Answer:
aef = fed = 51 degrees,
and the full angle aed = 102 degrees
Step-by-step explanation:
If ef bisects the angle aed, then the two angles it defines: aef and fed, must measure the same.
Therefore we can asume that aef = fed which numerically means:
4 x + 3 = 7 x - 33
so we solve for x:
33 + 3 = 7 x - 4 x
36 = 3 x
x = 36/3
x = 12 degrees
That means that the half angle aef measures:
aef = 4 x + 3 = 4 (12) + 3 = 48 + 3 = 51 degrees
Then we have that aef = fed = 51 degrees,
and the full angle aed = 51 + 51 = 102 degrees
8x - 27 - 10 - 6x = 15
2x - 27 - 10 = 15
2x - 17 = 15
+ 17 + 17
2x = 32
X = 16
Step-by-step explanation:
8x-37-6x=15
2x=15+37
2x=52divide both sides by 2
x=26
An auditorium has 50 rows of seats. The first row has 20 seats, the second row has 21 seats, the third row has 22 seats, and so on, each row having one more seat than the previous row. How many seats are there altogether?
Answer:
1050
Step-by-step explanation:
I'm pretty positive it would be 1050 by multiplying 50 and 20 and adding 50
The total number of seats in the auditorium are 2225.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that an auditorium has 50 rows of seats. The first row has 20 seats, the second row has 21 seats, the third row has 22 seats.
We can write the sequence as -
20, 21, 22, 23, 24, .......,
It is a arithmetic sequence. We can write the total number of seats in the auditorium as the sum of the terms of the sequence. We can write -
S{n} = (50/2)(2 x 20 + 49 x 1)
S{n} = 25(40 + 49)
S{n} = 25 x 89
S{n} = 2225
Therefore, the total number of seats in the auditorium are 2225.
To solve more questions on sequences, visit the link below -
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The width of a rectangle is 4 inches less than the length. The perimeter is 60 inches. Find the length and the
width
Answer:
Length=17
width=13
Step-by-step explanation:
W=width
L=length
Perimeter = 2w+2l since it's a rectangle
W=l-4 (given)
Plug into perimeter equation
Perimeter =(2l-8)+2l
=4l-8
60=4l-8
68=4l
17 =l
W=l-4=17-4=13
Last week Asanji ran 17 miles more than Scott. Asanji ran 22 miles. How many miles did Scott run?
Answer:
Scott ran 5 miles
Step-by-step explanation:
22-17=5
Reasonableness...
5+17=22
Answer: 39 <3 ^_^
Step-by-step explanation: Last week Asanji ran 17 miles more than Scott. Asanji ran 22 miles. How many miles did Scott run? 17+22=
What is the next term In the sequence? 1, 4, 9, 16, __
Answer:
25
Step-by-step explanation:
Everytime, you add a value number 2 greater than the previous.
1+3=4
4+5=9
9+7=16
16+9=25
━━━━━━━☆☆━━━━━━━
▹ Answer
25
▹ Step-by-Step Explanation
1 + 3 = 4
4 + 5 = 9
9 + 7 = 16
16 + 9 = 25
The pattern is increasing the value of which is added by two each time:
3 + 2 = 5
5 + 2 = 7
7 + 9 = 16
9 + 16 = 25
Hope this helps!
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━━━━━━━☆☆━━━━━━━
what is 2 times 4 equal
Answer:
8
Step-by-step explanation:
Step 1: Convert to math
2 times 4 = 2 x 4
Step 2: Multiply
2 x 4 = 8
This is the same as 2 x 2 x 2 or 2³
Answer:
2 x 4 = 8
Step-by-step explanation:
2(4)=8
2+2+2+2=8
Diego arranges the students in his math class from shortest to tallest and measures the height in inches of each student in the class. Use the shape of the distribution to compare the mean and median. Are the mean and median equal? If not, which is greater? Explain your reasoning.
Answer:
Explained below.
Step-by-step explanation:
A graph is formed using the height of students in Diego's math class.
It is provided that he arranges the students from shortest to tallest and measures the height in inches of each student in the class.
A distribution is known as to be skewed to the right, or positively skewed, when maximum of the data are collected on the left of the distribution and the graph has a longer tail towards the right.
For a positively skewed data: Mean > Median
A distribution is said to be skewed to the left, or negatively skewed, if maximum of the data are collected on the right of the distribution and the graph has a longer tail towards the left.
For a negatively skewed data: Mean < Median
A distribution is said to be symmetric, if maximum of the data are collected in the middle of the distribution and the graph has equal proportion of tails on both sides.
For a symmetric data: Mean = Median
Write the rule for the table, use x for the input.
Input Output
-1,0,1,2,3,4 1,9,17,25,33,41
Step-by-step explanation:
so you take the numbers and put them in order from least to greatest. so it would be negative -1, 0, 1, 1, 2, 3, 4, 9, 17, 25, 33, 41 .
It takes 15 minutes to preheat your oven to 325 degrees. For an oven preheated to 325 degrees, the recommended cooking time for a turkey is about 16 minutes per pound
(a) Use a formula to express the total time T, in minutes, needed to preheat the oven and then bake a turkey weighing p pounds.
(b) Use your formula from part (a) to find the approximate time required to prepare a turkey weighing 14 pounds.
(a) The formula for the total time T, in minutes, needed to preheat the oven and bake a turkey weighing p pounds is T = 15 + 16p.
(b) The approximate time required to prepare a turkey weighing 14 pounds is 239 minutes.
We have,
(a)
To express the total time T, in minutes, needed to preheat the oven and then bake a turkey weighing p pounds, we can use the formula:
T = 15 + 16p
The first term, 15, represents the time needed to preheat the oven to 325 degrees (in minutes).
The second term, 16p, represents the recommended cooking time per pound for a turkey weighing p pounds (in minutes).
(b)
Using the formula T = 15 + 16p, we can find the approximate time required to prepare a turkey weighing 14 pounds:
T = 15 + 16 * 14
T = 15 + 224
T = 239
Therefore, the approximate time required to prepare a turkey weighing 14 pounds is 239 minutes.
Thus,
(a) The formula for the total time T, in minutes, needed to preheat the oven and bake a turkey weighing p pounds is T = 15 + 16p.
(b) The approximate time required to prepare a turkey weighing 14 pounds is 239 minutes.
Learn more about equations here:
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The chi-square goodness-of-fit test can be used to test for:
Answer:
In the blue area, people live closely because of its 1.Indutrialised area 2. The land is costly. 3.urbanisation In lighter color areas its farther because 1.Village 2.Farming area 3.Less popular rural area
Step-by-step explanation:
In the blue area, people live closely because of its 1.Indutrialised area 2. The land is costly. 3.urbanisation In lighter color areas its farther because 1.Village 2.Farming area 3.Less popular rural area
61 points!!! The line is perpendicular to the x-axis and passes through (1,2) The equation of t he line is
Example of non-statistical question , statistical question
Answer: A non-statistical For example, the question, 'What is 2 plus 2?' is a non-statistical question. This question has only one correct answer that doesn't change
A statistical question For example, there will likely be variability in the data collected to answer the question, "How much do the animals at Fancy Farm weigh?"
hoped this helped
Matt has two very active dogs...
7x2x2x2 is the prime factorization for which of the following
А
72
B
56
С
44
D
28
Angle 1 and Angle 2 are supplementary. The measure of Angle 2 is 78
less than the measure of Angle 1. Find the measure of Angle 2
Answer: Angle 1 is 129 degrees. Angle 2 is 51 degrees.
Step-by-step explanation: 129+51=180 129-51=78
I NEED HELP PLEASE! The approach ramp used by a daredevil motorcyclist for flying over a pit of venomous snakes has a rise of 52 feet for every 80 feet in horizontal distance. Find the grade of the ramp. Round to the nearest whole percent.
Answer:
65%
Step-by-step explanation:
The formula for the grade of the ramp = Rise of the ramp/ horizontal distance of the ramp
Rise of the ramp = 52 feet
Horizontal distance = 80 feet
Grade of the ramp = 52 feet/80 feet
= 0.65
The grade of the ramp is 0.65
Rounding up to the nearest whole percent
Grade of the ramp = 0.65 × 100
= 65%
Therefore, the grade of the ramp to the nearest whole percent = 65%
which of the following is the correct conversion rate to multiply by in order to convert from meters per second to centimeters per second 100 seconds/1 m 100 m/ 1 cm 100 cm/1 second 100 cm/ 1 m
Answer:100cm/1m
Step-by-step explanation:
An education center offers a total of 400 math, physics and
chemistry courses. The ratio of the number of math to physics
to chemistry courses is 3:4:3.
The cost of a math class is $25 per class and the cost of a
physics class is $20 per class. If you took all 400 classes, it
would cost a total of $9,800. What is the price of each
chemistry class?
$
Answer:
$30
Step-by-step explanation:
The price of each chemistry class is $30.
f(x) = 2x g(x) = x + 5 h(X) = 3x - 7 What is the correct set up for h(f(x))?? *
A. 2(3x - 7)
B. 3(2x) - 7
C. (3x - 7) + 5
D. 3(x + 5) - 7
Answer:
bStep-by-step explanation:
2
15) John traveled 166.25 miles and used 9
gallons of gas. How many miles per gallon
does John's car get?
Answer:
18.472 miles
Step-by-step explanation:
[tex]166.25 \: miles = 9 \: gallons \\ x \: miles = 1 \: gallons[/tex]
Cross Multiply
[tex]9x = 166.25[/tex]
Divide both sides of the equation by 9
[tex] \frac{9x}{9} = \frac{166.25}{9} [/tex]
[tex]x = 18.472[/tex]
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{18.472 \: miles}}}}}[/tex]
Step-by-step explanation:
Distance travelled = 166.25 miles
gallons of gas used = 9 gallons
To find : 1 gallons of gas = ? miles
In unitary method, we have to obtain unit quantity. So, to find the distance travelled using 1 gallons of gas, 166.25 is divided by 9
[tex] \sf{ \frac{166.25}{9} }[/tex]
[tex] \dashrightarrow{ \sf{18.472 \: miles}}[/tex]
Hope I helped!
Best regards!
The price of an item has been reduced by $8.35. The new sale price is $21.36. What was the original price. answer fast!
Answer:
$29.71
Step-by-step explanation:
just add the reduced price to the amount you took away: 8.35+21.36=29.71
Answer:
$29.71
Step-by-step explanation:
$21.36 + $8.35 = $29.71
hope this helps pls give brainliest
9
Dusty found out that each grain of sand weighs 40000 or .000025 of a pound. He decides to write this
number in scientific notation.
2.5 x 10
What value should Dusty record in the box?
Record your answer and fill in the bubbles on your answer
document. Be sure to use the correct place value.
Answer:
[tex]n = -5[/tex]
Step-by-step explanation:
Given
[tex]Digit = 0.000025[/tex]
Required
Rewrite using scientific notation, then find n
[tex]Digit = 0.000025[/tex]
Express as fraction
[tex]Digit =\frac{25}{1000000}[/tex]
This can be splitted to
[tex]Digit = 25 * 10^{-6}[/tex]
The first number must be between 1 and 10; hence, 25 can be expressed as 2..5 * 10
[tex]Digit = 2.5 * 10* 10^{-6}[/tex]
Apply law of indices
[tex]Digit = 2.5 * 10^{1-6}[/tex]
[tex]Digit = 2.5 * 10^{-5}[/tex]
Comparing n, the given options
[tex]n = -5[/tex]
Find the volume of the parallelepiped with the given vertices:(1,2,1), (2,3,4), (3,4,5), (2,3,2), (3,3,3), (4,4,6), (4,4,4), (5,5,7)
Answer:
0
Step-by-step explanation:
three vectors are
[tex]u=(2,3,4)-(1,2,1)=(1,1,3)[/tex]
[tex]v=(3,4,5)-(1,2,1)=(2,2,4)[/tex]
[tex]w=(2,3,2)-(1,2,1)=(1,1,1)[/tex]
volume is given by [tex]V=u \cdot(v \times w)[/tex] [tex]v \times w=\left|\begin{array}{ccc}i & j & k \\ 2 & 2 & 4 \\ 1 & 1 & 1\end{array}\right|=(-2,2,0)[/tex]
so volume is [tex]V=(1,1,3) \cdot(-2,2,0)=0[/tex]
2
three vectors are [tex]u=(4,4,6)-(3,3,3)=(1,1,3)[/tex]
[tex]v=(4,4,4)-(3,3,3)=(1,1,1)[/tex]
[tex]w=(5,5,7)-(3,3,3)=(2,2,4)[/tex]
volume is given by [tex]V=u \cdot(v \times w)[/tex] [tex]v \times w=\left|\begin{array}{ccc}i & j & k \\ 1 & 1 & 1 \\ 2 & 2 & 4\end{array}\right|=(2,-2,0)[/tex]
so volume is [tex]V=(1,1,3) \cdot(-2,2,0)=0[/tex]
I can't figure it out
Answer:
Domain: x ≥ 7
Range: y ≥ -1
Step-by-step explanation:
Domain is the set of x-values that can be inputted into function f(x).
Range is the set of y-values that can be outputted from function f(x).
We know that we can't take a square root of a negative and get a real number. The closest we can get is the square root of zero, no less.
What x-value renders the square root 0? x = 7 does, and we can't go less than that or we will get imaginary numbers. Therefore, the domain is x ≥ 7.
To find the range, we simply solve the rest of the function when x = 7, as we cannot go any lower.
y = 0 - 1
y = -1
Therefore, our range has to be y ≥ -1 because that would be the lowest y-value outputted from the lowest x-value.
Hurry
Write 7.63 as a mixed number in simplest form.
[tex]7\frac{63}{100}[/tex]
Step-by-step explanation:
Hey there!
ANSWER: [tex]7\frac{63}{100}[/tex]EXPLANATION:7.63 as a mixed number form
If you want to write 7.63 as a mixed number form, you have to make 7 the whole number because it is in the ones and 63 is the fraction because it comes after the decimal point.
[tex]7.63=7\frac{63}{100} \text{(ANSWER)}[/tex]
Hope this helps!
[tex]\text{-TestedHyperr}[/tex]
What is 10 decreased by m
Answer:
m-10
Step-by-step explanation:
If it said M decreased by 10, it would be 10-m, but because it says 10 decreased by m, the answer is m-10
Ordering Rational Numbers
Answer:
0.07 < 7/50 < 0.5
Step-by-step explanation:
7/50=0.14
=>0.07<0.14<0.5
I received a letter from your competitor that mentions a savings of 15% over your prices. Can you match this offer? My current rate is $129.00 per month
Complete question :
I received a letter from your competitor that mentions a savings of 15% over your prices. Can you match this offer? My current rate is $129.00 per month." Representative: "We will match any competitive offer. Your adjusted rate will be __________ dollars per month."
Answer:
$109.65
Step-by-step explanation:
Given the following :
Current rate = $129.00
Savings on current rate = 15%
Therefore, the adjusted rate will be 15% off the currently charged rate.
15% of $129.00
(15/ 100) × $129.00
0.15 × $129.00 = $19.35
Adjusted rate = current rate - adjustment
Adjusted rate = $129.00 - $19.35
Adjusted rate = $109.65
Hence, complete response :
We will match any competitive offer. Your adjusted rate will be $109.65 dollars per month."
Vanessa runs a dog kennel. There are 45 dogs at the kennel today, and she needs to collect the correct size bowls for feeding time. 1/5 of the dogs need a small size bowl 20 of the dogs need a medium size bowl the rest need a large size bowl How many dogs need a large size bowl?
Answer:
20
Step-by-step explanation:
Answer:
16
Step-by-step explanation:
One fifth of 45 = 45/5=9
This means 9 dogs require small bowls.
If 9 require small, 20 require medium and the rest require large, then 45-9-20=16
16 dogs need large size bowl.
Hope this helped!
They will build another fence that is 48 feet long. The posts can be a minimum of 5 feet apart and a maximum of 9 feet apart. The posts should be equally separated. Design a fence that uses the fewest posts possible. How far apart should each post be placed?