This statement is TRUE. When we are doing a problem, we could use these questions " what is the equation asking you do? what is your plan to solve?" as the part of starting solving the problem in math about equation matter.
About equationIn mathematics, an equation is an equation statement that contains one or more variables. Solving equations consists of determining which variable values makes an equality true. The variable is also called "unknown" and the value of an "unknown" that satisfies the equation is called the equation solution. There are two types of equations: identity and conditional equations. True identity for all variable values. The conditional equation is true only for certain variable values.
An equation is a mathematical statement in the form of a symbol which states that two things are exactly the same. Equations are written with an equal sign (=), as follows:
x + 3 = 5, which states that value x = 2.
2x + 3 = 5, which states that the value x = 1.
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The question y=4x; (1 4) yes or no question makes me really confused and I don't know if it's a yes or no
[tex](\stackrel{x}{1}~~,~~\stackrel{y}{4})\hspace{5em}y=4x \\\\[-0.35em] ~\dotfill\\\\ \underset{y}{4}~~ = ~~4(\underset{x}{1})\implies 4~~ = ~~4\textit{\LARGE \checkmark}[/tex]
Answer:
y = 4x; (1, 4) = TRUE
Step-by-step explanation:
(1, 4) basically means:
x = 1
y = 4
So we put these values into our equation:
4 = 4 x 1
4 = 4
Amir is growing three plants.
He keeps track of each plant's height over time.
Which plant is growing the slowest?
Slowest growing plant is plant A.
What is slope?The Slope (also called Gradient) of a line shows how steep it is.
To calculate the Slope:
Divide the change in vertical distance by the change in horizontal distance
Given,
Amir grows three plants,
Graph of plant A is given with straight line,
Height is denoted on x axis,
Time is denoted on y axis
Slope of the line will represent growth rate.
Line passes through (1,2) and (2,4)
slope of the line
= y-y'/x-x'
= 2 - 4/1 - 2
= - 2 / - 1
= 2
Growth rate = 2 inches per month
For plant 2
by the table,
Height is 15 inches in 6 months.
Growth rate = 15/6 = 2.5 inches per month
Equation for plant 3
h = 3.5t
Slope of the equation = 3.5
Growth rate = 3.5 inches per month
By the above calculation,
Growth rate of plant A is least.
Hence, Plant A is growing slowest.
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find p(-2) and p(3) for each function
p(x)=-7x^2+5x+9
p(x)=3x^3 - x^2 + 2x - 5
According to the Function, p(-2) = -29 and p(3) = 73 are the values that we have.
How do you know if something has a purpose or not?The vertical line test has been used to determine if a graph accurately depicts a function. If a trendline created across the chart is moved and only ever hits it once, the chart is functional. If the line graph crosses the chart at least once, it is not a function.
The core concept of mathematics' calculus is functions. The functions are special types of relations. A function is a rule that generates a unique outcome for each input x in mathematics. A mapping or transformation in mathematics represents a function. Usually, letters like f, g, and h are used to designate these functions. The domain is the set of all possible values that can be passed into a function while it is specified. The term "range" refers to the whole set of values that the function's output is capable of producing. The co-domain is the set of possible values for a function's outputs.
put the value of x = -2 and x = 3 into the polynomials .
[tex]p(-2) = -7(-2)^{2} + 5(-2) + 9 = -7 \times 4 + (-10) + 9 = -28 + (-10) + 9 = -29\\p(3) = 3(3)^{3} - (3)^{2} + 2(3) - 5 = 3 \times 27 - 9 + 6 - 5 = 81 - 9 + 6 - 5 = 73\\So, for p(x) = -7x^{2} + 5x + 9, p(-2) = -29 $and$ p(3) = 73.\\For p(x) = 3x^3 - x^{2} + 2x - 5, p(-2) = -29 $and$ p(3) = 73.\\For p(x) = 3x^{3} - x^{2} + 2x - 5, p(-2) = -29 $and$ p(3) = 73.\\[/tex]
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In the diagram below, D E ‾ DE is parallel to A B ‾ AB . If D E DE is 5 5 less than D C DC, A C = 56 AC=56, and A B = 48 AB=48, find the length of D C ‾ DC . Figures are not necessarily drawn to scale. State your answer in simplest radical form, if necessary.
The length of line segment Dc is equal to 35 units.
How to determine the length of DC?In Mathematics, two geometric figures are considered to be congruent only when their corresponding side lengths are congruent and the magnitude of their angles are congruent.
Since side length DE is parallel to AB and side DE is 5 less than side length DC, we have the following:
DE = DC - 5
In Geometry, the corresponding side lengths of two similar geometric figures are proportionate and as such, we have the following:
DC/AC = DE/AB
DC/56 = DC - 5/48
48DC = 56(DC - 5)
48DC = 56DC - 280
56DC - 48DC = 280
8DC = 280
DC = 280/8
DC = 35 units.
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Solve the system of equations.
−
2
�
+
9
�
=
11
−
5
�
+
2
�
=
−
34
−2x+9y=11
−5x+2y=−34
Crissy took out an installment loan to pay for her new car. She borrowed $22500 for 40
months with a $6743.25 finance charge. Find her APR to the nearest hundredth of a
percent. Don't forget to include the percentage symbol (%).
O 16.91%
O 16.19%
O 19.16%
O 19.61%
The APR, given the finance charge, the amount borrowed, and the number of months, is b. 16. 19 %
How to find the APR?You can find the APR by using the RATE function on Spreadsheet.
The number of periods = 40 months
The Payment per month was:
= ( Loan amount + Finance charge )
= ( 22, 500 + 6, 743 .25 ) / 40 months
= $ 731.08125
The present value is the loan amount of $ 22, 500
The monthly rate is 1. 13456 %
The APR is:
= 1. 3456 x 12 %
= 16. 19 %
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If the mean of 6 numbers is 36, what is the 6th number if 5 of the numbers are 27, 42, 43, 45, and 35?
The sixth number in the data is 24.
What is mean of a data?Mean is an arithmetic average of the data set, and it can be calculated by dividing a sum of all the data points with the number of data points in the data.
Given that, the mean of 6 numbers is 36, we need to find the 6th number if 5 of the numbers are 27, 42, 43, 45, and 35
We know that,
Mean = (sum of observations) ÷ (total number of observations)
Let the sixth number be x,
Therefore,
36 = (27 + 42 + 43 + 45 + 35 + x) / 6
216 = 192 + x
x = 24
Hence, the sixth number in the data is 24.
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Solve for x in the equation 2x^2 + 5x - 3 = 0:
A) x = -3, 1/2
B) x = 1/2, -3
C) x = -1/2, 3
D) x = 3, -1/2
B)
Step-by-step explanation:To solve the equation 2x^2 + 5x - 3 = 0, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
Where a = 2, b = 5, and c = -3.
Plugging in the values, we get:
x = (-5 ± √(5^2 - 4 * 2 * -3)) / 2 * 2
x = (-5 ± √(25 + 24)) / 4
x = (-5 ± √49) / 4
x = (-5 ± 7) / 4
So, the two solutions are:
x = ( -5 + 7 ) / 4 = (2) / 4 = 1/2
x = ( -5 - 7 ) / 4 = (-12) / 4 = -3
So, the two solutions to the equation 2x^2 + 5x - 3 = 0 are x = 1/2 and x = -3.
Answer:
The answer is B) x = 1/2, -3.
Step-by-step explanation:
The equation 2x^2 + 5x - 3 = 0 can be solved using the quadratic formula, which states that the solutions to a quadratic equation of the form ax^2 + bx + c = 0 are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
where a, b, and c are the coefficients of the equation and ± represents both the positive and negative square root.
In this case, a = 2, b = 5, and c = -3. Plugging these values into the formula gives us:
x = (-5 ± √(5^2 - 4 * 2 * -3)) / (2 * 2)
x = (-5 ± √(25 + 24)) / 4
x = (-5 ± √(49)) / 4
x = (-5 ± 7) / 4
So the two solutions are:
x = (-5 + 7) / 4 = 2 / 4 = 1/2
x = (-5 - 7) / 4 = -12 / 4 = -3
Therefore, the solutions to the equation 2x^2 + 5x - 3 = 0 are x = 1/2 and x = -3, which corresponds to option B) x = 1/2, -3.
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Type the probability notation for chooing a car or a truck. Type the probability notation for chooing a plate and then a bowl. Would the following group of probabilitie be valid or not valid: 23%, 45%, 17%?
After her annual eye exam, Gianna will randomly elect a pair of contact from the baket containing 5 brown pair, 7 green pair, and 4 blue pair of colored contact. What i the probability that Gianna will randomly elect a brown pair or a green pair?
The probability that Gianna will randomly elect a brown pair or a green pair is 0.75 or 75%.
What is meant by probability notation?A practical technique to express the likelihood that an event will occur or not is through probability notation. When working with Venn diagrams, set notation is employed, and we use it to accomplish this.
Capital letters and various Greek characters are frequently used while notating events.
It is also possible to express probability as a percentage and it can only range from 0 to 1. The likelihood that event A will occur is frequently expressed as P (A) P(A) P(A)P, left parenthesis, A, right parenthesis.
The P(A/B) formula is written as P(A/B) = P(AB) / P(B), where the symbol denotes the intersection of events "A" and "B."
A basket containing 5 brown pair, 7 green pair, and 4 blue pair of coloured contacts. total pair of coloured contacts in basket =5+7+4=16
Gianna will randomly select,
P(a brown pair or green pair) =
[tex]\dfrac{\text{number of brown or green pair of colored contacts in basket}}{\text{total pair of colored contacts in basket}}[/tex]
= [tex]$\frac{5 + 7}{16}[/tex]
= [tex]$\frac{12}{16}[/tex]
= 3/4
= 0.75
Thus, the probability that Gianna will randomly elect a brown pair or a green pair is 0.75 or 75%.
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Part D Use the results from Parts B and C in the product rule of differentiation to find a simplified expression for the vertical velocity of the car, vy(t) = View Available Hint(s) vy(t) = Owyo'e-21 -yde (a cos(wt) +w sin(at)) cos(wt) sin(wt) yoe- (cos(wt)+aw cos(wt)) O ayo’e-20t -w cos(wt) sin(wt) Submit Previous Answers ✓ Correct In this example we used both the chain and product rules of differentiation to obtain an expression for the (vertical) velocity-time relationship for the car from its position-time relationship Part E Evaluate the numerical value of the vertical velocity of the car at time t = 0.25 s using the expression from Part D, where yo = 0.75 m, a=0.95 s-, and w = 6.3s-1 View Available Hint(s) μΑ ? (0.25 s) =
(0.25 s) = -1.8 m/s ,the numerical value of the vertical velocity of the car at time t = 0.25s, which was found to be -1.8m/s.
Part D:
In order to find the expression for the vertical velocity of the car, we need to use both the chain and product rules of differentiation. The chain rule states that if f(x) is a function of g(x), then the derivative of the function is equal to the derivative of g(x) multiplied by the derivative of f(x). The product rule states that if two functions, f(x) and g(x), are multiplied together, then the derivative of the product is equal to the derivative of f(x) multiplied by g(x) plus the derivative of g(x) multiplied by f(x).
Using the chain rule, we can find the derivative of the position-time equation:
y'(t) = yo'e-21 -yde (a cos(wt) + w sin(wt))
Using the product rule, we can find the derivative of the position-time equation:
v(t) = owyo'e-21 -yde (a cos(wt) + w sin(wt)) cos(wt) sin(wt) + yoe- (cos(wt) + aw cos(wt))
Simplifying the expression, we find:
v(t) = ayo'e-20t -w cos(wt) sin(wt)
Part E:
In order to evaluate the numerical value of the vertical velocity of the car at time t = 0.25s, we need to plug the given values for yo, a, and w into the expression for the vertical velocity.
Substituting the given values into the expression, we find:
v(0.25s) = 0.75e-20(-6.3)cos(6.3*0.25)sin(6.3*0.25)
Simplifying the expression, we find:
v(0.25s) = -1.8 m/s
In this example, we used the chain and product rules of differentiation to find the expression for the vertical velocity-time relationship for the car from its position-time relationship. We then used this expression to evaluate the numerical value of the vertical velocity of the car at time t = 0.25s, which was found to be -1.8m/s.
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Using the origin as the center of dilation and a scale factor of k=1/2, find the coordinates of the vertices of the image of the polygon below.
(Show Work PLEASE)
Answer:
A' (-2, -1.5)
B' (-2, 1.5)
C' (1, 1.5)
D' (1, -1.5)
Step-by-step explanation:
If you start at (0,0) and go to Point A, you go 4 to the left and down 2. Half of that is left 3 and down 1.5. That is where A' will go. Do the same thing to the other 3 points.
Exponential Functions
The amount of money left after 8 quarters is $3,547,878
How much of your original money will you have after 8 quarters?The theory used in this question is exponential decay, which describes how the value of a quantity decreases over time.
In this case, the value of the original investment decreases by 7% each quarter.
The steps for this process are as follows
Convert the percentage to a decimal. 7% = 0.07
Substitute the values into the equation: y = 5,000,000(1 - 0.07)t
Simplify the equation by multiplying the numbers in the parentheses: y = 5,000,000(0.93)t
Substitute the number of quarters into the equation: y = 5,000,000(0.93)8
Calculate the amount of money left after 8 quarters: y = 5,000,000(0.93)8 = 3,547,878
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Determine if the following statements are true or false. The magnitude of a vector can be different in different coordinate systems. It is possible to add a scalar to a vector. A 2D vector can have a magnitude equal to zero even when one of its components it nonzero. The direction of a vector can be different in different coordinate systems. A 2D vector can have a component equal to zero even when its magnitude is nonzero. The components of a vector can be different in different coordinate systems. It is possible to multiply a vector by a scalar. Determine if the following statements are true or false. Remember that for a mathematical statement to be true it must be true in all cases. If V_3 = V_1 + V_2, then V_4 = 3V_1 + 3V_2 is parallel to V_3. If V_3 = V_1 + V_2, then V_3 - V_2 is parallel to V_1. If V_3 = V_1 + V_2, then V_3 = V_1 + V_2. If V_3 = V_1 + V_2, then V_3 > V_1.
The statements given are mostly true, except for the statements that V_4 is parallel to V_3 and that V_3 is greater than V_1.
The magnitude of a vector can be different in different coordinate systems. True
It is possible to add a scalar to a vector. True
A 2D vector can have a magnitude equal to zero even when one of its components it nonzero. True
The direction of a vector can be different in different coordinate systems. True
A 2D vector can have a component equal to zero even when its magnitude is nonzero. True
The components of a vector can be different in different coordinate systems. True
It is possible to multiply a vector by a scalar. True
If V_3 = V_1 + V_2, then V_4 = 3V_1 + 3V_2 is parallel to V_3. False
If V_3 = V_1 + V_2, then V_3 - V_2 is parallel to V_1. True
If V_3 = V_1 + V_2, then V_3 = V_1 + V_2. True
If V_3 = V_1 + V_2, then V_3 > V_1. False
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what is this one ??
i have 4 more
Answer:
see below
Step-by-step explanation:
year 1
7000*(1+13%) = 7910
year 2
7910*(1+13%) =8940
How much would you need to depoit in an account now in order to have $20,000 in the account in 4 year? Aume the account earn 5% interet
The amount that is needed to be deposited is $15,609.61
According to the Question
The formula for the future value of an investment may be used to determine the amount that must be deposited today in order to have $20,000 in 4 years:
FV = PV * (1 + r)^n
Where:
FV = future value = $20,000
PV = present value = x
r = annual interest rate = 5%
n = number of years = 4
To solve for PV, rewrite the formula as follows:
PV = FV / (1 + r)^n
Putting the values:
x = $20,000 / (1 + 0.05)^4
⇒ x = $15,609.61
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The amount that is needed to be deposited is $15,609.61
According to the Question
The formula for the future value of an investment may be used to determine the amount that must be deposited today in order to have $20,000 in 4 years:
FV = PV * (1 + r)^n
Where:
FV = future value = $20,000
PV = present value = x
r = annual interest rate = 5%
n = number of years = 4
To solve for PV, rewrite the formula as follows:
PV = FV / (1 + r)^n
Putting the values:
x = $20,000 / (1 + 0.05)^4
⇒ x = $15,609.61
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how did we get value 0.0004?
Unfortunately, without more context about the origin of the value 0.0004, it is not possible to provide a detailed explanation of how it was obtained. The method for obtaining this value will depend on the context in which it is used.
For example, if 0.0004 is a decimal fraction, it may have been obtained by dividing a small number by a larger number. If it is a monetary amount, it may have been the result of a calculation involving currencies, exchange rates, or taxes. If it is a measurement of physical quantity, it may have been obtained using a scale, ruler, or other measuring device.
The value 0.0004 can have different meanings depending on the context in which it is used. For example, it could represent a decimal fraction, a monetary amount, or a measurement of physical quantity.
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Answer:
Step-by-step explanation:
Find the volume of this sphere.
Use 3 for
Volume of a sphere would be 6912.
What is Volume of this sphere ?
The volume of a sphere is calculated as V = 4/3πr^3, where V = volume and r is radius.
The fact that a sphere can be measured for its volume and surface area is due to the fact that it is a three-dimensional shape as opposed to a circle, which is a two-dimensional shape.
According to given question,
[tex]Volume\ of \ sphere=\frac{4}{3} \pi r^{3} \\\\Volume\ of \ sphere=\frac{4}{3} \pi 12^{3} \\\\Volume\ of \ sphere=\frac{4}{3} (3){1728}\\\\Volume\ of \ sphere=6912[/tex]
Hence, Volume of a sphere would be 6912.
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Samtech manufacturing purchased land and building for $4 million. In addition to the purchase price, samtech made the following expenditures in connection with the purchase of the land and building:.
The initial valuation of each asset Samtech acquired in transactions:
Value capitalized = $4,000,000 + $16,000 + $5,000 + $4,000
Value capitalized = $4,025,000
Assets Fair value Total percentage Proportional value
1.Land $3,300,000 75% $2,475,000
2.Building $1,100,000 25% $275,000
Total $4,400,000 100 % $2,750,000
Working Notes :
Land =($3,300,000 ÷ $4,400,000) =75%
Building =($1,100,000 ÷ $4,400,000) = 25%
Land Improvement =$82,000 + $40,000 =$122,000
2) The initial valuation of each asset assumes that immediately after acquisition that Samtech demolished the building:
Entries Amounts
1. Purchase cost $4,000,000
2. Add: Title insurance of $16,000
3. Add: Legal fees for drawing the contract $5,000
4. Add: State transfer fee of $4,000
5. Add: Demolition cost $250,000
6. Add: Cleaning and grading cost $86,000
7. Less: Salvage material $6,000
Total Cost of land $4,355,000
Land Improvement = $82,000 + $40,000 = $122,000
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The complete question is:
Samtech Manufacturing purchased land and building for $4 million. In addition to the purchase price, Samtech made the following expenditures in connection with the purchase of the land and building: Title insurance $ 16,000 Legal fees for drawing the contract 5,000 Pro-rated property taxes for the period after acquisition 36,000 State transfer fees 4,000 An independent appraisal estimated the fair values of the land and building if purchased separately, at $3.3 and $1.1 million, respectively. Shortly after the acquisition, Samtech spent $82,000 to construct a parking lot and $40,000 for landscaping. Required: 1. Determine the initial valuation of each asset Samtech acquired in these transactions. 2. Determine the initial valuation of each asset, assuming that immediately after acquisition, Samtech demolished the building. Demolition costs were $250,000 and the salvaged materials were sold for $6,000. In addition, Samtech spent $86,000 clearing and grading the land in preparation for the construction of a new building.
Each of the two congruent sides of an isosceles trapezoid measures 9 cm. The little base measures 11 cm less than the large base. The perimeter of this trapezoid is 43 cm. What is the measurement of the large base?
The length of the large base of the trapezoid is 18cm.
What is the measurement of the large base of the trapezoid?An isosceles trapezoid is simply a convex quadrilateral having a line of symmetry equally dividing one pair of opposite sides.
Given the data in the question
Let the large base be represented by 'x'
Large base = xLittle base = x - 11Each of the two congruent sides = 9cmPerimeter = 43The perimeter of the trapezoid is the sum of all the sides of all its sides.
Perimeter = side a + side b + side c + side d
Hence;
43 = x + ( x - 11 ) + 9 + 9
Solve for x
43 + x + x - 11 + 18
43 = 2x + 7
43 - 7 = 2x
36 = 2x
2x = 36
x = 36/2
x = 18
Hence;
Large base = x = 18cm.
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a tree is a graph with no cycle. show by induction that a tree with n nodes contains n −1 edges.
The statement holds for all positive integers n, and a tree with n nodes contains n-1 edges.
The statement can be proven by induction.
Base case: If a tree has one node, then it has no edges (n = 1, n-1 = 0).
Inductive step: Assume the statement is true for n = k (i.e. a tree with k nodes contains k-1 edges). We prove it is true for n = k+1.
Let T be a tree with k + 1 nodes, and let v be any node in T. Then, since T is a tree, v must have exactly one parent node and k-1 child nodes (or no child nodes at all). Let T' be the subtree of T rooted at v, which has k nodes. By the inductive hypothesis, T' has k-1 edges.
Since v has exactly one parent node, there is exactly one edge connecting it to its parent in T. Thus, T has k-1 + 1 = k edges, which means the statement holds for n = k + 1.
Therefore, by induction, the statement holds for all positive integers n, and a tree with n nodes contains n-1 edges.
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6 - 9b = - 10b - 4 =
Answer:
B = 10/19 it's a fraction btw
How to Evaluate the Expression in Algebra Calculator
you have to substitute a number for each variable and perform the arithmetic operations. In the example above, the variable x is equal to 6 since 6 + 6 = 12. If we know the value of our variables, we can replace the variables with their values and then evaluate the expression.
What is meant by arithmetic ?
The Father of Arithmetic is an Indian mathematician and astronomer by the name of Brahmagupta.The area of mathematics known as arithmetic deals with the study of numbers and the numerous operations that can be performed on them. Addition, subtraction, multiplication, and division are the fundamental mathematical operations.The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic. The difference between consecutive words is always minus five, hence the sequence 21, 16, 11, 6,... is also arithmetic.Since arithmetic is the most fundamental area of mathematics, it is crucial to learn and comprehend it thoroughly. Every other area of mathematics is impacted by arithmetic, which functions somewhat like the fundamental blocks for more challenging and sophisticated topics.To learn more about arithmetic refer to
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Porter is visiting india and would like to purchase some local spices. He finds some spices that cost 452. 95 rupees. If the current exchange rate is 1 dollar:73. 6500 rupees, how much do the spices cost in u. S. Dollars?.
The spices cost 6.15 in dollars. Porter is visiting India and bought species cost 6.15 dollars.
Here, these values are given, which is important for our solution,
So, after putting the values,
Porter bought species cost 452.95 rupees after visiting to India.
Current exchange rate = 1 dollar = 73.6500 rupees.
Here , 73.6500 rupees = 1 dollar
So, 1 rupee = 1/ 73. 6500 dollar
Then , 452. 95 rupees = 452. 95/ 73.6500 dollar.
After diving the rupees value by dollar values,
We get these values,
So, here, 452.95 rupees became 6.15 dollars.
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Answer: $6.15
Step-by-step explanation:
Porter bought species cost 452.95 rupees after visiting to India.Current exchange rate = 1 dollar = 73.6500 rupees.Here, 73.6500 rupees = 1 dollarSo, 1 rupee = 1/ 73. 6500 dollarThen, 452. 95 rupees = 452. 95/ 73.6500 dollar.After diving the rupees value by dollar values,We get these values,So, here, 452.95 rupees became 6.15 dollars.now imagine that you know the volume of the solid (v, measured in cm 3 ) and the length of two of the three sides, b and c (measured in cm). explain in words or with an equation how you can calculate the length of the remaining side, a.
If you know the volume of the solid and the length of two of the three sides, b and c the length of the remaining side, a can be calculated by putting this values in the formula of volume(height*breadth*length).
The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.
Various forms have various volumes. We have studied the several solids and forms that are specified in three dimensions, such as cubes, cuboids, cylinders, cones, etc., in 3D geometry. We will discover how to find the volume for each of these shapes.
Volume = a× b× c
a = V / b×c
Cubic units are used to quantify a solid's volume. For instance, the volume will be given in cubic metres if the dimensions are given in metres. The International System of Units uses this as the reference unit for volume (SI). Cubic metres, cubic feet, cubic inches, etc. are additional volume units.
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simplify:6(y^2)^2(x^-2y)^-1 /3x^-3 y^5
What are the four important properties of a parallelogram?
Answer:
see below
Step-by-step explanation:
Opposite sides are congruent (AB = DC).
Opposite angels are congruent (D = B).
Consecutive angles are supplementary (A + D = 180°).
If one angle is right, then all angles are right.
The four properties of parallelogram are:
i) Opposite sides are parallel & equal.
ii) Sum of adjacent interior angles is 180°
iii) Opposite angles are equal.
iv) Diagonals bisect each other.
What is an parallelogram?The quadrilateral with two pairs of parallel sides is known as a parallelogram. Equal in length and width on both sides is required. Four vertices make up a parallelogram, which also has four edges.
A parallelogram is a two-dimensional (2D) shape that has two matching pairs of opposite sides that are parallel and equal in length. The angles inside the two sides of the shape must add up to 180 degrees, which means that all of the angles must add up to 360 degrees.
A rectangle that has been pushed over slightly is all that a parallelogram really is. Because of this, finding the area of a parallelogram can be done using the same formula as finding the area of a rectangle.
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find the equation of the tangent line to the graph of the function f(x)=(x2 9)(x−4) at the point (1,−30) .
The point-slope formula can be used to get the equation of the tangent line to the graph of the function f(x)=(x2 - 9)(x - 4) at the point (1, -30).
To get the slope at the position (1, -30), first take the derivative of the function:
f'(x) = (x2 - 9) (x2 - 9)
(x - 4)' = 2x - 9/x - 4
Check the derivative at x = 1 now:
f'(1) = 2(1) - 9/(1) - 4 = -93
The line has a -93 slope.
Now, enter the point-slope formula the point (1, -30) and the slope (-93):
y - (-30) = -93(x - 1) (x - 1)
If we simplify, we get:
y = -93x + 22
As a result, y = -93x + 22 is the equation of the tangent line to the graph of the function f(x)=(x2 - 9)(x - 4) at the point (1, -30).
The point-slope formula can be used to get the equation of the tangent line to the graph of the function f(x)=(x2 - 9)(x - 4) at the point (1, -30). According to the point-slope formula, the equation of the line is y - y1 = m for a given point (x1, y1) and slope (m) (x - x1). The specified point in this instance is (1, -30), and the slope of the line may be calculated by calculating the function's derivative and evaluating it at x = 1. The derivative of the function f(x) is 2x - 9/x - 4, which for x = 1 translates to -93. When the point and slope are entered into the point-slope equation, we obtain the result y - (-30) = -93(x - 1), which is abbreviated to y = -93x + 22. As a result, y = -93x + 22 is the equation of the tangent line to the graph of the function f(x)=(x2 - 9)(x - 4) at the point (1, -30).
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HELP ME
how do i do this. im terrifingly confused
find an equation of the sphere with center (-5, -3, 0) and radius 1
Equation of the sphere with center (-5, -3, 0) and radius 1 is (x + 5)² + (y + 3)² + z² = 1.
The Sphere is what?All points on a sphere are at a set distance from the centre, making it a three-dimensional geometric object. It is thought to be one of the most basic three-dimensional shapes and is a perfect circle.
Both a circle and a sphere are round, if you compare them. The fact that we can measure the volume and area of a sphere is due to the fact that a sphere is three-dimensional as opposed to a circle, which is a two-dimensional shape.
It is possible to formulate the equation for a sphere with centre (h, k, l) and radius r as follows:
(x - h)² + (y - k)² + (z - l)² = r²
Using the given center (-5, -3, 0) and radius 1, we can write the equation of the sphere as:
(x + 5)² + (y + 3)² + (z)² = 1²
which simplifies to:
(x + 5)² + (y + 3)² + z² = 1.
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How to find the zeros of a function?
The zeros of a function can be obtained by factor method, by solving equation or on a graph.
What are zeros of a function?
The values of x for which a function f(x) becomes zero, or f(x)=0, are known as the zeros of the function.
There are 3 different ways by which we can find zeros of a function.
The 3 ways are:
1. By factor method
In order to use this strategy, we must first identify a function's factors. The roots of a function are then obtained by equating the factors with zero.
2. By solving an equation
In some functions, it can be challenging to identify the factors directly. In these situations, we first create an equation by equating the polynomial function with zero. The equation is then resolved. A function's roots are the roots of an equation.
3. On a graph
This is the simplest method for locating a function's zeros. With this approach, we must identify the point at which a function's graph touches or cuts the x-axis (i.e., the x-intercept). The zeros of a function are the locations where the graph cuts or touches the x-axis.
Hence, by these ways we can find the zeros of a function.
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