Answers
[tex] \frac{25-y^2}{16} + \frac{y^2}{9} = 1[/tex]
Explanation:
For the first given equation, we will need to isolate the x². This can be done as follows:
x² + y² = 25
x² + y² - y² = 25 - y²
x² = 25 - y² ..................> I
For the second given equation:
We will remove every x² and substitute with its equivalence from I as follows:
[tex] \frac{x^2}{16} + \frac{y^2}{9} = 1[/tex]
[tex] \frac{25-y^2}{16} + \frac{y^2}{9} = 1[/tex]
Hope this helps :)
It is the c)25-y^2-y^2 by 16-9 = 1
Related Questions
what is 103.468 rounded to the nearest liter
Answers
Hope this helps!
A rubber ball dropped on a hard surface takes a sequence of bounces, each one 4/5 as high as the preceding one. If this ball is dropped from a height of 10 feet, what is the total vertical distance it has traveled at the time when it hits the surface for its fifth bounce?
A) 28 77/125 feet
B) 49 1/25 feet
C) 57 29/125 feet
D) 59 29/125 feet
Answers
Answer:
The answer is 57 29/125 feet ⇒ answer (C)
Step-by-step explanation:
∵ The ball dropped from a height 10 feet
∴ The vertical distance = 10 feet
∵ It bounces 4/5 as high as the preceding one
∴ 1st bounce = 10 × 4/5 = 8 (move down another 8)
∴ The vertical distance = 8 + 8 = 16 feet
∴ 2nd bounce = 8 × 4/5 = 6.4 (move down another 6.4)
∴ The vertical distance = 6.4 + 6.4 = 12.8 feet
∴ 3rd bounce = 6.4 × 4/5 = 5.12 (move down another 5.12)
∴ The vertical distance = 5.12 + 5.12 = 10.24 feet
∴ 4th bounce = 5.12 × 4/5 = 4.096 (move down another 4.096)
∴ The vertical distance = 4.096 + 4.096 = 8.192 feet
∵ The ball will hit the surface to make the 5th bounce
∴ The total vertical distance is :
10 + 16 + 12.8 + 10.24 + 8.192 = 57.232 = 57 29/125
Another way:
* We can use the formula of geometric sequence with
1st bounce distance (a) = 8 + 8 = 16 and ratio (r) = 4/5
and number of bounces (n) = 4 (hit the surface for its 5th bounce)
∵ [tex]S_{n}=\frac{a(1-(r^{n}))}{1-r}[/tex]
∴ [tex]S_{4}=\frac{16(1-(\frac{4}{5})^{4})}{1-\frac{4}{5}}=47\frac{29}{125}[/tex]
* Then we must to add the 10 feet
(the ball dropped from height 10 feet)
∴ The total vertical distance = 10 + 47 29/125 = 57 29/125 feet
an organization surveyed a random sample of their employees about their new vacation policy. Out of the employees surveyed, 83% rated the vacation policy as "delightful" with a margin of error of ±2% and a confidence interval of 95%. What does the margin of error imply?
Answers
Answer:
Given is:
Out of the employees surveyed, 83% rated the vacation policy as "delightful" with a margin of error of ±2% and a confidence interval of 95%.
±2% means plus 2% from 83% and minus 2% from 83%, making the interval between 81% and 85%.
In general the margin of error tells that, how many percentage points the results will differ from the real population value. A small margin of error shows trustworthy results whereas a large margin of error means the results are not accurate.
Therefore, it can be concluded, with 95% confidence, that between 81% and 85% of all employees will rate the vacation policy as "delightful."
Ken started saving for retirement at age 35 with plans to retire at age 70. He invested an average of $600 per month in various securities, with an average annual return of 5% adjusted for inflation. Assuming monthly compounding, how much has Kent saved at the start of retirement
A: $54,192.18
B: $825,655.45
C: $499,355.18
D: $681,655.46
Answers
Peter is working for an hourly wage of 12$ if he worked for 20 hours last week what is his gross pay
Answers
Number of hours Peter worked = 20 hours
Gross Pay = Hourly Wage x Number of Hours worked
Using the values, we get:
Gross Pay = 12 x 20 = $240
Thus, the gross pay of Peter was $240 for his work of last week
the slope of the line below is -3. which of the following is the point-slope form of the line? A.) y+2=3(x-2) B.) y+2=-3(x-2) C.) y-2=-3(x+2) D.) y-2=3(x+2)
Answers
[tex]y-y_1=m(x-x_1)\\\\(x_1;\ y_1)\ is\ a\ known\ point\\\\m\ is\ the\ slope\ of\ the\ line[/tex]
We have:
[tex]m=-3;\ (x_1;\ y_1)=(2;-2)[/tex]
Substitute
[tex]y-(-2)=-3(x-2)\\\\y+2=-3(x-2)[/tex]
Answer: B. y + 2 = -3(x - 2)
Answer:
B) y + 2 = -3(x - 2)
Step-by-step explanation:
it's what I got
a season ticket for bolton f.c. this season cost £410 it is to go up by 34% next season how.much will a season ticket cost next season?
Answers
100 + 34 = 134
÷ 100 = 1.34
1.34 is your multiplier. So if you do 410 x 1.34 you'll have £549.40
I may be wrong, but I'm quite sure this is right!
What are a) the ratio of the perimeter’s b) and the ratio of areas of the larger figure to the smaller figure?
Answers
a) We have been given two similar figures and we have to find ratio of perimeters of these figures.
Let a be given side of larger figure and b be the given side of smaller figure. Let [tex]p_{1} \text{ and } p_{2}[/tex] be the perimeters of two figures and [tex]A_{1} \text{ and } A_{2}[/tex] be the areas of the two figures.
We know that perimeters of two similar figures are in the ratio of corresponding sides.
[tex]\frac{p_{1}}{p_{2}}=\frac{a}{b}[/tex]
We have been given, [tex]a=26\text{ and }b=6[/tex]
Therefore, upon substituting these values in the above equation, we get
[tex]\frac{p_{1}}{p_{2}}=\frac{26}{6}[/tex]
[tex]\frac{p_{1}}{p_{2}}=\frac{13}{3}[/tex]
(b)
Further we know that areas of two similar figures are in the ratio of squares of corresponding sides.
[tex]\frac{A_{1}}{A_{2}}=\frac{a^{2}}{b^{2}}\\ \frac{A_{1}}{A_{2}}=\frac{26^{2}}{6^{2}}\\ \frac{A_{1}}{A_{2}}=\frac{676}{36}\\ \frac{A_{1}}{A_{2}}=\frac{169}{9}\\[/tex]
Therefore, first option is the correct answer.
hey can you please help me posted picture of question
Answers
If Disc> 0, the function has two distinct roots
If Disc = 0, the function has a repeated root
If Disc < 0, the function has no real root.
Since the given graph has no real root, i.e. it does not cross x-axis at any point, so we can say that the discriminant of the given function is negative.
So the answer to this question is option C
At a school for performance art students
2/5
of the girls study music,
3/5
of the girls study dance and
1/6
of the girls study music and dance. What fraction of those who study music also study dance?
Answers
A father is giving his child a 30-inch long softball bat for her birthday.He has a rectangular box that has the dimensions of 5 inches by 6 inches by 25 inches. Will the bat fit in the box ? Explain
Answers
The bat is 30 in.
So, I think it will fit.
Hope this helped☺☺
Answer:
No, the bat will not fit. Using the Pythagorean theorem, the length of a diagonal of a face of the box is about 24 inches, and the length of the diagonal of the cube is about 29.4 inches. This is less than the length of the bat.
Step-by-step explanation:
Edguenity
Solve the system using the substituiton method
branliest offered
3x-7y=10
x-4y=5
Answers
To solve this problem using substitution, we need to set x equal to a value and substitute it into the other equation.
Since
x - 4y = 5,
x = 5 + 4y
3x - 7y = 10
3(5 + 4y) - 7y = 10
15 + 12y - 7y = 10
15 + 5y = 10
5y = -5
y = -1
Now that we know y is -1, we can substitute it back into the equation to find x:
y = -1
x - 4y = 5
x - 4(-1) = 5
x - (-4) = 5
x + 4 = 5
x = 1
So, your answers are x = 1 and y = -1.
Hope this helps!
PLEASE HELP!!! Find the equation , in the standard form of the line passing through the points (3,-4) and (5,1)
Answers
[tex]\bf y=\cfrac{5}{2}x-\cfrac{15}{2}-4\implies y=\cfrac{5}{2}x-\cfrac{23}{2}\impliedby \begin{array}{llll} \textit{now let's multiply both}\\ \textit{sides by }\stackrel{LCD}{2} \end{array} \\\\\\ 2(y)=2\left( \cfrac{5}{2}x-\cfrac{23}{2} \right)\implies 2y=5x-23\implies \stackrel{standard~form}{-5x+2y=-23} \\\\\\ \textit{and if we multiply both sides by -1}\qquad 5x-2y=23[/tex]
side note: multiplying by the LCD of both sides is just to get rid of the denominators
hey can you please help me posted picture of question
Answers
(5 + 3i)(4+ 2i)
= 5(4+2i) + 3i(4+2i)
= 20 +10i + 12i +6i²
= 20 +22i +6(-1)
= 20 + 22i - 6
= 14 + 22i
Choose the correct factorization for the polynomial 21xy+15x+35ry+25r
Answers
3x(7y+5)+ 5r(7y+5)
(3x+5r)(7y+5)
Please rate
In a survey conducted in an Office, 60% of the sample respondents agreed that employees should have flexible working hours.
If the margin of error is +-2%, the expected population proportion that wanted flexible working hours is between -------% and------%
Answers
Answer:
Yes, the answer is between 58% and 62%
Step-by-step explanation:
I just did it on Edmentum
Q # 17 , Find the slope
Answers
From the above graph we can see that the points (-4,-1) and (0, -3) lie on the line. So using these two points we can find the slope.
[tex]Slope=m= \frac{-3-(-1)}{0-(-4)} \\ \\ m= \frac{-3+1}{0+4} \\ \\ m= \frac{-2}{4} \\ \\ m= \frac{-1}{2} [/tex]
So, first option is the correct answer
m = (y2-y1) / (x2-x1)
Substituting values we have:
m = (- 4 - (- 3)) / (2-0)
Rewriting we have:
m = (- 4 + 3) / (2-0)
m = (- 1) / (2)
m = -1 / 2
Answer:
The slope is given by:
m = -1 / 2
option 1
the sum of a number and 7 is the same as double the number increased by 3
Answers
n+7=2n+3
Subtract both sides by 3:
n+4=2n
Now by n:
2n=4
Divide:
n=2
The number is 2
x + 7 = 2x + 3
We want to solve for x in these types of problems. To do so, we must get all of the "x"s on one side of the equal sign and the constants on the other.
7 - 3 = 2x - x
4 = x
Our answer is x = 4.
what is sqrt p^5 q^10 expressed in simplified form?
Answers
The simplified form of the expression [tex]\sqrt{p^5q^{10}}[/tex] is p²q⁵√p, obtained by separating and simplifying the square roots of the individual factors.
The expression [tex]\sqrt{p^5q^{10}}[/tex] can be simplified by separating the square roots of the individual factors and simplifying each one individually.
First, let's rewrite the square root of the entire expression:
[tex]\sqrt{p^5}[/tex] = p²√p because we are taking the square root of p to the fifth power which results in p squared and the square root of p remaining.[tex]\sqrt{q^{10}}[/tex] = q⁵ because q to the tenth power is a perfect square, and taking the square root gives us q to the fifth power.Therefore, the simplified form of [tex]\sqrt{p^5q^{10}}[/tex] is p²q⁵√p.
which is an example x-intercept of the graph of the function y=tan(x-(5pi/6))
Answers
Explanation:
1) Given function:
[tex]y=tan(x- \frac{5 \pi }{6} )[/tex]
2) x-intercept are the roots of the function, i.e. the solution to y = 0
3) to find when y = 0, you can either solve the equation or look at the graph.
4) Solving the equation you get:
y = 0 ⇒ tan(x - 5π/6) = 0 ⇒ x - 5π/6 = arctan(0)
arctan(0) is the angle whose tangent is zero,so this is 0
⇒ x - 5π/6 = 0 ⇒ x = 5π/6.
Then, one example of an x-intercept is x = 5π/6, which means that when x = 5π/6, the value of the function is 0.
Since, the tangent function is a periodic function, there are infinite x-intecepts, that is why the questions asks for one example and not all the values.
You can verify by replacing the value x = 5π/6 in the given function:
y = tan (5π/6 - 5π/6) = tan(0) = 0.
Answer:
D?
Step-by-step explanation:
True or False? The shortest distance from the center of the circumscribed circle to the sides of the inscribed triangle is the circle's radius
Answers
Answer:
false
Step-by-step explanation:
The statement that the shortest distance from the center of the circumscribed circle to the side of the inscribed triangle is the circle's radius is false.
How to find the radius of the circumscribed circle around a triangle?The intersection of the perpendicular bisectors of any two sides(or all three sides if you want) is the center of the circumscribed circle for that triangle.
The length of that intersection point from any of the vertices of the triangle is the radius of the circumscribed circle of that triangle.
When a triangle is placed in a circle such that the side of the circle touch the circumference of the circle, then the circle is a circumscribed circle.
The line drawn from the center of the circle to the side of the triangle is the shortest possible line.
However, it is certain that this line is the radius.
This is so because the side of the triangle lie on the circumference of the circle
Hence, the statement that the shortest distance from the center of the circle is false.
Read more about circumscribed circle at:
brainly.com/question/2699432
#SPJ5
Jack had $80 more than Eric. When Jack spent $30, he found that the amount of money he had left was twice s much as Eric had. How much did the boys have altogether at the beginning?
Answers
x: amount of money Jack has
y: amount of money Eric has
We write the system of equations:
x = y + 80
x - 30 = 2y
Solving the system we have:
x = $130
y = $ 50
Therefore, the amount of money they had at the beginning is:
130 + 50 = $ 180
Answer:
the boys had $ 180 altogether at the beginning
The table below shows a correct representation that 15 pounds (lb) of sugar cost $3: lb lb lb lb lb lb lb lb lb lb lb lb lb lb lb $1 $1 $1
Answers
Answer:
true
Step-by-step explanation:
Hey can you please help me posted picture of question
Answers
Explanation:
These type of questions can easily be solved using the Venn diagram. Below is the image attached that shows the Venn diagram and the solution.
so the answer for your question is D.7
I hope I can show the solution but I cant post the picture right now :(
Hope Ihelped
A batch of cookies requires 3/8 cup of butter. Butter can be purchased in boxes, each containing 4 sticks, with 1 stick equivalent to 1/2 cup of butter. If Monica is to bake 15 batches of cookies, which of the following is the best estimate for the total number of boxes of butter she needs to buy?
Answers
So, the answer is [tex]\boxed{3}.[/tex]
when is periodic data useful? give examples to support your answer please
Answers
(i) when you want to know the valency to male compounds
for example :
when H2 and O2 react in normal conditions they form H2O, amd here we needed crossmultiplication of their valencies.
(ii) To know masses while calculating mass number.
For example In case you wanna find mass of 100 molecules of H2O.
(iii) To find electronegativity (to determine type of bond formed).
For example: which kind of bond Hydrogen and Clorine will form.
identify the slope and Y- intercept of the graph of the equation.Then graph the equation, Y = - 5/4X + 1
Answers
The slope = -5/4
#1. if i have a circle with a radius of 6 in and it is cut into 8 equal slices (like a pie) and the coordinates are (8, 5) then what is the central angle, what is the measure of the arc that 2 pieces together would intercept, and the equation that represents as well as the circumference?
I also need the same answers for these:
#2. radius 10 inches, 14 equal pieces, and points of (3, 7)
#3. radius 25 cm, 16 pieces and 14 and 53
#4. radius 12 inches, 8 pieces and points of (2, 5)
#5. radius 4 inches, 12 equal pieces, and points of (3, 6)
Answers
coordinates of the center (8,5)
radius=6 in
is cut into 8 equal slices-----> 360°/8-----> 45° each slice
a) equation of a circumference
(x-h)²+(y-k)²=r²--------> (x-8)²+(y-5)²=6²
b) circumference=2*pi*r-----> 2*pi*6---> 37.68 in
if 360° (full circle) has a length of---------> 37.68 in
90° (2 pieces together)---------> x
x=90*37.68/360-----> x=9.42 in
the measure of the arc that 2 pieces together would intercept is 9.42 in
c) The central angle of one slice is 45 degrees
Part 2)
coordinates of the center (3,7)
radius=10 in
is cut into 14 equal slices-----> 360°/14-----> 25.71° each slice
a) equation of a circumference
(x-h)²+(y-k)²=r²--------> (x-3)²+(y-7)²=10²
b) circumference=2*pi*r-----> 2*pi*10---> 62.8 in
if 360° (full circle) has a length of---------> 62.8 in
51.42° (2 pieces together)---------> x
x=51.42*62.8/360-----> x=8.97 in
the measure of the arc that 2 pieces together would intercept is 8.97 in
c) The central angle of one slice is 25.71 degrees
Part 3)
coordinates of the center (14,53)
radius=25 cm
is cut into 16 equal slices-----> 360°/16-----> 22.5° each slice
a) equation of a circumference
(x-h)²+(y-k)²=r²--------> (x-14)²+(y-53)²=25²
b) circumference=2*pi*r-----> 2*pi*25---> 157 cm
if 360° (full circle) has a length of---------> 157 cm
45° (2 pieces together)---------> x
x=45*157/360-----> x=19.63 cm
the measure of the arc that 2 pieces together would intercept is 19.63 cm
c) The central angle of one slice is 22.5 degrees
Part 4)
coordinates of the center (2,5)
radius=12 in
is cut into 8 equal slices-----> 360°/8-----> 45° each slice
a) equation of a circumference
(x-h)²+(y-k)²=r²--------> (x-2)²+(y-5)²=12²
b) circumference=2*pi*r-----> 2*pi*12---> 75.36 in
if 360° (full circle) has a length of---------> 75.36 in
90° (2 pieces together)---------> x
x=90*75.36/360-----> x=18.84 in
the measure of the arc that 2 pieces together would intercept is 18.84 in
c) The central angle of one slice is 45 degrees
Part 5)
coordinates of the center (3,6)
radius=4 in
is cut into 12 equal slices-----> 360°/12-----> 30° each slice
a) equation of a circumference
(x-h)²+(y-k)²=r²--------> (x-3)²+(y-6)²=4²
b) circumference=2*pi*r-----> 2*pi*4---> 25.12 in
if 360° (full circle) has a length of---------> 25.12 in
60° (2 pieces together)---------> x
x=60*25.12/360-----> x=4.19 in
the measure of the arc that 2 pieces together would intercept is 4.19 in
c) The central angle of one slice is 30 degrees
Solve triangle PQR is PQ 9, PR 7, and QR 8. POR is NOT a right triangle.
Answers
PR = 7 unit
QR = 8 unit
To find => Area of triangle PQR
We can find area of triangle by Heron's Formula.
Where,
s = (9+7+8)/3
= 24/3
= 8
and,
a = 9
b = 7
c = 8
Heron's Formula = [tex] \sqrt{s(s - a)(s - b)(s - c)} [/tex]
= [tex] \sqrt{8(8 - 9)(8 - 7)(8 - 8)} [/tex]
= [tex] \sqrt{8( - 1)(1)} [/tex]
= [tex] \sqrt{ - 8} [/tex]
= [tex]2i \sqrt{2} [/tex]
Area of triangle = 2i√2 units
Hope this helps!
[tex]\text {Formula = } \sqrt{p(p-a)(p-b)(p-c)} , \text { where p is half the perimeter}[/tex]
We will start off by find p:
[tex]\text {p = } \dfrac{9+7+8}{2} = \dfrac{24}{2}= 12 [/tex]
Now we know, p = 12, we plug in a = 9, b = 8 and c = 7 into the formula to find the area:
[tex]\text {area = } \sqrt{12(12-9)(12-8)(12-7)}[/tex]
[tex]\text {area = } \sqrt{12(3)(4)(5)}[/tex]
[tex]\text {area = } 26.83 \text{ units}^2[/tex]
suppose you toss a fair coin and roll a fair six-sided die. What is the probability your actions result in tails on the coin and 3 on the die