If angle 1 and angle 2 form a linear pair, and the m<1= (4x+7) degrees and the m<2= (2x-1) degrees, what is the value of x, and the measure of angle 1 and angle 2?
Answers
Answer: The value of x is 29°, the measure of angle 1 is 123°, and the measure of angle 2 is 57°.
Step-by-step explanation:
A linear pair is the same as a straight line meaning that the sum of the two angles has to equal 180 degrees.
In this case, add both angles and set them to equal to 180 in order to solve for x.
(4x + 7) + (2x-1) = 180 Combine like terms on the left side.
(4x + 2x) + ( 7 - 1) = 180
6x + 6 = 180 Now subtract 6 from both sides
-6 -6
6x = 174 Divide both sides by 6
x = 29
Since x is 29 degrees we will input it into the expression for the angles and solve for the real value.
m ∠1 = 4(29) + 7
m ∠1 = 116 + 7
m ∠1 = 123
If the measure of angle 1 is 123 degrees then you can subtract that from 180 to find the measure of angle two or you can use the expression.
m ∠2 = 2(29) -1
m ∠2 = 58 - 1
m ∠2 = 57
Related Questions
What is the answer ???????
Answers
.A rectangle is constructed with its base on the diameter of a semicircle with radius 16 and with its two other vertices on the semicircle. What are the dimensions of the rectangle with maximum area?
The rectangle with maximum area has base __ and height __.
Answers
To find the dimensions of the rectangle with maximum area, we need to consider the relationship between the rectangle and the semicircle.
Let's assume that the base of the rectangle is the diameter of the semicircle. Since the radius of the semicircle is given as 16, the diameter (and base of the rectangle) will be 2 * 16 = 32.
Now, we need to determine the height of the rectangle. Since the other two vertices of the rectangle lie on the semicircle, the height of the rectangle will be the distance from the center of the semicircle to the top edge of the rectangle.
The center of the semicircle is also the midpoint of the base of the rectangle, so the distance from the center to the top edge of the rectangle will be equal to the radius of the semicircle.
Therefore, the height of the rectangle will be 16.
Hence, the dimensions of the rectangle with maximum area are:
Base: 32
Height: 16
To know more about Vertices visit-
brainly.com/question/29154919
#SPJ11
Of the balloons recently sold by party store, 4 were purple and 8 were other colors. Considering the data, how many of the next 66 balloons sold would you expect to be purple
Answers
Answer: 22
Step-by-step explanation:
From the question, we are given the information that of the balloons recently sold by party store, 4 were purple and 8 were other colors. This means that the fraction of those that was purple is:
= 4/(4+8)
= 4/12
= 1/3.
Therefore, if there are 66 balloons, the number expected to be purple will be:
= 1/3 × 66
= 22
There'll be 22 purple balloons
Answer:
22
Step-by-step explanation:
= 4/(4+8)
= 4/12
= 1/3.
= 1/3 × 66
= 22
There'll be 22 purple balloons.
please help i’m gonna cry
Answers
Answer:
She Flipped the symbol
Step-by-step explanation:
Please don't cry. I will explain it to you. Just please don't cry.
She multiplied correctly. But in her end result, she flipped the symbol.
You only flip symbols when multiplying or dividing by a negative number.
I hope this helps! Please don't cry :)
A store that sells skis buys them from a manufacturer at a wholesale price of $57. The store's markup rate is 40%.
a. What price does the store charge its customers for the skis?
b. What percent of the original price is the final price?
c. What is the percent increase from the original price to the final price?
Answers
a) The selling price of the skis is $79.80.
b) The final price is 140% of the original price.
c) The percent increase from the original price to the final price is 40%.
a) Calculation of selling price:
Markup rate is 40%
Original cost = $57
Selling price = (100% + Markup percentage) × Original cost
Selling price = (100% + 40%) × $57
Selling price = 1.4 × $57
Selling price = $79.80
b) Calculation of percentage of the original price that is the final price
Percentage of original price that is the final price = (Final price / Original price) × 100%
Percentage of original price that is the final price = ($79.80 / $57) × 100%
Percentage of original price that is the final price = 140%
c) Calculation of the percentage increase
Percentage increase = (Final value − Initial value) / Initial value × 100%
Percentage increase = ($79.80 − $57) / $57 × 100%
Percentage increase = $22.80 / $57 × 100%
Percentage increase = 40%
Therefore, The store charges $79.80 for the skis. The final price is 140% of the original price and the percent increase from the original price to the final price is 40%.
To learn more about the Selling Price, refer to:
https://brainly.com/question/29273267
#SPJ11
what is the measure of angle A?
Answers
Answer:
Step-by-step explanation:
138° - 80° = 58°
There are 32 females cast in the school play. The ratio of male roles to female roles is 3:8. How many males are cast in
the school play?
Answers
Answer:
12
Step-by-step explanation:
32×3/8
.................
The point of concurrency of the angle bisectors of a triangle is known as_____. a) Incentre. b) Centroid. c) Orthocentre. d) None
Answers
The required final answer is option a) Incentre
What is concurrency of the angle?The point of concurrency of the angle bisectors of a triangle is known as the "Incentre".
It is the center of the circle inscribed within the triangle, which is equidistant from all three sides of the triangle.
The incentre is the point where the angle bisectors of a triangle intersect, forming the incircle, which is the largest circle that can be inscribed inside the triangle.
The incentre is always within the triangle and is equidistant from all three sides of the triangle, making
it a useful tool in construction and design applications. In summary, the incentre is the center of the incircle of a triangle, and it is the point where the angle bisectors of the triangle intersect.
Thus, required answer is "Incentre".
To know more about Triangle visit:
brainly.com/question/2773823
#SPJ4
(2x+15) What is the measure, in degrees, of angle D ?
Answers
The measure of angle D is ∠D = 65°.
What are similar triangles?Two triangles are said to be similar if there corresponding sides are proportional and their corresponding angles are equal.
Given is that triangle ΔABC is similar to triangle ΔDEF.
We can write -
∠D + x + 90° = 180°
∠D = 90° - x
Since both the triangles are similar, we can write -
∠D = ∠A
{90° - x} = {2x + 15}°
3x = 75°
x = 25°
∠D = 90 - x = 65°
∠D = 65°
Therefore, the measure of angle D is ∠D = 65°.
To solve more questions on angles, visit the link below-
brainly.com/question/1041084
#SPJ1
Find the distance between the two points rounding to the nearest tenth (if necessary)
(8,7) and (1,-2)
Answers
Answer:
≈ 11.4
Step-by-step explanation:
Calculate the distance using the distance formula
d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)
with (x₁, y₁ ) = (8, 7) and (x₂, y₂ ) = (1, - 2)
d = \(\sqrt{(1-8)^2+(-2-7)^2}\)
= \(\sqrt{(-7)^2+(-9)^2}\)
= \(\sqrt{49+81}\)
= \(\sqrt{130}\)
≈ 11.4 ( to the nearest tenth )
She swam 800 meters in 16 minutes, find how many minutes would it take her to swim 1,600 meters?
Answers
A simple random sample of 15 year old boys from one city is obtained in their weights are listed below use a 0.01 significance level to test the claim the these sample ways come from a population with a mean equal to 148 pounds. Assume that the standard deviation of the weight of a 15-year-old boys in the city is known to be 16.1 pounds. Use the traditional method of testing hypotheses.
Answers
Answer:
\/\/\/
Step-by-step explanation:
What you are testing is a distribution of means, because you have a sample of eleven individuals (N=11), a population mean, and the population variance. Basically, the problem is asking: what is the likelihood that the sample mean (153.45 lbs) could have been obtained from a population where (M=149) if the null hypothesis is true?
p1: 15 year old boys with a mean weight of 153.45 lbs from City "Unknown".
p2: 15 year old boys with a mean weight of 149.00 lbs from the population.
H1: The sample of boys from City "Unknown" was not drawn from a population where the average weight of 15 year old boys = 149lbs.
H0: The sample of boys from City "Unknown" was drawn from a population where the average weight of 15 year old boys = 149lbs.
Mean = 149 [μM = μ = 149]
Variance = 16.2squared/11 = 262.44/11 = 23.86 [σM2 = σ2/N]
Standard Deviation = 4.88 [σM = √σM2 = √(σ2/N)]
Shape = normal
Using .01 level of significance for a two-tailed test, the cutoff sample score is +/- 2.575
Z = (M-µ) / σM = (153.45 - 149) / 4.88 = .91
.91 < 2.575
σM or the Standard Error of the Mean is 4.88 so...
for 99% confidence interval,
lower limit = 153.45 + (-2.575)(4.88) = 140.88
upper limit = 153.45 + (2.575)(4.88) = 166.02
the 99% confidence interval = 140.88 — 166.02 (lbs)
the population mean (µ=149.00) is included in the interval, which confirms results of Z test.
Conclusion: retain null, there is <.01 probability that the sample from City "Unknown" was drawn from a population where the mean weight is NOT = 149.00lbs.
a score of x = 70 on an exam with µ = 82 and σ = 8, or a score of x = 60 on an exam with µ = 72 and σ = 12?
Answers
A score of x = 60 on an exam with μ = 72 and σ = 12 is comparatively better than a score of x = 70 on an exam with μ = 82 and σ = 8.
To compare the two scores, we can convert them to z-scores, which tell us how many standard deviations a particular value is from the mean. The formula for z-score is:
z = (x - μ) / σ
where x is the value, μ is the mean, and σ is the standard deviation.
For the first score of x = 70 on an exam with μ = 82 and σ = 8, the z-score is:
z = (70 - 82) / 8 = -1.5
For the second score of x = 60 on an exam with μ = 72 and σ = 12, the z-score is:
z = (60 - 72) / 12 = -1.0
The z-score for the first score is lower than the z-score for the second score, which means that the first score is further below its mean than the second score is below its mean. Therefore, we can say that a score of x = 60 on an exam with μ = 72 and σ = 12 is comparatively better than a score of x = 70 on an exam with μ = 82 and σ = 8.
For more questions on Z-Score
https://brainly.com/question/28000192
#SPJ4
A force of 3 pounds is required to hold a spring stretched 0.6 feet beyond its natural length. how much work (in foot-pounds) is done in stretching the spring from its natural length to 0.7 feet beyond its natural length? answer exactly or round to 2 decimal places.
Answers
The work done (in foot-pounds) in stretching the spring from its natural length to 0.7 feet beyond its natural length is 1.23 foot-pound
Data obtained from the questionFrom the question given above, the following data were obtained:
Force (F) = 3 poundsExtension (e) = 0.6 feetWork done (Wd) =?How to determine the spring constantForce (F) = 3 poundsExtension (e) = 0.6 feetSpring constant (K) =?F = Ke
Divide both sides by e
K = F/ e
K = 3 / 0.6
K = 5 pound/foot
Thus, the spring constant of the spring is 5 pound/foot
How to determine the work doneSpring constant (K) = 5 pound/footExtention (e) = 0.7 feetWork done (Wd) =?Wd = ½Ke²
Wd = ½ × 5 × 0.7²
Wd = 2.5 × 0.49
Wd = 1.23 foot-pound
Therefore, the work done in stretching the spring 0.7 feet is 1.23 foot-pound
Learn more about spring constant:
https://brainly.com/question/9199238
#SPJ1
Kathy ell ome pie at a bakery he cut each pie into 6 piece to ell individually he ell 5/6 of a pie each hour How many whole pie did Kathy ell in 36 hour?
Answers
Step-by-step explanation:
she sell 5piece out of 6 per hour
for 36 hour, she sell:
5 × 36 = 180piece of pie
one pie is cut to 6 piece
180/6 = 30pie
HELP ME. PLEASE !!! WILL MARK BRAINLIEST IF YOU HELP . and explain.
Answers
1.4 + 3.5 =
A. 17.20
B. 4.9
C. 1
D. 7.10
Answers
1.4 + 3.5
Add the terms
4.9
Hope this helps! :)
Consider the enlargement of the rectangle. A small rectangle with length of 4 and width of 2. A larger rectangle with length of 12 and width of 6. Which proportional statements are true of the enlargement? check all that apply. Startfraction width original over length original endfraction = startfraction width enlargement over length enlargement endfraction startfraction length original over length enlargement endfraction = startfraction width original over width enlargement endfraction startfraction width original over length enlargement endfraction = startfraction length original over width enlargement endfraction startfraction width enlargement over length enlargement endfraction = startfraction width original over length original endfraction startfraction length original over width enlargement endfraction = startfraction length enlargement over width original endfraction.
Answers
The two given rectangles are proportional to each other since they have a width-to-length ratio of 2 and the area ratio between them is equal to 9.
Two rectangles are proportional to each other when both have the same length-to-width ratio. The area ratio is defined by the following formula:
r' = (l' · h')/(l · h) (1)
Where:
l' - Length of the enlarged rectangle.
l - Length of the original rectangle.
h' - Length of the enlarged rectangle.
h - Length of the original rectangle.
Now we determine the length-to-width ratio of each rectangle:
Original rectangle
s = 4/2
s = 2
Enlarge rectangle
s' = 12/6
s' = 2
The two rectangles have the same length-to-width ratio.
The area ratio is:
r' = (12 · 6)/(4 · 2)
r' = 72/8
r' = 9
To learn more about rectangles visit: brainly.com/question/29123947
#SPJ4
Two rectangles are proportional to each other when both have the same length-to-width ratio. The area ratio is defined by the following formula:
r' = (l' · h')/(l · h) (1)
Now we determine the length-to-width ratio of each rectangle:
Original rectangle
s = 4/2
s = 2
Enlarge rectangle
s' = 12/6
s' = 2
The two rectangles have the same length-to-width ratio.
The area ratio is:
r' = (12 · 6)/(4 · 2)
r' = 72/8
r' = 9
given that £1 = $1.62
how much is £650 in $
Answers
Answer:
$1053
Step-by-step explanation:
If we have that £1 = $1.62, then we can multiply both sides by 650 in order to get £650 on the left side of the equality. We must multiply the right side also by 650, and so we get £650=$1.62 * 650.
To do this multiplication, we can break 1.62 down simply into $1.00 +$0.6+$0.02
650*$1.00=$650, 650*$0.6=650*6/10=65*6=$390, and 650*$0.02=650*2/100=6.5*2=$13.
When we add these three products together, we get $650+$390+$13=$1053. And so, £650=$1053
Two variables are connected by the relation: P∝1/Q^2
Q is increased by 40%
To the nearest percent, describe the change in P
in percentage terms.
Answers
The change in P in percentage terms is 51% decrease.
How to illustrate the information?Since the two variables are connected by the relation, this will be illustrated as:
P=k/Q^2
where k is the proportionality constant.
Now, If Q is increased by 40%, i.e. the update Q' = Q + 0.4Q.
Now, we have
P1 = k/Q^2 and P2 = k/(Q+0.4Q)^2
P2/P1 = {k/(Q+0.4Q)^2}/{k/Q^2}
P2/P1 = 1/(1.4)^2
P2=0.51*P1
P2 = 0.5P1
Hence P reduces by 51%.
Learn more about variables on:
https://brainly.com/question/25223322
#SPJ1
suppose a stick of length 1 is broken into two pieces uniformly randomly. what is the expected length of the smaller piece?
Answers
Assume a stick of length 1 is randomly broken into two portions. The smaller piece's estimated length is 0.25.
The random variable L (the length for the shorter stick) has a uniform distribution.
Thus the probability density function for L is as follows:
L = \(\frac{1}{0.5-0} = 2\)This means 2 for all length in the range 0 - 0.5
Now, we calculate the expected value for random variable L as seen on the attachment. Based on the calculation, 0.25 is the smaller piece's estimated length for the randomly broken stick.
Learn more about probability density function here: brainly.com/question/15714810
#SPJ4
This meal costs $19.00 .A sales tax is applied, followed by an automatic tip of 18 %.What is the total with tax and tip?
Answers
The total cost of he meat with tax and tip is $ 22.42
How to find the totalTo calculate the total cost with tax and tip, we need to follow these steps:
multiply the meal cost by the tip rate. when the tip rate is 18%, we have:
Tip amount = $19.00 * 0.18 = $3.42
Add the meal cost, sales tax, and tip amount to get the total cost:
Total cost = Meal cost + Sales tax + Tip amount
= $19.00 + $3.42
= $ 22.42
Therefore, the total cost with tax and tip is $22.42
Learn more about total cost at
https://brainly.com/question/5168855
#SPJ1
Jorden wanted to leave a 15% tip on a $48.00 bill. What amount should he leave?
Answers
Answer:
7.20
Step-by-step explanation:
15% of 48 = 7.20
Answer:
Jordan should leave $7.20 tip
Step-by-step explanation:
%15 off of $48.00 is $40.80; $7.20 + $40.80 = $48.00
✧brainliest appreciated✧
Find the mode of the following data for data sets a-d (Remember what the steps are for finding the mode ).Rewrite the problem as learned in finding the mode. (B) 15,22,17,19,22,17,29,24,17,15
Answers
Answer:
The mode would be
Step-by-step explanation:
To find the mode, or modal value, it is best to put the numbers in order. Then count how many of each number. A number that appears most often is the mode.
15, 15, 17, 17, 17, 19, 22, 24, 29
If this is the rewritten version then we can conquer that the mode would be 17 since 17 is displayed the greatest amount of times. (out of the other numbers.)
Hope this helped! If it did please consider marking this as brainliest! :)
The graph of f(x) and g(x) are shown below. How many solutions does the system of equations have?
Click pic to see whole problem
Answers
Answer:
Step-by-step explanation:
Solving systems of equations gives the points of intersection when the equations are graphed.
The answer is 3.
A square has side lengths of 9, which of the following is a correct formula for finding the area of a square? Select all that apply. i will give u brainlist
Answers
what the other person said. 9^2
please help with this.
Answers
9514 1404 393
Answer:
d. The triangles are not similar
Step-by-step explanation:
The angle between the given sides is the same, so we need to compare the side ratios. In ΔQRS, we have ...
QR/RS = 4/15
In ΔVTU, we have ...
VT/TU = 8/32 = 1/4 ≠ 4/15
The triangles are not similar because corresponding sides are not proportional.
Multiply. Write each product in simplest form.
9. 3×11
10. //
13. 021-
12.
20
=
=
=
11. 2×4=
8 9
X
18 20
14.
=
Answers
Answer:
Te conozco y sé qué
Como Nuevo de fabrica el otro
Simplify -8a(-6a) Show each step of your work.
i will mark you brainiest
Answers
Answer:
\(48a^{2}\)
Step-by-step explanation:
First, multiply the numbers
-8a ( -6)a
48aa
Next, We can combine the exponents
\(48a^{2}\)
That is all you need to do. : - )
question 19 the list 76, 56, 93, 24, 45, 88, 13, 7 , 37 is sorted using bucket sort with 4 buckets. which buck will contain 45?
Answers
Bucket number 2 will contain 45 after sorting the data.
According to the statement, we are given that a data list is sorted using bucket sort with 4 buckets and we have to find which bucket will contain the number 45.
So, the given data list is:
76, 56, 93, 24, 45, 88, 13, 7, 37
The list of data is sorted into buckets and the data contains numbers from 0 to 100.
We know that the 100 numbers are being sorted with 4 buckets which means each bucket contains 25 numbers.
So, let us consider
BUCKET 1: 0 to 25
It contains data numbers 7, 13, and 24.
Now,
BUCKET 2: 25 to 50
It contains data numbers 37 and 45.
Now,
BUCKET 3: 50 to 75
It contains data number 56.
Now,
BUCKET 4: 75 to 100
It contains data numbers 76, 88, and 93.
From sorting, the 45 number sort in bucket 2.
So, bucket number 2 will contain 45 after the list is sorted.
To learn more about Bucket sorting or bin sorting;
https://brainly.com/question/31481690
#SPJ4