Answer:
[tex](x-9)^{2}+(y+4)^{2}=81[/tex]
Step-by-step explanation:
we know that
The equation of a circle in standard form is equal to
[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]
where
(h,k) is the center
r is the radius
In this problem we have
[tex](h,k)=(9,-4)[/tex]
[tex]r=9\ units[/tex]
substitute
[tex](x-9)^{2}+(y+4)^{2}=9^{2}[/tex]
[tex](x-9)^{2}+(y+4)^{2}=81[/tex] ----> equation of the circle in standard form
POP QUIZ
First person to answer correctly gets brainliest
1. 1-1
2. (1248/56)^0
3. 2*0
Answer:
What's the question? All you posted was the potential answers.
Step-by-step explanation:
This seems really easy, but
1) 0
2) 0
3) 0
which of the following is a point on the plane curved defined by the parametric equations?
x=4t
y=12t^2+4t-1
a. (4,7)
b. (4,207)
c.(-2,4)
d.(-2,0)
Answer:
d.(-2,0)
Step-by-step explanation:
The given parametric equation is:
[tex]x=4t[/tex]
[tex]y=12t^2+4t-1[/tex]
We make t the subject in the first equation;
[tex]t=\frac{x}{4}[/tex]
We substitute into the second equation to get:
[tex]y=12(\frac{x}{4})^2+4(\frac{x}{4})-1[/tex]
[tex]y=\frac{3}{4}x^2+x-1[/tex]
When x=4 , [tex]y=\frac{3}{4}(4)^2+4-1=15[/tex]
When x=-2 , [tex]y=\frac{3}{4}(-2)^2+-2-1=0[/tex]
Therefore the point (-2,0) lies on the given parametric curve.
An end table costs $69.85 today. If the CPI is 194, what would an end table cost in 1983, to the nearest cent? a. $135.51 b. $124.15 c. $36.00 d. $23.76
Answer:
$36.00
Step-by-step explanation:
The cost performance index (CPI) is a measure of the financial effectiveness and efficiency of a project. As a ratio it is calculated by dividing the budgeted cost of work completed, or earned value, by the actual cost of the work performed, that is to say:
CPI = Budgeted cost of work / Actual cost of work
From the statement we know that:
CPI = 1.94
Budgeted cost of work= $69.85
Cost of work in 1983 = Budgeted cost of work / CPI
Cost of work in 1983 = $69.85 / 1.94 = $36.00
Answer:
The answer is C
Step-by-step explanation:
Approximately how much water does the average american use every day?
Answer: Estimates vary, but each person uses about 80-100 gallons of water per day
I need help
A rectangular shelf has a perimeter of 46 inches. Its area is 76 square inches. What are the dimensions of the shelf?
Answer:
19 in × 4 inStep-by-step explanation:
l - length
w - width
The formula of a perimeter of a rectangle: P = 2(l + w)
The formula of an area of a rectangle: A = lw
We have P = 46in and A = 76in² Substitute:
(1) 2(l + w) = 46
(2) lw = 76
2(l + w) = 46 divide both sides by 2
l + w = 23 subtract w from both sides
l = 23 - w
subtitute it to (2):
(23 - w)w = 76 use the distributive property
23w - w² = 76 subtract 76 from both sides
-w² + 23w - 76 = 0 change the signs
w² - 23w + 76 = 0
w² - 4w - 19w + 76 = 0
w(w - 4) - 19(w - 4) = 0
(w - 4)(w - 19) = 0 ⇔ w - 4 = 0 or w - 19 = 0
w - 4 = 0 add 4 to both sides
w = 4
w - 19 = 0 add 19 to both sides
w = 19
Put the values of w to (1):
l = 23 - 4 = 19 or l = 23 - 19 = 4
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
Choose the correct formula for the function g.
Answer: C) g(x) = 2ˣ⁻³ + 2
Step-by-step explanation:
The general form of an exponential equation is: g(x) = 2ˣ⁻ᵃ + b where
"a" is a horizontal shift to the left if positive (or right if negative)"b" is a vertical shift up if positive (or down if negative)The new function is shifted UP 2 units and RIGHT 3 units
a = 3b = 2--> g(x) = 2ˣ⁻³ + 2
Identify the volume of the composite figure rounded to the nearest tenth. HELP PLEASE!!
Answer:
V = 115.3 ft³
Step-by-step explanation:
The left part of the figure shows a cube of side length 4.2 ft. The volume of a cube is V = s³, where s is the side length. Hence, the volume of this particular cube is V = (4.2 ft)³ = 74.088.
The volume of a pyramid is V = (1/3)(base area)(height).
Here V = (1/3)(4.2 ft)²(7 ft) = 41.16 ft³.
Summing up the two distinct areas, we get V = 41.16 ft³ + 74.088 ft³, or
V = 115.3 ft³ after rounding up to the nearest tenth.
The volume of the composite figure is 115.2 cu.ft. , Option A is the correct answer.
What are Three Dimensional Figures ?Those figures that required x,y and z axis for their representation are three dimensional figures.
They have length , breadth and height.
All the object that we see around us can be categorized into Three Dimensional Figure.
In the given figure
It can be seen that it consists of a cube and a square pyramid
To determine the volume we have to determine the volume of each figure and then add
Volume of a cube = side * side * side
Side of the cube = 4.2 ft.
Substituting the values
Volume of cube = 4.2 * 4.2 * 4.2
Volume of cube = 74.088 cu.ft
Volume of a square pyramid is given by
(1/3) * a² * h
a is the area of the base
area of the base = area of the square = side * side
Area of the base = 4.2 * 4.2
Area of the base = 17.64 sq.ft
Height of the pyramid = 7 ft.
Volume of square pyramid = (1/3)* 17.64 *7
Volume of a square pyramid = 41.16 cu.ft
Total volume = 74.088 + 41.16
Total Volume = 115.2 cu.ft
Therefore , The volume of the composite figure is 115.2 cu.ft. , Option A is the correct answer.
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Sketch the following in standard position.
Determine the quadrant the angle lies in (if it is on an axis, state which axis it is on and if it is + or - axis)
Then determine the reference angle.
Answer: 1) Quadrant: I, reference angle: [tex]\dfrac{2\pi}{5}[/tex]
2) Quadrant: III, reference angle: 85°
3) Quadrant: IV, reference angle: [tex]\dfrac{\pi}{4}[/tex]
Step-by-step explanation:
Reference angle is the angle closest to the x-axis
1) The given angle is (2/5)π. The first quadrantal (π/2) would be (2.5/5)π
Since (2/5)π < (2.5/5)π then it must be in Quadrant 1.
The angle closest to the x-axis is the same as the given angle.
2) The given angle is -95°. It is measured clockwise since it is a negative angle. Since it is greater than 90°, it is greater than the 270° quadrantal. So it must be in Quadrant III.
The angle closest to the x-axis is 85°.
3) The given angle is (23/4)π. Since (8/4)π is one rotation, this is greater than one rotation. (23/4)π - (8/4)π - (8/4)π = (7/4)π. So, it rotates two complete rotations and lands at coterminal angle (7/4)π.
The angle closest to the x-axis is π/4
Tony is standing at sea level. From his location, the angle of elevation of the top of Blue Mountain is 23°. Staying at sea level, he walks 220 yards toward the mountain. The angle of elevation of the top is now 27°. Find the height of Blue Mountain. Round intermediate results to 3 decimal places and the final answer to 1 decimal place.
Answer:
559.2 yards.
Step-by-step explanation:
Let the height of the mountain be x yards and the distance from the second location to the base of the mountain be y yards.
Then we have the equations:
tan 27 = x/y
tan 23 = x / (220 + y)
From the first equation y = x/ tan27 so substituting in the second one we have:
tan 23 = x / (220 + x / tan 27)
Cross multiply:
x = 220 tan23 + x tan 23 / tan 27
x = 93.384 + 0.833 x
x - 0.833x = 93.384
x = 93.384 / 0.167
x = 559.2 yards to 1 dec place (answer).
BASIC MATH
Paul uses the expression 4.2 x 12.3 x 14.6 to determine the cost of tiling the floor of a room that measures 12.3 feet by 14.6 feet; each square foot of tile costs $4.20. How many decimal places will be in Paul’s final answer?
A. one
B. three
C. five
D. eight
B. Three. It is three because there is one decimal place in each factor.
Answer:
B. Three.
Explanation:
Three because there is one decimal place in each factor and there are 3 factors.
1. Find the phase shift of the function y = 5cos(2x + pi/2).
2. Which of the following functions has a maximum y value of 4?
y = 4cosx
y = cos4x
y = cosx + 4
y = cos(x + 4)
Answer:
see explanation
Step-by-step explanation:
1
The cosine function in standard form is
y = acos(bx + c)
where a is the amplitude, period = [tex]\frac{2\pi }{b}[/tex] and
phase shift = - [tex]\frac{c}{b}[/tex]
here b = 2 and c = [tex]\frac{\pi }{2}[/tex], thus
phase shift = - [tex]\frac{\frac{\pi }{2} }{2}[/tex] = - [tex]\frac{\pi }{4}[/tex]
2
the amplitude = | a |
which has a maximum of a and a minimum of - a
y = 4cosx ← has a maximum value of 4
Final answer:
The phase shift of the function y = 5cos(2x + π/2) is -π/4 radians. The functions y = 4cosx and y = cosx + 4 both have a maximum y value of 4.
Explanation:
To find the phase shift of the function y = 5cos(2x + π/2), we need to look at the argument of the cosine function. The general form is y = Acos(Bx - C) where C/B is the phase shift. In this case, the argument of the cosine is 2x + π/2, thus the phase shift is -π/2 divided by the coefficient of x, which is 2, giving us a phase shift of -π/4 or -0.785 radians.
To determine which of the provided functions has a maximum y value of 4, consider the amplitude of the cosine functions. For the functions y = 4cosx, y = cos4x, and y = cos(x + 4), the amplitude is 1, and thus the maximum y value is 1 for the latter two, and 4 for the first one. However, y = cosx + 4 is a cosine function shifted upward by 4 units, and hence its maximum y value is also 5. So, the functions with a maximum y value of 4 are y = 4cosx and y = cosx + 4.
The pie store is having a 20% , percent off sale on all of its pies. If the pie you want regularly costs $18 dollar sign, 18, how much would you save with the discount?
20% off, means that 20% of the regular price is how much you would save.
Multiply the original price by 20%
18 x 0.20 = 3.6
The discount is $3.60
Kenneth brings a partially-filled beaker of red liquid into is his laboratory and uses an apparatus to add drops of blue liquid to the beaker at a constant rate. The equation y = 5x + 15 describes the relationship between the number of minutes (x) since Kenneth began adding drops of blue liquid to the beaker and the total amount of liquid in the beaker (y), in milliliters. Which statement correctly describes a solution of the equation?
there are two ways you can do
[tex]y = 5x + 15 \\ \\ 1. \: y - 15 = 5x \\ 2. \: \frac{y - 15}{5} = x \\ 3. \: x = \frac{y - 15}{5} \\ \\ \\ 1. \: 5x + 15 = y \\ 2. \: 5x + 15 + - 15 = y + - 15 \\ 5x = y - 15 \\ 3. \: \frac{5x}{5} = \frac{y - 15}{5} \\ x = \frac{1}{5} y - 3[/tex]
A solution of the equation y = 5x + 15 represents a specific moment during Kenneth's experiment, where 'x' is the time elapsed since he started adding the blue liquid, and 'y' is the total volume of the liquid mixture in the beaker.
Explanation:The equation y = 5x + 15 provided is a linear equation, which is a mathematical expression showing a constant rate of change. In this context, Kenneth's experiment in the laboratory, 'x' is the number of minutes since Kenneth began adding drops of blue liquid to the beaker, and 'y' is the total amount of liquid, in milliliters, in the beaker.
A solution to this equation refers to specific values for 'x' and 'y' which make this equation true. For instance, if we choose x = 1 minute, then we can calculate 'y' by substituting 'x' into the equation which gives y = 5*1 + 15 = 20 mL. This means that after 1 minute, Kenneth has 20 mL of liquid in his beaker. Indeed, every solution to this equation reflects a specific moment (x, or number of minutes) in Kenneth's ongoing experiment and the corresponding total volume (y) of the mixture in the beaker.
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Using the keys above, enter an expression equivalent to (3x^2-8x-24)-(9x+6) using the fewest possible terms.
Answer:
Final answer in simplified form is [tex]3x^2-17x-30[/tex]
Step-by-step explanation:
Given expression is [tex](3x^2-8x-24)-(9x+6)[/tex]
Now we need to find an equivalent expression for [tex](3x^2-8x-24)-(9x+6)[/tex]
First we can distribute the negative sign and remove the parenthesis the combine like terms
[tex](3x^2-8x-24)-(9x+6)[/tex]
[tex]=3x^2-8x-24-9x-6[/tex]
[tex]=3x^2-17x-30[/tex]
Hence final answer in simplified form is [tex]3x^2-17x-30[/tex]
Which of the following correctly shows the length of each radius, the point where the circles intersect, and the equation of the tangent line at this point?
actually box 3 is correct.
because their radiuses are easy to find
but the tangent line is x=-4 or x=4
The option third radius for circle A is 4, the radius for circle B is 3 and the point of intersection is (4,3) and the tangent equation is x = 4 is correct.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
We have two circles in the graph plot:
From the graph plot:
For the circle:A the radius is 4
For the circle:B the radius is 3
The point of intersection point (4, 3)
The tangent line will be:
x = 4
Thus, the option third radius for circle A is 4, the radius for circle B is 3 and the point of intersection is (4,3) and the tangent equation is x = 4 is correct.
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Thomas has a collection of CDs that he plays regularly. He has five rock CDs, three country CDs, and four movie sound track CDs. If Thomas chooses a CD at random, what are the odds that he chooses a country CD?
Answer:
The answer is 1/4.
Step-by-step explanation:
5 rock CDs, plus 3 country CDs, plus 4 movie sound track CDs, equal 12 CDs in total. To find the odds of choosing a country CD, you divide the total number of CDs, by the number of what you choose (3/12).
Answer:
The odds that he choose a country CD is 1/3
Step-by-step explanation:
12/12 ÷ 3 = 1/3
An elevator travels 110 feet in 10 seconds. At that speed, how fac can this elevator travel in 12 seconds?
Divide 110 by 10 to get a rate if 11 feet per second. Multiply 11 by 12 seconds to get 132 feet
WILL GIVE BRAINLIEST
Answer:
12 m
Step-by-step explanation:
The formula for the area of a triangle is ...
A = 1/2bh . . . . . b represents the base; h represents the height
We are told that the height is 5 m less than the base, so we have ...
42 = (1/2)(b)(b -5)
84 = b(b-5) . . . . . . . . multiply by 2
We want two factors of 84 that differ by 5. The factors are ...
84 = 1·84 = 2·42 = 3·28 = 4·21 = 6·14 = 7·12
The relevant factors are 7 and 12, so now we know b-5 = 7 and b = 12.
The length of the base is 12 m.
4. About 30% of the U.S. population is under 20 years old. About 17% of the population is over 60, which of the following is the probability that a person chosen at random is under 20 or over 60?
-17%
-53%
-47%
-30%
A = person is under 20
B = person is over 60
P(A or B) = P(A) + P(B) ... works because A and B are mutually exclusive
P(A or B) = 0.30 + 0.17
P(A or B) = 0.47 = 47%
The probability that a person chosen at random is under 20 or over 60 is 47% , option C is the correct answer.
What is Probability ?Probability is a topic in mathematics where the likeliness of an event is studied.
The range of probability is 0 to 1 .
0 indicates uncertainty to 1 indicating certainty.
It is given in the question that
30% of the U.S. population is under 20 years old
About 17% of the population is over 60
probability that a person chosen at random is under 20 or over 60 = ?
Let P(A) represents person under 20
Let P(B) represents person over 60
As a person is chosen at random and the events cannot happen together so they are mutually exclusive events.
The probability for mutually exclusive event is given by
P(A or B) = P(A) + P(B)
P(A) = 17% = 0.17
P(B) = 30% = 0.3
P(A or B) = 0.30 + 0.17
P(A or B) = 0.47 = 47%
Therefore , the probability that a person chosen at random is under 20 or over 60 is 47% , option C is the correct answer.
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write a rational expression involving one variable for which the excluded values are -4 and -7. Please Help!!!!!!
Answer:
See below.
Step-by-step explanation:
Values are excluded if they make the denominator zero, so one rational expression could be:
(x^2 - 9) / (x + 4)(x + 7)
- when x = -4 or -7 then the denominator is zero so the values of the function is undefined for these values.
please show me how to do this, I need to show work
Answer:
x ≈ 11.68 ( to 2 dec. places )
Step-by-step explanation:
Given
[tex]6^{(x-8)}[/tex] = 730 ( take log of both sides )
log [tex]6^{(x-8)}[/tex] = log730
(x - 8)log6 = log730 ( divide both sides by log6 )
x - 8 = [tex]\frac{log730}{log6}[/tex] ≈ 3.68 ( add 8 to both sides )
x ≈ 11.68 ( to 2 dec. places )
Answer:
6^ 3.679648309
Step-by-step explanation:
Don't really have one. Went with trial and error. Set calculator to 2 d.p by the way
The equation of a circle is x2+y2−12x+6y+20=0 .
What is the radius of the circle?
r = ?
Answer:
The radius is r=5 units
Step-by-step explanation:
we know that
The equation of the circle in standard form is equal to
[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]
where
(h,k) is the center and r is the radius
we have
[tex]x^{2}+y^{2}-12x+6y+20=0[/tex]
Convert to standard form
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex](x^{2}-12x)+(y^{2}+6y)=-20[/tex]
Complete the square twice. Remember to balance the equation by adding the same constants to each side
[tex](x^{2}-12x+36)+(y^{2}+6y+9)=-20+36+9[/tex]
[tex](x^{2}-12x+36)+(y^{2}+6y+9)=25[/tex]
Rewrite as perfect squares
[tex](x-6)^{2}+(y+3)^{2}=5^{2}[/tex]
therefore
The center is the point (6,-3) and the radius is r=5 units
Joshua has a ladder that is 17 ft long. He wants to lean the ladder against a vertical wall so that the top of the ladder is 16.5 ft above the ground. For Safety reasons, he wants the angle the ladder makes with the ground to be no greater than 70°. Will the ladder be safe at this height? show your work
Answer:
No, it is not safe
Answer:
Hello!
The answer is no, he will not be safe. I had a similar problem on a test and got the answer correct. The only difference was they used slightly different numbers, so I am pretty sure this is correct. I hope this helps!
Step-by-step explanation:
Okay, so you are looking for x.
sin x= [tex]\frac{16.5}{17}[/tex]
x=[tex]sin^{-1}[/tex]([tex]\frac{16.5}{17}[/tex])
x≈76.07
76.07>70
Please answer this correctly
Answer:8462
Step-by-step explanation:
Answer:
8862 feet
Explanation:
The formula for circumference is C=pi*diameter. So, by substitution we can use 26586=(3)d and solve by dividing 26586 by 3 which gives us d=8862 feet.
Need help on these four and then I am done, please help, I'm slowly getting the hang of it, I've already done all the other ones!
For #11, the answer is C, I’m pretty sure.
For #12, KM = LN, and LM = KN.
I can’t help with the others though, sorry :/
Need help with the problem in the photo.
Answer:
B. 3x -2y = 10
Step-by-step explanation:
The given line rises three units for each two units of run to the right. Hence its slope is 3/2. A parallel line will also have a slope of 3/2.
Of the equations we can see, selection B has a slope of 3/2. It can be rewritten in slope-intercept form as ...
3x -10 = 2y . . . . . add 2y-10 to isolate the y-term; next divide by 2.
y = 3/2x -5 . . . . . the coefficient of x is the slope
Answer:
B. 3x -2y = 10
Step-by-step explanation:
The given line rises three units for each two units of run to the right. Hence its slope is 3/2. A parallel line will also have a slope of 3/2.
Of the equations we can see, selection B has a slope of 3/2. It can be rewritten in slope-intercept form as ...
3x -10 = 2y . . . . . add 2y-10 to isolate the y-term; next divide by 2.
y = 3/2x -5 . . . . . the coefficient of x is the slope
The image of point A is
A'
B'
C'
D'
Answer:
A' because it is translated to another position.
Hope this helps
Answer: A'
Step-by-step explanation:
From the given figure , it can be seen that the quadrilateral ABCD is translated to produce A'B'C'D' by some distance in a particular direction.
A translation is a kind of rigid motion used in geometry to trace a function that maps an shape a particular distance.The line segments joining a vertex in the pre-image to the corresponding vertex in the image are congruent and parallel.We can see that the point A' in the image is corresponding to the point A in the pre-image.
Hence, the image of point A is A' .
In a bag there are 5 red marbles, 10 blue marbles, and 15 green marbles. What is the probability that you will draw a blue marble?
1/2
1/3
2/3
3/4
probability of drawing a blue marble is 1/3
Please please help me..
The yellow and orange triangle is AA
It is AA because the orange triangle has two angles listed and, the yellow triangle has two angle listed.
Answer:
AA
Step-by-step explanation:
For the 2 triangles to be similar we require 2 corresponding angles to be congruent.
There are 2 angles of measure 30°
If we consider the yellow triangle the the third angle is
180° - ( 41 + 30)° = 180° - 71 = 109°
The 2 triangles have therefore 2 corresponding congruent angles
Hence the triangles are similar by the postulate AA
Two forces act on an object. The first Force has a magnitude of 400 Newtons and acts at an angle of 30 degrees as measured from the horizontal. Second Force has a magnitude of 280 Newtons in accident angle of 135 degrees is measured from the horizontal. Determine the vector v that represents the resultant Force.
a. v=(200-140rtsq2)i+(200rtsq3+140rtsq2)j
b. v=(200+140rtsq2)i+(200rtsq3+140rtsq2)j
c. v=(200rtsq3+140rtsq2)i+(200+140rtsq2)j
d. v=(200rtsq3-140rtsq2)i+(200+140rtsq2)j
ANSWER
Option D is correct
EXPLANATION
We resolve the forces into component forms.
[tex]F_1 = 400 \cos(30) i + 400 \sin(30) j[/tex]
[tex]F_1 = 200 \sqrt{3} i +200j[/tex]
Also the second is resolved to obtain,
[tex]F_2= 280 \cos(135) i + 280 \sin(135) j.[/tex]
[tex]F_2= - 140 \sqrt{2} i + 140 \sqrt{2} j[/tex]
To find the resultant vector, V, We add the corresponding components of the two forces to get:
[tex]V=F_1+F_2 [/tex]
[tex] \implies \: V = (200 \sqrt{3} - 140 \sqrt{2} )i + (200 + 140 \sqrt{2})j[/tex]
The correct answer is D.