Learning task 2
A. Solve the systems of equations by a) graphing b) elimination c) substitution
Eq. 1: 2x - 3y = -1; Eq. 2: y = x - 1
B. Solve the problem using any method.
The sum of two numbers is 32 and the difference is 2. Find the numbers
Answers
The given equations are
[tex]2x-3y=-1\cdots(i) \\\\y=x-1\cdots(ii)[/tex]
(a) Solution by graphing both the equations:
Graph for both the equations (i) and (ii) are in the figure. The point of intersection of both the graph is the solution of the equations.
From the graph, the point of intersection is (4,3)).
Hence, the required solution is (4,3).
(b) Solution by elimination method:
Equations (ii) can be written as -x+y=-1, now multiply it by 2, we have
[tex]-2x+2y=-2\cdots(iii)[/tex]
Add equations (i) and (iii), we have
2x-3y=-1
-2x+2y=-2
__________
[tex]\Rightarrow -3y+2y=-1-2\\\\ \Rightarrow -y=-3\\\\ \Rightarrow y=3.[/tex]
Putting the value of y=3 in equation (i), we have
[tex]2x-3\times 3=-1 \\\\\Rightarrow 2x=-1+9=8 \\\\\Rightarrow x=8/2=4[/tex]
Hence, the required solution is (4,4).
(c) Solution by substitution method:
Substituting the value of y from equation (ii) to equation (i), we have
[tex]2x-3(x-1)=-1 \\\\\Rightarrow 2x-3x+3=-1 \\\\\Rightarrow -x=-1-4=-4 \\\\\Rightarrow x=4[/tex]
Putting the value of x=4 in equation (i), we have
[tex]y=4-1=3[/tex].
Hence, the required solution is (4,3).
Related Questions
Allan can make 8 pizzas in 15 minutes at the pizza restaurant where he works. 28. __________ If the number of pizzas varies directly with minutes, how many pizzas can Allan make in 3 hours?
Answers
Answer:
96 pizzas
Step-by-step explanation:
First, we have to determine how many pizza he can make in one minute = 8/15 = 0.533
Convert 3 hours to minutes = 3 x 60 = 180 minutes
The number of pizzas he would make in 3 hours = 180 x 0.533 = 96 pizzas
There is a sale at your favorite clothing store. They have their jeans priced at $49.99 with a extra 20% off. How much will you pay for three pairs of jeans, not including tax? Exlpain how you got your answer.
Answers
Answer: You need to pay $119.98 for three pairs of jeans.
Step-by-step explanation:
Market price of 1 jeans = $49.99
Discount percent = 20% = 0.20
Market price for 3 jeans = 3 x ($49.99)
= $ 149.97
Discount price = 20% of (Market price for 3 jeans )
= .0.20 x ($149.97)
= $ 29.99
Price of 3 jeans after discount = (Market price for 3 jeans ) - ( Discount price)
= $ (149.97 - 29.99)
= $ 119.98
Hence, you need to pay $119.98 for three pairs of jeans.
all quadrilaterals are polygons true or false
Answers
Answer:
True
Step-by-step explanation: because they have 4 sides
All quadrilaterals are polygons because they are 2-dimensional closed shapes made up of interconnected straight lines, with four sides and angles.
Hence the given statement is true.
Sincw we know that,
A polygon is defined as a 2-dimensional closed shape made up of straight lines that are interconnected with each other at their endpoints. A Quadrilateral is a polyhedron that consists of four straight sides or edges.
The term quadrilateral is derived from two Latin words "quadri" meaning four and "latus" meaning sides.
It is important to note that not all polygons are quadrilaterals, but all quadrilaterals are indeed polygons.
Some examples of quadrilaterals include squares, rectangles, parallelograms, trapezoids, and rhombuses.
These shapes share certain properties such as having four sides and angles, with the sum of their interior angles adding up to 360 degrees.
To learn more about polygons visit:
https://brainly.com/question/23846997
#SPJ7
Given: SIn(A)= 4/5 ,pi/2 < A< pi and sin(B)= -2square5/5, pi < B < 3pi/2
What is the value of cos(A-B)
A. -2square5/25
B. -square5/5
C. 2square5/5
D. 11square5/25
Answers
Janna is looking for an apartment. She plans on paying no more than 25% of her monthly income in rent. If she earns $1,825 a month, which amount represents the most she plans to pay in rent every month?
Answers
Answer:
456.25
Step-by-step explanation:
25% as a decimal is .25
To find 25% of her monthly income, multiply 1,825 by .25
1825*.25=$456.25
I need help with this
Answers
Answer: 0.6 grams
Step-by-step explanation: divide grams by cm and its 0.6
What expressions are equivalent to 6.7 - (-2.5)
Answers
Answer:
[tex]6.7-\left(-2.5\right)=9.2[/tex]
Step-by-step explanation:
Given the expression
[tex]6.7-\left(-2.5\right)[/tex]
Solving the expression to get the equivalent function
[tex]6.7-\left(-2.5\right)[/tex]
[tex]\mathrm{Apply\:rule}\:-\left(-a\right)=a[/tex]
[tex]=6.7+2.5[/tex]
[tex]\mathrm{Add\:the\:numbers:}\:6.7+2.5=9.2[/tex]
[tex]=9.2[/tex]
Thus,
[tex]6.7-\left(-2.5\right)=9.2[/tex]
Order from least to greatest
6.8
The square root of 54/3
The square root of 13
26/3
PLEASE HELP
Answers
the square root of 14, the square root of 54/3, 6.8, the square root of 26/3.
Twice a number k plus 8 equals one-half times the quantity of four times a number k plus fourteen ?
Answers
Answer:
No solutions
Step-by-step explanation:
So putting that into an equation it equals
2k+8=(4k+14)÷2
Move the 2 to the other side.
2∙2k+8=4k+14
Simplify.
4k+8=4k+14
It doesn't make sense so No Solutions
Can someone please help
Answers
Answer:
2x+7
Step-by-step explanation:
F(x+3)=2(x+3)+1
F(x+3)= 2x+6 +1 =2x+7
i cant find my answer. You should really give your people the answer they are looking fo instead of giving sujestions.
Answers
Answer:
Did you ask a question? I just checked your profile to see if you posted any but i dont see anything except this
Step-by-step explanation:
Answer:
there is no question asked
Step-by-step explanation:
P(-6, 4), O-2, 7), R(-1, 0), S(-5, -3)
Please help ASAP
Answers
jnsxdhcdhcfhbh demdencec ecerfgv yes
Answers
Step-by-step explanation:
gvxghhujhggfffffddnnkiouucdss
Can someone help me with both these answers I’m marking brainliest
Answers
Answer:
X = 12/60%
60% = 0.6
X = 12/0.6
X = 20.
For the second one, multiply 350 by 0.02, which is just 2% in decimal form.
350*0.02 =7
That's 7 eggs.
Hope this helps!
At the end of the year, Close made the current year on mark down to make Room for next year models. One particular model had a sticker price of $28,640 when it was new. After being marked down, the price is now $27,208. What What is the percent of decrease in the price of the car
Answers
Answer: 5%.
Step-by-step explanation:
Given data:
Old price = $28,640
New price = $27,208
Solution:
Percentage of decrease
= old price - new price / old price * 100
= $28,640 - $27,208 /. $28,640 * 100
= $1432/$28,640*100
= 0.05*100
= 5%.
The percentage of decrease for the car is 5%.
The difference of two numbers is 3. Their sum is 13. Find the numbers.
Answers
Answer:
Answer:
The two numbers are 8 and 5
Explanation:
8 - 5 = 3
8 + 5 = 13
Hope this helps!
SHOW WORK PLZZZZZZZZZZZZZ!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
(x+1)(x+5)(5x−1)
x= 1/5, -5, -1
Step-by-step explanation:
5x^3+29x^2+19x-5
factor
(x+1)(x+5)(5x−1)
the zeros are
x+1=0
x=-1
x+5=0
x=-5
5x-1=0
5x=1
x=1/5
maybe this helps
How many solutions does the following function have? f(x)=4x^2-100
Answers
Answer: x = 5, -5
Step-by-step explanation:
Solve using the quadratic formula.
Of the 150 students that attended the science camp, 82 were sixth graders. Marco says that less than half of the campers were sixth graders. Is he correct? Tell why or why not. Use a benchmark percent to support your answer.
Answers
Answer:
Incorrect
Step-by-step explanation:
150 students are 100%,
82 students are x%
(82*100)/150=54,67%, so that is more than half of all students
Answer:
Marco is NOT correct
Step-by-step explanation:
150 / 2 = 75
so more than half of the students were 6th graders
55% of students were 6th graders, that's my benchmark but I'm not really sure.
Kimoni wants to purchase a pair of shoes that are on sale for 10% off the regular price
of $64.00. Which is the sale price of the shoes?
Answers
Answer:
57.60
Step-by-step explanation:
Multiply $64 by .1 which is the decimal form of 10%. You should get 6.4. Then you subtract 6.4 from 64, you get 57.60.
please answer please answer thank you
Answers
Answer:
367.62 in³
Step-by-step explanation:
The volume of a sphere is V = (4/3)πr³.
Here, that volume of the whole sphere is V = (4/3)(3.14)(5.6 in)³, or
V = 735.25 in³
A 'hemisphere' is half a sphere. Thus, the volume of each hemisphere shown here is
735.25 in³
---------------- = 367.62 in³ This just about matches the first answer choice.
2
HELPPPPPPPPPPPPPPPP!
Answers
Step-by-step explanation:
The answer is over stretching the ligament
Answer:
Sprain: over-streching the ligament
Tear: Torn or separated from bone
Dislocation: Bones separated from joint
Arthritis: Overuse injury that occurs over time
Nadia is a stockbroker. She earns 13% commission each week. Last week, she sold $4,500 worth of stocks. How much did she make last week in commission? If she averages that same amount each week, how much did she make in commission in 2011?
Answers
Multiply amount sold by commission rate:
4500 x 0.13 = 585
She made $585 last week.
Multiply amount made in 1 week by 52 weeks ( 1 year = 52 weeks)
585 x 52 = 30,420
She made $30,420 in 2011
Find P(5) when p = 0.38
i was swamped with work and my anxiety is flying off the charts rn
Answers
Step-by-step explanation:
p = 0.38
0.38 × 5
= 1.9
hope it helpful
The ratio of boys to girls in Mr. Woods class is 5:7.
If there are 60 students in all, how many are boys?
Answers
Answer:
25
Step-by-step explanation:
5+7 is 12, 60 divided by 12 is 5. 5x5 is 25
Find the measure of the each angle indicated. HELP
Answers
Answer:
(n-2)180 (this is the equation to find the sum of interior angles)
(4-2) 180 (plug in the amount of angles in the polygon and then solve)
2* 180
360
360 - 115 -100- 73= 72 (360 is the sum of all angles for this polygon. so subtract the known angles to find the unknown one)
measure of angle B is 72 degrees
Step-by-step explanation:
Answer:
b=72 degrees
Step-by-step explanation:
100+115+73=288
360-288= 72 degrees
Complete the steps to solve for x.
-0.51x + 0.21x = 6.3
- 0.51x + 0.21x = 6.3
x = 6.3
Answers
Answer:
Step-by-step explanation:
-0.51x+0.21x=6.3 combine like terms
-0.3x=6.3 divide by -0.3
x= -21
ANSWER ASAP FOR BRAINLIEST
Answers
Answer:
I CANT SEE THE IMAGE BUT I NEEED POINTS xD
Step-by-step explanation:
PERIODDDDDDDDD
Answer:
Laptops, 82 is the largest number when you look at the totals.
Step-by-step explanation:
gender| electronic tablet | Laptop | Both | Neither | Total
----------|----------------------------|------------|---------|-------------|--------
girl | 13 | 51 | 8 | 17 | 89
boy | 12 | 31 | 5 | 13 | 61
total | 25 | 82 | 13 | 30 | 150
LMK If I have to explain but I basically just got the 150 students from the directions and went from there.
Given L(-4, 3) and M(-7, -2), what is the length of segment LM?
Answers
Answer:
[tex]d = \sqrt{34}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra II
Distance Formula: [tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Step-by-step explanation:
Step 1: Define
Point L (-4, 3)
Point M (-7, -2)
Step 2: Find distance d
Simply plug in the 2 coordinates into the distance formula to find distance d.
Substitute [DF]: [tex]d = \sqrt{(-7+4)^2+(-2-3)^2}[/tex]Add/Subtract: [tex]d = \sqrt{(-3)^2+(-5)^2}[/tex]Exponents: [tex]d = \sqrt{9+25}[/tex]Add: [tex]d = \sqrt{34}[/tex]What is the slope and y-intercept of the equation 6x + 2y = 14
I
Answers
y-intercept: (0,7)