How far apart are the foci of an ellipse with a major axis of 32ft and minor axis of 14ft ?
The foci are placed 4 feet apart from the ellipse's center. Then the distance between the foci of the ellipse will be separated by 8 feet.
What is an ellipse?Ellipse is a locus of a point that moves in a plane such that the sum of its distances from the two points called foci adds up to a constant. It is taken from the cone by cutting it at an angle.
A major axis of 32 ft and a minor axis of 14 ft.
The major axis 2a of the ellipse will be
2a = 10 feet
a = 5 feet
The minor axis 2b of the ellipse will be
2b = 14
b = 7 feet
We must utilize the following connection to get the foci's coordinate:
b² = a² - c²
3² = 5² - c²
c² = 25 - 9
c² = 16
c = ± 4
As a result, the foci are placed 4 feet apart from the ellipse's center. As a result, the foci are separated by 4 + 4 = 8 feet.
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Draw a tessellation using the following shape(s).
octagon and square
The network of equilateral triangles, squares, and hexagons is used in just three regular tessellations.
What does tessellation of a form mean?
A flat surface is tessellated when one or more geometric forms, known as tiles, are used to tile the surface without any gaps or overlaps.Tessellations in mathematics can be expanded to greater dimensions and a wide range of geometries.A tiling is referred to as "non-periodic" if it doesn't have a repeating pattern.Only regular triangles, squares, and hexagons can tessellate on their own.
If you use more than one sort of form, you can create additional tessellations of regular shapes.
The network of equilateral triangles, squares, and hexagons is used in just three regular tessellations.
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Write each number as a percent.
1.23
.
Rather than being expressed as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100.
The number 1.23 as a percentage is 123 %.
What is a percentage?A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The percent sign, %, is frequently used to indicate it. There is no unit of measurement for a percentage. It is a dimensionless number (pure number).
Rather than being expressed as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You divide the part of the whole by the whole and multiply the result by 100 to get the percentage.
Let the number be 1.23
To find percentage multiply it by 100, we get
So, 1.23 × 100 = 123 %
Therefore, the number 1.23 as a percentage is 123 %.
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Given parallelogram LMNO with diagonals intersecting at point P. If MP = 2x + 5 and OP = 3x − 4, find OP.
−9
9
23
31
Given parallelogram LMNO with diagonals intersecting at point P, OP is equal to 23.
A parallelogram is a two-dimensional figure with two pairs of parallel sides. A parallelogram's pair of opposite sides are of equal length and its opposite angles are of equal measure.
The diagonals of a parallelogram bisect each other, divides each other into two equal lengths.
If the diagonals of parallelogram LMNO intersects at point P, then MP is equal to OP. If MP = 2x + 5 and OP = 3x − 4, solve for x.
MP = OP
2x + 5 = 3x − 4
5 + 4 = 3x - 2x
x = 9
Substitute the value of x to solve for OP.
OP = 3x − 4
OP = 3(9) - 4
OP = 27 - 4
OP = 23
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pls help, I need this ASAP, brainliest to the person with solution and right answer
Answer:
see explanation
Step-by-step explanation:
1
(5p² - 3) + (2p² - 3p³) ← remove parenthesis
= 5p² - 3 + 2p² - 3p³ ( collect like terms , largest exponent first )
= - 3p³ + 7p² - 3
2
(a³ - 2a²) - ( 3a² - 4a³) ← distribute second parenthesis by - 1
= a³ - 2a² - 3a² + 4a³ ( collect like terms, largest exponent first )
= 5a³ - 5a²
3
(- 4[tex]k^{4}[/tex] + 14 + 3k²) + (- 3[tex]k^{4}[/tex] - 14k² - 8) ← remove parenthesis
= - 4[tex]k^{4}[/tex] + 14 + 3k² - 3[tex]k^{4}[/tex] - 14k² - 8 ← collect like terms, largest exponent first
= - 7[tex]k^{4}[/tex] - 11k² + 6
4
(3 - 6[tex]n^{5}[/tex] - 8[tex]n^{4}[/tex]) - (- 6[tex]n^{4}[/tex] - 3n - 8[tex]n^{5}[/tex]) ← distribute second parenthesis by - 1
= 3 - 6[tex]n^{5}[/tex] - 8[tex]n^{4}[/tex] + 6[tex]n^{4}[/tex] + 3n + 8[tex]n^{5}[/tex] ( collect like terms, largest exponent first )
= 2[tex]n^{5}[/tex] - 2[tex]n^{4}[/tex] + 3n + 3
5
(y³ - 7[tex]x^{4}[/tex][tex]y^{4}[/tex]) + (- 10[tex]x^{4}[/tex]y³ + 6y³ + 4[tex]x^{4}[/tex][tex]y^{4}[/tex] ) - ( [tex]x^{4}[/tex]y³ + 6[tex]x^{4}[/tex][tex]y^{4}[/tex])
remove parenthesis from first 2 and distribute third by - 1
= y³ - 7[tex]x^{4}[/tex][tex]y^{4}[/tex] - 10[tex]x^{4}[/tex]y³ + 6y³ + 4[tex]x^{4}[/tex][tex]y^{4}[/tex] - [tex]x^{4}[/tex]y³ - 6[tex]x^{4}[/tex][tex]y^{4}[/tex]
collect like terms
note the term with the largest exponent is [tex]x^{4}[/tex][tex]y^{4}[/tex]
= (- 7[tex]x^{4}[/tex][tex]y^{4}[/tex] - 6[tex]x^{4}[/tex][tex]y^{4}[/tex] ) + (- 10[tex]x^{4}[/tex]y³ - [tex]x^{4}[/tex]y³) + (y³ + 6y³)
= - 13[tex]x^{4}[/tex][tex]y^{4}[/tex] - 11[tex]x^{4}[/tex]y³ + 7y³
COORDINATE GEOMETRY Find the measures of the sides of ΔJ K L and classify each triangle by the measures of its sides. (Lesson 4-1)
J(-7,10), K(15,0), L(-2,-1)
ΔJKL has 53.28 units of side length.
What is a triangle's definition?A triangle is a polygon with three sides and three edges.It is a fundamental geometric shape.Triangle ABC is a three-vertical triangle with the letters A, B, and C on each side.Any three non-collinear points define a unique triangle and, by extension, a unique plane in Euclidean geometry.So,
The formula for the perimeter of the side of a triangle: √(x₂−x₁)²+(y₂−y₁)²
Filling the values in the formula, we obtain:
= √(15−(-7))²+(0−10)²= 53.28 unitsThen, each side of the triangle will be: 53.28 units
Therefore, ΔJKL has 53.28 units of side length.
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round 0.6666 to 3 sf
Answer:
0.66 with a bar
Step-by-step explanation:
3n-21=2n (2-step equations)
Answer:
n=21
Step-by-step explanation:
3n-21=2n
subtract 3n from each side
-21=-1n
two negatives become a positive
6+2(2+3)divided by 2
Answer:
11
Step-by-step explanation:
[tex]6+2(2+3)/2[/tex]
[tex]6 + \frac{2 * (2+3) }2}[/tex] Cancel out 2* and the bottom 2
[tex]6+2+3[/tex] 6+2=8
⬇️
8 + 3
= 11
At a football game half time show, the marching band was in 3 sections, each with 8 rows of 8 players. The dancers were in 2 sections each with 6 rows of 7 dancers. What is the total number of band members and dancers in the halftime show?
The total number of band members and dancers in the halftime show in all rows were 276.
What is a row?A row is an arrangement of things in a straight line next to each other.
if there are n rows and each row has m members then total number of members = m* n
Given that marching band was in 3 sections and each section has 8 rows of 8 players , then players in each section of marching band = 8 *8 = 64
As, there are 3 such sections then total number of marching band players =3*(players in each section) = 3* 64 = 192
Given that there are 2 sections of dancers and each section has 6 rows of 7 dancers.
Then, dancers in each section of dancers = 6*7 =42
As there are two such sections, then the total dancers = 2* 42 = 84
total no of band members and dancers = 192+84 = 276
Therefore, The total number of band members and dancers in the halftime show were 276.
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Find the missing term of each arithmetic sequence.... 5, .. , 21,...
The missing terms of an arithmetic progression (AP) are -3, 5, 13, 21, 29.
What is meant by arithmetic progression (AP)?An arithmetic progression (AP) is a pattern in which each successive term has the same distinctions.
Each term in an arithmetic progression (except the first) is deduced by adding a specific range to the term preceding the first.The following arithmetic progression concepts are most often used to solve various AP problems for the initial term 'a' of an AP together with the common difference 'd.'The most common difference AP is 'd': d = a2 - a1 = a3 - a2 = a4 - a3 =...... = a - an-1. nth term of an AP: an = a + (n - 1) dThe sum of an AP's n terms is; Sn = n/2(2a+(n-1)d) = n/2(a + l), where l is the final term of the AP.The arithmetic sequence.... 5, .. , 21,...
There are total 5 terms in the series.
Let the initial term be 'a₁'.
Let the second term be 'a₂' = 5.
Let the third term be 'a₃'.
Let the fourth term is be 'a₄' = 21.
And final, the fifth term be 'a₅'.
The common difference of the AP are same. so,
d = a₃ - a₂ ........(equation 1)
d = a₄ - a₃ .......(equation 2)
Thus, equate the two formed equation;
a₃ - a₂ = a₄ - a₃
Substituting the values;
a₃ - 5 = 21 - a₃
Simplify the above equation;
a₃ = 26/2
a₃ = 13.
Put the value in equation 1 and find the common difference.
d = a₃ - a₂
d = 13 - 5 = 8
So, the first term will be;
d = a₂ - a₁
a₁ = a₂ - d
a₁ = 5 - 8
a₁ = -3
Now, the fifth term will be;
a₅ = a₄ + d
a₅ = 21 + 8
a₅ = 29.
Therefore, the arithmetic sequence of the AP formed as -3, 5, 13, 21, 29.
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She bought 0.85 pounds of ground beef for $5.60 per pound and 1 can of tomatoes for $1.79. if she had a coupon for $1.50 off, how much did she spend all together on the ingredients?
Answer:
$5.05
Step-by-step explanation:
.85($5.60) + $1.79 - $1.50
$4.76 + $1.79 - $1.50 = $5.05
Find the measure of the missing angles
Answer: d=90 degrees
e=69 degrees
f=111 degrees
Step-by-step explanation:
69+f=180 ==> a straight line is 180 degrees and is called a straight angle. The angles that make up the straight line add up to 180 degrees.
69-69+f=180-69
f=180-69
f=111 degrees
e+f=180 ==> a straight line is 180 degrees and is called a straight angle. The angles that make up the straight line add up to 180 degrees.
e+111=180
e+111-111=180-111
e=180-111
e=69 degrees
d+90=180 ==> if there is a tiny box between an angle, that means that the angle is a right angle which measures 90 degrees.
d-90+90=180-90
d=180-90
d=90 degrees
Use the Exterior Angle Inequality Theorem to list all of the angles that satisfy the stated condition. (Lesson 5-3)
measures less than m∠5
The exterior angle (∠ 5) is larger than either remote interior angle (∠ 7 and ∠ 8).
Exterior Angle Inequality Theorem
According to the exterior angle inequality theorem, the measure of any exterior angle of a triangle is greater than the measure of either of the opposite interior angles. The adjacent interior angle and the exterior angle are supplementary. A triangle's exterior angles add up to 360º.
A triangle's exterior angle is always greater than its two remote interior angles.
By the Exterior Angle Inequality Theorem, the exterior angle (∠ 5) is larger than either remote interior angle (∠ 7 and ∠ 8).
m ∠ 7 < m ∠ 5 and m ∠ 8 < m ∠ 5 .
Therefore, the correct answer is ∠ 7 and ∠ 8.
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Helen Mountain Tubing charges $25 for tube rental and $5 an hour to float down the river. Alpine Tubing charges $30 for tube rental and $2 an hour to float down the river. Create an equation to determine at what point the cost of both tubing companies is the same.
25x - 5 = 30x - 2
25x + 5 = 30x + 2
25 + 5x = 30 + 2x
25 - 5x = 30 + 2x
Answer:
25 + 5x = 30 + 2x
At 5/3s of an hour is when the cost of both tubing companies are the same.
This is when the price of both companies both hit $33.33
Step-by-step explanation:
25 + 5x = 30 + 2x
move variables by subtracting
25 + 3x = 30
move constants by subtracting
30 - 25 = 5
5 = 3x
x = 5/3
What is the value of r when s=-1 , t=4 and u = (1/5) ?
r=3s² + 5(t-2u)
A 7
B 15
C 21
D 22(1/5)
The value of r is 21 when s = -1 , t = 4 and u = 1/5 for the equation r = 3s² + 5 (t - 2u).
Quadratic Equation:
Quadratic equations are the polynomial equations of degree 2 in one variable of type.
The general form of a quadratic equation is,
f(x) = ax² + bx + c = 0
where a, b, c, ∈ R and a ≠ 0.
‘a’ is called the leading coefficient and
‘c’ is called the absolute term of f (x).
Given,
Equation is,
r = 3s² + 5 (t - 2u).
Here we need to find the value of r when the values of s = -1 , t = 4 and u = 1/5.
Apply the values on the given equation then we get,
=> r = 3 (-1)² + 5 ( 4 - 2(1/5))
Expand the values,
=> r = 3 (-1)² + 5( [20 -2] /5)
Here the value 5 is getting cancelled then we get,
=> r = 3(-1)² + 18
We know that the value of (-1)² = 1
So,
=> r = 3(1) + 18
=> r = 3 + 18
=> r = 21
Therefore, the value of r is 21.
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33 is 22% of what
number?
Answer:
150
Step-by-step explanation:
[tex]33 = 0.22(x)\\\\\\frac{33}{0.22} =\frac{0.22(x)}{0.22} \\\\\large\boxed{x=150}[/tex]
The angle adjacent to ∠ C is called an exterior angle of triangle A B C . Make a conjecture about the relationship among ∠A, ∠ B , and the exterior angle at C .
Here the conjecture we can made is :
The sum of interior angles i.e. ∠A and ∠B is equal to the exterior angle at C.
What is external and internal angles ?The exterior angle of any triangle is defined as the angle which is at the outside boundaries of that triangle. whereas, the interior angle is defined as the angle which is inside the triangle. In the other words if the triangle has the point within the angle it is in the interior of the angle , but if the point is outside then is it said to be in the exterior of the angle for that triangle.
What is adjacent angle ?In mathematics, the two angles are called as adjacent angles if they have a common vertex or we can say they are angle of a common vertex in the triangle.
we can define the adjacent angle as the angles which have common side and common vertex and they don't overlap.
Exterior angle PropertyAccording to the exterior angle property, if a side of a triangle is made, then the exterior angle formed is always equals to the sum of two interior angles opposite to each other in the triangle.
Thus on the basis of exterior angle property we can make the conjecture that, "the measure of an exterior angle is equal to the sum of measures of its nonadjacent interior angles".
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9th Grade Math - Geometry
Given: B is the midpoint of AC.
C is the midpoint of BD.
Prove AB = CD
Answer in two-column proof format, please.
If B is the midpoint of AC and C is the midpoint of BD, then AB=CD.
Given that B is midpoint of AC and C is the midpoint of BD.
We are required to prove that AB is equal to CD.
Midpoint is the point which divides the line segment into two equal parts.
If B is midpoint of AC then,
2AB=AC-----1
2BC=AC-----2
If C is midpoint of BD then,
2BC=BD-----3
2CD=BD-----4
From 1 & 2
2AB=2BC
AB=BC
Put the value of BC from 3.
AB=BD/2
Now put the value of BD from 4.
AB=2CD/2
AB=CD
Hence proved
Hence if B is the midpoint of AC and C is the midpoint of BD, then AB=CD.
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Solve the equation.
100 t=70 /240
The solution of t in 100 t=70 /240 is t= 7/2400
How to solve the equation?The equation is given as
100 t=70 /240
Divide both sides of the equation by 100
So, we have
t=70 /240 * 1/100
Evaluate
t= 7/2400
Hence, the solution of t in 100 t=70 /240 is t= 7/2400
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A baby weighs 20 pounds at her four-month appointment. Six months later, she weighs 24 pounds. By what percentage did the baby's weight increase? 22% 15% 25% 20%
The weight of the baby increased by a 20%
By what percentage did the baby's weight increase?We know that the initial weight of the baby is 20 pounds, so that will be our 100%, and we can write:
20lb = 100%
Then the weight is 24 lb, so that will represent another percentage X, we can write:
24lb = X
We can solve this for X, taking the quotient between the relations:
(24lb/20lb) = X/100%
(24lb/20lb)*100% = X = 120%
So we can see that the weight of the baby increased by a 20%
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Someone please help I’ll give brainles u gotta put the steps
Answer:
All answers in explanation
Step-by-step explanation:
Step 1: Unknown
Unknown is the number of refills purchased
Step 2 Key Information
Cost of souvenir cup, price per refill and total money spent
Step 3: Strategy (equation)
Define a variable x that represents the number of refills bought
The souvenir cup cost $14.25
Each refill costs $1.25
So x refills will cost 1.25x
Total cost = 14.25 + 1.25x
We are told she spent $23
So the equation is
14.25 + 1.25x = 23
Step 4: Solution
Equation is
14.25 + 1.25x = 23
a) Isolate the x term by subtracting 14.25 on both sides
14.25 - 14.25 + 1.25x = 23 - 14.25
1.25x = 8.75
b) Divide both sides by 1.25:
1.25x/1.25 = 8.75/1.25
x = 7
Solution is 7 refills
Step 5: Check your answer
Plug x = 7 back into the left side of the equation and check if it works out to 23
14.25 + 1.25 (7) = 14.25 + 8.75 = 23
So our answer is correct
An elevator was on floor number 27 of a hotel building when a guest on a different floor pushed the button to call the elevator. Over the next few minutes the elevator traveled up 6 floors, down 11 floors, up 3 floors, up 5 floors, and then down 14 floors. Write and evaluate an expression that models the situation. On what floor did the elevator finally stop?
The elevator finally stopped on the 16th floor.
What are expressions?In mathematics, an expression is a sentence that contains at least two numbers or variables and at least one mathematical operation. This math operation can be addition, subtraction, multiplication, or division. An expression has the following structure: (Number/variable, Math Operator, Number/variable)So, the expression would be:
6x - 11x + 3x + 5x - 14x = 2714x - 25x = 27-11x = 27Now,
27 - 11 = 16Therefore, the elevator finally stopped on the 16th floor.
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If £2000 is placed into a ban account that pays 3% compound interest per year how much will be in the account after 2 years
Answer:
There is 2121.80 in the account after 2 years.
Step-by-step explanation:
Use the formula A = P(1 + r)^t where P = initial amount, A = amount after t years and r = the rate (as a decimal).
So, for this problem:
Amount after 2 years = 2000(1 + 0.03)^2
= £2121.80
The women's 400m world record is 42.60 seconds. the 16th fastest women's 400m runner ran it in 49.24 seconds. what time is exactly halfway between these two times?
The time exactly halfway between 42.60 seconds and 49.24 seconds is 45.92 seconds.
Halfway simply means the midpoint between two values. It is the distance between two values divided by two. It can also mean the average of the two values.
If the women's 400m world record is 42.60 seconds and the 16th fastest women's 400m runner ran it in 49.24 seconds, to find the exact halfway of these two records means to find the average of these two records of time. Add the two records of time and divide by two.
n = (42.60 + 49.24)/2
n = 91.84/2
n = 45.92 seconds
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explicit rule 26,18,10,2
[tex]Answer:\ a_n=34-8n[/tex]
Step-by-step explanation:
26, 18, 10, 2
18-26=-8
10-18=-8
2-10=-8
This is an arithmetic progression:
[tex]a_n=a_1+(n-1)d,\\a_1=26\ \ \ \ \ d=-8\ \ \ \ n=1,\ 2,\ 3,\ 4\\a_n=26+(n-1)(-8)\\a_n=26+(n)(-8)+(-1)(-8)\\a_n=26-8n+8\\a_n=34-8n[/tex]
The cost of playing pool increases with the amount of time using the table. Identify the independent and dependent quantity I'm the situation
A tea bag is shaped like a regular square pyramid. Each edge of the base is 4 centimeters, and the slant height is 5 centimeters. What is the surface, area of the tea bag in square centimeters? Round to the nearest tenth if necessary.
Therefore, the surface area of the tea bag is 56 cm².
The slant height of the tea bag is l.
l = 5 cm
Each edge of the base of the tea bag = 4 cm
The lateral surface area of tea is L.
The Surface area of the tea bag is S.
The perimeter of the tea bag is p.
The lateral surface of the tea bag is,
[tex]Lateral \: Surface \: Area = \frac{1}{2} \times Perimeter × Slant \: height [/tex]
[tex]L = \frac{1}{2} \times p \times l[/tex]
[tex] = \frac{1}{2} \times 16 \times 5[/tex]
= 40 cm²
The lateral surface area of the tea bag is 40 cm².
Base Area = (4) ²
= 16 cm²
The surface area of the tea bag is,
Surface Area = Lateral surface area + Base area
S= 40 + 16
= 56 cm²
Therefore, the surface area of the tea bag is 56 cm².
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If a voltage of 110 V is applied across a
load and the resulting current flow is 2.2 A,
what is the resistance of the load in Ohms
Answer:
50 ohms.
Step-by-step explanation:
Volts = current * resistance
110 = 2.2 * r
R = 110 / 2.2
= 50 ohms.
Given point B is between A and C, where AC = 27 and AB = 10, What is BC?
Answer: BC=17
Step-by-step explanation:
AC=AB+BC
27=10+BC
27-10=10-10+BC
BC=27-10
BC=17
