Answers
Answer:
1). g(x) = [tex]5^{3x}[/tex]
2). g(x) = [tex]\frac{1}{3}5^{x}[/tex]
3). g(x) = [tex]3(5)^{x}[/tex]
4). g(x) = [tex]5^{\frac{1}{3}x}[/tex]
Step-by-step explanation:
Parent function f(x) = [tex]a^{x}[/tex] when transformed in the form of [tex]g(x)=h(a^{\frac{x}{k} })[/tex]
1). If h > 1, function is vertically stretched.
2). If 0 < h < 1, function is vertically compressed.
3). If k > 1, function is horizontally compressed.
4). If 0 < k < 1, function is horizontally stretched.
Parent function of the given functions in the question is f(x) = [tex]5^{x}[/tex]
g(x)= [tex]\frac{1}{3}(5^{x})[/tex], parent function is vertically compressed by a factor of [tex]\frac{1}{3}[/tex].
g(x) = [tex]5^{3x}[/tex], parent function 'f' is horizontally stretched by a factor of 3.
g(x) = [tex]5^{\frac{x}{3}}[/tex], parent function 'f' is horizontally compressed by a factor of [tex]\frac{1}{3}[/tex].
g(x) = [tex]3(5^{x})[/tex], parent function 'f' is vertically stretched by a factor of 3.
Related Questions
factor y=2x^2+10x+12
Answers
Answer:
y=2(x+2)(x+3)
Step-by-step explanation:
First, we need to factor the right side:
y=2(x^2+5x+6)
Now, we can have an incomplete equation like this:
y=2(x+_)(x+_)
In the blanks, we need to fill out numbers that add to be 5 and multiply to be 6. What are factors of 6? 6 and 1, 2 and 3. Do 6 and 1 add to be 5? No. Do 2 and 3 add to be 5? Yes!
So, our factored form is
y=2(x+2)(x+3)
ok I need help with this cylinder volume thing
ok so the volume is 20litres and the diameter is 13.5 but I need to find the length value. Length value needs to be in metres
Answers
Answer:
h = 0.139725
Step-by-step explanation:
Volume of a Cylinder Formula: V = πr²h
You are given V = 20 and r = 6.75.
20 = π(6.75)²h
20/45.5625π = h
h = 0.139725
I'm not sure if this is correct or not.
Answer:
≈1.4 m
Step-by-step explanation:
V= 20 l= 20 000 cm³
d= 13.5 cm ⇒ r= 13.5 cm / 2= 6.75 cm (assume it is cm)
V= πr²h
h= V/πr²= 20000/3.14*6.75² ≈ 140 cm= 1.4 m
Sheila plans to row across the lake from point A to point B as shown below.
To determine how far she will have to row, she has chosen a point Cand
calculated the labeled data. How many miles will she have to row? Round
your answer to two decimal places.
12.3 miles
15.6 miles
66.7°
Answers
Answer: 15.58 miles
Step-by-step explanation:
Given two sides and an included angle, segment AB can be calculated using the cosine rule :
Given a = 15.6 miles, b = 12.3 miles and C=α=66.7°
To find c:
c= √(a^2+b^2-2abcosα
c = √ 15.6^2 + 12.3^2 -(2 × 15.6 × 12.3)cos66.7°
c = √243.36 + 151.29 - 151.79454
c = √242.85545
c = 15.583820
c = 15.58 miles
Answer:
13.56
Step-by-step explanation:
hope that helps
.Write the following number in the standard form. a) 0.000000012
Answers
Answer:
[tex]1.2 * 10 ^{-8}[/tex]
Step-by-step explanation:
=> 0.000000012
Moving the decimal point after 1st non-zero digit:
=> [tex]1.2 * 10 ^{-8}[/tex]
Answer:
Scientific Notation: 1.2x10^-8, or 1.2e-8
Step-by-step explanation:
fractorise the following (a-b)²+(a-b)
Answers
Step-by-step explanation:
taking common (a-b)
so we get the answer
Jo paints some tennis balls and puts them in a bag. She picks a ball at random from the bag and replaces it. She repeats this 60 times, and gets a ball not painted 50 times. Find the experimental probability of getting a painted ball from Jo's bag.
Answers
Answer:
1/6
Step-by-step explanation:
An experimental probability is the number of times an event occurred when actually attempted.
So, if Jo does the experiment 60 times and receives 50 unpainted balls, then calculate how many painted balls she got:
60-50 = 10.
So, the probability of picking a painted ball = 10/60 = 1/6
Hope this helps
The parallelogram is rotated 90° anticlockwise about point G
Which of the points A , B , C and D is the image of point R ?
Answers
Answer:
C
Step-by-step explanation:
Let's say that point G is the origin, (0,0). Then, the coordinates of point R would be (-3, -5). Rotating the point 90° counter-clockwise would result in the final coordinates being (5, -3), therefore the answer is C.
PLEASEEE HELPPP IT DUE TODAYYY
Answers
Answer:
All angles in a rectangle are congruent, because in a rectangle, all angles are 90 degrees.
solve with ans : the compound interest of a sum of money in 1 years and 2 years are Rs 450 and Rs 945 respectively. find the rate of interest compounded yearly and the sum .
Answers
Answer:
The rate of interest compounded yearly =10%The sum compounded is Rs4,500Step-by-step explanation:
Compound Interest Formula, Amount, [tex]A(n)=P(1+r)^n[/tex]
Interest=Amount - Principal
[tex]I=P(1+r)^n-P[/tex]
At the end of 1 year, interest =Rs450, therefore:
[tex]450=P(1+r)-P\\450=P+Pr-P\\450=Pr[/tex]
At the end of 2 years, interest =Rs945, therefore:
[tex]945=P(1+r)^2-P\\945=P(1+r)(1+r)-P\\945=P(1+r+r+r^2)-P\\945=P(1+2r+r^2)-P\\945=P+2Pr+Pr^2-P\\945=2Pr+Pr^2[/tex]
Recall: Pr=450
Therefore:
[tex]945=2(450)+Pr^2\\945-900=Pr^2\\Pr^2=45[/tex]
Comparing Pr=450 and [tex]Pr^2=45[/tex]
[tex]\dfrac{Pr^2}{Pr}= \dfrac{45}{450}\\r=0.1[/tex]
Substitute r=0.1 to obtain P
0.1P=450
P=Rs4500
Therefore:
The rate of interest compounded yearly =0.1=10%The sum compounded is Rs4,500Which explains how to find the radius of a circle whose equation is in the form x2 + y2 = z? The radius is the constant term, z. The radius is the constant term, z, divided by 2. The radius is the square root of the constant term, z. The radius is the square of the constant term, z.
Answers
Answer:
The radius is the square root of the constant term, z
Step-by-step explanation:
makes sense, also took the test :)
Answer:
C. The radius is the square root of the constant term, z.
Step-by-step explanation:
Hope this helps :)
PLEASE help me with this question!!!!!!
Answers
Answer:
270[tex]\sqrt{3}[/tex] cm³
Step-by-step explanation:
A regular hexagon can be cut into 6 equilateral triangles.
The area (A) of an equilateral triangle can be calculated as
A = [tex]\frac{s^2\sqrt{3} }{4}[/tex] ← where s is the side length, here s = 6
A = [tex]\frac{6^2\sqrt{3} }{4}[/tex] = 9[tex]\sqrt{3}[/tex] cm² ← multiply by 6
area of base = 6 × 9[tex]\sqrt{3}[/tex] = 54[tex]\sqrt{3}[/tex] cm²
The volume (V) of the prism is calculated as
V = area of base × height = 54[tex]\sqrt{3}[/tex] × 5 = 270[tex]\sqrt{3}[/tex] cm³
What is the value for y? Enter your answer in the box. y = An isosceles triangle A B C with horizontal base A B and vertex C is below the base. Side A C and C B are labeled with single tick mark. All the three angles are labeled. Base angles C A B is labeled as 34 degrees and angle C B A is labeled as left parenthesis x minus 5 right parenthesis degrees. The angle A C B is labeled as 4y degrees.
Answers
Answer:
28.
Step-by-step explanation:
I just did the question and I got it right. The answer above is right. The image below is where I did the question and has the picture attached next to it too.
*And I accidentally clicked the one star option, that's why it has such a low score.
An isosceles triangle is a triangle where two sides are equal and the angles opposite to the sides are also equal.
The value of y is 28.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
An isosceles triangle is a triangle where two sides are equal and the angles opposite to the sides are also equal.
m∠CAB = 34
m∠CBA = x - 5
m∠ACB = 4y
Triangle ABC is an isosceles triangle.
AC and BC are sides are equal.
This means,
m∠CAB = m∠CBA
34 = x - 5
34 + 5 = x
x = 39
Now,
The sum of the angles in a triangle is 180 degrees.
This means,
34 + (x -5) + 4y = 180
34 + (39 - 5) + 4y = 180
34 + 34 + 4y = 180
68 + 4y = 180
4y = 180 - 68
y = 112 / 4
y = 28
We can cross-check.
34 + 34 + 4 x 28 = 180
34 + 34 + 112 = 180
180 = 180
Thus,
The value of y is 28.
Learn more about triangles here:
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Which equations represent a line that passes through the points given in the table? Check all that apply. y – 2 = –6(x + 10) y – 2 = –(x + 10) y – 1 = –(x + 4) y = –6x – 58 y = –x + y = –x + 5
Answers
Answer: b, c, and e
Step-by-step explanation:
I hope I helped
The standard form of the equation of straight line is given by
y - 1 = -1/6(x + 4)
What is the general equation of a Straight line?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
The equation of a straight line can be also written as -
Ax + By + C = 0
By = - Ax - C
y = (- A/B)x - (C/A)
We have a table as given in the image attached at the end of answer.
The slope of the line will be -
m = (y₂ - y₁)/(x₂ - x₁)
m = (1 - 2)/(- 4 + 10)
m = - 1/6
The standard form of the equation of straight line is given by -
y - y₂ = m(x - x₂)
y - 1 = -1/6(x + 4)
Therefore, the standard form of the equation of straight line is given by
y - 1 = -1/6(x + 4)
To solve more questions on straight lines, visit the link below-
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[Refer to the image attached for complete question]
Write the rule for finding the coordinates of a point that has undergone a dilation (with the origin as the point of dilation). Use this rule to find the coordinates of this point's dilation from the origin, with a scale factor of 3: (4, 10).
Answers
Answer:
(12, 40)
Step-by-step explanation:
The first thing is to assume that we have a point with the following coordinates (x, y).
Now, we can have two different cases since the meaning of the expansion of a point is moving to a new point that is a greater distance from the origin if we are expanding by a value, that is, an integer in the system of coordinates and the other case is that if we are dilating by a fraction that is between 0 <x <1, then the distance from the origin decreases.
Now, the point (x, y) goes through an expansion by a scale factor f (with the origin as the expansion point), then the new coordinate of the point = [f * x, f * y], that scale factor has the value of 3, so if we replace we have:
(3 * 4, 4 * 10) = (12, 40)
between which to whole numbers does the square root of 37 lie?
Answers
Between 6 and 7
6×6=36
7×7=49
hopefully this helped
The number √37 is lies between whole numbers 6 and 7.
We have to given,
A number is, √37
By the definition of square root, we get;
⇒ √37 = 6.08
And, We know that,
Number 6.08 is lies between whole number 6 and 7.
Hence, We get;
⇒ 6 < √37 < 7
Therefore, The number √37 is lies between whole numbers 6 and 7.
Learn more about Number system visit:
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evaluate 2x squared -1 when x=3
Answers
Hey there! :)
Answer:
17.
Step-by-step explanation:
Given:
f(x) = 2x² - 1
Substitute in 3 for x:
f(3) = 2(3)² - 1
f(3) = 2(9) - 1
Simplify:
f(3) = 18 - 1
f(3) = 17.
The company recently reduced its production to 1 million bicycles, but maintained its profit of 30 million dollars. What greater number of bicycles had the company previously produced to make the same profit? Round your answer to the nearest tenth.
Answers
Answer:
1.3 million bicycles!
Step-by-step explanation:
Answer:
1.3 million bicycles
Step-by-step explanation:
got it right on edge 2020
Alexa wants to have a bowling average of at least 210. If her scores are 230, 185, and 195, what does she need to score on her fourth game? Which inequality best represents the situation?
Answers
Step-by-step explanation:
so her minimum 4th score is calculated this way:
[tex] \frac{230 + 185 + 195 + x}{4} = 210 \\ 610 + x = 840 \\ x = 230[/tex]
so in round four
her score should be x in the way that:
x≥230
Simple and easy question
please help
Answers
Answer:
Volume = πr²h
= 3.14 * 5² * 4
= 314 cubic yards
Answer:
[tex]314 yd^3[/tex]
Step-by-step explanation:
Hey there!
Volume = π r^2 h
Plug in,
(3.14)(5^2)(4)
5•5 = 25
25 • 4 = 100
3.14 • 100
= 314
Hope this helps :)
A square has a side length x and a circle has a radius (x-1). At what value of x will the two figures have the same area?
a. 1.66
b. 2.29
c. 0.5
d. 1.25
Answers
Answer:
B
Step-by-step explanation:
The area of the square can be calculated using S^2 = x^2
The area of the circle is pi * r^2
= 22/7 * (x-1)^2
= 22(x-1)^2/7
So we need the value of x, that will make;
x^2 = 22(x-1)^2/7
In this kind of scenario, since we have options, it is best to test values instead of going through long calculations
Let’s try 2.29
So;
2.29^2 = 22/7(2.29-1)^2
5.2441 = 5.23
So close , but let’s see if any other value will
give us a closer value
Let’s work with 1.66
1.66^2 = 22/7(1.66-1)^2
2.7556 = 1.369
This is far from what we need
Let’s try 0.5
0.5^2 = 22/7(0.5-1)^2
Thus gives a negative answer on the right hand side, so no need trying
And lastly 1.25
1.25^2 = 22/7(1.25-1)^2
1.5625 = 0.1946
So the first test still gives the most probable answer to a decimal place accuracy
Answer:
b. 2.29
Step-by-step explanation:
the answer above is correct please give them the brainiest
Simplify the radical /81d^6.
O 9d2
81d3
O 9d3
O 906
Answers
Answer:
The answer is option C.
Step-by-step explanation:
[tex] \sqrt{ {81d}^{6} } = \sqrt{81} \times \sqrt{ {d}^{6} } \\ = 9 {d}^{3} [/tex]
Hope this helps you
Answer:c
Step-by-step explanation:
Three angles fits exactly around a point. Two of the angles are equal.The diffrence between the largest and the smallest angle is 30.Find the size ofthe three angles
Answers
Answer:
The angles are 110, 110 and 140
Step-by-step explanation:
Let the equal angles be x.
So we have angles x, x and another third one
Now, the other third angle is 30 degrees larger than x, this means that the other third angle is 30 + x
Since they are angles at a point, adding the three together will make or give 360.
Thus,
x + x + x + 30 = 360
3x + 30 = 360
3x = 360-30
3x = 330
x = 330/3
x = 110
So the other third angle is 110 + 30 = 140
So the angles are 110, 110 and 140
Which is the graph of f(x)=sqrt x?
Answers
Answer:
B
Step-by-step explanation:
a parabola would be x2 since it is square rooted it would be a curved so the answer would be the second graph
ayuda porfa se ruego :b
Answers
Answer:
b) 5u.
Step-by-step explanation:
El triangulo es 45-45-90, entonces los dos lados son iguales. Si un lado es 8u, el otro lado tambien es 8u.
Entonces, 8u + x = 13u.
x = 13u - 8u
x = 5u
Espero que esto te ayude!
express 1120 product of powers of its prime factors
Answers
Answer:
5x2x2x2x2x7x7
Step-by-step explanation:
First list all of the prime factors of 1120. You can do this by drawing a factor tree.
The results are:
5,2,2,2,2,7,7
To make 1120 a product of its prime factors, we just have to write it in the form:
5x2x2x2x2x7x7
Hope this helps
Hi can someone please help me.
The bases of a right triangle measure x-3 and x+4. If the hypotenuse of the triangle is 2x-3, what is the length of the hypotenuse?
Answers
Answer:
13 units.
Step-by-step explanation:
By Pythagoras:
(x -3)^2 + (x + 4)^2 = (2x - 3)^2
x^2 - 6x + 9 + x^2 + 8x + 16 = 4x^2 -12x + 9
4x^2 - x^2 - x^2 + 6x - 8x - 12x + 9 - 9 - 16 = 0
2x^2 -14x - 16 = 0
2(x^2 - 7x - 8) = 0
2(x -8)(x + 1) =0
x = 8, -1.
As x must be positive we take x = 8
So the hypotenuse is 2(8) - 3 = 13 units long.
What is the average rate of change for this exponential function for the
interval from x=2 to x= 4?
a.-6.
b.6
c.12
d.-12
Answers
Answer:
The correct answer is:
b. 6
Step-by-step explanation:
We are given the graph of an exponential function.
We have to find the average rate of change for this exponential function from x = 2 to x = 4.
First of all, let us plot the point on the graph on the points x = 2 and x = 4.
Please refer to the attached diagram.
We can easily find that the value of y at x = 2 is 4.
the value of y at x = 4 is 16.
[tex]\therefore[/tex] the coordinates are (2, 4) and (4, 16).
Let the points be A(2, 4) and B(4, 16)
Now, let us find the average rate of change for exponential function i.e. change in value of y divided by change in value of x from x = 2 to x = 4:
Formula:
[tex]\text{Average rate of change = } \dfrac{\text{Change in y coordinate}}{\text{Change in x coordinate}}[/tex]
[tex]\Rightarrow \dfrac{16-4}{4-2}\\\Rightarrow \dfrac{12}{2}\\\Rightarrow 6[/tex]
So, correct answer is option b. 6
3/4, 1, 4/3, 16/9,... which of the following are recursive formulas for the nth term of the following geometric sequence?
Answers
Answer:
nth term of geometric sequence = a(n) = [tex](3/4)(4/3)^{n-1}[/tex]
Step-by-step explanation:
nth term of geometric sequence = a(n)
nth term of geometric sequence = a(n) = [tex]ar^{n-1}[/tex]
Where,
a = first term
r = common ratio
n = number of term
So,
GP: 3/4, 1, 4/3, 16/9
a = 3/4
r = 1 / [3/4] = 4/3
n = n
nth term of geometric sequence = a(n) = [tex]ar^{n-1}[/tex]
nth term of geometric sequence = a(n) = [tex](3/4)(4/3)^{n-1}[/tex]
solve for x -48=6(x-3)
Answers
Answer:
[tex]\boxed{x = -6}[/tex]
Step-by-step explanation:
[tex]x-48 = 6(x-3)[/tex]
Resolving parenthesis
[tex]x - 48 = 6x-18[/tex]
Adding 18 to both sides
[tex]x-48+18 = 6x\\x-30 = 6x[/tex]
Subtracting x from both sides
[tex]-30 = 6x-x\\-30 = 5x[/tex]
Dividing both sides by 5
[tex]-30/5 = x[/tex]
[tex]-6 = x\\[/tex]
OR
x = -6
Answer:
x = - 6Step-by-step explanation:
x - 48 = 6(x - 3)
Expand the terms in the bracket
That's
x - 48 = 6x - 18
Group the constants at the right side of the equation and the ones with variables at the left side
x - 6x = 48 - 18
- 5x = 30
Divide both sides by - 5
x = - 6Hope this helps you
how far is 5 and a half from negative 1 and 3 fourths
Answers
Answer:
[tex] 7.25 \: units[/tex]
Step-by-step explanation:
[tex]d \bigg(5 \frac{1}{2}, \: \: - 1 \frac{3}{4} \bigg) \\ \\ = d \bigg( \frac{11}{2}, \: \: - \frac{7}{4} \bigg) \\ \\ = d \bigg( \frac{22}{4}, \: \: - \frac{7}{4} \bigg) \\ \\ = \frac{22}{4} - \bigg( - \frac{7}{4} \bigg) \\ \\ = \frac{22}{4} + \frac{7}{4} \\ \\ = \frac{22 + 7}{4} \\ \\ = \frac{29}{4} \\ \\ = 7. 25\: units[/tex]