If the linear system 6x-8y-10z=-48k, -5x+7y+9z=0, and -3x+4y+hz=0 has infinitely many solutions, x = 6(4) + z = 24 + z , y = -7/5 - z , z is free ,h=2 then k=4 and h=2.
We can rewrite the system of equations as an augmented matrix [A|B], where A is the coefficient matrix and B is the column vector on the right-hand side:
[ 6 -8 -10 | -48k ]
[-5 7 9 | 0 ]
[-3 4 h | 0 ]
We can perform row operations on the matrix to put it in reduced row echelon form, which will allow us to determine the solutions of the system. After performing row operations, we obtain:
[ 1 0 -1 | 6k ]
[ 0 1 1 | -7/5]
[ 0 0 h-2 | 0 ]
From the last row of the matrix, we see that h-2=0, which implies that h=2. From the first two rows of the matrix, we can see that x- z=6k and y+ z=-7/5. Since the system has infinitely many solutions, we can express x and y in terms of z, giving:
x = 6k + z
y = -7/5 - z
Substituting these expressions into the second row of the matrix, we obtain:
-5(6k+z) + 7(-7/5 - z) + 9z = 0
Simplifying this equation gives:
-30k - 10z - 7 + 9z = 0
Solving for k gives k=4.
Therefore, the solutions of the system are:
x= 6(4) + z = 24 + z
y = -7/5 - z
z is free
h=2
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Angles are not necessarily drown to scale.
Answer:
ask ur teacher its pointless
Step-by-step explanation:
no one knows
1. Use the inequality 12≥6(12x+2).
a. Apply the Distributive Property to the right side.
b. Solve the inequality.
At a store closing, a universal discount rate is applied to all items. If the original price of an item was $27.00 and the price
after the discount is $16.20, what is the discount rate at the store?
Answer:
Step-by-step explanation:
Your answer
40% discount
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(1x)/(2)=12
PLEASE SHOW THE WORK!!!
Answer:24
Step-by-step explanation:
simplify 1 * x to x
x/2=12
multiply both sides by 2
x=12 * 2
simplify 12 * 2 to24
x=24
Three pounds of flour are divided into 6 containers so that each container holds the same number of pounds of flour
Answer:
0.5 pounds per container.
Step-by-step explanation:
just divide 3 pound by 6 containers so it would be 3/6 which is equal to 1/2 which is the same as 0.5
There each container holds a number of pounds of flour which would be 0.5 pounds.
What is the division operation?In mathematics, divides left-hand operands into right-hand operands in the division operation.
If three pounds of flour are divided into 6 containers so that each container holds the same number of pounds of flour, we can find out how many pounds of flour each container holds by dividing the total amount of flour by the number of containers.
We can use the following equation to find out how many pounds of flour each container holds:
pounds of flour per container = total pounds of flour / number of containers
So, using this equation:
pounds of flour per container = 3 / 6
Apply the division operation, and we get
pounds of flour per container = 0.5
Each container holds 0.5 pounds of flour.
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There are 24 pints of juice in 2 containers, how many pints of juice in 1 container?
Question 1 options:
6
12
2
48
Ayuda!
Necesito el inciso k) por 10 puntos
Answer:
x=47is your answer
3x-11=130(alternate angle)
3x=130+11
x=141/3=47
Solve for x
X=4
3/2x+8=-1
Paisley invests money in an account paying a simple interest of 8.9% per year. If she invests $80 and no money will be added or removed from the investment, how much will she have in one year, in dollars and cents?
it will be removed
Step-by-step explanation:
help, look at picure
Answer:
x=3
Step-by-step explanation:
61/4=15 1/4
5(3)=15+(1/4)=15 1/4
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Answer:
tbh that doesnt make sense the easiest way to et the first one is to do 955 divided by 90.
Step-by-step explanation:
4
1
(12−8×)=
3
2
(6×)
creo que es 32 por la cultura
Rodrigo practiced playing the guitar 15 1/3 hours over the past 3 weeks. He practiced for 5 1/4 hours during the first week and 5 2/3 hours during the second week.
Answer:
[tex]4 \frac{5}{12}[/tex]
Step-by-step explanation:
The computation of the number of hours practiced on the third week is given below:
= Total hours over the past 3 weeks - first week - second week
[tex]= 15 \frac{1}{3} - 5 \frac{1}{4} -5 \frac{2}{3}\\\\= \frac{46}{3} - \frac{21}{4} - \frac{17}{3}\\\\= \frac{184 - 63 - 68}{12} \\\\= \frac{53}{12}\\\\= 4 \frac{5}{12}[/tex]
Answer: is is correct
Step-by-step explanation:
the figure it made of a square and right triangles. Find the area
PLZ help me
Answer:
720 inches squared
Step-by-step explanation:
for the square:
a = 24 x 24 = 576 inches squared
for the triangle:
36-24 =
a = 12 x 24 / 2
= 144 inches squared
576 + 144 = 720 inches squared
Answer:
720 inches squared
Step-by-step explanation:
i took test
define el concepto de renacimiento y el de humanismo
Answer:
Renacimiento es el nombre dado en el siglo XIX a un amplio movimiento cultural que se produjo en Europa Occidental durante los siglos XV y XVI. ... El Renacimiento fue fruto de la difusión de las ideas del humanismo, que determinaron una nueva concepción del hombre y del mundo.
Step-by-step explanation:
Please give thanks to all my answers and please mark as brilliant and please follow me
Yep here we go again :
In the diagram below lines HA and BC are parallel. If angle GEC = 135 what is angle HDF?
If you don't know the question, or not sure, please don't answer it!
Whoever answers it right gets brainliest.
Step-by-step explanation:
Angle HDF is also 135 degrees as well. Alternate exterior angles are congruent.
which one of the following is NOT a polynomial option 1. x^2-2x+3 option 2. 11x-9. option 3. 3/y
Answer:
option 3
Step-by-step explanation:
what is the surface area of the cylinder with height 3km and radius 7km
Answer:
A=439.82 or A=439
Step-by-step explanation:
~~~~~~~~:)
GUYS PLEASE ANSWER THIS QUESTION BELOW. I AM 1 BRAINLIEST AWAY FROM EXPERT AND NEED SOMEONE ELSE TO ANSWER THIS QUESTION SO I CAN GET BRAINLIEST! YOU DON'T NEED TO ANSWER IT RIGHT JUST TYPE SOMETHING RANDOM!! Thank you!!
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Answer:
Done :)
Step-by-step explanation:
Best of luck!
What is the correct vocabulary term for a number variable product or quotient in an expression
Answer the photo below thanks
Answer: rotation
Step-by-step explanation:
Twelve students share 3 pizzas equally. What fraction of a pizza does each student
get?
Answer: 4/12
Step-by-step explanation: 4 over 12
2. The weather forecast calls for 12 cm of snow. How many inches
can you expect?
4. You have a 1.5 gal jug. How many litres will it hold?
5. Joe is travelling in the United States. A road sign indicates he is
228 mi from his destination. How many kilometres is Joe from
his destination?
Answer:
2. 1 inch
4. 5.68 liters(if we estimate)
5. 366.96 kilometers
Step-by-step explanation:
2. centimeters to inches
4. gallons to liters
5. miles to kilometers
A teepee is designed to have a diameter of 10 ft and a volume of 366ft³ what is the height? A.15ft , b.14 ft, c 5ft, or 1 ft
Answer:
B. 14 ft approx
Step-by-step explanation:
Given data
A teepee has a conical shape
Diameter= 10ft
radius= 5 ft
Volume = 366ft³
Height = ????
The expression for the volume is
V= 1/3πr^2 h
substitute
366= 1/3*3.142*5^2*h
366= 1/3*78.55*h
366= 26.18h
h= 366/26.18
h=13.98 ft
h= 14 ft approx
Hence the Height is 14 ft approx
Answer:
14 ft
Step-by-step explanation:
a p e x!
Michael sells 136 newspapers each week. If there are 52 weeks in a year, how many newspapers does Michael sell in a year?
Answer:
7,072
Step-by-step explanation:
136 times 52 = 7,072
Answer:
7,072 newspaper in a year
Step-by-step explanation:
Multiply: 136*52=7,072
(I would put a picture of my work but I'm lazy right now lol)
Hope this helped!! :)
Stay safe and have a wonderful day/night!!!!!
Brainliest?!?!
find the unknown Angles in the given figure
Answer:
x = 50°, y = 50°
Step-by-step explanation:
⇒ x + x + 80° = 180°
⇒ 2x = 180° - 80° = 100°
⇒ x = 100°/2 = 50° ∴ y = x = 50°
Donna paid $3 to rent shoes and then $1 for each game she played at a bowling alley. She spent a total of $8 at the bowling alley.
Which equation can be used to find the number of games Donna played?
Answer:If shoes are for all games in row, P = 2 + 3 g If not, P = 5 g ,with g the number of games
Explanation: The price depends:if shoes are included for the whole games, you just have to pay them once and then you have to pay
g g a m e s , so P ( g ) = 2 + 3 g Else, you have to pay g s h o e s and g b o w l p a r t y ,so
P ( g ) = 2g + 3 g⇔ P ( g ) = 5 g
Hope this helped hope you get a good score on your assignment/test/quiz/homework-Tay did this
What is the Value of X
What is the Length of JM?
Answer:
JM = 17
x = 12
Step-by-step explanation:
The given triangles are similar with ASA rule if so then x + 5 must be equal to 2x - 7
x + 5 = 2x - 7 and 5 + 7 = 2x - x
12 = x
The length of JM
2x - 7 can be written as 2×12 - 7 = 17
What additional information would you need to prove
Answer:
A
Step-by-step explanation:
We use the Hypotenuse Leg Theorem
When we know the hypotenuse and a leg of a triangle.
We know The Hypotenuse (TO) so we need to know A leg of the triangle which the only leg is TM and OR.
√32+√42 ÷ √8 +√12 simplify
Note: It should be 48 instead of 42 because √42 cannot be simplified.
Given:
Consider the given expression is
[tex]\dfrac{\sqrt{32}+\sqrt{48}}{\sqrt{8}+\sqrt{12}}[/tex]
To find:
The simplified form of the given expression.
Solution:
We have,
[tex]\dfrac{\sqrt{32}+\sqrt{48}}{\sqrt{8}+\sqrt{12}}[/tex]
It can be written as
[tex]=\dfrac{\sqrt{16\times 2}+\sqrt{16\times 3}}{\sqrt{4\times 2}+\sqrt{4\times 3}}[/tex]
[tex]=\dfrac{4\sqrt{2}+4\sqrt{3}}{2\sqrt{2}+2\sqrt{3}}[/tex]
[tex]=\dfrac{4(\sqrt{2}+\sqrt{3})}{2(\sqrt{2}+\sqrt{3})}[/tex]
[tex]=\dfrac{4}{2}[/tex]
[tex]=2[/tex]
Therefore, the simplified form of the given expression is 2.