By completing squares, we will see that the radius is 12 units and the center is (-8, 1).
How to find the center and radius of the circle?The circle of center (x₁, y₁) and radius r is written as:
(x - x₁)² + (y - y₁)² = r²
Now we go to our equation:
x² + 16x + 64 + y² - 2y + 1 = 144
Now we need to complete squares:
(a + b)² = a² + 2ab + b²
Then we can rewrite:
(x² + 2*8*x + 8*8) + (y² - 2y + 1) = 12²
(x + 8)² + (y - 1)² = 12²
So the center is the point (-8, 1) and the radius is 12 units.
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Which is the equation of the line passing through (0,4) and (8,0)?
Answer:
[tex]\sf y = -\dfrac{1}{2} x +4[/tex]
Find slope (m):
[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
[tex]\rightarrow \sf slope \ (m): \dfrac{0-4}{4-0} = -\dfrac{1}{2}[/tex]
Now, find equation:
[tex]\sf y -y_1 = m(x - x_1) \ \ \ \ \textsc where \ (x_1, y_1 ) \ are \ points[/tex]
[tex]\rightarrow \sf y - 4 = -\dfrac{1}{2} (x - 0)[/tex]
[tex]\rightarrow \sf y = -\dfrac{1}{2} x +4[/tex]
The volume of air in a balloon is represented by the function v(r)=4/3 pi ^3, where r is the radius of the balloon, in
inches. The radius of the balloon increases with time, in seconds, by the function r(t) = 1².
Write a composite function that can be used to determine the volume of the balloon after t seconds. Then, select the
two true statements.
Question Progress
Work out the value of 4° x 16°
Answer:
20°0°0 is the correct answerQuadrilateral ABCD has the following coordinates: A(-6,3) B(-4,5) C(-1,6) and D(-3,2) and
maps onto A"B"C"D". It will undergo transformations that will consist of a reflection over
the y-axis followed by a translation. Point D" is shown plotted in the plane after the
transformation.
A) Write the translation rule that maps point D' to point D".
B) Write the coordinates of point A"
The translation rule that maps point D' to D" is (x + 3, y) and the coordinate of point A" is (9,3)
How to determine the translation rule?The coordinates are given as:
A(-6,3) B(-4,5) C(-1,6) and D(-3,2)
When reflected across the y-axis, the transformation rule is:
(x,y) -> (-x,y)
So, we have:
A' = (6,3)
D' = (3,2)
Point D" on the grid is (6,2).
This means that the translation rule that maps both point is (x + 3, y)
The coordinates of point AIn (a), we have:
A' = (6,3)
Using the translation rule (x + 3, y), we have:
A" = (6 + 3,3)
A" = (9,3)
Hence, the coordinate of point A" is (9,3)
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find the altitude of a kite where 120 feet of string makes a 64 degree angle to the ground
Answer:
107.86 to 2 d.p.
Step-by-step explanation:
makes a triangle. 120 feet is the hypotenuse.
we want to find the opposite so we will use sine.
sin(x) = opp/hyp which means opp = sin(x)hyp.
opp = sin(64)120
opp = 107.86 to 2d.p.
1 . A rope was 14.35 inches long. Megean cut the rope into 7 pieces of equal length. What was the length of each piece of rope in inches
2. Scott drank 3.5 bottles of water yesterday . Each bottle contained 1.2 pints of water. what was the number of pints of water Scott drank yesterday
Division is one of the four fundamental arithmetic operations. The number of pints of water Scott drank yesterday is 4.2 pints.
What is Division?Division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.
A rope was 14.35 inches long. Megean cut the rope into 7 pieces of equal length. Therefore, the length of each piece of rope in inches will be,
Length of piece = 14.35 inches/7 = 2.05 inches
Scott drank 3.5 bottles of water yesterday . Each bottle contained 1.2 pints of water. Therefore, the number of pints of water Scott drank yesterday is,
Number of pints = 3.5 bottles × 1.2 pints = 4.2 pints
Hence, The number of pints of water Scott drank yesterday is 4.2 pints.
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Solve for x. Round to the nearest tenth. 34° 90% (Figure is not necessarily drawn to scale) O x 3.1 0x 2.7 x=2 C= 5.9
Answer:
x=2.7
Step-by-step explanation:
tan34 = x/4
x = 4tan34 = 2.7
Points a and b lie on a circle centered at point o. if oa = 5 and what is the area of sector aob? use the value π = 3.14, and choose the closest answer. a. 19.6 square units b. 39.3 square units c. 7.85 square units d. 15.7 square units
The area of sector AOB whose radius OA 5 units is 19.6 sq. units.
What is the Sector?A sector is a portion of a circle which is enclosed between its two radii and the arc adjoining them. The most common sector of a circle is a semi-circle which represents half of a circle.
Here, Radius of Circle = 5 units
length of arc AB / circumference = 1/4
So, Area of Sector AOB = one fourth of area of circle
= 1/4 X π X r²
= 0.25 X 3.14 X 5²
= 0.25 X 3.14 X 25
= 19.625 sq. units
Thus, the area of sector AOB whose radius OA 5 units is 19.6 sq. units.
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Answer:
19.6
Step-by-step explanation:
Choose the expression that represents a linear expression.
6x + 6
O-6x² +8x-9
O8x3 + 9x² - 10x + 11
07x4-8x³+9x² - 10x + 11
Question 3(Multiple Choice Worth 1 points)
(06.01 LC)
Answer:
6x+6
Step-by-step explanation:
a linear expression has no power attached to the x (the unknown)
Factorise completely 12 x³y - 18 xy²
Answer:
6xy(2x²-3y)
Step-by-step explanation:
factorized completely
The troupe’s account balance first reached $500 on Day 4. The last day the account balance was $500 was
Day 8.
(a) Determine C(5), C(6), and C(7). Explain how you determined these amounts.
(b) Estimate C(1), C(2), and C(3). Explain how you determined these amounts.
(c) The stage manager said that the amount of money taken out of the account each day between Day 8
and Day 11 was the same amount of money put into the account each day between Day 0 and Day 4.
Recall that Day 11 is when the balance first reached $0. Without doing any calculations, how could
you show the stage manager was incorrect?
Answer:
The answer is c, hope this helps
Step-by-step explanation:
What is the length of the diagonal from vertex J to vertex L in the quadrilateral below?
Answer: 6.7 units for the diagonal from J to L
Step-by-step explanation:
you can use the Pythagorean theorem to find the diagonal (hypotenuse)
a^2 + b^2 = c^2
by counting units from M to J you have a length of 3 for the "a" value
by counting units from M to L you have a length of 6 for the "b" value
3^2 + 6^2 = c^2
9 + 36 = c^2
45 = c^2
take square root of both sides
6.7 = c
the diagonal is 6.7 units
Select the expression that’s is equivalent to (x-1)^2
Answer:
(x-1)^2
=x^2 - 2x + 1
Step-by-step explanation:
hope this helps
Find perimeter of this square with sides of length 5 cm
Answer:
P = 20 cm
Step-by-step explanation:
the perimeter (P) is the sum of the 4 sides (s) of the square
the sides of a square are congruent , then
P = 4s = 4 × 5 = 20 cm
I need to know how to solve this
Answer:
K=-6/11
Step-by-step explanation:
3(k/3+4-2k)=3(-9k)
K+12-6k=-27k
12-5k=-27k
12=-22k
K=-6/11
A rectangle is 21 meters long and 11 meters wide. what is the perimeter of this rectangle?
Step-by-step explanation:
the perimeter is simply the distance you would have to walk when going around the whole object once.
so, you would go a length, a width, another length and another width, until you are finally arriving back at the starting point.
so, the perimeter of a rectangle is
2×length + 2×width = 2×21 × 2×11 = 42 + 22 = 64 m
A cylindrical container is packaged inside a prism-shaped box. the box has a volume of 96 cubic units. if the container has a diameter of 4 units and a height of 6 units, what is the volume of the empty space between the cylinder and the box? round the answer to two decimal places. a. 20.60 cubic units b. 37.77 cubic units c. 51.27 cubic units d. 75.40 cubic units
Volume is a three-dimensional scalar quantity. The volume of the empty space is 20.602 units³.
What is volume?A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
Given the volume of the prism, the box is 96 units³ and the diameter of the cylindrical container is 4 units(Radius=2 units), while the height of the cylinder is 6 units. Therefore, The volume of the empty space is,
The volume of the empty space
= Volume of prism - Volume of the cylindrical container
= 96 units³ - (π×2²×6) units³
= 96 units³ - 75.398 units³
= 20.602 units³
Hence, the volume of the empty space is 20.602 units³.
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Which point is one fourth of the way between point A and point B on the line segment AB shown on the coordinate plane below?
The coordinate of the point between point A and point B on the line segment AB is [tex](\frac 92, -\frac{19}4)[/tex]
How to determine the point?The points are given as:
A = (4,-5)
B = (6,-4)
m : n = 1 : 3
The coordinate of the point is then calculated using:
[tex]P = \frac{1}{m + n}(mx_2 + nx_1,my_2 + ny_1)[/tex]
So, we have:
[tex]P = \frac{1}{1 + 3}(1 * 6 + 3 * 4, 1 * -4 + 3 * -5)[/tex]
Evaluate the sum of product
[tex]P = \frac{1}{4}(18, -19)[/tex]
Evaluate the product
[tex]P = (\frac 92, -\frac{19}4)[/tex]
Hence, the coordinate of the point is [tex](\frac 92, -\frac{19}4)[/tex]
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I dive to 17 metres for 47 minutes. after a 30 minute surface interval i do a second dive to 17 metres. losing track of time, i notice my bottom time is now 25 minutes. according to the general rules, what should i do
If your bottom time is 25 minutes, general rules recommend that you ascend immediately to 15 feet then remain there for 8 minutes. You should then go to the surface and not dive for 6 hours.
What do general rules on diving say about a 25 minute bottom time?The recommended bottom time is 24 minutes which means that staying there for 25 minutes will have exceeded this recommendation.
You should immediately ascend to 15 feet or 5 meters, and then wait there for 8 minutes. Then return to the surface and avoid diving for the next 6 hours.
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The diagram shows a regular polygon.
x
What is the value of x?
Write your answer as an integer or as a decimal rounded to the nearest tenth.
Answer:
To find the value of x, use the formula
(n-2) x 180, where n is the number of sides.
In this case, we have a TRIangle, which has THREE sides.
So, n=3
(3-2) x 180
1 x 180
180
If the total sum of the angles is 180, then the measure of one angle would be 180 divided by 3, which is 60.
Let me know if this helps, or if you got any more questions
how can i find area of abd triangle. .............
Answer:
6 square units
Step-by-step explanation:
The attachment shows the figure redrawn to scale, along with helpful semicircle O with diameter EB. Trig relations can be used to find the area of triangle ADB. The relation between an inscribed angle and its corresponding central angle is also helpful.
__
anglesAny right triangle can be inscribed in a semicircle whose diameter is the hypotenuse. Accordingly, we have constructed semicircle O whose center is the midpoint of EB. Hence its radius is EB/2 = 4/2 = 2.
Then angle EBD is an inscribed angle, hence half the measure of central angle EOD. Since ∠EOD is double the measure of ∠EBD, it is congruent to ∠EBC, which is also double the measure of ∠EBD. We have called the measure of this double angle θ. Its complement is the angle marked β.
segmentsThe fact that angles EOD and EBC are congruent means that segments OD and BC are parallel. Segment BC is the altitude of ΔADB with respect to base AD.
The tangent ratio is ...
Tan = Opposite/Adjacent
Applying that to angle β, we have
tan(β) = OD/AD [eqn 1]
tan(β) = BC/AC [eqn 2]
These two relations can be solved for the measures of AD and BC, which we need in order to find the area of ΔADB.
areaEquation [eqn 1] tells us ...
AD = OD/tan(β)
Equation [eqn 2] tells us ...
BC = AC·tan(β)
The area of ΔADB is ...
Area = 1/2bh
Area = 1/2(AD)(BC) = 1/2(OD/tan(β))·(AC·tan(β))
Area = 1/2(OD)(AC) . . . . . . factors tan(β) cancel
The length of AC is given as 6, and we know OD = 2, so the area is ...
Area = 1/2(2)(6) = 6
The area of triangle ADB is 6 square units.
The value of p in the equation 2p - 3 = p + 2 Is
Answer:
p = 5
Step-by-step explanation:
Given equation:
2p - 3 = p+2
To Find:
Value of pSoln:
2p - 3 = p + 2
Subtract p from both sides:
=>2p-3−p = p+2-p
=>p-3 = 2
Add 3 to both sides:
=>p−3+3 = 2+3
=>p = 5
Hence,the value of p would be 5.
We can plug the value we got to the original equation to verify:
=> 2p - 3 = p + 2
p = 5=> 2(5) -3 = 5 + 2
[Make sure to simplify using PEMDAS]=> 10 - 3 = 7
=> 7 = 7 [Proved]
Hence,this equation is true.
[tex]\rule{225pt}{2pt}[/tex]
Acronym PEMDAS rule means:
P:ParenthesesE:ExponentsM:MultiplicationD:DivisionA:AdditionS:SubtractionAnswer:
p = 5
Step-by-step explanation:
First we add 3 to both sides to make :
2p = p + 5
Now we subtract p from both sides :
p = 5
Hope this helped and brainliest please
Slope of (-9,-2) and (-9,-6)
Answer:
Slope is undefined.
Step-by-step explanation:
Help!! Also the questions says “Which of the following shows JUST a variable?”
Which of the following is the equation of the function below? y=2sec (x+pi/6)+2 y=sec2(x+pi/6)]+2 y=sec[2(x+2)] + pi/6 y=2sec(x+2) + pi/6
The equation of the function is y = sec(2(x + π/6)) + 2
How to determine the equation of the function?From the graph, we have the following parameters:
Local maximum = 3Local minimum = 1Period = 2Phase shift = π/6A secant function is represented as:
y = A sec(b(x + c)) + d
Where:
A = 0.5 * (max - min) = 0.5 * (3 - 1) = 1
b = Period = 2
c = Phase shift = π/6
d = 0.5 * (max + min) = 0.5 * (3 + 1) = 2
So, we have:
y = 1 * sec(2(x + π/6)) + 2
Evaluate
y = sec(2(x + π/6)) + 2
Hence, the equation of the function is y = sec(2(x + π/6)) + 2
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Answer
The answer is B on Edgenuit
Step-by-step explanation:
Desmos
I will choose brainlyist and 20 POINTS
Answer:
They are all non triangles, but I'm not in your math class, so I don't know.
Step-by-step explanation:
An mp3 player was reduced from $229.99 to $129.99. find the percent reduction in price. round the answer to the nearest tenth of a percent, if necessary.
Answer:
43.4%
Step-by-step explanation:
229.99 - 129.99
= 100
The percent reduction is:
100/229.99 * 100
=43.4%
55 POINTS!!!!!!!!! WILL GIVE BRAINLIEST!!!!!!!!!! PLS HELP ASAP!!!!!!!!!!
Danielle is trying to solve the equation [tex]8^x=\frac{1}{64}[/tex] Explain in detail how Danielle should solve this problem. Then solve it step by step showing all your work and tell Danielle what the answer should be.
Answer:
[tex]x=-2\\[/tex]
Step-by-step explanation:
[tex]8^x=\frac{1}{64}\\xlog8=log\frac{1}{64}\\x=\frac{log\frac{1}{64}}{\log8}\\x=-2[/tex]
First we write the equation given
Next we take the log of both sides. This turns [tex]x[/tex] into a normal term instead of an exponent, but turns [tex]8[/tex] and [tex]64[/tex] into the log version of themselves.
Next we can divide both sides by [tex]log8[/tex] to isolate [tex]x[/tex].
This gives us our answer of [tex]\boxed{-2}[/tex]
what is the distance from (7,0)- (-5,5)
Answer:
[tex]\frac{5}{-12}[/tex]
Step-by-step explanation:
If you use the formula [tex]m = \frac{y2 - y1} {x2 - x1}[/tex] with x1 being 7, y1 being 0, -5 being x2 and 5 being y2, then you can subtract. 5(y2) minus 0(y1) is 5, and -5(x2) minus 7(x1) is -12. The formula would look like this: [tex]m = \frac{5 - 0}{-5 - 7} \frac{5}{-12}[/tex].
(tip: you need to do rise over run, aka y over x, shown as [tex]\frac{y}{x}[/tex] or [tex]\frac{rise}{run}[/tex])
I hope I helped you answer your question, and helped better understand it as well
A dog eats 3 cans of dog food in 12 days. Write an equation to represent th
proportional relationship. Then find k, the constant of proportionality.
Let c =
Let d =
Equation:
= k•
k=-
The equation to represent the proportional relationship is c = 0.25d
How to determine the equation?Let c = the number of cans
Let d = the number of days
So, we have:
c = kd
Where k represents the constant of proportionality.
From the given parameters, we have:
3 = 12k
Divide both sides by 12
k = 0.25
Substitute k = 0.25 in c = kd
c = 0.25d
Hence, the equation to represent the proportional relationship is c = 0.25d
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