The equation is writen in the quatradtic form as [tex]g(x) = -3a(x - 2)^2 - 3b(x - 2) - 3c[/tex]
How to write the equationQuadratic equation is of the form
[tex]f(x) = ax^2 + bx + c[/tex]
the transformations
Reflect it in the x-axis: To reflect a function in the x-axis, we change the sign of the function.
[tex]g(x) = -ax^2 - bx - c[/tex]
Shift it horizontally to the right by 2 units: Our function becomes:
[tex]g(x) = -a(x - 2)^2 - b(x - 2) - c[/tex]
Stretch the function by a factor of 3: To stretch a function vertically, we multiply the function by the stretch factor, k.
[tex]g(x) = -3a(x - 2)^2 - 3b(x - 2) - 3c[/tex]
So, the final transformed quadratic function is: [tex]g(x) = -3a(x - 2)^2 - 3b(x - 2) - 3c[/tex]
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Write the inductive hypothesis for this statement
The inductive hypothesis is P₍ₐ₊₁₎ : 7 + 13 + 19 + ... + {6(a +1) +1} = (a + 1) {3(a + 1) + 4} is true for all (a+1) = n for the statement Pₙ : 7 + 13 + 19 + ... + (6n +1) = n(3n +4)
The statement is given as,
Pₙ : 7 + 13 + 19 + ... + (6n +1) = n(3n +4)
For n =1 we get,
P₁ : 6(1) + 1 =7
and, 1{3(1) + 4} = 7
Hence, 6n+ 1 = n(3n + 4) is true for n= 1.
Therefore assume that Pₐ is true for some a = n, we get,
Pₐ : 7 + 13 +19 +... + (6a +1 ) = a(3a + 4)
Let, n =a+1 , we get,
P₍ₐ₊₁₎ : 7 + 13 + 19 + ... + (6a +1) + {6(a +1) +1}
= Pₐ + (6a+ 7)
= a(3a + 4) + 6a + 7
= 3a² + 4a + 6a + 7
= 3a² +10a + 7
= 3a² + 7a + 3a + 7
= a( 3a + 7) + 1(3a + 7)
= (a + 1) ( 3a + 7)
= (a + 1) {3(a + 1) + 4}
Hence, (a +1) is true for all (a+1) = n by mathematical induction principle. Thus, the inductive hypothesis is true.
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help help help help help
El 60% de número de hombres es igual al 40% de mujeres. ¿qué tanto por ciento del total representa las mujeres?
The percentage of the total that women represent, would be 60% of the total.
How to find the percentage ?Given that 60 % of men is equal to 40 % of women, we have :
0. 6 M = 0. 4 W
Solving for women in terms of Men gives:
W = ( 0.6 x M) / 0.4
= 1.5 x M
We can then find the percentage of women to be:
= (W / Total ) x 100
= ((1.5 x M) / (2.5 x M)) x 100
= (1.5 / 2.5) x 100
= 0.6 x 100
= 60%
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3
Q
The diagram shows three shapes that are mathematically similar.
The heights of the shapes are in the ratio small: medium: large = 1:5:8.
Find the ratio shaded area : total unshaded area.
Give your answer in its simplest form.
NOT TO
SCALE
The ratio of the shaded area to the total unshaded area can be found to be 5 : 9.
How to find the ratio ?The three shapes are similar to each other which means that their areas must be similar as well.
The only shape that is shaded is the second largest shape and it has the value of 5 in the ratio. This means that the other two shapes are not shaded and their ratio values are 1 and 8.
This then means that the ratio of shaded area to unshaded area can be written as :
Shaded area : Unshaded area
5 x width : ( 1 x width) + ( 8 x width )
5 : 1 + 8
5 : 9
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Shane is 61 feet high on a ride at an amusement park. The angle of depression to the park entrance is 42°, and the angle of depression to his friends standing below is 80°. How far from the entrance are his
friends standing? Round to the nearest foot.
what’s the answer? To solve the law of cosine I don’t understand this math I rly need help.
The length of u to the nearest centimeter is about 30 cm.
We are given that;'
s = 730 cm, t = 270 cm and U=125°.
Now,
The Law of Cosines states that for any triangle with sides a, b and c and angle C opposite to side c, we have:
c2=a2+b2−2abcosC
To find c = u. Plugging in the values, we get:
u2=7302+2702−2×730×270×cos125°
Using a calculator, we get:
u2≈912.9
Taking the square root of both sides, we get:
u≈30.21
Rounding to the nearest centimeter, we get:
u≈30cm
Therefore, by the law of cosine the answer will be 30 cm.
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How many permutations do I have it I select 4 things from a total of 9 with replacement? (9P4)
There are 3024 possible arrangements of 4 items selected from a total of 9 with replacement.
It is required to find the number of permutations when 4 things are selected from a total of 9 with replacement.
Use the formula for permutations with replacement, which is:
= [tex]^np_r[/tex]
Here n is the total number of items and r is the number of selections.
As per the question, n = 9 and r = 4.
So, the number of permutations is:
= ⁹p₄
= 9!/5!
= 9 x 8 x 7 x 6
= 3024
Thus, there are 3024 possible arrangements of 4 items selected from a total of 9 with replacement.
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solvesolveslvesolbesolve
The maximum value of z = 28. I occurs at (x, y) = 4
How to go about this ?To solve thhis linear programming problem, we can use the graphical method..
Graph the feasible region defined by the constraints.....
x >= 0 and y >= 0 represent the non-negative quadrants.
x + y < = 8 represents the area below the line passing through ( 8, 0) and (0, 8).
x + y >= 2 represents the area above the line passing through ( 2 , 0) and (0 , 2).
Identify the corner points of the feasible region .....
(0, 2)
( 2, 0)
( 4, 4)
( 8, 0 )
Calculate tthe objective function at each corner point....
z(0, 2 ) = 3(0) + 4(2) = 8
z (2, 0 ) = 3(2) + 4(0) = 6
z(4, 4 ) = 3(4) + 4(4) = 28
z ( 8, 0) = 3(8) + 4(0) = 24
Determine the maximum value of the objective function and the values of x and y that give this maximum value
The maximum value of z is 28, which occurs at the corner point (4, 4).
So we c can be stated as follows --
Maximum value of z = 28
x = 4
y = 4
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A positive real number is 1 less than another. When 2 times the larger is added to the square of the smaller, the result is 13. Find the numbers. (If applicable, write your answers in the form p±q√r)
Can someone explain how to get the answer to…if 7p-4=8 what is the value of p?
The value of p in the equation 7p - 4 = 8 is p = 12/7
Solving for what is the value of p?From the question, we have the following parameters that can be used in our computation:
7p - 4 = 8
Add 4 to both sides
So, we have
7p = 12
Divide both sides by 7
So, we have
p = 12/7
Hence, the solution is p = 12/7
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What function is represented in the graph?
Select one:
y = 2(.5^x)
y = 2(3^x)
y = 3(.5^x)
y = 3(2^x)
The exponential function represented by the given graph is:
y = 2(.5^x)
What function is represented by the graph?Here we have an exponential decay, the general form of these functions is:
y = A*(b)^x
Where A is the initial value and b is the base, and it is a decay if 0 < b < 1.
Now let's look at the y-intercept, we can see that it is y = 2, then:
2 = A*(b)^0
2 = A
The function is of the form:
y = 2*(b)^x with 0 < b < 1.
The option that meets these conditions is the first one: y = 2(.5^x)
So that is the correct option.
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What is the value of Q3 of the data represented by the box plot?
Enter your answer in the box.
The value of Q₃ of the data represented by the box plot is,
⇒ Q₃ = 30
Given that;
A box plot is shown in figure.
Now, We have been given an image of a box plot and we are asked to find the value of third quartile represented by our given box plot.
Since, we know that the upper or 3rd quartile is represented by the last line of the box.
We can see that 1st line of our box is at 20 ,so it will be 1st or lower quartile.
And, The middle line is at 25, so median for our given box plot is 25.
The last line of the box is at 30, which is representing the upper or third quartile of our given box plot.
Therefore, the third quartile, is 30 for our given box-plot.
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A pyramid-shaped building is 318 ft tall and has a square base with sides of 580 ft. The sides of the building are made
from reflective glass. What is the surface area of the reflective glass?
The surface area of the glass is _____ ft².
(Round the final answer to the nearest whole number as needed. Round all intermediate values to four decimal places
as needed.)
Answer:
499,237 ft²
Step-by-step explanation:
You want the lateral area of a square pyramid 580 feet on a side and 318 feet tall.
AreaTo find the area of each triangular face, we must know its slant height. That can be found from the base and height of the pyramid using the Pythagorean theorem. Once we know the slant height, we can use the formula for the area of a triangle:
A = 1/2bh
There are 4 congruent triangular faces, so the lateral area of the pyramid will be 4 times the area of one face:
4A = 4(1/2bh) = 2bh
Slant heightThe slant height of a face of the pyramid is the hypotenuse of a right triangle with one leg equal to the height of the pyramid, and the other leg equal to half the length of a base edge. (This is the distance from the midpoint of the bottom edge of a face to the center of the base, under the peak of the pyramid.)
h = √((580/2)² + 318²) ≈ 430.3766 . . . . feet
Glass arealateral area = 2(580 ft)(430.3766 ft) ≈ 499237 ft²
The surface area of the glass is about 499237 square feet.
Find the area of this semi-circle with diameter, d = 20cm.
Give your answer rounded to 2 DP.
The area of the semicircle is 157. 00 cm
How to determine the area of the semi-circleTo determine the area of the semi-circle, we need to consider the formua.
the formula for calculating the area of a semi-circle is expressed with the equation;
A = 1/2π²
Such that the parameters of the formula are;
A is the area of the semi-circler is the radius of the semi-circleπ takes the constant value of 3.14It is important to note that
Formula for diameter is expressed as
Diameter = 2radius
Radius = 10cm
Substitute the values
Area = 1/2× 3.14 × 100
Multiply the values
Area = 157 cm²
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What is the value of z in the triangle?
Enter your answer in the box. Round your final answer to the nearest hundredth.
Answer:
z = 12.52 in.
Step-by-step explanation:
Because this is a right triangle, we can solve for z using on the trigonometric ratios.
If we allow 37° to be our reference angle, the 10 in. side is the adjacent side and z (directly across from the right angle) is the hypotenuse.
Thus, we can use the cosine ratio which is
[tex]cos(angle)=\frac{adjacent}{hypotenuse}[/tex]
Now, we can plug everything into the formula and solve for z, the hypotenuse:
[tex]cos(37)=10/z\\z*cos(37)=10\\z=10/cos(37)\\z=12.52135658\\z=12.52[/tex]
perimeter of a tabe is 228 inches and the length is 18 inches which is more than twice the width. How do I find the length and width of the worktable
The width of the worktable is 32 inches, and the length of the worktable is 82 inches.
Let's assume that the width of the worktable is "w" inches.
We are given that the length is 18 inches more than twice the width, which can be expressed as:
Length = 2w + 18
The perimeter of the worktable is the sum of the lengths of all four sides.
We know that the perimeter of the worktable is 228 inches, so we can write an equation:
Perimeter = 2 × (Length + Width)
228 = 2 × (2w + 18 + w)
228 = 2 × (3w + 18)
Dividing both sides by 2:
114 = 3w + 18
Subtracting 18 from both sides:
96 = 3w
Dividing both sides by 3:
w = 32
So, the width of the worktable is 32 inches.
Now we can use this value to find the length:
Length = 2w + 18
Length = 2 × 32 + 18
Length = 82
So, the length of the worktable is 82 inches.
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Write an explicit formula for an, the nth term of the sequence 36, 32, 28, ....
WORTH 20
Answer:
an = 36 + -4(n - 1)
Step-by-step explanation:
Explicit formula:
[tex]a_n=a_1+(n-1)d[/tex]
Where:
an = nth terma1 = first termd = common differenceHere, we are given the following:
Sequence: 36, 32, 28The first term is 36
To get to the next term, 4 is subtracted from the previous term so the common difference is -4.
So we have:
First term(a1) = 36Common difference = -4By plugging this into [tex]a_n=a_1+(n-1)d[/tex]
We acquire : [tex]a_n=36+(n-1)(-4)[/tex]
An hourglass is 6ft wide and 4 ft tall on top. On bottom the hourglass is 6ft wide and 2 feet tall. It can hold 2000 pounds. if the water takes exactly one year to pass through the hourglass, how much water pass through to the bottom each day? What is the linear function of the water passing through the hourglass?
The linear equation outlining the entire volume of water (y) which has coursed through the hourglass following x days. is
y = 5.48xThe volume of water passed each which is the slope is
5.48How to find the amount of water passing through the glass each dayTo ascertain the amount of water that is passing through the hourglass daily:
where:
Total water capacity: 2000 pounds
Time: 365 days
Water transpiring every day = Total water capacity / Time
Water pervading each day ≈ 200 / 365
Water pervading each day ≈ 5.48 pounds/day
the linear function of the water traveling through the hourglass.
Making x the number of days and y being the total quantity of water which has crossed through the hourglass after x days--as the fluid fluxes at a constant velocity--thus a linear relationship between x and y can be determined.
Every single day (x), the hourglass moves 5.48 pounds of water. This reveals the linear representation of:
y = 5.48x
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Kevin wants to save $600 to buy a TV. He saves $17 each week. The amount, A (in dollars), that he still needs after w weeks is given by the following function.
A (w)=600-17w
Answer the following questions.
(a) If Kevin still needs $277, how many weeks has he been saving?
weeks
(b) How much money does Kevin still need after 5 weeks?
$?
Answer:
A) Kevin has been saving money for 19 weeks.
B) Kevin still needs $515.
Step-by-step explanation:
A) 277=600-17x /-600
-17=-323 /÷(-17)
x=19
B) x=600-17×5
x=600-85
x= 515
The radius of a circle with area A is approximately $\sqrt{\frac{A}{3}}$
. The area of a circular mouse pad is 45 square inches. Estimate its radius to the nearest tenth.
in.
The radius of the circular mouse is 3.7 inches.
How to find the radius of a circle?The area of the circular mouse pad 45 square inches. Therefore, the radius of the circle can be found as follows:
area of the circle = πr²
where
r = radiusTherefore,
area of the circular mouse = 3.14 × r²
45 = 3.14r²
divide both sides by 3.14
r² = 45 / 3.14
r² = 14.3312101911
square root both sides
r = √14.331210911
r = 3.78565714243
r = 3.7 inches
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What is the measure of angle b?
A
90o
B
180o
C
43o
D
47o
Answer:
b
Step-by-step explanation: makes sense
This is the graph of a function in the form f(x)=a•b^x what’s the function
Answer:
Step-by-step explanation:
The function f(x) = a * b^x represents exponential growth or decay. The value of a represents the starting value or y-intercept, while the value of b represents the growth or decay factor. If b is greater than 1, the function represents exponential growth, while if b is between 0 and 1, the function represents exponential decay.
To determine the values of a and b from a graph, we need to look for specific features. The y-intercept represents the value of a, so we can read it directly from the graph. The growth or decay factor b can be found by examining the slope of the graph. If the graph is increasing, then b is greater than 1, and if it is decreasing, then b is between 0 and 1.
Ellie is going to see a movie and is taking her 2 kids. Each movie ticket costs $13 and there are an assortment of snacks available to purchase for $5 each. How much total money would Ellie have to pay for her family if she were to buy 4 snacks for everybody to share? How much would Ellie have to pay if she bought x snacks for everybody to share?
Total cost with 4 snacks:
Total cost with x snacks:
The total cost that Ellie would pay with 4 snacks is $59.
The total cost that Ellie would pay with x snacks is $29 + $5x.
What is the total cost?The first step is to determine the total number of people going to the movies. There are 3 people going to the movies.
The total cost spent by Ellie is the sum of the tickets and the total cost of the snacks.
Total cost = total cost of the tickets + total cost of the snacks
= (cost of one ticket x number of people going to the movie) + (number of snacks bought x price of one snack)
= (13 x 3) + ($5 x 4)
$39 + $20 = $59
Total cost if x snacks is bought: (13 x 3) + ($5 x x) = $39 + $5x
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In a roll of 50 pennies, 15 were made before 1985. What percent of the pennies in the roll were made before 1985?
The percentage of pennies in the roll is A = 30 %
Given data ,
Let the percentage of pennies in the roll made before 1985 be A
Now , the total number of pennies be = 50 pennies
And , the number of pennies made before 1985 is = 15 pennies
So , the percentage is A = ( 15 / 50 ) x 100
On simplifying the equation , we get
A = 3/10 x 100
A = 30 %
Hence , the percentage is 30 %
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Pls help thanks!!!!!!!!!!!
Answer:
Put your calculator in degree mode.
sin(13°) = 500/x
x sin(13°) = 500
x = 500/sin(13°) = 2,222.7 miles
Using a trigonometric relation we can see that x = 2,222.7 ft
How to find the value of x?We can see a right triangle, there we can see that one of the angles has a measure of 13°.
The opposite cathetus has a measure of 500ft, and we want to find x, which is the hypotenuse.
Then we can use the relation:
sin(a) = (opp cathetus)/hypotenuse
Replacing what we know, we will get:
sin(13°) = 500/x
Solving that for x:
x = 500/sin(13°) = 2,222.7 ft
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Write a polynomial function with the given zeros and their correspond possible answers. f(x) = Zeros 0 -6 -7 Mult. 1 3 1
[tex] - 13(t - 7) {6(t + 1) {8(t - 2)}^{?} }^{?} [/tex]
The value of a polynomial function with the given zeros would be,
⇒ f (x) = x (x + 7) (x + 6)³
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
Functions have zeroes 0, - 6, - 7 with multiplicity 1, 3, 1
Hence, We can formulate;
The value of a polynomial function with the given zeros would be,
⇒ f (x) = (x - 0)¹ (x - (- 6))³ (x - (- 7))¹
⇒ f (x) = x (x + 6)³ (x + 7)
⇒ f (x) = x (x + 7) (x + 6)³
Thus, The value of a polynomial function with the given zeros would be,
⇒ f (x) = x (x + 7) (x + 6)³
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What are the angles of rotation for a regular
pentagon? (Select all that apply)
a) 60
B) 72
c)90
d) 144
e) 180
f)216
g) 360
Answer:
c,,e,b,f
Step-by-step explanation:
What the answer for radius huryyyyyyyyyy pleaseeee
Answer: 12.6
Step-by-step explanation:
150/360*2*pi*r=10.
divide to get r alone
Assignment Active
The Economic Effect of Snowsheds
With so many snowsheds along the line, annual
maintenance soared. By 1910 many of the original
wooden structures needed replacing, and heavy snows in
the winter of 1912-13 crushed others. That year the
railway hired 1,800 workers to make shed improvements
along just 8 miles of track, and the need for additional
sheds was clear....
While making repairs on the Cascade Mountain
snowsheds in 1917, the Great Northern Railway used over
35 million board feet of timber that cost triple what it had
just eight years earlier. By this time, snowsheds and
tunnels covered 6.7 of the 9 track miles between
Wellington and Scenic.
According to this passage, how did snowsheds affect
the railroad in the long term?
O They decreased delays, which lowered the railroad
costs.
They required frequent repairs, which added to the
railroad costs.
They reduced the need for bridges, which lowered
the railroad costs.
O They required many workers to operate them,
which added to the railroad costs.
Classifying the polynomial
Answer: Polynomials can be classified by the degree of the polynomial. The degree of a polynomial is the degree of its highest degree term. So the degree of 2x3+3x2+8x+5 2 x 3 + 3 x 2 + 8 x + 5 is 3. A polynomial is said to be written in standard form when the terms are arranged from the highest degree to the lowest degree.