Answer:
1-ELIMINATION.
2- SUBSTITUTION.
3- GRAPHING.
Step-by-step explanation:
Methods:
1- Elimination:
- Line up the variables.
- To cancel out one of the variables, you need to make that the coefficient of that variable opposite. For example:
[tex]\left \{ {{3x+y=1} \atop {-3x+4y=3}} \right.[/tex]
As you can see, the coefficient of x in the first eqation is 3 and -3 in the second option.
- Add the equations.
- Solve for the the variable that is still present.
- Substitute the value of the variable obtained into one of the original equations.
- Solve for the other variable.
2- Substitution:
- Solve for one of the variables from any of the equations of the system.
- Substitute into the other equation for that variable.
- Solve for the other varible to find its value.
- Substitute the value obtained into any of the original equations and solve for the other variable.
3- Graphing:
- Rewrite the equations as equtions of the line slope intercept form ([tex]y=mx+b[/tex], where m is the slope nd b the y-intercept).
- Graph each line.
- Then:
If there ir an intersection point of the two lines, then that point is the solution to the system
If the lines are the same, there are infinitely many solutions.
If the lines are parallel, then there is no solution
Eva spent $11.61 downloading songs, each song cost $1.29. Four students wrote and solved equations to find s, the number of songs that she downloaded. Which student wrote and solved the equation correctly?
A. Seba’s work
1.29s=$11.61
S=10
B. Ari’s work
$1.29s=$11.61
S=9
C.Erick’s work
S/$1.29=11.61
S=14.98
D. Daniel’s work
S/$1.29=$11.61
S=9
Answer:
Option B.
Step-by-step explanation:
Let
s-----> the number of songs that Eva downloaded
we know that
The linear equation that represent the situation is
[tex]1.29s=11.61[/tex]
Solve for s
Divide by 1.29 both sides
[tex]s=11.61/1.29[/tex]
[tex]s=9\ songs[/tex]
therefore
Ari's work is correct
Answer:
answer b
Step-by-step explanation:
i took test
please help! 2 answer-choice math questions I give Brainliest, thanks, rattings, ect
its 50 POINTS
Question 2
What is the best approximation of the solution to the equations that these two lines represent?
(1, 1)
(1, 1.5)
(1.5, 1)
(0, 1)
Question 4
6x + 4y = 2
3x + 2y = 1
not enough information
coincident
inconsistent
consistent and independent
Answer:
2) (1,1.5)
4) Not enough information
Step-by-step explanation:
2) If you look along at the intersection point of the two lines it's (1,1.5).
4) Since only one equation is graphed, we can't tell anything.
write the expression in complete factored form. 3(a-7)-x(a-7) = (insert answer here)
Answer:
(a - 7)(3 - x)
Step-by-step explanation:
Given
3(a - 7) - x(a - 7) ← factor out (a - 7) from both terms
= (a - 7)(3 - x)
What is 16 cups converted to fluid ounces
Answer:
128 fluid ounces
Step-by-step explanation:
There are 8 fluid ounces in 1 cup.
There's 1 cup in 8 fluid ounces
16 cups x 8 = 128 fluid ounces
hey plz help me out i need all workings
a)x^2-4xy-12y^2 b)x^2+8x+12
Answer:
see explanation
Step-by-step explanation:
(a)
Consider the factors of the coefficient of the y² term ( - 12) which sum to give the coefficient of the xy- term (- 4)
The factors are - 6 and + 2
since - 6 × 2 = - 12 and - 6 + 2 = - 4, hence
x² - 4xy - 12y² = (x - 6y)(x + 2y)
----------------------------------------------------
(b)
Consider the factors of + 12 which sum to give + 8
The factors are + 2 and + 6, hence
x² + 8x + 12 = (x + 2)(x + 6)
selma is now 3 times older than joyce . four years ago , selma was 4 times as old as joyce was then . find their present ages
Present age of Selma = s
Present age of Joyce = j
Selma is now 3 times as old as joyce
s=3j........(1)
Four years ago,
s-4=j-4
then
Selma was 4 times as old as joyce
s-4=4(j-4)
s-4=4j-16
s=4j-16+4
s=4j-12.............(2)
Put the value of s in (2) from (1)
3j=4j-12
3j-4j=-12
-j=-12
Multiply by -1 both sides
j=12
Put the value of j in (1)
s=3j
s=3(12)
s=36
Present age of Selma = s = 36 years old
Present age of Joyce = j = 12 years old
(I RAISED THE POINTS AND THIS IS MULTIPLE CHOICE PLEASE TRY TO EXPLAIN WHY YOU GOT THAT ANSWER THANKS~~)
what is the 11th term in the sequence: an= -6n+13?
a)53
b) -79
c) -53
d)79
What is the sum of an infinite geometric series if a1 = 5 and r = 1⁄3?
A. 25⁄2
B. 30
C. 15⁄2
D. 15
Answer:
C
Step-by-step explanation:
The sum to infinity of a geometric series is
[tex]\frac{a_{1} }{1-r}[/tex] ( - 1 < r < 1 ) ← substitute values
S( ∞ ) = [tex]\frac{5}{1-\frac{1}{3} }[/tex] = [tex]\frac{5}{\frac{2}{3} }[/tex] = [tex]\frac{15}{2}[/tex]
The sum of the infinite geometric series is [tex]\frac{15}{2}[/tex]
What is infinite geometric series ?
The sum of all the terms of a geometric sequence is called infinite geometric series.
If a, ar, a[tex]r^{2}[/tex], ...., a[tex]r^{n-1}[/tex], .... is a geometric series, then a+ar+a[tex]r^{2}[/tex]+ ....+a[tex]r^{n-1}[/tex]+.... is the corresponding infinite geometric series.
where a is the 1st term & r is the common ratio between consecutive terms of the series.
Sum of infinite geometric series = [tex]\frac{a}{1-r}[/tex] ; |r|<1
What is the required sum of series ?Given, 1st term ([tex]a_{1}[/tex]) of the infinite geometric series = 5
Common ratio (r) = 1/3
∴ Sum of infinite geometric series = [tex]\frac{a_{1} }{1-r}[/tex]
= [tex]\frac{5}{1-\frac{1}{3} }[/tex]
= [tex]\frac{5}{\frac{2}{3} }[/tex]
= [tex]\frac{15}{2}[/tex]
Learn more about geometric series here :
https://brainly.com/question/24643676
#SPJ2
If Catherine traveled 1,600 miles in 8 hours on her plane flight to her vacation destination, at what rate was the plane traveling
Answer:
c.200
Step-by-step explanation:
can someone please help me with #9? (25 points)
Answer:
Step-by-step explanation:
General Solution
Left hand side
tan(30) + 1 / tan(30
tan^2(30) + 1
============
tan 30
but tan^2(30) + 1 = sec^2(30)
sec^2(theta) / tan(30) Let theta = 30o. This will work for any angle between 0 and 90
[tex]\dfrac{sec^2(theta)}{tan(theta)} = \dfrac{sec^2(theta)}{\dfrac{sin(theta)}{cos(theta)}} = \dfrac{1}{\dfrac{cos^2(theta)*sin(theta)}{cos(theta)}}[/tex]
Cancel out cos(theta) and one of cos^2(theta)
leaving your with
[tex]\dfrac{1}{sin(theta)*cos(theta)}[/tex]
which is exactly what the right hand side is.
This is the way this problem should be done. If you want to show what happens with 30o then
Thirty degree angle
tan(30) = 0.5774
Left hand side
0.5774 + 1/(0.5774) = 2.3093
Right hand side
1/(sin(30)*cos(30))
1/(0.5 * 0.8660)
1/(0.4330
2.3094
Which is about as close as you will get when you round.
Determine whether the following set of numbers is part of an arithmetic or geometric sequence. In the space provided, type arithmetic or geometric as your answer. -2, 4, -8, 16, ...
Answer:
Step-by-step explanation:
It's geometric.
You are starting with -2 and multiplying each successive term by - 2
r = - 2
a1 = -2
tn = ar^(n - 1)
So to try it out, let n be the 4th term
t4 = -2 * (-2)^(4 - 1)
t4 = - 2 * (-2)^3
t4 = - 2 * -8
t4 = 16 just as the series indicated.
number 6 please
F.$16.10
H.$15.25
G.$15.50
J.$14.50
The Answer Is J.14.50
Answer: $14.50
Step-by-step explanation:
Multiply $5.95 by 2.
Multiply $0.65 by 4.
Add both of the answers to the multiplying problems
Your final answer... I hope I was able to help!
Use the graph below. Is 21 inches, 24 inches, 25 inches
Answer:
21 inches
Step-by-step explanation:
May had just over 6 inches of rain, June had just about 9 inches of rain, and July had just under 6 inches of rain. Together, these months had 9 + 6 + 6 = 21 inches of rain.
In a recent survey, 0.4 of the people surveyed said their favorite beverage was coffee , 25 % said it was hot tea, andsaid it was millk 10 Which food was beverage by the greatest number of people?
Answer:
0.4
Step-by-step explanation:
0.4 as a percentage is 40%
25% is obviously 25%
10 is also obviously 10%
Solve the equation and check your solution 14 = 2y/5
14 = 2y/5 | *5
70 = 2y | :2
35 = y
Test :
14 = 2*35/5 TRUE
Answer:
y=35
Step-by-step explanation:
[tex]\frac{2y}{5}=14\\2y=14*5\\2y=70\\y=\frac{70}{2}\\y=35\\\\Checking\\\frac{2(35)}{5} \\\frac{70}{5} \\=14[/tex]
A store is having a sale where everything is discounted 30% find the discount and the sale price if a customer buys an item that normally sells for 365
Answer:
The discount is $109.50
The sale price is $255.50
Step-by-step explanation:
step 1
Find the discount
we know that
The discount is equal to the original price multiplied by the percentage rate of discount
we have
The original price is $365
The percentage of discount is equal to 30%
30%=30/100=0.30
so
the discount is equal to
0.30*($365)=$109.50
step 2
Find the sale price
The sale price is equal to the original price minus the discount
so
$365-$109.50=$255.50
Help is appreciated! :D
A field is undergoing construction and needs land to be removed in the shape of a rectangular prism. The land to be removed has a length of 1.4 × 104 in, a width of 4.3 × 103 in, and a height of 1.6 × 103 in. Find the volume of the land in scientific notation and in standard form. Answers should not be rounded. The volume of the land written in scientific notation is a × 10b cubic inches, where a____ is and B is____ .
The volume of the land written in standard form is____ cubic inches.
Answer:
a = 9.632 and b is 10
9.632*10^10 in^3 scientific form
96,320,000,000 in^3 standard form
Step-by-step explanation:
To find volume of a rectangular prism
V = l*w*h
= 1.4 * 10^4 ( 4.3 * 10^3) (1.6* 10^3)
When multiply powers of 10, we multiply the numbers out front
1.4*4.3*1.6 =9.632
Then we add the powers of 10
10^(4+3+3)
10^10
The volume is 9.632*10^10 in^3
a = 9.632 and b is 10
In standard form we move the decimal 10 places to the right. If there are not enough numbers we add zeros
9.632*10^10 in^3
96,320,000,000 in^3
Two fifth of the students in a class are male find the number of male students if there are 50 students in the class
There are 20 male students.
Hope this helps.
36/42 = 24/r solve the proportion to find r
[tex]36 \times r = 21 \times 12 \\ 36r = 252 \\ r = 252 \div36 \\ r = 7[/tex]
The question asks to solve a proportion 36/42 = 24/r. By cross-multiplication and solving the resulting equation for r, it is found that r = 28. Therefore, the correct value of r in this instance is 28.
Explanation:To solve the mathematical problem 36/42 = 24/r for the value of r, you should cross-multiply and then solve for r. Cross-multiplication means you multiply 36 by r and 42 by 24, which results in the equation 36r = 42 * 24. When you divide both sides by 36, you get r = 42 * 24 / 36 as the final form of the equation. After calculating the products and divison, you will find that r = 28.
Learn more about Solving Proportions here:https://brainly.com/question/15352418
#SPJ12
Which situation is best modeled by the inequality g ≤ 13?
A:You cannot play a game at age 13.
B:You must be no older than 13 to play a game.
C:You must be at least 13 to play a game.
D:You must be younger than 13 to play a game.
Answer:
You must be no older than 13 to play a game.
Step-by-step explanation:
≤ this sign means equal to or less than in this case it is 13
The situation that should be modeled by the inequality g ≤ 13 is option b.
Given information:
Inequality function g ≤ 13
Inequality function:We know that ≤ this sign represent that it is equal or lower than So here it should be no older than 13 for playing the game.
Learn more about inequality here: https://brainly.com/question/1778359
Which data value has the highest frequency? 1 1/6 3 1/6 3/8 5/8
Answer:
3 1/6
Step-by-step explanation:
To find the highest value, we have to evaluate each term individually,
1) 1 1/6 = 7/6 = 1.167
2) 3 1/6 = 19/6 = 3.16
3) 3/8 = 0.375
4) 5/8 = 0.625
Therefore, second data value (3 1/6) is highest.
Choose the best estimate for the length of a paperback book.
A.
4 in.
B.
8 in.
C.
14 in.
D.
18 in..
Answer:
I think its 14. If not, check other options. Bye!
Step-by-step explanation:
The estimated length of a paperback book is "8 inches".
paperback book:The paperback also called a paperback or softback, is a sort of book with a thick paper or paperboard cover that is often held together along with glue rather than stitches or staples.
Hardcover or hardcover books, but at the other extreme, are bonded with cardboard covered in linen, plastic, or leather.
Since 4 inches is far too short, and "14 and 18 " inches is longer than a ruler.
Therefore, the answer is "8 inches".
Find out more information about the book here:
brainly.com/question/1635505
I am not sure how to this pleases help
The subject of this question is Mathematics.
Explanation:The subject of this question is Mathematics.As a tutor, I would need more information about the specific question or problem you are working on to provide a detailed answer. Mathematics encompasses a wide range of topics including algebra, geometry, statistics, and calculus, among others. If you can provide more details about the specific topic or concept you are struggling with, I can provide a step-by-step explanation to help you understand.
Learn more about Mathematics here:https://brainly.com/question/27235369
#SPJ
9 plus x equals 5. Is my question and I’m really confused so some help would be appropriated
Answer:
x would equal -4
Step-by-step explanation:
What is the value of x in the product of powers below?
Answer:
= -7
Step-by-step explanation:
6 ⁹ ×6^x = 6²
From the laws of indices;
aⁿ × aⁿ = a^2n
Therefore;
6 ⁹ ×6^x = 6^(9+x)
6^(9+x) = 6²,
Since the bases are the same then the exponents are equal;
9+x = 2
x = -7
Answer:
x=-7
Step-by-step explanation:
[tex]6^9 \cdot 6^x = 6^2[/tex]
Apply exponential property to solve for x
[tex]a^m \cdot a^n = a^{m+n}[/tex]
[tex]6^9 \cdot 6^x = 6^{9+x}[/tex]
So the given equation becomes
[tex]6^{9+x}= 6^2[/tex]
Both sides of the equation has same base 6
So we equate the exponent and solve for x
[tex]9+x= 2[/tex]
Subtract 9 from both sides
[tex]x=-7[/tex]
Need help don’t understand
837.2 divided by 1:3 step my step
The value of the equation A = 837.2 / 1.3 is A = 644
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the first number be p
The value of p = 837.2
Let the second number be q
The value of q = 1.3
Now , the equation A = p/q
Substituting the values in the equation , we get
A = 837.2 / 1.3
On simplifying the equation , we get
A = 644
Therefore , the value of A is 644
Hence , the equation is A = 644
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ5
these types of questions are hurting me so if you could tell me the surface area of this shape. i have two questions left and can't miss anymore!
Answer:
The answer is D.
Step-by-step explanation:
Count how many l's there are, how many h's there are, and how many w's there are.
Answer:
[tex]\large\boxed{B.\ S.A.=2lw+2lh+2wh}[/tex]
Step-by-step explanation:
It's the net of a rectangular prism.
The formula of a surfave area of a rectangular prism:
[tex]S.A.=2lw+2lh+2wh[/tex]
We have two rectangles l × w, two rectangles l × h and two rectangles w × h.
Stephanie makes $200,000 annually and gets paid weekly. How much is her weekly paycheck
200,000/52 weeks in a year =$3846.153846 each week
Her weekly paycheck is 3835.82
Step-by-step explanation:As we know that there are 52.14 weeks in a year
So weekly paycheck will be 200,000 / 52.14 = 3835.82
Since she gets weekly check so her weekly paycheck is 3835.82