Answer:
minimum value = 10
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
To obtain this form using completing the square
add/subtract ( half the coefficient of the x- term )² to x² - 6x
f(x) = x² + 2(- 3)x + 9 - 9 + 19
= (x - 3)² + 10 ← in vertex form
with (h, k) = (3, 10 )
To determine maximum or minimum consider the value of a
• If a > 0 then minimum value of k
• If a < 0 then maximum value of k
Here a = 1 > 0, hence minimum value of k = 10
Question number 34 ?
An engineer drew the graph of a new tire on a coordinate plane. The equation of the tire was x^2+y^2-26y=0. How many feet will the tire roll in 100 complete revolutions. If necessary, round your calculations to the nearest hundredths, and your final answer to the nearest whole number. Complete the explanation (look at picture)
Answer:
Mr. Z ?
Step-by-step explanation:
An animal reserve has 28,000 elk. The population is at a rate of 15% per year. How long will it take for the population to reach 56,000?
Answer: In 5 years time the population will reach to 56,000.
Step-by-step explanation:
This can be calculated using yearly compound interest formula
Formula for yearly compound interest
CI = P(1+R/100)ⁿ
CI = 56,000
P = 28,000
R = 15%
n= number of years
Now,
56,000 = 28,000 (1+15/100)ⁿ
56,000 = 28,000 (1+.15)ⁿ = 28,000 (1.15)ⁿ
log (56,000/28,000) = n log(1.15)
log 2 = n log (1.15)
n = log 2/log 1.15
n≅ 5
At a recent audition school play, 1 out of 3 students who auditioned were asked to come to a second audition . After the second audition ,75% of those asked to the second audition were offered parts. If 18 students were offered parts , how many students were offered to the first audition
Answer:
The total students appearing in first audition = 72
Step-by-step explanation:
As given in the question:
1 out of 3 students were asked to come for second audition.
Let us assume the TOTAL STUDENT who came to first audition = m
So, [tex](\frac{1}{3}) m[/tex] appeared for the SECOND ROUND.
Now, 75% of students appearing in second audition were offered parts.
Calculating 75% of [tex](\frac{1}{3}) m[/tex]
[tex]\frac{75}{100} \times\frac{1}{3} m = 0.25 m[/tex]
Also, as said 18 students were offered parts.
⇒ 0. 25 m = 18
Now, solving for m, we get:
m = 18/0.25 = 72
or, m = 72
Hence, the total students appearing in first audition = 72
Final Answer:
- 24 students were asked to attend the second audition.
- 72 students auditioned initially for the first audition.
Explanation:
Let's tackle the problem step by step.
1. **Find the number of students asked to the second audition.**
We know that 18 students were eventually offered parts after the second audition. We're also given that 75% of those who were asked to the second audition were offered parts. To find out how many students were asked to the second audition, we can set up the following equation:
[tex]\[ \text{Number of students offered parts} =[/tex] [tex]\text{Percentage offered parts} \times \text{Number of students at the second audition} \][/tex]
From the given information:
[tex]\[ 18 = 0.75 \times \text{Number of students at the second audition} \][/tex]
Solving for the number of students at the second audition gives us:
[tex]\[ \text{Number of students at the second audition} = \frac{18}{0.75} = 24 \][/tex]
So 24 students were asked to the second audition.
2. **Find the total number of students who auditioned initially.**
If 1 out of 3 students who auditioned were asked to the second audition, we can infer that the ratio of students asked to the second audition to the total number of students who auditioned is 1:3.
Let's let X represent the number of students who auditioned initially. According to the ratio, we can write:
[tex]\[ \frac{1}{3} \times X = \text{Number of students at the second audition} \][/tex]
We've already solved for the number of students at the second audition, which is 24. Thus:
[tex]\[ \frac{1}{3} \times X = 24 \][/tex]
Solving for X, we get:
[tex]\[ X = 24 \times 3 = 72 \][/tex]
So 72 students auditioned initially for the first audition.
To summarize:
- 24 students were asked to attend the second audition.
- 72 students auditioned initially for the first audition.
Does anyone know what 2/6 plus 1/8 is?
Answer:
3/14
Step-by-step explanation:
hope this helps
Graph each function.
Answer:
Step-by-step explanation:
We can recognize that the parent function for all of these graphs is going to be y=x^2. What this means is that we can graph y=x^2 and then apply transformations to it to get to all of these new graphs.
1. y = -x^2 + 5
We can see that the coefficient of the x^2 term is negative which tells us that the graph will now open downwards.
We also know that we are adding 5 on the outside of the argument which means it affect vertical shift. Therefore, we will be moving 5 units up.
2. y = x^2 - 4
We can see that the only change made to this equation is subtracting 4 on the outside of the squared part of the equation. Again, this signifies vertical movement, but since it's negative we will be moving the entire y = x^2 graph down 4 units.
3. y = -x^2 - 1
What do you notice about this graph?
- negative coefficient
- subtracting 1 outside of the argument
What do these mean?
- negative coefficient: opens downwards
- subtracting 1: move entire y = x^2 graph down 1 unit
simplifica fractia 2n+6n supra 2
Answer:
Step-by-step explanation:
1234
2. Solve each equation and check your solution.
a.-3w - 4= w + 3
b. 3(3 – 3x) = 2(x + 3) - 30
c. 1/(2 + 4) – 6 = 2 (5 – 2)
Answer:
1. Solution
-3w-w=3+4
-4w=7
Therefore,w= -7/4
Step-by-step explanation:
2. Solution
3(3-3x)=2(x+3)-30
9-9x=2x+6-30
9+40-6=2x+9x
43=11x
Therefore, x=43/11
#Hope it helps u
What is the area of this trapezoid?
Check the picture below.
[tex]\bf \textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} a,b=\stackrel{parallel~sides}{bases}\\ h=height\\[-0.5em] \hrulefill\\ a=12\\ b=15\\ h=16 \end{cases}\implies A=\cfrac{16(12+15)}{2}\implies A=216[/tex]
JL has coordinates J(-6, 1) and L(-4,3).
Find the coordinates of the midpoint.
Answer:
The coordinates of the mid-point of JL are (-5 , 2)
Step-by-step explanation:
If point (x , y) is the mid-point of a segment whose end-points are [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex], then [tex]x=\frac{x_{1}+x_{2}}{2}[/tex] and [tex]y=\frac{y_{1}+y_{2}}{2}[/tex]
∵ JL is a segment
∵ The coordinates of J are (-6 , 1)
∴ [tex]x_{1}[/tex] = -6 and [tex]y_{1}[/tex] = 1
∵ The coordinates of L are (-4 , 3)
∴ [tex]x_{2}[/tex] = -4 and [tex]y_{2}[/tex] = 3
Lets use the rule above to find the mid-point of JL
∵ [tex]x=\frac{-6+-4}{2}=\frac{-10}{2}[/tex]
∴ x = -5
∴ The x-coordinate of the mid-point is -5
∵ [tex]y=\frac{1+3}{2}=\frac{4}{2}[/tex]
∴ y = 2
∴ The y-coordinate of the mid-point is 2
∴ The coordinates of the mid-point of JL are (-5 , 2)
Final answer:
The coordinates of the midpoint of the segment with endpoints J(-6, 1) and L(-4,3) are obtained by averaging the x and y coordinates of the endpoints, resulting in (-5, 2).
Explanation:
To find the coordinates of the midpoint of a segment with endpoints J(-6, 1) and L(-4,3), you use the midpoint formula which is ((x1 + x2)/2, (y1 + y2)/2). In this case, x1 is -6, x2 is -4, y1 is 1, and y2 is 3. Plugging these into the formula, we get the midpoint coordinates ((-6 - 4)/2, (1 + 3)/2) which simplifies to (-5, 2). Therefore, the midpoint of JL is at the coordinates (-5, 2).
In one day a movie theater collected $4275 from 675 people. The price of admission is $7 for an adult and $5 for a child. How many adults and how many children were admitted to the movie theater that day?
To find the number of adults and children admitted to the movie theater, we set up two equations based on the admission costs and total number of attendees. Solving these equations revealed that there were 450 adults and 225 children.
Explanation:The question involves a system of equations where we are required to determine the number of adults and children who were admitted to the movie theater given the total revenue and total number of attendees.
Let's denote the number of adults by A and the number of children by C. Given the price of admission is $7 for an adult and $5 for a child, we can represent the total revenue with the equation:
7A + 5C = 4275
Also, considering the total number of people is 675, we have another equation:
A + C = 675
To solve these equations, we'll use the substitution or elimination method:
From the second equation, express C in terms of A:Therefore, there were 450 adults and 225 children admitted to the movie theater that day.
Which method would be the most simplest way to solve the system? 7x+5y=19
-7x-2y=-16
Answer:
14x+3y=3
Step-by-step explanation:
Answer:
The answer is elimination and the equation evaluated would be (2,1)
Step-by-step explanation:
ASSIGNMENTS
COURSES
Assignment - 4. Ratios, Rates, and Unit Rates
Attempt 1 of 2
Decide which unit rate is greatest and explain why using complete sentences.
• 12 apples for $4
• 21 apples for $8
• 35 apples for $14
• 45 apples for $16
WRITER
Answer:
3 apples per $ is the greatest unit rate when someone buy 12 apples for $4, because we are able buy more apples with this rate for the same price.
Step-by-step explanation:
As we know that unit rate can be calculated by dividing the two quantities having different units.
For example, Madrid has been champions 10 times in 30 seasons,
i.e. 10 champions / 30 seasons = 0.33 champions per season
and
Barcelona has been champions 5 times in 30 seasons.
i.e. 5 champions / 30 seasons = 0.16 champions per season
Thus, the champion rate for Real Madrid is greater than the champion rate for Barcelona. It means, Real Madrid has been a better team.
Now, let us check and answer the question.
12 apples for $4 means:12 apples / $4 = 3 apples per $
21 apples for $8 means:21 apples / $8 = 2.62 apples per $
35 apples for $14 means:35 apples / $14 = 2.5 apples per $
45 apples for $16 means:45 apples / $16 = 2.81 apples per $
From the above calculations and observation, we can conclude that 3 apples per $ is the greatest unit rate when someone buy 12 apples for $4.
This unit rate is the greatest because we are able buy more apples with this rate for the same price.
In other words, the rate is cheaper than the unit rate of the rest, because can buy more apples with this rate for the same price.
In the early 1990s, the group was approached by film director Spike Lee to compose a song for his upcoming biopic on the life of Malcolm X.
Read the passage underlined (3).There may be a mistake in punctuation, capitalization, or spelling. If you find a mistake, choose the answer that corrects the mistake. If there is no mistake, choose ‘Correct as is.’
A) Correct as is.
B) In the Early 1990s, the group was approached
C) In the early 1990s the group was approached
D) In the early 1990s, the group, was approached
Answer: A
Step-by-step explanation: that’s the answer
Answer:
A
Step-by-step explanation:
Point G’ has coordinates (- 5, 2) If it was reflected across the y-axis, what were the coordinates of its pre image?
a.) (- 5, - 2)
b.) (5,2 )
c.) (2, - 5)
d.) (5, - 2)
Answer:
B. (5,2)
Step-by-step explanation:
Answer: b. 5, 2
Step-by-step explanation: got it right :p
Is 4/6 greater than 1/2
Yes because you have to convert the answers to 8/12 to 6/12
1/2 is not greater than 4/6 and the answer to the question "Is 1/2 greater than 4/6?" is no.
Someone help please
Answer I DONY KNOW SO LIKE BRUH
Step-by-step explanation: GOOD LUCK
his season, Lisa's lacrosse team has won $\frac 23$ of their home games (games played at Lisa's school), but just $\frac 25$ of their away games (games played at other schools). In total, Lisa's team has won $26$ games out of $49$ games they have played. How many home games has Lisa's team played?
Solution:
Let "h" be the number of home games
Let "a" be the number of away games
The total number of games is 49
Therefore,
h + a = 49 ---------- eqn 1
They won 2/3 of the home games and 2/5 of the away games
There were 26 games won
Thus we get,
[tex]\frac{2}{3}h + \frac{2}{5}a = 26\\\\10h + 6a = 26 \times 15\\\\10h + 6a = 390\\\\[/tex]
10h + 6a = 390 --------- eqn 2
Multiply eqn 1 by 6
6h + 6a = 294 ----------- eqn 3
Subtract eqn 3 from eqn 2
10h + 6a = 390
6h + 6a = 294
( - ) ------------------
4h = 96
h = 24
Thus 24 home games were played
A textbook store sold a combined total of 356 biology and psychology textbooks in a week. The number of biology textbooks sold was three times the number of psychology textbooks sold. How many textbooks of each type were sold?
Solve the quadratic equation 12x2 – 288 = 0 using the square root method.
Answer:
should be x = +2√6
Step-by-step explanation:
did test!
Multiplying Polynomials, Simplify with Work Shown.
(2x-10) (6x + 7)
20 Point offer for real, complete answer.
What is -9x+6=18 in slope intercept form ?
Answer:
y = 3/2 x + 3
Step-by-step explanation:
-9x + 6y = 18 is in standard form (ax + by = c).
Slope-intercept form isolates the "y" variable. It looks like this:
y = mx + b
Move anything that's not "y" to the right side. Move things in reverse BEDMAS order, using reverse operations of what you want to move.
[tex]-9x + 6y = 18[/tex] Move -9x by doing +9x to both sides
[tex]-9x + 9x + 6y = 18 + 9x[/tex] Simplify. -9x + 9x will cancel out.
[tex]6y = 18 + 9x[/tex] Move the "6" that multiplies with "y".
[tex]\frac{6y}{6} = \frac{18}{6} + \frac{9x}{6}[/tex] Divide each term by 6.
[tex]y = 3 + \frac{3x}{2}[/tex] "y" is isolated. Simplify the rest.
[tex]y = \frac{3}{2}x + 3[/tex] Rearrange to match slope-intercept form.
The solution to an inequality is 5≤x<9. What is the smallest value of x that will make the original inequality true?
Answer:
5
Step-by-step explanation:
It is given that the solution to an inequality is
[tex]5\leq x<9[/tex]
It means the original inequality is true for any values of x which is greater than or equal to 5 and less than 9.
We need to find the smallest value of x that will make the original inequality true.
[tex]5\leq x\text{ and }x<9[/tex]
Therefore, smallest value of x is 5 that will make the original inequality true.
Find the value of M. (please answer)
Answer:
M = 70
Step-by-step explanation:
Supplementary Angles = 180
180 - 110 = 70
Also linear pairs = 180.
m=70 degrees
I hope that helps you :)
The five-number summary for a set of data is 10, 14, 15.5, 21, 25 what is the interquartile range of the data?
Answer:
7
Step-by-step explanation:
Q1 = 14
Q3 = 21
Take 21 - 14 and it gives you the interquartile range of 7.
Final answer:
The interquartile range (IQR) for the data set with a five-number summary of 10, 14, 15.5, 21, 25 is 7, calculated as the difference between the third quartile (Q3) and the first quartile (Q1), which are 21 and 14 respectively.
Explanation:
The interquartile range (IQR) of a data set is calculated by subtracting the first quartile (Q1) from the third quartile (Q3). Given the five-number summary of 10, 14, 15.5, 21, 25, where 14 is Q1 and 21 is Q3, the IQR can be found using the formula:
IQR = Q3 - Q1
In this case:
IQR = 21 - 14
IQR = 7
Therefore, the interquartile range for this data set is 7.
A falling rock produces a force of 250 Newtons from acceleration due to gravity alone. What is the rock's mass in kilograms? Enter your answer rounded to the nearest tenth, such as: 42.5
Answer:
Convert 250 Newtons into Kilograms
25.5
Two ropes are attached to a large ballon in a parade. The people holding the ropes are 40 feet apart,and the angle between the two ropes is 86 degrees. The angle of elevation of one rope is 42 degrees. How long is each rope..Step by Step explanation..Please ..Thanks.
Answer:
We'll use the Law of Sines:
Sine (C) / c = Sine (B) / b
Sine (86) / 40 = Sine (52) / b
0.99756 / 40 = 0.78801 / b
0.024939 = .78801 / b
b = .78801 / .024939
side b = 31.5974978949 feet
Sine (42) / a = Sine (86) / 40
(0.66913 / a) = 0.024939
a = .66913 / .024939
side a = 26.8306668271 feet
******************************************************
I forgot to include the graphic.
Step-by-step explanation:
The arithmetic sequence 2, 4, 6, 8, 10, . . . represents the set of even natural numbers. What is the sum of the first 100 even natural numbers?
Answer:
1) 200
2) 10100
3) less than
explanation:
just did it :))
The sum of the first 100 even natural numbers will be 10,100.
What is the sum of an arithmetic sequence?Let a₁ be the first term, L be the last term, n be the number of terms, and d be a common difference.
Then the sum of the arithmetic sequence will be
S = (n / 2)[a₁ + L]
S = (n/2) [2a + (n − 1) d]
The arithmetic sequence is given below.
2, 4, 6, 8, 10, .....
The first term is 2 and the common difference is 2. Then the sum of the first 100 even natural numbers will be
S = (100/2) [2 x 2 + (100 − 1) x 2]
S = 50 [4 + 99 x 2]
S = 50 [4 + 198]
S = 50 [202]
S = 10,100
The sum of the first 100 even natural numbers will be 10,100.
More about the sum of arithmetic sequence link is given below.
https://brainly.com/question/25749583
#SPJ2
What is the value of X?
Answer:
x = 21 degrees
Step-by-step explanation:
The angles in a triangle add up to 180 degrees.
x - 4 + 3x + 100 = 180
x - 4 + 3x = 80
4x - 4 = 80
4x = 84
x = 21
I ONLY HAVE A LITTLE TIME ANS NEED HELP!!!!! can someone explain this to me
Answer:
x = 92
Step-by-step explanation:
[tex]\frac{x}{46} =\frac{78}{39}[/tex]
I did big side over small side, proportions.
Cross Multiply.
39x = 3,588
divide by 39x
x = 92
Answer:
92
Step-by-step explanation:
These triangles are similar because they share a common angle and two pairs of sides in the same ratio.
Sides of the bigger triangle are double of those of the smaller triangle
46+46 = 92