The horizontally compress the exponential function f(x)=2^x by a factor of 3 is f(3x)=2^3x
When we compress a function y=f(x) by a scale factor of 'k', where k >1, then the function after compression will become :
y=f(x), where k>1
We have given the Exponential function.
What is the scale factor?
The scale factor is a measure for similar figures, that look the same but have different scales or measures. Suppose, two circle looks similar but they could have varying radii. The scale factor states the scale by which a figure is bigger or smaller than the original figure.
The scale factor of the compression (k): 5
Then after horizontal compression, the exponential function will become
f(3x)=2^3x
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I need someone to solve this
The value of ? and X are 12 and 24 respectively
Similarity theorem of a triangleA triangles is 2D shape with three sides and angles.
From the given diagram, the ratio of similar sides is equal to a constant as shown;
15/20 = 9+15/20+x
Cross multiply
15/9+15 = 20/20+x
15/24 = 20/20+x
Comparing with the given ratio
? = 24
X = 20+x
Find x
15(20+x) = 480
300 + 15x = 480
15x = 180
x =12
Fro the given expression
x/32 = 9/?
12/32 = 9/?
12 ? = 32 * 9
? = 24
Hence the value of ?and x from the given diagram is 12 and 24 respectively
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Use the properties of 30-60-90 and 45-45-90 triangles to solve for x in each of the problems below. Then decode the secret message by matching the answer with the corresponding letter/symbol from the exercises.
The trigonometric function gives the ratio of different sides of a right-angle triangle. The given problems can be solved as given below.
What are Trigonometric functions?The trigonometric function gives the ratio of different sides of a right-angle triangle.
[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}\\\\\\Cosec \theta=\dfrac{Hypotenuse}{Perpendicular}\\\\\\Sec \theta=\dfrac{Hypotenuse}{Base}\\\\\\Cot \theta=\dfrac{Base}{Perpendicular}\\\\\\[/tex]
where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.
1st.) x = 5 /Sin(30°)
x = 10
!) sin(45°) = 4/x
x = 4/sin(45°)
x = 4√2
I) Cos(45°) = √3 / x
x = √3 / Cos(45°)
x = √6
E) Tan(60°) = 3√3 / x
x = 3√3 / 3
W) For isosceles right-triangle, the angle made by the legs and the hypotenuse is always 45°.
x = 45°
N) x² + x² = (7√2)²
x = 7
V) Tan(60°) = 7 / x
x = 7√3/3
K) x² + x² = (9)²
x = 9/√2
Y) Sin(60°) = 7√3/x
x = 14
M) Sin(30°) = x/11
x = 11/2
T) Sin(45°) = x/√10
x = √5
A) x + 2x + 90° = 180°
x = 30°
O) Sin(45°) = √2 / x
x = 2
R) Tan(30°) = x / 4
x = 4/√3 = 4√3 / 3
S) Sin(60°) = x / (10/3)
x = 5√3 / 3
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The following diagram represents all of the stages of a shrinking iceberg. The iceberg is circular, and when it started out, it had a radius of 100 feet. The iceberg shrank to a radius that was 75% of its original size every hour. Each circle in the drawing represents the size of the iceberg in each of the successive hours it was shrinking. Using this information, answer the questions having to do with the image:
a. Is this a geometric series or an arithmetic series? Explain why you chose this answer.
b. Describe the steps you would use to calculate the radius of the 6th circle.
c. Assuming this pattern continued forever, what would be the total length if you added all of the circles’ radii* together? Explain your answer.
A geometric progression is a sequence that involves a rate, causing a change in the subsequent values of the sequence with respect to the given rate.
The answers to the given question are as follows:
a. It is a geometric progression.
b. Radius of the 6th circle ≅ 23. 73 ft.
c. The total length, l, can be determined by: l = ∑0.75[tex]R_{i}[/tex], i = 1 to n.
Geometric progression involves a change in the subsequent values of a given sequence due to a rate. So considering the given question, the circular iceberg melts at a certain rate per hour. Thus its radius decreases at the given rate per hour.
a. Therefore it can be deduced that the question is on geometric progression.
b. To determine the radius of the 6th circle, the:
radius of the 1st circle = 100 ft
radius of the 2nd circle = 0.75 x 100
= 75 ft
radius of the t3rd circle = 0.75 x 75
= 56.25 ft
radius of the 4th circle = 0.75 x 56.25
= 42.1875 ft
radius of the 5th circle = 0.75 x 42.1875
= 31.640625 ft
radius of the 6th circle = 0.75 x 31.640625
= 23.73046875 ft
Thus the radius of the 6th circle is approximately 23. 73 ft.
c. Since the process is assumed to continue forever, let the number of hours required to be represented by n, and each radius of the iceberg be represented by R.
So then, we can say that the total length, l, of all the circles' radii is will be given by:
l = ∑0.75[tex]R_{i}[/tex], i = 1 to n
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Complete the following proof.
Given: SW is diameter of R
m = 30°
Prove: m RTW = 15°
Using the circle theorems, we have proven that m ∠RTW = 15°
Circle theoremsFrom the question, we are to prove that m ∠RTW = 15°
In the given diagram,
measure of arc ST = 30°
∴ m ∠SRT = 30°
m ∠SRT = ∠T + ∠W ( Exterior angle of a triangle equals the sum of the two remote angles)
Also,
∠T = ∠W (Radii of the same circle)
∴ m ∠SRT = ∠T + ∠T
m ∠SRT = 2 × ∠T
30° = 2 × ∠T
∠T = 30° /2
∠T = 15°
∴ m ∠RTW = 15°
Hence, we have proven that m ∠RTW = 15°
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If a line has a slope of -3 and goes through the point (-4, 10), then the equation for the line in slope-intercept form is ______________.
a.)
y = 3x - 26
b.)
y = 3x + 2
c.)
y = -3x - 2
d.)
y = -3x + 26
Answer:
c.) y = -3x - 2
Explanation:
Given following:
slope (m): -3pass point: (-4, 10)Equation:
[tex]\sf y - y_1 = m(x - x_1)[/tex]
[tex]\sf y - 10 = -3(x - (-4))[/tex]
[tex]\sf y - 10 = -3(x + 4)[/tex]
[tex]\sf y = -3x -12 + 10[/tex]
[tex]\sf y = -3x -2[/tex]
Which property was applied to create this equivalent expression? 7 x (5 6 x) right-arrow (7 x 5) 6 x the commutative property only the associative property only the distributive property only both the commutative property and the associative property
Step-by-step explanation:
7×5×6×x
7×5×6×392
210×392
82320
The option (B) is correct. Associative property was applied to create the given expression.
Given expression is 7x+(5+6x) rightarrow (7x+5)+6x.
Firstly, check the given expression by commutative property.
The commutative property of addition is a+b=b+a and the commutative property of multiplication is a×b=b×a.
The commutative property didn't satisfy the given expression.
Now, check the given expression by associative property.
The associative property of addition is (a+b)+c=a+(b+c) and the commutative property of multiplication is (a×b)×c=a×(b×c).
The associative property of addition satisfy the given expression.
Further, check the given expression by distributive property.
The distributive property is a×(b+c)=ab+bc.
The distributive property didn't satisfy the given expression.
Hence, the given expression 7x+(5+6x) rightarrow (7x+5)+5x s created by the associative property.
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NEED HELP ASAP
what is the mode of the data
(A) 3
(B) no mode
(C) 17
(D) 40
QUESTION #2
what is the mean of the data
(A) 17
(B) 19.5
(C) 22
(D) 19
use the picture for both of these questions
The function a(b) relates the area of a trapezoid with a given height of 12 and
one base length of 9 with the length of its other base.
It takes as input the other base value, and returns as output the area of the
trapezoid
a(b)=12
Which equation below represents the inverse function b(a), which takes the
trapezoid's area as input and returns as output the length of the other base?
OA 4(a)-+9
O B. o(a)-4-6
OC (a)-1-9
OD. (a)-+6
What is the measure of Angle D F E?
Answer:
Could you please put a picture of the problem?
Step-by-step explanation:
We don't know what you are trying to solve.
Pls help me with my hw.
I'm having difficulty in adjusting bases.
find x, here e is natural logarithm.
Answer:
See below
Step-by-step explanation:
7 + 15 e^(1-3x) = 10 start by subtracting 7 from both sides
15 e^(1-3x) = 3 now divide both sides by 15
e ^(1-3x) = .2 now take the ln of both sides
1-3x = -1.6094379 subtract 1 from both sides
-3x = = 2.6094379 divide both sides by -3
x = .869813
4% of ? Is $75 what is ? If the question
Answer:
1750
Step-by-step explanation:
(3,3p) and (4,p²+1) has gradient -1 find p
[tex] \frac{p {}^{2} + 1 - 3p }{4 - 3} = -1[/tex]
[tex]p {}^{2} - 3p + 1 = -1[/tex]
[tex]p {}^{2} - 3p +2 = 0[/tex]
[tex](p-2)(p - 1) = 0[/tex]
[tex]p = 2 \: \: \: \: \: p = 1[/tex]
The floor of a moving van is 3 ft off the ground. The ramp into the van is 14.5 feet and makes an angle with the ground. Which of the angle measures below is approximately the angle of elevation made with the angle of the ground and the ramp?
Answer:
SHould be 11.6 degrees
The cube of the sum of a number and 3.
The word expression the cube of the sum of a number and 3 can be written as (x + 3)³ or x³ + 9x² + 27x + 27.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
It is given that:
Let x be the number:
The word expression is:
The cube of the sum of a number and 3.
The sum of a number x and 3 is:
x + 3
The cube of the number (x + 3)
= (x + 3)³
After expanding the cube of (a + b)
(a + b)³ = a³ + 3a²b + 3ab² + b³
Similarly,
(x + 3)³ = x³ + 3x²(3) + 3(x)(3)² + (3)³
(x + 3)³ = x³ + 9x² + 27x + 27
Thus, the word expression the cube of the sum of a number and 3 can be written as (x + 3)³ or x³ + 9x² + 27x + 27.
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PLEASE HELP
Triangle not drawn to scale
Given: measure of angle A = 51 degrees, b = 12, and c = 8. What is the length of a to the nearest tenth?
PLEASE HELP QUICK!!
Question 1: About 80% of the packages on a delivery truck are internet orders. The driver delivered 644 packages that were internet orders. About how many total packages did the driver deliver that day?
Question 2: A librarian estimated that 60% of the books in the local library were fiction. She counted 8556 fiction books. About how many books are in the local library?
The total packages the driver delivered is 805.
The total number of books in the local library is 14,260.
What is the total packages delivered?Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred.
Total packages delivered = total number of internet orders / percentage of internet orders
644 / 80%
644 / 0.8 = 805
Total number of books = total number of fiction books / percentage of fiction books
8556 / 60%
8556 / 0.6 = 14,260
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Which exponential equation is equivalent to the logarithmic equation below 4^c=256
The following logarithmic equation is equivalent to the given exponential equation,
[tex]log_{4}(256) = c[/tex]
Computing the Equivalent Logarithmic Equation
The given exponential equation is,
[tex](4)^{c} = 256[/tex]
As per the fundamental properties of exponentiation, the logarithmic equivalent equation of any exponential equation has the same base as that in the corresponding exponential equation. Exponentiation refers to the act of raising a number to the power of another number.
In the exponential equation, [tex](4)^{c} = 256[/tex], $ is the base. So, the base in its equivalent logarithmic equation will also be 4.
The result of the exponential expression becomes the operand for the log.
Terms in a Logarithmic Equation
For the logarithmic equation, [tex]log_{4}(256) = c[/tex],
4 is called the base of the log. The variable 'c' is the logarithm of 256 to base 'a'.
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What are the domain and range of f(x)=logx-5
Hello and Good Morning/Afternoon:
Let's take this problem step-by-step:
Let's define some terms:
Domain: the set of inputs in the function (in this case, it is x)Range: the set of all of the possible outputs (in this case, it is y)Let's find the domain:
For log(x),
⇒ the only inputs that are accepted are nonnegative and nonzero
⇒ therefore: Domain is (0, ∞)
Now let's find out the range:
The biggest constraint of the output is log(x)
⇒ however log(x) has a range of (-∞,∞)
⇒ therefore the entire equation's range is
(-∞,∞)
Answer:
Domain: (0,∞)Range: (-∞,∞)Hope that helps!
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Greg walks 1/3 mile in 10 minutes
Answer:
Greg will walk 1 mile in 30 minutes, or 2 miles per hour.
Explanation:
Multiply the ratio of miles to minutes:
1/3 mi : 10 min
1 mi : 30 min
2 mi : 1 hr
I need this done urgently!
Answer:
1)65.9
2)326.6
3)13.6
4)8.0
Step-by-step explanation:
The trick is always to look at the number after the first decimal for rounding to 1 decimal place, if its above 5, you round it up to the next decimal; eg. 13.45 = 13.5 because the 5 will round it up,and if value below 5, you round it down; eg. 12.34 = 12.3 because the 4 is below 5 and the nearest 10th decimal is 3.
3. Try It #3 Write the point-slope form of an equation of a line with a slope of -2 that passes through the point (-2,2). Then rewrite it in the slope-intercept form.
Answer:
Point-slope form of equation given as [tex]$y-2=-2(x+2)$[/tex].
Slope-intercept form of equation is given as [tex]$y=-2 x-2$[/tex].
Step-by-step explanation:
In the question, it is given that the slope of a line is -2 and it passes from (-2,2).
It is asked to write the point-slope form of the equation and rewrite it as slope-intercept form.
To do so, first find the values which are given in the question and put it in the formula of point-slope form. Simplify the equation to rewrite as slope-intercept form.
Step 1 of 2
Passing point of the line is (-2,2).
Hence, [tex]$x_{1}=-2$[/tex] and
[tex]$$y_{1}=2 \text {. }$$[/tex]
Also, the slope of the line is -2.
Hence, m=-2
Substitute the above values in point-slope form of equation given by [tex]$y-y_{1}=m\left(x-x_{1}\right)$[/tex]
[tex]$$\begin{aligned}&y-y_{1}=m\left(x-x_{1}\right) \\&y-2=-2(x-(-2) \\&y-2=-2(x+2)\end{aligned}$$[/tex]
Hence, point-slope form of equation given as y-2=-2(x+2).
Step 2 of 2
Solve y-2=-2(x+2) to write it as slope-intercept form given by y=mx+c.
[tex]$$\begin{aligned}&y-2=-2(x+2) \\&y-2=-2 x-4 \\&y=-2 x-4+2 \\&y=-2 x-2\end{aligned}$$[/tex]
Hence, slope-intercept form of equation is given as y=-2x-2.
if X+1/x = 4 find x-1/x
what’s the answer??? Pls help asap this is due tonight
Answer:
30
Step-by-step explanation:
[tex]5(3) - 3( - 5)[/tex]
[tex]15 + 15[/tex]
[tex]30[/tex]
hope it was helpful. any confusion u may ask
Step-by-step explanation:
The answer is 30 the value of X and y is given that put them in 5x-3y
help me solve this thanks
Answer:
The amount after 6 years is $25,533.34.
Step-by-step explanation:
Use the formula f(t)=P(1+b)^t.
Plug in the information.
f(6)=18000(1+0.06)^6
Plug in 18000(1.06)^6 into calculator.
25,533.344020608.
Round to 2 decimal places.
25,533.34
The amount after 6 years is $25,533.34.
Hope this helps!
If not, I am sorry.
(LOOK AT IMAGE)
The sides of a regular 12-sided polygon have been extended to make a star, as shown below.
Calculate the size of angle x.
Give your answer in degrees (°).
Answer: 120
Step-by-step explanation:
The interior angle of the 12-sided polygon is
[tex]\frac{180(12-2)}{12}=150^{\circ}[/tex]
So, if we consider the triangle with angle x, two of its angles are each [tex]30^{\circ}[/tex] since they are supplementary to the interior angle of the 12-sided polygon.
Therefore, as angles in a triangle add to 180 degrees, x=120.
Loralei's dance team wants to purchase new uniforms for their national dance competition. They will get 25% of their total cookie dough sales to add to the money they already raised in the car wash they held. Her team raised $356.00 during their car wash and sold a total of $2,973.00 in cookie dough. How much money will they have in total to spend on new uniforms?
The total money the dance team would have to spend on the new uniforms is $1099.25.
How much money would the dance team have?Percentage can be described as a fraction of an amount expressed as a number out of hundred.
Total amount = (25% of the amount raised at the sale) + amount raised during the car wash
$356+ ( $25% x $2,973) = $1099.25
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26) Jenny drove 48 mph for 65 minutes. Which is true? a. Jenny drove exactly 48 miles b. Jenny drove more than 48 miles c. Jenny drove less than 48 miles
Answer:
B- Jenny must have driven more than 48 miles.
Step-by-step explanation:
If Jenny rode for 60 at 48 mph, it would be exactly 48 miles. Though there is only 60 minutes in an hour, and Jenny rode 5 minutes longer than that, her drive being 65 minutes. To find how much she rode, 5 extra minutes into an hour would divide equally into 60, resulting in 12. Divide 48 by 12, and Jenny would have driven 4 miles in the 5 minutes drive after 60 minutes.
(Jenny basically driven 52 miles in 65 minutes).
The black graph is the graph of y= f(x). Choose the equation for the red graph.
here is your answer
mark as brilliant and like pls in my answerif u want complete solution pls message meHow would you describe a transformation to someone who has never taken geometry before? Explain what a transformation is, and state how a transformation can be used to solve a problem in real life.
Transformation is the movement of a point from its initial location to a new location. Dilation can be used to scale down a map so that it can be plotted on a paper.
What is a transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, rotation, reflection and dilation.
Dilation is the increase or decrease in the size of a figure.
Dilation can be used to scale down a map so that it can be plotted on a paper.
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Complete the equation of the line through (-6,-5)(−6,−5)left parenthesis, minus, 6, comma, minus, 5, right parenthesis and (-4,-4)(−4,−4)left parenthesis, minus, 4, comma, minus, 4, right parenthesis.
Use exact numbers.
y=y=y, equals
Answer:
y = 1/2 x -2
Step-by-step explanation:
rise/run from (-6, -5) to (-4, -4) = 1/2
(rise 1, run 2)
meaning that slope (m) = 1/2
we can now rewrite our points in y=mx + b formatting:
y = mx + b
-5 = (1/2)(-6) + b
-4 = (1/2)(-4)+b
now, let's solve for b
-5 = (1/2)(-6) + b
-5 = -3 + b
-2 = b
-4 = (1/2)(-4)+b
-4 = -2 + b
-2 = b
So, the equation for our line is y = [tex]\frac{1}{2}[/tex] x- 2
hope this helps!! have a lovely day :)
Answer: y = 1/2x - 2
Step-by-step explanation: it’s right on khan academy (picture for proof)