Therefore , the solution of the given problem of equation comes out to be Focii (-2,5 ± (2√5 x 1/√5) and vertex ( − 2,5 ± 2√√5).
Explain the equation.An equation is a mathematical representation of two identical variables, one on each side of a "equals" sign. Common difficulties can be solved using equations. We commonly seek pre algebra help to resolve problems in real life. Pre-algebra is the fundamental building block of mathematics.
Here,
[tex](x + 2)^{2}[/tex] / [tex]a^{2}[/tex] + [tex](y-5)^{2}[/tex] /[tex]b^{2}[/tex] -=1 is (h, k).
the ellipse's nucleus
The major axis is the larger of the two axes, which are 2a and 26.
(H, a, k) and (H, k, b) are the vertices. Vertices are those along the major axis in this case, and covertices are those along the minor axis.
[tex](x + 2)^{2}[/tex]/16 + [tex](y-5)^{2}[/tex] /20 =1
can be written as
[tex](x + 2)^{2}[/tex]/ [tex]4^{2}[/tex] + [tex](y-5)^{2}[/tex] /(2√/5)2
hence centre is (-2, 5), maor axis is 2 x 2√√5 = 4√√5 and minor axis
is 2 x 4 = 8
Vertices are ( 2,5 25), or ( 2,5 25) and ( 2,5 + 25), while covertices are ( 2 4, 5) and ( 6,5), respectively.
As a result of the presence of a vertical major axis, eccentricity e and focii are
(h, k ± be). e is given by the relation a2 = b2(1 − e2) i.e.
=> e = [tex]\sqrt{1 - \frac{a^{2} }{b^{2}} }[/tex]
a2= 16 and b2= 62
=> e = 1/√5
Focii (-2,5 ± (2√5 x 1/√5)
or (-2,5±2) i.e. (-2, 7) and (-2, 3).
Therefore , the solution of the given problem of equation comes out to be Focii (-2,5 ± (2√5 x 1/√5) and vertex ( − 2,5 ± 2√√5).
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Use the rule x+8 to write a sequence of numbers. Then write the sequence as a list of ordered pairs. Start with and substitute at least six values for .
Answer:
Here is a sequence of numbers using the rule "x+8":
x+8=9 (x=1)
x+8=10 (x=2)
x+8=11 (x=3)
x+8=12 (x=4)
x+8=13 (x=5)
x+8=14 (x=6)
Here is the sequence of ordered pairs:
(1, 9)
(2, 10)
(3, 11)
(4, 12)
(5, 13)
(6, 14)
find quotient 5/4 divided by 13/12
Answer: 1.15384615385
Step-by-step explanation:
divide
Anna and Sharon both construct a triangle. Anna begins by drawing a segment with a length of 3 inches. Starting from one vertex, she draws another segment with a length of 5 inches so that the two segments have an included angle of 35°. Sharon constructs her triangle by drawing a segment with a length of 5 inches, measuring a 35° angle, and drawing a ray from one vertex. Then she measures and terminates the ray at 3 inches. Do Anna and Sharon create congruent triangles? Explain.
Answer:
Yes, Anna and Sharon both created triangles that are congruent. Their triangles are congruent because they have 2 corresponding, congruent side-lengths and an included angle that is congruent. Therefore, their triangles are congruent by SAS (Side-Angle-Side).
In the algebraic expression, 6x + 10, x is the (blank), 6 is the (blank), and 10 is the (blank)?
In the algebraic expression, 6x + 10, x is the variable, 6 is the coefficient and 10 is the constant.
What are algebraic expressions?
Algebraic expressions are mathematical phrases that can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. They can be used to represent mathematical operations and relationships between numbers.
Examples of algebraic expressions include:
2x + 3 (This is an expression that represents the sum of 2 times the value of x plus 3)
A letter or symbol that denotes an unknowable value is called a variable. The variable here is represented by x.
A coefficient is a number that is multiplied by a variable in an algebraic expression. In this case, 6 is the coefficient of x.
A constant is a value that does not change in an algebraic expression. In this case, 10 is the constant.
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for a pendulum with a length of l meters, the time in seconds that it takes the pendulum to swing back and forth is 2L^1/2. how long does it take a pendulum that is 9 meters long to swing back and forth
It will take 9 seconds a pendulum that is 9 meters long to swing back and forth.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
WE are Given the expression of length L in feet of a pendulum to the time t in seconds that it takes to swing back and forth modeled as;
T = 2√L
Given
Length of the pendulum = 9 meters
Required Time (period)
Substitute the given value into the formula
T = 2√L
T = 2√9
T = 2 x 3
T = 6 seconds
Hence the period is 6 seconds
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Find the distance between the points
(-5/2, 9/4) and(-1/2,-3/4)
Give the exact distance and an approximate distance rounded to at least 2 decimal places.
Make sure to fully simplify any radicals in first answer
Answer:
Step-by-step explanation:
distance = [tex]\sqrt{(-5/2+1/2)^{2} +(9/4+3/4)^{2} }=\sqrt{13}[/tex]=3.61
Help me please 35 points on the line
Answer shown in bold
401924109147The non-bolded values to the left are not to be typed in the answer box. They're present to keep track of the values. In other words, you'll type "40" without quotes into the first box, then "19" without quotes in the second box, and so on.
========================================================
Explanations:
Add up all of the values in the Venn diagram to find the total. Therefore, 9+10+14+7 = 40 students were surveyed.We add the values in the "social interaction activities" circle only. There are 9+10 = 19 students here.This time add up the values in the "technology driven activities" to get 10+14 = 24 students.The answer is 10 because this value is in the overlapped region between the two circles. The answer is 9 since this value is in the "social interaction activities" circle, but outside the other circle. The answer is 14 as this value is in the "technology driven activities" circle, but outside the other circle.The answer is 7 because this value is outside both circles.Let me know if you have any questions.
type an (x,y) ordered pair to put a point on this line.
The ordered pair (x, y) for the given line can be obtained from the graph as (-4, 1).
What is the equation for a straight line?A straight line can be written in the form of an equation as, y = mx + c.
Two straight lines intersect each other only at one point.
When two straight lines are parallel to each other the angle between them is zero.
The graph of the line is given.
In order to find the coordinate of a point do as follows,
Draw a perpendicular line from any point on the line to the x-axis.
The intersection of this line with the x-axis will give the x-coordinate.
Similarly, find the y-coordinate by drawing a perpendicular line to the y-axis.
Applying the above procedure, a point is obtained as (-4, 1).
Hence, the ordered pair for the line shown in the graph is (-4, 1).
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(2,1)
H
-8-6-4-2
(6,-3)
948
6+Q
4
y
·N··
2+
-2-
-6-
-8
P
2
4 6
R
8
What is the image of R for a dilation with center (0, 0) and a scale factor of
2
X
Answer: free allah long live
Step-by-step explanation:
46564
Find the LCM of the first five primes
Answer:
The first 5 prime numbers are 2, 3, 5, 7 and 11. Their LCM is 2310
What the answer to this 9 - 3y +3y =4
Answer:
its the answer
Step-by-step explanation:
the answer to the question is the answer
hehe
How do logarithmic functions model real-world problems and their solutions? Give a specific example and explain.
The process of logarithmic functions in real-worlds problems is given below.
And an example of an application of logarithmic function is given.
What is Logarithmic?The inverse of exponentiation is the logarithm. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b.
We know,
logarithmic function and exponential function are inverse of each other.
So, whenever we solve the exponential function,
we use the help of logarithmic functions.
To compute the number with bigger exponents,
we use the logarithms.
Because it reduces the size of the numbers.
Let the bacteria is growing exponentially,
b = 2ⁿ.
We know that the bacteria grows every hour.
We want to find time.
Here, we will use the inverse function to the exponential function.
How long will it take them to get 1000 bacteria?
1000 = 2ⁿ
Taking log on both sides,
log(1000) = n log2
n = log(1000)/log(2)
n = 9.96
n ≈ 10 hours.
Therefore, an application of logarithmic function is given above.
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19x+4 find the value of x
Answer:
x= -4/19
Step-by-step explanation:
19x+4
19x+4=0
19x= - 4
x= -4/19
On Saturday, a local hamburger shop sold a combined total of 396 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Saturday?
Let x be the number of hamburgers sold, then the number of cheeseburgers sold can be represented as 2x. The total number of hamburgers and cheeseburgers sold is the sum of these two quantities, so we can write an equation:
x + 2x = 396
To solve for x, we can combine like terms on the left side of the equation:
3x = 396
Then we can divide both sides by 3 to get:
x = 132
So, the number of hamburgers sold on Saturday is 132.
Toni runs around her school's baseball diamond. Each side is 27 m long. Note: A baseball diamond is square. How far does Toni run? m
Answer:
If we assume she runs around it once and since they tell us its a square: 27x4=108
Step-by-step explanation:
2. Avea checked out 18 books
from the library. Half of them
are nonfiction. How many
nonfiction books did she check
out?
Answer: she checked out 9 nonfiction books
Step-by-step explanation:
18-9=9
12 divided by four
plus 2 x 6+4
Answer:
19
Step-by-step explanation:
12 divided by four plus 2 x 6+4
assuming that the question is:
12 : 4 + 2 x 6 + 4 =
3 + 12 + 4 = (remember PEMDAS)
19
Help PLEASE IN A RUSH!
Which graph represents this system?
y = 3. x + y = 4.
On a coordinate plane, a horizontal line is at y = 3 and another line goes through (0, 4) and (4, 0).
On a coordinate plane, a vertical line is at x = 3 and another line goes through (0, 4) and (4, 0).
On a coordinate plane, a horizontal line is at y = 3 and another line goes through (0, 4) and (2, 6).
On a coordinate plane, a vertical line is at x = 3 and another line goes through (0, 4) and (3, 7).
Answer:
first option
Step-by-step explanation:
y = 3 is a horizontal line parallel to the x- axis and passing through all points with a y- coordinate of 3
x + y = 4 ← is the equation of a straight line
find the x and y- intercepts
to find the y- intercept let x = 0 in the equation and solve for y
0 + y = 4 , that is
y = 4 ⇒ (0, 4 ) is a point on line
to find the x- intercept let y = 0 in the equation and solve for x
x + 0 = 4 , that is
x = 4 ⇒ (4, 0 ) is a point on the line
the graph representing the system is
a horizontal line y = 3 and another line passing through (0, 4 ) and (4, 0 )
Find the difference between Mary's weight when she was 10 year's old and when she was born
The difference between Mary's weight when she was 10 year's old and when she was born will be;
⇒ 72 pounds
What is mean by Subtraction?Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
Given that;
When Mary was born, she weighed 8 pounds.
And, When she was 10 years old, she weighed 10 times as much.
Now,
Since, When she was 10 years old, she weighed 10 times as much.
Hence, When she was 10 years old, she weighed = 10 × 8 pounds
= 80 pounds
And, When Mary was born, she weighed 8 pounds.
Thus, The difference between Mary's weight when she was 10 year's old and when she was born is,
⇒ 80 - 8 pounds
⇒ 72 pounds
So, The difference between Mary's weight when she was 10 year's old and when she was born is 72 pounds.
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The complete question is this,
When Mary was born, she weighed 8 pounds. When she was 10 years old, she weighed 10 times as much. How much more did Mary weigh when she was 10 years old than she was born?
Does the table below represent a proportional relationship?
A. Yes, because all the ratios of y to x are equal to 2.
B. Yes, because all the ratios of y to x are equal to 3.
C. No, because all the ratios of y to x are not equal.
D. No, because all the numbers are positive.
The table represents a proportional relationship because all the ratios of y to x are equal to 3. (option B)
What is a proportional relationship?Two variables exhibit a proportional relationship if the constant of proportionality remains constant for all the given values in the table.
The equation that is used to represent a proportional relationship is:
y = kx
Where:
k = constant of proportionality
Value of k when x is 1:
3 = k
Value of k when x is 2:
6 = 2k
k = 6 / 2
k = 3
Value of k when x is 3:
9 = 3k
k = 9 / 3
k = 3
Value of k when x is 4:
12 = 4k
k = 12 / 4
k = 3
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A parade traveled 8 miles in 4 hours. How far did the parade travel per minute?
Answer:
1/30 of a mile per minute.
Step-by-step explanation:
8/4 = 2 miles per hour.
2/60 = 1/30 of a mile per minute.
A triangle has sides with lengths 8, 15, and 17. approximate the acute angles in this triangle to the nearest degree and list in ascending order
Answer:
28°, 62°
Step-by-step explanation:
As 8,15,17 is a Pythagorean Triple, the triangle must be a right triangle. Hence, we can use our common trig ratios to solve the problem. Let's assume our right triangle has a base of 8, a height of 15, and a hypotenuse of 17.
Here are all the acute angles in order:
[tex]\cos^{-1}(\frac{15}{17})\approx28^\circ[/tex]
[tex]\sin^{-1}(\frac{15}{17})\approx62^\circ[/tex]
Write the following expression in expanded form:9 to power of 3× 7to the power of 4
Exponential Expressions into Expanded Form into Answer:
[tex]9^{3}[/tex] = 9⋅9⋅9 = 729
[tex]7^{4}[/tex] = 7⋅7⋅7⋅7 = 2401
I hope this helps, have a good day!
Answer:
= 9⋅9⋅9 = 729
= 7⋅7⋅7⋅7 = 2401
Step-by-step explanation:
(Pythagorean Theorem and the Coordinate Plane MC)
Determine the perimeter of the right triangle shown
O 10 units
O 24 units
O 36 units
O 64 units
Answer:
A
Step-by-step explanation:
refer the sketch for step by step answer
Which of these systems of equations has infinitely many solutions? Explain your choice(s).
a. (1/2)x - 5y = 10
(-1/2)x + 5y = -10
b. 7x + 2y = -14
-7x + 2y = -14
c. x + 6y = -18
x - 6y = 18
d. (3/4)x - 9y = 12
(-3/4)x + 9y = 12
Find the volume of the given solid. Bounded by the cylinder y^2+z^2=4 and the planes x=2y, x=0, z=0 in the first octant
The volume of the given solid. Bounded by the cylinder y^2+z^2=4 and the planes x=2y, x=0, z=0 in the first octant is 16/3 unit cute
V = ∫ dV
= ∫0→2 ∫ 0→π/2 ∫ 0→ 2·r·sin(φ) [ r ] dzdφdr
Factorize to have
= ∫0→2 ∫ 0→π/2 [ r·2·r·sin(φ) - r·0 ] dφdr
= ∫0→2 ∫ 0→π/2 [ 2·r²·sin(φ) ] dφdr
= ∫0→2 [ -2·r²·cos(π/2) + 2·r²·cos(0) ] dr
= ∫0→2 [ 2·r² ] dr
= (2/3)·2³ - (2/3)·0³
Conclusively, this implies that the volume is = 16/3
In conclusion, the volume of the given solid is 16/3. cubic units
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Solve for -10 - 9/2 x <80
Answer:
X > -20
Step-by-step explanation:
-10 - 9/2 x < 80
Move 10 to the other side
- 9/2 x < 80 + 10
Simplify
-9/2 x < 90
-9 x < 180
x > -20
(We switch the inequality sign if we are dividing with negatives)
Hot dogs and corndogs were sold at last night's football game. A total of 81 were sold which allowed the concession stand to bring in $201. How many of each were sold?
The total number of corn dogs sold is 28 corn dogs and number of hotdogs is 53
What is total cost?Total cost is the overall expense incurred for a particular product, service, or project. It includes both fixed and variable costs, such as materials, labor, and overhead. It is often used in business and economic analysis as a measure of the efficiency and profitability of a particular venture. The total cost of a product or service can also be used to set prices and make pricing decisions.
According to question:-
step1
h = number of hotdogs
c = number of corndogs.
cost of hotdog = $3
corn dog = $1.50
The equation:
3h + 1.50c = 201 (1)
h = 2c - 3 (2)
step2
substitute (2) into (1)
3(2c - 3) + 1.50c = 201
6c - 9 + 1.50c = 201
7.50c - 9 = 201
7.50c = 201 + 9
7.50c = 210
c = 210/7.50
c = 28
Therefore,
h = 2c - 3
= 2(28) - 3
= 56 - 3
= 53
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List five vectors in Span (V₁ V₂). Do not make a sketch.
V₁ = (8 2 7 )
V₂ = (-6 4 0 )
List five vectors in Span (V₁ V₂).
(Use the matrix template in the math palette. Use a comma to separate vectors as needed. Type an integer or a simplified fraction for each vector element.)
Five vectors in Span (V₁ V₂) where V₁ = (8 2 7 ) and V₂ = (-6 4 0 ) is.
n(V₁ + V₂), n ∈ I, I = 1, 2, 3, 4, 5.
What is span in vector space?In mathematics, the set of all linear combinations of the vectors in S is referred to as the linear span, Denoted span(S), Either the intersection of all linear subspaces containing S, or the smallest subspace containing S, can be used to describe it. A vector space is therefore nothing more than the linear range of a set of vectors.
The vectors that are in the same span should be a multiple of the vectors
V₁ = (8 2 7 ), V₂ = (-6 4 0 )
Now, V₁ + V₂ = (2 6 7).
So, The five vectors in the span of V₁ and V₂ is,
2×(2 6 7).
= (4 12 14).
- 2×(2 6 7).
= (- 4 - 12 - 14).
3×(2 6 7).
= (6 18 21)
- 3×(2 6 7)
= (- 6 - 18 - 21).
5×(2 6 7).
= (10 30 35).
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5.7935 rounded to the nearest thousand
Answer:
5.794
Step-by-step explanation:
The seven after the decimal point is the tenth digit, the nine is the hundredth, and the 3 is the thousandth place. Therefore, we look at our neighbor (the number next to the thousandth place) and if its 5 or more we round up, but if its 4 or less we keep it the same.