Answer:
The latus rectum of an ellipse is a line segment that is perpendicular to the major axis of the ellipse and passes through one of its foci. If the ellipse has a major axis of length 2a, then the latus rectum will have a length of a. Therefore, if the latus rectum is equal to half of the major axis, then the major axis must have a length of 2a, and the latus rectum will have a length of a.
The point (√6, 1) can be the end point of the latus rectum if it lies on the ellipse. To determine if this is the case, you can substitute the coordinates of the point into the standard equation of an ellipse. If the point satisfies the equation, then it lies on the ellipse and can be the end point of the latus rectum.
The standard equation of an ellipse with major axis of length 2a and minor axis of length 2b is:
(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1
Where (h, k) is the center of the ellipse. In this case, we don't know the values of a, b, h, and k, so we can't determine if the point (√6, 1) lies on the ellipse. However, we can use the fact that the latus rectum has a length of a to find the center of the ellipse.
Since the latus rectum is perpendicular to the major axis and passes through the focus, it must also pass through the center of the ellipse. Therefore, the midpoint of the line segment defined by the coordinates (√6, 1) and the center of the ellipse must be the center of the ellipse. The coordinates of the center can be found by taking the average of the x-coordinates and the average of the y-coordinates. In this case, the center of the ellipse will have coordinates:
(x, y) = ((√6 + h) / 2, (1 + k) / 2)
Once you know the center of the ellipse, you can use the standard equation of an ellipse to find the values of a, b, h, and k. Once you have those values, you can determine if the point (√6, 1) lies on the ellipse and can be the end point of the latus rectum.
I hope this helps. Let me know if you have any other questions.
Emika has a monthly budget for her cell phone bill.
Last month she spent `120\%` of her budget, and the bill was `\$60`.
What is Emika’s monthly budget?
Using percentages, we know that Emika's monthly budget is $50.
What is the percentage?A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" is also used, the percent symbol, "%," is frequently used to indicate it.
A % is a number without dimensions and without a standard measurement.
For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).
So, if we multiply a fraction of a number by 100, you get a percentage. % is the symbol used to denote percentages.
Let x stand in for Emika's monthly cell phone budget.
Divide $60 by 120% to find his monthly spending limit.
x = $60 / 120%
x = $60 / 1.20
x = $50
Therefore, using percentages, we know that Emika's monthly budget is of $50.
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Find the equation of a line that passes through (-7,2) and is parallel to the line 7x+2y=0
Answer:
7x + 2y = - 45-----------------------
GivenLine 7x + 2y = 0,Point (-7, 2) on a parallel line.Find the equation of the parallel line.We know parallel lines have equal slopes.
Find the slope of the given line:
7x + 2y = 02y = - 7xy = - 3.5xThe slope is - 3.5.
Use point-slope equation to find the equation of the parallel line.
y - 2 = - 3.5(x - (-7))y - 2 = - 3.5x - 24.5y = - 3.5x - 22.5Convert it to standard form:
y = - 3.5x - 22.52y = - 7x - 45 7x + 2y = - 45Graph the linear inequality.
y> 3x+5
Answer:
Graph a solid line, then shade the area above the boundary line since y y is greater than −3x+5 - 3 x + 5 . y≥−3x+5 y ≥ - 3 x + 5.
Step-by-step explanation:
Find the arc length and sector area for the following:
(Use \large \pi=3.14...do not use the \large \pi button on your calculator!)
arc length =
sector area =
the value of arc length = 3.14 and the area of the sector = 4.71cm²
What is area of sector and length of an arc?The formula for the area of the sector of a circle is /360° (r2) where r is the radius of the circle and is the angle of the sector.
Arc length is the distance between two points along a section of a curve. It is given as
/360°×2r
= 180°, therefore /3 = 180/3= 60°
arc length = 60°/360 × 2×3.14×3
arc length = 3.14cm
The area of the sector = /360°×r²
60/360×3.14×3²
sector area = 3.14×3÷2
sector area = 4.71cm²
therefore the length of the arc and the area bounded by the arc and radius(sector) is 3.14cm and 4.17cm².
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Answer:the value of arc length = 3.14 and the area of the sector = 4.71cm²
Step-by-step explanation:
the value of arc length = 3.14 and the area of the sector = 4.71cm²
Find the common ratio of the geometric sequence -6, -48, -384, ...
Answer:
8
Step-by-step explanation:
-6 x 8=-48
-48 x 8=-384
So then I think that the common ratio is 8. ( If wrong, my sincere apology)
Please help!! I tried setting it up to 180 but I don’t feel right about it! Thanks! :)
Manuel has $20,000 in a savings account that earns 7% annually. The interest is not
compounded. How much interest will he earn in 2 years?
PLEASE HELP!!
Answer:
If Manuel has $20,000 in a savings account that earns 7% interest per year and the interest is not compounded, then after two years he will earn $2,800 in interest. This is because 7% of $20,000 is $1,400, and since the interest is not compounded, this amount will remain constant for each year. Therefore, after two years Manuel will earn a total of $1,400 + $1,400 = $2,800 in interest.
In general, if a savings account earns x% interest per year and the initial amount in the account is y dollars, then after n years the account will earn n * (x/100) * y dollars in interest. For example, if the interest rate is 7% and the initial amount is $20,000, then after two years the account will earn 2 * (7/100) * $20,000 = $2,800 in interest.
Step-by-step explanation:
Answer:
The answer is $2800.
Step-by-step explanation:
Given;Manuel has $20,000 in a savings account that earns 7% annually.To Find;Interest of 2 years.Now,
(20000 × 7) ÷ 100 = $1400
Here, we get for 1 year
for two years,
1400 × 2 = $2800
Thus, He will earn $2800 in 2 years.
A fish dives down into the ocean at a constant rate. From the surface, it
dives 2,060 feet in 5 minutes. The number -2,060 represents the
location of the sailfish in relation to the surface. What number
represents the location of the fish in relation to the surface 2 minutes
after beginning the dive?
Answer:
- 824 ft
Step-by-step explanation:
2 minutes out of 5 is a fraction 2/5
2/5 of the -2060 would be
2/5 *( -2060) = - 824 ft
Answer:
uhhh i think -824
Step-by-step explanation:
-2060/5
-412
-412x2
-824
Please help me understand this
Answer:
? understand whatt I think you ment to put a picture or something
ethe relationship between the data in the table is linear write a equation
in slope-itercept form that represent the data in the table
Answer:
give the data in the graph form and your answer is right..
Simplify:
[tex]\frac{sec(x)-csc(x)}{sec(x)+csc(x)}[/tex]
Hence, the value of [tex]\frac{sec(x)-csc(x)}{sec(x)+csc(x)}=1[/tex].
What is the trigonometry?
Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Here given that,
[tex]\frac{sec(x)-csc(x)}{sec(x)+csc(x)}[/tex]
As we know,
[tex]sec(x)=\frac{1}{csc(x)}\\\\\\1-1csc^2(x)=cot^2(x)\\\\\\1+csc^2(x)=cot^2(x)[/tex]
So,
[tex]\frac{sec(x)-csc(x)}{sec(x)+csc(x)}\\\\\\=\frac{\frac{1}{csc(x)}-csc(x)}{\frac{1}{csc(x)}+csc(x)}\\\\\\=\frac{\frac{1-csc^2(x)}{csc(x)}}{\frac{1+csc^2(x)}{csc(x)}}\\\\\\=\frac{{1-(1)csc^2(x)}}{{1+csc^2(x)}}\\\\\\=\frac{cot^2(x)}{cot^2(x)}\\\\\\=1[/tex]
Hence, the value of [tex]\frac{sec(x)-csc(x)}{sec(x)+csc(x)}=1[/tex].
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Here are the ages (in years) of 8 professors at a college. 46, 32, 57, 28, 42, 34, 29, 37. What is the percentage of these professors who are younger than 35?
Answer:
1/2
Step-by-step explanation:
There are 8 total professors and 4 are below the age of 35
32, 28, 34, 29
5). Jacob and Madison share a reward of $90 in a ratio of 1 : 4. What fraction of the total reward does Jacob get?
Answer:
$18
Step-by-step explanation:
RatioRatios are numerical proportions among different values.
Eg. 1 : 4 is 1 to 4.
SolutionGiven Total Shares = 1 + 4 = 5 = $90
Jacob gets 1 share.
1 Share = $90 ÷ 5 = $18
Therefore Jacob gets $18.
In a certain state, 43% of adults indicated that sausage is their favorite pizza. Suppose a simple random sample of adults in the state of size 25 is obtained and the number of adults who indicated that sausage is their favorite pizza was 19. What are values of the parameters n, p, and x in the binomial probability experiment?
If in a certain state, 43% of adults indicated that sausage is their favorite pizza. The values of the parameters n, p, and x in the binomial probability experiment are: n = 25, p = 43% x = 19.
What is binomial probability?Binomial probability can be defined as the tendency that two event will occur or the likelihood that an event will have two outcome such as good or bad, success or failure.
Analysis of the value of the parameters n,p,x:
n represent number of sample size = 25
p represent the probability of having success on a single trial = 43% or 0.43
x represent the number of success = 19
Therefore the values of the parameters n, p, and x in the binomial probability experiment are: n = 25, p = 43% x = 19.
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Jayden is deciding between two truck rental companies. Company A charges an initial fee of $85 for the rental plus $1.50 per mile driven. Company B charges an initial fee of $65 for the rental plus $2.50 per mile driven. Let AA represent the amount Company A would charge if Jayden drives xx miles, and let BB represent the amount Company B would charge if Jayden drives xx miles. Write an equation for each situation, in terms of x,x, and determine which company would be cheaper if Jayden needs to drive 5 miles with the rented truck.
Answer:
A = 85 +1.50xB = 65 +2.50xB is cheaper for 5 milesStep-by-step explanation:
You want cost equations and the cheaper company for driving 5 miles when A charges $85 plus $1.50 per mile, and B charges $65 plus $2.50 per mile.
(a) EquationsIn each case, the cost is the sum of the initial fee and the mileage charge. The mileage charge is the cost per mile, multiplied by the number of miles (x). Using the given fees and costs per mile, we have ...
A = 85 +1.50x
B = 65 +2.50x
(b) Cheaper companyThe difference in fees is $85 -65 = $20. The difference in mileage charges is $2.50 -1.50 = $1.00 (per mile). Then the two companies will charge the same for $20/($1 /mile) = 20 miles.
Five miles is less than that "break even" mileage, so the cheaper company will be the one with the lower initial fee. (The graph shows the charges for each company for 5 miles.) For more than 20 miles, the cheaper company is the one with the lower mileage charge.
Company B will be cheaper for a drive of 5 miles.
Solve the compound inequality.
-2x < -10 and x-5<6
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
Answer:
5 < x < 11 or x ∈ (5, 11)-----------------------------
Given compound inequality:
- 2x < - 10 and x - 5 < 6Solve each inequality:
- 2x < - 10 Divide both sides by - 2, it flips the inequality signx > 5 x - 5 < 6 Add 5 to both sidesx < 11Solution is:
5 < x < 11or
x ∈ (5, 11)Last week Cody ran 27 more miles than Joseph. Cody ran 34 miles. How many miles did Joseph run?
Which equation represents this situation?
A. x−27=34
B. x−34=27
C. x+27=34
D. x+34=27
Answer:
C
Step-by-step explanation:
The answer is 7 to the equation.
34-27 = 7
Another way to go about this is
x + 27 = 34
x = 7
27 + 7 = 34
:)
simplify 4(x -9y) + 8(3x + 2y)
Answer:
28x - 28y I think hope it is the answer
Lilah invested $400 in the stock market. She saw an 8% decrease in her money, what is the value of her stocks now
The value of Lilah's stock after the decrease of 8 % is $ 368
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the initial amount of money Lilah invested in stocks be = A
The value of A is = $ 400
Now , the percentage decrease in the value of stocks = 8 %
So , the equation will be
The value of the stocks after the decrease = initial amount of money Lilah invested in stocks - ( percentage decrease in the value of stocks x initial amount )
Substituting the values in the equation , we get
The value of the stocks after the decrease = 400 - ( 8/100 ) x 400
The value of the stocks after the decrease = 400 - ( 8 x 4 )
The value of the stocks after the decrease = 400 - 32
The value of the stocks after the decrease = $ 368
Therefore , the value of A is $ 368
Hence , The value of Lilah's stock after the decrease of 8 % is $ 368
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100 points will mark brainliest
Answer:
A is the answer
Step-by-step explanation:
if its wrong than its C
what is the decimal equivalent of 38/50
Answer: it is equal to 0.76
Answer: 0.76
Step-by-step explanation: 38 ÷ 50 = 0.76
You and a friend go to Tacos Galore for lunch. You order three soft tacos and three
burritos and your total bill is $11.25. Your friend's bill is $10.00 for four soft tacos
and two burritos. How much do soft tacos cost? How much do burritos cost?
please show work
Answer:
3 tacos and 3 burritos cost $11.25; 4 tacos and 2 burritos cost $10. The difference is 1 more taco and 1 less burrito, for $1.25 less.
So adjust the order repeatedly the same way, adding one taco and taking away one more burrito, and decreasing the cost by $1.25 each time.
3 tacos, 3 burritos, $11.25
4 tacos, 2 burritos, $10.00
5 tacos, 1 burrito, $8.75
6 tacos, 0 burritos, %7.50
The cost of each taco is $7.50/6 = $1.25.
3 of each cost $11.25, so 1 of each cost $3.75; the taco costs $1.25, so the burrito costs $2.50.
ANSWERS: taco $1.25, burrito $2.50
For the function f(x) =8(x+10), find f
Answer:
Step-by-step explanation:
The function for f(x)=8(x+10) is;
B. f^-1(x)=x-10/8
What is the equation of the horizontal line that passes through (8,-3) what is the slope of the line?
Answer: 0
Step-by-step explanation:
A horizontal line always has a slope of 0
in a class of 30 students, approximately what is the probability that two of the students have their birthday on the same day
The probability that two students out of 30 students have their birthday on the Same day is 0.706, that is nearly 71%
What is conditional probability?The possibility of an event or outcome happening contingent on the occurrence of a prior event or outcome is known as conditional probability.
How do you calculate conditional probability?the likelihood of the preceding event is multiplied by the probability of the subsequent,or conditional, occurrence to determine the conditional probability.
In a year we have 365 days
probability at least 2 people share the same birthday=1 - probability no people share the same birthday
the first student can be born on any day,so we'll give him a probability of 365/365
the probability of the next born is 364/365
the probability of the third born is 336/365
[tex] \frac{365 \: factorial}{335 \: factorial \: . {365}^{30} } [/tex]
this is the simplified form of the 30 probabilities product.= 0.294
therefore
probability at least 2 people share the same birthday=1 - probability no people share the same birthday
1 - 0.294= 0.706
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When Derrick turned 15, his grandparents put $10,000 into an account that yielded 1.4% interest, compounded quarterly, When Derrick turns 18, his grandparents
will give him the money to use toward his college education. How much does Derrick receive from his grandparents on his 18th birthday?
=======================================================
Explanation:
The compound interest formula is
A = P*(1+r/n)^(n*t)
where,
A = account balance after t yearsP = deposit amountr = annual interest rate in decimal formn = number of times the money is compounded per yeart = number of yearsThe deposit amount is P = 10000 dollars.
The value of r here is r = 0.014 which is the decimal form of 1.4%
n = 4 since we're compounding quarterly, i.e. 4 times a year.
The timespan from when Derrick was 15 to when he became 18 is 18-15 = 3 years, which is the value of t.
Summary of input values:
P = 10000r = 0.014n = 4t = 3Let's find the value of "A".
A = P*(1+r/n)^(n*t)
A = 10000*(1+0.014/4)^(4*3)
A = 10428.1800719861
A = 10428.18
a Ferris wheel can accommodate 35 people in 20 minutes. how many people could ride the Ferris wheel in 6 hours
Answer:
630 people could ride the Ferris wheel in 6 hours.
Step-by-step explanation:
First, let's find the people-per-hour amount:
Since there are 3 "20 minutes" in an hour, we multiply the amount it can accommodate by 3 as well:
35 * 3 = 105
Next, since we have 6 hours, we multiply our people-per-hour by 6:
105 * 6 = 630 people in 6 hours, final answer.
How do you slope intercept form and graph 4y-8x=12
The slope-intercept form of a line 4y - 8x = 12 is y = 2x + 3 and the slope is 2. The graph is attached below.
What is slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively.
Given:
4y - 8x = 12
Convert this equation to slope intercept form as shown below,
4y = 8x + 12
y = 8x / 4 + 12 / 4
y = 2x + 3
Here, the slope of the line is 2,
Therefore, the slope-intercept form of a line 4y - 8x = 12 is y = 2x + 3 and the slope is 2. The graph is attached below.
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retangular form of r=8 sin theta
Answer:
Step-by-step explanation:
r2=x2+y2,tanθ=yx,x=rcosθ,y=rsinθ
A square has sides of 18 units. Squares x + 1by x + 1units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume V of the box as a function in terms of x. V(x) =
The box's volume V expressed as a function of x V(x) =(x+1)(16 -2x) ².
A square form is what?A square has four equal sides, four vertices, and is a closed, two-dimensional object. It has parallel sides on either side. A square is also equivalent to a rectangle having equal length and width.
What are the four different kinds of squares?An equal-length rectangle with two neighboring sides. a quadrilateral having four straight angles and equal sides. a parallelogram with two sides that are equally spaced apart and one right angle. the shape of a right-angled rhombus.
Briefing:A distance of (x+1) is cut in from both sides, so the base dimensions are
18 - 2(x+1) = 16 - 2x
The depth of the fold is (x+1), so that is the depth of the box.
The volume V(x) = (x+1)(16 -2x)²
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