The following graph describes function 1, and the equation below it describes function 2:
Function 1
graph of function f of x equals negative x squared plus 8 multiplied by x minus 15
Function 2
f(x) = −x2 + 2x − 15
Function ____ has the larger maximum.
(Put 1 or 2 in the blank space)
Answers
Function 2 ⇒ [tex]- x^{2} +2x-15[/tex]
Both functions are shown in the graph below
As well as graphing, we can also find out the function with the highest maximum by using the formula to find the x-coordinate when the function is maximum/minimum
[tex]x=- \frac{b}{2a} [/tex]
Maximum vertex for function 1 is [tex]x=- \frac{8}{(2)(-1)} = \frac{-8}{-2} =4[/tex]
Maximum vertex for function 2 is [tex]x=- \frac{2}{(-2)(-1)}= \frac{-2}{-2}=1 [/tex]
Hence the function with the highest maximum is function 1
Answer:
The Function __1__ has the larger maximum.
Step-by-step explanation:
The given functions are
Function 1:
[tex]f(x)=-x^2+8x-15[/tex]
Function 2:
[tex]f(x)=-x^2+2x-15[/tex]
Both functions are downward parabola because the leading coefficient is negative. So, the vertex is the point of maxima.
If a function is [tex]f(x)=ax^2+bx+c[/tex], then its vertex is
[tex]Vertex=(\frac{-b}{2a}, f(\frac{-b}{2a}))[/tex]
The vertex of Function 1 is
[tex]Vertex=(\frac{-8}{2(-1)}, f(\frac{-8}{2(-1)}))[/tex]
[tex]Vertex=(4, f(4))[/tex]
The value of f(4) is
[tex]f(4)=-(4)^2+8(4)-15=1[/tex]
The vertex of Function 1 is (4,1). Therefore the maximum value of Function 1 is 1.
The vertex of Function 2 is
[tex]Vertex=(\frac{-2}{2(-1)}, f(\frac{-2}{2(-1)}))[/tex]
[tex]Vertex=(1, f(1))[/tex]
The value of f(1)is
[tex]f(1)=-(1)^2+2(1)-15=-14[/tex]
The vertex of Function 2 is (1,-14). Therefore the maximum value of Function 2 is -14.
Since 1>-14, therefore Function __1__ has the larger maximum.
Related Questions
HELP Please THANKS:((((
Answers
w + c <= 27
hope it helps
w>5.
Up to 27 acres will be filled with wheat and corn, so
w+c<=27
Final answer: A C
Choose the missing exponent to create a polynomial: 3x^4+4x^2-9x^-?+2
A)2
B)3
C)-9
D)7
E)4
Answers
we see we are given 9x^-?
so (-) times what=positive?
the answer is negative
so we must pick a negative exponent
so the answer is C -9
For a Polynominal 3x^4+4x^2-9x^-?+2 the missing part is mathematically given as
3x^4+4x^2-9x^-(-9)+2
-9, Option C is correct
What is a Polynomial?
Polynomials are summations of elements of the format of kxn, having k as any digit and n is +ve integer
Generally, the expression for the Polynominal is mathematically given as
3x^4+4x^2-9x^-?+2
In conclusion, the Polynominal must have all positive exponents, hence the value must be negative to give a positive exponent
Hence, -9 is correct
Read more about Polynomial
https://brainly.com/question/17822016
A roller coaster climbs 84 feet on the first hill then drop 60 feet down. on the second hill the roller coaster climb another 32 feet then drops 44 feet. what is te height at the end of the second hill ?
Answers
24 + 32 = 56
56 - 44 = 12
The answer is 12.
Answer:
12 feet.
Step-by-step explanation:
A roller coaster climbs the height on first hill = 84 feet.
Then drops down = 60 feet.
Height gained by the roller coaster = 84 - 60
= 24 feet
On other hill roller coaster climbs = 32 feet
Height gained by the roller coaster = 24 + 32 = 56 feet.
It drops again to the height = 44 feet
So the final height at the second hill = 56 - 44
= 12 feet
Therefore, height of roller coaster on the second hill is 12 feet.
Can square root of 32 be simplified
Answers
√32 = √8*4 = 4√2
Yes it can
First, we have to break 32 into its primes.
[tex]32=2^5[/tex]
[tex]=\sqrt{2^5}[/tex]
Since we don't want an odd number, we can split it into two.
[tex]=\sqrt{2^4\cdot \:2}[/tex]
[tex]=\sqrt{2}\sqrt{2^4}[/tex]
Since we want to remove one of the square roots, we have to do something like this: [tex]\sqrt{2^4}=2^{\frac{4}{2}}=2^2[/tex]
We would be left with,
[tex]=2^2\sqrt{2}[/tex]
Simplify the exponent.
[tex]=4\sqrt{2}[/tex]
This tells us that the square root of 32 can be simplified.
Thanks!
-TetraFish
Hot dogs come in packs of 10 and buns come in packs of 8. Whats the least amount of packs you can buy to have the same amount of hot dogs and buns.
Answers
The table below represents a linear function f(x) and the equation represents a function g(x):
x f(x)
−1 −3
0 0
1 3
g(x)
g(x) = 7x + 2
Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x). (6 points)
Part B: Which function has a greater y-intercept? Justify your answer. (4 points)
Answers
B. g(x) has a greater y intercept. Because g(x) is written in slope intercept form, we know that the intercept is simply the b value, which is 2 in this case. For f(x), we know that slope interceot is the value of y when x=0. When x=0 in this case, y=0. 2>0
Convert: 52 cups = ________ qt.
Answers
1 cup = 0.25 quarts
52 *0.25 = 13 quarts
13 is the answer HOPE THAT HELPS
If the discriminant of an equation is negative, which of the following is true of the equation
A it has two complex solutions
B it has one real solution
C it had two real solutions
Answers
Answer:
A. It has two complex roots.
Step-by-step explanation:
We are given that
Discriminant of an equation =negative
We have to find which is true about the equation .
Let quadratic equation
[tex]ax^2+bx+c=0[/tex]
Discriminant=[tex]D=b^2-4ac[/tex]
If D < 0 , then the equation has complex roots.
Therefore, if the discriminant of an equation is negative then the equation has two complex roots.
Answer:A. It has two complex roots.
The field hockey coach is purchasing new uniforms for the team. Company A charges a one-time printing fee of $100 and $12 per uniform. Company B charges a one-time fee of $61 and $15 per uniform. How many uniforms must the coach buy to get a better deal from Company A?
Answers
100 + 12x < 61 + 15x
39 < 3x
13 < x, so they must buy more than 13 to get a better deal.
which best describes the diameter of a circle?
A. The distance from the center to any point of the circle
B. The length of a chord that contains the center of the circle
C. The distance around the circle
D. The length of a chord that does not contain the center of the circle
Answers
Which best describes the diameter of a circle?
Statements
A. The distance from the center to any point of the circle
This statement describes the radius of the circle
B. The length of a chord that contains the center of the circle
This statement describes the diameter of the circle
C. The distance around the circle
This statement describes the circumference of the circle
D. The length of a chord that does not contain the center of the circle
This statement describes a line segment linking any two points on a circle that does not contain the center of the circle
therefore
the answer is the option
B. The length of a chord that contains the center of the circle
The correct answer is:
B) The length of a chord that contains the center of the circle
Explanation:
A chord is a segment that goes across a circle, with both endpoints on the circle.
A diameter goes through the center of a circle and has both endpoints on the circle; this makes it a chord that goes through the center.
An angle measures 7pi/9 radians. What is the degree measure of the angle?
Answers
1. You should know the percentage of the angle with respect to 2pi:
(7pi/9) / (2pi) = 7/18
2. Then, multiply the ratio to the 2pi angle in degrees, which is 360
360 * (7/18) = 140
140°
multiplying by 180/pi give you a degree measure
y=4x -1 and 12x=3y+7
Answers
Use the first equation to substitute 4x - 1 for y in the second equation:
12x = 3(4x - 1)+7
12x = 12x - 3 + 7
12x = 12x +4
0 = 4
The last equation is FALSE, indicating the system of two equations has no solution.
Does anyone know the answer to this question?
Answers
f(x) = x-3
g(x) = 2f(x)
g(2) = 2(2-3) = 2 * -1 = -2
- ( 1 + 7x ) - 6 ( -7 - x ) = 36
Please solve and show work
Answers
-1(1+7x) - 6(-7 - x) = 36
-1 - 7x + 42 + 6x = 36
41 - x = 36
41 = 36 + x
5 = x
Simplify.
-1 - 7x + 42 + 6x = 36
Add 1 to both sides.
-7x + 42 + 6x = 36 + 1
Simplify.
-x + 42= 37
Subtract 42 from both sides.
-x = 37 - 42
Simplify.
-x = -5
Divide both sides by -1.
x = 5
~Hope I helped!~
If (44)x = 432, what is the value of x?
4
7
8
28
Answers
44 x 4 = 176
44 x 7 =308
44 x 8 = 352
44 x 28 =1232
none of those will =432
are you sure you have the right numbers?
(44)x=432
x=432/44 = 9.8181
Not sure ^^^^^^^^^^^
Answers
y^2-7y-30
(y-10)(y+3)
(y-5)(2y+3)
If you divide out y-5, you are left with 2y+3
B
A square garden plot has an area of 75 ft2. a. Find the length of each side in simplest radical form. b. Calculate the length of each side to the nearest tenth of a foot.
Answers
a. Find the length of each side in simplest radical form.
First, a square area (A) = length (l)^2
A(ft2) = l^2 --> so l(ft) = square root (sr) of A
l = srA = sr75
Next, factor out 75 into number with even roots: 25•3 = 75
So l = sr25•sr3 --> l = 5•sr3 ft
5•sr3 is in the simplest radical form
b. Calculate the length of each side to the nearest tenth of a foot.
l = sr3 = 1.732 --> so 5•1.732 = 8.66ft
Tenth is one place to the right of the decimal, so l = 8.7 ft
Answer:
a)the length of each side is [tex]5\sqrt3[/tex] feet
b)In the nearest tenth the length of the side is 8.7 feet.
Step-by-step explanation:
The area of the square garden is 75 square feet.
a) Let x be the length of each side.
We know that,
[tex]\text{Area of square}=\text{(Side)}^2[/tex]
Hence, we have
[tex]75=x^2\\\\x=\sqrt{75}\\\\x=5\sqrt{3}[/tex]
Thus, the length of each side is [tex]5\sqrt3[/tex] feet
b)
In the nearest tenth the length of the side is 8.7 feet.
Given an arithmetic sequence in the table below, create the explicit formula and list any restrictions to the domain.
n | an
1 | 9
2 | 3
3 | −3
Answers
Concrete can be purchased by the cubic yard. How much will it cost to pour a slab 17 ft by 17 ft by 2 in. for a patio if the concrete costs $40.00 per cubic yard? (1 cubic yard = 27 cubic feet)
Answers
Answer:
It will cost approximately $71.360.
Step-by-step explanation:
Given,
The dimension of the concrete is 17 ft by 17 ft by 2 in.
1 ft = 12 inches ⇒ 2 inches = 1/12 × 2 = 1/6 ft.
Thus, the dimension of the concrete is 17 ft by 17 ft by 1/6 ft.
Now, the volume of the concrete = 17 × 17 × 1/6
[tex]=\frac{289}{6}\text{ cubic ft}[/tex]
We know that,
1 cubic yard = 27 cubic feet
[tex]\implies 1 \text{ cubic feet}=\frac{1}{27}\text{ cubic yards}[/tex]
[tex]\implies \frac{289}{6}\text{ cubic ft}=\frac{289}{6}\times \frac{1}{27} = \frac{289}{162}\text{ cubic yards}[/tex]
Since, the concrete costs $40.00 per cubic yard.
Hence, the total cost of concrete = [tex]\frac{289}{162}\times 40=\frac{11560}{162}=\$71.3580247\approx \$71.360[/tex]
The total cost of concrete is,
C = $71.4
We have to give that,
Dimensions of the concrete are,
17 ft by 17 ft by 2 in.
And, the concrete costs $40.00 per cubic yard.
Since we know that,
1 feet = 12 inches
Hence,
2 inches = 2/12 = 1/6 feet
Thus, the dimension of the concrete is 17 ft by 17 ft by 1/6 ft.
So, the Volume of the concrete,
V = 17 x 17 x 1/6
V = 48.2 cubic feet
Here, 1 cubic yard = 27 cubic feet
And, the concrete costs $40.00 per cubic yard.
Hence, the total cost of concrete is,
C = 48.2 × 40 / 27
C = $71.4
To learn more about the volume visit:
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How would I solve this?
Answers
2*(3(7)-1)
2*(21-1)
2*20
40
Final answer: 40
Remember the order of operations. Parentheses, then multiplication and division, followed by addition and subtraction.
A man paid $71.40 for a radio. The radio was marked 15% off the original selling price. What was the original selling price?
Answers
what is this answer
Answers
Divide both sides by 16
3.125=t^2
Find the square root of both sides (approximated)
1.77= t
Final answer: F
For the graphed function f(x) = (2)x + 2 + 1, calculate the average rate of change from x = −1 to x = 0. graph of f of x equals 2 to the x plus 2 power, plus 1. (6 points) −2 2 3 −3
Answers
Next time you should write the correct form of equation because it affects greatly the answer. I believe the correct form would be:
f (x) = 2 * x^2 + 1
where the second 2 is a power of x
The average rate of change is also defined as the slope of the equation. Therefore:
average rate of change = slope
Where slope is:
m = (y2 – y1) / (x2 – x1) = [f (0) – f (-1)] / (x2 – x1)
Calculating for f (0): x2 = 0
f (0) = 2 * 0^2 + 1 = 1
Calculating for f (-1): x1 = -1
f (-1) = 2 * (-1)^2 + 1 = 3
Substituting the known values to the slope equation:
average rate of change = (1 – 3) / (0 – 1)
average rate of change = -2 / -1
average rate of change = 2
Answer: 2
Answer:
I believe the proper form of this question is actually... as I have also come across this question.
"For the graphed function f(x) = (2)^(x + 2) + 1, calculate the average rate of change from x = −1 to x = 0."
Step-by-step explanation:
the y2 - y1/ x2 - x1, will actually be (-1,3) and (0,5).
This means you will get a 5 + 1 (because subtracting a -1 is the same as adding 1) over 0 - 3.
Next you have 6/-3 which will give you a answer of -2
Now I do believe the proper answer is actually 2 because the graph shows a chart that is growth, not decay, but the math gives a -2 which is confusing.
In a large bag of marbles, 30% of them are red. a child chooses 4 marbles from this bag. if the child chooses the marbles at random, what is the chance that the child gets exactly three red marbles? 0.0756 0.1764 0.2646 0.0810
Answers
P[k] = nCk * p^k *q^(n-k)
P[3] = 4c3 * 0.3^3 * 0.7 = 0.0756
The equation of a line is y = mx + 2. What is the value of m (the slope) if the line passes through point A(−5, −18)?
M=-4
M=4
M=1/4
M=7/8
Answers
remember that (x,y)
so we are given (-5,-18)
so when x=-5, y=-18
so
-18=-5m+2
minus 2 both sides
-20=-5m
divide both sides by -5
4=m
m=4
answer is 2nd option
If conner spent $36 to buy a new collar for each of his dogs.if each collar cost $6,how many dogs dose conner have?
Answers
Find a and b so that the polynomial, p(x)=x^2+ax-b passes through the points (6,-9) and (1, 16)
Answers
The given equation is:
p(x) = x^2 + ax - b
We write this in terms of y:
y = x^2 + ax – b
To solve for the values of the constants a and b, we are given the following conditions:
When x = 6, y = -9
When x = 1, y = 16
From these conditions, we can formulate two equation by substituting the values of y:
-9 = 6^2 + a(6) – b
6a = b – 45 ---> 1
16 = 1^2 + a(1) – b
a = b + 15 ---> 2
Combining equations 1 and 2:
6 (b + 15) = b – 45
6b + 90 = b – 45
5b = -135
b = -27
calculating for a using equation 1:
a = b + 15
a = -27 + 15
a = -12
Answers:
a = -12
b = -27
A triangle has side lengths 9, 10, and 12. is it acute, obtuse, or right? explain.
Answers
right if a² + b² = c²
аcute if a² + b² > c²
obtuse if a² + b² < c²
We have a=9, b=10 and c=12
a² + b² = 9² + 10² = 81 + 100 = 181
and
c² = 12² = 144
181 > 144 ⇒ аcute triangle.
Final answer:
By applying the Pythagorean theorem and comparing the square of the longest side to the sum of the squares of the other two sides, it is determined that a triangle with sides of 9, 10, and 12 is an acute triangle since 144 is less than 181.
Explanation:
To determine whether a triangle with side lengths of 9, 10, and 12 is acute, obtuse, or right, we can apply the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the lengths of the other two sides. If this condition is met, the triangle is right-angled. If the square of the longest side is greater than the sum of the squares of the other two sides, the triangle is obtuse. Conversely, if the square of the longest side is less than the sum of the squares of the other two sides, the triangle is acute.
For this triangle, the side lengths squared are:
9² = 8110² = 10012² = 144Adding the squares of the two shorter sides: 81 + 100 = 181.
Since 144 < 181, the square of the longest side (12²) is less than the sum of the squares of the other two sides, indicating that this triangle is acute.
A triangle has side lengths of 20 cm, 99 cm, and 108 cm. Classify it as acute, obtuse, or right.
A. acute
B. obtuse
C. right
Answers
If draw it out in your head, it's obviously obtuse.
The triangle will be:
right if a² + b² = c²
аcute if a² + b² > c²
obtuse if a² + b² < c²
We have a=20, b=99 and c=108
20² + 99² = 400 + 9801 = 10201
and
108² = 11664
10201 < 11664 ⇒ obtuse triangle.
Two sandboxes with the same area are shown. The equation w(3w+1)=5^2 represents the area of Sandbox 2 in terms of its width. Which is the approximate length of the longest side of Sandbox 2? Round the answer to the nearest hundredth of a meter.
A.) 2.72 meters
B.) 3.06 meters
C.) 9.16 meters
D.) 10.18 meters
Answers
sandbox 1 area = 5*5 = 25 square m
sandbox 2
25=w*(3w+1)=
3w^2+w-25=0
w=2.7248 (round to 2.72 m)
2.72*3=8.16+1 = 9.16
Longest side = 9.16 meters
Answer:
C.) 9.16 meters
Step-by-step explanation:
We are given that the two sandboxes have same area and the equation is given by 25 = w*(3w+1).
Now, we simplify this equation in order to find the value of unknown variable 'w'.
i.e. 25 = 3[tex]w^{2}[/tex]+w
i.e. 3[tex]w^{2}[/tex]+w-25=0
The two factors of this quadratic equation are w=2.72 and w= -3.05.
But, as 'w' represents the length of the box, so it cannot be negative.
Therefore, w = 2.72
So, the longest side of the box is (3w+1) = 3*2.72+1 = 9.16 meter
Hence, the length of longest side to the nearest hundredth is 9.16 meter.