What is the center of the circle given by the equation by the equation (x-3)2 + (y-9)2=16
Answer:
centre = (3, 9 )
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
(x - 3)² + (y - 9)² = 16 is in this form
with centre = (3, 9) and r = [tex]\sqrt{16}[/tex] = 4
Answer:
(3,9) -apex!!!!!!
Step-by-step explanation:
Harper knows he is 50 yards from the school. The map on his phone show that the school is 3/4 inches from current location. How far is Harper from home if map shows the distance as 3 inches
Answer: 200 yards
Step-by-step explanation:
So if 3/4 inches on the map is equal to 50 yards then you could divide the 3 inch distance from him to his home by 3/4 and then multiply that answer by 50. So 3 ÷ 3/4 = 4. 4 * 50 = 200. He is 200 yards from his home.
Answer:
Harper is 200 yards away home.Step-by-step explanation:
To solve this problem, we use the rule of three, if 50 yards represents 3/4 inches, how many yards would represent 3 inches?
[tex]x=3in\frac{50yd}{\frac{3}{4}in } =3\frac{200}{3}yd=200yd[/tex]
So, 3 inches represents 200 yards, that means Harper is 200 yards away home.
Remember that the rule of three is just about using the ratio that the problem already gave.
Therefore, the answer is 200 yards.
The area of a square is 729 square centimeter. How long is each side of the square?
Answer:
27 cm
Step-by-step explanation:
So the square root of 729 is 27
find the exact value of x
ΔABC and ΔCBD are similar. Therefore we have the proportion:
[tex]\dfrac{AB}{BC}=\dfrac{BC}{BD}\\\\AB=6;\ BC=x;\ BD=2[/tex]
Substitute:
[tex]\dfrac{6}{x}=\dfrac{x}{2}[/tex] cross multiply
[tex](x)(x)=(6)(2)\\\\x^2=12\to x=\sqrt{12}\\\\x=\sqrt{4\cdot3}\\\\x=\sqrt4\cdot\sqrt3\\\\\boxed{x=2\sqrt3}[/tex]
What is 15 to the 1/3 power in radical form
[tex]\sqrt[n]{a^m}=a^{\frac{m}{n}}\\\\\boxed{15^{\frac{1}{3}}=\sqrt[3]{15}}[/tex]
Radical form is the form of a equation in which the number or variable is written under some power of the root. The 15 to the 1/3 power in radical form is [tex]\sqrt[3]{15}[/tex].
Given information-15 to the 1/3 power is the 1/3 power of the number fifteen and it can be expressed as,
[tex]=(15)^{\dfrac{1}{3}[/tex]
This number has to be written in the radical form.
Radical form-Radical form is the form of a equation in which the number or variable is written under some power of the root.
When a fractional exponents of the number is given the numerator becomes the power and the denominator becomes the root. Let [tex]x^{\dfrac{a}{b}[/tex] is a number with fractional exponents where a and b are the real and positive integer, then a becomes the power and the b becomes the root of the number x.
[tex]x^{\dfrac{a}{b} }=\sqrt[b]{x^a}[/tex]
For the given number,
[tex]=(15)^{\dfrac{1}{3}}=\sqrt[3]{15}[/tex]
Hence the 15 to the 1/3 power in radical form is [tex]\sqrt[3]{15}[/tex].
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6691 ÷28. solved by long divison
To calculate 6691 divided by 28 using long division, divide each set of numbers step by step to arrive at a quotient of 238 with a remainder of 27, resulting in a decimal of approximately 238.96 when rounded.
The question involves the process of long division which is a method used in arithmetic. The student is trying to divide 6691 by 28:
Divide 66 by 28, which goes 2 times. Write 2 above the division bar, to the right of the first quotient place.
Multiply 2 by 28, which is 56, and subtract that from 66 to get a remainder of 10. Bring down the next digit, 9, to make 109.
Divide 109 by 28, which goes 3 times. Write 3 on the division bar. Multiply 3 by 28 (equals 84) and subtract from 109 to get 25.
Bring down the next digit, 1, to make 251. Divide this by 28, which goes 8 times. Eight times 28 is 224. Subtract this from 251 to get 27.
27 is less than 28, so the division process stops here. The answer up to this point is 238, with a remainder of 27.
The long division calculation of 6691 divided by 28 is 238 with a remainder of 27 or as a decimal, 238.96.
A special paint requires a mixture of paints: A, B and C. The ratio is: 60% A, 25% B, and 15% C. If you want 20 gallons of the special color, how many gallons of paint A will you need?
You would need 12 gallons of paint A. You can find this answer by finding what 60% of 20 is, and do that by multiplying 20 • (0.6). This is what gives you 12. Following that, you’ll need 3 gallons of C, and 5 gallons of B.
Which of the following is a factor of 2[tex]x^{4}[/tex] + 22x[tex]x^{3}[/tex] + 60x[tex]x^{2}[/tex]?
[tex]x^{3}[/tex]
[tex]x^{4}[/tex]
x + 4
x + 5
[tex]2x^4+22x^3+60x^2=2x^2(x^2+11x+30)=2x^2(x^2+6x+5x+30)\\\\=2x^2[x(x+6)+5(x+6)]=2x^2(x+6)(x+5)\\\\Answer:\ x+5[/tex]
Answer:
(x+5) is the final answer.
Step-by-step explanation:
We have to find the factors of [tex]2x^4+22x^3+60x^2[/tex]
Then select correct choice or choices from the given options.
[tex]2x^4+22x^3+60x^2[/tex]
[tex]=2x^2(x^2+11x+30)[/tex]
[tex]=2x^2(x^2+6x+5x+30)[/tex]
[tex]=2x^2(x(x+6)+5(x+6))[/tex]
[tex]=2x^2((x+5)(x+6))[/tex]
[tex]=2x^2(x+5)(x+6)[/tex]
From above factors, we see that only (x+5) is correct.
Hence (x+5) is the final answer.
if the cost of 3 pies is $20.What is the cost for 6 pies
Write the explicit formula for the sequence. -1, 4, -16, 64,... A) an = (4)(n-1) B) an = (-4)(n-1) C) an = -(4)(n-1) D) an = -(-4)(n-1)
Answer:
A
Step-by-step explanation:
Answer:
If on USA TEST PREP it is D
Step-by-step explanation:
The test grades of a science class are given.
78, 75, 70, 92, 69, 83, 98, 76, 75, 82, 91, 89
The grades are normally distributed with a mean of 81.5 and a standard deviation of 9.3.
What is the z-score of the highest grade in the test?
Round the answer to the nearest hundredth.
Answer:
1.77 to nearest hundredth
Step-by-step explanation:
Z-score = (score - mean) / standard deviation
98 is the highest score and its z-score is (98- 81.5) / 9.3
= 1.7742
Answer: 1.77
Step-by-step explanation:
Given : The test grades of a science class are given.
78, 75, 70, 92, 69, 83, 98, 76, 75, 82, 91, 89
The grades are normally distributed with a mean [tex]\mu= 81.5[/tex] and a standard deviation [tex]\sigma=9.3[/tex] .
let x be any random variable represents the test grades of a science class.
Formula for z-score:-
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
The highest score= 98
Then , the z-score of the highest grade in the test will be :-
[tex]z=\dfrac{98-81.5}{9.3}=1.77419354839\approx1.77[/tex]
Hence, the z-score of the highest grade in the test =1.77
Write the equation in slope intercept form of a line that goes through (4,9) and has a slope of 1/2
Answer:
y = [tex]\frac{1}{2}[/tex] x + 7
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
here m = [tex]\frac{1}{2}[/tex], hence
y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation
to find c substitute (4, 9) into the partial equation
9 = 2 + c ⇒ c = 9 - 2 = 7
y = [tex]\frac{1}{2}[/tex] x + 7 ← equation in slope-intercept form
3r-34r+80 please factor this
Answer:
(3r-10) (r+8)
Step-by-step explanation:
3r-34r+80
The first step is to combine like terms
3r - 34r
is -31r
-31r+80
We cannot factor since 31 is a prime number and 80 is not a multiple of 31
If you mean
3r^2-34r+80
(3r-10) (r+8)
A store owner bought a pair of headphones fo$150. He wanted to sell them for a profit of 30%. What price would he have to mark the headphones in order to make a profit?
Answer:
180
Step-by-step explanation:
30% of 150 = 30
because
30% of 15 = 3
30 + 150 = 180
Answer:
Step-by-step explanation:150+30=180
What are the zeros of the polynomial function f(x)=x^3+2x^2-24x?
Immediately, we can factor an x out of each term to simplify the polynomial.
x(x^2 + 2x - 24)
In doing this, we know the first zero will be x = 0.
Using the AC method, we can find the next two zeros.
x(x - 4)(x + 6)
The zeros, or x-intercepts of the polynomial, are 0, 4, and -6.The zeros of the polynomial function f(x) = x^3 + 2x^2 -24x are x = -6, 0, and 4.
Explanation:The question requires finding the zeros of the polynomial function f(x) = x^3 + 2x^2 -24x. The zeros of this function can be found by setting the function equal to zero and solving for x. So, we have 0 = x^3 + 2x^2 - 24x. All terms have an 'x', so we can factor out 'x' to give: 0 = x (x^2 + 2x - 24). The quadratic formula (which is used for expressions of the form ax^2 + bx + c = 0) to solve x^2 + 2x - 24 = 0, we get x = -6 and x = 4. Therefore, the zeros of the function are x = -6, 0, and 4.
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I'm really bad at math!
Here it goes: Find the sum
(5b-9) -3(8-26)
Help!!!!!
-Math Disaster
Given : (5b - 9) - 3(8 - 26)
⇒ (5b - 9) - 3(-18)
⇒ (5b - 9) + 54
⇒ 5b - 9 + 54
⇒ 5b + 45
Answer:
i think its 5b + 45
Step-by-step explanation:
im not 100% sure what your asking for but i just distributed the -3 to the 8 and -26 and got 5b -9 -24 + 78. then i combined the like terms to get 5b + 45.
hope this helps !!
Point slope form of (2,4) and (3,1)
Answer:
y-4 = 3 (x-2)
Step-by-step explanation:
To find the slope of a line
slope = (y2-y1)/(x2-x1)
slope = (1-4)/(2-3)
= -3/-1
=3
Now we use the point slope form for a line
y-y1 = m(x-x1)
y-4 = 3 (x-2)
Answer:
y-4 = 3 (x-2)
y=-3x+10
What is the y intercept of the line with the equation y=2x+8
Answer:
in the point slop form y=2x+8
the slope is 2
the y intercept is 8
The slope-intercept form of line:
y = mx + b
m - slope
b - y-intercept
We have y = 2x + 8. Therefore:
slope m = 2
y-intercept b = 8
Answer: y-intercept = 8.Please help with this ...Its very urgent..
Answer: q²x² - p³x + 3pqx + q = 0
Step-by-step explanation:
Since a and B are the roots of x² - px + q = 0, then x = a and x = B
⇒ (x - a)(x - B) = 0
⇒ x² - ax - Bx + aB = 0
⇒ x² - (a + B)x + aB = 0
Comparing this to the given equation of x² - px + q = 0, we discover that
p = a + Bq = aBNext, given the roots for the new equation as [tex]x = \dfrac{a}{B^2} \quad\text{and}\quad\ x=\dfrac{B}{a^2}[/tex]
⇒ [tex]\bigg(x - \dfrac{a}{B^2}\bigg)\bigg(x-\dfrac{B}{a^2}\bigg)=0[/tex]
⇒ (B²x - a)(a²x - B) = 0
⇒ a²B²x² - a³x - B³x + aB = 0
⇒ a²B²x² - (a³ + B³)x + aB = 0
Let's look at each term individually:
1st term: a²B²x² = (aB)²x² = q²x² (since q = aB)
2nd term: (a³ + B³)x cubic formula can be used
= [(a + B)(a² - aB + B²)]x
= [(a + B)(a² + (2aB - 3aB) + B²)]x
= [(a + B)(a² + 2aB + B² - 3aB)]x
= [(a + B)(a + B)² - 3aB)]x
= [( p )( p² - 3 q )]x since p = a + B and q = aB
= (p³ - 3pq)x distributed "p" into p² - 3q
= p³x - 3pqx distributed "x" into p³ - 3pq
3rd term: aB = q since q = aB
Put it all together:
q²x² - (p³x - 3pqx) + q = 0
⇒ q²x² - p³x + 3pqx + q = 0
Which of the following is the equation of a circle whose center is at the origin and whose diameter has end (-1,2) and (1,-2)
Answer:
x² + y² = 5
Step-by-step explanation:
The circle with center (h, k) and radius r has equation ...
... (x -h)² + (y -k)² = r²
You can find r² using the Pythagorean theorem or the distance formula, or you can simply calculate what it needs to be to make one or the other of the points lie on the circle.
For (h, k) = (0, 0), the equation is ...
... (x -0)² + (y -0)² = r²
Using (-1, 2) for (x, y), we can find r² as ...
... (-1 -0)² + (2 -0)² = r² = 1 + 4 = 5
Then the circle equation is ...
... x² + y² = 5
What is the slope of this line
What is the value of x in the equation 2x + 3y = 36, when y = 6?
8
9
27
36
THE ANSWER IS.......
Answer:
x=9
Step-by-step explanation:
2x+3y =36
We know y =6, so we can substitute this into the equation
2x+ 3(6) = 36
2x+18 = 36
Subtract 18 from each side
2x+18-18 = 36-18
2x =18
Divide each side by 2
2x/2 =18/2
x=9
I really like that you put the answer out there for other people. that's pretty cool! B) 9
F(x)=x^3+4x^2+x-6
What are the real zeros
To find the real zeros of the given function, set it equal to zero and solve the resulting equation.
Explanation:The real zeros of the function F(x) = x^3 + 4x^2 + x - 6 are the values of x that make the function equal to zero.
Step 1: Set the function equal to zero: x^3 + 4x^2 + x - 6 = 0.Step 2: Solve the equation by factoring, synthetic division, or using the Rational Root Theorem.Step 3: The real zeros of the function F(x) = x^3 + 4x^2 + x - 6 are the solutions obtained from Step 2.the graph below shows the relationship between the number of cookies made and the number of pans used:
Which statement best describes point A on the graph?
A: four pans make 16 cookies
B: four pans make 32 cookies
C: One pan makes 16 cookies
D: One pan makes 32 cookies
Answer:
B four pans make 32 cookies
Which equations have a value less than 6,766? A. one fourth x 6,766 = ________ B. 6 x 6,766 = ________ C. one half x 6,766 = ________ D. 1 x 6,766 = ________ A and C D and B A and B C and D
The values less than 6,766 are one fourth x 6,766 and one half x 6,766 (A and C options are correct)
What is an expression?Numbers, symbols and operators (such as and times) grouped together that show the value of something.
Given is an expression, 6,766
The values less than 6,766 are,
i) 1/4x6,766 = 1691.5
1691.5 < 6,766
ii) 1/2x6,766 = 3383
3383 < 6,766
Hence, one fourth x 6,766 and one half x 6,766 are correct answers.
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Oceanside bike rental shop charge 15 dollars plus 8 dollars an hours for renting a bike. Jason paid 79 dollars to rent a bike. How many hours did pay to have the bike checked checked out?
Answer:
8 hours
Step-by-step explanation:
Firstly, the cost for renting the bike needs to be subtracted from the total amount:
79 - 15 = 64
Now this can be divided by 8 to find the hours:
64 ÷ 8 = 8
So he paid for 8 hours.
Which equation is a point slope form equation for line AB ? y+1=32(x−1) y+1=−32(x−1) Four-quadrant Cartesian graph with integer tickmarks from -9 to 9 (or -10 to 10) for x and y axes, with a straight line with arrowheads drawn through two points labeled A and B. Point A is at (-3,5) and point B is at (1,-1).
Answer:
The second option is correct. The point slope form of AB is [tex]y+1=\frac{-3}{2}(x-1)[/tex].
Step-by-step explanation:
The given points are A(-3,5) and B(1,-1).
Slope of a line is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Slope of AB is
[tex]m=\frac{-1-5}{1-(-3)}[/tex]
[tex]m=\frac{-6}{4}[/tex]
[tex]m=\frac{-3}{2}[/tex]
The point slope form of a line is
[tex]y-y_1=m(x-x_1)[/tex]
Where, m is slope of the line.
Case 1: The slope of the line is [tex]\frac{-3}{2}[/tex] and the point is (-3,5). The point slope form of AB is
[tex]y-5=\frac{-3}{2}(x+3)[/tex]
Case 1: The slope of the line is [tex]\frac{-3}{2}[/tex] and the point is (1,-1). The point slope form of AB is
[tex]y+1=\frac{-3}{2}(x-1)[/tex]
Therefore the point slope form of AB is [tex]y+1=\frac{-3}{2}(x-1)[/tex]. Option 2 is correct.
The regular price for a sweater is $48. The store is having buy one get one 1/2 off sale. If you buy 2 sweaters for that price what percent discount is that ?
Answer: 25%
Step-by-step explanation:
Hi, if you buy 2 sweaters at full price (100%)
$48 x 2 = $96
"Buy one get one 1/2 off sale"´price
48 + (48/2) = 48 +24 = $72
So, the normal price for both sweaters (96) multiplied by a percentage is equal to the "buy one get one 1/2 off sale” price.
96 x =72
x =72/96 = 0.75
Multiplying by 100 to obtain the percentage form
0.75 =75%
So, the sale price is %75 of the full price.
To obtain the percent discount.
100%-75% = 25%
Tabitha walked 13.5 miles in 3 hours. at that speed how many miles will she wallk in seven hours?
Answer: 31.5 miles
Step-by-step explanation: know how many miles tabitha walked per hour, which is 4.5 miles. then multiply 13.5 x 2, and add 4.5 to receive your answer - 31.5.
Answer:
Step-by-step explanation: The answer is 31.5 miles. The way I got it is by multiplying 13.5 by 2 because that will be 6 hours already. That gives me 27. Then you divide 13.5 to get how much she walk for just 1 hour which is 4.5. When you add that to 27, you get 31.5. Hope this helps!!!!!
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The number p and −1.2 are additive inverses. Drag and drop −1.2 and p to their correct positions on the number line. Drag and drop the label “Sum” to the sum of −1.2 and p
Answer:
p=1.2
Step-by-step explanation:
Additive inverse of any number means a number which can be added to the original number to get
Two numbers are said to be additive inverse of each other if sum of both numbers is 0. For example if 5 is the given number then -5 will be it's additive inverse. So to find additive inverse, we basically change the sign of number.
Given number p is additive inverse off -1.2 so p must be 1.2.
Sum will obviously be 0.
So to graph them on number line, we make a point at -1.2, 1.2 and at 0 for their sum.
Answer:P=1.2
Step-by-step explanation: