Given data:
The first end point of the diameter is (-14, 1).
The second end point of the diameter is (-10, 9).
The centre of the circel is,
[tex]\begin{gathered} x=\frac{-14-10}{2} \\ =\frac{-24}{2} \\ =-12 \\ y=\frac{1+9}{2} \\ =5 \end{gathered}[/tex]The diameter of the circle is,
[tex]\begin{gathered} d=\sqrt[]{(-10+14)^2+(9-1)^2} \\ =\sqrt[]{16+6}4 \\ =4\sqrt[]{5} \end{gathered}[/tex]The radius is,
[tex]\begin{gathered} r=\frac{4\sqrt[]{5}}{2} \\ =2\sqrt[]{5} \end{gathered}[/tex]The equation for the circle is,
[tex]\begin{gathered} (x-(-12))^2+(y-5)^2=(2\sqrt[]{5})^2 \\ (x+12)^2+(y-5)^2=20 \end{gathered}[/tex]Thus, the equation for the circle is (x+12)^2 +(y-5)^2 =20.
How many units are in a hundred?
Solution
There are 100 units
[tex]100\text{ units}[/tex]Brief Explanation
[tex]\begin{gathered} 1\text{ unit}=1unit \\ \\ 1tens=10units \\ \\ 1hundred=10tens=10(10)units \\ \\ 1hundred=100units \end{gathered}[/tex]The cost of printing the cover of the book is Rs Y. while the cost of printing a page of the book is Rs P. If the book has 45 pages and it costs Rs C to print one copy of it. Construct a formula for C in terms of P and Y
Answer:
y = 3? (A) −192 ... If P = a² + a −1 and R = −a − 1, which expression represents P + R.
Step-by-step explanation:
Assume the cost of a taxi is one dollar per ride and $2.30 per mile what function represents your total cab fare be sure to indicate any domain restrictions.
The total cost of a taxi is given by the sum of a fixed amount of $1.00 per ride and an additional amount of $2.30 per mile driven. Then, the total cost f in function of the total number of miles driven x is given by:
[tex]f(x)=1+2.3x[/tex]Notice that, since there is no sense in considering "negative miles driven" the domain of this function is given by:
[tex]\mleft\lbrace x\in\mathfrak{\Re }\mright|x\ge0\}[/tex]This is equivalent to state "x is a real number greater than or equal to 0"
Solve (1/2 - 1/5) / 2/3 Simplify if necessary.
The Simplification of the fractional expression (1/2 - 1/5) / 2/3 is 9/20
How to simplify fraction?A fraction is a number which consists of a numerator and a denominator.
A numerator is the top or upper value of a fraction while a denominator is the bottom or lower value of a fraction.
(1/2 - 1/5) / 2/3
= (5-2) / 10 ÷ 2/3
= 3/10 ÷ 2/3
multiply by the reciprocal of 2/3= 3/10 × 3/2
= (3 × 3) / (10 × 2)
= 9/20
In conclusion, (1/2 - 1/5) / 2/3 when simplified is given by 9/20
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A car travels at an average speed of 56 miles per hour. How many miles does it travel in 4 hours and 45minutes?
We can use the following formula to solve the exercise.
[tex]\text{ Distance }=\text{ Rate}*\text{ Time}[/tex]Then, we have:
[tex]\begin{gathered} \text{ Distance = ?} \\ \text{ Rate = 56 mph} \\ \text{ Time }=4\frac{3}{4}=\frac{4*4+3}{4}=\frac{19}{4}=4.75\text{ hours} \\ \text{ Because }\frac{45\text{ minutes}}{60\text{ minutes}}=\frac{45}{60}=\frac{15*3}{15*4}=\frac{3}{4} \end{gathered}[/tex]We replace the know values in the formula.
[tex]\begin{gathered} \begin{equation*} \text{ Distance }=\text{ Rate}*\text{ Time} \end{equation*} \\ \text{ Distance }=56\text{ mph}*4.75\text{ hours} \\ \text{ Distance }=266\text{ mi} \end{gathered}[/tex]AnswerThe car travels 266 miles in 4 hours and 45minutes.
help meeeeeeeeeeeeeee pleaseeeeeeehelp meeeeeeeeeeeeeee pleaseeeeeee
Answer: 10.8 seconds
Step-by-step explanation:
[tex]-16t^2 + 170t+40=10\\\\16t^2 -170t-30=0\\\\t=\frac{-(-170) \pm \sqrt{(-170)^2 -4(16)(-30)}}{2(16)}\\\\t \approx 10.8 \text{ } (t > 0)[/tex]
Write the product using exponents.3.3.3.3Using exponents, the product is
In the product
3×3×3×3
you have 4 threes, then it's equivalent to the next expression:
[tex]3\cdot3\cdot3\cdot3=3^4[/tex]write an expression for the perimeter of the bedroom shown below
In this case, we'll have to carry out several steps to find the solution.
Step 01:
perimeter = ?
x + 4 = width
2x - 3 = length
Step 02:
perimeter = 2* width + 2*lenght
perimeter = 2 * (x + 4) + 2 * (2x -3)
= 2x + 8 + 4x - 6
= 6x + 2
The answer is:
The perimeter of the bedroom is 6x - 2
Determine the GCF of 6x²y - 12xy + 9x³y²
A
B 3x³y²
C
36x³y²
D
36xy
3ry
The greatest common factor(gcf) of the given expression is 3xy.
The expression is 6x²y - 12xy + 9x³y².
From all the terms we take the coefficients. 6 ,12 and 9
The GCF of these three numbers is 3 as it divides all the three numbers.
Now for the variable x. the lowest power will be the gcf. Hence the gcf will have x.
Now for the variable y. the lowest power will be the gcf. Hence the gcf will have y.
Therefore the gcf of the given expression will be 3xy .
6x²y - 12xy + 9x³y² = 3xy (2x - 4 + 3x²y)
The HCF, or highest common factor, is the largest number that divides each of the two or more numbers. HCF is also known by the titles The Greatest Common Measure (GCM) and The Greatest Common Divisor (GCD).
The smallest common multiple of any two or more numbers is found using the least common multiple, or LCM. There are two distinct methods: LCM and HCM. The HCF of two numbers is the highest factor that will exactly any divide two integers equally.
It is the most effective divisor for any pair of integers that may evenly or completely divide the inputted numbers.
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Write an equation of the form y = mx for the line shown below. If appropriate,use the decimal form for the slope.(4,3)
SOLUTION
Step 1 :
In this question, we are expected to find the equation of the line,
y = m x + c
where y = dependent variable,
x = dependent variable,
m = gradient of the line
c = intercept on the y - axis.
Step 2 :
We are given that :
[tex]\begin{gathered} \text{The gradient of the line, } \\ m\text{ }=\text{ }\frac{y_2-y_1}{x_{2_{}}-x_1} \\ \text{where (x }_{1\text{ , }}y_{1\text{ }}\text{ ) = ( 4, 3)} \\ (x_{2\text{ , }}y_2\text{ ) = ( -4 ,- 3 )} \\ \text{Then we have that :} \\ m\text{ = }\frac{(\text{ -3 - 3 ) }}{-\text{ 4 - 4}} \\ m\text{ = }\frac{-6}{-8} \\ m\text{ =}\frac{3}{4} \end{gathered}[/tex]Step 3 :
Since ( x 1, y 1) = ( 4, 3 ) and
[tex]\begin{gathered} \text{the gradient m = }\frac{3}{4}\text{. } \\ y-y_{1\text{ }}=m(x-x_1) \\ y\text{ - 3 =}\frac{3}{4}\text{ ( x - 4 )} \\ \text{simplifying further, we have that:} \\ 4\text{ y - 12 = 3 x - }12 \\ 4y\text{ - 3x - 12 + 12 = 0} \\ 4\text{ y - 3 x = 0} \\ \operatorname{Re}-\text{arranging the equation, we have that:} \\ 4\text{ y = 3 x } \end{gathered}[/tex]CONCLUSION:
The final answer is :
[tex]y=\text{ }\frac{3}{4}\text{ x }[/tex]A box contains five cards lettered A,A,B,C,D. If one card is selected at random from the box and NOT replaced, what is the probability that Jill will draw an A and then a C?
A box contains five cards lettered A,A,B,C,D. If one card is selected at random from the box and NOT replaced, what is the probability that Jill will draw an A and then a C?
step 1
Find the probability that Jill draw an A
P=2/5
step 2
Find the probability that jill draw a C
P=1/4
therefore
the probability that Jill will draw an A and then a C is
P=(2/5)(1/4)
P=2/20
P=1/10 or 10%What’s is the probability of spinning a 4 on the spinner below
The probability of spinning a 4 on the spinner is 1/12.
Given, a spinner having two numbers 4 & 9
the sector having number 9 has an angle of 30°.
We have to find the probability of spinning a 4 on the spinner
So, the probability of spinning a 4 is,
Probability = (Area of sector having number 4)/(Area of the circle)
Probability = (30°/360°×π×r²)/(π×r²)
Probability = 1/12
Hence, the probability of spinning a 4 on the spinner is 1/12.
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help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer: 19.6 feet
Step-by-step explanation:
Using the Pythagorean theorem,
[tex]x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6[/tex]
The student council sold two types of ice cream, sundaes and cones, during homecoming week. Each sundaes cost the same amount, and each cones cost the same amount.
One the first day they earned $210 for selling 125 cones and 10 sundaes
One the second day they earned $256 for selling 100 cones and 30 sundaes.
What was the cost in dollars for each cone sold by the student council?
Answer:
1 cone = $1.36
Step-by-step explanation:
125 c + 10 s = $210
100 c + 30 s = $256
make one of the terms the same (easier one = 30 sundaes)
125 × 3 = 375 c
10 × 3 = 30 s
210 × 3 = $630
375 c + 30 s = $630
375 c + 30 s = $630
100 c + 30 s = $256
same sign = subtract
375 - 100 = 275 c
30 - 30 = 0 s
630 - 256 = $374
275 c = $374
÷ 275 on both sides to get c
c = $1.36
Jada drank 12 ounces of water from her bottle. This is 60% of the water the bottle holds. How much water does the bottle hold?
Jada's water bottle holds 20 ounces of water.
Let the water bottle holds x ounces of water.
She drank 12 ounces of water.
this is equivalent to 60%
Hence 60% of x = 12
or, 0.6x = 12
or, x = 20 ounces
Therefore the bottle holds 20 ounces of water.
The English word percentage which refers to fractions with a denominator of 100, was derived from the Slang term "per centum," which means "by the hundred."
In other words, it is a connection where it is always assumed that the value of the whole is 100. The proportion of each reading to the total value is represented by the actual number whenever we have two or more readings that sum up to 100.
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pls help me i will fail if i get this wrong ):
The position of museum relative to hotel will be (9,1) as the starting position will be (0,0) that is her hotel then the position of coffee shop is (-2,4) and at the end position of museum is (7,5).
What is coordinate?A set of values indicating an exact position. On graphs, it is typically represented by a pair of numbers: the first number represents the distance along, and the second number represents the distance up or down. The location in the cartesian plane will be defined by the coordinate points. The distance between two points is known as the x-coordinate, or abscissa, and the distance between two points is known as the y-coordinate. To find the coordinates of a point in a coordinate system, do the inverse. Start at the point and trace a vertical line up or down to the x-axis. There you have your x-coordinate. Then repeat the process, but this time follow a horizontal line to find the y-coordinate.
Here,
The starting coordinate=0,0
The second coordinate=-2,4
The ending coordinate=7,5
The required coordinate will be
=7--2-0,5-4-0
=9,1
The position of the museum in relation to the hotel is (9,1) because the starting point is (0,0) that is her hotel and the position of the coffee shop is (-2,4) and the position of museum is (7,5).
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Someone please help me
Answer:
3. Texas (1), timeline (2), tryouts (3), two-step (4)
4. wail (1), waved (2), wriggled (3), write (4)
Step-by-step explanation:
3. All start with T
go onto the next letter
Texas
Two-step
Tryout
Timeline
Therefore,
Texas (1)
Timeline(2)
Tryout(3)
two-step (4)
4. Same process as before, we are going to the third letters for wail and waved, the fourth letter for wiggled and write.
Wriggled
Write
Wail
Waved
g comes before t
i comes before v
Therefore,
wail (1)
waved (2)
wriggled(3)
write(4)
describe the translation of the point to its image: (-4,-6) to (-6,-12)
We want to translate from point (- 4, - 6) to (- 6, - 12)
If we translate a point with coordinates, (x, y) by c units to the left and d units downwards, the new coordinates would be (x - c, y - d)
Looking at the given points,
- 4 - 2 = - 6
- 6 - 6 = - 12
Thus, the point was translated by 2 units to the left and 6 units downwards
Let A={1,2,3,4,5,6} and B={4,6,8}. Which of the following is an element of A∩B?Select the correct answer below:3682
Given the following set:
A = {1,2,3,4,5,6}
B = {4,6,8}
∩ means "intersection" of two sets. In other words, the data that the two sets have in common.
Checking the given sets,
A = {1,2,3,4,5,6}
B = {4,6,8}
A∩B or A and B have a common data of 4 and 6. These two are the intersections of A and B.
Among the given choices, only Choice B is correct which is 6.
Therefore, the answer is CHOICE B : 6
i really need help with math i am not the best at it
a Given:-
A image.
To find the total area of the given image.
So the given image is splitted into three images they are a triangle at the top and a rectangle at the middle and parallelogram at the bottom.
So the formula for triangle is,
[tex]A=\frac{1}{2}\times b\times h[/tex]So the formula for rectangle is,
[tex]A=l\times b[/tex]So the formula for parallogram is,
[tex]A=b\times h[/tex]So from the given image we have the values as,
Triangle has,
[tex]b=3,h=4[/tex]Rectangle has,
[tex]l=10,b=3[/tex]Paralleogram has,
[tex]b=5,h=2[/tex]So now we substitute the following values. so we get,
For Triangle,
[tex]\begin{gathered} A=\frac{1}{2}\times3\times4 \\ A=3\times2 \\ A=6 \end{gathered}[/tex]For Rectangle,
[tex]\begin{gathered} A=10\times3 \\ A=30 \end{gathered}[/tex]For paralleogram,
[tex]\begin{gathered} A=5\times2 \\ A=10 \end{gathered}[/tex]So the total area is,
[tex]\begin{gathered} A=6+30+10 \\ A=46 \end{gathered}[/tex]So the total area is 46 in.sq.
Please help me solve this problem
Answer:
The amount invested at an 8% rate would be $184
The amount invested at a 3% rate would be $69
Step-by-step explanation:
The amount invested at an 8% rate would be $184 because 2,300 x 0.08 (8% in a decimal form) x 1 (since it was after 1 year) would come to 184.
The amount invested at an 3% rate would be $69 because 2,300 x 0.03 (3% in a decimal form) x 1 (since it was after 1 year) would come to 69.
What is the point slope form of the line with slope -1/4 that passes through the
point (9, 2)?
Answer:
[tex]y - 2 = - \frac{1}{4} (x - 9)[/tex]
find the 12th term of the geometric sequence 1,3,9,...
find the 12th term of the geometric sequence 1,3,9,...
we have
a1=1 ------> first term
a2=3
a3=9
Find the value of r (common ratio)
we have that
a2/a1=3/1=3
a3/a2=9/3=3
so
the common ratio is
r=3
we know that the general equation for a geometric sequence is
[tex]a_n=a_1\cdot r^{(n-1)}[/tex]we have
a1=1
r=3
substitute
[tex]\begin{gathered} a_n=1\cdot3^{(n-1)} \\ a_n=3^{(n-1)} \end{gathered}[/tex]Find the 12th term
so
For n=12
substitute in the equation
[tex]\begin{gathered} a_{12}=3^{(12-1)} \\ a_{12}=3^{(11)} \\ a_{12}=177,147 \end{gathered}[/tex]therefore
the answer is177,147Evaluate the expressions. 0 3 9 Х Ś ? (-2) =
Question:
Solution:
Every number different from zero, with zero power, is always equal to 1. Then we can conclude that:
[tex]3(\frac{4}{9})^0\text{ = 3(1) = 3}[/tex]and
[tex](-2)^0\text{ = 1}[/tex]Is the point (-2,11) on the circle with radius 5 and center (2,13)?
From the question;
we are to determine if the point (-2, 11) is on the circle with radius 5 and center (2, 13)
The equation of a circle with a radius r and center (a, b) is given as
[tex](x-a)^2+(y-b)^2=r^2[/tex]Hence, the equation of the circle with radius 5 and center (2, 13)
[tex]\begin{gathered} (x-2)^2+(y-13)^2=5^2 \\ (x-2)^2+(y-13)^2\text{ = 25} \end{gathered}[/tex]Considering the point (-2, 11), we need to substitute the values for x and y
therefore, x = -2, y = 11
[tex]\begin{gathered} (-2-2)^2+(11-13)^2\text{ }\ne\text{ 25} \\ (-4)^2+(-2)^2\text{ }\ne\text{ 25} \\ 16\text{ + 4 }\ne\text{ 25} \\ 20\text{ }\ne\text{ 25} \end{gathered}[/tex]Since LHS is not equal to RHS then the point (-2, 11) is not on the circle.
The graph below has the same shape as the graph of G(x) = {4, but it isshifted two units to the right. Complete its equation. Enter exponents usingthe caret (-); for example, enter x4 as x^4. Do not include "G(X) =" in youranswer.5.G(X) =
ANSWER:
[tex]G(x)=(x-2)^4[/tex]STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]G(x)=x^4[/tex]In a function, to move it to the right or to the left we must add if we want to move to the left and we must subtract if we want to move to the right.
But we must add or subtract within the exponent, since it moved 2 to the right we must subtract 2 units, just like this:
[tex]G(x)=(x-2)^4[/tex]if a_1=2 and a_n=2a_n-1 find the first five terms of the sequence
Answer:
a1 = 2, a2 = 4, a3 = 8, a4 = 16, and a5 = 32
Explanation:
Given the first term and the nth term of the sequence as;
[tex]\begin{gathered} a_1=2 \\ a_n=2a_{n-1} \end{gathered}[/tex]Since the first term is given already to be 2, let's go ahead and find the 2nd term;
[tex]\begin{gathered} a_2=2a_{2-1} \\ a_2=2a_1 \\ a_2=2\ast2 \\ \therefore a_2=4_{} \end{gathered}[/tex]The 3rd term will be;
[tex]\begin{gathered} a_3=2a_{3-1} \\ =2a_2 \\ =2\ast4 \\ \therefore a_3=8 \end{gathered}[/tex]The 4th term can be found as follows;
[tex]\begin{gathered} a_4=2a_{4-1} \\ =2a_3 \\ =2\ast8 \\ \therefore a_4=16 \end{gathered}[/tex]The 5th term can found as follows;
[tex]\begin{gathered} a_5=2a_{5-1} \\ =2a_4 \\ =2\ast16 \\ \therefore a_5=32 \end{gathered}[/tex]Find the arc length of the semicircle.
Either enter an exact answer in terms of π or use 3.14 point, 14 for π and enter your answer as a decimal.
Answer:
28.26 units
Step-by-step explanation:
circumference equals 2r times pi. radius is 9 so the circumference is 2 x 9 x pi (which is 3.14). This would give is 56.52 but since its a half circle you divide it by two
3. Shown above is the graph for which of the following equations?
O A. y=-x-3
O B.y=x+3
O C. y=x-3
O D.y=3-x
Using the equation of slope intercept form, the equation of the given graph is y=x-3.
In the given question we have to find equation of the given graph.
From the given graph the points are (3,0) and (0,-3).
We know the standrd equation of the line is y=mx+c
where m=slope and c=value of y at the y intercept form.
So the value of c= -3
Now finding the value of m.
m={y(2)-y(1)}/{x(2)-x(1)}
From the points, x(1)=3, x(2)=0, y(1)=0, y(2)= -3
Putting the value
m=(-3-0)/(0-3)
m=-3/-3
m=1
Now putting the value of m and c in the equation
y=mx+c
y=1*x+(-3)
y=x-3
Hence, the equation of the given graph is y=x-3.
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At the beginning of a snowstorm, Hassan had 2 inches of snow on his lawn.
The snow then began to fall at a constant rate of 2.5 inches per hour.
Assuming no snow was melting, how much snow would Hassan have on his
lawn 5 hours after the snow began to fall? How much snow would Hassan
have on his lawn after t hours of snow falling?
Hassan will have 14.5 inches of snow on his lawn after 5 hours of snow falling.
How to find amount snow ?Individual ice crystals that make up snow develop while suspended in the atmosphere, typically within clouds, before falling and accumulating on the ground, where they go through additional changes.
It starts out as frozen crystalline water that forms in the atmosphere under favourable conditions, grows to millimetre size, precipitates and builds up on surfaces, then undergoes a metamorphosis in place, and finally melts, slides, or sublimates away.
2 inches of snow on the lawn
Rate of snow falling = 2.5 inches per hour
Snow did not melt
Let y = height of snow on the lawn
Let t = time in hours
y = 2 + 2.5t
To find how much snow is on the lawn after 5 hours of snowing, substitute t = 5 into the found equation and solve for y:
⇒ y = 2 + 2.5(5)
⇒ y = 2 + 12.5
⇒ y = 14.5 inches
Therefore, Hassan will have 14.5 inches of snow on his lawn after 5 hours of snow falling.
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