Answers
EXPLANATION
Given the Matrix:
[tex]\begin{bmatrix}{2} & {-4} & {4} \\ {1} & {2} & {11} \\ {} & {} & {}\end{bmatrix}[/tex]Our system of equations will be:
[tex]\begin{bmatrix}{x1} & {y2} & {c1} \\ {x2} & {y2} & {c1} \\ {} & {} & {}\end{bmatrix}[/tex](1) x1 + y1 = c1
(2) x2 + y2 = c2
So, replacing values of given Matrix, this will give us:
Equation (1): 2x -4y = 4
Equation (2): x +2y = 11
Related Questions
Simplify each expression by using the Distributive Property and combine like terms to simplify the expression.Algebra 1-a+11b-7-2a-b
Answers
Explanation:
The initial expression is:
-a + 11b - 7 - 2a - b
The terms -a and -2a are like terms. In the same way, 11b and -b are like terms.
So, using the distributive property, we get:
-a + 11b - 7 - 2a - b
-a - 2a + 11b - b - 7
(-1 - 2)a + (11 - 1)b - 7
-3a + 10b - 7
Therefore, the simplified expression is: -3a + 10b - 7.
Answer: -3a + 10b - 7
is √100 a whole number, irrational number, rational number, or an integer?
Answers
The given number is
[tex]\sqrt[]{100}[/tex]The square root of 100 is 10.
So, this is a whole, integer, and rational number.Remember that whole and integers are also rational because they are a subset of rational numbers set.
Solve the system of equations by the substitution method. 7x- y=58 5x+6y=28
Answers
ANSWER
The solution is (8, -2)
EXPLANATION
The substitution method consists in solving one of the equation for one of the variables - it will be as a function of the other variable, then substitute that variable by this expression into the other equation. There we'll have an equation for one of the variables, we solve that and the substitute the value into the expression we found first.
For this problem let's solve the first equation for y:
[tex]7x-y=58[/tex]We can just add y to both sides of the equation and then subtract 58 from both sides:
[tex]\begin{gathered} 7x-y+y=58+y \\ 7x=58+y \end{gathered}[/tex][tex]7x-58=y[/tex]Now we substitute y by this expression into the second equation:
[tex]5x+6(7x-58)=28[/tex]And solve for x. First apply the distributive property to the second term:
[tex]\begin{gathered} 5x+6\cdot7x-6\cdot58=28 \\ 5x+42x-348=28 \end{gathered}[/tex]Add like terms - this means adding the coefficients of x:
[tex]\begin{gathered} (5+42)x-348=28 \\ 47x-348=28 \end{gathered}[/tex]Then add 348 to both sides of the equation:
[tex]\begin{gathered} 47x-348+348=28+348 \\ 47x=376 \end{gathered}[/tex]Finally, divide both sides by 47:
[tex]\begin{gathered} \frac{47x}{47}=\frac{376}{47} \\ x=8 \end{gathered}[/tex]Now, to find y we just have to substitute x = 8 into the expression we found for y as a function of x:
[tex]y=7x-58[/tex][tex]y=7\cdot8-58=56-58=-2[/tex]So the solution to the equation is x = 8 and y = -2, which is the point (8, -2)
Find three consecutive odd Integers such that the sum of the largest and twice the smallest is 25.x represents the smallest integer, then which equation could be used to solve the problem?
Answers
ANSWER
7, 9, 11
EXPLANATION
We want to find three consecutive odd numbers.
Let the smallest number be x.
Then, the next odd number is (x + 2).
The last odd number is (x + 4).
The sum of the largest odd number and twice the smallest number is 25:
(x + 4) + 2x = 25
=> x + 4 + 2x = 25
3x + 4 = 25
3x = 25 - 4
3x = 21
x = 21 / 3
x = 7
Therefore, the three consecutive numbers are:
7
(7 + 2) = 9
(7 + 4) = 11
They are 7, 9, 11
10. Use the Distributive Property to solve the equation 3(x - 6) + 6= 5x - 6.
Answers
3(x-6)+6 = 5x-6
Apply distributive property:
3x-18+6= 5x-6
Combine like terms
3x-12 = 5x-6
Move x terms to the right:
3x-5x = -6+12
-2x = 6
divide both sides by -2
x=-3
answer the question below show work write the x and y intercepts
Answers
ANSWER:
STEP-BY-STEP EXPLANATION:
We have the following system of inequalities:
[tex]\begin{gathered} f(x)>|x| \\ \: g(x)<-\frac{1}{2}x+1 \end{gathered}[/tex]This system can only be solved graphically, therefore
for f(x):
The x and y intercept is (0, 0)
for g(x)
The x-intercept is (2, 0) and y-intercept is (0, 1)
The solution to the system will be the area where the shadows of each inequality overlap
Just like that:
Mortgages (47-49)Eli is buying a townhouse that costs $276,650. He has $28,000 in savings and earns $4,475 a month. Eli would liketo spend no more than 30% of his income on his mortgage payment. Which loan option would give Eli the lowestmonthly payment? Show your work.A. 30 year FHA, 3.5% down and a fixed rate of 6.5%B. 30 year fixed, 5% down at a fixed rate of 6.25%C. 30 year fixed, 6.5% down and a fixed rate of 5.75%D. 30 year fixed, 10% down at a fixed rate of 5%
Answers
Cost C = $276,650
Initial quote = $28000
If Eli spends 30% of 4,475 = $1342.5 monthly
Then now calculate
3.5% down of $276,650 = $9682.75
Substract $28000- $9682.75 = 18317.25
Now find ,fixed rates
For 6.5% , interest is.
She have to pay a quote of (276,650- 9682.75)/12•30
. = $741.57
For 5% down of $276,650 = 13832.5
Eli have now $28000- $13832.5 = 14167.5
She have to pay a quote of (276,650- 13832)/30•12 = $262818/360
. = $730
Interest fixed rate 6.25%
Then find 730• ( 1+ 6.25/100)^ 30 = 4500 in 30 years
Now option C)
6.5% down = $276,650x 6.5/100 = $17982.25
Eli have now $28000 - 17982.25 = 10017.75
She have to pay a quote of (276,650 - 17982)/30•12
. = $718.52
Then find 718.52•( 1+ 5.75/100)^30 = 3844.6. in 30 years
Option D)
10% down = $276,650x10/100 = $27,665
Eli have now $28000- 27,665 = $335
She have to pay a quote of (276,650 - 27665)/30•12 =
. = $691.625
Then find now 691.625•(1+ 5/100)^30 = $2989.16 in 30 years
So ,in conclusion we have to choose the minor value of quote. In this case is
ANSWER IS
OPTION D) $2989,16
Hello! Need a little help on part B. Thank you!
Answers
we have the system of equations
[tex]\begin{gathered} f(x)=\log_2x+2 \\ g(x)=\log_2x^3-6 \end{gathered}[/tex]Equate the functions f(x) and g(x)
[tex]\log_2x+2=\log_2x^3-6[/tex]Apply property of logarithms
[tex]\begin{gathered} \operatorname{\log}_2x+2=3\operatorname{\log}_2x-6 \\ 3\operatorname{\log}_2x-\operatorname{\log}_2x=2+6 \\ 2\operatorname{\log}_2x=8 \\ \operatorname{\log}_2x=4 \end{gathered}[/tex]Apply the definition of logarithm
[tex]\begin{gathered} 2^4=x \\ x=16 \end{gathered}[/tex]Express the product shown as a fraction in simplest form: -2/5 . 2/5
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Answer:
7/25
Step-by-step explanation:
2/5 x 7/10 =14/50 divide by 2/2 = 7/25
I need help with this Question 5 and Question 6
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5) The rate of change from 2000 to 2012 is 0.80
6) The rate of change from 2012 to 2015 is 0.32
From the question, we have
5) Rate of change from 2000 to 2012 = (3.64-2.02)/2.02
=1.62/2.02
=0.80
6) Rate of change from 2012 to 2015 = (3.64-2.45)/3.64
=1.19/3.64
=0.32
Subtraction:
Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.
The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.
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The profit in dollars of running an assembly line that produces custom uniforms each day is given by P(t)=−40t2+960t−4,000
where t represents the number of hours the line is in operation. Determine the number of hours the assembly line should run in order to make a profit of $1,760 per day.
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Answer:
12
Step-by-step explanation:
[tex]-40t^2+960t-4000=1760 \\ \\ -t^2+24t-100=44 \\ \\ t^2-24t+144=0 \\ \\ (t-12)^2=0 \\ \\ t=12[/tex]
The number of bacteria in a culture is given by the function n(t)=920e^.2twhere t is measured in hours.(a) What is the relative rate of growth of this bacterium population?(b) What is the initial population of the culture (at t=0)?(c) How many bacteria will the culture contain at time t=5?
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Answer:
a. Relative rate of growth = 0.2
b. Initial population: 920
c. 2501
Explanation:
If we have an exponential function of the form
[tex]y=A_0e^{kt}[/tex]Then
A0 = inital amount
k = relative rate of growth
t = time
Now in our case we have
[tex]n(t)=920e^{0.2t}[/tex]Therefore,
Inital population = 920
Relative rate of growth = 0.2
Now at t = 5, the above formula gives
[tex]n(5)=920e^{0.2*5}[/tex]
which evaluates to give
[tex]n(5)=2500.8[/tex]which rounded to the nearest whole number is
[tex]\boxed{n(5)=2501.}[/tex]The property taxes on a house were $1140. What was the tax rate if the house was valued at $190,000? Follow the problem-solvingprocess and round your answer to the nearest hundredth of a percent, if necessary.
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Okay, here we have this:
Considering the provided information we obtain that:
$1140 is x%
$190,000 is 100%
So, here we have the following proportion:
[tex]\frac{190000}{1140}=\frac{100}{x}[/tex]Now, let's solve for x:
[tex]\begin{gathered} x=\frac{1140\cdot100}{190000} \\ x=\frac{114000}{190000} \\ x=\frac{3}{5} \\ x=0.6 \end{gathered}[/tex]Finally we obtain that the tax rate was 0.6%.
What is the constant of variation, k, of the direct variation, y = kx, through (5, 8)?k = – k equals negative (8 Over 5).k = – k equals negative (5 Over 8 ).k = k equals (5 Over 8).k = k equals (8 Over 5 ).I dont understand how to solve this.
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Hello! If we rewrite this expression y = kx, we will see that k will have a variation according to y and x values, look:
Now, notice that the exercise has given a point to us: (5, 8).
Remember that (5, 8) = (x, y), so, let's replace it in the formula:
Right answer:
k = k equals (8 Over 5 ).
Helen mean receives a travel allowance of $180 each week from her company from time away from home. If this allowance is taxable and she has 24% income tax rate, what amount will she have to pay in taxes for this employee benefit? (Round your final answer to two decimal places)
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The tax rate she needs to pay is 24% of the $180.
Then first, we convert the 24% to decimal, by dividing by 100:
[tex]\frac{24}{100}=0.24[/tex]Now we multiply the total amount by the percentage in decimal:
[tex]0.24\cdot180=43.2[/tex]The amount she will have to pay in taxes is $43.20
I need help with this question I appreciate the help
Answers
when
y = 2
x = 10
Therefore,
[tex]\begin{gathered} y=kx \\ k=\frac{y}{x} \\ k=\frac{2}{10}=\frac{1}{5}=0.2 \end{gathered}[/tex]C = 0.2 g
√2 + √5 + √5 =A. √2 + 3√5 or B. √2 + 2√5Which one?
Answers
You have the following expression:
√2 + √5 + √5
In order to simplify the given expressions, you consider the terms with square roots as factor that you can simplify in the same way of the simplification in algebra. That is, if you have √5 + √5, you can sum the coefficients of these terms. Thus, what you have is √5 + √5 = 2√5.
Then, for the given expression you obtain:
√2 + √5 + √5 = √2 + 2√5
Determine whethersecx cotx-cosxsin(-x) cot²xand cotx are equivalent. Justify your answer.
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we have the expression
[tex]\frac{secxcot^2x-cosx}{sin(-x)cot^2x}[/tex]Rewrite the given expression
Remember that
sin(-x)=-sin(x)
[tex]\frac{\frac{1}{cosx}\frac{cos^2x}{sin^2x}-cosx}{-sinx\frac{cos^{2}x}{s\imaginaryI n^{2}x}}[/tex]Simplify the expression
[tex]\begin{gathered} \frac{\frac{cosx}{s\imaginaryI n^2x}-cosx}{-\frac{cos^2x}{s\imaginaryI nx}} \\ \\ \frac{\frac{cosx-sin^2xcosx}{sin^2x}}{-\frac{cos^2x}{sinx}} \\ \\ \frac{cosx-s\imaginaryI n^{2}xcosx}{s\imaginaryI n^{2}x}\colon-\frac{cos^{2}x}{s\imaginaryI nx} \\ \\ \frac{sinx(cosx-sin^2xcosx)}{sin^2x(cos^2x)} \\ \\ \frac{(cosx-sin^2xcosx)}{sin^x(cos^2x)} \\ \\ \frac{cosx(1-s\imaginaryI n^2)}{s\imaginaryI nx(cos^2x)} \\ \\ \frac{(1-s\imaginaryI n^2)}{s\imaginaryI nx(cosx)} \\ \\ \frac{cos^2x}{s\imaginaryI nx(cosx)} \\ \\ \frac{cosx}{sinx} \\ \\ cotx \end{gathered}[/tex]therefore
The answer is
yes, the expression is equivalent to cot(x)A realtor wanted to determine if there was a relationship between the size (in 100 square feet) of a new custom-built home and the price (in thousands of dollars) of the home.
Size, x Price, y
26 235
27 273
41 387
29 253
33 295
34 335
36 395
45 475
22 203
a) Determine the Person Correlation Coefficient.
b) Test whether there is a relation between size and price.
c) Draw the scatter diagram
d) Determine the Least Square line.
e) If a new custom-built home is of a size 3700 square feet what would be its price.
¬¬
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The graphs , solutions and table are attached below and check out the calculation part just by scrolling down.
What is statistics ?In the field of applied mathematics known as statistics, gathering, describing, analyzing, and drawing conclusions from numerical data are important tasks. Probability theory, linear algebra, and differential and integral calculus are the main mathematical foundations of statistics.
Calculationsee the graphs and table attached below
a ) The cluster (points) shows upward direction and nearly to linear form. So it is positive Correlation.)
b ) calculation part for this part has been attached in pictures below since it was not possible to write here .
the regression line of y on x is =
Y = 11.5355X - 58.7667
c ) r^2 = 58313.22 / 62507.5556 = 0.9328
It is high correlation, So the regression equation is good fit to the given data. 93% of the total variation in y occurs because of the variation in their x.
d ) H0: Slope of Regression Coefficient is Zero
H1: Slope of Regression coefficient is not Zero.
calculation part in pictures attached .
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A person tosses a coin twice. Find the set representing the event E that the first toss is tails.
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Solution:
Given that;
A person tosses a coin twice.
The tree diagram representing when a coin is tossed twice is shown below
From the tree diagram above;
The set representing the event E that the first toss is tails is
[tex]TH,TT[/tex]Hence, the answer is
[tex]\lbrace TT,TH\rbrace[/tex]Find the image of (4, 5) under S0.5 withcenter at (1, 6)
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We have a pre-image that is the point (4, 5).
We applied a dilation with scale 0.5 and center at (1, 6).
As the center is not the center of coordinates, we applied a change of coordinates to make (1, 6) the center of coordinates.
Then, the point (4, 5) becomes:
[tex](4,5)\longrightarrow(4-1,5-6)=(3,-1)[/tex]We apply the dilation to the point and get:
[tex](3,-1)\longrightarrow(0.5\cdot3,0.5\cdot(-1))=(1.5,-0.5)[/tex]Now, we go back to the original coordinates:
[tex](1.5,-0.5)\longrightarrow(1.5+1,-0.5+6)=(2.5,5.5)[/tex]We can verify the transformation in a graph:
The graph makes sense, as the image point is half the distance from the center of dilation that the pre-image point.
Three friends go on a road trip from Phoenix, AZ toLas Vegas, NV, a distance of 286 miles. The car theyare driving gets 33 miles per gallon. If the price ofgasoline averages $3.86/gallon, how much willeach student have to pay for the trip
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First, let's find how many gallons are needed:
[tex]\begin{gathered} \frac{286miles}{33\text{ }\frac{miles}{gallon}} \\ 8.7gallons \end{gathered}[/tex]If the price of one gallon is $3.86, then they will have to pay:
[tex]\begin{gathered} 3.86*8.7 \\ 33.58 \end{gathered}[/tex]The price they will have to pay is $33.58.
Dividing the price by 3 (each student):
[tex]\begin{gathered} \frac{33.58}{3} \\ 11.2 \end{gathered}[/tex]Answer: Each student will have to pay $11.20.
What is the average rate of change from point A to point B in the graph below? A(1/3) B(3/7) C(3) D(6)
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Step 1: Define the formula
The formula for finding the average rate of change is :
[tex]\text{Average rate of change = }\frac{y_2-y_1}{x_2-x_1}[/tex]Step 2: Identify the coordinates of the points on the line
A(-3, -1), B(6, 2)
Step 3: Apply the formula
[tex]\begin{gathered} \text{Average rate of change = }\frac{2-(-1)}{6-(-3)} \\ =\text{ }\frac{2\text{ + 1}}{6\text{ + 3}} \\ =\text{ }\frac{3}{9} \\ =\text{ }\frac{1}{3} \end{gathered}[/tex]Hence, the average rate of change is 1/3
Answer: Option A
1) use the equation below to answer part A-Cy=3x-1Part A : What is the slopeA) 3B)3xC)(-1,0)D)(0,-1)Part B : what is the y-intercept? A) (0,-1)B)3xC)(-1,0)D)3Part C: graph y=3x-1
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We are given the following equation
[tex]y=3x-1[/tex]Part A: What is the slope?
The standard equation of a line in slope-intercept form is given by
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
Comparing the given equation with the standard form, we see that the slope is 3.
m = 3
Option (A) is correct.
Part B: What is the y-intercept?
Comparing the given equation with the standard form, we see that the y-intercept is -1.
b = -1
The y-intercept is the value when the line cuts the y-axis, so the corresponding x-value is 0.
So the point is
(0, -1)
Option (A) is correct
Part C: graph y = 3x - 1
The above equation can be graphed by taking some coordinates (substitute x-values into the function and get the y-values from the function.
When x = -1
y = 3x - 1 = 3(-1) - 1 = -3 - 1 = -4
(-1, -4)
When x = 1
y = 3x - 1 = 3(1) - 1 = 3 - 1 = 2
(1, 2)
When x = 2
y = 3x - 1 = 3(2) - 1 = 6 - 1 = 5
(2, 5)
Let us sketch these points to form a line.
The above is a rough graph for the given equation y = 3x - 1
What is the solution for the equation 6 (3x - 2) = -4(5x - 3) + 8?
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Okay, here we have this:
Considering the provided equation, we are going to solve it, so we obtain the following:
6 (3x - 2) = -4(5x - 3) + 8
18x - 12 = -20x + 12 + 8
18x - 12 = -20x +20
18x+20x=+20+12
38x=32
x=32/38
x=16/19
Finally we obtain that the solution for the equation is 16/19.
In the statement 'If it is sunny Thursday, we will go to a ball game', the phrase 'we will go to a ball game' is thehypothesis.conclusion.converse.conditional statement.
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Answer:
(B) Conclusion.
Explanation:
Given the statement:
If it is sunny Thursday, we will go to a ball game
The phrase: 'we will go to a ball game' is the conclusion.
Consider the following table with information about a sample of students from Phoenix HighSchool and where they live. If a person is randomly selected determine the following probability:P(Female or Suwanee).SnellvilleSuwaneeTotalFemaleValeTotal102030StoneMountain121426S16243050803023B.c.D. TOA.8040
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The total number of students are T = 80.
Determine the number of students who are Female od Suwanee.
[tex]10+12+8+16=46[/tex]The probability for slected person is Student or Suwanee is,
[tex]\begin{gathered} P\text{ (Female or Suwanee)=}\frac{46}{80} \\ =\frac{23\cdot2}{40\cdot2} \\ =\frac{23}{40} \end{gathered}[/tex]So answer is 23/40.
Option A is correct.
how do you do 0.52 divided by 2?
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Given the Division:
[tex]0.52\div2[/tex]You can identify that, in this case, the Dividend is:
[tex]0.52[/tex]And the Divisor is:
[tex]2[/tex]Then, you can rewrite it in this form:
Notice that the Dividend is a Decimal Number. Then, you can follow these steps to solve the Division:
1. Take the first digit of the Dividend. Since it is 0, any number multiplied by zero is zero, you can place 0 at the top. Place 0 under the first digit of the Dividend too.
2. Subtract the numbers:
3. Bring down the next digit. Since it is the first digit after the Decimal Point, you need to write a Decimal Point at the top:
4. Divide the new number by the Divisor.
5. Find a number whose multiplication with the Divisor 2 gives you 5 as the result or a number closer to 5. These would be 2.
6. Place the number 2 at the top and multiply the divisor by it.
7. Place the result below the number 5 and subtract them.
8. Apply the same procedures with the other digits.
Then:
Hence, the answer is:
[tex]=0.26[/tex]A race car travels 2 9/16 miles per minute. How far will it travel in 1 1/4 ?
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Directions - Find the x and y-intercepts for each Standard Form equation. Write your answer as an ordered pair.2x + 4y = 8x - intercept =y - intercept =
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We have the following:
[tex]2x+4y=8[/tex]solving for y:
[tex]\begin{gathered} \frac{2}{4}x+\frac{4}{4}y=\frac{8}{4} \\ \frac{1}{2}x+y=2 \\ y=-\frac{1}{2}x+2 \end{gathered}[/tex]now, x- intercept is when y is equal to 0, therefore
[tex]\begin{gathered} 0=-\frac{1}{2}x+2 \\ \frac{1}{2}x=2 \\ x=2\cdot2 \\ x=4 \end{gathered}[/tex]y-intercept is when x is equal to 0, therefore
[tex]\begin{gathered} y=-\frac{1}{2}\cdot0+2 \\ y=2 \end{gathered}[/tex]The answer is:
x - intercept = (4, 0)
y - intercept = (0, 2)