Find the value of x. If necessary, found your answer to the nearest tenth. The figure is not drawn to scale
Answers
Related Questions
Which ordered pair is the vertex of y = [x - 3]+ 2?
A.(2, –3)
B.(–3, 2)
C.(3, 2)
D.(2, 3)
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Factor \2x^2-11x+5=0
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2x² - x - 10x + 5
x(2x - 1) - 5(2x - 1)
(2x - 1)(x- 5) is your answer.
The quadratic equation [tex]2x^2[/tex]-11x+5=0 is factored into (2x - 1)(x - 5), and it has solutions x = 0.5 and x = 5.
Explanation:The question asks us to factor the quadratic equation[tex]2x^2[/tex]-11x+5=0. To do this, we need to find two numbers that multiply to give ac (where a is the coefficient of x^2 and c is the constant term) and add to give b (the coefficient of x). Here, ac is (2)(5)=10, and b is -11. The two numbers that satisfy this are -10 and -1 because -10 * -1 = 10 and -10 + -1 = -11.
We rewrite the middle term using these two numbers and then group the terms to factor by grouping:
[tex]2x^2[/tex]- 10x - x + 5 = 0([tex]2x^2[/tex]- 10x) - (x - 5) = 0
2x(x - 5) - 1(x - 5) = 0
(2x - 1)(x - 5) = 0
The factored form of the quadratic equation is (2x - 1)(x - 5). Therefore, the solutions to the equation are x = 0.5 and x = 5, found by setting each factor equal to zero.
What is the vertex of the quadratic function f(x) = (x - 8)(x - 2)
Answers
Answer: (5, -9)
What is the vertex of the quadratic function f(x) = (x – 8)(x – 2)?
PLz help!
Write the equation of the line that passes through (3, −2) and has a slope of 4 in point-slope form. (2 points)
1 y + 2 = 4(x − 3)
2 y − 3 = 4(x + 2)
3 x − 3 = 4(y + 2)
4 x + 2 = 4(y − 3)
Answers
It's the first answer.
Given that the slope = 4 and the coordinate is (3, -2),
[tex]4 = \dfrac{y + 2}{x + 3} [/tex]
[tex] y + 2 = 4(x - 3) [/tex]
Answer : y + 2 = 4(x - 3) (Answer A)
Which of the following functions are their own inverses? Select all that apply.
a. t(p) = p
b. y(j) = -1/j
c. w(y) = -2/y
d. d(p) = 1/x^2
Answers
The appropriate choices are ...
a. t(p) = p
b. y(j) = -1/j
c. w(y) = -2/y
Answer:
a,b and c.
Step-by-step explanation:
We have to find the the functions that are their own inverses.
a.t(p)=p
Then the inverse function of given function is
[tex]p=t^{-1}(p)[/tex]
Therefore, the given function is inverse function of itself.
Hence, option a is true.
b.y(j)=[tex]-\frac{1}{j}
Let y(j)=y then we get
[tex]y=-\frac{1}{j}[/tex]
[tex]j=-\frac{1}{y}[/tex]
[tex]j=-\frac{1}{y(j)}[/tex]
[tex]j=-\frac{1}{\frac{-1}{j}}[/tex]
[tex]j=j[/tex]
Hence, the function is inverse of itself.Therefore, option b is true.
c.[tex]w(y)=-\frac{2}{y}[/tex]
Suppose that w(y)=w
Then [tex]w=-\frac{2}{y}[/tex]
[tex]y=-\frac{2}{w}[/tex]
[tex]w(y)=-\frac{2}{-\frac{2}{w}}[/tex]
[tex]w(y)=w[/tex]
[tex]w(y)=-\frac{2}{y}[/tex]
Hence, the function is inverse function of itself.Therefore, option c is true.
d.[tex]d(p)=\frac{1}{x^2}[/tex]
Let d(p)=d
If we replace [tex]\frac{1}{x^2}by p then we get
[tex]d=\frac{1}{x^2}[/tex]
[tex]x^2=\frac{1}{d}[/tex]
[tex]x=\sqrt{\frac{1}{d}}[/tex]
[tex]x=\sqrt{\frac{1}{d(p)}[/tex]
Hence, the function is not self inverse function.Therefore, option d is false.
Two events are independent when the following is true:
a. the outcome of one event determines the outcome of the other event
b. there is no correlation between the two events
c. the outcome of one event does NOT determine the outcome of the other event
d. The outcome of the event is determined by the theoretical probability of the event
Answers
Solution:
Independent Events:
Consider an experiment of Rolling a die, then getting an even number and multiple of 3.
Total favorable outcome = {1,2,3,4,5,6}=6
A=Even number = {2,4,6}
B=Multiple of 3 = {3,6}
A ∩ B={6}
P(A)=[tex]\frac{3}{6}=\frac{1}{2}[/tex], P(B)= [tex]\frac{2}{6}=\frac{1}{3}[/tex]
P(A ∩ B)=[tex]\frac{1}{6}[/tex]
So, P(A)× P( B)=[tex]\frac{1}{2}\times\frac{1}{3}=\frac{1}{6}[/tex]=P(A ∩ B)
Hence two events A and B are independent.
Option (c). the outcome of one event does NOT determine the outcome of the other event
Answer:
C on edge or the outcome of one event does NOT determine the outcome of the other event
Step-by-step explanation:
The table shows the number of boys and girls that have black, blonde, brown, or red hair color. What is the probability that a student is a boy with red hair? (round to nearest hundredth)
Hair Color Boys Girls
Black 4 5
Blonde 4 6
Brown 10 8
Red 2 1
Answers
the probability that the student is a boy with red hair is 2/40 = 0.05.
Answer:
0.05
Step-by-step explanation:
Given :
Hair Color Boys Girls
Black 4 5
Blonde 4 6
Brown 10 8
Red 2 1
Solution :
Since ware required to find the probability that a student is a boy with red hair.
Total no. of boys with red hair = 2
Total no. of students = 4+4+10+2+5+6+8+1=40
Thus the probability that a student is a boy with red hair = [tex]\frac{\text{No. of boys with red hair }}{\text{total no. of students }}[/tex]
⇒[tex]\frac{2}{40}[/tex]
⇒[tex]\frac{1}{20}[/tex]
⇒[tex]0.05[/tex]
Hence the probability that a student is a boy with red hair is 0.05
What is the area of sector GPH?
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The area of the shaded area = (40/360) * pi r^2
r = 9 cm
Area of the shaded area = 1/9 * 3.14 * 9^2
Area of the shaded area = 3.14 * 9
Area of the shaded area = 28.26
Notice one of the 9s disappeared. Where did it go?
You could begin the problem by writing out 9^2
Area = 1/9 * 3.14 * 9 * 9 Notice that 1/9 will cancel out 1 of the nines.
28.26 yds = Shaded area.
The area of sector GPH is [tex]\(\frac{1}{4}\pi r^2\).[/tex]
To find the area of sector GPH, we use the formula for the area of a sector of a circle, which is given by [tex]\(\frac{\theta}{360^\circ} \times \pi r^2\)[/tex], where [tex]\(\theta\)[/tex] is the central angle of the sector in degrees, and [tex]\(r\)[/tex] is the radius of the circle.
Given that the central angle of sector GPH is [tex]\(90^\circ\) (or \(\frac{\pi}{2}\)[/tex] radians, since[tex]\(180^\circ\) is \(\pi\) radians)[/tex], and the radius [tex]\(r\)[/tex] is unspecified, we can express the area of the sector in terms of [tex]\(r\).[/tex]
Using the formula for the area of a sector:
[tex]\[ \text{Area of sector GPH} = \frac{\theta}{360^\circ} \times \pi r^2 \][/tex]
Substituting [tex]\(\theta = 90^\circ\):[/tex]
[tex]\[ \text{Area of sector GPH} = \frac{90^\circ}{360^\circ} \times \pi r^2 \][/tex]
Simplifying the fraction:
[tex]\[ \text{Area of sector GPH} = \frac{1}{4} \times \pi r^2 \][/tex]
So, the area of sector GPH is [tex]\(\frac{1}{4}\pi r^2\)[/tex], which is one-fourth of the area of the entire circle. This makes sense because the sector represents a quarter of the circle's area due to its [tex]\(90^\circ\)[/tex] central angle.
Given: KLMN is a trapezoid, KF =10 MF ║ LK AKLMF = AFMN Find: KN
Answers
We know:
LK // MF
KF = 10
A(KLMF) = A(FMN)
Since LM // KF (because they are bases of the trapezoid) and LK // MF because is given in the hypothesis, KLMF is a parallelogram.
The area of a parallelogram is given by the base times the height.
A(KLMF) = b × h
= 10 × h
The area of a triangle is given by the formula:
A(FMN) = (b × h) / 2
= (FN × h) / 2
We know that the two areas are congruent, therefore:
A(KLMF) = A(FMN)
10 × h = FN × h / 2
The two "h" cancel out because they are the same and we can solve for FN:
10 = FN / 2
FN = 20
Now we can calculate:
KN = KF + FN = 10 + 20 = 30
Hence, KN is 30 units long.
In a trapezoid with parallel sides, if a pair of opposite sides are equal, then the other pair of opposite sides are also equal. Therefore, in the given trapezoid KLMN, KN is equal to AN + 10.
Explanation:In the given trapezoid KLMN, the sides KF and LM are parallel. We are given that KF = 10 and AFMN = AKLMF. We need to find KN.
Since KF and LM are parallel, KF = LM. Therefore, LM = 10.
Since AFMN = AKLMF, we can say that AN = KL. So, AN + LM = KL + KF. Substituting the given values, we get AN + 10 = KL + 10. Therefore, AN = KL.
Hence, KN = KL + LM = AN + LM = AN + 10.
Therefore, KN = AN + 10.
Yanis fires pottery in a kiln. He decides to measure the rate of change of temperature of the pottery over time. What would be an appropriate unit for Yanis's purpose?
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Answer with explanation:
Pottery is on a Kiln.
Unit of temperature can be Kelvin(°K) or Degree Celsius(°C) or Fahrenheit(°F).
Unit of time is second, minute and hour.
Rate of change of temperature of the pottery over time can be written as
[tex]1.=\frac{\text{Degree Celsius}}{\text{Second}}\\\\2.=\frac{\text{Degree Celsius}}{\text{Minute}}[/tex]
Internationally , Kelvin is used as S.I unit of Temperature.
So,Yanin can use
[tex]1.=\frac{\text{Kelvin}}{\text{Second}}\\\\2.=\frac{\text{Kelvin}}{\text{Minute}}[/tex]
as Rate of change of temperature of the pottery over time.
Solve the equation 3x+5y=4
for y
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Answer:
y = (4 -3x)/5
Step-by-step explanation:
Find the terms containing y. If they are all on one side of the equation (it is), then identify the terms not containing y. Subtract those. Then, divide by the coefficient of y.
3x +5y = 4
5y = 4 - 3x . . . . . non-y term subtracted
y = (4 -3x)/5 . . . . divide by the coefficient of y
_____
If you like, you can rearrange this to slope-intercept form:
... y = -3/5x +4/5
A cirlce with a radius of 8 cm rotates 30 degrees in one second. Determine the angle of rotation in radians.
Angle:___ w:___ v:___
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[tex]\bf \begin{array}{ccll} de grees&radians\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 180&\pi \\\\ 30&x \end{array}\implies \cfrac{180}{30}=\cfrac{\pi }{x}\implies x=\cfrac{30\pi }{180}\implies x=\cfrac{\pi }{6}\\\\ -------------------------------\\\\ \stackrel{angular~velocity}{w}=\cfrac{\stackrel{central~angle}{\frac{\pi }{6}}}{\stackrel{time}{1~s}}\implies w=\cfrac{\pi }{6}~\frac{radians}{seconds}[/tex]
[tex]\bf \textit{arc's length}\\\\ s=r\theta ~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\ ------\\ r=8\\ \theta =\frac{\pi }{6} \end{cases}\implies s=8\cdot \cfrac{\pi }{6}\implies s=\cfrac{4\pi }{3} \\\\\\ \stackrel{linear~velocity}{v}=\cfrac{\stackrel{arc's~length}{\frac{4\pi }{3}}}{\stackrel{time}{1~s}}\implies v=\cfrac{4\pi }{3}~\frac{cm}{seconds}[/tex]
Chloe puts 4 soaps and two bottles of lotion in each gift basket. She has 127 soaps and 85 bottles of lotion. How many gift baskets can Chloe complete?
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85/2 = 42.5 = 43
She can only make 31 full gift baskets with the amount of soap she has.
Therefore, Chloe can make 31 gift baskets.
Help ASAP PLEASE!!! match the term with the appropriate definition.
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2) 5x+1>=11→5x+1-1>=11-1→5x>=10→5x/5>=10/5→x>=2: Option J. x>=2, closed dot at 2 and shaded to the right
3) x-7>-4→x-7+7>-4+7→x>3: Option H. x>3, open dot at 3 and shaded to the right
4) -2x<6→(-1/2)(-2x<6)→(-1/2)(-2x)>(-1/2)(6)→x>-3: Option G. x>-3, open dot at -3 and shaded to the right
5) 4<-4x→(-1/4)(4<-4x)→(-1/4)(4)>(-1/4)(-4x)→-1>x→x<-1: Option B. x<-1, open dot at -1 and shaded to the left
6) -2x+3<-7→-2x+3-3<-7-3→-2x<-10→(-1/2)(-2x<-10)→
(-1/2)(-2x)>(-1/2)(-10)→x>5: Option A. x>5, open dot at 5 and shaded to the right
7) 2x<=6→2x/2<=6/2→x<=3: Option I. x<=3, closed dot at 3 and shaded to the left
8) 3(x+4)>8x-6→3x+12>8x-6→3x+12-3x+6>8x-6-3x+6→18>5x→
18/5>5x/5→18/5>x→x<18/5: Option E. x<18/5, open dot at 18/5 and shaded to the left
9) -3x+4<-x+2→-3x+4+3x-2<-x+2+3x-2→2<2x→2x>2→2x/2>2/2→x>1: Option C. x>1, open dot at 1 and shaded to the right
10) -2(x-4)>5-(x+2)→-2x+8>5-x-2→-2x+8>3-x→-2x+8+2x-3>3-x+2x-3→
5>x→x<5: Option D. x<5, open dot at 5 and shaded to the left
To win at lotto in a certain state, one must correctly select 6 numbers from a collection of 50 numbers (one through 50). the order in which the selections is made does not matter. how many different selections are possible?
Answers
https://brainly.com/question/10013755
We have been given that the order doesn't matter in the selection procedure. Hence, the case is of combination.
The formula for the combination is given by
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
Now, in order to win at lotto, one must correctly select 6 numbers from a collection of 50 numbers. Thus, the required ways should be
[tex]^{50}C_6[/tex]
Using the above formula, the number of different selections are
[tex]^{50}C_6=\frac{50!}{6!(50-6)!}\\ \\ =\frac{50!}{6!44!}\\ \\ =\frac{44!\times 45\times 46\times 47 \times 48\times 49\times 50}{6!44!}\\ \\ =15890700[/tex]
Therefore, 15890700 different selections are possible.
Amy has 5 yards of border to put around a garden. She uses all the border to make four sections that are the same length. Which expession does not equal the length of one these sections in yards?
Answers
Answer:
F. 4 ÷ 5
Explanation:
We know that Amy has 5 yards of boarders and that she will use them to make 4 equal borders.
This means that:
she will divide 5 yards by 4 to know the length of each border
Among the given choices, choices G, H and J show the division of 5 by 4 which is correct representation of the length
On the other hand. choice F shows the division of 4 by 5 which is an incorrect representation of the length.
Hope this helps :)
Answer:
4 ÷ 5
Step-by-step explanation: becuz i said so
HELP
______________________
Answers
x*50 = y
Answer:
The answer is the third option/choice.
which transformations are needed to change the parent some function to the sine function below?
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Vertical compression of 1/2 compresses the range from -1/2 to 1/2
Phase shift of pi/2 to the left
Horizontal stretch to a period of 4pi, as the crests are at -4pi, 0, 4pi
Vertical shift of 1 unit up moves the range to 1/2 to 3/2
So the first choice looks like a good answer.
Solution:
the function y = sin x, which would have range from -1 to 1 and period of 2pi:
So the answer would be:Vertical compression of 1/2 compresses the range from -1/2 to 1/2Phase shift of pi/2 to the leftHorizontal stretch to a period of 4pi, as the crests are at -4pi, 0, 4piVertical shift of 1 unit up moves the range to 1/2 to 3/2
Q # 15 in the diagrams a || b a. Use the fiagrama o answer the question(diagrama not to scale.)
Answers
because ∠7 + ∠4 = 180°
The correct choice is number 1
///EAGLEPAW
Evaluate: 18.4 ÷ 2.3 × 3.4 + 13.812 =
Answers
A right triangle has one side, s, and a hypotenuse of 12 meters. Find the area of the triangle as a function of s.
A) A(s) = 2s
144 - s2
B) A(s) = s
144 - s2
C) A(s) = 2s
12 - s2
D) A(s) = 12s
144 - s2
10)
The base of a ladder is placed 5 feet away from a 13 foot tall wall. What is the minimum length ladder needed to reach the top of the wall (rounded to the nearest foot)?
A) 12 ft
B) 13 ft
C) 14 ft
D) 15 ft
Answers
Answer: A(s) = [tex]\frac{s\sqrt{144-s^{2} } }{2}[/tex] ; 10) c) 14ft
Step-by-step explanation: Area of a triangle is: A = [tex]\frac{b.h}{2}[/tex]
where:
b is base of a triangle
h is height of a triangle
For this right triangle, it is known one side, s, and hypotenuse, 12. To determine the other side, we use Pythagoras Theorem:
hypotenuse² = side² + side²
[tex]12^{2} = s^{2} + x^{2}[/tex]
[tex]x^{2} = 12^{2} - s^{2}[/tex]
[tex]x^{2} = 144 - s^{2}[/tex]
x = [tex]\sqrt{144 - s^{2} }[/tex]
To determine the Area of the right triangle as function of s:
A = [tex]\frac{b.h}{2}[/tex]
A = [tex]\frac{1}{2}[/tex](s.x)
A = [tex]\frac{1}{2}[/tex] . (s.[tex]\sqrt{144 - s^{2} }[/tex])
Therefore, the area of the right triangle is:
A = [tex]\frac{1}{2}[/tex] . (s.[tex]\sqrt{144 - s^{2} }[/tex])
The ladder and the wall form a right triangle. The height of it is 13 ft, the base is 5ft and the hypotenuse is the length of the ladder. So, to find the minimum length, use Pythagoras Theorem:
hypotenuse² = side² + side²
h² = 13² + 5²
h² = 169 + 25
h = [tex]\sqrt{194}[/tex]
h = 14
The minimum length the ladder has to have to reach the top is 14 ft.
ln(x+2)-ln(4x+3)=ln(1/2*x)
Answers
Using properties of logarithms
[tex] \frac{ln(x+2)}{ln(4x+3)} = ln \frac{x}{2} \\ \\ \frac{x+2}{4x+3} = \frac{x}{2} \\ \\2(x+2)=x(4x+3) 2x+4=4x^2+3x \\ \\ 4 x^{2} +x-4=0 \\ \\ x= \frac{-b+/- \sqrt{b^{2}-4ac} }{2a} \\ \\ x= \frac{ -1+/-\sqrt{1+64} }{8} \\ \\ x_{1} = \frac{-1+ \sqrt{65} }{8} \\ \\ x_{2} = \frac{-1- \sqrt{65} }{8} Check: When you substitute x_{2} into \\ \\ ln(4x+3)=ln(4* \frac{-1- \sqrt{65} }{8} ) =ln( \frac{-1- \sqrt{65} }{2} ) you will get negative number under ln, that is impossible , [/tex]
so x2 is not a solution of this logarithmic equation.
Only x1 is a solution.
Ben buys a car for $50,000. The value of the car decreases at a rate of 4% per year. How much will the car be worth in 3 years? A. $48,000 B. $44,237 C. $45,082 D. $43,270
Answers
y=abˣ
where:
a=initial value
b=decreasing rate
x=time in years
from the information:
a=50000, b=0.96, x=3
thus
y=50000(0.96)³
simplifying we get:
y=$44, 236.8
~$44237
Answer:
B. $44,237
BRAINLIEST!!!
Which statement about a dilation with a scale factor of 3 is true?
Answers
3/2 = 6/4
_____
The others are just plain false.
The statement which is true about the dilation is:
[tex]\dfrac{3}{2}=\dfrac{6}{4}[/tex]
Step-by-step explanation:We know that the dilation transformation changes the size of the original figure but the shape is preserved.
The dilation transformation either reduces the size of the original figure i.e. the scale factor is less than 1 or enlarges the size of the original figure i.e. the scale factor is greater than 1.
The ratio of the corresponding sides of the two figure are equal.
i.e.
[tex]\dfrac{3}{2}=\dfrac{6}{4}[/tex]
This is incredibly frustrating. PLEASE HELP ME
Answers
Explanation:
Given expression:
[tex]\sum_{i=1}^{25} 2^{2i}[/tex]
When i = 1: The answer is [tex]2^{2*1}[/tex] = 4
When i = 2: The answer is [tex]2^{2*2}[/tex] = 16
When i = 3: The answer is [tex]2^{2*3}[/tex] = 64
.
.
When i = 25: The answer is [tex]2^{2*25}[/tex] = [tex]2^{50}[/tex]
Which is the series mentioned in Option C
what is the product of r and t if R equals 5.33 and T equals 0.5
Answers
replace the letters with the numbers you have 5.33 x 0.5 = 2.665
The circle belowis centered at the point (-2 ,1) and has a radiusof length 3
Answers
Answer:
Option A, (x + 2)² + (y - 1) = 9
Explanation:
The equation form of a circle is (x - h)² + (y - k)² = r², where the center is ordered pair (h, k) and r represents the radius.
From the given information, the center is point (-2, 1) and the radius (r) is 3 units. With this, we can plug the information in and simplify:
(x - (-2))² + (y - (1))² = (3)²
(x + 2)² + (y - 1)² = 9
The equation for the given circle is (x + 2)² + (y - 1)² = 9
function that has the same domain as y=2√x
Answers
A.y= [tex] \sqrt{2x} [/tex]
B.y=[tex] \sqrt[3]{ x^{2} } [/tex]
C.y=[tex] \sqrt{x-2} [/tex]
D.y=[tex] \sqrt[3]{x-2} [/tex]
====================================================
We are given the function
y = 2 √x
The domain for the given function is this
{ x | x ≥ 0 }
The answer is A. y = √2x
In general any function that has a domain of x that is equal to or greater than 0. Some examples:
f(x) = √x - 2
f(x) = 5 √x
Answer:
The answer is A. y = √2x
Step-by-step explanation:
kaelyn has 14 coins that have a vaule of $ 1.20. she only has dimes and nickles. how many nickles does kaely have
Answers
Kaelyn has 14 coins made of dimes and nickels valued at $1.20. By setting up a system of equations and solving for the number of nickels, we determine that she has 4 nickels.
The student is asking a mathematical question involving coin values and combinations. When working with combinations of coins, we typically use a system of equations or algebraic expressions. Kaelyn has 14 coins consisting of dimes and nickels with a total value of $1.20. To systematize, let's let D be the number of dimes and N be the number of nickels. The following equations represent the relationships between the coins:
D + N = 14 (since there are 14 coins in total)0.10D + 0.05N = 1.20 (representing the total value of the coins in dollars)Multiply the second equation by 100 to deal with whole numbers:
10D + 5N = 120From the first equation, we can express D as:
D = 14 - NSubstitute this into the second equation:
10(14 - N) + 5N = 120140 - 10N + 5N = 120-5N = -20N = 4So, Kaelyn has 4 nickels and the rest are dimes.
hey can you please help me posted picture of question
Answers
Find the Vertex of y = 3x2+7x+2
Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 3 , is positive (greater than zero).
Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.
Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.
For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is -1.1667
Plugging into the parabola formula -1.1667 for x we can calculate the y -coordinate :
y = 3.0 * -1.17 * -1.17 + 7.0 * -1.17 + 2.0
or y = -2.083
Parabola, Graphing Vertex and X-Intercepts :
Root plot for : y = 3x2+7x+2
Axis of Symmetry (dashed) {x}={-1.17}
Vertex at {x,y} = {-1.17,-2.08}
x -Intercepts (Roots) :
Root 1 at {x,y} = {-2.00, 0.00}
Root 2 at {x,y} = {-0.33, 0.00}
3x²+7x+2=0
Solving using factorization.
3x²+6x+x+2=0
3x(x+2)+1(x+2)=0
(3x+1)(x+2)=0
This means the roots of the equation are x = -2 and x = -1/3
Now from the graphs determine which one has the roots at these two points. We can observe that Graph D has the roots at x=-2 and x=-1/3
So the answer to this question is option D