Answer:
Step-by-step explanation:
1. Equation of a circle:
(x - h)² + (y - k)² = r²
where (h, k) is the center and r is the radius.
If (h, k) is (2, 8) and r = 10:
(x - 2)² + (y - 8)² = 100
2. The vertex and focus have the same x-coordinate, so this is a vertical parabola. Equation of a vertical parabola is:
y = 1/(4p) (x - h)² + k
where (h, k) is the vertex and p is the distance from the vertex to the focus.
If (h, k) is (2, 2) and p = 5-2 = 3:
y = 1/12 (x - 2)² + 2
3. The directrix is a vertical line, so this is a horizontal parabola. Equation of a horizontal parabola is:
x = 1/(4p) (y - k)² + h
The distance between the directrix and the vertex is the same as p.
If (h, k) is (5, 2) and p = 5-3 = 2:
x = 1/8 (y - 2)² + 5
What is the solution to the equation below?
Answer:
[tex]\frac{38}{7}[/tex]
Step-by-step explanation:
Using the properties of logarithms,
[tex]\log(7)+\log(x-4)=1\\\log(7(x-4))=1\\\log(7x-28)[/tex]
Now think about what this is asking. The log function say 10 to the power of whats on the other side of the equals sign, equals whats in the parenthesis. So, this means whats is the parenthesis is equal to [tex]10^1[/tex] or just 10.
We can now solve to x.
[tex]7x-28 = 10\\7x=38\\x=\frac{38}{7}[/tex]
Answer:
x=38/7
Step-by-step explanation:
Just took the test
The figure below is rotated 270° clockwise about the origin .List the coordinates of the image.
A ( , )
B( , )
C( , )
D( , )
Answer:
A (-4, -4), B (-2, 6), C (-1, 1), D(-3, -5)
Step-by-step explanation:
Before the rotation:
A (-4, 4), B (6, 2), C (1, 1), D(-5, 3)
270° rotation clockwise is the same as 90° counterclockwise. To do that transformation:
(x, y) → (-y, x)
Therefore, the coordinates of the rotated figure are:
A (-4, -4), B (-2, 6), C (-1, 1), D(-3, -5)
The coordinates of the image are:
A'(-4,-4)B'(-2,6)C'(-1,1)D(-3,-5)---------------------------
This question is solved applying a 270° clockwise about the origin, which has the following rule:
[tex](x,y) = (-y,x)[/tex]
---------------------------
Coordinate A:
At the Figure, coordinate A is A(-4,4). Applying the rule:
[tex](-4,4) = (-4, -4)[/tex]
So the image of A is A'(-4,-4).
---------------------------
Coordinate B:
At the Figure, coordinate B is B(6,2). Applying the rule:
[tex](6,2) = (-2, 6)[/tex]
So the image of B is B'(-2,6).
---------------------------
Coordinate C:
At the Figure, coordinate C is C(1,1). Applying the rule:
[tex](1,1) = (-1, 1)[/tex]
So the image of C is C'(-1,1).
---------------------------
Coordinate D:
At the Figure, coordinate C is D(-5,3). Applying the rule:
[tex](-5,3) = (-3,-5)[/tex]
So the image of D is D'(-3,-5).
A similar question is given at https://brainly.com/question/3382538
Solve for x.
A. 6
B. 7
C. 4
D. 5
Answer:
D
Step-by-step explanation:
[tex]\frac{5x}{20} =\frac{45}{36}[/tex]
Cross multiply:
(5x)(36)=(20)(45)
180x = 900
divide by 180.
x=5
The value of x is 5.
How to find the value of x?Δ ACE ≅ Δ BCD (by AAA property)
Therefore
[tex]\frac{CD}{CE} = \frac{CB}{CA}[/tex] ( Similar triangle property)
[tex]\frac{20}{36} = \frac{5x}{45}[/tex]
5x = [tex]\frac{20 * 45}{36}[/tex]
5x = 25
x = 5
Therefore, option D. 5 is the correct answer
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Find the zeros of the function in the interval [-2xπ, 2π].
f(x)=3 cos x
Answer:
Option d.
±π/2 ; ±3π/2
Step-by-step explanation:
To quickly solve this problem, we can use a graphing tool or a calculator to plot the equation.
Please see the attached image below, to find more information about the graph
The equation is:
f(x)= 3*cos (x)
We can see from the graph that the zeros are
±π/2 ; ±3π/2
Correct option is d.
Use substitution to solve the system of equations x= -3y-13 2x+2y=-6
For this case we have a system of two equations with two unknowns:
[tex]x = -3y-13\\2x + 2y = -6[/tex]
To solve we follow the steps below:
We substitute the first equation in the second:
[tex]2 (-3y-13) + 2y = -6[/tex]
We apply distributive property to the terms of parentheses:
[tex]-6y-26 + 2y = -6[/tex]
We add 26 to both sides of the equation:
[tex]-6y + 2y = -6 + 26\\-4y = 20\\y = \frac {20} {- 4}\\y = -5[/tex]
We find the value of x:
[tex]x = -3 (-5) -13\\x = 15-13\\x = 2[/tex]
Answer:
[tex](x, y) :( 2, -5)[/tex]
The manager of cups R' Us handed out 125 coupons to his customers on Monday, c coupons on Tuesday, and 220 coupons on the Wednesday. Write an expression for the total number of coupons the manager handed out. Then simplify the expression.
Answer:125+220+c
if c= 20 then it would be 125+220+20=365
Step-by-step explanation:
PLEASE HELP!!!
What is -5/8 times 2/3?
Simplify for -5/8*2/3= -5/12
-0.416 as a mixed number
Find the partial fraction decomposition of
[tex]\dfrac1{x(x-1)}=\dfrac ax+\dfrac b{x-1}[/tex]
[tex]1=a(x-1)+bx[/tex]
If [tex]x=0[/tex], then
[tex]1=-a\implies a=-1[/tex]
If [tex]x=1[/tex], then
[tex]1=b[/tex]
So we have
[tex]\dfrac1{x(x-1)}=\dfrac1{x-1}-\dfrac1x[/tex]
1. A factory makes bicycles. Out of 300 bicycles, 2 were found to have defective brakes.
a. What is the experimental probability that the next bike manufactured will have defective brakes?
b. Predict how many bikes out of 2,100 will have defective brakes.
*Please explain how you found the answers*
Answer:
a. 1/150.
b. 14.
Step-by-step explanation:
a. That would be 2/300 = 1/150.
b. So we expect 1 out of every 150 bikes will have 1 with defective brakes so out of 2,100 it is (1/150) * 2,100
= 14.
Step-by-step explanation:
Which choice is equivalent to the quotient below shown here when x>0?
Answer:
Choice B is correct
Step-by-step explanation:
The given radical division can be expressed in the following form;
[tex]\frac{\sqrt{16x^{3} } }{\sqrt{8x} }[/tex]
Using the properties of radical division, the expression can be expressed in the following form;
[tex]\sqrt{\frac{16x^{3} }{8x} }=\sqrt{2x^{2} }[/tex]
Simplifying further yields;
[tex]\sqrt{2x^{2} }=\sqrt{2}*\sqrt{x^{2} }=x\sqrt{2}[/tex]
Choice B is thus the correct alternative
For this case we must simplify the following expression:
[tex]\frac {\sqrt {16x ^ 3}} {\sqrt {8x}} =[/tex]
Join the terms in a single radical:
\[tex]\sqrt {\frac {16x ^ 3} {8x}} =\\\sqrt {\frac {8 * (2x ^ 3)} {8x}} =\\\sqrt {\frac {2x ^ 3} {8x}} =\\\sqrt {2x ^ 2} =\\\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
So:
[tex]\sqrt {2x ^ 2} =\\x \sqrt {2}[/tex]
Answer:
Option B
Question 1 Find the maximum value of the function for the polygonal convex set determined by the given system of inequalities
Answer:
The maximum value is 126 occurs at (9 , 9)
Step-by-step explanation:
* Lets remember that a function with 2 variables can written
f(x , y) = ax + by + c
- We can find a maximum or minimum value that a function has for
the points in the polygonal convex set
- Solve the inequalities to find the vertex of the polygon
- Use f(x , y) = ax + by + c to find the maximum value
∵ 8x + 2y = 36 ⇒ (1)
∵ -3x + 6y = 27 ⇒ (2)
- Multiply (1) by -3
∴ -24x - 6y = -108 ⇒ (3)
- Add (2) and (3)
∴ -27x = -81 ⇒ divide both sides by -27
∴ x = 3 ⇒ substitute this value in (1)
∴ 8(3) + 2y = 36
∴ 24 + 2y = 36 ⇒ subtract 24 from both sides
∴ 2y = 12 ⇒ ÷ 2
∴ y = 6
- One vertex is (3 , 6)
∵ 8x + 2y = 36 ⇒ (1)
∵ -7x + 5y = -18 ⇒ (2)
- Multiply (1) by 5 and (2) by -2
∴ 40x + 10y = 180 ⇒ (3)
∴ 14x - 10y = 36 ⇒ (4)
- Add (3) and (4)
∴ 54x = 216 ⇒ ÷ 54
∴ x = 4 ⇒ substitute this value in (1)
∴ 8(4) + 2y = 36
∴ 32 + 2y = 36 ⇒ subtract 32 from both sides
∴ 2y = 4 ⇒ ÷ 2
∴ y = 2
- Another vertex is (4 , 2)
∵ -3x + 6y = 27 ⇒ (1)
∵ -7x + 5y = -18 ⇒ (2)
- Multiply (1) by 7 and (2) by -3
∴ -21x + 42y = 189 ⇒ (3)
∴ 21x - 15y = 54 ⇒ (4)
- Add (3) and (4)
∴ 27y = 243 ⇒ ÷ 27
∴ y = 9 ⇒ substitute this value in (1)
∴ -3x + 6(9) = 27
∴ -3x + 54 = 27 ⇒ subtract 54 from both sides
∴ -3x = -27 ⇒ ÷ -3
∴ x = 9
- Another vertex is (9 , 9)
* Now lets substitute them in f(x , y) to find the maximum value
∵ f(x , y) = 9x + 5y
∴ f(3 , 6) = 9(3) + 5(6) = 27 + 30 = 57
∴ f(4 , 2) = 9(4) + 5(2) = 36 + 10 = 46
∴ f(1 , 5) = 9(9) + 5(9) = 81 + 45 = 126
- The maximum value is 126 occurs at (9 , 9)
The maximum value of the function for the polygonal convex set determined by a system of inequalities can be found using linear programming. The key steps are to plot the inequalities, find the vertices of the feasible region, and substitute these points into the function to find the maximum value.
Explanation:This problem is related to linear programming, which is a method to achieve the best outcome in a mathematical model whose requirements are represented by linear relationships. To find the maximum value of the function for the polygonal convex set determined by the given system of inequalities, you essentially need to apply the rules of linear programming.
Firstly, plot the system of inequalities on a coordinate system to determine the feasible region, which is the polygonal convex set. Then, find each vertex of this polygonal convex set. These vertices are points where boundaries of the system of inequalities intersect. Once you have these vertices, substitute each of them into the function you are maximizing. The largest output will be the maximum value of the function within the given polygonal convex set.
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What is the effective annual interest rate on a savings account that earns interest at a rate of 1.55% compounded monthly?
A.
1.29%
B.
1.55%
C.
1.56%
D.
1.59%
Answer:
C
Step-by-step explanation:
The formula for effective annual interest rate is:
[tex]r=(1+\frac{i}{n})^{n}-1[/tex]
where
r is the effective annual interest rate
i is the stated interest rate (here, it is 1.55%, or 0.0155)
n is the number of compounding periods (here, compounded monthly, so it means 12 times a year, so n = 12)
plugging these info into the formula, we get:
[tex]r=(1+\frac{i}{n})^{n}-1\\r=(1+\frac{0.0155}{12})^{12}-1\\r=0.0156[/tex]
0.0156 * 100 = 1.56%
correct answer is C
Answer:
The answer is C
Step-by-step explanation:
i got it right on Plato : ) Brainliest?
Please help with this question. I don't understand!
Answer:
6135.9m^3
Step-by-step explanation:
V=3.14r^2 h/3
step by step
1. the radius is half so half of 25 is 12.5 that's the r in your equation
2.the height in your equation is 3 times more then the radius and your radius is 12.5X3 =37.5 for your height
3. plug everything in back into the equation v=3.14(12.5)^2(37.5/3)= 6135.923 when rounded it is 6135.9m^3
Please answer this multiple choice question CORRECTLY for 30 points and brainliest!
Answer:
D
Step-by-step explanation:
If you made a table and filled in the values, the rate column it would look like this:
d = r t
truck 80
car 90
So far so good. If we want the car to catch up with the truck, that means that in the end they travel the exact same amount of miles. So let's fill in the d:
d = r t
truck d 80
car d 90
Again, not too bad. If the car leaves 20 minutes later than the truck, that means that the time the truck is traveling is 20 minutes more than the car's time. So the car's time is t and the truck's time is t + 20:
d = r t
truck d 80 t+20
car d 90 t
Now because the distances are equal, we can set the rate times time for each vehicle equal to each other:
80(t + 20) = 90t
That is choice D
In the straightedge and compass construction of the equilateral triangle below, how do you know that AB ≈ AC?
Answer:
C
Step-by-step explanation:
C: AB is the radius of both circles.
Answer:
C. line segment AB is the radius of both circles.
Step-by-step explanation:
If point A is the center of the first circle and point B is the center of the second circle (in the figure), therefore Line segment AB is the radius of both circles and we write.
Line segment AB = line segment AC (radius of first circle ) and
line segment AB = line segment BC (radius of second circle).
Hence line segment AB is the radius of both circle is the correct option for AB =AC.
A sweater was on sale at %40 off the regular price. Ella saved $20 by buying the sweater on sale. What was the regular price of the sweater?
so she saved $20 and that was 40% of the regular price, let's say the regular price is "x".
if 20 is 40%, what is "x" or namely the 100%?
[tex]\bf \begin{array}{ccll} amount0&\%\\ \cline{1-2} 20&40\\ x&100 \end{array}\implies \cfrac{20}{x}=\cfrac{40}{100}\implies \cfrac{20}{x}=\cfrac{2}{5}\implies 100=2x \\\\\\ \cfrac{100}{2}=x\implies 50=x[/tex]
Answer:This is an equation! Solutions: x=1.
Step-by-step
For a normally distributed random variable x with m = 75 and s = 4, find the probability that 69 < x < 79 Use the table to help find the answer.
10-14-19-12-14-18-10-15-15
Translate the phrase into an algebraic expression
the sum of x and 6
Answer:
x + 6 =
Step-by-step explanation:
In math sum means addition, difference is subtraction, product is multiplication, and quotient is division
ANSWER
x+6
EXPLANATION
An algebraic expression contains letters and numbers that are connected with mathematical operators or symbols.
The sum of x and 6 as an algebraic up expression is:
x+6
This expression contains a variable , a mathematical symbol and a number.
The graph of the function, f(x) = 3^2 + x + 2, opens(down or up) and has a (minimum or maximum) value.
1. The parabola opens upward.
2. It has a minimum value
Step-by-step explanation:The explanation is shown below. Also, the graph of this function is shown below including the vertex.
A television manufacturer decides to increase its production by 25% per month to meet increasing customer demand. The company currently produces 2,000 television sets a month.
Which of the following graphs shows the total number of television sets, y, manufactured by the company in x months?
Answer:
The last graph
Step-by-step explanation:
The problem presented here is similar to a compound interest problem since we have an initial value, a growth constant and the aspect of time.
We can consider the number of television sets currently produced by the company to be our Principal amount;
P = 2000
The rate of increase in production per month can be considered as our interest rate earned;
r = 25% = 0.25
The total number of television sets y will be our Accumulated amount;
A = y
The duration x becomes our time n.
The compound interest formula is given as;
[tex]A=P(1+r)^{n}[/tex]
We simply substitute the given information into the formula;
[tex]y=2000(1.25)^{x}[/tex]
This is an exponential growth function since the base of the exponent x is greater than 1.
A graph of the function will be an exponential curve passing through ( 0, 2000) since 2000 is our initial value
Answer: the last ones
Step-by-step explanation: I put it and got it right:)
Write an equation in point-slope form for the line through the given point with the given slope. (–3, –7); m = -6/5x
The equation in point-slope form for the line through the point (-3, -7) with slope -6/5x is y - (-7) = -6/5(x - (-3)).
Explanation:To write the equation of a line in point-slope form, we can use the given point and slope. The point we have is (-3, -7) and the slope is -6/5. The point-slope form of a linear equation is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Plugging in the values, we get the equation as:
y - (-7) = -6/5(x - (-3))
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To write an equation in point-slope form, you need the coordinates of a point on the line and the slope of the line. In this case, the given point is (–3, –7) and the slope is -6/5. The equation in point-slope form is y + 7 = -6/5(x + 3).
Explanation:To write an equation in point-slope form, you need the coordinates of a point on the line and the slope of the line. In this case, the given point is (–3, –7) and the slope is -6/5.
The point-slope form of the equation is y - y1 = m(x - x1).
Plugging in the values, we get y - (-7) = -6/5(x - (-3)).
Simplifying, we have y + 7 = -6/5(x + 3).
Thus, the equation in point-slope form for the line through the point (–3, –7) with a slope of -6/5x is y + 7 = -6/5(x + 3).
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Bodhi has a collection of 175 dimes and nickels. The collection is worth $13.30. Which equation can be used to find n, the number of nickels in the collection? 0.1n + 0.05(n – 175) = 13.30 0.1n + 0.05(175 – n) = 13.30 0.1(n – 175) + 0.05 = 13.30 0.1(175 – n) + 0.05n = 13.30
Answer: 0.1(175-n)+0.05n=13.30
Step-by-step explanation: The question is asking you to make and simplify a system of equations.
The 2 equations are:
n+d=175
0.1d+0.05n=13.30.
d=175-n
Solve for n, then substitute into the second equation.
0.1(175-n)+0.05n=13.30
Hope this helps!
Kalaty bought 1/12 pounds of butter.How many ounces are 1/12 pounds of butter? Layla hatched 92 eggs.She used 43 and 1/5 of them how many eggs does she have left?
For this case we have that by definition:
1 pound is equivalent to 16 ounces.
We make a rule of three to determine the ounces of butter:
1lb ------------------------> 16onzas
[tex]\frac {1} {12}[/tex]----------> x
Where "x" represents the ounces of butter
[tex]x = \frac {\frac {1} {12} * 16} {1}\\x = \frac {16} {12}\\x = \frac {8} {6}\\x = \frac {4} {3}[/tex]
Thus, there are [tex]\frac {4} {3}[/tex]ounces of butter.
Now we must find the amount of eggs that remain:
[tex]92- (43+ \frac {1} {5}) =\\92 - (\frac {43 * 5 + 1} {5}) =\\92 - (\frac {215 + 1} {5}) =\\92 - (\frac {216} {5}) =\\92-43.2 =\\48.8[/tex]
Round down. There are 48 eggs left.
Answer:
There are [tex]\frac {4} {3}[/tex] ounces of butter.
48 eggs left
19. The areas of corresponding faces of two similar hexagonal prisms are 25 cm² and 121 cm². What is the ratios of the corresponding sides lengths? of the perimeter? of the volumes?
ANSWER
I) 5:11
ii) 5:11
iii) 125:1331
EXPLANATION
Let the side lengths be in the ratio:
x:y
This implies that the area will be in the ratio:
[tex] \frac{ {x}^{2} }{ {y}^{2} } = \frac{25}{121} [/tex]
Take positive square root.
[tex] \frac{x}{y} = \sqrt{ \frac{25}{121} } [/tex]
[tex] \frac{x}{y} = \frac{5}{11} [/tex]
Hence the sides are in the ratio:
x:y=5:11
The perimeter of the smaller hexagon is 6×5=30
The perimeter of the larger hexagon is 6×11=66
The ratio of the perimeter is
30:66=5:11
The volume will be in the ratio
5³:11³
125:1331
A Store is having two sales on popcorn. The original price of the popcorn is $10 for 10 oz. Sale A offers you 33% more popcorn for free. Sale B offers you the same amount of popcorn, but at 33% off of the original price. What is the better deal? Why?
Answer:
33% off is the better deal
Step-by-step explanation:
1.33 times as much popcorn for the same price is equivalent to 1/1.33 ≈ 0.75 times the price for the original amount of popcorn. That price is equivalent to a sale of 1 - 0.75 = 0.25 = 25% off.
The sale price of 33% off is a better deal (if you don't want the extra popcorn).
A rider is riding a bicycle on a 6 foot wall at a rate of 1 foot per second.The wheels have a radius of 1 foot and a piece of gum becomes stuck to the rear wheel as shown what's the gum minimum height and maximum height
Answer:
Gum’s Minimum height: 6ft
Gum’s Maximum height: 8ft
2nd part
How far does the gym travel in one revolution of the bicycle wheel?
2pi
Answer:
Minimum height of gum = 6 foot.
Maximum height of gum = 8 foot.
Step-by-step explanation:
A rider is riding a bicycle on a 6 foot wall, therefore the height of the lowest point of the rear wheel is 6 foot from the ground and highest point of the rear wheel is (6+2) foot = 8 foot ( because diameter of rear wheel =2 foot ).
If a piece of gum become stuck to the rear wheel, hence the minimum height of the gum is 6 foot from the ground and maximum height of the gum is 8 foot from the ground.
Identify the factors of 4x2 + 12x + 9
(4x − 3)(x − 3)
(4x + 3)(x + 3)
(2x − 3)(2x − 3)
(2x + 3)(2x + 3)
Answer:
(2x+3)(2x+3)
Step-by-step explanation:
a^2+2ab+b^2
Which of these shows the result of using the first equation to substitute for Y in the second equation, then combining like terms?
Y=2x
2x+3y=16
A. 8x=16
B. 4x=16
C. 5y=16
D. 5x=16
ANSWER
A. 8x=16
EXPLANATION
The given equations are:
1st equation: y=2x
2nd equation: 2x+3y=16
We substitute the first equation into the second equation to get:
2x+3(2x)=16
This implies that:
2x+6x=16
We combine like terms to get:
8x=16
The correct choice is A. 8x=16
30 POINTS PLEASE HELP!
Which division problem does the model represent?
Answer:
first 1
Step-by-step explanation:
first 1
Answer:
7/4 ÷ 1/2= 3 1/2
Step-by-step explanation:
This is the answer hope it help's :)
What are the period and amplitude of the function?
ANSWER
Period: 2π , amplitude: 4
EXPLANATION
The graphed function is
[tex]y = 4\cos(x) [/tex]
The amplitude of this function is
[tex] |4| = 4[/tex]
The period is 2π because there is no phase shift hence the period is still equal to the parent function.
Period: 2π , amplitude: 4
Answer:
The correct option is 3.
Step-by-step explanation:
The general form of a cosine function is
[tex]f(x)=A\cos (Bx+C)+D[/tex]
where, A is amplitude, 2π/B is period, C is phase sift and D is midline.
[tex]A=midline=\frac{Maximum-Minimum}{2}[/tex]
[tex]A=midline=\frac{4-(-4)}{2}[/tex]
[tex]A=midline=4[/tex]
The amplitude of the function is 4.
The given graph complete a cycle in the interval [0,2π], therefore the period of the graph is 2π.
Therefore the correct option is 3.