Answer:
The solutions I found to this system of equations are (1, 0) and (⁸/₁₅, -7).
I keep second guessing and recalculating the second point there, so I'd suggest double-checking it by going through the work yourself. The first one checks out though.
Step-by-step explanation:
Let's solve this by substitution, where one equation is solved for one variable and substituted in to the other. As the latter equation is already solved for y, we can simply substitute it into the other:
given:
y = 3x² - 4x + 1
3x - 5y = 3
then:
3x - 5(3x² - 4x + 1) = 3
Which we can then simplify and solve:
3x - 15x² + 20x - 5 = 3
-3x + 15x² - 20x + 5 = -3
15x² - 23x = -8
Now we can find find the solution by completing the square:
15(15x² - 23x) = 15(-8)
225x² - 345x = -120
225x² - 345x + (23/2)² = -120 + (23/2)²
225x² - 345x + 529/4 = -120 + 529/4
(15x - 11.5)² = -120 + 132.25
(15x - 11.5)² = 12.25
15x - 11.5 = ± √12.25
15x - 11.5 = ± 3.5
15x = 11.5 ± 3.5
x = (11.5 ± 3.5) / 15
x = 15 / 15, and 8 / 15
x = 1, and 0.5333...
Now that we have x, we can solve for y.
given: 3x - 5y = 3
for x = 1:
3 - 5y = 3
y = 0
for x = ⁸/₁₅:
3(⁸/₁₅) - 5y = 3
5y = 3(⁸/₁₅) - 3
5y = ²⁴/₁₅ - ⁴⁵/₁₅
5y = -²¹/₁₅
y = -²¹/₃
y = -7
So the solutions to this system of equations are (1, 0) and (⁸/₁₅, -7).
If k=9 and x=5, find the value of the expression:
2k - X
Please hurry
Answer:
[tex]\huge\boxed{13}[/tex]
Step-by-step explanation:
= 2k - x
Given that k = 9, x = 5
= 2(9) - 5
= 18 - 5
= 13
[tex]\rule[225]{225}{2}[/tex]
Hope his helped!
~AH18078. Determine the area of a sector
with a central angle of 42° in a
circle with radius 3 inches.
NEED IT ASAP
Answer:
[tex]\boxed {\boxed {\sf A \approx 3.3 \ in^2}}[/tex]
Step-by-step explanation:
Since we are given the central angle in degrees, we should use the following formula for sector area.
[tex]A= \frac {\theta}{360}* \pi r^2[/tex]
The angle is 42 degrees and the radius is 3 inches. Therefore,
[tex]\theta= 42 \\r=3 \ in[/tex]
[tex]A=\frac {42}{360} * \pi (3 \ in)^2[/tex]
Solve the exponent.
(3 in)²= 3 in*3in = 9 in²[tex]A=\frac {42}{360} * \pi (9 \ in^2)[/tex]
Multiply all three numbers together.
[tex]A= 0.116666666667* 3.14159265359 * 9 \ in^2[/tex]
[tex]A=3.29867228627 \ in^2[/tex]
Let's round to the tenth place. The 9 in the hundredth place tells us to round the 2 up to a 3.
[tex]A \approx 3.3 \ in^2[/tex]
The area of the sector is approximately 3.3 square inches.
HELP ME PLS ITS URGENT .. !❗❗❗❗❗❗❗❗❗❗❗❗❗
The commuting distances, in miles, of 10 employees were used to make the box plot shown above. Which of the sets of distances below matches the given box plot?
A.
Commuting Distances: 10, 15, 15, 20, 20, 20, 30, 30, 45, 45
B.
Commuting Distances: 10, 15, 15, 20, 20, 30, 30, 30, 45, 45
C.
Commuting Distances: 10, 15, 20, 20, 20, 20, 30, 30, 45, 45
D.
Commuting Distances: 10, 15, 15, 20, 20, 20, 30, 45, 45, 45
Answer:
A the answer is A ^w^ hope this helps
If John gets paid $45.00 an hour and works 10 hours, how much does he earn?
HELP PLS MIGHT GIVE BRAINLIST BUT ONLY IF 2 PEOPLE ANSWER!
Answer:
area of rectangle =72in
area of triangle = 3in
square in of plastic in ruler =69in
I need help finding the area and perimeter to this question. Pls help!! Thank you!
Answer:
Perimeter: 50.27
Area: 201.06
Step-by-step explanation:
The perimeter (circumference) is radius times pi times 2
This would be 8 times pi tomes 2 and when you do that you get 50.27
For the area you would do radius squared times pi
This would be 8 squared times pi which is 201.06
Hope this is helpful
- Please mark brainliest :)
Asha is tiling the lobby of the school with one-foot square tiles. She has 6 bags
of tiles with 50 tiles in each. The lobby is a 30-foot by 8-foot rectangle. How
many tiles will Asha have left over after she tiles the lobby?
Answer:
60 tiles left over
Step-by-step explanation:
the lobby needs 30 x 8 = 240 tiles.
she has 6 x 50 = 300 tiles
300 - 240 = 60 left over
Suppose that 20% of voters are in favor of a certain legislation. A large number n of voters are polled and a relative frequency estimate fA(n) for the above proportion is estimated. How many voters should be polled so that the probability is at least 0.95 that fA(n) differs from 0.20 by less than 0.02?
Answer:
8000 voters
Step-by-step explanation:
E is the difference between probability that is real and those which are estimated
Sd² = p(1-p)
When solve this, using the formula in the attachment,
0.95 = 1-0.2(0.2)²/n(0.02)
0.95 = 1 - 0.16/n(0.02)²
1-0.95 = 0.16/n(0.02)²
0.05 = 0.16/0.0004n
We cross multiply here
0.05 x 0.0004n = 0.16
0.00002n = 0.16
Divide through by 0.00002 to get n
n = 8000
This is the number of voters that should be polled
A particular fruit's weights are normally distributed, with a mean of 372 grams and a standard deviation of 26 grams. If you pick 36 fruit at random, what is the probability that their mean weight will be between 365 grams and 380 grams
Answer: 90.93%
Step-by-step explanation:
M= 372
s= 26
n=36
P(365<x<380)
1. Find Z ----> 365-372 [tex]\sqrt{36}[/tex] = -1.6 Next Z----> 380 - 372 [tex]\sqrt{36}[/tex]= 1.8
26 26
2. plug into calculator to find probablity: normalcdf(-1.6 , 1.8 ) = .90927 or 90.93% that the prob is between 365 and 380
1, 3, 5, 7, 9, 9, 11, 11, 13, 14 }
Which box plot represents the data set?
What is the midpoint of the segment below? (-12, -3) (3, -8)
What is the slope of the line below?
(1-2)
(
4-2)
A. negative
B. undefined
C. positive
D. Zero
Answer: D. Zero
Step-by-step explanation:
It’s a flat line. Flat horizontal lines are ALWAYS zero
Please help!!!!!!!!!!!!!!!!!!!!!!
What is the COEFFICIENT in the expression s + 16?
Answer:
I think its 16
Step-by-step explanation:
SOMEONE HELP ME PLEASE!!!!?
Answer:
139
Step-by-step explanation:
supplementary angles add up to equal 180
so to find the measure of angle ABC we subtract the given angle from 180
180-41=139
so we can conclude that angle ABC= 139
Step-by-step explanation:
< ABC and < CBD are supplementary angles.
< CBD = 41°
< ABC + < CBD = 180° ( Being supplementary angles)
< ABC + 41° = 180°
< ABC = 180° - 41°
< ABC = 139°
Hope it will help :)❤
Which expressions are equivalent to 5x-15? Select three options.
5(X+15)
5(x-3)
4x+3y-15-3y+X
-7y-6x-8y + x
0-20-3x+5+ 8x
Answer:
The number 2 for sure but i dont know the rest
Step-by-step explanation:
I GIVE BRAINLIEST FOR EXPLANATION AND CORRECT ANSWER EXTRA POINTS
Mrs Sogiba is catering for her son's birthday party. She has invited some of
her son's friends to theparty. The number of friends is a compositemultiple of her
son's age on his birthday. She has baked 48 cup cakes and each childwill receive
exactly the same number of cupcakes. Use your knowledge of factors and multiples
to find out how old her son will be on this birthday.
Answer:
48 cupcakes divided by the boys age equals amout of cupcakes per person.
Step-by-step explanation:
Pls help if not that’s fine just pls stop with the links
Answer:
C. 73 and 73
Step-by-step explanation:
An isosceles triangle has two angles that are the same, that narrows it down to C and D. The question states that there is only one 34° angle so it has to be C.
Answer:
C. 73° and 73°
Step-by-step explanation:
We know that the sum of interior angles in a triangle is equal to 180° and
Isosceles triangles has two angles with same measurement
it stated in the question that exactly one angle has measure of 34°
So the other two angles must be equal for the triangle to be isosceles
180 - 34 = 146 and this divided by 2
73° and 73° is the answer.
Round 7.54 please I need help
Write an equation of a line that has a slope of 3/4and passes through point (8,7)
The probability distribution for a
random variable x is given in the table.
-10
-5
0
5
10
15
20
Probability
.20
.15
.05
.1
.25
.1
.15
Find the probability that x = -10
Answer:
.20
Step-by-step explanation:
According to what are written in the table the probability for x=-10 is .20
The probability distribution at x= -10 is 0.20.
What is Probability distribution?A mathematical function called a probability distribution explains the likelihood of many alternative values for a variable. Graphs or probability tables are frequently used to represent probability distributions.
Given:
We have table as,
x -10 -5 0 5 10 15 20
Probability 0.20 0.15 0.05 0.10 0.25 0.10 0.15
So , we have to find probability that x = -10 then by looking at table the corresponding value to x= -10 the probability is 0.20.
Learn more about Probability distribution here:
https://brainly.com/question/14210034
#SPJ2
One interior angle of a triangle is 60⁰. The other angle measures are x⁰ and y⁰. Which of the following could be the values of x and y? Select all that apply. A. x = 50, y = 90 B. x = 45, y = 45 C. x = 40, y = 80 D. x = 100, y = 20 E. x = 60, y = 60
Answer:
B,C,D
Step-by-step explanation:
WILL MARK B!
Please I need help I have a quiz
Answer:
a) 2x² - x + 3 = x(2x + 1) - 2x
<=> 2x² - x + 3 = 2x² + x - 2x
<=> 3 - x = - x
<=> 3 = 0
=> no solution
b) x/2 - x/3 - x/4 = 1/12
[tex] \frac{6x}{12} - \frac{4x}{12} - \frac{3x}{12} = \frac{1}{12} \\ \\ \frac{ - x}{12} = \frac{1}{12} \\ \\ = > - x = 1 \\ \\ \\ < = > x = 1[/tex]
=> the euqation has the solution x = 1
c) |x - 5| = 2|x|
=> x - 5 = 2x
or x - 5 = -2x
<=> x = -5
or 3x = 5
<=> x = -5
x = -5or x = 5/3
d) defined conditions: 2 - x 》 0
<=> x 《 2
we have:
[tex] \sqrt{x + 4} = 2 - x \\ < = > x + 4 = (2 - x) {}^{2} \\ < = > x + 4 = {x}^{2} - 4x + 4 \\ < = > {x}^{2} - 5x = 0 \\ < = > x(x - 5) = 0 \\ [/tex]
<=> x = 0 (because x 《 2)
e)
[tex] \sqrt{5} = \frac{1}{25 {}^{x} } \\ = > 5 = \frac{1}{25 {}^{2x} } \\ < = > 5.25 {}^{2x} = 1 \\ < = > 5.5 {}^{4x} = 1 \\ < = > 5 {}^{4x + 1} = 1 \\ = > 4x + 1 = 0[/tex]
<=> x = -1/4
Answer:
[tex]a) [x: - \infty < x < \infty ][/tex]
[tex]b)[x: - 1][/tex]
[tex]c) [x:- \frac{5}{3} ][/tex]
[tex]d) [x: 3, 0][/tex]
[tex]e) [x: - \frac{1}{4} ][/tex]
Which equation represents "The sum of a number n and 8, subtracted from 20, is 16."
A. n + 8-20 = 16
B. 8n - 20 = 16
C. 20 - (n + 8) = 16
D. 20- 8n = 16
Convince yourself that there are 3 similar triangles in the diagram. Choose the
similarity statement that represents the relationship among the 3 triangles.
Please only answer if your sure
Answer:
second option.
Step-by-step explanation:
Account (A) is a saving account , the interest earned after 1 year is $12 .If the interest rate is 3.2% for account (A). How much is the principle for account (A) ?3
Answer:
The principal for the account is $375.
Step-by-step explanation:
This is a simple interest problem.
The simple interest formula is given by:
[tex]E = P*I*t[/tex]
In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.
The interest earned after 1 year is $12 .If the interest rate is 3.2% for account (A).
This means, respectively, that [tex]t = 1, E = 12, I = 0.032[/tex]
We want to find P.
[tex]E = P*I*t[/tex]
[tex]12 = P*0.032*1[/tex]
[tex]P = \frac{12}{0.032}[/tex]
[tex]P = 375[/tex]
The principal for the account is $375.
Please Help!!!!! Ill give thanks and rate best!
Answer:
1/216
1/8 *1/3³ ( cross multiply ) = 1/216
Did you only need the answer for the one on the top right?? Or all of them because If you need all of them I can do that too I am just assuming you just needed that one because it was selected.
First one to answer gets BRAINLIEST no cap look at the picture.
Answer:460
Step-by-step explanation:
Calculate the SQRT485 Express answer to nearest hundredth.
*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆
Answer: 22.02
Explanation:
I hope this helped!
<!> Brainliest is appreciated! <!>
- Zack Slocum
*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆