Answer:
27
Step-by-step explanation:
If this is a right angle triangle, we will do this.
45^2 - 36^2 =
√729 = 27
Therefore, the missing leg = 27
Hope that helps!
What is the vertex form of a line
The vertex form of line f(x) = ax² + bx + c is y = a(x - h)² + k where the vertex is (h, k).
What is the vertex form of a line and what is its formula?The vertex form of a line is one of the representations of the line in an equation format. Here the line focused on the coordinates of the vertex.
For a line, f(x) = ax² + bx + c, the vertex form is y = a(x - h)² + k; vertex at (h, k).
To convert the general form to the vertex form, the general equation is simplified as below:
y = ax² + bx + c
= ax² + bx + c + b²/4a - b²/4a
= a(x² + b²/4a² + b/a) + (c - b²/4a)
= a(x² + (b/2a)² + 2b/2a) + (c - b²/4a)
= a(x + b/2a)² + (c - b²/4a)
⇒ y = a(x - (-b/2a))² + (c - b²/4a)
Consider -b/2a = h and (c - b²/4a) = k, then we get
y = a(x -h)² + k; vertex form of the given line.
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How do you find the degree of a polynomial step by step?
Put the polynomial in conventional form. Count the number of terms in the polynomial. The degree of the polynomial is one more than the number of terms.
Begin by writing the polynomial in standard form. This means that the terms should be written in descending order of degree, with the coefficient of the leading term being positive. Make sure that each term is separated by a plus or minus sign.Count the number of terms in the polynomial. Include the constant term, even if it is equal to zero.The degree of the polynomial is one more than the number of terms. For example, if the polynomial has two terms, its degree is three. If the polynomial has three terms, its degree is four.If the polynomial has an exponent that is not a whole number, it is called a rational polynomial. The degree of a rational polynomial is equal to the degree of the numerator of the rational expression. If the polynomial has a negative exponent, it is called an inverse polynomial. The degree of an inverse polynomial is equal to the negative of the exponent. If the polynomial is a combination of rational and inverse polynomials, the degree is equal to the highest
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in how many ways can two representatives be picked so that one is a mathematics major and the other is a computer science major?
There probability two ways to pick two representatives with one majoring in mathematics and the other majoring in computer science.
In order to pick two representatives with one majoring in mathematics and the other majoring in computer science, there are two approaches that can be taken. The first approach is to pick one representative who majors in mathematics first, then the second representative who majors in computer science. The second approach is to pick one representative who majors in computer science first, then the second representative who majors in mathematics. Both of these approaches would yield two representatives, one with a mathematics major and the other with a computer science major. It is important to note that whichever approach is taken, both representatives must be chosen from the same pool of potential representatives. Thus, the pool of potential representatives should be large enough to encompass both mathematics and computer science majors in order to successfully pick two representatives with one majoring in mathematics and the other majoring in computer science.
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Sanjay needs 9090 meters of fence to surround a rectangular garden. The length of the garden is three times its width, ww. Which of these equations give the correct formula for the perimeter?.
Sanjay needs 90 meters of fence to surround a rectangular garden. The length of the garden is three times its width, w.
What is an equation in maths?
An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.
Given that we have all the equations set up, we need to solve for W.
1.) w+3w=90
4w=90
w=22.5
2.) w+3w+w+3w=90
8w=90
w=11.25
3.) 2*w+2*3w=90
2w+6w=90
8w=90
w=11.25
4.) 2*(3w+w)=90
6w+2w=90
8w=90
w=11.25
Now, out of all those which one was different?
A. (w+3w=90)
This equation did not match with all the others is (w+3w = 90)
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what is the product of -8x^7 and -2xy^3
Answer:
16x^8y^3
Step-by-step explanation:
Simplify the expression.
Answer:
[tex]-8x^7(-2xy^3) = 16x^8y^3[/tex]
Step-by-step explanation:
⭐Multiplication rules
negative * negative = positivenegative * positive = negativepositive * positive = positive⭐ Exponent multiplication rule
[tex]a^n * a^m = a^{n+m}[/tex]⭐ Multiplying two terms with variables
multiply the coefficients (the numbers next to the variables) and the variablesWe need to utilize these 3 key points (⭐) when multiplying to terms with variables.
First, let's multiply the coefficients:
-8 * -2 = 16
negative * negative = positiveNext, let's multiply the variables:
[tex]x^7 * xy^3[/tex]
These two variables have the same base (x), so we will add their exponents up.
* remember: if you see a variable without an exponent, it has an exponent of 1 *
[tex]x^7 * x = x^8[/tex]
[tex]a^n * a^m = a^{n+m}[/tex]The variable [tex]y^3[/tex] will stay the same because there is no other y variable.
= [tex]x^8y^3[/tex]
Now, "attach" the variables to the product of the coefficients:
= [tex]16x^8y^3[/tex]
what is the value of the limit [tex]\lim_{x \to \5} \sqrt{x^{2}+4 }[/tex]
Answer:
Refer to the attached photo.
Step-by-step explanation:
How do you write a geometric function?
A geometric sequence is an exponential function. Instead of y=ax, we write an=crn where r is the common ratio and c is a constant (not the first term of the sequence, however). A recursive definition, since each term is found by multiplying the previous term by the common ratio, ak+1=ak * r.
Geometric function theory is the study of geometric properties of analytic functions. A fundamental result in the theory is the Riemann mapping theorem.
There are many shapes in geometry based on their dimensions. Circle, Triangle, Square, Rectangle, Kite, Trapezium, Parallelogram, Rhombus and different types of polygons are the 2-d shapes. Cube, Cuboid, Sphere, Cone and Cylinder are the basic three-dimensional shapes.
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Which type of polynomial is 3x3?
Answer:
3x3 is a cubic polynomial
Step-by-step explanation:
Since the highest degree of exponent in 3x3 is 3, the polynomial is a cubic polynomial.
... Hope this helped! Have a wonderful New Year!
Points a, b, and c are collinear. If bc = 8. 5 and ac = 13. 2, select all possible values of ab.
Chen rode his skateboard 3 3/4 miles in 3/4 of an hour. What was his average speed in miles per hour?
A 2 13/16
B 4
C 4 1/2
D 5
The average speed of Chen when skating is 5 miles per hour
How to determine the average speed of Chen ?From the question, we have the following parameters that can be used in our computation:
Time = 3/4 of an hour
Distance covered = 3 3/4 miles
The average speed can be calculated using the following equation
Average speed = Distance covered/Time
Substitute the known values in the above equation, so, we have the following representation
Average speed = (3 3/4)/(3/4)
Evaluate the quotient
Average speed = 5
Hence, the average speed is 5 miles per hour
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Consider the functions f(x) = 23x + 5 and g(x) = 32x + 7. what do the slopes indicate about the lines?
As per the given function, the line of the functions has the same intersecting point (-0.2, 0).
The term function in math refers a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Here we have the consider the functions f(x) = 23x + 5 and g(x) = 32x + 7.
And we need to find the slopes indicate about the lines.
While we looking into the given functions,
f(x) = 23x + 5
g(x) = 32x + 7
Now, we have to identified that the slope of the function f(x) is 23 and the slope of the function g(x) is 32.
And now we have to apply some sample values on the function, then we get the following table of values.
And by using the table we have to plot the graph then we get the graph like the following.
Through graph we have identified that both functions has the same intersecting point (-0.2, 0).
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How do you find the height of a pyramid if you know the length and slant height?
The height of pyramid if the length and slant height is known is . h² = S² - (x/2)².
Define the term height of a pyramid?The perpendicular distance between a pyramid's base and apex determines the pyramid's height. The altitude of the pyramid is the length of the line that extends from the base to the apex and is perpendicular to the base.We can employ the Pythagoras theorem to accomplish this as the triangle is right-angled and is created by the slant height (s), its altitude (h), and 1⁄2 of side length of a base (x/2).
As a result, (x/2)² + h² = s².
We can utilize this while figuring out how to find the pyramid's volume given the slant height.
h² = S² - (x/2)²
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What are the factors of x³ 4x² x 6?
The factors of x³ 4x² x 6 are (1) x³, (2) 4x², (3) x and (4) 6. These factors are the numbers that can be multiplied together to give x³ 4x² x 6 as the product.
To find the factors of x³ 4x² x 6, we must first expand the expression. x³ 4x² x 6 can be expanded to x³ x x 4x² x 6, which can be further simplified to x³ + 4x² + 6. The factors of this expression are the numbers that can be multiplied together to give x³ 4x² x 6 as the product. In this case, the factors are (1) x³, (2) 4x², (3) x, and (4) 6. In other words, x³ 4x² x 6 can be written as (x³)(4x²)(x)(6). Understanding the factors of an expression is an important skill in algebra, as it can help you simplify and solve equations.
The factors of x³ 4x² x 6 can be calculated by factoring the expression:
x³ 4x² x 6 = (x³)(4x²)(x)(6)
This can be further simplified to:
x³ 4x² x 6 = x⁴ (4x²)(6)
Therefore, the factors of
x³ 4x² x 6 are (1) x³, (2) 4x², (3) x, and (4) 6.
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given JK || MN and L is the midpoint of JM proven JKL = MNL
The triangle JKL is similar to triangle MNL by AA similarity and all three sides of the triangle are equal, so JKL = MNL.
What is the triangle?One of the fundamental shapes in geometry is represented by the symbol Δ and consists of three connected vertices. Any one of a triangle's three sides can serve as its base, however typically the bottom side is used.
Given:
JK || MN and L is the midpoint of JM,
As the line JK || MN then,
∠ MNL = ∠ JKL (The alternate angle of the parallel line are equal)
∠ LMN = ∠ LJK (The alternate angle of the parallel line are equal)
∠ JLK = ∠ NLM (The corresponding angle of the parallel line are equal)
Thus, all the sides will also be equal as the angles are equal.
Hence, the area will also be equal.
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How do you solve three consecutive numbers?
The solution of three consecutive numbers is the addition of one more value to a base number.
For example, the solution of three consecutive numbers of 5 is 6, 7, 8.
What are consecutive numbers?Consecutive numbers are those numerical values that are found just after a specific number or value, for example consecutive numbers from 5 will be 6 onwards.
When we want to find the consecutive numbers of a base number we only have to do a sum, which we can express in the following way:
Cn = N + n
Cn : Consecutive numberN : Base numbern : Position of the consecutive numberExample:
N = 5
Three consecutive numbers are:
n= 1, 2, 3
Cn = 5 + 1 = 6Cn = 5 + 2 = 7Cn = 5 + 3 = 8Learn more about consecutive numbers in:
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help me out on this
The standard form of the complex number is respectively 2√3 i - 15 + √300 i,4 - 7 i, and -14 + 9 i.
What is a complex number?Complex numbers are helpful in finding the square root of negative numbers.
A complex number is the sum of a real number and an imaginary number.
(a)
As per the given, 2√-3 - 15 + √-300
Since, √-1 = i thus,
2√3 i - 15 + √300 i
(b)
As per the given, (15 - 10i)/(2 + i)
By rationalization,
(15 - 10i)/(2 + i) x (2 - i)/(2 - i)
⇒ (30 - 15 i - 20 i + 10 i²)/(2² - i²)
⇒ (30 - 10 - 35 i)/(4 + 1)
⇒ 4 - 7 i
(c)
As per the given, 3(2 + i) - 4(5 - 2i)
⇒ 6 + 3i - 20 + 8i
⇒ -14 + 9 i
Hence "The complex number has the following conventional forms: 2√3 i - 15 + √300 i,4 - 7 i, and -14 + 9 i".
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he cost of a parking permit consists of a one-time administration fee plus a monthly fee. A permit purchased for 12 months costs $660. A permit purchased for 15 months costs $810.
What is the administration fee?
$50
$54
$55
$60
The one-time administration fee is (d) $60
How to determine the administration fee?From the question, we have the following parameters that can be used in our computation:
12 months costs $660.
15 months costs $810.
This means that
(x, y) = (12, 660) and (15, 810)
For the one-time administration fee, we have
(x, y) = (0, y)
So, we calculate the slope using
slope = (y₂ - y₁)/(x₂ - x₁)
So, we have
(y - 660)/(0 - 12) = (810 - 660)/(15 - 12)
This gives
(660 - y)/12 = 50
So, we have
660 - y=600
This gives
y = 60
Hence, the administration fee is $60
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if 10 people appear at random to give blood, what is the probability that at least 1 of them is a universal donor
Probability that at least one of them is a universal donar is 0.5263.
What is probability ?
What is probability explain?
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
Have given,
Probability of getting a universal donor is 0.072.
X be the “random variable” which “describes the number of universal donors” in the “sample of 10 people”.
X follows a “binomial distribution” with n=10 and p=0.072
P(X=x) = ([tex]{n}C^{x}[/tex])*([tex]p^{x}[/tex])*([tex]q^{n-x}[/tex]) ; x=1(1)10 ; q=1-p
Required probability,
P(X≥1)= 1 - P(X=0)
= 1 - (10C0)*([tex]0.072^{0}[/tex])*([tex]0.928^{10}[/tex])
= 1 - 0.4737 = 0.5263
Probability that at least one of them is a universal donar is 0.5263.
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Graph the line. 2x+y=8
Answer:
Step-by-step explanation:
put it into the y=mx+c equation
y=-2x+8
therefore th y intercept is at (0,8)
and the gradient in -2
Select all the true statements.if vertical angles are congruent, then two lines cut by a transversal are parallel. if two parallel lines are cut by a transversal, then corresponding angles are congruent. if two parallel lines are cut by a transversal, then alternate interior angles are congruent. points on a perpendicular bisector of a line segment are equidistant from the segment’s endpoints. points on a perpendicular bisector of a line segment are never equidistant from the segment’s endpoints.
By the property of alternate interior angles, Option (1) is the correct statement.
∠XWY ≅ ∠ZYW
Property of the alternate angles states, if two parallel lines are cut by a transversal, then the alternate angles are congruent.
By this property,
Lines XW and YZ are the parallel lines intersected by a transversal WY.
Here, ∠XWY and ∠ZYW represent the interior angles between the parallel lines and the transversal.
Therefore, interior alternate angles ∠XWY and ∠ZYW will be congruent.
Hence, Option (1) will be the correct option.
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The Abubakar family household uses 850 kWh of electricity per month (kWh stands for Kilowatt hour, a measure of electricity usage). They want to decrease their electricity usage, so they begin to decrease their usage by 25 kWh per month. The equation y = –25x + 850 can be used to model this scenario.
How many kWh of electricity will they be using 12 months after they've started doing this?
Answer:
550 kWh
Step-by-step explanation:
To find the number of kilowatt hours of electricity the Abubakar family will be using 12 months after they've started decreasing their usage, we can substitute 12 for x in the equation y = –25x + 850. This gives us y = –25 * 12 + 850 = –300 + 850 = 550.
Therefore, the Abubakar family will be using 550 kilowatt hours of electricity 12 months after they've started decreasing their usage.
A windowpane is 63 inches tall and the diagonal distance from one corner to the other is 65 inches. How wide is the windowpane?
Answer:
16 inches
Step-by-step explanation:
Using the Pythagorean theorem, the distance is [tex]\sqrt{65^2-63^2}=16[/tex].
a ball of radius 17 has a round hole of radius 3 drilled through its center. find the volume of the resulting solid.
Refer to the photo taken.
Find dy/dx for the function y=3x^0
Answer:0
Step-by-step explanation:
So this is an exponential equation. And the dy/dx is impossible because anything time 0 is 0. So there is no Rise over run, most commonly known as your slope.
Option. A ) 0 is correct
It is given that,y = 3x⁰ = 3
we have asked to differentiate the function y with respect to x.
for constants, the slope is always zero and the graph looks like a line parallel to the x-axis
[tex]dy/dx[/tex] = 0
therefore, the differentiation of y=3 is 0.
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Find the solution to the following system by substitution.
y=-2x-3
y = 3x + 12
O A. (-1/2, 3/)
O B. (3,21)
O
C. (-3,3)
о
D. (-3,-9)
What is mode maths example?
The mode for a particular set of observations is 5 since it occurs the majority of the time.
What is mode?The mode formula is described in statistics as the formula for calculating the mode of a given collection of data. The value that occurs most frequently in a particular set is referred to as the mode, and the mode differs across grouped and ungrouped data sets. The mode may be calculated quite easily. Put all of the numbers in a given set in order, either lowest to highest or highest to lowest, and then count how many times each number appears in the set. The mode is the one that appears the most.
Here,
given set of observation:
5, 7, 8, 5, 7, 6, 9, 5, 10, 6
Mode is the number which occurs the highest time.
So here 5 occurs the highest times(3 times).
So,5 is the mode.
The mode for given set of observation is 5 as it occurs most time.
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What is the slope of 3x y =- 12?
The slope of the given straight line equation 3x+y=-12 is m=-3.
How slope can be find on graph?Finding the change in values divided by the change in values will reveal the slope between two places. As long as the line is linear, you can really use any two locations along the line to get the slope (straight line). An easy approach to do it is to use the end points since they are provided.
What are four types of slope?Negative, positive, zero and undefined are four types of slope.
The equation is given as:
3x+y= -12
Separate y we get:
y= -3x-12
This is a straight line equation and we can compare it with y=mx+c where m is the slope.
Upon comparison with general equation slope m=-3.
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What is the difference between a figure also called a pre-image and an image?
The image is the final appearance of a figure after a transformation operation. The pre-image is the original appearance of a figure in a transformation operation.
What is transformation?A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's final shape and location.
Preimages are the original, unaltered shapes, and images are the new (transformed) shapes. To put it another way, a transformation is a process that maps a preimage onto an image.
Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's final shape and location.
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A snail travels 15m in 3000 seconds. What is the snail's average speed?
Answer:
the snail was going 0.005m/second
Step-by-step explanation:
15m/3000
(c) what is the average rate of change of the inductor's energy between t = 0.0 and t = 1.0 s?
The average rate of change of the inductor's energy between t = 0.0 to t = 1 .0 is 6
The term circuit in defined as an inductor and a resistor is called an RL-circuit here the inductor resists any current change in the circuit and the resistor dissipates energy, then the resulting in the exponential decay of current if no current or voltage source is present.
Here we need to calculate the average rate of change for the inductor's energy,
Here we know that the values of t1 = 0, and t2 = 1
Similarly, here we know the value of flow of current as f(t1) = 12 and f(t2) = 18.
Now, the average rate of change is calculated as
=> [18 - 12]/1 - 0
When we simplify the expression, then we get,
=> 6/1
=> 6
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