Which statements about the graph of the exponential function f(x) are TRUE?The x-intercept is 1.The y-intercept is 3.The asymptote is y = -3The range is all real numbers greater than -3The domain is all real numbers.f(x) is positive for all x-values greater than 1As x increases, f(x) approaches, but never reaches, -3.
Answers
1 The x-intercept is the value of x where the graph intersects the x-axis. The graph crosses the x-axis at x = 1. This statement is true.
2 The y-intercept is the value of y where the graph intersects the y-axis. The graph crosses the y-axis at y = -2. This statement is false.
3 The horizontal asymptote is the value of y to which the graph approaches but never reaches. This value seems to be y = -3, thus this statement is true.
4 The range is the set of values of y where the function exists. The graph exists only for values of y greater than -3. This statement is true.
5 We can give x any real value and the function exists, i.e., any vertical line would eventually intersect the graph. This statement is true.
To find the domain of a function when we are given the graph, we use the vertical line test. This consists of drawing an imaginary vertical line throughout the x-axis. If the line intersects the graph, that value of x is part of the domain.
This imaginary exercise gives us the centainty that there is no value of x that won't intercept the graph, thus the domain is the set of all the real values.
6 We can see the graph is positive exactly when the function has its x-intercept, thus This statement is true.
7 As x increases, y goes to infinity. The value of -3 is not a number where f(x) approaches when x increases, but when x decreases. This statement is false.
Related Questions
Look at the figure below. 8 8 4 4 Which expression can be evaluated to find the area of this figure?
Answers
Answer
[tex]8^2-4^2[/tex]Step-by-step explanation
The figure consists of a square with sides of 8 units from which a square of sides of 4 units has been subtracted.
The area of a square is calculated as follows:
[tex]A=a^2[/tex]where a is the length of each side.
Substituting a = 8, the area of the bigger square is:
[tex]A_1=8^2[/tex]Substituting a = 4, the area of the smaller square is:
[tex]A_2=4^2[/tex]Finally, the area of the figure is:
[tex]A_1-A_2=8^2-4^2[/tex]Find The distance DB from Cassini yo Tethys when AD is tangent to the circular orbit. Round to the nearest kilometer
Answers
we have that
triangle ABD is a right triangle , because AD is a tangent
so
Apply the Pythagorean Theorem
DB^2=AB^2+AD^2
we have
AB is a diameter (two times rhe radius)
AB=2*295,000=590,000 km
AD=203,000 km
substitute
DB^2=590,000^2+203,000^2
DB=623,946 kmsolve for missing variable: 11y-36=63
Answers
The equation can be solved as,
[tex]\begin{gathered} 11y-36=63 \\ 11y=63+36 \\ 11y=99 \\ y=\frac{99}{11} \\ y=9 \end{gathered}[/tex]Therefore, the value of y is 9.
14) A positive number is two fifths of another positive number. The sum of the numbers is 49. What arethe two numbers?
Answers
Let's use the variable x to represent the second number. The first number is two fifths of x, so the first number is 2x/5.
If the sum of the numbers is 49, we can write the following equation:
[tex]\frac{2}{5}x+x=49[/tex]Now, solving the equation for x, we have:
[tex]\begin{gathered} \frac{2}{5}x+\frac{5}{5}x=49\\ \\ \frac{7}{5}x=49\\ \\ \frac{1}{5}x=7\\ \\ x=7\cdot5\\ \\ x=35 \end{gathered}[/tex]Let's calculate the first number:
[tex]\frac{2}{5}x=\frac{2}{5}\operatorname{\cdot}35=2\cdot7=14[/tex]Therefore the numbers are 14 and 35.
Two ships are sailing across the Atlantic ocean at the equator. The dofference in solar time between them is two hours. How many degrees of longitude are they apart?
Answers
Answer:
30 degrees
Step-by-step explanation:
There are 360 degrees of longitude ( 360 degrees is a complete circle)
It takes 24 hours to complete a complete rotation of the earth
360 degrees / 24 hours = 15 degrees / hr
15 degrees/ hr * 2 hr = 30 degrees
In a survey, 12 people were asked how much they spent on their child's last birthday gift. The results wereroughly bell-shaped with a mean of $39.1 and standard deviation of $17.4. Estimate how much a typical parentwould spend on their child's birthday gift (use a 99% confidence level). Give your answers to 3 decimal places.Express your answer in the format of ī + Error.$£ $
Answers
Given:
number of people (n) = 12
mean = 39.1
standard deviation = 17.4
99% confidence level
Using the confidence level formula, we can find the estimate of how much a typical parent would spend on their child's birthday:
[tex]\begin{gathered} CI\text{ = x }\pm\text{ }\frac{z\varphi}{\sqrt[]{n}} \\ \text{where x is the mean} \\ z\text{ is the z-score at 99\% confidence interval} \\ \varphi\text{ is the standard deviation} \\ n\text{ is the number of people asked} \end{gathered}[/tex]The z-score at 99% confidence level is 2.576
Substituting, we have:
[tex]\begin{gathered} CI\text{ = 39.1 }\pm\text{ }\frac{2.576\text{ }\times\text{ 17.4}}{\sqrt[]{12}} \\ =26.161\text{ and 52}.039 \end{gathered}[/tex]Hence, a typical parent would spend between $26.161 and $52.039 or :
[tex]39.1\text{ }\pm\text{ 12.939}[/tex]STRUCTURE Quadrilateral DEFG has vertices D(-1, 2), E(-2, 0), F(-1,-1) and G(1, 3). A translation maps quadrilateral DEFG to
quadrilateral D'EFG. The image of D is D'(-2,-2). What are the coordinates of E, F, and G'?
E (
FD
G' (
Answers
The coordinates are;
E' = (-3, -4)F' = (-2, -5)G' = (0, -1)Given,
Quadrilateral DEFG with vertices;
D = (-1, 2)E = (-2, 0)F = (-1,-1) G = (1, 3)We have to find the coordinates of E', F', G'.
A figure is translated when it is moved to the left, right, up, or down.
The original figure's points are all translated (moved) by the same amount and in the same direction.
Here,
Compare the coordinates of D with the coordinates of D' to determine the mapping rule that converts DEFG to D'E'F'G'.
D = (-1, 2)
D' = (-2, -2)
The x-coordinate has be translated 1 unit to the left.
The y-coordinate has been translated 4 units down.
Then,
The mapping rule is:
(x, y) → (x-1, y-4)
To find the coordinates of E', F' and G', apply the mapping rule to the given vertices of the pre-image:
⇒ E' = (-2-1, 0-4) = (-3, -4)
⇒ F' = (-1-1, -1-4) = (-2, -5)
⇒ G' = (1-1, 3-4) = (0, -1)
That is,
The coordinates are;
E' = (-3, -4)F' = (-2, -5)G' = (0, -1)Learn more about translation maps here;
https://brainly.com/question/13007985
#SPJ1
Solve the method.simultaneous equation by graphicaly + 3x = 6y - 2x = 1
Answers
The equations given are
[tex]\begin{gathered} y+3x=6............1 \\ y-2x=1............2 \end{gathered}[/tex]The graph of the equations will be shown below
Hence, the solution to the equations is the point where the two equations intersect.
Therefore, the solution is
[tex](1,3)[/tex]URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100 POINTS!!!!!
Order the numbers from least to greatest
Answers
Answer:
-1, √4/5, -6/5, √3, 2, -3√9, 2√125
Step-by-step explanation:
An auto mechanic recommends that 3 ounces of isopropyl alcohol be mixed with a tankful of gas (14 gallons ) to increase the octane of the gasoline for better engine performance. At this rate, how many gallons of gas can be treated with a 16-ounce bottle of alcohol (You don’t need to translate or understand just solve the word problem please )
Answers
Let be "x" the number of gallons of gas that can be treated with a 16-ounce bottle of alcohol.
According to the information given in the exercise, 3 ounces of isopropyl alcohol should be mixed with 14 gallons of gas.
Then, you can set up the following proportion:
[tex]\frac{14}{3}=\frac{x}{16}[/tex]Now you have to solve for "x":
[tex]\begin{gathered} (16)(\frac{14}{3})=x \\ \\ \frac{224}{3}=x \\ \\ x\approx74.67 \end{gathered}[/tex]Therefore, the answer is:
[tex]\approx74.67\text{ }gallons[/tex]
Lily likes to collect records. Last year she had 12 records in her collection. Now she has 15 records. What is the percent increase of
her collection?
The percent increase of her collection is
Answers
Maya started to run on a treadmill after setting its timer for 96 minutes. The display says that she has finished 47% of her run. How many minutes have gone by? Round your answer to the nearest tenth.
Answers
Answer:
45.1
Step-by-step explanation:
96 x .47 = 45.12
Rounded to the nearest tenth is 45.1
Percent means per hundred [tex]\frac{47}{100}[/tex] to divide by 100 you move the decimal place to places to the left.
Question 1-3
The distance traveled by car, for a duration of time, can be modeled with the equation s= 45t, where s is the distance, in miles, and it is
the time, in hours. Which graph represents this proportional relationship correctly?
120
105
90
Distance (mi)
Distance (mi)
75
60
45
120
30
105
90
15
75
60
45
30
0
15
2
Time (hr)
Time (hr)
100
lon
3
+X
X
120
105
90
Distance (mi)
75
60
45
30
15
0
1
2
Time (hr)
co
X
Answers
The equation s = 45t, where s is the distance in miles and it is the time in hours, can be used to simulate the distance driven by a car over a period of time then the car will travel 135 hours in 3 hours.
What is meant by the constant of proportionality?The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. Constant ratio, constant rate, unit rate, constant of variation, and even rate of change are other names for the constant of proportionality.
Given: The distance traveled by car at a constant rate is proportional to the time spent driving.
In the equation d = 45 t, d denotes the distance (in miles) and t denotes the time (in hours).
d / t = 45 miles per hour
The constant of proportionality = 45 miles per hour.
Also, the distance traveled by car in 1 hour = 45 miles
The distance traveled by car in 3 hours = 3 × 45 = 135 miles
Therefore, a car will travel 135 hours in 3 hours.
The complete question is:
The distance traveled by car at a constant rate is proportional to the time spent driving. In equation d = 45t, d represents the distance (in miles) and t represents the time (in hours).
A. What is the constant of proportionality? _____ miles per hour
B. How far will the car travel in 3 hours? _______ miles
To learn more about constant of proportionality refer to:
https://brainly.com/question/28413384
#SPJ13
First try was incorrect Fill in the blank. Constant: a number that is next to a variable.
Answers
A number that is right next to a variable. For instance,
[tex]5x+6[/tex]the number 6 is a constant.
Factor by grouping:y^3-5y^2+3y-15
Answers
we have the expression
y^3-5y^2+3y-15
Grouping terms
(y^3-5y^2)+(3y-15)
factor y^2
y^2(y-5)+(3y-15)
factor 3
y^2(y-5)+3(y-5)
factor (y-5)
(y-5)[y^2+3]24. The base of a 13-foot ladder stands 5 feet from a house. Sketch a drawing to model this situation. How many feet up the side of the house does the ladder reach? Explain how drawing the picture helped you solve the problem.
Answers
The draw that describes this situation looks like this:
Drawing this helped us to know that the ladder forms a right triangle with one of the walls of the house.
When we have right triangles we can apply the Pythagoras theorem, from the Pythagoras theorem we can express:
[tex]13^2=5^2+h^2[/tex]Solving for h, we get:
[tex]\begin{gathered} 13^2-5^2=5^2-5^2+h^2 \\ 13^2-5^2=h^2 \\ h=\sqrt[]{13^2-5^2}=\sqrt[]{169-25}=\sqrt[]{144}=12 \end{gathered}[/tex]Then, the ladder reach 12 feet up the side of the house
what us the area of the triangle if the perimeter is 16
Answers
We are asked to find the area of the given triangle.
Recall that the area of a triangle is given by
[tex]A=\frac{1}{2}\cdot b\cdot h[/tex]Where b is the base and h is the height of the triangle.
Let us find the base and height from the given figure.
As you can see,
base = 6
height = 4
[tex]\begin{gathered} A=\frac{1}{2}\cdot b\cdot h \\ A=\frac{1}{2}\cdot6\cdot4 \\ A=\frac{1}{2}\cdot24 \\ A=12 \end{gathered}[/tex]Therefore, the area of the triangle is 12 square units.
can anyone help me? solve using system of linear equations using elimination x – y - 3z = 4 2x + 3y – 3z = -2 x + 3y – 2z = -4
Answers
The solution is x = 2, y = -2 and z =0
How to solve the system of equations?The system of equations is given as
x – y - 3z = 4
2x + 3y – 3z = -2
x + 3y – 2z = -4
Start by eliminating y
To do that, we subtract (2) from (3)
x + 3y – 2z = -4 - (2x + 3y – 3z = -2)
This gives
-x + z = -2
Make x the subject in the above equation
x = z + 2
Substitute x = z + 2 in (1) and (2)
z + 2 – y - 3z = 4
z + 2 + 3y – 2z = -4
Solve the equations
-2z - y = 2
-z + 3y = -6
Multiply -z + 3y = -6 by 2
-2z + 6y = -12
Start by eliminating z
Subtract -2z + 6y = -12 from -2z - y = 2
7y = -14
Evaluate
y = -2
Substitute y = -2 in -z + 3y = -6
-z + 3(-2) = -6
Evaluate
-z - 6 = -6
Evaluate
z = 0
Recall that x – y - 3z = 4
So, we have
x + 2 - 3(0) = 4
Evaluate
x = 2
Hence, the values of the variables are x = 2, y = -2 and z =0
Read more about system of equations at
https://brainly.com/question/13729904
#SPJ1
Remember to write a let statement and answer the question. A collection of dimes abs quarters has a value of $1.35. List all possible combinations of dimes abs quarters.
Answers
Let d represents dimes and q represents quarter.
Note that a dime is 10 cent, which is same as one over ten, and a quarter is one over four
[tex]\begin{gathered} d=\frac{1}{10}=0.1 \\ q=\frac{1}{4}=0.25 \end{gathered}[/tex]Given that a collection of dimes abs quarters has a value of $1.35, then this can be represented as below:
[tex]0.1d+0.25q=1.35[/tex]Multiply through by 100 to get
[tex]\begin{gathered} 100\times0.1d+100\times0.25q=100\times1.35 \\ 10d+25q=135 \end{gathered}[/tex]To get the possible combinations of dimes and quarters, lets the try different values of that will satisfy the equation.
When q is 1,
[tex]\begin{gathered} 10d+25q=135 \\ q=1 \\ 10d+25(1)=135 \\ 10d+25=135 \\ 10d=135-25 \\ 10d=110 \\ d=\frac{110}{10}=11 \end{gathered}[/tex]Therefore, 11 dimes and 1 quarter abs is a possible combination
When q is 3
[tex]\begin{gathered} 10d+25(3)=135 \\ 10d+75=135 \\ 10d=135-75 \\ 10d=60 \\ d=\frac{60}{10} \\ d=6 \end{gathered}[/tex]Also, 6 dimes and 3 quarter abs is a possible combination
When q is 5
[tex]\begin{gathered} 10d+25(5)=135 \\ 10d+125=135 \\ 10d=135-125 \\ 10d=10 \\ d=\frac{10}{10} \\ d=1 \end{gathered}[/tex]Also, 1 dime and 5 quarter abs is a possible combination
When q is 7
[tex]\begin{gathered} 10d+25(7)=135 \\ 10d+175=135 \\ 10d=135-175 \\ 10d=-40 \\ d=\frac{-40}{10}=-4 \end{gathered}[/tex]Since negative answer was gotten for dimes, 7 quater wouldn't give any possible combination.
Hence, there are It can be found that there are there are three possible combinations, these are:
11 dimes and 1 quarter abs
6 dimes and 3 quarter abs
1 dime and 5 quarter abs
Answer parts a through E for the function shown below
Answers
Solution
We are given the function
[tex]f(x)=x^3+4x^2-x-4[/tex]First, Let us do the simplification or factorization
[tex]\begin{gathered} f(x)=x^2(x+4)-1(x+4) \\ f(x)=(x^2-1)(x+4) \\ f(x)=(x-1)(x+1)(x+4) \end{gathered}[/tex](a).
The coefficient of x^3 is positive
(b).
So basically, we set f(x) = 0 to get the x - intercepts
[tex]\begin{gathered} f(x)=(x-1)(x+1)(x+4) \\ (x-1)(x+1)(x+4)=0 \\ x=1,-1,-4 \end{gathered}[/tex]The x - intercepts are
[tex]x=1, -1, -4[/tex]The graph of f(x) is also given below
Square ABCD is inscribed in a circle with radius 20 m . What is the area of the part of the circle outside of the square
Answers
ANSWER:
456 square meters
STEP-BY-STEP EXPLANATION:
The first thing is to represent the problem in the following figure:
To calculate the area of the part of the circle outside of the square, we must calculate the area of the circle and subtract the area of the inscribed square.
To calculate the area of the square, we plant the following, taking into account that the diagonal of the square is equal to twice the radius and the sides equal to the radius times the root of two, like this:
Knowing the value of the side of the square, we can directly calculate the area of the part of the circle outside of the square, subtracting the corresponding areas like this:
[tex]\begin{gathered} A=A_C-A_S_{} \\ A=\pi\cdot r^2-\mleft(r\cdot\sqrt{2}\mright)^2 \\ \text{replacing} \\ A=3.14\cdot20^2-\mleft(20\cdot\sqrt{2}\mright)^2 \\ A=1256-800 \\ A=456 \end{gathered}[/tex]The area of the part of the circle outside of the square is equal to 456 square meters
A triangular pyramid has a base shaped like an equilateral triangle. The legs of the equilateral triangle are all 5 millimeters long, and the height of the equilateral triangle is 4.3 millimeters. The pyramid's slant height is 3 millimeters. What is its surface area?
Answers
The surface area of the triangular base pyramid is 19.75 mm².
How to find the surface area of a pyramid?The surface area of a triangular pyramid is the sum of the area of the whole sides of the triangular pyramid.
Therefore,
Surface area of a triangular pyramid = base area + 1 / 2 (perimeter × slant height)
The base of the triangular pyramid is an equilateral triangle. An equilateral triangle has congruent sides.
Therefore,
base area = 1 / 2 × 5 × 4.3
base area = 10.75 mm²
Hence,
perimeter of the base = 5 + 5 + 5 = 15 mm
Surface area of a triangular pyramid = 10.75 + 1 / 2 (15 × 3)
Surface area of a triangular pyramid = 10.75 + 1 / 2(18)
Surface area of a triangular pyramid = 10.75 + 9
Surface area of a triangular pyramid = 19.75 mm²
learn more on pyramid here: https://brainly.com/question/16472037
#SPJ1
Pls someone help me! Giving brainless
Answers
Answer:
ANSWER=5
Step-by-step explanation:
GIVEN=8+(-3)
(+)×(-)=(-)
SO 8-3=5
PLEASE MARK ME AS BRILLINT
To graph the inequality y>-3x-4, you would draw a dashed line.O A. TrueO B. False
Answers
True.
Since it is strictly greater
prism x imprison wire similar. the volume of prison why is 92 cm3 find the volume of prism x.
Answers
If they are similar, then their side measures are proportional
Prism X, volume = 92 cm^3
Lola needs 2/3 cup of lemon-lime soda for every 2 cups of punch. Find ____ cups of soda/cup of punch
Answers
We know that
• There are needed 2/3 cups of lemon soda for every 2 cups of punch.
To find the answer, we have to divide.
[tex]\frac{\frac{2}{3}}{2}=\frac{2}{6}=\frac{1}{3}[/tex]Therefore, the answer is 1/3 of soda/cup of punch.Every week a company provides fruit for its office employees. They canchoose from among five kinds of fruit. Which probabilities correctly completethis probability distribution for the 50 pieces of fruit, in the order listed?
Answers
Given:
Total number of pieces = 50
So, the probabilities are:
Apples
[tex]P(apples)=\frac{8}{50}=0.16[/tex]Bananas
[tex]P(bananas)=\frac{10}{50}=0.2[/tex]Lemons
[tex]P(lemons)=\frac{5}{50}=0.1[/tex]Oranges
[tex]P(oranges)=\frac{15}{50}=0.3[/tex]Pears
[tex]P(pears)=\frac{12}{50}=0.24[/tex]Answer: A.
Jordan owns a house painting service. For each house, they charge $95 plus $60 per hour of work. A linear equation that expresses the total amount of money Jordan earns per house is y=60x+95. What are the independent and dependent variables? What is the y-intercept and the slope?
Answers
Answer:
The slope is 60
The y intercept is 95
The independent variable is x (the number of hours)
The dependent variable is y (The amount earned.)
Step-by-step explanation:
What is the inverse function of y = (x-4)^2+2
Answers
One way to find the inverse of a function is by first swapping x and y, then solving for y, like this:
[tex]\begin{gathered} y=(x-4)^2+2\text{ }\Rightarrow x=(y-4)^2+2 \\ \end{gathered}[/tex]Now, let's solve for y, like this:
[tex]\begin{gathered} x=(y-4)^2+2 \\ x-2=(y-4)^2+2-2 \\ (y-4)^2=x-2 \\ \sqrt[]{\mleft(y-4\mright)^2}=\sqrt[]{x-2} \\ y-4=\sqrt[]{x-2} \\ y-4+4=\sqrt[]{x-2}+4 \\ y=\sqrt[]{x-2}+4 \end{gathered}[/tex]Then, the inverse function of y = (x-4)^2+2 is:
[tex]y=\sqrt[]{x-2}+4[/tex]the sum of the angle measures of a polygon with n sides is given find n1440
Answers
Given in the question:
a.) The sum of all angles of a polygon is 1,440 degrees.
To be able to determine what polygon has a total sum of angles of 1,440 degrees, we will be using the following formula:
[tex]\text{ }\Theta=(n-2)x180^{\circ}[/tex]We get,
[tex]\text{ 1},440^{\circ}=(n-2)x180^{\circ}[/tex][tex]\text{ 1},440^{\circ}=180n-360^{\circ}[/tex][tex]180n=1,440^{\circ}\text{ + 360}^{\circ}[/tex][tex]180n=1,800^{\circ}[/tex][tex]\frac{180n}{180}=\frac{1,800^{\circ}}{180}[/tex][tex]n\text{ = 10}[/tex]Therefore, that polygon is a decagon or a polygon with 10 sides.