solve equation (n-1)(n+6)(n+5)=0
Which equation represents the general form a circle with a center at (–2, –3) and a diameter of 8 units?
A.) x^2+y^2+4x+6y-51=0
B.) x^2+y^2-4x-6y-51=0
C.) x^2+y^2+4x+6y-3=0
D.) x^2+y^2-4x-6y-3=0
To find the equation, we will form the general equation of a circle and then will find the equation that matches the equation we formed.
General equation of a circleThe general equation of a circle is given as
[tex](x-h)^2+(y-k)^2 = R^2[/tex]
where, the (h, k) are the coordinates of the center of the circle, and R is the radius of the circle.
The correct option is c.
Given to uscircle with a center at (–2, –3) diameter of 8 unitsTo findthe equation of the circle that represents the general form of a circle with a center at (–2, –3) and a diameter of 8 units.
Radius of the CircleGiven that the diameter of the circle is 8 units. therefore,
[tex]\rm{ Radius\ of\ the\ circle =\dfrac{Diameter}{2} = \dfrac{8}{2}[/tex]
Equation of a circleThe equation of the circle that represents the general form of a circle with a center at (–2, –3) and a radius of 4 units can be found by substituting the values in the equation of a circle:
[tex](x-h)^2+(y-k)^2 = R^2[/tex]
Substituting the values,
[tex][x-(-2)]^2+[y-(-3)]^2 = 4^2\\\\ (x+2)^2+(y+3)^2 = 16[/tex]
[tex](x+2)^2+(y+3)^2 = 16\\\\ (x^2 + 4 + 4x)+(y^2+9+6y) = 16\\\\ x^2 + 4 + 4x+y^2+9+6y = 16\\\\ x^2 + 4x+y^2+6y = 16-4-9\\\\ x^2 + 4x+y^2+6y = 3\\\\ x^2 + 4x+y^2+6y -3 = 0[/tex]
Therefore, the equation which will be in the above form will be the equation we want. As we can see the above equation is similar to option c.
VerificationTo verify that we will plot the graph. The image given below represents the general form of a circle with a center at (–2, –3) and a diameter of 8 units.
Hence, the correct option is c.
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this math problem is hard
By the Triangle Inequality Theorem, if two sides of a triangle have lengths of 6 and 13, what are the possible lengths of the third side?
In this exercise we have to use the knowledge of triangles to calculate the value of the third side, so we have:
[tex]7
organizing the information given in the statement we find that:
a=6 b=13 c=xRecognition of the Pythagorean theorem we have that will be:
[tex]c
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translation rule to describe the translation of x that is 3 units to the left and 4 units up
the length of a rectangular foam packing block is 9 in the width is 3 and 1/4 in and the height is 2/3 of an inch what is the volume of the foam block
The volume of a rectangle is the product of it length, width and height, the volume of the rectangle in this example is 19 1/2 cubic inched
Volume of RectangleGiven Data
Length of block = 9 inches
Width of block = 3 1/4 inches = 13/4 inches
Height of block = 2/3 of an inches
We know that the expression for volume of rectangle is given as
Volume = Length * With * Height
Substituting our given data we have
Volume = 9* 13/4 * 2/3
Volume = 9*13*2/1*4*3
Volume = 234/12
Volume = 19 1/2 cubic inches
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24r3-64r2-21r+56 answer
Create a 5th degree polynomial with four terms in standard form
"What is the value of-3|15-s|+2^3 when s-=3"?
Which of the expressions below can be factor using the difference of squares method
Evaluate 0.3 y+\dfrac yz0.3y+zy0, point, 3, y, plus, start fraction, y, divided by, z, end fraction when y=10y=10y, equals, 10 and z=5z=5z, equals, 5.
When [tex]\( y = 10 \) and \( z = 5 \)[/tex], [tex]\( 0.3y + \frac{y}{z} \) equals \( 5 \)[/tex].
Step 1 :To evaluate the expression [tex]\(0.3y + \frac{y}{z}\) when \(y = 10\) and \(z = 5\)[/tex], follow these steps:
1. Substitute the given values of [tex]\(y\) and \(z\)[/tex] into the expression:
[tex]\[0.3 \times 10 + \frac{10}{5}\][/tex]
2. Calculate each term separately:
- [tex]\(0.3 \times 10 = 3\)[/tex]
- [tex]\(\frac{10}{5} = 2\)[/tex]
3. Add the results:
[tex]\[3 + 2 = 5\][/tex]
So, when [tex]\(y = 10\) and \(z = 5\)[/tex], the expression [tex]\(0.3y + \frac{y}{z}\) equals \(5\).[/tex]
Step 2 :1. Multiply 0.3 by 10:
[tex]\[0.3 \times 10 = 3\][/tex]
2. Divide 10 by 5:
[tex]\[\frac{10}{5} = 2\][/tex]
3. Add the results:
[tex]\[3 + 2 = 5\][/tex]
Thus, when [tex]\(y = 10\) and \(z = 5\)[/tex], the expression [tex]\(0.3y + \frac{y}{z}\) equals \(5\).[/tex]
How many times is function f called in the code segment below? 25 points?
It's 3/5 of the wall is made from brick how do you determine the height of the brick proportion of the wall
To find the height of the brick proportion of a wall, multiply the total wall height by the fraction representing the brick portion. For instance, if the wall is 220 cm high and 3/5 is brick, the brick portion's height would be 132 cm.
To determine the height of the brick proportion of the wall, you would need to know the total height of the wall first. Once you have the total height, you can calculate the height of the brick section by multiplying the total height by the fraction of the wall that is brick. For example, if 3/5 of the wall is made from brick, and the wall is 220 cm high, the calculation would be as follows:
Height of brick portion = Total height of the wall × Fraction of wall that is brick
Height of brick portion = 220 cm × (3/5) = 132 cm
Therefore, the height of the brick proportion of the wall would be 132 cm.
4z - 7 in terms of z
Which prefix means 1/10 of a unit in the metric system?
A. milli
B. Deci
C. Hecto
D. Centi
Complete the expansion of (a + b)6 with a = 1 and b = 0.3.
(dont add everything together)
(1 + 0.3)^6 = (____)^6 + 6(____)^5(____) + 15(____)^4(____)^2 + 20(____)^3(____)3 + 15(____)^2(____)^4 + 6(___)(___)^5 + (____)^6
Answer:
[tex](1+0.3)^{6}=(1)^6+6(1)^{5}(0.3)+15(1)^{4}(0.3)^{2}+20(1)^{3}(0.3)^{3}+15(1)^{2}(0.3)^{4}+6(1)^{1}(0.3)^{5}+(0.3)^{6}[/tex]
Step-by-step explanation:
This is an expansion of the expression [tex](a+b)^{6}[/tex]. In general you can expand expressions of this form by a formula known as the binomial theorem. This formula establishes that
[tex](a+b)^{n}=\sum_{k=0}^{n} {n\choose k} a^{n-k}b^{k}[/tex]
Where the coeficients [tex]n\choose k[/tex] are called binomial coeficients, and can be computed by the formula
[tex]{n\choose k} =\frac{n!}{(n-k)! k!}[/tex]
where [tex]n!=1\times 2\times 3\times \cdots\times n[/tex].
The average of 25, 29, and x is 29. Find x.
29 * 3 = 87
25 +29 = 54
x = 87 - 54 = 33
x = 33
The smallest angle in a triangle is 1/5 as large as the largest angle. The third angle is twice the smallest angle. Find the three angles.
Answer:
x + 5x + 2x = 180
8x = 180
x = 22.5 degrees ( smallest angle), Largest Angle = 112.5 degrees and the third angle = 45 degrees
Let's call the smallest angle x. Then the largest angle is 5x and then the third angle is 2x since it is twice the smallest angle. We know that the sum of all the angles in a triangle is 180 degrees.
Step-by-step explanation:
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What are the 3 steps for factoring completely?
2. How did the technique of “Factoring by Grouping” get it’s name?
3. How can you tell if Factoring by Grouping works for a problem?
4. What is a perfect square trinomial?
5. a.) How can you tell if a binomial is the difference of two squares.
b.) What is the factored form of the difference of two squares.
6. How do you find the zero’s of a polynomial function?
Factoring completely involves three steps: identifying the GCF, applying the appropriate factoring method, and checking for additional factors. Factoring by grouping is used when there are four terms in an expression and common factors can be factored out separately. An example is given to illustrate the factoring by grouping process.
Explanation:Factoring Completely:Identify the greatest common factor (GCF) of the terms in the expression and factor it out.Apply the difference of squares, trinomial, or grouping method to factor the remaining expression.Check if there are any additional factors that can be factored further.Factoring By Grouping:This technique is used when there are four terms in an expression and there is a common factor between the first two terms and the last two terms. The common factor is factored out separately from the two pairs, and then the resulting binomials are factored further.
Factoring by Grouping Example:Consider the expression 2x + 3y + 4x + 6y. In this case, we can group the terms as (2x + 3y) + (4x + 6y). Common factors can be factored out separately, resulting in (2x + 3y)(1 + 2).
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-3x = 4y = 8
X and y intercepts of this equations . Then graph line
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For what value of x is the square of the binomial x+1 twenty greater than the square of the binomial x–3?
Answer:
x=3.5 they did nothing wrong but I am pretty sure you meant not twenty but one hundred and twenty for that the answer is x=16
Step-by-step explanation:
who is the fastest man alive?
Usain Bolt set world records for the 100-m and 200-m dashes with impressive maximum speeds and accelerations.
Usain Bolt of Jamaica set the world record for the men's 100-m dash in the 2008 Olympic Games in Beijing. He accelerated for 3.00 s to reach his maximum speed and maintained it for the race. Calculating his maximum speed and acceleration involves understanding his performance data.
For the 100-m dash, Bolt's maximum speed was approximately 12.19 m/s and his acceleration was 2.63 m/s². In the 200-m dash, his maximum speed using the same assumptions was 10.36 m/s. This insight into Bolt's remarkable athleticism showcases his exceptional speed and acceleration capabilities on the track.
What is the mode of the data set?
103, 77, 90, 102, 103, 81, 78, 84, 84, 87, 99, 103, 118
Question 3 options:
84
90
93
103
If the sum of six consecutive even integers is 354 what is the smallest of the six integers
Find two numbers, if Their sum is 3/5 and their difference is 7 1/5
Answer:
3.9 and -3.3
Step-by-step explanation:
sinθ=1/4, 0<θ<90; cosθ
A rectangle is dilated by a scale factor of 4.
a) The original rectangle is 8 cm by 3 cm. What are the dimensions of the new rectangle?
b) Is the new image a reduction or enlargement? Explain.
HELP PLEASE
What is the rule for this pattern of numbers?
Some amount of billiard balls were arranged in an equilateral triangle. And 13 balls were extra. When the same set of billiard balls were arranged into triangle in which each side has one more ball than in the first arrangement there were 7 balls shortage. How many balls were at the set?
Please help if you absolutly know the answer!!!!!!!!!!!
write the rate as a fraction? 17 meters per second