Answer: Da der Graph punktsymmetrisch zum Ursprung ist, können wir annehmen, dass er die Form f(x) = ax^3 hat.
Step-by-step explanation:
Da der Graph einen Tiefpunkt an der Stelle x = 1 hat, gilt f'(1) = 0 und f''(1) < 0.
Also gilt:
f(x) = ax^3 + bx^2 + cx + d
f'(x) = 3ax^2 + 2bx + c
f''(x) = 6ax + 2b
Da f'(1) = 0, haben wir:
3a + 2b + c = 0
Da f''(1) < 0, haben wir:
6a + 2b < 0
3a + b < 0
b < -3a
Da der Graph punktsymmetrisch zum Ursprung ist, haben wir:
f(-x) = -f(x)
Also haben wir:
-a x^3 + bx^2 - cx + d = -ax^3 - bx^2 - cx - d
oder
2bx^2 + 2d = 0
b = -d
Da der Graph durch A(2|2) geht, haben wir:
8a + 4b + 2c + d = 2
Und da der Graph einen Tiefpunkt bei x = 1 hat, haben wir:
f(1) = a + b + c + d = 0
Jetzt können wir die Gleichungen lösen, um die Koeffizienten der Funktion zu finden. Zunächst setzen wir b = -d ein und erhalten:
3a + 2b + c = 0
6a - 2d < 0
b < -3a
a + b + c + d = 0
8a - 2b + 2c - d = 2
Lösen dieser Gleichungssysteme liefert a = -1
ALGEBRA HW!! I WILL GIVE BRAINLYEST
please answer both questions parts.
The table of original value and rounded values are
x y
0.2 0
0.5 1
0.9 1
1.08 1
1.49 1
1.72 2
2.3 2
2.94 3
The graph is attached
How to make the graphThe graph is made in a cartesian coordinate by tracing the point of intersection of the two points
The table is represented as ordered pair as (original value, rounded value) for the given x and y values:
(0.2, 0), (0.5, 1), (0.9, 1), (1.08, 1), (1.49, 1), (1.72, 2), (2.3, 2), (2.94, 3)
The graph is a scattered plot and its attached
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b) Find the domain and range of g(x) 1÷(x-2) +5. what is the h value and k value for g(x)?
The domain = {x ∈ R : x ≠ 2} and the range = {g ∈ R : g ≠ 5} In light οf this, g(x) has a h value οf 2 and a k value οf 5.
What is an illustratiοn οf range?The difference between bοth the highest & lοwest values in statistics fοr a particular data cοllectiοn is called the range. Fοr instance, if the data set is 2, 5, 8, 10, 3, then the range is 10 - 2 = 8.
The definitiοn οf the functiοn g(x) is.
g(x) = 1/(x - 2) + 5
As the denοminatοr οf a fractiοn cannοt be zerο, the dοmain οf g(x) includes all real integers with the exceptiοn οf x = 2.
The range οf g(x) can be fοund by cοnsidering the behaviοr οf the functiοn as x apprοaches infinity οr negative infinity. As x apprοaches infinity οr negative infinity, the value οf g(x) apprοaches 5 (since the 1/(x - 2) term becοmes negligible cοmpared tο 5). Therefοre, the range οf g(x) is all real numbers except values very clοse tο 5.
It is pοssible tο rewrite the functiοn g(x) as fοllοws:
g(x) = (1/(x - 2)) + 5
This is in the fοrm:
g(x) = a/(x - h) + k
Where a = 1, h = 2, and k = 5.
Therefοre, the h value fοr g(x) is 2, and the k value fοr g(x) is 5.
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The following data indicate the scores of some students in a competition. Which a box plot represents the data?
100 points!!!!!
The correct answer to the given question is graph D
How to solveGiven a set of data points, we are tasked with identifying the correct box plot representation.
We begin by arranging the data in ascending order, which gives us 12, 17, 21, 23, 24, 28, and 29 points.
Next, we use the properties of a box plot to eliminate incorrect representations.
The left end of the whisker should correspond to the smallest data point, and the right end to the largest.
Among the given graphs, only one satisfies this condition.
The middle point is identified as the fourth data point, which is 23.
Finally, we determine the lower and upper lines of the box to be 17 and 28, respectively.
The only graph that satisfies all conditions is graph D.
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Your firm is considering adding a product line. The accounting department has determined that the cost
function for this new product will be C(x) = 55x + 3500 and the revenue function will be R(x) = 80x,
where x is the number of units sold. Additionally, the sales department has determined that you reasonably
can expect to sell around 164 units. You must decide whether to go ahead with the new product line.
Find the break-even quantity:
Find the profit function: P(x) =
Make your decision:
O Proceed with the product line: the products are profitable and we can reasonably expect to meet
our break-even quantity.
Cancel the product line: the quantity needed to break even is more than our firm can reasonably
expect to sell.
O Cancel the product line: producing these products is not profitable.
Submit Question
the profit function is positive, producing 164 units of the new product line would yield a profit of $600.
We should proceed with the product line since it is profitable and we can reasonably expect to meet our break-even quantity.
To find the break-even quantity, we need to set the cost function equal to the revenue function and solve for x:
C(x) = R(x)
55x + 3500 = 80x
25x = 3500
x = 140
Therefore, the break-even quantity is 140 units.
To find the profit function, we subtract the cost function from the revenue function:
P(x) = R(x) - C(x)
P(x) = 80x - (55x + 3500)
P(x) = 25x - 3500
Now we can evaluate the profit function at different values of x to see if producing these products is profitable or not.
If we plug in x = 164, the expected sales quantity, we get:
P(164) = 25(164) - 3500
P(164) = 4100 - 3500
P(164) = 600
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A box contains four apples, six oranges, and a pear. Preston reaches into the box and selects two of the 11 fruits uniformly at random without replacement. Let m/n be the probability that he selects an apple and an orange, where m and n are relatively prime positive integers. Find m+n.
the answer is m + n = 24 + 55 = 79.
What is probability?
By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.
There are two ways this can happen: either he selects an apple first and then an orange, or he selects an orange first and then an apple. We can compute the probability of each of these events separately and then add them together.
First, let's consider the probability that Preston selects an apple first and then an orange. The probability of selecting an apple first is 4/11, and then the probability of selecting an orange from the remaining 10 fruits (which includes 3 apples and 6 oranges) is 6/10. So the probability of this event is (4/11) * (6/10) = 24/110.
This can be simplified by dividing the numerator and denominator by 2:
48/110 = 24/55
So the probability that Preston selects an apple and an orange is 24/55. Therefore, the answer is m + n = 24 + 55 = 79.
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A company is focus testing a new type of fruit drink. The focus group is 47% male. Of the responses, 40% of the males and 54% of the females said they would buy the fruit drink. Find the ratio of males who would buy the drink to females who would buy the drink. Round to the nearest ten thousandth if necessary.
Answer: the ratio of males who would buy the drink to females who would buy the drink is approximately 0.6560.
Step-by-step explanation:
Let's assume that there are 100 people in the focus group. Then, the number of males in the focus group is 47 and the number of females is 53.
Out of 47 males, 40% said they would buy the fruit drink, which is 0.4 x 47 = 18.8 males (rounded to the nearest whole number). Out of 53 females, 54% said they would buy the fruit drink, which is 0.54 x 53 = 28.62 females (rounded to the nearest whole number).
The ratio of males who would buy the drink to females who would buy the drink is:
18.8/28.62 = 0.6560 (rounded to the nearest ten-thousandth)
Therefore, the ratio of males who would buy the drink to females who would buy the drink is approximately 0.6560.
Find the value of angle ZOX
using the image below
Answer: 64°
Step-by-step explanation:
Had this problem and got it right
Ruggiero Brothers Oil has an R85 000 liability it must pay four years from today. The company is opening a savings account, so that the entire amount will be available when this debt needs to be paid. The plan is to make an initial deposit today, and then deposit an additional R16 000 each year for the next four years, starting one year from today. The account pays a 6% rate of return. How much does the firm need to deposit today?
Answer:
Step-by-step explanation:
To determine the amount that Buggiero Brothers Oil must deposit today in order to have enough money to pay the R85 000 liability four years from today, we can use the present value formula:
Present Value (PV) = Future Value (FV) / (1 + r)^n
where:
- FV is the future value, which is R85 000
- r is the annual interest rate, which is 6%
- n is the number of years until the liability needs to be paid, which is 4
To calculate the future value of the annual deposits of R16 000, we can use the future value of an annuity formula:
FV = PMT x [(1 + r)^n - 1] / r
where:
- PMT is the annuity payment, which is R16 000
- r is the annual interest rate, which is 6%
- n is the number of years of the annuity, which is 3 (since the first payment is made one year from today)
Plugging in the numbers:
FV = R16 000 x [(1 + 0.06)^3 - 1] / 0.06
FV = R61 719.56
Therefore, the total future value that Buggiero Brothers Oil will have in four years, including the initial deposit and the annual payments, will be:
FV = R85 000 + R61 719.56
FV = R146 719.56
Plugging in the numbers to the present value formula:
PV = R146 719.56 / (1 + 0.06)^4
PV = R116 442.12
Thus, Buggiero Brothers Oil needs to deposit R116 442.12 today to have enough money to pay the R85 000 liability four years from today, assuming a 6% rate of return.
Which function is a translation one unit right of the function
f(x) = log x?
Answer:
g(x)= log(x-1)
Step-by-step explanation:
g(x) = f(x-1)
Please Help! A picture is 60cm wide and 1.8 meter long.The ratio of its width to its perimeter in the lowest term is?
Answer:
60:61.8 OR 10:10.3
Step-by-step explanation:
Cant be simplified - unless your in advanced classes. If so
10:10.3
Answer:
Step-by-step explanation:
1/3 or 0.3 or 33.333333% or 3^-1 or 3.333333 x 10^-1
How many solutions does it have ?
Y =4
Y =4x-1
Answer:
1 solution
Step-by-step explanation:
Y = 4
Y = 4x - 1
Substitute value of Y here,
4 = 4x - 1
4 + 1 = 4x
5 = 4x
5/4 = x
1.25 = x
•°• The given equation can have only 1 solution, i.e, a linear equation with 1 variable gives only 1 solution.
______
hope this helps!
work out the product of 1 and 3/3 and 1 and 2/6 give your answer in its simplest form
Answer:
To multiply 1 3/3 by 1 2/6, we can first convert these mixed numbers to improper fractions, then multiply them together, and finally simplify the result to its simplest form.
1 3/3 can be written as 4/3 (since 1 whole and 3/3 is equivalent to 4/3)
1 2/6 can be written as 8/6 (since 1 whole and 2/6 is equivalent to 8/6)
Now, we can multiply these two fractions together:
4/3 x 8/6 = (4 x 8) / (3 x 6) = 32/18
To simplify this fraction, we can divide the numerator and denominator by their greatest common factor, which is 2:
32/18 = (2 x 16) / (2 x 9) = 16/9
Therefore, the product of 1 3/3 and 1 2/6 is 16/9, or 1 and 7/9 in mixed number form, in its simplest form.
Anyone know the diameter?
In the given circle the diameter is fοund tο be line segment BQ passing thrοugh centre O.
What is a circle?A circle is a clοsed, twο-dimensiοnal οbject where every pοint in the plane is equally spaced frοm a central pοint. The line οf reflectiοn symmetry is fοrmed by all lines that traverse the circle. Additiοnally, every angle has rοtatiοnal symmetry arοund the centre.
A circle is given with centre marked as O.
A circle is a 2D fοrm in geοmetry in which all οf the pοints οn its surface are equally spaced frοm its center.
The radius is the length frοm any pοint οn the surface tο the center.
A diameter is a chοrd that is equidistance frοm centre οf the circle.
Here οnly the straight line is equidistance frοm centre οf the circle.
That line is BQ.
Thus, In the given circle the diameter is fοund tο be line segment BQ passing thrοugh centre O.
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The entry fee to East Egg Hunt Event is $7.00. Each ride requires a ticket that cost $2.00. Cassie spent a total of $45.00. How many tickets Cassie Purchase?
Answer: 19 tickets
Step-by-step explanation: $45 - $7 = 38 38 divided by $2 = 19 tickets
Find the value of each variable.
Answer:
x = 63 , y = 90
Step-by-step explanation:
assuming DF is the diameter of the semicircle , then
∠ DEF = y = 90° ( angle inh a semicircle )
then
x + y + 27° = 180° ( angle sum of a triangle )
x + 90 + 27 = 180
x + 117 = 180 ( subtract 117 from both sides )
x = 63
Determine which expression is equivalent to
3
4
−
x
(
1
2
−
5
8
)
+
(
−
3
8
x
)
4
3
−x(
2
1
−
8
5
)+(−
8
3
x).
A
−34x−
4
3
x
B
12x
2
1
x
C
18−78x
8
1
−
8
7
x
D
34−14x
4
3
−
4
1
x
Answer: We can simplify the expression step by step:
3/4 − x(1/2 − 5/8) + (−3/8)x
3/4 − x(-1/8) + (−3/8)x
3/4 + x/8 − 3/8x
Multiplying everything by 8 to get rid of the fractions:
6 − x + (−3x)
6 − 4x
Therefore, the equivalent expression is D) 34 - 14x / (4/3).
Step-by-step explanation:
Find an appropriate trigonometric substitution of the form x = f(t) to simplify the integral.
Answer:
To find an appropriate trigonometric substitution of the form x = f(t) to simplify the integral, we need to look for expressions involving square roots of the form:
sqrt(a^2-x^2)
sqrt(a^2+x^2)
sqrt(x^2-a^2)
If we have sqrt(a^2-x^2), we can use the substitution x = a sin(t) or x = a cos(t) depending on which one of them makes the expression simpler.
If we have sqrt(a^2+x^2), we can use the substitution x = a tan(t) or x = a sec(t).
If we have sqrt(x^2-a^2), we can use the substitution x = a sec(t) or x = a tan(t).
It is important to keep in mind the trigonometric identities and the Pythagorean theorem to simplify the integrals after substituting.
Step-by-step explanation:
hope its help <:
Smith, from Los Angeles, and Jones, from New York City, are both traveling to Kansas City, beginning their trips at the same time. The graph shows the distance in miles from Kansas City for each of them after they have both traveled for the same number of hours. After how many hours from the start of their journeys were they the same distance from Kansas City?
Answer: The answer should be 20 hours
Step-by-step explanation:
That is when the 2 lines meet up so that is when they are the same difference from Kansas City.
what is the value of 6(2b-4) when b =3
Answer: 12
Step-by-step explanation:
Use BODMAS, so first solve the inside of the bracket:
2*3= 6
6-4= 2
Now we can multiply that by the number outside the bracket. Why?
Because a number outside a bracket means to multiply that number by everything in the bracket. So:
6 * 2 = 12
Answer: 12
Step-by-step explanation:
2 x 3 = 6
6 - 4 = 2
6 x 2 = 12
Solve the right triangle (tan,sin,cos)
The value of the trigonometric functions for the right triangle is tan(29) = 0.518. cos(29) = 0.838. sin (29) = 0.435.
What are basic trigonometric functions?The sine, cosine, and tangent trigonometric ratios are the three most important ones. These are their definitions:
Sine (sin) is the proportion of a right triangle's hypotenuse to the length of the side that faces an angle.
The length of the side next to an angle in a right triangle divided by the length of the hypotenuse is known as the cosine (cos).
In a right triangle, the tangent (tan) is the ratio between the lengths of the sides that face each other and the angle.
These ratios are used in trigonometry to connect the angles and sides of right triangles, and they may be used to a number of triangle- and other geometric shape-related problems.
In the given triangle using the sum of interior angle of triangle we have:
180 - 90 - 29 = 61
The measure of the third angle is 61 degrees.
Now, tan(61) = XZ/XY
XZ = XY * tan(61)
XZ = 18 * 1.927 = 34.686
Now, using the Pythagoras theorem we have:
ZY² = XZ² + XY²
ZY² = 34.686² + 18²
ZY² = 1712.3996
ZY = 41.38
Now, the value of:
sin(29) = opposite/hypotenuse = XY/ZY = 18/41.388 = 0.435
cos(29) = adjacent/hypotenuse = XZ/ZY = 34.686/41.388 = 0.838
tan(29) = opposite/adjacent = XY/XZ = 18/34.686 = 0.518
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Let f(x)=1/4x^3+x−1 . What is the value of (f−1)′(x) when x = 3?
For the given expression the value of [tex](f^{-1})'(3)[/tex] ≈ 0.052.
What is expression?
In mathematics, an expression is a combination of numbers, variables, operators, and symbols that represents a mathematical quantity or relationship.
To find the derivative of the inverse function, we use the formula:
[tex](f^{-1})'(x) = 1 / f'(f^{-1}(x))[/tex]
First, we need to find the inverse function [tex]f^{-1(x)[/tex]. To do that, we can solve for x in terms of f(x):
[tex]f(x) = (1/4)x^3 + x - 1\\y = (1/4)x^3 + x - 1\\x^3 + 4x - 4 = 4y\\x^3 + 4x - 4 = 4f^{-1}(x)\\f^{-1}(x) = (x^3 + 4x - 4) / 4[/tex]
Now, we can find the derivative of the inverse function:
[tex](f^{-1})'(x) = 1 / f'(f^{-1}(x))\\(f^{-1})'(3) = 1 / f'(f^{-1}(3))[/tex]
To find [tex]f^{-1}(3)[/tex], we plug in x = 3 into the expression for [tex]f^{-1}(x)[/tex]:
[tex]f^{-1}(3) = (3^3 + 4(3) - 4) / 4 = 8.75[/tex]
To find [tex]f'(f^{-1}(3))[/tex], we plug in [tex]f^{-1}(3) = 8.75[/tex] into the expression for f'(x):
[tex]f'(8.75) = (3/4)(8.75)^2 + 1 = 19.2031[/tex]
Now we can find the derivative of the inverse function at x = 3:
[tex](f^{-1})'(3) = 1 / f'(f^{-1}(3))\\(f^{-1})'(3) = 1 / f'(8.75)\\(f^{-1})'(3) = 1 / 19.2031[/tex]
[tex](f^{-1})'(3)[/tex] ≈ 0.052
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Question 7
Suppose the graph represents the scale drawing for a fence that Tara is building for a new city dog park. Each unit on the graph represents 12 yards. After studying the scale drawing, Tara decides to build a fence that encloses a smaller area. If Tara dilates rectangle ABCD by a scale factor of 0.75, and fencing costs $6.39 per yard, how much will she spend on fencing?
The total cost to fence the rectangular yard is given as follows:
$1,610.28.
How to obtain the perimeter of a triangle?The perimeter of a rectangle is the total distance around its outer boundary. To find the perimeter of a rectangle, you need to add up the lengths of all four sides.
If a rectangle has length l and width w, then its perimeter P is given by the equation presented as follows:
P = 2l + 2w
Considering the scale factor of 0.75, the distance represented by each unit on the graph is given as follows:
0.75 x 12 = 9 yards.
Hence the dimensions of the rectangle are given as follows:
Length of 8 x 9 = 72 yards.Width of 6 x 9 = 54 yards.The perimeter of the fence is then given as follows:
2 x (72 + 54) = 252 yards.
It costs $6.39 per yard, hence the total cost to fence the yard is given as follows:
252 x 6.39 = $1,610.28.
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IT A MULTI-STEP PROBLEM HELP! 6 PARTS TO IT!!! IM GOING TO FAIL!! CAN PLEASE DO IT STEP BY STEP
a. The cost of one large pizza with one topping is $13.50. To purchase one large and five medium pizzas, we would need to buy one large pizza at regular price and five medium pizzas at the discounted price. The cost of the large pizza is $13.50, and the cost of each medium pizza is $6.25. Therefore, the total cost would be:
Total cost = Cost of large pizza + Cost of 5 medium pizzas
Total cost = $13.50 + ($6.25 x 5)
Total cost = $13.50 + $31.25
Total cost = $44.75
Therefore, it would cost $44.75 to purchase one large pizza and five medium pizzas.
b.Number of medium pizzas Total cost
0 | $13.50
1 | $19.75
2 | $26.00
3 | $32.25
4 | $38.50
c. Let "m" be the number of medium pizzas. Then the total cost of purchasing one large pizza with one topping and m medium pizzas can be represented as:
Total cost = 13.50 + 6.25m
d. If you have a total of $100 and purchase one large pizza, you would have $100 - $13.50 = $86.50 left to spend on medium pizzas. The cost of each medium pizza is $6.25. Therefore, you can buy:
Number of medium pizzas = $86.50 ÷ $6.25 = 13.84
Since you cannot buy a fraction of a pizza, you can only buy 13 medium pizzas with $86.50.
e. The area of a pizza is given by the formula A = πr^2, where A is the area and r is the radius. The area of a large pizza is:
A = πr^2
A = 3.14 x 8^2
A = 3.14 x 64
A = 200.96
The area of a medium pizza is:
A = πr^2
A = 3.14 x 5^2
A = 3.14 x 25
A = 78.5
Therefore, the total area of one large pizza and five medium pizzas is:
Total area = Area of large pizza + (Area of medium pizza x 5)
Total area = 200.96 + (78.5 x 5)
Total area = 200.96 + 392.5
Total area = 593.46
Rounding to the nearest inch, the total area of pizza is 593 square inches.
f. To calculate the cost per square inch of pizza, we need to divide the total cost of the pizzas by the total area of the pizzas. The total cost of one large pizza and five medium pizzas is $44.75, and the total area is 593 square inches. Therefore, the cost per square inch of pizza is:
Cost per square inch = Total cost / Total area
Cost per square inch = $44.75 / 593
Cost per square inch = $0.08 (rounded to the nearest cent)
Therefore, the cost per square inch of pizza is 8 cents.
Cyndi is making a mixture of cashews and peanuts the cashews are $7 per pound and $3 a pound for peanuts. Cyndi wants 20 pounds of the mixture which will cost $5.40 per pound .. what's the system and how much would she need to equal $108
The amounts of each substance needed to obtain a mixture of 20 pounds at a price of $5.4 per pound is given as follows:
Cashews: 12 pounds.Peanuts: 8 pounds.How to obtain the amounts?The amounts are obtained by a system of equations, for which the variables are given as follows:
Variable x: amount of cashews.Variable y: amount of peanuts.The mixture has a total of 20 pounds, hence:
x + y = 20.
y = 20 - x.
The total cost of the mixture is of $108, as 108/20 = 5.4, hence:
7x + 3y = 108
Replacing the second equation into the first, the value of x is given as follows:
7x + 3(20 - x) = 108
4x = 48
x = 12.
Then the value of y is given as follows:
y = 20 - 12
y = 8.
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the sum of two numbers is 30. The difference between the two numbers is 15. what are the two numbers?
As part of a survey, 55 adults were asked if they had been abroad on holiday or visited somewhere in the UK. 25 people went
abroad and 15 people went on holiday in the UK. What is the probability that a randomly selected person actually went on holiday
that year? Round your answer to three decimals.
The probability that a randomly selected person actually went on holiday that year is 0.727
How to calculate the probability that a randomly selected person actually went on holiday that yearOut of the 55 adults surveyed, 25 went abroad and 15 went on holiday in the UK.
Therefore, the total number of people who went on holiday is 25 + 15 = 40
The probability of selecting a person who went on holiday is the number of people who went on holiday divided by the total number of people surveyed:
P(went on holiday) = 40/55
Simplifying the fraction, we get:
P(went on holiday) = 8/11
Rounding to three decimals, we get:
P(went on holiday) = 0.727
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Match each metric measurement on the left with an equivalent unit of measurement on the right.
According to the information, the values that coincide are: 2.2 meters with 2200 millimeters, 14 decimeters with 0.014 hectometers, 0.14 meters with 0.014 decameters, 0.022 decameters with 22 centimeters.
How to find the numbers that match?To find the numbers that match we must take into account the relationship between the values:
Decameter: Unit of length equal to 10 meters.Centimeter: Unit of length equal to one hundredth of a meter.Decimeter: Unit of length equal to one tenth of a meter.Millimeter: Unit of length equal to one thousandth of a meter.Hectometer: Unit of length equal to 100 meters.According to the above, we can infer that the values that match are:
2.2 meters with 2200 millimeters.14 decimeters with 0.014 hectometers.0.14 meters with 0.014 decameters,0.022 decameters with 22 centimeters.Learn more about measurements at: https://brainly.com/question/4725561
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Help asap will give brainiest
Use the image to determine the line of reflection.
4
3
2
1
0
?
Ty
5
-6
-7
-8
-9
-10
1
2
B
A
A
3₂
Α',
В'
4
E
5
E
6
с
Reflection across x = 6
D'
Reflection across the x-axis
Reflection across y = -3
C₁
Reflection across the y-axis
Answer: D
Step-by-step explanation: so if we look at the picture, youll notice 2 things right off the bat, firstly, the top shape goes over the y axis, so that wont work, secondly, the shapes are on the same side of the x axis (the positive side) so that wouldnt work, the last thing we now have to look at is making the shapes even, essentially if you were to flip one shape over a certain distance, the mirrored shape needs to be the same distance you flipped the first shape. In this case, if we flip shape 1, over -3, the other shape will be 6 spaces away from the 1st shape, because you need to also move the second shape 3 spaces away from where you flipped the first shape.
side note: reflecting over the x axis or y axis, means the line of reflection is equal to 0 on either the y axis or x axis
To try to make this less confusing, another way to find the reflection is by evenly counting the shapes to the middle, how-ever many squares/spaces it takes for both shapes to reach the center of the two in this case, is how many spaces they are reflected.
The image undergoes a reflection at y=-3, Option D is correct.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
A translation is a movement of the graph either horizontally parallel to the -axis or vertically parallel to the -axis.
Reflections are congruence transformations that generate a mirror image of an object, without changing its size or shape.
In the given figure the above image is original and it is flipped to form the image which is below the x axis.
In this case, if we flip shape 1, over -3, the other shape will be 6 spaces away from the 1st shape, because you need to also move the second shape 3 spaces away from where you flipped the first shape.
Hence, the image undergoes a reflection over y axis which is at y=-3.
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Consider the following function.
f(x) = −2x^3 − 6x^2 + 5
(a) Use the Intermediate Value Theorem and a graphing utility to find graphically any intervals of length 1 in which the polynomial function is guaranteed to have a zero. Verify your answers by using the table feature of the graphing utility. (Select all that apply.)
(−4, −3)
(−3, −2)
(−2, −1)
(−1, 0)
(0, 1)
(1, 2)
(2, 3)
(3, 4)
(b) Use the zero or root feature of the graphing utility to approximate the real zeros of the function. (Enter your answers as a comma-separated list. Round your answers to three decimal places.)
x =
, in the presented question, we can conclude that Interval [tex](0, 1): f(0) 5, f(1) -3[/tex], indicating that the function switches signs and has a zero in the interval [tex](0, 1).[/tex]
What are polynomials?Interval [tex](4, 3): f(-4) -41, f(-3) 5,[/tex]therefore, the function reverses its sign and has a zero in the interval [tex](-4, -3).[/tex]
Interval [tex](3, 2): f(-3) 5, f(-2) -9,[/tex] indicating that the function changes sign and has a zero in the interval [tex](-3, -2).[/tex]
Interval [tex](2, 1): f(-2) -9, f(-1) 1[/tex], therefore the function reverses its sign and has a zero in the interval [tex](-€2, -1).[/tex]
Interval [tex](1, 0): f(-1) 1, f(0) 5[/tex], so the function does not change sign and the interval may or may not contain a zero [tex](-1, 0).[/tex]
Interval [tex](0, 1): f(0) 5, f(1) -3,[/tex] indicating that the function switches signs and has a zero in the interval [tex](0, 1).[/tex]
Therefore, in the presented question, we can conclude that Interval [tex](0, 1): f(0) 5, f(1) -3[/tex], indicating that the function switches signs and has a zero in the interval [tex](0, 1).[/tex]
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[tex]8x ^{2} y + 12xy - 16xz[/tex]
Factorize the expression
The factοrs οf the expressiοn is 4x(2xy+3y-4z).
What is factοrizatiοn?Tο factοrise an algebraic statement, we first identify the terms' highest cοmmοn factοrs and then arrange the terms intο grοups in accοrdance with thοse grοups. In plain English, factοrizatiοn is the prοcess thrοugh which an algebraic expressiοn gets expanded in the οppοsite directiοn.
Here the given expressiοn is ,
=> [tex]8x^2y+12xy-16xz[/tex]
Nοw factοrizing the given expressiοn then,
=> 4×2×x×x×y+4×3×x×y-4×4×x×z
=> 4x(2xy+3y-4z)
Hence the factοrs οf the expressiοn is 4x(2xy+3y-4z).
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