The equation of the hyperbola is -(1/16) (x +4)² + (1/4) (y +2)² = 1
What is Hyperbola?
A hyperbola is a particular kind of smooth curve that lies in a plane and is classified by its geometric characteristics or by equations for which it is the solution set. A hyperbola is made up of two mirror images of one another that resemble two infinite bows. These two sections are known as connected components or branches.
The intersection of the two asymptotes is where the hyperbola's center is located. This is the key idea (-4,-2)
We have y orientation because the vertex at (-4,0) is above this location. The equation will take the form as a result.
-a (x + 4)
2 + b (y + 2)
In the case of certain a and b, 2 Equals 1.
Inputting (-4,0) reveals that b = 1/4.
Finally, requiring that y = x/2 be an asymptote reveals that a = 1/16.
-(1/16) (x +4)² + (1/4) (y +2)² = 1
Hence, The equation of hyperbola is -(1/16) (x +4)² + (1/4) (y +2)² = 1
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Supergym is a national chain of gyms. This year, its employees sold 10,412 gym memberships, which turns out to be 52% more than they sold last year. How many memberships did they sell last year?
The supergym sold 15,826.24 membership last year
How to calculate the number of membership sold ?
This year it's employees sold 10,412
This number is 52% more that they sold last year
The first step is to calculate 52% of 10,412
52/100 × 10,412
= 0.52 × 10412
= 5,414.24
The number of membership sold this year can be calculated as follows
= 5414.24 + 10,412
= 15,826.24
Hence the number of membership they sold last year is 15,826.24
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Hakeem is starting a running plan to train
for a race. In the first week of his running
plan, Hakeem will run 11 miles. The plan
calls for Hakeem to increase his weekly
milage by 2 miles every week. If Hakeem
sticks to the plan, how many miles would
he be expected to run during his 8th week
of the training plan?
Answer:
25 miles
Step-by-step explanation:
Hakeem is starting a running plan to train for a race. In the first week of his running plan, Hakeem will run 11 miles. The plan calls for Hakeem to increase his weekly milage by 2 miles every week. If Hakeem sticks to the plan, how many miles would he be expected to run during his 8th week of the training plan?
This can be described as:
11 + 2w
when w = week
because he runs 11 miles the first week, he only has 7 weeks of 2 mile increases:
11 + 2(7) = 25 miles
The probability of rolling a six on a bias dice
is 1/5
Work out the probability of rolling exactly
one six
The probability of rolling exactly one six = 0.04
what is probability ?
Probability is a branch of mathematics that deals with the occurrence from of a random event . the value is expressed from zero to one .Probability has been introduced in mathematics to predict how likely events are to happen .
So , acc the question "exactly one six " means that one roll so that probability must be doubled the probability of " not six " is 4/5 . the probability of a 6 on the roll and not on the second is 1/5 x 4/5 =4/ 25 .
The six could come on the second roll so thst probability must be doubled .
the overall probability of exactly one six 8/25 or 0.32
completing toatl probability -no sixes =4/25 x 4/25 =16/25 =0.04
two sixes =1/5x 1/5 =1/25= 0.04
Hence , the probability of rolling exactly one six = 0.04
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B.10 Midpoint formula: find the midpoint 2YG
A line segment has the endpoints U(19, 6) and V(17, -3). Find the coordinates of its midpoint
M.
Write the coordinates as decimals or integers.
M =
Submit
Work it out
Please help
Answer:
Midpoint formula is given as [(x1+x2)÷2, (y1+y2)÷2], where x and y are coordinates of the points.
Midpoint = [(19+17)÷2, (6+(-3))÷2]
= (36÷2, 3÷2)
= (18, 1.5)
Whats this answer?? I need it
Please help immediately!!
Question 2 (10 points)
Answer:
125.
Step-by-step explanation:
5^3
= 5 * 5 * 5
= 25 * 5
= 125.
A rectangle with a width of x feet and height of StartFraction 7 over 2 EndFraction feet.
Jack is building a rectangular fence for his ferret. He has 20 feet of fencing and wants the short side of the fence to be 7
2
feet. How long will the other side of the fence be? Write the answer in decimal form.
The long side will be
feet.
The other side of the fence based on the information illustrated is 6.5 feet.
How to calculate the length?It should be noted that the perimeter of a rectangle is illustrated as:
= 2(length + width)
In this case, the width is given as 7/2 = 3.5 feet.
It should be noted that the perimeter is given as 20 feet.
Therefore, the length will be:
2(length + width) = 30
2(length + 3.5) = 20
2Length + 7 = 20
2L = 20 - 7
2L = 13
L = 13/2
L = 6.5
Therefore, the length is 6.5 feet.
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"I NEED HELP PLS" The following figure is made of 1 triangle and 2 rectangles.
Find the area of each part of the figure and the whole figure.
Figure Area (square units)
Rectangle A
Triangle B
Rectangle C
Whole figure
The value of the area are;
Rectangle A = 54 square units
Triangle B = 2 square units
Rectangle C = 6 square units
Whole figure = 62 square units
How to determine the area of the composite figureThe formula for determining the area of a rectangle is expressed as;
Area = lw
Where;
l is the length of the rectanglew is the width of the rectangleFrom the figure shown, we have two rectangles
Area of the bigger rectangle;
Length = 9
Width = 6
Now, substitute the value
Area = 9(6)
Multiply through
Area = 54 square units
Area of the smaller rectangle
Length = 9 - 7 = 2
Width = 9 - 6 = 3
Substitute the values
Area = 2(3)
Multiply through
Area = 6square units
The formula for area of a triangle is expressed as;
Area = 1/2 base× height
Base = 9 - 6 = 3
Height = 9 - 2 = 3
Substitute the value
Area = 1/ 2 ×2(3)
Area = 6/ 3
Area = 2
The total area = Rectangle A + rectangle B + Triangle
Total area = 54 + 6 + 2
Total area = 62 square units
Hence, the area is 62square units
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Answer:
A=54 B=3 Whole=73
Step-by-step explanation:
I know this because i did this aswell
10^-3 x 10^6
please write in the form of powers/ index notation (for example, 7^5 or 10^-4)
It should be noted that 10^-3 × 10^6 in scientific notation is 10³.
How to illustrate the information?It should be noted that scientific notation is simply used in Mathematics to express the numbers that are either too small or too large.
This will be illustrated based on the information given. In this case, we want to multiply 10^-3 × 10^6. This will be illustrated thus:
= 10^-3 × 10^6.
It should be noted that since the question is about multiplication, the powers will be added.
= 10^-3 × 10^6.
= 10³
The answer is 10³.
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What is the value of z in the system shown below?
x+y+z=6
x + 2y = 5
2x+z = 5
========================================================
Explanation:
I'll use the substitution method to solve this system of equations.
Solve the third equation for z
2x+z = 5
z = 5-2x
Then solve the second equation for y
x+2y = 5
2y = 5-x
y = (5-x)/2
y = -0.5x+2.5
Plug each of these into the first equation so we can solve for x.
x+y+z = 6
x+(-0.5x+2.5)+(5-2x) = 6
-1.5x+7.5 = 6
-1.5x = 6-7.5
-1.5x = -1.5
x = (-1.5)/(-1.5)
x = 1
Let's use this to find y and z
y = -0.5x+2.5 = -0.5*1+2.5 = 2
z = 5-2x = 5-2*1 = 3
Therefore,
x = 1
y = 2
z = 3
Or we can write it like this: (x,y,z) = (1,2,3)
-------------------
Check:
Plug these values into equation 1 and simplify
x+y+z = 6
1+2+3 = 6
6 = 6
We get the same thing on both sides.
This confirms equation 1.
Repeat for equation 2.
x+2y = 5
1+2*2 = 5
1+4 = 5
5 = 5
This confirms equation 2.
Lastly, plug those values into equation 3
2x+z = 5
2*1+3 = 5
2+3 = 5
5 = 5
Equation 3 is confirmed.
All three equations are true when (x,y,z) = (1,2,3). The solution is fully confirmed.
omsomfigure2.52base a 20 cmfigure B:ta20 cm5 pmfigure.boromomsomfigure D:tasarea 2018.paretAmong these figures, gureand figurehave the same volume
We will compute the volume of each figure.
1) Figure A
We have a cone with:
• Ab = base area = 20 cm²,
,• h = heigh = 5 cm.
The volume of the cone is:
[tex]V_A=\frac{1}{3}\cdot A_b\cdot h=\frac{1}{3}\cdot(20cm^2)\cdot5\operatorname{cm}\cong33.3cm^3\text{.}[/tex]2) Figure B
We have a cylinder with:
• Ab = base area = 20 cm²,
,• h = heigh = 6 cm.
The volume of the cylinder is:
[tex]V_B=A_b\cdot h=20cm^2\cdot6\operatorname{cm}=120cm^3.[/tex]3) Figure C
We have an inclined cylinder with:
• Ab = base area = 20 cm²,
,• h = heigh = 5 cm.
The volume of the inclined cylinder is:
[tex]V_C=A_b\cdot h=20cm^2\cdot5\operatorname{cm}=100cm^3.[/tex]4) Figure D
We have a parallelepiped with:
• Ab = base area = 20 cm²,
,• h = heigh = 5 cm.
The volume of the parallelepiped is:
[tex]V_D=A_b\cdot h=20cm^2\cdot5\operatorname{cm}=100cm^3.[/tex]5) Figure E
We have an inclined square pyramid with:
• Ab = base area = 20 cm²,
,• h = heigh = 10 cm.
The volume of the square pyramid is:
[tex]V_E=\frac{1}{3}\cdot A_b\cdot h=\frac{1}{3}\cdot(20cm^2)\cdot10\operatorname{cm}\cong66.67cm^3\text{.}[/tex]Answer
Among these figures, figure C and figure D have the same volume.
How do you fully factorise 15p^2+24p
Given that 2 = 6.
Which theorem proves that line d is parallel to line e.
Converse of the alternate exterior angle
theorem
Converse of the alternate interior angle
theorem
Alternate Exterior angle theorem
Alternate interior angle theorem
The theorem that proves that lines d and e are parallel is the: A. converse of the alternate exterior angles theorem.
What is the Converse of the Alternate Exterior Angles Theorem?The alternate exterior angles that are formed on each lines that are cross by the transversal are said to be congruent or equal to each other if both lines they lie on are parallel, based on the alternate exterior angles theorem.
Also, we can prove that if the alternate exterior angles are congruent, then the lines they lie on are parallel lines, using the converse of the alternate exterior angles theorem.
Thus, we are given that angle 2 = angle 6. Angles 2 and 6 lie on lines d and e. Since they are equal to each other, they are congruent angles. Therefore, lines d and e are parallel lines based on the converse of the alternate exterior angles theorem.
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will the bakery have enough time to bake 5 batches of bagels
can't understand Ur question nicely
how do you know if shapes are congruent
Answer:
Congruent shapes are shapes that are exactly the same. The corresponding sides are the same and the corresponding angles are the same.
Answer: Congruent mean same/equal
Step-by-step explanation: So if the have the same height,width, radius,or even angles, they can be congruent.
mom walks at a speed of 6 miles per hour. how long will it take her to walk 1 mile?
$1,500 for 1,080 square feet of carpet
When the price is $1,500 for 1,080 square feet of carpet, the price per square feet is $1.389.
How to illustrate the information?It should be noted that from the information, it was stated that the price is $1,500 for 1,080 square feet of carpet.
In this case, it should be noted that the price per square feet will be:
= Total amount / Number of square feet
= $1500 / 1080
= $1.389 per square feet.
Therefore, the price is $1.389.
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$1,500 for 1,080 square feet of carpet. Find the. price per square feet
What are the rules for the order of calculations/operations in an expression?
Answer:
Parentheses, Exponents, Multiplication, Division, Addition, Subtraction
PEMDAS
multiplication and division are on the same level, when you see both work from left to right
addition and subtraction are also on the same leve, work from left to Right
P > E > M = D > A = S
Answer:
p e m d a s
Step-by-step explanation:
I hope it's helpful for you
PLEASE, PLEASE HELP WILL GIVE BRAIBNLIEST PLEASE HELP!!! QUESTION IN THE IMAGE BELOW.
Answer:
25/6
Step-by-step explanation:
We determine the scale factor by comparing the lengths of corresponding sides of the square.
The length of O’N’=15 and the length of ¯¯¯¯¯¯¯¯¯¯¯ON=9
The equation for the scale factor, k is then given by:
O’N’=kON
15=9k
K= 15/9= 5/3.
The scale factor is k= 5/3
How many square feet of outdoor carpet will
we need for this hole?
Hey you man what are you doing here go to there
find the slope of the line that passes through ( 7,1 ) and (10,3)
simplify your answer and write it as a proper fraction. improper fraction, or integer.
Answer:
2/3
Step-by-step explanation:
The formula for the slope is:
[tex]\frac{y2-y1}{x2-x1}[/tex]
Plug in (7,1) and (10, 3):
[tex]\frac{3-1}{10-7} = 2/3[/tex]
What is the slope of the line represented by the equation y = 4/5x -3?
Answer: 4/5
Step-by-step explanation:
y = mx + b
m represents the slope in this line.
Answer:
4/5
Step-by-step explanation:
Equation is in slope intercept form:
[tex]y = mx + b[/tex]
where m is the slope and b us the y-intercept
so, slope is 4/5
Drawn to scale
find the area of the figure
Check the picture below.
[tex]\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ a=8\\ b=12\\ h=7 \end{cases}\implies A=\cfrac{7(8+12)}{2}\implies A=70[/tex]
Tessa has a coin jar full of dimes and pennies. When she took the coin jar to the bank, she was told that it contained exactly $27.34. Give three different combinations of the number of dimes and pennies that could have been in the coin jar.
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Find the probability that at most 2 heads occured when 5 fair coins are tossed
Answer:
Five coins are tossed the probability of getting two heads is 5/16.
Step-by-step explanation:
I hope it will be helpful for you.
how do I find the correct answer for the blank?
Consider a rectangular prism with a volume of 24 cubic centimeters. What could be the dimensions of the rectangular prism? Match each set of length and width with the correct height to complete the possible dimensions of rectangular prisms with volumes of 24 cubic centimeters. Prism M Length = 4 cm Width = 1 cm Prism W Length = 2 cm Width = 2 cm Prism Z Length = 6 cm Width = 1 cm Prism J Length = 2 cm Width = 4 cm Prism R Length = 2 cm Width = 3 cm Prism F Length = 1 cm Width = 8 cm
The dimensions of the rectangular prisms are:
Prism M: l=4 cm , w=1 cm and h=6 cm
Prism W: l=2 cm , w=2 cm and h=6 cm
Prism Z: l=6 cm , w=1 cm and h=4 cm
Prism J: l=2 cm , w=4 cm and h=3 cm
Prism R: l=2 cm , w=3 cm and h=4 cm
Prism F: l=1 cm , w=8 cm and h=3 cm
Given, a rectangular prism with a volume of 24 cm³
Dimensions of the prism if the volume is 24 cm³.
Prism M:
l=4 cm and w=1 cm
we know that volume = h×l×w
h×4×1=24
4h=24
h=24/4
h=6 cm
Prism W:
l=4 cm and w=2 cm
we know that volume = h×l×w
h×2×2=24
4h=24
h=24/4
h=6 cm
Prism Z:
l=4 cm and w=1 cm
we know that volume = h×l×w
h×6×1=24
6h=24
h=24/6
h=4 cm
Prism J:
l=2 cm and w=4 cm
we know that volume = h×l×w
h×2×4=24
8h=24
h=24/8
h=3 cm
Prism R:
l=2 cm and w=3 cm
we know that volume = h×l×w
h×2×3=24
6h=24
h=24/6
h=4 cm
Prism F:
l=1 cm and w=8 cm
we know that volume = h×l×w
h×1×8=24
8h=24
h=24/8
h=3 cm
hence we get the required dimensions.
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Mason and his children went into a movie theater and he bought $36.50
worth of candies and pretzels. Each candy costs $4.25 and each pretzel costs
$3.50. He bought 6 more pretzels than candies. Write a system of equations
that could be used to determine the number of candies and the number of
pretzels that Mason bought. Define the variables that you use to write the
system.
Answer:
Let C=the number of candies (because the first variable starts with c)
Let p= the number of pretzels (because the second variable starts with p)
SYSTEM OF EQUATIONS:
4.25c+3.50p=36.50 (first variable number + 2nd variable number equals total amount
p=c+6 (we know we have 6 more pretzels than candies to we have to add candies(c)+6 how many more pretzels than candy we have to find pretzels total number.
Write the equation of the line that goes through the point (3,-3) and has a slope of -5/3 (in slope intercept form).
The equation of the line that goes through the point (3,-3) and has a slope of -5/3 is y=(-5x+6)/3.
What is a slope?In mathematics, line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. The letter m is frequently used to represent a slope; reason for this is unclear, although it is first used in English by O'Brien in 1844, who wrote the equation for a straight line as "y = mx + b," and by Todhunter in 1888, who wrote it as "y = mx + c."
The ratio of "vertical change" to "horizontal change" between (any) two unique points on a line is used to compute slope. The ratio can also be written as quotient ("rise over run"), which produces same number for every two distinct points on the same line. A declining line has negative "rise." The line might be useful, as determined by road surveyor, or it might appear in a diagram that represents a road or a roof as a description or a design.
The slope's absolute value serves as a gauge for line's steepness, incline, or grade. A steeper line is indicated by slope with a higher absolute value. A line can be drawn with one of four directions: upward, downward, horizontal, or vertical.
if we let y = mx + b, where m is the slope and b is the intercept, and y - y1 = m (x - x1), then:
3(y + 3) = - 5 (X - (-3))
3y + 9 = - 5 X + 15
3y = -5 X + 6
y=(-5x+6)/3
Check:
When x = 3, y should equal - 3, so:
Y = (- 5 (3) + 6)/3 = -3
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