Answer:
The standard form of the ellipse is [tex]\frac{(x-4)^{2}}{9} + \frac{(y-7)^{2}}{49} = 1[/tex].
Step-by-step explanation:
The major axis of the ellipse is located in the y axis, whereas the minor axis is in the x axis. The center of the ellipse is the midpoint of the line segment between vertices, this is:
[tex](h, k) =\frac{1}{2}\cdot V_{1} (x,y) + \frac{1}{2}\cdot V_{2} (x,y)[/tex] (1)
If we know that [tex]V_{1} (x,y) = (4,0)[/tex] and [tex]V_{2}(x,y) = (4, 14)[/tex], then the coordinates of the center are, respectively:
[tex](h,k) = \frac{1}{2}\cdot (4, 0) + \frac{1}{2}\cdot (4,14)[/tex]
[tex](h,k) = (2,0) + (2, 7)[/tex]
[tex](h, k) = (4, 7)[/tex]
The length of each semiaxis is, respectively:
[tex]a = \sqrt{(1 - 4)^{2}+(7-7)^{2}}[/tex]
[tex]a = 3[/tex]
[tex]b = \sqrt{(4-4)^{2}+(0-7)^{2}}[/tex]
[tex]b = 7[/tex]
The standard equation of the ellipse is described by the following formula:
[tex]\frac{(x-h)^{2}}{a^{2}}+ \frac{(y-k)^{2}}{b^{2}} = 1[/tex]
Where:
[tex]h[/tex], [tex]k[/tex] - Coordinates of the center of the ellipse.
[tex]a[/tex], [tex]b[/tex] - Length of the orthogonal semiaxes.
If we know that [tex]h = 4[/tex], [tex]k = 7[/tex], [tex]a = 3[/tex] and [tex]b = 7[/tex], then the standard form of the ellipse is:
[tex]\frac{(x-4)^{2}}{9} + \frac{(y-7)^{2}}{49} = 1[/tex]
PLS HELP 40 POINTS
If the dimensions of the following cylinder are quadrupled, what will be the volume of the new similar cylinder?
340,426.24 in. 3
20,724 in. 3
63,829.92 in. 3
110,528 in. 3
Volume of the new similar cylinder is equals to 340,426.24 in.³.
What is volume?
" Volume is defined as the total space occupied by any three dimensional objects enclosed in it."
Formula used
Volume of the cylinder = πr²h
r = radius of the cylinder
h = height of the cylinder
value of π = 3.14
According to the question,
radius of the cylinder = 11 in.
height of the cylinder = 14 in.
Dimensions of new cylinder are quadrupled means 4times.
New radius = 44 in.
New height = 56 in.
Substitute the value in the formula we get,
Volume of the new cylinder = (3.14) ×(44)² × (56)
= 340,426.24 in.³
Hence, volume of the new similar cylinder is equals to 340,426.24 in.³.
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the nth term of a sequence is 4n-3. finf the number in the sequence that is closest to 150
Answer:
149
Step-by-step explanation:
nth term = 4n - 3 ..............(1)
Now,
For The tern closer to 150
150 = 4n - 3
or, 153 = 4n
or, n = 38.25
Now,
Since n can not be in decimal,
Put n = 38 in (1) (Rounding off 38.25 to 38)
or, nth term = 38*4 -3
= 152 - 3 = 149
∴ The number of sequence closer to 150 is 149
Explain why sin(A)=sin(D)
I NEED HELP ASAP
becouse The size does not differ whether it is big or small, the degree remains the same
can someone help me
55 x 7 = 385
dadadsdsadssdgregeg
Find all working solutions for x.
✓(x-5) - 5 = 3
Answer:
Step-by-step explanation:
✓(x-5) - 5 = 3
✓(x-5) - 8 = 0
(✓(x-5))² - 8² = 0
x-5 - 64 = 0
x - 69 = 0
x = 69
Show that the transformation T defined by
T(x1, x2) = (2x1 - 3x2, X1+4, 5x2) is not linear.
Let u = (1, 0) and v = (0, 1). Then
T (u) = (2*1 - 3*0, 1 + 4, 5*0) = (2, 5, 0)
T (v) = (2*0 - 3*1, 0 + 4, 5*1) = (-3, 4, 5)
=> T (u) + T (v) = (-1, 9, 5)
but
T (u + v) = T (1, 1) = (2*1 - 3*1, 1 + 4, 5*1) = (-1, 5, 5)
=> T (u + v) ≠ T (u) + T (v)
which means T does not preserve addition, so it is not linear.
Round 386.565 to the nearest hundredth.
The measure of (angle) 6 is 120. The measure of (angle) 5 is 100. What is the measure of (angle) 4
Answer:
80
Step-by-step explanation:
4x20=80
The area of a rectangle is given by the expression x^2 + 6x – 16. What are the dimensions of the rectangle?
(x+4) by (x+4)
(x+4) by (x-4)
(x+8) by (x-2)
(x-8) by (x+2)
Answer:
I don't no answer sorry sorryPlease help me find x and y
Answer:
x = 33
y = 5
Step-by-step explanation:
Line BD splits AC in half so y is also 5Since the triangles are congruent (is known because of the congruence lines) and you know two angles you can find x57+90=147 and 180-147= 33 which is xPls help I’ll brainlest
Answer:
Choice B
Step-by-step explanation:
7.1×10⁵ = 710,000
Answer:
The answer is B. 7.1 times 10^5.
Step-by-step explanation:
To convert a number to scientific notation, place or move the decimal point of a number until the coefficient of the number is greater than 1 and less than 10. Record down the coefficient and count the number of steps the decimal point was moved. The number of steps moved is taken as the exponent.
In 710,000, the decimal is moved to the left 5 times. Thus, causing 710,000 to written as 7.1 times 10^5 in scientific notation.
Marie had 12 pizzas. She wanted to give each person of a 1/4
pizza. How many people would receive a piece of pizza?
Answer:
48 people.
Step-by-step explanation:
Each person gets 1/4 of a pizza meaning that one pizza can serve 4 people. If one pizza can serve 4 people, 12 pizzas can serve 48 people, because 4x12=48.
Tickets to the theater cost $8.00 for adults and $3.00 for children. A group of 2
total people showed up to the theater. They spent $93.00 total on tickets. How
many adults and children were in the group?
Answer: 9 adults 7 children
Step-by-step explanation:
A rectangular in ground pool needs to be filled with water. The pool is 20 feet long 9 1/2 feet wide, and 5 1/2 feet deep determin the maximum amount of water the pool can hold? PLS ANSWER IM GOING TO FAIL
Answer:
1045 ft³ of water
Step-by-step explanation:
Given :
Length = 20 feets
Width = 9 1/2 feets
Height = 5 1/2 feets
The maximum of water the pool can hold is equivalent to the volume of the pool ;
Hence, Volume = Length * width * height
Volume = 20 * 9 1/2 * 5 1/2
Volume = 1045 ft³ of water
What does the digit 8 represent in 687, 413?
Answer:
80,000
hope this helps
have a good day :)
Step-by-step explanation:
Answer:
Hundreths
Step-by-step explanation:
Suppose that, as course instructor, you decide instead that you want to calculate a 95% confidence interval for the population proportion of all Cal Poly students who have ever marched in a Memorial Day Parade, and that you would like the margin of error of your 95% confidence interval to be .05, and that you would like to use a (most) conservative sample size for this task. What sample size should you use
Answer: 385
Step-by-step explanation:
If prior population proportion p is unknown, then the formula to compute sample size will be:
[tex]n= 0.25(\frac{z^*}{E})^2[/tex]
where, E= Margin of error, z* = Critical zvalue
Given: E= 0.05
Critical value for 95% confidence = 1.96
Required sample size: [tex]n=0.25(\frac{1.96}{0.05})^2[/tex]
[tex]\\=384.16\approx385[/tex]
Hence, the required sample size = 385
Perform the operation. Enter your answer in scientific notation. 7 × 102 − 5.6 × 102 =
urgent..
not explanation just answer plzz
Answer:
D 1
Step-by-step explanation:
The question is in the picture (Alegbra 1)
Answer:
[tex] \frac{s}{s + 3} [/tex]
Answer:
S/S+3
Step-by-step explanation:
Hope this helps...
At the start of the day, Megan has the following items for sale:
60 Sandwiches £2.40
40 Baguettes a £2.70
25 Jacket potatoes £3.25
She sells all the jacket potatoes, 65% of the sandwiches and 85% of the
baguettes.
What is the total value of her sales that day?
Answer:
266.65
Step-by-step explanation:
65% of 60 = 39 sandwiches sold
85% of 40 = 34 baguettes sold
all Jacket potatoes sold 3.25 x 25
34 x 2.70
39 x 2.40
add the total and comes to 266.65
09.03 MC) What is the domain of the following parabola? (5 points) u-shaped graph that opens down with a vertex of 2, 3 Select one: a. x ≥ 2 b. x ≤ −1 c. y ≤ 3 d. All real numbers
Answer:
The correct option is d: All real numbers.
Step-by-step explanation:
For a function f(x), the domain is the set of all the possible values of x that we can input in that function.
A general way to find the domain of a function is:
First, assume that the domain is the set of all real numbers.
Then, look at restrictions implied:
like in functions like:
f(x) = 4 if x > 3
Here the domain of the function is implied.
Third, let's find values of x that make "problems" with our function (for example, a zero in the denominator) and then remove these points from the domain.
In this case, we have a quadratic function:
y = a*x^2 + b*x + c
Here we do not have any problem (like a zero in a denominator), and we do not have any restrictions (We only know that the parabola is U shaped, so it is a function, and that its vertex is (2, 3) )
Then we can conclude that the domain of this function is the set of all real numbers.
The correct option is d: All real numbers.
What is the length of NP?
Answer:
c. √174
Step-by-step explanation:
NP²= 10²+7²+5²=100+49+25= 174
NP = √174
The length of NP would be; √174
What is Pythagoras' Theorem?If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
|AC|^2 = |AB|^2 + |BC|^2
where |AB| = length of line segment AB. (AB and BC are the rest of the two sides of that triangle ABC, AC being the hypotenuse).
We are given the measure of sides;
NP²= 10²+7²+5²
NP²=100+49+25
NP²= 174
NP = √174
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someone tell me 1+1= 11 and not 2 - -
to
Angle JKL is a straight angle.
The measure of angle MKL is 25°.
The measure of angle JKM is xº.
What is the value of x?
M
25°
K
n
Answer:
180-25=155 degrees
Step-by-step explanation:
Select the correct answer.
This graph represents a function.
y
A
8-
61
+
2-
X
-8
-6
-4
- 2
2
4
6
8
-2
-4
-6-
-8
Which table contains points from the inverse of the graphed function?
A.
X х
-4
-3
-2.
-1
3
- 3
y
-1
1
B.
Х
-3
-1
3
1
у
-4
-3
-1
-2
.
-3
Х
3
- 1
2.
1
3
1
y
4
D.
Х
1
4
2
3
y
-3
-1
3
9514 1404 393
Answer:
B
Step-by-step explanation:
To find the graph of the inverse function, swap the labels x and y on the axes of the given graph.
There are no x-values common to all the tables, but you can make a determination of the correct one by looking at x=1 and x=-1.
After you swap the axis labels you see that the points ...
(x, y) = (1, -2) or (-1, -3)
are on the graph. These points are only found in the table of selection B.
The table contains points from the inverse of the graphed function is B. Table 2.
What is a graph?A graph simply means a diagram that represents the variation of a variable when being compared with other variables.
In this case, the inverse of the graphed function will simply be done by switching all the values of x and y in each point. This is clearly illustrated in the second table.
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1. How far is KFC from RCBC Savings Bank? 2. How far is BaliwagLetchon Manok from RCBC Savings Bank? 3. How far is Baliwag Lechon from his residence? 4. How far is KFC from his residence? 5. What is the measure of angle ERK ?
Answer:
Following are the solution to the given question.
Step-by-step explanation:
Please find the graph file and its solution in the attachment.
[tex]4x-15=3x+28\\\\4x-3x=28+15\\\\x=43\\\\[/tex]
Similarly:
[tex]3y+5=2y+50\\\\3y-2y=-5+50\\\\y=45\\\\[/tex]
For point 1:[tex]\to KR=4x-15= 4\times 43-15=172-15=157[/tex]
For point 2: [tex]\to BR=2y+50= 2\times 43+50=86+50=136[/tex]
For point 3:[tex]\to BE=KR=157[/tex]
For point 4:[tex]\to Kf=BR=130[/tex]
For point 5:[tex]\to ERK=KFB=180^{\circ} -\angle B-\angle ERB = 180^{\circ}-92^{\circ}-18^{\circ}=70^{\circ}[/tex]
Given that ΔKER and ΔBRE are congruent triangles, therefore:
1. How far KFC is from RCBC = KR = 157 m
2. How far BaliwagLetchon Manok is from RCBC Savings Bank = BR = 140 m
3. How far Baliwag Lechon is from his residence = BE = KR = 157 m
4. How far KFC is from his residence = KE = BR = 140 m
5. The measure of ∠ERK = 70°
What are Congruent Triangles?Congruent triangles have corresponding parts hat are congruent to each other.
Thus, given that ΔKER ≅ ΔBRE, find the values of x and y as shown below:
KR = BE
4x - 15 = 3x + 28
4x - 3x = 15 + 28
x = 43
KE = BR
3y + 5 = 2y + 50
3y - 2y = -5 + 50
y = 45
Thus:
1. How far KFC is from RCBC = KR
KR = 4x - 15
Plug in the value of x
KR = 4(43) - 15
KR = 157 m
2. How far BaliwagLetchon Manok is from RCBC Savings Bank = BR
BR = 2y + 50
Plug in the value of y
BR = 2(45) + 50
BR = 140 m
3. How far Baliwag Lechon is from his residence = BE = KR = 157 m
4. How far KFC is from his residence = KE = BR = 140 m
5. The measure of ∠ERK = 180 - (92 + 18) = 70°
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Exam grades: Scores on a statistics final in a large class were normally distributed with a mean of 77 and a standard deviation of
10. Use the TI-84 PLUS calculator to answer the following. Round the answers to at least two decimals.
(a) Find the 28th percentile of the scores.
(b) Find the 65th percentile of the scores.
(c) The instructor wants to give an A to the students whose scores were in the top 12% of the class. What is the minimum score
needed to get an A?
(d) Between what two values are the middle 64% of the scores? (Enter the smaller number in the first box.)
On a particular day, 112 of 280 passengers on a particular DTW-LAX flight used the e-ticket check-in kiosk to obtain boarding passes. In a random sample of eight passengers, use the binomial model to find the approximate hypergeometric probability that four will have used the e-ticket check-in kiosk to obtain boarding passes.
Answer:
0.2348 = 23.48% probability that four will have used the e-ticket check-in kiosk to obtain boarding passes.
Step-by-step explanation:
Hypergeometric distribution:
The probability of x sucesses is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of sucesses.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
Population of 280, which means that [tex]N = 280[/tex]
112 use e-ticket check-in kiosk, which means that [tex]k = 112[/tex]
Sample of eight passengers means that [tex]n = 8[/tex]
Find the approximate hypergeometric probability that four will have used the e-ticket check-in kiosk to obtain boarding passes.
This is P(X = 4). So
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 4) = h(4,280,8,112) = \frac{C_{112,4}*C_{168,4}}{C_{280,4}} = 0.2348[/tex]
0.2348 = 23.48% probability that four will have used the e-ticket check-in kiosk to obtain boarding passes.
1. Given f(x) = x2 – X and g(x) = 3x + 2, find f(g(2))
Answer:
56
Step-by-step explanation:
g(2) = 3(2) + 2
= 6 + 2
= 8
f(8) = 8^2 - 8
= 64 - 8
= 56
Find...
2/7 of 36
I really need help!
Answer:
10 2/7
Step-by-step explanation:
Of means multiply
2/7 *36
72/7
Changing from an improper fraction
70/7 +2/7
10 2/7
Answer:
[tex] \frac{2}{7 } \: of \: \: 36 \\ = \frac{2}{7} \times 36 \\ = \frac{2 \times 36}{7} \\ = \frac{72}{7} \\ = 10 \frac{2}{7} \\ = 10.28[/tex]
✐ The answer in fraction form is 72/7, & in decimal form is 10.28.
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