what is the distance between the y intercept of the function f(x)=3(2)^x and the y intercept of the function g(x) represented by the table below
A: 2 units
B: 3 units
C: 8 units
D: 9 units
Answers
The distance between the y-intercept of the function f(x)=3(2)ˣ and the y-intercept of the function g(x) for this case is given by: Option C: 8 units
What is y-intercept of a function?The intersection of the graph of the function with the y-axis gives y-intercept of that function. The y-intercept is the value of y on the y-axis at which the considered function intersects it.
Assume that we've got: y = f(x)
At y-axis, we've got x = 0, so putting it will give us the y-intercept.
Thus, y-intercept of y = f(x) is y = f(0)
What is the equation of a line passing through two given points in 2 dimensional plane?Suppose the given points are [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex], then the equation of the straight line joining both two points is given by
[tex](y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)[/tex]
We're given that:
[tex]f(x) = 3(2)^x[/tex]
Its y-intercept is:
[tex]y = f(0) = 3(2)^0 = 3\times 1 = 3[/tex]
Assuming y = g(x) is a linear function, from the first two points [tex](x_1, y_1) = (-5,15)[/tex] and [tex](x_2, y_2) = (-2, 3)[/tex], we get:
[tex](y - 15) = \dfrac{3 - 15}{-2 - (-5)} (x -(-5))\\\\y -15 = -\dfrac{12}{3} (x+5)\\\\y-15 = -4x - 20\\y = -4x - 5[/tex]
Checking if really y = g(x) is linear or not by evaluating it on its rest of the points:
[tex]y = g(2) = -4(2) -5 =-8-5 = -13\\\\y = g(5) = -4(5) -5 = -25[/tex]
These outputs matches with the table output, so we can take:
[tex]g(x) = -4x -5[/tex]
Its y-intercept is:
[tex]y = g(0) = -4(0) -5 = -5[/tex]
The distance between 3 and -5 on the y-axis is the absolute difference between these values of y, evaluated as:
[tex]d = |3 - (-5)| = |8| = 8[/tex] units.
Thus, the distance between the y-intercept of the function f(x)=3(2)ˣ and the y-intercept of the function g(x) for this case is given by: Option C: 8 units.
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Related Questions
Which number sentence has a difference of 5?
8-(-3)
0
-3-8
-3-(-8)
3-(-8)
Answers
Answer:
The 4th one
Step-by-step explanation:
-3-(-8)=5
Kiko baked a batch of cookies. She ate 3 cookies and then gave half of the remaining cookies to her friends. If c represents the number of cookies that Kiko baked, which expression shows the number of cookies she gave to her friends?
Answers
Answer: (c - 3) / 2 = x
Step-by-step explanation:
If c represents the cookies, then you remove 3 because she ate 3 of the cookies. Since half of the remainder of the cookies were given to her friend, you must divide the product of c - 3, by 2. The reason for the parenthesis is so that it overrules PEMDAS, as parenthesis goes before division.
Can somebody answer this worksheet. Sorry before it didnt let me.
Answers
Answer:
1: L = 5
W = 7
2: A = lw
3: 35
4: 18
5: You have to add them up because it is 1 shape broken up into different parts.
6: 53
(08.01 LC)
A biologist created the following graph to show the relationship between the temperature of water (x), in degrees Celsius, and the number of insect larvae (y) in the water:
graph of y = -2x^2 + 20x + 400
What does the y-intercept of the graph represent?
Answers
Answer:
400
Step-by-step explanation:
Remember y=mx+b
b=y-intercept
it's the starting point on a graph.
Which expression has the same value as -18 divided by -9?
-18 divided by 2
-12 divided by (-3)
-10 divided by 5
-8 divided by (-4)
Answers
Answer:
-8 divided by (-4)Step-by-step explanation:
-18 divided by -9 is +2 and that is what you want.
-18 divided by 2 is -9, not correct.
-12 divided by (-3) is +4, not correct.
-10 divided by 5 is -2, not correct.
Leaving the correct answer: -8 divided by (-4) is +2.
Remember: a negative times a negative equals a positive.
HELP ITS MATH U CAN DO IT!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
1/3
Step-by-step explanation:
1/3 x 1/3 x 1/3 = 1/27
if was negitive would be 1/-27
if 1/9^3 would be 1/729
if negitive 1/-729
HELP PLSS WILL GIVE BRAINLIEST
Solve N = 3rt^4 - 5rz
(solve for z)
Answers
Answer:
Step-by-step explanation:
N = 3rt^4 - 5rz
now factor r out
N = r(3t^4-5z)
divide by r on both sides
N/r = (3t^4 - 5z)
subtract (3t^4)
N/r - 3t^4 = -5z
now divide by -5 to isolate the variable (z)
[tex]\frac{(n/r)-3t^4}{-5}[/tex] = z
Answer:
(N-3rt^4) / -5r = z
Step-by-step explanation:
N = 3rt^4 - 5rz
Subtract 3rt^4 from each side
N-3rt^4 = 3rt^4-3rt^4 - 5rz
N-3rt^4 = - 5rz
Divide each side by -5r
(N-3rt^4) / -5r = - 5rz/ -5r
(N-3rt^4) / -5r = z
400 people are asked if they drink tea
7/10 say yes and 20% of the people who say yes drink three cups a day
Answers
Answer:
56 people drink 3 cups daily
Step-by-step explanation:
What's the total number of people that drink 3 cups?
Total number of people = 400
7 / 10 were asked said yes
Number of people that said yes = (7 / 10) × 400 = 280
280 people drink tea.
20% of 280 people drink 3 cups daily, whats the number = ?
20% of 280 = ?
20 / 100 = x / 280
(20 × 280) = (100 × x)
5600 = 100x
X = 5600 / 100
X = 56 people
56 people drink 3 cups of tea daily.
Answer:
56 people drink 3 cups daily
Step-by-step explanation:
What fractional part of 84 is 14?
Answers
Answer:
1/6
Step-by-step explanation:
14/84 = 7/42 = 1/6
Please give me the answer
Answers
Answer:
50 degrees
Step-by-step explanation:
Since the two sides have the same length of 7 cm, it is an isosceles triangle so x = (180-80) / 2 = 50
What is the value of the expression 30 divided by (negative 6)?
Answers
Answer:
30 divided by (negative 6) would be : 30/(-6) = -5
Hope this helps!
:)
What is the value of x in the equation .5x+.08=1.68?
A.3.28
B.3.2
C. .88
D. .32
Answers
Answer:
Step-by-step explanation:
Answer:
x = 0.88/5
Step-by-step explanation:
5x+0.8=1.68
5x = 1.68 - 0.8
5x = 0.88
x = 0.88/5
What are some real-life examples of objects that are rectangles and made of
square tiles in rows and columns?
Answers
Answer:
a cube like the one with color things I forgot the name but is that one
The manager of a plant nursery bought 120 lb of soil to use for potting plants. The manager can put 5 lb into each of the small pots and 12 lb into each of the large pots. The manager made a sketch to show the line representing the different combinations of pots that can be used. The x-axis represented the number of small pots and the y-axis represented the number of large pots. The manager labeled only the intercepts.
Which points did the manager label?
(0, 24) and (10, 0)
(0, 5) and (12, 0)
(0, 10) and (24, 0)
(0, 12) and (5, 0)
Answers
Answer:
(0, 24) and (10, 0)
Step-by-step explanation:
hope it's helpful
A branch point where currents divide or combine is known as a ______
A. Principal node
B. Common node
C. Ground node
D. Reference node
Answers
what is the value of this expression 4 + 6 (4.3 + 8 )
-2.1
Answers
Answer:
The answer is 20.2
Step-by-step explanation:
always start with the number is parentheses
Answer:75.7
Step-by-step explanation:

What is the perimeter of rectangle EFGH?
Answers
Answer:
Step-by-step explanation:
Perimeter of rectangle = sum of all the four sides
= length + width + length + width
= 2 length + 2 width
= 2 * ( length + width)
what is 5+105?
:) :) :) :)
Answers
Answer:
110
Step-by-step explanation:
Answer:
Your answer friend...
Step-by-step explanation:
Q. What is 5 + 105?
A. 5 + 105 = 110
I hope its helpful...
What is the area of triangle ABC? Round to the nearest square unit.
Triangle A B C is shown. The length of A C is 16, the length of C B is 8, and the length of A B is 10.
Heron’s formula: Area
8 square units
15 square units
33 square units
618 square units
Answers
The area of the triangle ABC is 33 square units
We have given that,
Triangle A B C is shown. The length of A C is 16, the length of C B is 8, and the length of A B is 10.
We have to determine the area of the triangle
What is the area of the triangle?[tex]\text{ Area }=\sqrt{s(s-a)(s-b)(s-c)}[/tex]
A = area
s = semi-perimeter
a = length of side a
b = length of side b
c = length of side c\text{ Area } = area
s = semi-perimeter
use the given value in the above formula we get the area of the triangle ABC is,
Therefore the correct answer is 33 square units.
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Answer:
33 square units
Step-by-step explanation:
How can the point (12, 16) be explained? The highest point of the mountain defined by the function is 12 feet. The highest point of the mountain defined by the function is 16 feet. The width of the base of the mountain defined by the function is 12 feet. The width of the base of the mountain defined by the function is 16 feet.
Answers
Answer:
B The highest point of the mountain is defined by the function is 16 feet.
Step-by-step explanation:
Saw it somewhere
The points (12, 16) can be explained as,
The highest point of the mountain defined by the function is 16 feet.
The width of the base of the mountain defined by the function is 12 feet.
Co ordinatesWhat are co ordinates?a group of variables that accurately depict a position. The first number on a graph represents the distance along, while the second number represents the distance up or down. For instance, the point (2,15) is located 2 units down and 15 units up.
What is Abscissa?The "x" coordinate of a point, as represented on the horizontal line, is another name for the abscissa.
What is Ordinates?The co ordinate that is displayed on the vertical line, commonly known as the "y" coordinate is called ordinates.
Description for the co ordinates (12, 16)As, 12 is written first on the co ordinates, that's why 12 is showing the abscissa on the horizontal line which is the width of the base of the mountain.
While, 16 here shows the ordinates on the vertical line which is the highest point of the mountain.
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Simplify the given expression.
13 + (14a+5b)
HELP
Answers
Answer:
13 + 14a + 5b
Step-by-step explanation:
when there's a + in front of a expression
in parentheses the expression remains the same
Answer:
14a + 5b + 13
Step-by-step explanation:
You maintain an average balance of $1050 on your credit card which carries a 12% annual interest rate. The monthly interest payment is
Answers
Answer:
157.5
Step-by-step explanation:
This diagram shows triangles ABC and PQR. ABC is mapped to PQR by combining two single transformations. The first is a rotation of 90 degrees clockwise about C. Describe fully the second transformation.
Answers
Answer:
enlarge by -2 by centre point (3,1)
Step-by-step explanation:
What is the product of 2x + y and 5x – y + 3?
Answers
Answer:
10[tex]x^{2}[/tex] + 6x + 3xy + 3y - [tex]y^{2}[/tex]
Step-by-step explanation:
(2x + y)(5x – y + 3)
=10[tex]x^{2}[/tex] - 2xy + 6x + 5xy - [tex]y^{2}[/tex] +3y
=10[tex]x^{2}[/tex] + 6x + 3xy + 3y - [tex]y^{2}[/tex]
A special truck cleans the surface of the ice shown above. The figure is composed of a square and two semicircles.
Answers
Answer:
Surface Area Truck Cleans; 232.5625π + 930.25 ( square meters )
Step-by-step explanation:
See attachment below;
Find x and y
Need done before 11:59
Answers
Answer:
Step-by-step explanation:
(3x + 6)° = 78°
3x = 72°
x = 24°
z = 180° - 78° = 102°
Answer:
x= 102
z= 24
Hope it will help you :)
100 points!!!!! if you help me A semitruck and its load is measured to weigh 31 tons. A toll is assessed such that $0.01 is paid for every 10 pounds of weight. What is the amount of the toll this truck should pay?
Answers
Answer:
$62
Step-by-step explanation:
The total weight of the semitruck and its load is 31 tons. Let's convert this to pounds:
1 ton = 2000 lb
31 tons = 2000 * 31 = 62000 lb
We know every 10 lb will be priced at $0.01, so divide 62000 by 10 to find how many times we need to pay $0.01:
62000 ÷ 10 = 6200
Each of these 6200 times, we need to pay $0.01 so multiply these together:
6200 * 0.01 = 62
The answer is $62.
Answer:
its 62 dollars
Step-by-step explanation:
Please help! Will give brainliest, thanks and more points.
Look at the picture.
Answers
Answer:
rectangular prism
Step-by-step explanation:
their is four sides and a top and bottom
Answer:
it's a rectangular prism and their is four sides and a top and bottom
Step-by-step explanation:
boom
PLEASE ANSWER!!!!! I WILL MARK YOUR ANSWER AS BRAINLIEST!!!!!
Answers
Answer:
3/4=0.75
Step-by-step explanation:
The radius of a spherical glass ornament is 6 centimeters. Twenty-seven ornaments are packed in a cube shaped box with a side length of 36 centimeters. What is the volume of the empty space in the box, rounded to the near whole number?
Answers
Answer:
45.413 cm³
Step-by-step explanation:
Because the volume of a orament is 57 cm³ . The volume of twenty-seven oraments is 1242 cm³ . The volume of a cube is 46656 cm³
⇒The empty space is :
46656-1242=45414 ( cm³)
So the empty space is 45414 cm³
The volume of the empty space in the box, rounded to the nearest whole number, is 22,247 cubic centimeters.
What is a sphere?It is a three-dimensional figure.
The volume of one spherical glass ornament can be found using the formula V = (4/3)πr³, where r is the radius.
We have,
V = (4/3)π(6³)
= 904.78 cm³ (rounded to two decimal places)
The volume of 27 such ornaments is:
= 27 V
= 27 × 904.78
= 24,409.06 cm³ (rounded to two decimal places)
The volume of the cube-shaped box is given by V = s³,
where s is the side length.
Substituting the given side length, we get:
V = 36³
= 46,656 cm³
The empty space in the box is the difference between the volume of the box and the volume of the 27 ornaments:
Empty space = V(box) - 27V
= 46,656 - 24,409.06
= 22,246.94 cm³
Rounding this to the nearest whole number, we get:
Empty space ≈ 22,247 cm^3
Therefore,
The volume of the empty space in the box, rounded to the nearest whole number, is 22,247 cubic centimeters.
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