The equation of line passing through (-4, -16) and (5, 2) are y = 2x – 8, y - 2 = 2(x - 5) and y + 16 = 2(x + 4)
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.
The standard form for linear equation is:
y = mx + b
Where m is the slope and b is the y intercept
The equation of line passing through (5, 2) and (-4, -16) is:
y - 2 = [(-16-2)/(-4-5)](x - 5)
y - 2 = 2(x - 5)
y = 2x - 8
y + 16 = 2(x + 4)
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4. Find the length of a cylinder of volume 2 litres and radius 10 cm.
5. Find the radius of a cylinder of volume 45 cm³ and length 4 cm.
Remember 1
length of a cylinder of volume 2 litres and radius 10 cm is 0.0064cm and the radius of a cylinder of volume 45 cm³ and length 4 cm is 1.8928cm.
PART A
Volume of Cylinder = 2 Litres
Radius of cylinder = r = 10 cm
We need to find the length of a cylinder .
We know , Volume of Cylinder = π[tex]r^{2} h\\[/tex]
On substituting the values of Volume of Cylinder and r , we get
2 = π( [tex]10^{2}[/tex])h
h = 2 / 100π = 0.0064 cm
Here h = length of a cylinder
The length of a cylinder is 0.0064cm .
PART B
radius of a cylinder = r
volume of cylinder = 45 cm³
length of cylinder = h = 4 cm
Volume of Cylinder = π[tex]r^{2} h\\[/tex]
45 = 3.14 [tex]r^{2}[/tex] (4)
[tex]r^{2}[/tex] = 3.5828
r = 1.8928
Radius of a cylinder is 1.8928cm.
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Question 1 options:
Is the relation in this set of points a function?
{(-2, 6) , (4, 5) , (3, -3) , (6, 9), (4, -4)}
State whether the statement is true of false.
1. The relation is a function.
2. An element from the domain is paired with more than one element from the range.
Answer:
1.4 Relations and Functions
A relation is a correspondence between two sets. If x and y are two
elements in these sets and if a relation exists between x and y, then x
corresponds to y, or y depends on x.
DEFINITION OF A FUNCTION:
Let X and Y two nonempty sets. A function from X into Y is a relation that
associates with each element of X, exactly one element of Y.
However, an element of Y may have more than one elements of X
associated with it.
That is for each ordered pair (x,y), there is exactly one y value for each x,
but there may be multiple x values for each y. The variable x is called the
independent variable (also sometimes called the argument of the
function), and the variable y is called dependent variable (also
sometimes called the image of the function.) x = y2 is not a function from X into Y, because there
is not exactly one y value for each x.
Solving for y, you get y =
which means there are two possible values for y
Step-by-step explanation:
Statistics
Does the frequency distribution appear to have a normal distribution using a strict interpretation of the relevant criteria?
Speed-- Number of cars
0-29 4
30-59 16
60-89 60
90-119 20
No, the distribution is not symmetric THIS ONE
No, the frequency do not increase from the low frequency to a maximum frequency
Yes, all the requirements are met
Answer:
The answer to your question is: B
Explanation:
based on the statistics given, this answer best fits the Queston.
Find the missing integer that makes the following addition statement true.
+ 3 = 2+3=2
The missing integer that makes the following addition statement true is -1.
What is the commutative law of addition?The commutative law of addition is also known as the law of cumulative addition and it states that when two numbers are added together, then, the outcome is equal to the addition of their interchanged position because addition is considered as a binary operation.
Mathematically, the commutative law of addition can be represented using the following formula:
A + B = B + A.
What is an integer?An integer can be defined as a whole number that may either be positive, negative, or zero such as -1, 0, 1, 2, 3, etc.
Now, we would determine the missing number:
x + 3 = 2
x = 2 - 3
x = -1.
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Complete Question:
Find the missing integer that makes the following addition statement true.
+ 3 = 2
Hi, I need to send you the question as I have written
recall the formula for velocity, which involves distance and time:
velocity = distance / time
since the woman's velocity is: 4.5 Km/h, then in order to cover 10 km, we need to find the time in the equation:
4.5 km/h = 10 km / t
multiply both sides by the time (t)
4.5 * t = 10
divide both sides by 4.5 in order to isolate t completely
t = 10 / 4.5
then
t = 2 hours and 0.2222 hours which can be translated into minutes by multiplying this by 60: 40/3 = 13 minutes and 0.33333 minutes. which can be converted into seconds by multiplying it by 60: 20 seconds
Then she will cover that distance in 2 hours, 13 minutes and 20 seconds.
solve for x
8x=4x−32
Answer:
[tex]x = - 8[/tex]
Step-by-step explanation:
[tex]8x = 4x - 32 \\ 8x - 4x = - 32 \\ 4x = - 32 \\ x = - 8[/tex]
Convert the following phrase into a mathematical expression use x as the variable combine like terms when possible A number multiplied by -8 subtracted from the sum of 8 and two times the number
ANSWER:
[tex]-8x-(8+2x)[/tex]STEP-BY-STEP EXPLANATION:
We must convert the following statement "A number multiplied by -8 subtracted from the sum of 8 and two times the number" into a mathematical expression.
We know that "a number" would be x.
Therefore:
[tex]-8x-(8+2x)[/tex]Please help, you also need to explain your reasoning
The value of x that makes m parallel to n is 90 degrees.
The value of x that makes m and n parallel is 15.
How to find the angles in parallel lines?
When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, vertically opposite angles etc.
The value of x that makes the line ma and n parallel can be calculated as follows:
180 - x = x (alternate exterior angle)
180 = 2x
x = 180 / 2
x = 90 degrees
2.
3x - 15 + 150 = 180(supplementary angles)
3x = 180 - 150 + 15
3x = 45
x = 45 / 3
x = 15
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given: P(A) = 0.45, P(B) = 0.65, and P(A and B) = 0.35.
Find:
P (A or B)
P(A OR B) ( line on top)
P(A|B)
P(B|A)
Answer:
P(A or B) = 0.75P(A or B)' = 0.25P(A|B) = 0.54P(B|A) = 0.78Step-by-step explanation:
Normally we use the symbols U for set union corresponding to or and ∩ for set intersection corresponding to and.
But here i will use and and or
By the rules of probability
P(A or B) = P(A) + P(B) - P( A and B)
So P(A or b ) = 0.45 + 0.65 - 0.35 = 0.75
The complement of a set A is all the elements not in A
P(A') = 1 - P(A)
If we denote the complement of a set A as A' then your second expression is asking What is the complement of A or B or P(A or B)'
P(A and B)' = 1 - P(A or B) = 1- 0.75 = 0.25
P(A|B) = P(A and B)/P(B) = 0.35/0.65 = 0.54
P(B|A) = P(A and B)/P(A) = 0.35/0.45 = 0.78
The set of all numbers greater than or equal to -10 and less than 9
The The set of all numbers greater than or equal to -10 and less than 9 will be -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, and 8.
How to illustrate the information?It should be noted that from the information, we are to find the set of all numbers greater than or equal to -10 and less than 9.
This simply means the numbers from -10 to 8.
Therefore, the numbers will be -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, and 8.
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The heights of 10 year old children has a normal probability distribution with mean of 54.6 inches and standard deviation of 5.7 inches. What is the approximate probability that a randomly selected 10-year old child will be more than 51.75 inches tall?
The approximate probability that a randomly selected 10-year-old child will be more than 51.75 inches tall is 0.6915.
How to calculate the probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. From the information, the heights of 10-year-old children have a normal probability distribution with a mean of 54.6 inches and standard deviation of 5.7 inches.
Based on this, the probability that a randomly selected 10-year old child will be more than 51.75 inches tall will be:
P(X > 51.75)
= P(Z > [(number - mean) / standard deviation)]
= P(Z > [(51.75 - 54.6) / 5.7)]
= P(Z > -0.5)
= 1 - P(Z = -0.5)
This will be looked at in the z table.
= 1 - 0.3805
= 0.6915
Therefore, the probability is 0.6915.
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What is the largest five-digit multiple of 15 whose digits are all distinct and nonzero?
The largest five-digit multiple of 15 whose digits are all distinct and nonzero is 12345.
How can we express numbers belonging to decimal numeral system?Suppose that the number is abcd.efg and belongs to the decimal numerical system. Remember one thing that the place on the left of decimal point is called ones. Move one-one places to right, and divide by 10 and 10 more and more. Move one-one places to left, and multiply (un-divide) by 10 and 10 more and more. We will call d as ones digit, c as tens digit (it get multiplied by 10), b as hundreds digit etc.
WE need to find the five-digit multiple of 15 whose digits are all distinct and nonzero.
Thus, we can see that the largest five-digit multiple of 15 could be ;
12345
Since it must be all distinct and nonzero. so the correct digit is 12345.
Hence, the largest five-digit multiple of 15 whose digits are all distinct and nonzero is 12345.
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Which of the following is equivalent to −4(2x + 3y) − 6(3q + 7p)?
ill give coins or whatever its called...
Answer: −8x − 12y − 18q − 42p
Step-by-step explanation:
i did the exam xD
Match the polar equations to their rectangular forms-
Applying the rules for the polar equations, the correct pairs are given in the image at the end of the answer.
What are polar equations?
The most well known polar equation rules are given as follows:
For the first pair, when x = 2, we have that:
rcos(θ) = 2.
r = 2/cos(θ)
r = 2 sec(θ), as one divided by the cosine is the secant.
For the second pair, we have that:
x² + y² = 36.
x² + y² = r², hence:
r² = 36
r = 6.
For the third pair, we have that:
x² + y² = 2y
r² = 2rsin(θ).
r²/r = 2sin(θ).
r = 2sin(θ).
For the fourth pair, we have that:
[tex]x = \sqrt{3}y[/tex]
[tex]\frac{y}{x} = \frac{1}{\sqrt{3}}[/tex]
[tex]\frac{y}{x} = \frac{\sqrt{3}}{3}[/tex]
Then the angle theta is given as follows:
θ = arctan(sqrt(3)/3) = pi/6.
For the fifth pair, we have an angle in which the sine and the cosine are equal, hence this angle is of 45º = pi/4.
The image at the end of the answer shows all the matched pairs.
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What is the slope of the line that passes through the points (10, 4)(10,4) and (7, 3)(7,3)? Write your answer in simplest form.
The slope of the line that passes through points (10,4) and (7, 3) is 1/3
Here we are dealing with a slope of a line where a slope of a line is the change in the y coordinate with regard to the change in the x coordinate. If P(x1,y1) and Q(x2,y2) are the two points on a straight line, at that point the slope formula is given by:
m = Change in y-coordinates/Change in x-coordinates
m = (y₂– y₁)/(x₂ – x₁)
Since we are given two points (10,4) and (7, 3), where x₁ and x₂ are 10, 7 whereas y₁ and y₂ are 4, 3
From the formula we get,
m = (y₂-y₁)/(x₂-x₁)
= ( 3-4)/(7 - 10)
= -1/-3
=1/3
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The table below shows the probability distribution of a random variable Z. Z P(Z) -13 0.69-12 0.18 -11 0.04 -10 0.01 -9 0.01 -8 0.04 -7 0.03 What is the expected value of Z? Write your answer as a decimal.
To be able to get the expected value of Z, we will be using the following formula:
[tex]\text{ Expected Value = }\mu=Z_1P_1+Z_2P_2+Z_3P_3\text{ + }\ldots Z_nP_n[/tex]We get,
[tex]\text{ Expected Value = }\mu=Z_1P_1+Z_2P_2+Z_3P_3\text{ + }\ldots Z_nP_n[/tex][tex]\text{ = (-13)(0.69) + (-12)(0.18) + (-11)(0.04) + (-10)(0.01) + (-9)(0.01) + (-8)(0.04) + (-7)(0.03)}[/tex][tex]\text{ = (-8.97) + (-2.16) + (-0.44) + (-0.1) + (-0.09) + }(-0.32)\text{ + (-0.21)}[/tex][tex]\text{ = -8.97 - 2.16 - 0.44 - 0.1 - 0.09 }-0.32\text{ - 0.21}[/tex][tex]\text{ Expected Value = }\mu\text{ = -12.29}[/tex]Therefore, the expected value of Z is -12.29.
3000 for 2 years at 2% compounded quarterly
Based on the given parameters, the amount of the investment after 2 years is $3123
How to determine the amount?The given parameters about the compound interest are
Principal Amount, P = $3000
Interest Rate, R = 2%
Time, t = 2
Number of times, n = 4 i.e quarterly
Compound interests are different from simple interest, and they are calculated using the following compound interest formula
CI = P(1 + R/n)^nt - P
To calculate the amount, we have:
A = P + CI
So, the equation becomes
A = P + P(1 + R/n)^nt - P
Evaluate the like terms
A = P(1 + R/n)^nt
Substitute the known values in the above equation
A = 3000 * (1 + 2%/4)^(2 * 4)
Express 2% as decimal
A = 3000 * (1 + 0.02/4)^(2 * 4)
Evaluate the sum
A = 3000 * (1.005)^8
Evaluate the exponent
A = 3000 * 1.041
Evaluate the product
A = 3123
Hence, the value of the investment is $3123
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Directions: write an appropriate equation for the given graph using your knowledge of parent functions and (h,k)
The parent functions are defined with all coefficients with value 1.
They can be linear, quadratic, cubic, absolute, reciprocal, exponential, logarithmic, square root, sine, cosine, tangent...
Then we can pick a function and transform it in order to include the point (-1,5) in the function definition.
We will use the quadratic parent function:
[tex]y=x^2[/tex]We will adjust the coefficient a of the quadratic function in order to include (-1,5)
[tex]\begin{gathered} y=a\cdot x^2 \\ 5=a(-1)^2=a \\ a=5 \end{gathered}[/tex]Then, our transformed function is:
[tex]y=5a^2[/tex]
Geometry help please
Given
A right angle triangle is removed from the rectangle to create the shaded region.
That is,
To find: The area of the shaded region.
Explanation:
It is given that,
That implies,
The area of the shaded region is,
[tex]\begin{gathered} Area\text{ }of\text{ }the\text{ }shaded\text{ }region=Area\text{ }of\text{ }the\text{ }rectangle-Area\text{ }of\text{ }the\text{ }triangle \\ =l\times b-\frac{1}{2}\times b\times h \\ =5\times9-\frac{1}{2}\times4\times3 \\ =45-6 \\ =39ft^2 \end{gathered}[/tex]Hence, the area of the shaded region is 39ft^2.
which value of a make the solution of the equation 3(2x-4) = 4(ax-2)
The value of a that makes the solution of the equation is 1/2.
Given,
The equation: 3(2x - 4) = 4(ax - 2)
Solve,
3(2x - 4) = 4(ax - 2),
Open the bracket and multiply:
6x - 12 = 4ax - 8
Add 12 to both sides
6x -12 + 12 = 4ax + 12 - 8
We get,
6x = 4ax + 4
Add - 4ax to both sides:
6x - 4ax = 4ax - 4ax + 4
We get,
6x - 4ax = 4
Take x = 1
Then,
6 × 1 - 4a × 1 = 4
6 - 4a = 4
Now,
Add - 6 to both sides
6 - 6 - 4a = 4 - 6
We get,
-4a = -2
That is,
4a = 2
a = 2/4 = 1/2
That is,
The value of a that makes the solution of the equation is 1/2.
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Evalúe the limit. Show steps
After evaluating the limit we have came to find that the limit of [tex]\lim_{x\rightarrow -\infty }\frac{x^2}{x^2\ +4}[/tex] as x approaches ∞- is 1
What is limit?The value that a function, sequence, or index approaches as an input, or an index, approaches a particular value is known as a limit in mathematics. Limits, which are essential to calculus and mathematical analysis, are required by the definitions of continuity, derivatives, and integrals.
In addition to being closely related to the concepts of limit and direct limit in category theory, the idea of a limit of a sequence is further generalised to encompass the idea of a limit of a topological network.
A limit of a function is typically expressed in formulas as
[tex]{\displaystyle \lim _{x\to c}f(x)=L,}[/tex]
To find the limit we will use L'Hôpital's Rule
Find the derivative
⇒ [tex]\lim_{x\rightarrow -\infty }\frac{x^2}{x^2\ +4}[/tex]
⇒ [tex]\lim_{x\rightarrow -\infty }\frac{2x}{2x +0}[/tex]
⇒ [tex]\lim_{x\rightarrow -\infty }\frac{2x}{2x }[/tex]
Evalue -∞ as x
⇒ [tex]\frac{2(-\infty)}{2(-\infty)} }[/tex]
⇒ 1
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A contractor hired 150 workers to pave 30 miles of highway how many workers will they need to hire to pave 20 miles of highway in the same amount of time?
Answer: 100
Step-by-step explanation:
First, we need to know how many workers must be hired to pave one mile.
Which is 5 workers per 1 mile ( 150 / 30 )
Then you can either do
(5 + 5 +5 +5 + 5) + (5 + 5 +5 +5 + 5) + (5 + 5 +5 +5 + 5) + (5 + 5 +5 +5 + 5)
OR
5 x 20 = 100
( if I'm wrong it's like 3 am so I'm a bit slow but I hope I helped )
create an inequality expression with square root 8 and square root 16/2 thats shows how they compare
We are given the following two numbers to compare
[tex]\sqrt[]{8}\quad and\quad \frac{\sqrt[]{16}}{2}[/tex]Let us simplify them
[tex]\begin{gathered} \frac{\sqrt[]{16}}{2}=\frac{4}{2}=2\quad (\text{this is smaller)} \\ \sqrt[]{8}=2.828\quad (\text{this is greater)} \end{gathered}[/tex]So, we can compare them as
[tex]\sqrt[]{8}>\frac{\sqrt[]{16}}{2}[/tex]The quantity on the left side is greater than the quantity on the right side.
It cost Angel $6.75 to send 75 text messages. How much does it cost to send one text?
To know how much each message sent costs, knowing that 75 messages cost $6.75, we only have to divide the cost of the total of 75 text messages by the total number of the cost of the message,
So that:
$ 6.75 ➗75 text message = 0.09 $/text messagesWe say, that the cost of each text message is $0.09.
A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out the maximum amount of profit the company can make, to the nearest dollar. y = -x² + 64x - 292
Answer:
what
Step-by-step explanation:
i think maybe like… actually
Graph the compound function
Use the drawing tools to form the correct answer on the number line
Graph the solution set to this inequality.
-2(x + 6) > -4x
Answer:
Step-by-step explanation:
Answer:
x > 6 with an open point
Hope this helps!
Step-by-step explanation:
-2 ( x + 6 ) > -4x
-2x - 12 > -4x
-(-4x) - 2x > -(-12)
4x - 2x > 12
2x > 12
x > 6
Consider the function f(x) = -2/3x +5.
What is ƒ ( − 1/2 ) ?
After substituting x = -1/2 in f(x), the value of the function f(-1/2) is found to be 5.333.
What exactly is function?A function from a set X to a set Y assigns exactly one element of Y to each element of X.
What is the function's domain and codomain?The set X is known as the function's domain, and the set Y is known as the function's codomain.
The given function is f(x) = -2/3x +5.
To obtain f(-1/2), we must substitute the value of x with -(1/2).
f(x) = -2/3x +5
f(-1/2) = -2/3×(-1/2) + 5
f(-1/2) = (2/6) + 5
f(-1/2) = 0.333 + 5
∴ f(-1/2) = 5.3333
Therefore, the value of the function f(-1/2) obtained after substituting x = -1/2 is 5.333.
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10 less than the quotient of a number and 2 is -18"
The representation of the expression is x/2 - 10 = -18
How to translate the algebraic expression?The mathematical statement is given as
"10 less than the quotient of a number and 2 is -18"
In expressions, quotient mean divide i.e. /
So, we have the following representation
"10 less than the quotient of a number and 2 is -18" ⇒ 10 less than a number/2 is -18"
Let the number be x
So, we have
"10 less than the quotient of a number and 2 is -18" ⇒ 10 less than x/2 is -18"
Less than as used here means minus
So, we have
"10 less than the quotient of a number and 2 is -18" ⇒ x/2 - 10 is -18
Rewrite as
"10 less than the quotient of a number and 2 is -18" ⇒ x/2 - 10 = -18
Hence, the expression represented by "10 less than the quotient of a number and 2 is -18" is x/2 - 10 = -18
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To pay for a $22,800car, Mai made a down payment of $3,800and took out a loan for the rest. On the loan, she paid monthly payments of $420for 4 years. (a) What was the total amount Mai ended up paying for the car (including the down payment and monthly payments)? (b) How much interest did Mai pay on the loan?
1. The total amount that was paid for the car will be $23960.
2. The interest that Mai pay on the loan will be $1160.
How to calculate the value?1. From the information, in order to pay for a $22,800 car, Mai made a down payment of $3,800 and took out a loan for the rest and on the loan, she paid monthly payments of $420for 4 years.
The total amount that was paid for the car will be:
= $3800 + ($420 × 4 years)
= $3800 + ($420 × 48)
= $3800 + $20160
= $23960
2. The interest that Mai pay on the loan will be:
= $23960 - $22800
= $1160
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