Answer:
[4, -1]
Step-by-step explanation:
Using the Elimination Method:
3x + y = 11
5x - y = 21
__________
8x = 32
__ ___
8 8
x = 4 [Plug this back into both equations to get the y-coordinate of -1]; -1 = y
The y's are already additive inverses [result in 0], canceling each other out.
I am joyous to assist you anytime.
A town has accumulated 3 inches of snow, and the snow depth is increasing by 6 inches every hour. A nearby town has accumulated 6 inches, and the depth is increasing by 3 inches every hour. In about how many hours will the snowfall of the towns be equal?
Answer:
1 hour
Step-by-step explanation:
set town one equation to 3 + 6x and town two equation to 6+3x
set these two equations equal to each other and solve for x
3 + 6x = 6 + 3x
3x = 3
x = 1
1 hour
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In the lab, Tom has two solutions that contain alcohol and is mixing them with each other. He uses 500 milliliters less of Solution A than Solution B. Solution A is
14% alcohol and Solution B is 20% alcohol. How many milliliters of Solution B does he use, if the resulting mixture has 440 milliliters of pure alcohol?
Answer:
22 milliliters
step by step
solution B x 22
20 x 22 = 440 milliliters
Final answer:
Tom uses 1,500 mL of Solution B. By setting up equations using the volume percentage of alcohol in each solution and solving for 'x', the volume of Solution A, we find the required volume for Solution B.
Explanation:
To solve for the volume of Solution B that Tom uses, we first establish the equations based on the information given. Let's denote the volume of Solution A as x mL. Thus, the volume of Solution B will be x + 500 mL. The total amount of pure alcohol in the final mixture is 440 mL.
Using the volume percentage for alcohol content in each solution, we can set up two equations to find x. The first equation is based on Solution A (14% alcohol) and the second on Solution B (20% alcohol):
The total volume of alcohol combined from both solutions is equal to 440 mL, which gives us the equation:
0.14x + 0.20(x + 500) = 440
Solving for x we get:
Since x is the volume of Solution A and we know that Solution B is 500 mL more than Solution A, we calculate the volume of Solution B as follows:
x + 500 = 1,000 + 500 = 1,500 mL
Therefore, Tom uses 1,500 mL of Solution B.
3(6+5y)=2(-5+4y) help huhu
Answer:
-4 = y
Step-by-step explanation:
3(6+5y)=2(-5+4y)
18 + 15y = -10 + 8y
+10 +10
28 + 15y = 8y
- 15y -15y
28 = - 7y
28/-7 = -4
-7y/-7 = y
Answer:
y = -4
Step-by-step explanation:
distribute both 3 and 2 through the parenthesis, move the variable to the left side and change its sign, move constant to the right side and change its sign, collect like terms, calculate the difference, divide both sides of the equation by 7, and your answer would be -4
200 principal, 4% compounded annually for 5 years
[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$200\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &5 \end{cases} \\\\\\ A=200\left(1+\frac{0.04}{1}\right)^{1\cdot 5}\implies A=200(1.04)^5\implies A=243.33058048[/tex]
2x+10 + 4x+1 pleasee help!!
2x+10 + 4x+1
2x+4x+10+1 ( combine like terms)
2x+4x=6x
10+1=11
Answer: 6x+11
Answer:
6x+11
Step-by-step explanation:
Collect the like terms and add them up.
2x+4x and 10+1
=6x+11
Have a nice day!!!!!!! :-)
KA
Solve −2x2 − 16x − 44 = 0.
The solution to the quadratic equation -2x² - 16x - 44 = 0 are [tex]x = -4 -4\sqrt{6}i \ and \ x = -4 +4\sqrt{6}i[/tex]
Given the quadratic equation in the question:
-2x² - 16x - 44 = 0
To solve the quadratic equation -2x² - 16x - 44 = 0, we use the quadratic formula:
[tex]x = \frac{-b\±\sqrt{b^2 - 4ac} }{2a}[/tex]
From the equation:
a = -2, b = 16, c = -44
Plug these values into the above:
[tex]x = \frac{-b\±\sqrt{b^2 - 4ac} }{2a} \\\\x = \frac{-(-16)\±\sqrt{(-16)^2 - 4(-2)(-44)} }{2(-2)} \\\\x = \frac{16\±\sqrt{256 - 352} }{-4} \\\\x = \frac{16\±\sqrt{-96} }{-4} \\\\x = \frac{16\±4\sqrt{6}i }{-4} \\\\x = -4 \±4\sqrt{6}i\\\\x = -4 -4\sqrt{6}i \ or \ x = -4 +4\sqrt{6}i[/tex]
Therefore, the values of x are [tex]x = -4 -4\sqrt{6}i \ and \ x = -4 +4\sqrt{6}i[/tex]
Terry,Sasha, and Harry each chose a number.Terrys number is 10x as much as Sasha’s. Sasha’s number is 0.4. What number did each person choose?
i need help whoever got this answer right gets brainlist
Using the appropriate constant of proportionality, provide the value in the table that makes the quantities proportional to one another. Answer format: 8/9 *
Answer:
3
Step-by-step explanation:
If you look closely every X is changing by 3 so 3·y=x
Answer:
The value in the table that makes the quantities proportional to one another is y = 3
Step-by-step explanation:
Two quantities x and y are proportional one to another if they can be expressed as
y = kx
where k is the constant of proportionality. We can find k using an specific point. Take the first one
y = kx
k= y/x with (3.1 )
k= 1/3
So
y =1/3x for this case
If the two quantities are proportional, this rule must be true for any point (x,y) . Lets prove it
Point 2 (6,2)
2 =1/3*(6)
2= 2 True
Point 4 (12,4)
4 =1/3*(12)
4= 4 True
So to accomplish the rule in point 3, and finally in all table we must have that
y =1/3x is true for Point 3 (9,y) Then
y = 1/3 (9) = 9/3 = 3
y= 3
Y must be 3
Mr. Smith donated $378 to 2 charities. Charity A received 5 times as much as Charity B. How much did Charity B received from Mr Smith?
Answer:
$63
Step-by-step explanation:
let x represent Charity B then Charity A = 5x
Sum the two and equate to 378, that is
x + 5x = 378
6x = 378 ( divide both sides by 6 )
x = 63
Thus Charity B received $63
Jim believes he will receive 50 pieces of candy for Halloween. If Jim actually
received 75 pieces of candy, what is Jim's percent error? Round your answer to
the nearest tenth of a percent.
Find the slope of the line passing through each of the following pair of points. (4, 0), (-2, 8)
Answer:
-4
-----
3
Step-by-step
x1,y1
(4,0),
x2,y2
(-2,8)
y2-y1/x2-x2
8-0/(-2)-4=8/-6= -4
-----
3
If BD and AC are perpendicular , DBE = (2x - 1), and CBE = (5x - 42), find the value of x.
This equation graphed
I answered this question already.
9x+11y=-14
6x-5y=-34
Resolver por regla de cramer
Answer:
x=-4 y=2
Step-by-step explanation:
y=-14-9x÷9
6x-5 (14-9x÷9)=-34
6x-(70+45x÷9)=-34
Take LCM
and then do it
Use Order of Operations to simplify
8 + 7(4 exoponet 2 -3)
a salesman receives a salary rs 1000 per month and 10%commission on sales in excess of rs 5000.what is the amount of sales if he earns rs.2000. in a particular month
Answer:
Amount of sales = rs 10,000.
Step-by-step explanation:
He earns 2000 - 1000 = rs 1000 from sales.
This equals 10% ( = 0.10 as a fraction) of his sales so his sales must have been 1000 / 0.10
= rs 10,000.
Please answer this correctly
Answer:
Emmett
Step-by-step explanation:
Kira is younger than Nila
So Nila>Kira
Nila is older than Mike and Mike is older than Kira
Nila>Mike>Kira
Nila is younger than Emmett
Emmett>Nila>Mike>Kira
Answer:
Emmett is older
Nila is older than Kira.
Nila is older than Mike.
Nila is younger than Emmett.
Therefore, Emmett is older than Nila.
And if Nila is older than Kira, and Emmett is older than Kira, Emmett is oldest.
what is the answer to number 16
Answer:
b ≈ 13.80 in
Step-by-step explanation:
Since the triangle is right use the tangent ratio to solve for b
tan17.71° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AC}{BC}[/tex] = [tex]\frac{AC}{43.21}[/tex]
Multiply both sides by 43.21
43.21 × tan17.71° = AC, hence
AC = b ≈ 13.80 ( to 2 dec. places )
Round 17139.554963 to the nearest whole number.
menurut whole number.
Answer:
17140
Step-by-step explanation:
The number in the tenths place is 5 or higher so you need to round it up to 17140.
Answer:
17140
Step-by-step explanation:
If the number in the tenths place is 5 or more, round the number up.
As Laura's mother rushed off to work, she quickly gave Laura some instruct
me, try my cell ... if I don't answer it means I'm in a meeting, but don
neaps I'm in a meeting, but don't worry, the meeting
won't last more than 30 minutes and I'll call you back when it's over." Later than
needed her mother, but her mother was stuck in a meeting and couldn't answer ih
Laura concludes that she will have to wait no more than 30 minutes before she gete
from her mother. What law of logic did Laura use to draw this conclusion?
Answer:
I don't actually know the answer to this question please
Your watch Gains 0.5 minutes in 6hours. How much will it can in three days.
Answer:
6 Minutes
Step-by-step explanation:
3 days is 72 hours
72/6 = 12
12 * 0.5 = 6
write 0.3232323232... as a fraction
write 2.555555... as a mixed number
Answer: I believe first one is 32/99 and the second one is 2 whole numbers and 5/9
Step-by-step explanation:
The number 0.323232... can be written as a fraction 32/99, while the number 2.55555... can be written as the mixed number 2 5/9.
To write 0.323232... as a fraction, you can use the method for converting repeating decimals to fractions. Let's say X = 0.323232... Then 100X = 32.323232..., and subtracting the first equation from the second gives 99X = 32, or X = 32/99.
For the number 2.55555..., we will have our whole number as '2' and we need to convert .55555... into a fraction. Let's use the same method: if Y = .55555..., then 10Y = 5.55555.... Subtracting these gives 9Y = 5, which simplifies to Y = 5/9. So, 2.55555... as a mixed number is 2 5/9.
Learn more about Repeating Decimals here:
https://brainly.com/question/31325113
#SPJ6
Find the slope of the line with the equation 12x - 8y + 7 = 9.
-3/2
312
2/3
Final answer:
The slope of the line represented by the equation 12x - 8y + 7 = 9 is 3/2. To find this, the equation was rearranged into slope-intercept form, revealing the slope as the coefficient of x.
Explanation:
To find the slope of the line with the given equation 12x - 8y + 7 = 9, you first need to rearrange the equation into slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.
First, subtract 12x from both sides of the equation to isolate terms with y on one side:
-8y = -12x + 2
Next, divide each term by -8 to solve for y:
y = (12/8)x - 2/8
Simplify the fractions:
y = (3/2)x - 1/4
Now the equation is in slope-intercept form, and you can see that the slope m is 3/2 or 1.5. Therefore, the slope of the line is 3/2.
Mrs. Fronkos class for evry 6 boys there are 8 girls. Write the ratio of boys to girls in simplest form
Final answer:
The ratio of boys to girls in Mrs. Fronko's class in simplest form is 3:4, obtained by dividing both sides of the given ratio, 6:8, by the greatest common divisor, which is 2.
Explanation:
To find the ratio of boys to girls in Mrs. Fronko's class in its simplest form, we will start with the ratio given, which is 6 boys for every 8 girls. This can be written as 6:8. To simplify ratios, we divide both sides of the ratio by the greatest common divisor. In this case, the greatest common divisor of 6 and 8 is 2. Therefore, we divide both numbers by 2 to find the simplest form of the ratio.
6 ÷ 2 = 3 and 8 ÷ 2 = 4.
After dividing both numbers by 2, the ratio becomes 3:4. This indicates that for every 3 boys, there are 4 girls in Mrs. Fronko's class, and this is the simplest form of the ratio.
The equation 3w + 4j = 39 is used to determine the number of water bottles w and the number of juice bottles j that can be bought for $39. If you purchase 6 bottles of juice, how many bottles of water can you buy?
Juice bottles are J, replace j with 6 in the equation and solve for w:
3w + 4(6) = 39
3w + 24 =39
Subtract 24 from both sides:
3w = 15
Divide both sides by 3:
w = 15/3
w = 5
You can buy 5 water bottles.
Answer:
5
Step-by-step explanation:
The number of water bottles [tex]= w[/tex]
The number of juice bottles [tex]= j[/tex]
We have, [tex]3w + 4j = 39[/tex]
When we purchase 6 bottles of juice, [tex]j = 6[/tex]
So,
[tex]3w + 4j = 39[/tex]
[tex]3w + 4 \times 6 = 39[/tex]
[tex]3w + 24 = 39[/tex]
[tex]3w = 39 - 24[/tex]
[tex]3w = 15[/tex]
[tex]w = \frac{15}{3}[/tex]
[tex]w = 5[/tex]
Therefore, we can buy 5 bottles of water.
0.03 x 5=
How is this solved?
Answer: 0.15
Step-by-step explanation:
Multiply 0.03 by 5.
Answer:0.15
Step-by-step explanation:
First multiply 3 and 5. Then you will get 15. In the question it says 0.03 and its 2 digit from decimal so in 15 you will put a decimal 2 digit from the left and you will get 0.15
Y is inversely proportional to x. If y= 400 when x =2 find y when x= 200
Answer: 4
Step-by-step explanation:
Inversely proportional means xy = k, where k is the constant of proportionality
First, find k when x = 2 and y = 400 ----> 2(400) = k --> 800 = k
Then, find y when x = 200 (knowing that k = 800)
200y = 800
y = 4
factor x squared-6x+3x-18 by grouping
Answer:
(x - 6)(x + 3)
Step-by-step explanation:
Given
x² - 6x + 3x - 18 ( factor the first/second and third/fourth terms )
= x(x - 6) + 3(x - 6) ← factor out (x - 6) from each term
= (x - 6)(x + 3)
Ms. Thornton's class visited five freshwater lakes to learn more about the crocodiles and alligators living in them. The class counted the number of species in each lake as shown in the table.
Lake Crocodiles Alligators
A 4 5
B 21 35
C 3 9
D 6 16
E 24 30
The relationship between the number of crocodiles and the number of alligators is not proportional across all lakes. Only two of the lakes have crocodiles and alligators in the same proportion. Which two lakes are they?
A.
lake A and lake B
B.
lake B and lake C
C.
lake A and lake E
D.
lake C and lake D
Answer:
It's C. If you divide them you get 1.25 for both of them and its proportional
Please I need help?!
Answer:
1a. 460313
1b. 405040
1c. 100000 more
2a. 176960
2b. 12097
2c. 839000
2d. 452210
Step-by-step explanation:
2d. 442210
+ 10000
________
452210
2c. 849000
- 10000
________
839000
2b. 13097
- 1000
_______
12097
2a. 100000
+ 76960
________
176960
1c.
[tex] - 347077 + 447077 = 100000[/tex]
1b.
[tex]300000 + 90000 + 5000 + 40 = 395040 \\ \\ 10000 + 395040 = 405040[/tex]
1a.
[tex] -100000 + 560313 = 460313[/tex]
I am joyous to assist you anytime.