Answers
The exponential function formula for the parent function is found to be
[tex]f(x) = 2^x[/tex]
What is an exponential function?
The formula for an exponential function is [tex]f(x) = a^x[/tex], where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.
The general formula to find an exponential function is [tex]f(x) = ab^x[/tex]
From the given graph, we take two points on the graph : (1,2) and (2,4)
Substituting in the above equation, taking f(x) as y
[tex]ab^1 = 2\\\\ab^2 = 4[/tex]
Solving the above equations, we get
a= 1, b=2
So the parent function [tex]f(x) = 2^x[/tex].
Now using this function we can graph [tex]f(2x), -3f(x), 2f(2x)\\[/tex].
[tex]f(2x) = 2^{2x} = 4^x\\\\-3f(x) = -3 * 2^x\\2f(2x) = 2 * 4^x[/tex]
Therefore using the Desmos, the above exponential functions are graphed.
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Related Questions
PLEASE HELPPP I TOLD MY MOM I WOULD BE DONW ITH THIS CLASS TODAY SO SHE WOULDNT YELL AT ME BUT I HAVE 54 ASSIGNMENTS
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*ps the ^ means it’s a exponent
Hope I helped <3 sorry if I was wrong :(
50 PTS 50 PTS 50 PTS help.
Answers
Answer:
x = 90
Step-by-step explanation:
The diagram shows that angles 1 and 4 correspond with each other. Given that the two lines should be parallel, corresponding angles have the same answer. When corresponding angles cross at the same relative location (known as the junction), they will have the same angle measure.
So, set the 1st and 4th angles equal to each other.
3x-160 = x+20
2x = 180
x=90
Answer:x=90
Step-by-step explanation:Angles 1 and 4 must be equal to each other, as they are corresponding angles, so you set 3x-160 equal to x+20 and after solving, you get x is equal to 90.
What is the median of the distinct positive values of all of the fractions less than or equal to 1 with positive integer denominators less than or equal to 5
Answers
The median of the distinct positive values of all of the fractions less then or equal to 1 with positive integer denominators less than or equal to 5 is 11/20.
In the statistics, the median is the value in the middle of a data set. It means that 50% of data points have a value smaller or equal to the median and 50% of data points have a value higher or equal to the median. The middle number is found by ordering all data points and picking out the one in the middle or if there are two middle numbers, taking the mean of those two numbers. We have to arrange data values from lowest to highest value. The median is the data value in the middle of the set. If there are 2 data values in the middle the median is the mean of those 2 values.
The set of numbers are,
1 /5, 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 1
we have to take the average of middle two .
The middle of the set are 1/2 and 3/5. and the average of these two is 11/20.
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Claudius buys 6-cent plastic cups and spend a total of 3.60. He set the equation to help him determine the number of cups he bought. What is the value of c in claudius’s equation
Answers
Answer:
o
Step-by-step explanation:
Which value of b makes the equation b/4 =12 true? a. 48 b. 16 c. 9 d. 3
help please i have 4 mins to finish ;((
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The correct option is (a) 48.
In algebra, an equation is a statement of equality between two expressions. These expressions can be numbers, variables, or a combination of both.
In the equation:
b/4 = 12, the variable b is on one side of the equation and the value 12 is on the other side.
To find the value of b that makes the equation true, we need to isolate the variable b on one side of the equation.
In this case, we can do this by multiplying both sides of the equation by 4.
This cancels out the denominator of the fraction on the left side, and we get,
b = 12*4= 48.
This means that when b is equal to 48, the equation b/4 = 12 is true.
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How many blocks with dimensions of One-third times 1 times 1 can fit in a unit cube?
A block has a length of one-third, height of 1, and width of 1.
2
3
6
9
Answers
Answer: 3
Step-by-step explanation:
Given
The dimension of the small block is
[tex]\dfrac{1}{3}\times 1\times 1[/tex]
The Volume of the cube having unit length is
[tex]V=1\times 1\times 1\\V=1\ unit^3[/tex]
The number of blocks that can be in the unit cube is the division of the volume of the unit cube and block.
[tex]\Rightarrow \dfrac{1\times 1\times 1}{\dfrac{1}{3}\times 1\times 1}\\\\\Rightarrow \dfrac{3}{1}=3[/tex]
Answer:3
Step-by-step explanation:
Hey i know this question is linked to Pythagorean theorem but i am still confused. So, please help me if you can ❤️
Answers
Step-by-step explanation:
From Pythagorean theorem, one of the sides can be determined as x^2 + y^2 =8^2
or y = (8^2 - x^2)^(1/2)
we can write the perimeter P as
P = 2x + 2y ---> 20 = 2x + 2(8^2 - x^2)^(1/2)
Dividing by 2, we get
10 = x + (8^2 - x^2)^(1/2)
Move the x to the other side,
10 - x = (8^2 - x^2)^(1/2)
Take the square of both sides to get rid of the radical sign:
(10 - x)^2 = 8^2 - x^2
Move everything to the left and expand the quantity inside the parenthesis:
x^2 + (100 - 20x + x^2) - 64 = 0
2x^2 - 20x + 64 = 0
or
x^2 - 10x + 32 = 0
Now we can see that a = -10 and b = 32
Answer:
a = -10, b = 18
Step-by-step explanation:
The Pythagorean Theorem is, indeed, involved. Use it to find an expression (you won't get a number!) for the height of the rectangle.
Using the right triangle, one leg has length x and hypotenuse length 8. for a moment, label the height h. Then
[tex]x^2+h^2=8^3\\\\h^2=64-x^2\\\\h=\sqrt{64-x^2}[/tex]
This expression tells the height of the rectangle, so it is the length of the two vertical sides. The top and bottom sides each have length x.
Perimeter = 20 says that the total length of all the sides is 20. Set that up and do a heap of algebra!
[tex]x+x+\sqrt{64-x^2}+\sqrt{64-x^2}=20\\\\2x+2\sqrt{64-x^2}=20[/tex]
Divide by 2 (to simplify a bit).
[tex]x +\sqrt{64-x^2}=10[/tex]
Subtract x to get the square root by itself (you'll see why in the next step).
[tex]\sqrt{64-x^2}=10-x[/tex]
Square both sides of the equation.
[tex](\sqrt{64-x^2})^2=(10-x)^2\\\\\\64-x^2=100-20x+x^2\\\\64=100-20x+2x^2\\\\0=36-20x+2x^2[/tex]
Divide by 2 again (because you can)
[tex]0=18-10x+x^2[/tex]
Rearrange terms to match the order in the question.
[tex]x^2-10x+18=0[/tex]
The coefficient of x is a = -10. The constant is b = 18.
Simplify 14/15+11/15+1 1/15
last fraction is one one by fifteen mixed fraction
pleas answer
Answers
Answer: 2 11/15
Used this app called Cymath.
The population of a city is 5876000 in 1980. By 1990 it increased by 10.8%. In the 1990s it increased a further 4.7%. What was the population in the year 2000?
Answers
Answer: I think it's 6816606.576
Step-by-step explanation: Hope this helps?
Q1. In the given figure, ABCD is a parallelogram. Complete each statement along with the definition or property used.
(i) AD = ……….. (ii) DC = ……….. (iii) ∠DCB = ………..
(iv) ∠ADC = ……….. (v) ∠DAB = ……….. (vi) OC = ………..
(vii) OB = ……….. (viii) m∠DAB + m∠CDA = ………..
Answers
Step-by-step explanation:
i. AD = BC= 6cm (each two opposite sides are equal in length in parallelogram)
ii.DC=AB=9cm (each two opposite sides are equal in length in parallelogram)
iii.DCB=60 ,, bec DC and AB are parallel so their interior angles are supplementary their sum equals 180°
so DCB = 180-120=60°
iv.ADC=ABC = 120° because each two opposite angles are equal in measure in parallelogram
v. DAB=DCB =60° because each two opposite angles are equal in measure in parallelogram
vi. OC=AO =7cm because the diagonals of parallelogram bisect each other
vii. OB=DO=5cm because the diagonals of parallelogram bisect each other
viii . DAB=60° ,, CDA= 120 °
DAB+CDA =180°
or you could simply say that because DC and AB are parallel their interior angles are supplementary their sum is 180°
A student constructs a regular square pyramid with a base that has sides of 13. 2 cm and a
slant height of 6 cm. Find the surface area of the pyramid. Find the surface are of the pyramid
Answers
The surface area of a regular square pyramid is 332.64 square cm
We know that the surface area of pyramid is nothing but the sum of the areas of its lateral faces and its base.
surface area of pyramid
= areas of lateral faces of pyramid + area of base of pyramid
We know that the formula for the lateral surface area of regular pyramid is:
A = ½ × P × l
where P is the perimeter of the base and l is slant height
Here, a base of regular square pyramid with has sides of 13. 2 cm
a = 13.2 cm and slant height of 6 cm i.e., l = 6 cm
Using the formula of area of square, the base area of pyramid would be,
B = (13.2)²
B = 174.24 sq.cm.
the perimeter of base is:
P = 4 × 13.2
P = 52.8 cm
So, using the above formula of lateral surface area of pyramid the lateral surface area would be
A1 = 1/2 × 52.8 × 6
A1 = 158.4 sq. cm.
So, the surface area of the pyramid is:
A = A1 + B
A = 158.4 + 174.24
A = 332.64 square cm
Therefore, the surface area of the pyramid = 332.64 square cm
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One leg of triangle is 7 inches longer than the other leg. The hypotenuse is 8 inches longer than the shorter leg. The perimeter of the triangle is
Answers
Answer:
5 ; 12 ; 13
Step-by-step explanation:
Let :
Shorter leg = x
Other leg = x + 7
Hypotenus = x + 8
Recall:
Hypotenus² = opposite² + adjacent²
(x+8)² = x² + (x+7)²
x² + 16x + 64 = x² + x² + 14x + 49
x² - 2x - 15 = 0
x² - 5x + 3x - 15 = 0
x(x - 5) +3(x - 5) = 0
(x + 3) = 0 ; x = - 3
(x - 5) = 0 ; x = 5
Side can't be negative ;
Hence,
x = shorter side = 5
Other side = x + 7 = 5 + 7 = 12
Hypotenus = x + 8 = 5 + 8 = 13
You have to pay 25% income tax on all of the money you make. If you made $3000 this month, how much did you have to pay in taxes this month?
Please answer ASAP! :{
You get 20 points! :)
Answers
Answer: 750
Step-by-step explanation:
3000/4= 750
750
rewrite in y=mx+b form and show ur work 2x+y=3x-7
Answers
Write an exponential function to represent the spread of Ben's social media post. Write an exponential function to represent the spread of Carter's social media post
Answers
So, y = ab^x and y = ac^x are the exponential functions to represent the spread of Ben's and Carter's social media posts respectively.
An exponential function has the form y = ab^x, where a and b are constants and x is the independent variable (in this case, time).
For Ben's social media posts:
y = ab^x
For Carter's social media post:
y = ac^x
Please note that the value of a, b, and c will be different for Ben and Carter's post, as it will depend on the number of shares, likes, views, etc., and the rate of spread of the post.
This is an exponential function that represents the spread of Ben's social media posts and Carter's social media post.
Complete Question:
1. Write an exponential function to represent the spread of Ben's social media post 2. Write an exponential function to represent the spread of Carter's social media post. 3. Graph each function using at least three points for each curve. All graphs should be placed together on the same coordinate plane, so be sure to label each curve. You may graph your equation by hand on a piece of paper and scan your work, or you may use graphing technology. 4. Using the functions for each student, predict how many shares each student's post will be received on Day 3 and then on Day 10. Justify your answers 5. If Amber decides to mail copies of her photo to the 45 residents of her grandmother's assisted living facility, the new function representing her photo shares is . How does this graph compare with the original graph of Amber's photo share? 6. Based on your results, which students' post travels the fastest? How is this shown in the equation form of the functions? 7. If you had to choose, would you prefer a post with fewer friends initially but more shares, like Amber, or more friends initially but fewer shares? Justify your answer with your calculations from previous questions
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when you roll a pair of dice, what is the probability that your roll an even number or a 3?
a. 16.66%
b. 2/3
c. 1/2
d. 0.66?
Answers
Answer:
yv1dzybazu ai zai is zie
Step-by-step explanation:
side zue auebaiw ai was wiz
A 15-foot ladder is leaning against a building so that the top of the ladder is at a height of 12 feet.
building
Answers
Answer:
12
Step-by-step explanation:
Answer:12
feet
Step-by-step explanation:
Jeremias invested $20 at a rate of 8.5% compounded continuously. How long would it take to triple his money?
It will take _______ years
Answers
Answer:
13Step-by-step explanation:
Use formula for continuous interest:
A = [tex]Pe^{rt}[/tex], where r- interest rate, t- time in yearsIf A = 3P, and r = 0.085 then the equation is:
[tex]3P = Pe^{0.085t}[/tex][tex]3 = e^{0.085t}[/tex]ln 3 = 0.085t1.099 = 0.085tt = 1.099 / 0.085t = 12.9 ≈ 13 yearsThe formula for compounded continuously is A = Pe^rt where A if the final amount, P is the initial value, r is the rate and t is the length of time.
E is the constant for continuous interest.
Using the information from the problem $20 tripled would be 20x3 = $60
Now you have 60 = 20e^0.085(t)
We need to solve for t:
Divide both sides by 20:
e^0.085(t) =3
Apply the exponent rule:
0.085(t) = ln(3)
Solve for t:
T = ln(3)/0.085
T = 12.92 years. (Round off as needed)
cam someone please help me with this I don't know how it has to be reflection translation rotation pre image (By the way I said it out of order)
Answers
Answer:
it looks like a reflection or translation but my gut is saying translation
40 mi
9 mi
What is the length of the hypotenuse?
Answers
Answer:
[tex] = \sqrt{ {40}^{2} + {9}^{2} } \\ = \sqrt{1681} \\ = 41 \: mi[/tex]
Is her hair really that long... Possibly a brainly help me understand scientific notation better <3
Answers
Answer: 1 x 10^3
Step-by-step explanation:
1. Convert 9% into a decimal.
Answers
Hope this helped :))
What is the value of 3 in tan?
Answers
The value of tan 3° is 0.0524.
tangent is the trigonometric ratio.
we can find out the value of tangent by taking perpendicular of the triangle divided by base of the triangle.
tan Q = perpendicular of the triangle /base of the triangle.
sine theta divided by cos theta gives the value of tan theta.
tan Q = sin Q/ cos Q.
some formula of the tan Q are as follows,
1- tan Q = sin Q/cos Q
2- tan Q= 1 /cot Q
3-tan^2 Q =sec^2 Q -1
4- tan(90 - Q)=cot Q
5- tan (Q+π) = tan Q
6- tan (π-Q) = -tan Q
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A shoe company takes a random sample of 400 customers who visited their website last month and found that 275 of them actually purchased shoes. Determine the lower limit of a 95% confidence interval (z = 1.96) for the proportion of those people that will purchase shoes if they visit the website. Round the answer to 4 decimal places.
Answers
Answer:
0.6420758
Step-by-step explanation:
x = 275 ; n = 400
Phat = x / n = 275 / 400 = 0.6875
Z at 95% = 1.96
Confidence interval = phat ± margin of error
Margin of Error :
Z * √phat(1 - phat) / n
1.96 * √0.6875(0.3125) / 400
1.96 * 0.0231756
= 0.0454242
Lower boundary :
Phat - margin of error
0.6875 - 0.0454242
= 0.6420758
heyy! i’ll give brainliest please help.
Answers
Answer:
the city at a lower altitude would have a colder climate
helppp me plss its due tonight!!
Answers
Answer:
B.
Step-by-step explanation:
see photo above to anwser
Answers
Answer:
i can see
Step-by-step explanation:
UKDIAMOND is a great place for the people of sentence to get it 4out in a sense that you are a very
Answer:
b = 99°
Step-by-step explanation:
XY is a line segment and so it is a straight line which means that it is a straight angle - 180°
a = 28°
c = 53°
b = ?
=> a + b + c = 180°
=> 28° + b + 53° = 180°
=> b = 180° - (53 + 28)°
=> b = 180° - 81°
=> b = 99°
Therefore b = 99°
Hope it helps :)
Solve the following quadratic equation, leaving your answer in exact form:
2e²-8e +7= 0
Pls can anyone help it would rrly help out
Answers
Answer:
The two answers would be 0 and ln (7)
Step-by-step explanation:
Hope it helps:)
Find the difference of (6x2 + 3x – 5) and (4x² – 2x + 3).
Answers
Answer:
2x^2 + 5x - 8
Step-by-step explanation:
6x^2 + 3x - 5
- (4x^2 - 2x + 3)
--------------------------
2x^2 + 5x - 8
If the radius of a circle is 2 yards, what is the circles area?
Answers
Answer:
12.56 yards
Area of Triangle: [tex]\pi r^2[/tex]
So, [tex]\pi[/tex][tex]2^2[/tex]
Finally, 3.14*4 = 12.56
Step-by-step explanation: