Answer:
Step-by-step explanation:
The investment below is compounded semi-annually, while an investment of the same principal at the same rate compounded annually would have interest compounded once per year.
The formula for compound interest is A = P(1 + r/n)^nt where A is the final amount, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded per year and t is the number of years.
In the case of the semi-annual investment:
A = 9000(1 + 0.04/2)^(2*15) = $21,831.62
In the case of the annual investment:
A = 9000(1 + 0.04)^15 = $21,812.30
As we can see, the semi-annual investment yields a slightly larger return than the annual investment, $19.32 more. Compounding interest more frequently results in a larger return due to the interest earning interest.
1. A community garden has an area of 10 square yards. The community wants to divide it into plots that each
have an area of 1/2 square yard. How many plots can the garden be split into?
The garden can split into 20 plots.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
A community garden has an area of 10 square yards.
The community wants to divide it into plots that each have an area of 1/2 square yard.
The number of community garden,
= 10/(1/2)
= 20
Therefore, the number of required plots is 20.
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Nachelle decides to estimate the volume of a grapefruit by modeling it as a sphere. She measures its diameter as 11.4 cm. Find the grapefruit's volume in cubic centimeters. Round your answer to the nearest tenth if necessary.
The grapefruit's volume in cubic centimeters to the nearest tenth is equal to 775.8 cubic centimeters.
How to calculate the volume of a sphere?Mathematically, the volume of a sphere can be calculated by using this mathematical expression:
Volume = 4/3 × πr³
Where:
r represents the radius.
Based on the information provided about the grapefruit, the diameter of the sphere is given by;
Diameter of sphere = 11.4 cm
Radius = diameter/2 = 11.4/2 = 5.7 cm.
Substituting the given points into the volume of a sphere formula, we have the following;
Volume of sphere = 4/3 × 3.142 × 5.7³
Volume of sphere = 775.8 cubic centimeters.
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Mrs moth picked 24 flowers.Six of them each had 9 petals,7 of them had 8 petals, 5 of them each had 3 petals, and the rest had 10 petals.How many flowers had 10 petals?
Using the subtraction operation, the number of flowers with 10 petals that Mrs. Moth picked was 6.
What is a subtraction operation?A subtraction operation is one of the four basic mathematical operations, including addition, division, and multiplication.
The subtraction operation involves the minuend, the subtrahend, and the difference.
The minuend is the number or value being subtracted from by the subtrahend. The result of a subtraction operation is known as the difference.
The total number of picked flowers = 24
The number of flowers with 9 petals = 6
The number of flowers with 8 petals = 7
The number of flowers with 3 petals = 5
The total number of flowers identified = 18 (6 + 7 + 5)
The number of flowers with 10 petals = x
x = 24 - 18
= 6
Thus, 6 flowers had 10 petals out of the 24 Mrs. Moth picked.
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Please answer this question
The weighted average for A,B and C will be 0.333.
What is weighted average?
Weighted average is a mean calculated by giving values in a data set more influence according to some attribute of the data. It is an important section in CAT quantitative aptitude. Weighted average is an average in which each quantity to be averaged is assigned a weight, and these weightings determine the relative importance of each quantity on the average. Weightings are the equivalent of having that many like items with the same value involved in the average.
Now,
Given weight for A=0.5, B=0.1 and C=0.4
Weighted average=(A+B+C)/3
=(0.5+0.1+0.4)/3
=1/3
Weighted average=0.33
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Which expression is equivalent to 5.25×+1246x
Answer:
The expression "5.25x + 1246x" is equivalent to "1771x"
Question 1 (5 points) Match the correct definition to each word or term. a number that will be used in a function rule to determine the value of the output a relation in which each input has only one ouput the result of applying a function rule to the value of an input the set of possible outputs; dependent variable the set of allowable inputs: independent variable 1. Input 2. Output 3. Domain 4. Range 5. Function
The correct description of each function term is given as follows:
1. Input: A rule to determine the value of the output.
2. Output: The result of applying a function rule to the value of an input, and is the dependent variable.
3. Domain: the set of allowable inputs.
4. Range: The set of possible outputs.
5. Function: A relation in which each input has only one output.
What is a function?A function has the notation y = f(x), in which.
x is the input.y is the output.Hence the input is applied to the function to obtain the output, and these concepts, along with domain and range, are presented in this problem.
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When calculating simple interest, what must you do if you want to invest for months or weeks instead of years? a. Simple interest only pays yearly, so you should find another investment. b. The simple interest calculation does not use those units, so you should just calculate as normal. c. The units have changed, so the interest formula switches to I·t=P·r. d. Interest rates are annual, so you must convert the units into years. Please select the best answer from the choices provided A B C D
When calculating simple interest, if we want to invest for months or weeks instead of years we must convert the interest rate units into years.
Option D is the correct answer
What is simple interest?It is the interest calculated on the principal at a given rate for a time period.
We have,
The formula for simple interest.
SI = PRT/100
P = principa
R = rate
T = time
Now,
Time is in years when we are calculating the simple interest.
Example:
If time is in months.
T = 4 months
T = 4/12 = 1/3 years.
Thus,
We must convert the units into years.
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Which of these is a way to show that two figures are congruent
If two figures can be mapped onto one another or if all pairings of angles and side lengths are congruent, the figures are said to be congruent.
What is Triangle?
A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.
What is the condition to be congruent?
If two triangles are the same size and shape, they are said to be congruent. To establish that two triangles are congruent, not all six matching elements of either triangle must be located. There are five requirements for two triangles to be congruent, according to studies and trials. The congruence properties are SSS, SAS, ASA, AAS, and RHS.
Both triangles are said to be congruent if the three angles and three sides of one triangle match the corresponding angles and sides of the other triangle.
In Δ PQR and ΔXYZ, as shown in figure,
we can identify that PQ = XY, PR = XZ,
and QR = YZ
and ∠P = ∠X,
∠Q = ∠Y and ∠R = ∠Z.
Then we can say that Δ PQR ≅ ΔXYZ.
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Find the least positive integer m such that m^2 −m+11 is a product of at least four not necessarily distinct primes.
The least positive integer is m=132.
m(m−1)+11=N
It is clear that N must be odd and that can be divisible by the prime 11.
However, the following congruences have no solution as it is easy to prove directly by checking the few possibilities with m(m−1) not divisible by 3,5 and 7 respectively
{m(m-1)+2=0(mod 3)
{m(m-1)+1=0(mod 5)
{m(m-1)+4=0(mod 7)
Thus N=∏ with pi≥11
A necessary condition is that (solving the quadratic in m)
√4N-43=x² and from this, we need that
N≡1,3,7(mod10)
By chance, we find the minimum N=113⋅13 which corresponds to m=132
and that could have been calculated by direct trials but the next solution seems to be far from 132.
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A quadrilateral has diagonal that are perpendicular but not congruent
A quadrilateral has diagonals that are perpendicular but not congruent
is a rhombus.
What is a rhombus?A quadrilateral with all equal sides is a rhombus. Rhombuses are a particular kind of parallelogram in which all of the sides are equal since the opposite sides of a parallelogram are equal.
From the properties of a rhombus, we know,
A rhombus has an equal number of sides. In this case, ABCD equals DA.
At an angle of 90° divides each of the diagonals. In this instance, diagonals AC and BD split at a 90° angle.
A rhombus has parallel opposite sides. In this case, AB || CD and AD || BC.
In a rhombus, the opposite angles are equal. ∠A = ∠C, while ∠B = ∠D.
The sum of adjacent angles is 180°.
Diagonals of a rhombus bisect each other at the right angles but they are not congruent.
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Solve the equation. 3x^2-4y-2=0 please help.
The solution for the equation 3x²-4x-2=0 is 1.72076 and 0.387426.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
3x²-4x-2=0
Now, solving the above Quadratic Equation
D= √b² - 4ac
From the given equation
a= 3, b-4, c=-2
Then, D= √(-4)² - 4(3)(-2)
D= √16 +24
D = √40
Now, x= (-b ±D)/ 2a
x= -(-4) ± √40/ (6)
x= 4+ √40/6 or x= 4-√40/6
x = 1.72076 or x=−0.387426
Hence, the value of x is 1.72076 and 0.387426.
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A picture measures 60 cm by 30 cm. The mat around the picture is 6 cm wide.
Find the area of the mat.
Answer:
1224 cm²
Step-by-step explanation:
The picture is a rectangle with length 60 cm and width 30 cm.
area of rectangle = length × width
area of picture = 60 cm × 30 cm = 1800 cm²
Now we add the mat to the picture. The width of the mat is 6 cm, so when you add mat to two opposite sides, the total length of the picture and mat becomes 60 cm + 6 cm + 6 cm = 72 cm. When you add mat to the other two opposite sides, the total width of the picture and mat becomes 30 cm + 6 cm + 6 cm = 42 cm. Now we have a rectangle 72 cm by 42 cm.
area of picture and mat = 72 cm × 42 cm = 3024 cm²
The area of the mat is the difference in area between the picture with mat and the picture without mat.
area of mat = 3024 cm² - 1800 cm² = 1224 cm²
3) A mechanism used to encrypt and decrypt data
a) Data flow
b)Algorithm
c) cryptography
d)None of these
Answer:
c) cryptography
Step-by-step explanation:
Cryptography is a mechanism used to encrypt and decrypt data.
Debt payments of $2,100 and $1,950 are due in six months and nine months, respectively. What single payment is required to settle both debts in one month? Assume a simple interest rate of 6.30% p.a. and use one month from now as the focal date.
The single payment that is required to settle both debts is given as follows:
$3,897.9.
How to obtain the balance?The balance of an account after t years, using simple interest, that is, a single compounding per year, is given by the equation presented as follows:
A(t) = P(1 + rt).
In which:
P is the principal.r is the rate, as a decimal.t is the time, in years.For the $2,100 payment in 6 months = 0.5 years, the principal is obtained as follows:
(1 + 0.5 x 0.063) P = 2100
P = 2100/(1 + 0.5 x 0.063)
P = $2,035.88.
For the $1,950 payment in 9 months = 0.75 years, the principal is obtained as follows:
(1 + 0.75 x 0.063) P = 1950
P = 1950/(1 + 0.75 x 0.063)
P = $1,862.02.
Hence the single payment is obtained as follows:
2035.88 + 1862.02 = $3,897.9.
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Describe the possible lengths of the third side of the triangle given that the lengths of the other two sides are 5 inches and 12 inches.
The possible length of the third side of a triangle, say x, with the other two sides are 5 inches and 12 inches. is
7 ≥ x ≥ 17
How to determine the possible length of third sideThe length of the third side is within the range of
sum of the two sidesdifference of the two sidesThe sum of the two ides is the highest possible length of the third side
= 12 inches + 5 inches
= 17 inches
The difference of the two ides is the lowest possible length of the third side
= 12 inches - 5 inches
= 7 inches
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Use differences to find a pattern in the sequence.
2,9,22,45,82,137,214
Assuming that the pattern continues, the eighth term should be.
If the sequence be 2, 9, 22, 45, 82, 137, 214 then the pattern be 6, 13, 23, 37, 55, 77.
What is meant by sequence ?The term "patterns" describes common, repeatable sorts of practices or regulations. To forecast what has happened or what might happen, patterns are helpful. come following a group of integers that are ordered specifically. Sequence describes this grouping of numbers.
Putting events or information in a precise order is referred to as sequencing. Higher-order thinking abilities—such as those for detecting patterns, figuring out causes and effects, and more—are necessary for sequencing. Sequencing aids students in both understanding and organizing the material they have learnt and in problem-solving.
Let the given sequence be 2, 9, 22, 45, 82, 137, 214
The differences to a pattern in the sequence be
= 9 - 2, 22 - 9, 45 - 22, 82 - 45, 137 - 82, 214 - 137
= 6, 13, 23, 37, 55, 77
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Below is the seating chart of 50 students in a STP226 class. You are tasked with selecting a sample of 5 students from the class in order to accurately estimate the average Exam 1 score for the entire class.
Front Desk
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Post
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
Post
Door
1) Considering the STP 226 class seating chart above, suppose you randomly selected a student from each row: students in seats 3, 18, 21, 34, and 50 were selected for your sample.
a) What was the sampling method used?
b) Is this sample going to be representative or do you see any issues with the sample? Answer briefly.
The sampling method used in this case is random sampling and the sample is representative.
What is a sample and what makes a sample to be representative?A sample is a small proportion of individuals taken from the general population to be studied. For a sample to be representative it is expected that all the individuals represent the population, for example, if the population includes people of different ages the sample should include this too.
Is the sample representative?The random sample selected is representative because the seats of the students selected are distributed within the class rather than in only one row or line.
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PLEASE DONT IGNORE :( I NEED HELP THIS IS DUE IN A COUPLE MINUTES
Lines AB, BC, and AC have an equal slope, with a slope value of 2/3.
What is a Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
Given a line AC that has an x-intercept of "2"
Since,
AB is part of line AC thus the slope of AB will be the same as the slope of line AC and the Slope of line BC.
For the slope of line AB:
Since there is no Additional data given on the problem we will assume that every square is a unit square in the graph
Thus, Coordinates of A = (-5, -2)
Since Point B is the x-intercept of line AB thus its coordinates = (-2, 0)
from the formula of the slope of a line:
m = (y₂ -y₁)/(x₂ - x₁)
Thus, the slope of line AB:
m = (0+2)/-2 +5)
m = 2/3
therefore, the slope of the line AB, BC, and AC are equal and the value of the slope is 2/3.
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what size bands would result from cutting the following plasmid using hind iii, eagi and smai? the plasmid has a total of 5541 base pairs
The size of the bands that would result from cutting the plasmid with Hind III, Eco RI and Sma I would be 5530
The size of bands resulting from cutting a plasmid with Hind III, EagI and SmaI can be determined using the following formula:
Size of Band = Plasmid Size - (Hind III + EagI + SmaI)
The size of the bands that would result from cutting the plasmid with Hind III, Eco RI and Sma I can be calculated using the following formula:
For this example, the plasmid has a size of 5541 base pairs. After cutting with Hind III, EagI and SmaI, the size of the bands will be:
Size of Band = 5541 - (6 + 4 + 4)
Size of Band = 5527 base pairs
Band size = Total base pairs - [size of sites (Hind III + Eco RI + Sma I)] + 1
In this case, the band size would be calculated as follows:
Band size = 5541 - (6 + 6 + 4) + 1
Band size = 5530 bp
Therefore, the size of the bands that would result from cutting the plasmid with Hind III, Eco RI and Sma I would be 5530
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Complete question:
What size bands would result from cutting the following plasmid using Hind III, EcoRI and SmaI? The plasmid has a total of 5541 base pairs.
Find the inverse of y=2x²+3x+5
According to the given information in the question the inverse of y=2x²+3x+5 is x = (y - 5 - 3x)/2.
What does the math term "inverse" mean?Inverse operations, such as subtraction and addition multiplication and division, are pairs of mathematical operations where one operation reverses the effect of the other. The opposite of a number, or "inverse," is what is meant by the phrase. i.e., x - 1 = 1 / x.
Does inverse imply a negative value?Negative correlation and inverse relationships are interchangeable terms. Any two or more variables that consistently move in the opposing directions can be described by both. The outcome of measuring an inverse association will result in a negative sign.
To find the inverse of a function, you first need to switch the x and y variables, and then solve for y.
So, the inverse of y=2x²+3x+5 is x = (y - 5 - 3x)/2
Note that the inverse of a function is only possible if the function is a one-to-one function.
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What is the circumference of the circle? Use 3.14 for π.
circle with a segment drawn from the center of the circle to a point on the circle labeled 4 inches
A. 157.75 inches
B. 50.24 inches
C. 25.12 inches
D. 12.56 inches
Answer:
C. 25.12 inches
Step-by-step explanation:
radius = 4 inches
circumference = 2πr
circumference = 2 × 3.14 × 4 inches
circumference = 25.12 inches
Answer:c is correct 25.12
Step-by-step explanation:
a significant number of accidents are caused by vehicle equipment failure such as the following except:
A significant number of accidents are caused by vehicle equipment failure such as the following except Operative lights.
Operative lights are also called Surgical lights which are medical equipment devices used to illuminate the operating field during surgery.
Surgical lights are referred to by many names: Operating lights, OR lights, operating room lights, surgical lamps, and surgical light heads.
The primary function of surgical lighting is to illuminate the operative site on and/or within a patient for ideal visualization by OR staff during a surgical procedure.
With proper lighting, operating room staff can achieve a higher level of efficacy during surgery and reduce the risk of complications.
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a 5 ich photo was enlarged to make a poster as shown. if the dimensions of the poster are (x^2 - 6) inches by (x^ + 12) inches, what is the area of the poster
The dimensions of the poster are given as (x^2 - 6) inches by (x^2 + 12) inches.
The area of the poster is given by the product of these two dimensions:
Area = (x^2 - 6) inches * (x^2 + 12) inches
Area = x^4 - 6x^2 + 12x^2 - 72
Area = x^4 + 6x^2 - 72 inches^2
So, the area of the poster is x^4 + 6x^2 - 72 inches^2.
How to solve (2n+7)=(3n+3)
Answer:
n = 4
Step-by-step explanation:
Let's put all of our variables on one side, and all of our non-variable numbers on the other. (I like to do this so that the variable isn't negative. You'll still get the same answer.)
So we can minus 2n on both sides, giving us 7 = n + 3.
Then, let's do our non-variables and subtract 3 from each side. This gives us 4 = n or n = 4.
Therefore, n = 4.
Sine/Cosine of Complementary Angles Solve for x
In a right triangle, sin (8x-9) = cos (x+6) Solve for X Round your answer to the nearest tenth
Using complementary angles, the value of x = 10.3
What are complementary angles?Complementary angles are angles in which the sum add up to 90°.
How to find the value of x in the given right triangle?Since in a right triangle, sin(8x - 9) = cos(x + 6). To solve the problem, we proceed as follows.
sin(8x - 9) = cos(x + 6).
Given that cosФ = sin(90 - Ф), we have that
cos(x + 6) = sin[90 - (x + 6)]
So, susbstituting this into the equation, we have that
sin(8x - 9) = cos(x + 6)
sin(8x - 9) = sin[90 - (x + 6)]
This implies that
8x - 9 = 90 - (x + 6)
8x - 9 = 90 - x - 6
8x - 9 = 84 - x
Adding x to both sides of the equation, we have
8x + x - 9 = 84 - x + x
9x - 9 = 84 + 0
9x - 9 = 84
Adding 9 to both sides of the equation, we have that
9x - 9 + 9 = 84 + 9
9x + 0 = 93
9x = 93
x = 93/9
x = 10.33
x ≅ 10.3
So, the value of x = 10.3
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help me please asap!!
Answer:
The length of the longer ladder is 36ft
Step-by-step explanation:
30ft/10ft = 3
12ft x 3 = 36ft
Another way to solve this is by cross multiplying
[tex]\frac{10}{12}[/tex] = [tex]\frac{30}{x}[/tex]
10x = 360
x = 36ft
Consider the graph of the function f(x) shown above. It consists of two line segments, an arc of a semi-circle centered at (-4,0) with radius 3, and an arc of a quarter-circle centered at (1,0) with radius 2. Find the value of [tex]\int\limits^4_ {-7} \, f(x) dx[/tex]
The value of the integral is given as follows:
C. -7π/2.
How to obtain the result of the integral?The result of the integral is given by the total area of the figure.
From x = -7 to x = -1, the figure is a semi-circle of radius 3, below the y-axis, hence it's area is given as follows:
A1 = -0.5π x 3²
A1 = -4.5π.
From x = -1 to x = 1, with the line, the figure is a right triangle with sides 2 and 2, hence the area is given as follows:
A2 = 0.5 x 2 x 2
A2 = 2.
From x = 1 to x = 3, the figure is quarter circle with radius 2, hence the area is given as follows:
A3 = 0.25π x 2²
A3 = π.
From x = 3 to x = 4, the figure is a right triangle with sides 1 and 4, below the y-axis, hence the area is given as follows:
A4 = 0.5 x 1 x 4
A4 = -2.
Hence the total area, representing the integral, is given as follows:
A = A1 + A2 + A3 + A4
A = -4.5π + 2 + π - 2
A = -3.5π
A = -7π/2.
(the result of the integral is negative but the area is positive).
Meaning that the correct option is given by option C.
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Factor the expression using the GCF.
49 - 28 = ?
By calculating, The GCF of the given numbers 49 and 28 is 7.
What is Algebraic expression ?
An algebraic expression is an expression that consists of numbers, variables and operators such as addition, subtraction, multiplication and division. These expressions can be used to solve equations and other mathematical problems. Algebraic expressions can also be used to represent relationships between different variables. For example, the expression 4x + 2y can be used to represent the relationship between two variables, x and y.
So lets first find the prime factorization of 28
prime factorization of 28 = 2 × 2 × 7
So lets first find the prime factorization of 49
prime factorization of 49 = 7 × 7
To find the GCF, multiply all the prime factors common to both numbers:
Therefore, The GCF of the given numbers 49 and 28 is 7.
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What is the value or x?
Answer:
x = 25
Step-by-step explanation:
Since the given triangle is a right triangle and we are also given two sides which are opposite (height) = 24 units and adjacent (base ) = 7 units. We can apply the Pythagoras Theorem where:
[tex]\displaystyle{\text{opposite}^2 + \text{adjacent}^2 = \text{hypotenuse}^2}[/tex]
In simpler words, it is:
[tex]\displaystyle{\text{height}^2 + \text{base}^2 = \text{slope}^2}[/tex]
Substitute in given values:
[tex]\displaystyle{24^2+7^2=x^2}[/tex]
Evaluate and solve for x:
[tex]\displaystyle{576+49=x^2}\\\\\displaystyle{625=x^2}\\\\\displaystyle{\sqrt{625}=\sqrt{x^2}}\\\\\displaystyle{\pm \sqrt{625}=x}\\\\\displaystyle{\pm 25=x}[/tex]
However, x is a length value and length's value cannot be negative so x can only be 25.
Hence, x = 25 units
find the slope of a line perpendicular to the line whose equation is2x+3y=-3 . Fully simply your answer.
3/2 is a slope of a line perpendicular to the line whose equation of
2x+3y=-3 .
What is meant by perpendicular ?One specific example of the more broad mathematical concept of orthogonality is the concept of perpendicularity, which is the orthogonality of traditional geometric objects.
As a result, in higher mathematics, the term "perpendicular" is occasionally used to represent considerably more intricate geometric orthogonality criteria, like the relationship between a surface and its normal vector.
If two lines cross at a right angle, they are said to be perpendicular to one another.
A first line is explicitly said to be perpendicular to a second line if the two lines meet and the straight angle on one side of the first line is cut by the second line into two congruent angles at the point of junction.
This can be done by rearranging the equation into the slope intercept form.
2x +3y = -3
3y = -2x -3
y = -2/3x - 1
Thus, the slope of the given line is -2/3.
The slope of the perpendicular line is the negative reciprocal of the given line.
Slope of perpendicular line = 3/2
The slope-intercept form was:
(i) The reciprocal of m is 1/m.
(ii) The negative reciprocal of m is -1/m.
Negative reciprocal of -2/3
= -1 ÷ (- 2/3)
= -1 × (-3/2)
= 3/2
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