Answers
Answer:
x = 14° and z = 83°
Step-by-step explanation:
We know that the vertical angles of intersecting lines are equal.
Thus, 13x - 85 = 97
i.e. 13x = 97 + 85
i.e. 13x = 182
i.e. [tex]x=\frac{182}{13}[/tex]
i.e. x = 14°
Since, the sum of all the four angles formed by intersecting line is 360°.
We get,
(13x-85) + 97 + 2z = 360° (Take 2z as opposite angles are equal)
i.e. 2z = 360 - 97 + 85 - 13 × 14
i.e. 2z = 360 - 12 - 182
i.e. 2z = 360 - 194
i.e. 2z = 166
i.e. [tex]z=\frac{166}{2}[/tex]
i.e. z = 83°
Hence, we get the angles x = 14° and z = 83°.
Related Questions
Which expression is the correct one?
Answers
The logarithmic property of base change says that
loga (b) = logc (b) / logc (a)
Therefore the same property applies to this problem and the correct expression for this question is:
logb (x) / logb (a)
Find the area. The figure is not drawn to scale
Answers
Find the value of x
Please answer fast
Thx
Answers
A 6-foot tall person standing with her back to the sun casts an 8-foot long shadow. To the nearest degree, what angle does the sun make with the ground?
Answers
α≈37 °
Answer:
Step-by-step explanation:
Alright, lets get started.
Please refer the diagram I have attached.
Let us suppose the sun has angle of elevation x
The triangle formed will be a right triangle, so
[tex]tan x= \frac{opposite}{adjacent}[/tex]
[tex]tanx = \frac{6}{8}[/tex]
taking tan inverse
[tex]x=tan^{-1}(\frac{6}{8} )[/tex]
[tex]x=36.87[/tex]
To the nearest degree, the angle will be 37 degrees. : Answer
Hope it will help :)
Lyla took a total of 16 quizzes over the course of 4 weeks. After attending 8 weeks of school this quarter, how many quizzes will Lyla have taken in total? Assume the relationship is directly proportional.
Answers
Lyla takes 4 quizzes per week. Over 8 weeks, she will have taken a total of 32 quizzes, if the relationship is directly proportional.
Explanation:Lyla took 16 quizzes over the course of 4 weeks. This indicates that Lyla takes 4 quizzes per week (16 quizzes divided by 4 weeks). We can apply this rate to an 8-week period to find out how many quizzes she will have taken after 8 weeks of school. To do this, you multiply the number of quizzes she takes per week (4) by the number of weeks (8), which results in 32 quizzes. Hence, Lyla will have taken a total of 32 quizzes after 8 weeks. This calculation assumes that the relationship is directly proportional, meaning the number of quizzes she takes each week remains constant.
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a zookeeper measured the length of 5 snakes at the zoo he recorded the results in a table. what is the main snake length?
____cm
Answers
A combined total of $49,000 is invested in two bonds that pay 2% and 6.5%simple interest. The annual interest is $2,5100. How much is invested in each bond?
Answers
x + y = 49,000 so x = 49,000 - y
0.02x + 0.065y = 2,510
substitute x = 49,000 - y into 0.02x + 0.065y = 2,510
0.02x + 0.065y = 2,510
0.02(49,000 - y) + 0.065y = 2,510
980 - 0.02y + 0.065y = 2,510
0.045y = 1,530
y = 34,000
x = 49,000 - y = 49,000 - 34,000 = 15,000
answer
invested $34,000 in the bond that pays 6.5% rate and $15,000 in bond that pays 2% rate
The amount invested in the 2% bond is $7,500, and the amount invested in the 6.5% bond is $41,500.
Explanation:Let's assume that the amount invested in the 2% bond is x dollars. Then, the amount invested in the 6.5% bond is $49,000 - x dollars.
The interest earned from the 2% bond is 0.02x dollars, and the interest earned from the 6.5% bond is 0.065($49,000 - x) dollars.
According to the problem, the sum of these two interests is $2,510. So, we have the equation:
0.02x + 0.065($49,000 - x) = $2,510
Simplifying and solving this equation, we find that x = $7,500. Therefore, $7,500 is invested in the 2% bond, and $41,500 is invested in the 6.5% bond.
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Please Help Me with this problem.
Answers
A flagpole casts a showdown 15 feet long the 6 foot tall man casts a shadow 4 feet long how tall is the flag pole
Answers
mans shadow over mans height (4/6 ) equals flag pole shadow over flag pole height (15/x)
set them to equal each other:
4/6 = 15/x
cross multiply: 4*x =4x, 15*6 = 90
so you have 4x = 90
now divide both sides by 5 to solve for x, which is the height of the flag pole:
x = 90 / 4 = 22.5 feet tall
Evaluate the expression. If necessary, round to the nearest hundredth. ln 4.4
Answers
While it's possible to approximate the value of this log (using a series representation for the ln function), the more usual approach at this course level is to look up or calculate the value.
On my TI-83 Plus calculator, I entered "ln 4.4" and obtained the result 1.48. This is approximate.
A cube has a surface area of 864 square inches.
Find the volume of the cube.
Answer Choices
12 cubic inches
144 cubic inches
1,664 cubic inches
1,728 cubic inches
Answers
Name the complementary to m
Answers
Answer:
The complement of m∠WXV is m∠UXV
Explanation:
Complementary angles are two (or more) angles with a sum of 90 degrees.
Because line WT is dissected perpendicularly by line UX, two 90° angles are formed in ∠TXU and ∠WXU. We know that they are both 90° because of the box on ∠TXU. ∠TXU and ∠WXU are supplementary angles -- two angles that occupy the same line but are dissected by a perpendicular line forming two angles with a sum of 180 degrees.
If ∠TXU + ∠WXU = 180, and ∠TXU = 90, then ∠WXU must also equal 90:
90 + ∠WXU = 180
90 - 90 + ∠WXU = 180 - 90
0 + ∠WXU = 90
∠WXU = 90°
As we see in the diagram, ∠WXU is dissected by line SV. Because of this, it is broken into the two angles of ∠WXV and ∠UXV. We already established that ∠WXU is 90°. Therefore the sum of these two angles formed must equal 90°, which, in turn, means they are complementary angles. They complement one another.
Therefore, the complement of ∠WXV is ∠UXV
Charlene has a budget of $65. Beau and Belle dresses are $76.48. What inequality can be used to calculate how much of a markdown Beau and Belle must take for Charlene to stay in her budget
Answers
- 65.00
----------
$11.48
The answer for how much of a markdown would be 15%
The inequality
[tex]76.48 \geqslant 65 + .15[/tex]
76.48 is greater than or equal to 65 + 15%
Final answer:
To find out how much Beau and Belle must markdown the dress for Charlene to stay within her budget of $65, we use the inequality 76.48 - m ≤ 65, which solves to m ≥ 11.48, meaning the dress needs a markdown of at least $11.48.
Explanation:
To determine the markdown Beau and Belle must offer for Charlene to afford the dress within her budget, we can set up an inequality. Let's denote the markdown as m. The original price of the dress is $76.48, and Charlene's budget is $65. Therefore, the dress's price after the markdown should be less than or equal to $65. The inequality that models this scenario is:
76.48 - m ≤ 65
This inequality states that the original price of the dress minus the markdown m should be less than or equal to Charlene's budget of $65. To find out how much of a markdown is needed, we will solve for m.
Subtracting $76.48 from both sides of the inequality:
-m ≤ 65 - 76.48
-m ≤ -11.48 (This indicates that the markdown must be at least $11.48)
To express m as a positive number, we multiply both sides of the inequality by -1, remembering to reverse the inequality symbol:
m ≥ 11.48
Therefore, Beau and Belle must markdown the dress by at least $11.48 for Charlene to stay within her budget constraint.
Okay my question is : Rachael’s backyard swimming pool is being empty by a pump. The amount of water in the pool W in gallons at any time t in hours is given by the following equation :W=9000-150t deep how many gallons of water are being pumped out each hour??that is my question plzzz answer asap
Answers
250 1 times 250 substract by 9000 gives 8750 them find loss of water by 9000 substracted by 8750.
Have a nice day
corresponding sides of two squares are in the ratio 13to 19. what is the ratio of their perimeters
Answers
The ratio of their perimeters is 13 to 19.
State whether a side of the aquarium is best modeled by a point, a line, a ray, or a plane.
A) RAY B) POINT C) LINE D )PLANE
Answers
Hope this helps!
Plz mark Brainliest!
a bell curve ____
A. Normal Distribution
B. Negatively Skewed
C. Positively Skewed
Answers
The sum of 6 consecutive integers is 519. What is the third number in this sequence?
Answers
n-2+n-1+n+n+1+n+2+n+3=519
6n+3=519
6n=516
n=86
So the third number is 86.
What does the phrase “at the eleventh hour” mean in this sentence
The members of the House of Representatives approved the budget “ at the eleventh hour”
A) at a particular time of day
B) with unanimous agreement
C) before they needed to
D) at the last minute
Answers
Answer:um
Step-by-step explanation:d
What is the measure of ∠PQR ?
Enter your answer in the box. °
Answers
you are given 70 and 80 which = 150 degrees ( 70 +80 = 150)
so the missing angle (PQR) = 180 - 150 = 30 degrees
it is an algebra 2 question I do not know if that is allowed. please if anyone can help anyway.
[tex]x \div x - 4 = 2[/tex]
Answers
what is the slope w(2,4) and x(-5,-5)
Answers
Please help me? Show your work please! I give brainiest! (Or whatever it’s called :) )
Answers
4² + 9² = c²
16 + 81 = c²
97 = c²
9.85 = c
There are 5,280 ft in a mile.
Multiply 9.85 by 5,280.
9.85 × 5,280 = 52,008
Multiply 52,008 by 110.
52,008 × 110 = 5,720,880
The estimated cost for constructing the street would be $5,720,880.
Which expression is equivalent to the expression shown please help!!!!!!!!!!!
Answers
= 7^14 ÷ 7^2
= 7^(14-2)
= 7^12
ANSWER: 7^12 (top right answer)
Hope this helps! :)
Help me! :)
The edges of a polyhedron are the line segments bordering each face.
True or False?
Answers
The answer is True :3
solve 2x-3y=5 x=4y+5 using the substitution method
Answers
Substitute x=4y+5 into the first equation
2(4y+5)-3y=5
8y+10-3y=5
Subtract both sides by 10
5y=-5
Divide both sides by 5
y=-1
Now that we have a value of y we can put that value into any equation and we will get the value of x
I will do it to both equations to prove it
2x-3(-1)=5
2x+3=5
Subtract both sides by 3
2x=2
Divide both sides by 2
x=1
x=4(-1)+5
x=1
So your final answer is x=1 and y=-1
A round of table has a diameter of 28 inches. What is the area of the tabletop? Use 22/7 for pi
Answers
Area = π r² = 22/7 x (14)² = 616 in²
Answer: 616 in²
1936 or 616
Probably 616 though
watermelon seed is 4mm long. How far would a line of 120 watermelon seeds stretch? Write your answer in meters.
Answers
To find the total length of 120 watermelon seeds, each 4mm long, we just need to multiply the length of one seed by the total number of seeds. Then, to convert the total length from millimeters to meters, we divide by 1000. So, a line of 120 watermelon seeds would be 0.48 meters long.
Explanation:This problem involves simple multiplication to solve it. Since each watermelon seed is 4mm long, to find the length of 120 seeds lined up, we just need to multiply 120 by 4. So, 120 seeds * 4mm/seed = 480mm. To convert millimeters to meters, we divide by 1000 (as there are 1000mm in a meter). So, 480mm = 0.48 meters. Therefore, a line of 120 watermelon seeds would stretch 0.48 meters.
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Which of the following equations can be used to solve for acceleration
A) acceleration= distance * time
B) acceleration=(change in velocity)/time
C) acceleration = force* distance
D) acceleration = (change in displacement)/time
Answers
Hello!
The answer should be the second option B.
Acceleration is a rate of change in velocity. It involves a change in speed and direction. Change of velocity over a period of time.
Acceleration formula
↓↓↓↓↓↓↓
A=Δv/t
Hope this helps!
Thank you for posting your question at here on Brainly.
-Charlie
The equation that can be used to solve for acceleration is acceleration = (change in velocity)/time (Option B).
Explanation:The equation that can be used to solve for acceleration is acceleration = (change in velocity)/time (Option B).
This equation calculates acceleration by dividing the change in velocity by the time taken.
For example, if an object's velocity changes from 10 m/s to 20 m/s in 5 seconds, the acceleration can be calculated using this equation as (20 m/s - 10 m/s) / 5 s = 2 m/s2.
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A local coffee shop serves 2/9 as many customers as a shop run by a national coffee chain. The shop run by the chain serves 502 customers day. About how many customers does the local shop serve in a day
Answers
Answer:
about 112 customers
Step-by-step explanation:
we know that
To find out how many customers does the local shop serve in a day, multiply the fraction 2/9 by the number of customers that the shop run serve in a day
Let
x ----> the number of customers that the shop run serve in a day
y ----> the number of customers that the local shop serve in a day
[tex]y=\frac{2}{9}x[/tex]
we have
x=502
substitute the value of x in the equation
[tex]y=\frac{2}{9}(502)[/tex]
[tex]y=111.6[/tex]
Round up
so
about 112 customers
The local shop serves about 112 customers in a day
Further explanationOrder of Operations in Mathematics follow this following rule :
ParenthesesExponentsMultiplication and DivisionAddition and SubtractionThis rule is known as the PEMDAS method.
In working on a mathematical problem, we first calculate operation that is in parentheses, follow by exponentiation, then multiplication or division, and finally addition or subtraction.
Let us tackle the problem.
[tex]\texttt{ }[/tex]
This problem is about Percentage.
A local coffee shop serves 2/9 as many customers as a shop run by a national coffee chain.
[tex]\texttt{Local Shop's customers} = \frac{2}{9} \times \texttt{National Chain's customers}[/tex]
[tex]\texttt{ }[/tex]
The shop run by the chain serves 502 customers day.
[tex]\texttt{National Chain's customers} = 502[/tex]
[tex]\texttt{ }[/tex]
[tex]\texttt{Local Shop's customers} = \frac{2}{9} \times \texttt{National Chain's customers}[/tex]
[tex]\texttt{Local Shop's customers} = \frac{2}{9} \times 502[/tex]
[tex]\texttt{Local Shop's customers} = 111\frac{5}{9}[/tex]
[tex]\texttt{Local Shop's customers} \approx 112[/tex]
[tex]\texttt{ }[/tex]
Conclusion:The local shop serves about 112 customers in a day
[tex]\texttt{ }[/tex]
Learn moreInfinite Number of Solutions : https://brainly.com/question/5450548System of Equations : https://brainly.com/question/1995493System of Linear equations : https://brainly.com/question/3291576Answer detailsGrade: Middle School
Subject: Mathematics
Chapter: Percentage
Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point , Multiplication , Division , Exponent , PEMDAS , percentange , percent