Answers
f(x) is a quadratic function having roots 1,-3
For function creation of f(x) visit attachment 2
f(x)=x^2+2x-3Now
\(\\ \sf\longmapsto f(-2)=(-2)^2+2(-2)-3=4-4-3=-3\)
\(\\ \sf\longmapsto g(-2)=|-(-2)+2|+|2+2|=|4|=4\)
Hence
\(\\ \sf\longmapsto (f+g)(-2)\)
\(\\ \sf\longmapsto f(-2)+g(-2)\)
\(\\ \sf\longmapsto -3+4\)
\(\\ \sf\longmapsto 1\)
Answer:
(f + g) (-2) = 1
Step-by-step explanation:
First, it is important to determine the quadratic and absolute value functions in order to perform the given function operations.
Quadratic Function: f(x)Given the vertex (h, k) occurring at point, (-1, -4), substitute the value of these coordinates into the vertex form:
f(x) = a(x - h)² + k
where:
(h, k) = vertex
a = determines whether the graph opens up or down, and makes the parent function wider or narrower.
h = determines how far left or right the parent function is translated.
k = determines how far up or down the parent function is translated.
f(x) = a(x - h)² + k
f(x) = a(x + 1)² - 4
Next, to solve for the value of a, we need another point from the graph. Let's use one of the x-intercepts, (-3, 0):
f(x) = a(x + 1)² - 4
0 = a(-3 + 1)² - 4
0 = a(-2)² - 4
0 + 4 = 4a - 4 + 4
4 = 4a
4/4 = 4a/4
1 = a
Therefore, the quadratic function in vertex form is: f(x) = (x + 1)² - 4
Absolute value function, g(x):Given the vertex (h, k) occurring at point, (2, 0), substitute the value of these coordinates into the absolute value function:
g(x) = a |x - h | + k
The definitions for a and the vertex, (h, k) remains the same.
Choose another point on the graph, (3, 1) and substitute the values of its coordinates, along with the vertex into the absolute value function to solve for the value of a:
g(x) = a |x - 2 | + 0
1 = a |3 - 2|
1 = a | 1 |
1 = a
Therefore, the absolute value function is: g(x) = |x - 2|.
Now, we are ready to solve for (f + g)(-2) = f(-2) + g(-2)
We'll solve each functions separately, then combine the solutions later on.
f(-2):f(-2) = (-2 + 1)² - 4
f(-2) = (-1)² - 4
f(-2) = 1 - 4
f(-2) = -3
g(-2):g(-2) = |-2 - 2|
g(-2) = | -4 |
g(-2) = 4
(f + g)(-2) = f(-2) + g(-2) = -3 + 4 = 1
Therefore, the correct answer is 1.
Related Questions
Find x. √11 X = √17 VIRI X
Answers
1.243 is the measure of the value of x from the given expression
Solving rational equationsRational equations are those that contain rational expressions. A rational expression is a fraction with polynomial numerator and denominator. A rational expression, in other terms, is a ratio between two polynomials.
Given the following rational equation
√11 x = √17
We need to determine the measure of the value of x.
Taking the square of both sides we will have:
(√11 x)² = (√17)²
11x² = 17
x² = 17/11
x² = 1.545
Take the square root of both sides
√x² = √1.545
x = 1.243
Hence the measure of the value of x from the given equation is 1.243.
Learn more on rational equation here: https://brainly.com/question/12223525
#SPJ1
Multiply (2x + 2y)(2x + 2y)
Answers
Answer:
4x² + 4y² + 8xy
Step-by-step explanation:
( 2x + 2y ) ( 2x + 2y ) = ( 2x + 2y )²
Formula : -
( a + b )² = a² + b² + 2ab
Here,
a = 2x
b = 2y
( 2x + 2y )²
= ( 2x )² + ( 2y )² + 2 ( 2x ) ( 2y )
= 2²x² + 2²y² + 8xy
= 4x² + 4y² + 8xy
$7.99 by 16.2 ounces
Answers
Answer:
.49 if you're dividing them.
Step-by-step explanation:
What is the fractional equivalent of the repeating decimal n = 0.1515...?
Answer the questions to find out.
1. How many repeating digits does the number represented by n have?
Write your answer in the space below.
Answers
Answer:
The fractional equal is n = \(\frac{1.3636...}{9}\)
Step-by-step explanation:
I. When n = 0.1515...
10 * n = 0.1515 * 10
10n = 1.515...
So 10n - n = 1.515... + 0.151...
9n = 1.363...
n = \(\frac{1.3636...}{9}\) or 0.1515...
Back to the question, How many repeating digits does is infinity.
You can prove it by use calculator.
Hope that help :)
Two sides of a triangle have lengths 10 and 30. The third side has a length that is
Answers
Answer:
2h4o
Step-by-step explanation:
It took Ms. Hernandes 4/5 hours
to drive 3/10 of the way to her
uncles house. How many hours
did it take to drive to her unde
house?
Answers
Answer:
2 2/3 hours or 2 hours and 4o minutes
Step-by-step explanation:
set up a proportion
\(\frac{time}{distance}\) = \(\frac{time}{distance}\)
\(\frac{\frac{4}{5} }{\frac{3}{10} }\) = \(\frac{h}{1}\)cross multiply and solve for h
\(\frac{3}{10}\) h = \(\frac{4}{5}\) Multiply both sides by \(\frac{10}{3}\)
\((\frac{10}{3})\)\(\frac{3}{10}\) h = \((\frac{10}{3})\)\(\frac{4}{5}\) Multiply and then divide the top and bottom by 5
h = \(\frac{8}{3}\) o r2 \(\frac{2}{3}\)
Colin pays £766.45 a year on his car insurance.
The insurance company increases the price by 5.4%.
How much does the insurance cost now?
Give your answer rounded to 2 DP.
Answers
=766.45x(1+0.054)
=766.45x1.054
= 807.8383
=807.84
75% of the apple pies are sold on Tuesday and the remainder with thrown out if 12 apple pies were sold on Tuesday then how many worth grown out
Answers
Answer:
75 % of 12 = (75 * 12 ) / 100 = 9 were sold
12 - 9 = 3 were thrown out
Step-by-step explanation:
circle columns to break apart the array into two parts 6rolls 7columns
Answers
complete the following statements. in general, % of the values in a data set lie at or below the 70th percentile. % of the values in a data set lie at or above the 20th percentile.. if a sample consists of 600 test scores, of them would be at or below the 86th percentile. if a sample consists of 600 test scores, of them would be at or above the 62th percentile.
Answers
If a sample consists of 600 test scores, 516 of them would be at or below the 86th percentile. If a sample consists of 600 test scores, 228 of them would be at or above the 62th percentile.
What is percentile?A percentile is a score that compares a specific score to the scores of the other members of a group. It displays the proportion of other scores that a given score outperformed. For instance, if you have a test score of 75 and are placed in the 85th percentile, it signifies that your score is greater than those of 85% of other test takers.
Given that,
In general, 70 % of the values in a data set lie at or below the 70th percentile.
20 % of the values in a data set lie at or above the 20th percentile.
Generally percentile defines the percentage of a data set that is below or at a value that is being considered.
Hence the percentage of the values of a data set that lies below or at the 16th percentile is 16%
Also the values of a data set that lies below or at the 24th percentile is 24%
Given a sample of 600 test scores , the number of test scores that will be at or below the 86th percentile is 86% of 600 which is mathematically represented as:
K = \(\frac{86}{100}\) × 600
K = 516 test scores
Given a sample of 600 test scores , the number number of test scores that will be above the 62 th percentile is (100 - 62 = 38 )% of 600 which is mathematically represented as:
a = \(\frac{38}{100}\) × 600
a = 228 test scores.
To know more about percentile refer to:
https://brainly.com/question/28509003
#SPJ4
Let the factors, a1, a2, … a9 of a9 be written in a square 3 by 3 array as indicated. Let a1 Help me plz
Answers
Answer:
61.2
Step-by-step explanation:
To solve this, we would have to use the arithmetic progression formula
S(n) = a + (n - 1) d, where
S(n) = is the value of the nth term
a = value of the first term
n = the nth term we're interested in
d = difference between successive terms
We're given that the first term, a1 = 1.we also know that the 6th term, a6 = 44
If so, we can use this to get our "d", saying
44 = 1 + (6 - 1) d
where
44 is the value of the 6th term, and n is 6. Also, the first term a = 1. Simplifying further we have
44 = 1 + 5d
5d = 44 - 1
5d = 43
d = 43/5
d = 8.6
This means that the difference between successive term is 8.6, we then use this "d" to find our 8th term
S(n) = 1 + (8 - 1) 8.6
S(n) = 1 + 7 * 8.6
S(n) = 1 + 60.2
S(n) = 61.2
Therefore, the 8th term is 61.2
Given the set S = {a, b, c, d}, answer the following.
(a) How many one-element subsets does S have?
(b) How many two-element subsets does S have?
(c) How many three-element subsets does S have?
(d) How many four-element subsets does S have?
(e) How many zero-element subsets does S have?
(f) How many subsets does S have?
(g) If
n(S) = k,
how many subsets will S have?
Answers
Answer:
Step-by-step explanation:
Convert the decimal 0.65 to a fraction in its lowest terms.
Answers
Answer:
The correct fraction is 13/20.
Step-by-step explanation:
\(.65 = \frac{65}{100} = \frac{13}{20} \)
Reasoning: :)
Given: a || b, transversal k
Prove <3 = <6
Answers
By the property of corresponding angles ∠3 ≅ ∠5.
What is transversal line?In geometry, a transversal is any line that intersects two straight lines at distinct points.
If two parallel lines are cut by a transversal, then each pair of corresponding angles are equals.
That is, ∠3 = ∠5 and ∠4 = ∠6.
Therefore the given angles ∠3 and ∠5 are equal.
Hence ∠3 ≅ ∠5 .
Know more about transversal line here :
https://brainly.com/question/17432060
#SPJ1
Triangle XYZ is rotated 90° counterclockwise about the origin to produce X'Y'Z'. What are the coordinates of X'Y'Z'?
Answers
Answer:
59
Step-by-step explanation:
6 plus 4 equals 8 plus 9
Identify the coordinates of each vertex of triangle XYZ.
Apply the 90° counterclockwise rotation rule, which states that when rotating a point 90° counterclockwise about the origin, the new coordinates of the point will be (-y, x).
Substitute the coordinates of each vertex into the rotation rule to find the coordinates of the corresponding vertex in X'Y'Z'.
For example, let's say that the coordinates of triangle XYZ are:
X = (2, 3)
Y = (-1, 4)
Z = (0, -2)
To find the coordinates of X'Y'Z', we can apply the rotation rule to each vertex as follows:
X' = (-3, 2)
Y' = (-4, -1)
Z' = (2, 0)
Therefore, the coordinates of X'Y'Z' after rotating triangle XYZ 90° counterclockwise about the origin are:
X' = (-3, 2)
Y' = (-4, -1)
Z' = (2, 0)
Note that the order of the vertices may change after the rotation, but the coordinates of each vertex will correspond to the same vertex in the original triangle.
please help
What is the distance to the earth’s horizon from point P?
Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.
x =
mi
Answers
The measure of distance x, that is, the distance between a point P and the point of horizon, is equal to 284.372 miles.
How to find the distance to the earth horizon from a given point
In this problem we must determine the distance between a point P located about earth's circumference and the point of horizon, located on earth's circumference. Since the line between these two points is tangent to earth, then, distance x can be found by Pythagorean theorem:
x = √[(3959 mi + 10.2 mi)² - (3959 mi)²]
x = 284.372 mi
The distance x is equal to 284.372 miles.
To learn more on Pythagorean theorem: https://brainly.com/question/14930619
#SPJ1
HELP HELP HELPPPP
ILL GIVE BRAINLIEST HELPPPPPPPPP
100 POINTSSS
Answers
Answer:
C. 0.48
Step-by-step explanation:
Probability = number of required outcome
_______________________
number of possible outcome
= total volleyball game events
_______________________
total sophomore + junior
= 66/137
= 0.48
Answer: D) 0.31
Step-by-step explanation:
Let A denote the event that a person is a sophomore.
Let B denote the event that a person has attended volleyball game.
A∩B denote the event that a person is a sophomore and attend volleyball game.
Let P denote the probability of an event.
We are asked to find:
P(A∩B)
From the table provided to us we see that:
A∩B=42
Hence,
P(A∩B)=42/137=0.3065 which is approximately equal to 0.31. Therefore ur answer will be 0.31.
Pls help me fast!!!!!!!
Answers
Answer:
-x. is the answer maksjjsjsjsbbshs
Roger made a table showing how he spent his time in one day. How many days
will go by before Rodger has slept the equivalent of one day. Explain how you found your answer!
Data:
work : 1/3 day
sleep : 3/8 day
meals: 1/8 day
computer : 1/6 day
PLSSS.... Answer must be whole #
Answers
Answer:
Roger will have to sleep 2.667 days.
Step-by-step explanation:
If Roger sleeps 3 / 8 of a day in one day.
Then for Roger to sleep the equivalent of one day he will have to sleep
=
Given that set A has 73 elements and set B has 29 elements, determine the maximum possible number of elements in A ∩ B
Answers
help me please i would appreciate it so so much
Answers
Answer:
w = 120
x = 60
y = 120
z = 60
Step-by-step explanation:
w = 120 (vertically opposite angles)
sum of co interior angles is 180
⇒ w + x = 180 and x + y = 180
w + x = 180
⇒ 120 + x = 180
⇒ x = 180 - 120
⇒ x = 60
x + y = 180
⇒ 60 + y = 180
⇒ y = 180 - 60
⇒ y = 120
z = x (corresponding angles)
z = 60
Newton and Descartes have a 70-day summer vacation. They go to camp for 23/70 of their vacation, and they travel for 6/35 of their vacation. They stay home the rest of their vacation. How many weeks do Newton and Descartes spend at home?
Answers
5 weeks do Newton and Descartes spend at home. This can be solved using the concept of fractions.
What is fractions?In mathematics, the portion or component of the complete item is represented by a fraction. It stands for the equal components of the whole. Both the numerator and denominator are components of a fraction. The top number is referred to as the numerator, while the bottom number is referred to as the denominator.
Given that,
Newton and Descartes have a 70-day summer vacation
They go to camp for 23/70 of their vacation
= 70 × (23/70)
= 23
Next, they travel for 6/35 of their vacation
= 70 × (6/35)
= 12
So, they stay home the rest of their vacation
= 70 - 23 - 12
= 35
Now, they stay home (35 ÷ 7) = 5 weeks.
Therefore, 5 weeks do Newton and Descartes spend at home.
To know more about fractions refer to:
brainly.com/question/17220365
#SPJ1
not sure what the answer is but I need the interpets
Answers
The x-intercepts of the given expression which is a rational function is calculated to be 0 and the y-intercepts are ±√25.
What does rational function mean?The given expression is a rational function and can be written as the quotient of two polynomials.
The numerator of the rational expression is -x⁷ and the denominator is x²−25. The numerator is a degree 7 polynomial and the denominator is a degree 2 polynomial.
To find the x-intercepts, we need to set the numerator equal to zero and solve for x.
-x⁷ = 0
x⁷ = 0
x = 0
To find the y-intercepts, we need to set the denominator equal to zero and solve for x.
x²−25 = 0
x² = 25
x = ± √25
Therefore, the x-intercepts of the given expression are 0 and the y-intercepts are ± √25.
For more questions related to intercepts
https://brainly.com/question/24212383
#SPJ1
Question :
Find the intercepts of the given function.
y = (-x⁷)/(x²−25)
Cynthia invests some
money in a bank which
5% compound interest per year.
pays
She
wants it to be worth
over £8000 at the end of 3
years.
What is the smallest amount, to the nearest pound, she can invest?
I
Answers
Answer:
The smallest amount is £6911
Step-by-step explanation:
Rate of Interest = R = 5% per year
Duration in years = n = 3 year
Amount expected after three years when compounded annually = A = £8000
Formula for Amount of compound interest annually is a follows
A = P( 1 + R/100)^n
In our case Principal P = x , Amount A = 8000 , R = 5% and n = 3( since compounded annually). On substituting these values in above formula we get
8000 = x ( 1 + 5/100)^3
⇒8000 = x ( 105/100)^3
⇒8000 = x ( 21/20 )^3
⇒(8000 × 20 × 20 × 20)/(21×21×21) = x
⇒x = 6910.70≈6911
5 out of 25 girls said that they like pink as their favorite color. If you were to ask 325 girls, how many would say they liked pink?
Answers
Answer:
65 girls
Step-by-step explanation:
325/25=13 13x5=65
geometry math problems
which one would be the correct answer
Answers
=======================================================
Explanation:
Your teacher wants you to use the angle-angle-side congruence theorem, which abbreviates to AAS. Note in the diagram that we have two pairs of angles marked.
Angle P = Angle U (double arcs)Angle Q = Angle S (single arcs)So we have the info about the angles being congruent, and that takes care of the two "A"s in AAS.
We just need a pair of sides to be congruent. Specifically, we need the pair of sides that are not between the angles mentioned for either triangle. If we went for this option, then we'd go for ASA instead of AAS. The order is important.
So we have two possible answers
PR = UTQR = STIf either of those were given to us, then we can use the AAS theorem. Unfortunately PR = UT isn't listed, but QR = ST is listed. So this is why choice B is the answer.
Side note: Both QR and ST are opposite the double arc angle.
Answer:
QR≅ST
Step-by-step explanation:
With AAS congruence, you need 2 angles and a non-included side. On ΔPQR, that could be either PR or QR. PQ is the included side as it is between the angles, and therefore cant be used for this congruence theorem.
As said above, it can be either PR or QR, but it has to be QR in this case as there is no answer option for PR.
On the other triangle, the corresponding side is ST. ∠S and ∠Q are corresponding, and US is the included side, so that leaves only ST.
Finally, the information you need to prove that the triangles are congruent is QR≅ST.
Consider the information about the economy of Pakistan. Note that the currency of Pakistan is the rupee.
The government purchases: 3.30 trillion of rupees.
Individuals consume: 9.50 trillions of rupees.
Individuals save: 5.44 trillions of rupees.
Businesses invest: 1.20 trillions of rupees.
Foreigners spend: 0.50 trillions of rupees to purchase Pakistani firms.
Pakistan imports: 2.13 trillions of rupees.
Pakistan exports: 1.40 trillions of rupees.
Calculate Pakistan's GDP. Assume that the values are all current and no conversions need to be made. Give your answer in terms of trillions of rupees, and round to two decimals.
Answers
Pakistan's GDP is 13.27 trillion rupees.
What is GDP?GDP is the total value of all products manufactured and goods provided within that territory during a specific period.
We have,
Government purchases = 3.30 trillion rupees.
Individuals consume = 9.50 trillion rupees.
Individuals save = 5.44 trillion rupees.
Businesses invest = 1.20 trillion rupees.
Foreigners spend =0.50 trillion rupees to purchase Pakistani firms.
Pakistan imports = 2.13 trillion rupees.
Pakistan exports = 1.40 trillion rupees
GDP is given by:
C + I + G + NX
Where,
C = Consumption
I - Investment
G - Government Purchases
NX - Net Exports = Export - Import
So,
C = 9.50
I = 1.20
G= 3.30
NX = ( 1.40 - 2.13 ) = -0.73
GDP = 9.50 + 1.20 + 3.30 - 0.73
GDP = 13.27 trillion rupees.
Thus Pakistan's GDP is 13.27 trillion rupees.
Learn more about GDP here:
https://brainly.com/question/15868608
#SPJ1
Will mark brianliest if correct,
If Oliver paid $22,how many times did he ride the Ferris wheel?
Math
If u need more information please tell me. Look at the picture
Answers
Answer:
11 times
Step-by-step explanation:
So if you look at the point where the line is on two real numbers at the top of the grid, it shows that it cost $10 for every 5 rides. So if you find the unit rate, divide 10 by 5 to see how much each ride cost, you get that each ride cost $2. Then just divide $22 by $2 and you get 11. Hope this helps, comment if you need more help
In the figure below, G is between E and H, and F is the midpoint of EG. If EH = 10 and FG = 4, find GH.
Answers
Answer:
GH = 2
Step-by-step explanation:
since F is the midpoint of EG , then EF = FG = 4
EF + FG + GH = EH , that is
4 + 4 + GH = 10
8 + GH = 10 ( subtract 8 from both sides )
GH = 2
Write the equation of the line that passes through (−1, 5) and has a slope of 3 in point-slope form. (2 points)
Answers
-1 = 15 + b
-16 = b
y = 3x -16
y - 5 = 3(x +1)