Answer:
y=1/2(x-6)^2+3/2
Step-by-step explanation:
General equation of parabola centered at (h,k) and axis of symmetry is parallel to y-axis is given as
(x-h)^2=4p(y-k)^2
where
vertex is at (h,k)
p shows the distance of focus from vertex, f = (h, k + p)
and directrix is given at y = k - p
if value of p is >0 then the focus is above vertex
if value of p<0 then focus is below vertex
Given:
focus= (6,2)
directrix y=1
Comparing above with standard formula of parabola, we get
Also distance p is half the distance from the (6,2) to the directix y=1 which is
1/2=p
As p>0, that means given parabola focus lies above vertex
hence parabola opens upwards
Finding vertex of parabola:
As focus is is at (6,2) and also 1/2 above the vertex so we get vertex at
V=(6,2-1/2)
V=(6,1.5)
Now by comparing above with the standard formula of parabola we have
h=6, k=1.5
Putting values in the formula we get
(x-6)^2=4(1/2)(y-1.5)
(x-6)^2=2(y-1.5)
(x-6)^2=2y-3
Or by re-arranging the terms equation can also be written as
f(x)=1/2(x-6)^2+3/2 !
The equation for a parabola with a focus at (6,2) and a directrix at y=1 is y = (x²-12x+37)/2. It is derived using the definition of a parabola.
Explanation:The equation of a parabola can be derived using the definition of a parabola: the set of all points that are equidistant from a given point (the focus) and a given line (the directrix). The distance between a point (x,y) on the parabola and the focus (6,2) is equal to the absolute value of the difference between y-coordinate of the point and y-coordinate of the directrix line.
Mathematically, the distance to the focus is (x-6)² + (y-2)² and the distance to the directrix is |y-1|. For any point on the parabola, these distances are equal, so we have (x-6)² + (y-2)² = (y-1)². Solving for y, we obtain the quadratic equation y = (x²-12x+37)/2, which represents the equation of a parabola with a focus at (6,2) and a directrix at y=1.
Learn more about Derivation of Parabola Equation here:https://brainly.com/question/29045743
#SPJ3
find the equation!!!!!! asap
Answer:
[tex]y=\frac{1}{36}x^2[/tex]
Step-by-step explanation:
The focus of the parabola is (0,9)
and the directrix is y=-9.
The equation of this parabola is given by:
[tex]x^2=4py[/tex]
The vertex of this parabola is at the origin.
The value of p is the distance from the vertex to the focus.
p=9-0=9
The equation of the parabola is
[tex]x^2=4(9)y[/tex]
[tex]x^2=36y[/tex]
Or
[tex]y=\frac{1}{36}x^2[/tex]
Use polynomial division to completely factor y=x^3+3x^2-13x-15 by x+5
Answer:
(x - 3)(x + 1)(x + 5)
Step-by-step explanation:
I'd use synthetic division instead. If we were to find the roots of the given polynomial, we could from them write the factors as well.
The divisor x + 5 corresponds to root x = -5. Setting up synthetic div.,
-5 ) 1 3 -13 -15
-5 10 +15
-----------------------------
1 -2 -3 0
Since the remainder is 0, we know that -5 is a root and (x + 5) is a factor. Moreover, we know that the coefficients of the quotient are 1, -2 and -3.
1x² - 2x - 3 can be factored: the factors are (x - 3) and (x + 1).
So the end result for this problem is (x - 3)(x + 1)(x + 5).
Find the perimeter of this figure.
Answers choices
40 m
20 m
100 m
80 m
4 congruent sides, each 10 m, so perimeter 10+10+10+10 =
Answer: 40 m
Please help! This is 6th grade math on surface area.
Answer:
144
Step-by-step explanation:
Ok. I love problems like this.
You just have to find the surface are of each part and add it up!
To find the surface area of a rectangle, you multiple the base and the height. To find the surface area of a triangle, you multiple the base and height, and divide by 2 (because its half of a rectangle).
Left rectangle: 3*ll=33
Middle rectangle: 4*ll=44
Right rectangle: 5*ll=55
Top triangle: 3*4=12
12/2=6
Bottom triangle: 3*4=12
12/2=6
ADD THEM ALL!!! 33+44+55+6+6=144
(Also can I please please please have brainliest? I need it to level up!)
what happens when you subtract a fraction with the same denominators and numerators
Answer:
0
Step-by-step explanation:
Example : [tex]\frac{2}{5} - \frac{2}{5}[/tex] = 0
Is this relation a function?
Simplify the expression (-7)2.
Answer: -14
Step-by-step explanation:
Answer:
Step-by-step explanation:
(-7)2
-7 • 2
-14
Find the unknown angle measure: please help..not sure if child's answers are correct?
Answer:
Part 1) The measure of angle PSL is 45°
Part 2) The measure of angle XYZ is 70°
Part 3) The measure of angle HJZ is 100°
Part 4) The measure of angle PHL is 120°
Part 5) The measure of angle WXZ is 140°
Part 6) The measure of angle UTG is 62°
Step-by-step explanation:
Part 1) Find the measure of angle PSL
we know that
∠PSL+∠LSM=90° -----> by complementary angles
we have
∠LSM=45°
substitute
∠PSL+45°=90°
∠PSL=45°
Part 2) Find the measure of angle XYZ
we know that
∠WYX+∠XYZ=180° -----> by supplementary angles
we have
∠WYX=110°
substitute
110°+∠XYZ=180°
∠XYZ=70°
Part 3) Find the measure of angle HJZ
we know that
∠HJZ=∠HJK+∠KJZ
we have
∠HJK=20°
∠KJZ=80°
substitute
∠HJZ=20°+80°=100°
Part 4) Find the measure of angle PHL
we know that
∠PHL=∠PHS+∠SHL
we have
∠PHS=46°
∠SHL=74°
substitute
∠PHL=46°+74°=120°
Part 5) Find the measure of angle WXZ
we know that
∠WXZ=∠WXY+∠YXZ
we have
∠WXY=15°
∠YXZ=125°
substitute
∠WXZ=15°+125°=140°
Part 6) Find the measure of angle UTG
we know that
∠UTG=∠ATG-∠ATU
we have
∠ATG=120°
∠ATU=58°
substitute
∠UTG=120°-58°=62°
The difference between the two numbers is 48. The ratio of the two number is 7:3, what are the two numbers?
Answer:
84 and 36
Step-by-step explanation:
The ratio of two numbers is 7:3.
We don't know what the numbers are, but since their ratio is 7:3, we can let the numbers be 7x and 3x. Notice that the ratio between 7x and 3x is 7x/3x = 7/3, so we still have the same ratio, 7:3.
The difference between the numbers is 48.
7x - 3x = 48
4x = 48
x = 12
7x = 7(12) = 84
3x = 3(12) = 36
The numbers are 84 and 36.
Check:
7/3 = 2.333...
84/36 = 2.333...
84 and 36 are int he same 7:3 ratio as 7:3.
84 - 36 = 48
The difference between 84 and 36 is 48 like the problem states.
This shows our answer, 84 and 36, is correct.
Hi, hope you’re having a good day today!!!
Answer:
84:36
(The explanation is really really long, so you may want to skip it, unless this is a test or you want a better understanding then, yeah)
So first, you have 7:3
Then, you have to multiply both by the same number to get an equal ratio to 7:3,
Let’s try 7*10=70 and 3*10=30 70-30=40, so you know that the answer is close,
Then, let’s try 7*11=77 and 3*11=33, subtract and you get 44. Nope, not the answer
So, finally let’s try 7*12=84 and 3*12=36, and 84-36=48!!!!
So, the answer is explained! Wait, but you still have to put them like ratios (if this chapter is ratios and proportions)
84:36 or 84 to 36, either way.
Have a great day!! ❤️❤️2 Enter the power of 10 that makes an expression
equivalent to 900
9x
Answer:
10^2
Step-by-step explanation:
10^2 = 10x10 = 100
100 x 9 = 900
Perry’s pizza parlor sells pepperoni pizza for $1.15 per piece and plain pizza for $0.90. Paul purchased 37 pieces of pizza for Pam’s party, paying $39.05. How many pieces of pepperoni pizza did Paul purchased?
Answer:
Paul purchased 23 pieces of pepperoni pizza
Step-by-step explanation:
Let pepperoni pizza pieces = x
and plain pizza pieces = y
So, the equations will be:
AS pepperoni pizza piece is sold for $1.15 and plain pizza is sold for $0.90 and Paul paid $39.05
1.15 x + 0.90 y = 39.05 eq(1)
Paul bought total 37 pieces of pizza so,
x + y = 37 eq(2)
Solving eq(1) and (2) we can find the pieces of pepperoni pizza bought by Paul.
Multiplying equation (2) with 1.15 and subtracting eq(1) and eq(2)
1.15 x + 0.90 y = 39.05
1.15 x + 1.15 y = 42.55
- - -
__________________
0 x - 0.25 y = -3.5
y = -3.5/-0.25
y = 14
Putting value of y in equation(2)
x+y = 37
x + 14 = 37
x = 37 - 14
x = 23
So, Paul purchased 23 pieces of pepperoni pizza as x represents pepperoni pizza pieces.
By setting up and solving a system of linear equations, we determined that Paul purchased 23 pieces of pepperoni pizza for Pam's party.
To determine how many pieces of pepperoni pizza Paul purchased for Pam's party from Perry's pizza parlor, we can set up a system of equations based on the cost of each piece and the total amount spent. Let x represent the number of pepperoni pizzas at $1.15 each and y represent the number of plain pizzas at $0.90 each. We have the following equations based on the given information:
x + y = 37 (total pieces of pizza purchased)
1.15x + 0.90y = $39.05 (total amount spent)
By solving these equations simultaneously, we can find the exact number of pepperoni and plain pizzas that Paul purchased. Multiplying the second equation by 100 to clear the decimals, we get:
115x + 90y = 3905
Now, multiply the first equation by 90:
90x + 90y = 3330
Subtract the modified first equation from the modified second equation:
(115x + 90y) - (90x + 90y) = 3905 - 3330
25x = 575
x = 23
Paul purchased 23 pieces of pepperoni pizza.
A college-entrance exam is designed so that scores are normally distributed with a mean of 500 and a standard deviation of 100. Using the eight‐part symmetry of the area under a normal curve, what is the probability that a randomly chosen exam score is less than 200 or greater than 800?
The probability is__?
Final answer:
The combined probability of scoring less than 200 or greater than 800 on a normally distributed college-entrance exam with mean 500 and standard deviation 100 is approximately 0.3%.
Explanation:
The probability that a randomly chosen exam score is less than 200 or greater than 800 in a normally distributed college-entrance exam can be found by using the properties of the normal distribution. Since the mean score is 500 and the standard deviation is 100, scores below 200 are three standard deviations below the mean, and scores above 800 are three standard deviations above the mean. Given the symmetry and the empirical rule of normal distribution, approximately 99.7% of values lie within three standard deviations from the mean, leaving roughly 0.3% of the values outside this range. Therefore, since both tails (below 200 and above 800) are considered, we need to split this percentage, which gives us approximately 0.15% (or 0.0015 in probability terms) for each tail. Thus, the combined probability of scoring less than 200 or greater than 800 is approximately 0.3% (or 0.003 in probability terms).
Find the volume and explain please ASAP.
Answer:
1395in^3
Step-by-step explanation:
First find the volume of the cuboid, 15in x 9in x 7in = 945in^3
Then find the volume of the rectangular pyramid using the formula V=lwh/3, the total height is 17in so subtract the height of the cuboid from the total height, giving you 10in.
V=(15in)(9in)(10in)/3 = 450in^3
450in^3 + 945in^3 = 1395in^3
which sampling method divides the samples into precincts?
A. simple random sampling
B. systematic random sampling
C. stratified random sampling
D. Cluster sampling
Answer:
D. Cluster sampling
Step-by-step explanation:
Dealing with the whole population can be cumbersome, time-consuming and very expensive. In order to make it more feasible for researchers they can employ cluster sampling. In cluster sampling, the population are divided into precincts, or gropus. The researcher then selects the groups that will be included in the study through simple random samping or systematic sampling. The researcher can opt to choose let the whole cluster or group to participate in the study or they can randomly select the individuals within the groups.
Answer:
d
Step-by-step explanation:
Evaluate the expression 7x^2y, when x = 5 and y=3
Answer:
It is 525
Step-by-step explanation:
Your school needs 9 buses for this field trip. additonly, you must include a $100 tip. If your school spends $1829.82,how much does each bus cost
The cost of each bus for the school's field trip is approximately $192.20.
To calculate the cost of each bus, you first subtract the tip from the total expenses.
So, $1829.82 - $100 = $1729.82.
This is the total cost for the 9 buses without the tip.
Next, you divide this amount by the number of buses to find the cost per bus. $1729.82 / 9 = $192.20.
Therefore, each bus costs about $192.20.
You are trying to dunk a basketball. You need to jump 2.5 feet. In the air to dunk the ball. The height that your feet are above the ground is given by the function h (t)=-16ft+12. What is the maximum height your feet will be above the ground? Will you be able to dunk the basketball
Answer:
1)he maximum height your feet will be above the ground is 12
2)Will you be able to dunk the ball= yes
Step-by-step explanation:
Given:
In order to dunk the basket ball, height needed to jump= 2.5 feet
The height that your feet need to be of the ground is given by the function h(t)= -16t^2+12
1) the maximum height your feet will be above the ground=?
Given function of height,h(x)=-16t^2+12
finding maximum of the above function
The maximum of any function written in form of ax^2+bx+c is given by
max= c - (b2 / 4a)
Putting values c=12, b=0 and a=16, we get
max= 12-(0^2/4(-16))
= 12 -0
=12 feet
he maximum height your feet will be above the ground is 12 feet.
2) Will you be able to dunk the ball=?
As the maximum height the feet will be above the ground is 12 feet which is greater than the height needed to jump in the air to dunk the ball 2.5 feet i.e.
12>2.25
hence yes you will not be able to dunk the ball !
How many layers of material were the Romanroads made of?
A.two
B.three
C.four
D.five
PLEASE HELP ME NOW!!
Answer:
[tex]x=4+-2\sqrt{7}[/tex]
Step-by-step explanation:
To solve, we need to take square root of both sides first:
[tex](x-4)^2=28\\\sqrt{(x-4)^2} =+-\sqrt{28} \\x-4=+-\sqrt{28}[/tex]
Now we use the property of radical shown below to simplify square root of 28:
Property: [tex]\sqrt{x*y}=\sqrt{x} \sqrt{y}[/tex]
Now, we have:
[tex]x-4=+-\sqrt{28}\\x-4=+-\sqrt{4*7}\\x-4=+-\sqrt{4}\sqrt{7}\\x-4=+-2\sqrt{7}[/tex]
Now we take 4 to the other side and isolate x:
[tex]x-4=+-2\sqrt{7} \\x=4+-2\sqrt{7}[/tex]
first answer choice is right.
The answer is:
The correct answer is the first option.
[tex](x-4)^{2}=4+-2\sqrt{7}[/tex]
Why?To solve the problem, we must remember the following square root property:
[tex]\sqrt{ab}=\sqrt{a}\sqrt{b}[/tex]
So,
We are given the expression:
[tex](x-4)^{2}=28[/tex]
Now, isolating we have:
First, applying square root to both sides of the equation in order to simplify the quadratic term, we have:
[tex]\sqrt{(x-4)^{2} }=\sqrt{28}\\(x-4)=\sqrt{4*7}\\\\x=4+-(\sqrt{4}*\sqrt{7})\\\\x=4+-2\sqrt{7}[/tex]
Hence, the correct answer is the first option.
[tex](x-4)^{2}=4+-2\sqrt{7}[/tex]
Have a nice day!
What is the total amount that Matthew's bank will receive after lending him $8,000 for four years at an interest rate of 6 percent, compounded annually?
Answer:
Total amount that Matthew's bank will receive is $10099.81.
Step-by-step explanation:
We need to find the amount Matthew's bank will receive after lending him $8,000 for four years at an interest rate of 6 percent, compounded annually.
The formula for compound interest is:
[tex]A=P(1+r)^n[/tex]
Where A = future value
P= Principal Amount
r = interest rate
and n= time
So in the question we are given:
P= $8000
r = 6% or 0.06
t = 4 (since 4 yeras compounded annually)
A= 8000*(1+0.06)^4
A= 8000*(1.06)^4
A= 10099.81
So, total amount that Matthew's bank will receive is $10099.81.
Answer:
the answer is 10,099.80
Step-by-step explanation:
Choose the correct simplification of the expression a2 ⋅ a3. a a6 a5 a−1
Answer: The correct option is (C) [tex]a^5.[/tex]
Step-by-step explanation: We are given to choose the correct simplification for the following expression :
[tex]P=a^2.a^3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We will be using the following property of exponents :
[tex]x^a.x^b=x^{a+b}.[/tex]
So, the simplification of expression (i) is as follows :
[tex]P\\\\=a^2.a^3\\\\=a^{2+3}\\\\=a^5.[/tex]
Thus, the correct simplification of the given expression is [tex]a^5.[/tex]
Option (C) is CORRECT.
Monique planted seeds to grow pansies, Snapdragons, and petunias. After several weeks, 18 out of 40 pansy seeds, 21 out of 50 snapdragon seeds, and 12 out of 30 petunia seeds grew into plants. Write the named of the plants in order from least percentage of plants that grew to the greatest percentage of plants that grew.
Answer:
petunias, snapdragons, then pansy
Step-by-step explanation:
Ok first, lets find the percentage of 18 out of 40: 18/40= 0.45
The 21 out of 50= 21/50= 0.42
Lastly, 12/30= 0.40
And its very simple to put from least to greatest:
0.40, 0.42, 0.45
Hope this helped ;)
The answer is petunias, snapdragons, then pansies.
Hope this helps!
A collection of quarters and nickels contains at least 42 coins and is worth at most $8.00. If the collection contains 25 quarters, how many nickels can be in the collection? Let x = the number of quarters. Let y = the number of nickels. There are at least nickels, but no more than nickels.
Answer:
17
35
Step-by-step explanation:
Answer:
17
35
Step-by-step explanation:
Solve this problem using the substitution method 2y-1/2y=2
Answer:
y=3/2and x =2
Step-by-step explanation:
If you buy five of the XYZ bonds with $8 commission for each how much will it cost?
Answer:
B) 5065
Step-by-step explanation:
100.5 times 5 = 502.5
502.5 times 100
+ 8 times 5 (commission)
The question asks for the total commission fee when buying five XYZ bonds. Each bond has $8 commission. Therefore, 5 bonds * $8 = $40.
Explanation:To determine the total cost of purchasing five XYZ bonds with a commission fee of $8 each, you have to multiply the number of bonds by the commission fee. So, the calculation will be:
Identify the number of bonds: 5 bonds.Identify the commission fee per bond: $8.Multiply the number of bonds by the commission fee: 5 bonds * $8 = $40.This means the total cost just for purchasing (not including the face value of the bonds themselves) is $40.
Learn more about Bond Purchase Cost here:https://brainly.com/question/2506248
#SPJ3
Which change (in percent) is larger: a increasing the price from $400 to $500 or increasing the price from $500 to $600?
Worth 86 points!!!!!
Answer:
400 to 500
Step-by-step explanation:
The increase in the price from $400 to $500 has got the larger change, that is the change of 25%.
What is the Percentage?The Latin term "per centum," which signifies "by the hundredth," was the source of the English word "percentage." Segments with a denominator of 100 are considered percentages. In other terms, it is a relationship where the worth of the entire is always considered to be 100.
As per the data provided in the question,
Percentage change from $400 to $500
% change = (500 - 400)/400 × 100
% change = 25%
Percentage change from $500 to $600,
% change = (600 - 500)/500 × 100
% change = 20%
Therefore, $400 to $500 has the largest change.
To know more about Percentage:
https://brainly.com/question/29306119
#SPJ2
I don’t get this problem
Answer:
Line B
Step-by-step explanation:
It is the line that most of the dots surround
Answer:
Line b
Step-by-step explanation:
Line b has the most black dots positioned close to it, and therefore is the best fit line.
John is at a local bait shop; he wants to buy bait for his fishing trip. At the store, they are selling live bait for $12 a pound and natural bait for $7 a pound. John would like to get at least 3 pounds of live bait, but he only has a budget of $63. Let x be the amount of live bait and y be the amount of natural bait. Model the scenario with a system of inequalities.
Answer:
[tex]x\geq3[/tex]
[tex]12x+7y\leq63[/tex]
[tex]y\geq0[/tex]
Step-by-step explanation:
If we let x be the amount of live bait and y be the amount of natural bait, Then we can come up with the following inequalities;
We are told that John would like to get at least 3 pounds of live bait. At least 3 means 3 or more. Since x represents the amount of live bait, we have;
[tex]x\geq3[/tex]
Moreover,we are informed that;
The store sells live bait for $12 a pound and natural bait for $7 a pound. x pounds of live bait would cost 12x while y pounds of natural bait would cost 7y. The total cost would thus be;
12x + 7y
but John only has a budget of $63. This implies that he can spend $63 at most, thus;
[tex]12x+7y\leq63[/tex]
Finally we can have our last inequality as;
[tex]y\geq0[/tex]
|x| + |y|
Evaluate the expression if x = 16 and y = 13.
Answer:
|x| + |y| = 29
Step-by-step explanation:
We have been given the expression;
|x| + |y|
We are required to evaluate the above expression if;
x = 16 and y = 13
The parallel vertical lines imply that we are dealing with the absolute value of x and y;
|x| + |y| = |16| + |13|
= 16 + 13
= 29
Answer:
The correct answer is 29
Step-by-step explanation:
Points to remember
|x| = x
|-x| = x
It is given an expression, |x| + |y|
To find the value of given expression
|x| + |y| if x = 16 and y = 13
Substitute the value of x and y in the above expression,
|x| + |y| = |16| + |13|
= 16 + 13 = 29
Therefore the correct answer is 29
If you roll a number cube 30 times, how many times do you expect to roll a five
Answer:
5
Step-by-step explanation:
There are 6 numbers on a die, one of them is 5 so we expect to get a five one of six times
P (5) = 1/6
If we roll the die 30 times, we expect to get a five 30 * 1/6 = 5 times