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.
What is the slope of the line that contains the points in the table?
х
У
15
-2
9
ON
3
4
-3
O A. 3
O B. -6
O c. 2
O D. -3
Answer:
https://www.dasd.org › 4444PDF
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Entering Algebra 2: Answer Key
Hi I need help with this question please!!! I don’t understand it :/
Answer:
- 22.5
Step-by-step explanation:
Substitute x = 3 into f(x) and x = 16 into h(x) , then
[tex]\frac{1}{2}[/tex] g(3) - h(16)
= [tex]\frac{1}{2}[/tex] × - 3(3)² - (2[tex]\sqrt{16}[/tex] + 1)
= [tex]\frac{1}{2}[/tex] × - 3(9) - (2(4) + 1)
= [tex]\frac{1}{2}[/tex] × - 27 - (8 + 1)
= - 13.5 - 9
= - 22.5
Given a right triangle with an acute angle Θ , if sin Θ = cos Θ , describe what this triangle would look like.
For sinø = cosø, ø = 45°. Because it is right, it is also a right, isosceles triangle
If a = 1/2, then a^2=
(A) -1
(B) 4
(C) 0
(D) 1
Answer:
1/4
Step-by-step explanation:
a^2
Let a= 1/2
(1/2)^2
(1/4)
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\mathsf{a^2}\\\\\mathsf{= \ (\dfrac{1}{2})^2}\\\\\mathsf{= \ \dfrac{1}{2}\times\dfrac{1}{2}}\\\\\mathsf{= \ \dfrac{1\times1}{2\times2}}\\\\\mathsf{= \ \bf \dfrac{1}{4}}[/tex]
[tex]\boxed{\boxed{\large\textsf{Therefore, the ANSWER is: }\boxed{\mathsf{\bf \dfrac{1}{4}}}}}\huge\checkmark[/tex]
[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
I need help with this math problem
GP
We have
(a + bx) / (a - bx) = (b + cx) / (b - cx)
==> (a + bx) (b - cx) = (a - bx) (b + cx)
==> ab + (b ² - ac) x - bcx ² = ab + (ac - b ²) x - bcx ²
==> (b ² - ac) x = (ac - b ²) x
==> b ² - ac = ac - b ²
==> 2b ² = 2ac
==> b ² = ac … … … [1]
Similarly, you would find
(a + bx) / (a - bx) = (c + dx) / (c - dx)
==> ad = bc … … … [2]
and
(b + cx) / (b - cx) = (c + dx) / (c - dx)
==> c ² = bd … … … [3]
Now:
c ² = bd ==> b = c ² / d
b ² = ac ==> c = b ² / a
ad = bc ==> d = bc / a
and we find
d / c = (bc / a) / (b ² / a) = c / b
and
c / b = (b ² / a) / (c ² / d) = (b ² d) / (a c ²) = b / a
which is to say, the ratio between d and c is equal to the ratio between c and b, and also equal to the ratio between b and a. Therefore (a, b, c, d) are in a geometric progression.
Can someone help me in this plz
Answer:
a =2 5
b =50
Step-by-step explanation:
Find the slope between (-2,-2) and (0,-3)
Answer:
Step-by-step explanation:
x1 y1 x2 y2
-2 -2 0 3
ΔY 5
ΔX 2
slope= 2 1/2
B= 3
Y =2.5X +3
SEE QUESTION IN IMAGE
Answer:
Step-by-step explanation:
[tex]Mean=\frac{all.ages.added.together.of.all.kids}{total.number.of.kids}[/tex] Hopefully, that makes sense! To get the numerator of that problem, we take the number of kids and multiply it by the corresponding age and add them all together. To get the denominator, we add the total number of kids together. That will look like this mathematically, setting the mean equal to 14.44, as stated:
[tex]14.44=\frac{13(15)+14(42)+15X+16(10)+17(3)}{15+42+X+10+3}[/tex] and simplify that a bit to
[tex]14.44=\frac{195+588+15X+160+51}{70+X}[/tex] and a bit more to
[tex]14.44=\frac{994+15X}{70+X}[/tex] and cross multiply
14.44(70 + X) = 994 + 15X and
1010.8 + 14.44X = 994 + 15X and
16.8 = .56X so
X = 30
30 kids are 15 years old for the mean age to be 14.44
d.30
Answer:
Solution given:
x. [tex] \:\:\:[/tex] f. [tex] \:\:\:[/tex] fx
13. [tex] \:\:\:[/tex] 15. [tex] \:\:\:[/tex] 195
14.[tex] \:\:\:[/tex] 42 [tex] \:\:\:[/tex] 588
15. [tex] \:\:\:[/tex] x. [tex] \:\:\:[/tex] 15x
16. [tex] \:\:\:[/tex] 10. [tex] \:\:\:[/tex] 160
17. [tex] \:\:\:[/tex] 3. [tex] \:\:\:[/tex] 51
. n=70+x. [tex]\sum[/tex]=994+15x
we have
mean=sum/n
14.44=[tex]\bold{\frac{\sum}{n}}[/tex]
14.44=[tex]\bold{\frac{994+15x}{70+x}}[/tex]
doing crisscrossed multiplication
(70+x)*14.44=994+15x
1010.8+14.44x=994+15x
15x-14.44x=1010.8-994
0.56x=16.8
x=16.8/0.56
x=30
Can someone Answer this
Answer:
tan x = c/b
cos x = b/a
sin x = c/a
Step-by-step explanation:
an easy way to memorize it would be SOH CAH TOA
SOH = sin, opposite, hypotunese
-- you find the angle and you divide it's opposite and hypotunese when it asks for sin
CAH = cos, adjacent, hypotunese
-- you find the angle's adjacent side and hypotunese, then divide
TOA = tan, opposite, adjacent
-- you find the angle's opposite side and divide it by the adjacent side
36. Factorize x-12x + 20
Parallelogram PARL is similar to parallelogram WXYZ. If AP = 7, PL = 15, and WZ = 45, find the value of c.
Answer:
c = 21
Step-by-step explanation:
**I assume that side WX in my diagram (attached as an image below) is the value of C that we're looking for. ALSO, the sizes and lengths of the parallelograms are NOT to scale.**
If two parallelograms are similar, that means the lengths of the corresponding sides have EQUAL ratios.
PL corresponds with WZ. To get from 15 to 45, you would multiply 15 by 3, so the ratio of the legnths of the corresponding sides between these two parallelograms is 1:3.
With that in mind, we can apply this ratio to find WX.
We know that AP has a length of 7, so we will multiply that by 3, getting a value of 21, and 7:21 ratio is the same as 1:3.
c = 21
Hope this helps (●'◡'●)
Help, please, I'll give brainliest
HHHHELP ME!!!!!! PLZ
Total gasoline = 10 gallons
Gasoline left after 100 miles = 5 gallons
Gasoline used in 100 miles
= Total gasoline - Gasoline left after 100 miles
= 10 gallons - 5 gallons
= 5 gallons
Gasoline used in 1 mile
= Gasoline used in 100 miles/100
= 5 gallons/100
= 0.05 gallons
Be sure to show your work and solve for e:
17 + e + 11 = 56
-2/3a+5/6a-1/5a-1/6
Answer:
[tex]\frac{-1}{30} a - \frac{1}{6}[/tex]
Step-by-step explanation:
Which statements are correct? Check all that apply.
Answer:
e s r
Step-by-step explanation:
Multiply. (Use photo). Enter your answer in simplest radical form.
Answer:
72√2
Step-by-step explanation:
3√2 × 2√8 × √3 × √6
The above can be simplified as follow:
3√2 × 2√8 × √3 × √6
Recall
a√c × b√d = (a×b)√(c×d)
3√2 × 2√8 × √3 × √6 = (3×2)√(2×8×3×6)
= 6√288
Recall
288 = 144 × 2
6√288 = 6√(144 × 2)
Recall
√(a×b) = √a × √b
6√(144 × 2) = 6 × √144 × √2
= 6 × 12 × √2
= 72√2
Therefore,
3√2 × 2√8 × √3 × √6 = 72√2
Fill in the following statements.
DE ||
2DE =
Answer:
DE ║ BC
BC = 2(DE)
Step-by-step explanation:
From the picture attached,
AD = DB [Given]
AE = EC [Given]
Therefore, points D and E will be the midpoints of the sides AB and AC.
By midsegment theorem,
Segment joining midpoints of the two sides of a triangle is parallel and measures the half of the third side of the triangle.
DE ║ BC
DE = [tex]\frac{1}{2}(BC)[/tex]
BC = 2(DE)
find the measure of acute angle of a right angle triangle when one angle is 60°
Answer:
30 degrees.
Step-by-step explanation:
Let the acute angle be x.
Then as the 2 acute angles in a right triangle sum to 90 degrees,
x = 90 - 60
= 30.
We used the information we know to give us this equation.
90°+60°+x=180°
We add 90° and 60° to give 150°
150°+x=180°
x must therefore be 30°The value of 9.6 x 10000 lies between
a) 800 and 900
b)300 and 400
c) 80 and 90
d) 30 and 40
Answer:
option A is write answer
I hope you help
Answer:
none of these
Step-by-step explanation:
it's 96000 so none
Please I need some help!
Answer:
A
Step-by-step explanation:
A compressed by a factor of 1/4 in the y or vertical direction
ZEFG and ZGFH are a linear pair, mZEFG = 2n + 16, and mZGFH = 3n+24. What are mZEFG and mZGFH?
mZEFG =
Answer:
m<EFG = 72°
m<GFH = 108°
Step-by-step explanation:
m<EFG = 2n + 16
m<GFH = 3n + 24
Linear pairs are supplementary, therefore,
m<EFG + m<GFH = 180°
Substitute
2n + 16 + 3n + 24 = 180
Add like terms
5n + 40 = 180
5n + 40 - 40 = 180 - 40 (subtraction property of equality)
5n = 140
5n/5 = 140/5 (division property of equality)
n = 28
✔️m<EFG = 2n + 16
Plug in the value of n
m<EFG = 2(28) + 16 = 72°
✔️m<GFH = 3n + 24
Plug in the value of n
m<GFH = 3(28) + 24 = 108°
What is a graph of g(x)=(2/3)x-2?
The graph above or below should answer the question.
What is the equation of the line of reflection? please help, due in 30 minutes!!!
Answer:
The line of reflection is usually given in the form y = m x + b y = mx + b y=mx+by, equals, m, x, plus, b.
Step-by-step explanation:
Answer:
The line of reflection in [tex]y=mx+b[/tex] form is [tex]y=\frac{1}{3} x-2[/tex]
Step-by-step explanation:
An object is launched at 19.6 meters per second (m/s) from a 58.8-meter tall platform. The equation for the
object's height s at time t seconds after launch is s(t) = - 4.9t2 + 19.6t + 58.8, where s is in meters. Create a
table of values and graph the function. Approximately what is the maximum height that the object will get?
O 76.4 meters
113.5 meters
O 78.4 meters
58.8 meters
Answer:
Step-by-step explanation:
The easiest way to do this is to complete the square on the quadratic. This allows us to see what the vertex is and answer the question without having to plug in a ton of numbers to see what the max y value is. Completing the square will naturally put the equation into vertex form:
[tex]y=-a(x-h)^2+k[/tex] where h will be the time it takes to get to a height of k.
Begin by setting the quadratic equal to 0 and then moving over the constant, like this:
[tex]-4.9t^2+19.6t=-58.8[/tex] and the rule is that the leading coefficient has to be a 1. Ours is a -4.9 so we have to factor it out:
[tex]-4.9(t^2-4t)=-58.8[/tex] Now take half the linear term, square it, and add it to both sides. Our linear term is a -4, from -4t. Half of -4 is -2, and -2 squared is 4, so we add a 4 to both sides. BUT on the left we have that -4.9 out front there as a multiplier, so we ACTUALLY added on to the left was -4.9(4) which is -19.6:
[tex]-4.9(t^2-4t+4)=-58.8-19.6[/tex] and now we have to clean this up. The right side is easy, that is -78.4. The left side...not so much.
The reason we complete the square is to create a perfect square binomial, which is the [tex](x-h)^2[/tex] part from above. Completing the square does this naturally, now it's just up to us to write the binomial created during the process:
[tex]-4.9(t-2)^2=-78.4[/tex] Now, move the constant back over and set the equation back equal to y:
[tex]-4.9(t-2)^2+78.4=s(t)[/tex] and we see that the vertex is (2, 78.4). That means that 2 seconds after launch, the object reached its max height of 78.4 meters, the third choice down.
Pls help me this is my homework
Answer:
C) 840
C) 87
D) 3000-150n
Step-by-step explanation:
Answer:
c
c
d
Step-by-step explanation:
A survey was done that asked students to indicate whether they enjoy reading or playing video games.
What is the ratio of those who do not enjoy reading and those who do not enjoy playing video games?
Enter your answer, in simplified form without using decimals, in the boxes.
please help me :D
Answer:
9 to 3
Step-by-step explanation:
Those who don't enjoy reading: 8+1=9
Those who don't enjoy playing video games: 1+2=3
Ratio is 9 to 3.
What is the tangent ratio of angle x?
tan x= 20/21
tan x= 21/29
tan x= 20/29
tan x= 21/20
Answer:
[tex]\tan x=21/20[/tex]
Step-by-step explanation:
In any right triangle, the tangent of an angle is equal to its opposite side divided by its adjacent side. (o/a)
For angle [tex]x[/tex], its opposite side is 21 feet and its adjacent side is 20 feet. Therefore, we have:
[tex]\boxed{\tan x=21/20}[/tex]
An airplane from Singapore to Melbourne takes about 7 1/2 hours to cover a distance of 6057 km. What is the average speed of the airplane.
Answer: 13.46 km/h
Step-by-step explanation:
7 1/2 hr= 450 min
6057/450= 13.46
WILL MARK BRAINLIEST
picture included^^^^
need help asap please n thank you!
^^^^
Answer:
14
Step-by-step explanation:
The a value is from the center to the maximum
We want from minimum to max so we need 2 times the amplitude
a = 7
2 *7 = 14
