Answer:
[tex]x=1\,,\,y=-1[/tex]
Step-by-step explanation:
Given: [tex]ax+by=a-b\,,\,bx-ay=a+b[/tex]
To solve: the given linear equations
Solution:
Consider the equations:
[tex]A_1x+B_1y+C_1=0\\A_2x+B_2y+C_2=0[/tex]
By method of cross multiplication:
[tex]\frac{x}{B_1C_2-B_2C_1}=\frac{y}{C_1A_2-C_2A_1}=\frac{1}{A_1B_2-A_2B_1}[/tex]
For equations: [tex]ax+by=a-b\,,\,bx-ay=a+b[/tex]
[tex]ax+by-(a-b)=0\\bx-ay-(a+b)=0[/tex]
Take [tex]A_1=a\,,\,B_1=b\,,\,C_1=-(a-b)\,,\,A_2=b\,,\,B_2=-a\,,\,C_2=-(a+b)[/tex]
So,
[tex]\frac{x}{-b(a+b)-a(a-b)}=\frac{y}{-b(a-b)+a(a+b)}=\frac{1}{-a^2-b^2}\\\frac{x}{-ab-b^2-a^2+ab}=\frac{y}{-ab+b^2+a^2+ab}=\frac{1}{-(a^2+b^2)}\\\frac{x}{-(a^2+b^2)}=\frac{y}{a^2+b^2}=\frac{1}{-(a^2+b^2)}\\\frac{x}{-(a^2+b^2)}=\frac{1}{-(a^2+b^2)}\,,\,\frac{y}{a^2+b^2}=\frac{1}{-(a^2+b^2)}\\x=1\,,\,y=-1[/tex]
2,-4,8,-16
What is the next term in the sequence?
Answer:
32
Step-by-step explanation:
every time we are multiplying by -2 so if we do -16 x -2 we will get postive 32
Answer:
36
Step-by-step explanation:
it is a pattern of times -2
The graph of equation (3,-2) passes through which point
Answer:
If the y-intercept is 0, then this graph passes through [3,-2][6,-4][9,-6] and so forth.
Step-by-step explanation:
Rise over run, 3 is the rise, and -2 is the run. Using this you can find any point on the line up to infinity.
Answer:
it passes through y intercept
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Please answer correctly !!!!!!!! Will mark brainliest !!!!!!!!
Answer:
(7,7)
Step-by-step explanation:
The maximum point in a graph is where the y value is the highest. On this graph, the point (7,7) has the highest y value of 7 of the entire graph, making it the maximum. Hope this helps!
Each of three friends flips a coin 71 times. The results for each friend are shown in the tables. Find the Each of three friends flips a coin 71 times. The results for each friend are shown in the tables. Find the relative frequency for the event "heads" for each friend. If the friends combine their results to get 101 heads and 112 tails, what is the relative frequency for the event "heads"? Use pencil and paper. Suppose each friend flips a coin 710 times. Is there a value you would expect the relative frequency for the event "heads" to be close to?
For friend 1, the relative frequency is [tex]\frac{25}{71}\approx 0.352.[/tex]
For friend 2, it's [tex]\frac{53}{71}\approx 0.746,[/tex] and for friend 3, it's [tex]\frac{23}{71}\approx 0.319.[/tex]
Combining the data of all three would give a relative frequency of [tex]\frac{101}{213}\approx 0.474.[/tex]
If each friend were to flip a coin 710 times, assuming the coin to be a fair coin, we'd expect about half of the flips to be heads, so the relative frequency would be close to 0.5.
15) Martha wants to put carpet in a rectangular room that measures 14 feet by 16 feet. There is a section in front of
the door which measures 3 feet by 4 feet that will remain tiled. How many square feet of carpet will Martha need?
Answer:
5 ft
Step-by-step explanation:
write down in terms of n an expression of the following sequences
a) 12 10 8 6 4
b) 25 20 15 10 5
Answer:
[tex]-2n+14[/tex]
[tex]-5n+30[/tex]
Step-by-step explanation:
-2 difference.
[tex]u_{n} =-2n+c[/tex]
[tex]u_{1} =-2(1)+c=12[/tex]
[tex]c=14[/tex]
-5 difference.
[tex]u_{n} =-5n+c[/tex]
[tex]u_{1} =-5(1)+c=25[/tex]
[tex]c=30[/tex]
9. y=-2(x-3)
10. 12x + 30 y = 10
11. y = -5x+2
12. y=6+36-1)
13. y-3 = 2x
14. y=-3-4(x+9)
intercept form
Answer:
9. y= -2x+6
10. y= -0.4x+ [tex]\frac{1}{3}[/tex]
11. y = -5x+2
12. y=41
13. y=2x+3
14. y= -4x-39
Step-by-step explanation:
9.
y= -2(x-3)
y= -2x+6
10.
12x+30y=10
Subtract 12x from both sides
30y=10-12x
Divide both sides by 30
y= -0.4x+ [tex]\frac{1}{3}[/tex]
11.
y = -5x+2
(Already solved)
12.
y=6+36-1
y=41
13.
y-3=2x
Add 3 to both sides
y=2x+3
14.
y= -3-4(x+9)
y= -3-4x-36
y= -4x-39
need help ezy points plz
Answer:
24 cubic inches.
Step-by-step explanation:
[tex]2a \times a^{2} +a^{3} \\2a^{3} +a^{3}[/tex]
[tex]3a^3\\3(2)^3\\3 \times 8[/tex]
A bag contains 14 green tiles,10 red tiles, and 16 blue tiles. Brodie randomly draws a tiel, records the color , and replaces the tile.if he does this 80 times, how many times should he expect to draw a red tile
Answer:
20 red tiles
Step-by-step explanation:
14 green tiles,10 red tiles, and 16 blue tiles. = 40 tiles
P(red) = 10/40 = 1/4
If we draw 80 tiles
80 * 1/4 = 20
We should expect 20 red tiles
Analyze Nick's solution. Is he correct? If not, what was
his mistake?
Yes, Nick is correct.
O No, the power multiplied to 8.64 should have an
exponent of 0.
No, he needed to subtract the coefficients.
X No, he needed to add the exponents.
Answer: No, the power multiplied to 8.64 should have an exponent of 0. B pretty much
Step-by-step explanation: just got that question trust me it’s right.
Answer:
No, the power multiplied to 8.64 should have an exponent of 0.
A 13-foot board is cut into two pieces. The length of the shorter piece is 1 ft more than half the length of the longer piece. Find the length (in ft) of the shorter piece.
Answer: 1
Step-by-step explanation: 1
Length of the shorter piece of board is equals to 5foot.
What is length?
" Length is defined as the distance between two end points of any object."
According to the question,
Length of the board = 13foot
'l' represents the length of the longer piece
As per the condition given we have,
Length of the shorter piece = [tex]\frac{l}{2} +1[/tex]
Therefore,
[tex]l + \frac{l}{2}+1=13[/tex]
⇒ [tex]\frac{3l}{2} =13-1[/tex]
⇒[tex]l= \frac{2}{3} (12)[/tex]
⇒ [tex]l= 8foot[/tex]
Length of the shorter piece = [tex]\frac{8}{2} +1[/tex]
= [tex]5foot[/tex]
Hence, length of the shorter piece of board is equals to 5foot.
Learn more about length here
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Samy's car can hold 20 gallons of
gasoline in its fuel tank. It is 3/4 full. He
can travel 15 miles for every gallon of
gasoline.
Rosa car has 13 gallons of gasoline in
the fuel tank and she can travel 19 miles
for every gallon of gasoline.
If they both start at the same place and
travel at the same constant speed, who
will go farther?
Answer:.
Justification:
Answer:
Rosa will go farther.
Step-by-step explanation:
1. Samy's travel distance.
3/4 of 20
3/4 * 20 = 15 gallons
15 miles for every gallon
15 * 15 = 225
Samy's travel distance is 225 mIles
2. Rosa travel distance.
13 gallons
19 miles for every gallon
19 * 13 = 247 mIles
Rosa's travel distance is 247 mIles.
If a line is perpendicular to a line segment, what angle do they form at their
intersection?
A. 90°
B. 45°
C. 180°
D. 09
Select the correct answer.
The sum of two numbers is -18. If the first number is 10, which equation represents this situation, and what is the second number?
A. The equation that represents this situation is 10 - x= -18. The second number is 28.
OB.
The equation that represents this situation is 10+ x=-18. The second number is -28.
C.
The equation that represents this situation is r- 10 =-18. The second number is -8.
D. The equation that represents this situation is -10+ x = -18. The second number is -8.
Answer:
Thw answer would be B
Step-by-step explanation:
Answer:
OB.
The equation that represents this situation is 10+ x=-18. The second number is -28.
Step-by-step explanation:
First, sum means added together.
Second, one value in the sum is given so:
10+(var)=-18
var=8
and if we solve, we get -28.
(2x+3y)+(8x+10y) simplify the following
Answer:
10x+13y
Step-by-step explanation:
remove parentheses:
2x+3y+8x+10y
add like-terms:
2x+8x+3y+10y
add numbers with the same variables/elements
10x+3y+10y-->10x+13y
hope this helps
Hello!
Answer:[tex]\boxed{ \bf The~correct~answer~is~10x~+~13y.}[/tex]
________________________________________________
Explanation:(2x + 3y) + (8x + 10y)
First, drop the brackets:
2x + 3y + 8x + 10y
Next, collect like terms:
2x + 8x + 3y + 10y
Finally, add the like terms together:
10x + 13y
Please answer correctly !!!!!!!!!! Will mark brainliest !!!!!!!!!!!!
Answer:
see explanation
Step-by-step explanation:
(1)
Given
g(r) = (r + 14)² - 49
To obtain the zeros, let g(r) = 0 , that is
(r + 14)² - 49 = 0 ( add 49 to both sides )
(r + 14)² = 49 ( take the square root of both sides )
r + 14 = ± [tex]\sqrt{49}[/tex] = ± 7 ( subtract 14 from both sides )
r = - 14 ± 7, then
r = - 14 - 7 = - 21 ← smaller r
r = - 14 + 7 = - 7 ← larger r
(2)
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
g(r) = (r + 14)² - 49 ← is in vertex form
with vertex = (- 14, - 49 )
please help i don’t know what to do and this will help me pass 7th grade thank you!!!
Height of table is 18 inches
Height of one block is 2 inches
The height would be 34 inches with 8 blocks ✌️
Answer:
Well each block is 2
Step-by-step explanation:
cause the height of the table is 18 itself it says in the table and one block just adds 2
i hope it's right sorry if it's not
I understand the struggle
Question 7
The equation of a straight line AB is
[tex] \frac{x}{2} + \frac{y}{2} = 1[/tex]
(a) Find the gradient of line AB.
(b) Find the y-intercept of line AB.
(c) A second line PQ is parallel to the line AB and passes through a point (2, -8).
Show that the second line PQ also passes through the point(-1,-5)
Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
[tex]\frac{x}{2}[/tex] + [tex]\frac{y}{2}[/tex] = 1 ( multiply through by 2 to clear the fractions )
x + y = 2 ( subtract x from both sides )
y = - x + 2 ← in slope- intercept form
(a) with slope m = - 1
(b) with y- intercept c = 2
(c)
Parallel lines have equal slopes, thus
y = - x + c ← is the partial equation of PQ
To find c substitute (2, - 8) into the partial equation
- 8 = - 2 + c ⇒ c = - 8 + 2 = - 6
y = - x - 6 ← equation of PQ
To show (- 1, - 5) lies on PQ, substitute x = - 1 into the equation and evaluate for y.
y = - (- 1) - 6 = 1 - 6 = - 5 ← the given y- coordinate
Thus PQ passes through (- 1, - 5 )
Micaela tried to rotate the square 180° about the origin.
Is her rotation correct? If not, explain why.
No, she translated the figure instead of rotating it.
No, she reflected the figure instead of rotating it.
No, the vertices of the image and pre-image do not
correspond
Yes, the rotation is correct.
Answer:
No, the vertices of the image and pre-image do not correspond.
Step-by-step explanation:
Answer: its C
Step-by-step explanation: you got this
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Lisa receives a net pay of $619.06 biweekly. She has $143 withheld from her pay each pay period. What is her annual gross salary?
Answer:
Step-by-step explanation:
i have provided an attachment for you to take a look at that may help with your example please mark brainliest im new to brainly and son hoping to earn a reputation thank You
Number 4 please I need help please I need help please help me
Answer:
The perimeter is 112 m
Step-by-step explanation:
The perimeter is the sum of all the edges
26+ 12 + 18 +? + ?+ 30
The two question marks add to 26 so replace them with 26
26+ 12 + 18 +26+ 30
112
The perimeter is 112 m
PLEASE HELP I WILL MARK BRAINLIEST
Answer:
(cos^2(x)-1) cot (-x); last expression.
Step-by-step explanation:
You'll first need to simplify the given expression. Then look at each option. To find out whether or not two expressions are equivalent see if they have the same value irrespective of the value of the variables in them.
1) (1-cos^2(x)) cot (-x) is equivalent
2) (cos^2(x)-1) cot(x) is equivalent
3) (sin62(x)-10 tan (x) is equivalent
4) (cos^2(x)-1) cot (-x) is not equivalent.
PLZ HELP ME W DIS ASAP!!!
Answer:81/m^7(D)
Step-by-step explanation:
81m^5/12
81/m^7
the scale on the map is 1: 20000. The area of a lake on a map is1.6 square centimetres. give the actual area of the lake
Answer:
6.4 × 10^8
Step-by-step explanation:
A person is listening to a 500 Hz tone sitting from a distance of 450 m from the sound source. What is the time interval between successive compressions from the source?
Answer:
So, the time interval between successive compression from the source is 0.002 seconds.
Step-by-step explanation:
Given that,
Frequency of the tone, f = 500 Hz
It is sitting at a distance of 450 m from the source of sound, d = 450 m
Let t is the time interval between successive compression from the source. We know that the relation between the frequency and the time period is :
[tex]T=\dfrac{1}{f}T=\dfrac{1}{500}\\\\T = 0.002 s[/tex]
So, the time interval between successive compression from the source is 0.002 seconds.Find the volume of the pyramid. 100 points
120 yd^3
Step-by-step explanation:
The formula for the volume of a pyramid is...
[tex]V=\frac{1}{3}Bh[/tex]
B is the area of the base and h is the height from the middle of the pyramid to the top. Since we know both of these we can plug them in.
[tex]V=\frac{1}{3}(45*8)[/tex]
[tex]V=\frac{1}{3}*360[/tex]
[tex]V=[/tex]
120
The volume for the pyramid is 120 yd^3.
Answer:
120 yards ^3
Step-by-step explanation:
To solve we need to know the formula.
The formula for the volume of a pyramid is 1/3 B * H
B= 45 and H = 8. We can sub those values in to the formula to solve.
= 1/3 45*8
= 1/3 360
=120
Since we multiplied yd^2 by yd, we get yd^3
So the answer is 120 yd^3
What is the value of x in the figure? Enter your answer in the box.
PLease answer fasttttt
Answer:
65
145=145
thats the answer
Which triangles are similar? c d a b If someone replies really fast to this I would amazingly appreciate it
Answer:
b and d
Step-by-step explanation:
b and d from the picture
same angle of 25 between sides with 1:2 side to base ratio
9. What is the volume of the triangular prism
below?
5cm
3 cm
4cm
3 cm
Need help ASAP
could someone help me please I don't quite understand this.
Answer:
you clicked the correct one!
Step-by-step explanation:
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