Based on the calculations, the equation for the locus of these points is equal to x² + y² = 9.
How to find the locus of a point?First of all, we would determine the distance between points A and B as follows:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance = √[(-3 - 3)² + (0 - 0)²]
Distance = √[-9² + 0]
Distance = √81
Distance = 9.
Four (4) times the distance between points A and B is given by:
Distance = 9 × 4
Distance = 36.
Translating the word problem into a mathematical expression, we have:
a² + b² = 36
Also, from the distance formula we have:
a = √[(h + 3)² + (k - 0)²]
a² = h² + 6h + 9 + k²
Similarly, b² is given by:
b = √[(h - 3)² + (k - 0)²]
b² = h² - 6h + 9 + k²
Equating the equations, we have:
a² + b² = 36
h² + 6h + 9 + k² + h² - 6h + 9 + k² = 36
2h² + 2k² = 36 - 18
2h² + 2k² = 18
Dividing both sides by 2, we have:
h² + k² = 9 ⇒ x² + y² = 9.
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find the area of the shaded regions.
Answer: [tex]27\pi \text{ cm}^{2}[/tex]
Step-by-step explanation:
The area of the entire circle is [tex](\pi)(6^{2})=36\pi[/tex]
The area of the sector with the right angle is [tex]\frac{36\pi}{4}=9\pi[/tex]
Subtracting these areas, we get [tex]27\pi \text{ cm}^{2}[/tex]
The population P ( ) of a culture of the bacterium Pseudomonas aeruginosa is given by P ( t ) 1684 + 83,000 + 10,000 , where is the time in hours the culture was started .
The maximum time in hours will be equal to 24.64 hours.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given function is P(t) = -1684t² +83000t + 10000
The maximum time will be calculated by differentiating the given function with respect to 't' and equate with zero.
[tex]\dfrac{dP(t)}{dt}[/tex] = -1684t² +83000t + 10000 = 0
[tex]\dfrac{d}{dt}[/tex][-1684t² +83000t + 10000] = 0
-3368t + 83000 = 0
3368t = 83000
t = 24.64 hours
Therefore the maximum time in hours will be equal to 24.64 hours.
The correct question is given below:-
The population p(t) of a culture of the bacterium Pseudomonas aeruginosa is given by,p(t)= -1684t² +83000t + 10000 which is the time in hours since the culture was started. Determine the time the population was at its maximum. Round to the nearest hour.
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Marc mixes blue and yellow paint to make his favorite shade of green, which he'll use to paint his house. He has 14 cans of blue paint and 20 cans of yellow paint when he starts.
He wants the same green color every time he mixes, so the amounts of blue and yellow must always be proportional to the original mixture.
On day 1, he mixes 4 cans of blue and 6 cans of yellow.
On day 2, he mixes 6 cans of blue and 9 cans of yellow.
Fill in the blanks to find the highest number of cans of each color Marc can mix to make the same shade of green on day 3.
In the simplest form, the ratio of blue paint to yellow paint is 2 : 3.
The number of blue paint he used on the first and second day is 10.
The number of yellow paint he used on the first and second day is 15.
On the third day, the highest number of can of blue paint he can use is 2
On the third day, the highest number of can of yellow paint he can use is 3.
What is the highest number of blue and yellow paint he can use?The ratio of blue paint to yellow paint can be determined by determining the simplest form of the paints used: 4 : 6 = 2: 3
Total blue paint used on the first and second day = 4 + 6 = 10
Blue cans remaining = 14 - 10 = 4
Total yellow paint used on the first and second day = 6 + 9 = 15 cans
Yellow cans remaining = 20 - 15 = 5 cans
Maximum ratio of blue and yellow cans that can be used is 2 : 3.
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In order to slove the following system of equations by addition, which of the following could you do before adding the equations so that one variable will be eliminated when you add them?
4x-2y=7
3x-3y=15
Answer:
B. use multipliers -3 and 2
Step-by-step explanation:
If you're solving the system by "addition," multiplying the equations by the chosen numbers needs to result in opposite coefficients for one of the variables.
Effect of answer choicesA. The system becomes ...
12x -6y = 2112x -12y = 60No variable has opposite coefficients.
__
B. The system becomes ...
-12x +6y = -216x -6y = 30The y-variable has opposite coefficients. This is a good choice.
__
C. The system becomes ...
12x -6y = 216x -6y = 30No variable has opposite coefficients.
__
D. The system becomes ...
4/3x -2/3y = 7/33x -3y = 15No variable has opposite coefficients.
__
Additional comment
The simplest "no brainer" solution is to use the coefficients of one of the variables, negating one of them. Multiply each equation by the opposite equation's coefficient. Here, the y-coefficients are -2 and -3, and the multipliers of answer choice B are -3 and 2, consistent with this advice. (The sign of 2 was changed.)
Answer:
B.
Step-by-step explanation:
Multiply the top equation by -3 and the bottom equation by 2
-12x+6y=-21
6x-6y= 30
-6x = 9 Variable "y" is removed
Hope this helps
the graph shows the equation x^2+y^2=5 use the slider for a to move the vertical line on the graph based on the vertical line test is this equation a function why or why not
Answer:
Not a function.
Step-by-step explanation:
The vertical line touches the graph at more than one point at once.
The Green Party at a large university plans to line both sides of a 24-foot-long hallway with posters endorsing a candidate for state senate. Each of the posters costs them $6.25 , they’re 3 feet wide, and there will be 4 feet between posters. Assume the first poster on each end will be exactly even with the start of the hall. Estimate how much this will cost.
The total cost of putting the posters on the wall is $25.
What is the cost of putting the posters on the wall?
If the first poster on each end will be exactly even with the start of the wall, it means that after the two posters have been placed on either side of the wall, the total space left would be 10 feet (24 - 3 - 3 - 4 - 4).
After the first poster has been placed on both ends of the wall, a second poster would be placed on either ends of the wall. Total space now left is 4 feet (10 - 3 - 3). So there can only be four posters on the wall.
Total cost of 4 posters = 4 x $6.25 = $25
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Mike is c years old, he is half as old as Steve. How old was Steve two years ago?
Answer:
2(c-1)
Step-by-step explanation:
MIke is c
Steve is 2c
Steve was 2c -2 two years ago
20. An amount of money was shared among five boys Ali, Juma, Musa, Khalid and Mustafa. Ali got /8 of the total amount while Juma got /5 of the remainder. The remaining amount was shared equally among Musa, Khalid and Mustafa, each of which received Kshs 600. a) How much did Juma get? b) How much was shared among the five boys. (3 marks) (2 marks)
Answer:
[tex]x=\frac{18000}{7}=2571\frac{3}{7}[/tex]
Step-by-step explanation:
Let the total amount be x
Then Ali got 1/8x With 7/8x left
Juma got 7/40x with 7/10x left
Musa, Khalid and Mustafa got 7/30x each
since [tex]\frac{7}{30}x=600[/tex]
7x=18000
[tex]x=\frac{18000}{7}=2571\frac{3}{7}[/tex]
If A and B are 7 x 2 matrices, and C is a 4x7
matrix, which of the following are defined?
A. CA
B. B - A
C. B-C
D. ABT
E. AC
F. CT
Answer:
A, B, D, F
Step-by-step explanation:
Matrix operations require that the matrix dimensions make sense for the operation being performed.
Matrix multiplication forms the dot product of a row in the left matrix and a column in the right matrix. That can only happen if those vectors have the same dimension. That is the number of columns in the left matrix must equal the number of rows in the right matrix.
Matrix addition or subtraction operates on corresponding terms, so the matrices must have the same dimension.
The transpose operation interchanges rows and columns, so reverses the dimension numbers. It is a defined operation for any size matrix.
Defined operationsA. CA ⇒ (4×7) × (7×2) . . . . defined
B. B -A ⇒ (7×2) -(7×2) . . . . defined
C. B -C ⇒ (7×2) -(4×7) . . . undefined
D. AB' ⇒ (7×2) × (2×7) . . . . defined
E. AC ⇒ (7×2) × (4×7) . . . undefined
F. C' ⇒ (7×4) . . . . defined
Beginning with the graph of f(x) = x2, what transformations are needed to form g of x equals one third times the quantity x plus 3 end quantity squared minus 3 question mark?
To transform f(x) into g(x) we need to use addition, subtraction and multiplication.
Given f(x)=[tex]x^{2}[/tex] and g(x)=[tex]x/3+3(x^{2} -3)[/tex]
We need to transform function f(x)into g(x).
A function refers to a relation which expresses relationship between two variables. It contains one value for each value of x. If there are more than one value for one value of x then it is not said to be a function.
f(x)=[tex]x^{2}[/tex], g(x)=[tex]x/3+3(x^{2} -3)[/tex]
To transform f(x) into g(x) we need to follow the following steps:
First subtract 3 from f(x).Then multiply the expression received from above step by 3.Next step is to add x/3 to the expression received from the above step.Now we will get the g(x)=[tex]x/3+3(x^{2} -3)[/tex].Hence we have to use addition, subtraction and multiplication for transformation.
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The graph of g(x) is wider than f(x) and is shifted to the left 4 units and down 3 units.
Step-by-step explanation:
PLEASE HELP
Find the point that splits segment CD in half if point C is located at (−2, 4) and point D is located at (3, 7)
(2.5, 1.5)
(1, 5)
(0.5, 5.5)
(3, 2)
Answer:
0.5, 5.5
Step-by-step explanation:
ive done this worksheet before
Answer: Choice C
(0.5, 5.5)
===========================================================
Explanation:
Draw out a number line with -2 and 3 on it. These are the x coordinates of the given points. Add up these values and divide by 2 to get the midpoint on the number line.
(A+B)/2 = (-2+3)/2 = 1/2 = 0.5
The value 0.5 is the midpoint of -2 and 3. This midpoint is equally spaced from both endpoints.
Therefore, the x coordinate of the midpoint is 0.5
Repeat this idea for the y coordinates
Add: 4 + 7 = 11
Divide the result in half: 11/2 = 5.5
The y coordinate of the midpoint is 5.5
The overall midpoint itself is located at (x,y) = (0.5, 5.5)
This is why choice C is the final answer.
Visual confirmation is shown below. GeoGebra has a nice handy feature to find the midpoint very quickly with just a few clicks.
A textile factory wants to start incorporating silk into their cotton fabric. The factory currently has 200lbs of cotton, which costs $0.75 per pound. Silk, however, costs $15 per pound. If the factory wants the cost of their blended fabric to be $5 per pouund, how much silk will they need to buy?
Answer:
cos4B=1-8sin^2B+8sin^4B
If a = 3 and b = -2, what is the value of
a²+3ab-6²?
Answer:
-45
Step-by-step explanation: Plug the numbers of a and b into the equation.
Answer:
-45
Step-by-step explanation:
ok so basically since a is 3 a2 will be 9 then you put back the plus sign then 3×a×b will be -18 then 6square will be 36.
=9+(-18)-36
= -9-36
=-45
Hi- I need help please to get my HS diploma...did not graduate :(
Find the remainder when f(x)=x3−6x2+3x−1 is divided by 2x−3.
The remainder from the division of the algebraic equation is -53/8.
What is the remainder of the algebraic expression?The remainder of the algebraic expression can be determined by using the long division method.
Given that:
[tex]\mathbf{f(x) = \dfrac{x^3 - 6x^2 + 3x - 1}{2x-3}}[/tex]
where:
The divisor = 2x -3Using the long division method, we have:
[tex]\mathbf{= \dfrac{x^2}{2} +\dfrac{-\dfrac{9x^2}{2}+3x -1 }{2x-3}}[/tex]
[tex]\mathbf{= \dfrac{x^2}{2}-\dfrac{9x}{4} +\dfrac{-\dfrac{-15x}{4}-1 }{2x-3}}[/tex]
[tex]\mathbf{= \dfrac{x^2}{2}-\dfrac{9x}{4} -\dfrac{15}{8}+\dfrac{-\dfrac{53}{8} }{2x-3}}[/tex]
[tex]\mathbf{= \dfrac{x^2}{2}-\dfrac{9x}{4} -\dfrac{15}{8}-\dfrac{53 }{8(2x-3)}}[/tex]
Therefore, we can conclude that the remainder is -53/8.
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Which statement regarding the diagram is true?
m∠WXY = m∠YXZ
m∠WXY < m∠YZX
m∠WXY + m∠YXZ = 180°
m∠WXY + m∠XYZ = 180°
Find the area of the following figure:
The area of the figure is 11. 27 cm²
How to find the areaThe figure given is a parallelogram
Note that the formula for area of a parallelogram is given as;
Area = base × height
Base = 2. 3cm
height = 4. 9cm
Area = 2. 3 × 4. 9
Area = 11. 27 cm²
Thus, the area of the figure is 11. 27 cm²
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Work out 0.8 million - 1.76 thousand
The value of the given task 0.8 million - 1.76 thousand is 798,240.
Place value0.8 million
= 0.8 × 1,000,000
= 800,000
1.76 thousand
= 1.76 × 1000
= 1,760
So,
0.8 million - 1.76 thousand
= 800,000 - 1,760
= 798,240
Therefore, 0.8 million - 1.76 thousand is 798,240
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Please help!! Very much appreciated!! Consider the following set of real numbers. Which of the following lists all of the rational numbers in the set?
Answer:
The second choice.
Step-by-step explanation:
A rational number means that you are able to write the number as a fraction with integers in the numerator and the denominator. An integers are the whole numbers and their opposites ...-3,-2,-1,0,1,2,3...
The square root of 4 is 2. 2 can be written 2/1 (an integer over and integer)
-square root of 2 cannot be written as an integer over an integer. When this number is written as a decimal number it never repeats and it never terminates so it cannot be written as an integer over and integer.
-2/3 is written in the form of an integer over and integer.
1 can be written 1/1
9/8 is written as an integer over an integer.
The square root of 9/4 would be 3/2. (3/2)(3/2) = 9/4.
2.4 repeating can be written as an integer over an integer. Any decimal that repeats or terminates can be written as an integer over and integer. It actual happens to be 22/9.
The square root of 10 written as a decimal does not repeat or terminate so it is not rational. Only perfect squares are rational.
what is the approximate radius of a sphere with the volume of
Answer:
4.6cm
Step-by-step explanation:
v=4/3πr^3
128π=4/3π^3
128π×3=4πr^3
384π\4=πr^3
96π\π=r^3
96=r^3
3√96=r
r=4.579
r=4 6cm
Which of the following determines a plane?
A. 3 non-collinear points
B. line and a point on the line
C. three collinear points
D. a straight line
Answer: A 3 non collinear pts
a plane is a flat surface like a wall
Jacob can take any one of three routes from school to the mall, and one of five possible routes from the mall to his house. If he doesn’t retrace his steps, how many different ways can Jacob walk from school to home?
Answer:
15 routes
Step-by-step explanation:
3 x 5 = 15 routes
What is f(x) = 8x² + 4x written in vertex form?
F(x) = 8x + - 1.
f(x) = 8√(x + 1)² - 1/6
f(x) = 8√x+¹²-2
f(x) = 8(x + 1)² - 4
[tex]8x^{2}+4x\\\\=8\left(x^{2}+\frac{1}{2}x \right)\\\\=8\left(x+\frac{1}{4} \right)^{2}-8\left(\frac{1}{16} \right)\\\\\boxed{f(x)=8\left(x+\frac{1}{4} \right)^{2}-\frac{1}{2}}[/tex]
NO LINKS!! Please help me with this problem
Answer:
-8Step-by-step explanation:
[tex] \bf \cfrac{f(x + h) - f(x)}{h} [/tex]
[tex]\bf f(x) -8x + 1[/tex]
[tex]\bf f(x+h) = -8x-8h+1[/tex]
[tex]\bf \cfrac{ - 8x - 8h + 1 + 8x - 1}{h} [/tex]
[tex] \bf =\cfrac{ - 8h}{h} [/tex]
[tex] \bf = - 8[/tex]
▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎
Answer:
Given function:
[tex]f(x) = -8x + 1.[/tex]
Let's find the difference quotient:
[tex]\frac{f(x+h)-f(x)}{h}\\\\= \frac{[-8(x+h)+1] - (-8x + 1)}{h}\\\\= \frac{-8x-8h+1+8x-1}{h}\\\\ = \frac{-8h}{h}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(h\neq 0)\\\\= -8.[/tex]
PLEASE HELP ME I NEED YO FINISH THIS QUESTION !!!!!!!!!!!The cylinder below has a cross-sectional area of
19 m².
What is the volume of the cylinder?
If your answer is a decimal, give it to 1 d.p. and
remember to give the correct units.
area = 19 m²
13 m
Not drawn accurately
Answer:
247m³
Step-by-step explanation:
volume of cylinder = πr²*h
volume of cylinder = 19m²*13m
volume of cylinder = 247m³
247 cubic meters is the volume of the cylinder.
What is volume?Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface. The cubic meter (m³), a derived unit, is the SI unit of volume. Volume is another word for capacity.
The area of the circular face of the cylinder is given by:
A = πr²
where r is the radius of the circular face. Since the area of the circular face is given as 19 m², we can solve for the radius as follows:
19 = πr²
r² = 19/π
The volume of the cylinder is given by:
V = Ah
where h is the height of the cylinder. Since the height is given as 13 m and we have just found the radius to be approximately 2.197 m, we can calculate the volume as follows:
V = πr²h
=19*13
≈ 247 m³
Therefore, the volume of the cylinder is approximately 247 cubic meters.
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Classify the triangle by its angle and sides
Answer:
isosceles obtuse triangleStep-by-step explanation:
isosceles obtuse triangle
An isosceles obtuse triangle is a triangle in which one of the three angles is obtuse (lies between 90 degrees and 180 degrees) and the other two acute angles are equal in measurement, and 2 equal sides.
fg⊥op, rs⊥qr. FG = 40, RS = 40, OP = 15. Find x.
A. 17
B. 21
C. 20
D. 15
The measure of x from the diagram is 15
Circle theoremsFrom the given diagrams, we are told that fg⊥op, rs⊥qr. Given the following parameters
FG = 40,
RS = 40,
OP = 15.
Since the measure of FG is equal to RS, hence the measure of Op will be equal to OQ to have:
OQ = OP = x
x = 15
Hence the measure of x from the diagram is 15
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Answer: 15
Step-by-step explanation:
OP = OQ
they are congruent
Which could be the entire interval over which the
function, f(x), is positive?
O (-∞, 1)
O (-2, 1)
O (-∞, 0)
O (1,4)
Answer:
(-2, 1)
Step-by-step explanation:
So assuming this table contains all the zeroes of f(x) and all of them having a multiplicity of 0. This quadratic equation can be defined as
[tex]f(x) = a(x+2)(x-1)[/tex]. So if you look at the top where its f(-3) then f(-2) then f(-1) it appears to be increasing and then somewhere in between f(-1) and f(0) it has a turning point in which it starts decreasing. and then after f(1) it no longer outputs positive values and appears to be going towards negative infinity. So the interval in which f(x) is positive seems to be finite and using this table it appears to be at (-2, 1) and make sure to use parenthesis since at f(-2) and f(1) it's not positive, because 0 is not positive, so it's not included in the interval
A container is shaped like a cylinder with half spheres on each end. The cylinder has a length of 30 centimeters and a radius is 5 centimeters. To the nearest cubic centimeter, how many cubic centimeters can one container hold? Do not round calculations until the final answer. For the final answer, round to the nearest cubic centimeter (no decimals) and use a comma to separate the thousands place. cubic centimeters
The cubic centimeter one container can hold is 2,878.33 cm³.
What is the cubic centimeter one container can hold ?In order to determine the cubic centimeter one container can hold, the volume of the container has to be determined.
Volume of the container = volume of the cylinder + (2 x volume of the hemisphere)
Volume of the cylinder = πr²h
Where:
π = 3.14 r = radius h = height3.14 x 5² x 30 = 2355 cm³
Volume of a hemisphere = (2/3) x π x r³
2 x (2/3 x 3.14 x 5³) = 523.33 cm³
Volume of the container = 523.33 cm³ + 2355 cm³ = 2,878.33 cm³
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Fifteen hungry kittens found a bucket of sausages. Each time
they cut a sausage or a part of a sausage, they cut it into exactly
two new pieces. They made 18 cuts in all and each kitten got 2
(maybe unequal) pieces of sausage. How many sausages were in
the bucket?
Answer:
2.4 SAUSAGES
Step-by-step explanation:
18 x 2 = 36
36/ 15 = 2.4
Which line has no slope?
a
O Line a
O Line b
O Line c
O Line d