The equation of the circle is (x + 7)² + (y + 6)² = 4 if the center and radius are (-7,-6) and 2 respectively.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
We have center of the circle(h, k) = (-7, -6)
The radius of the circle r = 2
The standard form of a circle:
(x - h)² + (y - k)² = r²
(x - (-7))² + (y - (-6))² = 2²
(x + 7)² + (y + 6)² = 4
Thus, the equation of the circle is (x + 7)² + (y + 6)² = 4 if the center and radius are (-7,-6) and 2 respectively.
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The area of a rectangle is 119 square units. Find the length and width of the rectangular
Answer: 7 and 17
Step-by-step explanation:
Since the area of a rectangle is the product of the two sides, the product of these two numbers must be 119.
The factors pairs of 119 are 1 and 119, and 7 and 17.
x+7 and x-3 have a difference of 10. The difference of 7 and 17 is also 10. Hope this helped!
In the future, please take a less blurry photo because I had to guess the part where I think it said x-3.
Write the arithmetic series 3+9+15+21+27 using summation notation
Answer:
_ t&byds
ty grk gtrwwfh
Find the h.c.f of
[tex] {x}^{3} + {y}^{3} \: and \: \: {x}^{2} - xy + {y}^{2} [/tex]
The greatest common factor will be (x² – xy + y²).
Greatest common factorThis is a value or expression that can divide the given expressions without leaving a remainder.
Given the following expressions
x^3+^3 and x^2 - xy + y^2
Expand x^3+y^3
x^3+y^3 =(x + y)(x² – xy + y²).
Since (x² – xy + y²) is common to both expression, hence the greatest common factor will be (x² – xy + y²).
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find the length of segment AC if AB=7.8 cm and BC=25 mm. how many solutions are there in each case? Point B lies on segment AC
Answer:
10.3. and One solution
Step-by-step explanation:
I had this question, tho it might be different
33. Three consecutive
integers exist such that five
times the first number is
equal to one more than twice
the sum of the second and
third numbers.
Which equation accurately
solves for the integers?
Let n represent the first
number.
The equation which accurately solves for the integers is; 5n = 2(2n +3) +1.
Which equation accurately solves for the integers?It follows from the task content that the first number is represented by n.
On this note, it follows that the second, and third numbers are; (n+1) and (n+2) respectively.
On this note, since five times the first number is equal to one more than twice the sum of the second and third numbers; we have;
5n = 2(n+1+n+2) +1
5n = 2(2n+3)+1.
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A principal of $5500 is invested in an account paying an annual rate of 7%. Find the amount in the account after 4 years if the account is compounded semiannually, quarterly, and monthly.
Answer:
Formulae is Future value, see in picture I've done example 1 for u.
Last week Sharon's mother order 60 roses for her shop this week she will order five times as many roses how many roses will she order write an expression and then find the solution
Answer:
60(5) = 300 :D
Step-by-step explanation:
First lets make the equation :)
Orders 60 roses
This week will order 5x as many as last week
60 x 5 OR 60(5)
60(5) = 300 :)
Have an amazing day!!
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What happens when you reflect an object over intersecting line( combination of reflection)?
Answer:
Step-by-step explanation:
The Compositions of Reflections Over Intersecting Lines Theorem states that if we perform a composition of two reflections over two lines that intersect, the result is equivalent to a single rotation transformation of the original object.
hope it helps! (✿◠‿◠)
The result concluded is equivalent to a single rotation transformation of the original object.
Explanation of how reflection across axis works?When a graph is reflected along an axis, say x-axis, then that leads the graph to go just on the opposite side of the axis as if we're seeing it in a mirror.
The Compositions of Reflections Over Intersecting Lines states that if we perform a composition of two reflections over two lines that intersect.
The result concluded is equivalent to a single rotation transformation of the original object.
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what is the perimeter of a rectangle with the of 10cm and width 20cm
Find the value of x.
helpppp
Answer: [tex]55^{\circ}[/tex]
Step-by-step explanation:
The measure of the third unknown arc is
[tex]360^{\circ}-70^{\circ}-110^{\circ}=180^{\circ}[/tex].
So, [tex]x=\frac{180^{\circ}-70^{\circ}}{2}=\boxed{55^{\circ}}[/tex]
Area of a Parallelogram
i 13 cm
20 cm
15 cm
View One Minute Version
Overview
Answer:
260 cm^2
Step-by-step explanation:
The area of a parallelogram is calculated by multiplying its height and base:
The base for this parallelogram is given as 20 and the height is 13
13*20 = 260
The area is stated in square units so the answer is 260 cm^2
Question 1
At room temperature, one liter of water can dissolve over 300 grams of salt.
What is the solvent in this solution?
temperature
water
salt
grams
It's the water
The salt would be the solute that dissolves in the solvent.
Temp - is a factor
(affecting rate at which salt dissolves)
grams - unit of measure
Hope this helps!
Suppose that F(x) = x² and G(x) = 2/5 x². Which statement best compares the
graph of G(x) with the graph of F(x)?
A. The graph of G(x) is the graph of F(x) stretched vertically and
flipped over the x-axis.
B. The graph of G(x) is the graph of F(x) stretched vertically.
C. The graph of G(x) is the graph of F(x) compressed vertically and
flipped over the x-axis.
OD. The graph of G(x) is the graph of F(x) compressed vertically.
Answer: The graph of G(x) is the graph of F(x) compressed vertically.
Step-by-step explanation:
See attached image.
For the given functions f and g find f•g and state it’s domain
f(x) = 3x - 6; g(x) = 8x +4
f.g and its domain is 24x²-36x-24; all real numbers.
Given, f(x) = 3x - 6; g(x) = 8x +4.
We need to find the value of f.g
What is a domain?The domain of a function; In mathematics, the domain of a function is the set of inputs accepted by the function.
Now, (f.g)(x)=(3x-6)(8x+4)
=24x²-48x+12x-24
=24x²-36x-24
Therefore, f.g and its domain is 24x²-36x-24; all real numbers.
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Part D
Explain how an insurance company can pay a large benefit even if it hasn't collected that amount from an individual's premiums.
Pooling can be referred to the process of how an insurance company can pay a large benefit even if it hasn't collected that amount from an individual's or company premium in this type of context.
What is Insurance?This is referred to as a type of protection against financial loss or other forms of incidents or risks and there are different types which cater for different purpose or reasons and they include life, vehicle insurance etc. The insurance plan is usually sold by designated insurance companies and are accessible to the public.
Pooling is the process which involves the smaller firms purchasing better interest rates which helps to lessen the cost of coverage. This also ensures that benefits are paid at the right time so as to avoid hassle and other forms of issues which may arise from this important process.
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Simplify. Write your answers without exponents.
Answer:
1. 1/27 2. 1/16
Step-by-step explanation:
First can be rewritten as (1/9)^(1/2 * 3) and anything to the power of 1/2 is a sqrt. So it is sqrt(1/9)^3. Then (1/3)^3 which is 1/27
Second, the negative bring the number to the bottom, 1/(32)^4/5. Then can be written as [tex]\sqrt[5]{1/32}[/tex]^4. 5th root of 1/32 is 1/2 then 1/2^4 is 1/16
The residence of a city voted on whether to raise property taxes the ratio of yes votes to know votes was 5 to 6 if there was 5844 Novos what was the total number of votes
Given the function r(x)=x−4x 9, find the values of x that make the function less than or equal to zero. write the solution in interval notation.
Inequalities help us to compare two unequal expressions. The solution that will make the value of the function r(x) less than equal to 0 is [3,∞).
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.
It is mostly denoted by the symbol <, >, ≤, and ≥.
To find the value of x that will make the function r(x)=x-4x+9 less than or equal to 0 solve the inequality,
x - 4x + 9 ≤ 0
x - 4x ≤ -9
-3x ≤ -9
x ≥ (-9)(-3)
x ≥ 3
Hence, the solution that will make the value of the function r(x) less than equal to 0 is [3,∞).
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g(x)= l2xl +2
find domain and range
The domain of the function g(x)=l2xl +2 is all real numbers and the range is from (0,∞).
Given g(x)= l2xl +2
First of all we know that modulas gives two values for x<0 and x>=0.
The function g(x) if opened gives two values.
for x>=0 g(x)=2x+2
for x<0 g(x)=-2x+2
because we have not told about the description about x so we can put any value in the function.
So the domain is all real numbers.
Now when we take g(x)=2x+2 for x>=0
putting x=0 we get 2 and rest are positive values so the value of g(x) keeps increasing as we increase the value of x. So here range is [2,∞).
Now take g(x)=-2x+2 for x<0
putting smallest number starting from zero but not 0 we will get a number near to 0 but not zero and because when a negative number multiplies with -2 it becomes positive and increase the value of g(x) so here the range becomes (0,∞).
When we talk about overall range it will be [2,∞) ∪(0,∞)
it will be (0,∞).
Hence the domain of the function g(x) is all real numbers and range is from 0 to infinity.
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Use the function below to find F(3).
Answer:
The choice D.
Step-by-step explanation:
[tex]f(x) = {( \frac{1}{6} })^{x} \\ \\ f(3) = {( \frac{1}{6} })^{3} = \frac{ ({1})^{3} }{( {6})^{3} } = \frac{1}{216} [/tex]
Find the x-intercept of the graph of the linear equation y = −1
2
x + 3.
x-intercept
Answer:
Step-by-step explanation:
x intercept equals pi
Answer:
x intercept= 6
Step-by-step explanation:
Alexander is working two summer jobs, making $10 per hour washing cars and $8 per hour landscaping. Last week Alexander worked twice as many hours washing cars as he worked hours landscaping hours and earned a total of $84. Write a system of equations that could be used to determine the number of hours Alexander worked washing cars last week and the number of hours he worked landscaping last week. Define the variables that you use to write the system.
The system of equations is:
x = 2y
x*$10 + y*8 = $84
Solving it, we see that he worked 3 hours landscaping and 6 hours washing cars.
How to write the system of equations?
First, we need to define the variables:
x = number of hours washing cars.y = number of hours landscaping.We know that Alexander worked twice as many hours washing cars as he worked hours landscaping, then:
x = 2y
We also know that he earned a total of $84, then:
x*$10 + y*8 = $84
So the system of equations is:
x = 2y
x*$10 + y*8 = $84
To solve it, we just replace the first equation into the second one:
(2y)*$10 + y*8 = $84
y*$28 = $84
y = $84/$28 = 3
So He worked 3 hours landscaping, and:
x = 2*y = 2*3 = 6
6 hours washing cars.
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A dinghy is pulled toward a dock by a rope from the bow through a ring on the dock 8 ft above the bow. The rope is hauled in at the rate of 1 ft/sec. Complete parts (a) and (b). a. How fast is the boat approaching the dock when 10 ft of rope are out? ft/sec (Type an integer or a simplified fraction.) b. At what rate is the angle changing at this instant? rad/sec (Type an integer or a simplified fraction.)
a) The speed of the boat is 3/5 ft/sec
b) The rate at which the angle changes is 8/125 rad/sec
What is a right angled triangle?A right angled triangle is a type of the triangle with one of its angles 90°.
The longest side of the triangle is called the hypotenuse which is the side that faces the right angle. other sides are called the adjacent sides.
Analysis:
The analysis is in the attached file below.
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Solve inequality -8x+4≤36.
[tex]\bf{-8x+4\leq 36 }[/tex]
Subtract 4 from both sides.
[tex]\bf{-8x\leq 36-4 }[/tex]
Subtract 4 from 36 to get 32.
[tex]\bf{-8x\leq 32 }[/tex]
Divide both sides by −8. Since −8 is <0, the inequality direction is changed.
[tex]\bf{x\geq \dfrac{32}{-8} }[/tex]
Divide 32 by −8 to get −4.
[tex]\bf{x\geq -4 \ \ \Rightarrow \ \ \ Answer }[/tex]
{ Pisces04 }Question :
Solve inequality -8x + 4 ≤ 36Solution :
⇒ -8x + 4 ≤ 36
⇒ -8x ≤ 36 - 4
⇒ -8x ≤ 32
⇒ -x ≤ 32 / 8
⇒ -x ≤ 16 / 4
⇒ -x ≤ 8 / 2
⇒ -x ≤ 4
⇒ x ≥ -4
Choose the proportion that is true.
3/8=15/40
12/13=2/3
9/13=27/36
16/49=4/7
Answer:
3/8=15/40
Step-by-step explanation:
Multiply both the numerator and the denominator of the first term by 5 and you'll see that it's the same fraction.
represent the complex number graphically, and find the trignometric form of the number. 1 + 3i
The trigonometric form of the complex number 1 + 3i is 3.16[cos(71.57)° + isin(71.57°)]
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Complex number is in the form z = a + bi, where a, b are real numbers.
Given the complex number z = 1 + 3i
In polar form: r = √(1² + 3²) = 3.16
Ф = tan⁻¹ (3/1) = 71.57⁰
The trigonometric form of the complex number 1 + 3i is 3.16[cos(71.57)° + isin(71.57°)]
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In a story about a doctor trying to treat a patient with mysterious symptoms, which scene would most likely be the climax?
What does it mean to the rise over run when the slope is an integer? a. the rise number is one c. the run part of the slope is going to be one b. the run number is always negative d. there will be no slope Please select the best answer from the choices provided
Answer:
C
Step-by-step explanation:
When the run part (the difference between x-coordinates of the two points on the line) is 1, the slope is an integer.
If f(x) = 2x²-5, f(5) =
Answer:
f(5) = 45
Step-by-step explanation:
If f(x) = 2x²-5 , f(5) =
f(5) = 2(5)² - 5
f(5) = 2(25) - 5
f(5) = 50 - 5
f(5) = 45
HELP................................................
Answer:
D. g(x) = 5x^2
Step-by-step explanation:
Answer:
D.
Step-by-step explanation:
A point of the function g(x) is known: (1, 5)
The proper function is
[tex]g(x)=5x^{2}[/tex]
Demonstration calculating g(1)
[tex]g(1)=5(1)^{2} =5(1)=5[/tex]
The point (1, 5 ) belongs to this function
Hope this helps