Answer:
Length=8
Step-by-step explanation:
128= Length×Width
W=2L
so we can rewrite the first equation as:
128=L×2L
128=2L²
64=L²
8=L
and W=2L so:
W=2(8)
W=16
f(x) = 2[tex]x^{2}[/tex]+ x − 4 for x ∈R, a ≤ x ≤ a+3. If the range of the function f is −2 ≤ f(x) ≤ 16, find the possible values of a.
Answer:
No answer is possible
Step-by-step explanation:
First, we can identify what the parabola looks like.
A parabola of form ax²+bx+c opens upward if a > 0 and downward if a < 0. The a is what the x² is multiplied by, and in this case, it is positive 2. Therefore, this parabola opens upward.
Next, the vertex of a parabola is equal to -b/(2a). Here, b (what x is multiplied by) is 1 and a =2, so -b/(2a) = -1/4 = -0.25.
This means that the parabola opens upward, and is going down until it reaches the vertex of x=-0.25 and up after that point. Graphing the function confirms this.
Given these, we can then solve for when the endpoints of the interval are reached and go from there.
The first endpoint in -2 ≤ f(x) ≤ 16 is f(x) = 2. Therefore, we can solve for f(x)=-2 by saying
2x²+x-4 = -2
add 2 to both sides to put everything on one side into a quadratic formula
2x²+x-2 = 0
To factor this, we first can identify, in ax²+bx+c, that a=2, b=1, and c=-2. We must find two values that add up to b=1 and multiply to c*a = -2 * 2 = -4. As (2,-2), (4,-1), and (-1,4) are the only integer values that multiply to -4, this will not work. We must apply the quadratic formula, so
x= (-b ± √(b²-4ac))/(2a)
x = (-1 ± √(1-(-4*2*2)))/(2*2)
= (-1 ± √(1+16))/4
= (-1 ± √17) / 4
when f(x) = -2
Next, we can solve for when f(x) = 16
2x²+x-4 = 16
subtract 16 from both sides to make this a quadratic equation
2x²+x-20 = 0
To factor, we must find two values that multiply to -40 and add up to 1. Nothing seems to work here in terms of whole numbers, so we can apply the quadratic formula, so
x = (-1 ± √(1-(-20*2*4)))/(2*2)
= (-1 ± √(1+160))/4
= (-1 ± √161)/4
Our two values of f(x) = -2 are (-1 ± √17) / 4 and our two values of f(x) = 16 are (-1 ± √161)/4 . Our vertex is at x=-0.25, so all values less than that are going down and all values greater than that are going up. We can notice that
(-1 - √17)/4 ≈ -1.3 and (-1-√161)/4 ≈ -3.4 are less than that value, while (-1+√17)/4 ≈ 0.8 and (-1+√161)/4 ≈ 2.9 are greater than that value. This means that when −2 ≤ f(x) ≤ 16 , we have two ranges -- from -3.4 to -1.3 and from 0.8 to 2.9 . Between -1.3 and 0.8, the function goes down then up, with all values less than f(x)=-2. Below -3.4 and above 2.9, all values are greater than f(x) = 16. One thing we can notice is that both ranges have a difference of approximately 2.1 between its high and low x values. The question asks for a value of a where a ≤ x ≤ a+3. As the difference between the high and low values are only 2.1, it would be impossible to have a range of greater than that.
Help asap sorry for the blurry pic
Total mass = 8 kg
Mass of tool 1 = 4 kg
Mass of tool 2 = 2 kg
So,
Total mass = Mass of tool 1 + Mass of tool 2 + Mass of tool 3
=> 8 kg = 4 kg + 2 kg + Mass of tool 3
=> 8 kg = 6 kg + Mass of tool 3
=> 8 kg - 6 kg = Mass of tool 3
=> 2 kg = Mass of tool 3
The sporting goods store sells 6 different brands of tennis rackets and 4 different brands of tennis balls. If Amanda buys one brand of tennis racket and one brand of tennis balls, how many different combinations of brands can she buy ?
10
12
16
24
Answer:
24
Step-by-step explanation:
There are 6 different types of rackets and 4 different types of balls.
To determine the number of different combinations
6 rackets * 4 balls
24 combinations
Answer:
24
Step-by-step explanation:
Here are the numbers of children in 11 elementary school classes.
18, 18, 17, 18, 19, 20, 17, 17, 17, 18, 20
Find the modes of this data set.
Hey there!
Mode is basically the number(s) in a data plot you see MORE THAN once
• 18 appeared four times (this could be a possible answer)
• 17 appeared four times (this could be a possible answer)
• 19 appeared one time (this can’t be your answer)
• 20 appeared two times (this could be a possible answer)
Possible answers: 17,18, & 20
Since 17 & 18 appeared the MOST in the data plot those numbers could be your mode in your given data plot
Answer: 17 & 18
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
I don’t understand how to find the height
Answer:
height, x is 235 ft
Step-by-step explanation:
From trigonometric ratios:
[tex] \cos( \theta) = \frac{adjacent}{hypotenuse} [/tex]
but:
[tex] \theta = 90 \degree - 36 \degree \\ \theta = 54 \degree[/tex]
adjacent is x
hypotenuse is 400 ft
[tex] \ \cos ( 54 \degree) = \frac{x}{400} \\ \\ x = 400 \ \cos (54 \degree) \\ x = 235 \: \: feet[/tex]
Answer:
[tex]235\ ft[/tex]
Step-by-step explanation:
In this problem, one is given two parallel lines and a few transversals that form a triangle between these parallel lines. The parallel lines, one from the parasailer, and one from the boat have an angle of depression between them. This means the angle of elevation from the boat to the parasailer is also (36) degrees. This is due to the alternate interior angles theorem, which states that when two parallel lines are intersected by a transversal, then the alternate interior angles are congruent.
The triangle formed in this situation is a right triangle, this is indicated by the box around one of the angles. Now that one has found another angle measure in this triangle, one can use right angle trigonometry. Right angle trigonometry is a series of ratios that describe the relationship between the sides and angles of a right triangle. These ratios are as follows:
[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}[/tex]
Please note that the names (opposite) and (adjacent) are subjective, and change relative to the angle one is looking at, however (hypotenuse) refers to the side opposite the right angle. This side doesn't change its name. In this situation, it would be most logical to use the ratio of sine, (sin), as one has the measure of the hypotenuse, and one is trying to find the measure of the side opposite the angle. Substitute the given information into the ratio of (sin) and solve to find the unknown:
[tex]sin(\theta)=\frac{opposite}{hypotenuse}[/tex]
[tex]sin(36)=\frac{x}{400}[/tex]
Inverse operations,
[tex]sin(36)=\frac{x}{400}[/tex]
[tex]400(sin(36))=x[/tex]
[tex]235.114=x[/tex]
What is the midpoint of the segment shown below?
10
O A. (-1,-1)
(-11, 0)
O B. (-2, -3)
O C. (-1, -3)
- 10
10
(9,-1)
- 10
D. (-2, -1)
Answer:
(-1,-0.5)
Step-by-step explanation:
Find the solution to this problem by using the midpoint formula which is (x1+x2/2,y1+y2/2) plug in the values of y and x to get -11+9/2+0-1/2. simplify to get the solution of (-1,-0.5)
Divide Rs.45000 among 2 students Mina and Rita in the ratio of marks they got 40 and 50 respectively
Let
Money share of Mina=40xMoney shae of Rita=50xATQ
[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow 40x+50x=45000[/tex]
[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow 90x=45000[/tex]
[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow x=\dfrac{45000}{90}[/tex]
[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow x=500[/tex]
Now
[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow Rita=50x=50(500)=25000[/tex]
[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow Mina=40x=40(500)=20000[/tex]
The graph below could be the graph of which exponential function?
Answer:
B
Step-by-step explanation:
Please answer before 2:30!!!
There are 189 apples in a basket. How many children can share them equally?
List all numbers that apply.
For the equal distribution each child can take either 1 or 3 or 7 or 9 or 21 or 27 or 63 or 189 apple.
What is equal distribution?
The distribution of a something in a way that each will get same amount.
How 189 can be divided equally?
If the distribution is equally then each child should take, either 1 or 2 or 3 an so on means same amount.
For this we will check that 189 is divisible by which numbers.
Now we can see that 189 is divisible by 1, 3, 7, 9, 21, 27, 63, 189. It is clear that each child can take either 1 or 3 or 7 or 9 or 21 or 27 or 63 or 189 apple then the distribution will be equal means every child will have same amount of apple.
Therefore, the correct answer is 1, 3, 7, 9, 21, 27, 63, 189.
Learn more: https://brainly.ph/question/4734029
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What is the value of l n e Superscript 4
Answer:
4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
what is meant by derivative
Answer:
its basically just rate of change or slope. with derivatoves you can find the slope of a tangent line which is a line that touches the curve at a point.
Please help explanation if possible
Answer:
(x,y) —> (–1 ,1)
I hope I helped you ^_^
Help find the equivalent fraction with the correct steps please !
-2/5 x 6/-1 ÷ 5/-2
What’s the equivalent fraction ? Please help! Tysm (:
Answer:
: = ÷
[tex]\frac{-2}{5}*\frac{6}{-1} : \frac{5}{-2} = \frac{-12}{-5} : \frac{5}{-2} = \frac{12}{5}*\frac{-2}{5}=\frac{-24}{25}[/tex]
An equivalent fraction is -24 over 25.
Ariana is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Ariana will earn $40 every time one of her songs is played in a commercial and she will earn $110 every time one of her songs is played in a movie. Ariana earned a total of $500 in royalties on 9 commercials and movies. Write a system of equations that could be used to determine the number of commercials and the number of movies on which Ariana's songs were played. Define the variables that you use to write the system.
A bookstore is selling books for $10 each. Which graph shows the relationship between the number of books, x, the store sold and the total amount of money, y, paid from the book sales?
Answer:
Graph B
Explanation:
(t + 1)(t2 + 2t + 4)
find the product.
Answer:
5+5t
Step-by-step explanation:
The answer you are looking for is t^3+3t^2+6t+4.
Solution:
(t+1)(t^2+2t+4)
t^3+2t^2+4t+t^2+2t+4
t^3+3t^2+6t+4
Write an equation in slope-intercept form for the line with slope 3/5 and y-intercept -1.
Answer:
y=3/5x-1
Step-by-step explanation:
Help me with this pls IM FAILING PYTHAGOREAN THEOREM
Answer: 33
Work Shown:
Apply the pythagorean theorem to get
[tex]a^2 + b^2 = c^2\\\\x^2 + 44^2 = 55^2\\\\x^2 + 1936 = 3025\\\\x^2 = 3025 - 1936\\\\x^2 = 1089\\\\x = 33[/tex]
16. Mrs. Acosta wants to buy 2 flag pins
for each of the 168 band members for
the Fourth of July Parade. Pins cost
$0.09 each. Which is the best estimate
of the cost of the pins?
What describes the correct way to convert minutes to an hour
Answer:
Yo mean correct way??
yo can divide minute by 60 to convert minute into hour
For example
To convert 10 minute into hour. then we should divide 10 by 60. 10/60
Answer:
In any conversion you have to establish ratios (or rates) for the different units being converted.
The process will be performed by a series of multiplications that will cancel out the "unwanted" units.
multiplication by one (1) does not change the value in an equation.
you have to multiply by a "series of ones" that take into account the units being converted..
for example
1 minute/60 seconds or 1 inch = 2.54 cm or 1 day = 24 hours
in your problem you have minutes... lets say you have 100 minutes
100 minutes * 1 hour minutes cancel and you have 100/60 = 1 [tex]\frac{2}{3}[/tex] hrs
60 minutes
Step-by-step explanation:
khan academy
help:,)
Answer:
5
Step-by-step explanation:
It is 5 because you just have to count by using a jumping math tectechnique.
Please anyoneeeeeeee.....i am almost done just please help me
Answer:
B. XV and XY
Step-by-step explanation:
you can eliminate the top two options because those aren't rays. XV and XY are the only ones that end in X
Need answer asap algebra 2 math
Answer:
B
Step-by-step explanation:
f(x) = 2x^2 - 4x + 5 Put brackets around the first 2 terms.
f(x) = (2x^2 - 4x) + 5 Take out the common factor of 2
f(x) = 2(x^2 - 2x) + 5 1/2 the second term and square.
f(x) = 2(x^2 -2x + (2/2)^2) + 5 Express brackets as a perfect square.
f(x) = 2(x - 1)^2 + 5 Multiply 2 * 1 (the term without an x. Subtract.
f(x) = 2(x - 1)^2 + 5 - 2 Combine
f(x) = 2(x - 1)^2 + 3
A room is twice as long as it is broad and its height is 8 m. if the cost of painting its walls at Rs. 20 per m² is Rs 9600 , find the cost of carpeting its floor at Rs. 400 per m²
let breadth be X
length = 2x
height = 8m
rate of painting the four wall= 20/m^2
cost of painting=9600
Area of four wall= cost of painting / rate
= 9600/20
= 480m^2
again,
Area of four wall = 2 h(l+b)
or, 480=2×8(X+2x)
or, 480/16=3x
or, 30/3=X
or, X= 10m
again,
2x= 2×10m=20m
again,
Area of floor = length × breadth
= 20×10
=200m^2
again,
rate of carpeting the floor= 400/m^2
cost of carpeting the floor = rate × area
= 400× 200
= Rs. 80000
Use factoring to determine the x-intercepts and vertex of the quadratic function
y = 2x2 + 5x - 3 (pls answer)
consindering the equation ""yvariable m is the intercept ,,c constant
therefore from the equation by comparing...=mx+c where y
Select the best answer to describe the parabola
Answer:
B
Step-by-step explanation:
It opens downwards, so the parabola is negative. This also means the vertex of the parabola is the highest point, therefore it is a maximum.
Fifthteen of student took a math test. Eight student scored 75, five scored 82 and two scored 95. What was the average of there score
Answer:
84
Step-by-step explanation:
To find the average of the data or the mean, add 75, 82, and 95 which is 252, then 252 divided by 3 = 84. Hopefully, this helps :)
What should the equations look like for each number? 17-20
Answer:
See below.
Step-by-step explanation:
17.)
[tex]x+100+120+100=360\\x+320=360\\x=40[/tex]
18.)
[tex]x+150+77+48=360\\x+275=360\\x=85[/tex]
19.)
[tex]x+122+92+76=360\\x+290=360\\x=70[/tex]
20.)
[tex]x+115+85+60=360\\x+260=360\\x=100[/tex]
three consecutive even numbers add up to 105 determine the product of the three numbers
Answer:
34 + 35 + 36 = 105
Step-by-step explanation:
Find the length of the third side. If necessary, round to the nearest tenth.
12
13
Answer:
Submit Answer
attempt 1 out of 2
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PLS HELP ASAP
Answer:
5
Step-by-step explanation:
Use pythagorean theorem. A^2+B^2=C^2
13 is c because it is the hypotenuse and across from the right angle
a is unknown and b is 12
A^2+12^2=13^2
A^2 +144 = 169
A^2 = 169- 144
A^2= 25
now take the sq root of both side
A = 5
Answer:
17.7
Step-by-step explanation:
