Answers
The equation of an ellipse for the graph shown is [tex]\frac{x^2}{5^2} + \frac{y^2}{21^2} = 1[/tex]
How to determine the equation?Since the given coordinates of the vertices and foci have the form (-5, 0) and (5, 0) and (-2, 0) and (2, 0) respectively, this ultimately implies that the major axis of this ellipse is the x-axis.
Thus, the standard form of the equation of this ellipse is given by:
[tex]\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1[/tex]
Next, we would solve for b² by using this equation:
b² = a² - c²
b² = 5² - 2²
b² = 25 - 4
b² = 21.
Substituting the parameters into the standard equation of an ellipse, we have;
[tex]\frac{x^2}{5^2} + \frac{y^2}{21^2} = 1[/tex]
Read more on ellipse here: https://brainly.com/question/14468579
#SPJ1
Related Questions
In the triangle below, what is the cosine of 62 degrees?
Answers
Answer:
A. 8/17
Step-by-step explanation:
Cosine = adjacent over hypotenuse
Adjacent to angle 62 is 8 (The two angles are said to be adjacent angles when they share the common vertex and side).
The hypotenuse is 17 (opposite of right angle)
what would be this answer for the algebra thing
Answers
Answer:
c. 4x + 20 = 140
Step-by-step explanation:
Perimeter = 140 feet
Width = L + 10
P = 2w + 2L
P = 2(L + 10) + 2L
P = 2L + 20 + 2L
P = 4L + 20
Find the area of each figure. GEOMETRY PLS HELPPPP
Answers
Answer:
180
Step-by-step explanation:
For each of the two right triangles, by the Pythagorean theorem, she shared side is of length 15. So, the area of each of the top two rectangles is (½)(8)(15), so their combined area is 120.
Moving onto the trapezoid, we can use the formula for the area of a trapezoid to determine its area is (½)(14+16)(4)=60.
So, the answer is 120+60=180.
S
V
E
M
<
Which of the following inequalities are correct?
Some of the numbers involved are shown on the number line below.
Choose all answers that apply:
12-18
-20
-18-12
-12 < 18
-12
←||||*|||||
-10
0
10
18
20
Answers
Answer:
I think -10 is the answer
help asappppp
please
Answers
A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely.
What is the equation of a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is the y-intercept.
The graphs can be described as shown below.
A.) The first graph has the y-intercept at 2. Therefore, the first graph can be described by the equation, y =5x + 2.
B.) For the second graph, the graph passes through the point (-1,0). Therefore, if we substitute the value of y as 0 in the equation y=3x+3, we will get x=-1.
Hence, the equation of the second graph is y=3x+3.
C.) For the third graph, the graph passes through the point (-1.5,0). Therefore, if we substitute the value of y as 0 in the equation y=2x+3, we will get x=-1.5.
Hence, the equation of the second graph is y=2x+3.
Learn more about Equation of Line:
https://brainly.com/question/21511618
#SPJ1
Identify the type i error and the type ii error that corresponds to the given hypothesis. The proportion of people who write with their left hand is equal to.
Answers
Option D: Type I error ("Reject the claim that the proportion of people who write with their left hand is 0.15 when the proportion is actually 0.15").
Option B: Type II error ("Fail to reject the claim that the proportion of people who write with their left hand is 0.15 when the proportion is actually different from 0.15").
Type I error:
A. Fail to reject the claim that the proportion of people who write with their left hand is 0.15 when the proportion is actually different from 0.15.
B. Reject the claim that the proportion of people who write with their left hand is 0.15 when the proportion is actually different from 0.15.
C. Fail to reject the claim that the proportion of people who write with their left hand is 0.15 when the proportion is actually 0.15.
D. Reject the claim that the proportion of people who write with their left hand is 0.15 when the proportion is actually 0.15.
A Type I error is when the null hypothesis is rejected when it is true. In this case, the null hypothesis is that "the proportion of people who write with their left hand is equal to 0.15".
The right option is D (reject the null hypothesis when it is true).
Type II error:
A. Fail to reject the claim that the proportion of people who write with their left hand is 0.15 when the proportion is actually 0.15.
B. Fail to reject the claim that the proportion of people who write with their left hand is 0.15 when the proportion is actually different from 0.15.
C. Reject the claim that the proportion of people who write with their left hand is 0.15 when the proportion is actually different from 0.15.
D. Reject the claim that the proportion of people who write with their left hand is 0.15 when the proportion is actually 0.15.
A Type II error is when the null hypothesis is failed to be rejected when the alternative hypothesis is true. In this case, the null hypothesis is that "the proportion of people who write with their left hand is equal to 0.15".
The right option is B (failed to reject the null hypothesis when it is false).
The options A and C are correct decisions, as reject the null hypothesis when it is false (Option C) and not reject the null hypothesis when it is true (Option A).
Learn more about Errors on:
https://brainly.in/question/14970496
#SPJ4
Question 3 of 6
Drag the tiles to the correct boxes to complete the pairs.
Match each equation with its solution set.
H
5 = 81
FOL
625
125
256
+243
= 32
Submit
64
Answers
Step-by-step explanation:
HOPE THIS HELPS!.....
ATTACHED IS THE SOLUTION!Answer: i hope this helps
Step-by-step explanation:
Samual has a collection of toy cars his favorites are the 27 red ones which makes up 60% of his collection how many toy cars dose he have??
Answers
Answer:
45
Step-by-step explanation:
Use khan acedaemy
please help its timed i will give brainlyest
Answers
Answer:
20
Step-by-step explanation:
Long Division, cancel the zeroes, then 80/4 which is 20
Answer:
20
Step-by-step explanation:
8000/400= 20
Question 5 of 10
What is the first step in solving a quadratic equation of the form given below?
(ax+ b)² = c
O A. Divide both sides by c
OB. Factor out a common factor
OC. Use the zero product rule
OD. Take the square root of both sides
Answers
Answer:
D
Step-by-step explanation:
(ax + b)² = c
step 1 : take square root of both sides
ax + b = ± [tex]\sqrt{c}[/tex]
step 2 : subtract b from both sides
ax = - b ± [tex]\sqrt{c}[/tex]
step 3 : divide both sides by a
x = - [tex]\frac{b}{a}[/tex] ± [tex]\frac{\sqrt{c} }{a}[/tex]
Answer:
D. Take the square root of both sides
Step-by-step explanation:
Given quadratic equation:
[tex](ax+b)^2=c[/tex]
To solve, square root both sides:
[tex]\implies \sqrt{(ax+b)^2}=\sqrt{c}[/tex]
[tex]\textsf{Apply radical rule} \quad \sqrt{n^2}=n, \quad \textsf{assuming }n \geq 0:[/tex]
[tex]\implies ax+b=\pm\sqrt{c}[/tex]
Subtract b from both sides:
[tex]\implies ax=-b\pm\sqrt{c}[/tex]
Divide both sides by a:
[tex]\implies x=\dfrac{-b\pm\sqrt{c}}{a}, \quad a\neq 0[/tex]
Question 5
Sam wants to build a toy box in the shape of a rectangular prism that will
hold 36 cubic feet. If the height needs to be 1 foot less than the width and
the length is twice the width, find the height of the toy box.
Answers
Considering the volume of the given rectangular prism, the height is of 5.03 feet.
What is the volume of a rectangular prism?The volume of a rectangular prism of length l, width w and height h is given by:
V = lwh.
In this problem, we have that:
h = w - 1 -> w = h + 1.l = 2w = 2(h + 1) = 2h + 2.The volume is of 365 cubic feet, hence:
lwh = 365
(2h + 2)(h + 1)h = 365
(2h² + 4h + 2)h - 365 = 0
2h³ + 4h² + 2h - 365 = 0.
Using a cubic equation calculator, the height is of h = 5.03 feet.
More can be learned about the volume of a rectangular prism at https://brainly.com/question/17223528
#SPJ1
which 2 number have the mean of 10 and range of 4
Answers
Answer:
12 and 8
Step-by-step explanation:
→ Set up two equations
x - y = 4
[tex]\frac{x+y}{2} =10 \\ \\x + y = 20[/tex]
→ Add the 2 equations together
2x = 24
→ Solve for x
x = 12
→ Substitute into original equation
12 - y = 4
→ Solve
y = 8
For the following exercises, determine whether the functions are even, odd, or neither.
19. Solve |2x − 3 | = 17.
Answers
Answer:
The solutions of the equation |2 x-3|=17
are x=10
and x=-7
Step-by-step explanation:
Given equations is |2 x-3|=17.
It is required to find out the values of x satisfying the given equation.
To find it out, use the fact that the solution of this type of equation is 2x-3=17.
Or 2x-3=-17 and simplify the equations using simple mathematical operations.
Step 1 of 2
Solve the equation 2x-3=17,
Add 3 on both sides of the equation 2x-3=17,
2x-3+3=17+3
2x=20
Divide by 2 on both sides of the equation 2x=20,
[tex]$$\begin{aligned}&\frac{2 x}{2}=\frac{20}{2} \\&x=10\end{aligned}$$[/tex]
Step 2 of 2
Solve the equation 2x-3=-17,
Add 3 on both sides of the equation 2x-3=-17,
[tex]$2 x-3+3=-17+3$\\ $2 x=-14$[/tex]
Divide by 2 on both sides of the equation 2x=-14,
[tex]$$\begin{aligned}&\frac{2 x}{2}=\frac{-14}{2} \\&x=-7\end{aligned}$$[/tex]
What is the relationship between the angles?
Another answer is none of the above.
Answers
Reason - they are adjacent angles
Not vertical
Not complementary
Not supplementary
Fernando and Maria are at opposite sides of a park. They plan to meet later at a fountain that is located somewhere between them. Maria will arrive at the fountain first, before Fernando even leaves his starting location. The ratio of Maria's starting location to the fountain to Fernando's starting place is 5:3. What is the location of the fountain? Round to the nearest tenth, if necessary.
(, )
Answers
The location of the fountain based on the information given is (-1, 0.5).
How to illustrate the location?From the graph, the coordinates are (4, 2) and (-4, -2).
The ratio is given as 5:3.
The coordinates of the fountain will be:
[(5 × -4 + 3 × 4)/(5 + 3), (5 × -3 + 3 × 2)/(5 + 3)]
= (-1, -0.5)
Learn more about location on:
brainly.com/question/11940101
#SPJ1
Suppose a batch of steel rods produced at a steel plant have a mean length of 176 millimeters, and a variance of 100. If 446 rods are sampled at random from the batch, what is the probability that the mean length of the sample rods would differ from the population mean by greater than 0.65 millimeters
Answers
The probability that the mean length of the sample rods would differ from the population mean by greater than 0.65 mm is 0.1698 or 16.98%.
Mean length of the population (μ) = 176 mm.
Variance of the population (σ²) = 100.
Therefore, the standard deviation of the population (σ) = √100 = 10.
The sample size (n) = 446.
The mean of the sample = the mean of the population = μ = 176 mm.
The standard deviation of the sample (s) = σ/√n = 0.4735137.
We are asked to find the probability that the sample rods would differ the population mean by greater than 0.65 mm, that is,
either the length of the sample rods is less than (176 - 0.65) =175.35
or the length of the sample rods is more than (176 + 0.65) = 176.65.
This can be shown as P(X < 175.35 or X > 176.65) = 1 - P(175.35 < X < 176.65) = 1 - Normalcdf(175.35,176.65,176,0.4735137) = 1 - 0.8302 = 0.1698 or 16.98%.
Thus, the probability that the mean length of the sample rods would differ from the population mean by greater than 0.65 mm is 0.1698 or 16.98%.
Learn more about the probability of sampling distributions at
https://brainly.com/question/15291567
#SPJ4
For the following exercises, graph the given functions by hand.
41. y = −| x |
Answers
Using translation concepts, the graph of the function y = -|x| is given at the end of this answer.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
Graph y = -|x| is a reflection over the x-axis of the function y = |x|, and both functions(|x| in red, -|x| in blue) are given in the graph at the end of this answer.
More can be learned about translation concepts at https://brainly.com/question/4521517
#SPJ1
Could use some Geometry help
Answers
I am not 100% sure but I think it is 85 degrees
DO NOT take my word for it
Step-by-step explanation:
I'm not sure but I think it is 75 degree
solve this mathematical equation 3x=5+7
Answers
Answer:
x=4
Step-by-step explanation:
3x=5+7
7+5=12
12/3=4
x=4
Hope this helps!!
Answer:
x=4
Step-by-step explanation:
add like terms
3x =5+7
3x=12
divide both sides by 3
3x=12
3 3
x=4
Find the inverse of f(x)=5x^2-3
Answers
[tex]\large\boxed{y=\pm\sqrt{\frac{x+3}{5}}}[/tex]
To find the inverse, swap the [tex]y[/tex] (or [tex]f(x)[/tex] in this case) and the [tex]x[/tex], then solve for [tex]y[/tex].
[tex]\begin{aligned}y&=5x^2-3\\x&=5y^2-3\\x+3&=5y^2-3+3\\x+3&=5y^2\\\frac{x+3}{5}&=\frac{5y^2}{5}\\\frac{x+3}{5}&=y^2\\\pm\sqrt{\frac{x+3}{5}}&=\sqrt{y^2}\\\pm\sqrt{\frac{x+3}{5}}&=y\end{aligned}[/tex]
What 3D shape does this make? I think it's a cube but the only options are rectangular prism, rectangular pyramid, triangular prism, or no shape. Please help!
Answers
Answer:
the answer would be no shape.
Step-by-step explanation:
imagine you have the paper in your hands, if you start from the left you would have to fold the paper 3 times, then when it comes to the last 2 squares, you wouldnt be able to close the cube. hope this helps
Answer:
an open cube
Step-by-step explanation:
your welcome
Draw an angle that measures 260° in standard position.
Answers
Answer:
attached
Step-by-step explanation:
Fracciones heterogeneas
Answers
The information given illustrates that the equivalent fraction will be 2/6.
How to calculate the fraction?It should be noted that equivalent fraction simply means the fractions that are the same.
In this case, we are given 4/6 and 1/3. They have different numerators and denominators. The question is simply to change 1/3 to another fraction that has a denominator of 6.
This will be illustrated. The equivalent faction to 1/3 will be:
= 1/3 × 2/2
= 2/6
Therefore, the answer is 2/6.
Learn more about fractions on:
brainly.com/question/78672
#SPJ1
HELP! BRainliest +20
A function f is defined such that 8f(x)=f([tex]\frac{1}{8}[/tex]x) for all values of x, and f(4) = 24. What is the value of f(32) ?
Answers
The value of f(32) is 3
What is a Function ?A function is a mathematical statement used to relate two variables .
It is given that
8f(x) = f((1/8)x)
It is also given that
f(4) = 24
now to determine the value of f(32)
8 * f(32) = f((1/8) *32)
8 * f(32) = f(4 )
f(32) = 24 /8 = 3
Therefore the value of f(32) is 3
To know more about function
https://brainly.com/question/12431044
#SPJ1
What's the equation of a line that passes through points (–1, –5) and (1, 3)? Question 20 options: y=-2x
y=1/4x-2
y=-x+4
y=4x-1
Answers
Come up with two examples of ratio relationships that are interesting to you.
In mathematics a ratio is a comparison of two or more numbers that indicates their sizes in relation to each other
Answers
Answer:
1:3 is an example and for every two boy there are 5 girls is another example
Edited: I go out Five times as much as My sister does. My sister goes out only 3 times. Which is 15:1
I see 5 blue cars for every 6 red cars. Which is 5:6
Ratio is always represented in terms of ':' like a:b
Examples
#1
Sam has 2 apples Jane has 4 applesThe ratio of apples is 2:4 or 1:2
#2
dummy stars present at your home =10Stars present in Big dipper =7The ratio is 10:7
An 11 3/8-inch wide board can be cut into how many strips of width 5/8 inch, if each cut takes 1/8 inch of the width? (Must the answer be a whole
number?)
Answers
Answer:
15.
Step-by-step explanation:
Width of the strip + cut = 5/8 + 1/8 = 3/4.
11 3/8 / 3/4
= 91/8 / 3/4
= 91/8 * 4/3
= 91/6
= 15 1/6
So the answer is 15
Which model represents the factors of 4x^2-9
Answers
The model (x+a)(x-a) will represents the factors of 4x²-9 as (2x+3)(2x-3).
What are the quadratic equations in one variable completing the squares method?The "completing the squares" method aims to construct a quadratic equation of the form where the x variable is entirely covered by a single squared term, which is the square of a linear expression in x, as the name suggests.
The quadratic equation can resemble this:
x²-a² = (x+a)(x-a)
Given equation;
⇒4x²-9
⇒(2x)²-3²
The equation can be modeled as;
(2x+3)(2x-3)
Hence the model (x+a)(x-b) will represents the factors of 4x²-9 as (2x+3)(2x-3).
To learn more about completing the squares method refer to:
https://brainly.com/question/16800259
#SPJ1
1. A small garden has a perimeter of 24 1/4 ft. If the lengths is 8 ft, what is the area of the garden.
2. Lynn is putting tiles on her bathroom floor. Each tile measures 1 square foot each. The floor measures 4 1/2 ft by 3 3/4 ft. How many tiles will she need to cover the floor?
3. A dog pen is 3 1/3 yards wide by 5 2/3 yards long. What is the area of the dog pen?
Answers
The area of the garden is 33 ft².
The number of tiles required to cover the floor is 17 tiles.
The area of a dog pen is 170/9 square yards.
We need to find the area and perimeter for the given questions.
What are the formulas to find the perimeter and the area of a rectangle?The formula to find the perimeter of a rectangle=2(Length+Breadth)
The formula to find the area of a rectangle=Length×Breadth.
Given that, a small garden has a perimeter of 24 1/4 ft and the length is 8 ft.
Now, perimeter = 2(8+Breadth)
⇒24 1/4=16+2×Breadth
⇒97/4-16=2×Breadth
⇒Breadth=97-64/4×2=33/8 ft
Now, Area=8×33/8=33 ft²
Therefore, the area of the garden is 33 ft².
Given that, the floor measures 4 1/2 ft by 3 3/4 ft.
The area of a floor=Length×Breadth=9/2×15/4=135/8 ft²
Number of tiles to cover the floor=135/8=16.875
Therefore, the number of tiles required to cover the floor is 17 tiles.
Given that, a dog pen is 3 1/3 yards wide by 5 2/3 yards long.
Now, the area of a dog pen=10/3×17/3=170/9 square yards.
Therefore, the area of a dog pen is 170/9 square yards.
To learn more about the area and the perimeter visit:
https://brainly.com/question/11957651.
#SPJ1
A rectangular shaped desk has a length of 30 inches and a width of 24 inches. A desk with a similar shape has a length of 48 inches. What is the width of this desk? ((solve fast!!))
Answers
The width of the desk will be 38.4inches
Similar shapesA rectangle is a quadrilateral that has 4 sides and angles.
If a rectangular shaped desk has a length of 30 inches and a width of 24 inches and a desk with a similar shape has a length of 48 inches, the width of the desk will be calculated using this expression;
l/w = L/W
30/24 =48/W
Cross multiply
30W = 24 * 48
W = 38.4inches
Hence the width of the desk will be 38.4inches
Learn more on similar shapes here: https://brainly.com/question/14285697
#SPJ1