6x+4y=42 -3x+3y=-6 by elimination
Answer:
x=5, y=2
Step-by-step explanation:
To solve this system, we need to find x and y. First, let's find x. In the first equation (6x+4y=42), subtract 4y on both sides to isolate 6x. This will result in 6x=42-4y. Divide by 6 on both sides to isolate x and get x=7-[tex]\frac{2}{3}[/tex]y. Now we know what x equals. Go to the second equation ad plug this into it. So instead of -3x+3y=-6, you'll have -3(7-[tex]\frac{2}{3}[/tex]y)+3y=-6. Use the distributive property to get -21+2y+3y=-6. Add 2y and 3y to get -21+5y=-6. Add 21 to both sides to isolate 5y and get 5y=15. Divide by 5 on both sides to isolate y and get y=3. Now that we know that y=3, we can plug this back into the equation that was bolded above so that we can find x, so we'll have x=7-[tex]\frac{2}{3}[/tex](3) since y=3, and we'll get x=7-[tex]\frac{6}{3}[/tex], or x=7-2, or x=5.
x=5
y=2
Answer: (5, 3)
Step-by-step explanation:
Solve by Addition/Elimination
6x + 4y = 42 −3x + 3y = −6
Multiply each equation by the value that makes the coefficients of x opposite.
6x + 4y = 42
(2) ⋅ (−3x + 3y) = (2) (−6)
Simplify (2) ⋅ (−3x + 3y).
6x + 4y = 42
−6x + 6y = (2) (−6)
Multiply 2 by −6. 6x + 4y = 42
−6x + 6y = −12
Add the two equations together to e liminate x from the system.
6x + 4y = 42
±6x + 6y = −12
1 0y= 30
Divide each term in 10y = 30 by 10.
10y = 30
10 10
Cancel the common factor of 10.
y = 30/10
Divide 30 by 10.
y = 3
Substitute the value found for y into one of the original equations, then solve for x.
Substitute the value found for y into one of the original equations to solve for x. 6x + 4 (3) = 42
Multiply 4 by 3.
6x + 12 = 42
Move all terms not containing x to the right side of the equation.
6x = 30
Divide each term by 6 and simplify.
x = 5
The solution to the independent system of equations can be represented as a point.
(5, 3)
The result can be shown in multiple forms.
Point Form:
(5, 3)
Equation Form:
x = 5, y = 3
I'm very confused, I don't know where to even start! Please help me!!
Answer/Step-by-step explanation:
✔️Using trigonometric ratio, find width of the rectangle, BD:
Thus:
[tex] tan(\theta) = \frac{opposite}{adjacent} [/tex]
Where,
[tex] tan(\theta) = tan(60) = \sqrt{3} [/tex]
Opposite = BD
Adjacent = 7 cm
Plug in the values
[tex] \sqrt{3} = \frac{BD}{7} [/tex]
Multiply both sides by 7
[tex] 7\sqrt{3} = BD [/tex]
[tex] BD = 7\sqrt{3} [/tex]
✔️Using trigonometric ratio, find height of the rectangle, BF:
Thus:
[tex] tan(\theta) = \frac{opposite}{adjacent} [/tex]
Where,
[tex] tan(\theta) = tan(60) = \sqrt{3} [/tex]
Opposite = 6 cm
Adjacent = BF
Plug in the values
[tex] \sqrt{3} = \frac{6}{BF} [/tex]
[tex] BF = \frac{6}{\sqrt{3}} [/tex]
Rationalize
[tex] BF = \frac{6 \times \sqrt{3}}{\sqrt{3} \times \sqrt{3}} [/tex]
[tex] BF = \frac{6\sqrt{3}}{3} [/tex]
[tex] BF = 2\sqrt{3} [/tex]
✔️Perimeter of rectangle BDEF:
Perimeter = 2(BD + BF)
Plug in the values
[tex] Perimeter = 2(7\sqrt{3} + 2\sqrt{3}) [/tex]
[tex] Perimeter = 2(9\sqrt{3}) [/tex]
[tex] Perimeter = 18\sqrt{3} [/tex]
✔️Area of the rectangle BDEF:
Area = BD × BF
Plug in the values
[tex] Area = 7\sqrt{3} \times 2\sqrt{3} [/tex]
[tex] Area = 7 \times 2\sqrt{3 \times 3} [/tex]
[tex] Area = 14 \times 3 [/tex]
[tex] Area = 42 [/tex]
PLEASE HELP ASAP Which of the following expressions is equivalent to the expression 42 + 90?
Answer:
6(7+15)
Step-by-step explanation:
6×7=42
6×15=90
Ms. McGuirk wants to know if she built her son's new sandbox with a perfect right angle or not? The shorter sides are 15 feet and 8 feet what should the measure of the 3rd side be to make it a perfect right angle?
Answer:
17 feet
Step-by-step explanation:
A right angle has 3 sides: the adjacent, the opposite and the hypotenuse.
The hypotenuse is the largest side of the right angle
The shorter sides are 15 feet and 8 feet which should represent opposite and adjacent sides respectively
Opposite = 15 feet
Adjacent = 8 feet
Hypotenuse = x feet
Using Pythagoras theorem to solve
Hypotenuse ² = opposite ² + adjacent ²
x² = 15² + 8²
x² = 225 + 64
x² = 289
Find the square root of both sides
√x² = √289
x = 17 feet
The 3rd side is 17 feet
Can somebody help me on this
Answer/Step-by-step explanation:
a. 3x + 13 = 12x - 2x
Add like terms
3x + 13 = 10x
3x = 10x - 13 (subtraction property of equality)
3x - 10x = - 13 (substraction property of equality)
-7x = -13
-7x = -13/-7 (division property of equality)
x = 13/7
b. 6j - 12 + 4j - 8 = 10
Add like terms
6j + 4j - 12 - 8 = 10
10j - 20 = 10
10j = 10 + 20 (addition property of equality)
10j = 30
10j/10 = 30/10 (division property of equality)
j = 3
c. 10y - 4y = 14 + 2y - 3y
Add like terms
6y = 14 - y
6y + y = 14 (addition property of equality)
7y = 14
7y/7 = 14/7
y = 2
d. 4p + 8 - 3p = 33
Add like terms
4p - 3p + 8 = 33
p + 8 = 33
p = 33 - 8 (subtraction property of equality)
p = 25
Plz help I’m getting timed
Answer:
$38,465
Step-by-step explanation:
35 x 1,099 = 38,465
I am very confused with this problem please help me
Answer:
The answer is -0.5
Step-by-step explanation:
Divide both side by the numeric factor on the left side then solve
what is the sum of four consecutive odd numbers is 80?
Answer:
Let first number be x , so other numbers will be x+2,x+4 and x+6. Now sum of all these number is 4x+12=80 or x=(80–12)/4=68/4=17 . So numbers are 17,19,21 and 23.
Answer:
90% of people marry there 7th grade love. since u have read this, u will be told good news tonight. if u don't pass this on nine comments your worst week starts now this isn't fake. apparently if u copy and paste this on ten comments in the next ten minutes you will have the best day of your life tomorrow. you will either get kissed or asked out in the next 53 minutes someone will say i love you
Step-by-step explanation:
I’ll give the Brainliest to who answers the question with and reasonable explanation.
When is the constant of proportionality the same as the unit rate when comparing two quantities?
A. Only when the two quantities are indirectly proportional
B. Only when the two quantities are directly proportional
C. Always
D. Never
Thank you!
Answer:
it's A
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
Just got it correct
solve -1 < x + 1 ≤ 6
Answer:
-2<x≤5
Step-by-step :
-1<x+1≤6 So fisrt what every we do to one side we must do to the other. In this case it's a bit different since we are dealing with inequalities.
-1<x+1≤6 I would start off by isolating x in the middle.
-1<x+1≤6 I subtracted 1 from all three sides.
-1 -1 -1
Now your equation should look like this:
-2<x≤5 Now there is really nothing much we can do here since we were just trying to get x by its self.
Answer : -2<x≤5
find the greatest common factor and the least common multiple of 12 and 20 explain
I’ll give brainleast
Answer:
GCF: 4
LCM: 60
HELP
ME
PLEASE!!!!!NOWWW
Answer:
1.a
2.j
3.g
4.d
5.i
6.l
7.b
8.c
9.f
10.h
11.e
12.k
Step-by-step explanation:
solve for x (log) PLEASE HELP ASAP! thank you!!!! *will give brainliest ofc*
Answer:
( D ) x = 6
Hope this helps !! :)
What is the measure of ∠ ACD?
Answer:
so 1st, subtract 33 and 117 from 180
180-117-33= 30
then you subtract 30 from 180
180-30= 150
and your measurement of angle ACD is 150
A school hoped to raise $30,000 at an auction to pay for
new computers. After the auction was over, the school
found they had made $34,800. What percent of their goal
did the school raise?
A
186%
B
116%
с
86%
D
16%
Andrew buys 8 pounds of apples for $11.60. He wants to know and use the unit rate of the cost per pound.
True or False: Two pounds of apples cost more than $3.
Answer:true
Step-by-step explanation:
Maggie says the LCM of 8 and 12 is 24. Her friend Glen says the answer is 4. Who is rigth?
Answer:
Maggie
Step-by-step explanation:
Pls help me solve for x ill give 10 points away
Answer:
.53 pounds of dog food each day.
Step-by-step explanation:
Use PEMDAS to solve
can someone answer the problem, please?
158
× 4
Answer:
the answer is 632
Step-by-step explanation:
just do some normal multiplication. :)
(take 2 bc i messed up) What is √30 simplified
Answer: the square root of 30 is simplified to 5...
Hope this helps! :D
Step-by-step explanation:
Answer:
Square root of 30 simplified is 5
Step-by-step explanation:
Hope this helps! c:
1 3 Which is the best estimate of 11. 113 2 4? O 4 O 6 o 22 O 33
Answer:22
Step-by-step explanation:
What is the value of (2)⁶?
Answer:
64
Step-by-step explanation:
2 to the sixth power would be 2 multiplied by itself 6 times
What is three hundred forty two thousandths in decimal form?
Answer:
C
Step-by-step explanation:
it says thousandths and a number group with a th at the end is on the right of the decimal.
Answer:
C: 0.342
Step-by-step explanation:
Here's how it works:
.(tenth)(hundredth)(thousandth)
Therefore,
"Three hundred forty-two thousandths" is 0.342.
2 pens in each pack of black pens 5 pens in each pack of red pens 6 pens in each pack of green pens On Monday number of packs sold of black, red and green pens = 7 : 3 : 4 A total of 212 were sold.
Answer:
The number of green pens sold is 96.
Step-by-step explanation:
Note: This question is not complete. The complete question is therefore provided before answering the question as follows:
A shop sells packs of black pens, packs of red pens and packs of green pens. There are:
2 pens in each pack of black pens
5 pens in each pack of red pens
6 pens in each pack of green pens
On Monday, number of packs of black pens sold : number of packs of red pens sold : number of packs of green pens sold = 7:3:4
A total of 212 pens were sold.
Work out the number of green pens sold.
The explanation of the answer is now given as follows:
Since the ratio is given in packs of pens, we have to first convert it to number of pens based on the number of pens in each pack. Therefore, we have:
7:3:4 is converted to (7 * 2) : (3 * 5) : (4 * 6) = 14 : 15 : 24
Based the new ratio, we have:
Weight of contribution of the green pens to the total number of pens sold = 24 / (14 + 15 + 24) = 24 / 53 = 0.452830188679245
The number of green pens sold can now be calculated as follows:
Number of green pens sold = Total pens sold * Weight of contribution of the green pens to the total number of pens sold = 212 * 0.452830188679245 = 96
Therefore, the number of green pens sold is 96.
Evaluate x – y if x = 5 and y = -2.
Answer:
7
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
x - y
x = 5
y = -2
Step 2: Evaluate
Substitute: 5 - -2Simplify: 5 + 2Add: 7Evaluate the following expression using the values given: Find LaTeX: 3r^2-5s+6t3 r 2 − 5 s + 6 t if LaTeX: r=2,\:s=-4,\:t=-1r = 2 , s = − 4 , t = − 1
Answers:
-2
26
38
-14
Answer:
26
Step-by-step explanation:
These problems always really confuse me but I took a quiz with this question and this is my answer 26
Answer:26
Step-by-step explanation:
i just took the test
Solve the inequality 3(x - 7) + 2(4x + 9) > 0.
Answer:
x>3/11
3x - 21 + 8x + 18 >0
11x - 3 >0
11x >3
x>3/11
Answer:
Step-by-step explanation:
3(x - 7) + 2(4x + 9) > 0
3x-21+8x+18>0
11x-3>0
11x>3
x>3/11
Line m has the equation y = 1/2x - 4
If lines m and n are parallel to each other, which of the following equations could represent line n?
2x+y=4
2x-y=4
X+2y=4
X-2y=4
Answer:
As the slopes of both lines 'm' and 'n' are the same.Therefore, we conclude that the equation x-2y=4 represents the equation of the line 'n' if lines m and n are parallel to each other.
Step-by-step explanation:
We know that the slope-intercept of line equation is
[tex]y=mx+b[/tex]
Where m is the slope and b is the y-intercept
Given the equation of the line m
y = 1/2x - 4
comparing with the slope-intercept form of the line equation
y = mx + b
Therefore,
The slope of line 'm' will be = 1/2
We know that parallel lines have the 'same slopes, thus the slope of the line 'n' must be also the same i.e. 1/2
Checking the equation of the line 'n'
[tex]x-2y=4[/tex]
solving for y to writing the equation in the slope-intercept form and determining the slope
[tex]x-2y=4[/tex]
Add -x to both sides.
[tex]x - 2y + (-x) = 4+(-x)[/tex]
[tex]-2y = 4 - x[/tex]
Divide both sides by -2
[tex]\frac{-2y}{-2}=\frac{-x+4}{-2}[/tex]
[tex]y=\frac{1}{2}x-2[/tex]
comparing ith the slope-intercept form of the line equation
Thus, the slope of the line 'n' will be: 1/2
As the slopes of both lines 'm' and 'n' are the same.Therefore, we conclude that the equation x-2y=4 represents the equation of the line 'n' if lines m and n are parallel to each other.
NEED HELP ASAP!
The sum of two numbers is 105. The larger number is 6 less than twice the smaller
number. What are the numbers?
Answer: x=68, y=37
Step-by-step explanation:
The equation for the sum of two numbers is 105 would be x+y=105. You can say the larger number would be x and the smaller would be y. So, x=2y-6. then you plug that into the x in the first equation.
2y-6+y=105
3y-6=105
3y=111
y=37
Then you would plug in the y to one of the equations. I will do the second one but you can do either one.
x=2y-6
x=2*37-6
x=74-6
x=68
I need help with this question pls
Answer:
A. would be a.
Step-by-step explanation:
Answer:
a) D
b) 4.09 cm
Step-by-step explanation:
a) P of a circle is 22/7 D
Half a circle 1/2 22/7 D
D= 2r
1/2 22/7 2x (D)
b) Find Radius
P = (3.142 * (2r) )
25.71 = 3.142 *2r
r= 4.09 cm