Answer:62
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.
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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
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
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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A suitcase measures 14 inches long and 20 inches high. What is the diagonal length of the suitcase
Answer:
Step-by-step explanation:
14^2+20^2=c^2
196+400=c^2
square root of 596=c^2
c^2=24.4
The diagonal length of the suitcase is 24.41 inches if the suitcase measures 14 inches long and 20 inches high.
What is a right-angle triangle?It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
We have a suitcase measures 14 inches long and 20 inches high.
The diagonal, length, and height will make a right angle triangle.
Let's suppose the length of the diagonal is x inches
From the Pythagoras theorem:
x² = 14² + 20²
x² = 596
x = 24.41 inches
Thus, the diagonal length of the suitcase is 24.41 inches if the suitcase measures 14 inches long and 20 inches high.
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find the slope.................................
Answer:
1/1
Step-by-step explanation:
We can use the points (0, -1) and (1, 0) to solve.
Slope formula: y2-y1/x2-x1
= 0-(-1)/1-0
= 1/1
= 1 (Answer)
Hope This Helped! Good Luck!
If m(x)=x+5/x-1 and n(x) = x – 3, which function has the same domain as (m.n)(x)
The function m(x) = x + 5/(x-1) has the same domain as the composition of functions (m.n)(x) because they both have the domain of all real numbers except 1.
Explanation:The domain of a function is the set of all possible input values (often called 'x-values') which will give valid output values. In other words, it's all the values x can take on. The function m(x) = x +5/(x-1) will be undefined when the denominator equals zero, so x cannot equal 1. Therefore, the domain of m(x) is all real numbers except 1.
On the other hand, the function n(x) = x - 3 doesn't have any restrictions and can take on all real numbers. However, (m.n)(x) refers to a composition of functions, specifically m(n(x)). This will inherit the domain restrictions from m(x). Therefore, the function that has the same domain as (m.n)(x) is m(x) because the composition will allow inputs for all real numbers except 1, as dictated by m(x).
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If you ask all your classmates for their favorite colors, you are gathering what kind of data?
A) bivariate
B) categorical
C) numerical
D) quantitative
When you ask all your classmates for their favorite colors, you are gathering data that can be grouped into categories based on color names, such as "red," "blue," "green," and so on. This type of data is known as categorical data.
Categorical data, also sometimes referred to as qualitative data, consists of information that is not numerical in nature and can be separated into different categories according to some quality or attribute. In the case of favorite colors, you're dealing with categories as you cannot perform arithmetic operations on them (you can't add 'red' to 'blue' and get a sum, for instance).
Let's review the other options:
A) Bivariate data involves two variables and the relationship between them. Since the question only refers to one variable—favorite color—this is not bivariate data.
C) Numerical data involves numbers, and operations such as addition, subtraction, multiplication, and division can be performed on it. Since favorite colors are not numbers, this is not numerical data.
D) Quantitative data is another term for numerical data; it involves quantities that can be measured and expressed using numbers. Since we're not measuring anything in numbers when asking about favorite colors, this is not quantitative data.
Thus, the correct answer is:
B) Categorical
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
Solve using substitution or elimination.
y = x + 1
2x - 5y = 4
Substitute y = x + 1 into 2x - 5y = 4
-3x - 5 = 4
Solve for x in -3x - 5 = 4
x = -3
Substitute x = -3 into y = x + 1
y = -2
Therefore,
x = -3
y = -2
Evaluate 3b + 2 when b=4
[tex]
3\times4+2=12+2=\boxed{14}
[/tex]
Answer: 14
Step-by-step explanation: if you substitute B in for 4, You then multiply 3 by 4 and get a product of 12. Then the question says to add 2. Add 2 to what you already have and you get the sum of 14.
Have a great Day!
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
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
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 .
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
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.
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
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.
Which expression is equivalent to this expression
t - 6(-2t + 1)
[tex]t - 6( - 2t + 1) \\ t + 12t - 6 \\ 13t - 6 \\ 13t = 6 \\ t = \frac{13}{6} [/tex]
The correct expression which is equivalent to this expression t - 6(-2t + 1) is,
⇒ 13t - 6
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The expression is,
⇒ t - 6 (- 2t + 1)
Now, We can simplify as;
⇒ t - 6 (- 2t + 1)
⇒ t + 12t - 6
⇒ 13t - 6
Thus, The correct expression which is equivalent to this expression
t - 6(-2t + 1) is,
⇒ 13t - 6
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Plz help me with this
it's the third choice because of your radius like how it's 2πR^2
Answer: [tex]\bold{D)\quad y = 2sin(3x)}[/tex]
Step-by-step explanation:
[tex]\text{The standard form of a sine equation is: y=A sin(Bx - C) + D}\\\\\bullet\text{A = amplitude}\\\\\bullet\text{Period = }\dfrac{2\pi}{B}\\\\\bullet\text{Phase Shift = }\dfrac{C}{B}\\\\\bullet\text{D = vertical shift (up if positive, down if negative)}[/tex]
In the given graph,
A (amplitude) = 2P (period) = [tex]\dfrac{2\pi}{3}[/tex] --> B = 3Phase Shift [tex]\bigg(\dfrac{C}{B}\bigg)[/tex] = 0 --> C = 0D (vertical shift) = 0[tex]\implies \large\boxed{y = 2sin(3x)}[/tex]
see graph below for verification
The height of a fireworks rocket in meters can be approximated by h= -5t^2+30t, where h is the height in meters and t is the time in seconds. Find the time it takes the rocket to reach the ground after it has been launched
It takes 45 seconds. the easiest way to do these is to use a graphic calculator and replace the variables with x and y, for example, this equation would become -5x^2+30x, and if you don't have access to a graphing calculator, you can always use desmos online.
Answer:
It takes 6 seconds to the rocket to reach the ground after it has been launched
Step-by-step explanation:
The height of a fireworks rocket in meters can be approximated by :
h = -5t² + 30t, where h is the height in meters and t is the time in seconds
Now, we need to find the time it takes the rocket to reach the ground after it has been launched
So, When it touches the ground height will be 0
⇒ h = 0
⇒ 0 = -5t² + 30t
⇒ t² - 6t = 0
⇒ t(t - 6) = 0
Now, since the rocket is launched from above the ground ⇒ t ≠ 0
⇒ t - 6 = 0
⇒ t = 6
Hence, It takes 6 seconds to the rocket to reach the ground after it has been launched
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%.
How many real number solutions does the equation have. Y=3x^2-5x-5
Answer:
2
Step-by-step explanation:
To find how many real solution a quadratic equation has, we just need to find the value of its discriminant. If the discriminant is zero, the quadratic only has one real solution; if the discriminant is positive, the quadratic has two real solution; if the discriminate is negative, the quadratic doesn't has any real solutions.
The discriminant of a quadratic equation of the form [tex]ax^2+bx+c[/tex] is given by: [tex]b^2-4ac[/tex]
We know from our quadratic that [tex]a=3[/tex], [tex]b=-5[/tex], and [tex]c=-5[/tex].
Replacing values:
[tex](-5)^2-4(3)(-5)[/tex]
[tex]25+60[/tex]
[tex]85[/tex]
Since the discriminant is positive, we can conclude that our quadratic equation has two real solutions.
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.
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!:)
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.
4. An adult African elephant weighs
approximately 8 tons. Which comparis
is true?
8 tons = 20,000 pounds
6 8 tons < 20,000 pounds
8 tons < 100,000 ounces
08 tons = 24,000 pounds
5. A water bottle contains 2,000 milliliters
so what is the answer A,B,C,D
Answer:
8 tons < 20,000
Step-by-step explanation:
1 ton = 2000 pounds
so 8 tons would be 16,000 which makes it less than 20,000
Final answer:
An adult African elephant that weighs approximately 8 tons is not equal to 20,000 pounds; instead, 8 tons equals 16,000 pounds. The provided comparison in the question is incorrect.
Explanation:
To determine if an adult African elephant that weighs approximately 8 tons is equal to 20,000 pounds, we need to convert tons to pounds using the unit equivalence 1 ton = 2,000 pounds. Multiplying 8 tons by the unit equivalence gives us:
8 × 2,000 = 16,000 pounds.
Knowing that the range of weight of a male African elephant is between 12,000 and 16,000 pounds, we can see that 8 tons does not equal 20,000 pounds. Therefore, the comparison 8 tons = 20,000 pounds is incorrect.
A correct comparison would be 8 tons = 16,000 pounds, which is not one of the options provided in the question.
As for the water bottle containing 2,000 milliliters, this is simply stating the volume capacity of the bottle but does not relate to the conversion between tons and pounds.
The rectangle below has an area of x^2-9 square meters and a width of x-3 meters.What expression represents the length of the rectangle?
The area of a rectangle can be found by using this formula: Area = Length • Width
The question gives us the area and the width, so all we need to look for is the length. To do this, we manipulate the formula so we are solving for length, like so: Length = Area / Width
Area = x^2 -9
Width = x-3
Length = unknown
Now, we plug in what we know (Area and Width) into the formula for Length:
Length = (x^2 - 9) / (x - 3)
x^2 - 9 simplifies to (x - 3)(x+3) so we are left with: Length = (x - 3)(x + 3) / (x - 3) and we see that (x - 3) cancels out
The final answer is that *Length = x + 3*
To check your work, you can plug in each part into the formula for area and see if the answers match
The question is asking for the length of a rectangle given the area and width. This can be found by using the formula for the area of a rectangle which is width * length = area. Dividing the given area by the width results in the length.
Explanation:To solve the problem, we need to use the formula for the area of a rectangle which is width*length=area. Given the area is x^2-9 and the width is x-3, we can find the length by dividing the area by the width. Therefore, the length of the rectangle is (x^2 - 9) / (x - 3).
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Which of the following can be modeled with an exponential function? Select all that apply.
1) Height over time that a football is thrown across the field.
2) The cost to attend Universal Studios increases by 1% each year.
3) An endangered species population is decreasing by 12% each year.
4) The distance a bicyclist travels when cycling a constant speed of 25 mph.
5) The population of a town that is growing by 5% each year.
Answer:
Step-by-step explanation:
The answers would be 2, 3, and 5.
The first situation represents a quadratic equation and the fourth situation represents a linear equation.