The value of a if HL is perpendicular to HJ is 20
How to determine the value
From the information given, we have that;
HL = angle 2 = a + 15HJ = angle 3 = HJIt is important to note that perpendicular lines always intersect each other and the angle between perpendicular lines is equivalent to 90 degrees.
Then, we have that;
Angle 2 + angle 3 = 90 degrees
Substitute the values
a + 15 + a + 35 = 90
collect like terms
2a + 50 = 90
2a = 90 - 50
subtract like terms
2a = 40
Make 'a' the subject
Divide both sides by 2
2a/2 = 40/2
a = 20
Thus, the value of a if HL is perpendicular to HJ is 20
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Helps solve Application
The percentage of 0 - 17 in 2015 is 23.97% and the percentage is decreasing by 0.048% in 2015
The percentage of 0 - 17 in 2015The equation of the function is given as
P(x) = 26x^-0.03
In 2015, x = 15
Substitute x = 15 in the equation P(x) = 26x^-0.03
P(15) = 26 * 15^-0.03
Evaluate the expression
P(15) = 23.97
Hence, the percentage of 0 - 17 in 2015 is 23.97%
How fast is the percentage decreasing in 2015The equation of the function is given as
P(x) = 26x^-0.03
Differentiate the function
P'(x) = -0.03 * 26x^-1.03
In 2015, x = 15
Substitute x = 15 in the equation
P'(15) = -0.03 * 26 * 15^-1.03
Evaluate
P'(15) = -0.048
Hence, the percentage is decreasing by 0.048% in 2015
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Can someone please help me I will mark u brilliant
Answer:
M would be at (0,-2)
Step-by-step explanation:
The question asks you to rotate the image 180 degrees clockwise. Clockwise means towards the right, such as how a clock moves. Each axis is 90 degrees, so by moving it twice would land at (0,-2).
A horizontal line (such as the x-axis) is 180 degrees, so by mirroring the point, you would see the point is at (0,-2).
Mate m.1 is so hard help me pls someone
Determine the end behavior of each function.
(a)
p(x) = a(x + b)5(x − c)3
, where a, b, and c are constants and
a < 0
.
p(x) → as x → −∞
p(x) → as x → ∞
(b)
f(x) =
9x2 − 11x + 2
8x2 − 6
f(x) → as x → −∞
f(x) → as x → ∞
(c)
g(x) = 9 + e−6x
g(x) → as x → −∞
g(x) → as x → ∞
Step-by-step explanation:
(a)
a, b, c are constants and play no role with their value when it goes relative to enormous numbers and to infinity.
but the sign is important.
a < 0, so, it will stay < 0 for all eternity/infinity.
(x + b)⁵ for x going to infinity, this goes to infinity.
for x going to -infinity, this also goes to -infinity (the exponent 5 is odd, so a negative value put to an odd power will create a negative result value).
(x - c)³ for x going to infinity, this goes to infinity.
for x going to -infinity, this also goes to -infinity (for the same reasons - 3 is an odd number).
x going to -infinity,
p(x) = -×-infinity×-infinity = -infinity
x going to infinity,
p(x) = -×infinity×infinity = -infinity
(b)
the x² terms drown out all other terms with lower x exponent (so, incl. -11x or any constants).
what remains for very, very large x is
9x²/8x² = 9/8 = 1.125
since we have x² terms, it does not matter, if x is positive or negative, the result is always positive.
so, x going to infinity or to -infinity, p(x) is the same again :
p(x) = 9/8 = 1.125
(c)
finally, we have a different result for x going to -infinity or to infinity.
x going to -infinity :
the exponent of e is then -6×-infinity = infinity. and e to the power of infinity is infinity.
p(x) = 9 + infinity = infinity
x going to infinity :
the exponent of e is then -6×infinity = -infinity. and e to the power of -infinity is 1/e to the power of infinity.
and that is 1/infinity. the limit for that is 0.
p(x) = 9 + 0 = 9
There are 50 minutes left before the event begins. You have 20 balloons to inflate before the event. How much time can you spend inflating each one equally?
Answer: 24 seconds
Step-by-step explanation:
20/50=0.4
0.4*60=24
6.48 x 10 5
-------------------------
(2.4 x 10 4) (1.8 x 10 -2)
Answer:
1.5×10³
Step-by-step explanation:
You want to know the value of the expression given with numbers in scientific notation.
EvaluationThe usual rules of arithmetic and exponents apply. Your calculator or spreadsheet can use and display the numbers in scientific notation for you.
[tex]\dfrac{6.48\times10^5}{(2.4\times10^4)(1.8\times10^{-2})}=\dfrac{6.48}{2.4\times1.8}\times10^{5-4-(-2)}=\boxed{1.5\times10^3}[/tex]
3 1/3 divided by 3/8
Enter your answer, as a mixed number in simplest form,in the boxes
What geométric symbol would be represented by a baseball bat
Answer: i think the overall shape of a baseball bat would be more rectangular
Step-by-step explanation:
reason for thinking so: because a baseball bat depending on size, would normally fit into a rectangular box
Challenge: A scuba diver has 30 cubic feet of air in his tank and dives under the water at
3:15pm. When he resurfaced at 3:30pm, he had 12 cubic feet of air left. How many cubic
feet of air per minute did he use?
The cubic feet of air the scuba diver used per minute is 1.2 cubic feet of air per minute
Unit rateQuantity of air in his tank = 30 cubic feetTime he dives in = 3:15pmTime he resurfaced = 3:30pmQuantity of air remaining in the tank = 12 cubic feetCubic feet of air used per minute = Difference in quantity of air in his tank / difference in time
= (30 - 12) / (3:30pm - 3:15pm)
= 18 / 15
= 1.2 cubic feet of air per minute
Therefore, the cubic feet of air the scuba diver used per minute is 1.2 cubic feet of air per minute
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x[tex]x^{2}+ 10x =11[/tex]
Answer:
For this problem, x has multiple values, so we will solve for both.
Step-by-step explanation:
[tex]x^2+10x-11=11-11\\x^2+10x-11=0\\[/tex]
Quadratic rule
[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]\mathrm{For\:} a=1,\:b=10,\:c=-11[/tex]
[tex]x_{1,\:2}=\frac{-10\pm \sqrt{10^2-4\cdot \:1\cdot \left(-11\right)}}{2\cdot \:1}[/tex]
Dealing with radicals
[tex]\sqrt{10^2-4\cdot \:1\cdot \left(-11\right)}\\=\sqrt{10^2+4\cdot \:1\cdot \:11}\\=\sqrt{10^2+44}\\=\sqrt{100+44}\\=\sqrt{144}\\=\sqrt{12^2}\\=12\\[/tex]
Multi-solution expression
[tex]x_1=\frac{-10+12}{2\cdot \:1},\:x_2=\frac{-10-12}{2\cdot \:1}[/tex]
Solve for x₁
[tex]\frac{-10+12}{2\cdot \:1}\\=\frac{2}{2\cdot \:1}\\=\frac{2}{2}\\=1[/tex]
Solve for x₂
[tex]\frac{-10-12}{2\cdot \:1}\\=\frac{-22}{2\cdot \:1}\\=\frac{-22}{2}\\= -\frac{22}{2}\\= -11[/tex]
Thus, x has 2 values for 2 different numbers:
x₁ = 1
x₂ = -11
➲ Hope this helps!
To make five cups of lemonade you mix three cups of water with two cups of lemon
juice. If there are sixteen cups in a gallon, how many cups of lemon juice are needed to
make ten gallons of lemonade?
A: 16
B: 32
C: 40
D: 48
E: 64
(I know the answer is E but I don't know how to get it)
Use the multiplier method to decrease £56 by 14%
You must show your working.
- 7.84 is actual difference of percentage by multiplier method to decrease.
What percentage means?
Percentage, which is a relative figure used to denote hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.56 - Percentage decrease =
56 - (14% × 56) =
56 - 14% × 56 =
(1 - 14%) × 56 =
(100% - 14%) × 56 =
86% × 56 =
86 ÷ 100 × 56 =
86 × 56 ÷ 100 =
4,816 ÷ 100 =
48.16
56 decreased by 14% = 48.16
Absolute change (actual difference):
48.16 - 56 = - 7.84
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Of the following fractions which one is the largest 9/19 , 5/11 ,7/15
Answer: 9/19
Step-by-step explanation:
9/19=0.4737
5/11=0.4545
7/15=0.4666
9/19 has the largest decimal making it largest.
PLEASE PLEASE HELP!!!
Answer:
Step 1: 1605 - 75 = 1530
Step 2: 1530 / 255 = 6
Step-by-step explanation:
ayudaaaa c x 4=32 porfaaa :vvv
Answer:C=8
Step-by-step explanation:
32 divided by 4 = 8
The sum of first five prime numbers is
An architect charges $1800 for a first draft of a three-bedroom house. If the work takes longer than 8
hours, the architect charges $105 for each additional hour. What would be the total cost for a first draft
that took 14 hours to complete?
The total cost for a first draft that took 14 hours to complete is $2430.
How to illustrate the expression?It should be noted that when the work takes longer than 8 hours, the architect charges $105 for each additional hour. For 14 hours, the additional hours will be:
= 14 - 8
= 6 hours
Therefore, the total cost will be:
= 1800 + (105 × 6)
= 1800 + 630
= 2430
Therefore, the total cost for a first draft that took 14 hours to complete is $2430.
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Home Depot entered fiscal 2017 with a total capitalization of $21,904 million. In 2017, debt investors received interest income of $877 million. Net income to shareholders was $8,654 million. (Assume a tax rate of 21%.)
Calculate the economic value added assuming its cost of capital is 10%. (Do not round intermediate calculations. Enter your answer in millions rounded to 2 decimal places.)
The economic value added (EVA) for Home Depot in the fiscal year, 2017, is $6,463.60 million.
What is the economic value added?Economic value added (EVA) measures a company's financial performance or economic profit.
EVA is based on the residual wealth of the company for the fiscal year. It measures the value a company generates from its invested funds at the cost of capital.
EVA is calculated by deducting the cost of capital from the operating profit after tax (NOPAT).
Data and Calculations:2017 total capitalization = $21,904 million
2017 interest paid to debt investors = $877 million
Net income to shareholders = $8,654 million
Corporate tax rate = 21%
Profit before taxes = $10,954 million ($8,654/ 1 - 0.21)
Cost of capital = 10%
= $2,190.4 million ($21,904 x 10%)
EVA = NOPAT - (Invested Capital * WACC)
= $8,654 million - $2,190.4 million
= $6,463.60 million.
Thus, the economic value added (EVA) for Home Depot in the fiscal year, 2017, is $6,463.60 million.
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Write a rule for the relation shown in the table.
X: 1, 2, 3, 4
Y: 10, 12, 14, 16
Is 7 hundreds + 4 thousands + 27 ones greater than, less than or equal to 6 thousands + 4 hundreds? *
Answer:
6 thousands + 4 hundreds
4727>6400
Step-by-step explanation:
4727<6400
At end of the first half of a football game, Nathan had carried the ball for 50.5 yards. By the end of the game, he carried the ball for a total of 75 yards. Find the percent of increase in the number of yards he carried. Round to the nearest whole tenth if necessary
The percent increase in the number of yards is 32.7%
How to calculate the percent increase ?At the end of the football game, Nathan carried the ball for 50.5 yards
At the end of the game, the ball was carried for a total of 75 yards
The percent increase in the number of yards can be calculated dividing the percentage change by the original value and multiplying by 100
= 75 - 50.5/75 × 100
= 24.5/75 × 100
= 0.3266 × 100
= 32.66
= 32.7%
Hence the percent increase in the number of yards is 32.7%
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A contract was made to be completed in 40 days and 24 men were put to work. After 28 days, 11 more men were engaged and the work was completed just in time. if not extra men engaged, how many days would the work have taken.
If no extra men were engaged then the work would have been completed in 45.5 days.
What is work?In physics, work is a measure of energy transfer that occurs when an object is moved over a distance by an external force, at least a portion of which is applied in the direction of displacement.So,
= (24 × 28) + (24 + 11) × 12= 672 + 420= 1092The time required by 24 men to complete their work is:
= 1092/24= 45.5Therefore, if no extra men were engaged then the work would have been completed in 45.5 days.
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4/z >= 3; z = 2
Please solve
The inequality expression 4/z >= 3 is false, when z = 2 because 2 is not greater than or equal to 3
How to evaluate the expression?The inequality expression is given as
4/z >= 3
The value of z is given as
z = 2
Substitute 2 for z in the inequality expression given as
4/z >= 3
So, we have:
4/2 >= 3
Evaluate the quotient
2 >= 3
The above inequality expression is false.
This is so because 2 is not greater than or equal to 3
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A bee flies at 12 feet per second directly to a flowerbed from its hive. The bee stays at the flowerbed for 17 minutes, and then flies directly back to the hive at feet per second. It is away from the hive for a total of 19 minutes.
a. What equation can you use to find the distance of the flowerbed from the hive?
b. How far is the flowerbed from the hive?
Answer: (a) The equation is so called "time equation"
D/12 + 16*60 + D/8 = 19*60 seconds
(b) To determine the distance D, solve the equation
D/12 + D/8 = 19*60 - 16*60 = 3*60
multiply both sides by 24
2D + 3D = 3*60*24
5D =4320
D =4320/5 = 864 ft
Step-by-step explanation:
A friend comes to visit and mentions the temperature in their hometown is currently 25 degrees
Celsius. What is this in Fahrenheit? (Write your answer as a whole number.)
Answer:
77
Step-by-step explanation:
If w = 18, what is the value of 3w − 11?
A: 307
B: 65
C:43
D: 10
Answer: 43 ==> C
Step-by-step explanation:
3w − 11=
3(18)-11=
54-11=43 ==> C
Answer:
c, 43
Step-by-step explanation:
3 times 18, minus 11
36x+9 equals what
big blak vjndjgd
We can conclude that the equation 36x + 9 equals -1/4.
What exactly is an equation?An equation, in its most basic form, is a mathematical statement demonstrating that two mathematical expressions are equal.3x + 5 = 14, for example, is an equation in which the expressions 3x + 5 and 14 are separated by a 'equal' sign.So,
36x + 936x + 9 = 036x = -9x = -9/36x = -1/4Therefore, we can conclude that the equation 36x + 9 equals -1/4.
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Round 782,317.772 to the nearest whole number.
Nearest whole number will be 782318.
Nearest ones whole number is the first digit before the decimal point of a number.
For example nearest ones of 9.6 is equal to 10.
If the tenth digit (first number before decimal point) of the number is greater than or equal to 5 we round up and add 1 to ones of number, If the tenth digit of the number is less than 5 we remove the decimal part. Example:
124.6
The first number of right of decimal point is 6
6 is greater than 5, so we add 1.
Result = 125
Now given number is 782317.772
since the first digit after decimal is 7 which is greater than 5 thus the nearest whole number will be 782318.
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Hey beinggreat78, the ones with a large amount of points are for u and they also mention your name so its easier to spot them (not that i dont want u to answer all the questions)
Answer:
C.
Step-by-step explanation:
[tex]3 \div 10 = 0.3 < 0.4[/tex]
Answer:
C
Step-by-step explanation:
All work and the answer is provided in the attached screenshot! :)
Write two expressions
that represent the volume of the cube, one with
exponents and one without.
The two expressions for the volume of a cube with a side length of S are:
V = S^3
V = S*S*S
How to express the volume of the cube?A cube is a rectangular prism where the 3 dimensions have the same measure, which we will call the side-length of the cube.
So, if S is the sidelength of the cube, the volume will be given by the product between the product between the dimensions of the cube, and the 3 dimensions measure the same thing, which is S, then:
V = S*S*S
That is the expression without exponents, and the expression with an exponent is really trivial, we have S multiplied by itself 3 times, so we get:
V = S^3
These are the two expressions for the volume.
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