Answer: Option D
[tex]f(x)=(x+3)^2 -k[/tex]
Step-by-step explanation:
For a quadratic function of the form
[tex]ax ^ 2 + bx + c[/tex]
The x coordinate of the vertice is:
[tex]x =-\frac{b}{2a}[/tex]
In this case the function is:
[tex]f(x)=x^2+6x-2\\\\[/tex]
So
[tex]a=1\\b=6\\c=-2[/tex]
The x coordinate of the vertice is:
[tex]x=-\frac{6}{2*1}\\\\x=-3[/tex]
The y coordinate of the vertice is:
[tex]f(-3) = (-3)^2 +6(-3) -2\\\\f(-3)=-11[/tex]
The vertice is: (-3, -11)
The form e vertice for a quadratic equation is:
[tex]f(x)=(x-h)^2 +k[/tex]
Where
the x coordinate of the vertice is h and the y coordinate of the vertice is k.
Then h=-3 and k =-11
Finally the equation [tex]f(x)=x^2+6x-2\\\\[/tex] in vertex form is:
[tex]f(x)=(x+3)^2 -k[/tex]
Answer:
The correct answer option is D. f(x) = (x + 3)² - 11.
Step-by-step explanation:
We know that the standard form of a quadratic function is given by:
y = ax² + bx + c
The vertex form of a parabola is given by
y = a(x - h)² + k
where (h, k) is the vertex of the parabola.
h = -b / 2a and k = f(h)
In the given equation f(x) = x² + 6x - 2
a = 1, b = 6 and c = -2
Finding h:
h = -6 / (2 × 1)
h = -6/2
h = -3
Finding k:
k = 1(-3)² + 6(-3) + 3
k = 9 - 18 - 2
k = -11
Therefore, the given quadratic function in vertex form: f(x) = (x + 3)² - 11
Susan owns a small business there was a loss of $11 on Monday and a profit of $18 on Tuesday on Wednesday there was a loss of $7 and on Thursday there was a profit of $8 find the total of profit or loss
A. $13 loss
B. $8 profit
C. $44 profit
D. $18 profit
Answer:
B. $8 profit
Step-by-step explanation:
Loss is negative and profit is positive
Monday : -11
Tuesday: +18
Wednesday: -7
Thursday: +8
------------
+8
We have a profit of 8
Answer:
8
Step-by-step explanation:
What happens to the value of the expression 5/x +5 as x decreases from a large positive number to a small positive number
Answer:
The value increases
Step-by-step explanation:
the smaller the divisor, the larger the quotient.
It increases I am taking the quiz right now and I checked.
1.Henry’s age is equals to Felicia’s age cubed . If Henry is 64 years old, how old is Felicia?
2. Which function is nonlinear?
a) y=3x(x+5)+4
b) y=-5x-2/3
c) y=2(6x-2)-5x
d) y=5x-2/4
Please help.
1. 4 cubed is 64 (4 x 4 = 16 x 4 = 64
2. Choice A. y=3x(x+5)+4 is a parabola
which expression has a value greater than 4 raise to 3?
there are :
-2 raise to 5
-7 raise to 2
-3 raise to 4
and
-5 raise to 2
We just have to evaluate and compare the numbers:
[tex]4^3 = 64\\(-2)^5 = 32\\(-7)^2=49\\(-3)^4 = 81\\(-5)^2=25[/tex]
So, the only expression that exceeds 4^3 is (-3)^4
(-3)^4
Step-by-step explanation:
The annual rate on a loan is 12% which can be represented using the expression 1.12t write an expression that represents the 6 months interest rate
Answer:
1.06t
Step-by-step explanation:
When the annual rate on a loan is 12% , which was represented using the expression 1.12t. Where t is the time. We are asked to write an expression that represents the 6 months interest rate applied. Assuming the rate of interest for 6 months be 6% half yearly, the expression for the same will be 1.06t
Answer:
1.06t
Step-by-step explanation:
When the annual rate on a loan is 12% , which was represented using the expression 1.12t. Where t is the time. We are asked to write an expression that represents the 6 months interest rate applied. Assuming the rate of interest for 6 months be 6% half yearly, the expression for the same will be 1.06t
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Select the all the numbers that would be apart of the pattern rule, "multiply by 6 and subtract 2
A. 34
B. 40
C. 55
D. 88
E. 119
Answer:
A. 34; B. 40. D. 88
Step-by-step explanation:
The rule is, "multiply by six and subtract two."
So, if we add two to the number, it should be evenly divisible by 6.
We can check each number.
A. 34 + 2 = 36; 36/6 = 6. TRUE.
B. 40 + 2 = 42; 42/6 = 7. TRUE.
C. 55 + 2 = 57; 57/6 = 9½. False.
D. 88 + 2 = 90; 90/6 = 15. TRUE.
E. 119 + 2 = 121; 121/6 = 20⅙. False.
The numbers that satisfy the rule are 34, 40, and 88.
The slope of the line below is 5 which of the following is the point slope form of the line
Answer:
Option D. [tex]y-3=5(x+1)[/tex]
Step-by-step explanation:
we know that
The equation of the line into point slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
In this problem we have
[tex]m=5[/tex]
[tex](x1,y1)=(-1,3)[/tex]
substitute the values
[tex]y-3=5(x+1)[/tex]
If you sleep 6 hours out of 24 hours, what percent of the time do you sleep?
Answer: 1/4
Step-by-step explanation: Since there are 24 hours in a day, 1/4 would be equal to 6 hours out of the day.
Answer: (25%)
Correct Answer 100%! Pls, give me brainliest. Thank You
What is the product of (2x^2+4x-2) and (3x+6)
Answer:
6x³ + 24x² + 18x - 12
Step-by-step explanation:
We require the product
(2x² + 4x - 2)(3x + 6)
Each term in the second factor is multiplied by each term in the first factor, that is
2x²(3x + 6) + 4x(3x + 6) - 2(3x + 6) ← distribute all parenthesis
= 6x³ + 12x² + 12x² + 24x - 6x - 12 ← collect like terms
= 6x³ + 24x² + 18x - 12
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What are the zeros of the function?
Use the zeros to find all of the linear factors of the polynomial function.
Write the equation of the graphed function f(x), where a is the leading coefficient. Use the factors found in the previous question. Express the function as the product of its leading coefficient and the expanded form of the equation in standard form.
Use the y-intercept of the graph and your equation from part E to calculate the value of a.
Given what you found in all of the previous parts, write the equation for the function shown in the graph.
Answer:
Step-by-step explanation:
The zeros of this cubing function are easily read from the graph: {-20, -5, 15}.
The factors of this polynomial are therefore (x + 20), (x + 5) and (x - 15).
The y-intercept is (0, 1).
The function is thus f(x) = a(x + 20)(x + 5)(x - 15).
According to the y-intercept, if x = 0, y = 1.
Thus, y = 1 = f(0) = a(20)(5)(-15), or 1 = a(100)(-15), or 1 = -1500a.
Then a = -1/1500, and the function is:
f(x) = (-1/1500)(x^3 + .. + .. + ... ). We must multiply out (x + 20)(x + 5)(x - 15) to obtain f(x) in finished form.
Answer:
zeros: (-20, 0), (-5, 0) and (15, 0)
factors: (x + 20), (x + 5) and (x - 15)
f(x) = a*(x + 20)*(x + 5)*(x - 15)
a = -1/1500
f(x) = -1/1500*(x + 20)*(x + 5)*(x - 15)
f(x) = -1/1500*x^3 - 1/100*x^2 + 11/60x + 1
Step-by-step explanation:
The zeros of the function are those points where the function intercepts the x-axis. They are: (-20, 0), (-5, 0) and (15, 0)
The zeros of a polynomial are expressed as factors as follows: (x - a) where a is a zero. Then, for this case, the factors are (x + 20), (x + 5) and (x - 15)
The equation of f(x) use the factors and the leading coefficient as follows: f(x) = a*(x + 20)*(x + 5)*(x - 15)
Applying the distributive property of multiplication, we get the expanded form:
f(x) = a*(x + 20)*(x + 5)*(x - 15)
(x + 20)*(x + 5) = x^2 + 5x + 20x + 20*5 = x^2 + 25x + 100
f(x) = a*(x^2 + 25x + 100)*(x - 15)
(x^2 + 25x + 100)*(x - 15) = x^3 - 15x^2 + 25x^2 - 15*25x + 100x - 100*15 = x^3 + 15x^2 - 275x - 1500
f(x) = a*(x^3 + 15x^2 - 275x - 1500)
The y-intercept of the graph is (0, 1). Replacing this point into the function equation:
1 = a*(0 + 20)*(0 + 5)*(0 - 15)
1 = a*20*5*(-15)
1 = a*(-1500)
a = -1/1500
Replacing this value into the function equation:
f(x) = (-1/1500)*(x^3 + 15x^2 - 275x - 1500)
f(x) = -1/1500*x^3 - 1/100*x^2 + 11/60x + 1
HELPPPPPPPPPP Add & subtract matrices .....
PLZ GIVE THE ANSWER .. THANKSSSSS .
Answer:
[tex]\left[\begin{array}{ccc}-2&-1&1\\6&0&3\end{array}\right][/tex]
Explanation
Given in the question two matrix, a matrix can only be added to (or subtracted from) another matrix if the two matrices have the same dimensions.
Here the dimensions are 2x3 and 2x3.
[tex]\left[\begin{array}{ccc}0&2&4\\4&4&1\end{array}\right][/tex][tex]-\left[\begin{array}{ccc}2&3&3\\-2&4&-2\end{array}\right][/tex]
To subtract two matrices, just subtract the corresponding entries
[tex]\left[\begin{array}{ccc}0-2&2-3&4-3\\4+2&4-4&1+2\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}-2&-1&1\\6&0&3\end{array}\right][/tex]
Change 50% to a decimal, then a fraction.
Answer:
0.5 and 1/2
Step-by-step explanation:
half of 100 is 50 so thats the 1/2 put 1/2 into decimal form and its 0.5
Sixty percent of the flowers in Karen’s garden are roses. Which of the following shows 60% roses?
Answer:
A
Step-by-step explanation:
3/5 of the letters are roses and 3/5 = 6/10 = 60%
Final answer:
The correct option that shows 60% roses is b. 50% of the flowers are blue and 50% of the flowers are red.
Explanation:
The question asks which option shows 60% roses. The correct option would be b. 50% of the flowers are blue and 50% of the flowers are red. This is because 60% of the flowers in Karen's garden are roses, and the remaining 40% would consist of other flowers, such as blue and red flowers.
Which line is the best model for the data in the scatter plot?
Answer:
A.) is the best option
Step-by-step explanation:
Find the second, fourth, and eleventh terms of the
sequence described by each explicit formula.
A(n) = -9 + (n - 1)(3)
Answer:
The second term is -6 , the fourth term is 0 , the eleventh term is 21
Step-by-step explanation:
* Lets revise the explicit formula
- An explicit formula will create a sequence using n, the number
position of each term.
- If you can find an explicit formula for a sequence, you will be able
to quickly and easily find any term in the sequence by replacing
n with the number of the term you want
- It defines the sequence as a formula in terms of n.
* Now lets solve the problem
- The formula of the sequence is A(n) = -9 + (n - 1)(3)
- A(n) is any term in the sequence
- n is the position of the number
- To find the second term put n = 2
∵ n = 2
∴ A(2) = -9 + (2 - 1)(3) = -9 + (1)(3) = -9 + 3 = -6
* The second term is -6
- To find the fourth term put n = 4
∵ n = 4
∴ A(4) = -9 + (4 - 1)(3) = -9 + (3)(3) = -9 + 9 = 0
* The fourth term is 0
- To find the eleventh term put n = 11
∵ n = 11
∴ A(11) = -9 + (11 - 1)(3) = -9 + (10)(3) = -9 + 30 = 21
* The eleventh term is 21
Answer:
Second term = -6
Fourth term = 0
Eleventh term = 21
Step-by-step explanation:
We are given the following explicit formula of an arithmetic sequence and we are to find the second, fourth and the eleventh terms of this sequence:
[tex]a_n=-9+(n-1)(3)[/tex]
where [tex]a_n[/tex] = nth term, [tex]a_1=-9[/tex] and [tex]n[/tex] = number of term.
Second term [tex](a_2) = -9+(2-1)(3)[/tex] = -6
Fourth term [tex](a_4) = -9+(4-1)(3)[/tex] = 0
Eleventh term [tex](a_{11}) = -9+(11-1)(3)[/tex] = 21
110 is 21.1% of what number?
Answer: 23.21
Explanation: I did 110x21.21 divided by 100
The number 110 is 21.1% of the number 521.33, as of the given percentage.
Given that,
To determine the number whose 21.1% is 110.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
here,
let the number be x,
110 = 21.1% of x,
x = 110 / 0.211
x = 521.33
Thus, the number 110 is 21.1% of the number 521.33.
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Which group of numbers is listed from greatest to least?
|-3|, |-4|, |-7|, |-8|, |-9|
8, |-6|, 5, |-4|, |1|
-3, |-1|, 0, 2, 7
9, 7, |6|, -5, |-4|
Answer:
The second option is the correct answer
Step-by-step explanation: Hope this helps
The group of numbers is listed from greatest to least will be 8, |-6|, 5, |-4|, |1|
What is descending order?The descending order is one in which the numbers are in decreasing pattern or numbers vary from the greatest to the lowest.
In the question there are four options:-
|-3|, |-4|, |-7|, |-8|, |-9|
8, |-6|, 5, |-4|, |1|
-3, |-1|, 0, 2, 7
9, 7, |6|, -5, |-4|
We can clearly see that option second has a series of descending numbers. The series is descending from the number 8 to 1 in the decreasing pattern of the numbers.
Hence a group of numbers are listed from greatest to least will be 8, |-6|, 5, |-4|, |1|
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What is a common mistake when evaluating and documenting skill sets
Answer:
confusing activities with accomplishments
Step-by-step explanation:
Answer:
confusing activities with accomplishments.
Step-by-step explanation:
A and B are independent events if...
Answer:
(C) The probability of buying bread and cheese is 0.12
Step-by-step explanation:
P(Event A) = 0.6
P(Event B) = 0.2
If Event A and Event B are independent,
Then P(Event A and Event B) = 0.6 x 0.2 = 0.12
A and B are independent events if:
C. The probability of buying bread and cheese is : 0.12
Step-by-step explanation:Two events A and B are said to be independent.
if P(A∩B)=P(A)×P(B)
where P denote the probability of an event.
Here,
Event A= A shopper buys bread
and Event B=A shopper buys cheese
Also we have:
P(A)= 0.60 and P(B)= 0.20
If A and B are independent events then,
P(A∩B)=0.60×0.20
i.e.
P(A∩B)=0.12
i.e.If A and B are independent then the probability of buying bread and cheese is: 0.12
Also we know that:
P(A∪B)=P(A)+P(B)-P(A∩B)
If A and B are independent then,
P(A∪B)=0.60+0.20-0.12
i.e.
P(A∪B)=0.68
If A and B are independent then the probability of buying bread or cheese is: 0.68
a 96 foot transmission tower casts a 72 foot long shadow. an anchor wire runs from the top of the tower to the tip of the shadow. a ladder is set up vertically 66 feet from the base of the tower so the top of the ladder touches the wire. what is the height of the ladder
Answer:
63.5
Step-by-step explanation:
they all form a triangle, and the formula for that is a²+b²=c²
a=96 b=wire c=72
96²+b²=72²
9216+b²=5184
-9216 -9216
b²= -4032
square root of -4032 = 63.5
Juice boxes are sold in a local store for 65 cents each. The factory has $1400 in fixed costs plus 15 cents of additional expense for each juice box made. Assuming all juice boxes manufactured can be sold, find the break-even point.
Answer:
Break even occurs at 2800 juice boxes.
Step-by-step explanation:
Fixed cost form the factor = $1400
Variable cost per unit juice box = 15 cents = $0.15
Let number of juice boxed produced to get brek even point = x
Then total cost = c(x)= 1400+0.15x
Selling price per unit juice box = 65 cents = $0.65
Then total sales = R(x)= 0.65x
At break even both sales and cost will be equal so we get:
[tex]0.65x=1400+0.15x[/tex]
[tex]0.65x-0.15x=1400[/tex]
[tex]0.50x=1400[/tex]
[tex]x=\frac{1400}{0.50}[/tex]
[tex]x=2800[/tex]
Hence break even occurs at 2800 juice boxes.
Randall purchased a plot of land for his business. The figure represents a plan of the land showing the location of the office space, parking lot and open space for a yard so that the employees and visitors can enjoy time outside. The coordinates represent points on a rectangular grid with units in feet. What is the perimeter of the plot of land rounded to the nearest tenth of a foot?
Answer:
482.8
Step-by-step explanation:
Answer:
The perimeter of the plot of land is approximately 482.8 feets.
Step-by-step explanation:
By the given diagram,
The perimeter of the plot of land = The perimeter of the quadrilateral having the vertices (0,0), (0,120), (140,100) and (140,20),
Since, the perimeter of the quadrilateral having the vertices (0,0), (0,120), (140,100) and (140,20) = The distance between (0,0) and (0,120) + The distance between (0,120) and (140,100) + The distance between (140,100) and (140,20) + The distance between (140,20) and (0,0)
By the distance formula,
[tex]=\sqrt{(0-0)^2+(120-0)^2}+\sqrt{(140-0)^2+(100-120)^2}+\sqrt{(140-140)^2+(20-100)^2}+\sqrt{(0-140)^2+(20-0)^2}[/tex]
[tex]=\sqrt{120^2}+\sqrt{19600+400}+\sqrt{0+80^2}+\sqrt{19600+400}[/tex]
[tex]=120+100\sqrt{2}+80+100\sqrt{2}[/tex]
[tex]=200+200\sqrt{2}[/tex]
[tex]=482.842712475[/tex]
[tex]\approx 482.8\text{ feet}[/tex]
Hence, the perimeter of the plot land is approximately 482.8 feets.
Can someone please explain how to get the answer plzzzzz
Multiply the two numbers first
6*3= 18
Divide the total volume by 18
144/18=6
Answer: Missing length is 6 ft .
What is the range of the function f(x) = 3x2 + 6x – 8?
Answer: C... {y|y ≥ -1}
Step-by-step explanation:
f(x) is a quadratic equation with the x-side squared and a is positive which means that the graph of the function is a parabola facing up. The range of f(x) is given by {y|y ≥ k}, where k is the y-coordinate of the vertex.
in vertex form (h, k) = (-1, -11)
This meaning the range ={y|y ≥ -11}
Answer:
the answer is C
Step-by-step explanation:
Find the minimum/maximum of y=2x^2+12x-22
Answer:
The minimum value of this function is -40.
Step-by-step explanation:
Recall that the minimum of a quadratic whose graph is a parabola that opens up, as this one does, is the vertex of the graph. The x-coordinate of the vertex is given by x = -b / (2a), where a is the coefficient of the x^2 term and b is that of the x term.
Here, x = -12 / (2*2), or x = -12/4, or x = -3.
Find the y-value at this x-value: f(-3) = 2(-3)^2 + 12(-3) - 22, or
f(-3) = 2(9) - 36 - 22, or -40.
The vertex is at (-3, -40). The minimum value of this function is -40.
The provided quadratic function y=2x²+12x-22 has no local minimum or maximum, as indicated by the application of the second derivative test, which results in a point of inflection rather than an extrema.
The minimum or maximum of the quadratic function y=2x²+12x-22. To locate the extrema of a quadratic function, we often use the first derivative test. However, the information provided indicates the derivative vanishes at x = 2 (y' = 0), but the second derivative test (y" = 6x - 12) reveals that this point is a point of inflection rather than a minimum or maximum. The second derivative being zero at x = 2 implies that there is no concavity change and hence, no local extrema. Therefore, for this particular quadratic function, there is no local minimum or maximum. The function can be rewritten as y = (x - 2)³ + 8, which shifts the function y = x³ two units to the right and eight units upwards, further emphasizing that it indeed has no local extrema.
what is the value of s in the equation 4s x 4 = 64
Answer:
s = 4
Step-by-step explanation:
4s * 4 = 64
Simplify: 16s = 64
Divide: s = 64/16
Simplify: s = 4
“ s “ equals 4 therefore 4 is the answer
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Jamie has a deck of 60 sports cards, of which some are baseball cards and some are football cards. Jamie pulls out a card randomly from the deck, records its type, and replaces it in the deck. Jamie has already recorded nine baseball cards and 11 football cards. Based on these data, what is, most likely, the number of baseball cards in the deck?
20
22
25
27
Answer:
Option D is correct .i.e., Most likely, the number of baseball cards in the deck is 27.Step-by-step explanation:we find probability of getting a Base ball card and compare it with probability of Baseball card from whole data.let,Total No. of Sports Cards in Data 1= 60and No. of Base ball card in Data 1 = xIn Data2,Jamie recorded data for 20 times⇒Total No. of cards in Data 2 = 20In which 9 cards are of Baseball and 11 cards are of Football.⇒ No. of Baseball card in Data 2 = 9Now by comparing,Therefore, Option D is correct .i.e., Most likely, the number of baseball cards in the deck is 27.
Step-by-step explanation:
2. By selling an article for ₹1636.25, a dealer gains ₹96.25. Find his gain percentage.
Answer is..
5.88%
(96.25/1636.25)%
= 5.88%
Final answer:
To calculate the gain percentage, subtract the gain from the selling price to get the cost price, and then divide the gain by the cost price and multiply by 100. The dealer's gain percentage is approximately 6.25%.
Explanation:
The subject of the question is to calculate the gain percentage of a dealer who sells an article for ₹1636.25 and gains ₹96.25. To find the gain percentage, we need to identify the cost price first. The cost price (CP) can be calculated by subtracting the gain from the selling price (SP), which gives us CP = SP - Gain = ₹1636.25 - ₹96.25 = ₹1540.
Next, we calculate the gain percentage using the formula:
Gain Percentage = (Gain / Cost Price) * 100
Substituting the values, we get:
Gain Percentage = (₹96.25 / ₹1540) * 100
Therefore, the gain percentage of the dealer is approximately 6.25%.
Which side lengths form a right triangle 30 POINTS!! I DONT HAVE MUCH TIME
Answer:
To solve this problem, we can use Pythagorean theorem, it tells us that the square of the hypotenuse is equal to the sum of the square of the other two sides.
When we look at these side lengths, we can see that only the second answer is suitable because from the lengths, we can predict that 13 is the length of the hypotenuse, 5 is the length of the shorter leg and 12 is the length of the other leg, and when you actually calculate it, the result is correct as well:
5² + 12² = 25 + 144 = 169
13² = 169
So the answer is B
I’m thinking that the answer is B! Sorry if I’m wrong!:)
The histogram represents the number of gallons of gasoline that drivers purchase weekly. Which bar represents the number of gallons most drivers purchase during the week?
A) Bar 1
B) Bar 2
C) Bar 3
D) Bar 5
Answer:
option B) Bar 2
Step-by-step explanation:
The histogram represent the number of gallons of gasoline on x axis.
The number of drivers purchase weekly on y axis.
In this histogram 5 Bars are shown.
First bar represents = 5 drivers
Second bar represents = 6 drivers
Third bar represents = 1 driver
Fourth bar represents = 3 drivers
Fifth bar represents = = 4 drivers
So the second bar represents the the number of gallons most drivers purchased during the week.
Therefore, option B) Bar 2 is the correct answer.
Answer:
bar2
Step-by-step explanation: