Answers
Answer:
∠1 is 150°
∠2 is 30°
∠3 is 150°
∠4 is 30°
Step-by-step explanation:
∠1 is vertically opposite to ∠3 so they are equal
360° - (150° + 150°) = 360° - 300° = 60°
∠2 and ∠4 must sum to 60°
Step-by-step explanation:
From the question
∠1 is opposite to ∠ 3 and vertically opposite angles are equal
So
∠1 = ∠ 3
That's
∠ 3 = 150°∠ 3 and ∠ 4 are on a straight line and angles on a straight line add up to 180°
So to find ∠4, subtract ∠3 from 180°
That's
∠ 4 = 180 - ∠ 3
∠ 4 = 180 - 150
∠ 4 = 30°Since ∠ 4 and ∠ 2 are opposite they are also equal
That's
∠ 4 = ∠ 2
Therefore
∠ 2 = 30°Hope this helps you
Related Questions
A test was marked out of 80. Aboy scored
60% of the marks on the test. How many
marks did he score?
(A)20
(B)48
(C)60
(D)75
Answers
Answer:
B
Step-by-step explanation:
To solve this you do 80/100=.8
You than do .8×60= 48
The length l, width w, and height h of a box change with time. At a certain instant the dimensions are l = 3 m and w = h = 6 m, and l and w are increasing at a rate of 3 m/s while h is decreasing at a rate of 6 m/s. At that instant find the rates at which the following quantities are changing.
(a) The volume.
m3/s
(b) The surface area.
m2/s
(c) The length of a diagonal. (Round your answer to two decimal places.)
m/s
Answers
Answer:
a) The rate of change associated with the volume of the box is 54 cubic meters per second, b) The rate of change associated with the surface area of the box is 18 square meters per second, c) The rate of change of the length of the diagonal is -1 meters per second.
Step-by-step explanation:
a) Given that box is a parallelepiped, the volume of the parallelepiped, measured in cubic meters, is represented by this formula:
[tex]V = w \cdot h \cdot l[/tex]
Where:
[tex]w[/tex] - Width, measured in meters.
[tex]h[/tex] - Height, measured in meters.
[tex]l[/tex] - Length, measured in meters.
The rate of change in the volume of the box, measured in cubic meters per second, is deducted by deriving the volume function in terms of time:
[tex]\dot V = h\cdot l \cdot \dot w + w\cdot l \cdot \dot h + w\cdot h \cdot \dot l[/tex]
Where [tex]\dot w[/tex], [tex]\dot h[/tex] and [tex]\dot l[/tex] are the rates of change related to the width, height and length, measured in meters per second.
Given that [tex]w = 6\,m[/tex], [tex]h = 6\,m[/tex], [tex]l = 3\,m[/tex], [tex]\dot w =3\,\frac{m}{s}[/tex], [tex]\dot h = -6\,\frac{m}{s}[/tex] and [tex]\dot l = 3\,\frac{m}{s}[/tex], the rate of change in the volume of the box is:
[tex]\dot V = (6\,m)\cdot (3\,m)\cdot \left(3\,\frac{m}{s} \right)+(6\,m)\cdot (3\,m)\cdot \left(-6\,\frac{m}{s} \right)+(6\,m)\cdot (6\,m)\cdot \left(3\,\frac{m}{s}\right)[/tex]
[tex]\dot V = 54\,\frac{m^{3}}{s}[/tex]
The rate of change associated with the volume of the box is 54 cubic meters per second.
b) The surface area of the parallelepiped, measured in square meters, is represented by this model:
[tex]A_{s} = 2\cdot (w\cdot l + l\cdot h + w\cdot h)[/tex]
The rate of change in the surface area of the box, measured in square meters per second, is deducted by deriving the surface area function in terms of time:
[tex]\dot A_{s} = 2\cdot (l+h)\cdot \dot w + 2\cdot (w+h)\cdot \dot l + 2\cdot (w+l)\cdot \dot h[/tex]
Given that [tex]w = 6\,m[/tex], [tex]h = 6\,m[/tex], [tex]l = 3\,m[/tex], [tex]\dot w =3\,\frac{m}{s}[/tex], [tex]\dot h = -6\,\frac{m}{s}[/tex] and [tex]\dot l = 3\,\frac{m}{s}[/tex], the rate of change in the surface area of the box is:
[tex]\dot A_{s} = 2\cdot (6\,m + 3\,m)\cdot \left(3\,\frac{m}{s} \right) + 2\cdot (6\,m+6\,m)\cdot \left(3\,\frac{m}{s} \right) + 2\cdot (6\,m + 3\,m)\cdot \left(-6\,\frac{m}{s} \right)[/tex]
[tex]\dot A_{s} = 18\,\frac{m^{2}}{s}[/tex]
The rate of change associated with the surface area of the box is 18 square meters per second.
c) The length of the diagonal, measured in meters, is represented by the following Pythagorean identity:
[tex]r^{2} = w^{2}+h^{2}+l^{2}[/tex]
The rate of change in the surface area of the box, measured in square meters per second, is deducted by deriving the surface area function in terms of time before simplification:
[tex]2\cdot r \cdot \dot r = 2\cdot w \cdot \dot w + 2\cdot h \cdot \dot h + 2\cdot l \cdot \dot l[/tex]
[tex]r\cdot \dot r = w\cdot \dot w + h\cdot \dot h + l\cdot \dot l[/tex]
[tex]\dot r = \frac{w\cdot \dot w + h \cdot \dot h + l \cdot \dot l}{\sqrt{w^{2}+h^{2}+l^{2}}}[/tex]
Given that [tex]w = 6\,m[/tex], [tex]h = 6\,m[/tex], [tex]l = 3\,m[/tex], [tex]\dot w =3\,\frac{m}{s}[/tex], [tex]\dot h = -6\,\frac{m}{s}[/tex] and [tex]\dot l = 3\,\frac{m}{s}[/tex], the rate of change in the length of the diagonal of the box is:
[tex]\dot r = \frac{(6\,m)\cdot \left(3\,\frac{m}{s} \right)+(6\,m)\cdot \left(-6\,\frac{m}{s} \right)+(3\,m)\cdot \left(3\,\frac{m}{s} \right)}{\sqrt{(6\,m)^{2}+(6\,m)^{2}+(3\,m)^{2}}}[/tex]
[tex]\dot r = -1\,\frac{m}{s}[/tex]
The rate of change of the length of the diagonal is -1 meters per second.
Simplify the expression:
4w + 10(7w+1)
Answers
Answer:
74w+10
Step-by-step explanation:
That's the answer
The geometric probability function is f (x) = (1-P) x-1 P. what is the approximate probability of rolling a standard die and getting the first 6 on the 3rd try?
Answers
Answer:
We know that for a standard dice the probability of obtain a 6 is:
[tex] P=\frac{1}{6}[/tex]
And for this case our value of x=3 and replacing we got:
[tex] f(x=3) = (1- \frac{1}{6})^{3-1} \frac{1}{6}[/tex]
[tex]f(x=3)=\frac{25}{36} \frac{1}{6}= \frac{25}{216}= 0.116[/tex]
Step-by-step explanation:
For this case we have the following function:
[tex] f(x) = (1-P)^{x-1} P[/tex]
We want to find the approximate probability of rolling a standard die and getting the first 6 on the 3rd try
We know that for a standard dice the probability of obtain a 6 is:
[tex] P=\frac{1}{6}[/tex]
And for this case our value of x=3 and replacing we got:
[tex] f(x=3) = (1- \frac{1}{6})^{3-1} \frac{1}{6}[/tex]
[tex]f(x=3)=\frac{25}{36} \frac{1}{6}= \frac{25}{216}= 0.116[/tex]
Devaughn is 8 years older than Sydney. The sum of their ages is 64. What is Sydney's age?
Answers
Answer:
Sydney's age is 28
Step-by-step explanation:
Let Devaughn be D
And Sydney be S
D=S+8..... equation 1
D+S=64...... equation 2
Substitute equation 1 to equation 2
S+8+S=64
2S+8=64
2S=64-8
2S=56
S=56/2
S=28
Hope it helps
Good luck
And Devaughn age as 8+x
Equation will be
8+x+x=64
8+2x=64
2x=64-8
2x=56
x=28
Therefore Sydney is 28years old
Bubba Bulldog and all of his dog friends love to hide bones! Bubba hid 4 bones, Barry hid 5 bones, Larry hid 10 bones, and Goby hid 13 bones.
Find the mean number of dog bones.
_______dog bones
Answers
Answer:8
Step-by-step explanation:
You find the average which is adding them all together then dividing by how many numbers you added.
Help a man out, ive been stuck on this for a while.
Answers
Answer:
1. true - dilating figures does not change their angle measure
2. true - dilating figures does not change the orientation, so AD would still be on a horizontal line parallel to its current position
What is the measure of
Answers
Answer:
x= 78
Step-by-step explanation:
Focus on the blue traingle:
∠BHI= 180° -47° -31° (∠sum of triangle)
∠BHI= 102°
x°= 180° -102° (adj. ∠s on a str. line)
x°= 78°
x= 78
Alternatively,
x°= 47° +31° (ext. ∠ of triangle)
x°= 78°
x= 78
Joes employer will reimburse him $0.17 per mile driven. If Joe drives 107.78 miles on a business trip,
what is his mileage reimbursement?
Answers
Answer:
$18.3236
Step-by-step explanation:
If the employer reimburses $0.17 per mile driven, we just need to multiply $0.17 by the number of miles that Joe drives.
So, the mileage reimbursement for Joe is:
$0.17 * 107.78 = $18.3236
What is the inequality
Answers
Answer:
x ≥ 4
Step-by-step explanation:
Well to find the inequality we need to single out x,
4x - 1 ≥ 15
+1 to both sides
4x ≥ 16
Divide 4 by both sides
x ≥ 4
Thus,
x is greater than or equal to 4.
Hope this helps :)
Help! PLZ, 20 PTS in 10 mins if possible thx !!!! A gym charges $55 for a monthly membership and an additional $4.50 for each yoga class a member attends. Simba can spend at most $70 at the gym each month. Write an inequality that shows the maximum number of yoga classes, y, that Simba can attend while staying within his gym budget. _________
Answers
Answer:
(70-55)/4.5=y rounded down to the nearest whole number
Step-by-step explanation:
The first step is to take away the $55 from $70
70-55=15
Simba has $15 to spend on the yoga classes, to find the number of yoga classes she can attend, you divide 15 by the amount a yoga class costs, $4.50
15/4.50=3 1/3
Because she can not have 1/3 of a yoga class, she can attend 3 yoga classes in her budget.
Hope this helps, if you have any questions feel free to ask
Have a good day! :)
-7(5-3x)=-35 what is the x in the problem
Answers
Answer:
x = 0
Step-by-step explanation:
-7(5-3x)=-35
Divide by -7
-7/-7(5-3x)=-35/-7
5 -3x = 5
Subtract 5 from each side
5-3x-5 = 5-5
-3x=0
Divide by -3
x=0
Answer: x = 0
Step-by-step explanation: Start by distributing the -7 through the parenthses on the left side of the equation.
-7(5) is -35 and -7(-3x) is 21x.
So we have -35 + 21x = -35.
Next, isolate the x term by adding 35 to both sides.
When we do this, we get 21x = 0.
Now divide both sides by 21 and x = 0.
What is the answer, plz help. 5(x-7) + 42 = 5x+7
Answers
Answer:
x is all real numbers
Step-by-step explanation:
5(x-7) + 42 = 5x+7
Distribute
5x - 35 +42 = 5x+7
Combine like terms
5x +7 = 5x+7
Subtract 5x from each side
7=7
This is always true, so x can be any number
Answer:
Hey there!
5(x-7)+42=5x+7
5x-35+42=5x+7
7=7
Infinite solutions.
Hope this helps :)
Toni runs around her school's baseball diamond. Each side is 27 m long. Note: A baseball diamond is square. How far does Toni run?
Answers
Answer:
108 m
Step-by-step explanation:
Betty has $33 to buy plants for her greenhouse. Each plant costs $8. How
many plants can she buy? Do not include units in your answer.
Answers
Answer:
4 plants
Step-by-step explanation:
If betty has $33 dollars and each plant is $8, than 33/8 ≈ 4
(8 * 4 is 32)
She will have one dollar left but she can't buy another plant since that's not enough.
Answer:
4 plants
Step-by-step explanation:
Take the amount of money she has and divide by the cost per plant
33/8
The amount is 4 with 1 dollar left over
4 plants
Please answer this correctly without making mistakes.Please simplify the correct answer
Answers
Answer:
19/70 of NASA shuttle missions were carried out by Discovery.
9/140 of NASA shuttle missions were carried out by Challenger.
17/70 of NASA shuttle missions were carried out by Endeavour.
Step-by-step explanation:
Adding the number of missions carried out by NASA gives us 140 in total.
Discovery's total amount of missions simplified is 19/70.
Challenger's total amount of missions is already in the simplest form.
Endeavour's total amount of missions simplified is 17/70.
Answer:
81/140
Step-by-step explanation:
Well to find the fraction we first need to total amount of NASA missions.
38 + 32 = 70
70 + 34 = 104
104 + 27 = 131
131 + 9 = 140
Now we need to find out the amount of Discovery, Challenger, and Endeavour missions.
38 + 9 + 34 = 81
Now we can make the following fraction,
81/140
This is already in simplest form.
Thus,
the answer is 81/140.
Hope this helps :)
A 5 hour conference booking is required fir an office party for 120 people which includes a buffet dinner hotel 5 has recently increased the Total chargers by 10% how much would thia Booking now cost from hotel 5
Answers
Answer:
Total cost = $4,873
Therefore, the booking cost of hotel 5 would be $4,873
Step-by-step explanation:
Please refer to the attached table.
The total cost includes the cost of the room and the cost of buffet dinner.
From the given table hotel 5,
The cost of the room for 120 people is found to be $166 per hour.
The conference will last for 5 hours so the total cost of the room is
Cost of room = 5*$166 = $830
From the given table hotel 5,
The cost of the buffet dinner per head is found to be $30.
Since there are total 120 people so the total cost of dinner is
Cost of dinner = 120*$30 = $3600
Total cost = $830 + $3600 = $4430
We are given that hotel 5 has recently increased the total chargers by 10%
Total cost = $4430*1.10
Total cost = $4,873
Therefore, the booking cost of hotel 5 would be $4,873.
A P E X!!!! URGENT :The annual interest rate of Belinda's savings account is 8.6% and simple interest is calculated quarterly. What is the periodic interest rate of Belinda's account?
Answers
Answer:
The answer is 2.15%
Step-by-step explanatio
which graph represents a function? Please help!
Answers
Answer:
The last graph (to the far right).
Step-by-step explanation:
As long as each x-value has one y-value, it is a function. However, the last graph has an x-value at -1 where there are two y-values. So, it does not pass the Vertical Line Test, and it is a relation rather than a function.
Hope this helps!
Which of the following proves ABC DEF?
A.
SAS
B.
SSS
C.
SSA
D.
ASA
Answers
Option A is the correct answer.
Answer:
SAS
Step-by-step explanation:
According to the given information both the triangles are congruent by SAS postulate.
The given triangles are congruent by SAS rule.
What is congruency in triangles?Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.
Given are two triangles, ABC and DEF,
They have congruent parts, given;
AB ≅ DE
BC ≅ EF
∠ B ≅ ∠ E
The triangles have two congruent sides and one congruent angle between them.
The Side-Angle-Side theorem of congruency states that, if two sides and the angle formed by these two sides are equal to two sides and the included angle of another triangle, then these triangles are said to be congruent.
Hence, The given triangles are congruent by SAS rule.
For more reference on congruent triangles, click;
https://brainly.com/question/12413243
#SPJ2
Find (g/f)(x) for the given functions: f(x) = 5/x and g(x) = 3 + x/5
Answers
Step-by-step explanation:
just substitute the value of g(X) and f(X)
The equation of the graphed line is 2x – y = –6. A coordinate plane with a line passing through (negative 3, 0) and (0, 6). What is the x-intercept of the graph? –3 –2 2 6
Answers
Answer:
-3
Step-by-step explanation:
-3 is the answer
Answer:
-3
Step-by-step explanation:
Tim and Jim are working on a school project together. If he had to work by himself, it would take
Tim 10 hours to complete the school project. If Jim worked alone, it would take him 15 hours.
Working together, how long will it take Tim and Jim to complete the school project together?
Answers
Answer: 6 hours
Step-by-step explanation:
Given, Tim and Jim are working on a school project together.
Tim takes 10 hours to complete the school project.
If Jim worked alone, it would take him 15 hours
Let t be the time they both take if they work together.
Then, [tex]\dfrac{1}{t}=\dfrac{1}{\text{Time taken by Tim}}+\dfrac{1}{\text{Time taken by jim}}[/tex]
[tex]\Rightarrow\ \dfrac{1}{t}=\dfrac{1}{10}+\dfrac{1}{15}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{3+2}{30}=\dfrac{5}{30}\\\\\Rightarrow\dfrac{1}{t}=\dfrac{1}{6}\\\\\Rightarrow t=6[/tex]
So, it will take 6 hours to complete the school project together .
graph the function f(x)=3/2(x-4)^2+3
Answers
Answer:
its 23
Step-by-step explanation:
Find the surface area of the triangular prism using its net (below).
Answers
Answer:
It is 96 square units
Step-by-step explanation:
Two friends are playing tic-tac-toe. If Amy wins 3/8 of the time, Lily wins 3/10 of the time, and they tie the rest of the time, then what fraction of the time do they tie?
Answers
Answer:
13/40
Step-by-step explanation:
The period they have played can be divided into 3 parts:
● The time Amy wins
● The time Lily wins
● The time they tie
So the sum of them is the total time of playing.
Let A be the time Amy wins, L the tile Lily wins and T the time they tie .
●●●●●●●●●●●●●●●●●●●●●●●
Since we have expressed the times using fractions then the total period of playing is 1 wich is 100%.
So:
A + P + T = 1
3/8 + 3/10 + T = 1
Multiply 8 by 10 and 10 by 8 so that you get a common denominator.
Cross multiply the numerators and the denominators.
(3*10+3*8)/80 + T = 1
(30 + 24)/80 + T =1
54/80 + T = 1
(27*2)/(40*2) + T = 1
Simplify by 2
27/40 + T = 1
T = 1 - 27/40
Multiply one by 40 to get a common denominator
T = (40-27)/40
T = 13/40
So they have tied 13/40 of the time
Need help with this math problem
Answers
Answer:
4
Step-by-step explanation:
f(x) = 4 ^ ( x-2)
Let x=3
f(3) = 4 ^ ( 3-2)
= 4 ^ 1
= 4
Answer:
4
Step-by-step explanation:
4^(x - 2)
Plug x as 3.
4^(3 - 2)
Subtract.
4^(1)
4^1 = 4
Identify the CONCLUSION of a hypothesis test of the following claim and sample data: Claim: "The average annual household income in Warren County is $47,500." A random sample of 86 households from this county is obtained, and they have an average annual income of $48,061 with a standard deviation of $2,351. Test the claim at the 0.02 significance level.
Answers
Complete Question
The options for the above question is
a There is not sufficient evidence to warrant rejection of the claim.
b There is sufficient evidence to warrant rejection of the claim.
c There is sufficient evidence to support the claim.
d There is not sufficient evidence to support the claim.
Answer:
Option A is correct
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu =[/tex]$47,500
The sample size is [tex]n = 86[/tex]
The sample mean is [tex]\= x =[/tex]$48,061
The standard deviation is [tex]\sigma =[/tex]$2,351
The level of significance is [tex]\alpha = 0.02[/tex]
The null hypothesis is
[tex]H_o : \mu =[/tex]$47,500
The alternative hypothesis is
[tex]H_a : \mu \ne[/tex] $47,500
The critical value of [tex]\alpha[/tex] from the t-Distribution table is [tex]Z_{\frac{\alpha }{2} } = 2.326[/tex]
Now the test statistics is mathematically evaluated as
[tex]t = \frac{\= x - \mu }{ \frac{\sigma }{\sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{48061 - 47500 }{\frac{2351}{\sqrt{86} } }[/tex]
[tex]t = 2.21[/tex]
Now from the values obtained we can see that
[tex]Z_{\frac{\alpha }{2} } > t[/tex]
hence we fail to reject the null hypothesis
Hence there is not sufficient evidence to warrant rejection of the claim
Answer it pls option c
Answers
Answer:
[tex]x = \frac{1}{4}[/tex]
Step-by-step explanation:
[tex]\frac{x}{2} +\frac{3}{4} =\frac{7}{8}[/tex]
→ Find the LCM of the denominators (2,4 and 8)
LCM = 8
→ Multiply the whole equation by 8 to get rid of the fractions
4x + 6 = 7
→ Minus 6 from both sides to isolate 4x
4x = 1
→ Divide both sides by 4 to isolate x
[tex]x = \frac{1}{4}[/tex]
Answer:
[tex]x = \frac{1}{4} [/tex]Step-by-step explanation:
[tex] \frac{x}{2} + \frac{3}{4} = \frac{7}{8} [/tex]
Multiply both sides of the equation by 8
[tex] \frac{x}{2} \times 8 + \frac{3}{4} \times 8 = \frac{7}{8} [/tex]
[tex]4x + 6 = 7[/tex]
Move constant to R.H.S and change its sign
[tex]4x = 7 - 6[/tex]
Subtract the numbers
[tex]4x = 1[/tex]
Divide both sides of the equation by 4
[tex] \frac{4x}{4} = \frac{1}{4} [/tex]
Calculate
[tex]x = \frac{1}{4} [/tex]
hope this helps..
Best regards!!
What is the measure of x?
Answers
Answer:
9 in.
Step-by-step explanation:
Given that the 4 in and 10 in. lines are parallel, the two triangles are similar.
As such, the ratio of the sides would give the same results.
Hence,
4/6 = 10/(6 + x)
cross multiplying
4(6 + x) = 60
Dividing both sides by 4
6 + x = 15
collecting like terms
x = 15 - 6
= 9