WILL MARK BRAINLIEST!!! PLZ HELP! The following graph describes function 1, and the equation below it describes function 2. Determine which function has a greater maximum value, and provide the ordered pair. Function 1 Function 2 f(x) = −x2 + 4x + 1 Function 1 has the larger maximum at (4, 1). Function 1 has the larger maximum at (1, 4). Function 2 has the larger maximum at (2, 5). Function 2 has the larger maximum at (3, 2).
Answers
Answer:
C: Function 2 has the larger maximum at (2, 5).
Step-by-step explanation:
We are given two functions, with Function 1 being described by the graph and Function 2 given by the function:
[tex]f(x)=-x^2+4x+1[/tex]
Notice that the leading coefficient of Function 2 is negative. The graph of Function 1 is curving downwards. So, both functions will have maximum values.
Recall that for a parobala, the maximum (or minimum) values is the y-value of the vertex point. So, let's find the vertex for each function.
For Function 1, we can see that the vertex is at (4,1). Thus, its maximum value is y = 1.
For Function 2, we will need to work out the vertex. Recall that the vertex is given by:
[tex]\displaystyle \left(-\frac{b}{2a},f\left(-\frac{b}{2a}\right)\right)[/tex]
Function 2 is defined by:
[tex]f(x)=-x^2+4x+1[/tex]
Therefore, a = -1, b = 4, and c = 1.
Find the x-coorindate of the vertex:
[tex]\displaystyle x=-\frac{(4)}{2(-1)}=2[/tex]
Substitute this back into the function to find the y-coordinate.
[tex]f(2)=-(2)^2+4(2)+1=5[/tex]
So, the vertex of Function 2 is (2,5). Therefore, the maximum value of Function 2 is y = 5.
Since 5 is greater than 1, the maximum value of Function 2 is greater.
The answer is choice C.
Related Questions
Factor completely x3 + 8x2 − 3x − 24. (x − 8)(x2 − 3) (x + 8)(x2 + 3) (x − 8)(x2 + 3) (x + 8)(x2 − 3)
Answers
Answer:
(x + 8) (x² - 3)
Step-by-step explanation:
Given:
x³ + 8x² - 3x - 24
Find:
Factors
Computation:
x³ + 8x² - 3x - 24
x²(x + 8) -3(x + 8)
(x + 8) (x² - 3)
Factor of the given equation is (x + 8) (x² - 3)
Answer:
(x + 8) (x² - 3)
Step-by-step explanation:
A classroom floor has an area of
(30x^3 + 8x^2, with a width of 2x feet.
What is the length of the floor?
Answers
Answer:
15x² + 4x feet
Step-by-step explanation:
We need to calculate (30x³ + 8x²) / 2x.
(30x³ + 8x²) / 2x
= 30x³ / 2x + 8x² / 2x
= 15x² + 4x
which of the following statements must be true about this diagram ? check ALL that apply
Answers
Answer:
Check A, B and DStep-by-step explanation:
A. m∠4 = 180° - m∠3
m∠1 = 180° - (m∠3 + m∠2)
m∠3 < m∠3 + m∠2 ⇒ m∠4 >m∠1
B. m∠4 = 180° - m∠3
m∠2 = 180° - (m∠3 + m∠1)
m∠3 < m∠3 + m∠1 ⇒ m∠4 >m∠2
C. Not necessarily {could be but not always}
D. m∠4 = 180° - m∠3
m∠1 + m∠2 + m∠3 = 180° ⇒ m∠1 + m∠2 = 180° - m∠3 = m∠4
E. m∠3 = m∠1 + m∠2 only if m∠3 = 90°
F. Not necessarily. {Could be but also could not be. In the picture is, but we don't know if the diagram is accurate or just approximate.}
Cody is a lifeguard and spots a drowning child 40 meters along the shore and 70 meters from the shore to the child. Cody runs along the shore for a while and then jumps into the water and swims from there directly to the child. Cody can run at a rate of 4 meters per second and swim at a rate of 1.1 meters per second. How far along the shore should Cody run before jumping into the water in order to save the child? Round your answer to three decimal places.
Answers
Answer:
Cody should run approximately 19.978 meters along the shore before jumping into the water in order to save the child.Thus,
Step-by-step explanation:
Consider the diagram below.
In this case we need to minimize the time it takes Cody to save the child.
Total time to save the child (T) = Time taken along the shore (A) + Time taken from the shore (B)
The formula to compute time is:
[tex]time=\frac{distance}{speed}[/tex]
Compute the time taken along the shore as follows:
[tex]A=\frac{x}{4}[/tex]
Compute the time taken from the shore as follows:
[tex]B=\frac{\sqrt{70^{2}+(40-x)^{2}}}{1.1}[/tex]
Then the total time taken to save the child is:
[tex]T=\frac{x}{4}+\frac{\sqrt{70^{2}+(40-x)^{2}}}{1.1}[/tex]
Differentiate T with respect to x as follows:
[tex]\frac{dT}{dx}=\frac{d}{dx}[\frac{x}{4}]+\frac{d}{dx}[\frac{\sqrt{70^{2}+(40-x)^{2}}}{1.1}][/tex]
[tex]=\frac{1}{4}-\frac{1}{1.1}\cdot \frac{(40-x)}{\sqrt{70^{2}+(40-x)^{2}}}[/tex]
Equate the derivative to 0 to compute the value of x as follows:
[tex]\frac{dT}{dx}=0[/tex]
[tex]\frac{1}{4}-\frac{1}{1.1}\cdot \frac{(40-x)}{\sqrt{70^{2}+(40-x)^{2}}}=0\\\\\frac{1}{1.1}\cdot \frac{(40-x)}{\sqrt{70^{2}+(40-x)^{2}}}=\frac{1}{4}\\\\4\cdot (40-x)=1.1\cdot [\sqrt{70^{2}+(40-x)^{2}}]\\\\\{4\cdot (40-x)\}^{2}=\{1.1\cdot [\sqrt{70^{2}+(40-x)^{2}}]\}^{2}\\\\16\cdot (40-x)^{2}=1.21\cdot [70^{2}+(40-x)^{2}}]\\\\16\cdot (40-x)^{2}-1.21\cdot (40-x)^{2}=5929\\\\14.79\cdot (40-x)^{2}=5929\\\\(40-x)^{2}=400.88\\\\40-x\approx 20.022\\\\x\approx 40-20.022\\\\x\approx 19.978[/tex]
Thus, Cody should run approximately 19.978 meters along the shore before jumping into the water in order to save the child.
Dante is baking two different recipes, cookies and brownies. The cookie recipe requires 1.5 cups of sugar, and the brownie recipe requires 1.25 cups of sugar. Write an addition equation to represent the total amount of sugar Dante needs. Enter your answer as an addition equation, like this: 42+(-53)=-11
Answers
Answer:
2.75 cups of sugar
Step-by-step explanation:
Hello!
To find the total amount of sugar Dante needs we need to add the amount need for each recipe
Cookie recipe needs 1.5 cups
Brownie recipe needs 1.25 cups
1.5 + 1.25 = 2.75 cups of sugar
The answer is 2.75 cups of sugar
Hope this helps!
Answer:
the answer is 1.5+1.25=1.75
Step-by-step explanation:
i just added them together
your welcome ( it also depends on how many times he uses the recipes)
Which property is shown in the matrix addition below?
5
-1
0
5
-7
0.4
0
-7
0
0.4
+
+
+
6.2
-8.5
-9.9
6.2
-9.9
-8.5
12
0
2
12
0
2
inverse property
identity property
commutative property
associative property
Help please!
Answers
Answer:
associative property
The solution is, property is shown in the matrix addition below is
associative property.
Here, we have,
The property shown in the given matrix addition is associative property.
Let's define associative property first,
The Associative Property of Addition for Matrices states :
Let A , B and C be m×n matrices .
Then, (A+B)+C=A+(B+C) .
Associative Law of Addition of Matrix:
Matrix addition is associative. This says that, if A, B and C are Three matrices of the same order such that the matrices B + C, A + (B + C), A + B, (A + B) + C are defined then A + (B + C) = (A + B) + C.
Since P and Q are of the same order and pij = qij then, P = Q.
Here, from the given information,
we get, A , B and C be 4×1 matrices,
and, (A+B)+C=A+(B+C)
So, The solution is, property is shown in the matrix addition below is
associative property.
To learn more on matrix click:
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What is the solution for 5x-9 is less than or equal to 21
Answers
Answer:
Step-by-step explanation:
5x - 9 <= 21
5x <=30
x <= 6
A geometric series has a common ratio of (-2) and the first term is 3.
Show that the sum of the first eight positive terms of the series is 65 535.
Answers
Answer:
see explanation
Step-by-step explanation:
The sum to n terms of a geometric series is
[tex]S_{n}[/tex] = [tex]\frac{a_{1}(r^{n}-1) }{r-1}[/tex]
where a₁ is the first term and r the common ratio
Given a₁ = 3 and r = - 2 , then
3 × - 2 = - 6
- 6 × -2 = 12
12 × - 2 = - 24
- 24 × - 2 = 48
48 × - 2 = - 96
- 96 × - 2 = 192
The positive terms are in a geometric progression
3, 12, 48, 192, ....
with a₁ = 3 and r = 12 ÷ 3 = 48 ÷ 12 = 4 , then
S₈ = [tex]\frac{3(4^{8}-1) }{4-1}[/tex] = [tex]\frac{3(65536-1)}{3}[/tex] = 65536 - 1 = 65535
BRAINLIEST
HOW CAN POSTULATES AND THEOREMS RELATING TO SIMILAR AND CONGRUENT ANGLES BE USED TO WRITE A PROOF?
Answers
Answer:
How can postulates and theorems relating to similar and congruent triangles be used to write a proof? If the three sets of corresponding sides of two triangles are in proportion, the triangles are similar. ... If the three sets of corresponding sides of two triangles are in proportion, the triangles are similar.
Step-by-step explanation:
Hope this helps :D good luck!!
What is the value of this expression when c = -4 and d = 10?
Answers
Answer:
[tex]\Large \boxed{\mathrm{\bold{B. \ 9}}}[/tex]
Step-by-step explanation:
Plug in c = -4 and d = 10 for the expression.
1/4(-4³ + 10²)
Evaluate the expression.
1/4(-64 + 100)
1/4(36)
36/4 = 9
Answer:
[tex]\huge\boxed{B. \ \ 9}[/tex]
Step-by-step explanation:
1/4 (c³ + d²)
Given that c = -4 and d = 10
1/4 ( -4³ + 10²)
1/4 ( -64+100)
1/4 ( 36 )
=> 9
Quina is cooking fish for a group of travelers quina has 78 huge fish and each fish can feed 3 travelers. how many travelers can Quina feed?
Answers
Answer:
234 people
Step-by-step explanation:
1 fish = 3 people
Multiply each side by 78
1*78 = 3 *78
78 fish = 234 people
Answer:
234 traveling people
Step-by-step explanation:
78 times 3 equals 234
Jaden’s teacher had 4 boxes of pens that each contained y pens. She took 6 pens out of one of the boxes and told her 17 students to divide the remaining pens equally among themselves. Which expression shows the number of pens each student got?
Answers
Answer:
x = (4y-6)/17
where x is the number of pens each student got.
Step-by-step explanation:
No. of boxes = 4
no. of pen in 1 box = y
total no, of pens in 4 box = No. of boxes *no. of pen in 1 box = 4y
No. of pen took away by Jaden's teacher = 6
no. of pens left = 4y - 6
This, 4y - 6 pen has to be divided among 17 students.
Let each student get x pen
thus, total no. of pen got by 17 student = 17x
This, 17x should be equal to total no. of pens available which is 4y-6
17x = 4y-6
=> x = (4y-6)/17
Thus, expression to represent number of pens each student got
is x = (4y-6)/17
Answer:
4y-6/17
Step-by-step explanation:
Jaden’s teacher had 4 boxes of pens that each contained y pens.
Number of boxes of pen = 4
Number of pens per box = y
Total number of pens = 4 x y = 4y
She took 6 pens out of one of the boxes told her 17 students to divide the remaining pens equally among themselves.
Total number of pens left = 4y - 6
Number of students = 17
A united states presidential coin is made from an alloy of 4 metals-copper, zinc, manganese, and nickel- with weights in the ratio of 177:12:7:4 respectively. The coin weighs a total of 8 grams. What is the weight of the zinc in this coin?
Answers
Answer:
0.32 grams
Step-by-step explanation:
ratio of weight of -copper, zinc, manganese, and nickel = 177:12:7:4
let the
weight of copper = 177x
weight of zinc = 12x
weight of manganese = 7x
weight of nickel = 4x
Total weight of this alloy in terms of x = 177x + 12x+ 7x + 4x = 300x
given weight of alloy = 8 grams
thus,
weight of this alloy in terms of x =given weight of alloy
300x = 8 grams
x = 8/300 grams =
weight of zinc = 12x = 12 * 8/300 grams = 96/300 grams = 0.32 grams
You land a job as an police officer. Your salary for the 1st year is $43,125. You will receive a 7% increase every year. How much will your salary be at the start of year six?
Answers
Answer:
Salary after 5 year(A) = $60,485 (Approx)
Step-by-step explanation:
Given:
Staring salary(P) = $43,125
Growth rate(r) = 7%
Number of year (n) = (6-1) = 5
Find:
Salary after 5 year(A)
Computation:
[tex]A=P(1+r)^n \\\\ A = 43125(1+0.07)^5 \\\\ A = 60485[/tex]
Salary after 5 year(A) = $60,485 (Approx)
Ethan bought 4 packages of pencils. After he gave 8 pencils to his friends, he had 40 pencils
left over. How many pencils were in each package? Use the drop-down menus to solve the
problem arithmetically and algebraically.
Answers
Answer:
12
Step-by-step explanation:
Because you add 8 to the 40 which is 48 then divide equaling 12
Answer:
12
Step-by-step explanation:
40+8=48
48/4=12
If x^a=y^b=z^c and y^2=zx ,show that :. 1 by a + 1 by c = 2 by b.
Answers
Answer:
1/a + 1/c = 2/b
Step-by-step explanation:
.......................
A local museum charges $25 per adult and $12 per child for admission fees. At the end of a day, the museum made $9,014 in total admission revenue, not including sales tax, and had a total of 450 guests. The system of equations below can be used to model the number of guests that were children, x, and the number of guests that were adults, y.
Answers
Answer:
Answer on Edmentum! :)
Step-by-step explanation:
Hope this helps!
The number of children were 172 and number of adults were 278.
What is linear equation?An equation that makes a straight line when it is graphed.
Given that, A local museum charges $25 per adult and $12 per child for admission fees. At the end of a day, the museum made $9,014 in total admission revenue, not including sales tax, and had a total of 450 guests
According to question,
12x+25y = 9014
x+y = 450
Solving using elimination method, we get,
x = 172 and y = 278
Hence, The number of children were 172 and number of adults were 278.
For more references on linear equation, click;
https://brainly.com/question/11897796
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Select the graph of the solution. Click until the correct graph appears.
|x| = 2
Answers
Answer:
the question seems incomplete or maybe am unable to solve it
Answer:
the number line with the clear circles
Step-by-step explanation:
whats the factored form of 6x 2 - 8x - 8 = 0
Answers
Answer:
2(x -2)² = 0
Step-by-step explanation:
2(x² - 4x - 4) = 0
2(x -2)² = 0
x = 2
Answer:
[tex]2(3x-2)(x+2)=6x^2-8x-8[/tex]
The factored form of [tex]6x^2-8x-8=0[/tex] is [tex]2(3x-2)(x+2)=0[/tex]
Step-by-step explanation:
[tex]6x^2-8x-8=0[/tex]
The way the quadratic equation was given, we can't have a factored form in the format: [tex](ax-b)(cx+d)[/tex]
First, divide both sides by 2
[tex]3x^2-4x-4=0[/tex]
Now, it is about thinking. From the equation, we will get something in the format: [tex](ax-b)(cx+d)[/tex]
Let's expand this: [tex](ax-b)(cx+d) = acx^2+adx-bcx-bd[/tex]
From here, we can give some values for those variables, based on the quadratic equation [tex]3x^2-4x-4=0[/tex]:
[tex](3x-b)(x+d) = 3\cdot 1\cdot x^2+3dx-b\cdot 1 \cdot x-bd= \boxed{3x^2+3dx-bx-bd}[/tex]
Once we want the middle term to be -4 and bd to be 4, we can easily evaluate the other variables.
[tex](3x-2)(x+2) = 3\cdot 1\cdot x^2+3(2)x-(2)\cdot 1 \cdot x-(2)(2)= \boxed{3x^2+6x-4x-4}[/tex]
Therefore,
[tex](3x-2)(x+2)=3x^2-4x-4[/tex]
But we are not ready yet!
This is the factored form of [tex]3x^2-4x-4=0[/tex], to get the factored form of the problem equation, just multiply the factored form we got by 2.
[tex]2(3x-2)(x+2)=6x^2-8x-8[/tex]
pls help me asap!!!!!!!!
Answers
Answer:
Center: (9,3)
Radius: 9 units
Step-by-step explanation:
[tex]x^{2} -y^{2} -18x-6y+9=0[/tex]
[tex]x^{2} -18x+81+y^{2} -6y+9=-9+81+9[/tex]
[tex](x-9)^{2} +(y-3)^{2} =81[/tex]
Center: (9,3)
[tex]r^{2} =81[/tex] → [tex]r=9[/tex]
Radius : 9 units
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OAmalOHopeO
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Please help!!! Find the length of MK
Answers
Answer:
HK = 42
HM = 23
MK = ??
23 + MK = 42
MK = 19
^^^ so you're correct :)
Let me know if this helps!
Find the area. Round to the nearest tenth.
6 ft
3 ft
12.16 ft
9.16 ft
Answers
Answer:
100.5 ft^2
Step-by-step explanation:
First find the area of the rectangle
A = l*w
A = 12.16 * 6
A =72.96 ft^2
Then find the area of the triangle
A = 1/2 bh
The base is 12 ft - 6ft = 6ft
The height is 9.16 ft
A = 1/2 ( 9.16) * 6
A = 27.48 ft^2
Add them together
27.48+72.96
100.44 ft^2
Round to the nearest tenth
100.5 ft^2
Answer:
[tex]\huge \boxed{\mathrm{100.4 \ ft^2 }}[/tex]
Step-by-step explanation:
To find the area of the shape, we can add the area of the rectangle with the area of the triangle.
Area of rectangle :
base × height
6 ft × 12.16 ft
72.96 ft²
Area of triangle :
base × height × 1/2
(12 ft - 6 ft) × 9.16 ft × 1/2
6ft × 9.16 ft × 1/2
27.48 ft²
Adding the areas.
72.96 ft² + 27.48 ft²
100.44 ft²
≈ 100.4 ft² (rounded to nearest tenth)
Msr walkers class set up an online fund with a goal to raise 1280
Answers
Answer: is brainly broken for u too??
Step-by-step explanation:
the area of a parallelogram is 48cm².if the two adjacent sides are 8cm and 6cm, find the length of its diagonal .
Answers
Answer:
10cm
Step-by-step explanation:
Assuming the shape is a rectangle since it's already stated that it's a parallelogram, and the area is stated, we can use the Pythagorean theorem to find the length
[tex]a^{2} +b^2=c^2[/tex], where c will be the length
isolate c
[tex]c^2=a^2+b^2[/tex]
[tex]c=\sqrt{a^2+b^2}[/tex]
substitute for a and b
[tex]c=\sqrt{8^2+6^2}[/tex]
[tex]c=\sqrt{64+36}[/tex]
[tex]c=\sqrt{100}[/tex]
[tex]c=10[/tex]
1. Why is f(x)=(3x+13)2+89 not the vertex form of f(x)=9x2+2x+1? 2. What is the vertex of the parabola with the equation y=(x−2)2+10?
Answers
Answer:
Step-by-step explanation: u hv 2 make a table for x and y and put in #'s like 1,2,3,4 so u get 1 side of the parabola. x-1, y-11/x-2,y-11/x-3,y-11/x-4,y-14; here u c that u have 2 y's=11 so the points between are the Vertex Points of (2,10)
X has a coefficient, the vertext is (2,10)
2 divided by 3 + 2 divedes by 3 +3 divided by 3 =?
Answers
Answer:
1/5
Step-by-step explanation:
1/5
2/3+3/3+4/3
=2/5*3/6
= 1/5
I'm not sure.
Answer:
The answer should be 0.022
The distance of planet Mercury from the Sun is approximately 5.8. 107 kilometers, and the distance of planet Venus from the Sun is 1.1. 10 kilometers. About how many more kilometers is the
distance of Venus from the Sun than the distance of Mercury from the Sun?
Answers
Answer:
I would say about 5 times but I am not sure so if it is wrong am sorry.
Solve without calculator log54 base 10
Answers
Step-by-step explanation:
log54 = log(2×3³)
= log2 + log3³
= log2 + 3log3
does it matter in what order we divide our our prime factors explain
Answers
Answer:
No, it does not matter.
Step-by-step explanation:
In prime factorization there is only one way to be factored. Once these numbers are broken down, into prime numbers you will get the same result no matter what list of prime numbers you use and what order you use them in.
A beach is 7.3 miles wide and 30 miles long. If one inch of rain falls on this beach, how many cubic feet of rain fell in this area? Hint: convert units to feet first.
Answers
Answer:
Step-by-step explanation:
volume=7.3×1760×3×30×1760×3×1/12=73×176×90×440=508780800 ft³
Answer:
508,780,800 ft³ of rain
Step-by-step explanation:
In order to do the computation, we need to express all the given lengths in feet.
recall that 1 mile = 5280 feet
hence,
width = 7.3 miles = 7.3 x 5280 = 38,544 feet
length = 30 miles = 30 x 5280 = 158,400 feet
also recall that 1 inch = 1/12 feet
hence,
depth of rainfall = 1 inch = 1/12 feet
Volume of rain = width of beach x length of beach x depth of rainfall
= 38,544 x 158,400 x (1/12)
= 508,780,800 ft³ of rain