Answer:
The equations have one solution at (5, -5).
Step-by-step explanation:
We are given a system of equations:
[tex]\displaystyle{\left \{ {{-2x+5y=-35} \atop {7x+2y=25}} \right.}[/tex]
This system of equations can be solved in three different ways:
Graphing the equations (method used)Substituting values into the equationsEliminating variables from the equationsGraphing the Equations
We need to solve each equation and place it in slope-intercept form first. Slope-intercept form is [tex]\text{y = mx + b}[/tex].
Equation 1 is [tex]-2x+5y = -35[/tex]. We need to isolate y.
[tex]\displaystyle{-2x + 5y = -35}\\\\5y = 2x - 35\\\\\frac{5y}{5} = \frac{2x - 35}{5}\\\\y = \frac{2}{5}x - 7[/tex]
Equation 1 is now [tex]y=\frac{2}{5}x-7[/tex].
Equation 2 also needs y to be isolated.
[tex]\displaystyle{7x+2y=25}\\\\2y=-7x+25\\\\\frac{2y}{2}=\frac{-7x+25}{2}\\\\y = -\frac{7}{2}x + \frac{25}{2}[/tex]
Equation 2 is now [tex]y=-\frac{7}{2}x+\frac{25}{2}[/tex].
Now, we can graph both of these using a data table and plotting points on the graph. If the two lines intersect at a point, this is a solution for the system of equations.
The table below has unsolved y-values - we need to insert the value of x and solve for y and input these values in the table.
[tex]\begin{array}{|c|c|} \cline{1-2} \textbf{x} & \textbf{y} \\ \cline{1-2} 0 & a \\ \cline{1-2} 1 & b \\ \cline{1-2} 2 & c \\ \cline{1-2} 3 & d \\ \cline{1-2} 4 & e \\ \cline{1-2} 5 & f \\ \cline{1-2} \end{array}[/tex]
[tex]\bullet \ \text{For x = 0,}[/tex]
[tex]\displaystyle{y = \frac{2}{5}(0) - 7}\\\\y = 0 - 7\\\\y = -7[/tex]
[tex]\bullet \ \text{For x = 1,}[/tex]
[tex]\displaystyle{y=\frac{2}{5}(1)-7}\\\\y=\frac{2}{5}-7\\\\y = -\frac{33}{5}[/tex]
[tex]\bullet \ \text{For x = 2,}[/tex]
[tex]\displaystyle{y=\frac{2}{5}(2)-7}\\\\y = \frac{4}{5}-7\\\\y = -\frac{31}{5}[/tex]
[tex]\bullet \ \text{For x = 3,}[/tex]
[tex]\displaystyle{y=\frac{2}{5}(3)-7}\\\\y= \frac{6}{5}-7\\\\y=-\frac{29}{5}[/tex]
[tex]\bullet \ \text{For x = 4,}[/tex]
[tex]\displaystyle{y=\frac{2}{5}(4)-7}\\\\y = \frac{8}{5}-7\\\\y=-\frac{27}{5}[/tex]
[tex]\bullet \ \text{For x = 5,}[/tex]
[tex]\displaystyle{y=\frac{2}{5}(5)-7}\\\\y=2-7\\\\y=-5[/tex]
Now, we can place these values in our table.
[tex]\begin{array}{|c|c|} \cline{1-2} \textbf{x} & \textbf{y} \\ \cline{1-2} 0 & -7 \\ \cline{1-2} 1 & -33/5 \\ \cline{1-2} 2 & -31/5 \\ \cline{1-2} 3 & -29/5 \\ \cline{1-2} 4 & -27/5 \\ \cline{1-2} 5 & -5 \\ \cline{1-2} \end{array}[/tex]
As we can see in our table, the rate of decrease is [tex]-\frac{2}{5}[/tex]. In case we need to determine more values, we can easily either replace x with a new value in the equation or just subtract [tex]-\frac{2}{5}[/tex] from the previous value.
For Equation 2, we need to use the same process. Equation 2 has been resolved to be [tex]y=-\frac{7}{2}x+\frac{25}{2}[/tex]. Therefore, we just use the same process as before to solve for the values.
[tex]\bullet \ \text{For x = 0,}[/tex]
[tex]\displaystyle{y=-\frac{7}{2}(0)+\frac{25}{2}}\\\\y = 0 + \frac{25}{2}\\\\y = \frac{25}{2}[/tex]
[tex]\bullet \ \text{For x = 1,}[/tex]
[tex]\displaystyle{y=-\frac{7}{2}(1)+\frac{25}{2}}\\\\y = -\frac{7}{2} + \frac{25}{2}\\\\y = 9[/tex]
[tex]\bullet \ \text{For x = 2,}[/tex]
[tex]\displaystyle{y=-\frac{7}{2}(2)+\frac{25}{2}}\\\\y = -7+\frac{25}{2}\\\\y = \frac{11}{2}[/tex]
[tex]\bullet \ \text{For x = 3,}[/tex]
[tex]\displaystyle{y=-\frac{7}{2}(3)+\frac{25}{2}}\\\\y = -\frac{21}{2}+\frac{25}{2}\\\\y = 2[/tex]
[tex]\bullet \ \text{For x = 4,}[/tex]
[tex]\displaystyle{y=-\frac{7}{2}(4)+\frac{25}{2}}\\\\y=-14+\frac{25}{2}\\\\y = -\frac{3}{2}[/tex]
[tex]\bullet \ \text{For x = 5,}[/tex]
[tex]\displaystyle{y=-\frac{7}{2}(5)+\frac{25}{2}}\\\\y = -\frac{35}{2}+\frac{25}{2}\\\\y = -5[/tex]
And now, we place these values into the table.
[tex]\begin{array}{|c|c|} \cline{1-2} \textbf{x} & \textbf{y} \\ \cline{1-2} 0 & 25/2 \\ \cline{1-2} 1 & 9 \\ \cline{1-2} 2 & 11/2 \\ \cline{1-2} 3 & 2 \\ \cline{1-2} 4 & -3/2 \\ \cline{1-2} 5 & -5 \\ \cline{1-2} \end{array}[/tex]
When we compare our two tables, we can see that we have one similarity - the points are the same at x = 5.
Equation 1 Equation 2
[tex]\begin{array}{|c|c|} \cline{1-2} \textbf{x} & \textbf{y} \\ \cline{1-2} 0 & -7 \\ \cline{1-2} 1 & -33/5 \\ \cline{1-2} 2 & -31/5 \\ \cline{1-2} 3 & -29/5 \\ \cline{1-2} 4 & -27/5 \\ \cline{1-2} 5 & -5 \\ \cline{1-2} \end{array}[/tex] [tex]\begin{array}{|c|c|} \cline{1-2} \textbf{x} & \textbf{y} \\ \cline{1-2} 0 & 25/2 \\ \cline{1-2} 1 & 9 \\ \cline{1-2} 2 & 11/2 \\ \cline{1-2} 3 & 2 \\ \cline{1-2} 4 & -3/2 \\ \cline{1-2} 5 & -5 \\ \cline{1-2} \end{array}[/tex]
Therefore, using this data, we have one solution at (5, -5).
Which type of cloud is mostly made up of ice crystals? A. Altostratus B. Cirrus C. Cumulus D. Stratus
I know not math But please help
Answer:
The answer is B
Step-by-step explanation:
look it up on google.
Answer:
The answer is B
Mostly its of B but some clouds are also made up of cmulus(option C)
the highest temperture ever recorded in continent was 45 celcius and lowest was-55 C what are corressponding tempurtures in degrees fahenheight? highest temperture was _ F
Answer:
113°F is the highest temperature and -67° is the lowest temperature.
Step-by-step explanation:
(45°C × 9/5) + 32 = 113°F
(-55°C × 9/5) + 32 = -67°F
Corey, Laura, Paige and Jacob, all turkeys, are wandering through the beautiful forest. They spot seven bees and five cockroaches, and in the trees, they see eight spiders. There are also four deer and four boars. Behind a bush, they can see a pair of antlers. How many legs are there in total?
A) 196
B) 148
C) 180
D) 176
Answer:
I think it would be A
Step-by-step explanation:
Answer: D
Step-by-step explanation:
Use calculator as putting numbers
8+42+30+64+28+4=176
The discount price of a hat is $18. What is the regular price? $
PLZ HURRY!!!!!
how to simplify -7/3
Answer: -7/23
Step-by-step explanation:
this is the answers pls brainlist me
Will mark as brainliest if correct!
Answer:
the answer is A
Step-by-step explanation:
48/50 x 100% = 96% of student wearing tennis shoes
100% - 96% = 4% students not wearing tennis shoes
Stephanie ate 12 of the 40 chips in a bag. What percentage of the chips did Stephanie eat?
Answer:
30%
Step-by-step explanation:
Answer:30%
Step-by-step explanation:
find questionsToday, everything at a store is on sale. The store offers a 20% discount.
a) The regular price of a T-shirt is $18. What is the discount price? $
3.6
b) If the regular price of an item is x dollars, what is the discount price in dollars? Write an expression. $
3.28
c) The discount price of a hat is $18. What is the regular price? $
Answer a is 14.40 the discount price is 14.40
Choose the solutions to the quadratic equation
x2 - 8x - 9 = 0.
-21
ex? - 8x = 9 to
-1
9
29
DONE
IL Directions: Encircle the letter of the correct answer.
1. When you add the decimal numbers 0.25, 0.033 and 1.78 the result is ?
A. 0.263
B. 0.0263
C. 2.063
D.2.2063
2. What is the difference when 43.67 is subtracted from 125.5?
A. 81.83
B. 81.17
C. 81.87
D. 81.57
3. Valerie, Gianna and Candice went to school clinic to find out their weights. Valerie's weight is 28.58
kilograms, Gianna's weight is 30.55 kilograms and Candice's weight is 25.48 kilograms. What is the total
weight of the three pupils?
A. 84.61 kilograms B. 84.16 kilograms C. 59.13 kilograms D. 54.06 kilograms
4. Keziah spent P24.85 for sandwich and P11.20 for juice. How much change did he receive if she gave the
vendor P100?
A. P 63.05
B. P 63.95
CP 73.05
D.P 73.95
5. At 6:00 in the morning, the temperature was 23.8 °C. At 12:00 noon, the temperature rose by 5.7°C. What
was the temperature at 12:00 noon?
A. 29.5 °C
B. 18.1 °C
C. 33.5 °C
D. 35.5 °C
Answer:
The answers are as follows:
1 . Option C: 2.063
2. Option A: 81.83
3. Option A: 84.61 kilograms
4. Option B: P63.95
5. Option A: 29.5°C
Step-by-step explanation:
Lets look at the questions one by one.
1. When you add the decimal numbers 0.25, 0.033 and 1.78 the result is ?
The question simply requires adding the three quantities.
The result is 2.063
Hence, Option C is correct.
2. What is the difference when 43.67 is subtracted from 125.5?
Subtracting 43.67 from 125.5, we get
125.5 - 43.67 = 81.83
Hence,
Option A is correct
3. Valerie, Gianna and Candice went to school clinic to find out their weights. Valerie's weight is 28.58 kilograms, Gianna's weight is 30.55 kilograms and Candice's weight is 25.48 kilograms. What is the total weight of the three pupils?
Adding all the weights
28.58+30.55+25.48 = 84.61
Hence, Option A is correct.
4. Keziah spent P24.85 for sandwich and P11.20 for juice. How much change did he receive if she gave the vendor P100?
For this first we have to calculate the total cost
24.85+11.20 = 36.05
Now to find the change he will get
Subtracting total expense from 100
100-36.05 = 63.95
Hence, Option B is the correct answer.
5. At 6:00 in the morning, the temperature was 23.8 °C. At 12:00 noon, the temperature rose by 5.7°C. What was the temperature at 12:00 noon?
The sum of temperature at 6:00 and the rise will tell us the temperature at 12:00
So,
23.8+5.7 = 29.5
Hence,
Option A is correct
The answers are as follows:
1 . Option C: 2.063
2. Option A: 81.83
3. Option A: 84.61 kilograms
4. Option B: P63.95
5. Option A: 29.5°C
Please help me!!!!!!!
Answer:
D) 5 miles to 1 hour.
Step-by-step explanation:
If each small box is 1 mile you can count the boxes to line up with the 1 hour graph. Hence, 5 boxes to 1 hour box equals 5 miles to the hour.
Answer:
D.)5 miles to 1 hour
I need help on this problem. Not good with word problems
Answer:
the one where your mouse is at
Step-by-step explanation:
first one
Answer:
2f + 10 = 20
Step-by-step explanation:
If he wants to give two candy bars to each friend, then each friend is worth 2f.
He wants to have 10 left over, so 10 + 2f must be equal to 20. In other words 2f = 20 - 10, which means 2f + 10 = 20.
I hope this makes sense.
Pls need answer fast
Answer:
B
Step-by-step explanation:
The answer is B
Pls with right answer
Answer:
$2,000
Step-by-step explanation:
They already raised
$5358
$2834
$4132
Total: $12,324
They need $14,000
-$12,324 =$1,676 is how much more they need
$2,000 more.....round 1676 to 2000
ed
A running track has two straight sides with length 130 m and two semicircle
ends with radius 40 m. It takes Kat 20 seconds to jog 80 m. How long would
it take her to jog around the track 42 times? Give your answer in hours and
minutes, to the nearest minute.
40 m
130 m
Answer:
1 hour 29 minutes and 29 seconds
Step-by-step explanation:
We need to find the circumference of the two semicircles of the track (which forms a full circle of radius 40m):
pi×40×2 = 80pi
The total length of the track to be travelled would be:
(80pi+130+130) × 42 = (80pi+260) ×42
= 21 476m (Rounded to 5 s.f.)
80m/20s
1s = 80÷20
= 4m
For every 1 second, Kat travels 4m.
Total Time taken:
21 476÷4 = 5369 seconds
= 1 hour 29 minutes and 29 seconds
simplify ...........x^4/3+1=3
Answer:
2 3/4 or 2.75
Step-by-step explanation:
How to find the domain and range of numbers
Answer:
m a g i c t h a t ' s h o w
(79,35+7,32) x 42,2-95,3
Answer:
3562.174
Step-by-step explanation:
happy thanksgiving
An arithmetic sequence has a first term of 8 and sixth term of 38. What is the 50th term of this sequence?
Answer:
302
Step-by-step explanation:
Tn=a+(n-1)d
38=8+[6-1)d
38-8=5d
30/5=d
6=d
Tn=a+(n-1)d
8+(50-1)6
=8+(49)6
302
PLZ HURRY IT'S URGENT!!!
The USC basketball team scored over 100 points in its last game. Some baskets were worth 2 points and others were worth 3 points. Which is a possible combination of the different baskets scored?
options:
20 two point shots
10 three point shots
25 two point shots
15 three point shots
15 two point shots
20 three point shots
25 two point shots
25 three point shots
The USC basketball team scored over 100 points in its last game. Some baskets, x, were worth 2 points and other baskets, y, were worth 3 points. Write an inequality to represent the score.
options:
2x+3y 100
2x+3y≤100
Answer:
25 two point shots
25 three point shots
2x+3y<100 is that the one missing the sign?
Step-by-step explanation:
25*2=50
25*3= 75
50+75= 125
2x+3y has to be over 100 points
so 2x+3y<100
11. MONEY You earn 8x + 7y dollars for working x hours at a restaurant and y hours at a bus
station. How much do you earn for working 12 hours at the restaurant and 16 hours at the bus
station?
Answer:
$208
Step-by-step explanation:
Total amount earned is given as:= 8x + 7y
The number of hours worked at a restaurant = x hours
The number of hours worked at a bus
station = y hours
How much do you earn for working 12 hours at the restaurant and 16 hours at the bus station?
= 8(12) + 7(16)
=96 + 112
= $208
what ratio is equavelent to 5:4
Answer:
the two equivalent ratios of 4 : 5 are 8 : 10 and 12 : 15.
Step-by-step explanation:
the two equivalent ratios of 4 : 5 are 8 : 10 and 12 : 15.
Write 7/25 as a decimal show your work
Answer:
0.28 is a decimal and 28/100 or 28% is the percentage for 7/25.
Step-by-step explanation:
i needhelp one more little crown plzz
25x4=100
7x4=28
28/100
0.28
28%
i barely remember how to do this
should b a decimal in between 7 and 00 i think idk
Gregg manages a small cleaning business. He has 18 employees. The cleaners get paid $14.00per hour. The cleaning supervisors get paid $19.00 per hour. His budget has set aside a payroll expense of $282.00 per hour if all of his employees are working. How many cleaners and how many supervisors does he employ?
Gregg employed
nothing cleaners and
nothing supervisors.
Answer:
Gregg employed 12 cleaners and 6 cleaning supervisors.
Step-by-step explanation:
Set up a system of equations where c is the number of cleaners and s is the number of cleaning supervisors:
c + s = 18
14c + 19s = 282
Solve by substitution by solving for c in the first equation:
c + s = 18
c = 18 - s
Then, plug in 18 - s as c into the second equation:
14c + 19s = 282
14(18 - s) + 19s = 282
Solve for s:
252 - 14s + 19s = 282
252 + 5s = 282
5s = 30
s = 6
Then, plug in 6 as s into the first equation:
c + s = 18
c + 6 = 18
c = 12
So, Gregg employed 12 cleaners and 6 cleaning supervisors.
A tree is 72 feet (ft) tall. How many inches (in) is this? First fill in the blank on the left side of the equation using one of the ratios. Then write your answer on the right side of the equation.
1 foot = 12 inches:
1/72 = 12/x
Cross multiply:
1x = 72 * 12
x = 864 inches
Display the graph of y=2+1/x
Answer:
Step-by-step explanation:
After living in his house for 15 years, a man sold it for Rs. 7,000 profit and purchased a new
one for Rs. 1,000 more than twice the selling price of his old one. If the new house cost 3 times
the original price of the old one, what did he pay for each?
please answer it asap. thanks in advance:)
Answer:
He paid 5,000 for the old home, which was the original price of it.
And he paid 15,000 for the new home.
Step-by-step explanation
Twice the selling price of his old one, the selling price was 7,000
7,000 * 2 = 14000.
14000 + 1000 = 15000.
15,000 is three times more than he originally paid for his old home.
n Purchased a new one for 1,000 more than twice the selling price.
2. Jim makes $12 an hour and worked 47 hours this week? (remember the overtime)
What is the volume of the following rectangular prism?
Answer:
we kinda need to see the prism
Answer:
what is the prisim
Step-by-step explanation:
What about this one I kinda don’t get it