The value of a is 1/4 and the value of h and k is (2,-7/4)
What is a Parabola ?A parabola is a u shaped curve. It is a plane curve whose all points are at a fixed distance form a point called focus.
(x-h)² = 4a(y-k)
It is given that the parabola goes through the point (3, -1), and the vertex is at (2, -2).
Therefore
(x -2)² = 4a(y +2)
The parabola passes through the point (3,-1)
(3-2)² = 4*a(-1+2)
1 = 4 a
a = 1/4
Now to determine the value of focus point , (h,k)
(h = 2)
k = - 2 +1/4 = -7/4
Therefore The value of a is 1/4 and the value of h and k is (2,-7/4)
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Fill in the blanks in each rule.
1. Ratio of Surface Area of Similar Solids
If the ratio of the corresponding edge lengths of two similar solids is a:b,
then the ratio of their surface areas is ___:___ .
2. Ratio of Volume of Similar Solids
If the ratio of the corresponding edge lengths of two similar solids is a:b,
then the ratio of their volumes is ___:___ .
The ratio of their surface areas will be a²/b². And the ratio of their volumes a³/b³.
What are the surface area and the volume of an object?The size is the amount of space covered by a two-dimensional hard surface.
The volume of an element or compound is the sufficient space it takes up, calculated in cubic units.
1. The ratio of the surface area of similar solids
If the ratio of the corresponding edge lengths of two similar solids is a:b, then the ratio of their surface areas will be a²/b².
2. The ratio of the volume of similar solids
If the ratio of the corresponding edge lengths of two similar solids is a:b, then the ratio of their volumes a³/b³.
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integrated mathematics 2. need help with chapter 5 test please
Answer:
1/4
Step-by-step explanation:
[tex]\text{Diamonds, spades, clubs and hearts make up the 4 suits of a deck of cards, }[/tex]
[tex]\text{which contains 52 cards. There are 13 diamonds in a pack.}[/tex]
[tex]\text{Probability of an event:}[/tex]
[tex]\text{ Number of favorable outcomes / Total number of outcomes}[/tex]
[tex]\text{Probability of getting a diamon}d = \frac{13}{52} = \frac{1}{4}.[/tex]
[tex]\text{So the chance that you draw out a diamond from a deck}=\frac{1}{4}[/tex] .
Which graph has a slope 4/5?
Answer:
The middle option on the top row
Step-by-step explanation:
Slope is calculated as rise/run between two points.
In this case it takes 4 up and 5 to the right to get between the two points, so the rise would be 4 and run 5.
5 oranges are shared equally by 2 people.
About how many oranges does each person get
Answer:
2.5
Step-by-step explanation:
5 divided by 2 is 2.5
Answer:
Each person would get around 2.5 oranges.
Step-by-step explanation:
There are five oranges to split between two people- this can set up the equation 5 divided by 2 equals x. The answer to 5 divided by 2 is 2.5, meaning that each person would get around 2.5 oranges. I hope this helps! :)
What is the value of x? x = 2.25 x = 11.25 x = 13 x = 22
Answer:
x = 2.25 x = 11.25 x = 13 x = 22
Step-by-step explanation:
Fiona asked her team to suggest ways of surveying the population of their middle school to find out how many students use bottled water.
Which student has the method that is most representative of the school’s population?
Raina suggested that she ask everyone in her math class on Friday.
Miya suggested that she ask students sitting in the first row of her classes on Friday.
Ryo suggested that he ask the basketball players at his practice on Friday.
Amir suggested that he ask every tenth student as he or she walks into school in the morning.
The students who has the method that is most representative of the school’s population is Amir.
What is a population?Population refers to the group of people being studied in an experiment or the group from which a sample is drawn.
Amir has the method that is most representative of the school’s population because the method includes all students in the school studying different subjects but picked at random (every tenth students)
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What should your units on your base area calculations be, and why? how is this different from the units on your volume calculations? explain in two to three sentences.
The units used for area are squared length units, where the length units are: meter, inch, feet, etc.
Which units are used for surface areas?
The units used for surface areas are length units (meters, inches, feet, etc) squared.
Why we use those? Because area is defined as the product between the two dimensions (two sides of rectangle, for example) of a figure. And these dimensions are given in length units. So if we take the product of two of these, we will get squared length units.
The difference with volume units, is that for volume we need 3 dimensions, then we will have cubed length units.
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5. you work at a t-shirt printing business. 175 of 3,500 t-shirts shipped are printed improperly. what is the experimental probability that a t-shirt is printed improperly?
a: 6%
b: 1.75%
c: 5%
d: 35%
Answer:
C: 5%
Step-by-step explanation:
175 out of 3500 = 175/3500
175/3500 = 1/20
1/20 = 0.05
0.05 = 5%
Answer:
C 5%
Step-by-step explanation:
I am smart so trust me
The average vehicle releases 1.39 grams of nox per mile driven. if a vehicle is driven 22,000 miles per year for 15 years, how much nox does that vehicle release
In 15 years, the average car releases 458.7 kilograms of nox.
How much nox does that vehicle release?
We know that the average vehicle releases 1.39 grams per mile driven.
And, in average, that car drives 22,000 miles per year.
So in a year, a car releases:
M = (22,000)*1.39 g = 30,580 g = 30.58 kg
In one year, the average car releases around 30.58 kilograms of nox.
Then in 15 years, the car releases 15 times that amount, then we have the product:
T = 15*30.58 kg = 458.7 kg
In 15 years, the average car releases 458.7 kilograms of nox.
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Find f(-3) for f(x)=4•(2)^x
A. 1/2
B. -32
C. -24
D. 1/8
a triangle has sides lenghts of 6.8cm, 28.5cm and 29.3cm. is this a right angled triangle
Answer:
Yes it is a right angled triangle
Step-by-step explanation:
If its a right triangle it would satisfy the Pythagoras theorem.
29.3^2 = 858.49
28.5^2 = 812.25
6.8^2 = 46.24
Adding the last 2 values:
812.25 + 46.24
= 858.49
So YES.
that’s the question
Answer:
all real numbers
ez clappp
Draw and label a net to find the surface area of the original juice box. it costs
supreme packaging $0.02 per square inch to create one juice box. the company
groups eight juice boxes together as one package. how much does it cost to
create one package?
Based on the area of the juicebox and the cost per square inch, the cost to create one package is $7.20.
What is the cost of one package?First, find the area of the juice box. The formula is:
= 2lh + 2lw + 2hw
= (2 x 3 x 4) + (2 x 3 x 1.5) + (2 x 4 x 1.5)
= 45 inch²
The Cost is $0.02 per square inch and the number per package is 8 juice boxes. The total cost is:
= 45 x 0.02 x 8 boxes
= $7.20
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Which equation can be simplified to find the inverse of y = 5x² + 10?
Answer:
See below
Step-by-step explanation:
Here is how to start....you didn't include the equations in question, so I do not know what the answer may be
solve for x
y-10 = 5 x^2 divide thru by 5
(y-10)/5 = x^2 'sqrt' both sides
± sqrt( (y-10) / 5 = x change x's and y's
± sqrt ((x-10)/5) = y
Car 2 passes car 1. To a stationary observer, car 1 has a velocity of 28 m/s to the east and car 2 has a velocity of 33 m/s to the east. How much time will pass before car 2 is 14 m ahead of car 1?
Answer:
2.8 s
Step-by-step explanation:
33x = 28x + 14(m)
5x = 14(m)
x = 2.8(s)
I need help with question two please, it’s due tomorrow first thing so kinda need to get it done
At a football game, the quarterback threw the football and the receiver caught it for a 12-yard gain. What integer represents the yards gained?
1/12
12
-12
6
The volume of a brick 3 inches wide, 8 inches long, and 4 inches tall is:
15 square inches
36 square inches
44 square inches
96 square inches
Answer:
96 cubic inches
Step-by-step explanation:
Volume=length*width*height
Your unknown is volume, which we can simplify as V.
Plugging in for the values of length, width, and height, we get [tex]v=8*3*4[/tex]
From there, we can simplify.
[tex]V=8*3*4\\V=24*4\\V=96[/tex]
To get the units, we know that the length, the width, and the height all are measured in inches.
[tex]V=inches*inches*inches\\V=inches^2*inches\\V=inches^3[/tex]
[tex]inches^3[/tex] can also be written as cubic inches, or inches cubed.
This gives you the answer of 96 cubic inches.
Record the letters in your triangle from left to right
Answer:
.
Step-by-step explanation:
Quadrilateral a'b'c'd' is the result of dilating quadrilateral abcd about point p by a scale factor of
5/2
The two statements about the dilated quadrilateral a'b'c'd' are false.
bc and bc' are on the same line ( False)
The length of the cd and c'd' are the same. (False)
The complete question is attached with the answer below.
What is dilation?Dilation is the process of increasing the size of an object while maintaining its shape. Depending on the scale factor, the object's size can be increased or decreased.
Here the quadrilateral abcd is dilated by the scale factor 5 / 2.So the new quadrilateral is a'b'c'd'.
The given two statements are false:-
bc and bc' are on the same line ( False)
The length of the cd and c'd' are the same. (False)
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Write
7(2p+4)-2(p-5)
Where a and b are integers.
in the form ap+b
[tex]7(2p+4)-2(p-5)=14p+28-2p+10=12p+38[/tex]
Answer:
12p+38
Step-by-step explanation:
Expand the brackets and simplify :
14p+28 -2p+10 (-2×-5=+10 as the product of 2 negatives is always positive)
12p+38
This is our final answer as 12 and 38 are integers
Hope this helped and brainliest please
if population function x has mean M(x)=2 and M(x²)=8, find its standard deviation
The standard deviation of the population function is 2
How to determine the standard deviation?The given parameters are:
M(x) = 2
M(x²)=8
The standard deviation is calculated using:
[tex]\sigma = \sqrt{M(x^2) - (M(x))^2[/tex]
Substitute known values
[tex]\sigma = \sqrt{8 - 2^2[/tex]
Evaluate the expression
[tex]\sigma = 2[/tex]
Hence, the standard deviation of the population function is 2
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Write the slope-intercept form of the equation for the line.
y = -10/3x + 1/2
y = -3/10x + 1/2
y = 1/2x +3/10
y = 3/10x +1/2
Answer:
y=-3/10x+1/2
use the coordinates to find the gradient (m)then substitute it in this formula y=mx+c
find c by substituting one of the coordinate
After 4 years, approximately how much will marcia have saved in interest by consolidating the two balances? a. $1,890.24 b. $133.92 c. $543.84 d. $1,346.40
The amount that Marcia will have saved in interest by consolidating the two balances is: b.$133.92.
Amount saved in interestFirst step
Calculating for credit card A monthly payment (12% APR) using financial calculator
=pmt(rate,nper,-pv,fv)
Where:
Rate=12%/12=1%
Nper =12 months×4 years=48
PV = $1,389.47
FV=0
Hence:
=pmt(1%,48,-1389.47,0)
=$ 36.59
Second step
Monthly payments 16% APR=$39.38×48
Monthly payments 16% APR =$1890.24
Monthly payments 12% APR=$36.59×48
Monthly payment 12% APR=$1756.32
Third step
Amount saved in interest=$1890.24 -$1756.32
Amount saved in interest=$133.92
Therefore the correct option is B.
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Using f(x) = log x, what is the x-intercept of g(x) = log (x + 4)? Explain your reasoning. help please! Even these simplest questions get me stuck.
Answer:
The x-intercept is at (-3, 0).
Step-by-step explanation:
log 1 = 0, so the x intercept of y = log x is at (1, 0).
The + 4 in the parentheses moves the whole graph 4 units to the left.
Therefore the x-intercept of log(x + 4) is where x = 1-4 = -3.
2. Determine if the set of ordered pairs is a relation or a function.
{(-3,0), (-1,3), (1,0), (3,3)}
O relation
O function
O both
Function
According to defination
A relation is called to be a function if every domain of the relation has an unique range .
Or
f(x)=yHere
f(-3)=0f(-1)=3f(1)=0f(3)=3Every domain has unique range
Hence it's a function
Answer:
Function
Step-by-step explanation:
The point is a function because it passes the vertical line test
It is not a relationship because each input have only 1 out put
several local communities planted 2,360 trees this year on arbor day. and 360 more trees this year than they did last year. how many trees did they plant last year?
Answer:
2000
Step-by-step explanation:
2360-360
because it's says more trees tan last year so u minus
Sally has 10 pounds she wants to buy 28 cans of soda which cost 28p each does she have enough money
Answer:
Yes, Sally has enough money to buy 28 cans of soda.
Step-by-step explanation:
Yes, because £10 = 1000p
1000p / 28p = 35 cans
35 cans < 28 cans
So Sally has enough money for 28 cans.
hi I need help answering this question please worth 20 points
question is : how many people went on the fishing trip ?
solve
-11 2/3 x (-4 1/5
Answer:
733
Step-by-step explanation:
write it into improper fraction
simplify by finding the lcm