One quadratic function has the formula h(x) = -x 2 + 4x - 2. Another quadratic function, g(x), has the graph shown below
Which option below best describes the maximums of these two functions?
Functions g and h have the same maximum of -2.
Functions g and h have the same maximum of 2.
Function h has the greater maximum of -2.
Function g has the greater maximum of 2.
Answers
Complete the square of h(x) = -x^2 + 4x - 2:
h(x) = -x^2 + 4x - 2 = -(x^2 - 4x) -2
= -(x^2 - 4x + 4 - 4) - 2
=-(x^2 - 4x + 4) -2+4
= -(x-2)^2 + 2 The equation describing this parabola is y=-(x-2)^2 + 2, from which we know that the maximum value is 2, reached when x = 2.
The 2 graphs have the same max, one at x = -2 and one at x = + 2.
Answer:
Functions g and h have the same maximum of 2.
Step-by-step explanation:
Related Questions
In a poll of students at basketball champoin 82% of the students say that basketball is better than fottball.
Answers
Find the area of the surface of the part of y=4x+z^2 that lies between the planes
Answers
[tex]y=z^2+4x[/tex]
X)Solve for [tex]x[/tex] by simplifying both sides of the equation, then isolate the variable
[tex]x=- \frac{ z^{2} }{4}+ \frac{y}{4} [/tex]
Z)Take the root of both sides and solve.
[tex]z= \sqrt{-4x+y}, - \sqrt{-4x+y} [/tex]
To the nearest hundredth, what is the area of a circle with a radius of 3 units
Answers
28.27 square units (APEX)
Answer:
28.27
Step-by-step explanation:
gl on test
WILL MARK BRAINLIEST
There are 50 red beans and 50 white beans in a bag. The first bean selected is red. The red bean is returned to the bag. What are the chances of the second bean selected being red?
Answers
Hope this helps :)
Recently, the texas junior college teachers association annual conference was held in austin. at the time a taxi ride in austin was $ 1.75 $1.75 for the first 1 5 15 of a mile and $ 0.25 $0.25 for each additional 1 5 15 of a mile. if the distance from one of the convention hotels to the airport is 5.8 5.8 miles, how much will it cost to take a taxi from that hotel to the airport?
Answers
Recently, the texas junior college teachers association annual conference was held in austin. at the time a taxi ride in austin was $ 1.75 for the first 1/5 of a mile and $ 0.25 for each additional 1/5 of a mile. if the distance from one of the convention hotels to the airport is 5.8 miles, how much will it cost to take a taxi from that hotel to the airport?
we know that
(1/5) miles is equal to 0.20 miles
so
for the first 0.20 miles----------> $1.75
Remaining Distance = 5.8 - 0.2 miles = 5.6 miles
5.6/(0.2) =28 (this is the number of (1/5)th of a mile after the 1st (1/5)th
Each of these costs 0.25 dollars
28*0.25 = 7 dollars
total cost=$1.75+$7------> $8.75
the answer is
$8.75
To calculate the total taxi fare in Austin, first calculate the initial fee for the first 1/15 mile and then the cost for each additional 1/15 mile. For 5.8 miles, the total cost amounts to $23.25, comprising a $1.75 initial fare and $21.50 for the subsequent distance.
Let's break down the cost of a taxi ride based on the given pricing structure. To find the total cost of a taxi ride for a given distance, we need to calculate the cost for the first 1/5 mile and the additional cost for the remaining distance.
The initial cost for the first 1/5 mile is given as $1.75.
We know the total distance is 5.8 miles. Since the first 1/5 mile is included in the initial cost, the distance to be charged in increments of 1/5 mile is:
[tex]\[ 5.8 - \frac{1}{5} = 5.8 - 0.2 = 5.6 \, \text{miles} \][/tex]
To find the number of 1/5 mile increments in 5.6 miles, divide by 0.2:
[tex]\[ \frac{5.6}{0.2} = 28 \][/tex]
Thus, there are 28 additional 1/5 mile increments.
Each additional 1/5 mile increment costs $0.25. Thus, the total cost for the additional distance is:
[tex]\[ 28 \times 0.25 = 7.00 \][/tex]
The total cost is the initial cost plus the cost for the additional distance:
[tex]\[ 1.75 + 7.00 = 8.75 \][/tex]
Thus, the total cost to take a taxi from the hotel to the airport, given a distance of 5.8 miles, is $8.75.
How many questions can i miss on a 28 question test to get a 70%?
Answers
0.7(28) = 19.6
You need to get 19.6 points for a 70%. To calculate the points missed, subtract this from the total points on the test:
28 - 19.6 = 8.4
You can only miss 8.4 points on the test, or no more than 8 questions, to get a grade of 70%.
For $360, a rock-climbing gym offers a yearly membership where members can climb as many days as they want and pay $4 per day for equipment rental. Nonmembers pay $10 per day to use the gym and $6 per day for equipment rental. Find the total number of visits when the cost for a member and nonmember will be the same.
Answers
360+4x=16x
360=12x
x=30
After 30 days they visit, they will spend the same amount.
The cost for a member and a nonmember of a rock-climbing gym will be the same at 30 visits.
Explanation:To find the total number of visits when the cost for a member and a nonmember will be the same, we need to set up an equation based on the problem statement, which we can then solve.
For the member, the cost is the $360 yearly fee plus $4 per visit (for equipment rental) - so if 'x' represents the number of visits, the total cost for a member would be $360 + 4x.
For a nonmember, the cost is $10 per visit (for gym use) plus $6 per visit (for equipment rental) - so the total cost for a nonmember is $16x.
So, to find the number of visits 'x' where both costs are equal, we need to solve this equation: $360 + 4x = $16x.
Solving the equation gives us $360 = 12x, which simplifies to x = 30.
So, the cost for a member and a nonmember would be the same at 30 visits.
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What is the radian measure of a 150° angle?
Answers
[tex]\bf \begin{array}{ccll} radians&de grees\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ \pi &180\\ x&150 \end{array}\implies \cfrac{\pi }{x}=\cfrac{180}{150}\implies \cfrac{\pi \cdot 150}{180}\implies \stackrel{simplified}{\cfrac{5\pi }{6}}[/tex]
The radian measure of a 150° angle is (5/6) π rad, found by multiplying 150° by the conversion factor π/180.
To find the radian measure of a 150° angle, we use the relationship between degrees and radians. Recall that a full circle in degrees is 360° and in radians is 2π rad. Therefore, we can say that 360° equals 2π radians. To convert degrees to radians, we multiply the degree measure by the fraction π/180.
For a 150° angle, the calculation would be:
150° multiplied by the conversion factor π/180
150° * (π/180) = (150/180) * π = (5/6) * π rad
Thus, the radian measure of a 150° angle is (5/6) π rad.
What is log base 5(4*7 )+log base 5 of 2 written as a single log?
A.log base 5 of 21
B.log base 5 of 26
C.log base 5 of 30
D.log base 5 of 56
Answers
D. log base 5 of 56
The explanation is show below:
1. You have the following logarithm expresssion:
log5(4*7 )+log5(2)
2. By the logarithms properties, you can rewrite the logarithm expression as following:
log5(28)(2)
log5(56)
3. Therefore, as you can see, the answer is the option mention before.
Answer:
D. log base 5 of 56
Step-by-step explanation:
Since, by the multiplication law of logarithm,
[tex]log_a(m)+log_a(n) = log_a(mn)[/tex]
Given expression is,
log base 5(4*7 )+log base 5 of 2
[tex]=log_5(4\times 7)+log_5(2)[/tex]
[tex]=log_5(28)+log_5(2)[/tex]
By the above property,
[tex]=log_5(28\times 2)[/tex]
[tex]=log_5(56)[/tex]
= log base 5 of 56
Hence, Option D is correct.
A box contains 16 transistors, 5 of which are defective. if 5 are selected at random, find the probability that
a. all are defective. and. none are defective.
Answers
Only one way of selecting the 5 defective transistors:
Number of ways of selections available = 6C5 = 16!/[5!*(15-5)!] = 4368
Probability they are all defective = Number of ways of selecting 5 defectives/Total number of ways possible = 1/4368 ≈ 0.000229
Part (b): None are defective
Total number of non defectives = 16 -5 = 11
Number of ways of selecting 5 non defective = 11C5 = 462 ways
Total number of ways possible = 16C5 = 4368
Probability of selecting 5 non defectives = 462/4368 = 11/104 ≈ 0.1058
A - all defective
B - none defective
[tex] \displaystyle
|\Omega|=\binom{16}{5}=\dfrac{16!}{5!11!}=\dfrac{12\cdot13\cdot14\cdot15\cdot16}{2\cdot3\cdot4\cdot5}=4368\\
|A|=1\\
|B|=\binom{11}{5}=\dfrac{11!}{5!6!}=\dfrac{7\cdot8\cdot9\cdot10\cdot11}{2\cdot3\cdot4\cdot5}=462\\\\
P(A)=\dfrac{1}{4368}\approx0.02\%\\
P(B)=\dfrac{462}{480480}=\dfrac{1}{1040}\approx0.1\% [/tex]
HELP ! I've been stuck on this for over 15 mins. :(
What are the explicit equation and domain for an arithmetic sequence with a first term of 8 and a second term of 5?
an = 8 − 5(n − 1); all integers where n ≥ 1
an = 8 − 5(n − 1); all integers where n ≥ 0
an = 8 − 3(n − 1); all integers where n ≥ 1
an = 8 − 3(n − 1); all integers where n ≥ 0
Answers
Plug in a1 = 8:
an = 8 + (n - 1)d
FInd d:
Given that a2 = 5
5 = 8 + (2-1)d
5 = 8 + d
d = -3
Plug in d = -3:
an = 8 -3(n - 1)
Answer: an = 8 -3(n - 1) ; n ≥ 1
does anyone know what the measuure of Ф should be . is so i will mark brainliest.
Answers
A triangle's angles measure 180°, so we just have to subtract the other two angle measures:
180 - 50 - 70 = Ф
60 = Ф
Express the complex number in trigonometric form. -2 + 2square root of three i
Answers
Answer:
The required trigonometric form is [tex]4(\cos(60)-i\sin(60))[/tex]
Step-by-step explanation:
Given : Complex number [tex]-2+2\sqrt{3}i[/tex]
To find : Express the complex number in trigonometric form?
Solution :
The complex number [tex]a+ib[/tex] trigonometric form is [tex]r(\cos\theta+i\sin\theta)[/tex]
Where, [tex]r=\sqrt{a^2+b^2}[/tex]
and [tex]\theta=\tan^{-1}(\frac{b}{a})[/tex]
On comparing with given complex number [tex]-2+2\sqrt{3}i[/tex]
a=-2 and [tex]b=2\sqrt{3}[/tex]
Substitute the value,
[tex]r=\sqrt{a^2+b^2}[/tex]
[tex]r=\sqrt{(-2)^2+(2\sqrt{3})^2}[/tex]
[tex]r=\sqrt{4+12}[/tex]
[tex]r=\sqrt{16}[/tex]
[tex]r=4[/tex]
[tex]\theta=\tan^{-1}(\frac{b}{a})[/tex]
[tex]\theta=\tan^{-1}(\frac{2\sqrt3}{-2})[/tex]
[tex]\theta=\tan^{-1}(-sqrt3)[/tex]
[tex]\theta=\tan^{-1}(\tan(-60))[/tex]
[tex]\theta=-60[/tex]
Substituting all values in the formula,
[tex]r(\cos\theta+i\sin\theta)[/tex]
[tex]4(\cos(-60)+i\sin(-60))[/tex]
[tex]4(\cos(60)-i\sin(60))[/tex]
Therefore, The required trigonometric form is [tex]4(\cos(60)-i\sin(60))[/tex]
Which sequence is modeled by the graph below? coordinate plane showing the points (1, 1) (2, 2) (3, 4) and (4, 8)
a. an = 1(2)n − 1
b. an = 2(1)n − 1
c. an = 1 + (2)n − 1
d. an = (2)(n − 1)
Answers
Answer: The correct option is d.
Explanation:
From the given information it is noticed that the coordinate plane showing the points (1, 1) (2, 2) (3, 4) and (4, 8).
The coordinates are in the form of (x,y), it means the value of xth term of the sequence is y.
The point (1,1) represents that the first term is 1. Similarly from (2, 2) (3, 4) and (4, 8) points we can say that the second term is 2, third term is 4 and fourth term is 8.
The sequence is 1,2,4,8.
It can be written as,
[tex]2^0,2^1,2^2,2^3[/tex]
Since the base is common that is 2 and the power is one less than the position of term. So the sequence is in the form of,
[tex]a_n=2^{n-1}[/tex]
Therefore, the correct option is d.
Norma stopped to get gas for her car before beginning a trip. her odometer read 2587 miles, and she filled up her tank with 26 gallons. at the end of her trip, her odometer read 3295 miles. what is her car's miles per gallon?(round to the closest gallon)
Answers
Assuming that at the end of the trip all the gas had been consumed, a total of 26 gallons was consumed.
Therefore,
Car consumption = 708/26 = 27.23 miles/gallon
License plates are made using 2 letters followed by 3 digits. how many plates can be made ifrepetition of letters and digits is allowed
Answers
20 PTS AND I'LL MARK BRAINLIEST
∠1 and ∠2 are a linear pair, and ∠2 and ∠3 are vertical angles. m∠2=(5+4y)∘ and m∠3=(6y−25)∘ . What is m∠1 ?
Answers
5+4y=6y-25 (We'll add the degrees symbol later)
5 = 2y - 25
30 = 2y
y = 15°
We can plug the y-value into the value for m∠2.
5 + 4(15) = 65°
Now, we can easily find m∠1, since they are a linear pair.
m∠1 + m∠2 = 180
m∠1 + 65 = 180
m∠1 = 115°.
m∠1 equals 115°.
Hope this helps!
given function f(x)=x^2-x+8, find each of the following. f(9) f(-6) f(0)
Answers
f(9) - substract x = 9 to the equation of the function:
[tex]f(9)=9^2-9+8=81-9+8=80\\\\f(-6)=(-6)^2-(-6)+8=36+6+8=50\\\\f(0)=0^2-0+8=8[/tex]
Show work please (6th grade math)
Answers
rate = 36 miles / 45 min = 0.8 miles per mindistance traveled = 0.8 miles per min ( 60 min ) = 48 miles
Hope this answers the question. Have a nice day.
To find how long the bus travels in 60 minutes, we need to find a ratio of how long the bus travels every 15 minutes.
We do this by dividing 45 minutes by 3. We now have 15 minutes.
You then divide the miles by 3 as well. 36 divided by 3 is 12.
A bus travels 12 miles every 15 minutes.
Now, this still isn't the answer. We need to find how many miles the bus travels in 60 minutes.
To find this, we need to find how many 15 minute intervals are in 60 minutes. To do this, we divide 60 by 15 to get 4. We use this 4 to multiply it by 12 to find the total number of miles in 60 minutes.
12 times 4 is 48 miles.
Therefore, the bus travels 48 miles in 60 minutes.
A pretzel maker was interested in knowing the number of pretzels in each bag it sold. The results of their research are shown in the box-and-whisker plot. What is the median number of pretzels?
Answers
The median number of pretzels is 54.
What is Box and whisker plot?The lower and upper quartiles are represented by the left and right sides of the box in a box and whisker plot. The box encompasses the interquartile interval, which contains 50% of the data. The median is the vertical line that divides the box in half. On the box plot, the mean is sometimes shown by a dot or a cross.
From the given box plot we can have the following information:
Minimum = 45
Lower Quartile = 47
Median= 54
Upper Quartile= 61
Maximum = 68
Thus, the Required median is 54.
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The height of a triangle is 8 inches more than its base. the area of the triangle is 104.5 square inches. find the base and height.
Answers
b------> the base of the triangle
h------> the height of the triangle
we know that
area of the triangle=b*h/2
h=b+8-----> equation 1
area=104.5 in²
104.5=b*h/2-----> 209=b*h-----> equation 2
substitute equation 1 in equation 2
209=b*[b+8]----> 209=b²+8b-----> b²+8b-209=0
using a graph tool---> to resolve the second order equation
see the attache figure
the solution is
b=11 in
h=b+8----> h=19 in
the answer is
the base is 11 in and the height is 19 in
What is the value, after 7 years...
Answers
Answer:
13946
Step-by-step explanation:
answer this question please and right
Answers
Given center of the circle at (-10,6) and radius 4,
(x + 10)² + (y - 6)² = 4²
(x + 10)² + (y - 6)² = 16
Answer: (x + 10)² + (y - 6)² = 16
Center of circle: (-10, 6)
Radius: 4
(x - -10)² + (y - 6)² = 4²
Equation: (x + 10)² + (y - 6)² = 16
If the person can't accommodate and the glasses is + 2.50d, at which distance will the person see clearly
Answers
At a + diopter measurement is a nearsighted person take the value of 2.5 and make it the denominator with 1 as the numerator to find the distance in meters that they can see clearly past their face.
1/2.5 = 2/5 of a meter.
Answer:
40 cm or 2/5 of a meter.
Step-by-step explanation:
A short-sighted person, at a positive diopter, will take an estimation of about 2.5 and make it the denominator by 1 as the numerator to find out the distance (in meters) that they can see clearly.
We can find the value of f, given the value for P:
P = +2.50
f = 1 / p = 1 / 2.50
(changing the units, it will be) ---> 100 / 2.50 which is equal to 40 cm.
Therefore, 40 cm which is 2/5 of a meter is the distance a person with glasses +2.5d can see clearly.
The spoke of a wheel reaches from the center of the wheel to its room if the circumference of the rim of the wheel is 42 inches how long is each spoke
Answers
so to find the (d) you divide 48÷3.14=15.29 inches. As the spoke goes from the center to its rim, it it is the radius, which is half of the diameter.15.29/2 is
B) 7.64 inches.
Any answers please??
Answers
X-axis= (x,y) --->(x,-y)
Y-axis= (x,y) --->(-x,y)
X-axis= (-4,4) --->(-4,-4)
Y-axis= (-4,-4) --->(4,-4)
X-axis= (4,-4) --->(4,4)
Hope this Helps! :)
can someone please explain the steps to solve these questions.
Answers
A class had 30 pupils at the beginning of this school term, but now has 5 more pupils. What is the percent of increase?
The question is basically asking how much 5 is in ratio to 30. So just divide 5 (the given amount) by 30 (the total amount). The answer is 0.16, or 16%
Triangle rst is circumscribed about the circle below. What is the perimeter of the triangle?
Answers
Answer:
perimeter of the triangle = 24 units
Explanation:
Using the grid, we can note that:
RS = 6 units
ST = 8 units
We know that the triangle inscribed in a circle is a right-angled triangle. Therefore, we can use the Pythagorean theorem to get the third side as follows:
(RT)² = (RS)² + (ST)²
(RT)² = (6)² + (8)²
(RT)² = 100
RT = 10 units
Now, we can get the perimeter as follows:
perimeter = RS + ST + RT
perimeter = 6 + 8 + 10
perimeter = 24 units
Hope this helps :)
Not sure what the answer is but this guy didnt attach the dang picture so here.
Find the following measure for this figure.
Volume =
18 cubic units
24 cubic units
36 cubic units
Answers
In your case, l=4 units, w=2 units, h=3 units and V=4×2×3=24 cubic units.
Answer:
So the answer is 24 cubic units
Step-by-step explanation:
l=4 units,
w=2 units,
h=3 units and
V=4×2×3=24 cubic units.
Find all solutions to the equation sin2x+sinx-2cosx-1=0 in the interval [0, 2pi)
Answers
_____
Replacing sin(2x) with 2sin(x)cos(x), you have
2sin(x)cos(x) +sin(x) -2cos(x) -1 = 0
sin(x)(2cos(x) +1) -(2cos(x) +1) = 0 . . . . factor by grouping
(sin(x) -1)(2cos(x) +1) = 0
This has solutions
sin(x) = 1
x = π/2
and
2cos(x) = -1
cos(x) = -1/2
x = {2π/3, 4π/3}