Write the system of equations as a matrix equation AX=B, with A as the coefficient matrix of the system.x+2y=−112x+6y=−30
Answers
The matrix equation is given to be:
[tex]AX=B[/tex]where A is the coefficient matrix of the system.
To get the value of X, we need to multiply both sides of the equation by the inverse of A, since:
[tex]A\cdot A^{-1}=1[/tex]Therefore, we have:
[tex]X=A^{-1}\cdot B[/tex]he TLAST OPTION is correct.
Related Questions
[tex]3-\sqrt{x} 5[/tex]
Answers
The value of the expression given as 3 - √x⁵ is 3 - x^2√x
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to evaluate the expression?The expression is given as
3 - √x⁵
Express 5 as the sum of 4 and 1
So, we have the following equation
3 - √x⁵ = 3 - √x^(4 + 1)
Apply the law of indices to expand the equation
So, we have the following equation
3 - √x⁵ = 3 - √(x^4 * x)
Next, we expand the equation
So, we have the following equation
3 - √x⁵ = 3 - √x^4 * √x
Evaluate the square root of x^4
So, we have the following equation
3 - √x⁵ = 3 - x^2 * √x
Evaluate the product
So, we have the following equation
3 - √x⁵ = 3 - x^2√x
Hence, the value of the expression is 3 - x^2√x
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a group of people are waiting in line for a movie premier. every 14th person in line will win a free movie ticket . every 10th person will receive a gift card of 30 dollars. which person is the first to win both prizes.if there are 200 people in line how many will receive both prizes?
Answers
In order to determine which person is the first to win both prizes, you have to find the least common multiple to both numbers 14 and 10.
To determine what is the least common multiple number you proceed as follow:
You list different multiples of each number 14 and 10.
For 14: 14 28 42 56 70 84 98 112
For 10: 10 20 30 40 50 60 70 80
The least common multiple is 70, becasue is the first common number in each list.
Hence the 70th person in the line will win both prizes.
12. The perimeter of a triangle with sides 5x-1, 5x-1, 2.2x +10, and the perimeter of a square with a side length of 6.5x -11.8 are the same. What is the value of x?
Answers
The value of x is 4.
The perimeter of any shape is the sum of lengths of all its sides.
We are provided with the sides of triangle i.e., 5x-1, 5x-1 and 2.2x +10.
So, The perimeter of a triangle = sum of length of all three sides = (5x-1) + (5x-1) + (2.2x +10)
The perimeter of a triangle = 12.2x + 8 equation 1
Also, we are provided with the side of square i.e., 6.5x -11.8.
The perimeter of a square = 4 (side) = 4 (6.5x - 11.8)
The perimeter of a square = 26x - 47.2 equation 2
As per question,
Perimeter of a triangle = Perimeter of a square
12.2x + 8 = 26x - 47.2
13.8x = 55.2
x = 4
So we can write, the value of x is 4.
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Classify the following functions as growth or decay: f(x) = 10 (6/7)^x, g(x)= 1/3e^x, h(x)=5e^-x, k(x)= -10(6/7)^x
Answers
It is known that any exponential function with the form f(x)=a^x is an increasing function while a function of the form g(x)=a^(-x) is a decreasing function.
Furthermore, it a function h(x) is increasing, then the function -h(x) is decreasing. By analogy, if a function k(x) is decreasing, then -k(x) is increasing.
Now let's analyze the functions from the problem.
[tex]\text{ Let }f(x)=10\cdot(\frac{6}{7})^x[/tex]Since (6/7)^x is increasing and the multiplying factor of 10 is positive, then the function f(x) is also increasing.
Use these rules to find whether each function is increasing or decreasing.
Remember that increasing functions are used to represent growth while decreasing functions are used to represent decay.
Provide the correct reason for the statement in line 1. (please help)
Answers
Answer:
d) given
Step-by-step explanation:
nothing has been done yet, the statement is given as stated above the statement
on a highway there are billboards located every 1 1/2 km there are 14 billboards in that highway how long is the highway
Answers
Answer:
1 1/2 = 3/2
3/2 x 14
= 42/2
=21
Step-by-step explanation:
Please help me I was sick today and missed out on class and I don’t understand this question
Answers
Answer: 72 i think
Step-by-step explanation:
1. Write the regression2.r =3. what does the r mean?I predict there will be a [blank] relationship between [blank] and [blank] I think it’s because [blank] and I’m gonna send a photo about my graphing points
Answers
First of all, we have to find the mean of x values.
According to the given graph, the x values are: 0, 1, 2, 2, 3, 3, 4, 5, 6, 7.
So, the mean is
[tex]\bar{x}=\frac{0+1+2+2+3+3+4+5+6+7}{10}=\frac{33}{10}=3.3[/tex]The mean of x values is 3.3.
The y values are: 2, 2, 3, 4, 4, 4, 5, 6, 8, 9.
The mean would be
[tex]\bar{y}=\frac{2+2+3+4+4+4+5+6+8+9}{10}=\frac{44}{10}=4.4[/tex]The mean of y values is 4.4.
Now, we find the standard deviation for x values and y values.
[tex]undefined[/tex]Sarah enrolled $10,000 worth of debt with National Debt Relief. We negotiated with the creditors and reduced the debt by 50%. Sarah’s fee for our services was 25% of the enrolled debt ($10,000). How much did Sarah end up saving after reducing her debt and paying us our fee?*
Answers
Answer:
7500$
Step-by-step explanation:
A teacher is organizing binders for her students. She has 54 pieces of lined paper, 36 pieces of grid paper, and 72 dividers. What is the greatest number of identical binders that she can make? Please help!
Answers
Using the highest common factor, the greatest number of identical binders that the teacher can make is 18.
What is the highest common factor?The highest common factor or multiple of the given numbers is the highest number that can divide them without a remainder.
We know that 2, 9, and 18 can divide 54, 36, and 72 without leaving a remainder.
We can see that the highest common factor is 18.
When we divide 54 by 18, the quotient is 3. If you divide 36 by 18, the quotient is 2. When you divide 72 by 18, the result is 4.
The number of lined paper = 54 pieces
The number of grid paper = 36 pieces
The number of dividers = 72 dividers
The common factors of 54, 36, and 72 are 2, 9, and 18.
The highest common factor of 54, 36, and 72 is 18.
Thus, 18 binders containing 3 pieces of lined paper, 2 pieces of grid paper, and 4 dividers can be made from the collection, using their HCF.
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If a ball is thrown directly upward with a velocity of 88 ft/s, its height (in feet) after t seconds is
given by y = 88t - 16t².
When does the ball reach its maximum height? (Round to two decimal places)
Answers
If a ball is thrown directly upward with a velocity of 88 ft/s, its height (in feet) after t seconds is given by y = 88t - 16t².The ball will reach its maximum height at 121 feet.
Maximum heightGiven equation:
y = 88t - 16t²
Maximum height dy/dt = 0
88-32t = 0
32t = 88
t = 88/32sec
t = 2.75sec
Hence,
Maximum height attained by the ball :
Maximum height attained by the ball = 88(2.75)-16(2.75)²
Maximum height attained by the ball = 242 - 121
Maximum height attained by the ball = 121 feet
Therefore the maximum height is 121 feet.
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Find the value of (-3/8) x (+8/15)
A. -1/5
B. -1/3
C. 11/15
D. 11/23
Answers
Answer: [tex]\Large\boxed{A. -\dfrac{1}{ 5}}[/tex]
Step-by-step explanation:
Given expression
[tex]-\dfrac{3}{8} \times \dfrac{8}{15}[/tex]
Combine the fractions
[tex]=\dfrac{-3\times 8}{8 \times 15}[/tex]
Cancel out the 8 on both the numerator and denominator
[tex]=\dfrac{-3}{ 15}[/tex]
Divide 3 on both the numerator and denominator
[tex]=\dfrac{-3\div 3}{ 15\div 3}[/tex]
[tex]=\Large\boxed{-\dfrac{1}{ 5}}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Step by step
Multiply across and simplify
-3/8 x 8/15
-3 x 8 = -24 over 120
Simplified to -1/5
Fill in the blanks below with the correct units.(a) The school bus had a mass of about 9000 ?(b) Last week, Ravi drove about 13?to visit his uncle.(c) Goran added 5 ?e of cream to his coffee.
Answers
The first unit is kilograms because the bus is really heavy.
The second is kilometers because meters are too small.
The third one is milliliters because liters are too much for ice cream.
HELP ME QUICK!! I’LL MARK YOU BRAINLIEST!!
3-8. Find the distance between each pair of points if they were graphed on a number line. Represent your work
using absolute value symbols.
a. -10 and 10
b. -15 and -7
Answers
a-21
n-23
Horatio left a campsite, hiking at a rate of 1 mile per hour. Ivan left 3 hours later, hiking at a rate of 2 miles per hour. How long will it take Ivan to catch up to Horatio?
Answers
Ivan will catch up to Horatio in 3 hours .
In the question ,
it is given that
speed of Horatio is 1 miles per hour
speed of Ivan is 2 miles per hour .
and Ivan leaves 3 hours late than Horatio .
Let "t" be the time ( in hours ) taken for Ivan to meet Horatio ,
So, the distance covered by Ivan will be 2*t .
Since Horatio left 3 hours before so the time taken for Horatio to meet Ivan is (t+3).
So, the distance covered by Horatio will be 1*(t+3) .
The distance covered for Horatio and Ivan will be equal ,
which means
2*t = 1*(t+3)
2t = t + 3
2t - t = 3
t = 3
Therefore , Ivan will catch up to Horatio in 3 hours .
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A certain standardized test has a mean of 421 and a standard deviation of 18. For a student to score higher than 30.85% of those who took the exam, what score would be necessary?
Answers
The score required for the exam so that the score is higher than 30.85% is 412 for certain standardized test.
What is defined as the z-score?A Z-Score is a measurable statistic of a score's connection to the mean among a set of scores.A Z-score can tell a trader whether a value is characteristic for a given data set or atypical.In overall, a Z-score of less than 1.8 indicates that a company may be on the verge of bankruptcy, whereas a score nearer to 3 indicates that a company is in good financial standing.The formula for finding the z-score is;
z = (x - μ)/σ
x = sample size
μ = mean of the population
σ = standard deviation of the population.
The given values are-
μ = 421
σ = 18
Probability = 30.85% = 0.3085
Check the z-score from the negative z table for 0.3085
z score = -0.5
Put the values in z formula and find x.
z = (x - μ)/σ
-0.5 = (x - 421)/18
Simplifying;
x = -9 + 421
x = 412
Thus, the score required for the standardized test is found as 412.
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Find the equation for the circle with a diameter whose endpoints are (5,5) and (3,−5).
Answers
The equation of the circle in standard form whose center is at (h, k) = (4, 0) is (x - 4)² + y² = 26.
How to derive the standard equation of the circle based on the coordinates of diameter endpoints
In this question we find the coordinates of the endpoints of the diameter of the circle, then, the center of the circle is the midpoint of the line segment. The center of the circle is found by midpoint formula:
(h, k) = 0.5 · (5, 5) + 0.5 · (3, - 5)
(h, k) = (4, 0)
And the radius of the circle is determined by Pythagorean theorem:
r = √[(4 - 5)² + (0 - 5)²]
r = √[(- 1)² + (- 5)²]
r = √26
Then, the equation of the circle in standard form is describe below:
(x - h)² + (y - k)² = r²
If we know that (h, k) = (4, 0) and r = √26, then the equation of the circle is:
(x - 4)² + y² = 26
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Through how many radians does the minute hand of a clock rotate from12:40 PM to 1:10 PM?o10- 10The minute hand rotates through radians.(Simplify your answer. Type an exact answer in terms of Use integers orfractions for any numbers in the expression)-10
Answers
As you can see in the given figure the minute hand of a clock rotate from 12:40 to 1:10 formig a straigth angle.
A straight angle in radians is π radians.
Then, the minute hand rotates π radiansThe numbers of trading cards owned by 9 middle-school students are given below.
(Note that these are already ordered from least to greatest.)
352, 409, 424, 471, 497, 503, 515, 525, 561
Send data to calculator
Suppose that the number 561 from this list changes to 768. Answer the following.
(a) What happens to the mean?
(b) What happens to the median?
OOO
It decreases by
It increases by
It stays the same.
It decreases by .
0.
It increases by 0.
It stays the same.
X
S
Answers
The mean increases by 23 and the median stays the same.
What are the mean and median?A data set's mean (average) is calculated by summing all of the numbers in the set, then dividing by the total number of values in the set. When a data collection is ranked from least to greatest, the median is the middle value.
Given the data set: 352, 409, 424, 471, 497, 503, 515, 525, 561
(a) Mean = [tex]\frac{352+409+424+471+497+503+515+525+561}{9}[/tex]
Mean = [tex]\frac{4257}{9}[/tex]
= 473
The number 561 from this list changes to 768.
New mean = [tex]\frac{352+409+424+471+497+503+515+525+768}{9}[/tex]
= [tex]\frac{4464}{9}[/tex]
= 496
Thus, the mean increases by 496 - 473 = 23.
(b) Median = mid value
= 497
When the number 561 changes to 768, still the mid value will remain the same i.e. the median remains the same.
Therefore, the mean increases by 23 and the median stays the same.
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What is a different common Denominator you could use in problem 2
Answers
Answer:
what is the problem ???
Step-by-step explanation:
2320 is what percent of 2000
Answers
Solve the equation for x.
6(x + 3) - 8 = 4x + 2(4 + x)
Answers
Hello! So...
We are given the following to solve:
Solve for x.
[tex]6(x+3)-8=4x+2(4+x)[/tex]
_______________________________________________________
1. Expand both sides of the equation.
[tex]6(x+3)-8=6x+10[/tex]
[tex]4x+2(4+x)=6x+8[/tex]
[tex]6x+10=6x+8[/tex]
______________________________
2. Subtract 10 from both sides.
[tex]6x+10-10=6x+8-10[/tex]
_______________________________
3. Simplify.
[tex]6x=6x - 2[/tex]
_______________________________
4. Subtract 6x from both sides.
[tex]6x-6x=6x-2-6x[/tex]
_______________________________
5. Simplify.
[tex]0=-2[/tex]
^Notice, the sides are not equal in the solution. This being said, there would be no solution.
___________________________________________________
Hope this helps! If you need anything else, feel free to comment below. Thanks and good luck!
the original price of an article was 240.00. The price is increased by 12½%. The new price of the article is?
Answers
Answer:
The new price of the article is $270
Step-by-step explanation:
270-240/240
x 100% = 12.5%
12.5x240/100
= 30
find all real and complex zeros for f(x)=x^3-x^2+3x-3
Answers
The real and complex zeros for the function given as .f(x) = x³ - x² + 3x - 3 are x = 1 and x = ±i√3, respectively
How to determine the zeros of the function?The equation of the function is given as
f(x) = x³ - x² + 3x - 3
Group the terms of the function in two's
So, we have the equation
f(x) = (x³ - x²) + (3x - 3)
Factor each group in the function
f(x) = x²(x - 1) + 3(x - 1)
Factor out x - 1
f(x) = (x² + 3)(x - 1)
Set to 0
(x² + 3)(x - 1) = 0
This gives
x² = - 3 and x = 1
Evaluate the roots
x = ±i√3 and x = 1
Hence, the zeros of the equation are x = ±i√3 and x = 1
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How many months does it take $428 to double at a simple interest rate of 12%
Answers
When $428 doubles, it means that the
help meeeeeeeeeeeeeeeeeeeeeee
Answers
Answer:
600
Step-by-step explanation:
[tex]R(1)=400 \\ \\ R(2)=1000 \\ \\ R(2)-R(1)=600[/tex]
find the answer to this problem (15/16) - ( -3/16)
A. 3/4
B. -3/4
C. -1 1/8
D. 1 1/8
Answers
First you would do change change and it would be (15/16)+3/16,then do 15+3=18,then put it over 16,18/16,then you simplify and it would be 9/8,but you can’t have a bigger numerator over a denominator,so you would divide 9/8 and it would be 1 1/8.
Leroi is using coordinate geometry to prove this theorem.
Theorem: The diagonals of a parallelogram bisect one another.
Given: AD//BC; AB//CD; AC and BD intersect at M.
Prove: M bisects AC and BD.
Which of these is the BEST strategy for this proof?
A) Use the Midpoint Formula to find the coordinates of M, then use the Distance Formula to verify that AC= BD
B) Use the equations of line AC and line BD to find the coordinates of M, then use the Distance Formula to verify that AC= BD
C) Use the equations of line AC and line BD to find the coordinates of M, then use the midpoint Formula to verify that M is the midpoint of both AC and BD
D) Use the Distance Formula to find the coordinates of M, then use the Midpoint Formula to verify that M is the midpoint of both AC and BD
Answers
The BEST strategy for this proof is (A) Use the Midpoint Formula to find the coordinates of M, then use the Distance Formula to verify that AC= BD
How to determine the best strategy for the proof?The theorem is given as
Theorem: The diagonals of a parallelogram bisect one another.
Also, we have the following given parameters
AD//BC; AB//CD;
AC and BD intersect at M.
The above means that:
Lines AD and BC are parallel lines, and AB and CD are parallel lines
The statement AC and BD intersect at M implies that
AM = MC and BM = MD.
The above means that we need to calculate the lengths of the above segments, and then make comparison
The lengths of the segments can be calculated using the distance formula
Other than that, the coordinate of the point M needs to be calculated
The option that satisfies the above conditions is (a)
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Rectangle ABCD is shown with the dimensions given in units. The length of AB is greater than the length of AD which inequality represents this situation?
A: 9x-16<1.5+42
B: 9x-16>1.5x+42
C: 10.5x<26
D: 10.5x>26
Answers
Answer:
B
Step-by-step explanation:
it is simple.
because AB > AD, their size representations must have the same relationship.
therefore,
9x - 16 > 1.5x + 42
that could be simplified to
7.5x > 58
The inequality that represents AB > AD is B: 9x - 16 > 1.5x + 42.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, In Rectangle ABCD the length of AB is greater than the length of AD.
∴ The inequality that represents this is AB > AD which is,
9x - 16 > 1.5x + 42.
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HELP! 100 POINTS!!!
A baking company has developed two new cookie recipes, however, they only have the resources to add one item to their product line. They decide to randomly sample three groups of 100 people to determine which cookie recipe, A or B, is preferred. The results are shown in the following table.
Recipe A Recipe B
Sample #1 26 67
Sample #2 48 89
Sample #3 22 56
A. Based on the collected data, which recipe should the baking company add to their product line? How confident should the company be in their decision? Explain your reasoning using complete sentences.
B. Using the mean of the data for Recipe A, approximately what percentage of people would you expect to prefer Recipe A over Recipe B?
Answers
Answer:
Question A: They should add product B because it has a 69% rate of approval. They can be 69% confident that the addition of product B will be successful.
Question B: 31% of people would prefer cookie A over cookie B
Step-by-step explanation: