Answer:
To find an expression that is equivalent to `y = x^2 + 8x + 18`, we can try to complete the square, factorize, or use the quadratic formula.
Completing the square:
We can add and subtract (8/2)^2 = 16 to the right-hand side of the equation to get:
y = x^2 + 8x + 18 + 16 - 16
y = (x + 4)^2 + 2
So an equivalent expression for `y = x^2 + 8x + 18` is `y = (x + 4)^2 + 2`.
Factorizing:
We can try to factorize the quadratic expression on the right-hand side of the equation. To do this, we need to find two numbers whose sum is 8 and whose product is 18. These numbers are 2 and 6, so we can write:
y = x^2 + 2x + 6x + 18
y = (x^2 + 2x) + (6x + 18)
y = x(x + 2) + 6(x + 3)
y = (x + 2)(x + 6)
So an equivalent expression for `y = x^2 + 8x + 18` is `y = (x + 2)(x + 6)`.
Using the quadratic formula:
We can use the quadratic formula to solve for x in the equation `y = x^2 + 8x + 18`. The quadratic formula states that for an equation of the form `ax^2 + bx + c = 0`, the solutions for x are given by:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
In our case, a = 1, b = 8, and c = 18. Substituting these values into the quadratic formula, we get:
x = (-8 ± sqrt(8^2 - 4(1)(18))) / 2(1)
x = (-8 ± sqrt(4)) / 2
x = -4 ± 1
So the solutions for x are x = -5 and x = -3. If we substitute these values into the original equation `y = x^2 + 8x + 18`, we get:
When x = -5, y = (-5)^2 + 8(-5) + 18 = 5 - 40 + 18 = -17
When x = -3, y = (-3)^2 + 8(-3) + 18 = 9 - 24 + 18 = 3
So an equivalent expression for `y = x^2 + 8x + 18` is `y = (x + 5)(x - 3)`.
Tom drinks 8 oz of water for every 3
miles he bikes. After 21 miles, how
much water did he drink?
Answer:
56 oz of water
Step-by-step explanation:
Answer:
56 oz
Step-by-step explanation:
He stops 7 times in 21 miles because he stops every 3 miles and 21 divided by 3 equals 7. He also drinks 8 oz of water every time he stops, and if he stops 7 times then we just multiply 8 and 7, and since 8×7=56 he drank 56 oz of water after 21 miles.
Could I please have BRAINLIEST?simplify: sin theta {1/sin theta - 1/cosec theta}
Answer:
SORRY I DIDN'T KNOW
Step-by-step explanation:
PLEASE SOLVE THIS PROBLEM
Write an equation and solve.
Bobby needs to buy a new
bicycle. If he already has $50 and
he gets $15 per week for his
allowance, how many weeks will
it take him to get the $200 he
needs to purchase the bike he
wants?
What’s the value of this expression
3x6-4+8/2
Kyla applied rm ◦ T0,3 to triangle ABC. What mistakes did she make? Check all that apply.
She applied the rotation to the triangle first.
She applied the reflection to the triangle first.
She changed the size of the triangle instead of just applying a translation.
She translated the triangle down instead of just applying a reflection.
She applied a rotation instead of a reflection
Answer: she applied the reflection to the triangle first
&
she changed the size of the triangle instead of just applying a translation.
Step-by-step explanation:
Answer:
B & C
Step-by-step explanation:
C2 Let x,y,ze R³ and s,t € R. Prove the following properties of the dot product. (a) ≥ 0 (b) *.x = 0 if and only if x = 0 (c) x.y = y.x (d) x (sy + tz) = s(X ·Ý) + t(X · Z) .
The dot product of vectors in R³ has several properties.
Firstly, it is non-negative, meaning it is greater than or equal to zero. Secondly, the dot product of a vector with the zero vector is zero if and only if the vector itself is also the zero vector. Thirdly, the dot product is commutative, so x·y = y·x. Lastly, the dot product distributes over scalar addition, allowing us to factor out scalars. Specifically, x(sy + tz) = s(x·y) + t(x·z).
(a) To prove that the dot product is non-negative, we can use the fact that the dot product of a vector with itself is equal to the sum of the squares of its components. Since the square of any real number is non-negative, the sum of squares is also non-negative, and thus the dot product is non-negative.
(b) If the dot product of a vector x with the zero vector is zero, it implies that the sum of the squares of the components of x is zero. The only way for this to be true is if all the components of x are zero, which means x itself is the zero vector. Conversely, if x is the zero vector, then the dot product of x with any vector y will be zero, as all the components of x are zero.
(c) The commutativity of the dot product can be proven by expanding the dot product formula, which is the sum of the products of corresponding components of the vectors. Since the multiplication of real numbers is commutative, the order of the components does not affect the final sum.
(d) The distributive property of the dot product over scalar addition can be demonstrated by expanding both sides of the equation and simplifying. Using the distributive property of scalar multiplication over vector addition, we can split the left side of the equation into two dot products. Then, by distributing the scalars, we obtain the right side of the equation. Thus, the equation holds true.
Learn more about dot product here:
https://brainly.com/question/29097076
#SPJ11
Data were collected on the following viables. Which variable is LEAST likely to be approximated with a normal model? The distribution of heights of tomato plants growing at an agncultural Center, where most heights cluster around the center and there are some very short and very tail heights The distribution of times that a certain brand of house paint lasts on a house where the distribution is symmetric and bell-shaped The distribution of lengths of the trout living in a certain roam where the dist tion is unimodal and clustered around the center and the left hair is a mirror image of the night hall The distribution of weighs of mold samples growing in a laboratory where the distribution is symmetric, un model and does not have any outliers . E ) The distribution of ages in years of the residents of a town where the tail of the distribution is longer than the left
The distribution of heights of tomato plants growing at an agricultural center is the least likely to be approximated with a normal model.
The variable that is least likely to be approximated with a normal model is the distribution of heights of tomato plants growing at an agricultural center, where most heights cluster around the center and there are some very short and very tall heights.
A normal distribution assumes that the data follows a symmetric, bell-shaped pattern.
However, in the case of tomato plant heights described, the distribution is not symmetric and does not exhibit a bell-shaped pattern. Instead, it has a cluster around the center with some very short and very tall heights, indicating a skewed distribution.
The other options mentioned in the question, such as the distribution of times that a certain brand of house paint lasts, the distribution of lengths of trout, the distribution of weights of mold samples, and the distribution of ages of residents in a town,
all exhibit characteristics that are more likely to be approximated with a normal model, as they either display symmetric, unimodal patterns or have no outliers. Therefore, the distribution of heights of tomato plants growing at an agricultural center is the least likely to be approximated with a normal model.
To know more about cluster refer here:
https://brainly.com/question/15016224#
#SPJ11
Rewrite the following as a decimal
-5 1/11
Answer:
-5.09
Step-by-step explanation:
Convert 5 1/11 to an improper fraction.
Exact Form:
-56/11
Decimal Form:
-5.09
Mixed Number Form:
-5 1/11
Molly went shopping and her bank account got below $7.50
What is x equal to in the problem.
Answer:
have no idea mate actually is 69
Step-by-step explanation:
yebamabsi
Answer:
52°
Step-by-step explanation:
x is the same angle as opposite to 52°, making x 52°
It costs Joanna $17,200 to open her new shoe store and then $24 for each pair of shoes she stocks. Joanna decides to charge her customers $45 per pair of shoes. a) What is her Cost Function? b) What is her Revenue Function? c) What is her Profit Function? d) What is her Break-Even Point? (a) Joanna's Cost Function is C(x) = |7
a. C(x) = 17,200 + 24x, where x represents the number of pairs of shoes stocked.
b. R(x) = 45x, where x represents the number of pairs of shoes sold.
c. 21x - 17,200, where x represents the number of pairs of shoes sold.
d. Joanna's break-even point is approximately 819 pairs of shoes.
Apologies for the cutoff in your previous message. Based on the provided information, let's calculate Joanna's Cost Function, Revenue Function, Profit Function, and Break-Even Point:
a) Cost Function (C(x)):
The fixed cost to open her shoe store is $17,200, and Joanna incurs an additional cost of $24 for each pair of shoes she stocks. Therefore, the cost function is:
C(x) = 17,200 + 24x, where x represents the number of pairs of shoes stocked.
b) Revenue Function (R(x)):
Joanna charges her customers $45 per pair of shoes, so the revenue function is:
R(x) = 45x, where x represents the number of pairs of shoes sold.
c) Profit Function (P(x)):
Profit can be calculated by subtracting the total cost from the total revenue. The profit function is:
P(x) = R(x) - C(x)
= 45x - (17,200 + 24x)
= 45x - 17,200 - 24x
= 21x - 17,200, where x represents the number of pairs of shoes sold.
d) Break-Even Point:
The break-even point occurs when the profit is zero, indicating that Joanna has covered all her costs. To find the break-even point, we set P(x) = 0 and solve for x:
21x - 17,200 = 0
21x = 17,200
x = 17,200 / 21 ≈ 819.05
Therefore, Joanna's break-even point is approximately 819 pairs of shoes.
Note: Since the number of pairs of shoes cannot be fractional, the actual break-even point would be either 819 or 820 pairs of shoes, depending on the context.
Learn more about number from
https://brainly.com/question/27894163
#SPJ11
Colin Sarah and Gordon share some sweets in the ratio 2:5:3 calling gets 26 sweets how many sweets are there at altogether together
Answer:
Collin: 26, Sarah: 65, Gordon: 39, so 130 altogether
Step-by-step explanation:
Dan invests £1300 into his bank account.
He receives 5% per year simple interest.
How much will Dan have after 2 years?
Give your answer to the nearest penny where appropriate
Given parameters:
Principal = £1300
Interest rate = 5%
Duration = 2yrs
Unknown:
Total amount of Dan's principal = ?
To solve this problem, we apply the equation below:
Total investment worth = Principal + interest
Interest = [tex]\frac{PRT}{100}[/tex]
where P is the principal
R is the rate
T is the time
Now, input the parameters;
Total investment worth = £1300 + £ [tex]\frac{1300 x 5 x 2}{100}[/tex]
= £1300 + £130
= £1430
The amount after two years is £1430
Suppose Amanda LaCount dances on a rectangular stage that is 60 feet long and 25 feet deep. How long is the diagonal length of the stage?
(achieve 3000 , In step With Amanda LaCount)
65feet
60feet
70feet
63feet
Answer:
65 feet
Step-by-step explanation:
Given that,
Length of a rectangle, L = 60 feet
Breadth of a rectangle, B = 25 feet
We need to find the diagonal length of the stage. We know that for a rectangle each angle is 90 degrees. Let x is the length of the diagonal. So,
[tex]x=\sqrt{L^2+B^2} \\\\x=\sqrt{(60)^2+(25)^2} \\\\x=\sqrt{3600+625} \\\\x=65\ \text{feet}[/tex]
So, the length of the diagonal is 65 feet. Hence, the correct option is (a).
Each hour, the number of bacteria in Dr. Nall’s petri dish tripled. What percent is the population compared to the population the hour before?
3%
30%
130%
300%
Answer: D. 300%
Step-by-step explanation:
#0 I think I should get brainliest answer because...
I am about to add my evidence of how I found my answer AND proof for edge so I think I should get brainliest because I added more proof and evidence
#1: How I found my answer
Well, the bacteria on Dr. Nall's dish starts with 100% bacteria in it and after an hour, it tripples, so after an hour, it would have to be 100x3=300 and now all we have to do is add the percent so 300% and so, the answer is: D. 300%
#2: Proof:
edge test 100% correct shone on this question
Answer:
The Answer is the last one
Step-by-step explanation:
4(5-2)(5-3)+7(5-2)(5-5)-6(5-3)(5-5)
Answer:
24 is the answer
Step-by-step explanation:
did a quiz on it yesterday lol !
- mark me brainliest !
Answer:
24 is the answer.
Step-by-step explanation:
answer that is CORRECT gets brainliest
Answer:
0.65 third option
Step-by-step explanation:
95×0.65= $61.75
The population of Stockmoon is increasing at 2% every year. The population was 550 in 1990. How many people are living in Stockmoon today? Round your answer to the nearest person.
Answer:996
Step-by-step explanation:
the number of calories is correlated with the amount of vitamin c
Step-by-step explanation:
World's Healthiest Foods rich in
vitamin C
Food calories
Papaya119224%
Bell Peppers29157%
Broccoli55135%
Brussels Sprouts56129%
Strawberries46113%
Pineapple83105%
Oranges6293%
Kiwifruit4285%
Cantaloupe5478%
Cauliflower2973%
Answer: The number of calories is [Not] correlated with the amount of vitamin C
Step-by-step explanation:
Edg2021
Evaluate (-3a+4b)32c-1 when a = 3, b = 1, and c = 4.
Answer:
-641.
Step-by-step explanation:
hope that helps:))
Richard and Teo have a combined age of 31. Richard is 13 years older than twice Teo's age. How old are Richard and Teo?
Answer:
Richard is 22 and Teo is 9
Step-by-step explanation:
Teo's age:
31-13
=18 divided by 2
=9
Richard's age:
31-9
=22
Another 2 needed. 50 points!
Please show work, Thanks! :)
Answer:
1) B
2) C
Step-by-step explanation:
Question 1)
We have the function:
[tex]y=2x^2+24x-16[/tex]
Note that this is in the standard quadratic form:
[tex]y=ax^2+bx+c[/tex]
Unfortunately, since this isn't in vertex form, we need to do a bit more work for our vertex.
Remember that we can find our vertex using the following formulas:
[tex]x=-\frac{b}{2a},\ y=f(-\frac{b}{2a})[/tex]
Let's label our coefficients. Our a is 2, b is 24, and c is -16.
Let's find our vertex. Substitute 24 for b and 2 for a. This yields:
[tex]x=-\frac{24}{2(2)}[/tex]
Multiply:
[tex]x=-\frac{24}{4}[/tex]
Divide:
[tex]x=-6[/tex]
So, the x-coordinate of our vertex is -6.
Now, to find the y-coordinate, we simply need to substitute x for our equation. We have:
[tex]y=2x^2+24x-16[/tex]
Substitute -6 for x:
[tex]y=2(-6)^2+24(-6)-16[/tex]
Evaluate. Square:
[tex]y=2(36)+24(-6)-16[/tex]
Multiply:
[tex]y=72-144-16[/tex]
Subtract. So, the y-coordinate of our vertex is:
[tex]y=-88[/tex]
So, our vertex point is (-6, -88).
Remember that the axis of symmetry is the same as the x-coordinate of our vertex. So, our axis of symmetry is at x=-6.
Therefore, our answer is B.
Question 2)
We have the equation:
[tex]y=-2x^2+8x-20[/tex]
Again, we can use the above formula. Let's label of coefficients.
Our a is -2, b is 8, and c is -20.
So, let's find the x-coordinate of our vertex:
[tex]x=-\frac{b}{2a}[/tex]
Substitute 8 for b and -2 for a:
[tex]x=-\frac{8}{2(-2)}[/tex]
Multiply:
[tex]x=-\frac{8}{-4}[/tex]
Divide. The negatives cancel. So, our x-coordinate is:
[tex]x=2[/tex]
Now, substitute this back into the equation to find the y-coordinate:
[tex]y=-2(2)^2+8(2)-20[/tex]
Square:
[tex]y=-2(4)+8(2)-20[/tex]
Multiply:
[tex]y=-8+16-20[/tex]
Add:
[tex]y=-12[/tex]
Therefore, our vertex is (2, -12).
And the axis of symmetry is at x=2.
Our answer is C.
And we're done!
Answer:
Coordinate geometry is one of the most important and exciting ideas of mathematics. In particular it is central to the mathematics students meet at school. It provides a connection between algebra and geometry through graphs of lines and curves. This enables geometric problems to be solved algebraically and provides geometric insights into algebra.
The invention of calculus was an extremely important development in mathematics that enabled mathematicians and physicists to model the real world in ways that was previously impossible. It brought together nearly all of algebra and geometry using the coordinate plane. The invention of calculus depended on the development of coordinate geometry.
Step-by-step explanation:
the net annual sales of a sample of small retail clothing stores were organized into the following relative frequency distribution. net sales (in $ millions) percent of total 1 up to 4 13 4 up to 7 14 7 up to 10 40 10 up to 13 23 13 or more 10 what is the mean net sales (in $ millions)? group of answer choices mean cannot be computed. $8.59 $7.09 $10.09
The mean net sales, rounded to two decimal places, is approximately $8.64 million.
To calculate the mean net sales, we need to multiply each class midpoint by its corresponding percent of the total, then sum up these values.
Let's calculate the class midpoints for each category:
1 up to 4: (1 + 4) / 2 = 2.5
4 up to 7: (4 + 7) / 2 = 5.5
7 up to 10: (7 + 10) / 2 = 8.5
10 up to 13: (10 + 13) / 2 = 11.5
13 or more: We'll assume the midpoint to be 15 (higher than the upper limit).
Now, let's calculate the contributions to the mean:
(2.5 * 13%) + (5.5 * 14%) + (8.5 * 40%) + (11.5 * 23%) + (15 * 10%)
= (0.325) + (0.77) + (3.4) + (2.645) + (1.5)
= 8.64
The mean net sales are therefore $8.64 million, rounded to two decimal places.
for such more question on mean
https://brainly.com/question/14532771
#SPJ8
Plz help with this right now
Answer:
Step-by-step explanation:
use slope formula m=(y2-y1)/(x2-x1)
m=(6-8)/(0-2)
m=-2/-2
m=1
y-intercept is the value of y when x=0, so it is 6
The answer is B
-5x + 3 > - 72
O x > -26
O x < 15
O x > 15
O x < -26
Which statement is true regarding the traits of scatter plots
Answer: A
Step-by-step explanation:
JUST TOOK THE QUIZ
Point N is on line segment MO. Given MO = 18 and MN = 3, determine the
length NO.
Answer:
Length of NO is 15
Step-by-step explanation:
because
NO = MO-MN
what do you get when you divide 4/9 / 3/7
Answer:
1.03703703704
Step-by-step explanation:
did it on paper and then finished the equation in my head
what number line represents the solutions to |x+4|=22?
Answer:
or, x= 22 - 4
Step-by-step explanation:
or, x = 18
therefore x = 18
Question 7 12.5 pts A network consists of the following list. Times are given in weeks Activity Predecessor a mb A 5 11 14 B 8 14 20 C A 6 10 14 D B 3 5 7 E C, D 4 6 11 F E 6 8 13 G E 10 18 22 a. What
The given information presents a network with a list of activities and their respective durations in weeks. The activities are interconnected, indicating their dependencies and the time required to complete each activity. The question asks for the earliest start time, earliest finish time, latest start time, and latest finish time for each activity in the network.
To determine the earliest start time, earliest finish time, latest start time, and latest finish time for each activity, we can utilize the concept of the Critical Path Method (CPM).
The CPM allows us to analyze the network and identify the critical path, which is the sequence of activities that determines the longest duration for completing the project.
To calculate the earliest start time (ES) and earliest finish time (EF) for each activity, we start by assigning ES = 0 for the first activity. Then, for each subsequent activity, ES is calculated as the maximum EF of its preceding activities. EF is then calculated by adding the activity duration to ES.
Next, we determine the latest finish time (LF) and latest start time (LS) for each activity. LF is initially set as the project duration, and LS is calculated by subtracting the activity duration from LF.
For each preceding activity, LF is determined as the minimum LS of its succeeding activities.
The critical path is identified by comparing the ES and LF values for each activity. Activities with ES equal to LS and EF equal to LF are part of the critical path.
The critical path represents the activities that, if delayed, would extend the project's overall duration.
By performing these calculations for the given network, we can determine the earliest start time, earliest finish time, latest start time, and latest finish time for each activity.
Additionally, the critical path can be identified based on the ES, EF, LS, and LF values.
To learn more about Critical Path Method visit:
brainly.com/question/30715657
#SPJ11
