Answers
A horizontal shift is indicated by addition/subtraction to x rather than the function.
A right shift is indicated by subtracting the number from x. So a right shift of F(x) will be indicated by F(x-2)
Thus,
G(x) = F(x-2)
G(x) = (x-2)²
So, the answer to this question is option B
Related Questions
a gardener at Blair's Arboretum is making displays of roses with 192 red 120 yellow and 168 pink roses to choose from if she wants to use all of the flowers in the displays need to be identical what is the greatest number of displays she can create
Answers
The four vertices of a rectangle drawn on a complex plane are defined by 1 + 4i, -2 + 4i, -2 – 3i, and 1 – 3i. The area of the rectangle is square units.
Answers
Answer:
The area of rectangle =21 sq units .
Step-by-step explanation:
Given the four vertices of rectangle are 1+4i,-2+4i, -2-3i and 1-3i.
Consider ABCD is a rectangle and its vertices are 1+4i,-2+4i,-2-3i and 1-3i.
First we find sides of rectangle
AB=vertices of B- vertices of A
AB= -2+4i-(1+4i)=-3
If complex number=a+biThen modulus=[tex]\sqrt{a^2+b^2}[/tex]Length of AB= [tex]\sqrt{(-3)^2}[/tex]=3 ( Because magnitude = length always positive )BC= Vertices of C - vertices of B
BC=-2-3i-(-2+4i)=-7i
Length of BC=[tex]\sqrt{(-7)^2}[/tex]=7 ( Magnitude always positive)
CD= vertices of D- vertices of C
CD= 1-3i-(-2-3i)=3
Length of CD= [tex]\sqrt{3^2}[/tex]=3 ( Magnitude always positive)
DA= vertices of A - vertices of D
DA= 1+4i-(1-3i) =7i
Length of DA= [tex]\sqrt{7^2}[/tex]=7 ( Magnitude always positive)
AB=CD and DA= BC
Length BC=7 units
Breadth AB=3 units
Area of the rectangle = [tex]length\times breadth[/tex]
Area of rectangle =[tex]AB\times BC[/tex]
Area of rectangle= [tex]3\times 7[/tex]=21 sq units .Victor Malala has a net income of $1240.00 per month. If he spends $150.00 on food, $244.00 on a car payment, $300.00 on rent, and $ 50.00 on savings, what percent of his net income can he spend on other things?
Answers
Food: F=$150.00
Car payment: C=$244.00
Rent: R=$300.00
Saving: S=$50.00
Other things: O=?
F+C+R+S+O=I
$150.00+$244.00+$300.00+$50.00+O=$1240.00
Solving for O:
$744.00+O=$1240.00
$744.00+O-$744.00=$1240.00-$744.00
O=$496.00
Percent of his net income Victor can spend on other things: P=?
P=(O/I)*100%
P=($496.00/$1240.00)*100%
P=(0.40)*100%
P=40%
Answer: 40% of his net income Victor can spend on other things.
-3x - 7 = -6x + 2 ......................
Answers
+7 +7
---------------------------------------------------------------------------------------------------------------------
-3x = -6x+9
+6x +6x
---------------------------------------------------------------------------------------------------------------------
3x = 9
x = 3
PLEASE PLEASE PLEASE HELP ME WITH ALGEBRA 1 PLEASE!?!?!?!?!!!?!?!?!?!?! I WILL GIVE LOTS OF POINTS AND BRAINLEST PLEEEEEEEEEEEEEEEEASE!!?!?!?!?!?!!?!?!?!?
What are the different types of solutions that you can get when you solve a system of linear equations? Describe the graphs of these different types of systems.
Answers
Answer:
there are no solutions (lines do not intersect)there is one solution (lines intersect at one point)there are an infinite number of solutions (lines overlap—are the same line)Step-by-step explanation:
"A system of linear equations" covers a lot of territory. In Algebra 1, it usually means two linear equations in two unknowns. Each of those equations will graph as a line on a coordinate plane.
A solution is a point that satisfies all the equations. That is, it is a point that is on all the lines described by the system of equations.
The geometry of lines on a plane comes into play with regard to solutions.
The lines may be parallel, hence never intersect. (No points will be on all the lines.)The lines may intersect at one point.The lines may be the same line, overlapping, identical, coincident, consisting of all the same points, an infinite number.for triangle cab find the length of a Side a
Answers
the law of cosines establishes that
a²=c²+b²-2*c*b*cos A
in this problem
a=?
b=21
c=32
A=40°
a²=32²+21²-2*32*21*cos 40-----> a²=435.44---------> a=20.87 units
Solve for r.
4r-9s=K
Answers
Final answer:
To solve for 'r' in the given equation, add 9s to both sides and then divide by 4, resulting in r = (9s + K) / 4.
Explanation:
To solve for r in the equation 4r - 9s = K, we need to isolate r on one side of the equation. Here's how we can do this:
Add 9s to both sides of the equation to get 4r = 9s + K.Divide both sides of the equation by 4 to solve for r, resulting in r = (9s + K) / 4.Now, we have r expressed in terms of s and K, which is the desired form.Q9 Q11.) Complete the first and second equations of the system of equations.
Answers
See picture below for the answer. Let me know if you have questions about the answer.
Which quadratic equation equation is equivalent to (x^2-1)^2 -11(^2-1) +24=0
Answers
Use substitution: [tex]x^2-1=t[/tex]
[tex]t^2-11t+24=0\\\\t^2-8t-3t+24=0\\\\t(t-8)-3(t-8)=0\\\\(t-8)(t-3)=0\iff t-8=0\ \vee\ t-3=0\\\\t=8\ \vee\ t=3[/tex]
we're going back to substitution:
[tex]x^2-1=8\ \vee\ x^2-1=3\ \ \ \ |add\ 1\ to\ both\ sides\ of\ the\ equations\\\\x^2=9\ \vee\ x^2=4[/tex]
therefore
[tex]x=\pm\sqrt9\ \vee\ x=\pm\sqrt4\\\\\boxed{x=-3\ \vee\ x=3\ \vee\ x=-2\ \vee\ x=2}[/tex]
Answer:
x = ± 3 and ± 2
Step-by-step explanation:
The given quadratic equation is
[tex](x^{2}-1)^{2}-11(x^{2}-1)+24=0[/tex]
To make this question easier we will consume ( x² -1 ) = a
a² - 11a + 24 = 0
Now we can factorize this equation easily
a²- 8a - 3a + 24 = 0
a (a-8) - 3 ( a-8) = 0
( a-3 ) ( a-8 ) = 0
Therefore, a - 3 = 0 ⇒ a = 3
or a - 8 = 0 ⇒ a = 8
Now we put the value a
when a = 3 (x² - 1) = 3
x² = 3 + 1 = 4
x = √4
= ± 2
when a = 8 (x² - 1) = 8
x² = 9
x = √9
= ± 3
Therefore, x = ± 3 and ± 2 will be the answer.
hey can you please help me posted picture of question
Answers
y = f (x)
The domain of the function is:
values of x for which it is defined.
The range is:
values of and for which it is defined.
The inverse is:
x = f (y)
The domain of the function is:
values of and for which it is defined.
Answer:
TRUE
option A
Domain of the function is Range of its Inverse.
Range of the function is Domain of its Inverse.
This is because the function and its inverse are a reflection about the line x= y, as a result the x values get translated to y values.
hey can you please help me posted picture of question
Answers
The solution is shown below:
(8 - 3i)(6 + 5i)
= 8(6 +5i) - 3i(6 + 5i)
= 48 + 40i - 18i - 15i²
= 22i + 48 - 15(-1)
= 22i + 48 + 15
= 22i + 63
= 63 + 22i
A triangle has side lengths of 7, 24, and 26. Is the triangle right, acute, or obtuse? a. right c. obtuse b. acute Please select the best answer from the choices provided A B C
Answers
Answer:
Option C. Obtuse
Step-by-step explanation:
we know that
Applying the Pythagoras Theorem
If [tex]c^{2}=a^{2} +b^{2}[/tex] ----> is a right triangle
If [tex]c^{2}>a^{2} +b^{2}[/tex] ----> is a obtuse triangle
If [tex]c^{2}<a^{2} +b^{2}[/tex] ----> is an acute triangle
where
c is the greater side
Verify
[tex]c^{2}=26^{2}= 676[/tex]
[tex]a^{2} +b^{2}=7^{2} +24^{2}=625[/tex]
therefore
[tex]676>625[/tex]
[tex]c^{2}>a^{2} +b^{2}[/tex] -----> is a obtuse triangle
hey can you please help me posted picture of question
Answers
(11 - 7i) - (16 - 11i)
= 11 - 7i - 16 + 11i
= -5 + 4i
So, the answer to this question is option B
1. You have the following expression:
(11-7i)-(16-11i)
2. If you want to substract both terms, you obtain:
11-7i-16+11i
(11-16)+(-7+11)
3. Then, you obtain the following result:
-5+4i
4. Therefore, as you can see, the correct answer is the second option (option B), which is:
B. -5+4i
The average score on a standardized test is 750 points with a standard deviation of 50 points. What is the probability that a student scored more than 850 on the standardized test ?
Answers
z=(x-μ)/σ
where:
x=850
μ=750
σ=50
thus
z=(850-750)/50
z=2
thus
P(x>850)=1-P(x<850)=1-P(z<2)=1-0.9772=0.0228
Answer: P(x>850)=0.0228
Answer:
2%
Step-by-step explanation:
A person in a balloon which is 2,000 feet above the airport finds that the angle of depression to a ship out at sea is 21°. Find the horizontal distance between the balloon and the ship.
Answers
The horizontal distance between the balloon and the ship can be calculated using the tangent function is 1639 feet.
To find the horizontal distance between the balloon and the ship, we can use the tangent function in trigonometry. Let's denote the horizontal distance as x, and the distance between the balloon and the ship along the ground as y.
We have the angle of depression (21°) and the altitude of the balloon (2,000 feet). We can set up the equation:
tan(21°) = y / (2,000 + y)
Now, we need to solve for y:
tan(21°) * (2,000 + y) = y
y * tan(21°) = 2,000 * tan(21°) - y * tan(21°)
y * (1 - tan(21°)) = 2,000 * tan(21°)
y = (2,000 * tan(21°)) / (1 - tan(21°))
Now, calculate the value:
y ≈ (2,000 * 0.364) / (1 - 0.364)
y ≈ 728 / 0.636
y ≈ 1,148.17
Now that we have the value of y, we can find the horizontal distance x using the Pythagorean theorem:
[tex]x^2 + y^2 = (2,000)^2\\x^2 + (1,148.17)^2 = 4,000,000\\x^2 = 4,000,000 - 1,319,441.98\\x^2 = 2,680,558.02\\x = 1,638.84 (rounded)[/tex]
The horizontal distance between the balloon and the ship is approximately 1,639 feet.
Horizontal distance = height of balloon / tangent(angle of depression) = 2000 / tan(21°) ≈ 5243.87 feet.
To find the horizontal distance between the balloon and the ship, we can use trigonometry, specifically the tangent function.
Let's denote:
- [tex]\( h \)[/tex] as the height of the balloon above the ground (2,000 feet in this case).
- [tex]\( \theta \)[/tex] as the angle of depression (the angle formed between the line of sight from the balloon to the ship and the horizontal ground).
Given that the angle of depression [tex]\( \theta \)[/tex] is 21°, we can use the tangent function:
[tex]\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \][/tex]
In this case, the opposite side is the height of the balloon above the ground (2,000 feet), and we want to find the adjacent side, which represents the horizontal distance between the balloon and the ship.
So, we have:
[tex]\[ \tan(21°) = \frac{2000}{\text{horizontal distance}} \][/tex]
To find the horizontal distance, we rearrange the equation:
[tex]\[ \text{horizontal distance} = \frac{2000}{\tan(21°)} \][/tex]
Now, we can calculate this:
[tex]\[ \text{horizontal distance} = \frac{2000}{\tan(21°)} \approx \frac{2000}{0.381} \approx 5243.87 \text{ feet} \][/tex]
So, the horizontal distance between the balloon and the ship is approximately 5243.87 feet.
using the quadratic formula to solve 7x^2-x=7, what are the values of x?
Answers
[tex]a x^{2} +bx+c=0[/tex]
So, to make this true subtract 7 from each side.
The equation is now 7[tex] x^{2} [/tex] - x - 7 = 0
Values for a, b, and c: a = 7, b = -1, c = -7
Plug these variables into the quadratic equation.
[tex] x= \frac{1 {\pm} \sqrt{ -1^{2}-4*7*-7}}{2*-7} [/tex]
Square -1 to get 1 and multiply -4 x 7 x -7 to get 196.
[tex]x= \frac{1 {\pm} \sqrt{1+196}}{2*-7}[/tex]
Multiply 2 x -7 to get -14, the denominator, and add 1 to 196.
[tex]x= \frac{1 {\pm} \sqrt{197}}{-14}[/tex]
Since 197 is not a square number, and I don't know if you want to leave it in radical form or not, I will just because it's easier to understand.
Hope this helps!
7-x = -2 whats the awnser
Answers
9 = x
If you're wanting the value of x, the answer is ...
x = 9
_____
You can always solve an equation like this by subtracting one side, then dividing by the coefficient of x, then adding the opposite of the constant. If you choose to subtract the right side, these steps will give you ...
9 -x = 0 . . . . . . subtract -2 from both sides
-9 +x = 0 . . . . . divide by the coefficient of x, which was -1
x = 9 . . . . . . . . .add the opposite of the constant, so add 9
Whatever you do to one side of the equation, you must also do to the other side. When we say "subtract -2", we mean "subtract -2 from both sides of the equation."
The circle graph shows the different types of books that Yubo enjoys reading
Which two types of books does Yubo spend a total of of her time reading?
Choose exactly two answers that are correct.
A.
Fiction
B.
Mystery
C.
Poetry
D.
History
Answers
History=0.4~40%
Poetry=0.3~30%
hence we can conclude that the answer is:
C. Poetry
D. History
Answer:
its really History and Mystery hope i hlaaaaaaaaaaaaaaaaped
Find the value of x for which m//n
A.
10
B.
12
C.
40
D.
52.
Answers
(3x+12)°=48°
Solving for x:
3x+12=48
3x+12-12=48-12
3x=36
3x/3=36/3
x=12
Answer: Option B. 12
Answer:
The answer is D. 52
Step-by-step explanation:
edg 2020
At the grocery store, an 8-inch cherry pie costs $4.39 and a similar 10-inch cherry pie cost $6.15. which is the better deal?
Answers
for the 10 inch pie you are paying about 61 cents per inch
so the 8 inch pie is a better deal
hope this helped
oh and to get those numbers divide 4.39 by 8 and 6.15 by 10
Devonte used the change of base formula to approximate log 8 25. Which expression did Devonte use?
A.log 8/25 B.log8/log25 C.log 25/8 D.log25/log8
Answers
Answer:
D.
Step-by-step explanation:
Nikhil gets paid a 5 percent commission on every pair of shoes that he sells. He earned $1.00 on the last pair of shoes that he sold. The expression that can be used to represent x, the price of the shoes, is mc005-1.jpg What was the price of the shoes?
Answers
.05s=f(s)
.05s=1
s= $20
Answer:
$20.00 is the correct answer
Step-by-step explanation:
I promise this is correct
The poplution of Las vegas, Nevada has been increasing at an annual rate of 7.0%. If the poplution of las vegas was 478,434 in the year 1999, predict its population in 2010.
Answers
p(x) = 478,434*1.07^x
For x=11, this is
p(11) = 478,434*1.07^11 ≈ 1,007,033
The relation predicts the Las Vegas population in 2010 to be 1,007,033.
Jewelry is commonly weight in carats.Five carats are equivalent to one gram.How many grams of gold are contained in 24-carat gold chain
Answers
Suppose we calculate a 95% confidence interval for the population mean to be (6.93, 11.45). how do we interpret this?
Answers
The [tex]95\%[/tex] confidence interval for the population mean is [tex]\left( {6.93,11.45}\right)[/tex] means that there are [tex]95\%[/tex] chances of the population mean lies in the interval.
Further Explanation:
Explanation:
The formula for confidence interval can be expressed as follows,
[tex]\boxed{{\text{Confidence interval}}=\left( {\overline X \pm ME} \right)}[/tex]
ME represents the Margin of Error.
The confidence interval has two limits.
(1). Upper Limit
(2). Lower Limit
The upper limit can be calculated as follows,
[tex]{\text{Upper limit}}=\left( {X + ME}\right)[/tex]
The lower limit can be calculated as follows,
[tex]{\text{Lower limit}} = \left( {X - ME}\right)[/tex]
The given confidence interval is [tex]\left( {6.93,11.45}\right).[/tex]
The upper limit of the confidence interval is 11.45.
The lower limit of the confidence interval is 6.93.
The 95\% confidence interval for the population mean is [tex]\left( {6.93,11.45}\right)[/tex] means that there are [tex]95\%[/tex] chances of the population mean lies in the interval.
Learn more:
1. Learn more about normal distribution https://brainly.com/question/12698949
2. Learn more about standard normal distribution https://brainly.com/question/13006989
3. Learn more about confidence interval of mean https://brainly.com/question/12986589
Answer details:
Grade: College
Subject: Statistics
Chapter: Confidence Interval
Keywords: Z-score, Z-value, confidence interval, confidence limit, 95 percent, standard normal distribution, standard deviation, test, measure, probability, low score, mean, repeating, indicated, normal distribution, percentile, percentage, undesirable behavior, proportion, empirical rule.
A pizza that was ordered for a party was already cut into 6 slices. If each serving of pizza was 1 3 of a slice, how many servings of pizza were available? A) 18 Eliminate B) 2 C) 1 18 D) 1 2
Answers
I serving size was 1/3 of a slice
1/3 * 3 = 1
3 serving sizes made one slice
Multiply this by the amount of slices
3 * 6 = 18
There are 18 serving sizes
The answer is 18
Hope this helps!
f(x)=e^(x) where it is translated 1 unit right and 2 units down
Answers
1) It is tanslated 1 unit right:
g(x)=f(x-1)→g(x)=e^(x-1)
2) and 2 units down:
h(x)=g(x)-2→h(x)=e^(x-1)-2
Answer: e^(x-1)-2
A taxi driver estimates that his earnings are $240 on a fine day and $320 on a wet day. What are his expected earnings on a day with probability of rain of 0.45?
Answers
Probability of not raining=1-0.45=0.55
The expected earning will be given by:
E(x)=240(0.55)+320(0.45)
E(x)=132+144
E(x)=276
Answer: $276
You have $25 in your bank account. You make $7 per hour babysitting. How many hours must you babysit to have a total of $165 in your account?
Answers
You start with 25 dollars, you make 7 an hour:
7x + 25
Set this to 165:
7x + 25 = 165
Now subtract 25 from both sides:
7x = 140
Divide both sides by 7:
x = 20
So, you must babysit 20 hours.
Hope this helps!
25 + 7h = 165
h is the total number of hours you spend babysitting.
Solve for h to find how many hours you need to babysit to have a total of $165 in your bank account.
25 + 7h = 165
Subtract 25 from both sides.
7h = 140
Divide both sides by 7.
h = 20
You must spend 20 hours babysitting to have $165 in your bank account.
What is the inverse function of f(x)=5x-3
Answers
The inverse function of f(x) = 5x - 3 is found by switching x and y to solve for x, resulting in the inverse function f⁻¹(x) = (x + 3) / 5. This process is part of understanding function transformations that change a function's graph.
Finding the Inverse Function
Find the inverse function of f(x) = 5x - 3. To find the inverse, we need to switch the roles of x and y. So we first write y = 5x - 3. We then solve this equation for x to get x as a function of y. Performing the steps:
Add 3 to both sides: y + 3 = 5x.
Divide both sides by 5: (y + 3) / 5 = x.
This new equation x = (y + 3) / 5 represents the inverse function. To use the proper notation, we replace y with f⁻¹(x) and x with y, giving us f⁻¹(x) = (x + 3) / 5.
Understanding Function Transformations
When considering transformations such as f(-x) or f(2x), these changes to the independent variable result in specific alterations to the graph of the function, such as reflections across the y-axis or horizontal shrinkage by half.