Answers
Answer:
I tink D?
Step-by-step explanation:
The function after the reflection over y-axis is f' ( x ) = √( -x )
What is Reflection?Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point. The line of reflection is the line that a figure is reflected over. If a point is on the line of reflection then the image is the same as the pre-image. Images are always congruent to pre-images.
The reflection of point (x, y) across the x-axis is (x, -y). When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).
Given data ,
Let the function be represented as f ( x )
Now , the value of f ( x ) is
f ( x ) = √x
Now , when you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y)
So , the reflected function is f' ( x ) = √( -x ) and the graph is plotted
Hence , the reflected function is f' ( x ) = √( -x )
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Related Questions
4 groups of 3 give me answer
Answers
The question 4 groups of 3 can be calculated to be a total of 12 objects across all groups.
How to solve for the total number in the groupThe total number of groups are 4 in number
Each of the 4 groups have 3 objects in it.
That is 3 in 4 places
This can be solved by 4 * 3 = 12
Hence we can say that the solution for the questions that says 4 groups of 3 is 12
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What is 2.4 divided by -0.06?
(With work pls)
Answers
Answer:
To find the result of 2.4 divided by -0.06, we need to use the following steps:
Step 1: Change the division problem into a multiplication problem by flipping the divisor and multiplying by its reciprocal.
-0.06 ÷ 2.4 = -0.06 x 1/(2.4)
Step 2: To find the reciprocal of 2.4, we need to divide 1 by 2.4
1/(2.4) = 0.416666666666667
Step 3: Multiply the original dividend (2.4) by the reciprocal of the divisor (0.416666666666667)
2.4 x 0.416666666666667 = -0.1
So, 2.4 divided by -0.06 is equal to -0.1
It's worth noting that -0.1 is a negative number which makes sense since the divisor is negative, hence the result is the opposite of the result when dividing by a positive number.
Your kite is stuck in a tree that is 45 feet tall. The angle your string makes with the ground is 68°. Rather than worrying about the kite, you decide to calculate how much string you have let out. Assuming the string is held tight and makes a straight line to the ground, how much string have you let out?
Answers
Answer:
48.53 = 49 feet
Step-by-step explanation:
sin 0 = opposite/hypotenuse
sin 68 = AB/AC = 45/x
x = 45/sin 68 = 45/0.9272 = 48.53
48.53 rounded = 49 feet
Answer:
You have let out 48.5 feet of string
Step-by-step explanation:
Attached is a sketch of the problem.
We can use SOH CAH TOA to find our answer.
In this acronym, O is the opposite side, A is the adjacent side, and H is the hypotenuse. S is for the SIN function. C is for the COS function. T is for the TAN function.
We can calculate the length of the string by using the SIN function.
So we can say the sine of angle x is the opposite side divided by the hypotenuse.
[tex]sin(x)=\frac{O}{H}[/tex]
Lets solve for [tex]H[/tex].
Multiply each term by [tex]H[/tex].
[tex]H*sin(x)=\frac{O}{H} *H[/tex]
Simplify the right side by cancelling the common factor of [tex]H[/tex].
[tex]H*sin(x)=O[/tex]
Divide both sides of the equation by [tex]sin(x)[/tex].
[tex]\frac{H*sin(x)}{sin(x)} =\frac{O}{sin(x)}[/tex]
Simplify the right side by cancelling the common factor of [tex]sin(x)[/tex].
[tex]H=\frac{O}{sin(x)}[/tex]
Now lets evaluate the length of the string.
In this example we are given
[tex]x=68\\O=45[/tex]
[tex]H=\frac{45}{sin(68)}[/tex]
[tex]H=48.5341[/tex]
what is the hypothesis of the following conditional statement?
If we walk home from school, it takes 30 minutes.
a. we walk home from school
b. it takes 30 minutes
c. we do not walk home from school
d. we walk
Answers
The hypothesis of the conditional statement is;
Option A: we walk home from school
How to identify the hypothesis?A hypothesis is defined as an educated guess while using reasonable thought patterns, about the answer to a scientific question. Now, the hypothesis can either be supported or not supported at all, but then it depends on the data gathered.
A conditional statement is defined as a set of rules performed provided a certain condition is met. Thus, it is sometimes referred to as If-Then statement because if a condition is said to be met, then an action is said to have been performed " .
Thus, the conditional statement here is: " we walk home from school ".
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Determine the intercepts of the line.
�
yy-intercept:
(
(left parenthesis
,
,comma
)
)right parenthesis
�
xx-intercept:
(
(left parenthesis
,
,comma
)
)right parenthesis
A coordinate plane. The x- and y-axes each scale by one-tenth. A graph of a line intersects the points zero, four-tenths and three-tenths, zero.
Answers
shola collects N2x salary every month. when he takes away his expenditure of N5000, the salary is less than or equal to N2500. How much does Shila collects every months?
Answers
Answer:
less than or equal to N7500
Step-by-step explanation:
N2x - N5000 = N2500
N2x = N7500
#7 in need help with this problem please
Answers
You cannot use the Hypotenuse-Leg congruence theorem to prove the similarity of triangles JKM and LKM, as they are not right triangles.
What is the HL congruence theorem?The Hypotenuse-Leg congruence theorem states that if the hypotenuse and one leg of two right triangles have the same measure then these two triangles are said to be congruent to each other.
The triangles JKM and LKM are not right triangles, as they do not have an angle of 90º, hence the HL congruence theorem cannot be used to prove their similarity.
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What is the effect on the graph of f(x) = x² when it is transformed to
• h(x) = 5x2 + 10?
Answers
The transformation applied is the one in option D, a vertical dilation of scale factor of 5, and a shift of 10 units up.
What is the effect of the transformation?Here we start with the parent quadratic function:
f(x) = x²
And we have the transformed function:
h(x) = 5x² + 10
We can write this as:
A vertical dilation of a scale factor 5, which will give:
h(x) = 5*f(x)
And then a translation of 10 units upwards, which gives:
h(x) = 5*f(x) + 10
Replacing the function f(x) we will get:
h(x) = 5*x² + 10
Then the correct option is D.
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How many full 2 3/4-in. sheets can be cut from 26 1/8-in. stock?
Answers
The required number of sheets cut from the stock are 9.
What is mixed fraction?A mixed fraction is one that is represented by both its quotient and remainder. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.
According to question:
We have,
We need sheets of length = 2 (3/4) in from 26 (1/8) in stock.
So, 2 (3/4) = 11/4 in
26 (1/8) = 209/8
Then,
Number of sheets = 209/8 / 11/4
Number of sheets = 836/88
Number of sheets = 9.5
So, 9 sheets can be cut.
Thus, required number of sheets are 9.
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PLEASE HELP
A recipe for soup calls for 4 tablespoons of lemon juice and 1/2 cup of olive oil. The given recipe serves 4 people, but a cook wants to make a larger batch that serves 120 .
a) How many cups of lemon juice will the chef need for the larger batch?
b) How many pints of olive oil will the chef need for the larger batch?
Answers
So the chef will need 30 times the amount of lemon juice that the original recipe calls for.
The original recipe calls for 4 tablespoons of lemon juice, so 4 tablespoons x 30 = 120 tablespoons of lemon juice needed for the larger batch.
Since there are 16 tablespoons in a cup, 120 tablespoons is equivalent to 120/16 = 7.5 cups.
b) To determine the amount of olive oil needed for the larger batch, we will again multiply the original amount by the ratio of the larger batch to the original, which is 30.
The original recipe calls for 1/2 cup of olive oil, so 1/2 cup x 30 = 15 cups of olive oil needed for the larger batch.
Since there are 2 cups in a pint, 15 cups is equivalent to 15/2 = 7.5 pints of olive oil.
So the chef will need 7.5 pints of olive oil for the larger batch.
120 table spoons of lemon juice.
15 cups of olive oil.
NO LINKS!!!
55, Write an equation satisfying the given conditions.
Answers
Part (a)
The two limit statements tell us that this an exponential decay function.
The curve goes up forever when heading to the left (negative infinity) as indicated by the notation [tex]\displaystyle \lim_{\text{x}\to-\infty}f(x) = \infty[/tex]
At the same time, the curve slowly approaches the horizontal asymptote y = -2, when moving to the right, because of this notation [tex]\displaystyle \lim_{\text{x}\to\infty}f(x) = -2[/tex]
An exponential decay function like [tex]\text{y} = (0.5)^{\text{x}}[/tex] has a horizontal asymptote of y = 0, aka the x axis. The y value approaches 0 but never gets there. Each output is positive.
Shift everything down 2 units to arrive at [tex]\text{y} = (0.5)^{\text{x}}-2[/tex] and this will move the horizontal asymptote down the same amount.
There's nothing really special about the 0.5; you can replace it with any value in the interval 0 < b < 1.
---------
Answer: [tex]\text{f(x)} = (0.5)^{\text{x}}-2[/tex]====================================================
Part (b)
I'll use this template
[tex]\text{y} = ab^{\text{x}}+c[/tex]
Plugging in x = 0 leads to y = a+c which is the y intercept. Set this equal to the stated y intercept 7 and we get a+c = 7.
We want the [tex]ab^{\text{x}}[/tex] portion to approach zero, which leads to c = 4 so we approach the stated horizontal asymptote.
So,
a+c = 7
a+4 = 7
a = 7-4
a = 3
We go from this
[tex]\text{y} = ab^{\text{x}}+c[/tex]
to this
[tex]\text{y} = 3b^{\text{x}}+4[/tex]
The value of b doesn't matter.
I'll go for b = 0.7 so we get to [tex]\text{f(x)} = 3(0.7)^{\text{x}}+4[/tex]
---------
Answer: [tex]\text{g(x)} = 3(0.7)^{\text{x}}+4[/tex]====================================================
Part (c)
The parent function [tex]\text{y} = \log(\text{x}})[/tex] has a domain of [tex](0, \infty)[/tex]. In other words it is the interval [tex]0 < \text{x} < \infty[/tex]
If we replaced each input x with x-5, then we shift the xy axis 5 units to the left. It gives the illusion the log curve moves 5 units to the right.
The vertical asymptote also moves 5 units to the right. We go from a domain of [tex](0, \infty)[/tex] to a domain of [tex](5, \infty)[/tex]
The base of the log doesn't matter.
---------
Answer: [tex]\text{h(x)} = \log(\text{x}-5)[/tex]Check out the graphs below. I used GeoGebra, but Desmos is another good option.
Jose is building a rectangular shaped garden and needs to know how many square feet it will cover. The dimensions of the garden will be 8 feet in length and (3n+2) in width. What is the area of the garden space?
A) 24n+16
B) 11n+10
C) 40n
Thank you!!!
Answers
Answer:
The equation for the area of a rectangle is length*width. For this problem, it says the length is 8 and the width is (3n+2). All you have to do is multiply 8 by (3n+2).
8(3n+2)=A
24n+16=A
Option A is correct
A grocery chain determines the cost and revenue models using the following functions: C(x)=1.2x−0.012x2, 0≤x≤150 R(x)=3.6x−0.06x20≤x≤150, where x is the number of unit items sold. Determine the interval on which the profit function P(x) = R(x) − C(x) is increasing.
Answers
Answer:
Yesterday I have received amount of be with you i need to pay
The interval on which the profit function is increasing is [0, 25).
Given that:
The cost function is, C(x) = 1.2x - 0.012x²
The revenue function is, R(x) = 3.6x - 0.06x²
Here, x i is the number of units sold, and 0 ≤ x ≤ 150.
The profit function is:
P(x) = R(x) - C(x)
= (3.6x - 0.06x²) - (1.2x - 0.012x²)
= 2.4x - 0.048x²
Find P'(x).
P'(x) = 2.4 - 0.096x
The profit function is increasing when P'(x) > 0.
2.4 - 0.096x > 0
2.4 > 0.096x
25 > x
That is x < 25.
Hence the function is increasing in the interval [0, 25).
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Find the component form of u + v given the lengths of u and v and the angles that u and v make with the positive x-axis. ||u||= 4, θu =6 , ||v|| = 1, θv = 4
Answers
The component of u+v along the length of u and v is (6.3, 0.66).
A vector is quantity which has both magnitude and direction. A magnitude is the length of the vector.
Here in the question u and v makes angle with the positive x axis.
||u||= 4 and θu =6 and ||v|| = 1, θv = 4
To determine the component of u = |u||(cosu, sinu)
Component of u = 6(0.9, 0.1) = (5.4, 0.6)
Component of v = ||v||(cosv sinv)
Component of v along the x axis = 1(0.9, 0.06 ) = (0.9, 0.06)
In the question value of u+v needs to be find.
Value of u + v = (5.4 + 0.9 , 0.6+ 0.06)
Value of the component form of u + v = (6.3, 0.66).
Hence, the component of u+v along the length of u and v is (6.3, 0.66).
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A cylinder has a height of 7 yards and a diameter of 26 yards. What is its volume? Use ≈ 3.14 and round your answer to the nearest hundredth.
Answers
The volume of the cylinder is 3,714.62 cubic yards.
How to get the volume of the cylinder?We know that the volume of a cylinder of radius R and height H is given by:
V = pi*R²*H
where pi = 3.14
In this case, we also know that:
H = 7yd
And the diameter is 26 yards, the radius is half of that, then:
R = 26yd/2 = 13yd
Then the volume is:
V = 3.14*(13 yd)²*7yd = 3,714.62 yd³
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Standardized tests for certain subjects, given to high school students, are scored on a scale of 1 to 5. Let A represent the score on a randomly selected exam for subject A and let B represent the score on a randomly selected exam for subject B. The distributions of scores for each subject’s standardized tests are displayed in the table and the histograms.
Answers
The probability of a score lower than three is given as follows:
0.38.
How to obtain the probabilities?A probability is obtained as the division of the number of desired outcomes by the number of total outcomes.
As the table gives the probability distribution, we must just take the probabilities of the desired events from the table.
The probability of a score lower than three is given as follows:
P(X < 3) = P(X = 1) + P(X = 2).
Taking the values from the table, the probability is of:
P(X < 3) = 0.18 + 0.20
P(X < 3) = 0.38.
Missing InformationThe problem is given by the image presented at the end of the answer.
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Sam has 3 1/4 pounds of blueberries. Ben also has some blueberries. Together, they have 9 2/3 pounds of blueberries. Create an equation to represent the number of pounds of blueberries, b, Ben has.
Answers
The required blueberries Ben has 6 5/12 pounds.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
Let the amount of blueberries Ben has to be x,
According to the question,
Together, they have 9 2/3 pounds of blueberries.
x + 3 1/4 = 9 2/3
x = 9 2/3 - 3 1/4
x = 9 + 2/3 - 3 -1/4
x = 6 + 5/12
x = 6 5/12 pounds
Thus, the required blueberries Ben has 6 5/12 pounds.
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Santiago has planned a basketball game for the weekend.
The chance of snow on Saturday is 35%, with a 70% chance on
Sunday. If these probabilities are independent, what is the
chance that it will snow on both days?
Answers
The probability that it will snow on both days, given the chances of snow on Saturday and Sunday, is 24.5%.
How to find the probability ?The chance of it snowing on both days is calculated by multiplying the probability of it snowing on Saturday by the probability of it snowing on Sunday. If the probabilities are independent, we can assume that one event occurring doesn't affect the other event, therefore the probability of both events happening is just the product of the individual event probabilities.
So, the chance of it snowing on both days is:
P(Saturday and Sunday) = P(Saturday) x P(Sunday)
P(Saturday and Sunday) = 0.35 x 0.70
P(Saturday and Sunday) = 24.5 %
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A new apartment building has 33 floors, with 24 apartments on each floor. How many apartments are in the building?
(Partial product)
Red :
Blue :
Green :
Yellow :
Total Product:
Answers
Simple equation when u break it down: 33 x 24=792 apartments
How many apartments are in the building?A building, or edifice, is an enclosed structure with a roof and walls that is standing in one location more or less permanently, such as a house or factory (although there are also portable buildings). Buildings come in a variety of sizes, shapes, and uses, and they have been modified throughout history for a wide range of reasons, including the availability of building materials, weather, land prices, ground conditions, particular uses, prestige, and aesthetic considerations.
given:
new apartments' building =33 floor
apartments on each =24 floor
33*24=792
792 apartments are in the building
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Pythagoras is very tall for ancient Greck standards: 1.78 m. He notices that when he stands with his back to the sun, his shadow is 3.08 m in length, while the shadow cast by the lighthouse is 26 m long How tall is the lighthouse?
Answers
The lighthouse is 8.88 m tall.
What is the ratio?
A ratio is a mathematical comparison of two or more quantities. It expresses the relationship between the values of the quantities in terms of a numerical fraction.
This problem can be solved using similar triangles. Since the ratio of the heights of Pythagoras and the lighthouse is the same as the ratio of their corresponding shadow lengths, we can set up the following proportion:
(Height of lighthouse) / (Height of Pythagoras) = (Shadow length of lighthouse) / (Shadow length of Pythagoras)
Plugging in the given values:
(Height of lighthouse) / 1.78 = 26 / 3.08
To solve for the height of the lighthouse, we can cross-multiply and divide:
(Height of lighthouse) = (26 / 3.08) * 1.78
The lighthouse is approximately:
(26/3.08)*1.78 = 8.88 m
Hence, The lighthouse is 8.88 m tall.
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Which inequality is true when x= 4?
Answers
For the value of x = 4, the inequality equation that is true is option C: x/2 < 3.
What is an inequality?
In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.
The first inequality equation is - x + 5 < 3
Substitute the value of x = 4 in the equation.
4 + 5 < 3
Now, simplify the equation -
9 < 3
It is known that 9 is not less than 3, but greater than 3.
Therefore, this inequality is false.
The second inequality equation is - 9x > 36
Substitute the value of x = 4 in the equation.
9(4) > 36
Now, simplify the equation -
36 < 36
It is known that 36 is not less than 36, but equal 36.
Therefore, this inequality is false.
The third inequality equation is - x/2 < 3
Substitute the value of x = 4 in the equation.
4/2 < 3
Now, simplify the equation -
2 < 3
It is known that 2 is less than 3.
Therefore, this inequality is true.
The fourth inequality equation is - 18 < x + 8
Substitute the value of x = 4 in the equation.
18 < 4 + 8
Now, simplify the equation -
18 < 12
It is known that 18 is not less than 12, but greater than 12.
Therefore, this inequality is false.
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Which inequality is true when x = 4?
A. x + 5 < 3
B. 9x > 36
C. ×/2 < 3
D. 18 < x + 8
Write two different expressions you could use to represent the
combined area of the Activities and Quotations sections. What
information about the sections does each expression show?
Answers
The area expressions are (2x + 1) * (x^2 + 4x - 5) and 2x^3 + 9x^2 - 6x - 5
How to determine the area expressionsThe missing figure is added as an attachment
From the question, we have the following parameters that can be used in our computation:
Length = 2x + 1
Width = x^2 + 4x - 5
The area is calculated as
Area = (2x + 1) * (x^2 + 4x - 5)
When expanded, we have
Area = 2x^3 + 8x^2 -10x + x^2 + 4x - 5
Evaluate the like terms
Area = 2x^3 + 9x^2 - 6x - 5
Hence, the area expression is 2x^3 + 9x^2 - 6x - 5
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I need assistance for this problem below:
Answers
The image of quadratic function f(x) = x² is equal to g(x) = 6 · x².
How to derive and graph the image of a quadratic equation
In this question we see the representation of quadratic equation f(x) = x², from which we need to generate the image of this function, this can be done by a rigid transformation known as vertical dilation:
g(x) = k · f(x), k > 1
Where:
f(x) - Original functiong(x) - Resulting functionIf we know that f(x) = x² and k = 6, then the image of function is:
g(x) = 6 · x²
Whose representation on Cartesian plane is shown in the image attached below.
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Check image for questions!
(Answers are already there, just gotta figure out where they go)
50 points!
Answers
The equation y is 2x - 3 describes the line with a slope of 2 and a Y-intercept of -3.
Linear equation?Use m is used to show the slope of a line.
m = 2
c is used to signify the line's y-intercept. c = -3
For the line's equation, the slope-intercept is: y = mx + c
In the equation above, replace c = -3 with m = 2 ,y = 2x - 3
Consequently, the equation of the line with a Y-intercept of -3 and a slope of 2 is as follows: y = 2x - 3.
For the line's equation, the slope-intercept is: y = mx + c
In the equation above, replace c = -3 with m = 2 ,y = 2x - 3
Consequently, the equation of the line with a Y-intercept of -3 and a slope of 2 is as follows: y = 2x - 3.
The complete question is,
The line with a -3 Y-intercept and a 2 slope has what equation?
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part a: the number of transistors per ic in 1972 seems to be about 4,000 (a rough estimate by eye). using this estimate and moore's law, what would you predict the number of transistors per ic to be 20 years later, in 1992? prediction
Answers
Using Moore's Law, which states that the number of transistors on a chip doubles approximately every two years, the estimated number of transistors per IC in 1992 would be 64,000.
The law claims that we can expect the speed and capability of our computers to increase every two years because of this, yet we will pay less for them. In more simple terms, the observation by Gordon Moore in 1965 that the number of transistors in a dense integrated circuit (IC) doubles roughly every two years is known as Moore's law.
This is calculated by doubling the estimate of 4,000 transistors every two years for a total of 8 doublings (16 years).
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if the relation represents a function, find the domain and range. (enter your answers using interval notation. if the relation is not a function, enter none in the domain and range answer blanks.)
Answers
If the relation is represented by the equation y = 2x + 1, the domain would be all real numbers (-infinity, +infinity) and the range would be all real numbers greater than or equal to 1 (1, +infinity).
A relation is a function if for every input (x) there is exactly one output (y). To determine if a relation is a function, we can use the vertical line test, which states that if a vertical line can be drawn through the graph and intersects the relation more than once, then the relation is not a function.
If the relation is a function, we can find the domain and range by analyzing the relation. The domain is the set of all x-values and the range is the set of all y-values. In interval notation, the domain is written as (a, b) and the range is written as (c, d).
So, the domain and range answers depend on the relation which is given and it should be specified.
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determine the relative order of the metric prefixes of kilo-, micro-, centi-, and milli-. for the same base unit, choose... is less than choose... , which is less than choose... , which is less than choose... .
Answers
The relative order of the metric prefixes Milli- < Centi- < Micro- < Kilo-
The relative order of the metric prefixes of kilo-, micro-, centi-, and milli- is milli-, centi-, micro-, and kilo-. This order is determined by the exponential values of each prefix.
Milli- is equal to 10-3, centi- is equal to 10-2, micro- is equal to 10-6 and kilo- is equal to 103. The exponential values are used to determine the relative order of the prefixes. The lowest exponential value is milli-, making it the smallest metric prefix and the highest exponential value is kilo-, making it the largest metric prefix.
When the exponential values are compared, it is clear that the order of the prefixes is milli- < centi- < micro- < kilo-. This order is used to determine the relative size of the metric prefixes when measuring the same base unit.
For example, if the base unit is meter, then millimeter is the smallest measure and kilometer is the largest measure. The exponential values of the metric prefixes determine the relative order of the base unit.
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In the equation 10+4y=-4y+2,the variable y represents the same value. Is y = 1, 0, -1, or -2 the solution of this equation explain
Answers
The solution to the equation 10+4y=-4y+2 is -1 because the variable y represents the same value.
What is equation?An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =. In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the relationship between two expressions on opposite sides of the sign. It mostly consists of one variable and one equal to symbol. 2x - 4 = 2 is an example.
Here,
10+4y=-4y+2
8y=-8
y=-1
The solution of equation 10+4y=-4y+2 is -1 as the variable y represents the same value.
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60⁰
m
Find the area of each triangle round to the nearest tenth
For math thanks !!!!!
Answers
Answer:
5.2 square units
Step-by-step explanation:
You want the area of a triangle with sides 4 and 3, and the angle between them measuring 60°.
AreaThe formula for the area of a triangle is ...
A = 1/2ab·sin(C)
ApplicationHere, we have a=4, b=3, C=60°, so the area is ...
A = 1/2·4·3·sin(60°) = 3√3 ≈ 5.2 . . . . square units
The area of the triangle is about 5.2 square units.
for each of the following sets of functions either find a function f(x) in their span such that f(x) > 0 for all x
Answers
f(x) = 7x - 1, which is a linear equation with a positive leading coefficient, making f(x) > 0 for all x.
Set 1: {f(x) = x + 1, f(x) = x - 1}
Function f(x) = x^2 + 2 can be found in the span of the two given functions. This can be seen by expanding the equation:
f(x) = x^2 + 2 = (x + 1) + (x - 1) = 2x;
thus, f(x) = 2x + 2, which is a quadratic equation with a positive leading coefficient, making f(x) > 0 for all x.
Set 2: {f(x) = 4x - 2, f(x) = 3x + 1}
Function f(x) = 7x - 1 can be found in the span of the two given functions. This can be seen by expanding the equation:
f(x) = 7x - 1 = (4x - 2) + (3x + 1) = 7x;
thus, f(x) = 7x - 1, which is a linear equation with a positive leading coefficient, making f(x) > 0 for all x.
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Complete question:Find a function f(x) in the span of the functions f1(x) = x and f2(x) = -x such that f(x) > 0 for all x.