Answer:
√85
Step-by-step explanation:
a² + b² = c²
6² + b² = 11²
36 + b² = 121
b² = 121 - 36
b² = 85
b = √85
Answer:
Hello! The answer is \(b = \sqrt{85}\).
Step-by-step explanation:
To solve this question, we have to use the Pythagorean theorem. We are given one of the legs and the hypotenuse. (The hypotenuse is opposite the right angle).
a^2 and b^2 represent our legs while c^2 represents the hypotenuse.
We have to substitute our values in for a^2 and c^2:
6^2 + b^2 = 11^2
This leaves us with 36 + b^2 = 121
To get b^2 by itself, we have to subtract 36 from both sides:
36 + b^2 = 121
-36 -36
This leaves us with b^2 = 85
To get just b, we have to take the square root:
√b^2 = √85
This leaves us with \(b = \sqrt{85}\).
Question 10 of 10
If you know the circumference of a circle, which step(s) can you follow to find
its radius?
O
A. Divide by 2, then multiply by .
B. Divide by .
C. Divide by 2.
D. Divide by , then divide by 2.
Answer: Divide by \(\pi\), then divide it by 2
Step-by-step explanation:
Circumference formula: \(\pi\)*(r*2)
\(\pi\)*(r*2)/\(\pi\)=r*2
(r*2)/2=r
So, divide by exactly pi (or 3.14), then divide by 2. DON'T divide by 2 first, then pi because you won't end up with the same answer.
Find the slope & y-intercept of the equation y = -2x + 3. slope = y-intercept
Answer:
slope: -2, y-intercept: 3
Step-by-step explanation:
The question already gives you the answer. y=mx+b, so the slope is -2 and the y-intercept is 3.
Answer:
slope = 2
y int-(0,3)
Step-by-step explanation:
y = mx + b
m=slope
b= y int
Simplify
PLZ HELP QUICKLY
Answer:
c
Step-by-step explanation:
the volume of a rectangular prism is represented by the expression (x^3-2x^2-20x-24). if the length is (x-6) and the height and width are equal, what is the width of the prism?
The width of the prism is x+2. The smallest dimension of an item or figure on a planar surface is its width.
How do you find volume in rectangular prisms?When calculating the volume of a rectangular prism, we multiply the prism's length, width, and height.
A rectangular prism is a polyhedron in geometry that has two parallel and congruent bases. It also goes by the name cuboid. Six faces, each with a rectangle shape and twelve edges, make up a rectangular prism. It is referred to as a prism because of the length of its cross-section.
Given, the volume of the prism
= x³ + 2x²+ 20x - 24
length = (x- 6 )
height and width are equal then
h * w = x³ + 2x²+ 20x - 24 / (x - 6)
= (x + 2 ) (x + 2)
h = (x +2 )and
w = (x+2)
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Use the formula Pt= P0e^rt. where Pt is the amount after t years, P0 is the initial amount, t is the rate of interest, and t is the time period, to complete the table.
Answer:
Step-by-step explanation:
From the given formula,
\(P(t)=P(0)e^{rt}\)
\(\frac{P(t)}{P(0)}=e^{rt}\)
\(\text{ln}[\frac{P(t)}{P(0)}]=\text{ln}[e^{rt}]\)
\(\text{ln}[\frac{P(t)}{P(0)}]=rt\)
Now we put the values in the formula to get the values of the blank spaces in the table,
1). \(\text{ln}[\frac{984}{800}]=5r\)
r = \(\frac{0.207}{5}\)
r ≈ 4.2%
2). \(\text{ln}[\frac{1464}{1200}]=4r\)
r = \(\frac{0.19885}{4}\)
r = 0.0497
r = 5%
3). \(\text{ln}[\frac{1111.5}{950}]=0.045t\)
t = \(\frac{0.157}{0.045}\)
t = 3.5 years
4). \(\text{ln}[\frac{775}{620}]=3.7t\)
t = \(\frac{0.22314}{0.037}\)
t ≈ 6 years
5). \(\text{ln}[\frac{1066.8}{840}]=8r\)
r = \(\frac{0.239}{8}\)
r ≈ 3%
a collection of methods for collecting, displaying, analyzing, and drawing conclusions from data
The term you are looking for is "data analysis". It refers to a set of techniques and tools used to transform raw data into meaningful information, which can then be used to make informed decisions.
This process typically involves several stages, including data collection, data cleaning, data transformation, data modeling, and data visualization.
By using these methods, analysts can identify patterns, trends, and insights that might otherwise be hidden in large or complex datasets.
Data analysis refers to the process of collecting, cleaning, transforming, modeling, and visualizing data to draw meaningful conclusions. It involves a range of techniques and tools, such as statistical analysis, machine learning, and data visualization, to identify patterns, trends, and insights. Data analysis is a crucial part of many fields, including business, science, healthcare, and government, where data-driven decisions are becoming increasingly important. By using data analysis methods, analysts can turn raw data into actionable information that can be used to improve processes, optimize performance, and make informed decisions.
In today's data-driven world, the ability to collect, analyze, and draw conclusions from data is becoming increasingly valuable. Whether you're a business owner, scientist, or government official, data analysis can help you make more informed decisions and drive better outcomes. By using a collection of methods for collecting, displaying, analyzing, and drawing conclusions from data, you can unlock the full potential of your data and gain a competitive edge in your industry.
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–2 • 4? what is the anserw do you now
Answer:
Step-by-step explanation:
-8 because a negative times a positive is a negative so w times 4 equals I and since it’s a negative sign it’s -8
g a spinning wheel on a playground with a radius of 3 feet rotates 6 revolutions every 7 seconds. find the linear speed in feet/second of a point on edge of the wheel
The linear speed of a point on the edge of the wheel is approximately 18.857 feet/second.
What is the linear speed in feet/second of a point on edge of the wheel?To find the linear speed of a point on the edge of the spinning wheel, we need to calculate the distance traveled by that point in one second.
Given:
- Radius of the wheel (r) = 3 feet
- Number of revolutions per second (n) = 6/7 revolutions/second
To convert revolutions per second to radians per second, we need to multiply the number of revolutions by 2π (the conversion factor between revolutions and radians).
n (in radians/second) = (6/7) * 2π
Now, to calculate the linear speed (v) at the edge of the wheel, we can use the formula:
v = r * n
Substituting the values:
v = 3 feet * (6/7) * 2π radians/second
Simplifying:
v ≈ 3 * (6/7) * 2 * 3.14 feet/second
v ≈ 18.857 feet/second
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Which ordered pair describes the location of the point shown on the
coordinate system below?
10.
10
10
A. (3,-5)
B. (-5,3)
C. (3,5)
D. (-5, -3)
Your answer is A!
Step-by-step explanation:
Your answer is A!
The coordinate point from the given graph is (3, -5). Therefore, option A is the correct answer.
What is coordinate plane?A coordinate plane is a two-dimensional surface formed by two number lines. It is formed when a horizontal line (the X-axis) and a vertical line (the Y-axis) intersect at a point called the origin. The numbers on a coordinate grid are used to locate points.
From the given coordinate plane, the coordinate point lies in fourth quadrant.
Where, x-coordinate is positive and y-coordinate is is negative.
The coordinate point correspond to x-axis is 3 and coordinate point correspond to y-axis is 5.
So, the coordinate point is (3, -5)
Therefore, option A is the correct answer.
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(a +11)(11a +1)
Simplify
Answer:
11a^2 + 122a + 11
Step-by-step explanation:
First, multiply a by 11a, which gives you 11a^2. Then you multiply 11 to 11a, which gives you 122a, then last just multiply 11 to 1 and you get 11. Hope this helps.
Find the value of x. Find the measures of the two supplementary angles
Answer:
x = 32
<1 = 102 degrees
<2 = 78 degrees
Step-by-step explanation:
3x + 6 + 2x + 14 = 180
5x + 20 = 180
5x = 180 - 20
x = 160/5
x = 32
3(32) + 6 = 102 degrees
180 - 102 = 78 degrees
7. How much bleach would you use to prepare 1000 mL of a 1:32 solution?
1 : 32 = X : 1000
To prepare a 1000 mL of a 1:32 ratio bleach solution, you would need to mix 31.25 mL of bleach with 968.75 mL of water.
To calculate the amount of bleach needed to make a 1000 mL solution, we can set up the following proportion:
1 part bleach / 32 parts water = X mL bleach / 1000 mL total solution
Cross-multiplying, we get:
32X = 1000
Solving for X, we get:
X = 1000 / 32 = 31.25 mL of bleach
Therefore, to prepare a 1000 mL 1:32 bleach solution, you would need to mix 31.25 mL of bleach with 968.75 mL of water.
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Lincoln went to the grocery store and purchased cans of soup and frozen dinners. Each can of soup has 250 mg of sodium and each frozen dinner has 550 mg of sodium. Lincoln purchased a total of 13 cans of soup and frozen dinners which collectively contain 4450 mg of sodium. Determine the number of cans of soup purchased and the number of frozen dinners purchased.
There are 9 cans of soup and the 4 frozen dinners that were purchased.
How to explain the information?Let x = the number of cans of soup purchased.
Let y = the number of frozen dinners purchased.
Lincoln purchased a total of 13 cans of soup and frozen dinners. This means that
x + y = 13 ..... i
x = 13 - y
The equation will be illustrated as
250x + 550y = 4450 .... ii
Substituting x = 13 - y into equation ii, it becomes
250(13 - y) + 550y = 4450
3250 - 250y + 550y = 4450
- 250y + 550y = 4450 - 3250
300y = 1200
y = 1200/300
y = 4
4 frozen dinners
Substituting y = 4 into x = 13 - y, it becomes
x = 13 - 4 = 9
9 cans of soup.
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What is the value of "c" in the following quadratic? (Make sure the equation is in
standard form: ax2 + bx+c=0)
4x² + 10X - 24 = 0
c=-24
Step-by-step explanation:
a=4, b=10 and c=-24
Use the numbers 3, 4, and 5 to complete the math sentence.
___+___•___= 19
Answer:
Step-by-step explanation:
cook
Answer:
4 + 5*3 = 19
Step-by-step explanation:
Remember PEMDAS so you would multiply first :)
5*3 = 15 + 4 = 19
Please solve with explanation
Answer:
a. 49/2
b. -2/9
If I make any mistakes, I'm sorry.
Find the slope of the tangent line to the parabola at the point.
The equation of the tangent line to the parabola at the point (1,5) is y = 4x + 1.
To find the slope of the tangent line to the parabola at the point (1,5), we need to find the derivative of the equation y = 6x - x² and evaluate it at x = 1.
Taking the derivative of y with respect to x:
dy/dx = d(6x - x²)/dx
= 6 - 2x
Now, we can substitute x = 1 into the derivative to find the slope at that point:
slope = 6 - 2(1)
= 6 - 2
= 4
So, the slope of the tangent line to the parabola at the point (1,5) is 4.
To find the equation of the tangent line, we need to use the point-slope form of a line.
The equation is given by:
y - y₁ = m(x - x₁)
Substituting the values we have:
y - 5 = 4(x - 1)
Expanding and simplifying:
y - 5 = 4x - 4
Moving the constant term to the other side:
y = 4x + 1
Therefore, the equation of the tangent line to the parabola at the point (1,5) is y = 4x + 1.
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Complete question =
Find the slope of the tangent line to the parabola at the point (1,5). y = 6x-x². find an equation of the tangent line.
Solve for Z =
Please answer
Answer:
z = 32°
vertical angles are equal to each other. 32° ≅ z°
An auditorium with 30 rows of seats has 10 seats in the first row. Each successive row has one more seat than the previous row. If students taking an exam are permitted to sit in any row, but not next to another student in that row, what is the maximum number of students that can be seated for an exam
Answer:
Step-by-step explanation:
380 rows in total
bcs
use sense
how do you multiply a square root by a square root and a whole number?
for example, the square root of 5 times (4 times the square root of 5) is 20, but i don’t understand how rob solve for this thanks!
To multiply a square root by a square root and a whole number, you can use the distributive property of multiplication
Given data ,
Let the numbers be represented by the expression A
Now , the value of A is
A = √2 × 3√5
First, you can simplify each square root:
√2 = 1.4142 (rounded to 4 decimal places)
3√5 = 5.1962 (rounded to 4 decimal places)
Next, you can multiply the two simplified square roots and the whole number:
√2 × 3√5 = 1.4142 × 5.1962 × 3
= 22.3607 × 3
= 67.0821
Hence , the expression is A = √2 × 3√5 = 67.0821
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question 1 find two consecutive even numbers such that the sum of the smaller number and twice the larger number is 70A.) 10 and 30B.) 16 and 27C.) 20 and 22D.) 22 and 24
hello
to solve this problem, let's represent the first consecutive number with x and the second with x + 2
from the information on the question, we can set out an equation here
\(\begin{gathered} x\text{ +2}\times(x+2)=70 \\ 2x+2x+2=70 \\ 4x+2=70 \end{gathered}\)let's solve this equation
step 1
collect like terms
\(\begin{gathered} 6x+4=70 \\ 6x=70-4 \\ 6x=66 \end{gathered}\)step two
divide both sides by the coefficient of x
what is 80=-20b? plz help
Answer:
b=-4
Step-by-step explanation:
80=-20b
If you divide -20 from both sides, you get -4=b. That's the answer.
PLZ MARK BRAINLIEST!!!
Answer:
-4
Step-by-step explanation:
80= - 20b
divide both by -20
that gives us -4=b
so, b= -4
Have a great day
1. Write a story about Sylvia's bike ride home. Include as many details as you
can about distance, time, and speed. (You can refer to the segment #'s in
your story if you find it helpful)
Answer:
sylvia is biking home (segment 1) she is traveling at a constant rate of a mile every 15 minutes, she then takes a 20 minute break relizing she dropped something, she goes back and finds it ten minutes later (3) then she bikes home at a rate of 7 miles per 30 minutes.
Step-by-step explanation:
The first four Laguerre polynomials are 1,1-1,2-4+e". and 6 - 18+91?-1. Show that these polynomials form a basis of P3 To show that these polynomials fom a basis of P3, what theorem should be used? O A. If a vector space V has a basis of n vectors, then every basis of V must consist of exactly n vectors O B. Let V be a p-cimensional vector space, p21. Any linearly independent set of exactly p elements in V is automatically a basis for V. Oc. If a vector space V has a basis B (by bn, then any set in V containing more than n vectors must be linearly dependent OD Let H be a subspace of a finite-dimensional vector space V. Any linearly independent set in H can be expanded, if necessary, to a basis for H. Write the standard basis of the space Pg of polynomials, in order of ascending degree. (Simplify your answers. Type expressions using t as the variable. Use a comma to separate answers as needed.) Express each of the polynomials as coordinate vectors relative to the standard polynomial basis of P3 The coordinate vector in Pg for 1 is The coordinate vector in Ps for 1-tis The coordinate vector in Pg for 2 - 4 +12 is The coordinate vector in P, for 6-18 + 9-2 -1is How can these vectors be shown be linearly independent? O A. Form a matrix using the vectors as columns and find its inverse. O B. Form a matrix using the vectors as columns and solve the equation Ax = 0 using this matrix as A. OC. Form a matrix using the vectors as columns and determine the number of pivots in the matrix. OD. Form a matrix using the vectors as columns and augment it with a vector b. Form a matrix using the four coordinate vectors in Bg for the Laguerre polynomials. In order from left to right, use the vectors for 1, 1--2-41 +1, and 6-18+91° -1. Click to select your answer(s). ?
The theorem that should be used to show that the Laguerre polynomials form a basis of P3 is option B: Let V be a p-dimensional vector space, p>1. Any linearly independent set of exactly p elements in V is automatically a basis for V.
The standard basis of the space P3 of polynomials is {1, t, t^2, t^3}.
The coordinate vector in P3 for 1 is (1, 0, 0, 0).
The coordinate vector in P3 for 1-t is (1, -1, 0, 0).
The coordinate vector in P3 for 2-4t+t^2 is (2, -4, 1, 0).
The coordinate vector in P3 for 6-18t+9t^2-2t^3 is (6, -18, 9, -2).
To show that these vectors are linearly independent, we need to form a matrix using the four coordinate vectors as columns and solve the equation Ax = 0, where A is the matrix, and x is a column vector of coefficients. If the only solution to this equation is x=0, then the vectors are linearly independent. Therefore, option B is the correct answer.
Forming the matrix and solving for x, we get:
| 1 1 2 6 | | x1 | | 0 |
| 0 -1 -4 -18 | | x2 | | 0 |
| 0 0 1 9 | | x3 | = | 0 |
| 0 0 0 -2 | | x4 | | 0 |
The solution to this system is x1 = x2 = x3 = x4 = 0, which means that the vectors are linearly independent. Therefore, the Laguerre polynomials form a basis of P3.
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The graph shows a scuba diver's ascent over time. Use the graph to write an equation in slope-intercept
form that represents the diver's depth over time.
The equation that represents this situation is
The equation that represents the situation is m= 1/8s-10
What is a Graph?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.
When
s= 0, m= -10
When
s= 80, m= 0
\(\frac{0-(0-10)}{80-0} = \frac{10}{80} = \frac{1}{8}\)
m-0 = 1/8(s-80)
m= 1/8s-10. The equation
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A theater wants to build movable steps that they can use to go on and off the stage. They want the steps to
have enough space inside so they can also be used to store props.
0.2 m
0.3 m
0.15 m
0.5 m
0.4 m
How much space is inside the steps?
The space inside the steps will be 0.04 cubic meter
What is volume?The space in a three dimensional region occupied by any body is called as volume.
Assume the steps have the dimensions shown in the diagram below.
We can decompose them into two rectangular prisms.
The lower prism has the dimensions 20 in × 16 in × 6 in.
The upper prism has the dimensions 20 in × 8 in × 6 in.
1. Volume of lower prism
V = lwh = 20 in × 16 in × 6 in = 1920 in³
2. Volume of upper prism
V = lwh = 20 in × 8 in × 6 in = 960 in³
3. Volume of steps
V = 1920 in³ + 960 in³ = 2880 in³
Or the volume in meter will be 2880 cubic inches = 0.04 cubic meters.
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X=
4
7
9
Does anyone know this please help quick !
Answer:
9
Step-by-step explanation:
Intersecting Chords Formula:
a • b = c • d
where a and b are the segments on one chord and c and d are the segments on the other chord
3*6 = 2*x
18 = 2x
Divide by 2
18/2 =2x/2
9 =x
McDonalds sells a 20-piece chicken nugget for $5.20. What is the cost per nugget?
Answer:
O.26
Step-by-step explanation:
Divide The cost from the pieces
Answer:
26 cents a nugget
Step-by-step explanation:
I just did 5.20 divided by 20.
if v⃗ 1=[−4−5]v→1=[−4−5] and v⃗ 2=[30]v→2=[30] are eigenvectors of a matrix aa corresponding to the eigenvalues λ1=4λ1=4 and λ2=2λ2=2, respectively,
Yes, v⃗ 1=[−4−5]v→1=[−4−5] and v⃗ 2=[30]v→2=[30] are eigenvectors of matrix A corresponding to eigenvalues λ1=4λ1=4 and λ2=2λ2=2, respectively.
Are v⃗ 1=[−4−5]v→1=[−4−5] and v⃗ 2=[30]v→2=[30] eigenvectors of matrix A?Yes, v⃗ 1=[−4−5]v→1=[−4−5] and v⃗ 2=[30]v→2=[30] are indeed eigenvectors of matrix A.
An eigenvector of a matrix represents a direction that remains unchanged after applying the matrix transformation, except for a scalar multiplication known as the eigenvalue.
In this case, v⃗ 1=[−4−5]v→1=[−4−5] and v⃗ 2=[30]v→2=[30] satisfy this property. When matrix A acts on v⃗ 1, the resulting vector is obtained by scaling v⃗ 1 by a factor of λ1=4λ1=4.
Similarly, when matrix A acts on v⃗ 2, the resulting vector is obtained by scaling v⃗ 2 by a factor of λ2=2λ2=2.
Thus, v⃗ 1 and v⃗ 2 are eigenvectors of matrix A corresponding to the given eigenvalues.
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Work out the unknown value
\( {8}^{a} \times {8}^{a} = {8}^{ - 12} \)
\(a \: = \)
Variables are the name for the unknown.You must isolate the variable in order to get a solution for it (such as x).
Find the unknown value in the proportion ?Unknown value.Variables are the name for the unknown.You must isolate the variable in order to get a solution for it (such as x).
The variable can be separated from the equation by performing inverse operations.Adding and multiplying are the opposites of subtracting and dividing, respectively.
Starting with the proportion:
12/? = 4/3
Since it should be equal to 4/3, notice that if we divide both numerator and denominator by 3, then we should get 4 and 3 respectively:
Therefore, ?÷3 is equal to 3.
Which number is equal to 3 when we divide it by 3?
That number is 9. 9÷3=3
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