Function g can be thought of as a translated (shifted) version of f(x)=x^2.
PLEASE HELP I NEED THISSS!!!
Answers
Answer:
g(x) = x² - 3
Step-by-step explanation:
A quadratic function has been given as,
f(x) = x²
If the function f is translated by 'h' unit down over the y-axis, the new function obtained by the translation is,
g(x) = x² - h
From the graph attached, h = 3 units (shift of 3 units downwards)
Therefore, g(x) = x² - 3 will be the translated version of f(x).
Related Questions
What is the solution set of -|-x| = -12
Answers
Answer:
{-12,12}
Step-by-step explanation:
-|-x| = -12 multiply both sides by -1
|-x| = 12 apply rule for solving absolute value equations
-x = 12 and -x = -12 solve
x = -12 and x =12
Use the method of cylindrical shells to find the volume of the solid generated by rotating the region bounded by the curves y=cos(πx/2), y=0, x=0, and x=1 about the y-axis
Answers
Answer:
1,45 cubic units
Step-by-step explanation:
The method of cylindrical shells demands that the volume of the solid is given by:
[tex]V=2\pi\int_a^b xf(x)dx[/tex] (1)
In this case you have that f(x) is:
[tex]f(x)=cos(\frac{\pi}{2}x)[/tex]
a = 0
b = 1
First, you solve the integral, by parts:
[tex]\int xf(x)dx=\int xcos(\frac{\pi}{2}x)dx=x(\frac{2}{\pi})sin(\frac{\pi}{2}x)-\int (\frac{2}{\pi})sin(\frac{\pi}{2}x)dx\\\\=(\frac{2}{\pi})xsin(\frac{\pi}{2}x)+(\frac{2}{\pi})^2cos(\frac{\pi}{2}x)+C[/tex]
Next, you calculate the volume of the solid, by replacing the solution to the integral in the equation (1):
[tex]V=2\pi[(\frac{2}{\pi})xsin(\frac{\pi}{2}x)+(\frac{2}{\pi})^2cos(\frac{\pi}{2}x)]_0^1\\\\V=2\pi[(\frac{2}{\pi})-(\frac{2}{\pi})^2]=1,45u^3[/tex]
hence, the volume of the solid generated is 1,45 cubic units
work out the area of this circle when its the diameter 9m take pie to be 3.142 and give your answer to 2 decimal places.
Answers
3.142*4.5²=63.6255
Answer=63.63
Please see the attached picture for full solution
Hope it helps
Good luck on your assignment..
What is the diameter of the smallest circle that would enclose 2,000 pennies?
Answers
Answer:
Almost about 4500 mm
Step-by-step explanation:
Measure the pennies width and estimate. Multilpy by 2000 and there you go!
Please answer correctly !!!!!!! Will mark brainliest !!!!!!!!!!!
Answers
Answer:
-8
Step-by-step explanation:
f(1) = -2
g(4)= 6
-8 *(-2) -4 * 6 = 16 -24 = -8
Which expression represents the algebraic phrase “the sum of negative three-eighths and four times x minus nine times z”?
Answers
Answer:
-3/8 +4x -9z
Step-by-step explanation:
this should be the translated answer, the variables don't need a multiplication sign because they aren't written as numbers
Which are linear pairs? Check all that apply.
A. ∠DAE and ∠EAD
B. ∠BAC and ∠CAD
C. ∠BAE and ∠EAD
D. ∠EAD and ∠DAC
E. ∠CAE and ∠BAD
Answers
Answer:
Options B, C and D
Step-by-step explanation:
Linear pair of angles means sum of the angles of the pair is 180° which are formed at a point of a line.
In other words, pair of supplementary angles is the linear pair.
From the figure attached,
Pair of the linear angles are,
1). ∠BAC and ∠CAD
2). ∠BAE and ∠EAD
3). ∠EAD and ∠DAC
Therefore, Options B, C and D are correct.
Answer:
B, C, and D
Step-by-step explanation:
Given that 3x/8 = 9y/4, Find the ratio of x:y
Answers
Answer:
1:6
Step-by-step explanation:
3x/8 = 9y/4
Multiply by 8
3x = 9y/4 *8
3x = 18 y
Divide by 3
x = 18y/3
x = 6y
The ratio is of x to y is
1:6
Answer:
Step-by-step explanation:
3x/8=9y/4
3x/2=9y
1.5x=9y
1.5x:9y
. (10 points) Based on pre-trial speculation, the probability that a jury returns a guilty verdict in a certain high-profile murder case is thought to be 15% if the defense can discredit the police department, and 80% if they cannot. Veteran court observers believe that the skilled defense attorneys have a 70% chance of convincing the jury that the police either contaminated or planted some evidence. What is the probabiliy that the jury returns a guilty verdict?
Answers
Answer:
34.5% probability that the jury returns a guilty verdict
Step-by-step explanation:
We have these following probabilities:
If the police can discredit the police department, 15% probability of a guilty verdict.
70% probability of the police department being discredited by the defense.
If the police can discredit the police department, 80% probability of a guilty verdict.
100 - 70 = 30% probability of the defense not discrediting the police.
What is the probability that the jury returns a guilty verdict?
15% of 70% and 80% of 30%. So
p = 0.15*0.7 + 0.8*0.3 = 0.345
34.5% probability that the jury returns a guilty verdict
Which situation is best modeled with a division expression?
finding the number of equal-sized parts into which a number can be split
finding the combined value of several different numbers
finding the distance between two numbers on a number line
finding the total value when several of the same number are grouped together
Answers
Answer: Finding the number of equal-sized parts into which a number can be split
Step-by-step explanation:
Hi, a division expression is the division of 2 numbers that results in a quotient.
The quotient is the number of times that the second number in the division is contained in the first number.
For example 20 ÷ 2 = 10
Number 2 is contained 10 times in the number 10, or in other words, 20 can be split into ten equal-sized parts.
Feel free to ask for more if needed or if you did not understand something.
Answer:
A
Step-by-step explanation:
for edge
A high square prism has a length L and width W units. if its height is H Units long the find the lateral surface area of the prism .
Answers
Answer:
2(L+W)H
Step-by-step explanation:
The lateral surface area of a prism is the total of the area of the faces.The lateral area of the prism is equal to the perimeter of the base times the altitude.Surface area= 2(L+W)H
12(3x)=12 what does x equal
Answers
Answer:
x=0.333
Step-by-step explanation:
12(3x)=12
36x=12
/36 on both sides
x=0.333
18. QS bisects ZPQR. If mZPQS = 3x and
mZROS = 2x + 6, then mZPQR =
?
A. 18°
B. 36°
C. 30°
D. 6°
Answers
I need which other form can you represent the number 2 1/3
Answers
To keep the same denominator, multiple the number two by three.
You should get the number 6.
Once you have this number, add it to the remaining 1/3.
It should look like this:
7/3
Answer:
You can also represent it as [tex]\sqrt[3]{2}[/tex]
Step-by-step explanation:
[tex](\sqrt[3]{2})^{3} =2\\2^{\frac{1}{3} } =2[/tex]
What is the value of y when x = 6?
-3x + 9y = 18
Answers
Answer:
y = 6
Step-by-step explanation:
-3x + 9y = 18
-3(6) +6y = 18
-18 +6y = 18
Add 18 to each side
-18+18 +6y =18+18
6y = 36
Divide each side by 6
6y/6 = 36/6
y = 6
PLS HELP ME WITH THIS
Answers
Answer:
so the answer is the second one. Hope this working helps
if ten coins are spun together, the probability of four or more heads is 0.83. the probability of eight or more is 0.05. find the probability of:
I) less than four. II)fewer than 8
Answers
Answer:
a. 0.17
b. 0.95
Step-by-step explanation:
The key to answering both questions is that we should understand that the probability of an event happening = 1 - the probability of the event not happening
Firstly, we want to calculate the probability of less than four
Probability of less than four = 1 - probability of four or more heads
that is 1 - 0.83 = 0.17
Probability of less than 8 = 1 - probability of 8 or more = 1-0.05 = 0.95
Please if you know this please help me I’m stuck I don’t know
Answers
Answer:
The vertical angles theorem
Step-by-step explanation:
The Vertical Angles Theorem states that vertical angles, angles that are opposite each other and formed by two intersecting straight lines, are congruent.
Angles ∠JKN and ∠MKL fit the criteria of the vertical angles theorem, meaning they are congruent.
What is the vertex of the function f(x)=3(x-4)^2+5
Answers
Answer:
vertex = (4, 5 )
Step-by-step explanation:
The equation of a parabola in vertex form is
f(x) = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
f(x) = 3(x - 4)² + 5 ← is in vertex form
with vertex = (4, 5 )
can someone answer number 11 and show the work? I need it bad, please .
Answers
Answer: 8
Evaluating the function for x = -1
[tex]f(x)=x^2+7\\f(-1)= (-1)^2+7\\f(-1)=8[/tex]
3x-2y=-4 can someone find the slope and y intercept for this? thank you.
Answers
Answer:
[tex]Slope:\frac{3}{2}\\y-intercept:2[/tex]
Step-by-step explanation:
21. A quantity of food would last a
family of 5 for 21 days. How long
would the same quantity last a
family of 7 if thev all eat at the same
rate?
Answers
Answer:
15 days
Step-by-step explanation:
5 x 21 = 105
105/7 = 15
Answer:
15 days
Step-by-step explanation:
As the number of people in that family increases the time taken reduces, so the time is in inverse proportion to the number of people in that family.
Let the number of days taken by a family of 7 to finish a quantity of food be x.
⇒ [tex]\frac{x}{21}[/tex] = [tex]\frac{1}{\frac{7}{5} }[/tex]
⇒ [tex]\frac{x}{21}[/tex] = [tex]\frac{5}{7}[/tex]
⇒ x = [tex]\frac{21 * 5}{7}[/tex]
x = 15
∴ It would take a family of 7 15 days to finish a quantity of food.
Hope this helps!!!
19. A bakery sold three kinds of muffins on Monday. The ratio of cranberry to blueberry muffins sold was 2/3 . The ratio of blueberry to cinnamon muffins sold was 1. If 60 blueberry muffins were sold on Monday, how 4/1 many more cranberry muffins than cinnamon muffins did the bakery sell? *
Answers
Answer:
25
Step-by-step explanation:
The ratio of cranberry to blueberry muffins sold was 2/3.
This means that for every 3 blueberry muffins, 2 cranberry muffins were sold.
The ratio of blueberry to cinnamon muffins sold was 4/1.
This means that for every cinnamon muffin, 4 blueberry muffins were sold.
In other words, the ratio of cinnamon muffins to blueberry was 1/4.
60 blueberry muffins were sold on Monday.
This means that the number of cranberry muffins sold was:
2/3 * 60 = 40 cranberry muffins
This also means that the number of cinnamon muffins sold was:
1/4 * 60 = 15 cinnamon muffins
To find how many more cranberry muffins were sold than cinnamon muffins:
40 - 15 = 25 muffins
25 more cranberry muffins were sold.
Answer:
25
Step-by-step explanation:
A car drives at a speed of 90 km/h for 2 hours and 20 minutes.
How far does the car drive?
Answers
Answer:
210 KM
Step-by-step explanation:
first 20minutes is 1/3 of an hour
20/60=1/3 hour
how far does the car drive =time *speed
=2 1/3 hour *90= 210 km
i wiil be happy if you mark me as brainliest
the area of a right angled triangle is 600cm^.if base of the base of the exceeds the altitude by 10,find the dimensions of the triangle
Answers
Answer:
b => base => 40 cm
h => altitude => 30 cm
A = h*b/2
h=b-10
600=(b-10)b/2
600 = (b^2-10b)/2
1200=b^2-10b
b^2-10b-1200=0
(b-40)(b+30)=0
b=40 cm
h=b-10 = 40-10=30
Simultaneous equation
Answers
Answer:
x = 5, y = 9.
Step-by-step explanation:
8^x / 2^y = 64
3^4x * (1/9)^(y -1) = 81
From the first equation
2^3x / 2^y = 2^6
2^(3x-y) = 2^6
So 3x - y = 6 ..........(1)
From the second equation:
3^4x * 9^(-(y-1)) = 3^4
3^4x * 3^2(-(y-1)) = 3^4
3^(4x+ 2(1 - y)) = 3^4
So 4x + 2(1 - y) = 4
4x - 2y = 2
2x - y = 1 .............(2)
Subtract: (1) - (2):
x = 5.
and 2(5) - y = 1
so y = 9.
Solving the simultaneous equations we get x is 5 and y is 9 .
Simultaneous equations in algebra are those that concurrently involve two or more variables, such as x and y. Even though they are solved simultaneously, the equations are known as simultaneous equations. Just these equations alone have innumerable answers.
A system of equations, often known as an equation system, is a collection of finite equations for which common solutions are sought.
The two given equations can be simplified as:
[tex]8^x \div 2^y = 64\\\\or,\frac{2^{3x}}{2^y} =2^6\\\\or, 2^{3x-y}=2^6\\\\or, 3x-y = 6[/tex]
And :
[tex]3^{4x} \times (\frac{1}{9})^{y-1}=81\\\\or, 3^{4x} \times 3^{-2(y-1)}=3^4\\\\or, 3^{4x+2-2y}=3^4\\\\or, 4x-2y = 2\\\\or,2x-y=1[/tex]
Now we can solve the two simultaneous equations :
3x - y = 6 and 2x - y = 1
Subtracting the equations we get:
x = 5
and
y = 9
Solving the simultaneous equations we get the value of x as 5 and the value of y as 9 .
To learn more about simultaneous equations visit:
brainly.com/question/16763389
#SPJ1
Help me with this question please
Answers
Answer:
x < 6
Step-by-step explanation:
There is an open circle ( no equals) at 6 and the line goes to the left
This means that it is less than 6
x < 6
Mark asked each student in a class to name their favourite colour. For this class, the number of students who said blue is three times the number of students who said green. Write down the ratio of the number of students who said blue to the number of students who said green.
Answers
Answer:
3:1
Step-by-step explanation:
Since there are 3 times more blue favorite kids, the ratio is
3:1
The ratio of the number of students who said blue to the number of students who said green is 3 : 1.
What is ratio?The ratio is a numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.
Given:
Mark asked each student in a class to name their favorite color.
For this class,
the number of students who said blue is three times the number of students who said green.
Let n be the number of students who said green.
Then, 3n, the number of students who said blue.
The ratio of the number of students who said blue to the number of students who said green.
= 3n/ n
= 3/1
= 3: 1.
Therefore, the ratio is 3 : 1.
To learn more about the ratio;
https://brainly.com/question/13419413
#SPJ2
If the diameter of a circle is 7 inches,
which is closest to the circumference?
F 21.98 in.
G 38.47 in.
H 43.96 in.
J 153.86 in.
Answers
Work Shown:
Circumference = pi*diameter
Circumference = 3.14*7
Circumference = 21.98 inches approximately
This is approximate since pi = 3.14 is approximate.
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). A florist currently makes a profit of $20 on each of her celebration bouquets and sells an average of 30 bouquets every week. She noticed that when she reduces the price such that she earns $1 less in profit from each bouquet, she then sells three more bouquets per week. The relationship between her weekly profit, P(x), after x one-dollar decreases is shown in the graph below. Use the graph to complete each statement about this situation. The maximum profit the florist will earn from selling celebration bouquets is $___ . The florist will break-even after ______ one-dollar decreases. The interval of the number of one-dollar decreases for which the florist makes a profit from celebration bouquets is (___,____).
Answers
Answer:
First space: 15
Second space: 20
Third space: 0
Fourth space: 20
Step-by-step explanation:
If the florist decrease x times the value of the bouquet by 1, the number of bouquets sold is 30 plus 3 times x, so we have that:
P(x) = (20 - x)*(30+3x)
P(x) = 600 +30x - 3x2
The vertical axis of the graph represents the profit P(x) of the florist.
So observing the graph, we can see that the maximum profit is 675, and occurs when the value of x is 5, that is, the price of the bouquet is 20 - 5*1 = $15
Looking again to the graph, we see that when x = 20 her profit is zero (the price of each bouquet will be 20 - 20*1 = 0)
The interval of x for which the florist have a positive profit (P(x) > 0) is between x = -10 and x = 20, but the florist cannot make a negative number of one-dollar decrease, so the lower number in the interval should be 0.
Answer:
675
20
(0,20)
Step-by-step explanation:
