The process to show the vector field V(x,y,z) as conservative is show below and the scalar potential f is [tex]f(x,y,z) =xyz^{2} + e^{\pi }[/tex] .
A Vector field can be called as conservative if we are able to find the potential function "f" , whose gradient is field .
The Gradient is vector that is made from partial derivatives of potential function .
The Vector function is given as , V(x,y,z) = [tex](yz^{2} )i + (xz^{2} )j + (2xyz)k[/tex] ,
So , we can write the partial derivatives function of potential function as :
[tex]\frac{\partial f}{\partial x} = yz^{2}[/tex] ; [tex]\frac{\partial f}{\partial y} = xz^{2}[/tex] ; [tex]\frac{\partial f}{\partial z} = 2xyz[/tex],
On Antidifferentiating any of the above three partial derivatives ,
we get ; [tex]f=xyz^{2} + C[/tex] , here the constant C can take any value ,
so , we take C as [tex]e^{\pi }[/tex] .
Therefore , the potential Function is [tex]f(x,y,z) =xyz^{2} + e^{\pi }[/tex] .
The given question is incomplete , the complete question is
Show that the vector field defined by the vector function V(x,y,z) = (yz²)i + (xz²)j + (2xyz)k is conservative by finding a scalar potential f .
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What are quadrants examples?
The examples for each of the quadrant is explained below.
Quadrant in math is defined as one of the four regions or sections of the coordinate system and the quadrants are separated by the x-axis and the y-axis and these axes are perpendicular to each other.
Here we have to know the value that must be placed on each quadrant.
Here the first quadrant has both x and y-coordinates are positive.
The second quadrant has the value of the x-coordinate is negative and the y-coordinate is positive.
The third quadrant has both x and y-coordinates are negative.
The fourth quadrant has the value of the x-coordinate is positive and the y-coordinate is negative.
Therefore, the example for each of them are written as
=> Quadrant I = (1, 1)
=> Quadrant II = (-1, 1)
=> Quadrant III = (-1, -1)
=> Quadrant IV = (1, -1)
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Tony performs a dilation on Figure R. He uses a scale factor of 4 with a center of dilation at the orgin.
What are the coordinates of the image of vertex P?
The x- coordinate of the vertex P is -4 and the y coordinate is -3. The coordinates of the image of vertex P is thus, (-4, -3).
What are coordinates?Coordinates are numbers describing the position of a point or shape in a line or particular space. We can represent a line or shape in the space between number lines with both positive and negative coordinates.
The vertical axis in the number line is called y-axis and the horizontal axis is called the x- axis. The coordinate of a point is written as (x, y). The x, y represents the numbers on x-axis and y -axis touched at which the point lies in the graph.
For the given vertex P, the vertex lies on the point -4 on x-axis and on -3 in y axis. Hence, the coordinate of P is (-4, -3).
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Given that $x$ is a positive integer less than 100, how many solutions does the congruence $x 13 \equiv 55 \pmod{34}$ have
There are three solutions to the congruence x+13=55 (mod 34).
What is congruence?Two figures are considered to be 'congruent' if they can be put exactly over each other. When you set one slice of bread on top of the other, you'll see that they're both the same shape and size. The phrase "congruent" refers to having exactly the same form and dimension. When two things or forms superimpose on each other, they are said to be congruent. Their shapes and sizes are identical. Line segments with the same length and angles of the same measure are congruent in the case of geometric forms.
Here,
something equaling 55 (mod 34) is unusual to say the least as 55 mod 34 = 21
do you mean x+13=21 (mod 34) ?
clearly x = 8 + 34k which gives 8, 42, 76 begin less than 100
The congruence x+13=55 (mod 34) has three solutions.
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a solid metal sphere of volume 1280cubic centimeters
is melted down and recast into 20 equal solid cubes.fund length of the side of each cube
a solid m or a solid m fear of volume
At a benefit concert, fifteen bands have volunteered to perform but there is only enough time for eight of the bands to play. How many lineups are possible?
On solving the provided question, we can say that - he need 56 answers he need to get correct if he want a grade of 80 percent on a test with 70 questions
what is percentage?A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. It has no measuring systems. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) * 100%.
Assuming that all of the questions are equally weighted, 56 is equal to 80% of 70. (.80)(70)=56 Therefore, 56 out of 70 is the lowest number you may get correct, or 80%.
So, the maximum number of questions you may omit is 14. As an alternative, if you desire 80% accuracy, you can have no more than 20% errors.
20% of 70
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Select the interval where the graph f is positive
Answer: A
Step-by-step explanation:
Based on the graph, we know that it is positive if it is above the x-axis. It is also indicated by the positive labels.
A: correct
Looking at choice A, it says the interval is from -2<x<-1. This means we have to find x=-2 and x=-1. On the graph, that interval is above the x-axis, so it is positive.
B: incorrect
Looking at choice B, it says the interval is from -1<x<0. This means we have to find x=-1 and x=1. On the graph, that interval is below the x-axis, so it is negative.
C: incorrect
Looking at choice C, it says the interval is from 0<x<1. This means we have to find x=0 and x=1. On the graph, that interval is below the x-axis, so it is negative.
Therefore, A is the correct answer.
A card i picked at random from a deck of 52 card. Find the probability that the card i either a queen or a diamond
the probability that the card is either a queen or a diamond is: 4/13
What is probability?A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
the proportion between the total number of conceivable outcomes and the number of outcomes in a comprehensive collection of equally probable alternatives that result in a particular occurrence.
Example: When flipping a coin, there are only two possible outcomes: either it will land on its head or on its tail.
Number of cards, n(S) = 52
Let E = Event of getting a diamond
F = Event of getting a queen
(E ∩ F) = Event of getting a diamond of queen.
Then, n(E) = 13
n(F) = 4 ,
n (E ∩ F)=1
P(E) = 13/52 = 1/4
P (F) = 4/52 = 1/13
P (E ∩ F) = 1/52
(E or F) = P(E ∪ F) = P(E) + P(F) × P(E ∩ F)
P (E or F) = 1/4 + 1/13 - 1/52
P (E or F) = (13 + 4 - 1)/52
P (E or F) = 16/52
P (E or F) = 4/13
The required probability of getting either diamond or a queen is 4/13
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There are 14 teams in a basketball league.
Each team plays every other team twice
during the season.
a) Suppose that you want to determine
how many games, in total, are played.
Suggest a simpler problem that you
could solve first.
b) How many games, in total, are played
during the season?
Please I need deep explaining.
Therefore , the solution of the given problem of combination comes out to be there were 182 games played in all.
Definition of combinationCombinations are operations in mathematics that count the number of possible combinations that can be created from a set of items, where the selection's direction is immaterial. You are free to select any arrangement of the parts. Permutations and combinations can be mixed up.
Here,
There still are 14 teams in all, but each team plays the other twice.
Every team plays almost every team twice, hence the total amount of games played is simply the permutations of 2 out of 14, which is determined by:
₁₄P₂
=14!/((14-2)!)
= (14×13×12!)/ 12!
= 14×13
=182
Consequently, there were 182 games played in all.
Therefore , the solution of the given problem of combination comes out to be there were 182 games played in all.
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Which ordered pairs are in the solution set of the system of linear inequalities?
y2-3x+2
y < 2x + 3
-6-5
-3-
(2. 2) (3. 1) (42)
The ordered pairs that are in the solution set of the system of linear inequalities are (2 ,2), (3 , 1) and (4 , 2).
What is system of equations?A finite collection of equations for which we searched for the common solutions is referred to in mathematics as a system of equations, sometimes known as a set of simultaneous equations or an equation system.
Given the system of linear inequalities:
y > -3x + 2
y< 2x + 3
Substitute the value of x and y for each given ordered pair.
For (2, 2) x=2 and y =2:
y > -3x + 2
2 > -3(2) +2
2> -4 True.
y< 2x + 3
2 < 2(2) +3
2< 7 True
For (3, 1) x=3 and y=1:
1 > -3(3) + 2
1 > -7 True
y< 2x + 3
1 < 2(3) + 3
1< 9 True
For (4 , 2) x=4 and y =2
y > -3x + 2
2 > -3(4) +2
2 > -10 True.
y< 2x + 3
2 < 2(4) + 3
2 < 11 True.
Hence the ordered pairs (2 ,2), (3 , 1) and (4 , 2) are in the solution set of the system of linear inequalities.
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At Hunter Elementary School, 73% of students buy their lunch. In a randomly selected first grade class of 19 children, find the probability that at least 12 buy their lunch. Round to 3 decimal places.
The probability that at least 12 buy their lunch = 0.887
Given that 73% of students buy their lunch.
⇒ p = 0.73
And q = 1-p
q = 0.27
sample size (the number of student selected) n = 19
We need to calculate the probability that at least 12 buy their lunch.
i.e., P(x ≥ 12)
We use binomial distribution formula, P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ
P(X ≥ 12)
= P(X= 12) + P(X= 13) + P(X= 14) + P(X= 15) + P(X= 16) + P(X= 17) + P(X= 18) + P(X= 19) [tex]=~ ^{19}C_{12}(0.73)^{12}(0.27)^{7} + ^{19}C_{13}(0.73)^{13}(0.27)^{6}+ ^{19}C_{14}(0.73)^{14}(0.27)^{5} + ^{19}C_{15}(0.73)^{15}(0.27)^{4} + ^{19}C_{16}(0.73)^{16}(0.27)^{3} + ^{19}C_{12}(0.73)^{17}(0.27)^{2}+ ^{19}C_{12}(0.73)^{18}(0.27)^{1}+ ^{19}C_{12}(0.73)^{19}(0.27)^{0}[/tex]
= 0.1207 + 0.1757 + 0.2036 + 0.1835 + 0.1240 + 0.0592 + 0.0178 + 0.0025
= 0.887
The required proability is 0.887
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For the initial 90 miles of a flight, the pilot heads 8° off course in order to avoid a storm. The pilot then changes direction to head toward the destination for the remainder of the flight, making a 157° angle to the first flight course. Determine the total distance of the flight
A. 48.4
B. 135.9
C. 138.4
D. 228.4
In the above scenario, note that the total distance of the flight is given as: 48.4 miles (approximately). This is solved using the law of Sines to find x.
What is the law of Sines?The connection between the sides and angles of non-right (oblique) triangles is defined by the Law of Sines. Simply put, it asserts that the ratio of the length of a triangle's side to the sine of the angle opposite that side is the same for all triangle sides and angles.
Thus, with regard to the problem modeled in the attached triangle, because two angles are given, the missing angle is 180° − (157° + 8°) or 15°. Use the Law of Sines to find x.
Using the law of ins we can state that:
Sin 8°/x = sin 15°/90
90 (Sin 8°) /x = Sin 15°
90 Sin 8° = x Sin 15°
90 Sin 8° / Sin 15° = x
90 (0.13917310096)/ 0.2588190451 = x
Thus,
x = 48.3951213156
x [tex]\approx[/tex] 48.4
Thus, the distance of the flight is approximately 48.4 miles.
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Work out the equation of the straight line
shown below.
Give your answer in the form y = mx + C,
where m and c are integers or fractions in
their simplest forms.
Y
6
5
4
3
2-
1
-6 -5 -4 -3 -2 -1 0
-14
-2-
-3+
-4-
-5-
-6-
1 2 3 4 5 6
X
Where m and c are integers or fractions, the equation of a straight line in the form of y = mx + c becomes y = x/2 + 8.
What is a straight line?A straight line is made up of many points connected at each end. Any straight line's slope, m, is determined by the formula. The slope-intercept formulation of a linear equation is y = mx + b. The equation's variables are X and Y. The slope of the line (m) and the value of y when x is 0 are represented by the values m and b, respectively.
[tex]m = \frac{y2-y1}{x2 - x1}[/tex]
given
the graph is,(0,8) and (9,2)
The slope of the line is,
m = 1/2
Because it crosses the y-axis at the point where the intercept C is equal to 8,
The equation of the line will be :
⇒ y = mx + c
⇒ y = (1/2)x + (8)
⇒ y = x/2 + 8
Where m and c are integers or fractions, the equation of a straight line in the form of y = mx + c becomes y = x/2 + 8.
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Can u please help.......
Using the centroid P on the triangle, the value of QN is 25.5 and PN is 8.5
What is Centroid of a TriangleThe centroid of a triangle is a point located at the intersection of the three medians (the lines that connect the vertices to the midpoints of the opposite sides). The centroid divides each median in two segments that have the same length. It is the center of gravity of the triangle and is the point at which the triangle's three medians intersect.
The centroid theorem states that the centroid of the triangle is at 2/3 of the distance from the vertex to the mid-point of the sides.
In this triangle, the centroid is at P and the QP is 17.
a) QN
The distance between QP is two-thirds the length of QN
The length of QP = 17
QP = 2/3 QN
17 = 2/3 QN
QN = (3 * 17) / 2
QN = 25.5
b) PN
The distance between PN is calculated as;
PN = QN - QP
PN = 25.5 - 17
PN = 8.5
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How do you solve for 4=2+W over 2
Need to know immediately
Solving for W in the equation 4 = (2 + W) / 2 gives W = 6
How to solve for WUsing the equation 4 = (2 + W) / 2, W is solved by making it the subject of the formula and this is means placing W alone at the left hand side of the equation'
This is achieved by the following procedure
clearing the fraction
4 = (2 + W) / 2,
8 = 2 + W
rearranging the equation
W + 2 = 8
subtracting 2 from both sides of the equation
W + 2 - 2 = 8 - 2
since 2 - 2 = 0 we have
W = 6
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Trejo says that if you know the x-intercepts,
y-intercepts, domain, and range of a
function then you automatically know the x-
intercepts, y-intercepts, domain, and range
of its inverse. Hilary disagrees. She says you
know the intercepts but that is all you know
for sure. Who is correct? Justify your
answer.
Trejo is correct, because if you know the x-intercepts, y-intercepts, domain, and range of a function then you automatically know the x- intercepts, y-intercepts, domain, and range of its inverse.
What is Function?A relation between a set of inputs having one output each is called a function.
Given that;
Trejo says that if you know the x-intercepts, y-intercepts, domain, and range of a function then you automatically know the x- intercepts, y-intercepts, domain, and range of its inverse.
But, Hilary disagrees, She says you know the intercepts but that is all you know for sure.
Now,
We know that;
In a function, If if you know the x-intercepts, y-intercepts, domain, and range of a function then you automatically know the x- intercepts, y-intercepts, domain, and range of its inverse.
Thus, The Trejo is correct.
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In the figure shown, what is the value of x?
Answer:
Step-by-step explanation:
SHOW HIGH CLARITY IMAGE, BUT USE CONGRUENCE OF TRINALGES AND FIND X BY EQUATING THE GIVEN SIDE I GUESS
IF YES MARK ME BRAINLIEST
when x equal 8 to the x^6-64x^4+x^2-7x-51
The expression (x - 8) is not the factor of the polynomial x⁶ - 64x⁴ + x² - 7x - 51.
What is factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
The polynomial is given below.
⇒ x⁶ - 64x⁴ + x² - 7x - 51
If the value of the polynomial is zero at x = 8. Then (x - 8) will be the factor of the polynomial.
At x = 8, the value of the polynomial is given as,
⇒ (8)⁶ - 64(8)⁴ + (8)² - 7(8) - 51
⇒ 262,144 - 262,141 + 64 - 56 - 51
⇒ - 43
The expression (x - 8) is not the factor of the polynomial x⁶ - 64x⁴ + x² - 7x - 51.
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Given g(x) = -4x - 4, find g(-2).
Answer:
4
Step-by-step explanation:
SolutionThis question basically asks you to substitute the value of x to find the value of function g(x).
Given x = -2,
g(-2) = -4(-2) - 4 = 8 - 4 = 4
Answer:
4
Step-by-step explanation:
g(x) = -4x - 4
Let x = -2
g(-2) = -4(-2) - 4
= 8 -4
=4
a 96 ounce container of juice cost 4.80. at what price should a 128 container be sold, in order for the unit rate for both items to be the same
Response is $6.40, a proportion is the relationship or equivalence between two ratios or fractions.
Is a proportion the same as a percentage?While the denominator of a percentage is always 100, a proportion is the relationship or equivalence between two ratios or fractions. Both proportion and percentage can be expressed as fractions.
A percentage is an equation in which two ratios are made equal to one another.
Out of a possible 100, the percentage is given.
Because 32 ounces is the difference between 128 and 96, making it 1/3 of 96, we can divide $4.80 by 3 to get $1.60, then add $1.60 to $4.80 to get $6.40.
Response is $6.40, a proportion is the relationship or equivalence between two ratios or fractions.
The complete question is,
It cost $4.80 for a 96-ounce bottle of orange juice. How much should be charged for a 128-ounce container in order to equalize the unit rates of the two sizes? Describe your thought process.
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3. At the grocery store, three flavors of Cheerios are sold.
Flavor A is 20 ounces and costs $4.49. The unit rate is ------------- per ounce.
For Flavor B, the equation y = 0.20x represents the cost (y) per ounce (x) in each box. The unit rate is------------------------ per ounce.
For Flavor C, the table below shows the amount paid per ounce. The unit rate is ---------------------- per ounce
Ray is making bouquets of balloons. In each bouquet 2 out of every 5 balloons are red. Write an equation to help Ray determine how many red balloons are needed compared to the the total number of balloons used.
7. Let x represent the number of balloons used compared to y which is the number of red balloons.
10.
Review the keywords below. Find at least 2 words commonly used for "Rate of Change". Drag and Drop them to the box for "Rate of Change" to earn full credit.
The unit rate of flavor A is; $0.2245 per ounce
The unit rate of flavor B is; $0.20 per ounce
An equation to help Ray determine how many red balloons are needed compared to the the total number of balloons used is; y = ²/₅x
How to find the unit rate?A unit rate is also called unit ratio and it describes how many units of the first type of quantity corresponds to one unit of the second type of quantity.
We are given that Flavor A is 20 ounces and costs $4.49. Thus;
Unit rate of flavour A = $4.49/20 = $0.2245 per ounce
For Flavor B, the equation y = 0.20x represents the cost (y) per ounce (x) in each box. Thus, the unit rate is $0.20 per ounce
Since ray is making bouquets of balloons. In each bouquet 2 out of every 5 balloons are red.
If x is the number of ounces, then the unit rate is 2/5 . Thus, the equation is; y = ²/₅x
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a taxi charges $2.35 fee plus $0.55 per mile. melissa has no more than $15 to spend on her taxi ride how many miles can she go?
Answer:
2.35 + 0.55 × 15 = 10.6
Therefore, she can go 10.6 miles.
Answer:
10.6
Step-by-step explanation:
2.35 + 0.55 x 15 = 10.6
What is the difference of polynomial and equation with example?
A polynomial is an expression involving variables and coefficients, which is formed by adding, subtracting, multiplying, and taking non-negative integer exponents of the variables. A mathematical statement that two expressions are equal is known as an equation.
A mathematical statement that two expressions are equal is known as an equation.
Example of a polynomial:
2x^2 + 3x + 5
Example of an equation:
2x^2 + 3x + 5 = 0
Let's say we are solving the equation 2x^2 + 3x + 5 = 0
Step 1: Subtract 5 from both sides.
2x^2 + 3x = -5
Step 2: Divide both sides by 2.
x^2 + 3/2 x = -5/2
Step 3: Use the quadratic formula to solve for x.
x = (-3 ± √17) / 4
Step 4: Simplify the answer.
x = (-3 ± 4.12) / 4
Step 5: Solve for the two values of x.
x = -0.78 or x = 3.28
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How do you solve an acute triangle using trigonometry?
An acute triangle is a triangle with all angles measuring less than 90°.
To solve an acute triangle using trigonometry, we need to know the length of at least one side and at least one angle of the triangle.
For example, let's assume the triangle has side lengths a = 6, b = 8, and we know the angle A = 30°.
First, we can use the Law of Cosines to calculate the length of the third side, c:
c² = a² + b² - 2abcos(A)
c² = 6² + 8² - 2(6)(8)cos(30°)
c² = 64 - 96cos(30°)
c² = 64 - 48
c² = 16
c = 4
Now we can calculate the other two angles, B and C, using the Law of Sines:
sin(B) = sin(A) * c/a
sin(B) = sin(30°) * 4/6
sin(B) = 0.5 * 2/3
sin(B) = 0.3333
B ≈ 19.47°
sin(C) = sin(A) * c/b
sin(C) = sin(30°) * 4/8
sin(C) = 0.5 * 0.5
sin(C) = 0.25
C ≈ 14.04°
Therefore, the three angles of the triangle are A = 30°, B = 19.47°, and C = 14.04°, and the three sides are a = 6, b = 8, and c = 4.
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Which of the parabolas has a maximum?
(1) y = 8x² + 6x + 6
(2) y = -2x² + 6x - 6
(3) y = 2x² - 6x + 6
(4) y = 6x² - 6x-6
Answer:
(2) y = -2x² + 6x - 6
Step-by-step explanation:
Notice that the only leading coefficient that is negative is in the 2nd equation. Hence, the shape of the parabola will be upside down, making it have a maximum.
If the m<1 = 17x - 30, and the <2 = 7x + 18, what is the value of x?
Answer:
X=8
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
17x−30+7x+18=180
17x+−30+7x+18=180
(17x+7x)+(−30+18)=180(Combine Like Terms)
24x+−12=180
24x−12=180
Step 2: Add 12 to both sides.
24x−12+12=180+12
24x=192
Step 3: Divide both sides by 24.
X=8
The manufacturer's price for a Jinko car is $x
Ben was given a 7% discount on the manufacturer's price when he bought a Jinko.
Ben paid $23 622 when he bought his Jinko.
(a) Calculate the value of x.
Answer:
x = $25,400 [the original price of the Junko car]
Step-by-step explanation:
The price Ben paid, $23,622, is after the 7% discount. Let x be the original price of the Jinko car. Ben's prices reflect a 7% discount:
x*(1-0.07) = $23,622 [The expression (1-0.07) means the original price, 1, is reduced by 7%, -0.07, to give the final price]
(0.93)x = $23,622
x = $25,400
How do you find the missing side of a triangle?
The missing sides of the triangle can be found by applying the Pythagoras Theorem .
What is Pythagoras Theorem ?
The Pythagoras Theorem states that square of hypotnuse (that is longest side) is equal to sum of the square of perpendicular and base .
that means : [tex]Hypotnuse^{2} = Perpendicular^{2} +Base^{2}[/tex] ;
let missing side of the Right triangle be hypotnuse ;
So , missing side is written as : [tex]Hypotnuse = \sqrt{Perpendicular^{2} +Base^{2}}[/tex] .
For Example : Let a right triangle has sides lengths of perpendicular = 6 and hypotnuse = 10 .
let , the length of side "base" be unknown.
So , in order to find length of side b (base) , we substitute the known values into Pythagoras theorem:
[tex]10^{2} =6^{2} +Base^{2}[/tex] ;
[tex]Base = 100-36[/tex] ;
So , missing side "base" is = 8 ;
Therefore , the missing side can be found by using the Pythagoras Theorem .
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For this exponential function,
what is the output value (y)
when the input value (x) is 2?
y = 4.2x
(2, [?])
Enter
The final statement is: y=16
What are functions?Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given here: The exponential function y=4×2ˣ
Therefore for x=2 we get
y=4×2²
y=16
Hence, The value of y at x equal to 2 is 16
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Please Help me find the area of the figure round to the nearest hundredth nessary
Answer:
912 cm²
Step-by-step explanation:
Formula for area of triangle: 1/2bh
So you'll first multiply the base by the height of the triangle
48 x 38 = 1,824
Then you'll multiply 1,824 by 1/2(which is the same as dividing it by 2)
1,824 ÷ 2 = 912
Can you help me with this
The graph of the line y = 4x + 3 is shown below.
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
y = 4x + 3
When x = 0, y = 3
When x = 1, y = 4 + 3 = 7
When x = 2, y = 11
Similarly for negative x values, we get,
x = -1, y = -4 + 3 = -1
x = -2, y = -8 + 3 = -5
So on......
So we must get the following coordinates:
(-1, -1), (-2, -5), (0, 3), (1, 7), (2, 11),, ........
Thus,
The graph is shown below.
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