5(2x^2-x-2)(x-2)
Step-by-step
Answer: [tex]5(\frac{10x^3}{5}+\frac{-25x^2}{5}+\frac{20}{5}) \\\\5(2x^3-5x^2+4)\\\\5(2x^2-x-2)(x-2)[/tex]
There is a language with 12 distinct letters. How many words that are less than four letters long can possibly be formed? (Assume any combination of letters is valid and letters can be repeated). Can you help me out with this one?
Answer:
1884
Step-by-step explanation:
1)If you hear the condition "less than four letters" it means that each word can consist of 3,2 or 1 letter. Firstly, consider the easiest situation with the word from one letter. There are 12 letters, so there are 12 words from one letter.
Then the words from two letters. The first letter of such a word can be chosen in 12 means(because 12 letters are available), then the second letter can be chosen in 12 means too. 12*12=144 words with 2 letters. (Multiplying, not adding, because each two words form one combination).
Then for the words from three letters, use the same rule, 12 means for the first letter, 12 means for the second letter, 12 means for the third letter. 12*12*12=1728 words.
Having particular words from 1,2,3 letters add them to get total quantity of words: 12+144+1728=1884words,that is the answer.
Mrs Lee had $7500 in her bank account. The bank paid 4% interest at the
end of each year. How much did she have in the bank at the end of 1 year?
Answer:
$7800
Step-by-step explanation:
1. Principal x interest x rate
So: $7500 + 4% (0.04) x 1 year = $300
2. Interest + Principal
So: $7500 + $300
Mrs Lee had $7800 in the bank.
Determine the remaining sides and angles of the triangle ABC.
c=6 mi, B = 38.71°, C = 32.51°
Find the measure of angle A.
A=°
(Type an integer or a decimal.)
Find the length of side a.
а:
mi
(Round to the nearest mile as needed.)
Find the length of side b.
b=mi
(Round to the nearest mile as needed.)
9514 1404 393
Answer:
A = 108.78°
a = 11 mi
b = 7 mi
Step-by-step explanation:
The sum of angles in a triangle is 180°, so the third angle is ...
A = 180° -38.71° -32.51°
A = 108.78°
__
The remaining sides can be found from the law of sines.
a/sin(A) = c/sin(C)
a = sin(A)·c/sin(C) ≈ 0.946762 × 11.163896
a ≈ 11 mi
b = sin(B)·11.163896 ≈ 0.625379 × 11.163896
b ≈ 7 mi
The Richter scale measures the magnitude, M, of an earthquake as a function of its intensity, I, and the intensity of a reference earthquake, .
Which equation calculates the magnitude of an earthquake with an intensity 10,000 times that of the reference earthquake?
Answer:
Option B. M = Log 10000
Step-by-step explanation:
From the question given above, we were told that the intensity (I) is 10000 times that of the reference earthquake (I₀).
Thus, we can obtain the magnitude (M) of the earthquake as follow:
Let the reference earthquake (I₀) = A
Then, the intensity (I) = 10000 × A
M = Log(I/I₀)
M = Log(10000A / A)
M = Log 10000
Thus, option B gives the right answer to the question.
Let U be a matrix where u_ij = 0 if i > j, and L be a matrix where l_ij = 0 if i < j.
(a) U is called an upper triangular matrix and L is a lower tri-angular matrix. Explain why.
(b) Prove or disprove: The sum of two upper triangular matrices is an upper triangular matrix.
(c) Prove or disprove: The product of two upper triangular matrices is an upper triangular matrix.
Answer:
A) U is called an upper triangular matrix because all entries below the principal diagonal element are zeros ( 0 ) since Uij = 0 if i >j also
L is a lower triangular matrix because all entries above the principal diagonal element are zero ( 0 )
B) sum of two upper triangular matrices = upper triangular matrix.
C) product of two upper triangular matrices = upper triangular matrix
Step-by-step explanation:
A) U is called an upper triangular matrix because all entries below the principal diagonal element are zeros ( 0 ) since Uij = 0 if i >j also
L is a lower triangular matrix because all entries above the principal diagonal element are zero ( 0 ) since Lij = 0 if i < j
B) To prove that sum of two upper triangular matrices
attached below
C) Prove or disprove that product of two upper triangular matrices is an upper triangular matrix
attached below
Work out m and c for the line: y = 6 x
Answer:
m = 6
c = 0
General Formulas and Concepts:
Algebra I
Slope-Intercept Form: y = mx + c
m - slope c - y-interceptStep-by-step explanation:
Step 1: Define
y = 6x
↓ Compare to Slope-Intercept Form
Slope m = 6
y-intercept c = 0
n eight-sided die, which may or may not be a fair die, has four colors on it; you have been tossing the die for an hour and have recorded the color rolled for each toss. What is the probability you will roll a blue on your next toss of the die
Answer:
The answer is "21%".
Step-by-step explanation:
[tex]\to 26 + 20 + 29 + 49 = 124\\\\=\frac{26\ \text{brown times}}{124 \ \text{total times}} \\\\= \frac{26}{ 124} \\\\ = 0.209677 \\\\[/tex]
Calculating the percentage:
[tex]= 20.9677 \times 100\\\\=20.9677\% \approx 21\%[/tex]
help i’ll give brainliest
Answer:
(0,-4)
Step-by-step explanation:
The plot for x intercept is at -4,0 and the y intercept is at 0,5
type it in as (0,-4), some require the (#,#) format
Write the equation of a line in slope intercept form that passes through the two points. (-1,3) and (2,9)
Answer:
[tex]y = 2x +5[/tex]
Step-by-step explanation:
Finding the Slope:
m = rise/run
[tex]m=\frac{9-3}{2-(-1)}=\frac{6}{3}=\boxed{2}[/tex]
The slope is 2.
Finding the y-intercept:
[tex]y = 2x + b\\\\9 = 2(2) + b\\\\9 = 4 + b\\\\9 - 4 = 4 - 4 + b\\\\\boxed{ 5 = b}[/tex]
The y-intercept is (0,5).
The equation should be: [tex]y = 2x +5[/tex].
Hope this helps.
Answer:
y = 2x+5
Step-by-step explanation:
To find the equation in slope intercept form, we first have to find the slope of the two points.
The formula for finding the slope is:
[tex]\frac{y2-y1}{x2-x1}[/tex]
We are given the points:
(-1, 3) and (2, 9)
x1, y1 and x2, y2.
[tex]\frac{9-3}{2-(-1)}[/tex]
[tex]\frac{6}{3}[/tex] or 2 (the slope).
The slope intercept form is written as:
y= mx + b
y=2x+b
To find b, we can plug in either of the points given. Personally, I like to work with positive numbers. I'll be using the point (2, 9), however, either point will get you to the same answer.
y=2x+b
9=2(2)+b
9=4+b
Now subtract 4 from both sides.
5=b
Which then leaves us with the equation:
y = 2x+5
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW. Find each measurement. Round your answers to the nearest tenth. Part 2dd
Answer:
see explanation
Step-by-step explanation:
Using the Sine rule in all 3 questions
[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex]
(2)
[tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex] , substitute values
[tex]\frac{45}{sin133}[/tex] = [tex]\frac{c}{sin26}[/tex] ( cross- multiply )
c × sin133° = 45 × sin26° ( divide both sides by sin133° )
c = [tex]\frac{45sin26}{sin133}[/tex] ≈ 27.0 ( to the nearest tenth )
(4)
[tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex] , substitute values
[tex]\frac{19}{sinB}[/tex] = [tex]\frac{30}{sin97}[/tex] ( cross- multiply )
30 sinB = 19 sin97° ( divide both sides by 30 )
sinB = [tex]\frac{19sin97}{30}[/tex] , then
∠ B = [tex]sin^{-1}[/tex] ( [tex]\frac{19sin37}{30}[/tex] ) ≈ 38.9° ( to the nearest tenth )
(6)
[tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex], substitute values
[tex]\frac{18}{sin102}[/tex] = [tex]\frac{xAB}{sin45}[/tex] ( cross- multiply )
AB sin102° = 18 sin45° ( divide both sides by sin102° )
AB = [tex]\frac{18sin45}{sin102}[/tex] ≈ 13.0 ( to the nearest tenth )
g U is the set of in the United States. A is the set of in the United States that have the in their name. B is the set of in the United States that have the in their name. Describe the set in words. Choose the correct answer below. A. is the set of in the United States that have the . B. is the set of in the United States that have the . C. is the set of in the United States that have the . D. is the set of in the United States that have the .
Question isn't well formatted picture if actual question is attached below :
Answer:
A' set of colleges in the United States which Don not have the word community in their name.
Step-by-step explanation:
If a universal set U is defined as :
U =set of colleges in the United States.
A = the set of colleges in the United States that have the word community in their name.
B is the set of colleges in the United States that have the name of an entertainer in their name.
The set A' is called the A complement. The complement of a particular refers to elements in the universal set which are not in A ;
A' = 1 - A'
Therefore, A' set of colleges in the United States which Don not have the word community in their name.
20 POINTS! The answer is x=4 and x= -5, how should I word it, saying how he is wrong?
Answer:
The student took the numbers for the factors 5, -4 for the zeros instead of solving the equation
The zeros are -5, 4
Step-by-step explanation:
x^2 +x - 20=0
What 2 number multiply to -20 and add to 1
5*-4 = -20
5+-4 = 1
(x+5)(x-4) =0
Using the zero product property
x+5 = 0 x-4 =0
x=-5 x=4
Answer:
Solution given:
equation is:
x²+x-20=0
doing middle term factorisation
note:we need to get 1 while subtracting factor of the product of constant and coefficient of x².
20*1=20=2*5*2*1
we get 1 while subtracting 5-2*2=5-4
now substitute value 5-4 at coefficient of x
we get
x²+(5-4)x-20=0
now
distribute
x²+5x-4x-20=0
taking common from each two term
x(x+5)-4(x+5)=0
again taking common (x+5) and keeping remaining at another bracket
(x+5)(x-4)=0
either
x+5=0
x=-5
or
x-4=0
x=4
Error is:
x= 4 not -4
x=-5 not 5.
Jeanne has a coupon for 1.95 off a jug of name brand laundry detergent that normally costs 14.99 . The store brand laundry detergent costs 11.53 How much will Jeanne save if she buys the store brand detergent instead of using her coupon and buying the name brand
Step-by-step explanation:
14.99 - 11.53= 3.46+1.95 =4.41
Roger can shovel his family's driveway in 1 hour. His older sister, Alexis, can shovel the driveway in 1/2 hour. If they work together, then how many minutes will it take them to shovel the driveway?
Answer:
40 min
Step-by-step explanation:
his sister can do it twice as fast so the boy does 1 and the sister does 2. he will do 1/3 of the work and it will take 1/3 of the time
Answer:
90 mins
Step-by-step explanation:
1 hour =60 mins
1/2 hour = 60/2=30
so, 60 +30=90
a store sells pencils pens and markers that sells two times as many markers as pencils and three times as many pens as pencils is the store sells a total of 1950 pencils and pens and markers in a week how many of each were sold
Answer:
Pencils = 325 ; Pens = 975 ; Markers = 650
Step-by-step explanation:
Let :
Number of Pencils = x
Number of pens = y
Number of markers = z
2 times as many markers as pencils
z = 2x
3 times as many pens as pencils
y = 3x
x + y + z = 1950
Write z and y in terms of x in the equation :
x + 3x + 2x = 1950
6x = 1950
Divide both sides by 6
6x / 6 = 1950 / 6
x = 325
Number of pencils = 325
Pens = 3 * 325 = 975
Markers = 2 * 325 = 650
Pencils = 325 ; Pens = 975 ; Markers = 650
solve 3x-4=√(2x^2-2x+2)
Answer:
Step-by-step explanation:
Begin the solution by squaring both sides of the given equation. We get:
(3x - 4)^2 = 2x^2 - 2x + 2, or:
9x^2 - 24x + 16 = 2x ^2 - 2x + 2
Combining like terms results in:
7x^2 - 22x + 14 = 0
and the coefficients are a = 7, b = -22, c = 14, so that the discriminant of the quadratic formula, b^2 - 4ac becomes (-22)^2 - 4(7)(14) = 92
According to the quadratic formula, the solutions are
-b ± √discriminant -(-22) ± √92 22 ± √92
x = ------------------------------- = ----------------------- = ------------------------
2a 14 14
I have a final for summer schoollll due midnight and it’s 10:23!!!!!!!!!!!!
Illustrate the 7th pattern of the sequence of square numbers.
1,4,9,16,25,36,49,........
7th pattern =49.....
Answer:
1, 4, 9, 16, 25, 36, 49…................the 7 the pattern is 49
Solve 9(7x-2) = 5 (10x - 1)
Answer:
[tex]9(7x - 2) = 5(10x - 1) \\ \\ 63x - 18 = 50x - 5 \\ \\ 63x - 50x = - 5 + 18 \\ \\ 13x = - 5 + 18 \\ \\ 13x = 13 \\ \\ x = \frac{13}{13} \\ \\ x = 1[/tex]
Answer:
[tex]9(7x - 2) = 5(10x - 1) \\ 9 \times 7x - 9 \times 2 = 5 \times 10x - 5 \\ 63x - 18 = 50x - 5 \\ 63x - 50x = - 5 + 18 \\ 13x = 13 \\ x = 1 \\ thank \: you[/tex]
solve the following equations
Answer:
x=0,5/2
Step-by-step explanation:
Find the missing side. Round your answer to the nearest tenth.
Answer:
[tex]sin\left(90\right)/x=sin\left(25\right)/16[/tex]
x = 37.85
Step-by-step explanation:
what is the square root of 24
Answer:
the square root of 24 is 4.89897948557
Answer:
4.89
Step-by-step explanation:
2root 6........***
how do you change 79/8 to a decimal
Answer:
Divide 79 by 8
Step-by-step explanation:
79/8
= 9.875
What are the zeros of this function?
Answer:
The zeros of this function would be: x = 4 and x = 6, assuming that option got caught off while you were taking a picture.
Step-by-step explanation:
When they're asking for the zeros of this type of function, where is forms this kind of U-shape or also known as a quadratic equation, they're asking what the x-value is when y = 0, or when the line of the function touches the x-axis. Notice that it happens when x = 4 and when x = 6.
In short, it's asking what the x-value is of the points of the function when it intersects the x-axis. Hopefully my explanation wasn't too confusing. Good luck on the rest of the quiz!
which shape is both a parallelogoram and a rhombus
Answer:
A square can be defined as a rhombus which is also a rectangle and a parellelogram with four congruent sides and four right angles
I hope this helps
Hey good morning I need help ASAP thank you guys
Answer:
B. x = 2.77
Step-by-step explanation:
3^x = 21
You first look for a base for 21 that is 3 to the power of something.
21 = 3^2.77
So 3^x = 2^2.77
They have the same base so
x= 2.77
Find the values for x and y using the diagram below. Explain what geometric relationships you used to solve the problem.
You DO NOT have to write a proof. An example would be "linear pair" or "right angles= 90◦
".
Answer:
2x, a linear pair
Step-by-step explanation:
2/5x/3/4 = 7/4 = 1 3/4
Write an equation for the graph below in terms of x
Answer:
x = -2
Step-by-step explanation:
the line goes through -2 on the x-axis
the line also goes through -3 on the y-axis
HELP PLEASE! INEEED HELPPP RIGHT NOW The graph of y=x−2−−−−√ is is transformed to become y=x+3−−−−√−2. Which of the following statements best describes the effect this transformation has on the graph of y=x−−√?
Answer:
I think it's D but I don't know how to do this, but I ask my Friend and he gave me this graph I hope it helps.
Option (C) the graph is translated 5 units left and 2 units down is the correct answer.
What is graph of a function?A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The graph of a function f is the set of all points in the plane of the form (x, f(x)).
For the given situation,
The function is [tex]y=\sqrt{x-2}[/tex]
This function is transformed to become the function as [tex]y=\sqrt{x+3}-2[/tex]
Now compare this transformation with the function [tex]y=\sqrt{x}[/tex].
These functions are plotted in the graph below.
On comparing this transformation,
The graph is translated 5 units left and 2 units down.
Hence we can conclude that option (C) the graph is translated 5 units left and 2 units down is the correct answer.
Learn more about graph of a function here
https://brainly.com/question/2275360
#SPJ2
If an 8" X 8" square cake serves 8 people, how many 24" X 24" square cakes are needed for a
wedding attended by 144 people?
Answer:
2 24" X 24" square cakes are needed.
Step-by-step explanation:
This question is solved by proportions.
Area of a square:
The area of a square of side l is given by:
[tex]A = l^2[/tex]
8" X 8" square cake serves 8 people
Thus:
[tex]A = 8*8 = 64[/tex]
Area of 64 serves 8 people, so for 1 people, an area of 64/8 = 8 is needed.
144 people
The total area needed is:
[tex]A = 144*8 = 1152[/tex]
How many 24" X 24" square cakes?
24*24 = 576
1 cake - 576
x cakes - 1152
Applying cross multiplication:
1152/576 = 2
2 24" X 24" square cakes are needed.
