what choice is a solution to the system of equations? y=2x-3 y-9=-x
Answer:
[tex](4,5)\ or\ x=4,y=5[/tex]
Step-by-step explanation:
[tex]We\ are\ given:\\y=2x-3\\y-9=-x\\Now,\ lets\ separate\ all\ the\ constant\ terms\ to\ the\ RHS\ and\ the\ variable\\ terms\ to\ the\ LHS.\\Hence,\\y-2x=-3\\y+x=9\\By\ subtracting\ the\ two\ equations:\\(y-2x)-(y+x)=(-3)-(9)\\Hence\ lets\ simplify\ this\ main\ equation: \\y-2x-(y+x)=-3-9\\y-2x-y-x=-12\\-3x=-12\\x=\frac{-12}{-3}=4\\\\Now,\ lets\ consider\ the\ second\ equation\ in\ the\ solution:\\y-9=-x\\Substituting\ x=4,\\y-9=-(4)\\y-9=-4\\y=-4+9\\y=5\\[/tex]
[tex]Now,\\We\ get\ the\ solution\ to\ this\ system\ of\ equations:\\x=4,y=5\\By\ putting\ this\ as\ a\ co-ordinate\ pair (x,y):\\(4,5)[/tex]
Answer:
The solution of the system of equations will be:
[tex]y=5,\:x=4[/tex]
Step-by-step explanation:
Given the system of equation
[tex]\begin{bmatrix}y=2x-3\\ y-9=-x\end{bmatrix}[/tex]
Arrange equation variables for elimination
[tex]\begin{bmatrix}y-2x=-3\\ y+x=9\end{bmatrix}[/tex]
so
[tex]y+x=9[/tex]
[tex]-[/tex]
[tex]\underline{y-2x=-3}[/tex]
[tex]3x=12[/tex]
so the system of equations becomes
[tex]\begin{bmatrix}y-2x=-3\\ 3x=12\end{bmatrix}[/tex]
solve 3x=12 for x
[tex]3x=12[/tex]
Divide both sides by 3
[tex]\frac{3x}{3}=\frac{12}{3}[/tex]
[tex]x=4[/tex]
[tex]\mathrm{For\:}y-2x=-3\mathrm{\:plug\:in\:}x=4[/tex]
[tex]y-2\cdot \:4=-3[/tex]
[tex]y-8=-3[/tex]
Add 8 to both sides
[tex]y-8+8=-3+8[/tex]
[tex]y=5[/tex]
Thus, the solution of the system of equations will be:
[tex]y=5,\:x=4[/tex]
Wayne bought blueberries. He uses 3/8 of the blueberries to make blueberry bread,
1/6 of the blueberries to make pancakes, and
5/12 of the blueberries to make jam. If Wayne uses 69 ounces of the blueberries he bought, how many ounces of blueberries did he buy?
Examen Compétence 1: Proportions et algèbre
1.
Dans un camp de jour, Marc essaie de te faire deviner le nombre d'élèves qu'il a
dans ses deux groupes. Dans le groupe A, le rapport entre les gars et les filles
est de 3:5 et celui du groupe B est de 2:3. Il y a 62 élèves en tout et il y a autant
de garçons dans le groupe A que dans le groupe B. Combien y a-t-il d'élèves dans
le groupe B?
Considérez qu'il y a "x" garçons dans chaque groupe et résolvez l'équation
algébrique.
Answer:
Check my link.
Step-by-step explanation:
Brainly keeps on saying my question either has a link or is inappropriate, and it neither has a link nor is inappropriate.
I have no clue as to what to correct.
Plzzzz help and also can you plz show how you got the answer
Answer:hi
Step-by-step explanation:
42.
*=3"y=9,- 27 and "y"? - 1, then abe is a
(a) 1
) (b) 27
(e)
( (d) 0
43. In given fig., the diagonals of a rectangle ABCD
Answer: (d) 0
we have:
[tex]y=9^{b}=(3^{2})^{b}=3^{2b}\\\\z=27^{c}=(3^{3})^{c}=3^{3c}\\\\\\x^{bc}.y^{ca}.z^{ab}=1\\\\<=>(3^{a})^{bc}.(3^{2b})^{ca}.(3^{3c})^{ab}=1\\\\\\<=>3^{abc}.3^{2abc}.3^{3abc}=1\\\\\\<=>3^{6abc}=3^{0}\\\\\\=>6abc=0\\\\\\<=>abc=0[/tex]
Step-by-step explanation:
Answer:
abc = 0
Step-by-step explanation:
[tex]x = {3}^{a} \\ y = {9}^{b} = {3}^{2b} \\ z = {27}^{c} = {3}^{3c} \\ \\ \because \: {x}^{bc} {y}^{ca} {z}^{ab} = 1 \\ \\ \therefore \: ( {3}^{a} )^{bc} ( {3}^{2b} )^{ca} ( {3}^{3c} )^{ab} = 1 \\ \\ {3}^{abc} .{3}^{2abc} .{3}^{3abc} = 1 \\ \\ {3}^{abc + 2abc + 3abc} = 1 \\ \\ {3}^{6abc} = {3}^{0} \: \\ ( \because \: {3}^{0} = 1) \\ \\ \because \: bases \: are \: equal \\ \therefore \: exponents \: will \: also \: be \: equal \\ \\ \implies \: 6abc = 0 \\ \\ \implies \: \red{ \bold{abc = 0 }}[/tex]
Rewrite each fraction with a denominator of 24 2/3 5/8
Answer:
A)16/24
B)15/24
Step-by-step explanation:
We were told to rewrite so that the denominator will be 24
A)2/3
This can be rewritten as 16/24, so that the denominator is now 24. And if we divide the numerator (16) by factor of 8 and the denominator (24) by factor of 8. Then we have 2/3.
OR
[2/3 × 8/8] = 16/24
B)5/8
This can be rewritten as 15/24, so that the denominator is now 24. And if we divide the numerator (15) by factor of 3 and the denominator (24) by factor of 3. Then we have 5/8
OR
(5/8 × 3/3)= 15/24
Perrie invests £25000 for 3 years in a saving account. She gets 2.7% per annum compound interest. Calculate the total amount of interest perrie will get after 3 years.
Answer:
I (interest) = £ 2,080.17
Step-by-step explanation:
Perrie invests £25000 for 3 years in a saving account. She gets 2.7% per annum compound interest. Calculate the total amount of interest perrie will get after 3 years.
To solve the above question, we would use the Periodic compound interest formula
A = P(1 + r) ^t
Where P = Principal = £25000
r = Interest rate = 2.7 % = 0.027
t = time in years = 3 years
Hence:
A = £25,000( 1 + 0.027)³
A = £27,080.17
A = P + I where
P (principal) = £ 25,000.00
I (interest) = £27,080.17 - £ 25,000.00
I (interest) = £ 2,080.17
The total amount of interest perrie will get after 3 years is £ 2,080.17
Which expression is equivalent to 0.5 × 0.6?
A. (5 × 10) × (6 × 10)
B. (5 × 110) × (6 × 1100)
C. (5 × 1100) × (6 × 1100)
D. (5 × 110) × (6 × 110)
Answer:
C.
Step-by-step explanation:
Because ( 5 x 1100) x (6 x 1100) yeay
The correct equivalent expression is (5 × 1/10) × (6 × 1/10)
The correct option is (D)
What are decimals?Decimals are one of the types of numbers, which has a whole number and the fractional part separated by a decimal point.
Given:
0.5 × 0.6
Is we expand it into fraction we get
=5/10 * 6*10
Hence, the equivalent fraction is 0.5 × 0.6.
Learn more about decimal here:
https://brainly.com/question/548650
#SPJ2
85 POINTS! If y is 2.5 when x is 5 and y varies directly with x, find y when x is 20.
Answer:
Y = 10 when X = 20
Step-by-step explanation:
Answer:
100
Step-by-step explanation:
y∝x∴y=k⋅x or k=y over x=2.50.5=5
(k is proportionality costant) When
x
=
20
;
y
=
5
⋅
20
=
100
[Ans]
please help me........
Answer:
x = 54
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Equality PropertiesStep-by-step explanation:
Step 1: Define
-12(x + 4) + 14x = 60
Step 2: Solve for x
Distribute -12: -12x - 48 + 14x = 60Combine like terms: 2x - 48 = 60Add 48 to both sides: 2x = 108Divide 2 on both sides: x = 54Answer:
x = 54
Step-by-step explanation:
-12(x + 4) + 14x = 60
i) distribute -12 to the whole parentheses of (x+4)
(-12 × x) + (-12 × 4) + 14x = 60
-12x - 48 + 14x = 60
ii) collect like terms
-12x + 14x - 48 = 60
2x - 48 = 60
iii) move constant to the right-hand side and change its sign
2x = 60 + 48
iv) add the numbers
2x = 108
v) divide both sides of the equation by 2
[tex] \frac{2x}{2} = \frac{108}{2} [/tex]
x = 54
The graph shows the relationship between the number of pounds of
apples purchased and the total cost of the apples.
What is the cost of 1 pound of apples? Enter the answer in the box.
Given:
The graph shows the relationship between the number of pounds of apples purchased and the total cost of the apples.
To find:
The cost of 1 pound of apples.
Solution:
We need to find the slope of the line to get the cost of 1 pound of apples.
From the given graph it is clear that the line passes through two points (0,0) and (2,3). So, the slope of the line is
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\dfrac{3-0}{2-0}[/tex]
[tex]m=\dfrac{3}{2}[/tex]
[tex]m=1.5[/tex]
Therefore, the cost of 1 pound of apples is $1.5.
Answer:
1.5
Step-by-step explanation:
Tim is going to an amusement park that cost 30.00 to get into.Treats like cotton candy carmel apples and funnel cakes cost 2.00 dollars each .Tim does not want to spend more than 62.00 in all. Solv for x ,where x equals the number of 2.00 treats tim can buy
Answer:
x = 16 treata
Step-by-step explanation:
Let us represent x = Number of treats that Tim can buy
We are told that: Tim does not want to spend more than $62.00 in all.
= Time wants to spend less than or equal to $62.00
Tim is going to an amusement park that cost $30.00 to get into.Treats like cotton candy carmel apples and funnel cakes cost 2.00 dollars each .
Therefore, our inequality equation =
$30.00 + $2.00 × x ≤ $62.00
30 + 2x ≤ 62
Solving for x
30 + 2x ≤ 62
2x ≤ 62 - 30
2x ≤ 32
x ≤ 32/2
x ≤ 16
Hence, Tim can buy no more than(less than or equal to ) 16 treats
Hurry please
:)))
I NEED HELP
Answer:
[tex] \huge\frac{ \sqrt{6} }{ \sqrt{5} } = \frac{ \sqrt{30} }{5} [/tex]
√30/5 is the right answer.write two equations that goes through the point 7, 4 and -3,8
Answer:
y=−2/5x+34/5 there is no other equation
Step-by-step explanation:
Answer:
y - 4 = -2/5(x - 7)
y = -2/5 + 6.8
Step-by-step explanation:
Graph it and see that they are both the same line and that they both go through the same points.
Mr Brown has 2 children are going to london by train 1 adult costs £24 and child ticket costs 12 1/3 off adults tickets and 60% off child ticket
Complete Question
Mr Brown has 2 children are going to london by train
1 adult costs £24 and child ticket costs 12
The Family Railcard offers:
1/3 off adults tickets and 60% off child ticket
What is the total cost of tickets when Mr Brown uses the Family Railcard
Answer:
£25.60
Step-by-step explanation:
From the question:
1 adult costs £24
The Family Railcard offers:
1/3 off adults tickets.
Hence:
1/3 × £24 = £8
The cost for Mr Brown = £24 - £8
= £16
Child ticket costs £12
The Family Railcard offers:
60% off child ticket
Hence = 60% × £12
= 60/100 × £12
= £7.2
The cost for 1 child = £12 - £7.2
= £4.8
The total cost of tickets when Mr Brown uses the Family Railcard is:
Cost for Mr Brown + Cost for his 2 Children
£16 + 2 × £4.8
£16 + £9.6
= £25.60
Can someone please help me? If it is correct ai will give Brainliest
Thank you
9514 1404 393
Answer:
A
Step-by-step explanation:
Collecting terms of the expression, we have ...
x + 0.1x = x(1 +0.1) = 1.1x
In words, adding 10% is the same as multiplying the value by 1.1. Choice A is appropriate.
Answer plzz I give will correct answer as brainliest
Answer: 13m
Step-by-step explanation:
A^2+ B^2= C^2
5^2+ 12^2= c^2
169= C^2
then square root the 169 to get 13
Ms. Albero decided to make juice to serve along with the pizza at the Student Government party. The directions said to mix 3 scoops of powdered drink mix with 1 gallon of water to make each pitcher of juice. One of Ms. Albero’s students said she will mix 12 scoops with 3 gallons of water to make 4 pitchers. How can you use the concept of proportional relationships to decide whether the student is correct?
Answer:
the student is wrong
Step-by-step explanation:
the og directions said 3 scoops / 1 gallon / 1 pitcher. if you are using 12 scoops, then the gallons of water will be proportional, meaning 3x4=12 scoops / 1x4=4 gallons / 1x4=4 pitchers. if you x4 to one of them, then the directly porportinal values also have to be multiplied by the same number, hence making the student wrong since they should have 4 gallons for 12 scoops
A square has a perimeter of 76 ft. What is the length of each side?
Answer:
19ft
Step-by-step explanation:
76÷4-- because a square has 4 sides
=19ft
19+19+19+19
=76
Answer:
nineteen. division by four
what is the answer to the question?
Answer:
120°
Step-by-step explanation:
m<ABD+m<DBC=m<ABC
61°+59°=120°
hope this helped!
Answer:
We conclude that the value of m∠ABC = 120°
Step-by-step explanation:
Given
m∠ABD = 61°
m ∠DBC = 59°
To Determine
m∠ABC = ?
It is clear that the value of m∠ABC can be determined by adding m∠ABD and m∠DBC because m∠ABC the segment BD divides the angle m∠ABC into two adjacent angles m∠ABD and ∠DBC.
Therefore,
m∠ABC = m∠ABD + m∠DBC
= 61° + 59° ∵ m∠ABD = 61°, m ∠DBC = 59°
= 120°
Therefore, we conclude that the value of m∠ABC = 120°
PLEASE HELP! and also please show your work!!
Answer: d) b = 12
2/3.b - 1/3.b + 12 = 16
⇔ 1/3. b = 16 - 12
⇔ 1/3.b = 4
⇔ b = 4.3 = 12
Step-by-step explanation:
Answer:
b = 12
Step-by-step explanation:
2/3 b - 1/3 b + 12 = 16
or, 2b/3 - b/3 + 12 = 16
or, 2b -b/ 3 + 12 = 16
or, 2b - b = 16 - 12
or, b = 4 × 3
therefore, b = 12
If at a toy store, 2 board games cost $13.40, what is the unit price of a board game?
Answer:
The unit price of a board game is $6.70
Step-by-step explanation:
1 board/2boards = x/13.4
Cross multiply:
13.4*1/2x
13.4/2x
x=6.7
Hope this helps plz hit the crown :D
plzzzzzzzzzzzzzzzzzzzzzz
Answer:
6[tex]x^{8}[/tex][tex]y^{5}[/tex]
Step-by-step explanation:
Using the rule of exponents
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] ⇔ [tex]a^{(m+n)}[/tex]
Given
3x²[tex]y^{4}[/tex] × 2[tex]x^{6}[/tex]y, then
3 × 2 × x² × [tex]x^{6}[/tex] × [tex]y^{4}[/tex] × [tex]y^{1}[/tex]
= 6 × [tex]x^{(2+6)}[/tex] × [tex]y^{(4+1)}[/tex]
= 6[tex]x^{8}[/tex][tex]y^{5}[/tex]
ASAP PLS HELP ME I NNED HELP
Answer:
perimeter=40.9ft
Step-by-step explanation:
The length at the top is 10ft,the length at the bottom is 10+4ft=14ft and the other lengths are8.9ft and 8ft
perimeter=10+14+8+8.9=40.9ft
Are the ratios 3:4 and 2:20 equivalent?
Answer:
no
Step-by-step explanation:
When Mr. Johnson check the newspaper on Monday he saw that the stock for Apple Inc. was worth $442.69 when he checked on Tuesday the stock had dropped $5.32 how much is the Apple Inc. stock worth on Tuesday
A. $437.37
B. $437.07
C. $448.01
D. $448.37
You are ordering a sandwich for lunch. If the sandwich shop boasts that they have 25 different toppings for their sandwiches, and you can choose up to five for no extra cost, how many combinations of toppings can you get on your sandwich without having to pay more?
Step-by-step explanation:
Number of Combinations
= 25C0 + 25C1 + 25C2 + 25C3 + 25C4 + 25C5
= 1 + 25 + 300 + 2300 + 12650 + 53130
= 68,406.
There are a total of 68,406 combinations.
Answer:
6
Step-by-step explanation:
What is the value of x in the equation 2(X+3) = 4(X-1)2
O1
O2
O3
O5
Please hurry ._.
Point E has a positive y-coordinate.
Answer:
please be more specific in your answer.
Step-by-step explanation:
i know that if it has a positive y coordinate then it would mean it has to be above the x-axis but thats all i can tell you from this.
I need help finding the missing side.
Answer:
x ≈ 25.1
Step-by-step explanation:
Using the cosine ratio in the right triangle, that is
cos64° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{11}{x}[/tex] ( multiply both sides by x )
x × cos64° = 11 ( divide both sides by cos64° )
x = [tex]\frac{11}{cos64}[/tex] ≈ 25.1 ( to the nearest tenth )