Answers
Answer:
22.5
Step-by-step explanation:
∠EAB=2x (alternate interior angles)
∠AEB=180°-4x (linear pair)
2x+180-4x=6x (exterior angle theorem)180-2x=6x180=8xx=22.5Related Questions
Holly earns 4% simple interest over 5 years. Which equation represents the amount in hollys account in terms of the principle?
Answers
A = p +0.2p
We don't know the value of P, so it stays unknown.
The r is the interest rate as a decimal. we know that r = 0.04 because we're told the interest rate is 4%. Note that 4% = 4/100 = 0.04
The time in years is t = 5
So this means...
A = P + P*r*t
A = P + P*0.04*t ... replace r with 0.04
A = P + P*0.04*5 ... replace t with 5
A = P + P*0.2 ... multiply
A = P + 0.2*P ... swap term
A = p +0.2p
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what is the HCF of 225 495 and 810
Answers
Step-by-step explanation:
Factor of 225
= 3 × 3 × 5 × 5
Factor of 495
= 3 × 3 × 5 × 11
Factor of 810
= 3 × 3 × 3 × 3 × 2 × 5
Now ,
HCF = Common Factor
= 3 × 3 × 5
= 45
[tex]...[/tex]
☘️☘️☘️...
The sum of one and six times a number is -113. What is the number?
Answers
Answer: -19
Step-by-step explanation:
n=number
6n+1=-113
6n=-114
n=-19
Which list shows the numbers in increasing order?
A) -0.5, 1.5, -2, -0.75, √7
C) -2, -0.75, -0.5, 1.5, √7
B) -0.5, -2, -0.75, 1.5, √7
D) √7, 1.5, -0.5, -0.75, -2
Answers
Answer:
Step-by-step explanation:
its ''C''
Simplify the following by combining all constants and
combining the a and b terms using exponential notation.
-3aaaaaa5bbbbb =
Answers
Answer:
-15a⁶b⁵
Step-by-step explanation:
-3aaaaaa5bbbbb
= -3a⁶5b⁵
= -15a⁶b⁵
I hope this helps!
What is the range of the function f(x) = 4x – 5 over the interval of 1 < x ≤ 5? Give your answer in interval notation.
Answers
Answer:
Hello,
Step-by-step explanation:
[tex]1 < x\leq 5 \ \\\Longrightarrow\ 4 < 4x \leq 20 \ \\\Longrightarrow\ -1 < 4x-5 \leq 15 \\\Longrightarrow\ -1 < f(x) \leq 15 \\\\range=]-1; 15][/tex]
The range of the function f(x) = 4x - 5 will range from -1 to 15.
What are the function and range?The expression that established the relationship between the dependent variable and independent variable is referred to as a function. In the function as the value of the independent variable varies the value of the dependent variable also varies.
A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
Given that the function f(x) = 4x – 5 and the interval is 1 < x ≤ 5. The range will be calculated as,
1 < x ≤ 5
4 < 4x ≤ 20
4-5<4x - 5< 20-5
-1 < 4x - 5 < 15
Therefore, the range of the function f(x) = 4x - 5 will range from -1 to 15.
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What is the expanded form of nine billion, eight hundred ninety-two million, eight hundred forty-six thousand, four hundred thirty-seven?
Answers
Answer:
9, 892, 846, 437
Step-by-step explanation:
9 billion = 9,000,000,000
8 hundred million = 800, 000, 000
9 ten million = 90, 000, 000
2 million = 2, 000, 000
8 hundred thousand = 800, 000
4 ten thousand = 40, 000
6 thousand = 6000
4 hundred = 400
3 ten = 30
7 one = 7
Add them all together = 9, 892, 846, 437
Hope this helped! ^^
Convert 50°F to degrees Celsius.
If necessary, round your answer to the nearest tenth of a degree.
Here are the formulas.
C=5/9(F-32)
F=9/5C+32
Answers
Answer:
10°C
Step-by-step explanation:
F = 50
C = 5/9 * (F - 32) = 5/9 * (50 - 32) = 5/9 * 18 = 5 * 2 = 10
What is the y intercept of the line
Answers
Answer:
2 is the y-int.
Step-by-step explanation:
Becuase the line runs through the y-axis at 2.
Find an equation of variation in which y varies jointly as x and z, and y= 48 when x = 8 and z=6
Answers
Answer:
y = xzStep-by-step explanation:
Joint variation equation:
y = kxz, where k- coefficient of variationGiveny = 48,x = 8,z = 6Find the value of k by plugging in the given values:
48 = 8*6k48 = 48kk = 1The equation is:
y = xzYou have two strands of decorative lights. Strand A changes color every 8 seconds and Strand B changes color every 12 seconds. Both strands just changed color. After how many seconds will the strands change color at the same time again?
Answers
Answer:
24 seconds
Step-by-step explanation:
Strand A: 3 × 8 secons =24 seconds
Strand B: 2 × 12 seconds= 24 seconds
3/4 + 7/8 + 3/4 + 1/2 + 7/8
Answers
Answer:
=
15/4
(Decimal: 3.75)
Step-by-step explanation:
The length of a rectangle is 4yd longer than its width.
If the perimeter of the rectangle is 68yd, find its length and width.
Answers
Pentagon Question
The sides add to 63, so:
[tex]11+3x+11+x+2+2x+3=63 \\ \\ 6x+27=63 \\ \\ 6x=36 \\ \\ x=6 \\ \\ \implies AB=2(6)+3=15[/tex]
Rectangle Question
If the width is w, then the length is w+4.
This means that 2(w+w+4)=68.
[tex] 2(2w+4)=68 \\ \\ 2w+4=34 \\ \\ 2w=30 \\ \\ w=15[/tex]
So, the length is 19 and the width is 15.
Using the associative property, rewrite the following expression. You do NOT need to simplify it. -3y - 6y + 10y
Answers
Another form of the given expression using associative property is 10y + (-3y -6y)
Associative propertyAssociative property shows that if two or more property are added or multiplied, the result remains the same. For instance;
a +(b + c) = (a+b) + c
Given the expression below;
-3y - 6y + 10y
Group to have
(-3y - 6y) + 10y
10y - 3y - 6y
This can also be grouped as;
(10y - 3y) - 6y = 10y + (-3y -6y)
Hence another form of the given expression using associative property is 10y + (-3y -6y)
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How do I solve this absolute value in quality problem
|2t + 2/3|≤4
Answers
Answer: -7/3≤t≤5/3
Step-by-step explanation:
|2t + 2/3|≤4
2t + 2/3≤4
(2t + 2/3≤4)*3
6t+2≤12
6t≤10
t≤10/6
t≤5/3
2t + 2/3>=-4
(2t + 2/3>=-4)*3
6t + 2>=-12
6t>=-14
t>=-14/6
t>=-7/3
-7/3≤t≤5/3
[tex]-6y + 4 = | 4y + 12 |[/tex]
Answers
Answer: its not equal.
Step-by-step explanation:
-6y + 4 = 2 (-3y + 2)
|4y + 12| = 4 (y + 3)
which expression represents an irrational number
Answers
The lateral surface area of cone A is exactly 1/2 the lateral surface area of
cylinder B.
OA. True
OB. False
Answers
Answer:
B. False
Step-by-step explanation:
You want to compare the lateral surface areas of a cone and cylinder, where the slant height of the cone is twice the height of the cylinder. Your proposition is that the cone's lateral area is half that of the cylinder.
Cone lateral areaEffectively, the lateral area of a cone is the area of a triangle whose base is the circumference of the cone, and whose height is the cone's slant height. The formula for the lateral area of a cone of radius r and slant-height s is ...
A = πrs
For the given dimensions (s=2h), the lateral area is ...
A = πr(2h) = 2πrh
Cylinder lateral areaThe lateral area of a cylinder is the area of a rectangle whose base is the circumference of the cylinder, and whose height is the cylinder's height. The formula for the lateral area of a cylinder of radius r and height h is ...
A = 2πrh
ComparisonThe lateral areas of the given figures are both 2πrh, so one is not half the other.
The proposition is False.
Evaluate the variable expression when a = 2 and c = −3. 2a − (c + a)2
Answers
the expression of the variable for a = 2 and c = 3. 2a − (c + a)2
2a+b^2 2a +b2
2(-3) +(-2)^2 2(-3) + (-2)
-6 +4 -6 -4
-2 -10
An expression is a set of terms combined using the operations +, -, x or ÷, for example 4 x − 3 or 5 x 2 − 3 x y + 17 . An equation is a statement with an equals sign, which states that two expressions are equal in value, for example 4 b − 2 = 6 .
Either the options are incorrect, or the problem is poorly written.
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The posts of a hockey goal are 6 ft. apart. A player attempts to score by shooting the puck from a
point that is 19 ft from one post and 24 ft from the other post. Within what angle & must the shot be
made? Express your answer to the nearest degree.
Answers
The angle at which the shot was made should be 17.53° degrees.
Let C denote the point where the player attempts to put in a goal.
Let A and B denote the two goalposts.
We are given the posts of a hockey goal are 6 ft apart.
The distance between the player and one goalpost is 19 ft.
The distance between the player and the other goalpost is 24 ft.
Then, we have AC = 19 ft, BC = 24 ft, and AB= 6 ft.
Refer to the diagram.
Let θ be the angle made when trying to shoot the goal towards goalpost A.
Then we have tan(θ) = 6/19
⇒ θ = 17.53° degrees.
Therefore, the angle at which the shot was made should be 17.53° degrees.
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What is the slope of the line represented by the equation y =4/5x-3?
Answers
Answer:
4/5 is the slope of the line
Allison ran 5 miles in 40 minutes before running an additional 3 miles in 27 minutes is this proportional are not pls help ASAP
Answers
Answer:
no it is not proportional...
Step-by-step explanation:
5 miles/40 minutes is 1/8
3 miles/27 minutes is 1/9...
Find the mystery number. It is a common multiple of 2,5 and 7. It has 3 digits. The sum of the digits is 10. The number is less than 500
Answers
The number is 280
In mathematics, Least Common Multiple is referred to by its entire name, whereas Highest Common Factor is its complete name. The L.C.M. defines the least number that is exactly divisible by two or more numbers, whereas the H.C.F. describes the biggest factor existing between any given pair of two or more numbers. LCM is also known as the Least Common Multiple (LCM), and HCF is also known as the Greatest Common Factor (GCF).
Two key techniques—the division method and the prime factorization approach—can be used to determine H.C.F. and L.C.M.
So we need to find the LCM of 2,5 and 7. Furthermore, we need to find multiply the LCM with a number which can make its sum of digits equal to 10.
LCM of 2,5 and 7 is 70
70 x 4 = 280
Sum of digits of 280 is 10, which is also less than 500
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One-seventh of a number, increased by twelve?
Answers
Answer:
x/7+12
Step-by-step explanation:
One seventh refers to 1/7.
Since we do not know what "a number" is it, it is written as "x."
Whenever you see the word "increased" think addition.
So in this case,
x / 7 + 12
Chef Smith will be serving a breakfast banquet for 300 guests. Each guest will be served a two-egg
omelet. How many dozen eggs should Chef Smith order?
Answers
Answer: 50
Step-by-step explanation:
Answer:
50
Step-by-step explanation:
300(2) bcuz 300 guests and each person gets 2
600(12) bcuz 300(2) is 600 and a dozen is 12
=50
A television sells for $550. Instead of paying the total amount at the time of the purchase, the same television can be
bought by paying $200 down and $50 a month for 14 months. How much is saved by paying the total amount at the
time of the purchase?
Answers
Kelsey made cupcakes to sell as a fundraiser for her trip to Washington DC.
She purchased one cupcake pan for $12. She calculated that the ingredients
cost her $0.25 per cupcake. She plans to sell the cupcakes for $0.75 each.
a. Write an equation that could be used to find the number of cupcakes
(x) she will need to sell to break even.
b. Solve the equation from part a. Explain how you know
is correct.
c. If she sold 184 cupcakes, what was her profit?
your answer
Answers
Answer:
a. 12= 0.50x
b. x=24 because if 0.5 times x is 12 then 12 *2 is x
c. 80$
Step-by-step explanation:
Its above.
Suppose you invest in an annuity that pays 5% annual interest, compounded quarterly. If you contribute $400 every quarter for 20 years, how much interest would you earn during the 20 years? Enter your answer, rounded to the nearest cent, without the dollar sign or comma ($23,678.1235 should be entered as 23678.12.)
Answers
If you contribute $400 every quarter for 20 years, the amount of interest you would earn during the 20 years is $22,447.52
What future value formula is applicable in this case?
The applicable future value formula is that of an ordinary annuity which determines the future worth of $400 quarterly savings for 20 years bearing in mind that the quarterly interest rate is the annual interest rate divided by 4
FV=PMT*(1+r)^N-1/r
FV=worth of the annuity after 20 years=unknown
PMT=quarterly deposit=$400
r=quarterly interest rate=5%/4=1.25%
N=number of quarterly savings in 20 years=20*4=80
FV=$400*(1+0.0125)^80-1/0.0125
FV=$54,447.52
interest=$54,447.52-($400*80)
interest=$ 22,447.52
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My child is struggling with the answer.
Answers
Using the relation between velocity, distance and time, the distances are given as follows:
A. d = 13/3 miles.
B. d = 4.25 miles.
C. d = M x 5/60(first five minutes) + N x 15/60(last 15 minutes).
What is the relation between velocity, distance and time?Velocity is distance divided by time, that is:
v = d/t.
Hence the distance is:
d = vt.
In item a, considering the time in hours, we have that:
v = 13, t = 20/60 = 1/3.
Hence:
d = 13/3 miles.
In item b, we have different definitions, then:
d = 15 x 5/60(first five minutes) + 12 x 15/60(last 15 minutes).
d = 15/12 + 15/5
d = 4.25 miles.
For item c, we have that:
d = M x 5/60(first five minutes) + N x 15/60(last 15 minutes).
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(A) Find the slope of the line that passes through the given points_
(B) Find the point-slope form of the equation of the line.
(C) Find the slope-intercept form of the equation of the line.
(D) Find the standard form of the equation of the line.
(4,2) and (11,8)
Answers
a) The slope of the line is 6 / 7.
b) The point-slope form of the equation of the line is y - 2 = (6 / 7) · (x - 4).
c) The slope-intercept form of the equation of the line is y = (6 / 7) · x - 17 / 7.
d) The point-slope form of the equation of the line is - 6 · x + 7 · y + 17 = 0.
How to find the equation of the line in three different forms
There are three different forms of the equation of the line:
Point-slope
y - y' = m · (x - x') (1)
Slope-intercept
y = m · x + k (2)
Standard
a · x + b · x + c = 0 (3)
Where:
m - Slopek - y-Intercepta) The slope that passes through the two given points is found by secant line formula:
m = [8 - 2] / [11 - 4]
m = 6 / 7
b) The point-slope form of the equation of the line is:
y - 2 = (6 / 7) · (x - 4)
c) The slope-intercept form of the equation of the line is:
y - 2 = (6 / 7) · x - 24 / 7
y = (6 / 7) · x - 17 / 7
d) The standard form of the equation of the line is:
7 · y = 6 · x - 17
- 6 · x + 7 · y + 17 = 0
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