Answer: I and III
Step-by-step explanation:
The graphs of f and g have the same axis of symmetry. The graph of f has a maximum point, and the graph of g has a minimum point. The graph is a result of a reflection of the graph pf g across the x-axis. The correct options are 1, 3, and 4.
What is quadratic function?A quadratic polynomial in mathematics is a polynomial of degree two in one or more variables. The polynomial function defined by a quadratic polynomial is known as a quadratic function.
We can use the fact that the points (3,2) and (7,2) are on the graphs of both functions to find out which of the given statements are true.
Let's start by using the fact that the graphs of the functions f and g pass through the points (3,2) and (7,2).
Since the y-coordinate is the same for both points, we can set the equations of the functions equal to 2 and solve for the unknown coefficients.
For the downward-opening quadratic function f, the equation is of the form:
[tex]f(x) = a(x - h)^2 + k[/tex]
Where (h,k) is the vertex of the parabola. Since f opens downward, the coefficient a is negative.
Using the point (3,2), we get:
[tex]2 = a(3 - h)^2 + k[/tex]
Using the point (7,2), we get:
[tex]2 = a(7 - h)^2 + k[/tex]
Subtracting the second equation from the first, we get:
[tex]0 = a[(3 - h)^2 - (7 - h)^2][/tex]
Simplifying this expression, we get:
0 = a[(3 - h + 7 - h)(3 - h - (7 - h))]
0 = a[-4(h - 5)]
Since a is non-zero (otherwise the parabola is not quadratic), we get:
h = 5
Plugging in h = 5 and using one of the equations above, we can solve for k:
[tex]2 = a(3 - 5)^2 + k[/tex]
2 = 4a + k
k = 2 - 4a
Therefore, the equation of the quadratic function f is:
[tex]f(x) = a(x - 5)^2 + (2 - 4a)[/tex]
Using the same method for the upward-opening quadratic function g, we get:
[tex]g(x) = b(x - 5)^2 + (2 + 4b)[/tex]
Where b is positive.
Now, let's check which of the given statements are true:
The graphs of f and g have the same axis of symmetry.
Since the vertex of f is (5, 2 - 4a) and the vertex of g is (5, 2 + 4b), the x-coordinate of the axis of symmetry for both functions is 5. Therefore, statement 1 is true.
The graphs of f and g have the same x-intercepts.
The x-intercepts of f are given by:
[tex]0 = a(x - 5)^2 + (2 - 4a)\\4a = a(x - 5)^2[/tex]
x - 5 = ±√(4/a)
x = 5 ± 2√(a)
The x-intercepts of g are given by:
[tex]0 = b(x - 5)^2 + (2 + 4b)[/tex]
-4b = [tex]b(x - 5)^2[/tex]
x - 5 = ±√(-4/b)
x = 5 ± 2i√(b)
Thus, since a and b have opposite signs, the x-intercepts of f and g are different. Therefore, statement 2 is false.
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surface area of a rectangular prism with length 11 meters, width 5 meters, and height 14 meters
Answer:
Step-by-step explanation:11
Can you guys help me find the area of this shape. I've literally tried everything and got it wrong.
Answer:
110 square centimeters.
Step-by-step explanation:
The area for a trapezoid can be figured out with the equation (a + b)h/2.
(9 * 5) + (9 + 4)10/2 {Work inside the parentheses first.}
45 + (13)10/2 {Divide 10 by 2 to get 5.}
45 + 13(5) {Multiply 13 by 5 to get 65.}
45 + 65 {Add 45 & 65 to get 110.}
110 square centimeters.
The area of the figure is 110 square centimeters.
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Answer:
A
Step-by-step explanation:
It will always go down if you put more wait.
Can I have Brainliest
how do you solve 27.5% of 88
answer:
im getting different answers so wait ill do it myself
Step-by-step explanation:
What is tip would you give to your waiter if your bill was $56.50 and the tip is 20% of the bill
$11.30
Step-by-step explanation:
First, convert the 20% to an actual number that can be used in a calculation.
For percents, this is always done by simply dividing the percent (in this case 20%) by 100%.
So, the conversational term "20%" becomes 20% / 100% = 0.20 in terms of a real mathematical number.
Second, you need to find out what 20% of your $56.50 meal cost is. This is always done by multiplying 0.20 by $56.50, or
0.20 x $56.50 = $11.30
So, the amount of tip you are going to leave is $11.30.
This makes the total cost of your meal (to write on your charge slip or other payment)
$56.50 + $11.30 = $67.80.
60 children were asked to chose their favourite vegetable from 5 options. Work out the number of children who chose each vegetable .
Answer:
carrots and cauliflower: 6
peas: 12
cabbage, sweetcorn: 18
Step-by-step explanation:
10 percent is 1/10, which is 6/60. Multiplied by two it's 12/60. Multiplied by 3 is 18/60.
Find m<1, m<2, and m<3
Answer:
<1 = 113
<2 = 67
<3 = 113
Step-by-step explanation:
m<2 = 67 (because of vertical angles)
<1 + 67 = 180
<1 = 113
<1 = <3 because of vertical angles
20% of ______ is 120
Answer:600
Step-by-step explanation:
Answer:
20
___ x X = 120
100
x100 x 100
20x = 120
divide by 20 on both sides.
x = 6
Problem PageQuestion A theater group made appearances in two cities. The hotel charge before tax in the second city was $1500 lower than in the first. The tax in the first city was 10%, and the tax in the second city was 8%. The total hotel tax paid for the two cities was $825. How much was the hotel charge in each city before tax?
Answer:
the hotel charge in the first city is $5250 while the hotel charge in the second city is $3750
Step-by-step explanation:
Let a represent the charge in the first city before tax and b represent the charge in the second city before tax.
Therefore tax in first city = 10% of a = 0.1a
Tax in second city = 8% of b = 0.08b
From the total tax as $825, hence:
0.1a + 0.08b = 825 (1)
The hotel charge before tax in the second city was $1500 lower than in the first. This gives the equation:
b = a - 1500
a - b = 1500 (2)
To find a and b, solve equation 1 and 2 simultaneously. Multiply equation 2 by 0.1 and subtract from equation 1:
0.18b = 675
b = $3750
a = b + 1500 = 3750 + 1500 = 5250
a = $5250
Therefore, the hotel charge in the first city is $5250 while the hotel charge in the second city is $3750
Please help asap I need this
Answer:
y= x+4
y=–4–2x
Step-by-step explanation:
using the formula (x–x1)/(x1–x2)= (y–y1)/(y1–y2)
Three paintings are shaped like an 8-foot square a 7-foot by 4-foot rectangle and a triangle with 6-foot base and height of 7 feet. If those paintings are hung together on the outside of the building how much of the building s wall they cover together ?
Answer:
113 square feet
Step-by-step explanation:
the total area covered can be determined by adding the area of the rectangle, triangle and square together
Area of a square = length² = 8² = 64 ft²
Area of a rectangle = length x width = 7 x 4 = 28 ft²
Area of a triangle = 1/2 x base x height = 1/2 x 6 x 7 = 21 ft²
64 + 28 + 21 = 113 ft²
Question below...15 points.
Answer: i think its c
Step-by-step explanation:
but im not totally sure
Answer:
B. s = 9 inches
Step-by-step explanation:
We are given a square with a perimeter of 36 inches, along with a key that the perimeter is given through the equation P = 4s, where "s" stands for the length of one side. We are then asked to find which number s is.
Perimeter is when you add 4 sides altogether, in our case we have 36 inches as our perimeter. Since 4s is the main factor as to how we got 36 inches, we need to set up one system equation.
P = 4s
36 = 4s
Now we need to find a number that multiplies with 4 to get us 36, simple as that. Let's get s alone to retrieve our answer :
36 = 4s
Divide 4 from both sides :
9 = s
s = 9
For an upcoming election, 500 registered voters were surveyed on a tax increase. 43% were for a tax increase and 51% were against a tax increase. The margin of error was 6%. What is an accurate conclusion from the poll?
a. Against a tax increase will win because it is above 50%.
b. The nal result is undecided because of the margin of error.
c. The nal result is undecided because percentages do not add up to 100%.
d. Against a tax increase will win because the margin of error will increase their percentage.
9/2 - 23/9=? plss help
Answer:
35/ 18
(Decimal: 1.944444)
Step-by-step explanation:
Answer
Step-by-step explanation:35/18
I WILL MARK BRAINLIEST! A parabola opening up or down has vertex (0,3) and passes through (4,7). Write its equation in vertex form.
Ok...so we have this........
y = ax2 + 4 ....... and we need to find "a"
So we have
-1 = a(-10)2 + 4
-5 = a (100)
(-1/20) = a ....... So we have ..........
y = (-1/20)(x- 0)2 + 4 or just (-1/20)x2 + 4
Note that this parabola opens downward...That makes sense since the vertex is above the x axis and the parabola passes through a point below the x axis.
Hope This Helped!
I couldn't copy paste the equation on here, so i attached it in pictures.
Helpppp asapppp I’ll give you a lot of points
Answer:
[tex]x = \frac{5a-2} {7+5a}\\[/tex]
Step-by-step explanation:
Given the expressions
[tex]x = \frac{5}{9y+5}....1\\y = \frac{5}{5a-2} ...2[/tex]
Substitute 2 into 1
[tex]x = \frac{5}{9(\frac{5}{5a-2} )+5} \\x = \frac{5}{(\frac{45}{5a-2} )+5} \\x = \frac{5}{\frac{45+5(5a-2)}{5a-2} } \\x= \frac{5}{\frac{35+25a}{5a-2} }\\x = \frac{5(5a-2)} {35+25a}\\x = \frac{5(5a-2)} {5(7+5a})\\\\x = \frac{5a-2} {7+5a}\\[/tex]
Someone please tell me the answers to this please I beg you
A triangle has two 12centimeter sides
. What are the possible lengths of third side?
Answer:
Step-by-step explanation:
if the two sides are 12, the third will have to be shorter so it could be:
( 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 )
good luck!can you choose me brainliest? :D
I rlly need help with this
You need to give more info so like show more of the question
from edgunuity please help asap! image attached above
When rolling a number cube, what is the probability of rolling a 2 or an even number. Express your answer as a fraction in lowest terms
Answer:
https://www.sketchywebsite.net/
Step-by-step explanation:
Identify the variable expression that is not a polynomial.
O A. 3 - 2
O B. 13
O C. y + 23
O D. x3
Answer:
the correct answer is d. x^3
D + -4 = 12
how do i find d?
Answer: D=16
Add 4 to both sides
D=16
Answer:
Answer: 16
Step-by-step explanation:
Do 12 -(-4 to get D
12 -(-4 = 16
8/9 ÷ 2/3 - 5/6
step by step fast
Answer:
is 1/2 or .5
Step-by-step explanation:
What is the PE of an object that is 15kg that is 5.0 M above the ground?
Answer:
735 JStep-by-step explanation:
The potential energy of a body can be found by using the formula
PE = mgh
where
m is the mass
h is the height
g is the acceleration due to gravity which is 9.8 m/s²
From the question we have
PE = 15 × 9.8 × 5
We have the final answer as
735 JHope this helps you
Jerry has four jackets in his closet. Without looking, he reached into his closet, pulled out a jacket, and then put it back in the closet. What is the probability that Jerry will randomly select the same jacket a second time?
Answer:
1%
Step-by-step explanation:
.
In the diagram below, BC = QR = x, AC = PR = y, and triangle PQR is a right
triangle. Use the drop-down menus to complete the proof that if the equation
22 + y2 = z2 is true of the side lengths in triangle ABC, then triangle ABC must be a right
triangle.
P
y у
y
B
R
х
Q
x2 + y2 = 22
Triangle PQR is a right triangle
Click the arrows to cho
from each menu.
Triangle PQR is given to be a right triangle, so the Pythagorean theorem can be used to
Applying the Pythagorean theorem, we have ΔPQR ≅ ΔABC. then we would have: ∠ACB = ∠PRQ = 90°
What is the Pythagroean Theorem?The pythagorean theorem states that the square of the longest side (hypotenuse) of a right triangle is always equal to the sum of the squares of the other two sides (legs) of the right triangle.
Since we know that ΔPQR is a right triangle, then:
x² + y² = PQ²
We are also given that x² + y² = z², so by substitution, we have:
z² = PQ², which makes both triangles have corresponding congruent sides. Therefore, ΔPQR ≅ ΔABC.
Using the corresponding parts of the congruent triangles, we can conclude that: ∠ACB = ∠PRQ = 90°.
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Can somebody help me??
Can someone pleaseeee help and if you’re correct i’ll give brainliest
Answer:
2,827.43
Step-by-step explanation:
HELP ASAP
What is the 10th term in the geometric sequence below?
−4, 12, −36, 108, ...
a)-236196
b)-78732
c)236196
d) 78732
Answer:
78732
Step-by-step explanation:
