Answer:
A. Stephanie correctly rewrote g(x) as a transformation of f(x), and she described the asymptotes of the two functions correctly.
Step-by-step explanation:
The statement is true because, g(x) = f(x) + 4 is indeed a transformation of f(x) by shifting the graph 4 units up, and because the horizontal asymptote is determined by the highest degree term in the function, which in this case is the same for both functions, so the two functions will have the same vertical asymptote, but the horizontal asymptote is determined by the leading coefficient which is different for both functions, so the two functions will have different horizontal asymptotes.
Geneva treated her parents to dinner at their favorite restaurant. The bill was $73.25. She wants to leave 24% of the total bill as a tip. How much should the tip be, in dollars?
Answer:
To calculate the tip, we first need to find 24% of the total bill. To do this, we can multiply the bill amount by 24% (expressed as a decimal).
Tip = 0.24 * 73.25
= 17.58
Therefore, the tip should be $17.58 in dollars.
The sum of three consecutive numbers is 120.
a) If x is the smallest of the three numbers,write down the equation that x satisfies.
b) Hence solve for x
Answer:
39
Step-by-step explanation:
x+x+1+x+2=120
3 consecutive numbers leading to x=39 !
Graph y=3/4x+5 which point lies on the graph of the line
Answer:
Graph is attached below
Step-by-step explanation:
To start off, let's find the y-intercept, which is when x=0
So, when x=0,
[tex]y=\frac{3}{4}(0)+5[/tex], which is y=5.
So we can put a point on (0, 5)
From there, since the slope is 3/4. We can go up 3 and right 4 to plot a point there, you can also do down 3 and down 4 from the y-intercept point, then keep going either, up 3 and right 4 or down 3 and left 4, which should give you a diagonal line that looks something like;
The top of a hill rises 64 feet above checkpoint -213. What is the altitude of the hill?
The altitude of the hill whose top rises 64 feet above checkpoint -213, is 277 feet above sea level.
What is the altitude?The altitude refers to the vertical distance or height of an object or point in relation to sea level (true altitude) or ground level (absolute altitude).
The altitude of a hill refers to its height measured from the ground level or the sea level, as the case may be.
In this situation, we can compute the altitude of the hill as the difference between the rise of the hill or mountain above the checkpoint and the given checkpoint.
The rise of the top of a hill = 64 feet
Given checkpoint = -213
The altitude of the hill = 277 feet [64 - (-213)]
Thus, the position or altitude of the hilltop in relation to the ground or sea level is 277 feet.
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Can someone help me do this problem? Can you do it in a ti-84 calculator? If so how?
Answer:
z = -8/3 - 5i
Step-by-step explanation:
Sorry, I don't know what a ti-84 calculator is.
But, I can solve this question normally.
Let the real part of z be x and the imaginary part be y.
z = x + iy
|z| = √(x²+y²)
z + |z| = x + iy + √(x²+y²) = 3 - 5i
Now, y has to be -5 as |z| is a real number so the only component affecting i is y. Therefore, y = -5.
Now, lets figure out the real part.
Cancel out imaginary part.
x + √(x² + 25) = 3
3 - x = √(x² + 25)
squaring on both sides,
9 + x² - 6x = x² + 25
6x = -16
x = -8/3
Hence the required complex number is -8/3 - 5i
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A man jogs from P to Q to M to R to Q back to P at an average speed of 150 yards per minute. To the nearest tenth of a minute, about how long does it take him to travel the entire distance
The time needed to travel the entire distance is given as follows:
1.27 minutes.
How to obtain the time it took to travel the entire distance?Before obtaining the time, we need to obtain the entire distance.
The distance is the perimeter of the rectangle, which is the sum of all the outer side lengths of the right triangle.
The sides of the right triangle are given as follows:
40 yards and 70 yards.
Applying the Pythagorean Theorem, the length of the hypotenuse is given as follows:
h² = 40² + 70²
[tex]\sqrt{40^2 + 70^2}[/tex]
h = 80.6 yards.
Then the total distance is given as follows:
40 + 70 + 80.6 = 190.6 yards.
The time is given by the division of the distance by the velocity of 150 yards per minute, hence:
t = 190.6/150
t = 1.27 minutes.
Missing InformationThe problem is given by the image presented at the end of the answer.
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Differentiate cos 5x
Answer
[tex] - 5 \sin(5x) [/tex]
On an island, frogs are always either green or blue in some initial ratio of blue to green frogs. The number of blue frogs increased by 60% while the number of green frogs decreased by 60%. It turns out that the new ratio of blue frogs to green frogs is the same as the previous ratio in the opposite order (green frogs to blue frogs). By what percentage did the overall number of frogs change?
When the number of blue frogs increased by 60% and the number of green frogs decreased by 60%, the percentage of the overall increase is solved to be 60%
How to find the percentage of the overall increaseAssuming the number of blue frogs and the number of green frogs are equal and = y
Then the total number of frogs = y + y = 2y
Increasing the percentage of each by 60%, the factor for percentage increase by 60% is 1.6
hence 1.6y + 1.6y = 3.2y
percentage change
= change in price / original price * 100
= (3.2y - 2y) / 2y * 100
= 1.2y / 2y * 100
= 0.6 * 100
= 60
hence the percentage change is 60%
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Josh Filled up the gas tank on his truck and decided to collect some data that he could use to determine the fuel Efficiency of his vehicle.
The x-intercept of the equation y=-13x+234 is (18,0).
What is the point slope form?The point slope form is used to find the equation of the straight line which is inclined at a given angle to the x-axis and passes through a given point.
The equation of the point slope form is: (y - y₁) = m(x - x₁)
where, (x, y) is a random point on the line and m is the slope of the line.
1) From the give table, we have (18, 0) and (15, 39).
Here, slope(m) = (39-0)/(15-18)
m= -13
2) Substitute m= -13 and (x₁, y₁)=(18, 0) in point slope form, we get
(y-0)= -13(x-18)
y=-13x+234
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): (18,0)
y-intercept(s): (0,234)
Therefore, the x-intercept of the equation y=-13x+234 is (18,0).
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Fatms is making a triangular Shaped Scarf, where the sides have Length's 78 cm, 78 cm, and 121cm. To finish the scarf, she will need to sew a binding perimeter around the scarf. Find the perimeter of of the of the scarf.
What type of proofs did Julie and Samuel use
What else is part of the problem?
[tex]98765÷325[/tex]98765÷325
Answer:
Not sure what you meant and could of used some specifics but I got this with my experience in algebra and geometry.
9906513923.77
98765 times triangle A 32598765÷325
At noon, a 36 foot building casts a 20 foot shadow. Find the shadow cast by a 6 foot tree. Set up a proportion and solve. Be sure to show all your work!
Using the concept of proportions and ratio, the building of 6ft casts a shadow of 3.33ft
What is ProportionsProportions are a way of comparing two or more quantities by expressing them as fractions or ratios. They are used to describe the relationship between parts of a whole.
A proportion can be written in different ways. For example, the proportion of red apples to total apples can be written as "3 out of 5", "3:5", or "3/5". In this case, 3 is the number of red apples, 5 is the total number of apples and 3/5 is the proportion of red apples.
Data;
Building = 36 ftshadow = 20 ftBuilding 2 = 6ftshadow = xSetting up a proportions or two ratios for this.
36 / 20 = 6 / x
cross multiply both sides and solve for x
36 * x = 20 * 6
36x = 120
x = 3.33
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Simplify the expression to a + bi form:
(
−
8
+
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)
+
(
2
+
2
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)
(−8+i)+(2+2i)Simplify the expression to a + bi form:
(
−
8
+
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)
+
(
2
+
2
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(−8+i)+(2+2i)
The simplified form of the given expression is 3(i-2)
What are expressions?A term can be a number, a variable, product of two or more variables or product of a number and a variable. An algebraic expression is formed by a single term or by a group of terms. For example, in the expression 4x + y, the two terms are 4x and y.
Given is an expression, (−8+i)+(2+2i)
Simplifying the expression,
(−8+i)+(2+2i)
= -8 + i + 2 + 2i
= -8+2+2i+i
= -6+31i
= 3(i-2)
Hence, the simplified expression is 3(i-2)
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Find the missing length.
Answer:
Pythagorean theorem:
[tex]a ^{2} + b ^{2} = c^{2} [/tex]
[tex]2 ^{2} + 11 ^{2} = c^{2} [/tex]
2×2=4 11×11=121
4+121=125
[tex]c = \sqrt{125} [/tex]
find x (will mark brainliest)
Using circle theorems, the value of x in the cyclic quadrilateral is 6 units
What is a Cyclic QuadrilateralA cyclic quadrilateral is a four-sided shape whose vertices all lie on the same circle. This means that all four angles of the quadrilateral are equal to one another.
This is further explained by circle theorem which is a branch of mathematics that deals with the properties of circles and their relationships with other shapes. It is based on the fact that all points on a circle are equidistant from the center of the circle. Circle theorem has many applications, such as finding the area of a circle, calculating the circumference of a circle, and even determining the angles of a triangle formed by three points on a circle.
In this given problem, to find the value of x, we have to use proportions or ratios of the sides given.
This becomes;
(x + 6) / x = 12 / x
when the denominators cancel out;
x + 6 = 12
Collect like terms
x = 12 - 6
x = 6
The value of x is 6
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(Look at picture)………..
Beginning at the y-intercept (0,35),Line is solid, slopes down one and over one, and is shaded beneath.
What is the graph?Choose your variables first.
If x is the amount of hours spent mowing lawns,
Let y equal the number of hours worked at the clothes business.
A minimum of $400 must be earned from both employment (400 or more)
15x + 10y ≥ 400
In order to graph y = -15/10x +35, get y.
10 hours minimum every day in the store.
35 hours maximum per week
x + y ≤ 35
To graph y = -x + 35, find y.
Making the graph: 0 to 35 for the x and y axes.
First equation: y = -15/10x + 35 y-intercept = 35 slope: solid line on the y-axis starting at 35, going down 12, over 10 Shade above solid line
Second formula: y 10
At y=10, draw a solid horizontal line; more than should be shaded above the line.
Third formula: y = -x + 35
beginning at the y-intercept (0,35)
Line is solid, slopes down one and over one, and is shaded beneath.
The overlapping region on the graph will appear as a little triangle with its points under the line from the third equation, above the horizontal line, and above the line from the first equation.
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Please look at the picture and answer the question thank you
Answer:
[tex]5y^3-2x^2+2[/tex]
Step-by-step explanation:
I like to start off by rearranging the like terms next to each other, going from the greatest power to the least, so that they are more clear.
So in this case it would be: [tex]2y^3+3y^3+x^2-3x^2+1+5-4[/tex]
Now you can add them together. Remember you can only add/subtract coefficient or variable with the same base and power.
And with that in mind, the final result should be,
[tex]5y^3-2x^2+2[/tex]
Hope this helps!
The results of a survey of students showed that 53 students had a Netflix account, 46 students had a Hulu account and 87 students had a Netflix or a Hulu account. How many students had both a Netflix and Hulu account? Show how you got your answer either by drawing a Venn diagram or by showing the math.
Answer:
12 students
Step-by-step explanation:
The number of students surveyed: 53 + 46 = 99 students
The number of student having both: 99 - 87 = 12 students
A frame is 10 inches wide and 6 inches tall. If it is reduced to a width of 3 inches then how tall will it be?
Considering the context of the question and the mathematical expression, the height of the frame. after the width is reduced to 3 inches will be 1.8 inches.
What are the Dimensions in MathematicsDimension is a term that is used to describe the measurement of the size or distance of an object or region or space in one direction.
Generally, the term dimension is the measurement of the length, width, and height of anything.
In this case, as given in the question
A frame is 10in wide and 6 in tall.
reduces to a width of 3 in
let us assume that the height of the frame after reducing the width to 3in be = x
then the equation becomes original width/ original length = reduced width/reduced length
put all the value, we get
[tex] = 10 \div 6 = 3 \div x[/tex]
solve the above
[tex]x = (6 \times 3) \div 10 \\ x \: = 1.8in[/tex]
Therefore, in this case, it is concluded that the correct answer is 1.8in, which will be the tall or height of the frame.
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At a particular job, workers' wages are linear and based on years of experience. You ask two workers what their
experience and wages are to determine the wage formula. One worker earns $16.10 per hour with 1 years of
experience. The other worker has 3 years of experience and earns $21.30 per hour.
Instructions: Change settings in the above tool as needed to assist in answering the following questions. All answers
could be calculated, or they can be read or estimated from the table or graph above after entering the correct
settings.
a) What is a worker's starting wage at this job? $
per hour
b) What wage can be expected after 7 years of experience? $
per hour
A worker's starting wage at this job is $13.5.
$31.70 per hour can be expected after 7 years of experience.
What is the system of equations?
System of equations, also known as simultaneous equations, Two or more equations to be solved together in algebra (i.e., the solution must satisfy all the equations in the system). The number of equations must equal the number of unknowns for a system to have a unique solution.
Given that a worker earns $16.10 per hour with 1 year of experience.
The other worker earns $21.30 per hour with 3 years of experience.
The model that represents the wages of a worker is
y = ax + b
Where x is the number of years of experience, and y is total wages.
Now putting x =1 and y = 16.10 in y = ax + b:
16.10 = a + b .....(i)
Now putting x =3 and y = 21.30 in y = ax + b:
21.30 = 3a + b .....(ii)
Subtract equation (ii) from equation (i)
3a + b =21.30
a + b = 16.10
(-) (-) (-)
__________
2a = 5.2
a = 2.6
Putting a = 2.6 in equation (i)
16.10 = 2.6 + b
b = 16.10 - 2.60
b = 13.5
The model is y = 2.6x + 13.5
A worker's starting wage is $13.5 at this job.
Putting x = 7 in y = 2.6x + 13.5:
y = 2.6×7 + 13.5
y = $31.70
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If 576 / 24 = 24, then 24² =
Answer:
Step-by-step explanation:
24²=24×24
Which is 576
A tree is 7 feet 1 inch tall. How tall is it in inches?
Answer:
85 inches
Step-by-step explanation:
7*12+1=84+1=85
A special drill is used at a construction site to dig holes. A hole is dug to a depth of 2.75 feet when the drill hits rock. The progress slows to 56 feet per hour of digging. The depth of the hole must be at least 1012 feet by the end of the day to stay on schedule.
What is the minimum amount of time the drill must continue at its present rate to complete the hole on schedule?
Select from the drop-down menus to correctly complete the statement.
To complete the hole on schedule the minimum amount of time the drill must continue to work is 18 hours
How to determine the minimum length of time the drill must workThe rate of the drill for the remaining part of creating the whole is 56 feet per hour of digging
The remaining depth of the hole = the total hole - the depth before the rock
The remaining depth of the hole = 1012 - 2.75
The remaining depth of the hole = 1009.25
At a rate of 56 feet per hour the number of hours to dig 1009.25
56 feet = 1 hour
1009.25 feet = ?
cross multiplying
? * 56 = 1 * 1009.25
? = 1009.25/56
? = 18
approximately 18 hours will take the drill to reach complete the hole
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Kelly and her brother won the lottery: Kelly took one half of the earnings, and her brother, Toey, took the other half. Kelly spent her entire half of the money. Joey spent & of his share.
What fraction of the total lottery winnings did Joey spend?
Answer:
Let's call the total amount of the lottery winnings x.
If Kelly took one half of the earnings, then she took 1/2x and Toey took 1/2x as well.
Toey spent 1/4 of his earnings, so he spent 1/4*(1/2x) = 1/8x
So Joey spent 1/8 of the total lottery winnings.
Identify what type of shape ABCD is if… the slope of BC= -5/4 and the length of DA=6.4
The shape of the ABCD is a rhombus. The diagonals are not equal to each other.
What is the 2-dimensional shape?
A two-dimensional shape with horizontal and vertical axes is known as a 2d shape (x-axis and y-axis). Two-dimensional shapes have only length and width. There is no thickness or height to these shapes.
Given the vertices of ABCD are A(-3,0), B (1,5), C(-3,10) and D(-7,5).
The formula distance between points (x₁, y₁) and (x₂, y₂) is √[(x₂ - x₁)² + (y₂ - y₁)²].
The distance between A and B is √[(1 - (-3))²+(5 - 0)²] = √(4²+5²) = 6.4
The distance between B and C is √[(-3 - 1)²+(10 - 5)²] = √(4²+5²) = 6.4
The distance between C and D is √[(-7 - (-3))²+(5 - 10)²] = √(4²+5²) = 6.4
The distance between A and D is √[(-7 - (-3))²+(5 - 0)²] = √(4²+5²) = 6.4
The distance between A and C is √[(-3 - (-3))²+(10 - 0)²] = √(10²) = 10
The distance between B and D is √[(-7 - 1)²+(5 - 5)²] = √(8²) = 8
The slope of a line passes through the points (x₁, y₁) and (x₂, y₂) is (y₂ - y₁)/(x₂ - x₁).
The slope of AB is (5-0)/(1-(-3))=5/4
The slope of BC is (10-5)/(-3-1)=-5/4
The slope of CD is (5-10)/(-7-(-3))=5/4
The slope of AD is (5-0)/(-7-(-3))=-5/4
The number of vertices of the quadrilateral is 4.
Thus it is either a square or rectangle or rhombus or parallelogram.
Since the length of all sides is equal thus it is either a square or rhombus.
Since the diagonals are not equal it is a rhombus.
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PLEASE ASSIST ME
The perimeter of a triangular garden is 72 feet Find the length of the three sides if the middle length side is 2 feet greater than twice the length of the smallest side, and the longest side is 2 feet less than 3 times the length of the smallest side
A rectangular prism has a square base. The height of the prism is equal to twice the edge length of its base. The base can be completely covered with no overlap by 16 squares that each have an edge length of 1 inch what is the total surface area of the rectangular prism
The total surface area of the rectangular prism is 160 inches².
How to calculate the surface area?Since the base of the rectangular prism is a square, we know that the edge length of the base is the square root of the area of the base. The area of the base is 16 square inches (since it can be completely covered by 16 squares with edge length of 1 inch), so the edge length of the base is 4 inches.
Since the height of the prism is twice the edge length of the base, the height of the prism is 8 inches.
The total surface area of a rectangular prism is given by the formula:
2lw + 2lh + 2wh
Where l is the length, w is the width and h is the height
So, the total surface area of the rectangular prism is:
2(4 inches * 4 inches) + 2(4 inches * 8 inches) + 2(4 inches * 8 inches)
= 160 square inches
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Use computer drawing software to construct a quadrilateral with two pairs of parallel sides and ywo angles measuring 125°. What geometric shape describes this quadrilateral
The geometric shape formed is a rhombus.
What is quadrilateral?A quadrilateral is a four-sided shape enclosed shape, where the sum of the internal angle is 180°.
Here,
It is mentioned in the question, we have to construct a quadrilateral with two pairs of parallel sides and two angles measuring 125°.
So, the construction of a quadrilateral is shown.
As seen in the figure, the figure is of a rhombus.
Thus, the geometric shape formed is a rhombus.
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Mick's zoo offers a promotional deal: get a free $3 cotton candy and a free
$2 soda with the purchase of five $12 admission tickets. A group of 20
students will each purchase a ticket. If half of them want cotton candy and
14 of them want soda, how many dollars would they save by using the
promotional deal?
The group of 20 students will save $144 by using the promotional deal. Half of the group, or 10 students, will get the free cotton candy, so that's $30 saved. 14 of the students will get the free soda, so that's another $28 saved. Added together the group of 20 students will save $58 on the cotton candy and $28 on the soda for a total savings of $144.
