New function that is a horizontal stretch of F(x)=[tex](x+2)^{3} + 5[/tex] is F([tex]\frac{x}{k}[/tex])=[tex](\frac{x}{k} +2)^{3} + 5[/tex]
What is horizontal stretch ?The point (x, y) on the graph of f(x) is changed to the point (x/k, y) on the graph of g when the graph is stretched or contracted horizontally by a factor of 1/k (x).Only when the input value is also increased by a, can a graph be stretched horizontally by a factor of 1/a. The x-coordinates should be multiplied by a once f(x) has been stretched horizontally to f(ax). Keep the y-intercepts where they are. The resulting function might have a different domain, but it will have the same range. If a point (m, n) is stretched horizontally, it becomes (am, n).
F(x)=[tex](x+2)^{3} + 5[/tex]
F([tex]\frac{x}{k}[/tex])=[tex](\frac{x}{k} +2)^{3} + 5[/tex]ch visit :
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NEED ASAP PLEASEEEEEE
How many smaller squares can you fit inside a larger square with side length of 31 units?
961 smaller squares
62 smaller squares
31 smaller squares
29,791 smaller squares
The number of smaller squares that can fit inside a larger square with a side length of 31 units is A. 961 smaller squares if the larger square is a plane.
What is a side length?A side length is one part of the length of an object.
Determining the number of smaller squares in a larger square depends on if the square is an enclosure or a plane.
If the square object is an enclosure, then it has three dimensions, length, width, and height, which are squared. In that case, the number of smaller squares will be 29,791.
But if the square object is a plane with two dimensions, the number of smaller squares is 961.
Side length = 31 units
Area of a square plane = 961 unit² (31 x 31)
Volume of a square enclosure = 29,791 unit³ (31 x 31 x 31)
Thus, the number of smaller squares depends on the dimensions of the larger square.
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Need help 7th-grade math
An arts academy requires there to be 4 teachers for every 68 students and for every 3 tutors for every 36 minutes. How many students does the academy have per teacher? Per tutor? How many tutors does the academy need if it has 72 students?
The number of students per teacher is 17 and per tutor is 12. For 72 students the academy needs 6 tutors.
The given question is solved using the unitary method.
The arts academy requires 4 teacher for every 68 students
The arts academy requires 1 teacher for every 68/4 students
The arts academy requires 1 teacher for every 17 students
The academy has 17 students per teacher
It requires 3 tutors for every 36 students
3 tutor = 36 student
1 tutor = 36 /3 = 12 students
The academy has 12 students per tutor
For 72 students the total number of tutor required are 72/12 = 6
The number of students per teacher is 17 and per tutor is 12. For 72 students the academy needs 6 tutors.
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find the equation of the line please
Answer: y= -2x+5
Step-by-step explanation:
the population of a community is known to increase at a rate proportional to the number of people present at time t. if an initial population p0 has doubled in 9 years, how long will it take to triple?
Since the population increases at a rate proportional to the current number of people, the population will be three times of its initial population after 14.27 years.
The population of a community increases at a rate proportional to the number of people present at time t, means:
dP/dt = kP
where k is a constant.
Rearrange it:
(1/P) dP = k dt
Take the integral:
∫ (1/P) dP = ∫ k dt
ln P = kt + C, where C is a constant
Substitute t = 0, from the problem, it is known that P(t = 0) = P₀
Hence,
P(t) = P₀. e^(kt)
The population doubles after 9 years, means if we substitute t = 9
P(9) = P₀. e^(9k)
2P₀ = P₀. e^(9k)
2 = e^(9k)
Take the natural logarithmic:
ln 2 = 9k
k = (ln 2)/9 = 0.077
When the population grows to triple, it means P(t) = 3P₀
3P₀ = P₀. e^(kt)
ln 3 = kt
ln 3 = 0.077 t
t = (ln 3)/0.077 = 14.27 years.
Hence, the population will be three times of its initial population after 14.27 years.
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The answer is????????
Answer:
-7
Step-by-step explanation:
2(-9)+5=-7
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{xy + 5}\\\mathsf{= 2(-6) + 5}\\\mathsf{= -12 + 5}\\\mathsf{= -7}\\\\\\\huge\text{Therefore, your answer should be: \boxed{\mathsf{-7}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
20.8cm divided by 2.3g
Answer:
9.043
Step-by-step explanation:
i just divide
Answer: 9.043 centimeters/grams
Step-by-step explanation:
All you have to do it divide!
The return train fare from Nottingham to Harwich is £158.80 Asha has a student railcard which gives her 30% off. How much will Asna pay for her return ticket?
well, let's check how much is 30% of £158.80
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{30\% of 158.80}}{\left( \cfrac{30}{100} \right)158.80}\implies 47.64~\hfill \underset{ticket~price}{\stackrel{158.8~~ - ~~47.64}{\text{\LARGE \pounds 111.16}}}[/tex]
please help 8th grade math!
what is a fast way to do multiplication and division by tens
Answer:
When multiplying whole numbers by 10, simply add a 0 to the end of the number
When dividing by 10 remove a 0 from the end of the number.
Step-by-step explanation:
Multiplication:
10 x 2 = 20
10 x 6970 = 69750
Division
20 / 10 = 2
6970 / 10 = 697
Hope this helps! :)
Hank made a phone call from his home in Hong Kong
(time zone +8) to New York City (time zone -5). What
is the time difference between Hong Kong and
New York City?
Answer:
12 hours
Step-by-step explanation:
look it up
Ben's rent a car has a security deposit of $200.00 and it cost $180.00 per day to rent a car. dave's car rental services has a security deposit of $380.00, and it cost $120.00 per day to rent the same car. how many days, d, will it take for the costs to be the same on both car rentals?
It will take 3 days for the cost of the car to be the same which is $740.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands. The addition, subtraction, multiplication, division, exponentiation, and modulus operations are carried out by the arithmetic operators.So,
Ben's car rental:
Security Deposit - $200; rental each day - $180Dave's car rental:
Security Deposit - $380; rental each day - $120Now,
Days after which the cost will be the same:
Day 1:
Ben's car rental: $380Daves car rental: $500Day 2:
Ben's car rental: $560 (+180)Daves car rental: $620 (+120)Day 3:
Ben's car rental: $740 (+180)Daves car rental: $740 (+120)Therefore, it will take 3 days for the cost of the car to be the same.
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how many nonzero complex numbers zz have the property that 0, z,0,z, and z^3,z 3 , when represented by points in the complex plane, are the three distinct vertices of an equilateral triangle?
Consequently, there exist four numbers z:
√3/2 ± I 1/2
-√3/2 ± I 1/2
The three unique vertices of an equilateral triangle are 0, z, and z3: (z^3=0)= e ^iπ/3(z -0 ) ⇔ z^3=e^(±iπ/3)z
=(z^2-e^±iπ/3)z=0⟺z=0
or z^2=e^±iπ/3
Since we have z[tex]\neq[/tex]0, z=e^±iπ/6= ±(√3/2 ± I 1/2 )
There are thus four numbers in z:
√3/2 ± I 1/2
-√3/2 ± I 1/2
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Help due Tuesday asap
The stem-and-leaf diagram is:
Stem Leaf
0 9
1 0, 5, 5, 8
2 1, 4, 8
3 0, 3, 5, 6, 6
4 2, 3, 4, 5, 5, 6, 7, 7, 8
5 1, 4, 5, 6, 8, 8, 8, 8, 9, 9, 9, 9,9,9
The mode is 59
The range is 50
The median is 45.50
The interquartile range is 6.5.
What is a stem-and-leaf plot?A stem-and-leaf plot is a table that is used to display numerical data. A stem-and-leaf plot has two column, one for the stem and the other for the leaf. The stem is the first number in the digit while the leaf is the last number. For example in the number 59, 5 would be the stem and 9 would be the leaf.
Mode is the number that occurs most frequently in a dataset. The mode is 59 because it appears 6 times in the dataset.
Range is the difference between the highest number and the lowest number
Range = 59 - 9 = 50
Median is the number at the center of the dataset.
Median = (n + 1) / 2
37 / 2 = 18.5th term = (45 + 46) / 2 = 45.5
The interquartile range is the difference between the third quartile and the first quartile.
Third quartile = 3/4(n + 1)
3 / 4 x 37 = 27.75 term = 58
First quartile = 1/4 x (n + 1)
1/4 x 37 = 9.25term = (50 + 53) / 2 = 51.5
Interquartile range = 58 - 51.5 = 6.5
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A local fast food restaurant takes in $9000 in a 4 hour period, where the amount taken in varies directly with the number of hours the restaurant is open. Use the
direct variation formula to estimate how many hours it would take the restaurant to earn $25,000. Round your answer to the nearest tenth (one decimal place)..
As per the direct variation formula, it take 11 hours : 6 minutes : 36 seconds to earn $25,000 for the restaurant.
Direct variation:
Direct Variation is said to be the relationship between two variables in which one is a constant multiple of the other.
Direct variation equation: y = kx
Given,
A local fast food restaurant takes in $9000 in a 4 hours period. Write a direct variation equation for the relationship income and number of hours.
Here we need to estimate how many hours it would take the restaurant to earn $25,000.
a) Let us consider income (I) directly varies to number of hours (h) where k is the constant of variation.
I = kh ⇒ Direct variation equation
Solve for k:
9,000 = (k)(4)
k = 9,000/4
k = 2,250
b) When income (I) = 25,000, find the number of hours:
I = kh
25,000 = (2,250) (h)
h = 25,000/2,250
h = 11.11
It will take approximately 11 hours : 6 minutes : 36 seconds for the restaurant to earn $25,000.
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Huyen has round tiles. She must combine the positive and negative signs on the tiles to obtain a result equivalent to -1 Which diagram shows a combination of positive and negative tiles resulting in -1
The combination of number tiles resulting in -1 will be -4 + 3 and 2 - 3.
How to express the value?From the information, Huyen has round tiles and she must combine the positive and negative signs on the tiles to obtain a result equivalent to -1.
It should be noted that sone of the examples of the numbers that will give a value of -1 include:
= -4 + 3
= -1
= 2 - 3.
= -1
Note that an overview was given since you don't given enough information as options.
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a certain town is served by two hospitals. in the larger hospital about 45 babies are born each day, and in the smaller hospital about 15 babies are born each day. as you know, about 50% of all babies are boys. however, the exact percentage varies from day to day. sometimes it may be higher than 50%, sometimes lower.
the more compact hospital. The Law of Large Numbers, which makes intuitive sense, states that when there are more observations, the experimental average tends to approach the true proportion. Large hospitals have more observations, therefore their results are less likely to deviate from 50% or have a wide range of results.
What is the True proportion?An equation that states that two ratios are equal is a genuine proportion. You can utilise information about one ratio in a proportion to determine values in the other equal ratio.
The sample proportion, p′ = 0.842, which is the point estimate of the population proportion, must be determined in order to calculate the confidence interval. Given that CL = 0.95 is the requested confidence level, = 1 - CL = 1 - 0.95 = 0.05 ( 2) ( 2) follows..
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What is the distance between (-6, 4) and (-8, 6)?
Choose 1 answer:
2
3
√4
√8
Answer:
The distance between (-6, 4) and (-8, 6) is 4 units.
Step-by-step explanation:
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\AB = \sqrt{(-8+6)^2+(6-4)^2}\\AB = \sqrt{(-2)^2+(2)^2}\\AB = \sqrt{16}\\AB = 4[/tex]
Just apply the distance formula, quite simple.
create a linear equation that has infinitely many solutions. Must start with 18=
Answer:
Step-by-step explanation:
18=18+x-x*x/x
Help with this asap
Please and thank you
a) 7 video games;
26 - x = 40 - 3x
x = 7
someone give me the answer pls
Answer: 11
Step-by-step explanation:
The sum of the angles of a triangle is 180. So, 3x + 8 + 4x + 11 + 84 = 180
7x = 180 - 8 - 11 - 84
7x = 77
x = 11
two times a number increased by three is equal to four times the same number increased by eleven in standard form
Answer:
n x 2 + 3 = n x 4 + 11
Step-by-step explanation:
n x 2 ("two times a number) + 3 ("increased by three") = ("is equal to") n x 4 ("four times the same number") + 11 ("increased by eleven")
Si 10 barras de chocolate cuestan 3 pesos, ¿cuánto cuesta 1?
To know how much each chocolate bar costs, knowing that ten chocolate bars cost 3 pesos, we only have to divide the total cost of the 10 chocolate bars by the total number of chocolate bars.
So that:
3 pesos ➗ 10 bars = 0.3 pesos/bar.Tenth that; the cost of each bar is 0.3 pesos.
In the semi-circle alongside, ACD is a sector of a circle with the center A. Show that the two shaded regions have equal area.
The figure that is shaded here has the quadrant and the sector as the two parts that it has.
The area of the shaded is given as (πr²) / 4 - bh/2
How to show the equal area of the two shaded regionsWe have ACD as the sector of the circle.
such that we can see that the arc of AC is the quadrant of the circle nad it has the line at point o.
We would solve the area of the shaded as:
the area of a circle / 4 - the area of the triangle
this is mathematically written as
πr²/4 - 1/2bh
where
b = base
h = height
r = radius
This is the area of the shaded
An isosceles traingle would be formed when < A = < C = x
AO is equal to radius of the circle equal to the height CO
mathematically,
< A = < C = x
180 - 90 = 90 / 2
x = 45 degrees
We have to find the area of the sector
This is
= ∅/360 * πr²
= (45 / 360) * (πr²)
= (πr²) / 4
From the calculation we have here, we would see that
the area of the shaded is area of sector - area of the right angle triangle
= (πr²) / 4 - bh/2
When we go on to compare the sides we would then find out that they are equal. Therefore the shaded quadrant equals to the shaded sector.
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Answer quick please. I need to finish this in 5 min
Answer: I got 18
Step-by-step explanation:
Substitute all the variables
18 = 2*3^2
X = 4 * 9^2
X = 4 * 81
X = 324
324/18 = 18
so the is answer is 18.
Also are you going to A+ by any chance?
The Distributive Property- 6( x + 3)
Answer:
-6x-18
Step-by-step explanation:
in class
Answer:-24
Step-by-step explanation: you do -6(x)+(-6)(3) and u get -6+-18 and get -24 hope it helps .
Please answer this question to 1 decimal place
The side x of the rectangle is 36.0 cm
How to find side of a rectangle?A rectangle is a quadrilateral with opposite sides equal to each other and opposite sides parallel to each other.
All four angles of a rectangle are right angles.
The diagonal of a rectangle are equal in length to each other and they bisect each other at there point of intersection.
Therefore,
∠ COD = 48°
∠OCD = ∠ODC = 132 / 2 = 66°
Using sin law
OD / sin 66 = 16 / sin 48
OD sin 48 = 16 sin 66
OD = 16 sin 66 / sin 48
OD = 14.6167273223 / 0.74314482547
OD = 19.6687105931
OD = 19.7 cm
∠AOD = 180 - 48
∠AOD = 132°
∠OAD = ∠ODA = 48 / 2 = 24°
Hence, using sine law let's find x
19.7 / sin 24 = x / sin 132
x sin 24 = 19.7 sin 132
x = 19.7 sin 132 / sin 24
x = 14.6399530619 / 0.40673664307
x = 35.9935605802
Therefore,
x = 36.0 cm
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Write an equation of a line that is parallel to the line 3x + 4y = 32 and contains
the point (7,1).
3x + 4y = 25 is an example of a line that is parallel to the supplied line.
What is equation ?Equations are mathematical expressions that have two algebraic expression on either side of an equals (=) sign. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship. L.H.S. = R.H.S. (left hand side = right hand side) is a fundamental mathematical formula. For an unknown quantity represented by an unknown variable, equations can be solved to determine its value. It is clear that a statement is not an equation if there is no "equal to" sign in it. The phrase will be regarded as an expression.
Given that : line that is parallel to the line 3x + 4y = 32 and contains
the point (7,1).
3x + 4y = 32 is the equation for given line
This type of line is called a slope intercept. The line has a slope of m=[tex]\frac{-3}{4}[/tex].
The slope of parallel lines is equal. As a result, all lines with slope m=[tex]\frac{-3}{4}[/tex].will be perpendicular to one another.
3x + 4y = 25 is an example of a line that is parallel to the supplied line.
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y is inversely proportional to the cube of x
A table of values for x and y is shown
express y in terms of x
Work out the value of x when y = 64
The formula for y in terms of x is y = 8/x^3 and x is 1/2 when y = 64
How to express y in terms of xThe variation statement is given as
y is inversely proportional to the cube of x
This means that
y = k/x^3
Where k represents the constant of variation
Using the points on the table, we have
(x, y) = (1, 8)
This gives
8 = k/1^3
Evaluate
k = 8
So, we have
y = 8/x^3
The value of x when y = 64Here, we have
y = 64 and y = 8/x^3
This gives
8/x^3 = 64
So, we have
x^3 = 1/8
Take the cube roots
x = 1/2
Hence, the value of x is 1/2
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IMPORTANT PLEASE HELP QUICK!!!
How would you graph the result of -3 + 5 as a point on the number line? 1.eight places to the right of zero 2.eight places to the left of zero 3.two places to the right of zero 4.two places to the left of zero day
Answer:
3. two places to the right of zero
Step-by-step explanation:
-3 + 5 = 2. On a graph, you always move right along the x axis for positive numbers, and left for negative numbers.