Answer:
x= -3 and y= 0
Step-by-step explanation:
5x+2y=-15
2x-2y=-6
7x =-21
x= -3
Putting value of x in equation 1
5(-3) +2y=-15
-15+2y= -15
2y= 0
y= 0
This can be solved with the help of matrices
In matrix form the above equations can be written in the form
[tex]\left[\begin{array}{ccc}5&2\\2&-2\/\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}-15\\-6\\\end{array}\right][/tex]
Let
[tex]\left[\begin{array}{ccc}5&2\\2&-2\/\end{array}\right][/tex] = A [tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex] = X and [tex]\left[\begin{array}{ccc}-15\\-6\\\end{array}\right][/tex]= B
Then AX= B
or X= A⁻¹ B
where A⁻¹= adj A/ ║A║ where mod A≠ 0
adj A= [tex]\left[\begin{array}{ccc}-2&-2\\-2&5\/\end{array}\right][/tex]
║A║= ( 5*-2- 2*2)= -10-4= -14≠0
X= A⁻¹ B
[tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex] =- 1/14 [tex]\left[\begin{array}{ccc}-2&-2\\-2&5\/\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}-15\\-6\\\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex] =- 1/14 [tex]\left[\begin{array}{ccc}-2*-15&+ -2*-6\\-2*-15&+ 5*-6\\\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex] =- 1/14 [tex]\left[\begin{array}{ccc} 30&+12\\30&+-30\\\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex] =- 1/14 [tex]\left[\begin{array}{ccc}42\\0\\\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}-42/14\\0/-14\\\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}-3\\0\\\end{array}\right][/tex]
From here x= -3 and y= 0
Solution Set = [(-3,0)]
Container A has 200 Liters of water, and is being filled at a rate of 6 liter per minute. Container B has 500 Liters of water, and is being drained at a rate of 6 liters per minute. How many minutes will it take for both containers to have the same amount of water.
Answer:
25 minutes
Step-by-step explanation:
let x represent total time when both containers to have the same amount of water.
the equation to represent container A = 200 + 6x
the equation to represent container B = 500 - 6x
Because both containers would have the same amount of water, the two equations would be equal to each other
200 + 6x = 500 - 6x
collect like terms
12x = 300
x = 300/12
x = 25 minutes
-3x + y = 7
5x+ 2y = 3
Substitution?
Answer: r=-1,y=4
Step-by-step explanation:
The balance in Al's account is $ 32.60 . The balance in Dee's account is 3 4 the balance in Al's account. The balance in Zac's account is $ 49.08 less than the balance in Dee's account. What is the balance in Zac's account?
Answer:
Balance in Zac's account = - $24.63
Step-by-step explanation:
Given:
Balance in Al's account = $32.60
Balance in Dee's account = 3/4 the balance in Al's account
Balance in Zac's account = balance in Dee's account - $49.08
Find:
Balance in Zac's account
Computation:
Balance in Dee's account = 3/4 the balance in Al's account
Balance in Dee's account = [3/4][32.60]
Balance in Dee's account = $24.45
Balance in Zac's account = balance in Dee's account - $49.08
Balance in Zac's account = $24.45 - $49.08
Balance in Zac's account = - $24.63
The perimeter of the square at the right is 48 inches. What is the area of the square at the right? Explain how you found your answer.
2 easy questions for 35 points
Answer:
for question 5
(1) 9x > 3x + 6
6x > 6
x=1
(2) $100-$10=$90
$90/5=18
Joan would need to work 18 hours
for question 6
P+ (PRT)/100
475 + 475(8.5)(12)/100
475+484.5
= 959.5
I hope this helped you ;)
The formula for throwing a baseball in the air is represented by h=-16t^2 + 12t + 40 where h is the height of the ball. What is the maximum height of the ball?
Answer:
the maximum height of the ball is 42.25 m
Step-by-step explanation:
Given the height function as;
h(t) = -16t² + 12t + 40
At maximum height, the final velocity of the ball will be zero.
The final velocity is calculated as follows;
[tex]v = \frac{dh(t)}{dt} = -32 t+ 12\\\\at \ maximum \ height\ v = 0\\\\Thus, -32 t+ 12 = 0\\\\32t = 12\\\\t = \frac{12}{32} \\\\t = 0.375 \ s[/tex]
At maximum height, the time of motion of the ball is 0.375 s.
The maximum height is calculated as follows;
h(t) = -16t² + 12t + 40
h(0.375) = -16(0.375)² + 12(0.375) + 40
h(0.375) = -2.25 + 4.5 + 40
h(0.375) = 42.25 m
Therefore, the maximum height of the ball is 42.25 m
The transformation of 'f' is represented by 'g'. Write a rule for g. f(x)=\root(3)(x). Then show your check steps.
Answer:
[tex]g(x)=-2\sqrt[3]x[/tex]
or
[tex]g(x) = -2f(x)[/tex]
Step-by-step explanation:
Given
[tex]f(x) = \sqrt[3]x[/tex]
Required
Write a rule for g(x)
See attachment for grid
From the attachment, we have:
[tex](x_1,y_1) = (-1,2)[/tex]
[tex](x_2,y_2) = (1,-2)[/tex]
We can represent g(x) as:
[tex]g(x) = n * f(x)[/tex]
So, we have:
[tex]g(x) = n * \sqrt[3]x[/tex]
For:
[tex](x_1,y_1) = (-1,2)[/tex]
[tex]2 = n * \sqrt[3]{-1}[/tex]
This gives:
[tex]2 = n * -1[/tex]
Solve for n
[tex]n = \frac{2}{-1}[/tex]
[tex]n = -2[/tex]
To confirm this value of n, we make use of:
[tex](x_2,y_2) = (1,-2)[/tex]
So, we have:
[tex]-2 = n * \sqrt[3]1[/tex]
This gives:
[tex]-2 = n * 1[/tex]
Solve for n
[tex]n = \frac{-2}{1}[/tex]
[tex]n = -2[/tex]
Hence:
[tex]g(x) = n * \sqrt[3]x[/tex]
[tex]g(x)=-2\sqrt[3]x[/tex]
or:
[tex]g(x) = -2f(x)[/tex]
Please answer need fast
Answer:
B is the correct ans
please mark brainliest
What is the PE of an object that is 15kg that is 5.0 M above the ground?
Answer:
735 JStep-by-step explanation:
The potential energy of a body can be found by using the formula
PE = mgh
where
m is the mass
h is the height
g is the acceleration due to gravity which is 9.8 m/s²
From the question we have
PE = 15 × 9.8 × 5
We have the final answer as
735 JHope this helps you
Which of the following expressions is a factor of 2x2 – 11x + 152
(2x-3)
(x+3)
(2x+5)
(2x-5)
(2x-1)
Step-by-step explanation:
option 3 and 4 are correct answer
A triangle has one side which is 1 foot long and another side which is 2 feet long.
Write a value that could be the length of the third side, in feet. Show your work.
Answer:
Is the triangle a right triangle?
Complete the square to re-write the quadratic function in vertex form: y = x ^ 2 - 2x - 8
Answer:
[tex]y=(x-1)^2-9[/tex]
Step-by-step explanation:
[tex]y=x^2-2x-8[/tex]
To complete the square:
[tex]\frac{b}{2}=(-1)^2=1[/tex]
[tex]y=x^2-2x-8[/tex]
[tex]+9[/tex] [tex]+9[/tex]
[tex]y+9=x^2-2x+1[/tex]
[tex](x-1)^2=y+9[/tex]
[tex]-9[/tex] [tex]-9[/tex]
[tex]y=(x-1)^2-9[/tex]
= ( + ) = ( + ) = ( + )
10. need help with this question plzz
Answer:
okay
Step-by-step explanation:
SO MARK THE PERIMETER AND THE FORMULA FOR FINDING TRAPEZUIM IS
area=1/2 (a+b)h
Answer:
144 cm²
Step-by-step explanation:
5x + 12x + 6x + 5x = 56
=> 28x = 56
=> x = 2
DC => 6x = 6(2) = 12
AB => 12x = 12(2) = 24
BC => 5x = 5(2) = 10
AD => 5x = 5(2) = 10
trapezium is an isosceles trapezium because a trapezium with a pair of non-parallel sides(BC&AD) that have equal distances, which are congruent, is an isosceles trapezium.
Thus, the base of the two triangles on each side are congruent.
base: (AB - DC) ÷ 2 = (24 - 12) ÷ 2 = 6
calculate the height using Pythagorean theorem => √10² - 6² = 8
area of the isosceles trapezium ABCD: (12 + 24) × 8 ÷ 2 = 144
Write an equation of the line that passes through the given points.
(-4,9) and (1, -1)
Answer:
y=-2x+1
Step-by-step explanation:
PLEASEEE I NEED HELP
Given the function f(x) = x2 – 8x + 9
a) Use completing the square to express the given function in vertex form.
b) State the coordinates of the vertex.
Find the sum: (x^5 - 2x^4 + 3x^2 - 6) + (3x^4 + 4x^2 + x + 4). Enter your answer as a
polynomial in descending order below, and use the caret (^) for exponents.
For example, you would write 4x2 as 4x^2.
Answer:
The sum of the two equation is [tex]x^5 + x^4 + 7x^2 + x -2[/tex]
Step-by-step explanation:
The given two equations are
[tex](x^5 - 2x^4 + 3x^2 - 6)\\ (3x^4 + 4x^2 + x + 4)[/tex]
Now rearranging the two equation in such a way that variables with similar with same power are grouped together -
[tex]x^5 - 2x^4 + 3x^4 + 3x^2 + 4x^2 + x- 6+ 4\\x^5 + x^4 (3-2) + x^2 (3+4) + x -6+4\\x^5 + x^4 + 7x^2 + x -2[/tex]
In ΔWXY,m∠W=(2x−12)m∠X=(2 x+17), and∠Y=(9x−7). Find∠X.
Answer:
x = 15
Step-by-step explanation:
2x + 17 = X
x=17-2
= 15
therefore x = 15
A data set has a lower quartile of 3 and an interquartile range of 5. Which box plot could represent this data set?
0
5
10
15
20
25
5
10
15
20
25
10
15
20
25
10
15
20
25
Answer:
could you put a picture up of the different box plots to choose from?
Step-by-step explanation:
hello please help i’ll give brainliest
Answer:
Step-by-step explanation:
Both arsenic and lead can be / are poisonous, so "poison" is the best response here.
Grant made a $2800 investment that piece is simple interest rate at 6% per year. To the nearest hundredth which of the following is the amount of interest here and after one year
F. $1,680.00
G. $46.67
H. $466.67
J. $168.00
Please help ASAP
Answer:
$1,680 - F
Step-by-step explanation:
You do 2800 x 0.6 in ur calculator which is 1680..
NOTE:I haven't done 5/6th grade math in so long.. So correct me if I am wrong please.But I tripple checked this.If the measure of two angles in a triangle are 60 and 100 degrees, what is the measure of the third angle? a. 20 degrees) b. 50 degrees) c. 30 degrees) d. 180 degrees)
Answer:
A. 20 degrees
Step-by-step explanation:
All triangles have 180 degrees in total !
using that info,
100+60= 160
180-160 = 20
Select all statements that show correct reasoning for finding 15 ÷ 2/9 * Multiply 15 by 2, then divide by 9. Multiply 15 by 9, then divide by 2. Multiply 15 by 1/9, then multiply by 2. Multiply 15 by 9, then multiply by 1/2
Answer:
Multiply 15 by 9, then divide by 2.
Step-by-step explanation:
We need to solve the given expression.
[tex]15\div \dfrac{2}{9}[/tex]
We know that, [tex]a\div \dfrac{b}{c}=a\times \dfrac{c}{b}[/tex]
We have,
a = 15, b = 2 and c = 9
So,
[tex]15\div \dfrac{2}{9}=15\times \dfrac{9}{2}\\\\=\dfrac{15\times 9}{2}\\\\=\dfrac{135}{2}\\\\=67.5[/tex]
So, the steps are "Multiply 15 by 9, then divide by 2".
8 7/8 divided by 2 1/2 feet
Answer:
3.55
Step-by-step explanation:
First you must reduce the problems so they do not have a whole. then just divide. You can also use a calculator.
Giving brainlist to whoever answers
Answer:
C 2496 in3
Step-by-step explanation:
Answer:
2496 in3
Step-by-step explanation:
Volume = LWH
24*8*13 = 2496
One dozen students each drop a brass tack six times from a height of six inches onto a level hard surface. They record the number of times the tack lands point up. The table below lists their results.
What was the experimental probability that the tack lands point-up for student 4?
Experimental Probability = 2/3
To find the experimental probability that the tack lands point-up for student 4, we can use the following equation
[tex]\frac{Point-up}{Attempts}\\\frac{4}{6} or\frac{2}{3}[/tex]
If this helped you a Brainliest would be appreciated!
Answer:
0.75
Step-by-step explanation:
Can someone pleaseeee help and if you’re correct i’ll give brainliest
Answer:
Hexagon
Step-by-step explanation:
It has more than 3 sides because it is more sides than a triangle and less than 5 since it has to be fewer sides than a pentagon. A hexagon has 6 sides meaning it has more sides than the pentagon.
Answer:
It should be hexagon
Step-by-step explanation:
Hex equals 6 and quad equals 4, so it would not be quadrilateral or square or recanatgle. So hexagon is your answer.
the triangle below has an area of 25 units2, find the missing side
Answer:
[tex]x=5[/tex]
Step-by-step explanation:
[tex]A= 0.5 bh[/tex]
[tex]25=0.5 (10)h\\\\[/tex]
[tex]25=5h[/tex]
[tex]5h=25[/tex]
[tex]h=5[/tex]
[tex]-------[/tex]
When placed end to end, 5 yellow lego bricks are 2 cm longer than 2 green lego bricks. While 3 green lego bricks are 2 cm longer than 7 yellow lego bricks. How long are 5 green lego bricks?
Answer:
5 green lego bricks are equal to 12 yellow lego bricks
Step-by-step explanation:
Let the yellow and green lego bricks be denoted by y and g respectively.
According to the given conditions
5y+ 2= 2g------ equation 1
3g+2= 7y----- equation 2
Rearranging the equations and adding
5y+ 2= 2g------ equation 3
7y-2= 3g----- equation 4
12y= 5g
5 green lego bricks are equal to 12 yellow lego bricks
Is that right? I'll post the pic
Answer:
I believe it is, I skimmed across it looks accurate to me
Step-by-step explanation: