Given:
The given function is:
[tex]y=-32x^2+90x+3[/tex]
To find:
The range of the given function.
Solution:
We have,
[tex]y=-32x^2+90x+3[/tex]
It is a quadratic function because the highest power of the variable x is 2.
Here, the leading coefficient is -32 which is negative. So, the graph of the given function is a downward parabola.
If a quadratic function is [tex]f(x)=ax^2+bx+c[/tex], then the vertex of the quadratic function is:
[tex]Vertex=\left(\dfrac{-b}{2a},f(\dfrac{-b}{2a})\right)[/tex]
In the given function, [tex]a=-32,b=90,c=3[/tex].
[tex]\dfrac{-b}{2a}=\dfrac{-90}{2(-32)}[/tex]
[tex]\dfrac{-b}{2a}=\dfrac{-90}{-64}[/tex]
[tex]\dfrac{-b}{2a}=\dfrac{45}{32}[/tex]
The value of the given function at [tex]x=\dfrac{45}{32}[/tex] is:
[tex]y=-32(\dfrac{45}{32})^2+90(\dfrac{45}{32})+3[/tex]
[tex]y=\dfrac{2121}{32}[/tex]
The vertex of the given downward parabola is [tex]\left(\dfrac{45}{32},\dfrac{2121}{32}\right)[/tex]. It means the maximum value of the function is [tex]y=\dfrac{2121}{32}[/tex]. So,
[tex]Range=\left\{y|y\leq \dfrac{2121}{32}\right\}[/tex]
[tex]Range=\left(-\infty, \dfrac{2121}{32}\right ][/tex]
Therefore, the range of the given function is [tex]\left (-\infty, \dfrac{2121}{32}\right ][/tex].
Find the radius when d=18
Answer:
9
Step-by-step explanation:
radius is half of the diameter
Find the value of angle A and angle B pls help (:
Answer:
m<A=97
m<B=97
Step-by-step explanation:
m<A=m<B
Congruent angles and they are vertical angles. The other two are also the same because the angles given have the same degrees.
m<A is supplementary to 83 degrees
Supplementary angles are two angles that sum up to 180 degrees.
180-83=97
97 degrees is the answer for each missing angles.
what type of lines are x-3y=-3 and 6x+2y=-12
Answer:
Perpendicular
Step-by-step explanation:
HELP ME!!! PLEASE I HAVE A G- MY PARENTS WILL KILL ME (LITERALLY PLEASE HELP)
Answer:
you should get math w ay it's good
Choose all the expressions that are equivalent to 4x-20.
x (4 - 20)
2 (2x - 10)
4(x - 20)
4(x - 5)
Answer:
4(x-5)= 4x-20
so the equivalent equation is 4(x-5)
Answer:
I don't actually know sorry
Step-by-step explanation:
I don't know
© A new car cost $14875. Three years later, the insurance company valued it at $10700. Calculate the percentage
reduction in value over the three years.
Answer: either I don't understand the question or its 72% and I'm fairly certain its 72%
I need help with this one. Please. thanks!
Answer:
x=6
Step-by-step explanation:
30=6+4x
you have to combine the number that are the same, like 2 and 4 or 3x and 4x
30-6=4x (you should always remember when you move a number if it was - it will turn +)
30-6=4x
24=4x
x=24/4
x=6
What is the slope of the line that passes through the points (-8, -6)(−8,−6) and (-18, 6) ?(−18,6)? Write your answer in simplest form.
11. One term, about 700 Statistics 2 students at the University of California, Berkeley, were asked how many college mathematics courses they had taken, other than Statistics 2. The average number of courses was about 1.1; the SD was about 1.5. Would the histogram for the data look like (i), (ii), or (iii)? Why?
Answer:
(i)
Step-by-step explanation:
Given that the mean value of the distribution is 1.1, then we can safely assume that the peak value will be reside around one with a variability measure, standard (1.5) represents changes in distribution away from the mean value. The could be to either side of the distribution. However, the cannot be a negative value for the number of courses taken, hence, the maximum value we can have to the left is 0. (figures to the far left of the distribution are negative). This means that the curve will fall towards the right, (positive direction hence giving a right skewed distribution.
Find an equivalent ratio in simplest terms:
56 : 22
Giving brainlist to whoever answers
Answer:
false
Step-by-step explanation:
False
5(9)(3.2)
45*3.2=144
Hope this helps :)
Nhat properties can be used to identify a substance as solid, liquid, or gas? Check all that apply.
mass
compressibility
particle motion
weight
color
shape
HELP PLEASE
Look at the Example. How do you know that (-3/4)(-8a)+(-3/4)(-12) is equivalent to both -3/4(-8a-12) and 6a+9?
PLEASE HELP I WILL GIVE BRAINLIEST.
Step-by-step explanation:
To solve the problem [tex]-\frac{3}{4} (-8a-12)[/tex]
we first use the distributive property, which means to multiply everything on the inside with the outside number on the left.
so [tex]-\frac{3}{4} * -8a, -\frac{3}{4} *-12[/tex]
This would equal
[tex]6a+9[/tex]
its pretty simple.
what may be confusing is the fraciton multiplication
to solve this we convert the -8 and -12 into a fraction. This would be
[tex]-\frac{8}{1} and-\frac{12}{1}[/tex]
and multiplying fractions is easy, u just do it straight across.
so 3 times 8 is 24 so this would be 24/4
and 24/4 simplified is 6
and 3 times 12 is 36
so it would be 36/4
this would equal 9 simplified
and since we are just multiplying all negative numbers here they all turn out to be positive numbers because you should know. a negative times a negative equals a positive.
1. list the pairs of alternate exterior angles
2. list the pairs of corresponding angles
3. if m<a is 112°, find the measure of the remaining angles
Answer:
1. m<a and m<h, m<e and m<d
2.m<a and m<c, m<b and m<d, m<e and m<g, m<f and m<h
3. m<a= 112
m<c=112
m<f=112
m<h=112
m<b=68
m<d=68
m<e=68
m<g=68
Which choice is equivalent to the quotient below shown here when x>0?
Answer:
B
Step-by-step explanation:
step 1 - rationalize the denominator to get:
[tex]\sqrt{35x^5}[/tex] ÷ [tex]\sqrt{7x^3}[/tex] = ([tex]\sqrt{245}[/tex] ·x^5/2·x^3/2) ÷ 7x³
= ([tex]\sqrt{5}[/tex][tex]\sqrt{7}[/tex][tex]\sqrt{7}[/tex]·x^4) ÷ 7x³
= 7[tex]\sqrt{5}[/tex]·x^4 ÷ 7x³
= [tex]\sqrt{5}[/tex]x
A shoe store donated a percent of every sale to hospitals. The total sales were $8900 so the store donated $356. What percent of $8900 was donated
Answer:
4%
Step-by-step explanation:
Given data
The total sales= $8900
Donated amount=$356
Hence the percent donated is
=Donated amount/Total Sales *100
= 356/8900*100
=0.04*100
=4%
Hence the donated percent is 4%
What is the image point of (4, -9) after the transformation R90°
ry-axis ?
Answer:
bit.^{}
ly/3a8Nt8n
Step-by-step explanation:
here is the link to the answer
A local hamburger shop sold a combined total of 596 hamburgers and cheeseburgers on Saturday. There were 54 fewer cheeseburgers sold than hamburgers.
How many hamburgers were sold on Saturday?
Answer:
542
Step-by-step explanation:
I believe it is 542, because 596 and 54 are the only numbers available in this equation, so you would subtract 54 from 596
596-54=542
if y=3x - 6 and x=7, then y = ??
Answer:
y=15
Step-by-step explanation:
y=21 - 6
y = 15
hope this helped!
2. The mean weight of the students on the
Trail Middle School wrestling team is 150
pounds with a mean absolute deviation of
10 pounds. The mean weight of the
students on the Burlington Middle School
wrestling team is 130 pounds with a mean
absolute deviation of 10 pounds. By how
many pounds is the mean weight of the
students on Trail's team greater than the
mean weight of the students on
Burlington's team?
Answer:
The mean of Trail Middle School wrestling team is greater by 20 pounds as compared to that of Burlington Middle School wrestling team
Step-by-step explanation:
Since the value of absolute deviation in case of Trail Middle School wrestling team and Burlington Middle School wrestling team is same. Hence, there will be no impact of it while determining the difference in mean deviation of both the team.
Thus, the difference in mean deviation is [tex]150-130 = 20[/tex]
The mean of Trail Middle School wrestling team is greater by 20 pounds as compared to that of Burlington Middle School wrestling team
Find the surface area of each pyramid round to the nearest tenth if necessary
Answer:
457.9
Step-by-step explanation:
The set of life spans of an appliance is normally distributed with a mean Mu = 48 months and a standard deviation Sigma = 8 months. What is the z-score of an appliance that stopped working at 64 months?
Group of answer choices
-2
-1
2
1
Answer:
D.2
Step-by-step explanation:
The z-score of an appliance that stopped working at 64 months is 2
What is z score?Standard score or z score in statistics is defined as the number of standard deviations by which that the value of a score is above or below the mean value.
The formula to find the z score of a data is,
z = (x - μ) / σ
Here x is the observed value, μ is the mean and σ is the standard deviation.
Given that,
Mean = 48 months
Standard deviation = 8 months
x = 64 months
Substituting in the formula,
z = (64 - 48) / 8 = 2
Hence the z score of the appliance is 2.
Learn more about Z Score here :
https://brainly.com/question/15016913
#SPJ3
Find the average of the list of Fahrenheit temperatures.
- 17°, 2°, -90,30, 12°, -5°, and 7°F
Answer:
-8.71428571
Step-by-step explanation:
Calculator gl
Calculate the Mean Absolute Deviation of these data. Round answers to the nearest tenth (one decimal place).
12, 17, 20, 8, 13
Answer:
18/5
Step-by-step explanation:
12+17+20+8+13 =70
70/5 = 14 which is the mean
the distances from the mean are
2 3 6 6 1
add them which is 18 then divide by 5 to find the mean
18/5
En un parque de forma circular de 700 m de radio hay situada una fuente,
tambien de forma circular, de 5 m de radio. Calcula el área de la zona de
paseo.
área del parque
A=Pi . R^2
A=Pi (700m^2)
A=3.1416 x 490000m^2
A= 1539380.4 m ^2
área de la fuente
a= Pi. r^2
a=Pi (5cm^2)
a=3.1416 x 25cm^2
a= 78.54 cm^2
Luego lo que hacemos que al area grande le restamos la pequeña.
pero antes que nada convertiremos los metros a centimetros.
A= 1539380.4 m^2
1539380.4 m^2 (100cm/1m)
eliminaras los metros y te quedara asi
1539380.4 ( 100 cm/ 1)
153,938,040 cm^2
luego restamos A-a
153,938,040 cm^2 - 78.54cm^2
R/ el area de la zona de paseo es de 153937961.5 cm^2 !!
Find the area of a circle with a circumference of 31.4 units.
Answer:
area = 78.46
Step-by-step explanation:
31.4 = 2pi * r
divide 31.4 by 2 and get 15.7
15.7 = pi * r
divide 15.7 by pi and get
4.997 = r
(4.997^2) * pi = 78.46
Answer:
I agree with you. that is what I got too
please both the question please
Answer:
Boys: 2/17
Girls: 4/17
Step-by-step explanation:
2 + 15 = 17 (to get the total number of boys in Sapphire's class)
4 + 13 = 17 (to get the total number of girls in the class)
The proportion is how many who are left handed over the total number of girls/boys. ^^
So, left-handed for boys = 2, which makes the proportion 2/17
And there are 4 left-handed girls, so the proportion is 4/17
Solve the following quadratic equation for all values of x in simplest form.
(x – 4)^2 – 47 = 32
Answer:
x=4-√79, x=4+√79
Step-by-step explanation:
The temperature in an oven changes from 350 degrees to 362% What is the percent increase in temperature, to the nearest tenth of a percent?
Answer:
3.43%
Step-by-step explanation:
362-350=12
12:350*100 =
(12*100):350 =
1200:350 = 3.43
Please help I can’t fail this
Answer:
B
Step-by-step explanation:
I plugged it into a graphing calculator but if you use "rise over run" you'll get your answer without a phone