The equation in the vertex form of g(x) is:
[tex]g(x) = (x + 1)^2 - 38[/tex]
How to get the equation of function g?
We know that g(x) is a translation of 2 units below and 3 units to the left of f(x).
So first, let's rewrite f(x) to its vertex form:
[tex]f(x) = x^2 - 4x - 32[/tex]
The vertex is at:
[tex]x = -(-4)/2*1 = 2[/tex]
The y-value of the vertex is:
[tex]f(2) = 2^2 - 4*2 - 32 = -36[/tex]
Then the vertex form of f(x) is:
[tex]f(x) = (x - 2)^2 - 36[/tex]
If we move this vertex 2 units below, and 3 units to the left, then we have:
[tex]g(x) = f(x +3) - 2\\\\g(x) = (x - 2 + 3)^2 - 36 - 2\\\\g(x) = (x + 1)^2 - 38[/tex]
That is the equation for g(x) in vertex form.
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What are the roots for the quadratic equation below?
3x^2+9x-2=0
Answer:
[tex]\sf{$a)$} \ x=\dfrac{-9\pm\sqrt{105}}{6}[/tex]
Step-by-step explanation:
Quadratic formula: [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Quadratic equation: ax² + bx + c = 0, where a ≠ 0
Given: 3x² + 9x - 2 = 0
⇒ a = 3, b = 9, c = -2
Substitute the given values into the formula and simplify:
[tex]x=\dfrac{-9\pm\sqrt{9^2-4(3)(-2)}}{2(3)}\\\\x=\dfrac{-9\pm\sqrt{81+24}}{6}\\\\x=\dfrac{-9\pm\sqrt{105}}{6}[/tex]
Therefore, the correct answer is A.
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which is the correct graph for the inequality
curved surface area of a cone = Trl, where r is the
radius and is the slant height.
The ice cream cone below is made from a piece of wafer.
Work out the area of wafer required to make the ice
cream cone.
Give your answer to 1 d.p.
2 cm
9 cm
The area of wafer required to make the ice cream cone 68.75 cm²
What is Area?The area is the amount of space within the perimeter of a 2D shape. It is measured in square units, such as cm², m², etc.
Given:
r= 2cm, l=9 cm
Surface area,
=πr(l +r)
=3.14*2(9 + 2)
= 6.25*11
=68.75 cm²
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3
O Find the perimeter of the following shape, given its curves are made from parts of circles.
Give your answers in terms of π.
4cm
4cm
4cm
The diagram is not drawn to scale.
Answer:
12pi cm
Step-by-step explanation:
The Perimeter of the full shape is the sum of the lengths of the edges of the parts. For convenience in referencing them, we'll call the large curve "[tex]curve_{big}[/tex]" and the three smaller curves "[tex]curve_1[/tex]" "[tex]curve_2[/tex]" "[tex]curve_3[/tex]" in order from left to right.
Thus, the Perimeter of the full shape can be written as an equation:
[tex]P_{overall} = Length(curve_{big})+Length(curve_1)+Length(curve_2)+Length(curve_3)[/tex]Since all of those edge lengths are curves, and the question states that all of the curves are made from parts of circles, then we need to know how to find the length of the edge of a circle.
Parts of a circle
Since values in the diagram are diameters, use the formula for the Perimeter of a circle [tex]P=\pi d[/tex] (where d is the diameter).
Let's call the diameters of each of our curves "[tex]d_{big}[/tex]" "[tex]d_1[/tex]" "[tex]d_2[/tex]" "[tex]d_3[/tex]", with the subscripts denoting which curve we're referring to.
Note that for each curve, the curve only represents half of a circle. So, to find the length of each curve, we'll need half of the full perimeter of each circle.
So for instance: [tex]Length(curve_{big})=\frac{1}{2} \pi d_{big}[/tex]
Substituting back into the main equation above:
[tex]P_{overall} = Length(curve_{big})+Length(curve_1)+Length(curve_2)+Length(curve_3)[/tex][tex]P_{overall}=\frac{1}{2} \pi d_{big} + \frac{1}{2} \pi d_{1} + \frac{1}{2} \pi d_{2} + \frac{1}{2} \pi d_{3}[/tex]
Note that all terms have common factors of "one-half" and "pi" in them. These can be factored out:
[tex]P_{overall}=\frac{1}{2} \pi (d_{big} + d_{1} + d_{2} +d_{3})[/tex]
The diameter for the large Curve, is the sum of the three small diameters, so [tex]d_{big}=12cm[/tex], and [tex]d_{1}=d_{2}=d_{3}=4cm[/tex]
Substituting and simplifying (in terms of pi):
[tex]P_{overall}=\frac{1}{2} \pi ( (12cm) + (4cm) + (4cm) + (4cm) )\\P_{overall}=\frac{1}{2} \pi ( 24cm)\\P_{overall}=12 \pi cm[/tex]
Additional Understanding
Interesting for this problem, since the diameters of the 3 small curves formed the diameter of the large curve [tex]d_{1} + d_{2} + d_{3} =d_{big}[/tex], one could make a different substitution into one of our formulas above:
[tex]P_{overall}=\frac{1}{2} \pi (d_{big} + d_{1} + d_{2} +d_{3})[/tex]
[tex]P_{overall}=\frac{1}{2} \pi (d_{big} + (d_{big}))[/tex]
[tex]P_{overall}=\frac{1}{2} \pi (2d_{big})[/tex]
[tex]P_{overall}=\pi d_{big}[/tex]
Notice that [tex]\pi d_{big}[/tex] is just the full perimeter of a circle with the big diameter.
So, if one imagined starting with a full circle with the big diameter, even though the bottom half of the circle was turned into a bunch of smaller half circles, since they were in a line along the diameter of the large circle, the full perimeter of the new shape didn't change.
The number of smaller circles doesn't need to be 3 either... as long as it goes the full distance across, right along the diameter.
*30pts*What is the value of x in the triangle?
Answer:
A.4
Step-by-step explanation:
Using the sine rule
sin(α)/A equals sin(β)/B
From the question & inserting values,
sin(90°)/8 equals sin(30°)/x
∴x equals[tex]\frac{sin(30)}{sin(90)}[/tex]×8
∴x equals 4
You can learn more on the sine rule in case you get confused.
Answer:
A
Step-by-step explanation:
using the sine ratio in the right triangle and the exact value
sin30° = [tex]\frac{1}{2}[/tex] , then
sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{8}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
2x = 8 ( divide both sides by 2 )
x = 4
35. Use the Change of Base Formula to evaluate logs 92. Then convert logs 92 to a logarithm in base 3. Round to the n
2.810; log3 55.2
2.810; log3 21.903
1.964, log3 55.2
4.522; log3 21.903
What is the surface area of the image below?
Answer:
Step-by-step explanation:
Comment
I'm going to assume that this is not a closed figure. The top is open like a water trough for horses.
There are 2 semicircular ends which add up to 1 whole circle.
There is 1 base area. The base area has a width of one of the semicircles. It has a length of 15 cm.
Solution
2 semi circles
r = d / 2
r = 20/2
r = 10
Area = pi r^2 This area is for 2 semicircles which = 1 circle.
Area = 3.14 * 10^2
Area = 3.14 * 100
Area = 314
Trough
r = d / 2
d= 20
r = 20/2
r= 10
w = 2*pi*r / 2
w = 2*3.14 *10/2
w = 31.4 cm
L = 15 cm
Area = 15 * 31.4
Area = 471
Total Area = 785
Find the measure of the indicated angle to the nearest degree.
?
58
30
Origami is the Japanese art of paper folding. The diagram below represents an unfolded paper kabuto, a samurai warrior's helmet. Which of the following are pairs of congruent segments? Check all that apply. A. PO and ON B. FR and NR C. NO and NM D. RC and RO E. DV and EW
Option (B) FR and NR, option (C) NO and NM, and option (D) RC and RO are correct.
What is congruence in geometry?The measurements of the sides and angles of two or more geometrical figures determine their congruence. For example triangle's size is determined by its three sides, and its shape is determined by its three angles.
We have:
The diagram represents an unfolded paper kabuto, a samurai warrior's helmet.
Unfolded paper can be seen in the provided figure. The sheet is square.
The diagonals, in this case, are FN and AK, and the midline is CM and OI. At point R, all of these lines converge.
FR ≅ NR
AO ≅ ON
RC ≅ RO
NO ≅ NM
DV ≅ HV
Thus, option (B) FR and NR, option (C) NO and NM, and option (D) RC and RO are correct.
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Find sin
A. 12/13
B. 1
C. 13/12
D. 13/5
Answer: A. [tex]\frac{12}{13}[/tex]
Step-by-step explanation:
The best way to remember this is SOH-CAH-TOA. For sin, it would be the opposite angle over the hypotenuse. The opposite angle of ∠C is 24 and the hypotenuse is 26. But that isn't in the answer choices, so you'll simplify the fraction.
[tex]\frac{24}{26} =\frac{12}{13}[/tex], therefore, the answer is A.
I hope this helps! Pls mark brainliest!! :)
Terick ran 2 3of a mile in 8 minutes. It took Chad 40 minutes to run 3 1 4miles. a. If Terick runs at that speed, how long will it take him to run one mile?
The time taken for Terick to run one complete mile is determined as 12 minutes
Speed of Chad
The speed of chad is calculated as follows;
s = distance/time
s = (3.25 miles)/(40)
s = 0.08125 miles/min
Total distance ran by Terick2/3 of a mile = 8 mins
1/3 of a mile = ?
1/3 of a mile = 4mins
1 mile = 8 mins + 4 mins = 12 mins
Thus, the time taken for Terick to run one complete mile is determined as 12 minutes.
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has a slope of 2 and contains what point? y-3=2(x+4)
We know immediately that the line must pass through (-4, 3).
Warm Shelters.org received a donation of $32,000 to buy beds and dressers for its new dormitories. Each bed will cost $320.00 and each dresser will be $75.00 each. A total of 132 pieces of beds and dressers are needed. What is the percentage of dressers with respect to the number of beds?
Please HELP
Answer:
you can buy 98 beds and buy dresses by rest of the money
simplify 3 + [5n - (2-n)]
Answer:
6n+1
Step-by-step explanation:
Eliminate the parenthesis by changing the symbol of each term inside
3+[5n-2+n]
Eliminate the bracket and group similar terms
5n+n+3-2
Simplify terms
6n+1
Select the correct answer from each drop-down menu.
The function f is given by the table of values as shown below.
x 1 2 3 4 5
f(x) 13 19 37 91 253
Use the given table to complete the statements.
If function f was translated down 4 units, the _
values would be _
A point in the table for the transformed function would be _
Using translation concepts, the correct statement is given by:
If function f was translated down 4 units, the f(x) values would be subtracted by 4. A point in the table for the transformed function would be (1,9).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
A translation down 4 units means that the output values are subtracted by 4, hence the table would be given by:
x 1 2 3 4 5
f(x) 9 15 33 87 249
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Answer:
The CORRECT answer is:
1. f(x)
2. decreased by 4
3. (4, 87)
Step-by-step explanation:
Took the test
what is the fraction 2500 of 3600
Answer:
25/36
Step-by-step explanation:
put 2500 over 3600 and you get 2500/3600 but you can simplify to get 25/36 but removing the 0's
I need the answer for number 4 please!!
Answer:
-3 - false
0 - true
1 - true
2 - false
4 - true
Step-by-step explanation:
the "zeros" of a function are its x-intercepts
(because that is when the function = zero [0])
So, we can look at the x-intercepts of the graph to find the zeros:
at 0, 1, and 4 the function = 0, meaning that those are zeros of the function
hope this helps!! have a lovely day :)
please help me with this problem ! would appreciate it!!!
[tex]1) \text{ } 2^{1/2}=\sqrt{2}\\\\2) \text{ } 2^{2/3}=\sqrt[3]{2^{2}}\\\\3) \text{ } 3^{3/2}=\sqrt{3^{3}}\\\\4) \text{ } 3^{1/3}=\sqrt[3]{3}[/tex]
Answer: correct radical forms are:
[tex]2^\frac{1}{2} = \sqrt{2}[/tex]
[tex]2^\frac{2}{3} = \sqrt[3]{2}[/tex]
[tex]3^\frac{3}{2} = \sqrt[]{3^3}[/tex]
[tex]3^\frac{1}{3} = \sqrt[3]{3}[/tex]
Step-by-step explanation:
Radical form : If n is a positive integer that is greater than 1 and a is a real number then, [tex]\sqrt[n]{a} =a^\frac{1}{n}[/tex] where n is called the index, a is called the radicand, and the symbol √ is called the radical.
therefore,
radical form of given values are :
[tex]2^\frac{1}{2} = \sqrt{2}[/tex]
[tex]2^\frac{2}{3} = \sqrt[3]{2}[/tex]
[tex]3^\frac{3}{2} = \sqrt[]{3^3}[/tex]
[tex]3^\frac{1}{3} = \sqrt[3]{3}[/tex]
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...............
................
Let the numbers be x and x/7
Now
sum=824x+x/7=8248x/7=8248x=824(7)8x=5768x=721The numbers are
721 and 721/7=103Answer:
7x+X=824
8X/8=834/8
x=108
Step-by-step explanation:
hope I helped
If the line segment AB is on a number line, and point A is at 6 and Point B is at 13, then the length of AB is ____.
Answer:
7
Step-by-step explanation:
The length of AB is the distance between A and B which is B-A -> 13-6= 7
Give the slope and the y-intercept of the line y=10x+9
Answer:
Slope: 10
Y-intercept: +9
Step-by-step explanation:
An equation written in slope-intercept form is y=mx+b. "m" is your slope and b is your y-intercept.
Fig. R24 shows a flower vase whose circular base is parallel to its circular top.
Use the dimensions in the figure to calculate the curved surface area of the flower vase
Answer:
operant conditioning and schedules of reinforcement
Mr.Baker is making a box using all of a 48-inch strip of oak. the box will be 14 inches wide. how long will the box be?
The length of the box made by Mr. Baker is 10-inch
Mr. Baker has strip of 48- inch long oak, by this strip he is making the rectangle box of width 14-inch.
The rectangle is 4 sided geometric shapes whose opposites are equal in lengths and all angles are about 90°.
As Mr. Baker has a strip that is 48-inch long and he made a rectangle box with it.
The width of the box = 14 inches
now the length of the box = (total length of the strip - 2* width of the box)/2
⇒ length of the box = (48 - 2*14)/2
⇒ length of the box = 10 inches
Thus the Mr. Baker made the box which is 10 inches long.
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9x+9y=9. Solve for Y
Answer:
y = 1 - x
Step-by-step explanation:
9x + 9y = 9 ( divide through by 9 )
x + y = 1 ( subtract x from both sides )
y = 1 - x
Answer:
y = 1 - x
Step-by-step explanation:
9x + 9y = 9
First, take 9x to the right side.
9y = 9 - 9x
9y = 9 ( 1 - x )
Divide both sides by 9.
y = 1 - x
Find f(x) and g(x) so that the
function given can be described
as y = f(g(x)).
y = e^sin x
Answer:
g(x) = sin(x)
f(x) = e^x
Step-by-step explanation:
Answer:
Step-by-step explanation:
[tex]f(x)=e^x\\g(x)=sin~x\\y=f(g(x))=f(sin~x)=e^{sin~x}[/tex]
A cooler contains five colas, seven root beers, and four ginger ales. Three people grab a drink at random, one at a time. a) What is the probability that the first person grabs a cola, the second person grabs a ginger ale, and the third person grabs b) What is the probability that the third person grabs a root beer given that the first two grabbed colas?
The probabilities are:
a) P = 0.024
b) P = 0.5
How to get the probabilities?
a) The probability that the first person grabs a cola is given by the quotient between the number of colas and the total number of drinks.
There are 5 colas, and 16 drinks in total, so the probability is:
P = 5/16
The second person needs to grab a ginger ale, now there are 15 drinks on the cooler (because one cola was taken) so this time the probability is:
Q = 4/15
Finally, the third person grabs (this is incomplete, I will assume that is another cola), this probability is:
Z = 4/14
The joint probability is:
prob = P*Q*Z = (5/16)*(4/15)*(4/14) = 0.024
b) If the two first persons grabed colas, then in the cooler we have:
3 colas, 7 root beers, and 4 ginger ales, for a total of 14 drinks.
Then the probability of grabbing a root beer is:
p = 7/14 = 1/2 = 0.5
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You must make 3 shots in a row to win the fairs basketball game. The hoop is uneven and the backboard curved. Only 5 players out of 100 win the game. What percentage of players do not win.
Answer:
95%
Step-by-step explanation:
5 player won, meaning 95 player didn't.
This means that 95% of the players didn't win.
What is:
[tex]5x + 5 = 5 \times (10 \div 5)[/tex]
Solve this equation.
Answer:
x = 1
Step-by-step explanation:
To solve an equation for a variable, we need to isolate (get the variable alone on one side)
(the order of the following was determined by PEMDAS)
5x + 5 = 5 (10 ÷ 5) [simplify inside parentheses]
5x + 5 = 5 (2)
5x + 5 = 10
- 5 -5 [subtract 5 from both sides to isolate x]
5x = 5
÷5 ÷5 [divide both sides to get x]
x = 1
hope this helps!!
solve for x -
[tex]\bold{x {}^{2} + 5x + 6 = 0}\\\\[/tex]
ty! ~
The solution of the given quadratic equation is x=-2 or x=-3.
The given quadratic equation is x²+5x+6=0.
What are different methods to solve a quadratic equation?The different methods of solving quadratic equations are factoring, completing the square or using the quadratic formula.
By using the splitting middle term method we can solve x²+5x+6=0.
That is, x²+2x+3x+6=0
⇒x(x+2)+3(x+2)=0
⇒(x+2)(x+3)=0
⇒(x+2)=0, (x+3)=0
⇒x=-2 or x=-3.
Therefore, the solution of the given quadratic equation is x=-2 or x=-3.
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A family originally bought a home for $654,030. Now, a few years later, the home is worth
$457,821. What was the percent of decrease in its value?
Answer:
30%
Step-by-step explanation:
First we find out the difference between them:
$654,030 - $457,821 = $196,209
Then we compare it with the original price:
196,209/654,030 = 0.3
Since 0.3 is 30%, that is 30% decrease in value.
