The new equation is
Y = (x-8)² .
The other way to write it is like this: (you might not recognize it in this form)
Y = x² - 16x + 64
The vertex of parabola [tex]y=x^{2}[/tex] is [tex](0,0)[/tex]
After shifting [tex]8[/tex] units towards the right, it will become [tex](8,0)[/tex].
Therefore, the equation of the new parabola will be [tex]y=(x-8)^{2}[/tex].
Hence, the answer is [tex]y=(x-8)^{2}[/tex].
The equation to the new parabola is [tex]y=(x-8)^{2}[/tex].
What is the equation of a parabola?
The general equation of a parabola is: y = a(x-h)2 + k or x = a(y-k)2 +h, where (h,k) denotes the vertex. The standard equation of a regular parabola is y2 = 4ax.
What is parabola and examples?A parabola is nothing but a U-shaped plane curve. Any point on the parabola is equidistant from a fixed point called the focus and a fixed straight line known as the directrix. Terms related to Parabola.
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Rectangle 1 has length x and width y. Rectangle 2 is made by multiplying each dimension of Rectangle 1 by a
factor of k, where k>0.
(a) Are Rectangle 1 and Rectangle 2 similar? Why or why not?
(b) Write a paragraph proof to show that the perimeter of Rectangle 2 is k times the perimeter of Rectangle 1.
(c) Write a paragraph proof to show that the area of Rectangle 2 is k2 times the area of Rectangle 1.
Answer:
(a) Rectangle 1 and rectangle 2 are similar
(b) The perimeter of Rectangle 2 is k times the perimeter of Rectangle 1
(c) The area of Rectangle 2 is k² times the area of Rectangle 1
Step-by-step explanation:
* Lets talk about the similarity
- Two rectangles are similar if there is a constant ratio between
their corresponding sides
- Rectangle 1 has dimensions x and y
- Rectangle 2 has dimensions kx and ky
- The ratio between their dimensions is:
kx/x = k and ky/y = k, so there is a constant ratio K between their
corresponding dimensions
(a) Rectangle 1 and rectangle 2 are similar
- The perimeter of any rectangle is 2(the sum of its two dimensions)
∵ Rectangle 1 has dimensions x and y
∴ Its perimeter = 2(x + y) = 2x + 2y ⇒ (1)
∵ Rectangle 2 has dimensions kx and ky
∴ Its perimeter = 2(kx + ky) = 2kx + 2ky
- By taking k as a common factor
∴ Its perimeter = k(2x + 2y) ⇒ (2)
- From (1) and (2)
∵ The perimeter of rectangle 1 = (2x + 2y)
∵ The perimeter of rectangle 2 = k(2x + 2y)
∴ The perimeter of rectangle 2 is k times the perimeter of rectangle 1
(b) The perimeter of Rectangle 2 is k times the perimeter of Rectangle 1
- The area of any rectangle is the product of its two dimensions
∵ Rectangle 1 has dimensions x and y
∴ Its area = x × y = xy ⇒ (1)
∵ Rectangle 2 has dimensions kx and ky
∴ Its area = kx × ky = k²xy ⇒ (2)
- From (1) and (2)
∵ The area of rectangle 1 = xy
∵ The area of rectangle 2 = k²xy
∴ The area of rectangle 2 is k² times the area of rectangle 1
(c) The area of Rectangle 2 is k² times the area of Rectangle 1
(a) Yes, Rectangle 1 and Rectangle 2 are similar. (b) It is proved that the perimeter of Rectangle 2 is k times the perimeter of Rectangle 1. (c) It is proved that the area of Rectangle 2 is [tex]k^2[/tex] times the area of Rectangle 1.
(a) Yes, Rectangle 1 and Rectangle 2 are similar. They are similar because each dimension of Rectangle 2 is k times the corresponding dimension of Rectangle 1, which means that all angles remain the same and the sides are in proportion.
(b) To prove that the perimeter of Rectangle 2 is k times the perimeter of Rectangle 1, we start by noting that the perimeter of a rectangle is the sum of all its sides. For Rectangle 1, the perimeter [tex]P_1[/tex] is given by :
[tex]P_1 = 2(x + y)[/tex]
For Rectangle 2, each dimension is multiplied by k, so the length becomes kx and the width becomes ky. Therefore, the perimeter [tex]P_2[/tex] of Rectangle 2 is:
[tex]P_2 = 2( kx + ky)[/tex]
[tex]P_2 = 2k(x + y)[/tex]
Since 2(x + y) is the perimeter of Rectangle 1, we can replace it with [tex]P_1[/tex], yielding [tex]P_2 =[/tex] [tex]kP1[/tex] . This shows that the perimeter of Rectangle 2 is indeed k times the perimeter of Rectangle 1.
(c) To prove that the area of Rectangle 2 is [tex]k^2[/tex] times the area of Rectangle 1, we consider the formula for the area of a rectangle, which is the product of its length and width.
The area [tex]A_1[/tex] of Rectangle 1 is:
[tex]A_1 = xy[/tex]
For Rectangle 2, the length and width are both multiplied by k, so the area [tex]A_2[/tex] is:
[tex]A_2 = (kx)(ky)[/tex]
When we multiply these out,
we get:
[tex]A2 =[/tex] [tex]k^2xy[/tex]
Since xy is the area of Rectangle 1, we can replace it with [tex]A_1[/tex], giving us [tex]A_2 =[/tex] [tex]k^2A_1[/tex] . This demonstrates that the area of Rectangle 2 is [tex]k^2[/tex] times the area of Rectangle 1.
The diagram of rectangles:
find the coefficient of Y^2 in the expansion of (2x+y)^3
Step-by-step explanation:
[tex]\text{Use}\ (a+b)^3=a^3+3a^2b+3ab^2+b^3.\\\\\text{We have}\ (2x+y)^3\\\\=(2x)^3+3(2x)^2(y)+3(2x)(y^2)+y^3\\\\\text{The coefficient of}\ y^2\ \text{is}\ (3)(2)=6[/tex]
A department store is having a sale. Skirts are on sale for 20% off the original price, p. Which equation could be used to find s, the sale price of a skirt?
The equation to calculate the sale price of the skirt, which is 's', given an original price 'p' and a discount of 20% on the original price would be s = p - (0.2 * p). This equation essentially subtracts the discount amount (20% of 'p') from 'p' to get the sale price 's'.
Explanation:To calculating a sale price, which is a Mathematical exercise commonly carried out in financial and business scenarios. In this context, there's a 20% sale on skirts. Given that the original price of the skirt is 'p', and the discount is 20% of 'p', we can denote that as '0.2p'. If the sale price is represented as 's', the equation to calculate the sale price would be s = p - (0.2 * p). This equation essentially subtracts the discount amount (20% of the original price) from the original price to obtain the price after discount, which is the sale price.
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the equation s = 0.80 * p. This accounts for a 20% reduction from the original price.
We need to determine the sale price using the original price (p) and the discount rate (20%).
Since the discount is 20% off, you can convert this percentage to a decimal
20% = 0.20.
To find the amount discounted, multiply the original price by 0.20,
Discount Amount = 0.20 * p.
Subtract the discount amount from the original price to get the sale price,
Sale Price (s) = p - 0.20 * p.
Alternatively, you can factor out p in the equation: s = p (1 - 0.20),
which simplifies to s = 0.80 * p.
One of the same side angles of two parallel lines is 20° smaller than the other one. Find the measures of these two angles.
Answer:
The measure of these two angles are 80° and 100°
Step-by-step explanation:
Let
x and y ----> the measure of the same side angles
we know that
The sum of of the same side angles of two parallel lines is equal to 180 degrees
x+y=180° -----> equation A
x=y-20° ----> equation B
substitute equation B in equation A and solve for y
(y-20°)+y=180°
2y=180°+20°
y=200°/2
y=100°
Find the value of x
x=100°-20°=80°
PLSSS HURRY!!!!!!!!
Solve the quadratic equation.
(x + 3)2 = 64
A) x = 5 or -11
B) x = 11 or -5
C) x = ± 3
D) x = ± 11
Answer:
A) x=5 or -11
Step-by-step explanation:
The given equation is:
[tex](x+3)^2=64[/tex]
The most suitable method so solve this quadratic equation is the square root method.
We take square root of both sides to obtain:
[tex]x+3=\pm \sqrt{64}[/tex]
[tex]\implies x+3=\pm8[/tex]
[tex]\implies x=-3\pm8[/tex]
We now split the plus or minus sign to get;
[tex]x=-3-8\:,x=-3+8[/tex]
This simplifies to:
[tex]x=-11\:,x=5[/tex]
The correct choice is A
-p+60 = = h + 10,000
In the equation above, h is a constant. If p = 10 is a solution to the equation, what is the value
of h?
By substituting p = 10 into the equation -p + 60 = h + 10,000 and solving for h, we find that the constant h is -9,950.
The solution cam be solved as:
To find the value of constant h when p = 10 is a solution to the equation -p + 60 = h + 10,000, we substitute p = 10 into the equation and solve for h.
-p + 60 = h + 10,000
-10 + 60 = h + 10,000
50 = h + 10,000
h = 50 - 10,000
h = -9,950
The value of h is therefore -9,950.
Find the measure of CD.
Round to the nearest tenth.
Please Help Me I Need It.
you need to find the median angle so you take the triangle (A) and solve for the angle using the inverse of sin.(B) take this angle and multiply it by 2 and you should have you arc length I think.
Answer:
89.0
Step-by-step explanation:
1/3 2/5 4/7 least to greatest
1.Change them all to having common denominators so it’s easier to compare the numerators
1/3=35/105 *35
2/5=42/105 *21
4/7=60/105 *15
2.Compare and order
3. Answer from smallest to largest =
1/3,2/5,4/7
Hope this helps :)
the angle of elevation from a point 25 feet from the base of a tree on level ground to the top of the tree is 30 degrees. which equation can be used to find the height of the tree
Answer:
the equation to find the height is: x = 25 * tan(30°) and the height is x = 14.43 feet
Step-by-step explanation:
Length of tree = 25 feet
Angle of elevation = 30 degrees
Equation for the height of tree=?
Let x represent the height.
We know that tan Ф = Perpendicular/Base
tan Ф = height of tree/ length of base
tan Ф = x/l
=> x = l*(tanФ)
x = 25 * tan(30°)
Now, putting values:
x= 25 * tan(30°)
x = 25 * 0.577
x = 14.43 feet
So, the equation to find the height is: x = 25 * tan(30°) and the height is x = 14.43 feet
A cylinder has a radius of 8 meters and a height of 4 meters. .
Given : Radius of cylinder = 8 m
Height = 4 m
Volume of cylinder = πr²h cu. units
= 22/7 × 8 × 8 × 4 m³
= 804.57 m³ (approx.)
Curved surface area = 2πrh sq. units
= 2 × 22/7 × 8 × 4 m²
= 201.14 m² (approx.)
Total surface area = 2πr(r + h) sq. units
= 2 × 22/7 × 8 (8 + 4) m²
= 2 × 22/7 × 8 × 12 m²
= 603.43 (approx.)
Final answer:
The volume of a cylinder with a radius of 8 meters and a height of 4 meters is calculated using the formula V = πr²h, which yields approximately 804.25 cubic meters when using π ≈ 3.14159.
Explanation:
To calculate the volume of a cylinder with a given radius and height, you can use the formula V = πr²h. In the case of a cylinder with a radius of 8 meters and a height of 4 meters, plug these values into the formula to get:
V = π × (8 m)² × 4 m
V = π × 64 m² × 4 m
V = 256π m³
Since π (pi) is approximately 3.14159, you can further calculate the volume as:
V ≈ 256 × 3.14159 m³
V ≈ 804.2477 m³
Thus, the volume of the cylinder is approximately 804.25 cubic meters, when expressed with four significant figures.
i need help asap ! 6th grade math surface area .
Answer:
136 un²
Step-by-step explanation:
Rectangles/linear faces: 7 * (5 + 6 + 5) = 7 * 16 = 112
Triangles/bases: 2 * 1/2(6 * 4) = 24
Total: 24 + 112 = 136 un²
The surface area-to-volume ratio is used in Biology to predict cell efficiency in eliminating wastes or procuring nutrients by diffusion.
Explanation:In Biology, the surface area-to-volume ratio is used to predict which cells might eliminate waste or procure nutrients faster by diffusion. This ratio is calculated by dividing the surface area of a cell by its volume. Cells with a larger surface area-to-volume ratio are more efficient at exchanging materials with their surroundings.
For example, consider a small cell with a high surface area-to-volume ratio. This cell has a relatively larger surface area compared to its volume, which allows for faster diffusion of nutrients into the cell and waste products out of the cell. In contrast, a larger cell with a lower surface area-to-volume ratio has a relatively smaller surface area compared to its volume, resulting in slower diffusion.
By analyzing the surface area-to-volume ratio, we can predict which cells have a greater capacity for diffusion and therefore can eliminate wastes or procure nutrients at a faster rate.
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Spencer puts an $1880 item on layaway by making 20% down payment and agreeing to pay $170 a month. How many months sooner would he pay off the item if he increased his monthly payment to $260?
Answer:
Spencer will pay off the item 3 months sooner if he pay $260 instead of $170 a month
Step-by-step explanation:
Total Amount = $1880
Down Payment = 20%
Monthly payment = $170
if Monthly payment increased from $170 to $260, How many months sonner Spencer will pay off?
So, First calculate the down payment
Down payment = 20% of 1880
= (20/100) * 1880
= 376
Amount left to be paid = 1880 - 376
= 1504
Total months to pay off for Spencer if he pay's $170 a month:
1504/170 = 8.8 ≈ 9 months
Total months to pay off for Spencer if he pay's $260 a month:
1504/260 = 5.7 ≈ 6 months
So, 9 -6 = 3 months
So, Spencer will pay off the item 3 months sooner if he pay $260 instead of $170 a month
A grocery store needed eight hundred ninety five cans of peas.If the peas came in boxes with thirty two cans in each box,how many boxes would they need to order?
Answer:
28 boxes
Step-by-step explanation:
We need to take the total number of cans needed and divide by the number of cans per box to determine the number of boxes
895 / 32 =27 with 31 left over
Making this a fraction
27 31/32 boxes
We cannot normally order part of a box
Rounding up to the next whole box
28 boxes
What is the value of z in this equation?:[tex]6z+10z=96[/tex]
Answer:
z = 6
Step-by-step explanation:
Given
6z + 10z = 96 ← collect terms on left side
16z = 96 ( divide both sides by 16 )
z = 6
A stadium has a seating capacity of 8,000. Suppose it is divided into 20 equal sections. How many seats are in each section?
Answer:
400 seats would be in each section.
Step-by-step explanation:
8,000/20 is equal to 400.
Hope this helps!
Please give brainliest :)
solve using the substitution method 3m-n=18 and 2m+n=-7
Answer:
m = 11/5, n= -57/5
Step-by-step explanation:
3m-n=18 and 2m+n=-7
Solve one of the equations for n
2m +n = -7
Subtract 2m from each side
2m-2m +n = -7 -2m
n = -7-2m
Substitute this into the first equation
3m -n =18
3m - (-7-2m) = 18
Distribute the minus sign
3m +7+2m = 18
Combine like terms
5m +7 = 18
Subtract 7 from each side
5m+7-7 = 18-7
5m = 11
Divide by 5
m = 11/5
Substitue this back into the equation for n
n = -7-2m
=-7 -2(11/5)
=-7-22/5
-35/5 -22/5
=-57/5
To solve the system using substitution, solve the first equation for n, substitute it into the second, and solve for m, which gives m = 11/5. Then, substitute m back into the expression for n to get n = -57/5.
To solve the system of equations using the substitution method, you can solve one of the equations for one variable and then substitute that expression into the other equation. Let's start with the two given equations:
3m - n = 18
2m + n = -7
First, solve the first equation for n:
n = 3m - 18
Now substitute this expression for n into the second equation:
2m + (3m - 18) = -7
Combine like terms:
5m - 18 = -7
Add 18 to both sides:
5m = 11
Divide by 5:
m = 11/5
Next, substitute the value of m back into the expression for n:
n = 3(11/5) - 18
n = 33/5 - 90/5
n = -57/5
Therefore, the solution to the system using the substitution method is m = 11/5 and n = -57/5.
what is value of x-(3x+5) when x=-2
Answer:
2
Step-by-step explanation:
3 * -2 = -6
-6 +5 = 1
-2 * -1 = 2
the value would be two
The perimeter of the rectangle is 28 units.
What is the value of w?
Step-by-step explanation:
The formula of a perimeter of a rectangle:
[tex]P=2l+2w[/tex]
We have P = 28. Substitute:
[tex]28=2l+2w[/tex]
Solve for w:
[tex]2l+2w=28[/tex] subtract 2l from both sides
[tex]2w=28-2l[/tex] divide both sides by 2
[tex]w=14-l[/tex]
Where [tex]0<l<14[/tex]
Answer:
answer is w = 14
Step by step???????????
Answer:
The measure of angle x is 12°
Step-by-step explanation:
we know that
(4x+4)°+(5x-22)°=90° ----> by complementary angles
Solve for x
(9x-18)°=90°
9x=90°+18°
9x=108°
x=12°
which of the following expressions cannot be factored?
A. 15x-10
B. 4x+8
C. 3x+8
D. 2x-2
Answer:
C. 3x + 8
Step-by-step explanation:
A. can be factored; Factor 5 from all terms:
(15x - 10)/5 = 3x - 2
B. can be factored; Factor 4 from all terms:
(4x + 8)/4 = x + 2
D. can be factored; Factor 2 from all terms:
(2x - 2)/2 = x - 1
~
Jackie bought a new 7.1 cubic foot chest freezer. The owners manual states that the temperature inside the freezer needs to be below 32°F before any perishable food can be stored. The ambient temperature is 78°F. If the freezer's temperature is modeled by the linear equation y = -
59
3
x + 78, how long will it be before Jackie can put steaks in her freezer?
Answer:
B) 2 hours 20 minutes
Answer:B 2HRS 20MINS
Step-by-step explanation:
( − 2 7 ) ( 5 − 8 ) Please solve .
Answer:
81
Step-by-step explanation:
We have to solve the following multiplication: (−27) (5−8)
First, we are going to simplify the second parenthesis, before performing the multiplication:
(−27) (5−8) = (−27)(-3) = 81.
The result is positive given that minus times minus equals plus.
Step 1: Solve the second parentheses
( − 2 7 ) ( 5 − 8 )
5 - 8 = -3
(-27)(-3)
Step 2: Multiply -27 by -3. Since these are both negative the answer will be positive
-27 * -3 = 81
Hope this helped!
~Just a girl in love with Shawn Mendes
Solve for x
3x+3/x-1=3x+2/x+4
Answer:
X=3.5
Step-by-step explanation:
Which interpretation for the given expression is correct? 5(3x-4)2 which one is right
A.
the quotient of 5 and the square of 3x - 4
B.
the product of 5 and the difference of 3x and the square of 4
C.
the product of 5 and the square of 3x - 4
D.
the difference of 5, 3x, and 4 squared
The correct interpretation for the expression 5(3x - 4)² is The product of 5 and the square of 3x - 4 ( option C)
An expression is a mathematical phrase containing variables, constants, and operators.
It represents a mathematical relationship or computation and does not have a specific value until the variables are assigned values.
Interpreting 5(3x - 4)²
is The product of 5 and the square of 3x - 4
Therefore, the correct interpretation for the expression 5(3x - 4)² is The product of 5 and the square of 3x - 4
15 points!!! The triangle ABC is dilated with respect to the point O(8,-3) and the scale factor 3 to a new triangle A'B'C'. What are the coordinates of B?
(24,-9)
(24,-3)
(12,-9)
(-4,-3)
Answer:
(-4,-3)
Step-by-step explanation:
we know that
The distance OB is equal to
(8-4)=4 units
To find the new distance OB', multiply the distance OB by the scale factor
so
OB'=OB*3
OB'=4*3=12 units
The x-coordinate of point B' is equal to
8-12=-4
The y-coordinate of point B' is the same that B -3
the coordinates of point B'are (-4,-3)
Can someone help me with this
Answer:
D) 3/25
Step-by-step explanation:
(3/5)/5 = .12
3/23 = .12
Hello There!
Your answer would be 3/25. Whenever you have two probabilities together you can multiply them and in this case, multiplying 3/5 by 1/5 will get you a product of 3/25
A bacteria culture begins with 4 bacteria which double in size every hour. How many bacteria exist in the culture after 8 hours.
Answer:
1024
Step-by-step explanation:
There are 4 bacteria at the start. We can make an equation to represent the phenomena explained in the question.
As it is written in the question that the bacteria culture doubles in every hour.
So,
Let t represent the unit of time
So the number of bacteria after t unit of time will be
Number of bacteria after t unit of time=4*2^t
We have to calculate number of bacteria after 8 hours, so t = 8
Number of bacteria after 8 hours=4*2^8
=4*256
=1024
So the bacteria after 8 hours in the culture will be 1024..
The initial population of the bacterium cells was 4, and after 8 hours, there would be 1024 bacteria in the culture.
The initial population of the bacterium cells at the beginning of the experiment was 4 bacteria.
Step-by-step calculation:
After 1 hour: 4 * 2 = 8 bacteriaAfter 2 hours: 8 * 2 = 16 bacteriaContinuing this pattern, after 8 hours: 4 * (2⁸) = 4 * 256 = 1024 bacteria.A Medical company tested a new drug on 100 people for possible side effects. This table shows the results...
Compare the probability that an adult has side effects with the probability that a child has side effects. Draw a conclusion based on your results.
Answer:
p(side effects|child) = 0.44
p(side effects|adult) = 0.14
Conclusion: children have a much greater chance of having side effects than adults.
Step-by-step explanation:
i just did it on apex. good luck!
Answer:
p(side effects/child) = 0.44
p(side effects/adult) = 0.14
Conclusion: Children have a much greater chance of having side effects than adults
~apex
a tree casts a shadow that is 20 feet long. if the tree is 35 feet tall, what is the angle of elevation from the end of the shadow to the top of the tree? round to the nearest tenth
Answer:
The angle of elevation is 60.3°
Step-by-step explanation:
* Lets revise the trigonometry functions
- In any right angle triangle:
# The side opposite to the right angle is called the hypotenuse
# The other two sides are called the legs of the right angle
* If the name of the triangle is ABC, where B is the right angle
∴ The hypotenuse is AC
∴ AB and BC are the legs of the right angle
- ∠A and ∠C are two acute angles
- For angle A
# sin(A) = opposite/hypotenuse
∵ The opposite to ∠A is BC
∵ The hypotenuse is AC
∴ sin(A) = BC/AC
# cos(A) = adjacent/hypotenuse
∵ The adjacent to ∠A is AB
∵ The hypotenuse is AC
∴ cos(A) = AB/AC
# tan(A) = opposite/adjacent
∵ The opposite to ∠A is BC
∵ The adjacent to ∠A is AB
∴ tan(A) = BC/AB
* Now lets solve the problem
∵ The shadow of the tree is 20 feet long
- The shadow of the tree is on the ground
∵ The height of the tree is 35 feet tall
∴ The shadow of the tree and the height of the tree formed the legs of
a right triangle
- The angle of elevation is opposite to the tree
∴ The shadow of the tree is the adjacent side of the angle of elevation
∴ The height of the tree is the opposite side of the angle of elevation
- let the name of the angle of elevation is Ф
∴ tan Ф = tree height/shadow length
∴ tan Ф = 35/20 = 7/4
∴ Ф = tan^-1(7/4) = 60.3°
* The angle of elevation is 60.3°
The radius of the base of cylinder is 38mm and it’s height 51mm find the surface area of the cylinder in terms of pi
For this case we have that by definition, the surface area of a cylinder is given by:
[tex]SA = 2 \pi * r * h + 2 \pi * r ^ 2[/tex]
Where:
r: It's the radio
h: It's the height
Substituting according to the data we have:
[tex]SA = 2 \pi * (38) * (51) +2 \pi * (38) ^ 2\\SA = 2 \pi * 1938 + 2 \pi * 1444\\SA = 3876 \pi + 2888 \pi\\SA = 6764 \pi[/tex]
Thus, the surface area of the cylinder is [tex]6764 \pi \ mm ^ 2[/tex]
Answer:
[tex]6764 \pi \ mm ^ 2[/tex]