Answers
Answer:
\(y=4^{x+1}.\)
Step-by-step explanation:
1. property of the exponential function [f(x)=a×] is: f(0)=1. If according to the data in the table f(0)=4, then the view of the required equation is
\(f(x)=a^{x+b}, \ where \ b-integer.\)
2. if according to the data in the table the values of 'y' are 4; 16; 64; 256, then the '4' is in the base of the exponential function.
3. finally, the step between 4,16,64 and 256 is 1, then the unknown integer 'b' is '1', and the required equation of the function is
\(y=4^{x+1};\)
Related Questions
Find the slope of the line that passes through (97, 21) and (54, -17).
Answers
Given data:
The first point given is (97, 21).
The second point given is (54, -17).
The slope of the line passing through the given points is,
m=(-17-21)/(54-97)
=-38/-43
=38/43
Thus, the slope of the line passing through the given points is 38/43.
Complete the equation of the line through (3, -8) and (6, -4).
Use exact numbers.
y =
Answers
Step by step
First we find slope by using formula
y2 - y1 over x2 - x1
Points (3, -8) and (6, -4)
-4 - -8 over 6 - 3
4 over 3 = 4/3 slope
Now we find our equation with point slope formula
y - y1 = m (x - x1)
Using points (6, -4)
y - -4 = 4/3 (x - 6)
Distribute
y + 4 = 4/3x - 8
subtract 4 from each side to isolate y
y + 4 -4 = 4/3x -8 -4
y = 4/3x -12
How much will a person pay for 8.2 pounds of bananas at a price of $2.46 per pound?
Answers
Answer:
$19.99
Step-by-step explanation:
1 lb = 16 oz
8.2 lb = (16 x 8) +2= 130
\(\frac{16}{2.46} =\frac{1}{x}\) ---> x = $0.154 per oz
0.154 x 130 = $19.99
Part IOnce you have constructed the parabola, use GeoGebra to display its equation. In the space below, rearrange the equation of the parabola shown in GeoGebra, and check whether it matches the equation in the vertex form that you wrote in part G. Show your work.How do I rearrange the equation?Here's the equation: y = 1/12 ( x - 6 )^2 +1
Answers
Given
\(1.33x^2-16x-16y=-64\)Transform it into its vertex form as shown below
\(\begin{gathered} \Rightarrow16y=1.33x^2-16x+64 \\ \Rightarrow y=\frac{1.33}{16}x^2-x+4 \end{gathered}\)Complete the square on the right side of the equation,
\(\begin{gathered} \\ \\ Set\text{ }b\text{ the term that completes the square} \\ \\ \\ \Rightarrow ax^2-2abx+ab^2=\frac{1.33x^2}{16}-x+c \end{gathered}\)\(\begin{gathered} \Rightarrow a=\frac{1.33}{16} \\ -2abx=-x \\ \Rightarrow2ab=1 \\ \Rightarrow b=\frac{1}{2a} \\ \Rightarrow b=\frac{16}{2*1.33} \end{gathered}\)Therefore,
\(\begin{gathered} \Rightarrow y=\frac{1.33}{16}x^2-x+4=\frac{1.33}{16}(x-\frac{8}{1.33})^2-(\frac{8}{1.33})^2+4 \\ \Rightarrow y=\frac{1.33}{16}(x-\frac{8}{1.33})^2-((\frac{8}{1.33})^2-4) \end{gathered}\)Thus, the obtained equation does not match the equation found in part G.However, consider that the leading coefficient is 1.33=1/3
Then, the given expression becomes
\(\begin{gathered} \frac{1}{3}x^2-16x-16y=-64 \\ \end{gathered}\)By the same token,
\(\begin{gathered} \Rightarrow y=\frac{1}{48}x^2-x+4 \\ \end{gathered}\)Completing the square,
\(\frac{1}{48}(x^2-48x)+4=\frac{1}{48}(x-24)^2-8\)\(\)There are 100 students enrolled in our school. 3/5 of the students are boys. How many students are girls?
Answers
Answer:
2/5 are girls so 40
Step-by-step explanation:
100 divided by 5 is 20.
BOYS: 20 x 3= 60
GIRLS: 20 x 2= 40
60+40=100
Hope this helps (:
I need help ASAP!!!!!! Plzzzzzzzzzzz!!!!!!
Answers
Answer:
The second graph, the extreme v
Step-by-step explanation:
We know that y=4x passes through 4 on 1. When absolute valued, we add the graph y=-4x. This gives us the graph second to the right.
By the way, can you follow me?
Thanks
Find a value of Z such that .6318 of the area lies between negative Z and Z.
Answers
The required value of z such that 0.6318 of the area lies between −z and z is 0.89.
If 0.6318 of the area lies between −z and z, then the area outside of this range is (1-0.6318) = 0.3682.
Since the normal distribution is symmetric, the area to the left of −z is equal to the area to the right of z. So, the area to the right of z is (0.3682 / 2) = 0.1841.
Using a standard normal distribution table, we can find the z-score corresponding to an area of 0.1841 to the right of z:
z = invNorm(0.1841) ≈ 0.89
Learn more about z-score here:
https://brainly.com/question/15016913
#SPJ1
please i’ll fail if i don’t get this right. please i’ll give brainlyist The current temperature of 15°F below zero is 18°F below the high temperature of the day. What is the high temperature for the
day?
OA. 5°F
ов. 33°F
OC. 3°F
OD. 33°F
Answers
Answer:
I think its C
Step-by-step explanation:
c. If Biff is rational, and has no intention of winning the hot dog eating contest, what is the optimal number of hot dogs he will eat
Answers
Answer:
8 units of Hot dog
Step-by-step explanation:
Total utility refers to the utility in which the is satisfaction after consuming the multiple units from a good or a service
As we can see from the attached figure that at the number of 8 hot dogs the total utility is maximum i.e 55
Therefore in the given case, the optimal number of hot dogs he will eat is 8 as at this point the total utility is more as compared to the other utilities
What is the answer 2/4
Answers
Answer:
1/2
Step-by-step explanation:
Divide the numerator and denominator by their common factor, to simplify in this case the common factor is 2.
2/4
1/2
Find AC, round to the nearest whole number
Answers
20
Triangles are 180 total so just add 118 and 22 then subtract it from 180 for your answer
#1 (7.6)
ABXC is a right triangle where mzXBC-90°, mzCXB-60°, and XB-5. Determine the length
of each side. Leave your answer as an exact answer.
1. Draw the triangle and label the given parts
2. Identify side types:
30-60-90 has hypotenuse, short, long
45-45-90 has hypotenuse, leg, leg
3. Write the formulas for the special right triangle. Plug in your values and solve.
To enter a square root answer, type the number outside and the number inside using the two
boxes provided. For example, 7√2 would look like 7
Length
Side
CB (long)
XB (hypotenuse)
Answers
The the length of each side of the triangle are: 5 units, 8.7 units and 10 units respective
What is a triangle?A triangle is a polygon with three sides, three angles, three vertices and sum of angles equal to 180 degrees
From the triangle, Using the trigonometric ratio of sine
Sin C = opposite/Hypothenuse
Sin30 = 5/H
Making h the subject of the relation we have
h= 5/sin30
h=5/0.5
Therefore the value of h=10 units
To find the third side use Pythagoras theorem
10² = 5²+p²
100-25 = p²
75 = p²
Taking the square of both sides
p=√75
p=8.7 units
Learn more about triangles on https://brainly.com/question/2773823
#SPJ1
Convert 25 to base 8
Answers
Remain =
25_(8*3)=1
Second devise 3/8 rem =3
Answer is (31 )base 8
HELP PLEASE AND HURRYY
Answers
Answer:
Part A: Answer: D.
Part B:
true
false
true
Step-by-step explanation:
Part A:
Use a tree.
Round 1 Round 2 Round 3
W W W
W W L
W L W
W L L
L W W
L W L
L L W
L L L
All possibilities are:
WWW, WWL, WLW, WLL, LWW, LWL, LLW, LLL
Answer: d.
Part B:
Winning 3 games is WWW.
WWW, WWL, WLW, WLL, LWW, LWL, LLW, LLL
Out of the 8 possible outcomes shown above, only 1 of them is WWW.
p(WWW) = 1/8
Answer: true
Winning exactly 2 games happens when there are exactly 2 W's:
WWW, WWL, WLW, WLL, LWW, LWL, LLW, LLL
p(exactly 2 wins) = 3/8
Answer: false
Wining at least 2 games means winning exactly 2 or exactly 3 times.
WWW, WWL, WLW, WLL, LWW, LWL, LLW, LLL
p(winning at least 2 games) = 4/8 = 1/2
Answer: true
You invested $1,000 in a savings account at the end of 7th grade. The account pays 5% annual interest. How much money will be in the account after 6 years? Round to the nearest hundredth. * 1 point
Answers
Step-by-step explanation:
1000 x .05= 50.
1000 + 50= 1050
1050 x 6= 6300
Define same side interior
Answers
Answer:
two angles that are on the same side of the transversal and on the interior of (between) the two lines.
Step-by-step explanation:
{ first 6 square numbers}
Answers
Answer:
{ 1, 4, 9 , 16 , 25, 36}
Step-by-step explanation:
hope that will help you
2. MATH!! I DO NOT KNOW IT!
Answers
Answer:
2) Quadrant IIis the right answer.
A rectangular prism has a width of x2 inches and a length of xy2 inches and a height of xy inches.
Which expression represents the volume of the rectangular prism in cubic inches?
2x^2y^2
2xy^3 + 2x^2y
2x^4y^3
x^3y^2
Answers
In this case, the width is x^2 inches, the length is xy^2 inches, and the height is xy inches.
Substituting these values into the formula, we get:
V = (xy^2)(x^2)(xy)
Simplifying, we get:
V = x^4y^3
Therefore, the expression that represents the volume of the rectangular prism in cubic inches is x^4y^3.
Recall that with base-ten blocks: 1 long 10 units, 1 flat 10 longs, and 1 block 10 flats. What is the fewest number of multibase blocks that can be used to represent the corresponding numeral in the given base?
a. 20 longs in base seven
b. 10 longs in base three
Answers
a. The answer is: The fewest number of multibase blocks required to represent 20 longs in base seven is 2 flats.
b. The answer is: The fewest number of multibase blocks required to represent 10 longs in base three is 3 flats and 1 unit.
a. To represent 20 longs in base seven, we need to find the fewest number of multibase blocks required.
In base seven, we have the following conversions:
1 long = 1 unit
1 flat = 10 units
1 block = 10 flats
To represent 20 longs, we can use 2 flats (each flat representing 10 units) and 0 units since there are no remaining units.
So, the fewest number of multibase blocks required would be 2 flats.
Therefore, the answer is: The fewest number of multibase blocks required to represent 20 longs in base seven is 2 flats.
b. To represent 10 longs in base three, we need to find the fewest number of multibase blocks required.
In base three, we have the following conversions:
1 long = 1 unit
1 flat = 3 units
1 block = 3 flats
To represent 10 longs, we can use 3 flats (each flat representing 3 units) and 1 unit since there is one remaining unit.
So, the fewest number of multibase blocks required would be 3 flats and 1 unit.
Therefore, the answer is: The fewest number of multibase blocks required to represent 10 longs in base three is 3 flats and 1 unit.
for such more question on fewest number
https://brainly.com/question/859564
#SPJ8
What would be the first step to solve this equation x - 5 (x-1) = x - (2x- 3 )
Answers
x−(5x−5)=x(2x−3)
Complete this sequence of numbers such that the difference between any two adjacent numbers is the same : 3/k, _, _, 9/2k.
Answers
The completed sequence is: 3/k, 3/k, 3/k, 9/2k.To complete the sequence of numbers with a constant difference between adjacent numbers, we can calculate the common difference by subtracting the first term from the second term.
Let's denote the missing terms as A and B.
The given sequence is: 3/k, A, B, 9/2k.
The common difference can be found by subtracting 3/k from A or B. Therefore:
A - 3/k = B - A = 9/2k - B.
To simplify, we can equate the two expressions for the common difference:
A - 3/k = 9/2k - B.
Next, we can solve for A and B using this equation.
Adding 3/k to both sides gives:
A = 3/k + 9/2k - B.
Now, we can substitute the value of A into the equation:
3/k + 9/2k - B - 3/k = 9/2k - B.
Simplifying further, we have:
9/2k - 3/k = 9/2k - B.
Cancelling out the common terms, we find:
-3/k = -B.
Multiplying both sides by -1, we get:
3/k = B.
For more such questions on Adjacent numbers:
https://brainly.com/question/28207765
#SPJ8
The equation 4(x-2)=100 is a true equation for a particular value of x.
Without solving, explain why 2(x-2)=50 is also true for the same value of
X. *
need this asap!!
Answers
Answer:
Yes because x=27
Step-by-step explanation:
4(x-27)=100
4(25)=100
100=100
and
2(27-2)=50
2(25)=50
50=50
4. For a spring break vacation, a student needs to spend $47 for gas, $311 for food, and $405 for a
hotel room. If the student takes $681.79 from savings, estimate how much more money is needed
for the vacation.
Answers
find all the cube roots of -8+8i(sqrt)3
Answers
Step-by-step explanation:
We need to find cube roots of
\( - 8 + 8i \sqrt{3} \)
Let put this into trig form.
\(r( \cos(x) + i \: sin(x)\)
To find the radius we do this formula,
\(r = \sqrt{ {a}^{2} + {b}^{2} } \)
where a is the real number and b is the coeffeicent of the imaginary term.
\(r = \sqrt{ - 8 {}^{2} + (8 \sqrt{3} ) {}^{2} } = \sqrt{64 + 192} = \sqrt{256} = 16\)
So our r value 16.
We need to find x, so we do this rule.
\( \tan(x) = \frac{b}{a} \)
\( \tan(x) = - \sqrt{3} \)
\((x) = \frac{2\pi}{3} \)
So our x is
\(x = \frac{2\pi}{3} \)
Now, we can simply our trig form,
\(16 ( \cos( \frac{2\pi}{3} ) + \sin( \frac{2\pi}{3} ) )\)
Now, we must find the cube roots of this.
This what we do,
Step 1: Take the cube root of 16., which is
\(2 \sqrt[3]{2} \)
Step 2: Divide the x values, which 2pi/3 by 3.
So now we get
\( \frac{ \frac{2\pi}{3} }{3} = \frac{2\pi}{9} \)
Step 3: Divide 2 pi by 3 and add that 2 times to 2pi/9.
\( \frac{2\pi}{9} + \frac{2\pi}{3} + \frac{2\pi}{3} = \frac{14\pi}{9} \)
So our cube root of this is
\( 2 \sqrt[3]{2} ( \cos \frac{14\pi}{9} + i \: sin \: \frac{14\pi}{9} ) \)
Solve the proportion:
5/X=12.5/20
A X=8
B X=9
C X=10
Answers
Answer:
A. X =8
Step-by-step explanation:
5/X=12.5/20
cross multiply
12.5X = 20*5
12.5X=100
X=100/12.5
X=8
determine f(2) for the function f(x)=4(3)^3+1
A. 36
B. 108
C. 432
D. 2916
Answers
Brainliest to correct!! Please help :)
Katie invested a total of $8,000, part at 3% simple interest and part at 4% simple interest. At the end of 1 year, the investments had earned $293 interest. How much was invested at each rate?
Katie invested $__ at a rate of 3% and $__ at a rate of 4%
Answers
Answers: 2700 and 5300 in that order
Katie invested $2700 at a rate of 3% and $5300 at a rate of 4%
===============================================================
Explanation:
x = amount invested at a rate of 3%y = amount invested at a rate of 4%Those two amounts must add to 8000 because this is how much she invests total. So x+y = 8000 is the first equation to set up.
The formula we'll be using is the simple interest formula, which is,
i = p*r*t
where p is the amount deposited or principal, r is the interest rate, and t is the number of years. Luckily, we don't have to worry about the time value t because t = 1 so it effectively goes away. We just need to worry about p and r.
The variable p will be tied directly to the values of x and y, as these are deposit amounts. The r values are decimal forms of the percentages (eg: 3% converts to 0.03)
In short, Katie will earn
0.03x dollars from the first account (3% account)0.04y dollars from the second account (4% account)In total, she earns 0.03x+0.04y dollars combined. This is set equal to 293 as this is the stated interest she earns over the entire year.
So another equation to set up is 0.03x+0.04y = 293
This only works for simple interest. Compound interest may likely be a different story.
----------------------------------------------------
To summarize so far, we found these two equations:
x+y = 80000.03x+0.04y = 293We have a number of options on how to solve this system. I'll use substitution.
Solve the first equation for y
x+y = 8000
y = 8000-x
Then we'll plug this into the other equation to solve for x like so,
0.03x+0.04y = 293
0.03x+0.04( y ) = 293
0.03x+0.04( 8000-x ) = 293
0.03x+0.04(8000)+0.04(-x) = 293
0.03x+320-0.04x = 293
-0.01x+320 = 293
-0.01x = 293-320
-0.01x = -27
x = -27/(-0.01)
x = 2700
This tells us that Katie invested $2700 at 3%
Use this x value to find y
y = 8000-x
y = 8000-2700
y = 5300
She also invested $5300 at 4%
----------------------------
As a quick check,
x+y = 2700+5300 = 8000so that works out
Also,
0.03*x = 0.03*2700 = 810.04*y = 0.04*5300 = 2120.03x+0.04y = 81+212 = 293which also works out. The answers are fully confirmed.
Cuánto le falta a 3/5para llegar a 9/10
Answers
Answer:
3/10
Step-by-step explanation:
3/5 se puede convertir en 6/10
(3x2)/(5x2).
9/10 - 6/10 = 3/10
le falta 3/10 para llegar a 9/10.
A radioactive isotope is decaying at a rate of 15% every hour. Currently there are 150 grams of the substance. Write an equation that will represent the number of grams present after n hours. How much will be left one day from now?A radioactive isotope is decaying at a rate of 15% every hour. Currently there are 150 grams of the substance. Write an equation that will represent the number of grams present after n hours. How much will be left one day from now?
Answers
Answer:
The equation that will represent the number of grams present after n hours is \(A(n) = 150(0.85)^n\)
3.035 grams will be left one day from now.
Step-by-step explanation:
Exponential equation for the amount of a substance:
The exponential equation for the amount of a substance is given by:
\(A(t) = A(0)(1-r)^t\)
In which A(0) is the initial amount and r is the decay rate, as a decimal, and t is the time period.
A radioactive isotope is decaying at a rate of 15% every hour.
This means that \(r = 0.15\)
Currently there are 150 grams of the substance.
This means that \(A(0) = 150\)
Write an equation that will represent the number of grams present after n hours.
\(A(n) = A(0)(1-r)^n\)
\(A(n) = 150(1-0.15)^n\)
\(A(n) = 150(0.85)^n\)
How much will be left one day from now?
One day is 24 hours, so this is A(24).
\(A(24) = 150(0.85)^{24} = 3.035\)
3.035 grams will be left one day from now.