible? If not help with a solution
Answers
--------------------------------------------------
Edit:
Assuming the lines are parallel, then refer to the image attachment for the angle labels
A = 14-4x
B = A = 14-4x
C = 5y-9
D = 8y+42
E = 180 - D = 180 - (8y+42) = -8y+138
B+C = 90
(14-4x)+(5y-9) = 90
-4x+5y+5 = 90
-4x+5y = 85
If the lines are parallel, then
A = E
14-4x = -8y+138
-4x+8y = 124
The system of equations is
-4x+5y = 85
-4x+8y = 124
Subtract equation 2 from equation 1 to get
-3y = -39
y = 13
Then use that y value to find x
-4x+8y = 124
-4x+8*13 = 124
-4x+104 = 124
-4x+104-104 = 124-104
-4x = 20
x = -5
So the final answer is x = -5
Once again this all depends on if the two lines are parallel.
A flat-screen television has a length that is 1 more inch than its width. The area of the television's screen is 1500 in cubed. To the nearest whole inch, what are the dimensions of the television
Answers
Final answer:
The dimensions of the flat-screen television with an area of 1500 square inches are approximately 38 inches in width and 39 inches in length.
Explanation:
To find the dimensions of a flat-screen television with an area of 1500 square inches and a length that is 1 inch more than its width, we can set up a quadratic equation. Let the width be w inches, then the length would be w + 1 inches. The area of the television's screen is given by the formula:
Area = width × length
Substituting the given values, we get:
1500 = w × (w + 1)
This simplifies to:
w² + w - 1500 = 0
Solving this quadratic equation, we find two potential solutions for w, but only the positive value makes sense in this context. Once we find the value of w, the width, we can then add 1 to get the length.
After calculating, we find that the width w is approximately 38 inches, and the length is approximately 39 inches. Therefore, the dimensions of the television are 38 inches by 39 inches to the nearest whole inch.
8 story building each story was 15 4/5 in height how tall was the building
Answers
Final answer:
To calculate the height of an 8-story building, where each story is 15 4/5 feet tall, multiply the height of one story by the number of stories, resulting in a total height of 126.4 feet.
Explanation:
The question asks how tall a building would be if it has 8 stories, with each story being 15 4/5 feet in height. To find the total height of the building, you need to multiply the height of one story by the number of stories. The height of one story is 15 4/5 feet, which can also be written as 15.8 feet when converted to a decimal. Therefore, the calculation would go as follows:
15.8 feet/story × 8 stories = 126.4 feet
This calculation shows that the total height of the building is 126.4 feet. This example demonstrates how to apply multiplication in real-life scenarios, specifically in calculating the height of structures based on the height of individual stories.
Answer:
[tex]\displaystyle \frac{632}{5} \;units\;\text{or}\; 126\;\frac{2}{5}\;units \;\text{or}\; 126.4\;units[/tex]
Step-by-step explanation:
We can multiply the number of stories (8) by the height of each story (15 4/5 units) to find how tall the building is.
[tex]\displaystyle 8*15\frac{4}{5}=8*\frac{79}{5} =\frac{8*79}{5} = \frac{632}{5} \;units\;\text{or}\; 126\;\frac{2}{5}\;units \;\text{or}\; 126.4\;units[/tex]
Why could the mean of the data set below be misleading? ages of teachers: 29, 38, 39, 26, 29, 29, 39, 77, 38, 29
Answers
Page: 20Critical ThinkingThinking that does not blindly accept arguments and conclusions. Rather, it examines assumptions, discerns hidden values, evaluates evidence, and assesses conclusions.
Page: 24TheoryAn explanation using an integrated set of principles that organizes observations and predicts behaviors or events.
Page: 25HypothesisA testable prediction, often implied by a theory.
Page: 25Operational DefinitionA statement of the procedures (operations) used to define research variables. For example, human intelligence may be operationally defined as what an intelligence test measures.
Page: 26ReplicationRepeating the essence of a research study, usually with different participants in different situations, to see whether the basic finding extends to other participants and circumstances.
Page: 26Case StudyAn observation technique in which one person is studied in depth in the hope of revealing universal
Tell wether the relationship is a proportional relationship or not.
Answers
The length of a particular rectangle is 4 greater than the width of the rectangle. If the perimeter of the rectangle is 16, what is the area of the rectangle?
Answers
w+4=l <=length is 4 greater than width
2w+2(w+4)=24 <= plug in the l in the first equation with the second equation
2w+2w+8=24 <= solve the equation
4w=16
w=4
and, since
w+4=l <= length is 4 greater than width
then l=4+4
l=8
Open up the parenthesis with the distributive property, and you get 2x + 8 + 2x = 16.
Subtract 8 from both sides.
2x + 2x = 8
Or
4x = 8
/4 /4
x = 2
So therefore, since the width is x, then the width is 2. The length is x+4, or 6.
The area is length times width.
2×6 = 12
So the area of the rectangle is 12 square units.
A friend asks you to think of a number, double it, then add 5. Write an algebraic expression to describe your friend's directions, and make a table of possible values.
Answers
divide use partial quotients. 2950÷67
Answers
On a grid Joe’s house is marked at ( -5, -3 ) and Andy’s house is marked at ( 3, -1 ). What is the distance, on the grid, between Joe’s house and Andy’s house?
Answers
Square root (x2-x1)^2+(y2-y1)^2
So,
i will do it without square first.
(3--5)^2+(-1--3)^2
(8)^2+(2)^2 ==== 64+4=68
answer is square root 68
Answer:
The distance is [tex]\sqrt{68} =2\sqrt{17}[/tex]
Step-by-step explanation:
Locating the points on the plane we can form a right triangle between them and solve the problem using the Pythagorean theorem.
*see attached image*
The sides of the triangle formed measure 8 and 2, so by pythagoras, the unknow side [tex]x[/tex] wich is the distance between the houses is:
[tex]x^2=8^2+2^2\\x^2=64+4\\x^2=68\\x=\sqrt{68}=\sqrt{4*17}=2\sqrt{17}[/tex]
So the distance, on the grid, between Joe’s house and Andy’s house is [tex]2\sqrt{17}[/tex]
Whole number between 9 4/9 and square root of 144
Answers
Answer:
Whole number between [tex]9\frac{4}{9}[/tex] and [tex]\sqrt{144}[/tex] are 10 and 11.
Step-by-step explanation:
To find : Whole number between [tex]9\frac{4}{9}[/tex] and [tex]\sqrt{144}[/tex]?
Solution :
Writing numbers into simpler forms,
[tex]9\frac{4}{9}=\frac{85}{9}\approx 9.44..[/tex]
[tex]\sqrt{144}=12[/tex]
So, The number between 9.44.. and 12.
i.e. [tex]9.44..<x<12[/tex]
Whole number is defined as a number without fractions or decimal.
Between 9 and 12 the whole numbers are 10 and 11.
Therefore, Whole number between [tex]9\frac{4}{9}[/tex] and [tex]\sqrt{144}[/tex] are 10 and 11.
Janita practices on the track field 1.5 hours each day before a track meet. If there are 6 days until the track meet, how many hours will Janita practice?
Answers
She would practice 9 hours.
Hope it helps!
8. The population of Grand City in 1990 was 5,250. Assume the population is increasing at 2.5% per year. What was the population in Grand City in 2010 (round answer to the nearest person)?
Answers
A = P x (1 + r/100)^t
A is the end amount
P is the initial (principal) amount
r is the rate
t is the amount of time
5250 x 1.025^20=8602.736312
Rounded to nearest person is 8603 people was the population of the city in 2010.
Solve the equation: -12 = 3x + 3
Answers
Subtract 3 from each side
-15=3x
Divide both sides by 3
-5=x
-12 - 3 = 3x subtract both sides by 3
-15 = 3x
-15/3 = x divide both sides by 3
-5 = x
hope this helps, God bless!
find the coordinates of the midpoint of HK if H(-1,2) and K(-7,-4)
Answers
Answer:
The midpoint of HK is (-4, 1)
Step-by-step explanation:
We are given two coordinates H(-1, 2) and K(-7, -4)
We need to find the midpoint of HK.
We have formula to find the midpoint.
[tex](\frac{x_1 + x_2}{2} , \frac{y_1 + y_2}{2} }[/tex]
Here [tex]x_1 = -1, y_1 = 2, x_2 = -7 and y_2 = -4[/tex]
Now plug in these values in the above formula, we get
[tex](\frac{-1 + (-7)}{2} , \frac{2 +(-4)}{2} )[/tex]
[tex](\frac{-8}{2}, \frac{-2}{2} ) = (-4, -1)[/tex]
So, the midpoint of HK is (-4, 1)
Starting at 1:00 pm the temperature changes -4 degrees per hour. How long will it take to reach -1 degrees?
please explain your anwser
Answers
Solve the equation, justify each step with an algebraic property:
3(2-x)=24
Answers
(2 * 3 + -1X * 3) = 24
(6 + -3X) = 24
6 + -6 + -3X = 24 + -6 0 + -3X = 24 + -6
-3X = 24 + -6
-3X = 18
X = -6
Work:
2−x=3242−x=8
−x=8−2
−x=6x=−6
A class of 12 girls and 14 boys is going to choose 3 students to represent them in student government. Allie suggested that the first 3 students to arrive in class the next day should be the representatives. Bobby suggested that each student roll 2 numbers cubes and the 3 students with the highest sum should be the representatives. Whose method would result in a fair sample that represents the class population, and why?
Answers
Roxanna earns 1.5 her normal hourly rate for overtime pay. Last week, Roxanna earned 72.00 I'm overtime pay for 4 hours. What is Roxanna's normal hourly pay?
Answers
Roxanna's normal hourly pay is $12.00.
Explanation:To find Roxanna's normal hourly pay, we need to first calculate her overtime pay rate. We know that she earns 1.5 her normal hourly rate for overtime pay. Since she earned $72.00 in overtime pay for 4 hours, we can set up an equation to solve for her normal hourly pay:
Overtime Pay = Normal Hourly Pay × Overtime Hours × Overtime Rate
$72.00 = Normal Hourly Pay × 4 × 1.5
Simplifying the equation, we have:
Normal Hourly Pay = $72.00 / (4 × 1.5)
Normal Hourly Pay = $72.00 / 6
Normal Hourly Pay = $12.00
Therefore, Roxanna's normal hourly pay is $12.00.
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Your friend has 5 more then twice as many game tokens as your sister. Let T be the number of game tokens your sister has. Write and expression for the number of game tokens your friend has
Answers
Hope this helps and please rate as brainliest!!! thx!!! ;)
The number of game tokens that the friend has can be represented as the algebraic expression '2T + 5', where 'T' represents the number of game tokens the sister has.
Explanation:The question asks to express the number of game tokens your friend has in terms of 'T', the number of game tokens your sister has. As the information provided states, your friend has '5 more than twice' the amount which your sister has.
The mathematical expression for this will be '2T + 5', where 2T is twice the number of tokens your sister has and 5 is the extra tokens your friend has over twice your sister's total.
So, if your sister has 'T' number of game tokens, your friend will have '2T + 5' number of game tokens.
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Cole had 3/4 of an hour of free time before dinner he spent 2/3 of that time playing the guitar how long did he play the guitar
Answers
The number of people who purchased a new car from Force Motor Company is 170% of the number of people who purchased a new car from Ampere Motors. If 60 people purchased a car from Ampere Motors, how many people purchased a car from Force Motor Company? A. 60 B. 70 C. 102 D. 170
Answers
Answer:
c
Step-by-step explanation:
102 people purchased a car from Force Motor Company
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
The number of people who purchased a new car from Force Motor Company is 170% of the number of people who purchased a new car from Ampere Motors.
If 60 people purchased a car from Ampere Motors, then we need to find number of people who purchased a car from Force Motor Company.
We will find it by
170%×60
170/100×60
1.7×60
102
Hence 102 people purchased a car from Force Motor Company
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