Solve the system of equations at right. 2^(x+y)=16 2^(2x+y)= 1/8
Answers
Answer:
(x, y) = (-7, 11)
Step-by-step explanation:
The system of exponential equations can be solved by the use of logarithms. Equivalently, the equations can be written so that exponents can be equated. This system is equivalent to two linear equations.
First equation:
2^(x+y) = 16
2^(x +y) = 2^4 . . . . use the same base to write the constant
x +y = 4 . . . . . . . . equate exponents of 2 (take log₂ of both sides)
Second equation:
2^(2x +y) = 1/8
2^(2x +y) = 2^(-3) . . . . use the same base to write the constant
2x +y = -3 . . . . . . equate exponents of 2
Solve the linear equations:
We can subtract the first equation from the second to get ...
(2x +y) -(x +y) = (-3) -(4)
x = -7
y = 4 -x = 4 -(-7) = 4 +7 = 11 . . . . use the first equation to find y
The solution to the system is (x, y) = (-7, 11).
Related Questions
THIS IS EXPONENTIAL FROM TWO POINTS
If f(x) is an exponential function where f(3.5)=21 and f(6.5)=69, then find the value of f(9), to the nearest hundredth.
Answers
Answer:
i think the answer is 144
Step-by-step explanation:
ohhh so first we should try finding the slope here. since we know the points are (3.5 , 21) and (6.5, 69) we can use the formula to look for the slope
the formula is:
y2 - y1 / x2 - x1
lets substitute
69 - 21 / 6.5 - 3.5
48 / 3
16
f(x) = 16x + b
now we just substitute
btw i dont think we need to find b because this inst a linear equation? im not sure but yea i dont think we need to find the y-intercept
so anyways
f(9) = 16(9)
= 144
You find a ring at a garage sale and purchase it for $2. Explain how you could use a simple balance and graduated cylinder to determine if it is made of gold or if it’s a fake.
Answers
Density of water is 1000kg/m^3
Gold should sink downIf yes then it's pure goldMark and Henry win some money and share it in the ratio 1:3. Mark gets £9. How much did Henry get?
Answers
Answer:
Hope this helps!!!!!!
Mark Brainlest!!!!!!!!!!
Step-by-step explanation:
Mark and Henry win some money and share it in the ratio 1:3. Mark gets £9. How much did Henry get?
Ratio = 1 : 3
Let Mark's share be 1x = x
and Henry's share be 3x
We know that Mark gets £9
So,
1x = x = £9
Then 3x = £(3 * 9) = £27
HENCE,
Mark's share = £9
Henry's share = £27
Total money = Mark's share + Henry's share = £9 + £27 = £36
Answer:
£27
Step-by-step explanation:
so it shows mark is 1 while Henry is 3
we know that Mark is 1/4 while Henry is 3/4
/4 because the total is 4 so whatever their ratio is over their total
so we do: 1 = 9
3 = ?
and then u cross multiply
3*9 = 27 ÷ 1 = 27
so Henry receives £27
Under his cell phone plan, Justin pays a flat cost of $56 per month and $5 per gigabyte. He wants to keep his bill under $65 per month. Write and solve an inequality which can be used to determine xx, the number of gigabytes Justin can use while staying within his budget
Answers
Answer:
56 + 5xx < 65
xx < 1.8
Step-by-step explanation:
56 + 5xx < 65
subtract 56 on both sides
56 + 5xx < 65
-56 -56
5xx < 9
divide by 5 on both sides
5xx/5 < 9/5
xx < 1.8 gigabytes
7
The number of chocolates, C. needed for a party is worked out using
the formula C = 6n, where n is the number of people attending,
How many chocolates are needed if there are:
b) 12 people?
a) 8 people?
C) 40 people?
d) 50 people?
Answers
Answer: (b) 72 (A) 48 (c) 240 (D) 300
Step-by-step explanation:I just multiplied
Answer:
6*12=72
6*8=48
6*40=240
6*50=200
Step-by-step explanation:
just substitute the given number for n and mulitply
f(x) = 3x - 2x - 5
Factoring quadratics
Answers
Answer:
[tex](3x -5)(x+1)[/tex]
Step-by-step explanation:
Factoring [tex]3x^{2} -2x-5=0[/tex] results in [tex](3x -5)(x+1)[/tex]
Can you please help me quickly!!
Answers
Answer:
to struggle to succeed when chances are bad
Step-by-step explanation:
She got nervous and froze when she thought she was going to lose.
White gold is made from gold, palladium, nickel and zinc in the ratio 15:2:2:1. A white gold ring contains 9g of gold. What is the mass of the ring?
Answers
Answer:
The mass of the ring is 12 grams.
Step-by-step explanation:
Total 20 parts
Gold 3/4 total mass (15/20)
3/4=9g
1/4=3g
4/4=12g
Answer:
mass of the ring = 12 g
Step-by-step explanation:
Given ratio
gold : palladium : nickel : zinc = 15 : 2 : 2 : 1
Add the ratios: 15 + 2 + 2 + 1 = 20
Therefore, as a fraction, gold is [tex]\sf \dfrac{15}{20}=\dfrac34[/tex] of the total mass of the ring.
Let the mass of the ring = x
As the ring containts 9 g of gold
[tex]\sf \implies \dfrac34x=9[/tex]
[tex]\sf \implies x=9 \cdot \dfrac43[/tex]
[tex]\sf \implies x=12[/tex]
Therefore, the mass of the ring is 12 g
comprising 9 g of gold, 1.2 g of palladium, 1.2 g of nickel and 0.6 g of zinc.
HAPPY BIRTHDAY!
You have decided to give your best friend a bag of red
and green marbles for his birthday. Your friend likes
green marbles better than red ones, so the bag has
twice as many green marbles as red. The label on the
bag says it contains a total of 84 marbles.
How many green marbles are in the bag? Write a
system of equations for this problem. Then solve the
problem using any method you like. Be sure to check
your solution
Answers
Answer:
56
Step-by-step explanation:
(84÷3) · 2 = x
28 · 2 = 56
Hope that helps!
The sixth-grade art students are making a mosaic using tiles in the shape of right triangles. each tile has leg measures of 5 cm and 6 cm. if there are
150 tiles in the mosaic, what is the area of the mosaic?
a 10 cm2
b 2250 cm 2
c 165 cm2
d 4500 cm2
Answers
Answer:
Below in bold.
Step-by-step explanation:
The area of each triangle = 1/2 * height * base
As it is a right triangle the height is equal to one of its sides, so
Area of 1 triangle = 1/2 * 6 * 5
= 15 cm^2
Area of mosaic = 150 * 15
= 2250cm^2.
Can someone help me with this
Answers
Answer:
NO, but I know who can
Step-by-step explanation:
Solve 58 - 10x< 20 + 9x.
-
O A. x2
O B. Xs2
O c. xs-2
O D. x2-2
Answers
I am not sure what you are asking by the options provided as the formatting has been messed up, but if you simplify the given equation you end up with:
x > 2
Step-by-step explanation:
Given
58 - 10x< 20 + 9x
Add 10x to both sides of the equatoin
58 < 20 + 19x
Subtract 20 from both sides of the equatoin
38 < 19x
2 < x
x > 2
Cora watched 30 movies for a combined total of 55 hours over her last summer break. Some of the movies were 1.5 hours long, and others were 2.5 hours long.
How many of Cora's movies were 2.5 hours long?
Answers
The number of movies that are 2.5 hours long that Cora watched is 10 hours.
What are the linear equations that represent this question?a + b = 30 equation 1
1.5a + 2.5b = 55 equation 2
Where:
a = movies that are 1.5 hours long
b = movies that are 2.5 hours long
How many movies are 2.5 hours long?Multiply equation 1 by 1.5
1.5a + 1.5b = 45 equation 3
Subtract equation 3 from 2
1b = 10 hours
To learn more about simultaneous equations, please check: https://brainly.com/question/25875552
Nil and Ethan are brothers. They left their home at the same time and drove to the same beach. Nil drove at a speed of 30 miles per hour. Ethan drove at a speed of 20 miles per hour. Nil arrived at the beach 0.5 hour earlier than Ethan. What is the distance between their home and the beach?
Answers
Answer:
10 miles
Step-by-step explanation:
Ethan drove at a speed of 20 miles per hour. Nil arrived at the beach 0.5 hour earlier than Ethan. What is the distance between their home and the beach? Every hour, Nil gets ahead of Ethan 30 - 20 = 10 miles.
If a coin is flipped 5 times and heads comes up 2 times, what is the relative frequency of heads coming up?
Answers
Answer:
0.40 is your answer
Step-by-step explanation:
0 .40 is your answer
Below are two parallel lines with a third line intersecting them.
(Please help T-T)
Answers
Answer:
x = 136
Step-by-step explanation:
44 + x = 180
x = 180 - 44
x = 136
Evaluate the function for the given value of x.
Answers
Answer:
f(-6)= -41 923
Step-by-step explanation:
f(-6)= -( -6)⁶ +5(-6)⁴+8(-6)³+2(-6) -7 you substitute x with -6 the you use a calculator which will then give you - 41923
3x+2x+6v-9g+hd+2v-1g
Answers
Answer:
5x+8x-10g+hd
Step-by-step explanation:
please mark me as brainlest
Hey there!
3x + 2x + 6v - 9g + hd + 2v - 1g
= 3x + 2x + 6v - 9g + 1hd + 2v - 1g
COMBINE the LIKE TERMS
= (3x + 2x) + (6v + 2v) - (9g - 1g) + (1hd)
= 3x + 2x + 6v + 2v - 9g - 1g + 1hd
= 5x + 7v - 10g + 1hd
= 5x + 7v - 10g + hd
= hd - 10g + 8v + 5x
Therefore, your answer is:
hd - 10g + 8v + 5x
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Can someone please help??? I can’t figure this out. Pleaseeee
Answers
Answer:
120°=1
Step-by-step explanation:
step 1 do 2/1
step 2 cut braket and ans will be 53
Concrete truck loaded with concrete was about 30 tons about how many pounds does the loaded concrete truck weigh
Answers
Answer:
30 tons of concrete
There are 2000 pounds in 1 ton
So 2000 pounds * 30 tons
30 * 2000 = 60000
60,000 pounds
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
In the equation n+5 - n- 10 = 1the value of n is
Answers
Answer:
No Solution
Step-by-step explanation:
If you grouped like terms, you would get [tex]n+(-n)+5-10=1[/tex]
Both n's would cancel each other out.
I hope this helps! (If it's wrong, then tell me, I'll try to find the correct answer...)
Joel has 24 sports trophies. Of the trophies 1/8 are soccer trophies. How many soccer does Joel have ?
Answers
Answer:
We are given that Joel has 24 sports trophies, of the 24 trophies there are 1/8 soccer trophies.
1/8 of 24 is 3.
24 divided by 8 = 3 soccer trophies
There are 3 soccer trophies all the rest of the trophies, which is 21 trophies, will be other sports. 21 trophies + 3 soccer trophies = 24 trophies in total
Step-by-step explanation:
Have a great rest of your day
#TheWizzer
Solve the system of equations below. Thankyou!
Answers
Answer:
x = - 9
y = 5
Step-by-step explanation:
EQ1 + EQ2
Substitute the value of X in either EQ1 or EQ2
7y-2x=53..........eqn 2
Add both eqns
-6x=54
x=54/-6
x=-9
Sub for x in eqn 1
-7y-4(-9)=1
-7y+36=1
-7y=1-36
-7y=-35
y=-35/-7
y=5
:x=-9 and y=5
A manager drew this box-and-whisker plot to represent the number of minutes each of the company's 360 employees took on their break.
How many employees took a break that lasted between 37 and 41 minutes?
Select from the drop-down menu to correctly complete the statement.
Answers
Given the box-and-whisker plot, the number of employees that took a break that lasted between 37 - 41 minutes is: 180.
What is a Box-and-whisker Plot?A box-and-whisker plot is a graphical representation of a data set showing how the data set is distributed into percentiles such as 25%, 50%, and 75%.
The range of the rectangular box covers 50% of the data set.
Thus, 37 - 41 minutes lies between 50% on the box-and-whisker plot, therefore:
50/100 × 360 = 180 employees.
In summary, given the box-and-whisker plot, the number of employees that took a break that lasted between 37 - 41 minutes is: 180.
Learn more about box-and-whisker plot on:
https://brainly.com/question/3473797
Answer:
The answer is 90
Step-by-step explanation:
Its not 180 I take k12 also.
ILL GIVE BRAINLIST THING IF YOU HELP PLEASE QUICK
Answers
Answer:
B and C are wrong
B: 7.89 x 10^-4
C: 3.15 x 10^2
Step-by-step explanation:
B is not written correctly. The purpose of scientific notation is to get rid of the decimal places with 0s. So instead of 0.789, it should be 7.89 x 10^-4
C is wrong, it should be 3.15 x 10^2
How many solutions are there for the quadratic equation?
Y=x^2+12x+36
Show work
Answers
Answer:
1 solution
x = -6Explanation:
[tex]\rightarrow \sf y=x^2+12x+36[/tex]
[tex]\rightarrow \sf x^2+12x+36=0[/tex]
[tex]\rightarrow \sf x^2+6x+6x+36=0[/tex]
[tex]\rightarrow \sf x(x+6)+6(x+6)=0[/tex]
[tex]\rightarrow \sf (x+6)(x+6)=0[/tex]
[tex]\rightarrow \sf x=-6[/tex]
Hence there is only one solution for this quadratic equation and the value is -6
[tex]\\ \rm\rightarrowtail x^2+12x+36=0[/tex]
[tex]\\ \rm\rightarrowtail x^2+6x+6x+36=0[/tex]
[tex]\\ \rm\rightarrowtail (x+6)(x+6)=0[/tex]
Only one solution present
x=-6
In this figure, ∠1 and ∠2 are located on a line.
Let m∠1=x° and m∠2=(45x)°.
What is the value of x?
Enter your answer in the box.
Answers
Answer:
Your answer would be 100
Step-by-step explanation:
4/5 of 100 is 80, 100 and 80 add up to 180, which makes it a supplementary angle, we know it is a supplementary angle because the figure has a line, so x = 100
a shopkeeper selling an article at discount of 20% looses rs 400 if he allow 10% discount he gains rs 200 find the marked price and the cost price of the article
Answers
Answer:700
Step-by-step explanation:
Let the M.P of the article be x .
A discount of 20% was given on the M.P .
So the selling price of the article ( S.P ) will be M.P - Discount .
Discount = 20 % of x
⇒ Discount = 20/100 of x
⇒ Discount = 1/5 × x
⇒ Discount = x/5
Now S.P = M.P - Discount .
⇒ S.P = x - x/5
⇒ S.P = ( 5 x - x ) / 5
⇒ S.P = 4 x / 5
The shopkeeper loses Rs 200 .
Loss = C.P - S.P
⇒ C.P = Loss + S.P
⇒ C.P = 200 + 4 x / 5
⇒ C.P = ( 1000 + 4 x )/5
Now if he allows 10 % discount then the gain is Rs 150 .
Gain = S.P - C.P
⇒ S.P = Gain + C.P
⇒ S.P = 150 + ( 1000 + 4 x )/5
⇒ S.P = ( 750 + 1000 + 4 x )/5
⇒ S.P = ( 1750 + 4 x )/5
Discount = 10 % of x .
⇒ Discount = 10/100 × x
⇒ Discount = x/10
S.P = M.P - Discount
⇒ ( 1750 + 4 x )/5 = x - x/10
⇒ ( 1750 + 4 x )/5 = 9 x / 10
⇒ 1750 + 4 x = 9 x / 2
⇒ 3500 + 4 x = 9 x
⇒ 9 x - 4 x = 3500
⇒ 5 x = 3500
⇒ x = 3500/5
⇒ x = 700
Select the correct answer.
which function is continuous across its domain?
Answers
Answer:
B
Step-by-step explanation:
A small bag of chips contains 0.3 of a cup of sugar. if a large bag of chips is the same as 6.4 small bags, how much sugar does a large bag contain?