Write an exponential function in the form y=ab^x that goes through points (0, 14) and (3,896).

Answers

Answer 1

The exponential function that goes through the points (0, 14) and (3, 896) is y = 14·3ˣ. This function has a base of 3 and a coefficient of 14.

An exponential function in the form y =abˣ is a function

where y is equal to a multiplied by b raised to the power of x.

To find the function that goes through the points (0, 14) and (3, 896),

We can write the following equation to find the base of the exponential function that goes through the points (0, 14) and (3, 896):

b³ = 896/14

We can then solve for b by taking the cube root of both sides of the equation to get:

b = 3

Now that we know the base of the function, we can use the point (0, 14) to find the value of the coefficient a.

Since the x-value of this point is 0, we can plug 0 in for x in the exponential function y=abˣ to get:

y = ab⁰ = a

Since the y-value of the point (0, 14) is 14, we can set this equal to a to solve for the value of a:

a = 14

So, the exponential function is y = 14·3ˣ

Learn more about exponential function here:

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Related Questions

Help plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz

Answers

Answer:

Step-by-step explanation:

Angle x is what I call "point to point" with the angle that measures 95 degrees. Because of this, they are vertical (the vertex of an angle makes a "v"; hence, the reason I call them point to point). Vertical angles are congruent. That means that they have the same measure. If x is vertical to an angle that measures 95 degrees, then x also measures 95 degrees.

Answer:

x is 95 degrees.

Step-by-step explanation:

worth 70 points PLZ HELLLLLLLLLLP
Four expressions are shown:

6(5x + 3)
6(6x + 2)
36x + 12
30x + 18
Which two expressions are equivalent to 6(5x + 2 + x)?

Answers

Answer:

B 6(6x + 2)

C 36x + 12

Step-by-step explanation:

I just did this question myself and I got it correct.

What is the volume of this rectangular prism?

Jasper built a dollhouse for his younger sister.

A rectangular prism has a length of 24 inches, width of 8 inches, and height of 10 inches. A triangular prism has a triangular base of 24 inches and height of 6 inches. The height of the prism is 8 inches.
Which equation shows how to determine the volume of the dollhouse?
V = 24 (10) (8) + one-half (6) (24) (8)
V = 24 (10) (8) + one-third (6) (24) (8)
V = 24 (10) (8) + one-half (6) (24) (10)
V = 24 (10) (8) + one-third (6) (24) (10)

Answers

Answer:

It's A :)

Also can i please have brainliest :)

Answer:

A

Step-by-step explanation:

3x+5y=27.50 & 6x+3y=27

I love you ​

Answers

Answer:

what do u want me to do withthis question

can u edit then I’ll edit

Step-by-step explanation:

Please help, solve for x

Answers

Answer:

x = 6

Step-by-step explanation:

10x = 5 x 12 = 60

x = 6

PLEASE PLEASE HELP!! I NEED THE ANSWERS ASAP

Answers

Answer:

Pictures below showing the answer :)

Step-by-step explanation:

.Distribute and combine like terms: −4(7r + 7)

Answers

Answer:

−28r−28

Step-by-step explanation:

−4(7r+7)

=(−4)(7r+7)

=(−4)(7r)+(−4)(7)

1. Determine the lateral and total surface
area of the pyramid.


(I need full explanation on how to solve

Answers

Answer:

Laterial surface area: 73 cm²Total surface area: 93 cm²

Step-by-step explanation:

The laterial surface area is the sum of the areas of the triangles. There are two triangles with dimensions: base = 4 cm, height = 8cm and two triangles with dimensions: base = 5cm, height = 8.2cm.

The laterial surface area LSA is:

LSA = 2 • ( 4.8/2) + 2 • ( 5 • 8.2/2)

LSA = 4 • 8 + 5 • 8.2

LSA = 73 cm²

The total surface area SA is the LSA plus the area of the base of the pyramid, which is a rectangle with dimensions: 4cm x 5cm:

SA = LSA + 4 5

SA = 73 cm + 20 cm²

SA = 93 cm²

Please help me with this it was due yesterday.

Answers

Answer:

domain= infinity on both sides.  range= -3<y<infinity

Step-by-step explanation:

hope this helps

Have a nice day :)

Help with 2 3 4 and 5 please!

Answers

Answer:

Number 2 is A

Number 3 is (5, -4)

Number 4 is (5, -4)

Number 5 is (4, 2)

Step-by-step explanation:

Answer:

B, maybe (5,-4), (5,-4), (4,2)

Step-by-step explanation:

Translate just means to move, and vertex T just means the dot labeled "T". Move just that point three to he left and two to the right is (-5,0). I would give (5,-4) as the answer for three, but I'm not too sure and don't wanna spread false information... onto number 4. (3,1) and the form is (x,y) Right is positive, so ADD 2 to 3. Down is negative, so SUBTRACT 5 to 1. You now have (5,-4). 2 multiplied by 2 is 4 and 1 multiplied by 2 is 2. (4,2)

Which is the vertex point of the equation y = (x - 1)2 - 16

Answers

Answer:

The vertex is at (h, k), which here is (1, -16).

Step-by-step explanation:

Compare the given y = (x - 1)2 - 16          (which should be y = (x - 1)^2 - 16 )

to                               y = (x - h)^2 - 16.

We can readily see that h = 1 and k = -16.

The vertex is at (h, k), which here is (1, -16).

please help me find the missing angles for each problem

Answers

Answer:

1) L1 = 123

L3 = 57

2) L1 = 49

L3 = 131

3) L2 = 116

L4 = 64

4) L1 = 108

L2 = 72

5) L3 = 69

L4 = 111

6) L3 = 124

L4 = 56

i need help with this​

Answers

Answer:

151

Step-by-step explanation:

Answer:

151

Step-by-step explanation:

PLEASE HELP ANSWER CORRECTLY !!!!!!!!!!!!!! WILL MARK BRIANLIEST !!!!!!!!!!!!!!

Answers

Hello again, hehelol12.

PQ is equal to CB. So the length of PQ must be 9.

Angle PQR is equal to CBA. Therefore the measure of angle PQR is 46.

I hope this helps!

Step-by-step explanation:

since they are congruent triangles, all your have to done is the compare the longest side of the first triangle is equal to that of the other; the smallest side of the first triangle is equal to that of the second, and so for the corresponding angles

using the above method,

Answer:

a) from mere observation line PQ is the longest therefore it is equal to the length of the longest side of the other triangle. so line PQ = 9

b) again, ang PQ is the smallest, using the method, ang PQ = 46 degrees

but mind you, you could use a ruler to measure the length to find the longest more accurately.

Rewrite the function in standard form.
f(x) = 4(x - 2)^2+ 3

Answers

Answer:

f(x) = 4x^2 - 13

Step-by-step explanation:

f(x)=4(x-2)^2 + 3 parentaties first

f(x) = 4 (x^2 - 4)+ 3 multiply by what's infront parentaties

f(x) = 4x^2 - 16 + 3 combine light terms

f(x) = 4x^2 - 13 Answer

Hope I helped :)

Solve the following quadratic equations using factoring.
a. x2 + 10x + 24 = 0

Answers

Answer:

x = - 6, x = - 4

Step-by-step explanation:

Given

x² + 10x + 24 = 0 ← in standard form

(x + 6)(x + 4) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 6 = 0 ⇒ x = - 6

x + 4 = 0 ⇒ x = - 4

. Find the sum of the infinite series, if it exists.

-270+135-67.5+⋯

Answers

Answer:

-180

Step-by-step explanation:

135/-270 = -1/2

67.5/135 = -1/2

The series is an infinite geometric series with r = -1/2

Since -1 < |r| < 1, the series has a sum

and equals a/(1 - r)       a = -270

S = a/(1 - r) = -270/(1 + 1/2) = -270/(3/2) = -180

For all values of x,
f(x) = 2x-3 and g(x) = x²+1

a) Find fg(x)
Simplify and give your answer in the form ax² + b

b) Find gf(x)
Simplify and give your answer in the form ax² + bx+c

Answers

Answer:

For f(x) = 2x + 3 and g(x) = -x 2 + 1, find the composite function defined by (f o g)(x)

(f o g)(x) = f(g(x))

= 2 (g(x)) + 3

= 2( -x 2 + 1 ) + 3

= - 2 x 2 + 5 Given f(2) = 3, g(3) = 2, f(3) = 4 and g(2) = 5, evaluate (f o g)(3)

Step-by-step explanation:

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Answers

Answer:

Side length = 5.8 in

Perimeter = 29

Area = 58 in²

Step-by-step explanation:

✔️Find Side length using trigonometric ratio:

Angle at center of a pentagon is always 36° (we have measure of a full circle, 360, divided by 10 smaller triangles = 36°)

So:

Reference angle = 36°

Adjacent side = 4 in.

Opp = ½ of the side length of the polygon = x (let's represent this as x)

Thus, apply TOA:

Tan 36 = Opp/Adj

Tan 36 = x/4

4*Tan 36 = x

x ≈ 2.9 in (nearest tenth)

Side length = 2*x = 2*2.9 = 5.8 in

✔️Perimeter = 5*side length

Perimeter = 5*5.8 = 29 in

✔️Area = ½aP

Where,

a = 4 in

P = 29

Plug in the values

A = ½*4*29

A = 58 in²

please help me answer this!

Answers

Answer:

right

Step-by-step explanation:

tell me if i was wrong

Caleb has at least $5. Which inequality is correct?

c < 5

or

c < 5

Answers

Answer:

It would be c is greater than or equal to five

Step-by-step explanation:

c≥5

5≤c

Help please, i give brainlist

Answers

1st one is -9x+6, -16x-14, 7x+3,4x-14, 3x+11,-9x-2,24x-40

PLEASE HELPP ILL GIVE BRAINLIEST

Answers

The answer would be 75%

A system of liner equation has been graphed in the diagram. Determine a responsible solution for the system of equation.

Answers

The answer is B. Even just looking at the negatives of the other solutions, you can see that it is B because the intersection has a negative x and a positive y.

find the value of each variables

Answers

Answer:

X=11

y=22

Step-by-step explanation:

[tex]tan60\frac{11\sqrt{3} }{x} \\\\\sqrt{3} =\frac{11\sqrt{3} }{x} \\\\x=\frac{11\sqrt{3} }{\sqrt{3} }[/tex]

⇒x=11

[tex]Sib 60=\frac{11\sqrt{3} }{y} \\\\\frac{\sqrt{3} }{2} =\frac{11\sqrt{3} }{y} \\\\y=\frac{11\sqrt{3} }{\sqrt{\frac{3}{2} } }[/tex]

⇒ y=22

hope it helps....

5th grade math. correct answer will be marked brainliest

Answers

Answer:

70/9

Step-by-step explanation:

You can rewrite 8 pounds as 72/9.

Take away 2/9 and you are left with 70/9.

Answer:

[tex]\frac{2}{9} x \frac{8}{1} = \frac{16}{9} = 1 \frac{7}{9}[/tex]

Van kept track of the number of hours that he spent at the
pool each week for several weeks. He spent 6, 2, 6, 3, and
3 hours.
What is the mean number of hours that Van spent at the pool each week?
A. 20 hours
B. 4 hours
C. 3 hours
D. 5 hours

Answers

Answer:

B. 4 hours

Step-by-step explanation:

add every number up

6+2+6+3+3= 20

then divide by the number of numbers you used to add with.

20÷5=4

4 hours

Is 80, 150, 170 a pythagorean triple?​

Answers

Answer:

Yes

Step-by-step explanation:

80² + 150² = 170²

6400 + 22500 = 28900

28900 = 28900

 ?!!!!!!!!!!!!!!!!!!!!!!!

Answers

The correct answer is B.

Can I please have brainliest?

geometry ^
please help me

Answers

2.99

by process of a elimination it can’t be the bottom two since the object is getting larger. If you take 6.21/5.4 you end up with 1.15. So now if you take 2.99/2.6 it also equals to 1.15.
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