[tex]\qquad\qquad\huge\underline{{\sf Answer}}☂[/tex]
Standard equation of circle ~
[tex]\qquad \sf \dashrightarrow \:(x - h) {}^{2} + (y - k) {}^{2} = r {}^{2} [/tex]
where,
h = x - coordinate of centre k = y - coordinate of centrer = radius of the circle
Now, let's plug in the values ~
[tex]\qquad \sf \dashrightarrow \:(x - (5)) {}^{2} + (y - ( - 8)) {}^{2} = {2}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \:(x + 5) {}^{2} + (y + 8) {}^{2} = {4}^{} [/tex]
Therefore, the correct choice is B
➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖
The equation of the circle with a center of (4,5) and a radius of 2 units is (x + 5)² +(y + 8)² = 4
How to determine the circle equation?The center of the circle is given as:
Center (a,b) = (-5, -8)
The radius is given as:
Radius, r = 2
The equation of the circle is calculated using:
(x - a)² + (y - b)² = r²
Substitute values for r and (a,b)
(x + 5)² +(y + 8)² = 2²
Evaluate the square of 2
(x + 5)² +(y + 8)² = 4
Hence, the equation of the circle is (x + 5)² +(y + 8)² = 4
Read more about circle equations at:
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Suppose we want to choose 6 letters, without replacement, from 10 distinct letters.
Answer:
Step-by-step explanation:
If order matters (much like forming... a 4 digit number-maybe for a safe?), you will be computing "permutations". The formula for "r" items chosen from "n" items, where order matters is Npermutations = nPr = n!/ (n-r)!
Npermutations = 10P6 = 10!/(10-6)= 10*9*8*7*6*5 = 151200
When order doesn't matter (such as in dealing a poker hand, its the cards you end up with that matter not the order in which they are dealt into your hand) you will be computing combinations. The formula for the number of combinations of "r "items from "n" choices is Ncombinations = nCr = n!/((n-r)!r!)
Ncombinations = 10C6 = 10!/((10-6)!6!) = (10*9*8*7)/(4*3*2*1) = 210
Notice how there are far fewer combinations than permutations. This makes sense because if you think about how 6 colors {red, blue, green, white, black, yellow} can be arranged, there are 6!=720 ways to arrange these 6 colors if order matters. If order doesn't matter, this set of 6 colors counts only once.
Same thing with numbers :)
Hope this helped, brainliest is always appreciated! :)
Have a nice day CX
~Mitsuna
A rectangle has a length of (x + 4) feet and a width of (x + 7) feet. The expression
2(x+)+2(x + 7) represents the perimeter of the rectangle.
Which expression also represents the perimeter of the rectangle, in feet?
A (x + 4) + (x + 4) + (x + 7) + (x + 7) W
B (x + 4)(x + 4)(x + 7)(x + 7)
C 4x + 11
D 22x
Answer:
A
Step-by-step explanation:
No need. It’s simple.
B can’t be it because it uses multiplication.
C can’t be it because it makes no sense.
D also makes no sense.
evaluate f ( - 5 ) =
Answer: −5
Step-by-step explanation:
simplify: (−5)
Re-order terms so constants are on the left:
(−5)f(−5)−5
ABDE is a rectangle on coordinate axes, the sides of the rectangle are parallel to the axes,
Point C is the centre of the rectangle
What are the coordinates of B and D
The coordinates of B and D are the location of the vertices B and D in the rectangle
The coordinates of B and D are (55, 30) and (55, 14)
How to determine the coordinates of B and D?From the figure of the rectangle, we have:
A = (25,30)
C = (40, 22)
Point B has the same y-coordinate as point A
So, we have:
B = (x, 30)
The x-coordinate is then calculated as:
Bx = 2Cx - Ax
This gives
Bx = 2*40 - 25
Bx = 55
So, the coordinates of B are:
B = (55, 30)
Point D has the same x-coordinate as point B
So, we have:
D = (55, y)
The y-coordinate is then calculated as:
Dy = Cy - (By - Cy)
This gives
Dy = 22 - (30 - 22)
Dy = 14
So, the coordinates of B are:
D = (55, 14)
Hence, the coordinates of B and D are (55, 30) and (55, 14)
Read more about rectangles at:
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Zoey purchased a new car in 1992 for $28,000. The value of the car has been depreciating exponentially at a constant rate. If the value of the car was $9,600 in the year 1996, then what would be the predicted value of the car in the year 1998, to the nearest dollar?
Answer:
V = V0 e^-k t where V is the value of the car and t the time in years
ln (V/V0) = - k t
k = -1/4 ln (96/280) = .268
V = V0 e^-k t = 28000 e^-.268 * 6 = 28000 e^-1.606 = $5621
Haley has $155 in savings, and her brother Hank has $230. Hayley is saving $10 each week and her brother is spending $15 each week. After how many weeks will their savings account have the same amount of money in them
Answer:
It will be 3 weeks until their savings account has the same amount of money in them.
Step-by-step explanation:
Have a great rest of your day
#TheWizzer
The pentagonal prism below has a height of 7.2 units and a volume of 309.6 units,
Find the area of one of its bases.
Answer:
Step-by-step explanation:
Volume of pentagonal prism = 309.6 cubic units
h = 7.2 units
[tex]\boxed{\text{Area of one of the base= $\dfrac{Volume}{h}$}}[/tex]
[tex]\sf=\dfrac{309.6}{7.2}\\\\= 43 \ square \ units[/tex]
Help I’ll give info help text me on ig 7mile.jr
The area of the rectangle is
432 square units. If the width
is 24 units, what is the length?
Answer:
18 units
Step-by-step explanation:
Area = length * width (A = L * w)
So, in order to find the length when given the width and area, you have to divide the area by the width.
432 / 24 = 18
I hope this helps! Have a lovely day!! :)
How do I solve for y?
Answer:
Step-by-step explanation:
The angle containing y and 63 are vertically opposite. They are equal.
y + 23 = 63 Subtract 23 from both sides
y +23-23 = 63 - 23
Answer y = 40
Let x and b be positive real numbers so that log_b(x^2) = 10. Find log_3sqrtb (1/x)
The value of the logarithm log₃ (x⁻¹)[tex]^{1/b}[/tex] where x and b positive real numbers is - 5 · b⁻¹ · log₃ b.
How to analyze and solve logarithmic expressionsLogarithms are trascendental functions, that is, functions that cannot be described algebraically.
In this question we must apply logarithm and algebraic properties to determine firstly the value of [tex]x[/tex] and later to find value of the latter logarithm. Now we proceed to find the value of [tex]x[/tex]:
[tex]\log_{b} x^{2} = 10[/tex]
[tex]2\cdot \log_{b} x = 10[/tex]
[tex]\log_{b} x = 5[/tex]
x = b⁵
Then, the value of the latter logarithm is:
log₃ (x⁻¹)[tex]^{1/b}[/tex]
- b⁻¹ · log₃ x
- b⁻¹ · log₃ b⁵
- 5 · b⁻¹ · log₃ b
The value of the logarithm log₃ (x⁻¹)[tex]^{1/b}[/tex] where x and b positive real numbers is - 5 · b⁻¹ · log₃ b. [tex]\blacksquare[/tex]
RemarkThe statement is poorly formated, correct form is described below:
Let [tex]x[/tex] and [tex]b[/tex] be positive real numbers so that [tex]\log_{b} x^{2} = 10[/tex]. Find [tex]\log_{3} \sqrt [b]{\frac{1}{x} }[/tex].
To learn more on logarithms, we kindly invite to check this verified question: https://brainly.com/question/3181916
50/100 in tenth fraction and decimal form
Answer:
5/10 and .5
Step-by-step explanation:
50/100 is 1/2 so 1/2 is equal to 5/10
5/10 is also 1/2 and 1/2 as a decimal is .5 or 0.5
hope it helps !
please help
cos40∘=sin(x+30∘)
Answer:
x = 20 degrees.
Step-by-step explanation:
cos40∘=sin(x+30∘)
sin (x + 30) = 0.766
x + 30 = arcsin 0.766 = 50
x = 50 - 30 = 20.
Answer:
x = 20
Step-by-step explanation:
cos(angle) = sin(complement of angle) , then
cos40 = sin(90 - 40) = sin50 , then
sin(x + 30) = sin50 , that is
x + 30 = 50 ( subtract 30 from both sides )
x = 20
Zahra is looking at a map of a park that has
a scale of 3 in. to 200 ft.
On the map, each side of the park is 6
inches long.
Zahra's distance to the park is 500 feet.
How long would this distance be on the
map?
Answer:
7.5 inches
peeeee
there are 45 marbles in a blue jar. the blue jar has 9 times as many marbles as a red jar. let m be the number of marbles in the red jar.
Write an equation that relates the number of marbles in the two jars. Use 9, m, and 45
Answer:
9m = 45
Step-by-step explanation:
if the blue jar has 9 times as many marbles as the red jar (which is 45 marbles), then that means that:
9m = 45
where m is the number of marbles in the red jar.
How do you figure out which statement is true?
Answer:
What question are you talking about though
help please thank you
Answer:
hmm i think its
1/2(x + y)
Step-by-step explanation:
because well... this would be eaiser for me if it said "of the" because "of the" is mostly used for multiply, but since it just said "the..." i can only guess. I think this may be the answer tho?
In a parallelogram ABCD, angle a=70, find 2angle d
Answer:
D = 110
Step-by-step explanation:
Given,
In a parallelogram ABCD,
∠A =70∘
∠A + ∠B = 180∘.. (supplementary angles)
∠B = 180∘ – 70∘ = 110∘
∠A = ∠C and ∠B = ∠D.. (Opposite angles of parallelogram)
∠A = 70∘, ∠B = 110∘, ∠C = 70∘, ∠D = 110
solve for X 3.5x/9= 4.2/5 Please help me
Answer:
x=2.16
Step-by-step explanation:
1. Cross multiply. 3.5x(5) = 9(4.2)
2. Simplify. 17.5x=37.8
3. Divide both sides by 17.5. x=2.16
One-fourth of the sum of a number and 10 is 2 less
than twice the number?
Answer:
The number is 2
Step-by-step explanation:
The equation is: 1/4 (x + 10) = 2x - 1
1/4x + 2.5 = 2x - 1
Multiply everything by 4 to get rid of the fraction
x + 10 = 8x - 4
Subtract x from both sides
10 = 7x - 4
Add 4 to both sides
14 = 7x
Divide both sides by 7
x = 2
What equals -9 when multiplied but -8 when added
Answer:
1 and -9
Step-by-step explanation:
We can find the number by looking at the factors of -9, which include 1 and -9, -1 and 9, and -3 and 3.
1 * -9 = -9
1 + (-9) = -8
-16t^2+100t+316=0
Solve the quadratic equation. Round to the nearest tenth.
Answer:
-2.3, 8.6 to the nearest tenth.
Step-by-step explanation:
-16t^2+100t+316=0
Simplify it first.
Divide by -4:
4t^2 - 25t - 79 = 0
Using the quadratic formula:
x = [-(-25) +/- √(-25)^2 - 4*4*-79) ] / 8
= (25 +/- √(1889)) / 8
= 3.125 +/- 43.463/8
= 3.125 +/- 5.433
= -2.308, 8.558
Answer:
quadratic formula normally normally applies in such cases
Help mee plsssssssss
Answer:
-3
Step-by-step explanation:
you can tell because 12-3=9 and 9 is the output. it's the same for the others. 15-3=12 and 20-3=17
Put the expressions in order from least to greatest.
Answer:
[tex]\frac{11^{4} }{11^{11} } ,\frac{1}{11^{-4} }, 11^{5}*11^{2}, (11^{-3})^{-3}[/tex]
Step-by-step explanation:
For this, you need to know the rules of exponents:
If the coefficient is the same, you can do things to it (which I will get into)
In this case, all the coefficients are 11, so we don't have to worry about the coefficients being different.
For the first one, you can subtract the denominator exponent by the numerator exponent like so:
[tex]11^{4} * 11^{-11} = 11^{-7}\\[/tex]
(When you multiply, you add the exponents)
Also, the rule is: [tex]x^{-y} = \frac{1}{x^{y} }[/tex] or [tex]\frac{1}{x^{-y} } = x^{y}[/tex]
For the second one, you can use the rule mentioned before:
[tex]\frac{1}{11^{-4} } = 11^{4}[/tex]
For the third one, you want to multiply the exponents (in these kinds of cases, you can multiply the exponent by the exponent)
So:
[tex](11^{-3} )^{-3} = 11^{9}[/tex]
Finally, the fourth one, you can simply just add the exponents:
[tex]11^{5} * 11^{2} = 11^{7}[/tex]
Then, just order them from least to greatest by their exponents value :)
Which number is a common multiple of 2 and 4?
A) 14
B) 24
C) 26
D) 34
LAST QUESTION MORE POINTS LETS TAKE IT TO 100!
Answer: B) 24
Step-by-step explanation:
All of these are multiples of 2 since they are all even numbers, so we will look to see which is a multiple of four.
Multiples of four are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, etc.
I bolded and underlined 24 because it is in the list of options. B) 24 is a common multiple of 2 and 4.
24 / 2 = 12
24 / 4 = 6
A jar contains 416 coins.1/4 of the coins are £1 coins.
280 of the coins are 20p coins.
The rest of the coins are 10p coins.
Work out the total value of the 416 coins.
Answer:
it's I think 250
Step-by-step explanation:
it's 250 from me...
What is 45% of 69/3???
Answer:
10.35
Step-by-step explanation:
69/3 = 23
45% of 23 = 10.35
Answer:
10.35
Step-by-step explanation:
69/3 = 23
45% of 23 = 10.35
Why are you deleting my answers??
| negative 9 | + | 12 | = what
a. negative 3
b. 3
c.negative 21
d.21
pleaz help might make brainliest
Answer:
21 (but see note)
Step-by-step explanation:
I am thinking you are showing the symbols for absolute values ( the vertical lines) so the absolute value of negative 9 is 9 and absolute value of positive 12 is 12 so it's just 9+12
Simplify the given expressions below.
I) 4x + 8 - 2x + 7
2) 2n ×5 ×2a
3) 6a power 5 over 3a power 2 ×2a
please work it out and clear
Step-by-step explanation:
1) [tex] \Rightarrow \: \sf \: 4x + 8 - 2x + 7[/tex]
Combine like terms
[tex] \rightarrow \: \sf \: ( 4x - \textcolor{green}{2}x) + (7 + \textcolor{green}{8})[/tex]
Add 4x and 2x , 7 + 8
[tex] \rightarrow \sf \: 2x + 15[/tex]
~Done~
2) [tex] \Rightarrow \sf 2n ×5 ×2a[/tex]
[tex] \rightarrow \sf \:( 2n) (5) (2a)[/tex]
[tex] \rightarrow \sf \: 20an[/tex]
~Done~
Find the value of x in this equation.
Answer: 5
Step-by-step explanation: