Construct a polar equation for the conic section with the focus at the origin and the following eccentricity and directrix.Conic Eccentricity Directrix1ellipsex= -75e =
Answers
In order to find the polar equation of the ellipse, first let's find the rectangular equation.
Since the directrix is a vertical line, the ellipse is horizontal, and the model equation is:
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]Where the center is located at (h, k), the directrix is x = -a/e and the eccentricity is e = c/a.
So, if the eccentricity is e = 1/5 and the directrix is x = -7, we have:
[tex]\begin{gathered} \frac{c}{a}=\frac{1}{5}\rightarrow a=5c\\ \\ -\frac{a}{e}=-7\\ \\ \frac{a}{\frac{c}{a}}=7\\ \\ \frac{a^2}{c}=7\\ \\ \frac{25c^2}{c}=7\\ \\ 25c=7\\ \\ c=\frac{7}{25}\\ \\ a=5\cdot\frac{7}{25}=\frac{7}{5} \end{gathered}[/tex]Now, let's calculate the value of b with the formula below:
[tex]\begin{gathered} c^2=a^2-b^2\\ \\ \frac{49}{625}=\frac{49}{25}-b^2\\ \\ b^2=\frac{25\cdot49}{625}-\frac{49}{625}\\ \\ b^2=\frac{24\cdot49}{625}\\ \\ b^2=\frac{1176}{625} \end{gathered}[/tex]Assuming h = 0 and k = 0, the rectangular equation is:
[tex]\frac{x^2}{\frac{49}{25}}+\frac{y^2}{\frac{1176}{625}}=1[/tex]Now, to convert to polar form, we can do the following steps:
[tex]\begin{gathered} \frac{25x^2}{49}+\frac{625y^2}{1176}=1\\ \\ 600x^2+625y^2=1176\\ \\ 600(r\cos\theta)^2+625(r\sin\theta)^2=1176\\ \\ 600r^2\cos^2\theta+625r^2\sin^2\theta=1176\\ \\ r^2(600\cos^2\theta+625\sin^2\theta)=1176\\ \\ r^2=\frac{1176}{600\cos^2\theta+625\sin^2\theta}\\ \\ r=\sqrt{\frac{1176}{600\cos^2\theta+625\sin^2\theta}}\\ \\ r=\sqrt{\frac{1176}{600+25\sin^2\theta}} \end{gathered}[/tex]Another way of writing this equation in polar form is:
[tex]r=\frac{ep}{1+\sin^2\theta}[/tex]Where p is the distance between the focus and the directrix.
Since the foci are located at (±c, 0) = (±7/25, 0) and the directrix is x = -7, the distance is:
[tex]p=7-\frac{7}{25}=\frac{175}{25}-\frac{7}{25}=\frac{168}{25}[/tex]So the equation is:
[tex]\begin{gathered} r=\frac{\frac{1}{5}\cdot\frac{168}{25}}{1+\sin^2\theta}\\ \\ r=\frac{\frac{168}{125}}{1+\sin^2\theta}\\ \\ r=\frac{1.344}{1+\sin^2\theta} \end{gathered}[/tex]Related Questions
Find the equation of the linear function represented by the table below inslope-intercept form.xy1-3 -723-114-15
Answers
To find the linear equation, we use two points from the table (1, -3) and (3, -11). First, we have to find the slope with the following formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where,
[tex]\begin{gathered} x_1=1 \\ x_2=3 \\ y_1=-3 \\ y_2=-11 \end{gathered}[/tex]Let's those coordinates to find the slope.
[tex]\begin{gathered} m=\frac{-11-(-3)_{}}{3-1}=\frac{-11+3}{2}=\frac{-8}{2}=-4\to m=-4 \\ \end{gathered}[/tex]The slope is -4.
Now, we use the point-slope formula to find the equation.
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-3)=-4(x-1) \\ y+3=-4x+4 \end{gathered}[/tex]Now, we solve for y to express it in slope-intercept form.
[tex]\begin{gathered} y+3=-4x+4 \\ y=-4x+4-3 \\ y=-4x+1 \end{gathered}[/tex]Therefore, the equation in slope-intercept form is y = -4x+1.Translate |f(x)=|x| so the vertex is at (-3,2)
Answers
we have the parent function
f(x)=|x| ------> vertex is (0,0)
Translate at (-3,2)
The rule of the translation is given by
(x,y) ----> (x-3,y+2)
that means ----> 3 units at the left and 2 units up
so
Applying the translation
the new function is equal to
h(x)=|x+3|+2The question is in the picture, couldn’t fit the last graph so sent it in a separate picture
Answers
Explanation:
Concept:
To figure out if a graph is a function, we will use the vertical line test below
The vertical line test is a graphical method of determining whether a curve in the plane represents the graph of a function by visually examining the number of intersections of the curve with vertical lines.
From the first graph we can see that the vertical line cuts the points at on intersection
The Second graph is given below as
Its has two intersections on both sides of the graph
The third graph is given below as
It has two intersections on the ride hand side of the graph
The Fourth graph ios given below as
Its has two intersection on the right hand side of the graph
In conclusion,
A graph is said to be a function if one value of x has a separate value of y
Therefore,
The final answer is
The FIRST OPTION is the correct answer
A washer and a dryer cost $765 combined. The washer costs $85 less than the dryer. What is the cost of the dryer?
Answers
The equation is formed and solved below
What is an equation?
Algebra is concerned with two types of equations: polynomial equations and the particular case of linear equations. Polynomial equations have the form P(x) = 0, where P is a polynomial, while linear equations have the form ax + b = 0, where a and b are parameters, when there is only one variable. To solve equations from either family, algorithmic or geometric approaches derived from linear algebra or mathematical analysis are used. Algebra also investigates Diophantine equations with integer coefficients and solutions. The approaches employed are unique and derive from number theory. In general, these equations are complex; one frequently searches just for the existence or lack of a solution, and, if they exist, the number of solutions.
Let the price of washer = $x
The cost of dryer = $x+85
The equation is formed as
x + x + 85 = 765
or, 2x = 765 - 85
or, x = 680/2 = 340
Price of dryer = $(340+85) = $425
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This problem is related to the linear equation and the required cost of the dryer is $425.
What is a linear equation?
If a variable's maximum power is always 1, an equation is said to be a linear equation. As a one-degree equation, it also goes by that name.
Let a washer costs be [tex]w[/tex] and a dryer costs be [tex]d[/tex].
Since the total cost of a washer and a dryer is $765, it follows:
[tex]w+d=765[/tex] ... (1)
Further, it is given that the washer costs $85 less than the dryer, it means that:
[tex]w=d-85[/tex] ... (2)
Using the two linear equations (1) and (2), it follows:
[tex]d-85+d=765\\2d-85=765\\2d=765+85\\2d=850\\d=\frac{850}{2}=425[/tex]
Therefore, the cost of a dryer is $425.
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The composition of functions
Answers
Answer: g(f(5)) = 352
Step-by-step explanation:
The question being asked is the same as finding g(f(5)).
What this means is to find f(5), and then plug that value into g(x) as x and solve.
f(5) = 4(5) + 1 = 20 + 1 = 21
g(f(5)) = g(21) = 21^2 - 4(21) - 5 = 441 - 84 - 5 = 357 - 5 = 352
Note: You could also find g(f(x)), and then plug 5 in as x and solve.
Start by plugging f(x) into g(x) such that you get g(x = f(x))
g(f(x)) = (4x + 1)^2 - 4(4x + 1) - 5
Now, replace x with 5 and solve to get g(f(5)).
g(f(5)) = (4(5) + 1)^2 - 4(4(5) + 1) - 5 = 352
Answer to the question
Answers
Find an equation in standard form of the parabola passing through the points. (2,-20),(-2,-4), (0, -8)
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The equation of a parabola in standard form is
[tex]y\text{ }=ax^2\text{ + bx + c}[/tex]So, we have the following equations,
For ( 2, -20) , -20 = a(2)^2 + b (2) + c,
For (-2, -4), -4 = a( -2)^2 + b (-2) + c,
For (0.-8), -8 = a (0) + b (0) + c
Then solving,
4a + 2b + c = -20 .............. equ 1
4a - 2b + c = -4 ................... equ 2
c= -8
put c= -8 in equ 1,
we have
4a + 2b -8 = -20 = 4a + 2b = -12 ------equ 3
put c= -8 in equ 2,
4a - 2b -8 = -4 = 4a - 2b = 4................... equ 4
Solving equ 3 and equ 4, a= -1 , b= -4
so a =-1, b= -4, c= -8
Then substituting the values in
[tex]y=ax^2\text{ + bx + c}[/tex][tex]y=-1(x^2)\text{ + -4(x) + }(-8)[/tex]
So, y= -x^2 -4x-8
what is 503472 rounded to the nearest thousend
Answers
Answer: 503,000
Step-by-step explanation:
The best way to understand the concept is to look at a round to the nearest thousand example: what is 52437 rounded to the nearest thousand?
As the hundredth digit is 4, which is less than 5, the number should be rounded down to 52000. As for 52678, as the hundredth digit is 6, which is larger than 4, it will be rounded up to 53000.
Break apart ones to add 18+5=
Answers
Answer: 23
Step-by-step explanation:
You have 1 ten and 8 ones + 5 ones. First, add the ones to get 13 ones. Then, split the ones into tens and ones to get 2 tens and 3 ones which is 23.
At a birthday party, guests ate 452 plates ofchocolate cupcakes and 2/3 plates of cherrycupcakes. How many did the guests eat altogether?If 5 plates of chocolate cupcakes and 5 plates ofcherry were made, how much of each are left?
Answers
Given
[tex]\begin{gathered} \text{Ate 4}\frac{5}{12}\text{Plates of chocolate cupcakes} \\ \text{And} \\ \text{Ate 2}\frac{1}{3}\text{plates of cherry} \end{gathered}[/tex]We are to add them together to know the total
[tex]4\frac{5}{12}+2\frac{1}{3}=6\frac{5+4}{12}=6\frac{9}{12}=6\frac{3}{4}[/tex]The final answer
[tex]6\frac{3}{4}[/tex]Steps Jeanne has a coupon for $1.95 off a jug of name-brand laundry detergent that normally costs $14.99. The store-brand laundry detergent costs $11.53. How much will Jeanne save if she buys the store-brand detergent instead of using her coupon and buying the name-brand?
Answers
we can do a subtraction to calculate the savings
[tex]14.99-11.53=3.46[/tex]will save 3.46 buying store-brand laundry detergent
and your savings from using the coupon are 1.95
We make a subtraction between the savings to know how much you save more with one method than with the other
[tex]3.46-1.95=1.51[/tex]she save $1.51 more buying store-brand
I survey found that 43 people like chocolate 39 people like peanut butter and 29 people like both draw an empty van diagram with intersections find how many people like only chocolate only peanut butter and both show your work fill in the V diagram according your numbers Calculate how many people are in the survey
Answers
Given:
There are 43 people who like chocolate 39 people like peanut butter and 29 people like both.
To draw: The ven diagram
Explanation:
Since 29 people like both chocolate and peanut butter.
Therefore,
The number of people who like chocolate only is,
[tex]43-29=14[/tex]The number of people who like peanut butter only is,
[tex]39-29=10[/tex]So, the total number of persons is,
[tex]14+29+10=53[/tex]The ven diagram is,
Where C represents the chocolate likers, B represents the peanut butter likers and U represents the total number of persons.
Final answer:
• The number of people who like chocolate only is 14.
,• The number of people who like peanut butter only is 10.
,• The total number of people is 53.
if QS in TV are parallel lines and m≤SRP=65°, what is m≤VUR
Answers
Angle SRP and Angle VUR are corresponding angles.
When two parallel lines are cut by a transversal, it creates several different pairs of angles that are equal, complements, and supplements.
In case of corresponding angles,
They are equal.
Given,
∠SRP = 65°
∠VUR = 65° also
Answer[tex]\angle\text{VUR}=65\degree[/tex]Find the x - and y -intercepts of the graph of the linear equation -6x + 9y = -18
Someone else got x=(3,0) y=(0,-2) but it was wrong
Answers
Answer:
x-intercept = 3y-intercept = -2Step-by-step explanation:
You want the intercepts of the equation -6x +9y = -18.
InterceptsThere are several ways to find the intercepts. In each case, the x-intercept is the value of x that satisfies the equation when y=0, and vice versa.
For y = 0, we find the x-intercept to be ...
-6x + 0 = -18
x = -18/-6 = 3
The x-intercept is 3; the point at that intercept is (3, 0).
For x = 0, we find the y-intercept to be ...
0 +9y = -18
y = -18/9 = -2
The y-intercept is -2; the point at that intercept is (0, -2).
Intercept formThe intercept form of the equation for a line is ...
x/a +y/b = 1
where 'a' is the x-intercept, and 'b' is the y-intercept.
We can get this form by dividing the original equation by -18.
-6x/-18 +9y/-18 = 1
x/3 +y/(-2) = 1
The x-intercept is 3; the y-intercept is -2.
__
Additional comment
When asked for the intercepts, it is sometimes not clear whether you are being asked for the value where the curve crosses the axis, or whether you are being asked for the coordinates of the point there.
Your previous "wrong" answer was given as point coordinates. Apparently, just the value at the axis crossing is required.
You have to have some understanding of your answer-entry and answer-checking software to tell the required form of the answer (or you can ask your teacher).
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could you help me no other tutor will help and its heartbreaking so please try your hardest
Answers
The triangle has sides
a=8
b=14
c=19
You need to determine the measure of x
To determine the value of x you have to use the Law of Cosines that states that:
[tex]a^2+b^2-ab\cos \theta=c^2[/tex]Where a, b, and c are the sides of the triangle, and theta represents the angle we are looking for.
So first step is to replace the formula with the given data and solve the exponents
[tex]\begin{gathered} 8^2+14^2-8\cdot14\cos thetha=19^2 \\ 64+196-112\cos \theta=361 \\ 260-112\cos \theta=361 \end{gathered}[/tex]Next solve for the cosine of theta:
[tex]\begin{gathered} -112\cos \theta=361-260 \\ -112\cos \theta=101 \\ \cos \theta=\frac{101}{-112} \\ \cos \theta=-\frac{101}{112} \end{gathered}[/tex]And calculate the inverse cosine to determine the measure of the angle
[tex]\begin{gathered} \theta=\cos ^{-1}(-\frac{101}{112}) \\ \theta=154.39 \end{gathered}[/tex]
A large western state consists of 3593 million acres of land. Approximately 14% of this land is federally owned. Find the number of acres that are not federally owned.
Answers
The number of acres that are not federally owned = 3089.98 million
What do you mean by western state?Land or other assets that are legally owned by the government or a government agency are referred to as government-owned property.
Federal, state, or local governments may be the owners of government-owned land, which may or may not be open to the general public without restriction.
If 14% of the land is federally owned, then 100 -14 = 86% of the land is not federally owned.
(14 *3593 ) / 100
50302 / 100 = 503.02
Federal owned land is 503.02 million acres of land.
3593 - 503.02 = 3089.98 = (86× 3593) ÷ 100
Land not owned by Federal Government = 3089.98 million acres of land.
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choose the correct letter ( this is not being graded it is review )
Answers
we have the points
(-2,6) and (-3,-7)
step 1
Find out the slope
m=(-7-6)/(-3+2)
m=-13/-1
m=13
step 2
Find out the equation in slope-intercept form
y=mx+b
we have
m=13
point (-2,6)
substitute and solve for b
6=13(-2)+b
6=-26+b
b=32
therefore
y=13x+32
step 3
Convert to standard form
AX+By=C
y=13x+32
13x-y=-32 -------> is equivalent to -13x+y=32
therefore
the answer is option DFind all real and imaginary solutions to the equation. Please help me tyy
Answers
Real solutions = 4/5 and 3
Imaginary solutions = 3i
Define real and imaginary solutions.The quadratic equation x² + 1 = 0 has a solution in the imaginary unit or unit imaginary number I Although there isn't a real number associated with this attribute, addition and multiplication can be employed to expand real numbers to so-called complex numbers. A real number is the real root of an equation. A complex root is a fictitious root that is represented by complex numbers in an equation. Imaginary numbers are "real" in the sense that they exist and are used in mathematics, even though they are not real numbers because they cannot be defined on a number line. Complex numbers, often known as imaginary numbers, are used in quadratic equations and in real-world applications like electricity.
Given,
Equation
4x³ + 5x² + 36x + 45 = 0
x²(4x + 5) + 9( 4x + 5) = 0
x² + 9 + (4x +5) = 0
(x - 3 ) (x +3) + (4x+5) = 0
x = 3i
x = [tex]\frac{4}{5}[/tex] and 3
Real solutions = 4/5 and 3
Imaginary solutions = 3i
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In 2011 Staci invested $13,000 in a savings account for her newborn son. The account pays 3.6% interest each year. Determine the accrued value of the account in the year 2029, when her son will go to college. Round your answer the nearest cent.In the year 2029, the accrued value will be $
Answers
To solve this problem, we can use the compound interest formula
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where A represents the accrued value, P represents the invested value, r represents the interest(in decimals), n represents the amount of times the interest is compounded per unit 't' and t represents the time.
Since the unit of the time 't' is years, and the interest is compounded yearly, n = 1.
To write a percentage as a decimal, we just have to divide the percentage value by 100.
[tex]3.6\%=0.036[/tex]To find the amount of time t, we just have to subtract the year the money was invested from the year we want to know the money accrued.
[tex]t=2029-2011=18[/tex]Then, using those values on the formula, we have
[tex]\begin{gathered} A=13,000(1+0.036)^6 \\ A=16073.1828298\ldots\approx16073.18 \end{gathered}[/tex]The accrued value in the year 2029 will be $16,073.18.
The functions f(m) = 18 + 0.4m and g(m) = 11.2 + 0.54m give the lengths of two differentsprings in centimeters, as mass is added in grams, m, to each separately.
Answers
STEP - BY - STEP EXPLANATION
What to do?
Graph each equation on the same set of axis.
Determine the mass that makes the spring the same length.
Determine the length of that mass.
Write a sentence comparing the two springs.
Given:
f(m) = 18 + 0.4m and g(m) = 11.2 + 0.54m
Step 1
Find the x and y-intercept of both function.
f(m) = 18 + 0.4m
f(0) = 18+0.4(0) = 18
0 = 18 + 0.4m
0.4m = -18
m=-45
The x and y -intercept of the function f(m) are (0, 18) and (-45, 0) respectively.
g(m) = 11.2 + 0.54m
g(0) = 11.2 + 0.54(0)
g(0) = 11.2
0 = 11.2+ 0.54m
0.54m = -11.2
m=20.7
The x and y - intercepts are (0, 11.2) and (20.7, 0).
Step 2
Graph the function.
Below is the graph of the function.
Observe from the graph that that the mass that makes the spring the same length is approximately 48.5 grams.
The length at that point is 37.4 centimeters.
Comparison between the two strings.
The string with the function f(m) started out longer, but does not stretch as quickly as the other spring with the function g(m).
ANSWER
b) 48.6 grams
c) 37.4 centimeters
d) The string with the function f(m) started out longer, but does not stretch as quickly as the other spring with the function g(m).
May you hello me and why did yall start making people pay?
Answers
Answer:
53.76
Explanation:
The volume of the triangular prism is given by
[tex]V=\frac{1}{2}\cdot h\cdot b\cdot l[/tex]where h is the height, b is the base, and l is the length of the prism.
Now in our case h = 3.2 m, b = 4.8 m, and l = 7m; therefore, the above equation gives
[tex]V=\frac{1}{2}\cdot3.2\cdot4.8\cdot7[/tex][tex]V=53.76\: m^3[/tex]which is our answer!
Hence, the volume of the triangular prism is 53.76 cubic meters.
Answer the questions about the figures below. 4 ft Figure A 6 ft 6 ft 4 ft (a) Which figures are parallelograms? Mark all that apply. Figure A O Figure B (b) Which figures are squares? Mark all that apply. Figure A Figure B (c) Which figures are rectangles? Mark all that apply. Figure A Figure B O Figure C Figure C Figure C 6 ft Figure B 4 ft 4 ft 6 ft None of the figures None of the figures None of the figures 6 ft X Figure C 6 ft 6 ft Ś 6 ft ?
Answers
A parallelogram is a 4 sided figures that has the opposite sides parallel.
Figure A has right angles so the opposite sides are parallel
Figure B has the opposite sides of equal length, so the opposite sides are parallel
Figure C has right angles so the opposite sides are parallel
For Question A, Figure A, B C are parallelograms
Squares have opposites sides parallel and all 4 sides of equal length and all angles right angles
The only figure with all 4 sides of equal length, all 4 angles right angles is Figure C ( opposites sides are parallel because 4 sides are equal length and all 4 angles are right angles)
The figure that is a square is Figure C
Rectangles are shapes that have opposite sides parallel and all 4 angles are right angles. Squares are special rectangles
Figure A has opposite sides parallel and all 4 angles equal length. Figure C is a square, which is a special rectangle
The rectangles are figures A and C
In a class of 10 boys and 12 girls, a committee of 4 members is to be formed. What is the probability to form a committee consisting of 2 boys and 2 girls?A. 0.3040B. 0.4060C. 0.5060D. 0.2060
Answers
Given:
Number of boys=10
Number of girls=12
Out of 22 members, 4 members is need to be selected.
To find probability to form a committee consisting of 2 boys and 2 girls:
So, we get
[tex]\begin{gathered} \frac{^{10}C_2\times^{12}C_2}{^{22}C_4}=\frac{\frac{10\times9}{2\times1}\times\frac{12\times11}{2\times1}}{\frac{22\times21\times20\times19}{4\times3\times2\times1}} \\ =\frac{5\times9\times6\times11}{11\times7\times5\times19} \\ =\frac{9\times6}{7\times19} \\ =\frac{54}{133} \\ =0.4060 \end{gathered}[/tex]Hence, the correct option is B.
A school choir needs to make t-shirts for its 75 members. A printing company charges $2 per shirt, plus a $50 fee for each color to be printed on the shirts. Write an equation that represents the relationship between the number of t- shirts ordered, the number of colors on the shirts and the total cost of the order. If you use a variable (letter) specify what it represents.
Answers
Let:
C(n,m) = Total cost
n = number of t- shirts ordered
m = fee for each color to be printed on the shirts
Therefore, the total cost of the order would be given by the following equation:
C(n,m) = $2n + $50m
Where:
n = 75
C(n,m) = $2(75) + $50m
C(n,m) = $150 + $50m
Select the table of values that contains ordered pairs that, when plotted, provide the best representation of the curve of the function
Answers
As given by the question
There are given that the equation:
[tex]y=-2(x+3)^2+4[/tex]Now,
Put the value of x into the given equation and find the value of y from all the tables one-by-one and match their value of x and y are equal or not.
Then,
Form the option third,
Put x = -2 to find the value of y, then match the value of y with the given value of y in the table.
So,
[tex]\begin{gathered} y=-2(x+3)^2+4 \\ y=-2(-2+3)^2+4 \\ y=-2(1)^2+4 \\ y=-2+4 \\ y=2 \end{gathered}[/tex]Now,
Put x = -1, then:
[tex]\begin{gathered} y=-2(x+3)^2+4 \\ y=-2(-1+3)^2+4 \\ y=-2(2)^2+4 \\ y=-2(4)+4 \\ y=-8+4 \\ y=-4 \end{gathered}[/tex]Then,
Put x = 0, then:
[tex]\begin{gathered} y=-2(x+3)^2+4 \\ y=-2(0+3)^2+4 \\ y=-2(3)^2+4 \\ y=-2(9)+4 \\ y=-18+4 \\ y=-14 \end{gathered}[/tex]Then,
Put 1 into the given equation instead of x:
So,
[tex]\begin{gathered} y=-2(x+3)^2+4 \\ y=-2(1+3)^2+4 \\ y=-2(4)^2+4 \\ y=-2(16)+4 \\ y=-32+4 \\ y=-28 \end{gathered}[/tex]And,
Put x = 2, so:
[tex]\begin{gathered} y=-2(2+3)^2+4 \\ y=-2(5)^2+4 \\ y=-2(25)+4 \\ y=-50+4 \\ y=-46 \end{gathered}[/tex]Now,
From option d, all values of x and y are matched also but curve representation is matched in option D.
Hence, the correct option is D.
Help I have use the calculator in degree mode for this problem
Answers
SOLUTION
The figure above consists of a triangle and a semi-circle.
Area of the figure = Area the of triangle + Area of the semi-circle
[tex]\begin{gathered} \text{Area of triangle = }\frac{1}{2}\times base\text{ }\times height\text{ } \\ \text{base of the triagle = 15 ft} \\ \text{height = }15\text{ ft } \\ \text{Area of triangle = }\frac{1}{2}\times15\text{ }\times15 \\ \text{Area of triangle = 112.5 ft}^2 \end{gathered}[/tex][tex]\begin{gathered} \text{Area of the semi circle = }\frac{1}{2}\times\pi r^2 \\ r,\text{ radius = }\frac{diameter}{2}\text{ = }\frac{15}{2}\text{ = 7.5} \\ \text{Area of semi-circle = }\frac{1}{2}\times3.14\times7.5^2 \\ \text{Area of semi-circle = }\frac{1}{2}\text{ }\times3.14\times56.25\text{ = 88.3125} \end{gathered}[/tex]Area of composite figure = 112.5 + 88.3125 = 200.8125
Therefore the Area of the figure = 200.81 squared feet to the nearest hundredth
Linda's mean speed on her drive home from Cincinnati is 54 mph. If the total trip is 378 miles, how long should she expect the drive to take? Round your answer totwo decimal places, if necessary,
Answers
We have that Linda's mean speed is 54 miles per hour. Since the total trip is 378 miles, we have the following rule of three:
[tex]\begin{gathered} 54\text{miles}\rightarrow1h \\ 378\text{miles}\rightarrow x \end{gathered}[/tex]therefore, we have:
[tex]\begin{gathered} x=\frac{378\cdot1}{54}=7 \\ x=7 \end{gathered}[/tex]Finally, we have that Linda should expect to drive 7 hours.
need help with a question
Answers
From the image, we have the equation:
3x - 6 = -2x + 4
Let's solve for x:
3x - 6 = -2x + 4
Add 2x to both sides of the equation:
3x - 6 + 2x = -2x + 2x + 4
3x + 2x - 6 = 4
5x - 6 = 4
Add 6 to both sides:
5x - 6 + 6 = 4 + 6
5x = 10
Divide both sides by 5:
[tex]\begin{gathered} \frac{5x}{5}=\frac{10}{5} \\ \\ x\text{ = 2} \end{gathered}[/tex]ANSWER:
x = 2
convert the equation of a parabola to vertex formy^2+4x-14y+57=0
Answers
first we need to solve X
[tex]\begin{gathered} -y^2+14y-57=4x \\ x=-\frac{1}{4}y^2+\frac{7}{2}y-\frac{57}{4} \\ \end{gathered}[/tex]we need to write the equation on this form
[tex]x=a(y-h)^2+k[/tex]where h=-(b/2a) and k=c- a (b/2a)2
we obtain a,b and c from the equation to solve x
so a=-1/4, b=7/2 and c=-57/4
now lets find h and k
[tex]\begin{gathered} h=-(\frac{b}{2a}) \\ h=-(\frac{\frac{7}{2}}{2\cdot-\frac{1}{4}}) \\ \\ h=-(\frac{\frac{7}{2}}{\frac{-1}{2}}) \\ \\ h=-(-7) \\ h=7 \end{gathered}[/tex][tex]\begin{gathered} k=c-a(\frac{b}{2a})^2 \\ \\ k=-\frac{57}{4}-(-\frac{1}{4})(\frac{\frac{7}{2}}{2\cdot-\frac{1}{4}})^2 \\ \\ k=-\frac{57}{4}+\frac{1}{4}(-7)^2 \\ \\ k=-\frac{57}{4}+\frac{1}{4}(49) \\ \\ k=-\frac{8}{4} \\ k=-2 \end{gathered}[/tex]now replace a, h and k on the equation
[tex]\begin{gathered} x=a(y-h)^2+k \\ \\ x=-\frac{1}{4}(y-7)^2-2 \end{gathered}[/tex]the evrtex is (h,k)=(7,-2)
Which choices are equivalent to the quotient below check all that apply. square root of 16 over square root of 8
Answers
To solve the quotient below;
[tex]\frac{\sqrt[]{16}}{\sqrt[]{4}}[/tex]We simply both the numerator and the denominator as follows;
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