Step-by-step explanation:
given :
2x - 3y = 11
-6x + 8y = 34
find : the solutions of the system by using Cramers Rule.
solutions:
in the matrix 2x2 form =>
[ 2 -3] [x] [11]
=
[-6 8] [ y] [34]
D =
| 2 -3 |
|-6 8 |
= 8×2 - (-3) (-6)
= 16-18 = -2
Dx = | 11 -3 |
| 34 8 |
= 11×8 - (-3) (34)
= 88 + 102
= 190
Dy = | 2 11 |
|-6 34 |
= 2×34 - (-6) (11)
= 68 + 66
= 134
x = Dx/D = 190/-2 = -95
y = Dy/D = 134/-2 = -67
the solutions = {-95, -67}
Answer:
(x , y ) = ( -95, -67)
Step-by-step explanation:
Given system :-
2x - 3y = 11
-6x + 8y = 34
Find :- Solutions of system by using Cramers rule.
Solution :-
To solve the system using Cramer's rule, list all needed determinants.
[tex] D = \left|\begin{array}{cc}2& - 3 \\ - 6 & 8\end{array}\right| [/tex]
[tex]D_1 = \left|\begin{array}{cc}11 & - 3 \\ 34 & 8\end{array}\right| [/tex]
[tex]D_2 = \left|\begin{array}{cc} 2& 11 \\ - 6 & 34\end{array}\right| [/tex]
Evaluate the determinants.D = 8 × 2 - ( -3) ( -6 )
= 16 - 18 = -2
[tex]D_1[/tex] = 11 × 8 - ( -3 ) ( 34 )
= 88 + 102 = 190
[tex]D_2[/tex] = 2 × 34 - ( 11 ) ( -6 )
= 68 + 66 = 134
Since D ≠ 0, Cramer'rs rule can be applied , so find x , y using the formulas;- x = [tex] \frac{D_1}{D}[/tex] , y = [tex]\frac{D_2}{D}[/tex].Plug the value into the formula:-
x = [tex] \frac{190}{-2}\\[/tex] , y = [tex]\frac{134}{-2} \\[/tex].
Divide
x = -95 , y = -67
The possible solution of the system is the ordered pair ( x , y ).(x , y ) = ( -95, -67)
Which point is located on the x-axis of a coordinate grid?
I don't see the grid? did you attach a photo?
In the United States, only Hawaii has a tropical wet climate. In some parts of Hawaii, rainfall is very heavy- over 400 inches per year on the windward side of the Hawaiian island of Kauai. The table shows the monthly rainfall for one year at a reporting station in Hawaii.
Answer:
Mean = 14.33333333
Median = 11
Mode= 9 and 11
Range = 42
Step-by-step explanation:
To find the mean, add all the numbers
(5+1+15+43+9+9+11+11+14+12+36+6) = 172
Divide by the number of numbers
172/12 = 14.33333333
Median is the middle number when listed from smallest to largest
1,5,6,9,9,11,11,12,14,15,36,43
Split into 2 even groups
1,5,6,9,9,11, 11,12,14,15,36,43
The middle is between 11 and 11
(11+11)/2 = 11
Mode is the number that appears mode often
This has 2 modes, 9 and 11
Range is largest number minus smallest number
43-1 = 42
Let h(x) = x*2 + kw - 8. If h(-1) = -5, what is the value of h(4)?
Help
Answer:
h(4) = 0
Step-by-step explanation:
Hoping its ' kx '
[tex]h(x) = x^2 + kx -8 \\\\h(-1) = (-1)^2 + k(-1) - 8\\\\-5 = 1 - k -8\\\\-5 = -k -7\\\\-5 + 7 = -k\\\\2 = -k\\-2 = k[/tex]
Now we have k = -2. We will find h(4).
[tex]h(4) = (4)^2 + (-2)(4) - 8 = 16 -8 - 8 = 0[/tex]
Answer:
h(4) = 0
Step-by-step explanation:
GIVEN :-
A quadratic function h(x) = x² + kx - 8h(-1) = -5TO FIND :-
Value of h(4)SOLUTION :-
To find the value of h(4) , you need to find 'k' first by using the given facts.
[tex]h(-1) = (-1)^2 + k(-1) - 8 = -5[/tex]
[tex]=> 1 - k - 8 = -5[/tex]
[tex]=> -k - 7 = -5[/tex]
Add both the sides by 7.[tex]=> -k - 7 + 7 = -5 + 7[/tex]
[tex]=> -k = 2[/tex]
Multiply both the sides by -1.[tex]=> -k(-1) = 2(-1)[/tex]
[tex]=> k = -2[/tex]
Putting the value of k,
[tex]h(4) = (4)^2 + (-2)(4) - 8[/tex]
[tex]= 16 - 8 - 8[/tex]
[tex]= 16 - 16[/tex]
[tex]= 0[/tex]
Help! Geometry Triangle Congruence
Answer:
Step-by-step explanation:
Thank your for revising and improving the image.
Assuming DF is a straight line,
Given E is the mid-point of DF
mCE = mGF
CE || GF
Then
mDE = mEF (E midpoint of DF)
Angle DEC = Angle EFG (corresponding angle, DF transversal of parallel lines CE and GF)
mCE = mGF (given)
Then triangles DCE and EGF are congruent by reason SAS (side-angle-side)
What is the slope of the line that contains the following 2 points (1,2) (4, 0)
URGENT
PLEASE ANSWER!!!!
Answer:I honestly don’t know.....
im so sorry
Step-by-step explanation:
What is the surface area of the triangular prism?
Answer:
9 x 24 x 1/2(basically dividing by 2) = 108 , 108 x 2(two triangles) = 216
40 x 15 = 600, 600 x 2(two slanted rectangles) = 1200
40 x 24 = 960 (area of base)
Add given areas:
216 + 1,200 + 960 = 2,376 square feet, B.
Answer:
(B) 2,376
Step-by-step explanation:
I was the first person to actually answer since the other person used you for points but it is B
A DVD case contains 4 comedies and 6 action movies. Suppose you select a movie at random on Friday night, don’t replace the movie because you don’t want to watch it again, and then select another movie on Saturday. What is the probability that you select a comedy on Friday and an action movie on Saturday? I HAVE 5 MINS
Step-by-step explanation:
P(C) = 4/10 = 2/5
P(A) = 6/10 = 3/5
Which of the following statements justifies why the triangle shown below is not a right triangle?
Answer:
C.
Step-by-step explanation:
15^2 not = 6^2 + 11^2.
A bean plant grows at a constant rate for month. After 10 days, the plant is
25 centimeters tall. After 20 days, the plant is 45 centimeters tall.
Which equation models the height of the plant, y, after x days?
Answer:
D or y-25=2(x-10)
Step-by-step explanation:
If you graph all or the answers the only one that hits both points is D.
9 yd
8 yd
8 yd
8 yd
Find the combined volume of the structure that is made
up of a prism and a pyramid.
Answer:
9YD THIS IS MY ANSWERStep-by-step explanation:
this is no wrong thi is perfect answer ok
heart follow and star
combine like terms, x-3+6
Answer:
x - 9
Step-by-step explanation:
That should be it, and let me know if I'm wrong. x is by itself and if you were to add 3 and 6 you'd get 9. So x - 9
What is the difference between a computer now from a computer in 1961?
Answer:
well first off the size we can fit compuers in our pockets nowadays
and hardware is insainly diffrent
Step-by-step explanation:
What is 6574893 + 7?????
Answer:
6574900
Step-by-step explanation:
Answer:
6,574,900
Step-by-step explanation:
have a good day
Help me!
I promise will chose Brainliest..
Answer:
IDR 3,651.04
Step-by-step explanation:
4x24=96
96x2,400=230,400
230,400+50,000=280,400
280,400x1.25=350,500
350,500/96=3,651.04
IDR 3,651.04
Answer:
3651 IDR
Step-by-step explanation:
I need to make some assumptions, as the problem description is sometimes too vague.
I assume the delivery charge to cover all 4 boxes as one lump sum.
4 boxes with 24 pouches each.
=> Roma has 96 pouches total.
each pouch cost 2400. that is in total
96×2400 = 230400 IDR
then there is the delivery charge of 50000 for everything.
so, the total costs for Roma are
230400 + 50000 = 280400 IDR
25% profit means that the total sales (assuming all pouches are sold) is 25% higher than the costs.
profit = 280400 + 25%
25% is 1/4 of the total (as 25%×4 = 100%).
25% = 280400 / 4 = 70100.
so, in order to make 25% profit the total sales price (for all pouches sold) has to be
280400 + 70100 = 350500 IDR
now, we have 96 pouches. after selling all 96 pouches we need to have an income of 350500 IDR.
the price for each pouch has to be an equal share of the 350500.
pouch price = 350500 / 96 = 3651 IDR.
Ayuda Porfavor !!!!!!!!
Answer:
44
Step-by-step explanation:
10 x 3 = 30
8 + 6 =14
30 + 14 = 44
Answer:
110ft²
Step-by-step explanation:
Area of figure=(10×8)+(1/2×6×8)
=80+24
=112 ft²
=110 ft² (to nearest tenth)
In circle P, PQ = 3 in. What is the circumference of the circle?
Answer:
6π
Step-by-step explanation:
Formula: C=2πr
C=2π3
C=6π
Find the length of the third side. If necessary, round to the nearest tenth 10 20
if only i knew I would love to help you sorry
Which cone has a volume of 24 x cm?
Answer:
cone a is the correct answer
the third choice is the cirrect answer.
the cone with a 4.5 cm height and a 8cm diameter
hope this helps :)
Help please...no links...
Answer:
a
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
x² = 4² + 7² = 16 + 49 = 65 ( take the square root of both sides )
x = [tex]\sqrt{65}[/tex] → a
Answer:
hopes this helps
Step-by-step explanation:
D 28
Josh was asked to solve the equation 15x-19=4x+11 His first step resulted in the equation 15x=4x=30 Describe what Josh did in his first step.
Answer:
added 19 and 11
Answer:
Added 19 to each side
Step-by-step explanation:
15x-19=4x+11
Add 19 to each side
5x-19+19=4x+11+19
5x = 4x+30
Im taking my algebra 1 final exam today... I'm nervous. Any advice? (I'm an 8th grader taking algebra and its challenging to me)
Take a deep breath and try to study right before the exam. Use your time on the exam wisely because it time goes away fast. Study the basics and formulas. Have a good exam your going to do good!!!
Evaluate the expression for p = 8.
4p =
Answer:
Answer = 32
Step-by-step explanation:
p= 8
4p
(4)(8)
=32
Answer:
I got, 8 x 4 = 32
Please please help me no links
Given:
In triangle ABC, AB = AC, AD is angle bisector and measure of angle C is 49 degrees.
To find:
The value of x and y.
Solution:
In triangle ABC,
[tex]AB=AC[/tex] (Given)
So, triangle ABC is an isosceles triangle and by the definition of base angles the base angles of isosceles triangle are congruent.
In isosceles triangle ABC,
[tex]\angle B\cong \angle C[/tex]
[tex]m\angle B\cong m\angle C[/tex]
[tex]m\angle B\cong 49^\circ[/tex]
The angle bisector of an isosceles triangle is the median and altitude of the triangle. So, the angle bisector is perpendicular to the base.
[tex]m\angle ADB=90^\circ[/tex]
[tex]x^\circ=90^\circ[/tex]
In triangle ABD,
[tex]m\angle DAB+m\angle ABD+m\angle ADB=180^\circ[/tex] [Angle sum property]
[tex]y^\circ+49^\circ+x^\circ=180^\circ[/tex]
[tex]y^\circ+49^\circ+90^\circ=180^\circ[/tex]
[tex]y^\circ=180^\circ-49^\circ-90^\circ[/tex]
[tex]y^\circ=41^\circ[/tex]
Therefore, the correct option is B.
Solve the right triangle. Round decimal answers to the nearest tenth.
Answer: c=a2+b2
Step-by-step explanation: the triangle is solvedlike that
Answer:
given 15 and 57˚
RS = 10 RT = 18 M<T = 0.6
Step-by-step explanation:
c = b/sin(ß) and a = √c^2-b^2 were used to find the answers. they are rounded.
What is the value of x?
Answer:
Step-by-step explanation:
Corresponding angles are congruent
x² - 72 = 6x
x² - 6x - 72 = 0
Sum = -6
Product = -72
Factor = -12 , 6 {-12*6 = -72 & -12 +6 = -6}
x² + 6x - 12x -72 = 0
x(x + 6) - 12(x + 6) = 0
(x + 6)(x -12)=0 {Ignore x + 6 = 0 because angles won't be in negative}
x - 12 = 0
x = 12
Jfndndndjjfjfjnsniwi
Answer:
soo abcdefghigklmnopqrstuvwzyz
its 50 with Fahrenheit
Step-by-step explanation:
becauze 4+5÷6=71
From a hot-air balloon, Andres measures a 31
∘
∘
angle of depression to a landmark that’s 847 feet away, measuring horizontally. What’s the balloon’s vertical distance above the ground? Round your answer to the nearest hundredth of a foot if necessary.
Answer:
508.93 feet
Step-by-step explanation:
Yep, I know this problem from Delta Math.
We use tangent, and then solve for tan(31). The work is attached below.
The balloons vertical distance above the ground is; h = 508.93 ft.
We are told that Andres measures the angle of depression to a landmark from a hot air balloon to be 31°.
Now horizontal distance of landmark to the air balloon is 847 ft.
This means that the vertical distance will be the vertical side of a triangle formed by the hot air balloon and the landmark.
Using trigonometric ratios, the vertical height is;
h = 847 tan 31°
h = 508.929 ft
Approximating to the nearest hundredths gives;
h = 508.93 ft.
Read more at; https://brainly.com/question/24780061
The original price of a bicycle was $400. Now it is on sale for $300. What percentage of the original price was the markdown?
Answer:
25%
Step-by-step explanation:
400/100•300/x=0.75
1.00-0.75= 0.25
25%
Answer:
25 percent of discount
Step-by-step explanation:
[tex]original_price=400\\final_price=300\\discount=100\\\\\frac{400*percent}{100}=100 =>percent=\frac{100^2}{400}=25[/tex]
I need help for today :( plz
Answer:
Step-by-step explanation:
Part C: (Explanation with steps)
Let the length of the swimming pool = l feet
And width of the pool = w feet
Perimeter of the pool = 2(l + w) feet
Since, perimeter of the pool = 8 feet
2(l + w) = 80
l + w = 40
l = (80 - w) -------(1)
Area of the pool = Length × width
A(w) = l × w
By substituting the value of l from equation (1)
A(w) = (80 - w) × w
A(w) = 80w - w²
To find the maximum area of the pool we will find the derivative of the function with respect to 'w' and equate it to zero.
A'(w) = 80 - 2w
(80 - 2w) = 0
w = [tex]\frac{80}{2}[/tex]
w = 40 feet
Therefore, for width (w) = 40 feet area of the pool will be maximum.
From equation (1),
l = 80 - 40
l = 40 feet
Therefore, maximum area of the pool = l × w
= 40 × 40
= 1600 square feet
Part A:
Function representing area of the pool,
A(w) = -w² + 80w
Part B:
Maximum area of the surface of the pool = 1600 square feet