Answer:
see explanation
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
To obtain this form use the method of completing the square on both the x and y terms
rearranging
x² + 6x + y² - 4y = 12
x² + 2(3)x + 9 + y² + 2(- 2)y + 4 = 12 + 9 + 4
(x + 3)² + (y - 2)² = 25 ← in standard form
with centre = (- 3, 2) and r = [tex]\sqrt{25}[/tex] = 5
Consider the steps to simplify the expression. Which property is used to reach Step 3?
Expression: -4
3
7
+ 7 + (-3
4
7
)
Step 1: = -4
3
7
+ (-3
4
7
) + 7
Step 2: = -4 + (-
3
7
) + (-3) + (-
4
7
) + 7
Step 3: = -4 + (-
3
7
) + (-
4
7
) + (-3) + 7
Step 4: = -4 + (-1) + (-3) + 7
Step 5: = -8 + 7
Step 6: = -1
A) The associate property of addition.
B) The commutative property of addition.
C) The opposite of a sum is the sum of its opposites.
D) Subtracting a number is the same as adding its inverse.
NOTE: I ACCIDENTALLY clicked one star. That DOES NOT count as a real rating, and this DOES NOT mean my answer is bad!
Answer:
Commutative Property of Addition
Step-by-step explanation:
Step 2: -4 + (-37) + (-3) + (-47) + 7
Step 3: -4 + (-37) + (-47) + (-3) + 7
Because the order was changed, it is the Commutative Property.
Which of the following could be the equation of the function below?
Answer:
Option C is the correct option.
Step-by-step explanation:
In the given cosine graph we can draw some parameters of the equation as below
y = a cos(bx + c) + d
1) amplitude a = (1+3)/2=2
2) Period = π
3) phase shift = -π ( to the left)
4) Vertical shift = -1 ( downwards on y-axis)
Therefore the equation of the graph will be
y = -2cos[2(x + π)] - 1
Option C is the correct answer.
Marshall Earns a salary of 36,000, and each year he receives a $4,000 raise. Jim earns a salary of $51,000, and each year he receives a $1,500 raise. How many years will it take before Marshall and Jim earn the same salary
Answer:
It will take 6 years
Step-by-step explanation:
Marshall starts at 36,000 dollars and Jim starts at 51,000, multiply the pay raises by 6 and for Jim you get $9,000 and Marshall gets $24,000 pay raise in 6 years.
Sorry If It Is a bit confusing, I'm not really good with words. :/
Both of them will get the same salary after 6 year.
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, Marshall Earns a salary of $36,000, and each year he receives a $4,000 raise. Jim earns a salary of $51,000, and each year he receives a $1,500 raise.
Let x be the year in which they will get the same salary
Establishing the equation, we get
36000+4000x = 51000+1500x
Simplifying the equation,
36+4x = 51+1.5x
2.5x = 15
x = 6
Hence, Both of them will get the same salary after 6 year.
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In a triangle the sides has 82 degrees ,2x+10 degrees and x degrees what is x
Answer:
x = 29 1/3 degrees
Step-by-step explanation:
A triangle has 3 angle that total 180 degrees.
The three angles given are 82 degrees ,2x+10 degrees and x degrees.
So,
82+ (2x+10) + x = 180
Combine like terms.
92 + 3x = 180
Subtract 92 from each side
3x = 180 -92
3x = 88
divide each side by 3
3x/3 = 88/3
Change 88/ 3 to a mixed number
3 goes in to 88 29 times with 1 left over.
x = 29 1/3 degrees
which is greater .513 or .5129
Answer:
.513 is larger
Step-by-step explanation:
1st method is the thousandths place larger or smaller
.1 tenths
.01 hundredths
.001 thousandths
In this case the thousandths is larger for .513
2nd method
subtract the two number
.513 - .5129 = .0001
Since the number recieved is positive this means .513 is larger
what is the midpoint between -9 and 15 on the number line? A. 3
B. 12
C. 6
D. 2
Answer:
A. 3
Step-by-step explanation:
To find the midpoint between two numbers, we add the two numbers and divide by 2
midpoint = (x1+x2)/2
midpoint = (-9+15)/2
midpoint = (6)/2
midpoint =3
Homer has four times as many hits in baseball than interceptions in football. Homer has made a total of 120 hits and interceptions. How many of each has Homer made? (Matrix on the calculator)
Answer:
If in football. Then Homer has made a total of 24 interceptions and 96 hits
Step-by-step explanation:
if we know that Homer has four times as many hits in baseball than interceptions that means how ever many interceptions he has its four times greater that that number so if he had 5 interceptions then you would do 5 x 4 and the number of hit would be 20 so if you already know the number of hits all together like we do you would divide by 5 cause the number of hits count as 4/5 and interceptions is 1/5 of that so we do 120/5 which gives us 24 and to find the number of hit we times that by 4 then we get 96 and to check our answer 96 + 24 = 120
Answer:
Step-by-step explanation:If in football. Then Homer has made a total of 24 interceptions and 96 hits
Step-by-step explanation:
if we know that Homer has four times as many hits in baseball than interceptions that means how ever many interceptions he has its four times greater that that number so if he had 5 interceptions then you would do 5 x 4 and the number of hit would be 20 so if you already know the number of hits all together like we do you would divide by 5 cause the number of hits count as 4/5 and interceptions is 1/5 of that so we do 120/5 which gives us 24 and to find the number of hit we times that by 4 then we get 96 and to check our answer 96 + 24 = 120
I do not get this. Evaluate.
Simplify your answer as much as possible.
3!6!/5!2!
Answer:
18
Step-by-step explanation:
[tex]\frac{3!6!}{5!2!}[/tex]
n! = n * (n-1)!
For example 7! can be written as 7 * 6!
3! is 3* 2!
6! is 6 * 5!
[tex]\frac{3!6!}{5!2!}[/tex]
[tex]\frac{3*2!6*5!}{5!2!}[/tex]
Cancel out 5! from the top and bottom . Also cancel out 2! from top and bottom.
[tex]\frac{3*2!6*5!}{5!2!}[/tex]
3*6= 18
Ashley is the utilities manager at a paper mill. She's watching over one of her holding tanks. It takes of an hour to fill the tank. At this rate, how many holding tanks will she fill in 1 hour?
Answer: 5/8
Step-by-step explanation:
"If a - 7 = b(x + 2), then x = ?"
Please help!!!!
I need a step by step explanation too.
Answer: choice (3), x = (2b+7)/(a-b)
==============================
Explanation:
The idea is to get all the x terms to one side (after distributing), then factoring out the common term x, finally divide both sides by (a-b) as shown below
ax-7 = b(x+2)
ax-7 = bx+2b .... distribute
ax-7+7 = bx+2b+7 ... add 7 to both sides
ax = bx+2b+7
ax-bx = bx+2b+7-bx ... subtract bx from both sides
ax-bx = 2b+7
(a-b)x = 2b+7 .... factor out the GCF x
x = (2b+7)/(a-b) ... divide both sides by (a-b)
We have all of "2b+7" over "a-b" as one big fraction. This is what choice (3) is showing.
Which of the functions below could have created this graph?
Answer:
A
Step-by-step explanation:
Two facts need to guide your answer.
One
The highest power is odd: you know this because an even power would start on the left come down do it's squiggles if had any and wind up on the right going up.
This graph comes down on the left does it's squiggles and then goes further down on the right. That's the behavior of something whose highest power is odd.
Two
The leading coefficient, the number in front of the highest power must be minus. If it was positive as in y = x^3 the graph would be the mirror image of what it is.
Argument
B and D cannot be true. The highest power is even.
C is false because the leading coefficient is + 1.
So that leave A which is the answer.
The graph is included with this answer
The position graph shown in the question represents an object that is undergoing uniform motion. To create this graph, you would need a linear function that describes linear motion.
Explanation:The position graph shown in the question represents an object that is undergoing uniform motion. Uniform motion occurs when an object travels at a constant speed in a straight line. The graph shows a linear relationship between position and time, with the object consistently moving in the same direction.
To create this graph, you would need a function that describes linear motion. A linear function in the form of y = mx + b, where y represents position, x represents time, m represents the slope (rate of change of position with respect to time), and b represents the initial position. The slope of the line in the graph represents the speed of the object.
For example, the function y = 2x would create a position vs. time graph with a slope of 2, indicating that the object is moving at a constant speed of 2 units per time interval. Similarly, any other linear function with a constant slope could create this graph.
Find all the zeros of the quadratic function:
y=x^2+15x+36
Answer:
x=-12 and -3
Step-by-step explanation:
The quadratic formula is
[tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex].
It is important because while some quadratics are factorable and can be solved not all are. The formula will solve all quadratic equations and can also give both real and imaginary solutions. We will substitute a=1, b=15 and c=36.
[tex]x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}\\x=\frac{-15+/-\sqrt{(15)^2-4(1)(36)} }{2(1)}\\x=\frac{-15+/-\sqrt{225-144} }{2}[/tex]
We will now simplify and solve.
[tex]x=\frac{-15+/-\sqrt{81}}{2}\\x=\frac{-15+/-9}{2}[/tex]
x=-12 and x=-3
A kite, flying 50 feet high in the air is attached by a string to a stake in the sand. How long is the string to the nearest tenth of a foot? A) 50.0 feet B) 70.7 feet C) 77.9 feet D) 88.6 feet
Answer:
Hello, the answer tho this question is C.) 70.7 feet.
Jack's pancakes recipe calls for 2 teaspoons baking powder and 3 cups of flour. How how much baking powder is needed if Jack uses 9 cups of flour
Answer:
6
Step-by-step explanation:
Jack would need 6 teaspoons of baking powder for 9 cups of flour to maintain the ratio given in the original recipe.
To determine how much baking powder is needed if Jack uses 9 cups of flour instead of 3, you can set up a proportional relationship because the quantity of baking powder required is directly proportional to the amount of flour used.
If the original recipe calls for 2 teaspoons of baking powder for every 3 cups of flour, for 9 cups of flour (which is 3 times as much), you would need 3 times as much baking powder. Hence, the calculation would be as follows:
2 teaspoons baking powder / 3 cups flour = x teaspoons baking powder / 9 cups flour
By cross-multiplication, we can find the value of x:
2/3 * 9 = x
x = 2 * 3 = 6 teaspoons of baking powder
Therefore, Jack would need 6 teaspoons of baking powder for 9 cups of flour to maintain the ratio given in the original recipe.
How to write 21/6 as a mixed number
The calculated fraction 21/6 to a mixed number is 3 1/2
How to change the fraction 21/6 to a mixed numberFrom the question, we have the following parameters that can be used in our computation:
Number = 21/6
Divide 21 by 6
So, we have
Quotient = 3
Next, we have
Remainder = 21 - 6 * 3
Evaluate the products
Remainder = 3
So, we have
Fraction = 3 3/6
Simplify
Fraction = 3 1/2
Hence, the fraction to a mixed number is 3 1/2
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What Is the Slope And Y Intercept Of This Line?
Y = X -5
Answer:
slope = 1 , y- intercept = - 5
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 )
y = x - 5 is in this form
with slope m = 1 and y- intercept c = - 5
In trapezoid ABCD AC is a diagonal and ∠ABC ≅ ∠ACD. Find AC if the lengths of the bases BC and AD are 14m and 28m respectively.
Answer:
[tex]AC=14\sqrt{2}m[/tex]
Step-by-step explanation:
we are given trapezoid ABCD
AC is a diagonal
∠ABC ≅ ∠ACD
we know that
BC and AD are parallel
so, <DAC = <ACB
so, ΔABC ≅ΔACD
Since, both triangles are similar
so, their ratios must be equal
we get
[tex]\frac{BC}{AC} =\frac{AC}{AD}[/tex]
now, we can plug values
[tex]\frac{14}{AC} =\frac{AC}{28}[/tex]
[tex]AC^2=14\times 28[/tex]
[tex]AC^2=14^2\times 2[/tex]
[tex]AC=14\sqrt{2}m[/tex]
To find the length of AC, the diagonal in trapezoid ABCD, we can use the fact that ∠ABC ≅ ∠ACD and the lengths of the bases BC and AD. By setting up a proportion using the corresponding sides of the similar triangles ABC and ACD, we can find that AB/AC = 1/2. Multiplying the length of AB by 2 gives us AC = 28m.
Explanation:Given that ∠ABC ≅ ∠ACD and the lengths of the bases BC and AD are 14m and 28m respectively, we can find the length of AC, which is a diagonal in trapezoid ABCD.
Because the two angles are congruent, triangle ABC is similar to triangle ACD. This means their corresponding sides are proportional.We can set up a proportion using the corresponding sides of the triangles:Autry made 45% of the shots he took during the basketball game. If he attempts 20 shots how many times did he score?
Final answer:
Autry scored 9 times during the basketball game by multiplying the shot percentage (0.45) by the total number of shots attempted (20).
Explanation:
The student's question is, how many shots did Autry score if he made 45% of his shots and attempted 20 shots in total? To calculate this, you can use the following steps:
Convert the percentage to a decimal by dividing by 100. So, 45% becomes 0.45.
Multiply this decimal by the total number of shots attempted. In this case, 0.45 multiplied by 20 shots.
The result gives you the number of successful shots Autry made.
So, performing the calculation:
0.45 × 20 = 9
Autry scored 9 times during the basketball game.
Simplify the expression below. (2n/6n+4)(3n+2/3n-2)What is the numerator of the simplified expression?
Answer:
n
Step-by-step explanation:
[tex](\frac{2n}{6n+4})(\frac{3n+2}{3n-2})[/tex]
We see that in the first rational expression, both the numerator and denominator are divisible by 2. This means we can factor a 2 out of the top and bottom and then cancel it:
[tex](\frac{2(n)}{2(3n+2)})(\frac{3n+2}{3n-2})\\\\=(\frac{n}{3n+2})(\frac{3n+2}{3n-2})[/tex]
Now we can multiply straight across:
[tex]\frac{n(3n+2)}{(3n+2)(3n-2)}[/tex]
Since we have the same factor on the top and bottom, this factor cancels:
[tex]\frac{n}{3n-2}[/tex]
The numerator is n.
The numerator of the simplified expression is [tex]n[/tex].
Given:
The given expression is:
[tex]\left(\dfrac{2n}{6n+4}\right)\left(\dfrac{3n+2}{3n-2}\right)[/tex]
To find:
The numerator of the simplified expression.
Explanation:
We have,
[tex]\left(\dfrac{2n}{6n+4}\right)\left(\dfrac{3n+2}{3n-2}\right)[/tex]
It can be written as:
[tex]=\left(\dfrac{2n}{2(3n+2)}\right)\left(\dfrac{3n+2}{3n-2}\right)[/tex]
[tex]=\dfrac{2n(3n+2)}{2(3n+2)(3n-2)}[/tex]
[tex]=\dfrac{n}{3n-2}[/tex]
Therefore, the numerator of the simplified expression is [tex]n[/tex].
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Hagrid plans to put up new fencing around his rectangular garden. He wants the width of his new garden to be 6 less than the length. The perimeter of the new garden will be 188 feet. Create and use an algebraic equation to find the dimensions (length and width) of Hagrid's new garden. Show your work!
Answer:
Lenght=50 feet.
Width=44 feet.
Step-by-step explanation:
1. He wants the width of his new garden to be 6 less than the length, this can be expressed as following:
[tex]W=L-6[/tex]
Where W is the width L is the length.
2. The perimeter of a rectangle can be calculated with:
[tex]P=2L+2W[/tex]
3. You know the perimeter, therefore, you can substitute [tex]W=L-6[/tex] into the equation of the perimeter and solve for the length:
[tex]2L+2(L-6)=188\\2L+2L-12=188\\4L=200\\L=50[/tex] (The length is 50 feet)
3. Then, the width is:
[tex]W=L-6[/tex]
[tex]W=50-6=44[/tex] (The width is 44 feet)
You roll a number cube twice what is the probability of rolling a 2
The probability of getting a 5 from the first rolling is 1/6. The probability of getting an even number is 1/2 (= 1/6 (for a 2) + 1/6 (for a 4) + 1/6 (for a 6)). As the two rollings are independent, you can just multiply two probability values to come up with a final answer. That is, (1/6)·(1/2) = 1/12.
Note that I did not write this. This answer comes from Wyzant. I am only linking this to you so that you'll get the answer quickly.
Answer:
i think its 1 out of 6 or 2 out of 12 depending on the way you meant the question im pretty sure this is right correct me if iam wrong
Step-by-step explanation:
Can I please get someone who is good at Geometry to help me? PLEASE AND THANK YOU!!!! (You just have to do problem A. Thanks again)
Answer:
x=6
Step-by-step explanation:
We can find < PMN by using the law of triangles.
The sum of the angles of a triangle adds to 180
<M + <N + < PMN = 180
32 + 64+ < PMN = 180
96 + < PMN = 180
Subtract 96 from each side
96 -96 < PMN = 180-96
< PMN =84
<PMN + <NPQ forms a straight line so it equals 180
<PMN + <NPQ=180
84 + <NPQ=180
Subtract 84 from each side
84-84 + <NPQ=180-84
<NPQ=96
<NPQ = 6x
96 = 6x
Divide each side by 6
96/6 = 6x/6
16 =x
simplify 12x+4(x+y)-6y ?
Answer:
16x - 2y
Step-by-step explanation:
12x+4(x+y)-6y
Distributive property
= 12x + 4x + 4y -6y
Combine like terms
= 16x - 2y
Expand
12x + 4x + 4y - 6y
Collect like terms
(12x + 4x) + (4y - 6y)
Simplify
16x - 2y
Find the equation (in terms of x) of the line through the points (-7,3),(-10,-3)
Answer:
y = 2x + 17
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 )
To calculate m use the gradient formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (- 7, 3) and (x₂, y₂ ) = (- 10, - 3)
m = [tex]\frac{-3-3}{-10+7}[/tex] = [tex]\frac{-6}{-3}[/tex] = 2
y = 2x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (- 7, 3 ), then
3 = - 14 + c ⇒ c = 3 + 14 = 17
y = 2x + 17 ← equation of line
Find the slip of the line that passes through each pair of point (-6,1), (4,8).
X1 = -6
Y1= 1
X2= 4
Y2 = 8
8 - 1
____
4 + 6
7
_ is your answer
10
i don’t get any of these :/// please help
1) From the total of 17 marbles, Jacob takes 2 out at random. There are
[tex]\dbinom{17}2=C(17,2)=C^{17}_2=\dfrac{P(17,2)}{2!}=\dfrac{P^{17}_2}{2!}=\dfrac{17!}{2!(17-2)!}=136[/tex]
possible outcomes of the draw. (Lots of different notations are used for the binomial coefficient; the first one is my preference.) The number of ways to draw exactly 2 orange marbles is
[tex]\dbinom70\dbinom{10}2=1\cdot1\cdot45=45[/tex]
That is, of the 3 red and 4 blue marbles - or the 7 non-orange marbles - we want 0; of the 10 oranges, we want 2.
So the probability of drawing exactly 2 orange marbles is [tex]\dfrac{45}{136}\approx0.33[/tex].
2) Now Jacob draws 3 marbles, for which there are
[tex]\dbinom{17}3=680[/tex]
possible combinations. The event that Jacob draws at least 1 orange marble is complementary to the event that Jacob draws 0 orange marbles. So if we find the probabilty of drawing 0 oranges, then we subtract this from 1 to find the probability of drawing at least 1.
There are
[tex]\dbinom73\dbinom{10}0=35\cdot1=35[/tex]
possible ways of doing, so the probability of drawing 0 oranges is [tex]\dfrac{35}{680}[/tex], in turn making the probability of drawing at least 1, [tex]1-\dfrac{35}{680}=\dfrac{645}{680}\approx0.95[/tex].
3) This question is kinda ambiguous. It's not clear whether Jacob draws a marble with or without replacement.
If he does return a drawn marble to the bag, then for each draw, there is a [tex]\dfrac{10}{17}[/tex] probability that he draws an orange marble, and a [tex]\dfrac7{17}[/tex] probability of not. The draws are presumably independent of one another, so that the probability of drawing the first orange marble on the fourth attempt would be
[tex]\dfrac7{17}\cdot\dfrac7{17}\cdot\dfrac7{17}\cdot\dfrac{10}{17}=\dfrac{3430}{83521}\approx0.041[/tex]
If no replacements are made, then as non-orange marbles are drawn from the bag, the number of non-oranges and the total number of marbles both decrease by 1. Then the probability of drawing orange on the fourth draw would be
[tex]\dfrac{\dbinom71\dbinom61\dbinom51\dbinom{10}1}{\dbinom{17}1\dbinom{16}1\dbinom{15}1\dbinom{14}1}=\dfrac5{136}\approx0.037[/tex]
If you're supposed to round to the nearest hundredths place, your final answer should be acceptable either way.
4) We want the probability that a boat is made of wood given that it has chrome accents:
[tex]P(\text{wood}\mid\text{chrome})=\dfrac{P(\text{wood AND chrome})}{P(\text{chrome})}=\dfrac{70\%}{75\%}\approx93\%[/tex]
5) We apply the inclusion/exclusion principle:
[tex]P(\text{wood OR chrome})=P(\text{wood})+P(\text{chrome})-P(\text{wood AND chrome})[/tex]
[tex]P(\text{wood OR chrome})=90\%+75\%-70\%=95\%[/tex]
6) The events of a boat having chrome accents and a boat being made of wood are independent if and only if
[tex]P(\text{wood AND chrome})=P(\text{wood})\cdot P(\text{chrome)}[/tex]
But [tex]90\%\cdot75\%=67.5\%\neq70\%[/tex], so these two events are not independent.
Which factors can be multiplied together to make the trinomial 5x2 + 8x – 4? Check all that apply. (x + 1) (2x + 1) (x + 2) (5x + 1) (5x – 2) Mark this and return Save and Exit
Answer:
(5x-2) and (x+2)
Step-by-step explanation:
Answer:
the factors are (5x-2) and (x+2)
Step-by-step explanation:
5x^2 + 8x – 4
first we multiply 5 and -4= -20
product is -20 and sum is +8
find out two factors whose product is -20 and add upto +8
10 * (-2) = 20
10 +(-2)= 8
5x^2 +10x-2x – 4
group the terms and factor out GCF
(5x^2 +10x)+(-2x – 4)
5(x+2) -2(x+2)
(5x-2)(x+2)
the factors are (5x-2) and (x+2)
Plz I need by tonight
Answer: Yes
Step-by-step explanation: 4x5 is 20 + 2 is 22 then when you multiply that by 9 you get 198
36x5 is 180 + 18 is 198
Both answers equal each other
Dai has 3 meters of fabric that he wants to cut into 5 equal sized pieces. what is true about the length of each piece of fabric. I need the answer as a fraction.
Answer:
The length of each piece of fabric is [tex]L=\frac{3}{5}[/tex]
Step-by-step explanation:
Given : Dai has 3 meters of fabric that he wants to cut into 5 equal sized pieces.
To find : What is true about the length of each piece of fabric ?
Solution :
Dai has 3 meters of fabric.
He cuts the fabric into 5 equal sized pieces.
So, The length of each piece is defined as
[tex]L=\frac{3}{5}[/tex]
Therefore, The length of each piece of fabric is [tex]L=\frac{3}{5}[/tex]
how do I solve for x - 5 = x + 7
Answer:
There are no values of x
that make the equation true.
Step-by-step explanation: No solution