Which of the following graphs is described by the function given below?
y=3x + 7x+2
O
O
A. Graph A
B. Graph B
O
C. Graph C
O
D. Graph D
Answers
This graph represents function of y = 3x²+7x+2, which is correct option(D).
What is Parabola?A parabola is a U-shaped curve this is drawn for a quadratic function,
f(x) = ax² + b x + c. The graph of the parabola is downward (or opens down), when the price of a is much less than 0, a < 0. The graph of the parabola is upward (or opens up) when the value of a is more than 0, a > 0.
Given function, y = 3x²+7x+2
Compare the given function to f(x) = ax² + b x + c ,
The graph of given function is upward (or opens up) because the value of 3 is more than 0, 3 > 0.
The x-intercept of given function are (-1/3, 0) and (-2,0)
The y-intercept of given function is (0,2)
Here is a graph represents function of y = 3x²+7x+2
Learn more about parabola here:
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The correct option is A. Graph A. It shows an upward-opening parabola with a vertex and y-intercept that match the derived values.
1. Direction of the Parabola : Since the coefficient of [tex]\( x^2 \)[/tex] (which is [tex]3[/tex]) is positive, the parabola opens upwards.
2. Vertex : The vertex of a parabola in the form [tex]\( y = ax^2 + bx + c \)[/tex] can be found using the formula for the x-coordinate of the vertex, [tex]\( x = -\frac{b}{2a} \)[/tex]
For the given function:
[tex]\[ a = 3, \quad b = 7 \][/tex]
So,
[tex]\[ x = -\frac{7}{2 \times 3} = -\frac{7}{6} \][/tex]
Next, we find the y-coordinate of the vertex by plugging [tex]\( x = -\frac{7}{6} \)[/tex] back into the equation:
[tex]\[ y = 3\left(-\frac{7}{6}\right)^2 + 7\left(-\frac{7}{6}\right) + 2 \][/tex]
Let's compute that:
[tex]\[ y = 3 \times \frac{49}{36} - \frac{49}{6} + 2 \][/tex]
[tex]\[ y = \frac{147}{36} - \frac{294}{36} + \frac{72}{36} \][/tex]
[tex]\[ y = \frac{147 - 294 + 72}{36} \][/tex]
[tex]\[ y = \frac{-75}{36} \][/tex]
[tex]\[ y = -\frac{25}{12} = -2.083 \][/tex]
Thus, the vertex is approximately at [tex]\(\left( -\frac{7}{6}, -\frac{25}{12} \right)\)[/tex]
3. Y-Intercept : This is the value of [tex]\( y \)[/tex] when [tex]\( x = 0 \)[/tex]
[tex]\[ y = 3(0)^2 + 7(0) + 2 = 2 \][/tex]
The graph should cross the y-axis at [tex]\( y = 2 \)[/tex]
Now, let's compare these features with the provided graphs:
The parabola should open upwards.
The y-intercept should be [tex]2[/tex].
The vertex should be approximately at [tex]\( \left( -\frac{7}{6}, -\frac{25}{12} \right) \)[/tex]
The complete question is
Which of the following graphs is described by the function given below? y=3x^2+7x+2
A. Graph A
B. Graph B
C. Graph C
D. Graph D
Related Questions
Translate this sentence into an algebraic inequality.x divided by the quantity y minus 9 is 18 or more.A.B.C.D.
Answers
Answer:
x/y-9 is grater than or equal to 18
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
x
___ ≥ 18
y-9
Tried my best to write it out like it would show it written out.
You are charged $16.7 in total for a meal. Assuming that the local
sales tax is 7.6%, what was the menu price of this item?
*How would I work this out I keep getting 15.43 but that’s not correct
Answers
Final answer:
To find the menu price of an item after a total charge of $16.7 with a 7.6% local sales tax, calculate the total sales tax amount and then deduct it from the total cost to obtain the menu price of $15.43.
Explanation:
To find the menu price of the item after being charged $16.7 in total for a meal with a 7.6% local sales tax:
Calculate the sales tax amount: 7.6% of $16.7 = $1.27
Subtract the sales tax from the total cost: $16.7 - $1.27 = $15.43
Therefore, the menu price of the item was $15.43. Make sure to round off correctly based on the question requirements.
what's the least common denominator of 5/6 2/3 and 3/5?
Answers
Answer:
30
Step-by-step explanation:
6*5= 30
3*10=30
5*6=30
Simplify.
1 – 2u + u + 4
Answers
Which expression is equivalent to 1/3 + 3/4 + 2/3
Answers
Answer:
7/4 or 1.75 or 1 3/4
Step-by-step explanation:
What is the radius of a base?
3 units
6 units
10 units
| 12 units
Answers
Answer:
Didn't give enough information..
Step-by-step explanation:
need to see the circle if need help ill give answer.
Factor the following and remember to factor out any common factors first.
x^2+8x+15
Enter the factors separated by semicolons. ( ; )
Answers
Answer:
(x+5) (x+3)
Step-by-step explanation:
x^2+8x+15
What two numbers multiply to 15 and add to 8
5*3 = 15
5+3 = 8
(x+5) (x+3)
Diego and Lin are drinking milkshakes. Lin starts with 12 ounces and drinks 1/4 an ounce per second. Diego starts with 20 ounces and drinks 2/3 an ounce per second. 1. How long will it take Lin and Diego to finish their milkshakes?
Answers
Answer:
Lin = 48 seconds
Diego = 30 seconds
Step-by-step explanation:
Hi, to answer this question we have to divide the total ounces of drink by the amount that each one drank per second, for each case.
Mathematically speaking:
Lin = 12 ounces / (1/4) ounces/second = 12/ (1/4) = 48 seconds
Diego = 20 ounces / (2/3) ounces/second = 20/ (2/3) = 30 seconds
Feel free to ask for more if needed or if you did not understand something.
Lin = 48 seconds
Diego = 30 seconds
The calculation is as follows:Lin = 12 ounces ÷ (1/4) ounces/second = 12 ÷ (1/4) = 48 seconds
Diego = 20 ounces ÷ (2/3) ounces/second = 20 ÷ (2/3) = 30 seconds
Learn more: https://brainly.com/question/4804019?referrer=searchResults
at the flea market, erin buys a phone that is 22% off and gloves that are reduced to $19.97. erin spends a total of $48.52. let g represent the cost of the phone. write an equation that correctly represents the cost of erin's shopping trip.
Answers
Answer:
g is approximately $129.77
Step-by-step explanation:
.22g+19.97=48.52
.22g=28.55
28.55/.22=129.77
Answer:
The cost of the phone: $28.55
The total price of the phone: $129.77
48.52 - 19.97 = 28.55
The phone was marked off by 22% so you divide by 22% to get the total cost of the phone, just incase you needed that.
Hope this helps <3
If answered correctly will give brainiest plz helpppppp!!!!!!
Answers
Answer:
50.29
Step-by-step explanation:
(25 1/7)/(22/7) = diameter
8 = diameter -->
4 = radius
4^2 pi = area
16pi=area
16*22/7 = area
352/7 = area
50.29 is (approx.) area
Estimate a 15% tip on a dinner bill of 31.51 by first rounding the bill amount to the nearest ten dollars.
Answers
Answer: The estimated 15% tip would be $4.50.
Step-by-step explanation: Basically, first you will need to round the bill amount, $31.51 to the nearest ten dollars. 31.51 rounded to the nearest ten dollars is $30. Next, you will need to find the estimated tip amount. To do this multiply $30 by the tip 15%. Before you can find the tip amount, you will need to covert 15% to a decimal. To convert 15% to a decimal, divide 15 by 100 to get 0.15. Now, you can multiply 30 by 0.15 to get 4.50. So, $4.50 would be the tip if $31.51 was rounded to the nearest ten dollars.
C) 0.2(x + 5) + 1 = 7
Answers
Answer:
x = 25
Step-by-step explanation:
Given
0.2(x + 5) + 1 = 7 ( subtract 1 from both sides )
0.2(x + 5) = 6 ( divide both sides by 0.2 )
x + 5 = 30 ( subtract 5 from both sides )
x = 25
00:00
In 1 hour, 32 cars pass through a particular intersection. At the same rate how long would it take for 96 cars to pass through the intersection?
A 2 hours
B. 3 hours
C
8 hours
D. 16 hours
Answers
Answer:
b,3 hours
Step-by-step explanation:
because you have 32 times 2 is 64 in 2 hours so that is not is so the times 8 is 256 in 8 hours so that is not it then times 16 is 512 so 512 in 16 hours that's not it so then times 3 it is 96 cars in 3 hours
five times as many girls as boys went to the dance. The total of 120 students went to the dance. How many boys and girls went to the dance?
Answers
Answer:
100 girls and 20 boys
Step-by-step explanation:
since its 5 times as many girls multiply 20 by 5 which is 100 and then boom 20 boys cause 100 divided by 5 is 20
What is the sum of the series? Write in expanded form making sure to show all steps used to find the sum.
Answers
Given:
[tex]\sum_{k=3}^{6}(-2 k+5)[/tex]
To find:
The sum of the series.
Solution:
[tex]$\sum_{k=3}^{6}-2 k+5[/tex]
Substitute k = 3, 4, 5 and 6.
[tex]$=[-2 (3)+5] +[ -2 (4) +5]+[-2 (5)+5]+[-2 (6)+5][/tex]
[tex]$=[-6+5] +[ -8 +5]+[-10+5]+[-12+5][/tex]
[tex]$=[-1] +[ -3]+[-5]+[-7][/tex]
Apply minus plus rule: [tex]+(-a)=-a[/tex]
[tex]$=-1 -3-5-7[/tex]
[tex]$=-16[/tex]
[tex]$\sum_{k=3}^{6}-2 k+5=-16[/tex]
Therefore the sum of the series is -16.
If a car has already traveled 10 miles and then continues for
another 6 hours at a steady rate of 30 miles per hour, how
many total miles will it have traveled?
miles
Answers
Answer:
190
Step-by-step explanation:
PLEASE MARK BRAINLY
What is the mean of the following numbers?
5, 7, 2,9,5
Answers
Answer:5.6
Step-by-step explanation:
Answer:
5.6
Step-by-step explanation:
[tex] \frac{5 + 7 + 2 + 9 + 5}{5} = \frac{28}{5} = 5.6[/tex]
What is sum 2/3 + 1/6?
Answers
Answer:
5/6
Step-by-step explanation:
convert 2/3 to 4/6 by multiplying by 2
4/6 + 1/6 = 5/6
Answer:
The answer is [tex]\frac{5}{6}[/tex]
Step-by-step explanation:
You need to find the GCF which is 6 so multiply the 2/3 to become 4/6 from then you can add the numerators.
Total savings
Misumi started with $217 in her bank account. She deposits
$25.50 each week and never withdraws any money. What
expression can Misumi use to determine her account balance
after w weeks?
Answers
Answer:
y=$25.50w+$217
w=10 weeks
$25.5(10)+$217
$255+$217
$472=y
11. An amusement park charges $45 per person for admission. A season pass
costs $112 per person.
a. Write the first five terms of an arithmetic sequence that represents the
total cost of admission for the number of visits in a season.
b. How many times does a person have to visit the park for a season pass
to be the better deal? Explain.
Answers
To represent the total cost of admission for the number of visits in a season, an arithmetic sequence can be created with a common difference of $45. The cost of admission for the first visit is $45, and the sequence can be extended to five terms. To determine when a season pass becomes the better deal, compare the total cost of admission with the cost of a season pass. A person would have to visit the park at least 3 times for a season pass to be the better deal.
Explanation:a. To represent the total cost of admission for the number of visits in a season, we can create an arithmetic sequence. The common difference will be the cost of admission each time a person visits the park, which is $45. The first term can be the cost of admission for the first visit, which is also $45. So, the arithmetic sequence will be:
Total: $45Total: $90Total: $135Total: $180Total: $225b. To find out how many times a person has to visit the park for a season pass to be the better deal, we need to compare the total cost of admission for the number of visits with the cost of a season pass. In this case, the season pass costs $112 per person, so we need to find the number of visits that would equal or exceed the cost of a season pass. From the arithmetic sequence we created in part a, we can see that a person would have to visit the park at least 3 times for the total cost of admission to equal or exceed the cost of a season pass. Therefore, a person would have to visit the park at least 3 times for a season pass to be the better deal.
. The equation d + 6400 = 3/1.3 x 10". 42
relates the distance d in kilometers of a
certain GPS satellite above the surface of
the Earth to the number of hours t it takes
the satellite to complete one orbit. The
average distance of this satellite above the
surface of the Earth is 20, 100 kilometers.
To the nearest hour, how long does it
take the GPS satellite to complete one
orbit of the Earth?
Answers
The satellite's speed is approximately 45,216 kilometers per hour.
Calculating the Satellite's Speed
To find the satellite's speed in kilometers per hour, we can follow these steps:
1. Calculate the total distance traveled in one orbit:
The satellite's orbital distance is the circumference of its circular orbit around the Earth.
Circumference = 2 * π * radius
where:
π (pi) is a mathematical constant approximately equal to 3.14159
radius = distance from the satellite to the Earth's center = 6400 km + 2000 km = 8400 km
2. Calculate the orbital period in seconds:
We know the orbital period is 12 hours, but we need it in seconds for our calculations.
Convert hours to seconds: 12 hours * 60 minutes/hour * 60 seconds/minute = 43,200 seconds
3. Calculate the speed:
Speed = distance / time
Speed = total distance / orbital period
Speed = (2 * π * radius) / orbital period
Speed = (2 * 3.14159 * 8400 km) / 43,200 seconds
Speed ≈ 12.56 km/s
4. Convert speed to kilometers per hour:
Speed = 12.56 km/s * 3600 seconds/hour = 45,216 km/hr
Therefore, the satellite's speed is approximately 45,216 kilometers per hour.
The probable question can be: A satellite has recently been placed in a nearby circular orbit 2000 kilometers above the earth surface. Given that the radius of the earth is approximately 6400 kilometers and that the satellite completes its orbit in 12 hours, CALCULATE THE SPEED OF THE SATELLITE IN KILOMETERS PER HOUR.
A bag contains white marbles and blue marbles, 54 in total. The number of white marbles is 1 less than 4 times the number of blue marbles. How many white marbles are there?
Answers
Answer: There are 43 white marbles.
Step-by-step explanation:
t = total number of marbles = 54
w = white marbles = 4b - 1
b = blue marbles
54 = b + (4b - 1)
b + 4b = 5b
54 = 5b - 1
+1
55 = 5b
/5
11 = b
There are 11 blue marbles.
4(11) - 1
44 - 1 = 43
43 + 11 = 54, therefore our solutions are correct.
Answer:
43
Step-by-step explanation:
W = 4B - 1
W + B = 54
4B - 1 + B = 54
5B = 55
B = 11
W = 4(11) - 1
W = 43
Which table represents a linear function?? Help plis
Answers
Answer:
The answer is the bottom left hand corner.
Step-by-step explanation:
Which pyramid has the greatest surface area?
Pyramid
Answers
Answer:
the greatest surface is A
Step-by-step explanation:
Answer:
answer is A have a great day
Step-by-step explanation:
Can someone do 11??? Please help I don’t want to fail my class
Answers
Recall that the tangent of an angle is equal to the ratio of the opposite over adjacent sides
tan(angle) = opposite/adjacent
For reference angle Y, the opposite side is XZ = 6 and the adjacent side is XY = 7, so,
tan(Y) = XZ/XY = 6/7
For tan(Z), things will swap. The opposite side is now XY = 7 and the adjacent side is now XZ = 6
tan(Z) = XY/XZ = 7/6
We do not use the hypotenuse sqrt(85) at all in this problem because the tangent ratio does not involve the hypotenuse.
Evaluate:
© 20
© 20.8
O 24
DONE
Answers
Answer:
24
Step-by-step explanation:
1. 24
2. 0
3. a [4.9] and [3.1] and c [-6] and [-6]
4. edge answer: The statement is not true for all real numbers. It is only true for decimal or fractional values of x . If x is an integer, then the ceiling function returns x when the input is x . But, the flooring function returns x + 1 when the input is x + 1. Since x does not equal x + 1 when x is an integer, the expressions are not equal when x is an integer.
5. edge answer: There are three steps. The steps are at 8 from 0 to 1, at 12 from 1 to 2, and at 16 from 2 to 3. Closed circles are on the left side of each step, and open circles are on the right.
6. all real numbers
7. all multiples of 4
8. multiples of 8 greater than 0
9. 3
10. real numbers ≥ 0
11. integers ≥ 0
12. f(x)=2.50[x-1]
here's your reminder to fix your posture (you know you're slouching, that'll hurt your back when you're old lol) and go get some water! hydration is best because your body uses it to regulate body temperature, keep joints lubricated, prevent infections, deliver nutrients to cells, and keep organs functioning properly. being well-hydrated also improves sleep quality, cognition, and mood! also, if you don't drink water for 3-21 days (depends on age and body and stuff) you'll die. so there's that too.
summary of that ^ fix your posture and drink some water <3
Coordinates of a Pre-image
The segments shown are dilations of each other about
the origin. Which statement could be true?
O
The coordinate (1, 0) is from a dilation using the
scale factor of
O
(1,0)
(5,0)
O
The coordinate (5,0) is from a dilation using the
scale factor of 4.
The coordinate (1, 0) is from a dilation using the
scale factor of 5.
The coordinate (5,0) is from a dilation using the
scale factor of
O
Answers
Answer:
The coordinate (1, 0) is from a dilation using the scale factor of One-fifth.
Step-by-step explanation:
this answer would be A. The coordinate (1, 0) is from a dilation using the scale factor of One-fifth.
hope this helps
WILL MARK BRAINLIEST
Write the equation to represent a line that contains the point (1, -7) and a slope of -4.
y =
Answers
Answer:
y= -4x - 3
Step-by-step explanation:
What is the y-intercept in the equation “y=4x-3”?
Answers
Ryan would like to save 15% of his take-home pay towards retirement. How much should
he save each month if he makes $5,000 each month?
$750
$1125
$75
$75,000
Answers
15%=0,15
5000×0,15=750$
Answer: He should save $750