Find the vertex of this parabola:
y = -x2 + 6x – 15
[tex]y = - x {}^{2} + 6x - 15[/tex]
[tex]y {}^{ \gamma } = - 2x + 6[/tex]
[tex]y {}^{ \gamma } = 0[/tex]
[tex] - 2x + 6 = 0[/tex]
[tex] - 2x = - 6[/tex]
[tex]2x = 6[/tex]
[tex]x = 3[/tex]
Substitute x=3 in y=-x²+6x-15[tex]y = - (3) {}^{2} + 6(3) - 15[/tex]
[tex]y = - 9 + 18 - 15[/tex]
[tex]y = - 9 + 3[/tex]
[tex]y = - 6[/tex]
Vertex: (3,-6)
[tex]==============================[/tex]
In order to find the vertex of a parabola, we use the following formula:
[tex]\mathfrak{\displaystyle\frac{-b}{2a} }[/tex]
Please remember that a parabola looks like this:
[tex]\tt{y=ax^2+bx+c}[/tex]
Now you know what a and b stand for.
In this case, a = -1, and b is 6:
[tex]\mathfrak{\displaystyle\frac{-6}{2(-1)} }[/tex]
Simplify:
[tex]\mathfrak{\displaystyle\frac{-6}{-2}}[/tex]
[tex]\mathfrak{3}\\=======================================[/tex]
Notes:Hope everything is clear.Let me know if you have any questions!Enjoy your day!Always remember: Knowledge is Power :)Answered by[tex]\mathcal{DiAmOnD}\\\tt{A~Creative~Helper}}}}[/tex]
Perform the indicated operation & simplify.
[tex](8-15i) +(11+24i) = 19+9i\\\\(8-15i)-(11+24i)=-3-39i=-3(1+13i)[/tex]
help I'm confused like always
Answer:
negative
Step-by-step explanation:
The good part about this question is you don't have to know the actual values of b or c, otherwise, I would be stumped too.
Given:
b is within 0 -> 1 b is positive
c is within -1 -> -2, c is negative
[tex]\frac{b}{c}[/tex] = b/c. When you have a fraction and one numerator is positive while the denominator is negative (or visa-versa, numerator is negative and denominator is positive), then the answer will ALWAYS be negative
so +b/-c = negative result
find the average of the following numbers -34 and -37
Answer:
35.5 is the average of 34 and 37
Step-by-step explanation:
Answer:
-35.5
Step-by-step explanation:
-34 + -37 = -71
-71/2 = -35.5
I hope this helps!
a retail owner can but a certain clock at an average price of $53 per clock and sell them for an average price of $84 per clock. his fixed costs are $8000 per month and his variable cost is $5 per clock. (A) how many clocks must he sell each month to break even? (B) how many clocks must he sell to have a profit of $3000?
Answer:
(A) 308 clocks
(B) 423 clocks
Step-by-step explanation:
The contribution margin is the amount by which the selling price of the clock exceeds the cost of the clock. The contribution margin is used to figure the break-even point, and the amount of profit from sales.
contribution margin = selling price - variable cost - purchase price
contribution margin = $84 -5 -53 = $26
__
(A)To break even, the contribution margin from 'b' clocks must equal or exceed the owner's fixed cost:
26b ≥ 8000
b ≥ 8000/26
b ≥ 307.7
The owner must sell 308 clocks each month to break even.
__
(B)To make a profit of $3000, the owner must sell enough clocks to cover the $8000 fixed cost and contribute an additional $3000. That is, the total contribution margin from selling p clocks must be about $3000+8000 = $11000.
26p ≈ 11000
p ≈ 11000/26 ≈ 423.08
The owner must sell about 423 clocks each month to earn a profit of about $3000.
__
Additional comment
Selling 423 clocks will yield a profit of $2998.
6.
Part I: Suppose a prism has a square base with each side of length 3.75 cm and a height
of 5.65 cm. Use the formula below to find the volume. Show your work and round your
answer to the nearest hundredth. (5 points)
79.45401²
Step-by-step explanation:[tex]1)\ V=B\ Sh[/tex]
[tex]\therefore\ V=3.15\times 3.75\times 5.65[/tex]
[tex]=79.403125[/tex]
[tex]\approx 79,45\ cm^3[/tex]
I hope this helps you
:)
Rounded to the nearest hundredth, the volume of the prism is approximately 79.50 cm^3.
To find the volume of a prism, we use the formula:
Volume = Base Area * Height
In this case, the prism has a square base with each side of length 3.75 cm and a height of 5.65 cm. The formula for the area of a square is:
Base Area = Side Length^2
So, the base area can be calculated as:
Base Area = 3.75 cm * 3.75 cm = 14.0625 cm^2
Now, we can find the volume using the formula:
Volume = Base Area * Height
Volume = 14.0625 cm^2 * 5.65 cm
Volume ≈ 79.5025 cm^3
To know more about volume:
https://brainly.com/question/32006008
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what is the area of the triangle
Answer:
6
Step-by-step explanation:
A=(bh)/2
a=(4*3)/2
a=12/2
a=6
Answer: 12 units 2
Step-by-step explanation:base times hight
R\ {0}→→ Ris defined by Jff: 1 f(x)=x³-1/x³-1then show that 2 f(x) + f(1/x)=0.
[tex]\orange\bigstar \bold{ solution}[/tex]
[tex]\bold{f(x) = x³ - \frac{1}{x³ } }[/tex]
[tex]\bold{f ( \frac{1}{x} )= \frac{1}{x³} -x³ } [/tex]
[tex]\bold{f (x) + f (\frac{1}{x}) = (x³- \frac{1}{x³} ) + ( \frac{1}{x³} -x³)}[/tex]
[tex]\bold{ = 0 }[/tex]
What is the mean for this list of numbers? 4, 12, 13, 7
Answer:
9
Step-by-step explanation:
Add all numbers together: 36
divide by the amount of numbers in the list: 9
:)
Kristy bought some rolls of wrapping paper and 2 bags of bows for less then $10. Each roll of wrapping paper and each bag of bows cost $1.50. Which inequality can be used to find w, the number of rolls of wrapping paper Kristy bought?
Answer:
[tex]w < 4 \frac{2}{3}[/tex]
Step-by-step explanation:
The inequality symbol for 'less than' is '<'.
Let's relate the cost and the number of each item bought together with an equation.
Total cost
= (number of rolls)(cost of each roll) +(number of bags)(cost per bag of bows)
= w(1.50) +2(1.50)
= 1.5w +3
Now, we can form the inequality.
Since the total cost is less than $10,
1.5w +3< 10
Subtract 3 from both sides:
1.5w < 10 -3
1.5w < 7
Divide both sides by 1.5:
[tex]w < 7 \div \frac{3}{2} [/tex]
[tex]w < 7 \times \frac{2}{3} [/tex]
[tex]w < \frac{14}{3} [/tex]
[tex]\textcolor{red}{w < 4 \frac{2}{3} }[/tex]
Factor each completely.one zero has been given
f(x)=x^3-4x+16;-2
F(x) = X^4+ 2x^-13x^2 -10x + 40;2
F(x)=x^3-3x^2-13x+15;-3
F(x)=x^4-8x^3+19x^2-12x;3
The polynomials in factored form are listed below:
f(x) = (x - 3.043) · (x - 1.521 - i 1.716) · (x - 1.521 + i 1.716) f(x) = (x - 2.236) · (x - 2) · (x + 2.236) · (x + 4)f(x) = (x + 3) · (x - 5) · (x - 1)f(x) = (x - 4) · (x - 3) · (x - 1) · xHow to factor polynomialsIn this question we must factor polynomials as there are both numerical and analytical methods. Mathematically speaking, factoring polynomials is represented by the following formula:
[tex]\sum^{n}_{i = 0} \,c_{i}\cdot x^{i} = \prod^{n}_{i=1}(x-r_{i})[/tex], [tex]\forall\,x, r_{i}\in \mathbb{C}[/tex] (1)
Where:
[tex]c_{i}[/tex] - [tex]i[/tex]-th Coefficient[tex]r_{i}[/tex] - [tex]i[/tex]-th RootRegarding fourth order polynomials we can solve them by Ferrari's method and third order polynomials by Descartes' method. Then, the solutions of each polynomials are given below:
Polynomial 1 ([tex]f(x) = x^{3}-4\cdot x +16[/tex])f(x) = (x - 4) · (x - 3) · (x - 1) · x
Polynomial 2 ([tex]f(x) = x^{4}+2\cdot x^{3}-13\cdot x^{2}-10\cdot x + 40[/tex])f(x) = (x - 2.236) · (x - 2) · (x + 2.236) · (x + 4)
Polynomial 3 ([tex]f(x) = x^{3}-3\cdot x^{2}-13\cdot x +15[/tex])f(x) = (x + 3) · (x - 5) · (x - 1)
Polynomial 4 ([tex]f(x) = x^{4}-8\cdot x^{3}+19\cdot x^{2}-12\cdot x[/tex])f(x) = (x - 4) · (x - 3) · (x - 1) · x
To learn more on polynomials, we kindly invite to check this verified question: https://brainly.com/question/17822016
Find the mean of the data.
8,14,22,7,2,11,25,7,5,9 PLEASE!!!!!!!!
Answer:
11
Step-by-step explanation:
To find the mean:
Add up all data values to get the sum then count the number of values in your data set. Lastly, divide the sum by the count.
Solution:
Thus,
2+ 5+7+7+8+9+11+ 14+22+25=110
110/10 = 11
Therefore, the mean is 11.
~lenvy~
Answer:
Step-by-step explanation:
just put them in order from least to greatest then find the middle number
Please help me find x
|x+8|=x+8
square two sides
x+8=(x+8)2
x+8=x2+16x+64
x2+16x+64-x-8=0
x2+15x+56
then rule a2+-l
If the distance from C to C’ is 8 and the scale factor is 5. What is the distance from A to C?
A. 8/5
B. 5/8
C. 10
D. 2
Consider the function f(x) = - 3x² + 30% - 3.
Determine, without graphing, whether the function has a minimum value or a maximum value.
Find the minimum or maximum value and determine where it occurs.
Identify the function's domain and its range.
O
..
a. The function has a
value.
b. The minimum/maximum value is
It occurs at x =
c. The domain offis
(Type your answer in interval notation.)
The range of fis 1 (Type your answer in interval notation.)
Copyright
Answer:
a. maximum value
b. x = 5
c. domain = all reals , range = y is less than or equal to 72
Step-by-step explanation:
a. maximum because it is a negative function and thats the highest value
b. thats the x value of the vertex which is the highest point
Is the table a linear or exponential function?
The table represents linear because the x represent the exponential functions
What is the value of the
expression? 1 7/8 - 6/4
Help!!!
Rationalize the denominator of;
[tex]1) \frac{1}{ \sqrt{7} } [/tex]
[tex]2) \frac{2}{ \sqrt{3} - \sqrt{2} } [/tex]
[tex]3) \frac{ \sqrt{6} + \sqrt{3} }{9 + 2 \sqrt{18} } [/tex]
Answer:
see below for explanation:-
Step-by-step explanation:
#1
[tex] \displaystyle{ \frac{1}{ \sqrt{7} } }[/tex]
[tex]\displaystyle{ \frac{1}{ \sqrt{7} } \times \frac{ \sqrt{7} }{ \sqrt{7} } }[/tex]
[tex]\displaystyle{ \frac{ \sqrt{7} }{7} }[/tex]
#2
[tex]\displaystyle{ \frac{2}{ \sqrt{3} - \sqrt{2} } }[/tex]
[tex]\displaystyle{ \frac{2}{ \sqrt{3} - \sqrt{2} } \times \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} + \sqrt{2} } }[/tex]
[tex]\displaystyle{ \frac{2( \sqrt{3} + \sqrt{2} }{( \sqrt{3} {)}^{2} - ( \sqrt{ 2 } {)}^{2} } }[/tex]
[tex]\displaystyle{ \frac{2( \sqrt{3} + \sqrt{2} ) }{3 - 2} }[/tex]
[tex]\displaystyle{2( \sqrt{3} + \sqrt{2} )}[/tex]
#3
[tex]\displaystyle{ \frac{ \sqrt{6} + \sqrt{3} }{9 + 2 \sqrt{18} } }[/tex]
[tex]\displaystyle{ \frac{ \sqrt{6} + \sqrt{3} }{ 9 + 2 \sqrt{9 \times 2} } }[/tex]
[tex]\displaystyle{ \frac{ \sqrt{6} + \sqrt{3} }{9 + 6 \sqrt{2} } }[/tex]
[tex]\displaystyle{ \frac{ \sqrt{6} + \sqrt{3} }{3(3 + 2 \sqrt{2}) } }[/tex]
[tex]\displaystyle{ \frac{ \sqrt{6} + \sqrt{3} }{3(3 + 2 \sqrt{2}) } \times \frac{3 - 2 \sqrt{2} }{3 - 2 \sqrt{2} } }[/tex]
[tex]\displaystyle{ \frac{3 \sqrt{6} - 2 \sqrt{12} + 3 \sqrt{3} - 2 \sqrt{6} }{3( {3}^{2} - (2 \sqrt{2} {)}^{2} ) } }[/tex]
[tex]\displaystyle{ \frac{ \sqrt{6} - 4 \sqrt{3} + 3 \sqrt{3} }{3(9 - 8)} }[/tex]
[tex]\displaystyle{ \frac{ \sqrt{6} - \sqrt{3} }{3} }[/tex]
Which of the following number sentences is an example of the associative property? Select all that apply.
[tex](1\frac{2}{5}*3\frac{1}{2} )*4=1\frac{2}{5} (3\frac{1}{2} *4)[/tex]
[tex]2.5*(1.8+6.3)=(2.5*1.8)+(2.5*6.3)[/tex]
10(4.6 × 3) = (10 × 4.6) × 3
6.3 × 1 = 6.3
Associative property:-
a+(b+c)=(a+b)+cLets check one by one
#1
Here the rule is
(ab)c=a(bc)Hence Yes associative property
#2
Here the rule is
a(b+c)=ab+acHence no it's distributive property
#3
a(bc)=(ab)cYes
#4
ab=baNo
Associative property meaning rearranging the parentheses in an expression which will not change the result.
✔A)
[tex]\rightarrow \sf (1\dfrac{2}{5} \ x \ 3\dfrac{1}{2} ) \ x \ 4 = 1\dfrac{2}{5} (3\dfrac{1}{2} \ x \ 4 )[/tex]
[tex]\rightarrow \sf \dfrac{98}{5} = \dfrac{98}{5}[/tex]
This uses associate property as it is rearranged in a different way and result same.
B)
[tex]\rightarrow \sf 2.5 \ x \ (1.8 +6.3) = (2.5 \ x \ 1.8)+(2.5 \ x \ 6.3 )[/tex]
This property is called distributive property. a(b + c) = a(b) + a(c)
✔C)
[tex]\sf \rightarrow 10(4.6 \ x \ 3) = (10 \ x \ 4.6) \ x \ 3[/tex]
[tex]\sf \rightarrow 138 = 138[/tex]
associate property as the following is rearranged inside the parentheses
D)
[tex]\rightarrow \sf 6.3 \ x \ 1 = 6.3[/tex]
This does not fall under any method or else multiplicative identity property.
Khairi has only 20¢ and 50¢ coins in his coin bank. There are twice as
many 20¢ coins as 50¢ coins. How many 20¢ coins are there in the coin
bank if all the coins add up to $17.10?
Answer:
There is 43 20¢ in the coin bank.
A company wants to decrease their
energy use by 15%. If their electric
bill is currently $2,100 a month,
what will their bill be if they are
successful? Give your answer
accurate to at least the nearest
dollar.
15% decrease means the bill would be 85% of the original bill ( 100% -15% = 85%)
multiply the current bill by 85%
2100 x 0.85 = 1.785
the bill would be $1,785
Airplane X left the airport, flying at a rate of 400 miles per hour. Airplane Y left 2 hours later, flying at a rate of 450 miles per hour. How long will it take airplane Y to catch up to airplane X?
Answer: i think it will take 48 hours
Step-by-step explanation:
here's how to get 48 so basically 450-400-2= 48
now if you end up doing 400 - 450 then you will get -50 if you do 400-450-2 you will get a -52 so you want to make sure you do the biggest number first and then do the smaller numbers to get 48 like 450 - 400 - 2 and then you will have 48
i hope this helps!
What is the volume of a rectangular prism that is 4 ft. by 12 ft. by 6 ft.? Question 21 options: 324 ft.³ 205 ft.³ 288 ft.³ 315 ft.³
Answer:
288 ft³
Step-by-step explanation:
The formula to find the volume of a rectangular prism is :
Volume = length × width × height
Let us find it now.
Volume = 4 ft × 12 ft × 6 ft
Volume = 48 ft² × 6 ft
Volume = 288 ft³
The circle graph shows how Lila spent her after-school time during the month of October.
Part A
If Lila spent a total of 92 hours on these activities in the month of October. How much time did she spent at Yoga?
Using proportions, it is found that she spent 25.76 hours at Yoga.
What is a proportion?A proportion is a fraction of a total amount.
Researching the problem on the internet, it is found that the circle graph shows that she spent 28% of her time of 92 hours on yoga, hence:
h = 0.28 x 92 = 25.76.
Hence, she spent 25.76 hours at Yoga.
More can be learned about proportions at https://brainly.com/question/24372153
Inez bought a shipping container at a packing store
Answer: ok? whats the question
Step-by-step explanation:
Answer:
I think u forgot to mention the question?
Step-by-step explanation:
A movie theater charges 9.00 for adults and $3.00 for senior citizens. On a day when 306 people paid for admission, the total receipts were $1554. How many who
paid were adults? How many were Seniors?
Answer: 2495
Step-by-step explanation:
9x + 7(325)-7x = 2495
2x = 220
x = 110 adults and 215 senior citizens
CHECKING our answer***
$990 + $1505 = $2495
Wish You the Best in your Studies.
416
Chapter 7 Graphing and Functions
16. 2y - 5 = 0
ху
Answer:
y=2
Step-by-step explanation:
add 5 to 0 then divide 5 with 2
A birthday cake weighs 7/8 pounds. If 2/3 of the cake is flour, how much is flour
find the measure of angles 2, 3, and 4. input the measures then click done. i-ready
please help i missed a day of class i cant figure this out
Answer:
m∠2 = 95°
m∠3 = 85°
m∠4 = 95°
Step-by-step explanation:
Vertical Angle Theorem:
When two straight lines intersect, the opposite vertical angles formed are always equal (congruent) to each other.
Therefore,
m∠3 = 85°
m∠2 = m∠4
Linear pair:
Two adjacent angles which, when combined, form a line, so the sum of a linear pair is 180°.
Therefore,
85° + m∠2 = 180°
m∠3 + m∠4 = 180°
If 85° + m∠2 = 180°
⇒ m∠2 = 180° - 85°
⇒ m∠2 = 95°
As m∠2 = m∠4 then m∠4 = 95°
PLEASE HELP!!! TOTAL 50 POINTS IF GIVEN BRAINLIEST ANSWER!!!
Find the average value of the function f over the given region.
f(x, y) =10x +3y over the triangle with vertices (0, 0), (9, 0), and (0, 2).
The average value of f(x, y) over the given region (I'll call it T) is
[tex]\dfrac{\displaystyle \iint_T f(x,y) \, dA}{\displaystyle \iint_T dA}[/tex]
In other words, it's the ratio of the integral of f(x, y) over the region to the area of the region.
The set T can be expressed as
[tex]T = \left\{(x,y) \,:\, 0\le x\le9 \text{ and } 0\le y\le -\dfrac29x+x\right\}[/tex]
Since it's a triangle, the denominator is easily computed to be
[tex]\displaystyle \iint_T dA = \frac12 \times 9 \times 2 = 9[/tex]
In the numerator, we have
[tex]\displaystyle \iint_T (10x+3y) \, dA = \int_0^9 \int_0^{-2x/9+2} (10x+3y) \, dy \, dx \\\\ = \int_0^9 \left(\frac32\left(-\frac{2x}9+2\right)^2+10x\left(-\frac{2x}9+2\right)\right) \, dx = 288[/tex]
and hence the average value is 288/9 = 32.