Answer:
4<x<6
Step-by-step explanation:
4 is smaller than x
and x is samller than 6
so its 5
The axis of symmetry for the function f(x) = −x2 − 10x + 16 is x = −5. What are the coordinates of the vertex of the graph?
(−5, 41)
(−5, 56)
(−5, 76)
(−5, 91)
Considering the definition of axis of symmetry and vertex of a quadratic function, the correct answer is the first option: the coordinates of the vertex of the graph is (-5,41).
Quadratic function
The general form of a quadratic function is f(x = ax²+ bx+ c, whose graph is a parabola.
Axis of symmetry and vertex of a quadratic function
Quadratic functions have a maximum (if a<0) or a minimum (if a>0). This point is the vertex of the parabola.
That is, the vertex of a quadratic equation or parabola is the highest or lowest point on the graph corresponding to that function. The vertex is in the plane of symmetry of the parabola; anything that happens to the left of this point will be an exact reflection of what happens to the right.
In other words, the vertex divides the graph into two halves that are mirror images of each other, so that the axis of symmetry always passes through the vertex.
Vertex of f(x) = −x² − 10x + 16
In this case, you know that the axis of symmetry for the function is x = −5.
So the vertex on the x-axis has a value of -5. To calculate the value of the vertex on the y-axis, you must substitute the value of the vertex on the x-axis in the function:
f(-5) = −(-5)² − 10×(-5) + 16
Solving:
f(-5)= 41
In summary, the correct answer is the first option: the coordinates of the vertex of the graph is (-5,41).
Learn more about the vertex of a quadratic function:
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Answer:
a
Step-by-step explanation:
a
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Question 2-14
Andy and Brett are selling tickets to their high school baseball game
• A total of 234 tickets were sold to the game
• Student tickets cost $5 each
. General tickets cost $ each
. The total revenue from ticket sales was $1268
Which statements are true? Choose all that are correct
The total revenue from the student tickets was $925.
A total of 185 student tickets were sold.
Olfg is the number of general tickets sold and s is the number
11
student tickets sold, the total revenue generated by the student and general tickets can be represented by the oquation 58 + 79 = 1,268
O Atotal of 98 general tickets were sold.
The revenue from the general tickets was greater than the revenue from the student tickets.
Ifg is the number of general tickets sold and s is the number of student tickets sold, thens + g = 234
POUS
Type here to search
O
BI
Answer:
the 1st, 2nd and 6th statements are true.
and probably the 3rd statement is true.
I am not sure about the 3rd statement, as I cannot read the original in your screenshot, and your transcribed description is probably not correct and contains typos.
but all you need is in the explanation below to decide, if the actual 3rd statement is true or not.
if "58 + 79 = 1268" actually means "5s + 7g = 1268" then it is true. otherwise it is false.
Step-by-step explanation:
g = number of general tickets sold
s = number of student tickets sold
so, in total
g + s = 234
tickets were sold.
and the revenue was
7g + 5s = $1,268
out of these 2 basic equating we get
g = 234 - s
and then
7(234 - s) + 5s = 1,268
1,638 - 7s + 5s = 1,268
-2s = -370
s = 185
g = 234 - s = 234 - 185 = 49
so, we know
185 student tickets were sold for 5×185 = $925
49 general tickets were sold for 7×49 = $343
[tex]\begin{equation}\text { Question: If } \ln (x+y)=4 \times y \text {. Find } \frac{d^{2} y}{d x^{2}} \text { at } x=0 \text {. }\end{equation}[/tex]
I think you meant to say
[tex]\ln(x+y) = 4xy[/tex]
and not "4 times y" on the right side (which would lead to a complex value for y when x = 0). Note that when x = 0, the equation reduces to ln(y) = 0, so that y = 1.
Implicitly differentiating both sides with respect to x, taking y = y(x), and solving for dy/dx gives
[tex]\dfrac{1+\frac{dy}{dx}}{x+y} = 4y + 4x\dfrac{dy}{dx}[/tex]
[tex]\implies \dfrac{dy}{dx} = \dfrac{4xy+4y^2-1}{1-4x^2-4xy}[/tex]
Note that when x = 0 and y = 1, we have dy/dx = 3.
Differentiate both sides again with respect to x :
[tex]\dfrac{d^2y}{dx^2} = \dfrac{(1-4x^2-4xy)\left(4y+4x\frac{dy}{dx}+8y\frac{dy}{dx}\right)-(4xy+4y^2-1)\left(-8x-4y-4x\frac{dy}{dx}\right)}{(1-4x^2-4xy)^2}[/tex]
No need to simplify; just plug in x = 0, y = 1, and dy/dx = 3 to get
[tex]\dfrac{d^2y}{dx^2} \bigg|_{x=0} = \boxed{40}[/tex]
2x +5 > -1 on the number line
Answer:
Below
Step-by-step explanation:
2x + 5 > -1
Treat the equality sign (ex. < >) as the costumary equal sign (=).
2x + 5 + (-5) > -1 + (-5) ---- -5 will cancel out the 5 on the left
2x/2 > -6/2 ------ divide by 2 to single out the x
x > -3
Remember to draw an open dot. Draw an arrow from -3 to the extreme right.
What is the normal approximation for pi?
Answer:
Most people use 3 or 3.14
Two forces of 560 N and 222 N act at a point. The resultant force is 634 N. Find the angle between the forces.
The angle between the two forces of 560 N and 222 N is 80.96°
What is the resultant of two vectors?The resultant of two vectors P and Q refer to the magnitudes of the vectors and it can be expressed by the formula [tex]\mathbf{R = \sqrt{P^2 +Q^2 +2PQ cos \theta }}[/tex]
Now, using the above equation, we can easily determine the angle between the forces of the two vectors as follows:
[tex]\mathbf{634 = \sqrt{560^2 +222^2 + 2(560 \times 222) \ Cos \theta }}[/tex]
[tex]\mathbf{401956 =313600 +49284 + 248640 \ Cos \theta }}[/tex]
[tex]\mathbf{401956 -313600 -49284 = 248640 \ Cos \theta }}[/tex]
[tex]\mathbf{39072= 248640 \ Cos \theta }}[/tex]
[tex]\mathbf{ Cos \theta = \dfrac{39072}{248640}}}[/tex]
[tex]\mathbf{Cos \theta =0.1571}[/tex]
[tex]\mathbf{ \theta =80.96^0}[/tex]
Therefore, we can conclude that the angle between the forces is 80.96°
Learn more about the resultant of two vectors here:
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What is the radius of the circle?
Answer:
13cm
Step-by-step explanation:
In this case you have to use the Pythagorean theorem.
cy = 24/2
cy=12 cm ( a perpendicular drawn to a chord from the center bisects the chord..
ac=5 cm (given)
now,
ay^2= 25cm + 144 cm
ay^2 = 169 cm
√169 = 13 cm
Answer:
13 cm
Step-by-step explanation:
Since AC is perpendicular to XY , and XA and AY are both radii of the same circle, you can say that AC is a perpendicular bisector.
From there, we can say that XC is 1/2 of 24 cm, or 12 cm.
We can then form triangle ACX use the Pythagorean theorem to find the length of AX.
The square root of 12^2 + 5^2 is 13.
Therefore, the radius of the circle is 13 cm
solve it in form of cos and sin pls
[tex]\text{L.H.S}\\\\=\dfrac{\cot A}{1- \tan A} + \dfrac{\tan A}{1- \cot A}\\\\\\=\dfrac{\tfrac{\cos A}{\sin A}}{1- \tfrac{\sin A}{\cos A}} + \dfrac{\tfrac{\sin A}{\cos A}}{1-\tfrac{\cos A}{\sin A}}\\\\\\=\dfrac{\tfrac{\cos A}{\sin A}}{\tfrac{\cos A- \sin A}{\cos A}} + \dfrac{\tfrac{\sin A}{\cos A}}{\tfrac{\sin A - \cos A}{\sin A}}\\\\\\=\dfrac{\cos^2 A}{\sin A(\cos A-\sin A)} + \dfrac{\sin^2 A}{\cos A(\sin A - \cos A)}\\\\\\[/tex]
[tex]=\dfrac{\cos^2 A}{\sin A(\cos A-\sin A)} - \dfrac{\sin^2 A}{\cos A(\cos A - \cos A)}\\\\\\=\dfrac 1{\cos A - \sin A} \left( \dfrac{\cos^2 A}{\sin A} - \dfrac{\sin^2 A}{\cos A}\right)\\\\\\=\dfrac 1{\cos A - \sin A} \left(\dfrac{\cos^3 A - \sin^3 A}{\sin A \cos A} \right)\\\\\\=\dfrac 1{\cos A - \sin A} \left[\dfrac{(\cos A - \sin A)(\cos^2 A + \sin^2 A + \sin A \cos A)}{\sin A \cos A} \right]\\\\\\=\dfrac{\cos^2 A + \sin^2 A+\sin A \cos A}{\sin A \cos A}\\\\\\[/tex]
[tex]=\dfrac{\cos^2 A}{\sin A \cos A}+\dfrac{\sin^2 A}{\sin A \cos A}+\dfrac{\sin A \cos A}{\sin A \cos A}\\\\\\=\dfrac{\cos A}{\sin A} + \dfrac{\sin A}{\cos A} + 1\\\\\\=\cot A + \tan A + 1\\\\\\=1 + \tan A + \cot A\\\\=\text{R.H.S}\\\\\text{Proved.}[/tex]
i need help please !!
Answer:
D. d-0.29
Step-by-step explanation:
29÷(0.29)=100
29÷0.29=100
They both equal 100 meaning that D is the answer.
22. Four years ago, age of X was 3 times Y. Six years from now X will be twice Y. Ages of X and Y
now are:
A.
034 and 14
B.
034 and 13
C.
033 and 14
D.
035 and 14
Answer:
a 34 and 14
Step-by-step explanation:
let present age be x and y
equation 1
x-4=3(y-4)
x=3y-8
equation 2
x+6=2(y+6)
x=2y+6
then
2y+6=3y-6
y=14
x=34
You invest $5000, add 50 each month, at 7.9% for 11 years.
Answer:
???
Step-by-step explanation:
The hypotenuse of a right triangle measures 7 cm and one of its legs measures 2 cm.
Find the measure of the other leg. If necessary, round to the nearest tenth
Help picture below problem 10
Answer:
E. APR
I hope this is what u want because I didn't quite get it is it like name the angle as like acute or obtuse or what
step by step
short answer please
Mrs Silverstein has 14 boys and Il girls in her
class. She must select two students at random to
serve as the class presidents What is the
probability that she will choose a boy followed by a
giri?
Answer:
Step-by-step explanation:
Here, I will instead go through the process for finding the probability of choosing two girls. Then once you understand how it was done, hopefully you will be able to answer the actual question for yourself.
Finding the probability of choosing two girls. Let's make it simpler by starting with the probability of choosing the first girl only.Probability of choosing the first girl. (Note: the letter chosen to represent the event is not important. Pick something that makes sense to you and be consistent)
P(G1) = # of girls / # of total outcomesSo the number of girls we know to be 11. What is the number of total outcomes? Well a boy or a girl can be chosen, and there are 14 boys and 11 girls, for a total of 25 students.
P(G1) = 11/ 25Let's find the probability of choosing the second girl from here.
P(G2) = # of girls / # of total outcomesHowever, this time things have changed. We've already chosen one girl, so the number of girls remaining to choose from is reduced 11 to 10. And the total number of students to choose from is reduced from 25 to 24.
P(G2) = 10 / 24Now we have the probability of choosing the first girl and the probability of choosing the second girl. From here, we just need to combine them to find the probability of both things happening together. To calculate the probability of two different events occurring, you multiply the two probabilities together.
Probability of choosing two girls. Let's use T for Two girls.
P(T) = P(G1) × P(G2) = (11 /25) × (10/24)
From here you can use a calculator to find the answer. This answer can either be written as a fraction, a decimal, or a percentage.
= 0.19 = 19 / 100 = 19%
Find teh value of teh coefficient a in the equation ax +2y =8 if a solution to the equation is the pair x=2 and y= 1
Answer:
a(2)+2(1)=8
2a+2=8
2a=8-2
2a=6
a=3
Affordable Auto offered to enter people into a drawing for a free car if they shared the company's advertisement on social media. This table gives the total number of times the advertisement was shared since the promotion began. The data can be modeled by a quadratic function.
Length of promotion (days) 2 4 6 8 10 12
Number of shares 1200 3219 6240 10264 15290 21318
What function best models the data?
y=1.2x^2+20.6x+280
y=125.3x^2+183.3
y=1.2x^2+280
y=125.3x^2+257.8x+183.3
Answer:
D; y=125.3x2+257.8x+183.3
Step-by-step explanation:
I just took the test
have a good day! :)
Triangle ABC is situated inside of a green square. The perimeter of the square is 33.6 feet. What is the area of triangle ABC?
Step-by-step explanation:
solution for the triangle ABC
convert 30 g 519 mg to g
Answer:
30.519 g
Step-by-step explanation:
The relation
1 g = 1000 mgSolving
30 g 519 mg30 g + 519 mg30 g + (519/1000) g30 g + 0.519 g30.519 gA=bh (b=8, h=5) what does A equal to evaluate this problem using the equation below
Answer:
40
Step-by-step explanation:
Please help me with these, first to answer receives 5 stars if correct and probably BRAINLIEST! The following are daily high temperatures (℉) in Auckland, New Zealand:
75 67 83 90 79 74 70 71 72 78 76 67 66 80 77 77 84 74
1. Using the data above, make a stem-and-leaf plot. (4 points)
2. Using the data above, make a box-and-whisker plot. If the set has outliers, use an * to show
them.
Answer:
6 6, 7, 7
7 0, 1, 2, 4, 4, 5, 6, 7, 7, 8
8 0, 3
9 0
Step-by-step explanation:
If you don't know how to make a stem and leaf plots this how. First you will draw a T-chart then you put the first integer or 10th place number on the left and the ones place number on the right.
Arnold is about to go on a 500-mile car trip. His mechanic recommends that he buy
a special highway engine oil that will save him 50 cents in gas for every 25 miles of the
trip. This new oil, however, will cost $20. Is it worthwhile for Arnold to buy the oil if he
has a coupon for $4 dollars off the price?
500 miles/ 25 = 20 x 0.50 = $10
He will save a total of $10
20-4 = $16
it will cost him $16 for the oil which is more than what he saves in gas so buying the oil is not worth it.
the day before yesterday is 2 days after Sunday what day is today
Thursday
Explanation:
Two days after Sunday is Tuesday
Tuesday would be the day before yesterday (Wednesday)
So today is Thursday
Answer:
The Day before the day before yesterday was two days after the day before my birthday. Today is Thursday. The following steps can be used in order to determine the day on birthday: Step 1 - Remember today is Thursday according to the given data. Step 2 - Now, the Day before the day before yesterday is Monday. Step 3 - The two days before Monday is Saturday. Step 4 - And the day of the birthday is after Saturday that is Sunday
Step-by-step explanation:
Someone please help me with this
Answer:
A
Step-by-step explanation:
writting only because answer need 20 words
i need this with the steps
If IN = 2x + 10 and AT = 26, find x. Group of answer choices 10 8 12 6
Answer:
your answer is B. 8
Step-by-step explanation:
Substitute x for 8.
2(8)+10
16+10=26
consecutive integers differ by, such as 15 and
Answer:
integers are not fractions so there you go
help me please :( I need this rlly badly no cap
Answer:
given below
Step-by-step explanation:
1 a. Sample space : 2 green, 1 red, 10 blue
b. Sample space : top surface, bottom surface, curved surface ( side)
c. shooting a free throw in a basketball game ( sorry I dont know this one )
Please help me solve this problem
Answer:
$46,800,000
Step-by-step explanation:
1. Find the total number of shares that Live Fund has. They have 24% of the total shares, which is 78,000. To find their portion of the shares, multiply the total amount by the percent they own; 78,000 * .24. This gives us 18720 shares.
2. Since they are selling half of their shares, divide their total number of shares by 2. This gives us 9360.
3. Each share is worth $5000, so multiply 9360 by 5000. This gives us a final answer of $46,800,000.
Alternatively, we could have just found half of the percent of shares that they own in step 1, so what 12% of 78,000 is instead, and multiplied by 5000.
On the southeast corner of Millennium Park, there is a garden walk. It is marked off in red in the drawing below. Side C, the hypotenuse of the triangle, shows the row along which flowers will be planted.
If side a measures 90 feet and side b measures 120 feet, how many feet of flowers will be planted along side c, the hypotenuse of the triangle? Show your work and explain your reasoning. (2 points)
Answer:
150 feet
Step-by-step explanation:
a²+b²=c²
90²+120²=c²
8100+14400=22500
√22500 = 150
c = 150 feet
