The solution of the system of equations is [tex]x=-2[/tex] and [tex]y=3[/tex]
Explanation:
The system of equations are [tex]4 x+5 y=7[/tex] and [tex]3 x-2 y=-12[/tex]
To determine the solution of the equation, let us solve the equations by elimination method.
Thus, multiplying the equation [tex]4 x+5 y=7[/tex] by 2, we get, [tex]8x+10y=14[/tex]
Multiplying the equation [tex]3 x-2 y=-12[/tex] by 5, we get, [tex]15x-10y=-60[/tex]
Adding these two equations, we have,
[tex]\ \ 8x+10y=14\\15x-10y=-60\\---------\\23x=-46[/tex]
Dividing both sides by 23, we have,
[tex]\frac{23x}{23} =\frac{46}{23}[/tex]
[tex]x=-2[/tex]
Thus, the value of x is [tex]x=-2[/tex]
Substituting [tex]x=-2[/tex] in the equation [tex]4 x+5 y=7[/tex], we get,
[tex]4 (-2)+5 y=7[/tex]
[tex]-8+5 y=7[/tex]
[tex]5y=15[/tex]
[tex]y=3[/tex]
Thus, the value of y is [tex]y=3[/tex]
Hence, the solution of the system of equations is [tex]x=-2[/tex] and [tex]y=3[/tex]
The solution to the system of equations, is: (-2, 3).
Solution to System of EquationsTo find the solution, you can use the elimination method by first making both equations equivalent. Then add or subtract to eliminate a variable.
Given:
4x + 5y = 7 --> Eqn. 13x – 2y = –12 --> Eqn. 2Multiply eqn. 1 by 3 and eqn. 2 by 4:
12x + 15y = 21 --> Eqn. 1
12x – 8y = –48 --> Eqn. 2
Subtract:23y = 69
Divide both sides by 23y = 3
Substitute y = 3 into eqn. 1.
4x + 5(3) = 7
4x + 15 = 7
4x = 7 - 15
4x = -8
x = -2
Therefore, the solution to the system of equations, is: (-2, 3).
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What was the value of x and y for the following equations? Equation 1: 2/3 (x-6) = 6 Equation 2: 2/3y - 6 = 6 x = 15, y = 15 x = 18, y = 15 x = 18, y = 18 x = 15, y = 18
The value of x is 15 and value of y is 18
Solution:
Given equations are:
[tex]\frac{2}{3}(x - 6) = 6\\\\\frac{2}{3}y - 6 = 6[/tex]
From first equation,
[tex]\frac{2}{3}(x - 6) = 6\\\\Remove\ the\ parenthesis\ and\ solve\\\\\frac{2}{3}x - \frac{2}{3} \times 6 = 6\\\\\frac{2}{3}x - 4 = 6\\\\Move\ the\ constant\ from\ left\ side\ to\ right\ side\\\\\frac{2}{3}x = 6 + 4\\\\\frac{2}{3}x= 10\\\\2x = 30\\\\Divide\ both\ sides\ by 2\\\\x = 15[/tex]
From second equation,
[tex]\frac{2}{3}y - 6 = 6\\\\Move\ the\ constant\ from\ left\ side\ to\ right\ side\ of\ equation\\\\\frac{2}{3}y = 6 + 6\\\\\frac{2}{3}y = 12\\\\2y = 36\\\\Divide\ both\ sides\ by\ 2\\\\y = 18[/tex]
Thus value of x is 15 and value of y is 18
Solve each equation.
a. 10 = 4y
b.5y = 17.5
c. 1.036 = 10y
d. 0.6y = 1.8
e. 15 = 0.1y
Answer:
a. y = 2.5
b. y = 3.5
c. y = 0.1036
d. y = 3
e. y = 150
Step-by-step explanation:
a. 10 ÷ 4 = 2.5
b. 17.5 ÷ 5 = 3.5
c. 1.036 ÷ 10 = 0.1036
d. 1.8 ÷ 0.6 = 3
e. 15 ÷ 0.1 = 150
Evaluate the expression.
(132−122)÷5
The value of the expression___ is
Final answer:
The value of the expression (132-122)÷5 is 2 after performing the subtraction followed by division.
Explanation:
Evaluating the expression (132−122)÷5 involves two operations: subtraction and division.
First, we subtract 122 from 132, which gives us 10.
Then, we divide the result by 5.
The division of 10 by 5 yields 2.
Therefore, the value of the expression (132−122)÷5 is 2.
Complete the table below
Answer:
10 100 1,000
30 60 1,800
40 40 1,600
Step-by-step explanation:
First you take each width and multiply it by 2 to get both widths.
Then you take 120 and subtract each width from it because it's 120 feet for the entire fence.
Next you end up with the length.
Finally you multiply the length by the width to get the area.
A recipe calls for 2 cups of flour of flour to make 3 dozen cookies. Is 3 cups of flour enough to make 60 cookies?
Answer:
no it is not
Step-by-step explanation:
it would be 54
Answer:
No
Step-by-step explanation:
2 cups of flour --> 36 cookies
3 cups of flour ----> x
2/3 = 36/x
x = 54 cookies
3 Cups of flour yields 54 cookies, but its not enough flour for 60 cookies.
A sketch of Jessie’s neighborhood is shown below. Which equation can Jessie use to determine x, the distance from home to school?
Answer:
Hello the Answer is A!
Step-by-step explanation:
Here's how to do it
When you have the triangle of her school you add your first to angles together and subtract from 180. Then you are going to set is up as law of sine. So the order would be 6/sin110* = x/sin50*
Hope this helps <3
The distance from home to school will be 5 meters.
Pythagorean theorem states that in the right angle triangle, the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
From the given image the distance between the home and school is followed by the square 3 meters from the home and the school is 4 meters making a right-angle triangle.
The minimum distance between the school and the home will be calculated as;-
D = √ ( 3² + 4² )
D = √ ( 25 )
D = 5 meters'
Therefore, the distance will be 5 meters.
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Kyra has a manufacturer's coupon for $5 off a box of diapers and a store coupon for 20% off any purchase. The store will let you use both coupons, but it does not have a policy about which coupon you must use first. What order should she use the coupons to get the maximum discount on a $40 box of diapers?
Answer: 20% of $40 is $8-$5=$3 or $40-$5=$35 and 20% of $35 is $7.
Step-by-step explanation: Based on this math you would want to apply the 20% discount first.
Jillian buys 3.6 meters of fabric. The fabric costs $5.75 for each meter. How much does Jillian spend for the fabric?I need help asap no need to give me example just answer
[help]
Sort the phrases according to whether or not they require a hyphen.
in eighty two days
Needs Hyphen
Does Not Need Hyphen
twenty six letters
the fourth person in line
three thousand years
two thirds of the class
Answer:
Needs hyphen: -in eighty two days -twenty six letter - two thirds do the class
Doesn’t need hyphen: -the fourth person in line -three thousand years
Step-by-step explanation:
Answer:
Needs hyphen:
in eighty two days
twenty six letters
two thirds of the class
Does not need Hyphen:
the fourth person in line
three thousand years
Step-by-step explanation:
Hyphen needed for numbers between 21-99
the area of a rectangular window is 7098cm^2 . if the length of. the window is 91 cm, what is it’s width?
Answer:
78
Step-by-step explanation:
7098 / 91 = 78
hope i helped
10. Write the number 2,049 in
expanded form.
Step-by-step explanation:
[tex]2049 = 2 \times 1000 + 0 \times 100 + 4 \times 10 + 9 \times 1 \\ = 2000 + 0 + 40 + 9 \\ = 2000 + 40 + 9[/tex]
Answer:
2,000 + 0 + 40 + 9
Explanation:
Expanded form or expanded notation is a way of writing numbers to see the math value of individual digits.
Hope this helps
- Amelia The Unknown
Which recursive definition represents the sequence {4,6,8,10...)?
A). a1 = 4; an-1-2
B). a1 = 4; an-1 + 2
C). a1 = 2; an-1 + 2
D). a1 = 4; 2an-1 - 2
Answer:It’s b
Step-by-step explanation:USA test prep answer
(9x2 + 10x + 4) − (9x2 + 5x − 1)
For this case we must simplify the following expression:
[tex](9x ^ 2 + 10x + 4) - (9x ^ 2 + 5x-1)[/tex]
We eliminate the parentheses taking into account that:
[tex]- * + = -\\- * - = +\\9x ^ 2 + 10x + 4-9x ^ 2-5x + 1 =[/tex]
We add similar terms taking into account that:
Equal signs are added and the same sign is placed.
Different signs are subtracted and the major sign is placed.
[tex]9x ^ 2-9x ^ 2 + 10x-5x + 4 + 1 =\\5x + 5[/tex]
Answer:
[tex]5x + 5[/tex]
Please Help with these 3 questions Please
How do you model 18 more than 27 on the number line?
Answer:
Step-by-step explanation:
make 18 a positive number on the number line and 27 a negative number on the number line
Which of the following expressions means "five factors of 3"?
35
0
05=3
[tex]\text{Hey there!}[/tex]
[tex]\large\text{Which of the following expressions means \underline{five factors of 3} ?}[/tex]
[tex]\large\text{Basically, it is telling you that 3 is expressed as it rises to the 5th}\\\large\text{power}[/tex]
[tex]\large\text{Based on SOME of the stuff we gathered above, we solved your}\\\large\text{equation/ question!}[/tex]
[tex]\boxed{\boxed{\mathsf{Your\ answer: \boxed{\mathsf{3^5}}}}}\checkmark[/tex]
[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\dfrac{\frak{LoveYourselfFirst}}{:)}[/tex]
Here is a balanced hanger:
If a square weighs 5 grams, and a triangle weighs 2 grams, how much does a circle weigh?
I don't know exactly i think its either 3 grams or 7 grams or 2 1/2 grams
sorry if its wrong
If f(x) = x ^ 3 + 2x ^ 2 - 3 , find f(2) . A ) -19 B ) -3 C) -1 D ) 5
Answer:
13
Step-by-step explanation:
f(x) = x ^ 3 + 2x ^ 2 - 3
Let x=2
f(2) = 2 ^ 3 + 2 *2 ^ 2 - 3
= 8 +2 *4 -3
= 8 +8 -3
=13
The farthest distance a satellite signal can directly reach
is the length of the segment tangent to the curve of Earth's
surface. If the measure of the angle formed by the tangent
satellite signals is 135, what is the measure of the intercepted
satellite
arc on Earth? (The figure is not drawn to scale.)
Answer:
45°
Step-by-step explanation:
The sum of interior angles of the quadrilateral that has vertices at the center of the Earth, the two points of tangency, and the satellite is 360°. The angles at the points of tangency are 90°, so the angle at the satellite and the central angle are supplementary.
The arc has a measure of 180° -135° = 45°.
Which inequality is equivalent to -m> 15
This inequality can be simplified.
~Divide -1 to both sides (flip the symbol since we're dividing a negative number)
-m/-1 < 15/-1
m < -15
Best of Luck!
Answer:
m < -15
Step-by-step explanation:
Step 1: Multiply both sides by -1
-m > 15
-m * -1 > 15 * -1
Since you multiply by a negative, you must flip the sign
-m * -1 > 15 * -1
m < -15
Answer: m < -15
Is the relation a function? Yes or No? (4,5),(4,-7), (4,2), (4,0), (4,9)
Answer:
No, because 4 is repeated in the domain.
Step-by-step explanation:
Answer:
No it's not a function
Step-by-step explanation:
When the domain repeats either once or more, it's never a function
Grace starts with 100 milligrams of a radioactive substance. The amount of the
substance decreases by each week for a number of weeks, w. She writes the
expression 100(-)w to find the amount of radioactive substance remaining after w
weeks.
Ryan starts with 1 milligram of a radioactive substance. The amount of the substance
decreases by 40% each week for a number of weeks, w. He writes the expression (1 -
0.4)" to find the amount of radioactive substance remaining after w weeks.
Use the drop-down menus to explain what each part of Grace's and Ryan's
expressions mean.
Answer:
100 is grace's initial amount. w is how much of the substance is being decrased each week. in ryan's equation, 1 is 100% of the substance, so the initial amount, and 0.4 is the amount that is being decreased.
Step-by-step explanation:
Answer:
100= Initial Amount
1/4= decay factor for each week
w= number of weeks
1/4w= decay factor after w weeks
1 - 0.4= decay factor for each week
w= number of weeks
0.4= percent decrease
Step-by-step explanation:
11. Simon arrived at work at 8:15 A.M. and left work at 10:30 P.M. If Simon gets paid by the hour at a
rate of $10 and time and / for any hours worked over 8 in a day. How much did Simon get paid?
A. $120.25
B. $160.75
C. $173.75
D. $180
E. $182.50
Answer:
D
Step-by-step explanation:
Draw and classify a quadrilateral that fits each description
4 right angles, opposite sides equal in length and parallel
Opposite sides equal in length and parallel
Answer:
It would be a square or a rectangle .
Step-by-step explanation:
The quadrilateral(s) has 4 sides, and each have have 4 right angles. The opposite lengths are both the same as the are parallel. Even though the rectangle has different lengths, the opposites match.
40 pts! please answer asap!
∠A and ∠B are supplementary angles. The measure of ∠A is three time the measure of ∠B.
Part A: Write an equation to represent the supplementary angle relationship between ∠A and ∠B.
Part B: Use the equation to find the measures of ∠A and ∠B.
[tex]\huge{\underline{\mathfrak{\red{Answer}}}}[/tex]
let A=3x then B=x
also given,
A+B=90°
3x+x=90
4x=90
x= 22.5°
then 3x= 3×22.5= 67.5
A= 67.5
B=22.5
Answer:
20 points
Step-by-step explanation:
Vertical and horizontal line (1,-4)—do X=blank and Y=blank
Answer:
x = 1 and y = - 4
Step-by-step explanation:
The equation of a vertical line is
x = c
where c is the value of the x- coordinates the line goes through.
Here the line passes through (1, - 4) with x- coordinate 1, thus
x = 1 ← equation of vertical line
The equation of a horizontal line is
y = c
where c is the value of the y- coordinates the line goes through.
Here the line passes through (1, - 4) with y- coordinate - 4, thus
y = - 4 ← equation of horizontal line
Rewrite the expression by favoring out the greatest common factor: 9b+12
Answer:
3(3b + 4)
the GCF is 3
Step-by-step explanation:
Solve for x.
8 - 4x - 28 = 4
x=_________
Answer:
x=6
Step-by-step explanat
solve the equation 14z=224
Answer:
16
Step-by-step explanation:
224/14=16
Answer: z=16
Step-by-step explanation:
take 224 and divide it by 14, whatever the answer is, equals z
Classify a triangle with angle measures of 63 degrees and 27 degrees.
A) Acute
B) Obtuse
C) Right
D) Not Possible
Yo sup??
63+27=90
therefore the other angle is 90
Hence it's a right angled triangle
correct answer is option C
Hope this helps