Answers
The first system matches with (-4, 5);
The second system matches with (2, 2);
The third system matches with (-1, -3);
The fourth system matches with (3, 4);
The fifth system matches with (2, -1); and
The sixth system matches with (-5, 6).
Explanation:
The sixth system is the easiest one to find. We are given the value of x and the value of y in the equations: x=-5 and y=6.
For all other systems, we must solve the system. For the first system:
[tex] \left \{ {{2x-y=-13} \atop {y=x+9}} \right. [/tex]
Since we have the y-variable isolated in the second equation, we will use substitution. We substitute this value in place of y in the first equation:
2x-y=-13
2x-(x+9)=-13
Distributing the subtraction sign,
2x-x-9=-13
Combining like terms:
x-9=-13
Add 9 to each side:
x-9+9=-13+9
x=-4
Substitute this into the second equation:
y=x+9
y=-4+9
y=5
The coordinates (-4, 5) represent the solution point.
For the second system:
[tex] \left \{ {{3x+2y=10} \atop {6x-y=10}} \right. [/tex]
We can make the coefficients of x the same and use elimination. To do this, we will multiply the first equation by 2:
[tex] \left \{ {{2(3x+2y=10)} \atop {6x-y=10}} \right. \\ \\ \left \{ {{6x+4y=20}
\atop {6x-y=10}} \right. [/tex]
Since the coefficients of x are now the same, we can cancel it. They are both positive, so we subtract:
[tex] \left \{ {{6x+4y=20} \atop {-(6x-y=10)}} \right. \\ \\5y=10[/tex]
Divide both sides by 5:
5y/5=10/5
y=2
Substitute this into the second equation
6x-y=10
6x-2=10
Add 2 to each side:
6x-2+2=10+2
6x=12
Divide both sides by 6:
6x/6 = 12/6
x=2
The coordinates (2, 2) represent the solution to this system.
For the third system:
[tex] \left \{ {{4x-3y=5} \atop {3x+2y=-9}} \right. [/tex]
We can make the coefficients of x the same by multiplying the first equation by 3 and the second by 4:
[tex] \left \{ {{3(4x-3y=5)} \atop {4(3x+2y=-9)}} \right. \\ \\ \left \{ {{12x-9y=15} \atop {12x+8y=-36}} \right. [/tex]
Since the coefficients of x are the same, we can cancel them. Since they are both positive, we will subtract:
[tex] \left \{ {{12x-9y=15} \atop {-(12x+8y=-36)}} \right. \\ \\-17y=51[/tex]
Divide both sides by -17:
-17y/-17 = 51/-17
y=-3
Substitute this into the first equation:
4x-3y=5
4x-3(-3)=5
4x--9=5
4x+9=5
Subtract 9 from each side:
4x+9-9=5-9
4x=-4
Divide each side by 4:
4x/4 = -4/4
x=-1
The coordinates (-1, -3) represent the solution of the third system..
For the fourth system:
[tex] \left \{ {{x+y=7} \atop {x-y=-1}} \right. [/tex]
Since the coordinates of x are the same and both are positive, we can cancel x by subtracting:
[tex] \left \{ {{x+y=7} \atop {-(x-y=-1)}} \right. \\ \\2y=8[/tex]
Divide both sides by 2:
2y/2 = 8/2
y=4
Substitute this into the first equation
x+y=7
x+4=7
Subtract 4 from each side:
x+4-4=7-4
x=3
The coordinates (3, 4) represent the solution to the fourth system.
For the fifth system:
[tex] \left \{ {{y=3x-7} \atop {y=2x-5}} \right. [/tex]
Since y is isolated in each equation, we can set them equation to each other:
3x-7=2x-5
Subtract 2x from each side:
3x-7-2x=2x-5-2x
x-7=-5
Add 7 to each side:
x-7+7=-5+7
x=2
Substitute this into the first equation:
y=3x-7
y=3(2)-7
y=6-7
y=-1
The coordinates (2, -1) represent the solution to the fifth system.
Related Questions
I need the answers to 5&6 explain how you found the answer and I'll give brainliest
Answers
Both of these problems can be solved through substitution using the variables that you know equal a number.
For example #5: 5(3)(3)-7(3)+4
45-21= 24, and 24+8=28
That is how you solve number 5 and can also solve 6 the same way using the same method.
Thirty five is what fraction of 80
Answers
35/80= 7/16
What is the answer to 2/5 + 7/20 and 6/15 + 14/40
Answers
6/15+14/40=3/4
In ABC what is the measure of C
Answers
To solve this equation, you know what each angle is equal to, and all triangles add to equal 180 degrees, so you can set it up like so:
6x + 2x + 2x = 180 Then combine all the x's and simplify by dividing.
Answer:
36 °
Step-by-step explanation:
Hello
In geometry an interior angle or an internal angle is an angle formed by two sides of a polygon that sharing a common end is contained within the polygon, and the sum of these angles is given by
sum=(n-2)*180°
where n is the number of sides of the polygon,in our case n= 3 (a triangle)
Step 1
find the sum o internal angles
sum=(3-2)*108°
sum=1*180°
(1)sum=180°
step 2
find x
now, according to the graph the sum of internal angles is
sum(graph)=6x+2x+2x
(2)sum=10x
(1) must be equal to (2)
180°=10x
isolating x
x=18
Step 3
find C
by the graph ,we know
C=2x
and x=18
replacing
C=2(18)
C=36°
Have a great day
HEEEEEEELP ASAP Janette went to Tire Mart and paid $122.57 per tire for 4 tires and a flat rate fee for installation for a total of $555.28 before taxes. Monique went to Fast Wheels and paid $136.71 per tire for 4 tires and a flat rate fee for installation for a total of $585.34 before taxes. The difference in the amount that they paid in installation charges is $____ WILL GIVE YOU BRAINLIEST
Answers
$136.71 • 4 + $585.34 = $1,132.18
$1,132.18 - $1,045.56 = $86.62
Please help me !!! Easy math
Answers
Answer:
i agree with answer above mine
Step-by-step explanation:
Lucy is a dress maker. She sews 4/7 of a dress in 3/4 hour. Lucy sews at a constant rate. At this rate, how many dresses does Lucy sew in one?
Answers
[tex]\sf\dfrac{4}{7}\div\dfrac{3}{4}[/tex]
When dividing fractions we flip the one we're dividing by and multiply:
[tex]\sf\dfrac{4}{7}\times\dfrac{4}{3}[/tex]
Multiply the numerators and denominators together:
[tex]\boxed{\sf\dfrac{16}{21}}[/tex]
So she sews 16/21 of a dress in one hour.
7.2 = 8t
t = ???
I need a little help with this one
sorry...
Answers
7.2/8= 0.9 and 8t/8=t
T=0.9
There is no problem with needing a little help, no need to apologize. To solve this use the inverse operation of multiplication (division) to solve. See photo :D
Cheers,
Izzy
what is yhe best approximation of the value of w?
A) 1.4 cm
B) 4.0 cm
C) 6.0 cm
D) 7.3 cm
Answers
B) 4.0 cm
ExplanationFirst, we can adapt the law of sines to the notation of our triangle:
[tex]\frac{sin(W)}{w} =\frac{sin(U)}{u}[/tex]
Now, we can infer from our diagram that [tex]W=39[/tex], [tex]U=31[/tex], and [tex]u=3.3[/tex], so we can replace the values in our previous expression:
[tex]\frac{sin(W)}{w} =\frac{sin(U)}{u}[/tex]
[tex]\frac{sin(39)}{w} =\frac{sin(31)}{3.3}[/tex]
Finally, we can solve for [tex]w[/tex]:
[tex]\frac{3.3sin(39)}{w} =sin(31)[/tex]
[tex]3.3sin(39)=wsin(31)[/tex]
[tex]\frac{3.3sin(39)}{sin(31)} =w[/tex]
[tex]w=\frac{3.3sin(39)}{sin(31)}[/tex]
[tex]w=4.03224[/tex]
Which rounds to [tex]w=4.0[/tex]
We can conclude that the best approximation of w is 4.0 cm
a 20 foot ladder leans against a wall so that the base of the ladder is 8 feet from the base of the building. what angle does the ladder make with the ground?
Answers
use cos(x)8/20
The ladder makes an angle of 63.43 degrees with the ground.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Given that 20 foot ladder leans against a wall so that the base of the ladder is 8 feet from the base of the building
We need to find the angle which the ladder make with the ground.
tan(x) = opposite side / adjacent side
In this case, the opposite side is the height of the building, which is 20 feet.
The adjacent side is the distance from the wall to the base of the ladder, which is 8 feet.
Plugging in the values:
tan(x) = 20 / 8
x=tan⁻¹(20/8)
x=63.43 degrees
x is the angle
Hence, the ladder makes an angle of 63.43 degrees with the ground.
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th original price of a computer was reduced by $250. if p= the computer original price in dollars. which algebraic expression represents the reduced price
Answers
p-250
Students in a class were asked to name their favorite sport they like to watch on television. The results are shown in the circle graph. How many times more students prefer to watch basketball than prefer to watch soccer? Soccer- 3% Basketball- 25.5%
Answers
8.5 times more student prefer basketball over soccer
Using the divison operation, we can conclude that students prefer Basksetball 8.5 times more than soccer.
Percentage who prefer soccer = 3%Percentage who prefer Basksetball = 25.5%To obtain the number of times basket ball preference is greater than soccer :
We use the division operation :
(percentage of basketball) ÷ (percentage of soccer)
(25.5) ÷ 3 = 8.5
Therefore, students prefer basketball 8.5 times more than soccer.
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Congruency means that two figures or items are exactly the same size and shape. Where in life would it be vitally important for two or more items to be congruent?
Answers
Hope this helps!
Brainliest? Please?
What is the surface area of this design/
Answers
4(2.1k-4)=6(3.4k-2) what does (K) equal?
Answers
4(2.1k - 4) = 6(3.4k - 2); apply the distributive property to remove the parenthesis.
8.4k - 16 = 20.4k - 12; Get the variable to one side, so subtract 8.4k.
-16 = 12k - 12; isolate the variable by adding 12.
-4 = 12k; divide by 12 to solve for our variable.
k = -1/3
I hope this helps!
show your work and simplify the expression (x – 2) (3x-4)
Answers
Remember F.O.I.L
First
Outside
Inside
Last
First: x * 3x = 3x^2
Outside: x * -4 = -4x
Inside: -2 * 3x = -6x
Last: -2 * -4 = 8
3x^2 - 4x -6x + 8
Now, combine like terms.
3x^2 - 10x + 8
Hope I helped!
I'd be very happy to help if you need anything else!
~ Zoe
The ratio of the number of boys to the number of girls in the class is 1:6. Which statement must describe the class?
A) There are exactly 7 students in the class.
B) There is 1 boy for every 6 girls in the class.
C) There are 5 more girls than boys in the class.
D) There is 1 boy out of the 6 students in the class.
Answers
: ) have a nice day
Answer: B
Step-by-step explanation: If it is asking the ratio from boys to girls the boy would be 1 and the girl would be 6 so the ratio is for every one boy is six girls. So it would be B.
The volume of a right rectangular shipping carton is 948.75 cubic meters. The height of the shipping carton is 11 meters, and the width is 7.5 meters. What is the length of the shipping carton? Enter your answer as a decimal in the box.
Answers
If volume of a right rectangular shipping carton is 948.75 cubic meters and the height of the shipping carton is 11 meters, and the width is 7.5 meters then length is 11.5 meters.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Given that volume of a right rectangular shipping carton is 948.75 cubic meters.
The height of the shipping carton is 11 meters, and the width is 7.5 meters.
We have to find the length of the shipping carton
V=Length × width × height
V= Length x 7.5 x 11
948.75 = 82.5 length
Divide both sides by 82.5
Length = 948.75/82.5
Length = 11.5 meters
Hence, if volume of a right rectangular shipping carton is 948.75 cubic meters and the height of the shipping carton is 11 meters, and the width is 7.5 meters then length is 11.5 meters.
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if the selling price is $18.00 and the markup is 33%.what is te dollar markdown?
Answers
If the markup is 33%, then the markdown is 67%
(18*67)/100 = x
1.206/100 = x
100x = 1.206
x = 1.206/100
x = 12,06$
What is 2x2 ? Plz I need the answer .
Answers
All you are doing is multiplying 2 by 2, doubling it.
Hope this helped<3
Charlene records the number of pieces of red colored candies in ten bags of candy of assorted colors. find and interpret the mean absolute deviation of the data
6,6,7,7,8,8,10,10,11
Answers
Please see the attached picture for the work.
The mean absolute deviation is approximately 1.48.
This means that the numbers of candies in the 10 bags are all very close to one another. There is not much variation.
Find the total surface area of the cube box below
Answers
everyday on her way home from school, Minnie usea $1 to buy a bag of chips. The bag cost $0.75, and she saves the remaining quarter in her change jar. Minnie buys 5 bags of chips per week. At this rate, how long will it take her to save $10.00
Answers
Can someone please help me??
Answers
Need help! Easy!! 7th grade Pre-algebra! Easy!
Answers
B is the appropriate selection.
_____
8. The vertex form will be
.. y = a(x +1)² -10 . . . . . matching selections F and H
When we substitute x=1, we get 4a-10 = 2; a=3
H is the appropriate selection
Gene has a gasoline budget of $275 per month. He uses an average of $7 of gasoline each day he drives. Which of the following equations represents how much money is left in his gasoline budget after x days of driving?
Answers
The equation to represent how much money is left in Gene's gasoline budget after driving for x days is y = 275 - 7x, where x is the number of days Gene drives and y is the money left in the budget.
Explanation:The equation representing how much money is left in Gene's gasoline budget after driving for x days can be expressed as y = 275 - 7x. Here, 275 represents the monthly gasoline budget, 7 is the cost of gasoline each day, and x is the number of days. If we plot y against x, we can visualize how Gene's monthly gasoline budget decreases by $7 for each day he drives.
This equation is a simple example of a linear equation, which describes a straight line in a coordinate system. The variable x is the independent variable (number of days driven) and y is the dependent variable (money left in the budget). The slope of the line (-7) represents the rate at which the budget decreases each day.
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"write an equation in slope-intercept form of the line satisfying the given conditions."
The line passes through (-3,2) and is parallel to the line whose equation is y = 4x + 1.
How do I do this problem? Show all work.
Answers
This is because y = 4x+1 is in the form y = mx+b (m = 4 is the slope)
Any line parallel to the given line is also going to have the same slope of m = 4
Plug in m = 4 and (x,y) = (-3,2) and then solve for b
y = mx+b
2 = 4(-3)+b
2 = -12+b
2+12 = -12+b+12
14 = b
b = 14
So m = 4 and b = 14 means that y = mx+b turns into y = 4x+14
----------------------------------------
Final Answer: y = 4x+14
Help with 3 and show all work
Answers
< is less than
> is greater than
Without him paying the extra fee is <=50
x is pounds.
Now, you have x<=50.
Hope this helped☺☺
The answer should be x<=50, or x is less than or equal to 50.
Your previous answer was almost correct, but the inequality actually has a less than or equal to sign since Michael could still be at exactly 50 pounds without having to pay extra. The charge only applies when the weight is more than 50 pounds.
Hope this helps!
The ratio of plates to napkins is 3:12. Write the ratio in simplest form.
Answers
I hope this helped! :-)
The common factor of 3 and 12 is 3.
3 divided by 3 is 1
12 divided by 3 is 4
So you get 1:4
Hope this helped! ♡
Can anyone help me? Or at least explain how you solved the problem
Answers
Answer is 2.