A 2-column table with 10 rows. The first column is labeled x with entries negative 4, negative 3, negative 2, negative 1, 0, 1, 2, 3, 4, 5. The second column is labeled f of x with entries 105, 0, negative 15, 0, 9, 0, negative 15, 0, 105, 384.
According to the table, which ordered pair is a local minimum of the function, f(x)?
(0, 9)
(4, 105)
(–1, 0)
(2, –15)
Answers
To determine which ordered pair is a local minimum of the function, f(x), we need to look for a point where the function value is smaller than the values of the function at the surrounding points.
From the table, we can see that the function value at x = 2 is -15, which is smaller than the function values at x = 1 and x = 3, which are both 0. Therefore, the ordered pair (2, -15) is a local minimum of the function, f(x).
Note that the ordered pairs (0, 9), (4, 105), and (-1, 0) are not local minima, as the function values at these points are all larger than the values at their surrounding points.
Answer:
D
Step-by-step explanation:
Related Questions
What’s is Arccsc .866 problem
Answers
Answer:
arccsc refers to "arc cosecant", or the radian measure of the arc on a circle corresponding to a given value of cosecant. Technical note: Since none of the six trig functions sine, cosine, tangent, cosecant, secant, and cotangent are one-to-one, their inverses are not functions.
what is arccsc equal to? The value of the arccsc function of any argument is an angle in radians whose cosecant function equals the given argument, that is, y = csc-1x if and only if x = cosec(y) for - /2 < y < /2 and y. ˗ˏˋ ❤︎ ࿐
Step-by-step explanation:
Consider f(x)= 4 cos x (1 – 3 cos 2x +3 cos² 2x − cos³ 2x).
Show that for f(x) dx = 3/2 sin7 m, where m is a positive real constant.
Answers
Answer:
We can start by simplifying the expression inside the parentheses using the identity:
cos 2x = 2 cos² x - 1
Substituting this in, we get:
1 – 3 cos 2x + 3 cos² 2x − cos³ 2x
= 1 – 3(2 cos² x - 1) + 3(2 cos² x - 1)² − (2 cos² x - 1)³
= 1 – 6 cos² x + 9 cos⁴ x - 4 cos⁶ x
Therefore, we can rewrite f(x) as:
f(x) = 4 cos x (1 – 6 cos² x + 9 cos⁴ x - 4 cos⁶ x)
Next, we can use the trigonometric identity:
sin 2x = 2 cos x sin x
to express cos x in terms of sin x:
cos x = √(1 - sin² x)
Substituting this in, we get:
f(x) = 4 sin x cos³ x (1 – 6 cos² x + 9 cos⁴ x - 4 cos⁶ x)
= 4 sin x (√(1 - sin² x))³ (1 – 6 (2 sin² x - 1) + 9 (2 sin² x - 1)² - 4 (2 sin² x - 1)³)
= 4 sin x (1 - sin² x)^(3/2) (16 sin⁶ x - 48 sin⁴ x + 36 sin² x - 8)
Next, we can use the substitution u = 1 - sin² x, du = -2 sin x cos x dx, to obtain:
f(x) dx = -2 du (u^(3/2)) (16 - 48u + 36u² - 8u³)
Integrating, we get:
f(x) dx = 2/3 (1 - sin² x)^(5/2) (8 - 36(1 - sin² x) + 36(1 - sin² x)² - 8(1 - sin² x)³) + C
Now, we can use the trigonometric identity:
sin² x = (1 - cos 2x)/2
to simplify the expression inside the parentheses. After some algebra, we obtain:
f(x) dx = 3/2 sin 7x + C
where C is the constant of integration. Since m is a positive real constant, we can set:
7x = m
and solve for x:
x = m/7
Substituting this in, we get:
f(x) dx = 3/2 sin(7m/7) = 3/2 sin m
Therefore, we have shown that:
f(x) dx = 3/2 sin m, where m is a positive real constant.
Please answer the question in the picture
Answers
answer:
(3x-2)(x+3)
explanation:
3x²+7x-6
3x²+9x-2x-6 [ least common multiple of 6 and 3 is 18: 9 * 2 ]
3x(x+3)-2(x+3) [ factorise them ]
(3x-2)(x+3) [ close the brackets and this is our final answer ]
An animal shelter provides a bowl with 1.25 liters of water for 5 cats.
About how much water will be left after the cats drink their average daily amount of water?
Water Consumption
Animal Average Amount
(Liters per day)
Canada Goose 0.24
Cat 0.15
Mink 0.10
Opossum 0.30
Bald Eagle 0.16
liter(s) of water will be left after the cats drink their average daily amount of water.
Answers
Answer:
.50 left
Step-by-step explanation:
You have to multiply .15 times 5, then get that and subtract that number by 1.25, but do not worry about the decimal just add that in later, and the answer is .50
Complete both transformations below. Then enter the final coordinates of the figure.
A (-4,0)
B
A" ([?], []) C" ([], [])
C (-3,-3)
1) Reflect across y-axis 2) < -5,2>
![Complete both transformations below. Then enter the final coordinates of the figure.A (-4,0)BA" ([?],](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/umMkj8c9UuIrrkMQzO5ODkH5kn0D9nDA.jpeg)
Answers
Answer:
A"(-1, 2)B"(-5, 1)C"(-2, -1)Step-by-step explanation:
You want points A(-4, 0), B(0, -1) and C(-3, -3) reflected across the y-axis and translated left 5 and up 2.
TransformationThe reflection across the y-axis changes the sign of the x-coordinate:
(x, y) ⇒ (-x, y)
The translation adds the translation vector to the reflected coordinates.
(x, y) ⇒ (x -5, y +2) . . . . . . translation (by itself)
Then the result of both transformations is ...
(x, y) ⇒ (-x -5, y +2)
For a number of points, this arithmetic is conveniently accomplished by a calculator. The result is ...
A"(-1, 2)B"(-5, 1)C"(-2, -1)![Complete both transformations below. Then enter the final coordinates of the figure.A (-4,0)BA" ([?],](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/NH04BEo7y2fNv0xtLdszczwiOvSwOMre.png)
You model your investment account using the formula y = 20000(1.035)x where x represents the
number of years and y represents the account balance after x years. What is the growth rate of your
investment?
Answers
Answer:
Step-by-step explanation:
The growth rate of the investment is represented by the constant multiplier in the exponential term of the formula y = 20000(1.035)x. In this case, the constant multiplier is 1.035, which represents the annual growth rate of the investment account.
To calculate the growth rate as a percentage, we can subtract 1 from the constant multiplier, and then multiply the result by 100.
So, the growth rate of the investment is:
1.035 - 1 = 0.035
0.035 * 100 = 3.5%
Therefore, the growth rate of the investment is 3.5%.
The growth rate of the investment can be found by subtracting 1 from the base of the exponential function and converting the result to a percentage:
growth rate = (base - 1) x 100%
growth rate = (1.035 - 1) x 100%
growth rate = 0.035 x 100%
growth rate = 3.5%
Therefore, the growth rate of the investment is 3.5%.
Using PT in the Coordinate System
Answers
Answer:
\(d = \sqrt{40} \)
Explanation:Distance between two points is given by the formula,
\(d= \sqrt{((x_2 - x_1)^{2} + (y_2 - y_1)^{2} )}\)
Let,
\( \sf Point \: 1 = (x_1,y_1)= (-3,2)\)
\(\sf Point \: 2 = (x_2,y_2)= (3,0)\)
Substituting the given coordinate in above formula,
\(d= \sqrt{((3 - ( - 3))^{2} + (0 - 2)^{2} )}\)
\(d = \sqrt{ {6}^{2} + ({ - 2})^{2} }\)
\(d = \sqrt{36 + 4} \)
\(d = \sqrt{40} \)
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Which value for x makes the open sentence true?
5+4⋅x=3²+x²
a. 5
b. 4
c. 3
d. 2
Answers
Answer:
D) 2
Step-by-step explanation:
First Method: Solve for xThere are two ways to find what value of x will make this equation true. The first method is to solve for x in the equation.
The given equation is:
\(5+4*x=3^2+x^2\)Rewrite this equation by evaluating the exponent on the right side of the equation, and make 4 * x = 4x.
\(5+4x=9+x^2\)Subtract \((5+4x)\) from both sides of the equation (so we can keep the \(x^2\) positive). It's just preference.
\(0=9+x^2-5-4x\)Simplify the right side of the equation by combining like terms and rearranging terms to follow the format of \(ax^2+bx+c\).
\(0=x^2-4x+4\)Factor this quadratic by seeing what two terms multiply to \(4\) and add up to \(-4\). These two terms are \(-2\). Notice that this is a perfect square.
\(0=(x-2)(x-2)\)Solve for x by setting the expressions inside the parentheses equal to 0.
\((x-2) = 0 \\ x - 2 = 0 \\ $Add to both sides of the equation.$\\ x =2\)This means that answer choice D) 2 is correct.
Second Method: Plug in the answer choicesThe second method is to substitute the given answer choices into the equation, which works when you are given answer choices. Otherwise, the first method is ideal.
Use the form of the equation where we set all the terms equal to 0.
\(0=x^2-4x+4\)Start with answer choice A, and work your way up to D to check all of them.
A) Substitute 5 for x into the equation.
\(0=(5)^2-4(5)+4 \\ 0 = 25 - 20 + 4 \\ 0=1\)This is a false statement; 0 does not equal 1.
B) Substitute 4 for x into the equation.
\(0=(4)^2-4(4)+4 \\ 0= 16-16+4 \\ 0=4\)This is a false statement; 0 does not equal 4.
C) Substitute 3 for x into the equation.
\(0=(3)^2-4(3)+4 \\ 0=9-12+4 \\ 0=1\)This is a false statement; 0 does not equal 1.
D) Substitute 2 for x into the equation.
\(0=(2)^2-4(2)+4 \\ 0=4-8+4 \\ 0=0\)This is a TRUE statement; thus, the answer is D) 2.
Find the lowest common denominator.
1 1 2
----------- , ------------ , -------------
(x+2)2 (x-2)2 x2-4
Answers
The LCD of 1/(x+2)^2, 3/(x-2)^2, and 4/(x^2-4) is (x+2)^2(x-2)^2(x+2)(x-2) = (x+2)^3(x-2)^3.
To find the lowest common denominator (LCD) of three fractions, we need to identify the factors of each denominator and select those factors that are common to all denominators.The given fractions are: 1/ (x+2)^2, 3/ (x-2)^2, and 4/ (x^2-4).
The first denominator (x+2)^2 can be factored using the formula for the difference of two squares. The denominator of 3/(x-2)^2 can also be factored using the formula for the difference of two squares.
Finally, the denominator of 4/(x^2-4) can be factored using the formula for the difference of two squares and the formula for the sum of two squares.
So, 1/(x+2)^2, 3/(x-2)^2, and 4/(x^2-4) can be rewritten as follows:1/ (x+2)^2 = A/(x+2) + B/(x+2)^2. Multiplying both sides by (x+2)^2 gives:1 = A(x+2) + B ... (1)3/ (x-2)^2 = C/(x-2) + D/(x-2)^2.
Multiplying both sides by (x-2)^2 gives:3 = C(x-2) + D ... (2)4/ (x^2-4) = E/(x-2) + F/(x+2). Multiplying both sides by (x^2-4) gives:4 = E(x-2)(x+2) + F(x+2)(x-2) ... (3)
Now, we need to solve these equations for A, B, C, D, E, and F. First, we will solve equation (1) for A and B by substituting x = -2, which gives A = -1/4. Then we will substitute x = -2 again and solve for B, which gives B = 1/4. Next, we will solve equation (2) for C and D by substituting x = 2, which gives C = 3/4.
Then we will substitute x = 2 again and solve for D, which gives D = -3/4. Finally, we will solve equation (3) for E and F by substituting x = 2 and x = -2, which gives E = 1/2 and F = 1/2.
Now, we have A = -1/4, B = 1/4, C = 3/4, D = -3/4, E = 1/2, and F = 1/2. The LCD is the product of all the factors that appear in the denominators of the fractions, each raised to the highest power that appears.
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3x+5y=14 and 6x-4y=9
Answers
Answer:
Step-by-step explanation:
Bấm máy tính hệ phương trình là ra
what percentage of the appies are yellow?
Answers
6 yellow apples
6/30=.2
.2*100=20
20%
Answer:
20%
Step-by-step explanation:
6 out of 30. = 1/5 = multiply 5*20= 100 and 1*20= 100 so it is 20% of 100.
Homework part2 need help asap
Answers
The key features of the given quadratic functions are listed below.
What is the graph of a quadratic function?In Mathematics and Geometry, the graph of any quadratic function would always form a parabolic curve because it is a u-shaped. Based on the first quadratic function, we can logically deduce that the graph is an upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0) i.e 3 > 0.
For the quadratic function y = 3x² - 5, the key features are as follows;
Axis of symmetry: x = 0.
Vertex: (0, -5).
Domain: [-∞, ∞]
Range: [-5, ∞]
For the quadratic function y = -2x² + 12x - 15, the key features are as follows;
Axis of symmetry: x = 3.
Vertex: (3, 3).
Domain: [-∞, ∞]
Range: [-∞, 3]
For the quadratic function y = -x² + 1, the key features are as follows;
Axis of symmetry: x = 0.
Vertex: (0, 1).
Domain: [-∞, ∞]
Range: [-∞, 1]
For the quadratic function y = 2x² - 16x + 30, the key features are as follows;
Axis of symmetry: x = 4.
Vertex: (4, -2).
Domain: [-∞, ∞]
Range: [-2, ∞]
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not sure need help
Answers
Answer:
x=10 degrees
Step-by-step explanation:
8x-12=6x+8
2x=20
x=10
A car rental company randomly assigns one of its 60 cars to a customer. Of the 60 cars, 4 of them are red.
How can you find the theoretical probability of a customer being assigned a red car?
a.Multiply the number of red cars by the total number of cars.
b.Divide the number of customers who are assigned red cars by the total number of cars.
c.Divide the number of red cars by the total number of cars.
d.Multiply the number of customers who are assigned red cars by the total number of cars.
Answers
What is the total weight of candy in a 5/6 pound bag site
Answers
We can see here that the total weight of candy in a 5/6 pound bag site is 377 grams.
What is weight?Weight is a measure of the force exerted by gravity on an object. It is the measure of how heavy an object is. Weight is typically expressed in units such as pounds or kilograms. The weight of an object can vary depending on the gravitational force acting on it.
There are 16 ounces in a pound.
Thus, a 5/6 pound bag of candy weighs
5/6 × 16 = 13.3 ounces.
If you want to know the weight in grams, 13.3 ounces is equal to 377 grams.
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Please help me Ive been struggling. Correct answer ill give you extra points and make brainliest
Answers
Answer:
Choice C 1.8 Million
Step-by-step explanation:
Average rate is also known as the slope.
Since the slope formula is m=rise/run, we can set up the equation:
m= (101-11)/(2000-1950)
= 90/50
= 1.8
PLS HELP ASAP! Given a cone with a height of 6 cm and a base diameter of 6 cm, what is the volume of the cone? Use 3.24 for π
π
Answers
Answer:
56.52 cm³
Step-by-step explanation:
\(\boxed{volume \: of \: cone = \frac{1}{3} \pi {r}^{2}h }\)
Diameter= 2 ×radius
Radius
= 6 ÷2
= 3cm
Height, h= 6cm
Volume of the cone
\( = \frac{1}{3} (3.14)( {3}^{2} )(6)\)
= 56.52 cm³
Two UNO students want to start a business selling slushies at the Gene Leahey Mall during the summer. They will have an initial cost of $500 to buy equipment and an additional $1.25 cost for each slushie they sell. They
plan to charge $3.50 for each slushie. Let C(x) represent the cost (in dollars) associated with starting and running the business and R(x) represent the revenue (in dollars) earned from sales. Let x represent the number
of slushies sold.
a. Write a linear function for cost.
C(x) =
b. Write a linear function for revenue.
R(x) =
Answers
Part (a)
The cost is the initial cost plus the cost per slushie multiplied by the number of slushies sold.
\(C(x)=500+1.25x\)
Part (b)
The revenue is the number of slushies sold multiplied by the amount charged per slushie.
\(R(x)=3.50x\)
Find the volume of the sphere. Sorry the pic isn’t the best! I tried lol!
Answers
Answer:
4,186.6 repeated (just round to .7 if it asks for it)
Step-by-step explanation:
The volume of a sphere is 4/3 pi r^3
plug in the radius and simplify that expression
Let f (x) = x - 4 . Graph g(x) = f (5x)
Choose the description of the transformation from the graph of f to the graph of g.
A.) The graph of g is a horizontal stretch of the graph of f by a factor of 5.
B) The graph of g is a horizontal shrink of the graph of f by a factor of 1/5
C) The graph of g is a vertical stretch of the graph of f by a factor of 5
D) The graph of g is a vertical shrink of the graph of f by a factor of 1/5
And what points would be plotted on a graph?
Answers
The graph of g(x) is on the image at the end, and the correct option for the transformation is B.
Which is the transformation applied?We define a horizontal dilation of scale factor k as:
g(x) = f(k*x)
if k > 1, we have a stretch.
if 0 < k < 1, we have a shink of scale factor 1/k
Here we have:
g(x) = f (5x) = 5x - 4
We can notice that k = 5, then we have a stretch, thus, the correct option is B.
The graph of function g(x) can be seen in the image at the end.,
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Clifton spent $14.30 to buy his class 26 ice
cream sandwiches. How much did each ice
cream sandwich cost?
Answers
Answer:
$0.55
Step-by-step explanation:
All you have to do is divide $14.30 by 26 and that equals 0.55 so he spent 55 cents on each sandwich
me me me me me me me me me me me pls
Answers
Answer:
Yes
Step-by-step explanation:
it is porportional
Answer:
yes it is proportional i agree with he or she they are correct as well
Step-by-step explanation:
Is √49 rational numher
Answers
Answer:
Yes
Step-by-step explanation:
Because 7x 7=49
Or 49 divided by 7 is 7
Answer:
yes
Step-by-step explanation:
b/c the sq root of 49 is 7
i need help plz i need to get a 100 plzz i need u
Answers
Answer:
84.2
Step-by-step explanation:
Answer:
The Answer is D
Step-by-step explanation:
you move the decimal to the right for each power of 10
Find the value of x in this equation.
Answers
Answer: 5
Step-by-step explanation:
Solve for x
I don’t know how i have to do it
Answers
Answer: x = 2
Intersecting Chords states:
⇒ 6 × x = 3 × (x + 2)
⇒ 6x = 3x + 6
⇒ 6x - 3x = 6
⇒ 3x = 6
⇒ x = 2
passes through (-4, 4) and (2, 10)
Answers
Answer:
Step-by-step explanation:
(10-4)/(2+4)= 6/6 =1
y - 10 = x - 2
y = x + 8
To find the number in a square, add the numbers in the two circles
connected to it.
Fill in the missing numbers.
Answers
The missing values in the quantitative reasoning given are : -2, 13 and 9
Given the rule :
square = circle + circleWe can deduce that :
circle = square - circleFor the left circle :
circle = -6 - (-4) = -6 + 4 = -2
For the right circle :
circle = 11 - (-2) = 11 + 2 = 13
For the left square :
square = 13 + (-4)
square = 13 -4 = 9
Therefore, the missing values are : -2, 13 and 9
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COMPLATE THE PAYTTERN
3, 3, 5, 8, 13, 21, ( ), ( )
Answers
Answer: 3; 3; 5; 8; 13; 21; 34; 55.
Try this option:
Step-by-step explanation:
the sum of the previous terms is the next term:3+5=8; 5+8=13; 8+13=21, then
13+21=34 and 21+34=55.
-3/2 divided by -6/11
Answers
Brainlist pls