Answers
Answer:
Step-by-step explanation:
I can't believe I'm doing this for 5 points, but ok!
For the first 3, we are going to multiply to find the value of that 3 x 3 matrix by picking up the first 2 columns and plopping them down at the end and then multiplying through using the rules for multiplying matrices:
[tex]\left[\begin{array}{ccccc}7&4&6&7&4\\-4&8&9&-4&8\\1&8&7&1&8\end{array}\right][/tex] and from there find the sum of the products of the main axes minus the sum of the products of the minor axes, as follows (I'm not going to state the process in the next 2 problems, so make sure you follow it here. This is called the determinate. The determinate is what you get when you evaluate or find the value of a matrix. Just so you know):
[tex](7*8*7)+(4*9*1)+(6*-4*8)-[(1*8*6)+(8*9*7)+(7*-4*4)][/tex] which gives us:
392 + 36 - 192 - [48 + 504 - 112] which simplifies to
236 - 440 which is -204
On to the second one:
[tex]\left[\begin{array}{ccccc}-8&-4&-1&-8&-4\\1&7&-3&1&7\\8&9&9&8&9\end{array}\right][/tex] and multiplying gives us
[tex](-8*7*9)+(-4*-3*8)+(-1*1*9)-[(8*7*-1)+(9*-3*-8)+(9*1*-4)][/tex] which gives us:
-504 + 96 - 9 - [-56 + 216 - 36] which simplifies to
-417 - 124 which is -541, choice c.
Now for the third one:
[tex]\left[\begin{array}{ccccc}-2&-2&-5&-2&-2\\2&7&-3&2&7\\8&9&9&8&9\end{array}\right][/tex] and multiplying gives us
[tex](-2*7*9)+(-2*-3*8)+(-5*2*9)-[(8*7*-5)+(9*-3*-2)+(9*2*-2)][/tex] which gives us:
[tex]-126+48-90-[-280+54-36][/tex] which simplifies to
-168 - (-262) which is 94, choice c again.
Now for the last one. I'll show you the set up for the matrix equation; I solved it using the inverse matrix. So I'll also show you the inverse and how I found it.
[tex]\left[\begin{array}{cc}-4&-5&\\-6&-8\\\end{array}\right][/tex] [tex]\left[\begin{array}{c}x\\y\\\end{array}\right][/tex] = [tex]\left[\begin{array}{c}-5\\-2\\\end{array}\right][/tex] and I found the inverse of the 2 x 2 matrix on the left.
Find the inverse by:
* finding the determinate
* putting the determinate under a 1
* multiply that by the "mixed up matrix (you'll see...)
First things first, the determinate:
|A| = (-4*-8) - (-6*-5) which simplifies to
|A| = 32 - 30 so
|A| = 2; now put that under a 1 and multiply it by the mixed up matrix. The mixed up matrix is shown in the next step:
[tex]\frac{1}{2}\left[\begin{array}{cc}-8&5\\6&-4\end{array}\right][/tex] (to get the mixed up matrix, swap the positions of the numbers on the main axis and then change the signs of the numbers on the minor axis). Now we multiply in the 1/2 to get the inverse:
[tex]\left[\begin{array}{cc}-4&\frac{5}{2}\\3&-2\\\end{array}\right][/tex] Multiply that inverse by both sides of the equation. This inverse "undoes" the matrix that's already there (like dividing the matrix that's already there by itself) which leaves us with just the matrix of x and y. Multiply the inverse matrix by the solution matrix:
[tex]\left[\begin{array}{c}x&y\end{array}\right] =\left[\begin{array}{cc}-4&\frac{5}{2} \\3&-2\end{array}\right] *\left[\begin{array}{c}-5&-2\\\end{array}\right][/tex] and that right side multiplies out to
x = 20 - 5 which is
x = 15 and
y = -15 + 4 which is
y = -11
(It works, I checked it)
Related Questions
What is 3/8 of 200?
pls show work
35 POINTS!!!
Answers
Answer:
The answer is 75
Step-by-step explanation:
3/8*200=75.
The diameter of a circle is 7 m. Find its area to the nearest tenth.
Answers
Area = pi x r^2
R = 7/2 = 3.5
Area = 3.14 x 3.5^2
Area = 38.5 m^2
38.5
Step-by-step explanation:
A = pi*r^2
A = pi*3.5^2
A = pi*12.25
A = 38.465
Click on the sentence that represents the following equation.
m - 15 = 22
A. The difference of a number and 15 is equal to 22.
B. A number plus 15 is equal to 22.
C. A number increased by 15 is equal to 22.
Answers
Answer:
A.
Step-by-step explanation:
'The difference' means minus or subtraction. 'plus' and 'increased' are both for addition.
Brainliest please!
Rohan is 2 years elder than rohit. Five years ago , one third of his age was equal to three-sevenths of rohit's age. Clalculate their present ages. pl tell with explanation
Answers
Answer:
I hope it will help you.
have a great day . ☺☺
Answer:
Step-by-step explanation:
Let Rohan age = xLet Rohit age =yx = y + 2
(1/3)* (x - 5 ) = (3/7)(y - 5) Multiply both sides by 3
(x - 5) = 9/7 (y -5) Multiply both sides by 7
7(x - 5) = 9(y - 5) Remove the brackets
7x - 35 = 9y - 45 Add 45 to both sides
7x + 10 = 9y
y = x - 2
7x + 10 = 9(x - 2)
7x + 10 = 9x - 18
7x +10 + 18 = 9x
28 = 2x
x = 14
y = 14 -2
y = 12
please help me is for my homework
Answers
Answer:
33.33%
Step-by-step explanation:
do divide 3÷9 and that is .333333333
and to convert a decimal to a percent you move the dot two number back so you get 33.33%
ASAP!! PLEASE Will mark the brainliest answer If a + b = 7 and ab = 12, then find the value of a2- ab+ b2 and a3+b3
Answers
Answer:
13 and 91
Step-by-step explanation:
(a + b)² = a² + 2ab + b² , substitute values
7² = a² + 2(12) + b²
49 = a² + 24 + b² ( subtract 24 from both sides )
25 = a² + b²
Then
a² - ab + b²
= a² + b² - ab , substitute values
= 25 - 12
= 13
-------------------------------------------
a³ + b³ = (a + b)(a² - ab + b²) ← substitute values
a³ + b³ = 7 × 13 = 91
The formula for the volume of a cylinder with a height of 5 units is V(r)=5 pi r^2 where r is the radius of the cylinder. What is the domain and range of this function?
a. r < 0, V(r) < 0
b. r > 0, V(r) < 0
c. r < 0, V(r) > 0
d. r > 0, V(r) > 0
Answers
Answer:
d. r > 0, V(r) > 0
Step-by-step explanation:
The radius represent a measure of lenght and the volume a measure of space, and both, lenght and space, cannot be negative, so both have to be > 0
If fx) = 3* + 10x and x) = 4x - 2, find (f+ g)(x).
Answers
Answer:
[tex]\boxed {\boxed {\sf B. \ 3^x + 14x-2}}[/tex]
Step-by-step explanation:
We are given 2 functions:
f(x)= 3ˣ + 10x g(x)= 4x-2We are asked to find (f+g)(x) or f(x)+ g(x). Essentially, we are finding the sum of the functions.
[tex](f+g)(x)=f(x)+ g(x)[/tex]
[tex](f+g)(x)=(3^x + 10x) + (4x-2)[/tex]
[tex](f+g)(x)= 3^x + 10x + 4x -2[/tex]
Simplify the expression by combining like terms. There are 2 terms with a variable of x, so they can be added together.
[tex](f+g)(x)= 3^x + ( 10x + 4x) -2[/tex]
[tex](f+g)(x)= 3^x + 14x -2[/tex]
The sum of the functions f(x) and g(x) is 3ˣ + 14x -2 and choice B is correct.
Simplify
3m + 3
What is the answer please
Answers
[tex]\rm \large \implies \: \: 3m \: + \: 3m[/tex]
[tex]\rm \large \implies \: \: 6m[/tex]
Answer:
6m
Step-by-step explanation:
those are like terms so you just have to add them
3m+3m=6m
i hope this helps
Find the length of the third side. If necessary, round to the nearest tenth.
15
12
Answer:
Submit Answer
attempt 1 out of 2
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Copyright 2021 DeltaMath.com. All Rights Reserved
PLS HELP ASAP
Answers
Answer:
The length of the third side is 9.
Step-by-step explanation:
Pythagorean Theorem: a² + b² = c²
12² + b² = 15²
144 + b² = 225
√b² = √81
b = 9
how do you solve this
Answers
Answer:
yo what concept is this
Step-by-step explanation:
Use the distributive property to write the expression without parentheses 6(7a+6)
Answers
Answer:
42a+36
Step-by-step explanation:
6(7a+6)
Distribute
6*7a + 6*6
42a+36
Answer:
42a + 36
Step-by-step explanation:
(-6127) + _____. = (-6127)
(+18) + _____ = (+20)
(+27) - ____ = (+20)
(+63) + _____= (+50)
(+21) - _____ = (+17)
Answers
Answer:
(-6127) + 0 = (-6127)
(+18) + 2 = (+20)
(+27) - 7 = (+20)
(+63) + (-13) = (+50)
(+21) - 4 = (+17)
Step-by-step explanation:
Find the coordinates of the image of R (2, 1) after the translation (x, y) → (x, y − 5).
Answers
Answer:
(2,-4)
Step-by-step explanation:
We subtract 5 to the y-coordinate, so we have (2,-4)
15. PLEASE HELP ME
A sports recreation company plans to manufacture a beach ball with a surface area of 7238 in.2 Find the radius of the beach ball. Use the formula A= 4\pir2, where A is the surface area and r is the radius of the sphere.
A. 48 in.
B. 24 in.
C. 75 in.
D. 576 in.
Answers
We know
[tex]\boxed{\sf Surface\:area=4\pi r^2}[/tex]
[tex]\\ \sf\longmapsto 4\pi r^2=7238[/tex]
[tex]\\ \sf\longmapsto 4\times \dfrac{22}{7}r^2=7238[/tex]
[tex]\\ \sf\longmapsto r^2=\dfrac{7238\times 7}{88}[/tex]
[tex]\\ \sf\longmapsto r^2=\dfrac{5066}{88}[/tex]
[tex]\\ \sf\longmapsto r^2=575.75[/tex]
[tex]\\ \sf\longmapsto r^2\approx576[/tex]
[tex]\\ \sf\longmapsto r\approx\sqrt{576}[/tex]
[tex]\\ \sf\longmapsto r\approx24in[/tex]
Option b is coreectAnswer:
B. 24 in.
Step-by-step explanation:
The given problem supplies as with the surface area of the beach ball and we are to look for the required radius. Assuming that the beach ball is perfectly shaped in the form of a sphere, then the formula for calculating the surface area of a sphere is given as:
SA = 4 π r^2
where r is the radius of the sphere and SA is the surface area which is given to be 7238 in^2
Rewriting the formula in terms of r:
r^2 = SA / 4 π
r = sqrt (SA / 4 π)
Solving for r:
r = sqrt (7238 in^2 / 4 π)
r = 24 in
Answer:
24 inches
Find the length of the third side. If necessary, round to the nearest tenth. 10 14
Answers
Answer:
9.8 units
Explanation:
According to Pythagoras theorem, the square of length of the hypotenuse is equal to the sum of squares of lengths of other two sides.
Let the third side be x units.
Then,
x² + 10² = 14²
=> x² + 100 = 196
=> x² = 196 - 100
=> x² = 96
=> x = √96
=> x = 4√6
=> x = 9.79....
=> x = 9.8 (Rounding to the nearest tenths)
So, the length of the third side is 9.8 units.
Consider the following points. (−4, −1) and (4, 2) Let Y'O' be the image of YO after a reflection across line . Suppose that ′ is located at (1, 4) and ′ is located at (−2, −4). Which of the following is true about line ?
Answers
The line was reflected about the line y = -x.
-----------------------------------------
This question is solved using reflection concepts.
There are various kinds of reflections, 90º clockwise about the origin, 90º counterclockwise, among other, and each of them has a rule.
-----------------------------------------
In this question:
Point (-4,-1) became (1,4).Point (4,2) became (-2,-4).From this, we have the following rule: (x,y) -> (-y,-x)
Checking the rules, it can be said that the line was reflected about the line y = -x.
A similar question can be found at https://brainly.com/question/16130908
Write a linear equation that goes through the points (-1,-10) and (5,2).
Answers
Answer:
y = 2x - 8
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 1, - 10) and (x₂, y₂ ) = (5, 2)
m = [tex]\frac{2-(-10)}{5-(-1)}[/tex] = [tex]\frac{2+10}{5+1}[/tex] = [tex]\frac{12}{6}[/tex] = 2 , then
y = 2x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (5, 2 ) , then
2 = 10 + c ⇒ c = 2 - 10 = - 8
y = 2x - 8 ← equation of line
(62.1) x (3.2) = ??
Please help urgent!!!
Answers
Answer:
198.72
Step-by-step explanation:
if u remove the brakctes and multiplay both of them by 10 and then multiply (621x32=19872 then u divide it by 100 and u get the answer 198.72
Only thing I need to know is what to do for the x on y = x + 3 and y = x
Answers
Answer:
Think of y = mx + b,
With y = x + 3, m = 1 so the slope is one, and b = 3 which is the y-intercept, so plot the point (0,3) on the y-axis.
To find the next point to plot go up 1 and over to the right 1 because slope is rise over run.
With y = x, the slope is still 1, but there is no y-intercept, so you plot the point (0,0), and to find the next point on that line, go up 1 and over the right 1 because m=1
If f(x)=7 find x=-3
A.4
B.-3
C.7
D.-4
Answers
Answer: the answer to your question is 7
Step-by-step explanation:
A student was given two data sets, Set A and Set B. Which of the following
statements is true?
Set A
-1
0
1
2
3
50
75
100
150
125
Set B
X
-1
0
1
2
3
0.60
3
15
75
375
A. Set A is a linear function and the values increase at the same rate
as Set B.
B. Set B is an exponential function and the values increase at a
faster rate than Set A.
C. Set A is a linear function and the values increase at a faster rate
than Set B
D. Set B is an exponential function and the values increase at the
same rate as Set A.
PREVIOUS
Answers
Answer:
b) is the correct option
Given that v=√u*u- 2qs. Make q the subject of the equation. Find the value of q in the equation if v=8, u=12, and s=40
Answers
Answer:
Step-by-step explanation:
v=√u*u- 2qs
[tex]\sqrt{20}[/tex] x 20 - 2q40 = 8[tex]2\sqrt{5}[/tex] x 20 - 2q40 = 840[tex]\sqrt{5}[/tex] - 2q40 = 8- 2q40 = 8 - 40[tex]\sqrt{5}[/tex]-80q = 8 - 40[tex]\sqrt{5}[/tex] q = (8-40[tex]\sqrt{5}[/tex] ) / -80 = [tex]\frac{-1 + 5\sqrt{5} }{10}[/tex] = 1.018Above given answer is correct.
You’re given two side lengths of 10 centimeters and 8 centimeters. The angle between the sides measures 40°. How many triangles can you construct using these measurements?
Answers
Answer:
1
Step-by-step explanation:
Once you have two sides and the included angle, there is only one triangle.
Answer: 1
Answer:
The answer is B. 1
Step-by-step explanation:
I hope I helped
In recent years, only 79% of the fruit sold at Fred's Fruit stand has been any good. Fred recently started buying fruit from new farmers and wants to know if there is a statistically significant increase in the percentage of good fruit. In a random sample if 475 pieces, 85 were bad. How would the conclusion change if the significance level went from 7% to 5%?
Answers
Answer:
The p-value of the test is 0.0485 < 0.05, also less than 0.07, so there is sufficient evidence to conclude that there is a statistically significant increase in the percentage of good fruit, for both significance levels, thus the change in significance levels do not change the conclusion.
Step-by-step explanation:
79% of the fruit sold at Fred's Fruit stand has been any good. Test if there has been an increase.
At the null hypothesis, we test if there has been no increase, that is, the proportion is still of 79%, so:
[tex]H_0: p = 0.79[/tex]
At the alternative hypothesis, we test if there has been an increase, that is, more than 79% being good, so:
[tex]H_1: p > 0.79[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.79 is tested at the null hypothesis:
This means that [tex]\mu = 0.79, \sigma = \sqrt{0.79*0.21}[/tex]
In a random sample if 475 pieces, 85 were bad.
So 475 - 85 = 390 were good, and:
[tex]n = 475, X = \frac{390}{475} = 0.8211[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.8211 - 0.79}{\frac{\sqrt{0.79*0.21}}{\sqrt{475}}}[/tex]
[tex]z = 1.66[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a sample proportion above 0.8211, which is 1 subtracted by the p-value of Z = 1.66.
Looking at the z-table, z = 1.66 has a p-value of 0.9515.
1 - 0.9515 = 0.0485
The p-value of the test is 0.0485 < 0.05, also less than 0.07, so there is sufficient evidence to conclude that there is a statistically significant increase in the percentage of good fruit, for both significance levels, thus the change in significance levels do not change the conclusion.
Drag the tiles to the correct boxes to complete the pairs.
Simplify the mathematical expressions to determine the product or quotient in scientific notation. Round so the first factor goes to the tenth
place.
HELP PLEASE!!!!!!
Answers
Answer:
Ans ; 1) 7.8 , 2) 3.3×10³ , 3) 2.1 ×10‐³ , 4) 3.7
I hope I helped you^_^
ILL MARK BRAINIEST IF YOU DO THIS CORRECTLY!!!
Answers
Answer:
C. 12 for $6.00
Step-by-step explanation:
Answer:
C. 12 for $6.00
Step-by-step explanation:
better than $13.00 for 24. as that'd be $6.50 for 12..
PLEASE HELP ME WITH THIS MATH QUESTION!
Answers
Answer:
C
Step-by-step explanation:
First, let's say 4³ is a and 5⁻² is b. We know that (a/b)ⁿ = aⁿ/bⁿ for any n, so
(a/b)⁵ = a⁵/b⁵
= (4³)⁵ /(5⁻²)⁵
Next, one power rule states that (4³)⁵ = 4 ⁽³ˣ⁵⁾ = 4¹⁵ and (5⁻²)⁵ = 5 ⁽⁻²ₓ⁵⁾=5⁻¹⁰, so
(4³)⁵ /(5⁻²)⁵ = 4¹⁵ / 5⁻¹⁰
Next, anything to a negative power (e.g. x⁻ⁿ) is equal to 1 over the absolute value of the power, so x⁻ⁿ = 1/xⁿ. Applying that here, we can say that
5⁻¹⁰ = 1/5¹⁰
4¹⁵ / 5⁻¹⁰ = 4¹⁵ / (1/5¹⁰) = (4¹⁵/1) / (1/5¹⁰) = 4¹⁵ * 5¹⁰
create a line that is perpendicular to AB and passes through C. you can use the tools available in geogebra to create perpendicular lines for this construction display the measurement of the angle of intersection between the two lines???
Answers
A linear relationship can be written as:
y = a*x + b
where a is the slope and b is the y-intercept.
If we know that the line passes through two points, (x₁, y₁) and (x₂, y₂), then we can write the slope as:
a = (y₂ - y₁)/(x₂ - x₁).
Also, for a given line:
y = m*x + s
A perpendicular line to that one must have a slope:
a = -(1/m)
And the intersection between two perpendicular lines forms four 90° angles.
So first, we need to find the slope of the line that passes through A and B.
A = (-3, 3)
B = (-1, -1)
Then the slope of the line is:
a = (-1 - 3)/(-1 - (-3)) = -4/2 = -2
a = -2
The slope of a perpendicular line should be:
slope = -(1/a) = -(1/-2) = 1/2
Then the perpendicular line will be something like:
y = (1/2)*x + b
To find the value of b, we can use the other restriction.
This line needs to pass through point C.
And we can see that point C is:
C = (1, 2)
This means that when x is equal to 1, y must be equal to 2.
Then replacing these in the above equation we get:
2 = (1/2)*1 + b
2 = 1/2 + b
2 - 1/2 = 4/2 - 1/2 = 3/2 = b
Then our equation is:
y = (1/2)*x+ 3/2
The graph of this line can be seen in the image below, the green line is the line that we found.
If you want to read more about linear relations, you can see:
https://brainly.com/question/19586594
Answer:
Step-by-step explanation:
find the missing side lengths answers are in simplest radical form with the denominator rationalized.
Answers
Answer:
Option B is the answer
Step-by-step explanation:
x= 8, y=4√2
We know from pythagorean's law
(Hypotenuse) ^2 = (base)^2 + (height) ^2
