The resulting function after all transformations have been carried out is; -7log6(-x) - 2.
Which function results from all the Transformations?The transformations which ensued on the function given are as follows;
Stretched vertically by a factor of 7; Hence, we have; 7f(x) = 7log6(x).Reflected over the x-axis; -7f(x) = -7log6(x).Reflected over the y-axis; -7f(x) = -7log6(-x).Shifted up by 2 units; -7f(x) -2 = -7log6(-x) - 2.On this note, it follows that the resulting function upon all the Transformations is; = -7log6(-x) - 2.
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How can I solve this?? Please help
Answer:yes
15x times 2=30x
15x times 3= 45x
3y tines 2 =6y
3y times 3=9y
Step-by-step explanation:
The triangles below are similar. Find x.
Answer: 105
Step-by-step explanation:
Corresponding sides of similar triangles are proportional, so
[tex]\frac{x}{14}=\frac{97.5}{13}\\\\=\frac{x}{14}=7.5\\\\x=\boxed{105}[/tex]
You have been saving $25 a week to make the trip; you now have $200. This money will be budgeted to include gas, food, and entertainment. Write an equation to model your savings plan and then graph it. What would be the domain and range in this situation?
Function g can be thought of as a translated (shifted) version of f(x)=x^2
Answer:
g(x)=x^2 -6x +5
Step-by-step explanation:
Answer:
g(x) = (x - 3)² - 4
Step-by-step explanation:
When values are directly added to the "x" variable (usually inside of parentheses), the function shifts to the left that many units.
When values are directly subtracted from the "x" variable, the function shifts to the right that many units.
When values are added to an overall function, the function shifts upwards that many units.
When a value is subtracted from an overall function, the function shifts downwards that many units.
We can determine how the function has been translated by looking at the changed position of the vertex (the lowest point of the line).
As you can see, the new vertex now lies on x = 3 rather than x = 0.This means that there should be a -3 directly next to the "x" variable in the new function.
The new vertex also now lies on y = -4 rather than y = 0. Therefore, there should be a -4 added to the overall equation.
These changes make the new function:
g(x) = (x - 3)² - 4
which equation would match the table the most?? pls help ☠️☠️
Decide if the function is an exponential function. If it is, state the initial value and the base. (5 points) y = - 6.1 ⋅ 3x
The function is an exponential function; the initial value is -6.1 and the base is 3
How to determine the function type?The equation of the function is given as:
y = -6.1 *(3^x)
An exponential function is represented as:
y = ab^x
Where:
Initial value = a
base = b
By comparison, we have
a = -6.1 and b = 3
Hence, the function is an exponential function; the initial value is -6.1 and the base is 3
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A fish tank has a length of 12 cm a width of 15 cm and a depth of 25 cm find the volume of the fish tank
Answer:
The formula of volume of cube is l*b*h
45*25*10=11250 cubic cm
Step-by-step explanation:
volume =length×width ×height
given:
length:45 cm
width:25 cm
height(depth):10 cm
according to the question
45 cm×25cm ×10cm
11250 cubic cm
Which of the following results in the difference of two squares?
The difference of two squares expression is (c) (5x + 3y)(5x - 3y)
How to determine the difference of two squares?The difference of two squares expression is represented as:
a^2 - b^2 = (a + b)(a - b)
Using the above as a guide, we have the following expression in option (c)
(5x + 3y)(5x - 3y)
Hence, the difference of two squares expression is (c) (5x + 3y)(5x - 3y)
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PLEASE HELP SOON THX SO MUCH
an airplane flies 3300 miles with the wind in 3 hrs 18 minutes. it takes 4 hrs 24 mins to make the return flight against the same wind. find speed of airplane and wind.
Answer:
The speed of aeroplane =875 miles/hr and the speed of wind =125 miles/hr.
Step-by-step explanation:
Let’s assume the speed of the plane =x miles/hr
And let the speed of wind =y miles/hr
So, the speed of the aeroplane in the direction of wind =(x+y) miles/hr
Speed of the aeroplane in the opposite direction of wind =(x–y) miles/hr
We know that, distance=speed×time
Then according to the given conditions, we have
3300=(x+y)×(3+(18/60))
here convert 18mins to hour by dividing by 60 and add to 3hrs.
⇒x+y= 3300/3.3
⇒x+y=1000 … (i)
And,
3300=(x-y)×(4+(24/60))
here convert 24mins to hour by dividing by 60 and add to 4hrs.
⇒x-y= 3300/4.4
⇒x-y=750 … (ii)
Adding equation (i) and (ii), we get
2x=1750
⇒x= 1750/2
=875
Substituting the value of x in equation (ii), we get
875−y=750
⇒y=875-750
⇒y=125
Therefore, the speed of aeroplane =875 miles/hr and the speed of wind =125 miles/hr.
emilio bought 5.65 of green grapes and 3.07 pounds of red grapes
The weight of each bag is 0.545 lb .
What is weight ?Weight in maths is the value of the mass of an object on a measuring scale , It is measured in pound , ounce , kilogram etc.
It is given that
Total weight of green grapes = 5.65 lb
Total weight of red grapes = 3.07lb
Total weight = 5.65 +3.07 = 8.72 lb
Total number of bags = 16
the weight of each bag
= 8.72 / 16
= 0.545 lb
Therefore the weight of each bag is 0.545 lb .
The complete question is
Emilio bought 5.65lb of green grapes and 3.07lb of red grapes. He divided the grapes equally into 16 bags. If each bag of grapes has the same weight, how much does each bag weigh?
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If f(x) = 3x + 2, what is f(5)?
Answer:
If a numbed substitutes x in f (x), you must substitute that number in the function for x.
Step-by-step explanation:
f(5) = 3(5) + 2
f(5 )= 17
Given that a bag of skittles has 15 blue candies, 16 orange candies, 12 yellow, 14 red, and 5 green candies, find the following probabilities.
Step-by-step explanation:
If you are asking about the probability of Getting Blue, Orange, Yellow, Red and Green
P=N(E)/N(S)
Probability of Blue=15/62
probability of Orange= 16/62
probability of yellow=12/62
probability of Red=14/62
probability of Green=5/62
QUESTION IS DOWN BELOW 15 POINTS EACH
Answer:
See below
Step-by-step explanation:
density = mass/volume
re-arrange to density * volume = mass
20 * 64 = 1280 gm
Density = mass/volume
re-arrange to volume = mass / density
560 / 14 = 40 cm^3
Select the correct answer.
A triangular tabletop has the given dimensions. Vinyl is placed around the outer edges of the tabletop.
3 ft
45°
45°
What is the approximate length of vinyl needed for the outer edges of the tabletop?
OA.
OB.
OC.
O D.
10.2 ft
14.2 ft
9 ft
11.2 ft
The length of the vinyl must be 10.2ft
How to get the length of the vinyl?We know that two of the angles of the triangle measure 45°, then we have a right triangle of 45°, 45°, 90°.
We know that the catheti measure 3 ft, using the pithagorean theorem, we know that the length of the hypotenuse is given by:
[tex]H^2 = (3ft)^2 + (3ft)^2[/tex]
[tex]H = \sqrt{2*(3ft)^2} = 4.2ft[/tex]
Then the perimeter of the triangle is:
P = 3ft + 3ft + 4.2ft = 10.2ft
The length of the vinyl must be 10.2ft
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how to estimate 11578995 to the nearest lakh
Answer:
1,16,00,000
Step-by-step explanation:
To round to the nearest lakh, identify the digit that is to the right of the number place representing 1 lakh. If it is 5 or greater, round up.
Round to nearest lakhThe value 1,15,78,995 is 115.78995 lakh. The digit to the right of the decimal point in this number is 7, which is greater than 4. Hence the nearest lakh is 116 lakh, or ...
1,16,00,000
Match the multiplication problem on the left with the simplified polynomial on the right.
4x(4x²-x+3)
16x²
(8x + 1)(2x - 3)
4x² (4x)
(2x + 3) (8x² - 4x + 3)
►
16x²-22x-3
16x³
16x³4x² + 12x
16x³4x² + 4x - 12
16x³ + 16x² - 6x +9
The match of the multiplication problem with the simplified expressions is as follows:
4x(4x²-x+3) ⇒ 16x³ - 4x² + 12x(8x + 1)(2x -3) ⇒ 16x² - 22x - 3 4x² (4x) ⇒ 16x³(2x + 3) (8x² - 4x + 3) ⇒ 16x³ + 16x² - 6x + 9Multiplication of polynomial expressions.The process involved in multiplying polynomial expression requires using all the parameters in parentheses to multiply each other.
From the given information:
[tex]\mathbf{4x(4x^2-x+3)}[/tex]
By using distributive law m(a+b+c) = ma + mb + mc
[tex]\mathbf{=4x(4x^2)+4x(-x)+4x(3))}[/tex]
= 16x³ - 4x² + 12x
(8x + 1)(2x -3)
By applying FOIL method: (a+b)(c+d) = ac + ad + bc + bd
= (8x (2x)) + (8x(-3)) + (1 × 2x) + (1 × (-3))
= 16x² - 22x - 3
4x² (4x)
Applying exponent rule; [tex]\mathbf{a^b*a^c = a^{b+c}}[/tex]
[tex]\mathbf{= 4x^2 (4x)= x^2*4^{1+1}x}[/tex]
[tex]\mathbf{= x^2*4^{2}x}[/tex]
[tex]\mathbf{= 4^{2}x^{2+1}}[/tex]
[tex]\mathbf{= 4^{2}x^{3}}[/tex]
[tex]\mathbf{= 16x^{3}}[/tex]
(2x + 3) (8x² - 4x + 3)
Using distributive parentheses:
= 2x(8x² - 4x + 3) + 3(8x² - 4x + 3)
= 16x³ + 16x² - 6x + 9
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Sound waves can be ranked by their intensity, I, given in this formula, where r is the distance from the source of a sound with a power output of P=4 πIr^2 Which equation correctly rewrites the formula to solve for I?
Answer:
See below
Step-by-step explanation:
P = 4pir^2 l divide both sides by 4 pi r^2
l = P /(4pir^2)
The diagonal of a rhombus is 24m and 10m. Find the perimeter.
Answer:
52m
Step-by-step explanation:
rhombus
its like a slanted square
all its 4 sides are equal like a square
both pairs of opposite sides are parallel
when the diagonals criss cross they make 4 triangles inside
the sides of the rhombus become the hypotenuse of a triangles inside
if the diagonal is 24 and 10 then
its radius is 12 and 5
the sides of the rhombus become the hypotenuse of a triangle that have the sides 12 and 5
hypotenuse of a triangle that has the sides 12 and 5 is
13
(its a special triangle: its a 5, 12, 13 right triangle)
13 times 4 is 52
In △ABC, we are told that c=11, ∡C=75∘, and ∡B=29∘. Solve for a and b.
The value of a and b are 5.5 and 11.0.
How to find side of a triangle?
The sides a and b of the triangle can be found as follows:
∠B = 29°
c = 11
∠C = 75°
∠A = 180 - 75 - 29 = 76°
Using sine ratio,
b / sin 29° = 11 / sin 75
b sin 75 = 11 sin 29
b = 11 sin 29 / sin 75
b = 5.33290582271 / 0.96592582628
b = 5.51816958277
b = 5.5
Let's find a,
a / sin 76 = 11 / sin 75
a sin 75 = 11 sin 76
a = 11 sin 76 / sin 75
a = 10.673252989 / 0.96592582628
a = 11.0466922042
a = 11.0
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Solve the quadratic equation by completing the square.
x^2+2x-2=0
The solution to the quadratic equation by completing the square is x = -1 + √3, x = -1 - √3
What is a quadratic equation?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
We have a quadratic equation:
x² + 2x - 2 = 0
x² + 2x + 1 - 1 - 2 = 0
(x + 1)² - 3 = 0
(x + 1)² = 3
x + 1 = ± √3
x = -1 ± √3
Thus, the solution to the quadratic equation by completing the square is x = -1 + √3, x = -1 - √3
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Note: When solving for k, round to four decimal places.
A country's population in 1994 was 107 million. In 1997 it was 112 million. Estimate the population in 2008 using the exponential growth formula. Round your answer to the nearest million.
Answer: 132 million
Exponential growth formula: [tex]P=A e^{rt}[/tex]
[P is final amount, A is initial amount, r is growth rate, x is time intervals]
To find growth rate:
[tex]112 = 107 e^{r(3)}[/tex]
[tex]3r= ln(112/107)[/tex]
[tex]r= ln(112/107)/3 = 0.01522334561[/tex]
Population in 2008:
[tex]P_{2008}=107 e^{(0.01522334561(14))}[/tex]
[tex]P_{2008}=132.4169522[/tex]
[tex]P_{2008}=132\:million \quad (rounded \:to\:nearest\:million)[/tex]
An international anime fan club surveyed 200 of its members regarding their viewing
habits over the long weekend: 120 watched Psycho-Pass, 90 watched Demon Slayer, 70 watched
My Hero Academia, 40 watched Psycho-Pass and Demon Slayer, 50 watched Psycho-Pass and
My Hero Academia, and 20 watched something else entirely.
a.
How many of the club members watched exactly one show?
b. What percentage of members watched all three anime?
Soil sells for 8 1/4 cents per pound. How much would you save if you bought a 100- pound sack for $7.45?
Answer:
$0.80
Step-by-step explanation:
If the 100 pounds was bought separately (of course in real life you will probably not)
= 100 pounds x $0.0825/pound
= $8.25
As you can see it will cost more than if you buy a 100 pound sack.
Cost Difference = $8.25 - $7.45 = $0.80
That means you will save $0.80 from it.
There will be a profit of $0.8 if the soil is bought for $7.45 for 100- pound sack and sold for 8 1/4 cents per pound.
What is Multiplication?Multiplication in mathematics is the process of adding a number repeatedly up to the times of another number. If two numbers, namely a and b are multiplied, this is denoted by a × b. This means that 'a' is added repeatedly to itself up to b times or b is added repeatedly up to 'a' times.
Amount got for 1 pound soil after selling = 8 [tex]\frac{1}{4}[/tex] cents
= 33/4 cents
= 8.25 cents
= 8.25 / 100 dollars
= 0.0825 dollars
For 100 - pound sack, amount got after selling = 0.0825 × 100
= 8.25 dollars
Cost for 100 - pound sack = $7.45
Profit = $8.25 - $7.45
= $0.8
$0.8 will be saved if you bought a 100- pound sack for $7.45.
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S and Tare mutually
exclusive events. Find P(sort)
P(S) = 12% P(T) =27%
The value of the probability P(S or T) is 39%
How to determine the probability?The probability values are given as:
P(S) = 12% P(T) =27%
For mutually exclusive events,
P(S or T) = P(S) + P(T)
This gives
P(S or T) = 12% + 27%
Evaluate the sum
P(S or T) = 39%
Hence, the value of the probability P(S or T) is 39%
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The slope indicates how fast y increases or decreases as x increases.
O True
O False
The answer is : True
Trust me char HAHA
BÁKLA KA POR TODEYS BEDYO.
what's the numerator for the following rational expression? 6/t+7/t=?/t
The numerator for the following rational expression is 13
How to determine the numeration?The rational expression is given as:
6/t + 7/t
Take the LCM of the denominator;
The LCM of t and t is t
So, we have:
6/t + 7/t = (6 + 7)/t
Evaluate the sum
6/t + 7/t = 13/t
13 is the numerator, while t is the denominator
Hence, the numerator for the following rational expression is 13
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a square pyramid has side length 9 in. and volume = 270 in^3. find the height.
If the square pyramid has side length 9 inches and volume of 270 inches cube then by putting the values within the formula of volume height are going to be 10 inches.
Given Length and volume of a square pyramid are 9 inches and 270 inches cube. Square pyramid is the pyramid having square base. It is a right square pyramid.
We know that the amount of square pyramid is 1/3 *[tex]l^{2} *h[/tex]
Put the values in formula to induce the values oh h.
Volume=1/3*[tex]9^{2}*h[/tex]
270=1/3* 81*h
h=(270*3)/81
h=810/81
h=10
Hence the peak of the square pyramid having length 9 inches and volume of 270 inches cube is 10 inches.
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Find the area of the following figure ( i don't know how to get that answer plsss, help)
The area of the figure is 11. 27 cm²
How to determine the areaThe figure given is a parallelogram
The formula for the area of a parallelogram is given thus;
Area = base × height
From the figure, we have that
base = 2. 3 cm
height = 4. 9 cm
Substitute into the formula
Area = 2. 3 × 4. 9
Area = 11. 27 cm²
Thus, the area of the figure is 11. 27 cm²
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Okay, I am getting familiar with quadratic equations by I'm not sure of X=m+/- n... Help!
The value of m and n to show the solution of the equation x² + 6x - 5 = 0 is m = -3 and n = ± √14
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Given the equation:
x² + 6x - 5 = 0
x² + 6x = 5
x² + 6x + 9 = 5 + 9
(x + 3)² = 14
x + 3 = ±√14
x = -3 ± √14
The value of m and n to show the solution of the equation x² + 6x - 5 = 0 is m = -3 and n = ± √14
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This circle is centered at the origin, and the length of its radius is 10. What is
the circle's equation?
A. x+y=10
B. x¹° + y¹° = 100
C. X²+ y² =10
D. X² +y²=100
Answer:
D
Step-by-step explanation:
If you substitute the radius, 10, and the center of the circle, the origin (also known as (0,0) into the equation of a circle, you should get: [tex](x - 0)^{2} + (y - 0)^{2} = 10 ^{2} [/tex]
Multiplying this out should leave you with D as your answer.