Answer:
a^2+b^2=c^2
a^2+b^2=8^2
a^2+b^2=64
32+32=64
5.66^2+5.66^2=8^2
Step-by-step explanation:
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How can you determine the number of solutions of a system of linear equations by inspecting its equations?
Step-by-step explanation:
To find - How can you determine the number of solutions of a system
of linear equations by inspecting its equations?
Proof -
There exists three types of solution for a system of linear equations.
1. No solution.
2. Unique solution.
3. Infinite many solutions.
Now,
Let the 2 linear equations are as follows :
y = ax + b
y = cx + d
1. For no solution -
a = c and b ≠d
For example-
y = -2x + 5
y = -2x - 1
Subtract first equation from second , we get
y - y = -2x - 1 - ( -2x + 5)
⇒0 = -2x - 1 + 2x - 5
⇒0 = -6
Not possible
So, There exist no solution.
2. For unique solution -
a ≠ c and b , d can be any value
For example -
If b and d are same ,
y = 2x - 4
y = -3x - 4
Subtract equation 1st from 2nd , we get
y - y = -3x - 4 - ( 2x - 4)
⇒0 = -3x - 4 - 2x + 4
⇒0 = -5x
⇒x = 0
⇒y = 2(0) - 4 = -4
∴ we get
x = 0, y = -4
If b and d are different
y = 2x - 4
y = -3x + 5
Subtract equation 1st from second
y - y = -3x + 5 - 2x + 4
⇒0 = -5x + 9
⇒-5x = -9
⇒x = [tex]\frac{9}{5}[/tex]
⇒y =2([tex]\frac{9}{5}[/tex]) - 4 = [tex]\frac{18}{5} - 4 = \frac{18 - 20}{5} = -\frac{2}{5}[/tex]
∴ we get
x = [tex]\frac{9}{5}[/tex] , y = [tex]-\frac{2}{5}[/tex]
3. Infinitely many solution -
a = c and b = d
For example -
y = -4x + 1
y = -4x + 1
Subtract equation first from equation second
y - y = -4x + 1 - ( -4x + 1)
⇒0 = -4x + 1 + 4x - 1
⇒0 = 0
Satisfied
So, Infinite many solution possible.
A bag contains 3 red, 5 yellow, and 7 purple marbles. Find the probability of drawing a purple marble followed by a red marble. The first marble is put back in the bag between draws.
Answer:
unsimplified : [tex]\frac{21}{225} or simplified: \: \frac{7}{75}[/tex]
Step-by-step explanation:
Work out : Look above at image.
A line includes the points (2, 10) and (1, 0). What is its equation in slope-intercept form?
Answer:
y=10x-10
Hope this helped <3
You rent an apartment that costs
$
1000
$1000 per month during the first year, but the rent is set to go up
$
160
$160 per year. What would be the monthly rent during the 10th year of living in the apartment?
Answer:
$2440
Step-by-step explanation:
a10 = a1 + (n-1)d <--- arithmetic sequence formula
a10 = 1000 + 9(160)
a10 = 2440
will mark brainliest and rate 5/5
Answer:
its c
Step-by-step explanation:
because i multuply
Answer:
320 cubic centimeters
Step-by-step explanation:
Multiply.
--
20 x 4 x 4 = 320
--
Finding Volume
Length x Width x Height = Volume
--
What is the diameter of a circle that has a radius of 5.2 yards?
** Do not put yards
Answer:
6.4
Step-by-step explanation:
Madelyn has x nickels and y dimes, having a maximum of 15 coins worth no
less than $1 combined. At least 2 of the coins are nickels and at least 9 of the
coins are dimes. Solve this system of inequalities graphically and determine
one possible solution.
9514 1404 393
Answer:
2 nickels, 9 dimes
Step-by-step explanation:
When there are a number of overlapping shaded areas on the graph, I find it convenient to use the reverse of the inequalities. That makes the unshaded area the solution space. Here, the vertices of the triangular solution space are ...
(2, 9), (2, 13), (6, 9)
Any of the grid points within (or on) this triangle is a possible solution. One of them is (2, 9) corresponding to 2 nickels and 9 dimes.
__
Three solutions are shown:
(x, y) = (2, 9), (3, 10), (4, 11)
Write in point-slope form an equation of the line that passes through the point (9, 8) with slope -6 .
Answer:
y= -6x+62
Step-by-step explanation:
y-y1=m(x-x1)
y-8=-6(x-9)
y-8=-6x+54
+8 +8
y= -6x+62
what does p equal please help me.
Answer: p < -3/5
Step-by-step explanation:
2p - 4 < -3p - 7
+3p +3p
------------------------
5p - 4 < -7
+4 +4
------------------------
5p < -3 (divide by 5)
p < -3/5
I'll give brainlist to the person that answers
Answer:
67.6
Step-by-step explanation:
area = 158/360 * 49 * pi = 67.56
help plssssssssssssssss
one question
8(5g+5−2) Distributive Property to simplify the expression.
Answer:
= 40g -24
Step-by-step explanation:
you would multiply everything in the bracket by 8 to expand this
e.g.
(8x5g )+ (8x5 )+ (8 x -2)
= 40g + 40 - 16
now simplify by subtracting the like terms
= 40g -24
>
<
=
pls help i beg u
Answer:
its less than <
Step-by-step explanation:
........
Answer:
>
Step-by-step explanation:
[tex]12 \times 1 \frac{2}{5} = 12 \times \frac{7}{5} = \frac{60}{5} \times \frac{7}{5} = \frac{420}{25} = 16 \frac{20}{25} [/tex]
Ron is making a triangular frame for a garden using three lengths of wood. He has three pieces of wood that measure 3 feet, 8 feet, and 4 feet in length. Ron claims that he can make a triangular frame with these three pieces of wood. Do you agree with Ron? Explain your reasoning.
Answer:
Step-by-step explanation:
A side of the triangle must be shorter than the sum of the remaining two sides.
He cannot make a triangle with 3, 4, and 8.
Trisha has $22.50 to spend at the movies. Her ticket is $11.50 , and she gets a large popcorn and soda . If the popcorn and soda each cost the same amount and she spends all her money, how much was the popcorn?
Answer:$5.50
Step-by-step explanation:
22.50 -11.50= 11
soda and popcorn (2 items)
11/2= 5.50
A rectangular playground has a width of 54 feet and a length of 81 feet. Martina makes a scale model of the playground using a scale of 1 in:3 ft.
What are the dimensions of Martina’s scale model?
Answer:
72 and 108
Step-by-step explanation:
540/30= 18 *4 = 72
and
810/30= 27*4=108
Ulet rolls 2 fair dice and adds the results from each. Work out the probability of getting a total of 7.
Answer:
7/ 36
Step-by-step explanation:
Roll of 2 fair six sided die :
Sample space = 6² = 36
Sum of 7:
(1,6) ; (6,1) ; (3,4) ; (4,3) ; (2,5) ; (5,2) = 6
Probability = required outcome / Total possible outcomes
Required outcome = 7
Total possible outcomes = 36
P(obtaining a sum of 7) = 7 / 36
Joseph plots the speed of his car and time on a scatter plot. The equation for the line of best fit on his scatter plot is y = -15x + 60, where x is the time in hours and y is the speed in miles/hour. Which statement describes the situation correctly?
A.
The initial speed is 60 miles/hour, and his speed decreases by 15 miles/hour every hour.
B.
The initial speed is 60 miles/hour, and his speed increases by 15 miles/hour every hour.
C.
The initial speed is 0 miles/hour, and his speed increases by 15 miles/hour every hour.
D.
The initial speed is 5 miles/hour, and his speed increases by 30 miles/hour every hour.
Answer:
A
Step-by-step explanation:
His speed change is the slope or -15, decreases by 15 miles/hour
when he starts, his speed is 0*-15+60 = 60 miles/hour
Answer:
a
Step-by-step explanation:
what's the value of y ?
[tex]y = ( { - 2 })^{2} [/tex]
pls help been waiitng for 2 hours now..
Answer:
(5,3)
Step-by-step explanation:
you would move 3 to the right and 2 down
please help with maths work
Given:
In a right angle triangle ABC, [tex]\angle B=90^\circ,x=8.7\ m[/tex], and [tex]\theta = 45^\circ[/tex]
To find:
The value of AC.
Solution:
In a right angle triangle,
[tex]\cos \theta =\dfrac{Adjacent}{Hypotenuse}[/tex]
[tex]\cos \theta =\dfrac{BC}{AC}[/tex]
[tex]\cos (45^\circ) =\dfrac{8.7}{AC}[/tex]
[tex]\dfrac{1}{\sqrt{2}}=\dfrac{8.7}{AC}[/tex]
On cross multiplication, we get
[tex]AC=8.7\times \sqrt{2}[/tex]
[tex]AC=12.30365799[/tex]
[tex]AC\approx 12.304[/tex]
Therefore, the measure of AC is 12.304 m.
6x + 8y + 6 ; x = 2 , y = 6
Answer:
66
Step-by-step explanation:
6x + 8y + 6
x=2
y=6
Replace the letters with the numbers:
6(2) + 8(6) +6
= 12 +48 + 6
= 66
Find the percent of change from 90 to 12.
Answer:
86.6667% decrease
Step-by-step explanation:
There are 7 students in cara art club . They need to share 2 rolls of clay equally . Cara wants to know how much clay she will get?
Answer:
2/7
Step-by-step explanation:
Solve for X. Please help ASAP! I have no idea how to do this and it’s due really soon!
Answer:
2
Step-by-step explanation:
5x+6=7x-2
5x+4=7x
4=2x
4/2
2
1. ) Explain the error in this simplification
2.) Show your work as you correct the error
Answer:
Given equation:
1 - 2/(x - 2) = (x + 1)/(x + 2)Correct solution:
(x - 2 - 2)/(x - 2) = (x + 1)/(x + 2) complete the fraction on the left(x - 4)(x + 2) = (x + 1)(x - 2) cross-multiplyx² + 2x - 4x - 8 = x² - 2x + x - 2 open parenthesis-2x - 8 = -x - 2 simplify-x = 6x = -6Errors
Step 1. not counting 1 as part of equation. It wasn't included into fraction.Step 1. not multiplying (x - 2) by 1.Step 4. - x + 2x = -2x is incorrect, it should be xWhat is the measure of angle x?
HURRY PLEASEEEEE I RLLY NEED THISSS
Answer:
Option 2
Step-by-step explanation:
Given function:
x=8 and y=6x=5 and y=20Option 1: ×
Table one: y=8-6
if y is 6 then 8-6 can’t be 6 it is 2.
Option 2: √
Table one:
y=8-2
y would be 6 then this would be correct..
Table two:
y=4x
if y=20 then x would be 5 and if y is 16 then x=4.
Option 3:×
y=4x
this is wrong since table 2 is y=4x..
Option 4:×
Table one
y=x-4
if y is 6 and x is 8 then this is wrong..
Therefore, option 2 is correct..
Helpppppp PLEASEEEEEEEEE MATH SUCKS AND I NEED YOUR BRAIN FOR HELP
pls number them by
6.
7.
8.
9.
:)
Answer:
Question 6: 3
Question 7: $1750
Question 8: 45 minutes
Question 9: $48
Step-by-step explanation:
Please help its due in a hour
Answer:
good luck
Step-by-step explanation: