Answers
Given: A matrix
[tex]\begin{bmatrix}{1} & {-3} & {2} \\ {3} & {9} & {5} \\ {} & & {}\end{bmatrix}[/tex]Required: To perform the following matrix row operation
[tex]-3R_1+R_2[/tex]Explanation: The operation is to be applied on the first row of the given matrix. Hence the second row will be same as that of the initial matrix.
The elements of the first row are first multiplied by 3 and then added with second row to give the required matrix.
Hence,
[tex]\begin{bmatrix}{-3+3} & {9+9} & {-6+5} \\ {3} & {9} & {5} \\ {} & {} & {}\end{bmatrix}[/tex]which gives
[tex]\begin{bmatrix}{0} & {18} & {-1} \\ {3} & {9} & {5} \\ {} & {} & {}\end{bmatrix}[/tex]Final Answer: The required matrix is
[tex]\begin{bmatrix}{0} & {18} & {-1} \\ {3} & {9} & {5} \\ {} & {} & {}\end{bmatrix}[/tex]Related Questions
Carl Heinrich had lateral filing cabinets that need to be placed along one wall of a storage closet. The filing cabinets are each 2 1/2 feet wide and the wall is 15 feet long. Decide how many cabinets can be placed along the wall
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In this case we have to divide the length of the wall by the width of a cabinet. Doing so, we have:
[tex]\begin{gathered} 2\frac{1}{2}=\frac{2\cdot2+1}{2}=\frac{5}{2}\text{ (Converting the mixed number to an improper fraction)} \\ \frac{15}{1}\div\frac{5}{2}=\frac{15\cdot2}{5}(\text{Dividing fractions)} \\ \frac{15\cdot2}{5}=\frac{30}{5}=6\text{ (Simplifying the result)} \\ \text{The answer is 6 cabinets.} \end{gathered}[/tex]What is the probability that a meal will include a hamburger
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ANSWER:
The probability that a meal will include a hamburger is 25%
SOLUTION:
The total combination of one entree and one drink is 4* 2 = 8
The total combination of one hamburger meal is 1*2 = 2
The probability is 2/8 or 1/4 or 25%
2/___=4/18What is the answer to the problem
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Explanation:
These are equivalent fractions, we have to find the missing denominator from the fraction on the left. Since the numerator of the fraction on the right is 4 and the numerator of the fraction on the left is 2, we can see that we have to divide by 2. Therefore 18 divided by 2 is 9. This is the numerat
Answer:
Determine the system of inequalities that represents the shaded area .
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For the upper line:
[tex]\begin{gathered} (x1,y1)=(0,2) \\ (x2,y2)=(2,3) \\ m=\frac{y2-y1}{x2-x1}=\frac{3-2}{2-0}=\frac{1}{2} \\ \text{ using the point-slope equation:} \\ y-y1=m(x-x1) \\ y-2=\frac{1}{2}(x-0) \\ y=\frac{1}{2}x+2 \end{gathered}[/tex]For the lower line:
[tex]\begin{gathered} (x1,y1)=(0,-3) \\ (x2,y2)=(2,-2) \\ m=\frac{-2-(-3)}{2}=\frac{1}{2} \\ \text{ Using the point-slope equation:} \\ y-y1=m(x-x1) \\ y-(-3)=\frac{1}{2}(x-0) \\ y+3=\frac{1}{2}x \\ y=\frac{1}{2}x-3 \end{gathered}[/tex]Therefore, the system of inequalities is given by:
[tex]\begin{gathered} y\le\frac{1}{2}x+2 \\ y\ge\frac{1}{2}x-3 \end{gathered}[/tex]A bag contains 6 red, 5 blue and 4 yellow marbles. Two marbles are drawn, but the first marble drawn is not replaced. Find P(red, then blue).
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5 + 6 + 4 = 15
red is 6/15 then taken out
then blue is 5/14
6/15 * 5/14 = 1/7
1/7 or about 0.143
Meghan measures the heights and arm spans of the girls on her basketball team. She plots the data and makes a scatterplot comparing heights and arm spans, in inches. Meghan finds that the trend line that best fits her results has the equation y=x+2 . if a girl on her team is 64 inches tall, What should Meggan expect her span to be?
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EXPLANATION
Let's see the facts:
The equation is given by the following expression y= x + 2
---> 64 inches tall
As we can see in the graph of arm span versus height, and with the given data the arm span should be:
arm span = y = 64 + 2 = 66 inches
So, the answer is 66 inches. [OPTION C]
The functions s and t are defined as follows.Find the value of t(s(- 4)) .t(x) = 2x ^ 2 + 1s(x) = - 2x + 1
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EXPLANATION
Since we have the functions:
[tex]s(x)=-2x+1[/tex][tex]t(x)=2x^2+1[/tex]Composing the functions:
[tex]t(s(-4))=2(-2(-4)+1)^2+1[/tex]Multiplying numbers:
[tex]t(s(-4))=2(8+1)^2+1[/tex]Adding numbers:
[tex]t(s(-4))=2(9)^2+1[/tex]Computing the powers:
[tex]t(s(-4))=2*81+1[/tex]Multiplying numbers:
[tex]t(s(-4))=162+1[/tex]Adding numbers:
[tex]t(s(-4))=163[/tex]In conclusion, the solution is 163
Find the surface area. Do not round please Formula: SA= p * h + 2 * b
Answers
The shape in the question has two hexagonal faces,
The Area of each of the heaxagonal faces is
[tex]=42\text{ square units}[/tex]The shape also has 6 rectangular faces with dimensions of
[tex]8.2\times4[/tex]The area of a rectangle is gotten with the formula below
[tex]\text{Area}=l\times b[/tex]By substituting the values, we will have
[tex]\begin{gathered} \text{Area}=l\times b \\ \text{Area}=8.2\times4 \\ \text{Area}=32.8\text{square units} \end{gathered}[/tex]To calculate The total surface area of the shape, we will add up the areas of the hexagonal faces and the rectangular faces
[tex]\text{Surface area=}2\times(area\text{ of hexagonal faces)+ 6(area of rectangular faces)}[/tex]By substituting the values, we will have
[tex]\begin{gathered} \text{Surface area=}2\times(area\text{ of hexagonal faces)+ 6(area of rectangular faces)} \\ \text{Surface area}=(2\times42)+(6\times32.8) \\ \text{Surface area}=84+196.8 \\ \text{Surface area}=280.8\text{ square units} \end{gathered}[/tex]Hence,
The Surface Area is = 280.8 square units
Angel Corporation produces calculators selling for $25.99. Its unit cost is $18.95. Assuming a fixed cost of $80,960, what is the breakeven point in units?
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The breakeven point of Angel Corporation equals to 11,500 units.
How do we get the breakeven point?Given that the unit price is $25.99, so if they sell a x units, then, the revenue is: R(x) = $25.99*x
Given that the cost per unit is $18.95, plus a fixed cost of $80,960, then, the cost of x units is: C(x) = $80,960 + $18.95*x
Now, the breakeven point is a value of x such that the cost is equal to the revenue, so we need to solve:
$25.99*x = $80,960 + $18.95*x
$25.99*x - $18.95*x = $80,960
$7.04*x = $80,960
x = $80,960/$7.04
x = 11,500 units
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Three-inch pieces are repeatedly cut from a 42-inch string. The length of the string after x cuts is given by y = 42 – 3x. Find and interpret the x- and y-intercepts.
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Answer:
y-intercept: 42
x-intercept: 14
Step-by-step explanation:
The y-intercept can be found with the given equation:
y = 42 - 3x
Either Let x = 0 to find the y-intercept. OR,
rearrange the equation to y=mx+b to see the y-intercept, which is b in the equation.
y = 3(0) + 42
y = 42
The y-intercept is 42 and this means that the original, uncut length of the string (zero cuts) is 42.
To find the x-intercept, let y = 0.
y = 42 - 3x
0 = 42 - 3x
Add 3x to both sides.
3x = 42
Divide by 3.
x = 42/3
x = 14
An x-intercept of 14, means that at 14 cuts there will be no more string left. The length of the string is now 0.
Find the sum of the arithmetic series given a₁ =A. 650B. 325C. 642D. 1266Reset SelectionPrevious Jixt45, an=85, and n = 5.
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SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: write the given details
[tex]a_1=45,a_n=85,n=5[/tex]STEP 2: Write the formula for calculating the sum of arithmetic series
STEP 3: Find the sum
By substitution,
[tex]\begin{gathered} S_n=5(\frac{45+85}{2}) \\ S_n=5(\frac{130}{2})=5\times65=325 \end{gathered}[/tex]Hence, the sum of the series is 325
Solve for y: 5 left parenthesis 3 y plus 4 right parenthesis equals 6 open parentheses 2 y minus 2 over 3 close parentheses The solution is Y = _______
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ANSWER:
-8
STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]5\cdot\mleft(3y+4\mright)=6\cdot\mleft(2y-\frac{2}{3}\mright)[/tex]Solving for y:
[tex]\begin{gathered} 15y+20=12y-4 \\ 15y-12y=-4-20 \\ 3y=-24 \\ y=-\frac{24}{3} \\ y=-8 \end{gathered}[/tex]The solution of y is equal to -8
Solve the triangle for the missing sides and angles. Round all side lengths to the nearest hundredth. (Triangle not to scale.)
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The Law of Cosines
Let a,b, and c be the length of the sides of a given triangle, and x the included angle between sides a and b, then the following relation applies:
[tex]c^2=a^2+b^2-2ab\cos x[/tex]The triangle shown in the figure has two side lengths of a=4 and b=5. The included angle between them is x=100°. We can find the side length c by substituting the given values in the formula:
[tex]c^2=4^2+5^2-2\cdot4\cdot5\cos 100^o[/tex]Calculating:
[tex]c^2=16+25-40\cdot(-0.17365)[/tex][tex]\begin{gathered} c^2=47.946 \\ c=\sqrt[]{47.946}=6.92 \end{gathered}[/tex]Now we can apply the law of the sines:
[tex]\frac{4}{\sin A}=\frac{5}{\sin B}=\frac{c}{\sin 100^o}[/tex]Combining the first and the last part of the expression above:
[tex]\begin{gathered} \frac{4}{\sin A}=\frac{c}{\sin100^o} \\ \text{Solving for sin A:} \\ \sin A=\frac{4\sin100^o}{c} \end{gathered}[/tex]Substituting the known values:
[tex]\begin{gathered} \sin A=0.57 \\ A=\arcsin 0.57=34.7^o \end{gathered}[/tex]The last angle can be ob
Please help! I think this is a simple question but I'm overthinking.
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We have the following:
We can solve this question by means of the Pythagorean theorem since it is a right triangle, in the following way:
[tex]c^2=a^2+b^2[/tex]a = 2.3
b = 3.4
replacing
[tex]\begin{gathered} c^2=2.3^2+3.4^2 \\ c^2=5.29+11.56 \\ c=\sqrt[]{16.85} \\ c=4.1 \end{gathered}[/tex]Therefore, the answer is 4.1
sandy made 8 friendship bracelets. she gave 1/8 to her best friend and 5/8 to her friends on the tennis team. write and solve an equation to find the fraction of her bracelets, b , sandy gave away1
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Answer:
(3/4)b
Explanation:
• Fraction given to her best friend = 1/8
,• Fraction given to her friends on the tennis team = 5/8
To calculate the total proportion of the bracelet she gave away, we add:
[tex]\begin{gathered} (\frac{1}{8}+\frac{5}{8})b \\ =\frac{6}{8}b \\ =\frac{3\times2}{4\times2}b \end{gathered}[/tex]Reducing the fraction to its lowest form by canceling out 2 gives:
[tex]=\frac{3}{4}b[/tex]57-92=17 -2c-ust +1 8x1322-1) = 677343 (x + 55-22-20 K 54+32--1 5x+363) = -1 5x+aen -6 8+2=6 2:6-8 -44)-5)-(2) 16-3942=12 18-y-18 -x-57-3222 - (-1)-sy-5633=2 2-35-17 = 2 2.3.3 -Byzo yo TARE 3) -x - 5y + z = 17 -5x - 5y +56=5 2x + 5y - 3z=-10 4) 4x + 4y + 2x - 4y+ 5x - 4y
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ANSWER:
[tex]\begin{gathered} x=4 \\ y=2 \\ z=0 \end{gathered}[/tex]STEP-BY-STEP EXPLANATION:
We have the following system of equations:
[tex]\begin{gathered} 4x+4y+z=24\text{ (1)} \\ 2x-4y+z=0\text{ (2)} \\ 5x-4y-5z=12\text{ (3)} \end{gathered}[/tex]We solve by elimination:
[tex]\begin{gathered} \text{ We add (1) and (2)} \\ 4x+4y+z+2x-4y+z=24+0 \\ 6x+2z=24\text{ }\rightarrow x=\frac{24-2z}{6}\text{ (4)} \\ \text{ We add (1) and (3)} \\ 4x+4y+z+5x-4y-5z=24+12 \\ 9x-4z=36\text{ (5)} \\ \text{ replacing (4) in (5)} \\ 9\cdot(\frac{24-2z}{6})-4z=36 \\ 36-3z-4z=36 \\ -7z=36-36 \\ z=\frac{0}{-7} \\ z=0 \end{gathered}[/tex]Now, replacing z in (4):
[tex]\begin{gathered} x=\frac{24-2\cdot0}{6} \\ x=\frac{24}{6} \\ x=4 \end{gathered}[/tex]Then, replacing z and x in (1):
[tex]\begin{gathered} 4\cdot4+4y+0=24 \\ 16+4y=24 \\ 4y=24-16 \\ y=\frac{8}{4} \\ y=2 \end{gathered}[/tex]Given that angle A lies in Quadrant I and sin(A)= 30/31, evaluate cos(A)
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Which of the followingrepresents this inequality?|4x – 61 > 10
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Solution:
Given the absolute inequality below:
[tex]\lvert4x-6\rvert>10[/tex]From the absolute law,
[tex]\begin{gathered} \lvert u\rvert>a \\ implies\text{ } \\ u>a\text{ } \\ or \\ u<-a \end{gathered}[/tex][tex]\begin{gathered} When\text{ 4x-6>10} \\ add\text{ 6 to both sides of the inequality,} \\ 4x-6+6>10+6 \\ \Rightarrow4x>16 \\ divide\text{ both sides by the coefficient of x, which is 4} \\ \frac{4x}{4}>\frac{16}{4} \\ \Rightarrow x>4 \end{gathered}[/tex][tex]\begin{gathered} When\text{ 4x-6<-10} \\ add\text{ 6 to both sides of the inequality,} \\ 4x-6+6<-10+6 \\ \Rightarrow4x<-4 \\ divide\text{ both sides by the coefficient of x, which is 4} \\ \frac{4x}{4}<-\frac{4}{4} \\ \Rightarrow x<-1 \end{gathered}[/tex]Plotting the solution to the inequality, we have the line graph of the inequality to be
Hence, the correct option is D.
Casey's Cookie Company opened with 24 cupcakes in the store display case. By noon, therewere only 15 cupcakes left. Was there a percent increase or decrease in the amount ofcupcakes? What was the increase or decrease amount?
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Percentage is the proportion between numbers
total initial of cakes for Casey's = 24
final number of cakes = 15
find proportion 15/24 how many represents
15/24 = 5/8
now divide 100/8 = 12.5
then multiply 12.5 x 5
12.5x5= 62.5 %
How do I do this ? I need to find the solution for it
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SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given equations
[tex]\begin{gathered} y=-\frac{4}{3}x \\ y=\frac{3}{2}x \end{gathered}[/tex]STEP 2: Define the point that is the solution for the given functions on the graph
The solution of such a system is the ordered pair that is a solution to both equations. To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect.
STEP 3: Determine the solution for the system of equations
It can be seen from the image below that the two lines intersect at the origin and hence they are given as the solutions to the given system of equations.
Hence, the solutions are:
[tex]x=0,y=0[/tex]Which function has a y-intercept of 4? a. f(x) = 3(1 + 0.05)* b.f(x) = 4(0.95)* c. f(x) = 5(1.1) d. f(x) = 5(0.8)
Answers
Answer:
The correct option is D
f(x) = 5(0.8)
has y-intercept of 4
Explanation:
To know which of the given functions has a y-intercept of 4, we test them one after the other.
a. f(x) = 3(1 + 0.05)
f(x) = 3.15 WRONG
b. f(x) = 4(0.95)
f(x) = 3.8 WRONG
c. f(x) = 5(1.1)
f(x) = 5.5 WRONG
d. f(x) = 5(0.8)
f(x) = 4 CORRECT
Which angles are adjacent and do NOT form a linear pair?
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Adjacent angles share a common side and a common vertex but do not overlap each other.
A linear pair is two adjacent angles that creat a straight line, thus adjacent angles which do not form a linear pair could be:
[tex]\angle2\text{ and }\angle3[/tex]Use the graph to evaluate the function for the given input value. 20 f(-1) = 10 f(1) = х 2 -10 -20 Activity
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we have that
[tex]f(-1)=-8,f(1)=-12[/tex]Hello! Need a little help on parts a,b, and c. The rubric is attached, Thank you!
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In this situation, The number of lionfish every year grows by 69%. This means that to the number of lionfish in a year, we need to add the 69% to get the number of fish in the next year.
This is a geometric sequence because the next term of the sequence is obtained by multiplying the previous term by a number.
The explicit formula for a geometric sequence is:
[tex]a_n=a_1\cdot r^{n-1}[/tex]We know that a₁ = 9000 (the number of fish after 1 year)
And the growth rate is 69%, to get the number of lionfish in the next year, we need to multiply by the rate og growth (in decimal) and add to the number of fish. First, let's find the growth rate in decimal, we need to divide by 100:
[tex]\frac{69}{100}=0.69[/tex]Then, if a₁ is the number of lionfish in the year 1, to find the number in the next year:
[tex]a_2=a_1+a_1\cdot0.69[/tex]We can rewrite:
[tex]a_2=a_1(1+0.69)=a_1(1.69)[/tex]With this, we have found the number r = 1.69. And now we can write the equation asked in A:
The answer to A is:
[tex]f(n)=9000\cdot1.69^{n-1}[/tex]Now, to solve B, we need to find the number of lionfish in the bay after 6 years. Then, we can use the equation of item A and evaluate for n = 6:
[tex]f(6)=9000\cdot1.69^{6-1}=9000\cdot1.69^5\approx124072.6427[/tex]To the nearest whole, the number of lionfish after 6 years is 124,072.
For part C, we need to use the recursive form of a geometric sequence:
[tex]a_n=r(a_{n-1})[/tex]We know that the first term of the sequence is 9000. After the first year, the scientists remove 1400 lionfish. We can write this as:
[tex]\begin{gathered} a_1=9000 \\ a_n=r\cdot(a_{n-1}-1400) \end{gathered}[/tex]Because to the number of lionfish in the previous year, we need to subtract the 1400 fish removed by the scientists.
The answer to B is:
[tex][/tex]If the revenue function for a certain item is R(x)=20x−0.25x2, what is the marginal revenue for the 8th item? Do not include the dollar sign in your answer.
Answers
The marginal revenue of the 8th item from the revenue function is 16
How to determine the marginal revenue?From the question, the revenue function is given as
R(x) = 20x - 0.25x^2
To calculate the marginal revenue, we start by differentiating the revenue function
This is calculated as follows
R(x) = 20x - 0.25x^2
Differentiate the function
R'(x) = 20 - 0.5x
The above represents the marginal revenue function
So, we have
M(x) = 20 - 0.5x
For the 8th item, we have
M(8) = 20 - 0.5 x 8
Evaluate
M(8) = 20 - 4
Evaluate
M(8) = 16
Hence, the marginal revenue is 16
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To find the length of a side, a, of a square divide the perimeter, P by 4. Use the above verbal representation to express the function s, symbolically, graphically, and numerically.
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Solution
- We are told to find the numerical, graphical, and symbolic expression for the side of a square, s, given its perimeter, P
Symbolic Representation:
- The symbolic representation simply means the formula we can use to represent the side of a square given its perimeter, P.
- The side of a square is simply the perimeter P divided by 4.
- Symbolically, we have:
[tex]\begin{gathered} s=\frac{P}{4} \\ \text{where,} \\ s=\text{side of the square} \\ P=\text{Perimeter of the square} \end{gathered}[/tex]Numerical Representation:
- We are given a set of numbers to create a table given some numbers for P.
- We are given a set of values for P: 4, 8, 10, 12.
- We can use the formula in the symbolic representation to find the corresponding values of s.
[tex]\begin{gathered} \text{When P = 4:} \\ s=\frac{4}{4}=1 \\ s=1 \\ \\ \text{When P=8:} \\ s=\frac{8}{4}=2 \\ s=2 \\ \\ \text{When P=10:} \\ s=\frac{10}{4}=2.5 \\ s=2.5 \\ \\ \text{When P=12:} \\ s=\frac{12}{4}=3 \\ s=3 \end{gathered}[/tex]- Now that we have the values of P and the corresponding values of s, we can proceed to create a table of values as the question asked of us.
Riley has $955 in a savings account that earns 15% interest, compounded annually.To the nearest cent, how much interest will she earn in 2 years?
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In order to calculate the interest generated in 2 years, we can use the formula below:
[tex]I=P((1+r)^t-1)[/tex]Where I is the interest generated after t years, P is the principal (initial amount) and r is the interest rate.
So, for P = 955, r = 0.15 and t = 2, we have:
[tex]\begin{gathered} I=955((1+0.15)^2-1) \\ I=955(1.15^2-1) \\ I=955(1.3225-1) \\ I=955\cdot0.3225 \\ I=307.99 \end{gathered}[/tex]Therefore the interest generated is $307.99.
Question 3 (5 points) Convert the decimal 0.929292... to a fraction. O 92 99 O 92 999 O 92 100 92 1000
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An architect is designing the roof for a house what is the height of the roof?
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An architect is designing the roof for a house
what is the height of the roof?
From the diagram,
We have that tan 30 = h/ 12
0.5774 = h/ 12
cross-multiply,
h = 12 x 0.5774
h = 6.9288 feet
Using data from the previous table, construct an exponential model for this situation.A ( t ) =What will be the value when t=8, rounded to 2 decimal places?
Answers
Answer
• Exponential model
[tex]A(t)=13.60(1+0.25)^{t}[/tex][tex]A(8)\approx81.06[/tex]Explanation
The exponential model equation can be given by:
[tex]A(t)=C(1+r)^t[/tex]where C is the initial value, r is the rate of growth and t is the time.
We can get the initial value by evaluating in the table when t = 0. In this case the value A(0) = 13.60. Then our equation is:
[tex]A(t)=13.60(1+r)^t[/tex]Now we have to get r by choosing any point and solving for r. For example, (3, 26.56). By replacing the values and solving we get:
[tex]26.56=13.60(1+r)^3[/tex][tex]\frac{26.56}{13.60}=(1+r)^3[/tex][tex](1+r)^3=\frac{26.56}{13.60}[/tex][tex]\sqrt[3]{(1+r)^3}=\sqrt[3]{\frac{26.56}{13.60}}[/tex][tex]1+r=\sqrt[3]{\frac{26.56}{13.60}}[/tex][tex]r=\sqrt[3]{\frac{26.56}{13.60}}-1\approx0.2500[/tex]Thus, our rate is 0.25, and we can add it to our equation:
[tex]A(t)=13.60(1+0.25)^t[/tex]Finally, we evaluate t = 8:
[tex]A(8)=13.60(1+0.25)^8=81.06[/tex]