Answer:
Step-by-step explanation:
The general formula for a horizontal hyperbola :
[tex]\frac{x^{2} }{a^{2} } -\frac{y^{2} }{b^{2} } =1[/tex]
Given: a = 1 we know a² = 1 ,and that c = 9 so we know c² = 9² = 81
We also know that the relation between a, b, c for a hyperbola is c²= a²+b²
c²= a²+b², substitute what we know
81 = 1 +b², subtract 1 from both sides of the equation
80 = b²
The equation of our hyperbola is:
[tex]\frac{x^{2} }{1 } -\frac{y^{2} }{80 } =1[/tex] or [tex]x^{2} -\frac{y^{2} }{80} =1[/tex]
9
Emily drives 186 miles in 3 hours.
(a) What is her average speed?
Answer:
Her average speed would be 62 mph.
Step-by-step explanation:
Step 1. Do 186 divided by 3
Step 2. The answer you would get is 62
Step 3. Label to get 62 miles per hour (mph)
I hope that this helps! :)
Step-by-step explanation:
Displacement = 186 miles
Time taken = 3hours
Average speed = ?
Now,
[tex]average \: speed = \frac{total \: distnce}{total \: time \: } \\ = \frac{186}{3} \\ [/tex]
= 62 miles per hour
How do I find the difference in the simplest form?
Answer:
2
Step-by-step explanation:
[tex] \frac{8x}{4x - 7} - \frac{14}{4x - 7} \\ \\ = \frac{8x - 14}{4x - 7} \\ \\ = \frac{2 \cancel{(4x - 7)}}{\cancel{(4x - 7)}} \\ \\ = 2[/tex]
Solve: 101x-99y=103
-99x+101y=-97
Answer:
[tex]x=2; y=1[/tex]
Step-by-step explanation:
Let's remember that if we replace one equation in a system with a linear combination of the equations (ie adding or subtracting them together, after multiplying them with some nice numbers) we are left with an equivalent system. So let's add and subtract them together, and use the new equations to work with.
[tex]I+II: 2x+2y=6\\I-II:200x-200y=200[/tex]
Better, now let's simplify the expression and let's use the new system
[tex]x+y=3\\x-y=1[/tex]
Done. At this point you can use whatever method you like to solve the system to get to the final solution. Adding and subtracting works great, and you get [tex]x=2, y=1[/tex] which, if you check by replacing in the original, is indeed a valid solution.
After plotting the data where x=the side of a polygon, and f(x) = the area of the polygon, Jack used technology and
determined the appropriate model to approximate the area of the polygon, F(x) = x^2 + 3x + 2. Use the model Jack
created to predict the area of a polygon that has a side length of 3.
10
18
19
020
Answer: 19
Step-by-step explanation:
As per the model created by Jack; f(x) determines the area and x represents length so f(3) = 9+9+1
Therefore, f(3) = 19
Problem 1: Verify whether these two functions are inverses: (x + 5) f(x) = (2x + 1) and g(x) = (5 - x) (2x - 1) What is g(x))? Use your keyboard and the keypad to enter your answer. Then click Done
g(f(x)) = x
What is inverse function?
An inverse function is defined as a function, which can reverse into another function.
[tex]f(x)= \frac{(x + 5)}{(2x + 1)}[/tex]
[tex]g(x)= \frac{(5 - x)}{(2x - 1)}[/tex]
[tex]g(f(x))=g( \frac{(x+5)}{(2x +1)})[/tex]
Substitute the value of f(x),
[tex]g(f(x))= \frac{(5 - \frac{(x + 5)}{(2x + 1)})}{(2 \frac{(x + 5)}{(2x + 1)} - 1)}[/tex]
[tex]g(f(x))= \frac{\frac{10x+5-x-5}{2x+1} }{ \frac{2x+10-2x-1}{2x+1}}[/tex]
[tex]g(f(x)) = \frac{9x}{9}[/tex]
g(f(x)) = x
Hence, g(f(x)) = x
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Solve by completing the square:
x2 + 2x-8= 0
-8
a.
x = -4 or 2
b. X= 4 or 2
-
=
c.
x= -4 or - 2
d. X= 4 or - 2
x
Find MQ in parallelogram LMNQ .
Answer:
MQ = 16.4
By the Parallelogram Diagonals Theorem , MP = PQ
So MQ = 2 · MP
Step-by-step explanation:
Parallelogram Diagonals Theorem
The diagonals of a parallelogram bisect each other, i.e. they divide each other into two equal parts.
P is the point of intersection of the diagonals.
Therefore, MP = PQ and LP = PN
If MP = 8.2, then PQ = 8.2
⇒ MQ = 8.2 + 8.2 = 16.4
Need help with math probelm if do 5 stars and brainly points
Set up:-
Find volume of closet storageFind volume of each cubeDivide and get no of cubesSolution:-
Here it's a cuboid
Length=L=6.5ftBreadth=B=4ftHeight=H=12.5ftVolume:-
[tex]\\ \rm\rightarrowtail V=LBH[/tex]
[tex]\\ \rm\rightarrowtail V=6.5(4)(12.5)[/tex]
[tex]\\ \rm\rightarrowtail V=325ft^3[/tex]
For cubes
sides=0.25ftVolume:-
[tex]\\ \rm\rightarrowtail V=side^3[/tex]
[tex]\\ \rm\rightarrowtail V=(0.25)^3[/tex]
[tex]\\ \rm\rightarrowtail V=0.015625ft^3[/tex]
Now
Total cubes:-
[tex]\\ \rm\rightarrowtail \dfrac{325}{0.015625}[/tex]
[tex]\\ \rm\rightarrowtail 20800cubes[/tex]
hey guys can you please help me with these questions please explained them
B for question 12
B for question 13
Step-by-step explanation:
U = Union
n= intercestion
B'= not b
A"= not a
so AnB'
should be B
if 2.50 = 1
2.50x8=
20
1×8 =
8
should be $8
The accompanying diagram show a cross-section of a rectangular pyramid. The cross sectional area is 36in and is 3 inches from the vertex of the pyramid. If the height of the pyramid is 5 inches, what is the area of the rectangular base?
The area of the rectangular base is the amount of space on the rectangular base
The area of the rectangular base is 60 square inches
How to determine the area of the rectangular base?The question is incomplete; as the diagram is not given.
So, I will apply the concept of similar shapes to determine the area of the rectangular base
To determine the area of the rectangular base, we make use of the following equivalent ratio:
Ratio = Height : Area
This gives
3 : 36 = 5 : Area
Express as fraction
36/3 = Area/5
Evaluate the quotient
12 = Area/5
Multiply both sides by 5
Area = 60
Hence, the area of the rectangular base is 60 square inches
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Martina is ordering an ice cream dessert. She must order a size and a flavor of ice cream. There are 4 sizes and 2 flavors to choose from. How many different
cream desserts could she order?
Answer: 8.
Step-by-step explanation: There are 4 sizes, so let's say that the sizes are small, medium, large, and extra large. There are 2 flavors, so let's say that the flavors are chocolate and vanilla. The possible combinations are below:
Small chocolateMedium chocolateLarge chocolateExtra large chocolateSmall vanillaMedium vanillaLarge vanillaExtra large vanillaAs you can see, there are 8 possible combinations that she can choose from as far as 4 sizes and 2 flavors go.
Have a great day! :)
2. Find the length of AD if the length of AB is 14 units, the length of BC is 5 units, and the length of CD is 8 units,
Answer: sqrt(285)
Step-by-step explanation:
Peter is buying a circular rug for his bedroom. The rug has an area of 40 square feet. What is the approximate diameter of the rug? Show your work or explain your answer.
The approximate diameter of the rug with an area of 40 ft² is 7.14 feet.
What is area?Area is the amount of space occupied by a two dimensional shape or object.
The area of a circle is given by:
Area = π * diameter²/4
The rug has an area of 40 square feet. Hence:
40 = π * diameter²/4
Diameter = 7.14 feet
The approximate diameter of the rug with an area of 40 ft² is 7.14 feet.
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A minibus drives with a constant speed
of 32 km/h. How long will it take to travel
a distance of 80 kilometers?
✰ Given Information :-
⠀
A minibus drives with a constant speed of 32 km/hr⠀
✰ To Find :-
⠀
Time taken to travel a distance of 80 kilometers⠀
✰ Formula Used :-
⠀
[tex] \qquad \star \: \red{ \underline{ \boxed{ \sf Time = \dfrac {Distance} {Speed} }}} \: \star[/tex]
⠀
✰ Solution :-
⠀
Putting the values in the formula, we get,
⠀
[tex] \sf \longrightarrow Time = \dfrac{80 }{32} \: \: \: \: \: \: \\ \\ \\ \sf \longrightarrow Time = \cancel{\frac{80}{32} } \: \: \: \: \: \: \\ \\ \\ \sf \longrightarrow Time = \dfrac{10}{4} \: \: \: \: \: \: \: \\ \\ \\ \sf \longrightarrow Time = 2.5 \: hrs \\ \\ [/tex]
Thus, the time taken to travel 80 km with that speed is 2.5 hours.
⠀
[tex] \underline{ \rule{227pt}{2pt}}[/tex]
⠀
Find the domain of
[tex]y = \frac{1}{(1 - \sin(x) } [/tex]
Let's see
Denominator must not be equal to zero or the function becomes undefined[tex]\\ \rm\rightarrowtail 1-sinx\neq 0[/tex]
[tex]\\ \rm\rightarrowtail sinx\neq 1[/tex]
[tex]\\ \rm\rightarrowtail x\neq \dfrac{n\pi}{2}[/tex]
So
[tex]\\ \rm\rightarrowtail Domain\in R-\left\{\dfrac{n\pi}{2}\right\}[/tex]
A rectangular room measures 18 ft by 37 ft. How many
square feet of tile are needed to cover the floor?
Step-by-step explanation:
the area of a rectangle is length × width.
in our case
37 × 18 = 666 ft²
so, we need 666 ft² of tiles.
Answer:
666 square feet
Step-by-step explanation:
To find the number of square feet of tile, we need to find the area:
A = L × W
A = 18 × 37
A = 666 ft²
Martin is an artist who molds plaster into unique shapes.
How much plaster can Martin fit into the mold shown?
Step-by-step explanation:
the volume of this object is the sum of the volume of the 2 blocks.
the large block is a cube of 4×4×4 = 64 ft³
the small block is 1×1×2 = 2 ft³
so, in total, he can fit 64+2 = 66 ft³ of plaster into the mold.
When 3(2x^2+4x+7)−(x^2−8x+11) is simplified, what is the coefficient of the x term?
Answer:
Step-by-step explanation:
when 3(2x^2+4x+7)−(x^2−8x+11) is solved you get
5x^2 + 20x + 10.
the x term is
−
2
+
√
2
,
0
)
,
(
−
2
−
√
2
,
0
)
[tex]3(2x^2+4x+7)-(x^2-8x+11)\\\\=6x^2 +12x + 21 -x^2+8x -11\\\\=5x^2+20x +10\\\\\text{The coefficient of the x term is 20}[/tex]
find x correct to 2 decimal places
Answer:
Step-by-step explanation:
The value of x in the triangle is 205.24 calculated by using tan function.
By using tan function we find the value of x.
Let us divide x to two parts which includes two right triangles.
We know than tan function is a ratio of opposite side and adjacent side.
tan 55 = 106/adj
adj= 106/1.428
adj=74.22
Now let us find the adjacent side length of larger triangle similarly.
tan 39 = 106/ adj
0.809 = 106/adj
adj=106/0.809
adj=131.025
So the value of x is 74.22+131.025
=205.245
Hence, the value of x in the triangle is 205.24.
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11. Maria's age is 3 years more than twice George's age. Which expression represents George's age in terms of Maria's?
Answer:
C
Step-by-step explanation:
Okay, the catch of this question is that they do a very good job of explaining Maria's age in terms of George's age, but they leave George's age in terms of Maria's all up to you.
First start off by doing an expression of what they explicitly give you. Maria's age in terms of George's age.
Let's use variables g, representing George's age and m representing Maria's age
m = 2g + 3
Okay, this is all dandy and all, but they ask us for George's age in terms of Maria's, so we need to isolate for g.
subtract the 3 from both sides, like so:
m - 3 = 2g
then divide 2 from both sides: (remember we're dividing the whole thing)
(m-3)/2 = g
Now we have an expression for George's age in terms of Maria's.
g = (m-3)/2 or [tex]g = \frac{m-3}{2}[/tex]
The answer that gives us this, is C.
If tanθ= 2/5 find cosθ using identities. This is in quad. 1.
Answer: 5/2
Step-by-step explanation:
What is the value of X?
Sin 55° = cos X.
Enter your answer in the box.
Answer:
x = 35°
Step-by-step explanation:
sin x = cos (90° - x)
sin 55° = cos (90° - 55°)
sin 55° = cos 35°
x = 35°
50 POINTS!
Exploiting for points will be reported.
Sophie deposited money into an account in which interest is compounded semiannually at a rate of 3.7%. She made no other deposits or withdrawals and the total amount in her account after 15 years was $12,158.10. How much did she deposit?
SHOW WORK FOR BRAINLIST
$7,015.11
total money accrued : $12,158.10years : 15 years rate of interest : 3.7%deposited : ADepth meanings:
P is deposited moneysemiannually : 2 times in a yearA is received or acquired moneyt is time in yearsr is rate in percentage[tex]\sf P = \dfrac{A} { (1 + \dfrac{r}{n})^{nt}}[/tex]
[tex]\rightarrow \sf P = \dfrac{12,158.10} { (1 + \dfrac{3.7\%}{2})^{(2)(15)}}[/tex]
[tex]\rightarrow \sf P = \dfrac{12,158.10} { (1 + \dfrac{0.037}{2})^{(2)(15)}}[/tex]
[tex]\rightarrow \sf P = 7015.113646[/tex]
Put the expressions in order from least to greatest.
Answer:
[tex]\frac{11^{4} }{11^{11} } ,\frac{1}{11^{-4} }, 11^{5}*11^{2}, (11^{-3})^{-3}[/tex]
Step-by-step explanation:
For this, you need to know the rules of exponents:
If the coefficient is the same, you can do things to it (which I will get into)
In this case, all the coefficients are 11, so we don't have to worry about the coefficients being different.
For the first one, you can subtract the denominator exponent by the numerator exponent like so:
[tex]11^{4} * 11^{-11} = 11^{-7}\\[/tex]
(When you multiply, you add the exponents)
Also, the rule is: [tex]x^{-y} = \frac{1}{x^{y} }[/tex] or [tex]\frac{1}{x^{-y} } = x^{y}[/tex]
For the second one, you can use the rule mentioned before:
[tex]\frac{1}{11^{-4} } = 11^{4}[/tex]
For the third one, you want to multiply the exponents (in these kinds of cases, you can multiply the exponent by the exponent)
So:
[tex](11^{-3} )^{-3} = 11^{9}[/tex]
Finally, the fourth one, you can simply just add the exponents:
[tex]11^{5} * 11^{2} = 11^{7}[/tex]
Then, just order them from least to greatest by their exponents value :)
In the diagram, the length of Line segment Y Z is twice the length of Line segment A Z.
Triangle X Y Z is shown. Angle X Y Z is a right angle. An altitude is drawn from point Y to point A on size Z X to form a right angle.
Line segment Y A is an altitude of ΔXYZ. What is the length of Line segment Y A?
5 StartRoot 3 EndRoot units
10 StartRoot 3 EndRoot units
15 units
20 units
Answer:
5 startrood 3 endroot units .
The length of YA from the figure is 10√3 units
Pythagoras theoremAccording to the pythagoras theorem;
YZ² = AZ² + YA²
Given that YZ = 2AZ, hence;
20² = 10² + YA²
YA² = 400 - 100
YA² = 300
YA = √300
YA = 10√3 units
Hence the length of YA from the figure is 10√3 units
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what is the volume of a rectangular prism with height of 12 inches and a base with an area of 2 square inches.
Answer:
24 cubic inches
Step-by-step explanation:
Volume is side x side x side. You already have done side x side so it is just side x area.
How do I solve for X?
The value of x in the special right triangle is 39.60 ft.
Right angle triangleRight angle triangle has one of its angles as 90 degrees. The side and angles can be found using trigonometric ratios.
Therefore, let's find the base of the triangle with 30 degrees.
sin 30° = opposite / hypotenuse
1 / 2 = 7 / b
b = 14 ft
Let's use the value(14 ft) to find the height of the biggest triangle.
sin 30 = opposite / hypotenuse
sin 30 = 14 / h
0.5h = 14
h = 14 / 0.5
h = 28 ft
Therefore, let's find the value of x .
sin 45° = 28 / x
x = 28 / 0.70710678118
x = 39.5979797464
x = 39.60 ft
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What happens to the coordinates of a shape when the shape reflects about the x-axis? What happens to the
coordinates when the shape reflects about the y-axls? Explain.
Hey there!
Here's what happens to the coordinates of a point when it's reflected around the x-axis:
(x, y) --> (x, -y) or (x, -y) --> (x, y)
So the point's x-coordinate hasn't changed.
Here's what happens to the coordinates of a point when it's reflected around the y-axis:
(x, y)--> (-x, y) or (-x, y) --> (x, y)
So the point's y-coordinate hasn't changed.
Hope everything is clear.
Let me know if you have any questions!
Always remember: Knowledge is power!
Choose the multiplication problem that correctly shows partial products.
A) A
B) B
C) C
Answer:
B
Step-by-step explanation:
62x4=248
4x2=8
6x4=24 and carry the 0 and get 240
240+8=248 and you get B
Determine the value of y, if x is -1
equation: y= | x |-4
Answer:
y = -3
Step-by-step explanation:
y = | x | - 4
y = | -1 | - 4
y = 1 - 4
y = -3
Comment any questions!