Answer:
x = 2
Step-by-step explanation:
f(x) = x + 8
f(x) = 10
10 = x + 8
minus 8 from the both sides
10 - 8 = x
2 = x
x = 2
Hope this is right correct me if im wrong!!!
Exponential function is a function between the dependent variable and independent variable in which the constant change in the independent variable gives the same proportional change in the dependent variable.
a) y intercept of the function is 10/3. b) Equation defining function is,[tex]y=\dfrac{10}{3} \times 3^x[/tex]
Given information-
The exponential function [tex]f[/tex] takes the value 10 when,
[tex]x=1[/tex]
The exponential function [tex]f[/tex] takes the value 2 when,
[tex]x=2[/tex]
What is exponential function?Exponential function is a function between the dependent variable and independent variable in which the constant change in the independent variable gives the same proportional change in the dependent variable.
The general form of the exponential function,
[tex]y=ab^x[/tex]
Here [tex]a[/tex] is the y intercept of the function and exponent of independent variable [tex]x[/tex].
The exponential function [tex]f[/tex] takes the value 10 when the value of x is 1.
thus,
[tex]10=ab^1\\10=ab\\a=\dfrac{10}{b}[/tex]
Let the above equation as equation number 1.
The exponential function [tex]f[/tex] takes the value 2 when the value of x is 2,
[tex]30=ab^2\\30=ab^2\\a=\dfrac{30}{b^2}[/tex]
Compare the values of a,
[tex]\frac{10}{b} =\frac{30}{b^2}\\ b=\dfrac{30}{10}\\ b=3[/tex]
Put the value of b in equation 1,
[tex]a=\dfrac{10}{3}[/tex]
Thus the y intercept of the function is 10/3.
Put the values to find the equation,
[tex]y=\dfrac{10}{3} \times 3^x[/tex]
Hence,
a) y intercept of the function is 10/3. b) Equation defining function is,[tex]y=\dfrac{10}{3} \times 3^x[/tex]
Learn more about the exponential function here;
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Graycie and her 6 friends are using 293 beads to make bracelets. They share the beads evenly but some were left over. How many beads does Graycie get if she gets the extra beads for her bracelets? Group of answer choices
Answer:
47
Step-by-step explanation:
What is the domain of the function below? {(1,6), (2, 6), (3,7) plzzzzzzzz
Answer:
the domin{1,2,3}
the range{6,7}
and its a function
Step-by-step explanation:
Need help asap very confusing to me picture included
Answer:
I attached an image of the graph, and as you can see the function approaches 1 as x approaches infinity and negative infinity.
So, the correct answer is D.
Let me know if this helps!
Answer:
I believe that it would be D. The Function approaches as x approaches - inf and inf
Mackenzie invested $770 in an account paying an interest rate of 6.1% compounded
continuously. Assuming no deposits or withdrawals are made, how long would it
take, to the nearest year, for the value of the account to reach $1,830?
Answer:
14
Step-by-step explanation:
The value of the account will reach to $1,830 in 15 years.
What is compound interest?Compound interest simply means that the interest associated with a bank account, loan, or investment increases exponentially over time.
Given that, Mackenzie invested $770 in an account paying an interest rate of 6.1% compounded continuously after a certain period of time the mount becomes $1830
We know that,
[tex]A = P(1+r)^n[/tex]
Where, A = amount, P = principal, r = rate and n = time.
1830 = 770(1+0.061)ⁿ
1830 / 770 = (1.061)ⁿ
2.37 = (1.061)ⁿ
Taking log both side,
log(2.37) = n log(1.061)
n = log(2.37) / log(1.061)
n = 14.57 ≈ 15
Hence, the value of the account will reach to $1,830 in 15 years.
For more references on Compound interest, click;
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Jada walks up to a tank of water than can hold up to 10 gallons. When it is active, a drain empties water from the tank at a constant rate. When Jada first sees the tank, it contains 7 gallons of water. Three minutes later, the tank contains 5 gallons of water.
a. At what rate is the amount of water in the tank changing? Use a signed number, and include the unit of measurement in your answer.
b. How many more minutes will it take for the tank to drain completely? Explain or show your reasoning.
c. How many minutes before Jada arrived was the water tank completely full? Explain or show your reasoning.
Answer:
a. rate to empty the tank = - 2/3 gal/min
b, 7.5 min to empty the tank
c. 4.5 min.
Step-by-step explanation:
I use the formula that the work done = rate of work times the time working = W = rt
The work in this problem is emptying the tank.
a. The rate to empty the tank is -2 gal/3 min or - 2/3 gal/min
b. 5/(2/3) = 15/2 = 7.5 min to empty the tank
c. Since 3 gal. had already drained, 3/(2/3) = 9/2 = 4.5 min.
pic attached- if x^4 * x^a = x^16 and (x^2)^b = x^8, what is the product of a and b?
Answer:
c
Step-by-step explanation:
x^4 * x^(4) = x^16
(x^2)^(4)=x^8
^(4)*^(4)=16
Sally bought 4 chocolate bars and 8 lollipops and paid $8.00. Josh bought 3 chocolate bars and 10 lollipops and paid $7.00.
What is the cost of a lollipop? Enter your answer as a decimal
Answer:
Lollipops cost $0.25
Step-by-step explanation:
4C + 8L = $8.00
3C + 10L = $7.00. We need to cancel out chocolate bars
-12C - 24L = $-24.00 Mulitply by -3
12 C + 40L = $28.00 Muliply by 4 Next simplify
16L = $4.00 Divide both sides by 16
L = $0.25
WE CAN EVEN CHECK OUR WORK
4C + 8(0.25) = $8.00
4C = $6.00
C = 1.5
3(1.5) + 10(.25) = $7.00
4.5 + 2.5 = 7
If a cylindrical vase has a 63 cubic centimeter volume an a cone has the same height and radius as the cylinder what is the volume of the cone
Answer:
[tex]21cm^{3}[/tex]
Step-by-step explanation:
According to the problem, calculation of given data are as follows,
Volume of cylindrical vase = [tex]63cm^{3}[/tex]
As, Cone has same height and radius as cylinder, than we can calculate volume of cone by using following formula,
Volume of cone = [tex]\frac{1}{3}[/tex] × Volume of cylindrical vase
By putting the value, we get
Volume of cone = [tex]\frac{1}{3}[/tex] × 63
Volume of cone = [tex]21cm^{3}[/tex]
i need help to solve for x
Answer: 15°
Step-by-step explanation:
Can anyone help please with 6 and 7 I’m in desperate need of can someone help please and God bless
I NEED HELP ASAP!!
Combined like terms to simplify: 5m exp2 +16k + 13m exp2
Answer:
5m^2 + 16k + 13m^2
(5m^2+13m^2) + 16k
18m^2 + 16k
Let me know if this helps!
Help
Consider function f. F(x) = ^3square8x + 4
Answer:
[tex]f^{-1}(x)=\frac{1}{8}(x-4)^{3}[/tex]
Step-by-step explanation:
Given function is,
f(x) = [tex]\sqrt[3]{8x}+4[/tex]
To find the inverse of this function,
Rewrite the function as a equation,
y = [tex]\sqrt[3]{8x}+4[/tex]
Interchange x by y and y by x,
x = [tex]\sqrt[3]{8y}+4[/tex]
Now solve this equation for y,
x - 4 = [tex]\sqrt[3]{8y}[/tex]
(x - 4)³ = [tex](\sqrt[3]{8y})^3[/tex]
(x - 4)³ = 8y
y = [tex]\frac{1}{8}(x-4)^{3}[/tex]
Now convert the equation into function,
[tex]f^{-1}(x)=\frac{1}{8}(x-4)^{3}[/tex]
Help Me Please !! THX!
Answer: decreases
Step-by-step explanation:
Which point is best represented by the ordered pair (2, -5.5)?
A point W
b point V
c point S
d point R
Answer:
the answer is b
Step-by-step explanation:
because the point is located at the number given the answer is b
Helpppppppppppppppppppppp
Answer:
c. 4x
Step-by-step explanation:
Which of the following are not perfect squares? Select all that apply.
16
44
81
6
49
24
Answer and Step-by-step explanation:
44, 6, and 24 do not have perfect squares.
To be a perfect square, they have to be able to have a number that, when it multiplies itself by itself (needs to be a whole number), it turns into the bigger number.
44, 6, and 24 can't do this when being square rooted.
16 turns into 4.
81 turns into 9.
49 turns into 7.
#teamtrees #PAW (Plant And Water)
Answer:
44, 6, and 24
Step-by-step explanation:
4²=16 so it's a perfect square
9²=81 so it's a prefect square
7²=49 so it's a perfect square
44, 6, and 24 all result in decimals so it's not a perfect square.
f(x) = x ^ 2 What is g(x)?
Answer:
A ; g(x) = (1/2 x)^2
Step-by-step explanation:
Here, we want to get g(x)
we have a point on the curve g(x)
The point is represented by (2,1)
What this mean here is that, when x = 2, y = 1
Looking at the first option;
Substitute 1 for y and 2 for x
1 = (1/2 * 2)^2
1 = 1
This means this is our answer
The equation for g(x) is;
g(x) = (1/2 x)^2
How will you use graph to solve Linear Inequalities?
Solve the proportion:
5
6
=
2
n
+
9
9
Step-by-step explanation:
[tex]56 = 2n + 99[/tex]
Collect like terms and simplify
[tex]56 - 99 = 2n \\ - 43 = 2n[/tex]
Divide both sides of the equation by 2
[tex] \frac{ - 43}{2} = \frac{2n}{2} [/tex]
Simplify
[tex]n = - \frac{43}{2} = - 21 \frac{1}{2} [/tex]
Find the distance between -6 and 8.
What is an expression that represents the distance
Answer:
14
Step-by-step explanation:
8 - |-6| = 14
|| means absolute value, or the distance the number has from 0 on the number line. ex. |-92| = 92 |8| = 8
can u help me
the question is: find the value of x for each equation below and the numbers is
-x+3=3x-2
1.5x-3=2.25x
-1/3x+2=3x-1
Answer:
1. x=5/4
2. x=-4
3. x= 9/10
Step-by-step explanation:
Let's solve your equation step-by-step.
−x+3=3x−2
Step 1: Subtract 3x from both sides.
−x+3−3x=3x−2−3x
−4x+3=−2
Step 2: Subtract 3 from both sides.
−4x+3−3=−2−3
−4x=−5
Step 3: Divide both sides by -4.
−4x/−4 = −5/ −4
x= 5/4
Answer:
x= 5/4 (5 over 4)
Let's solve your equation step-by-step.
1.5x−3=2.25x
Step 1: Subtract 2.25x from both sides.
1.5x−3−2.25x=2.25x−2.25x
−0.75x−3=0
Step 2: Add 3 to both sides.
−0.75x−3+3=0+3
−0.75x=3
Step 3: Divide both sides by -0.75.
−0.75x/−0.75=3/−0.75
x=−4
Answer:
x=−4
Let's solve your equation step-by-step.
−1/3x+2=3x−1
Step 1: Subtract 3x from both sides.
−1/3x+2−3x=3x−1−3x
−10/3x+2=−1
Step 2: Subtract 2 from both sides.
−10/3x+2−2=−1−2
−10/3x=−3
Step 3: Multiply both sides by 3/(-10).
(3/−10)*(−10/3x)=(3/−10)*(−3)
x=9/10
Answer:
x=9/10 (9 over 10)
Ms. Carson's art class made a large rectangular mural. The length of the mural is 9 feet, and its area is 72 square feet.
What is the width of the mural?
What is the perimeter of the mural?
Answer: 8 feet!
Step-by-step explanation:
To find the width, we have to find out what number multiplied by 9 gives us 72.
The width of the mural is 8 feet!
Name the quadrant or axis where each point lies.
Answer:
T is 1, S is 2, J is 3, D is 4 ... hope that helps : )
If 5(x + 2) = 5x + 10, then 6(x + 3) =?
Answer:
6
Answer:
6+18
Step-by-step explanation:
HELP ME SOMEONE PLS ANSWER MY QUESTION FROM MY PROFILE.
*Please if anyone understands this help! :) Also if you could show or explain your work It would be very helpful. *
Answer:
Step-by-step explanation:
A trapezoid with a height of 19 meters has a base of 26 meters and another base of 46 meters. What is the area of the trapezoid? The area of the trapezoid is
Answer:
684 meters 2
hope this helped
Help me pleaseeeeeee it would mean the world to me! .
Multiple choice answers:
A)14.7%
B)1187.5%
C)11.7%
D)26.4%
Answer:
I believe your answer is b
Saul makes trail mix with peanuts, raisins, and pretzels. The ratio of cups of raisins to cup of peanut is 1 to 6. The ratio of cups of pretzels to cups of raisin is 3 to 1. Decide if the statement is true or false. "Saul uses 6 times as many cups of peanuts as cups of raisin." *
1 point
True
False
Answer:
true
Step-by-step explanation:
Answer:
true
Step-by-step explanation:
In a right triangle, one acute angle is 22º and the hypotenuse is 70 cm. Find the
lengths of the legs and the other angle measure.
Answer:
Adjacent leg (In relation to the angle that is measure 22 degrees)= 70*Cosine 22 or 64.9; Opposite leg (In relation to the angle that is measure 22 degrees)=70* Sin 22 or 26.22
Step-by-step explanation:
The other angle measure is 90-22 or 68.
To find the length of the adjacent leg (a) use cosine. Remember cosine is Adjacent leg over hypotenuse.
Cosine 22= a/70- Multiply by 70
70* Cosine 22=a or about 64.9
To find the length of the opposite leg (o) use sine. Remember sine is Opposite leg over hypotenuse
Sine 22= o/70
70*Sine 22=o
o= about 26.22
Triangle Congruency please help!!
Answer:
A
Step-by-step explanation:
the nice thing about triangle is that the smallest angle is always opposite the smallest side, etc. also, we can get the remaining angle because we have 2 angles already and there are always 180 degrees in a triangle.
50+ 63= 113
180-113 =67
so, 50 is the smallest angle and thus the side opposite of it is the smallest. next is side bc because 63 is the next biggest angle measure. lastly, side ac is the largest because it's opposite of the largest angle measure
Answer:
a
Step-by-step explanation: