The equation for the ellipse centered at the origin is C. x²/4 + y²/49 = 1.
How to illustrate the information?Let the equation of the ellipse be:
x²/b² + y²/a² = 1
The co vertices are at (2, 0) and (-2, 0). The major axis is 14 units. Therefore, 2a = 14. This implies that a = 7 and a² = 7 × 7 = 49.
Therefore, since x²/b² + y²/a² = 1, this will be x²/4 + y²/49 = 1.
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Problem Set
Show instructions
Question 4 (1 point)
Given a triangle with sides of length 5 and 8, find the range of possible values for the third side. (Note: left
hand side of inequality in Blank 1 and right hand side in Blank 2)
Blank 1:
Blank 2:
____
Answer:
3 < x < 13
Step-by-step explanation:
Triangle Inequality Theorem
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
Let x be the length of the unknown side.
Therefore, x will either be the longest side or one of the shorter sides.
Therefore:
x < 5 + 8
⇒ x < 13
And:
8 < 5 + x
⇒ 3 < x
So the range of possible values of the third side is greater than 3 and less than 13: 3 < x < 13
In an interview of 45 students, 12 liked Mathematics and Science, 5 liked Mathematics and English, 25 liked Mathematics; 23 liked Science; 4 liked all three subjects; 15 liked English; 10 liked Science and English. How many students did not like any of the subjects?
Answer:
Step-by-step explanation:
plus 18 and subtract 4
Question 6 of 10
What is the solution to this equation?
2x+6=20
A. x = 13
B. x = 7
C. x = 52
OD. x=28
Answer:
x =7
Step-by-step explanation:
2x+6 = 20
To solve this equation, you first need to subtract 6 from each side
2x+6-6 = 20-6
2x = 14
Then divide each side by 2
2x/2 = 14/2
x = 7
Patrick and susie just welcomed a set of twins to their family and have to decide how to purchase health insurance for the babies. patrick’s employer pays for 100% of his monthly health insurance premium of $378, but will not pay for any of the $280 for each additional beneficiary. susie’s employer, who pays 63% of her $403 monthly premium, offers to pay 32% of the $310 monthly premium for each additional beneficiary. which would be the most economical way to purchase health insurance for the family? patrick's employer beneficiary monthly premium employer contribution patrick $378 100% additional (each) $280 0% susie's employer beneficiary monthly premium employer contribution susie $403 63% additional (each) $310 32% a. insure the entire family (patrick, susie, and the twins) with patrick’s employer. b. insure the entire family (patrick, susie, and the twins) with susie’s employer. c. insure patrick with his employer and susie and the twins with her employer. d. insure susie with her employer and patrick and the twins with his insurer.
The most economic way to purchase health insurance for the family would be to insure Patrick with his employer and Susie and the twins with her employer (Option c).
Reason behind the Choice
Patrick's employer pays for 100% of his monthly health insurance premium of $378
In this case, additional beneficiary for the twins = $280*2 = $560
Susie's employer pays 63% of her $403 monthly premium, and is ready to pay 32% of the $310 monthly premium for each additional beneficiary.
Total money to be paid in this case = 37% of $403 +2*(68% of $310)
= $570.71
Considering that Patrick's health insurance cost is lower than Susie's, it makes sense for him to get health insurance via Patrick's company.
For the twins, Susie's employer offers to pay 68% of $310 for each additional beneficiary. So, the most viable deal would be to buy Patrick's health insurance from his employer and Susie and the twin's health insurance from her employer.
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Answer:
C. Insure Patrick with his employer and Susie and the twins with her employer.
Solve for z square root of z^2-8- square root of 6z-17=0
[tex]\large\displaystyle\text{$\begin{gathered}\sf \sqrt{z^{2}-8 }-\sqrt{6z-17}=0 \end{gathered}$}[/tex]
Simplify the left side. Yes n is a positive integer greater than x and a is a real number or a factor, then [tex]\bf{\sqrt[n]{a^{x} }=a^{\frac{x}{n} }. }[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{(z^{2}-8)^{\frac{1}{2} }-\sqrt{6z-17}=0 } \end{gathered}$}[/tex]
If n is a positive integer greater than x and a is a real number or a factor, then [tex]\bf{\sqrt[n]{a^{x} }=a^{\frac{x}{n} }. }[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{(z^{2}-8)^{\frac{1}{2} }-(6z-17)^{\frac{1}{2}} =0 } \end{gathered}$}[/tex]
Draw each side of the equation. The solution is the x value of the point of intersection.
[tex]\red{\underbrace{\overbrace{\boxed{\boldsymbol{\sf{\green{z=3}}}}} \ \ \to \ \ \ Answer}}[/tex]
{ Pisces04 }Answer:
Step-by-step explanation:
[tex]\sqrt{z^2-8} -\sqrt{6z-17} =0\\\sqrt{z^2-8} =\sqrt{6z-17} \\6z > 17\\z > \frac{17}{6} \\z^2-8=0\\z^2 > 8\\so \\z < -\sqrt{8} \\or\\z > \sqrt{8} \\combining\\z > \frac{17}{6} \\again\\z^2-8=6z-17\\z^2-6z-8+17=0\\z^2-6z+9=0\\z^2-3z-3z+9=0\\z(z-3)-3(z-3)=0\\(z-3)(z-3)=0\\z=3[/tex]
Hurrry hellpppp!
A number is chosen at random from 1 to 50 find the provoking lf selecting an even number that is greater than 13
Answer:
15/50...may be/may not be......,,
The circumference of a circular painting is 56.52 feet. What is the diameter of the painting? Use 3.14 for π and do not round your answer.
Answer:
18 feetStep-by-step explanation:
The formula for circumference is 2πr
First, lets find the radius
3.14 * 2 = 6.28
56.52 / 6.28 = 9
The diameter = 2r
2 * 9 = 18
The diameter is 18 feet
Hope this helps!
Help please!
What’s the answer for graphing the piece wise function to get the right answer?
See attached plots.
The top one shows all three pieces plotted simultaneously, independent of their domains.
The bottom plot takes into account the domains and removes parts of each piece (the dashed gray parts) outside their respective domains.
A triangle has vertices as D(4,5), E(1,8) and F (1,2). Show that the height from D is also the median from D.
The x-coordinate of the altitude on EF is the same as the point D(4, 5) and by calculation, the height from D (1, 5) is also median from D (1, 5)
How can the height and median be calculated?The height from D is perpendicular to EF
The slope of EF = (8 - 2)/(1 - 1) = ∞
Therefore, the side EF is parallel to the y-axis.
Therefore, the coordinates of the point of intersection of the altitude from D and the line EF is (1, 5)
The median is the midpoint of the side EF
The coordinates of the midpoint is found as follows;
[tex] \mathbf{ \left(1 + \frac{1 - 1}{2}, \: 1 + \frac{8 - 2}{2}\right)} = (1 ,5)[/tex]
Therefore;
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How do I do this? :/
Answer:
13
Step-by-step explanation:
Since triangles CBA and DBA are equal, their lengths would also be equal, thus, DB = 13 as CA = 13
Answer:
CAB = DAB
CA is equivalent to BD
In this assignment, you will explore how the volume is changed when you adjust the height or radius of a cylinder. You will drag points of reference on an interactive tool to represent various changes. The interactive will display the changed volume visually and in the calculations and dimensions. You will then use what you see happening to answer questions.
The volume of a cylinder changes when you adjust the height or radius as the volume either increases or reduces.
How to illustrate the volume?Let's assume that the height and radius are 14cm and 7cm. The volume will be:
= πr²h
= 3.14 × 7² × 14
= 2154.04cm³
When the radius and height are reduced to 5cm and 9cm, the volume will be:
= πr²h
= 3.14 × 5² × 9
= 706.5cm³
This illustrates that the volume reduces when the height and radius reduces.
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Identical prizes are to be given to two winners from a group of 12 contestants. What counting formula would you use to determine how many ways the prizes could be given out
We will use a combination formula to determine how many ways the prizes could be given out.
In mathematics, a combination is a way of selecting items from a collection where the order of selection does not matter. Suppose we have a set of three numbers P, Q and R. Then in how many ways we can select two numbers from each set, is defined by combination.
The combination is defined as “An arrangement of objects where the order in which the objects are selected does not matter.” The combination means “Selection of things”, where the order of things has no importance.
The formulas nCk is popularly known as counting formula.
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Convert from Decimal Notation to Scientific Notation
In the following exercises, write each number in scientific notation.
552. 8,750,000
Answer:
Hence, 87,50,000 can be expressed as [tex]$8.75 \times 10^{6}$[/tex].
Step-by-step explanation:
- Given 87,50,000
- Use given, move the decimal point so that first factor is greater than or equal to 1 but less than 10 .
- Then count n and write in scientific notation.
Step 1 of 1
Consider 87,50,000.
8.75
So, 8.75 lies between 1 & 10 .
Now, Decimal moved to 6 places at left.
[tex]$8.75 \times 10^{6}$[/tex]
So, [tex]$87,50,000=8.75 \times 10^{6}$[/tex].
there are 12 students including 4 boys in a classroom. Find the number of girls in 8 such classrooms
Answer:
64 girls
Step-by-step explanation:
Number of boys in a classroom: 4
Total no. of students in the classroom: 12
Number of girls in 1 classroom: 12-4 = 8
Number of girls in 8 such classrooms: 8 × 8 = 64
pleasee help! :((
Select the correct answer.
Consider the graph of the function
f(x)=2^x
Which statement describes a key feature of function g if ?
g(x)= f(x-4)
A.
horizontal asymptote of
B.
horizontal asymptote of
C.
y-intercept at
D.
y-intercept at
Select the correct answer.
Consider the graph of the function .
A nonlinear function on a coordinate plane passes through (2.2, 5), (minus 5, 0) and intercepts the y axis at (1, 0).
Which statement describes a key feature of function g if ?
A.
horizontal asymptote of
B.
horizontal asymptote of
C.
y-intercept at
D.
y-intercept at
The option range of a function is (-∞, ∞), x-intercept of (0.1, 0), and the vertical asymptote is x = 0.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
As we can see in the picture, we have given a function:
We have a function:
g(x) = 4log(x) + 4
To find x-intercept plug g(x) = 0
0 = 4logx + 4
x = 0.1
(0.1, 0)
The vertical asymptote:
x = 0
The range of a function:
(-∞, ∞)
Thus, the option range of a function is (-∞, ∞), x-intercept of (0.1, 0), and the vertical asymptote is x = 0.
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(a) sin x° = 0.8
Given that x is an obtuse angle, find x.
(b) cos 127° = -cos yo
Given that y is an acute angle, find y.
The value of x is 126.87° and the value of y is 53°.
What is an obtuse and an acute angle?An obtuse angle is an angle that is greater than 90° but lesser than 180° while an acute angle is an angle between 0-90°.
From the given information:
sin x° = 0.8
x = sin⁻¹ (0.8)
x = 53.13°
x + 53.1° = 180°
x = 180° -53.13°
x = 126.87°
If cos 127° = -cos y°,
-cos y = -0.6018
cos y = 0.6018
y = cos⁻¹ (0.6018)
y = 53°
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BRAINLIEST, URGENT!!
Victoria dropped a basketball off the top of a building. Each time the basketball hit the ground, it bounced upward one-half the height that it fell. Victoria initially dropped the basketball from a distance of 60.0 feet above the ground. What was its maximum height above the ground, in feet, between the third and fourth time it hit the ground?
Answer:
7.5 ft
Step-by-step explanation:
1st drop = 60 ft
2nd drop = 60/2 = 30 ft
3rd drop = 30/2 = 15 ft
4th drop = 15/2 = 7.5 ft
Select the correct answer from each drop-down menu.
The endpoints of the longest chord on a circle are (4, 5.5) and (4, 10.5).
The center of the circle is at the point (-4, 6.75)(4, 8)(4, 9.25)(4, 16), and its radius is 1.252.53.756.25 units. The equation of this circle in standard form is (x - 4)^2 + (y - 8)^2 = 2.5(x + 4)^2 + (y + 8)^2 = 2.5(x - 4)^2 + (y - 8)^2 = 6.25(x + 4)^2 + (y + 8)^2 = 6.25.
The correct options regarding the circle with endpoints of the longest chord at (4, 5.5) and (4, 10.5) are:
The center is (4,8).The radius is of 2.5 units.[tex](x - 4)^2 + (y - 8)^2 = 6.25[/tex]What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
The center is the midpoint of the chords, hence:
[tex]x_0 = \frac{4 + 4}{2} = 4[/tex].[tex]y_0 = \frac{5.5 + 10.5}{2} = 8[/tex].The radius is half the distance between the chords, hence:
[tex]r = 0.5\sqrt{(4-4)^2 + (10.5 - 5.5)^2} = 0.5 = 2.5[/tex].
Hence the equation is:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
[tex](x - 4)^2 + (y - 8)^2 = 2.5^2[/tex]
[tex](x - 4)^2 + (y - 8)^2 = 6.25[/tex]
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What is the x-coordinate of the point that divides the directed line segment from k to j into a ratio of 1:3? x = (startfraction m over m n endfraction) (x 2 minus x 1) x 1 –1 3 7 11
The x-coordinate of the point which divide the line segment is 3.
Given the coordinates in the figure are J(1,-10) and K(9,2) and the 1:3 is the ratio in which the line segment is divided.
When the ratio of the length of a point from both line segments is m:n, the Sectional Formula can be used to get the coordinate of a point that is outside the line.
To find the x-coordinate we will use the formula x=(m/(m+n))(x₂-x₁)+x₁.
Here, m:n=1:3 and x₁=1 from the point J(1,-10) and x₂=9 from the point K(9,2).
Now, we will substitute these values in the formula, we get
x=(1/(1+3))(9-1)+1
x=(1/4)(8)+(1)
x=8/4+1
x=3
Hence, the x-coordinate of the point that divides the directed line segment from k to j into a ratio of 1:3 is 3 units.
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Answer:
b. 3
Step-by-step explanation:
got it correct
Li invests money in a savings account. She wants to know the amount of simple interest that she will earn in 6 years at 3.75 percent. What additional information does she need to find this amount?
Answer:
She needs the starting amount of money to create an equation.
Step-by-step explanation:
The formula that she can use when she has the starting amount or the y-intercept is this one: f(t)=P(1+b)^t.
t=time
b=percent
P=starting value
The formula with the information given is: f(6)=P(1+3.75)^6
Hope this helps!
If not, I am sorry.
Answer:
Principal
Step-by-step explanation:
Since, the amount in the simple interest is,
Where, P is the principal amount,
r is the annual rate,
t is the time ( in years ),
Here, r = 3.75 %, t = 6 years,
Thus, By the above explanation,
It is clear that, we need the value of P, that is, principal to find the amount.
For which value of b can the expression x2 + bx + 18 be factored?
An expression is defined as a set of numbers, variables, and mathematical operations. The value of b for which the expression x² + bx + 18 can be factored is 9.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The value of b for which the given expression x² + bx + 18 can be factored is 9. This will make the expression factored as (x+3) and (x+6).
Thus, the value of b for which the expression x² + bx + 18 can be factored is 9.
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The area of the triangle below is sq. units.
3
22
Answer:
So, what's the question?URGENT
Which of the following is the correct expanded form for the series below?
Σ
n=0
Hello,
[tex]$$\sum_{n=0}^4$$(\frac{1}{2})^{n} =(-\frac{1}{2})^{0}+(-\frac{1}{2})^{1}+(-\frac{1}{2})^{2}+(-\frac{1}{2})^{3}+(-\frac{1}{2})^{4}=1-\frac{1}{2} +\frac{1}{4} -\frac{1}{8}+\frac{1}{16}[/tex]
Find the area of the figure to the nearest square unit 3 cm and 8 cm
The area of the given composite figure is 74.24cm^2
Area of composite figureThe figure is made up of semi circle and rectangle
Area = area of semicircle + Area of rectangle
Area = 3.14(4)^2 + 3(8)
Area = 50.24 + 24
Area. = 74.24cm^2
Hence the area of the given composite figure is 74.24cm^2
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PLEASE HELP!!
Triangle not drawn to scale
Given: m & B = 18°, b = 9, and c = 20. Find
m & Co to nearest whole number.
Answer:
43°
Step-by-step explanation:
Calculating for the measure of angle C using
sine rule[tex] \frac{sin18}{9} = \frac{sinc}{20} \\ sinc = \frac{sin18 \times 20}{9} \\ sinc = 0.6867 \\ c = \csc(0.6867) \\ c = 43.3869 \\ c = 43 \: degrees[/tex]
Does dy/dx in a graph mean the value of f'(x), or the slope of f'(x) at the point?
What is the measure of the corresponding central angle for XY in radians?
Answer:
4 radians
Step-by-step explanation:
Arc Length (Radians) = rθ
Given Arc Length XY = 40cm and radius, r = 10cm,
we will substitute these 2 values into the formula to find θ.
(10)θ = 40
θ = 40 / 10
= 4 radians
Answer:
A
Step-by-step explanation:
the length of arc XY is calculated as
arc = circumference of circle × fraction of circle
= 2πr × [tex]\frac{0}{2\pi }[/tex] ( r is radius and Θ is central angle )
here arc = 40 and r = 10 , then
2π × 10 ×[tex]\frac{0}{2\pi }[/tex] = 40
20π × [tex]\frac{0}{2\pi }[/tex] = 40 ( cancel 20π and 2π by 2π )
10Θ = 40 ( divide both sides by 10 )
Θ = 4 radians
The table shows data from a survey about the number of times families eat at restaurants during a week. The families are either from Rome, Italy, or New York, New York:
High Low Q1 Q3 IQR Median Mean σ
Rome 21 1 1.5 7.5 6 4.5 6.5 6.6
New York 20 1 3.5 7.5 4 5 6.5 5.2
Which of the choices below best describes how to measure the center of these data?
Both centers are best described by the mean.
Both centers are best described by the median.
The Rome data center is best described by the mean. The New York data center is best described by the median.
The Rome data center is best described by the median. The New York data center is best described by the mean.
Choices for the measure of center that is best are: C. Rome data center is best described by the mean while that of New York data is best described by the median.
What are the Measures of Center?The measures of center include the mean and the median. Mean is best for a symmetrical data distribution while median is good for a skewed data distribution with an outlier.
The data for New work has an outlier, while that of Rome does not. Therefore, the best choices for the measure of center is: C. Rome data center is best described by the mean while that of New York data is best described by the median.
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I'm extremely bad at doing these
The first few terms of a geometric sequence with first term [tex]a[/tex] and common ratio [tex]r[/tex] look like
[tex]a, ar , ar^2, ar^3, \ldots[/tex]
and so on. Notice that the [tex]n[/tex]-th term (where [tex]n[/tex] is a natural number) is [tex]ar^{n-1}[/tex].
For this particular sequence, the first term is
[tex]a=3[/tex]
and the fourth term is
[tex]ar^{4-1} = ar^3 = 1029[/tex]
Substitute [tex]a=3[/tex] into the second equation and solve for [tex]r[/tex].
[tex]3r^3 = 1029 \implies r^3 = 343 \implies r = \sqrt[3]{343} = \sqrt[3]{7^3} = 7[/tex]
Then the two terms between the 1st and 4th - i.e. the 2nd and 3rd terms - are
[tex]ar = 3\times7 = \boxed{21}[/tex]
and
[tex]ar^2 = 3\times7^2 = \boxed{147}[/tex]
Answer:
Term 2 is 21, and term 3 is 147.
Step-by-step explanation:
The geometric sequence is 3, 3r, 3r^2, 1029.
[tex]r = \sqrt[3]{ \frac{1029}{3} } [/tex]
[tex]r = \sqrt[3]{343} = 7[/tex]
So we have 3, 21, 147, 1029.
Distribute and simplify these radicals.
√12•(-1+√5)
O-4√3
O-2√3+2√15
O 4√3
06√3
Answer:
√12×(-1)+√12×√5
-√12+√12×5
= -2√3+2√15