Answer:
(f+g)(2) = 1Step-by-step explanation:
Given :
f(x) = x − 3
g(x) = x² − x
Note : (f+g)(x) = f(x) + g(x)
then
(f+g)(2) = f(2) + g(2)
= (2 - 3) + (2² - 2)
= -1 + 2
= 1
another method:
(f+g)(x) = f(x) + g(x) = x − 3 + x² − x = x² - 3
then
(f+g)(2) = 2² - 3 = 4 - 3 = 1
The price of a jacket was increased from $110 to $126.5. What was the percent increase in the price of the jacket?
Answer:
15%
Step-by-step explanation:
percent increase is actual increase divided by starting value16.5/110 = 0.1515%Percent increase in the original price of jacket = 15%
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Given,
Original price of jacket = $110
Increased price of jacket = $126.5
Increased amount = $126.5 - $110
= $16.5
Increased amount in percentage = ($16.5/$110) × 100
= 0.15 × 100
= 15%
Hence, 15% is increase in the original price of jacket.
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9. The longitude of a geographic location is measured in degrees east (E) or west (W) from the
prime meridian (0°) to the international date line (180°). Quito, Ecuador, on the west coast of
South America, has a longitude of 78.5º W. Singapore, on the Malay Peninsula in Asia, has a
longitude of 104° E. Both cities are very close to the equator. The diameter of Earth at the
equator is 7928 miles. What is the shortest distance from Quito to Singapore? Explain how you
found your answer.
Based on the longitudes of Quito and Singapore, the shortest distance between the two areas is 19,702.5 km .
How far is Quito from Singapore?Because both cities are close to the equator, you use the longitudinal difference method to find the shortest distance.
First find the difference in longitudes:
= Singapore - Quito
= 104 - (-78.5) because Quito is west
= 104 + 78.5
= 182.5°
Then subtract this from 360°:
= 360 - 182.5
= 177.5°
Every 1° longitude along the Equator is 111 km so the shortest distance is:
= 177.5 x 111
= 19,702.5 km
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What are the y-intercept and the slope of the line represented in the graph?
A. y-intercept = -4 and slope = -2
B. y-interecept = 4 and slope = -2
C. y-interecept = 2 and slope = 4
D. y-interecept = 4 and slope = -4
Henry deposits $750 into a college savings account that is compounded annually when is his parents received as a stimulus package . If Henry let’s the money sit in the account without adding or removing any and receives a 8.5% interest rate , How much more money will he have total after 5 years ?
Answer:
The answer should be $1127.74
Find the value of y that satisfies the given conditions. Then graph the line on a separate sheet of paper. The line containing (−4, 9) and (4, 3) is parallel to the line containing (−8, 1) and (4, y).
Answer:
so first do nothing and just fail health class
The value of y that satisfies given conditions is y = - 8.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
We also know that slope(m) = (y₂ -y₁)/(x₂ - x₁).
So, lines parallel to each other have the same slope hence to find the value of y we'll equate their slopes.
∴ (3 - 9)/(4 + 4) = (y - 1)/(4 + 8).
-6/8 = (y - 1)/12.
-3/4 = (y - 1)/12.
-36/4 = y - 1.
- 9 = y - 1.
y = - 8.
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write two equations that when graphed look like this *see image*. please help its due soon and i will give ya 75 points for answering, thanks, 5 stars, and brainlist.
The graph is showing the equation of circle x²+y²=4
What is a circle?A circle is a two-dimensional geometry on the plane having a centre point and the circular line is drawn equidistant from the centre point.
The given graph in the question represents the equation of the circle cutting the points on the x-axis and y-axis at 4 which is the radius of the circle.
The equation will be as follows:-
x²+y²=4
Hence the graph is showing the equation of circle x²+y²=4
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A rectangular fence is to a total perimeter of 200 feet. If the length is twice the width, find the measurements of the length and width of the rectangular fence.
A rectangular fence is to a total perimeter of 200 feet. If the length is twice the width, find the measurements of the length and width of the rectangular fence.
✪ Explanation -:In this question we are provided with the perimeter of a rectangle fence that is 200 feet. It is also given that the length of the fence is twice its breadth. We are asked to calculate it's dimensions.
First we will form an equation.
Let us assume the breadth as x
Then, length = 2x
It is given that the perimeter is 200 feet.
We know,
[tex] \bull \: \small\boxed{ \rm{ Perimeter_{(rectangle)} = 2(length + breadth)}}[/tex]
Substituting the values we get
[tex] \small\sf{ 200 = 2(2x + x)}[/tex]
Now we will solve this equation and find out the value of x.
[tex] \small\sf{ 200 = 2(2x + x)}[/tex]
[tex] \longmapsto \small\rm{ 200 = 2(3x )}[/tex]
[tex] \longmapsto \small\rm{200 = 6x} [/tex]
[tex] \longmapsto \small\rm{ \dfrac{ \cancel{200} \: \: 33.33}{ \cancel{6}} = x } [/tex]
[tex] \small\sf{x = 33.33} [/tex]
We will substitute the value of x = 33.33.
Length = 2x = 2 × 33.33 = 66.66 feet
Breadth = x = 33.33 feet
Hence the length of the rectangular fence is 66.66 feet and the breadth is 33.33 feet.Need help for this please
Answer:
Using 22/7 as pi, the area of a circle with a diameter of 14 metres is:
154 m²
Step-by-step explanation:
To solve, use the formula for the area of a circle.
Formula for area of a circleRemember the formula for area of a circle. Be careful not to mix up the formula for area with the formula for circumference!
[tex]A = \pi r^{2}[/tex]
From the question, we know:
π = 22/7d = 14 mTo use the formula, we need the radius ("r").
Radius ("r")The radius is a line that goes from the centre point of the circle to the circle outline. It is half the length of the diameter.
Diameter ("d")The diagram shows the diameter ("d"), which goes through the centre point of the circle. It is twice the length of the radius.
Solve for "r".
r = d/2
r = (14 m)/2
r = 7 m
Solve for area using formulaSubstitute r = 7 m and π = 22/7 into the formula for the area of a circle.
[tex]A = \pi r^{2}[/tex] Start with the formula and substitute.
[tex]\displaystyle{A = \frac{22}{7} (7\ m)^{2}}[/tex] Square "7" and the "m".
Remember that the answer for area is always squared units.
[tex]\displaystyle{A = \frac{22}{7} (49\ m^{2})}[/tex]
Multiplying a fraction and whole number is the same as multiplying the whole number in the numerator (top of the fraction).
[tex]\displaystyle{A = \frac{22*49}{7}m^{2}}[/tex] Simplify the numerator.
[tex]\displaystyle{A = \frac{1078}{7}m^{2}}[/tex] Divide.
[tex]A = 154\ m^{2}[/tex] Final answer
∴ The area of the circle is 154 m².
In triangle ABC, mZA = 47° and mZB= 70°
B
70
47
A
С
What is the measure of angle C?
Enter your answer as the correct value. like this: 42
Need this answered ASAP can’t find it anywhere online
Answer:
The value of the rational expression when x = -3 is undefined.
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra II
Rational Functions
Asymptotes, HolesStep-by-step explanation:
Step 1: Define
Identify given.
[tex]\displaystyle \frac{x}{x^2 - 9} ,\ x = -3[/tex]
Step 2: Find Value
[Rational Expression] Substitute in x:∴ since we can't divide by 0, our rational expression when x = -3 will have to be undefined.
___
Topic: Algebra II
Two legs of a right triangle measure 3 inches and 4 inches. Which of the following choice for the
length of the third side will make the triangle a right triangle?
Answer:
5 inchStep-by-step explanation:
Two legs of a right triangle measure 3 inches and 4 inches. Which of the following choice for the length of the third side will make the triangle a right triangle?
not having the choices we solve with Pythagoraslet the unknow side xx = √(3²+4²)
x = √(9 + 16)
x = √25
x = 5William William mowed 75% of the lawn in 33 minutes. Part A Which equation can be used to find how many minutes it will take for William to mow the whole lawn if he continues at the same rate? 75n=33 33n=75 0.33n=75 75n100=33 Part B How many minutes will it take for William to mow the whole lawn?
The equation that can be used to find out the total time it will take to William to mow the lawn is (75n) / 100=33.
What is an equation?This is a mathematical expression that represents a situation including a value that is not known.
In this case the best equation would be 75n / 100=33 as this is the only one that includes all the factors:
75% out of a 100% that is unknown (n)100 (represents the percentage)33 (total of minutes completing 75%)What is the result of this equation?75n / 100=33n/ 100 = 33/75n/100 =0.44n= 0.44 x 100n = 44 minutesLearn more about equations in: https://brainly.com/question/10413253
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The diameter of a circle is 8 in. Find the circumference \textit{to the nearest tenth}to the nearest tenth.
Answer: C ≈ 25.1
Step-by-step explanation:
The circumference of a circle can be found with the following formula. We will plug in the diameter given, and solve.
C = dπ
C = (8)π
C ≈ 25.1
help please i need help
a) Line AE, and Line BC are parallel
b) Line ED, and Line CD
c) 3
Step-by-step explanation:
hi! how do i do this? the answer is 2k
[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]
[tex] log_{4}x = k \\ \\ \longrightarrow \: log_{4}x = log_{2 {}^{2} }x \\ \\ \longrightarrow \: 2 log_{2}x \\ \\ now , \\ \\ log_{2}x = k \\ \\ \therefore \: 2( log_{2}x) = 2(k) \\ \\ \longrightarrow \: 2k[/tex]
hope helpful ~
a Sam purchases a home for $1, 240, 500. Each year the value of the home appreciates by 3%. What is the value of the home after 6 years?
Answer:
lol
Step-by-step explanation:
On a place-value chart, you use exactly 12 counters to represent one decimal number and exactly 15 counters to represent another decimal number.
When you add the two numbers, you get a number you can represent with only 9 counters.
When you subtract the two numbers, you need more than 9 counters for the result.
• What could your numbers be For adding it be
• Explain how you came up with your numbers and why they work.
The possible number represented by the 9 counter is 27
How to determine the possible number?The counters are given as:
12 counters and 15 counters
When added, we get a number that can be represented by 9 counters.
This means that:
12 + 15 = 9x
Evaluate the sum
27 = 9x
Divide by 9
x = 3
When subtracted, you need more than 9 counters.
This means that:
x = 15 - 12 = 3
So, we conclude that the number is a multiple of 3 and 9
In other words, the decimal number is a multiple of 9 (i.e. 27)
Hence, the possible number is 27
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A news report suggested that an adult should drink a minimum of 4 pints of water per day. based on this report determine the minimum amount of water an adult should drink, in fluid ounces, per week.
Answer:
448 fl oz/week
Step-by-step explanation:
1 week = 7 days
4 pints per day × 7 days/week = 28 pints per week
1 pint = 16 fl oz
28 pints/week × 16 fl oz/pint = 448 fl oz/week
2
7
What is the area of the triangle?
units?
Step-by-step explanation:
the area of a triangle is always
baseline × height / 2
where baseline and height are perpendicular (at a 90° angle) to each other.
so, in our case the area is
7 × 2 / 2 = 7 × 1 = 7 units²
please solve the given problem
Answer:
x = -47.1
x = -3.35454... (2-digit repeat)
Step-by-step explanation:
Each of the absolute value functions causes the overall behavior of the equation to change where that absolute value function's argument is zero. Those values of x are -7, -5/2, -2/5.
These breakpoints cause the domain of the equation to be divided into 4 parts. A graphing calculator shows us that solutions exist only in the two regions ...
x < -7-7 ≤ x < -5/2In those regions, the equation simplifies to ...
x < -72(-(x +2/5)) -2(-(x +7)) = 2/3x +(-(x +5/2))
x(-2 +2) -4/5 +14 = x(2/3 -1) -5/2 . . . . collect terms
15.7 = -1/3x . . . . . . add 5/2
x = -47.1 . . . . . . . multiply by -3
__
-7 ≤ x < -5/22(-(x +2/5)) -2(x +7) = 2/3x +(-(x +5/2))
x(-2 -2) -4/5 -14 = x(2/3 -1) -5/2 . . . . collect terms
(-3 2/3)x = 12.3 . . . . . . . . add 1/3x +14.8
x = -36.9/11 = -369/110
x = -3 39/110 ≈ -3.35454... (2-digit repeat)
If 4x+2=11, what is the value of 2x-1 ?
Answer:
Step-by-step explanation:
4x + 2 = 11
4x = 9
x = 9/4
2(9/4) - 1
9/2 - 2/2= 7/2
Suppose the heights of the members of a population follow a normal
distribution. If the mean height of the population is 72 inches and the
standard deviation is 3 inches, 99.7% of the population will have a height
within which range?
A. 63 inches to 81 inches
B. 66 inches to 78 inches
C. 60 inches to 84 inches
D. 69 inches to 75 inches
The option (A) 63 inches to 81 inches is correct after using the empirical Rule.
What is the standard deviation?It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.
We have:
The mean height of the population is 72 inches and the standard deviation is 3 inches, 99.7% of the population will have a height
99.7% of data observed following a normal distribution lies within 3 standard deviations of the mean.
The lower range = 72 – 3(3) = 63 inches
The upper range = 72 + 3(3) = 81 inches
Thus, the option (A) 63 inches to 81 inches is correct after using the empirical Rule.
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It is found that children’s shoe size is correlated with scores on an achievement test. Explain, in words, if this is evidence that correlation implies causation.
Step-by-step explanation:
If you agree that increasing age (for elementary school children) causes increasing foot size, and therefore increasing shoe size, then you expect a correlation between age and shoe size. Correlation is symmetric, so shoe size and age are correlated.
The formula for the area of a triangle is, where b is the length of the base and h is the height.
Find the height of a triangle that has an area of 30 square units and a base measuring 12 units.
Answer: The formula for area of a triangle is area equals base times height divided by 2. the height is 5 units.
Step-by-step explanation:
3(x+1)=5(x−2)+7
solve for x
Simplify: (5 + i)(5 − i)
A) −12
B) 24i
C) 26
D) 8i
Answer:
C) 26
Simplify using the FOIL method--used to multiply binomials--and then combine real and imaginary parts of the problem.
5 × 5 = 25 + positive 1(i) = 26
Answer:
option c, 26
Step-by-step explanation:
(5 + i)(5 - i)
Apply complex arithmetic rule: (a + bi)(a - bi) = a^2 + b^2
a = 5, b =1
(5)^2 + (1)^2
(5)^2 = 25
(1)^2 = 1
25 + 1
please help me!!!
4) There are five nickels and seven dimes in
your pocket. You randomly pick a coin
out of your pocket and then return it to
your pocket. Then you randomly pick
another coin. The first coin is a nickel and
the second coin is a dime.
2
A) //1²
≈ 0.182
B) None of these
11
25
C)
≈ 0.29
D)
≈ 0.148
169
E)
49
169
1
4
= 0.25
5)
E
Answer:
B. None of these
Step-by-step explanation:
There are a total of 12 coins in your pocket.
The probability of drawing a nickel first is 5/12
Since you return the coin, the total number of coins in your pocket doesn't change.
The probability of drawing a dime second is 7/12
Since this is a compound probability problem, multiply the two probabilities together.
5/12 x 7/12 = 35/144
35/144 = 0.243
Please help! 5th-grade math!
It is a quadrilateral, parallelogram, and a rhombus
Answer:
quadrilateral, parallelogram, and rhombus.
Step-by-step explanation:
All quadrilaterals have 4 sides, all parallelograms have 2 sets of parallel sides, and a rhombus has diagonals that bisect each other perpendicularly.
help me pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeee
Since the variable x is the numerator of the fraction, we first need to multiply each side by 6, since the denominator is 6. After doing this, the equation should now look like this: [tex]18 = x + 31[/tex]. Next, we subtract 31 from 18 following the rule. 18 - 31 = -13. x is equal to -13.
For shown work in order:
[tex](6) 3 = x +31[/tex]
[tex]18 = x + 31[/tex]
[tex]18 - 31 = x[/tex]
[tex]x = -13[/tex]
Help please need quickly like rn
Answer:
288 m^3
Step-by-step explanation:
V=(1/3)Bh, where B is base, and h is height
The base will use the equation A=(1/2)bh
B = (1/2)12x9
B = 54
the height is given: 16m
substitute into Volume equation:
V=(1/3)54x16
V=288