The graphs of f of x is equal to 2 times x over the quantity x plus 4 end quantity and g(x) = −log3(x + 3) + 1 have which of the following features in common?
x-Intercept
Vertical asymptote
Range
End behavior
The x-intercept of both the functions is 0. Therefore, option A is the correct answer.
The given functions are f(x)=2x/(x+4) and g(x)= -log3(x+3)+1.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Find the horizontal asymptotes by comparing the degrees of the numerator and denominator.
For f(x)=2x/(x+4)
Vertical Asymptotes: x=-4
Horizontal Asymptotes: y=2
No Oblique Asymptotes
For g(x)= -log3(x+3)+1
An asymptote is a line that a curve approaches, but never touches. Find the horizontal, vertical, and oblique asymptotes.
No Vertical Asymptotes
No Horizontal Asymptotes
To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.
x-intercept(s): (0,0)
y-intercept(s): (0,0)
The x-intercept of both the functions is 0. Therefore, option A is the correct answer.
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Destiny scored 38 points during a recent basketball game. She only made 2-point shots and 3-point shots. In total, Farrah made 21 shots.
Create two unique equations that model the number of 2-point shots, x, and the number of 3-point shots, y, that Destiney made in the game.
The equation that that model the number of 2-point shots, x, and the number of 3-point shots, y is x + y = 21, 2x + 3y = 38
How to represent situation with an equation?Destiny scored 38 points during a recent basketball game. She only made 2-point shots and 3-point shots. In total, Farrah made 21 shots.
The unique equations that model the number of 2-point shots, x, and the number of 3-point shots, y, that Destiney made in the game is as follows:
where
x = number of 2-points shoty = number of 3-points shotTherefore, the equation that represent the situation is as follows:
x + y = 21
2x + 3y = 38
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Refer to the equation 2x - 6y = 12.
(a) Create a table of values for at least 4 points. Show your work.
(b) Use the table of values to graph
the line.
The points on the line 2x - 6y = 12 is
x y
0 -2
6 0
9 -1
12 2
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan \theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
a)The equation is 2x - 6y = 12
For x = 0,
[tex]2 \times 0- 6y = 12\\6y = -12\\y = -\frac{12}{6}\\y = -2[/tex]
For x = 6,
[tex]2 \times 6 - 6y = 12\\6y = 0\\y = 0[/tex]
For x = 9
[tex]2 \times 9 -6y = 12\\18 - 6y = 12\\6y = 12 - 18\\6y = -6\\y = -\frac{6}{6}\\y = -1[/tex]
For x = 12
[tex]2 \times 12 - 6y = 12\\-6y = 12 - 24\\-6y = -12\\y = \frac{12}{6}\\y = 2[/tex]
x y
0 -2
6 0
9 -1
12 2
b) The graph has been attached
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What is m∠B?
There is a seven sided polygon ABCDEFG in which the measure of angle BCD is 148 degrees, the measure of angle DEF is 142 degrees, the measure of angle EFG is 130 degrees, the measure of angle FGA is 129 degrees, and the measure of angle GAB is 120 degrees. Angle CDE is a right angle.
A. 51°
B. 129°
C. 134°
D. 141°
The measure of angle B is 141 degrees
Given,
In the question:
There is a seven sided polygon ABCDEFG
The measure of angle BCD is 148 degrees,
The measure of angle DEF is 142 degrees,
The measure of angle EFG is 130 degrees,
The measure of angle FGA is 129 degrees,
and the measure of angle GAB is 120 degrees.
Angle CDE is a right angle.
To find the m∠B.
Now, According to the question:
The sum of angles in a polygon adds up to 180(n - 2), where n is the number of sides of the polygon
The angles are given as:
∠BCD = 148
∠DEF = 142
∠EFG = 130
∠FGA = 129
∠GAB = 120
∠CDE = 90
So, the measure of angle B is calculated using:
∠B + 148 + 142 + 130 + 129 + 120 + 90 = 180(n - 2)
∠B + 759 = 180(n - 2)
The value of n is 7
∠B + 759 = 180(7 - 2)
∠B + 759 = 180 x 5
∠B = 900 - 759
∠B = 141
Hence, the measure of angle B is 141 degrees
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if f(x) = 2x + 7, what is the value of f(-10) and f(5)?
if f(x)= 2x+7
f(x)= two points
-10 and +5
the solution is : A,,,,f(-10)=2(-10)+7
= -20+7
= -13
and
B,,,,, f(5)= 2(5)+7
= 10+7
= 17
Find the additive inverse of 2x+5 .
Answer: -5-2x
Step-by-step explanation:
Which number line represents the solution to the inequality 3x−8≥7?
Answer:
Look at the attached image below
Step-by-step explanation:
[tex]\tt 3x-8\ge \:7[/tex]
Add 8 to both sides:-
[tex]\tt 3x\ge 7+8[/tex]
Add 7 and 8 to get 15:-
[tex]\tt 3x\ge 15[/tex]
Divide both sides by 3:-
[tex]\tt \cfrac{3x}{3}\ge \cfrac{15}{3}[/tex]
[tex]\tt x\ge \:5[/tex]
I don’t understand need help please. Calculate the line of best fit for the data in the table. The table below gives the number of hours spent studying for a science exam and the final exam grade. Show work
Study hours: 2 5 1 0 4 2 3
Grade: 77 92 70 63 90 75 84
Answer:
y = 6.08871x + 63.9274
Step-by-step explanation:
You can use Desmos a free graphing calculator to do this.
answer pls with work
The solution is Option C.
4cm , 6cm , 10 cm does not form a right angle triangle
What is a Triangle?
A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
Given data ,
Let the triangle be ABC which is a right angle triangle
Now , the sides of the triangle is given as
a)
6cm , 8cm , 10cm
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
So , substituting the values in the equation , we get
hypotenuse² = base² + height²
10² = 8² + 6²
100 = 64 + 36
100 = 100
Therefore , it is a right angle triangle
b)
12 cm , 35 cm , 37 cm
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
So , substituting the values in the equation , we get
hypotenuse² = base² + height²
37² = 35² + 12²
1369 = 1225 + 144
1369 = 1369
Therefore , it is a right angle triangle
c)
4 cm , 6 cm , 10 cm
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
So , substituting the values in the equation , we get
hypotenuse² = base² + height²
10² = 6² + 4²
100 = 36 + 16
100 ≠ 52
Therefore , it is not a right angle triangle
d)
10 cm , 24 cm , 26 cm
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
So , substituting the values in the equation , we get
hypotenuse² = base² + height²
26² = 24² + 10²
676 = 576 + 100
676 = 676
Therefore , it is a right angle triangle
Hence , the triangle with sides 4cm , 6cm , 10 cm does not form a right angle triangle
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how can you graph point with rational coordinates on a coordinate plane
Answer:
Locate the given point in the coordinate plane: for example; (−9,4)
Ans: Given that the x and y coordinate of the point are −9 and 4, respectively.
Here, the given point (−9,4) is located in the coordinate plane. It will be located on the top left side of the coordinate plane if you drew it out.
Step-by-step explanation:
1. You have to draw two perpendicular lines, \ (x-\)axis and \ (y-\)axis.
2. From the point of origin, you have to move 5 units to the right side along the positive \ (x-\)axis.
3. Now, you have to move \ (6\) units up, parallel to the positive \ (y-\)axis
4. Here, you mark the point of intersection and mark it as \ ((-9, 4).\)
Which graphs of ordered pairs represent functions? there's one more graph to so if all of those are wrong then its the one I could not get a image of
Ordered pairs of graphs III and IV represents a function.
How do you find out if a set of ordered pairs is a function or not?
For a set of ordered pairs to be a function, there must not be any two points that have the same first elements.
This means that, the x-coordinates must not repeat for any two given points.
According to the given question:
Graph I - Clearly x coordinate repeats for the ordered pairs (-8, 12) and (-8, -8). Therefore ordered pairs of Graph I does not represents a function.
Graph II - Clearly x coordinate repeats for the ordered pairs (9, 2) and (9, -10). Also for (18,4) and (18, -14) Therefore ordered pairs of Graph II does not represents a function.
Graph III - Every ordered pair of this graph is unique hence the ordered pairs of the graph III represents a function.
Graph IV - Every ordered pair of this graph is unique hence the ordered pairs of the graph IV represents a function.
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Data can be modeled by a cubic function when the Response area set of finite differences are Response area and Response area
Yes Data can be modeled by a cubic function
Using finite differences to determine the degree of the polynomial function that fits the data, you know when a set of data could be modeled by a cubic function if you obtain a third difference that is nonzero and constant.
The entities that contain the measures and dimensions make up the relational graph that is the Cube data model. The term "cubes" for entities in Cube was adopted from OLAP cubes. They are essentially data tables with a semantic meta layer that describes the measures, dimensions, and connections between the cubes.
The basic primitives of dimensions and measurements are the basis on which Cube operates. These primitives can be combined to create metrics by the user.
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Mrs. Chu is ordering senior portraits of her son to send to their relatives. A medium photo
costs $22 and a large photo costs $42. She wants to spend less than $400 in total.
Select the inequality in standard form that describes this situation. Use the given numbers
and the following variables.
x = the number of medium photos
y = the number of large photos
The inequality which represents the situation is 22x + 42y < 400.
What is inequality?A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.
In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.
As per the given,
Cost of medium photos = 22x
Cost of large photo = 42y
Total cost < 400
22x + 42y < 400
Hence "The scenario is represented by the inequality 22x + 42y < 400.".
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Christina and Spencer have 120 baseballs together. Spencer has 28 more baseballs than Christina. How many baseballs are in Spencer's collection? How many baseballs are in Christina's collection?
Christina has 46 baseballs and Spencer has 74 baseballs in their collections.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
Christina and Spencer have 120 baseballs together.
Let christina has x baseballs
Spencer has 28 more
than Christina
x+28 has Spencer
So x+x+28=120
2x+28=120
Subtract 28 from both sides
2x=120-28
2x=92
Divide both sides by 2
x=46
Hence, Christina has 46 baseballs and Spencer has 46+28=74 baseballs in their collections.
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Please, help. Simplify the expression in positive exponents.
Answer:
(r⁶s³t¹⁰)/uStep-by-step explanation:
= r⁻¹st⁻¹u⁻¹/(r⁽¹⁺¹⁻⁹⁾s⁽⁻²⁺⁰⁺⁰⁾t⁽⁻¹⁻⁹⁻¹⁾u⁽⁻⁶⁺⁰⁺⁶⁾)= r⁻¹st⁻¹u⁻¹/r⁻⁷s⁻²t⁻¹¹u⁰= r⁻¹⁺⁷s¹⁺²t⁻¹⁺¹¹/u⁰⁺¹= r⁶s³t¹⁰/uMr. Hill also teaches gym. He has 20 soccer balls and 3 teams of
students. He gives the same number of balls to each team.
Can Mr. Hill divide 20 balls into 3 equal groups?
»)
>>>
>>)
Yes
No
I am not sure.
Answer: No
Step-by-step explanation:
No, Mr.Hill can not divide 20 balls into 3 equal groups because 20/3 does not get you a whole number, and you can not have 0.66666667 of a ball.
Answer:
No.
Step-by-step explanation:
20/3 = 5 balls per team and five are left over. No he cannot, this is because Mr. Hill would need to have twenty one balls and he only has 20. So there is not enough. It’s because there are going to be leftovers.
function rule to find f(72)
Answer:
-10
Step-by-step explanation:
When a problem asks you to find f("a number"), it's just telling you to replace x with "a number." So, substitute x with 72 to get the equation [tex]f(72)=-12+\frac{72}{36}[/tex]. The fraction simplifies to 2, and -12 plus 2 is just -10.
The standard deviation provides insight into the distribution of values around the mean. If the standard deviation is small, in general, the more narrow the range between the lowest and highest value. That is, values will cluster close to the mean. From your descriptive statistics, describe the standard deviations of salary, hrly rate, yrs worked, education, and age. What does this tell you about the variables
The standard deviation gives information about how values are distributed around the mean. The range between the lowest and highest number is more constrained when the standard deviation is low. Values will so tend to group together around the mean.
What is explained by the standard deviation?
The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.
When comparing data sets that may have the same mean but a different range, it is helpful. The mean of the following two numbers, for instance, is the same: 15, 15, 15, 14, 16 and 2, 7, 14, 22, 30.
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consider the construction of a pen to enclose an area. you have 400 ft of fencing to make a pen for hogs. if you have a river on one side of your property, what are the dimensions (in ft) of the rectangular pen that maximize the area?
The length and width of the rectangular pen that optimizes the area are 400 feet and 200 feet, respectively, according to the perimeter of a rectangle.
what is perimeter ?The perimeter of a shape is the sum of the lengths of all its edges. For example, a triangle has three edges, hence its perimeter is equal to the sum of those three lengths.The perimeter of a form can be calculated by adding the lengths of all its sides. A perimeter example is what? A field with a length of 24 yards and a width of 15 yards, for instance, will have a perimeter of 78 yards.
calculation
In order to construct a hog pen, I have 800 feet of fencing.
Assume that "l" represents the rectangle's length and "w" its width.
One of your properties borders a river that I own.
I can secure my property with fencing on its three sides.
because of this, the fencing's necessary perimeter p = l + 2w
The fencing's perimeter is now equal to
⇒ l + 2w = 800
= l = 800 - 2w
now the rectangle's area = A = lw
Therefore, A = l * w = w ( 800 - 2w ) = 800w - [tex]2w^{2}[/tex]
By diffusing the area equation, we can figure out the rectangle's greatest area.
Therefore, A' = 800 - 4w
Again, A" = -4
The rectangle has the largest area since the second order differentiation is constant negative.
Put simply, we obtain: A' = 0 , A' = 800- 4w
⇒800- 4w = 0
⇒ 4 w = 800
⇒ w = 200
So the rectangle has a 200-foot width.
The rectangle's length is currently:
l = 800 - 2w = 800 - 2 ( 200 ) = l = 400 feet
The length and width of the rectangular pen that optimizes the area are 400 feet and 200 feet, respectively, according to the perimeter of a rectangle.
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can you help me thank you
someone help me please
Answer:
Step-by-step explanation:
The first step is combining like terms 3000 and 3000. The next step is to use the distributive property of equality. After that, combining like terms is the next step, and the last step will be the division property of equality to get the final answer.
hope this helps!! :3
Which type of graph would best compare the number of school days in California, Kansas, Alabama, and Rhode island?
Bar graph can best compare the number of school days in California, Kansas, Alabama, and Rhode island.
What is Bar graph?
A bar chart or bar chart is a chart or graph that represents categorical data in rectangular bars whose height or length is proportional to the value they represent. Bars can be drawn vertically or horizontally. Column charts are sometimes called vertical bar charts.
Bar charts show comparisons between discrete categories. One axis of the chart shows the specific category to be compared and the other axis represents the measured values. Some bar charts represent bars grouped into multiple groups to show values for multiple measurement variables.
Therefore, Bar graph can best compare the number of school days in California, Kansas, Alabama, and Rhode island.
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6x^2+60x+144 factor and is the first polynomial prime
Step-by-step explanation:
[tex]6x^2+60x+144\\\\6(x^2+10x+24)[/tex]
You are looking for two numbers that add to 10 and multiply to 24:
6 + 4 = 10
6 * 4 = 24
so [tex]x^2 + 10x + 24 = (x+6)(6+4)[/tex]
factored: [tex]6(x+6)(x+4)[/tex]
write in slope-intercept form of the line that passes through the points (-2,-2) and (5,12)
To write the equation of a line in slope-intercept form (y = mx + b), we need to find the slope of the line (m) and the y-intercept (the point where the line crosses the y-axis, which is represented by b).
We can use the point-slope formula to find the equation of the line that passes through the points (-2,-2) and (5,12):
y - y1 = m(x - x1)
Where (x1, y1) is a point on the line, and m is the slope of the line.
Plugging in the values for the given points and solving for m, we get:
m = (12 - (-2)) / (5 - (-2))
= 14 / 7
= 2
Now that we have the slope, we can use either of the given points to find the y-intercept (b). Let's use the point (-2,-2):
y = mx + b
-2 = 2(-2) + b
-2 = -4 + b
b = -2 + 4
b = 2
Therefore, the equation of the line in slope-intercept form is:
y = 2x + 2
This is the equation of the line that passes through the points (-2,-2) and (5,12).
Find EDED if AC=9x+1AC=9x+1 and BD=13x-11BD=13x−11 and ABCDABCD is a rectangle.
Rectangles are plane figures with common length of opposite sides. Thus the required value of ED is 14 units.
A rectangle is a family of quadrilateral which has two equal opposite sides, with two adjacent sides at right angle to each other. Some properties of a rectangle are:
opposite sides have equal length two adjacent sides are at right angle to each otherthe two diagonals are equalFrom rectangle ABCD, it can be deduced that:
AB = DC
AD = BC
AC = BD
So that;
9x + 1 = 13x - 11
11 + 1 = 13x - 9x
12 = 4x
x = [tex]\frac{12}{4}[/tex]
= 3
Therefore, we have;
BD = 13x - 11
= 13(3) - 11
BD = 39 - 11
= 28
But ED = [tex]\frac{BD}{2}[/tex]
So that;
ED = [tex]\frac{28}{2}[/tex]
= 14
ED = 14 units
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Find the length of the third side. If necessary, write in simplest radical form.
Answer: 5
Step-by-step explanation:
Pythagorean theorem a^2 + b^2 = c^2
5^2 + x^2 = 5sqrt(2) ^ 2
25 + x^2 = 50
x^2 = 25
x = 5 square root both sides
The function f(x)f(x) is graphed below. How many points on the graph represent a relative minimum?
A relative minimum is a point in which neighborhood values will be bigger thus, in the given graph the only "b" point is relative minima.
What is a graph?The graph is a geometrical representation of a function and can be plotted by taking x's and y's corresponding values within the interval.
For example plot of y = x³,y = sinx.
As per the given graph,
The point where the slope is zero and the smallest among its neighborhood points then it will be relative minima.
In the given graph the point b is the smallest among its neighborhood thus b will be the relative minimum.
Hence "A relative minimum is a point in which neighborhood values will be bigger thus, in the given graph the only "b" point is relative minima".
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Sofia bought a package of 20 bottles of water. Each bottle contains w ounces. Write an
expression that shows the total number of ounces.
Answer:
20w
Step-by-step explanation:
If you have 20 bottles, and each contains w ounces, we can use the following example to solve.
If there were 4oz per bottle,
20 * 4 = 80
80oz
We have w oz per bottle,
20 * w = ?
20w
The school is 3.64 miles from Tonya's house and 1.27 miles from Jamal's house. How much farther from school is Tonya's house than Jamal's house? Complete the explanation on how you can use a quick picture to solve the problem.
Answer: Tonya's house is 2.37 miles farther from the school than Jamal's house.
Step-by-step explanation: To solve this problem using a quick picture, we can draw a line segment to represent the distance from the school to Tonya's house, and another line segment to represent the distance from the school to Jamal's house. We can then use a ruler to measure the length of each line segment and subtract the length of the line segment representing the distance to Jamal's house from the length of the line segment representing the distance to Tonya's house.
For example, if we draw a line segment that is 3.64 inches long to represent the distance from the school to Tonya's house and a line segment that is 1.27 inches long to represent the distance from the school to Jamal's house, then we can use a ruler to measure the lengths of the line segments and find that the line segment representing the distance to Tonya's house is 3.64 - 1.27 = 2.37 inches longer than the line segment representing the distance to Jamal's house. This means that Tonya's house is 2.37 miles farther from the school than Jamal's house.
The management of a division National Motor Corporation that produces compact and subcompact cars has estimated that the quantity demanded of their compact models is 1400 units/week if the price of oil increases at a higher than normal rate, whereas the quantity demanded of their subcompact models is 2600 units/week under similar conditions. However, the quantity demanded of their compact models and subcompact models is 3500 units and 2300 units/week, respectively, if the price of oil increases at a normal rate. Determine the percentages of compact and subcompact cars the division should plan to manufacture to maximize the expected number of cars demanded each week. (Round your answers to the nearest percent.)
The percentages of compact and subcompact cars the division should plan to manufacture to maximize the expected number of cars demanded each week are 24.5% and 24.5%.
What is meant by percentage?The Latin word per centum, which means "hundred" or "by the hundred," is the source of the word "percent." The Italian term per cento, which means "for a hundred," gradually shrank to become the sign for "percent," which is now used globally. It eventually vanished entirely. The word "per" was frequently shortened to "p."
Given,
If the oil price increases at a higher than normal state,
Demand for the compact cars=1400
Demand for the sub-compact cars=2600
If the oil price increases at a normal rate,
Demand for the compact cars=3500
Demand for the sub-compact cars=2300
Assuming that the probability of price increases at higher than the normal rate is 50% and at a normal rate is 50%.
Then,
Demand for compact cars=50%(1400)+50%(3500)
=(50/100)×1400+(50/100)×3500
=700+1750
=2450
Demand for the sub-compact cars=50%(2600)+50%(2300)
=(50/100)×2600+(50/100)×2300
=1300+1150
=2450
Therefore, the percentages of compact and subcompact cars the division should plan to manufacture to maximize the expected number of cars demanded each week are 24.5% and 24.5%.
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