(1)×3 and (2)×5
15x-9y=33-(3)15x+20y=20-(4)Subtract both
[tex]\\ \sf\longmapsto -29y=13[/tex]
[tex]\\ \sf\longmapsto y=\dfrac{-13}{29}[/tex]
Put in eq(1)[tex]\\ \sf\longmapsto 5x+\dfrac{-117}{29}=11[/tex]
[tex]\\ \sf\longmapsto 5x=11+\dfrac{117}{29}=\dfrac{261+117}{29}=\dfrac{278}{29}[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{278}{145}[/tex]
Mary invests £12,000 in a savings account the account pays 1.5% compound interest per year work out the value of her investment after 2 years.
Answer:
The value of Mary's investment after two years = £12362.7
Step-by-step explanation:
P = Principal / initial amount
R = rate of interest per cent per year
T = number of years
A = final amount at the end of T years
Then:
A = P*(1 + R/100)^2
In our example:
P = £12000
R = 1.5 per cent per year
T = 2 years
Thus:
A = 12000*(1 + 1.5/100)^2
= 12000*(1 + 0.015)^2
= 12000*(1.015)^2
= 12000*(1.030225)
= 12362.7
Value of investment after two years = £12362.7
Tell whether the sequence is arithmetic, if it is, write a function rule to represent it.
4, 6.5, 9, 11.5, ...
is 4.212886… an rational or irrational number?
Answer:
irrational number
Step-by-step explanation:
An irrational number cannot be written as a ratio of two integers
i need help pls
7a/9bc ÷ 21a/12b
[tex]\displaystyle \frac{7a}{9bc} \div\frac{21a}{12b} =\frac{\backslash\!\!\!\!7a}{9 \backslash \!\!\!b \ c} \cdot \frac{4\backslash\!\!\!b}{\backslash\!\!\!\!7a} =\boxed{\frac{4}{9c} }[/tex]
Please help me to I’ll give 5 stars
Answer:
The correct answer is C [tex]3\frac{8}{33}[/tex]
Solution by separating the parts:
[tex]3\frac{8}{33}[/tex] = 3 + [tex]\frac{8}{33}[/tex]
We know that [tex]\frac{8}{33}[/tex] is 8 ÷ 33.
Therefore: [tex]3\frac{8}{33}=[/tex] 3 + (8 ÷ 33)
You then would have to use "Long Division" for 8 divided by 33
= 3 + 0.242 = 3.242424242424...
Hence giving you 3.24 repeated which is C
P.S. the quiz either looks like a PVS exam form, or a virtual school exam/quiz, I'm able to work and help with any other further questions.
What would be the denominator after rationalizing 7/(5√3-5√2)
Please tell fast
I will mark branliest please fast
Thank you ☺️
Step-by-step explanation:
=> 7/(5√3-5√2) × (5√3+5√2)/(5√3+5√2)
=> 7(5√3+5√2)/75-50
=> (35√3+35√2)/25.
after rationalising the denominator is 25.
hope this helps you.
At Rosa's Rose Shop, a bouquet containing a dozen roses costs $20. If the price of a bouquet is directly proportional to the number of roses it contains, how many dollars will a bouquet of 39 roses cost?
Answer:
It will cost $65.
Step-by-step explanation:
A dozen is 12. To find how much it will cost, we can divide the bouquet by 12.
39 ÷ 12 = 3 r3
with the remainder, we can
12 ÷ 3 = 4
3 is 1/4 of 12.
So we can multiply the price of bouquet by 1/2 to find the remainder's price. The whole equation would look like this:
(3x20) + (1/4 x 12)
60 + (1/4 x 20)
60 + 5
65
The answer is 65.
The plane Avia flies holds 2900 gallons of fuel. She landed the plane this morning with a reserve of 900 gallons. The plane is refueled at a rate of 300 gallons of fuel per minute. The function h(x)=900+300x represents the amount of fuel in her plane after x minutes of refueling. What is the meaning of h(5.5) in the context of this situation?
Answer:
h(5.5) = 2550
Step-by-step explanation:
when something is put inside of the parenthesis in a function like h(x) or f(x), it goes where the x is so the equation would look like this
900 + 300(5.5), 900 + 1650 = 2550
For the equation y=3x^2−6x−5, find the vertex showing all work.
Answer:
vertex: (1, –8)
Step-by-step explanation:
[tex]a=3 \\b=-6\\c=-5[/tex]
rewrite equation in vertex form: [tex]y=a(x-h)^2+k[/tex]
1. factor out 3
[tex]y=3x^{2} -6x-5\\y=3(x^{2}-2x)-5\\[/tex]
2. complete the square using [tex](\frac{b}{2} )^{2}[/tex]:
[tex](\frac{-2}{2})^2=1[/tex]
3. add the answer from step 2 to inside the parenthesis to create a factorable trinomial. subtract the answer from step 2 from –5 and multiply it by a. remember: a = 3
[tex]y=3(x^{2} -2x+1)-5-1(3)\\y=3(x-1)(x-1)-8\\y=3(x-1)^2-8[/tex]
4. find vertex
[tex]x-1=0\\x=1[/tex] [tex]y=-8[/tex]
vertex = [tex](1,-8)[/tex]
what is x? -8=-(x+4)
Answer:
x=4
Step-by-step explanation:
Write the augmented matrix for the following system of equations.
- 3x + 2y = 7
5 – 2x = 7y
Answer:
Point Form: [tex](-\frac{39}{25} , \frac{29}{25} )[/tex]
Equation Form: [tex]x=-\frac{39}{25} , y=\frac{29}{25}[/tex]
Step-by-step explanation:
Using its matrix, you are going to solve with
Write both equations in standard form. ...
Make the coefficients of one variable opposites. ...
Add the equations resulting from Step 2 to eliminate one variable.
Solve for the remaining variable.
Substitute the solution from Step 4 into one of the original equations.
7. People are migrating from one country or continent to the other in search of a better future. Many factors are being considered in
migration. Suppose x number of Filipinos migrate to Australia, express the following number of people migrating to other continents
(excluding Antarctica).
a. Africa : 20 less than the migration to Australia ( Answer: x - 20 )
b. Asia : 100 more than twice the migration to Australia (2 points)
c. North America : 15 more than 3 times the migration to Australia (2 points)
d. Europe: 10 more than twice the migration to Australia (2 points)
e. South America : 50 more than the migration to Australia (2 points)
f. Find the ratio (using fraction) of the migration to Europe over the migration to North America (Simplify your answer using
factoring) Show your solution. (5 points)
g. If x = 100, which continent has the biggest number of migration? Show your solution from a to e. (7 points)
Answer:
toyota innova 2.8 G A/T 2021 4x1
please explain and give answer
Angle 1=87°
Angle 2=88°
angle 1+2= 177
Step-by-step explanation:
I believe thsi should be right,
So angle 1 and 87° are the same because of some rule, then the angle above 2 would be 92 because of the same rule and its a straight line so 180-92=88 making angle 2, 88. When you add those it would be 177. Try that
Plz help i am so S t u p i d
Answer: 23, 5, 3
Step-by-step explanation:
Problem a)
5 + 2 x 3^2
5 + 2 x 9
5 + 18
23
Problem b)
7 + 8 / 5 - 2
15 / 3
5
Problem c)
18- 3 x 2/ 5 - 1^2
18 - 6/ 5 - 1
12/4
3
Answer:
a is 7×9=63 b is 15 /3=5c is 30 / 4 = 7.5I don't think you should doubt the ability to do well you should have confidence in your self .
PLEASE ANSWER QUICKLY AND CORRECTLY I APPRECIATE IT SO MUCH !!! :)))
Is (-1,4) a solution to the graph of
y= 3x + 7?
EXPLAIN WHY OR WHY NOT
Answer:
True
Step-by-step explanation:
(-1,4) = (x,y)
This means if "x = -1, then y should be 4"
y = 3x + 7
y = 3(-1) + 7
y = -3 + 7
y = 4
It is saying if x is -1, y is 4. This statement of "Is (-1,4) a solution to the graph of "y = 3x + 7?" Is true. You can also graph this and find the point (-1,4) and it would be on the line.
:D Hope it Helps (I dunno why I put it on this answer box now)
Answer:
Yes.
Step-by-step explanation:
Note that the point:
(x , y) = (-1 , 4)
x = -1
y = 4
Plug in the corresponding numbers for the corresponding variables in the given equation:
y = 3x + 7
(4) = 3(-1) + 7
Remember to follow PEMDAS. PEMDAS is the order of operation, and stands for:
Parenthesis, Exponent (& Roots), Multiplication, Division, Addition, Subtraction.
First, multiply 3 with -1:
4 = (3 * -1) + 7
4 = -3 + 7
Next, simplify by adding -3 with 7:
4 = (-3 + 7)
4 = 4
Yes. (-1 , 4) is a solution for y = 3x + 7, as the two sides of the equation equal.
~
||3x-4|-5|>1
Please Help Me!
20 points!
Answer:
4(3 −1)−5=75
Step-by-step explanation:
A child flies a kite at a height of 90 ft, the wind carrying the kite horizontally away from the child at a rate of 30 ft/sec. How fast must the child let out the string when the kite is 150 ft away from the child?
By Pythagorean theorem and differential calculus, the child must let out the string when the kite is 150 feet away at a rate of change of 25.725 feet per second.
How to determine the rate of change of the string
The geometric representation of this question is based on the Pythagorean theorem:
l² = x² + y² (1)
Where:
x - Horizontal distance of the kite from the kite, in feet.y - Height of the kine, in feet.l - Length of the string, in feet.The rate of change of the length of the string is obtained by differential calculus:
[tex]2 \cdot l \cdot \dot l = 2\cdot x \cdot \dot x[/tex]
[tex]\dot l = \frac{x\cdot \dot x}{l}[/tex]
[tex]\dot l = \frac{x\cdot \dot x}{\sqrt{x^{2}+y^{2}}}[/tex] (2)
If we know that x = 150 ft, y = 90 ft and [tex]\dot x = 30\,\frac{ft}{s}[/tex], then the rate of change of the length of the string is:
[tex]\dot l = \frac{(150\,ft) \cdot \left(30 \,\frac{ft}{s} \right)}{\sqrt{(150\,ft)^{2}+(90\,ft)^{2}}}[/tex]
[tex]\dot l \approx 25.725\,\frac{ft}{s}[/tex]
By Pythagorean theorem and differential calculus, the child must let out the string when the kite is 150 feet away at a rate of change of 25.725 feet per second.
To learn more on rates of change: https://brainly.com/question/13103052
#SPJ1
What is the domain of the function?
A ladder which is 4.7 m long is placed on the ground 0.5 m from a vertical wall and then leaned over to the wall.
How high up the wall can the ladder reach?
Give your answer rounded to 1 DP.
Answer:
the can reach up to 4.6 m
Jane's salary is increased by 2% to £23358.
How much was her salary before the rise?
Answer:
find two percent of 23358=467.18
minus the two percent from her salary 23358
23358-467.18=22890.84
please mark branliest
Could someone maybe help?
Answer:
9/11
Step-by-step explanation:
pick two points.
(x,y)
(5,4) and (-6,-5)
do rise/run (y2-y1/x2-x1)
4-(-5)/5-(-6)
subtracting a negative gives you a positive, so
4+5/5+6
9/11
HELP PLEASE?? Im confused caqn somone please help me ill make you brainliest .
Answer:
250.5 - 35 m = 300 - 35.25 m
Step-by-step explanation:
n ⇒ number of months it will take for both accounts to have the same amount of money
∴ the equation should be: 250.5 - 35 m = 300 - 45.25 m
⇒ 250.5 - 300 = -45.25m + 35m
⇒ -49.5 = -10 · 25m
m = 4950/1025
Answer:
b
Step-by-step explanation:
the correct equation is b
Recursive equation for -2, -5, -8, -11, -14
Answer:
f(0) = 1
f(x) = f(x-1) - 3
Step-by-step explanation:
probably use the style of your teacher
Sumita buys a set of earphones for £13.42.
She pays with £15.
How much change does she get?
Give your answer in £.
Answer:
Okay the answer is £1.56
Step-by-step explanation:
£15.00
-£13.42
£01.58
Brainliest if you liked the answer.
Under her cell phone plan, Grace pays a flat cost of $70 per month and $4 per gigabyte. She wants to keep her bill at $74.40 per month. Write and solve an equation which can be used to determine xx, the number of gigabytes of data Grace can use while staying within her budget. i don´t understand how to set up the problem.
The equation of the cell phone plan is y = 70 + 4x and the number of gigabyte is 1.10
How to determine the equation?The given parameters are:
Flat = $70 per month
Rate = $4 per gigabyte
Let the number of gigabyte be x, and the total cost be y.
So, we have:
y = Flat + Rate * x
So, we have:
y = 70 + 4x
When the bill is $74.40, we have:
74.40 = 70 + 4x
Subtract 70 from both sides
4x = 4.40
Divide both sides by 4
x = 1.10
Hence, the equation is y = 70 + 4x and the number of gigabyte is 1.10
Read more about linear equations at:
https://brainly.com/question/14323743
#SPJ4
when visiting baltimore md you need to rent a taxi to get from your hotel to the national aquarium. the taxi company charges a flat fee of $3 for using the taxi and $0.75 per mile. if you paid the taxi driver $24 how many miles did you travel
Answer:24-3 = 21 divided by .75 = 28 so the answer is 28 miles
Step-by-step explanation:
5(p+3)=37.95
help me with my homework
Answer:
p= 4.59
Step-by-step explanation:
Hope this helped :)
A shopkeeper bought a fan for rupees 840 at what price should he sell it to make a profit of 10% If he makes a loss of 5% by selling at what is the selling price
Answer with Step-by-step explanation:
10% of 840 can be found by multiplying 840 by 0.10 (or dividing 840 by 10)
10% of 840 = 84
To make a profit of 84 he needs to sell at 840 + 84 = 924 rs
5% of 840 can be found by multiplying 840 by 0.05 (or dividing 840 by 20)
5% of 840 = 42
To make a loss of 42 he needs to sell at 840 - 42 = 798 rs
For f(x)=4x+1 and g(x)=x^2-5, find (g/f)(x)
Answer:
[tex](g/f)(x) = \frac{g(x)}{f(x)} = \frac{ {x}^{2} - 5 }{4x + 1} [/tex]
I hope I helped you^_^
Mia is three years older than twice her sister Brooke's age. The sum of their ages is less than 30.
What is the greatest age Brooke could be?
a.) 7
b.) 8
c.) 9
d.) 10
the correct answer is b. 8