Answer:
Center: (6, -12)
Radius: 4
Step-by-step explanation:
Complete the squares
[tex]x^2+y^2-12x+24y-10=6\\\\x^2-12x-10+y^2+24y=6\\\\x^2-12x-10+46+y^2+24y+144=6+46+144\\\\(x^2-12x+36)+(y^2+24y+144)=196\\\\(x-6)^2+(y+12)^2=196[/tex]
Comparing with the standard form equation [tex](x-h)^2+(y-k)^2=r^2[/tex], since [tex]r^2=196[/tex], then the radius of the circle is [tex]r=14[/tex]. Also, the center of the circle would be [tex](h,k)\rightarrow(6,-12)[/tex].
What is the solution(s) to the system of equations y = x² +4 and y = 2x + 4
Answer:
[tex](x,y) = (0,4)~ \text{and}~ (x,y) = (2,8)[/tex]
Step by step explanation:
[tex]y = x^2 +4~~~~~~~~~...(i)\\\\y = 2x +4~~~~~~~~~...(ii)\\\\\text{From (i) and (ii):}\\\\~~~~~~x^2 +4 = 2x+4\\\\\implies x^2 = 2x\\\\\implies x^2 -2x = 0\\\\\implies x(x-2) = 0\\\\\implies x =0,~ x = 2[/tex]
[tex]\text{Substitute x = 0 in eq (i):}\\\\y = 0^2 +4 = 4\\\\\text{Substitute x = 2 in eq (i):}\\\\y=2^2+4 = 4+4 = 8\\\\\text{Hence,}~ (x,y)= \{(2,8), (0,4)\}[/tex]
What is the additive inverse of the complex number –8 + 3i?
–8 – 3i
–8 + 3i
8 – 3i
8 + 3i
The additive inverse of the complex number –8 + 3i will be 8 – 3i. Then the correct option is C.
What is Additive Inverse?To produce an answer equal to 0, additive inverse simply entails switching the sign of the quantity and adding it to the original figure.
The complex expression is given below.
⇒ –8 + 3i
Then the additive inverse of the complex number will be
Let x be the additive inverse of the complex number.
Then we have
x + (–8 + 3i) = 0
x = –(–8 + 3i)
x = 8 – 3i
Then the correct option is C.
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Answer:
C
Step-by-step explanation:
Edge 2022
please help me need the answer before 3:00
Answer:
26cm
Step-by-step explanation:
use the drop down menus to complete the statements about the function p(x)=x(x-1)+1
Answer:
a=1
b=-1
c=1
value of discriminant =-3
quadratic function will intersect x-axis 0 times
Step-by-step explanation:
The total length of a road trip was 18.4 hours. If highway signs are posted every 0.08 hours, including one at the end of the road trip, how many highway signs will there be on the road trip?
There are 230 highway signs during road trip.
What is length?Length is defined as the act of measuring the length of objects in some specified units which can be standard or non-standard.
Here, The total length of a road trip = 18.4 hours.
Highway signs are posted = after every 0.08 hours.
To find: Number of highway signs.
The number of highway signs is found = 18.4 / 0.08 = 230.
Thus there are 220 highway signs available during the road trip.
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Select the correct answer.
One leg of a right triangle is 10 units, and its hypotenuse is 12 units. What is the length of the other leg?
A.
about 7 units
B.
about 15 units
C.
about 25 units
D.
about 122 units
E.
about 224 units
A bag contains 14 gray, 7 black and 10 white marbles. A marble is drawn at random. What is the theoretical probability, as a decimal, of drawing a black marble? Round the decimal to the nearest hundredth
A pigeon was sitting 40 feet from the base of a telephone pole and flew 50 feet to reach the top of the pole. How tall is the telephone pole?
Answer:
90 feet
Step-by-step explanation:
40 + 50= 90 feet.
40 feet from the base is 40 feet high and 50 feet up is this equation.
Hope it helps sry if I’m wrong
Answer:
24 ft
Step-by-step explanation:
50 ^ 2 - 40 ^ 2 = b^2
2500 - 1600 = b^2
900 = b^2
√900 = √b^2
24 = b
Translate Triangle A by vector (3, -1) to give triangle B.
Then, rotate your triangle B 180° around the origin to give triangle C.
Describe fully the SINGLE transformation that maps triangle A onto triangle C.
Answer:
Translation as Triangle A has been translated by vector (3,-1) to now being (-2,-3)
Translation as Triangle A has been translated by a vector (3,-1) to now being (-2,-3).
What is translation?The process of changing the location of the image on the coordinate system will be known as the translation.
A translation in mathematics does not turn a shape; instead, it moves it left, right, up, or down. They are congruent if the translated shapes (or the image) seem to be the same size as the original shapes. They have merely changed their direction or directions.
Given that Translate Triangle A by a vector (3, -1) to give triangle B. Then, rotate your triangle B 180° around the origin to give triangle C.
Triangle A translation ⇒ (3,-1)
The second translation = (-2,-3).
Therefore, the translation as Triangle A has been translated by a vector (3,-1) to now being (-2,-3).
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Given the Equation y squared-Ay-6=0, where A is a constant, find the solutions for y in terms of A
Answer:
do u still need help with this
Jamiah bought two 125 ounce bags of flour for baking. He used up 32 ounces of flour to bake a batch of brownies. How much flour does Jamiah have now?
Answer: its 218
Step-by-step explanation: you just have to subtract 250 minus 32
Emma earned a grade of 95% on her multiple choice history final that had a total of
180 problems. How many problems on the final exam did Emma answer correctly?
Answer:
171
Step-by-step explanation:
180×95/100
180×95=17100
17100/100=171.
That is how I got my answer.
Write the product using exponents.
(-6)x(-6)x(-6)
The expression is
Answer:
(-6)³z² or -6³z²
Step-by-step explanation:
An exponent is used to signify the number of times a factor appears in a product.
__
In the expression (-6)·(-6)·(-6)·z·z, the factor (-6) appears 3 times, and the factor z appears 2 times. Written with exponents, this could be ...
(-6)³z²
_____
Additional comment
We can simplify this by realizing the product of the constant factors will be negative. (There is an odd number of minus signs.) The expression can also be written as ...
-6³z²
The version with (-6) being cubed is a more direct translation to the use of exponents.
If you pull a card from a standard deck of 52 and then pull a second card without replacing the first card, you have about a ____ chance(round to nearest percent) of pulling out a face card, followed by on ace.
The probability that you pull a card from a standard deck of 52 and then pull a second card without replacing the first card is 2%
How to determine the probability?The given parameters are:
Cards = 52
Face card = 12
Ace = 4
The probability of selecting a face card is:
P(Face card) = 12/52
Now, there are 51 cards.
The probability of selecting an ace is:
P(Ace) = 4/51
The required probability is:
P = 12/52 * 4/51
Evaluate
P = 0.0181
Express as percentage
P = 1.81%
Approximate
P = 2%
Hence, the probability is 2%
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Find the area of this circle. Use 3 for π.
A = πr²
r=10 cm
Answer:
A ≈ 300 cm²
Step-by-step explanation:
Area of a circle: πr² (where r is the radius)
π (pi) ≈ 3r (radius) = 10 cmSubstitute the given values into the formula:
⇒ A = πr²
⇒ A ≈ (3)(10)²
⇒ A ≈ 3(100)
⇒ A ≈ 300 cm²
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Hey there!
[tex] \red{\underline{\bold{\blue{Area \: of \: a \: circle}}}} [/tex]
[tex] \\ [/tex]
Answer :[tex] \red{\boxed{\bold{\blue{A \approx 300{cm}^{2}}}}} [/tex]
Explanation:The area of a circle is calculated using the following formula :
[tex] \sf{\blue{A} = \orange{\pi} \times \red{r}^{2}} \\ \sf{where \: \red{r}\: is \: the \: radius \: of \: the \: circle} [/tex]
⇢Here, we consider that π = 3 but in reality, π ≈ 3 replace [tex] \orange{\pi} [/tex] with 3 and [tex] \red{r} [/tex] with 10 :
[tex] \sf{\blue{A} = \orange{\pi} \times \red{r}^{2} } \: \: \: \\ \sf{\blue{A} \approx \orange{3} \times \red{10}^{2} } \\ \sf{\blue{A} \approx \orange{3} \times \red{100} } \\ \green{ \boxed{\sf{\blue{A} \approx300{cm}^{2}}}} [/tex]
⇒Therefore, the area of the circle is about 300cm².
[tex] \\ [/tex]
What is the y-intercept of the graph below?
Answer:
B
Step-by-step explanation:
the y- intercept is the point on the y- axis where the line crosses it
the line crosses the y - axis at (0, - 4 ) ← y- intercept
Erika is working on solving the exponential equation 50x = 17; however, she is not quite sure where to start. using complete sentences, describe to erika how to solve this equation.
hint: use the change of base formula: log base b of y equals log y over log b.
Erika is working on solving the exponential equation 50^x = 17; The solution is x = 0.7242.
What is logarithm?When you raise a number with an exponent, there comes a result.
Let's say you get
a^b = c
Then, you can write 'b' in terms of 'a' and 'c' using a logarithm as follows
[tex]b = \log_a(c)[/tex]
'a' is called base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'
Erika is working on solving the exponential equation 50^x = 17;
however, she is not quite sure where to start.
The equation is
[tex]50^x = 17\\[/tex]
By taking the log both sides
[tex]log_a b = x\\\\a_x = b[/tex]
By using the base formula
[tex]log_0 y = \dfrac{logy}{log b}[/tex]
So, [tex]log_{50} 17= x\\\\[/tex]
[tex]x = \dfrac{log17}{log 50}[/tex]
x = 0.7242
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pleeeeeeeeeeeeeeeeas FAST !!!!! i need help if a/b = (-7/9)^8 / (-7/9)^6 find the value of (a/b)^2.
Answer:
(-7/9)^4 = 2401/6561
Step-by-step explanation:
The rules of exponents apply.
(a^b)/(a^c) = a^(b-c) . . . . . quotient rule
(a^b)^c = a^(bc) . . . . . . . . power rule
__
value of a/bThe first rule of exponents shown above helps us find the value of a/b.
[tex]\dfrac{a}{b}=\dfrac{\left(\dfrac{-7}{9}\right)^8}{\left(\dfrac{-7}{9}\right)^6}=\left(\dfrac{-7}{9}\right)^{8-6}=\left(\dfrac{-7}{9}\right)^2[/tex]
value of (a/b)^2The second rule of exponents shown above tells us how to find the square.
[tex]\left(\dfrac{a}{b}\right)^2=\left(\left(\dfrac{-7}{9}\right)^2\right)^2=\left(\dfrac{-7}{9}\right)^{2\times2}\\\\\boxed{\left(\dfrac{a}{b}\right)^2=\left(\dfrac{-7}{9}\right)^4=\dfrac{2401}{6561}}[/tex]
_____
Additional comment
Since -7 is always to an even power in these expressions, its sign can be ignored. The product of an even number of negative values is positive.
What is the slope of the line represented by the equation y + 3 = -4(x-5)?
OA. 3
OB. 4
O C. -3
OD. -4
Answer:
-4
Step-by-step explanation:
if you graph it, we can find out two points are 0,17 and 1,13
we can find the slope from rise/run
-4 is the slope of the line represented by the equation y + 3 = -4(x-5)
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The equation of the line is y + 3 = -4(x-5)
We have to find slope
Let us simplify the equation to slope intercept form to find slope
y+3=-4x+20
y=-4x+17
Hence, -4 is the slope of the line represented by the equation y + 3 = -4(x-5)
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Triangle DEF has vertices D(0,2) , E(2,4) , and F(4,0) . Graph the image of the triangle after a reflection across the x-axis, followed by a dilation by a scale factor of 1.5.
The attached figure represents the image of the triangle after a reflection and a dilation
How to determine the image of the triangle?The vertices are given as:
D(0,2) , E(2,4) , and F(4,0) .
The transformations are given as:
Reflection across the x-axisDilation by a scale factor of 1.5.The rule of reflection across the x-axis is
(x,y) -> (x,-y)
So, we have:
D' = (0,-2)
E' = (2,-4)
F' = (4,0)
The rule of dilation by a scale factor of 1.5 is:
(x,y) -> 1.5(x,y)
So, we have:
D'' = 1.5 * (0,-2) = (0,-3)
E'' = 1.5 * (2,-4) = (3,-6)
F'' = 1.5 * (4,0) = (6,0)
See attachment for the image of the triangle
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What is the midpoint of FB
Point L is the midpoint
The midpoint is halfway between the two points. In this case, Point F and Point B are 10 units away from each other. The midpoint is the distance between the points (10) divided by 2.
What’s the inequality of x-3>8
Answer:
x>11
Step-by-step explanation:
To simplify this inequality, we add 3 from both sides to get x-3+3>8+3. Since -3+3 cancels out to 0, we are left with x>8+3. 8+3=11 so x>11.
Hope this helps! If you need further explanation let me know :)
What is the diameter of a hemisphere with a volume of 458 ft³, to the nearest tenth
of a foot?
Answer:
12.0 ft
Step-by-step explanation:
What is the orthocenter?
The midpoint of the base of the triangle
The point of intersection of the three medians
The point of intersection of the three altitudes
The orthocenter is the point of intersection of the three altitudes.
What is an orthocenter?An orthocenter can be defined as the point of intersection of altitudes which are perpendicular from the vertex to the opposite sides of a triangle.
Therefore, the orthocenter is the point of intersection of the three altitudes.
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What is the slop and the y-intercept of the line with the given equation: -x+4y= -24?
Answer:
Slope: 1/4
y - int: (0,-6)
Step-by-step explanation:
-x+4y=-24
4y = -24+x
y=1/4 * x - 6
Which are correct representations of the inequality -3(2x-5) <5(2-x)? Select two options.
x<5
-6x-5<10-x
-6x + 15 < 10-5x
5> ( number line )
-5< ( number line )
What is a divided by a% of a?
Answer:
[tex]\frac{100}{a}[/tex]
Step-by-step explanation:
Hello!
a% is the same as [tex]\frac a{100}[/tex].
a% of a can be found by multiplying them both, giving us [tex]\frac {a^2}{100}[/tex]
Solve:[tex]\frac{a}{\frac{a^2}{100}}[/tex][tex]a * \frac{100}{a^2}[/tex][tex]\frac{100a}{a^2}[/tex][tex]\frac{100}{a}[/tex]The value of the expression is [tex]\frac{100}{a}[/tex]
The measures of the angles of a triangle are shown in the figure below. Solve for x.
Step-by-step explanation:
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HELP PLEASE ‼️‼️‼️‼️ I WILL MARK BRAINLIEST
Answer:
102
Step-by-step explanation:
Find the slope of -8yx+5y=0
Answer:
0
Step-by-step explanation:
0, it is a flat line on a graph