hmmm was going to do a quick mockup, but it might be too wide, so let's nevermind that piece.
so let's see, the center of this ellipse is at (3,1), and a focus point is at (8,1), notice, the y-coordinate is the same, meaning the distance between those two points is "c", which is 5, so c = 5.
We also know that the directrix is x = 36.8, well, that's a vertical line, if the line is vertical, that means the ellipse is running perpendicular to that, namely it has a major axis over the x-axis, so is horizontal.
[tex]\bf \textit{ellipse, horizontal major axis} \\\\ \cfrac{(x- h)^2}{ a^2}+\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2- b ^2}\\ eccentricity\quad e=\cfrac{c}{a}\\\\ directrix=h\pm \cfrac{a^2}{c} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf \stackrel{\textit{its directrix}}{x=h\pm\cfrac{a^2}{c}}\implies \stackrel{\textit{using one directrix}}{36.8=h+\cfrac{a^2}{c}}\qquad \begin{cases} h=3\\ k=1\\ c=5 \end{cases}\implies 36.8=3+\cfrac{a^2}{5} \\\\\\ 33.8=\cfrac{a^2}{5}\implies \boxed{169=a^2}\implies 13=a \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \stackrel{\textit{recall that }}{c=\sqrt{a^2-b^2}}\implies 5=\sqrt{169-b^2}\implies 5^2=169-b^2\implies 5^2+b^2=169 \\\\\\ b^2=169-5^2\implies \boxed{b^2=144}\implies b=12 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \cfrac{(x-3)^2}{169}+\cfrac{(y-1)^2}{144}=1~\hfill[/tex]
Answer:
a on edgn btw
Step-by-step explanation:
f(x) = x^2 what is g(x)
ANSWER
[tex]g(x) = 9 {x}^{2} [/tex]
EXPLANATION
The given function is:
[tex]f(x) = {x}^{2} [/tex]
The function g(x) is a vertical compression of f(x).
This implies that:
[tex]g(x)=a\bullet f(x)[/tex]
[tex]g(x)=a\bullet {x}^{2} [/tex]
The function g(x) goes through (1,9).
[tex]g(1)=9[/tex]
[tex]a\bullet {(1)}^{2} = 9[/tex]
[tex]a = 9[/tex]
Hence the function is:
[tex]g(x) = 9 {x}^{2} [/tex]
This can be rewritten as:
[tex]g(x) = {(3x)}^{2} [/tex]
The correct choice is A.
Answer: g(x)=(3x)^2
Step by step:Ape
13) through: (1, 2), slope = 7
A) y = -5x+4 B) y = -5x+7
C) y = 4x - 5 D) y = 7x - 5
Answer: D
Step-by-step explanation:
if the slope is 7, mx + b =y the slope is m. that’s the only one that makes sense. hope this helps!
Answer:
D
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here slope m = 7, thus
y = 7x + c ← is the partial equation
To find c substitute (1, 2) into the partial equation
2 = 7 + c ⇒ c = 2 - 7 = - 5
y = 7x - 5 → D
Find the value of x.
x is equivalent to 20
Since this is a vertical angle, we can do this:
2+3x=62. Solve the equation:
3x=62-2
3x=60
x=20 is the answer.
Hope I helped!
~Potato
You deposited $120 in an account with an interest rate of 4%. In how many years will the simple interest earned be $1.92?
Answer: About 5 months
Equation:
t = I / Pr
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 4%/100 = 0.04 per year,
then, solving our equation
t = 1.92 / ( 120 × 0.04 ) = 0.4
t = 0.4 years
The time required to
accumulate simple interest of $ 1.92
from a principal of $ 120.00
at an interest rate of 4% per year
is 0.4 years (about 0 years 5 months).
A square grass field is being paved to convert it to a shopping mall. Each side of the field is 75 meters long. The plan is to reduce the side lengths of the grass field by 5
meters each week. Which function can be used to calculate the area of the grass field, A after T weeks?
(A)=75−(5t)^2
(A)=(75−5t)^2
(A)=75^2 −5
(A)=75^2 -(5t)^2
Answer: second option.
Step-by-step explanation:
The formula for calculate the area of a square is:
[tex]A=s^2[/tex]
Where "s" is the lenght of any side of the square.
You know that the square grass field is 75 meters long and they plan to reduce the side lengths of the grass field by 5 meters each week and the number of weeks is "t", then, the area after "t" weeks will be:
[tex]A=[s_{original}-(s_{eliminated})(number\ of\ week)]^2[/tex]
Substituting you get that the function that can be used to calculate the area of the grass field, "A" after "t" weeks is:
[tex]A=(75-5t)^2[/tex]
This matches with the second option.
If you only have a 1/10 measuring cup and a recipe calls for
4 3/10 cups of flour, how many 1/10 cups would you need to use?
Answer:
Step-by-step explanation:
well let break it down
you have 1/10
you need 4 and 3/10
that can be changed to 43/10 because you need 4 WHOLE or 40/10 (40/10 = 4)
if you can pour 1/10 and you need a total of 43/10, you'd need to use 43 of the 1/10 measuring cups
To measure out 4 3/10 cups of flour using only a 1/10 measuring cup, you would need to fill the 1/10 measuring cup 43 times.
Explanation:To determine how many 1/10 cups are needed to measure out 4 3/10 cups of flour, start by converting the desired amount into tenths.
4 3/10 cups can be thought of as 4 cups plus 3/10 of a cup, which is equivalent to 40/10 cups plus 3/10 cups, giving us 43/10 cups in total.
Since you only have a 1/10 measuring cup, you would need to use this cup a total of 43 times to get 43/10 cups of flour. Therefore, you would need to use the 1/10 measuring cup 43 times to obtain the necessary flour for the recipe.
Michael hires a cab that charges a fare of $0.50 per mile, plus an initial charge of $2. Jason hires a cab that charges a fare of $0.50 per mile, plus an initial charge of $3.50.
At how many miles will the fares paid by Michael and Jason become equal?
use reapeted addition and keep adding +$0.50 until you get $4.00 for it to be equal with Jason's total which was $4.00
so it will be at 3 miles.
or just multiply micheals total by 3.:) hope it helped!!
Answer:
The fares paid by Michael and Jason will never be equal.
Step-by-step explanation:
Helpp I’m so bad at this topic
Answer:
alternate angles
Step-by-step explanation:
the picture shows that there is a the Transversal (When two lines are crossed by another line)
on the inner side of each of those two lines are called Alternate Interior Angles
the definition of alternate angles is if the original two lines are parallel, the alternate angles are equal.
Remus is writing a book. If he wrote 34 chapters in 13 months, how long should it take Bob to write another chapter?
I love unit rate 13/34=0.38 months to write 1 chapter or write 2.62 in one month (34/13)
The graph shown represents a the rule y=x+1.5
Final answer:
The answer explains the graph of y=x+1.5, a direct relationship with a positive slope, and the graphical representation of the dependence of y on x.
Explanation:
Mathematics: The graph represents the rule y=x+1.5, showing a straight line with a positive slope where the y-intercept is 1.5. As x-values increase, the line gradually rises on the graph.
Direct Relationship: The line's slope remains the same, indicating a direct relationship between x and y.
Slope and Graphical Representation: By connecting points like (1,5), (2,10), (3,7), and (4,14), the dependence of y on x can be graphically illustrated.
Iteration question 6 please help
Answer:
option A
1 , 1 , 1 , 1
Step-by-step explanation:
Given in the question a function
f(x) = x²
initial value[tex]x_{0}[/tex] = -1
First iteration
f(-1) = (-1)²= 1
[tex]x_{1} =1[/tex]
Second iteration
f(1) = (1)² = 1
[tex]x_{2} =1[/tex]
Third iteration
f(1) = (1)² = 1
[tex]x_{3} =1[/tex]
Fourth iteration
f(1) = (1)² = 1
[tex]x_{4} =1[/tex]
Help please with these problems
the box is considered a prism
any prism the formula for volume is V=area of the base times height so
the first two boxes have the base of 16 plus the height of 3
so 16*3=48
48*2=96
the other box has the height of 5 so
16*5=80
in total they want the volume of all boxes so
96+80=176
answers B:)
if you need to elaborate lmk
Answer:
(B) 176 ft³
Step-by-step explanation:
Volume of the first box with 3 feet:
= 16 x 3
= 48 ft³
Volume of the second box with 3 feet:
= 16 x 3
= 48 ft³
Volume of the third box with 5 feet:
= 16 x 5
= 80 ft³
Total volume
= 48 + 48 + 80
= 176 ft³
Help me with 9 and 10 please! With explanation
The answer to Number 9 is D and the answer to number 10 is D because in number 9, City P is above 0 and City R is a negative number and below 0. In number 10, Point A is at -20 and Point B is 5 less. That would get you the equation -20-5. -20-5 = -25. On a number line, -25 is less than -20 and would be on the left side of Point A. Hope this helps!
Whatever he or she said is correct
The following box-and-whisker plots represent the fuel economy rates (combined city and highway) for the entire fleet of two major car manufacturers. Which of the following statements is not true? The median fuel economy rate of Car Manufacturer A is about 7 miles per gallon higher than the median fuel economy rate of Car Manufacturer B. The range of the middle half of the rates for both manufacturers is about the same. One of the vehicles in Car Manufacturer B's fleet has the lowest fuel economy rate of either manufacturer. Car Manufacturer A's fleet has a larger range of fuel economy rates than Car Manufacturer B's fleet.
Final answer:
Car Manufacturer B does not have the lowest fuel economy rate in the fleet, making this statement false.
Explanation:
Car Manufacturer A:
The median fuel economy rate of Car Manufacturer A is about 7 MPG higher than Car Manufacturer B.
Car Manufacturer A's fleet has a larger range of fuel economy rates than Car Manufacturer B's fleet.
Car Manufacturer B:
The range of the middle half of the rates for both manufacturers is about the same.
One of the vehicles in Car Manufacturer B's fleet has the lowest fuel economy rate of either manufacturer.
From the given box-and-whisker plots, it can be observed that the statement 'One of the vehicles in Car Manufacturer B's fleet has the lowest fuel economy rate of either manufacturer' is not true.
Graph the following inequality. Then click to show the correct graph. x < -1
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
x < -1
The solution is the interval ----> (-∞,-1)
All real numbers less than -1
On a number line the solution is the shaded area at the left of x=-1 (open circle)
using a graphing tool
see the attached figure
Answer:
Step-by-step explanation:
Trying to help everyone!
The number of paper clips that crystal has is 42 divided by the number of paper clips that gayle has. If gayle has 11 more paper clips than crystal does, how many paper clips does each have
Answer:
• Gayle: 14
• Crystal: 3
Step-by-step explanation:
Let g represent the number of paperclips Gayle has. Then 42/g is the number Crystal has. The relationship between the two numbers is said to be ...
g - (42/g) = 11
Multiplying by g gives ...
g^2 -42 = 11g
g^2 -11g -42 = 0 . . . . subtract 11 g to put into standard form
To factor this, you are looking for two factors of -42 that sum to -11.
-42 = -42·1 = -21·2 = -14·3 = -7·6
You can see that -14 and 3 sum to -11, so the factoring is ...
(g -14)(g +3) = 0
g = 14 . . . . . . . . . . makes the product zero. (The g=-3 solution is extraneous.)
Gayle has 14 paperclips and Crystal has 3.
Can someone help me please
OK the answer is (6,7). THis is true because you always put the x coordinate first and then the y coordinate and the x axis is horizontal and the y axis is vertical.
Answer:
From the Information provided by the graph shown above, i can conclude that Berlin's location on the graph is (6,7)
Answer the question in the picture.
Answer:
r=9
Step-by-step explanation:
We can use the Pythagorean to solve, since this is a right triangle
The leg lengths are r and 12
The hypotenuse is (r+6)
a^2 + b^2 = c^2
r^2 + 12^2 = (r+6)^2
Foiling out the right hand side
(r+6)(r+6_ = r^2+6r+6r+36
r^2 +144 = r^2 +12r+36
Subtracting r^2 from each side
r^2-r^2 +144 = r^2-r^2 +12r+36
144 = 12r+36
Subtract 36 from each side
144-36 = 12r+36-36
108 = 12r
Divide each side by 12
108/12 = 12r/12
9=r
AC=AB+BC
AC=6+r
AD=12
DC=r
by Pythagorus theorem
AC*2=AD*2+DC*2
(6+r)*2=12*2+r*2
36+12r+r*2=144+r*2
12r+r*2-r*2=144-36
12r=108
r=108/12
r=9
HELP QUICK
Mia bought some tomato plants for $9.98 and some potting soil for $6.89.
Round each amount to the nearest dollar.
About how much change did Mia get from $20.00?
A. about $1
B. about $5
C. about $17
D. about $3
Answer:
Mia bought some tomato plants for $9.98 and some potting soil for $6.89.
Round each amount to the nearest dollar.
About how much change did Mia get from $20.00?
A. about $1
B. about $5
C. about $17
D. about $3
Hope this helps :)
Have a great day !
5INGH
Step-by-step explanation:
$9.98 =$10
$6.89 = $7
10 + 7 =17
20 - 17 = 3
your answer would be d.
A jeweler has 15 diamond pendants and will display 4 of them from left to right in a glass case. In how many ways can he select and display the 4 pendants?
This is a problem of permutations. In this case, with 15 diamond pendants and selecting 4 at a time, there are 32,760 ways to select and arrange these pendants.
Explanation:This question is about permutations of a set of objects. A permutation is an arrangement of objects in a specific order. The number of permutations of n distinct objects taken r at a time, denoted by P(n, r), can be calculated as: n! / (n-r)! where the '!' symbol represents a factorial, the product of all positive integers less than or equal to the number.
In this case, the jeweler has 15 diamond pendants (n=15) and is selecting and arranging 4 of them (r=4). We can plug these values into the formula to find the number of ways: P(15, 4) = 15! / (15-4)! = 32,760. So, there are 32,760 ways to select and display the 4 pendants.
Learn more about Permutations here:https://brainly.com/question/23283166
#SPJ12
The potential energy of an object is jointly related with the mass of the object and the height of the object. A 40-kg object is 2
meters off the ground. The potential energy of the object is 784 joules. A 10-kg object is 3 meters off the ground. What is the
potential energy of the 10-kg object?
Answer:
294 Joules.
Step-by-step explanation:
For this all you have to do is use the equation for PE or Potential Energy. Which is given by ... PE = mgh.
m = the mass in kg
g = the accerlation due to gravity (9.8 m/s^2)
h = the height of the object in meters.
so... 10 kg (9.8)(3m) = 294 J
Answer:
294!
Step-by-step explanation:
edge 2021 enjoy
If x = 5 cm, y = 12 cm, and z = 13 cm, what is the surface area of the geometric shape formed by this net?
A. 82 sq. cm
B. 270 sq. cm
C. 210 sq. cm
D. 320 sq. cm
Answer:
the answer is C. 210 sq. cm
Step-by-step explanation:
Find the area of the triangle
The area of one of the triangular faces can be found by using the formula below.
a = 1/2 bh
a = 1/2 (5 cm) (12 cm)
a = 30 sq. cm
Since there are two triangular faces, multiply the area of one triangular face by 2. The area of two triangular faces is 60 cm2.
Next, find the area of each of the three rectangular faces using the formula, area = lw.
1st rectangle
a = lw
a = (5 cm) (5 cm)
a = 25 sq. cm
2nd rectangle
a = lw
a = (5 cm) (12 cm)
a = 60 sq. cm
3rd rectangle
a = lw
a = (5 cm) (13 cm)
a - 65 sq. cm
Add the three rectangle areas to find a total of 150 sq. cm.
To find the surface area of the triangular prism, add the area of the two triangular faces to the area of the three rectangular faces.
60 sq. cm + 150 sq. cm = 210 sq. cm
math help uwu,, please nd thank <3
Answer:
Step-by-step explanation:
The equation of a circle is:
(x - h)² + (y - k)² = r²
where (h, k) is the center and r is the radius.
So here, the center is (-2, 4), and the radius is 5.
Here's a graph: desmos.com/calculator/5zqdaam1w2
Can you please find tan z
If we are talking trigonometry, the answer is 24/32. If they want you to simplify your answer it would be 3/4.
The population of fish in a certain lake follows the logistic growth function , where t is the time in years.
When will the population reach 20,000?
Answer:
46 years
Step-by-step explanation:
We have the logistic growth function [tex]f(t)=\frac{25,000}{1+8.25e^{-0.076t}}[/tex] and we want to find the time when the population will reach 20,000, to do it we just need to replace [tex]f(x)[/tex] with 20,000 and solve for [tex]t[/tex]:
[tex]f(t)=\frac{25,000}{1+8.25e^{-0.076t}}[/tex]
[tex]20,000=\frac{25,000}{1+8.25e^{-0.076t}}[/tex]
Divide both sides by 25,000
[tex]\frac{20,000}{25,000} =\frac{1}{1+8.25e^{-0.076t}}[/tex]
[tex]0.8=\frac{1}{1+8.25e^{-0.076t}}[/tex]
Multiply both sides by [tex]1+8.25e^{-0.076t}[/tex] and divide them by 0.8
[tex]1+8.25e^{-0.076t}=1.25[/tex]
Subtract 1 from both sides
[tex]8.25e^{-0.076t}=0.25[/tex]
Divide both sides by 8.25
[tex]e^{-0.076t}=\frac{0.25}{8.25}[/tex]
[tex]e^{-0.076t}=\frac{1}{33}[/tex]
Take natural logarithm to both sides
[tex]ln(e^{-0.076t})=ln(\frac{1}{33} )[/tex]
[tex]-0.076t=ln(\frac{1}{33} )[/tex]
Divide both sides by -0.076
[tex]t=\frac{ln(\frac{1}{33} )}{-0.076}[/tex]
[tex]t[/tex] ≈ 46
We can conclude that the population will reach 20,000 after 46 years.
find the slope and write an equation with these to points (0,-2) (3,1)
plz explain
Hello There!
Slope: 1
Equation: y = x - 2
Let's start by finding the slope. To find the slope of a given equation, subtract the y values over the x values.
y1 - y2 / x1 - x2 ⇒ 3 - 0 / 1 - - 2 ⇒ 3 / 3 ⇒ 1
This means we have a slope value of 1.
Now, to find an equation. We will find the equation in slope intercept form, or y = mx + b. (In this case, m = the slope and b = the y-intercept, and x and y equal your x and y values fro a given point.)
To get the equation, we need to find the value of b, or the y intercept. To do this, we need to plug in the values we know into the equation.
we know m is the slope, and we know the slope is one so we can place that into the equation. We also know the points (0,-2) (3,1). We can place one of them into the equation for the values x and y.
1 = 1(3) + b
Now, simplify.
1 = 1(3) + b
1 = 3 + b
-2 = b
So, our y intercept is -2, we can plug that into the equation, making our final equation y = x - 2. We don't need to put y = 1x for the slope since multiplying something by 1 is doesn't change the number.
I hope this helps! I know my explanation might have been kind of confusing so if you need more help let me know in the comments !
Answer:
y = x - 2
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
To calculate m use the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (0, - 2) and (x₂, y₂ ) = (3, 1)
m = [tex]\frac{1+2}{3-0}[/tex] = [tex]\frac{3}{3}[/tex] = 1
Note the line crosses the y- axis at (0, - 2) ⇒ c = - 2
y = x - 2 ← equation of line
a circle has a circumference of 6. it has an arc of length 1/3
What is the central angle of the arc in degrees
Answer:
Ф = 10°
Step-by-step explanation:
Regarding arc length, s: s = r·Ф, where Ф is the central angle in radians and r is the radius.
We need to find the central angle, Ф, in this problem.
We know that C = circumference = 6, and that this leads to r = 6/π.
Substituting 6/π for r and 1/3 for s in Ф = s / r, we get:
Ф in radians = 1/3 / (6/π), or Ф = π/18 rad.
π 180°
Converting this into degrees, we multiply ------ by ----------
18 π rad
obtaining: Ф = 10°
Answer:
20
Step-by-step explanation:
How do I know if it’s closed or not? (Ignore the “Ben...”
Answer:
It is open if it is greater or less than >
It is closed if it is greater than or equal to or less than or equal to > (but with the line underneath it)
Step-by-step explanation:
Answer:
look at the point if it is closed it will look like a dot(10) if not it will look like an empty circle (11)
Step-by-step explanation:
x is greater than or equal to -2
x is less than -2
Which of the following functions is graphed below.
Answer: Option A
[tex]y=\left \{ {{x^2 +2;\ \ x<1 \atop {-x+2;\ \ x\geq1}} \right.[/tex]
Step-by-step explanation:
In the graph we have a piecewise function composed of a parabola and a line.
The parabola has the vertex in the point (0, 2) and cuts the y-axis in y = 2.
The equation of this parabola is [tex]y = x ^ 2 +2[/tex]
Then we have an equation line[tex] y = -x + 2 [/tex]
Note that the interval in which the parabola is defined is from -∞ to x = 1. Note that the parabola does not include the point x = 1 because it is marked with an empty circle " о ."
(this is [tex]x< 1[/tex])
Then the equation of the line goes from x = 1 to ∞ . In this case, the line includes x = 1 because the point at the end of the line is represented by a full circle .
(this is [tex]x\geq 1[/tex])
Then the function is:
[tex]y=\left \{ {{x^2 +2;\ \ x<1 \atop {-x+2;\ \ x\geq1}} \right.[/tex]
Chen is bringing fruit and veggies to serve at an afternoon meeting. He spends a total of $28.70 on 5 pints of cut veggies and 7 pints of cut fruit. The food cost is modeled by the equation , where v represents the cost of one pint of cut veggies and f represents the cost of one pint of cut fruit. If the cost of each pint of fruit is $2.85, what is the approximate price of a pint of veggies? (Round to the nearest cent.)
$1.75
$2.06
$2.39
$3.99
Answer: First Option
The approximate price of a pint of veggies is $1.75
Step-by-step explanation:
if v represents the cost of a pint of cut vegetables and f represents the cost of a pint of cut fruits then the equation that models the cost of "v" vegetables and "f" fruits is:
[tex]hv + 2.85f = z[/tex]
Where z represents the total cost of buying "v" vegetables and a "f" pints of fruits.
h represents the cost of a pint of cut vegetables .
We know that the cost "z" of 5 vegetables pints and 7 fruits pints is $ 28.70
So:
[tex]v = 5\\f = 7\\z = 28.70[/tex]
We substitute these values into the equation and solve for h.
[tex]h(5) + 2.85(7) = 28.70\\\\5h=28.70-2.85(7)\\\\5h=28.70-19.95\\\\5h=28.70-19.95\\\\h=\frac{8.75}{5}\\\\h=\$\ 1.75[/tex]