Answer:
(x, y, z) = (1, 12, 15)
Step-by-step explanation:
As with any set of linear equations, there are many possible routes to a solution. We might simplify the notation a bit by writing the coefficients in an augmented matrix. The columns, left to right, represent the coefficients of x, y, and z, in order, and the constant term.
The row operations we'll use are multiplying a row by a value and adding that result to another row, replacing the other row by the sum.
We can make things a little simpler by writing the second equation first. Then the augmented matrix we're starting with is ...
[tex]\left[\begin{array}{ccc|c}4&-1&1&7\\1&1&-1&-2\\1&-3&2&-5\end{array}\right][/tex]
Adding the second row to the first, we get ...
[tex]\left[\begin{array}{ccc|c}5&0&0&5\\1&1&-1&-2\\1&-3&2&-5\end{array}\right][/tex]
Dividing the first row by 5 gives ...
[tex]\left[\begin{array}{ccc|c}1&0&0&1\\1&1&-1&-2\\1&-3&2&-5\end{array}\right][/tex]
Subtracting this from the second row, and again from the third row, we are left with ...
[tex]\left[\begin{array}{ccc|c}1&0&0&1\\0&1&-1&-3\\0&-3&2&-6\end{array}\right][/tex]
Multiplying the second row by 3 and adding that to the third row, we get ...
[tex]\left[\begin{array}{ccc|c}1&0&0&1\\0&1&-1&-3\\0&0&-1&-15\end{array}\right][/tex]
Subtracting the third row from the second gives ...
[tex]\left[\begin{array}{ccc|c}1&0&0&1\\0&1&0&12\\0&0&-1&-15\end{array}\right][/tex]
Finally, multiplying the last row by -1, we have the solution:
[tex]\left[\begin{array}{ccc|c}1&0&0&1\\0&1&0&12\\0&0&1&15\end{array}\right][/tex]
This matrix corresponds to the equations ...
x = 1y = 12z = 15_____
The purpose of our choice of row operations is to make the diagonal elements 1 and the off-diagonal elements 0. That is how we end up with the final equations shown.
As we said, there are many ways to go about this. In general, one can ...
if necessary, swap rows until the diagonal term of interest is non-zero. If you are doing this using a computer program, generally you want the diagonal term to have the coefficient with the largest magnitude. When doing this by hand, you may want to arrange the rows to avoid fractions when you do the normalizing.divide the row by the coefficient of the diagonal element to "normalize" the diagonal element to a value of 1zero the other elements in that column by multiplying the row just normalized by the element in another row, then subtracting the product. (The 4th matrix shown above shows this for the first column.)proceed to the next diagonal element and repeat the process until all diagonal elements are 1. If you cannot make all diagonal elements 1, then the system of equations does not have a unique solution. If any row becomes all zeros, the system is "dependent" and has infinite solutions. If a row is zeros except for the rightmost column, the system is "inconsistent" and has no solutions.32k+24 i need the equivalent expression
Answer:
4k+3
Step-by-step explanation:
Given the sequence 2, 4, 8, , 16,........, where x = 0, 1, 2, 3, .......what is the function rule? f(x) = 2x + 2 f(x) = 2(2)x f(x) = (2x) f(x) = 2
Option C: [tex]f(x)=2^x[/tex] is the function rule.
Explanation:
The sequence is [tex]2,4,8,16, \dots \dots[/tex]
Let us find the common difference of this sequence.
Common ratio = [tex]\frac{4}{2} =2[/tex]
Hence, [tex]r=2[/tex]
Thus, the given sequence is a geometric progression.
To determine the function rule, let us substitute the values in the general formula of GP which is given by
[tex]f(x)=ar^{x-1}[/tex] where [tex]a=2, r=2[/tex]
Substituting we get,
[tex]f(x)=2(2)^{x-1}[/tex]
Simplifying, we get,
[tex]f(x)=2\times2^x\times2^{-1[/tex]
Adding the powers, we get,
[tex]f(x)=2^{1+x-1}[/tex]
Simplifying, we get,
[tex]f(x)=2^x[/tex]
Hence, the function rule is [tex]f(x)=2^x[/tex]
Thus, Option C is the correct answer.
There was 5 dogs and 1 dog got lost how many dogs are there now
Answer:
5 - 1 = 4
Step-by-step explanation:
In randomly selected family with two children, excluding multiple births , what is the probability of having two boys
Answer:
Therefor the probability of having two boys = [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
i) In randomly selected family with two children, excluding multiple births
the children can be in the following combinations:
a) one girl, one girl : GG
b) one girl, one boy : GB
c) one boy, one boy : BB
The order does not matter for this problem.
Therefor the probability of having two boys = [tex]\frac{1}{3}[/tex]
Dilly is 7 years younger than Dally. In 4 years time she will be half Dally’s age. What is the sum of their ages now?
Answer:
The sum of their ages now is 13
Step-by-step explanation:
Dally's age = x
Dilly's age = x - 7
In 4 years time Dilly will be half Dally’s age, therefore:
Dilly's age plus four equals to half of Dally’s age plus four,
replacing with the values and variables we know:
x - 7 + 4 = (x + 4) /2
x - 3 = (x + 4) /2
2x - 6 = x + 4 (Multiplying by 2 at both sides)
2x - x = 4 + 6 (Like terms)
x = 10 ⇒ x - 7 = 3
The sum of their ages now is 13 (10 + 3)
The sum of their ages now is 13 years
Let the age of Dilly be "x"
Let the age of Dally be "y"
If Dilly is 7 years younger than Dally, then;
x = y - 7 ....... 1
In 4 years time, their age will be:
Dilly = x+ 4
Dally = y + 4
If in 4 years' time she will be half Dally’s age, then;
x+4 = 1/2(y+4) ............... 2
Substitute equation 1 intp 2 to have:
y-7+4 = 1/2(y+4)
y - 3 = 1/2(y+4)
2y - 6 = y + 4
2y - y = 6 + 4
y = 10
Recall that x = y - 7
x = 10 - 7
x = 3
Sum of their ages will be x + y = 10 + 3 = 13 years
Hence the sum of their ages now is 13 years
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Urgent!!!!
5
11
7
9
Please help
Answer:
Its 7
Step-by-step explanation:
24÷8= 3
6×3=18
?×3=21
7×3=21
Awnser is 7
Kara works at a fine jewelry store and earns commission on her total sales for the week. Her weekly paycheck is $6,500 including her salary which is $1,000. Her sales for the week totaled to $45,000. Express her rate of commission as a percent rounded to the nearest whole number.
Rate of commission as a percent is 12 %
Solution:
Kara weekly paycheck is $6,500 including her salary which is $1,000
Therefore,
Commission amount = Weekly paycheck - salary
Commission amount = 6500 - 1000
Commission amount = 5500
Her sales for the week totaled to $45,000
Therefore rate of commission is given as:
[tex]Commission\ rate = \frac{\text{commission amount}}{\text{sales for week}} \times 100[/tex]
Substituting the values we get,
[tex]Commission\ rate = \frac{5500}{45000} \times 100\\\\Commission\ rate = \frac{550}{45}\\\\Commission\ rate = 12.2 \approx 12[/tex]
Thus rate of commission as a percent is 12 %
If the perimeter of the triangle is 32 cm what is the length of each two sides? Write and solve equation
Answer:
12 centimeters
Step-by-step explanation:
An isosceles triangle has two congruent sides which are legs(2 sides having same length )If x is length of each leg, then we ca write the equation like this
equation: x+x+8=32
combine like terms
2x +8 = 32
minus 8 from each side
2x=32-8
2x=24
divide both sides by 2
2x/2 = 24/2
x=12 centimeters
Please Do not answer with anything irrelevant to this subject,Thank you.
In a right triangle, side a is 3 times as long as side b, and side c is 30 cm. Using the Pythagorean Theorem, what are the lengths of sides a and b? Round your answers to the nearest tenth.Hypotenuse is 30,A and B are not known but we know A is 3 times more than B.
Answer:
a = 3√10 ≈ 9.5b = 9√10 ≈ 28.5Step-by-step explanation:
We are given two relations we can use to find "a" and "b":
a = 3b
a² + b² = 30²
Substituting for "a", we have ...
(3b)² +b² = 900
10b² = 900
b² = 90
b = √90 = 3√10 ≈ 9.5
Then "a" is ...
a = 3b = 3(3√10) = 9√10 ≈ 28.5
The values of "a" and "b" are about 28.5 and 9.5, respectively.
50 (5025
What is 50 divided by 5,025
Answer:
0.00995024875622
Step-by-step explanation:
Answer:
0.0099502487562189054726
Step-by-step explanation:
divide 50 by 5025
the two vertices of a triangle are (0,6) and (0,12). if the are of the triangle is 12 square units, where can the third vertex be? What if the triangle is also isosceles?
Answer:
1) (4,6),(-4,6), (4,12),(-4,12)
2) (4,9) or (-4,9)
Step-by-step explanation:
Observe that the two vertices given, (0,6) and (0,12) are on the y-axis.
The distance between this points is |12-6|=6
We know area of a triangle is [tex]A=\frac{1}{2}bh[/tex]
We were given area as 12.
[tex]\frac{1}{2}*b*6=12[/tex]
[tex]3b=12[/tex]
b=4 units
We can find a point 4 units horizontally away from any of the vertex.
So (4,6),(-4,6), (4,12),(-4,12) are feasible vertices.
For the triangle to be isosceles, then the third vertex must be on the horizontal line through the midpoint of (0,6) and (0,12) and must be 4 units away from the line x=0.
Therefore if thr triangle is isosceles, then third vertex must be at (4,9) or (-4,9)
David pays a 20% income tax on his 2,100-month salary. How much does he pay in taxes each year?
Andre Rick and ty were practicing for a track cycling race. Andre- 750 m in 3 minutes Rick 4 minutes 800m, Ty 950 in 5mmintues, who covered the last distance per minute?
A recipe for banana pudding calls for 2/3 cups of sugar for the flour and 1/4 cups of sugar for the meringue topping, how many cups of sugar is required to make that good banana pudding?
A phone originally price at $40 is now $30 what was the percent discount?
Answer:
2 5/8 to 1.
Step-by-step explanation:
That would be 1 3/4 divided by 2/3.
= 7/4 / 2/3
= 7/4 * 3/2
= 21 / 8
= 2 5/8
Answer 2 5/8 to 1.
I think
The senior class is planning a trip that will cost $35 per student if $3920 has been collected from the seniors for the trip, how many have paid for their trip? write and solve an equation.
Answer:
112 will have been paid for their trip
Step-by-step explanation:
You have to divide $3920 by $35 to get your answer
3 lines are shown. A line with points M, H, K intersects with a line with points J, H, L at point H. Another line extends from point H to point N in between angle K, H, J. Angle M H L is (3 x + 20) degrees, angle K H N is (x + 25) degrees, and angle J H N is (x + 20) degrees. What is the measure of AngleJHN? 25° 45° 50° 95°
Answer:
Option B.
Step-by-step explanation:
Given information: ∠MHL=(3x+20), ∠KHN=(x+25), and ∠JHN=(x+20).
We need to find the measure of ∠JHN.
[tex]\angle MHL=\angle JHK[/tex] (Vertical opposite angles)
[tex]\angle MHL=\angle JHN+\angle KHN[/tex]
Substitute the given values.
[tex]3x+20=(x+20)+(x+25)[/tex]
[tex]3x+20=2x+45[/tex]
[tex]3x-2x=45-20[/tex]
[tex]x=25[/tex]
The value of x is 25. So, the measure of ∠JHN is
[tex]\angle JHN=x+20=25+20=45[/tex]
The measure of ∠JHN is 45°.
Therefore, the correct option is B.
Answer:
it's B
Step-by-step explanation:
solve
-2x-y=1
y=3x-1
Answer:
x=-2/5
y=-1/5
Step-by-step explanation:
[tex]-2x-y=1\\y=3x-1[/tex]
Get the y variables onto 1 side
[tex]y+1=-2x\\y=3x-1[/tex]
Now shift the 1 over
[tex]y=-2x-1\\y=3x-1[/tex]
To solve for x, we can subtract the second equation from the first equation
[tex](y-y)=-2x-3x-1-1 = 0=-5x-2\\5x=-2\\x=-2/5[/tex]
Plug back into the first equation we found and solve for y
[tex]y=-2x-1\\y=-2(-2/5)-1\\y=4/5-1=-1/5[/tex]
PLEASE HELP ASAP PLEASE PLEASE PLEASE
Graph the solution to the scenario by dragging and dropping a circle/arrow onto the number line.
The roots of Billy's plant grew to 3 inches beneath Earth’s surface. Graph all the possible depths the roots can continue to grow.
Step-by-step explanation:
"At least x" means "that value x or more"
"At least 2" means "2 or more"
So Billy's plants grow 2 inches or more a month. The smallest increase possible is 2 inches.
We plot a closed circle at 2 on the number line. The closed circle tells us "include this value in the solution set". In contrast, the open circle says "exclude the endpoint from the solution set"
Then we shade to the right indicating all of the possible outcomes (growing 3 inches, growing 4 inches, etc.).
Convert 11/10 into a mixed number
Answer:
Divide 11 by 10 . Place this digit in the quotient on top of the division symbol. Multiply the newest quotient digit (1) by the divisor 10 . Subtract 10 from 11 . :) Hope this helps!
It can be a fraction of 11/10 as a mixed number is 1 1/10.
How to convert fractions into a mixed number?To convert a fraction into a mixed number, you need to divide the numerator (top number) by the denominator (bottom number).
The whole number part of the result is the whole number of the mixed number, and the remainder becomes the numerator of the fractional part.
As per the question, we have the fraction 11/10.
Dividing 11 by 10 gives:
11 ÷ 10 = 1 remainder 1
So the whole number part is 1, and the fractional part is 1/10. We can express this as a mixed number by writing:
11/10 = 1 1/10
Therefore, 11/10 as a mixed number is 1 1/10.
Learn more about the fraction here:
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How is 6.3 written in scientific notation?
6.3 x 10°
63 x 10-1
6.3 x 102
63 x 10°
Answer:
6.3 x 10°
Step-by-step explanation:
6.3 can be written as 6.3 x 1
recall that anything to the power of zero = 1
hence 10° = 1 substitute this back into the expression above to get:
6.3
= 6.3 x 1
= 6.3 x 10°
Julia went into a movie theater and bought 2 bags of popcorn and 5 pretzels, costing
a total of $37.25. Zoe went into the same movie theater and bought 8 bags of popcorn
and 9 pretzels, costing a total of $102.25. Determine the price of each bag of popcorn
and the price of each pretzel.
Answer:
A bag of pop corn costs $8, and each Pretzel costs $4.25.
Step-by-step explanation:
Let [tex]b[/tex] be the price of popcorn, and [tex]p[/tex] the price of Pretzels. If the girl bought 2 bags of popcorn and 5 Pretzels and it cost her $37.25, we have the equation
[tex]2b+5p=37.25[/tex] (this says that the cost of 2 popcorn bags plus 5 pretzels equals $37.25) .
And, since Zoe bought 8 popcorn bags and 9 Pretzels with a total price of $102.25, we get the equation
[tex]8b+9p=102.25[/tex] (this says that the cost of 8 popcorn bags plus 9 Pretzels equals $102.25).
Thus, we have two equations
1. [tex]2b+5p=37.25[/tex]
2. [tex]8b+9p=102.25[/tex]
and we solve them by first multiplying equation (1) by 4:
[tex]4(2b+5p=37.25 )\rightarrow (8b+20p=149)[/tex],
and then subtracting it from equation (2):
[tex]\:\:\:\:\: 8b+9p=102.25\\-(8b+20p=149)\\\line(1,0){3 cm}\\-11p=-46.75\\\\\boxed{p=\$4.25}[/tex]
Now we put this value of [tex]p[/tex] into equation (1) and get:
[tex]2b+5(4.25)=37.25[/tex]
and we solve for [tex]b[/tex] to get:
[tex]2b=37.25-21.5[/tex]
[tex]\boxed{ b=8}[/tex]
Therefore, a bag of popcorn costs $8, and each Pretzel costs $4.25.
Answer:
8 is your answer
Step-by-step explanation:
Suppose there is a strong positive correlation between m and n. Which of the
following must be true?
Option A. When m increases , n tends to increase.
Step-by-step explanation:
Positive correlation is a relationship between two variables in which both variables move in the same direction.
Option A. When m increases , n tends to increase.
Answer:
A. When m increase, n tends to increase
Without plotting the point (0,-10), tell in which quadrant or on
which axis it lies.
a. x-axis c. Quadrant I
b. y-axis d. Quadrant II
A diet food company is attempting to create a non-carb brownie composed entirely of fat and protein. The brownie must weigh at least 10 grams but no more than 100 calories. Fat has 9 calories per gram and protein has 4 calories per gram. Write and graph a system of inequalities that represents weight, in grams, of protein and fat.
Answer:
The system of inequalities is given by
i) x + y ≥ 10
ii) 9x + 4y ≤ 100
Step-by-step explanation:
i) let x be the number of grams of fat in the non-carb brownie.
ii) let y be the number of grams of protein in the non-carb brownie.
iii) The brownie must weigh at least 10 grams
iv) therefore we can write x + y ≥ 10
v) The brownie must have no more than 100 calories
vi) therefore we can write 9x + 4y ≤ 100
Simplify 8(3+5)
Help me please
Answer:
64
Step-by-step explanation:
pemdas says parenthesis first
3+5=8
8(8)
8 times 8 equals 64
We can add the numbers inside the parenthenses: 8(3+5)=8(8)
Now just multiply and we get 64.
So 64 is the simplified answer
Hope this helped!
13.
If the temperature drops from 35°F
to -12°F, how many degrees did it
change?
Answer: 47 degrees
Step-by-step explanation: If it dropped form 35 to 0. That is 35 degrees, if it dropped from 0 to -12 degrees that is 12 more degrees. 35 + 12 = 47
Answer:
it dropped 47°
add 12 to 35
Y=2x-3 a direct variation
What can the fraction 9/40 be converted into?
Answer:
a decimal 0.225
Step-by-step explanation:
Write an inequality that represents the statement "x is greater than -3 and less than or equal to 4."
A. -3
B. -3
C. -35X34
D. -35x<4
Answer:
-3<x<=4
Step-by-step explanation:
Which of the following sets of values correctly completes the T chart for the equation Y =|3x+1|. -5,1,7
7,1,7
5,-1,-7
5,1,7
Option C:
5, 1, 7
Solution:
Given equation:
y = |3x + 1|
In the chart, x values are given as –2, 0, 2.
To find the value of y for the corresponding x given.
Substitute x = –2 in the equation of y.
y = |3(–2) + 1|
= |–6 + 1|
= |–5| (Absolute value of a negative number is positive)
y = 5
Substitute x = 0 in the equation of y.
y = |3(0) + 1|
= |0 + 1|
= |1|
y = 1
Substitute x = 2 in the equation of y.
y = |3(2) + 1|
= |6 + 1|
= |7| (Absolute value of a negative number is positive)
y = 7
Option C is the correct answer.
The values of y are 5, 1, 7.
The answer image of the table is attached below.
Answer:
7,1,7
Step-by-step explanation:
Write the simplest polynomial function with the given roots -3,-2,1 and 5
The simplest polynomial function with the given roots is
[tex]x^4-x^3-19x^2-11x+30[/tex].
Solution:
Given roots of the polynomial are:
–3, –2, 1 and 5
If a is the root of the polynomial then the factor is (x –a).
So that, the factors of the given roots are:
(x –(–3)) = x + 3
(x –(–2)) = x + 2
(x – 1) = x – 1
(x – 5) = x –5
Polynomial = Product of the factors
= (x + 3)(x + 2)(x – 1)(x – 5)
Multiply first two factors.
[tex]=(x^2+2x+3x+6)(x-1)(x-5)[/tex]
[tex]=(x^2+5x+6)(x-1)(x-5)[/tex]
Now, multiply the next two factors.
[tex]=(x^2+5x+6)(x^2-5x-x+5)[/tex]
[tex]=(x^2+5x+6)(x^2-6x+5)[/tex]
Now multiply these two factors.
[tex]=x^2(x^2-6x+5)+5x(x^2-6x+5)+6(x^2-6x+5)[/tex]
[tex]=x^4-6x^3+5x^2+5x^3-30x^2+25x+6x^2-36x+30[/tex]
[tex]=x^4-x^3-19x^2-11x+30[/tex]
The simplest polynomial function with the given roots is
[tex]x^4-x^3-19x^2-11x+30[/tex].
What is approximate volume of a cone with a height of 9 feet and radius of 3 feet?
Answer:
84.82 ft³
Step-by-step explanation:
Answer:
84.823
Step-by-step explanation:
The formula of the volume of cone is v= 1/3 (PI* r^2) h
We have that h= 9feet , and r= 3
So, v =1/3 (Pi * 3^2) 9
V=84.82300