Answer:
(-7) (-10x - 3y = -18)
(10) (-7x - 8x = 11)
--------------------------
70x + 21y = 126
+ -70 - 80x = 110
---------------------------
-59x = 236
x = -4
Answer
[tex] \huge{ \boxed{ \text{(3 \:, - 4)}}}[/tex]
✑ [tex] \underline{ \underline{ \text{First ,\: let's \: know \: about \: elimination \: method}}}[/tex] :
☇ In this method , we add or subtract the given equations to eliminate one of the two variables by making their coefficients equal. Then , a single equation with one variable so obtained is solved to find the value of the variable. The value of the variable is substituted to any one equation to find the value of the eliminated variable.
☯ [tex] \underline{ \underline{ \text{Let's \: solve}}} : [/tex]
[tex] \underline{ \text{Original \: system}} : [/tex]
[tex] \text{ - 10x - 3y = - 18 - - - - Equation\: (i)}[/tex]
[tex] \text{ - 7x - 8y = 11 - - - - Equation \: (ii)}[/tex]
[tex] \text{Step \: 1} : [/tex] Take L.C.M ( Lowest Common Multiple ) of 10 and 7. For this , find the prime factors of each number. Then, take out the common prime factors and other remaining prime factors and multiply them.
prime factors of 10 = 1 × 2 × 5prime factors of 7 = 1 × 7L.C.M = Common factors × Remaining Factors
= 1 × 2 × 5 × 7
= 70
[tex] \text{Step \: 2} : [/tex] Multiply equation ( i ) by 7
[tex] \text{7( - 10x - 3y ) = - 18 * 7}[/tex]
⇢ [tex] \text{ - 70x - 21y = - 126 - - - - equation \: (iii)}[/tex]
[tex] \text{Step \: 3} : [/tex]Multiply equation ( ii ) by 10
[tex] \text{10( - 7x - 8y) = 11 \: * \: 10}[/tex]
⇢ [tex] \text{ - 70x - 80y = 110 - - - - equation \: (iv)}[/tex]
[tex] \text{Step \: 4} : [/tex] Subtract equation ( iv ) from equation ( iii ) :
Also Remember that while subtracting , sign of each term of the second equation changes. Here , we are eliminating x . So to make the coefficient of y same , equation ( i ) is multiplied by 7 and equation ( ii ) is multiplied by 10.⇩
[tex] \text{ - 70x - 21y = - 126}[/tex]
[tex]\text{+70x + 80y = - 110}[/tex]
___________________
[tex] \text{ \: \: \: \: \: \: 59y = - 236}[/tex]
Solve :
⇢ [tex] \text{59y/59 = - 236/59}[/tex]
⇢ [tex] \boxed{ \bold{ \text{y = - 4}}}[/tex]
[tex] \text{Step \: 5} : [/tex]
Substitute the value of y into equation ( iii ) , we get :
[tex] \text{ - 70x - 21y = - 126}[/tex]
➳ [tex] \text{ - 70x - 21( - 4) = - 126} [/tex]
➳ [tex] \text{ - 70x - ( - 84) = - 126} [/tex]
➳ [tex] \text{ - 70x + 84 = - 126}[/tex]
➳ [tex] \text{ - 70x = - 126 - 84}[/tex]
➳ [tex] \text{ - 70x = - 210}[/tex]
➳ [tex] \text{ - 70x/ - 70 = - 210/ - 70}[/tex]
➳ [tex] \boxed{ \bold{ \text{x = 3}}}[/tex]
[tex] \bold{ \underline{ \text{Hence ,\: x = 3 \: and \: y = - 4}}}[/tex]
Hope I helped!
♡ Have a wonderful day / night ツ
~ [tex] \sf{TheAnimeGirl} [/tex] ♪
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Triangle PQR is rotated 180 clockwise about point m and the image of point p is p and the image of point r is r what are the coordinates of the image of point Q
Answer:
Rotating 180 clockwise would mean that Q is Q if r is r, the coordinates of it pointing to Q would be in your picture , can I see a picture of the problem?
Step-by-step explanation:
The hypotenuse of a right triangle is 13ft long. The longer leg is 7ft longer than the shorter leg. Find the side lengths of the triangle.
Answer:
The side lengths are 5, 12, 13
Step-by-step explanation:
These are the side lengths we know before we have solved the problem.
a= x b= x+7 c= 13
If we put this into the Pythagorean theorem, we get
[tex]13^{2} = x^{2} +(x+7)^{2}[/tex]
Expand
[tex]169 = 2x^2+14x+49\\[/tex]
Subtract 169 from both sides
[tex]0 =2x^2+14x-120[/tex]
Solve using the quadratic formula
a= 2 b= 14 c= -120
[tex]\frac{-14\pm \sqrt{14^2-4\cdot \:2\left(-120\right)}}{2\cdot \:2}[/tex]
[tex]x= \frac{-14\pm \:34}{2\cdot \:2}[/tex]
If we separate the solutions we get
[tex]x= \frac{20}{4} = 5[/tex]
and
[tex]x= \frac{-48}{4} = -12[/tex]
Since this is a question about length, we can ignore the negative.
So the longer leg is 12ft and the shorter leg is 5ft
The shorter length is 5feet and the longer length is 12 feet
Let the shorter leg = x
Let the longer leg = x+7
Therefore,
x² + (x+7)² = 13²
x² + x² + 14x + 49 = 169
Collect like terms
2x² + 14x + 49 - 169 = 0
2x² + 14x - 120 = 0.
Divide by 2
x² + 7x - 60
By using quadratic equation
x² + 12x - 5x - 60
x(x + 12) - 5(x + 12)
Therefore, x - 5 = 0
x = 0 + 5.
x = 5
The shorter length is 5ft
Longer length = 5+7 = 12 feet
Read related link on:
https://brainly.com/question/19574344
Rosabell had 27 posters for the parade, she droppd 19 while marching in the parade. how many does she hav left.
What is the formula and slope of (18, -7) and (18, 2)
Answer:
Step-by-step explanation:
Coordinate points: (18, -7) and (18,2)
m= rise / run or [tex]\frac{ y_2 - y_1} {x_2 - x_1}[/tex]
m = slope
(x1, y1) = coordinates of first point in the line
(x2, y2) = coordinates of second point in the line
So your rise is...
2 - (-7)
and you run is...
18 -18
Rise = 9
Run = 0
Now, do you see the issue...
You can not have a number over 0 (* a great way to remember is N/0 spells no: "N" being number and "0" being zero)
The slope or the equation 9 / 0 (9 divided by 0 or 9 over 0) is ERROR in the calculator which means the slope of these points are undefined
The line is vertical when this happens
*Side Note: if you were to have 0 as you rise and 9 as your run, 0/9 is ok because that means you have a zero slope meaning that you have a horizontal line
0 divide by 9 is zero
Look at the equation. y=2x−2 Which situation is best described by the equation?
A. The temperature at 2.00AM 2°c and rises 2°C each hour for x hours
B. The temperature at 2.00AM is -2°C and rises 2°C each hour for x hours
C.The temperature at 2:00AM is 2°C and drops 2°C each hour for X hours
D. The temperature at 2:00AM is -2°C and drops 2°C each hour for x hours.
Answer: A
Step-by-step explanation:y=2x−2 2.00AM 2°c and rises 2°C each hour for x hours
How many 2/3 cup servings are in 1½ cups of cheese?
lol I know this but I'm too lazy
Answer:
2.25
Step-by-step explanation:
1.5 / 0.666 (repeating) = 2.25
Answer:
There are 2 one-quarter cup servings in 1 half cup
In 5.25 cups there are 21 one-quarter cup servings
Step-by-step explanation:
So 21 quarter cup servings divided by 2 quarter cup servings per half cup serving will yield the number of half cup servings.
21/2 is 10.5, so there are ten and half, half cup servings in 5.25 cups
express following
Following numbers in the
Standard form: 3.091403
for you
Answer:
[tex]3.10* 10^0[/tex]
Step-by-step explanation:
Given
[tex]3.091403[/tex]
Required
Express in standard form
A number in standard form can be expressed as:
[tex]a * 10^b[/tex]
Where
[tex]1 \leq a \leq 10[/tex]
i.e.
a is between 1 and 10 (inclusive) and preferable, a should be in 2 decimal places
We have that:
[tex]3.091403[/tex] is between 1 and 10.
So, in standard form it is:
[tex]3.091403 * 10^0[/tex]
Approximate to 2 decimal places
[tex]3.10* 10^0[/tex]
Hence, the standard form of [tex]3.091403[/tex] is [tex]3.10* 10^0[/tex]
It takes Andrew 4 min to swim 5 laps how many laps per min
Answer:
0.8 laps per min
Step-by-step explanation:
4 min / 5 laps
4/5 = 0.8
Kaitlyn is sharpening a pencil that is 19 cm. Each time she sharpens it goes down 2.5 cm. If she sharpens her pencil 4 times. How many centimeters of pencil does she have left?
Answer:
9 cm
Step-by-step explanation:
2.5x4=10
Draw the graph of y = 2x + 1
Answer:
Draw a dot at (0, 1)
Draw dot at (-1, -1)
Draw dot at (1, 3)
Connect the dots with a straight line
Step-by-step explanation:
The given equation is in slope-intercept form (y = mx + b). In this form, m is the slope and b is the y-intercept (where the line crosses through the y-axis).
The slope is 2, also written as [tex]\frac{2}{1}[/tex]. This means that the line goes up 2 units for each 1 unit to the right.
Nisha did the work below to solve an equation.
Step 1 7b+3.2b-5=18.92
Step 2 10.2b-5=18.92
Step 3 5.2b= 18.92
Step 4 b=3.64.
In which step did Nisha make her first error?
Step 1
Step 2
Step 3
Step 4
Answer:
Step 3.
Step-by-step explanation:
When 10.2b - 5 = 18.92, you cannot combine the unlike terms together on the left side to get 5.2b. Instead, add 5 to both sides:
10.2b = 18.92 + 5 = 23.92.
Answer: step 3
Step-by-step explanation:
1929 concert tickets were sold for a total of $31,062. If students paid $13 and nonstudents paid $20, how many student tickets were sold?
Answer:
answer is attached in the figure below hope it helps please mark it as brainlist
Sharon uses 1 1/2 cups of sugar to make 2 batches of cookies. How much sugar will she use to make 6 batches of Cooke’s?
Answer:
8 Batches
Step-by-step explanation:
Simple. Since it takes 2/3 of a cup for one batch, we divide 5 1/3 by 2/3, wich equals 8.
please help i have no idea
how much does 18cm are in mm
Explain how to solve the equation.
B - 7 = 12
Answer:
So if you take the 12 and add it to the 7 you get 19 then do 19 mines 7 and you get 12 so always add the sum to the number given to get the missing number
Step-by-step explanation:
Have a great day
pls help! will give brainliest!!!
Answer:?????
Step-by-step explanation:
what do u need help with/?//???/???
(Will mark brainlest Help please)out of 800 students at icenhower intermediate 208 live inside the city of mansfield
Answer:
Doesn't this mean that 592 students live outside the city of mansfield?
Step-by-step explanation:
800 - 208
The original cost of a sofa was $600. If it was discounted 40% and sales tax is 8%, what is the final cost of the sofa
Answer:
$312
Step-by-step explanation:
10% of $600 is $60
So $60*4=$240
$600-$240=$360
1%=$6
So $6*8=$48
$360-$48=$312
An electrician charges (1) an initial fee of $20 and then $30 per hour. What type of graph does this represent?
an increasing only graph
a decreasing only graph
an increasing and decreasing graph
Answer:
this is an increasing graph. of y = 30x + b
Step-by-step explanation:
since all that is happening is that people are adding money, the graph just goes up and up
Right 2 units and down 7 units
Answer:
-3.5
Step-by-step explanation:
Rise over run
I CAN GIVE BRAINLIEST!!!!!!
Answer: 2/1
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
Line is passing through the points (2, 3) & (5, 9)
Slope = (9 - 3)/ (5 - 2) = 6/3 = 2
Slope of the line is 2.
HELP FIVE STARS,THANKSAND BRAINLIEST (if your right)!!
What is the y-coordinate of the point shown in the graph?
P.S the graph is in the picture above.
Answer:
-7
Step-by-step explanation:
the full coordinate would be 3,-7. just line up the number directly above it and to the left/right and write it down x,y
Plz help- solve the inequality
-3(1 - z) < 9
Use distributive property
Answer:
z
=
9
2
Step-by-step explanation:
anyway
good luck
determine if the 2 triangles are similar or not. if they are similar choose the correct similarity theorem below.
A
B
C
D
Which function is represented by this graph
y=-1/2x +3 it's last one
$2665 is compounded annually at a rate of 9% for 1 year
Answer:
$2675
Step-by-step explanation:
plis help
Find the distance from the origin to the graph of 6x+3y+2=0
a.
0.33
b.
0.31
c.
0.3
d.
0.32
Answer:
Step-by-step explanation:
B is the answer
in the given figure, the side BC is produced to
the points o and E both sides. Prove that
ABE + ACD+ BAC = 180
the cost for fudge at candy lane is represented by the table.the graph the cost for similar fudge that best fudge shop sell. a. the unit rate for fudge at candy lane to equal the unit rate at best fudge shop. B.the unite rate for fudge at best fudge shop is less than unit rate at candy lane. C.the unite rate for fudge at candy lane is less than the unit rate at best fudge shop. D cost 3 pounds of fudge at best fudge shop is less than the cost of a pound of fudge at sweet treats
Answer:
B
Step-by-step explanation:
The correct statement of the given ones are - the unit rate of best fudge is less than unit rate of candy cane.
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
Where -
[m] is the slope of the line.
[c] is the y - intercept.
Given is a table that shows the cost for fudge at candy lane. The graph represents the cost for similar fudge that best fudge shop sell.
The slope of straight line represented by the table -
m[1] = (16 - 8)/(2 - 1)
m[1] = 8
The slope of the line plotted on graph -
m[2] = (9 - 6)/(3 - 2)
m[2] = 3
The slope is the measure of unit rate. Therefore, the unit rate of best fudge is less than unit rate of candy cane.
The cost 3 pounds of fudge at best fudge shop = 3 x 3 = $9
The cost 1 pound of fudge at candy lane = $8
Hence, cost 3 pounds of fudge at best fudge shop is greater than the cost of a pound of fudge at sweet treats.
Therefore, the correct statement of the given ones are - the unit rate of best fudge is less than unit rate of candy cane.
To solve more questions on straight line graphs, visit the link below-
brainly.com/question/2954112
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[Refer to the image attached for table and graph]