Answer: Center: (-3, 2). Radius: 4.
Step-by-step explanation:
The x-coordinate of the center of the circle is given by the constant within the parenthesis with variable x. Whatever number makes the equation x + 3 = 0 is the x-coordinate of the center of the circle, which in this case is -3.
The y-coordinate of the center of the circle is given by the constant within the parenthesis with variable y. Whatever number makes the equation y - 2 = 0 is the y-coordinate of the center of the circle, which in this case is -2.
The radius of the circle is the square root of the constant on the other side of the equation. So, r = [tex]\sqrt{16}[/tex] = 4.
The explanation is from the equation of a circle in a graph:
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
h and k in this equation stand for the coordinates of the center of the circle, with h being the x-coordinate and k being the y-coordinate. IN your equation, we have:
[tex](x+3)^2 + (y-2)^2 =16[/tex]
Which can also be written as
[tex](x-(-3))^2 + (y-(2))^2=16[/tex]
See the correlation of numbers -3 and 2 with h and k?
Notice also how the equation contains [tex]r^2[/tex], so to find the radius you do [tex]\sqrt{r^2}[/tex].
Solve for x.
Please help asap
find the missing number of each unit rate 24/8=?/1 40/20 = ?/1
Answer:
24/8 = 3/1
40/20 = 20/1
Step-by-step explanation:
I hope this helps!
Abigail Henderson has $1360 budgeted for spending money on an upcoming trip to country and country be countries currency is trading $1.30 per Curren$y a and country bees currencies trading at $1.60 per currency be she plans to spend more time In country a so she wants to four times as much of currency a as currency be
Abigail Henderson's budget of $1,360 and the $1.30 and $1.60 trading price of the currency of country A and country B gives;
The equation that represents the total cost is; 1.3·x + 1.4·y = 1,360The number of each currency Abigail plans to buy are;
The number of units of currency of country A, x = 800The number of units of the currency of country B, y = 200What is a budget?A budget provides an estimation of a person, business, or country's income and expenditure over a specified period or duration.
The amount Abigail Henderson budgeted = $1,360
The per currency exchange rate for country A = $1.30
The per currency exchange rate for country B = $1.60
The number of currency A Abigail wants = 4 × The number of currency B
Which gives; x = 4·y
The equation that represents Abigail's total cost of buying currencies is presented as follows;
1.3·x + 1.6·y = 1,360
Plugging in the value of x gives;
1.3 × (4·y) + 1.6·y = 1,360
6.8·y = 1,360
y = 1,360 ÷ 6.8 = 200
The number of currency of country B, Abigail purchases, y = 200
The number of currency of country A Abigail plans to buy, x = 4 × 200 = 800
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Man is ordering new tile for her kitchen floor the area of the floor is 115.4 ft.² and she wants to order between 15% and 20% extra of the material
The order for the extra materials that are ordered by the man will be between 17.31 ft² and 23.08 ft².
How to calculate the value?From the information, the man is ordering new tile for her kitchen floor the area of the floor is 115.4 ft.² and wants to order between 15% and 20% extra of the material.
It should be noted that 15% of the material will be:
= 15% × 115.4
= 17.31 ft²
It should be noted that 20% of the material will be:
= 20% × 115.4
= 23.08 ft²
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Quincy has a jewelry business in which he designs and sells bracelets. His daily profit, Q(x), can be modeled by the function Q(x) = 8.25x − 24.75, where x is the number of bracelets he sells. What is the value of Q(3), and what is its interpretation?
Q(3) = 0; If Quincy sells 3 bracelets, he will earn $0.
Q(3) = 0; If Quincy sells 0 bracelets, he will earn $3.
Q(3) = 3.36; If Quincy sells 3 bracelets, he will earn $3.36.
Q(3) = 3.36; If Quincy sells 3.36 bracelets, he will earn $3.
The correct interpretation is Q(3) = 0; If Quincy sells 3 bracelets, he will earn $0.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
Q(x) = 8.25x − 24.75, where x is the number of bracelets he sells.
So, for x= 3 them Q(3)
Q(3)= 8.25 (3) - 24.75
Q(3) = 24.75 - 24.75
Q(3) = 0
Hence, Q(3) = 0; If Quincy sells 3 bracelets, he will earn $0.
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A recent survey reported that 67% of Americans approve of human embryonic stem cell research. If an American is selected at random, find the probability that he or she will disapprove or have no opinion on the issue.
If an American is selected at random, the probability that he or she will disapprove or have no opinion on the issue is 33%.
How to find the probability?Given data:
Approved human embryonic stem cell research = 67% or 0.67
Now let find the probability that the human embryonic stem cell research will be disapprove using this formula
P(disapprove or no opinion) = 1 - Approved
Let plug in the formula
P(disapprove or no opinion) = 1 - 0.67
P(disapprove or no opinion) = 0.33 or 33%
Therefore 33% is the probability of disapprove or no opinion.
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A car drives 160 miles in the same amount of time that a plane flies 840 miles. The plane is going 170 mph faster than the car. How fast is the car going?
The speed of the car is 40mph
What is rate?A rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate.
Distance covered by car = 160 miles
distance covered by plane = 840 miles
let the time taken to cover 160 miles by car be x
speed of car = 160/x
speed of plane which is 170mph faster than speed of car = 170 + 160/x
time taken to cover 840 miles by plane,
time = distance/speed = [tex]\frac{840}{170 + \frac{160}{x} }[/tex]
By simplifying,
time taken by plane = [tex]\frac{840x}{170x + 160}[/tex]
since it takes same time for both to get to their destination,
Then,
x = [tex]\frac{840x}{170x + 160}[/tex]
By cross multiplying
x( 170x + 160) = 840x
divide both sides by x, it reduces to
170x + 160 = 840
170x = 840 - 160
170x = 680
x = 680/170
x = 4
Speed of car = 160/x
speed of car = 160/4
speed = 40mph
In conclusion, the care moves at the speed of 40mph
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Q4. Write (5-√5)² in the form a + b√5, where a and b are
integers.
(5-√5)² in the form a + b√5 can be written as 30 - 10√5 where, the integers a and b are 30 and -10 respectively.
What is integer?
Positive, negative, and zero are all examples of integers. The Latin word "integer" means to "whole" or "intact." Therefore, fractions and decimals are not included in integers. In this essay, we will learn more about integers, their definition, and their characteristics.
We know that,
[tex](a-b)^2= a^2 + b^2 - 2ab[/tex]
Using this mathematical identity, putting the values from question,
(5-√5)² = 5² + √5² - 2(5)(√5)
(5-√5)² = 25 + 5 - 10√5
(5-√5)² = 30 - 10√5
This is in the form a + b√5 where, the integers a and b are 30 and -10 respectively.
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Estimate 17.140 - 03.179 by first rounding each number to the nearest tenth.
Answer: 13.9
Step-by-step explanation:
17.140 rounded to the nearest tenth is 17.1
03.179 rounded to the nearest tenth is 3.2
17.1 - 3.2 = 13.9
Consider the equation and the following ordered pairs: (6,y) and (x,1).
y=−2x+5
The values of the variables x and y are 2 and -7.
We are given an equation. The equation is linear in nature. The equation represents a straight line. The equation is y = -2x + 5. We are given two sets of ordered pairs. The ordered pairs are (6, y) and (x, 1). These points satisfy the given equation. We need to find the values of the variables x and y. We will substitute the coordinates into the equation.
y = -2x + 5
First, we will put (6, y).
y = -2(6) + 5 = -12 + 5 = -7
Now, we will put (x, 1).
1 = -2x + 5
2x = 4
x = 2
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Eva says you can use the conversion for 60 km into
miles to convert 600 km into miles. Use Eva's
method to convert 600 km into miles.
300
miles
After using conversion of measurements , the answer is
60 km = 37.28 miles and 600km = 372.83 miles.
What is conversion of measurements?
By multiplying or dividing a number, a conversion factor can be used to change one set of units to another. If a conversion is required, it must be done using the correct conversion factor to get an identical value. The correct conversion factor, for instance, is 12 inches to 1 foot when converting between inches and feet. We must convert between different units in order to have accuracy and prevent measurement confusion.
Here the given we need to convert them km into miles.
To convert km to miles we need to divide the value by 1.609 .
=> 60 km
=> 60/1.609
=> 37.28 miles.
Now ,
=> 600 km
=> 600/1.609
=> 372.83 miles.
Therefore after conversion of measurement answer is
60 km = 37.28 miles and 600km = 372.83 miles.
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If A and B are independent events, P(A)=0.15, and P(B)=0.77, what is P(B|A)?
The Probability of P(B│A) is 0.77
What are independent events?Independent events are those events whose occurrence is independent on any other event. For example, if we flip a coin in the air and get the outcome as tail, then again if we flip the coin but this time we get the outcome as Head, In both cases, the occurrence of both events is independent of each other. It is a type of events in probability.
If A is the event that even number will appear when a die is rolled and B is when 4 or 6 appears
P(A)= 3/6 = 1/2 and P(B) = 2/6 = 1/3
Also A and B is the event ‘the number appearing is even and a multiple of 4 or 6 so that
P(A ∩ B) = 1/6
P(B│A) = P(A ∩ B)/ P(A)
= 1/6 /1/2= 1/3 = P(B)
Therefore P(B│A) = P(B)
if A= 0.15 and P(B)= 0.77
P(B│A) = 0.77
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Find all real numbers x such that
(3^x - 27)^3 + (27x - 3)^3 = (3x + 27x - 30)^3
All the real numbers x in the expression such that (3x - 27)³ + (27x - 3)³ = (3x + 27x - 30) is x = 1 .
In the question ,
it is given that the expression is
(3x - 27)³ + (27x - 3)³ = (3x + 27x - 30)
By using the identity a³ + b³ [tex]=[/tex] (a + b)(a² - ab + b² )
we get ,
[(3x - 27 + 27x - 3)] × [(3x - 27)² - (3x - 27)(27x - 3) + (27x - 3)² ] = 30x - 30
(30x - 30)×[(3(x - 9))² - (3(x - 9) × 3(9x - 1)) + (3(9x - 1))²] = 30x -30
using the identity (a-b)² [tex]=[/tex] a² -ab + b²
(30x - 30) × [9( x² - 18x + 81) - (9(9x² - 82x + 9)) + (9(81x² - 18x + 1)) = 30x-30
9(30x - 30)×[x² - 18x + 81 - 9x² + 82x - 9 + 81x² - 18x + 1] = 30x - 30
270×(x - 1)×[ 73x² + 46x + 73] = 30(x - 1)
taking (x-1) terms to LHS ,
we get
(270 - 30)×(x - 1)[ 73x² + 46x + 73 ] = 0
(240) (x - 1) [ 73x² + 46x + 73 ] = 0 ....because 270-30 = 240
Dividing both sides by 240
we get ,
(x - 1) [73x² + 46x + 73] = 0
So , either x - 1 = 0 or 73x² + 46x + 73 = 0
on solving 73x² + 46x + 73 = 0
we get the discriminant of 73x² + 46x + 73 a negative number , so it cannot have real root .
hence x -1 = 0
x = 1
Therefore , the only real solution is x = 1 .
The given question is incomplete , the complete question is
Find all real numbers x in the expression such that (3x - 27)³ + (27x - 3)³ = (3x + 27x - 30) ?
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What is the asymptote of the exponential function graph below?
y=1
y=5
y=2
y=0
Answer: y=5 is the asymptote answer
The note F# has a frequency of 1,480 hertz. The note B has a frequency of 988 hertz. Find the ratio of F# to B to two decimal places. Express the answer in integer-ratio form.
answer is a fraction.
The ratio of F# to B to two decimal places is 1.50:1.
What is ratio?A ratio is simply used to compare two things or numbers.
In this case, the note F# has a frequency of 1,480 hertz and the note B has a frequency of 988 hertz.
The ratio of F to B will be:
= 1480 / 988
= 1.50
The ratio is 1.50:1.
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Answer:
3/2
Step-by-step explanation:
Choose which property of equality is demonstrated.
a. AB = AB
Write the quadratic equation whose roots are -5 and 4, and whose leading coefficient is 5.
(Use the letter x to represent the variable.)
3
x
2
−
3
x
−
60
=
0
Explanation:
A quadratic equation whose roots are
α
and
β
and leading coefficient is
a
is
a
(
x
−
α
)
(
x
−
β
)
=
0
Hence, the quadratic equation whose roots are
5
and
−
4
and leading coefficient is
3
is
3
(
x
−
5
)
(
x
−
(
−
4
)
)
=
0
or
3
(
x
−
5
)
(
x
+
4
)
=
0
or
3
(
x
2
−
5
x
+
4
x
−
20
)
=
0
or
3
(
x
2
−
x
−
20
)
=
0
or
3
x
2
−
3
x
−
60
=
0
Answer:
5x^2+5x-100=0
Step-by-step explanation:
5(x+5)(x-4)=0
(x+5)(x-4)= 0
x= -5
x= 4
The quotient of a number and -4 is -20. Find the number
Answer:
80
Step-by-step explanation:
x/ -4 = -20
I hope this helps!
The equation of line s is y= – 4x– 5/3 . Line t includes the point ( – 3,3) and is parallel to line s. What is the equation of line t?
The equation of the parallel line t is y = -4x - 9
How to determine the line equation?The equation of line s given as
y = -4x - 5/3
Also, from the question
The point on line t is given as
Point = (-3, 3)
The equation of a line can be represented as
y = mx + c
Where
Slope = m
By comparing the equations, we have the following
m = -4
This means that the slope of y = -4x - 5/3 is -4
The slopes of parallel lines are equal
This means that the slope of the line t is -4
The equation of the parallel line is then calculated as
y = m(x - x₁) +y₁
Where
m = -4
(x₁, y₁) = (-3, 3)
Substitute the known values in the above equation
y = -4(x + 3) + 3
Evaluate
y = -4x - 12 + 3
Evaluate the sum
y = -4x - 9
Hence, the parallel line has an equation of y = -4x - 9
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A system consists of three identical components. In order for the system to perform as intended, all of the components must perform. Each has the same probability of performance. If the system is to have a .92 probability of performing, what is the minimum probability of performing needed by each of the individual components? Round your answer to three decimal places.
If each has the same probability of performance. If the system is to have a .92 probability of performing, The minimum probability of performing needed by each of the individual components is: 0.97126.
How to determine the probability:Given data:
Number of identical component = 3
Probability of performing = .92
Now let determine the probability
Probability = 0.92 ^(1/3)
Probability = 0.92^0.3333
Probability =.9726
Therefore the probability is .9726.
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Solve the application problem.
Find the area of a rectangular garden that measures 4 feet by 6/7 feet.
A. 3 3/7 ft
B. 9 5/7 ft^2
C. 9 5/7 ft
D. 3 3/7ft^2
Answer:
D. 3 3/7 ft²
Step-by-step explanation:
A = LW
A = 4 ft × 6/7 ft²
A = 24/7 ft²
A = 3 3/7 ft²
help asap thanks yall so much
Answer:
a and c
Step-by-step explanation:
if you evaluate each one on either side of the equal sign you get the same number on both sides
A rectangular ground is 121/4m long and 41/2 m broad. Find the perimeter and area of the ground.
Answer:
Thank you,Hope you like it and it will help you
There are 7 new books and 5 used books on a shelf.
(a) What is the ratio of new books to all books on the shelf?
0
(b) What is the ratio of used books to all books on the shelf?
0
Answer:
7 * 5 =35 because if you say 5 10 15 20 25 30 35 then that's your answer
Answer:
a) 7:13 b) 5:13
Step-by-step explanation:
There are 7 new books (-> 7:--) theres 5 used books, add the 7 new books and 5 used books together. it said "The ratio for new books to all books?" it must be in that order. with leads you to 7:13
do the same thing for b) using the same steps.
Please help 18points
Complete (assume $50,000 of overhead to be distributed): (Round your Ratio answers to the nearest hundredth.) Sq. Ft. Ratio Amount of Overhead Allocated Dept. A 20,000 A B Dept. B 80,000 C D
The calculation of the ratios, resulting from the square feet occupied by both departments, and the amounts of overhead allocated to the two departments are as follows:
Ratio Amount
Department A 1/5 $10,000
Department B 4/5 $40,000
What is the ratio?The ratio is the numerical relationship shared by two or more values.
Ratios are fractional values and are depicted using fractions, decimals, and percentages.
Ratios, like proportions, show how much a value or variable is contained in another.
Total overhead = $50,000
Department Square Feet Ratio Amount of Overhead Allocated
Dept. A 20,000 A = 1 B = $10,000 ($50,000 x 1/5)
Dept. B 80,000 C = 4 D = $40,000 ($50,000 x 4/5)
Ratios = 20,000:80,000
= 1:4
Sum of Ratios = 5
Thus, based on the cost driver allocation ratios, Department A will bear $10,000, while Department B will be allocated $40,000.
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I need help with this geometry question
The value of x will be 9.8 m.
The value of y will be 11.2 m.
What is mean by Triangle?
A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The two triangles are similar.
Now,
Since, The two triangles are similar.
So, We get the sides are proportional to each other.
Hence, We can formulate;
⇒ 4/5.6 = 7/x
Solve for x as;
⇒ x = 7 × 5.6 / 4
⇒ x = 9.8 m
And, 4/5.6 = 8/y
Solve for y;
⇒ y = 8 × 5.6 / 4
⇒ y = 11.2 m
Thus, The value of x will be 9.8 m.
The value of y will be 11.2 m.
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100 points answer asap
A park is shaped like a rectangle and measures 3.4 mi by 6.6 mi.
What are the perimeter and area of the park?
Enter your answers in the boxes.
Perimeter: ______ mi
Area: _____ mi²
Answer:
Perimeter: 20 mi
Area: 22.44 mi^2
Step-by-step explanation:
perimeter formula for a rectangle is 2 times length plus 2 times width
2(3.4)+2(6.6)
6.8+13.2
20 is the perimeter
Now for the are we multiplying the length and width to find area
3.4x6.6
22.44 is the area
Hopes this helps please mark brainliest
An exam has four multiple choice problems, each with five possible answers. If you guess on each problem, what is the probability of getting at least one answer correct? Round your answer to the nearest whole percent.
1/2 is the probability of getting at least one answer correct
How to find the probability of getting at least one answer correct?
Given that: the exam has 4 multiple choice with 5 possible answers. This means there are 20 possible choices ( 5×4 = 20).
That means each problem has a probability of 1/20 correct answer. The probability of getting at least one answer means you either get one, two, three or four correct answers. Thus:
P (at least one correct) = P(1) + P(2) + P(3) + P(4)
= 1/20 + 2/20 + 3/20 + 4/20
= (1+2+3+4)/20
= 10/20
= 1/2
Therefore, the probability of getting at least one answer correct is 1/2
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The probability of getting at least one answer correct is equal to 7
How to calculate for the probabilityThat I guess at least one answer correctly means that I could get all four answers correct or three answers correct or two answers correct or only one answer correct. The probability of getting any one answer is 1/4 and probability of not getting an answer is 1 - 1/4=3/4. Or implies addition.
probability of getting all four answers correct = 1/4 +1/4 + 1/4 + 1/4 = 4/4 = 1
probability of getting three answers correct = 1/4 +1/4 + 1/4 + 3/4 = 6/4 = 3/2
probability of getting two answers correct = 1/4 +1/4 + 3/4 + 3/4 = 8/4 = 2
probability of getting all four answers correct = 1/4 +3/4 + 3/4 + 3/4 = 10/4 = 5/2
The probability of getting at least one answer correct = 1 + 3/2 + 2 + 5/2
The probability of getting at least one answer correct = (2 + 3 + 4 + 5)/2
The probability of getting at least one answer correct = 14/2
Thefore, the probability of getting at least one answer correctly is the whole number 7
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Solve the following system of equations.
Provide your answer below:
-3x+4y= 7
7x- 12y = -11
Answer:
x = -5
y = -2
Step-by-step explanation:
-3x + 4y = 7 ⇒ ( 1 )
7x - 12y = -11 ⇒ ( 2 )
Multiply the equation ( 1 ) by 3.
( 1 ) × 3
3( -3x + 4y = 7 )
-9x + 12y = 21 ⇒ ( 3 )
Let us find the value of x.
Add equations ( 2 ) & ( 3 ).
( 2 ) + ( 3 )
7x - 12y - 9x + 12y = - 11 + 21
Combine like terms.
-2x = 10
Divide both sides by -2.
x = -5
Let us find the value of y.
For that, let us use equation ( 1 ) and replace x with -5 and make y the subject.
- 3x + 4y = 7
-3 × -5 + 4y = 7
15 + 4y = 7
Subtract 15 from both sides.
4y = 7 - 15
4y = -8
Divide both sides by 4.
y = -2
