Answer:
[tex](x + 1)^2 + (y-8)^2 = 173[/tex]
Step-by-step explanation:
[tex]\textsf{The standard form of the equation of a circle is }\\\\ \sf (x -h)^2 + (y-k)^2 = r^2 \;where\; (h, k) \textsf{ are the coordinates of the center of the circle and \;r\; is the radius}[/tex]
Here h = -1, k = 8
So we get
[tex](x - (-1)) ^2 + (y - 8)^2 = r^2[/tex]
[tex](x + 1)^2 + (y - 8)^2= r^2\\\\[/tex]
Since the circle passes through the point (-3, -5) we can plug in these values of x = -3 and y = -5 to get r squared
[tex](-3 + 1)^2 + (-5 -8)^2 = r^2\\\\(-2)^2 + (-13)^2 = r^2\\\\4 + 169 = r^2\\\\r^2 = 173\\\\\\[/tex]
So the equation of the circle is
[tex](x + 1)^2 + (y-8)^2 = 173[/tex]
Beth got a job painting dorm rooms at her college. At top speed, she could paint 5 identical rooms during one 6-hour shift.
How long did she take to paint
each room?
O 50 minutes
O 1 hour and 10 minutes
O 1 hour and 12 minutes
O 1 hour and 15 minutes
A die is rolled twice. What is the probability rolling a 3 first, followed by rolling an even number? Leave your answer as a reduced fraction.
The probability of rolling a 3 first, then an even number, is 1/12.
What do we mean by probability?Probability is simply the likelihood of something occurring. When we are uncertain about the outcome of an event, we can discuss the probabilities of various outcomes—how likely they are. Statistics is the study of events governed by probability.So, in the given situation the first roll has no effect on the second roll because they are separate events.
Because they are independent, the probabilities of the two events can be multiplied.
The probability of getting a 3 is 1/6.The probability of getting an even number is 1/2 (2, 4, 6).Now, we will multiply the two probabilities as follows:
1/6 × 1/2 = 1/12Therefore, the probability of rolling a 3 first, followed by rolling an even number is 1/12.
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I will give brainlist
Divide 4 and 5 over 6 ÷ negative 2 and 1 over 7.
negative 10 and 15 over 42
negative 8 and 5 over 42
negative 2 and 23 over 90
negative 2 and 1 over 2
The value of the expression given as [tex]4 \frac{5}{6} \div - 2\frac 17[/tex] is [tex]-2\frac{23}{90}[/tex]
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the solution to the expression?The expression is given as
Divide 4 and 5 over 6 ÷ negative 2 and 1 over 7.
Rewrite the above expression properly as follows:
Divide 4 5/6 ÷ -2 1/7
Using LaTeX, the above expression can be further represented as
[tex]4 \frac{5}{6} \div - 2\frac 17[/tex]
Rewrite the above fractions and express it as improper fractions
[tex]\frac{29}6 \div -\frac{15}7[/tex]
Rewrite the above fractions and express it as products
[tex]\frac{29}6 \times -\frac7{15}[/tex]
Evaluate the product in the above expression
[tex]-\frac{203}{90}[/tex]
Rewrite the above expression as a mixed fraction
[tex]-2\frac{23}{90}[/tex]
Hence, the value of the expression given as [tex]4 \frac{5}{6} \div - 2\frac 17[/tex] is [tex]-2\frac{23}{90}[/tex]
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A bag of sand originally weighing 144 lb was lifted at a constant rate. As it rose, sand also leaked out at a constant rate. The sand was half gone by the time the bag had been lifted to 18 ft. How much work was done lifting the sand this far? (Neglect the weight of the bag and lifting equipment.)
Using a linear function and the work integral, it is found that the work that was done lifting the sand this far is of 944 ft-lb.
What is a linear function?A linear function is modeled by the following rule:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, the change in y divided by the change in x.b is the y-intercept, which is the the value of y when the function crosses the x-axis, that is, when x = 0.For the weight of the bag of sand in this problem, we have that:
The initial weight of the bag was of 144 lb, hence the y-intercept is of b = 144.When the bag had been lifted 18 ft, 0.5 x 144 = 72 lb were gone, that is, 4 lb were gone for each ft the bag was lifted, hence the slope is of m = -4.Hence the weight of the bag after being lifted x feet is given by:
W(x) = 144 - 4x.
What is the work of a function?The work realized for a function f(x) in an interval [a,b] is given by the following integral:
[tex]W = \int_{a}^{b} f(x) dx[/tex]
For this problem, the function and the bounds of the interval are given as follows:
f(x) = 144 - 4x.a = 0, b = 18.Hence the work is given by:
[tex]W = \int_{a}^{b} (144 - 4x) dx[/tex]
W = 144x - 2x², from x = 0 to x = 18.
Applying the Fundamental Theorem of Calculus:
W = 144(18) - 2(18)² - 144(0) + 2(0)² = 1944 ft-lb.
The work that was done lifting the sand this far is of 944 ft-lb.
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The summary of the payroll for the monthly pay period ending July 15 indicated the following:
Sales salaries $125,000
Federal income tax withheld 32,300
Office salaries 35,000
Medical insurance withheld 7,370
Social security tax withheld 10,200
Medicare tax withheld 2,550
Required:
Journalize the entries to record (a) the payroll and (b) the employer's payroll tax expense for the month. The state unemployment tax rate is 3.1%, and the federal unemployment tax rate is 0.8%. Only $25,000 of salaries are subject to unemployment taxes. Refer to the Chart of Accounts for exact wording of account titles.
The journal entries to record (a) the payroll and (b) the employer's payroll tax expense for the month are as follows:
Journal Entries:a) The payroll:
Debit Sales salaries $125,000
Debit Office salaries 35,000
Credit:
Federal income tax withholding payable 32,300
Medical insurance withholding payable 7,370
Social security tax withholding payable 10,200
Medicare tax withholding payable 2,550
Cash $107,580
To record the monthly payroll.b) The employer's payroll tax expense:
Debit Payroll Tax Expense $975
Credit:
Federal Unemployment Tax Payable $200
State Unemployment Tax Payable $775
To record the employer's payroll tax expense for the month.Data and Transaction Analysis:SUTA = 3.1% of $25,000 = $775
FUTA = 0.8% of $25,000 = $200
Sales salaries $125,000
Federal income tax withheld 32,300
Office salaries 35,000
Medical insurance withheld 7,370
Social security tax withheld 10,200
Medicare tax withheld 2,550
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A. A car can go 33 miles on one gallon of gas. Gas costs $4.20 per gallon. How far can the car go for $25.00?
Set up a calculation with units to answer this question.
Type a 1 in any number boxes you don't need. Choose "no unit" for any unit pulldowns you don't need.
Answer:
199 miles
Step-by-step explanation:
if you multiply 33 in 6 places it gives 198 then you plus 1 to get $25.00
GOOD RIGHT please rate
Solve the system of equations by the elimination method.
-x + 2y = 0
x + 2y = 7
Answer:
[tex]\left \{ {{-x+2=0} \atop {x+2y=7}} \right.[/tex]
-x + 2 = 0 --> -x = -2
x + 2y = 7 --> x + 2y = 7
________
2y = 7-2 = 5 --> y = 5/2
x = -2y + 7 --> x = -5 + 7 --> x = 2
---
Have a nice day!
An elevator in a tall building goes up 7 floors then down 9 floors down 4 floors up 8 floors and down 2 floors now it it in floor 14 on what floor did the elevator start
Answer: I'm pretty sure its 14.
Step-by-step explanation: 14 + 7 - 9 - 4 + 8 - 2 = 14
Write a compound inequality for the graph shown below.
Use x for your variable.
Answer:
-7 ≤ x ≤ -4
Step-by-step explanation:
You want a compound inequality that expresses the same relation as a number line graph with solid dots at -7 and -4, and shading between.
Meaning of the graphThe graph shown is indicating values of x lie between -7 and -4, including those values. As an inequality, this is written ...
-7 ≤ x ≤ -4
x is less than or equal to 1.
0x<1
01sx
Ox21
Ox≤ 1
Answer:
the correct answer is O. x ≤ 1
Step-by-step explanation:
the rest are wrong because of the equal to sign in inequalities
How many gallons did the tub start with?
Answer:
15g i think sorry if i am rong but i tryed
Step-by-step explanation:
A woman traveled 2437.2 miles in 18 hours 20 minutes. Find the average speed of her flight in miles per hour. (Change
18 hours 20 minutes into hours and use the formula d=rt.)
Answer:Average Speed = 126.6 mph
Step-by-step explanation:
Select the correct answer.
What is the SI unit of time?
A second
B minute
C hour
D day
An object is moving at a speed of 5 kilometers every 4.5 hours. Express this
speed in miles per minute. Round your answer to the nearest hundredth.
(1 km
0.621 mile)
Speed is 0.01 miles per minute.
we know speed is = distance/ time
since we need speed in miles per minute we need to convert km into miles.
and hours in minute.
distance= 5km
1km= 0.621371 miles
5km= 50.621371 miles = 3.10686 miles= 3.12 miles
1hour= 60 minutes
4.5 hour = 4.5×60 minutes=270 minutes
speed= distance in km/time in minutes=3.12 miles/270 minutes
speed = 0.012 miles per minute
speed is 0.01 miles per second.
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Tell whether each equation is true, false, or open. Explain.
2.) 5x+7 = 17
1.) 85+ (-10) = 95
3.) -8(-2) - 7 = 14 – 5
Answer:
1.) 85+ (-10) = 95 is false.
2.) 5x+7 = 17 is false.
3.) -8(-2) - 7 = 14 – 5 is false.
Step-by-step explanation:
1. is false because since 85 ≠ 95, then 85 + ( - 10) = 95 is false.
2. is false because since 12 ≠ 17, then 5x + 7 = 17 is false.
3. is false because since -15 ≠ 14, then -8( - 2) - 7 = 14–5 is false.
I really need help I need to turn this in tmr can someone pls help I beg y a lot pósese
[2^3x(152 divided by 8)]-52
Answer:
152x-52
Step-by-step explanation:
The value of the expression after division is A = 100
What is an 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.
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 data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
A = 2³ ( 152 / 8 ) - 52 be equation (1)
On dividing the equation by 8 in the expression , we get
On simplifying the equation , we get
A = 8 ( 19 ) - 52
On further simplification , we get
A = 152 - 52
A = 100
Therefore , the value of A is after the division is 100
Hence , the equation is A = 100
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solve the literal equation 3y-6x=-2 for y
Answer:
y = -⅔+2x
Step-by-step explanation:
Hope this helps!!
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The equation in slope-intercept form is given as,
y = mx + c
Where m is the slope and c is the y-intercept.
The equation for y is y = 2x - 2/3
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 4 is an equation.
2x = 4x is an equation
We have,
3y - 6x = -2
Add 6x on both sides.
3y = -2 + 6x
3y = 6x - 2
Divide both sides by 3.
y = (6x - 2)/3
y = 2x - 2/3
This is in the form of an equation in slope-intercept form.
The equation in slope-intercept form is given as,
y = mx + c
Where m is the slope and c is the y-intercept.
Thus,
The equation for y is y = 2x - 2/3
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not tile A 10 x 12 plane
Answer:120
Step-by-step explanation:
so if its a 10x12 plane that would be 10 12 times so 10+10+10+10+10+10+10+10+10+10+10+10
or 12+12+12+12+12+12+12+12+12+12
What are the solutions to the system of equations?
{y=2x2−5x−7y=2x+2
The solutions to the system of equations are (x₁, y₁) = (9 / 2, 11) and (x₂, y₂) = (- 1, 0).
How to resolve a system of equation by algebra methods
Herein we find a system formed by one linear equation and one nonlinear equation (quadratic equation). First, we equalize the two equations to eliminate the variable y:
2 · x² - 5 · x - 7 = 2 · x + 2
2 · x² - 7 · x - 9 = 0
2 · [x² - (7 / 2) · x - 9 / 2] = 0
2 · (x - 9 / 2) · (x + 1)
There are two solutions to x: x₁ = 9 / 2, x₂ = - 1. And the solutions for y are:
x₁ = 9 / 2y₁ = 2 · (9 / 2) + 2
y₁ = 11
x₂ = - 1y₂ = 2 · (- 1) + 2
y₂ = 0
Then, the solutions to the system of equations are (x₁, y₁) = (9 / 2, 11) and (x₂, y₂) = (- 1, 0).
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Sue wrote a double fact. It has a sum less than 10 and greater than 4. The addends are each less than 5. What fact might she have written?
When Sue wrote a double fact. It has a sum less than 10 and greater than 4. The addends are each less than 5, the numbers that she wrote include 4+4 and 3+3.
How to illustrate the information?It is given that the sum is greater than 4 and smaller than 10.
If the sum is less than 10 and greater than 4 that limits you to 5,6,7,8,9
It should be noted that 5+5 is 10, and the sum has to be lower then 10.
The addends are less than 5 so it could be 4+4, 4+3, 4+2, 4+1
This shows that Sue might have written 5,6,7, or 8.
Therefore, the numbers are 3+3 and 4+4.
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write ____ as a single power of 5
Answer:
[tex]5^{14/5}[/tex]
Step-by-step explanation:
[tex]\frac{5^3}{5^{1/5}} \\ \\ 5^{3-\frac{1}{5}} \\ \\ =5^{14/5}[/tex]
In a game experience, the level of monsters, L, is measured by the formula L= 250M E, where M=number of monsters and E=experience of monsters. Solve the formula for E
The formula for E is given as E = L/250M
According to the question we have been given that the level of monsters is measured by as follows
L = 250M E (1)
where , M = number of monsters
E = experience of monsters.
Now we need to find the formula for E. For that we will solve equation (1) for E .
L = 250M E
Dividing both the sides by 250M we get
L/250M = E
or, E = L/250M
Thus above is the equation or the formula for E.
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ill give brainly and 10 points
|3.7−(−1.5)|
The initially reported temperature was 3.7 however the temperature changed to -1.5.
Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. y=45(0.974)^x
Given function y =45(0.974)ˣ is a function of exponential decay and percentage rate of decrease is 2.6%.
What is an exponential function?The exponential function is an function f(x) = a(b)ˣ
a = initial amount when x= 0
b= base that is multiplied and it is greater than 0
And x is the variable in the exponent
When b> 1 , the values of this function goes up and up and then this function shows exponential growth.
When 0< b< 1, the values of this function becomes smaller as x increases then this function shows exponential decay.
And r is the percentage rate of change where b =r +1
Given function is y = f(x) = 45(0.974)ˣ
When we compare it with standard function f(x) = a(b)ˣ
we get a = 45 and b =0.974
As b is between 0 and 1 in this case, therefore this function is exponential decay.
b =r+ 1
therefore r = b-1 = 0.974-1 = -0.026
converting 0.026 to percentage we get -0.026*100= -2.6% ( negative sign shows decrease)
Therefore, we can say that the given function represents exponential decay function and rate of decrease is 2.6%
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A ball is thrown with an initial height of 4 feet with an initial velocity of 36 ft/s.
The values of t for which the ball's height is 16 feet are 1.84s and 0.41s
From the question, we are to determine all values of t for which the ball's height is 16 feet
From the given information,
The equation that represents the ball's height (in feet) after t second is
h = 4 + 36t - 16t²
To determine all values of t for which the balls height is 16 feet, we will put h = 16 in the equation
That is,
h = 4 + 36t - 16t² becomes
16 = 4 + 36t - 16t²
Rearranging
16t² - 36t + 16 - 4 = 0
16t² - 36t + 12 = 0
Divide through by 4
4t² - 9t + 3 = 0
Solve the quadratic equation using the general formula
t = [-b±√(b²-4ac)]/2a
a = 4, b = -9, c = 3
t = [-(-9)±√((-9)²- 4(4)(3))]/2(4)
t = [9±√(81- 48)]/8
t = [9±√(33)]/8
t = [9±5.74]/8
t = [9+5.74]/8 or [9-5.74]/8
t = 14.74/8 or 3.26/8
t = 1.84 or 0.41
Hence, the values of t for which the ball's height is 16 feet are 1.84s and 0.41s
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-2x^2+4x=5
using the Quadratic formula, the equation needs to be in standard form first. Then label a, b and c and plug it into the quadratic formula and simplify using the order of operations. I
The solution by using the quadratic formula is,
x = 4 + 2√6 i / 4 and x = 4 - 2√6 i / 4
What is Quadratic formula?
To solve a quadratic equation ax²+ bx + c = 0 , we use the quadratic formula,
x = - b ± √b² - 4ac / 2a
The given expression is;
- 2x² + 4x = 5
Now, The given equation is solve by using Quadratic formula as;
- 2x² + 4x = 5
Move terms to the left side
- 2x² + 4x - 5 = 0
- ( 2x² - 4x + 5 ) = 0
2x² - 4x + 5 = 0
Compare with quadratic equation ax²+ bx + c = 0 we get;
a = 2, b = -4, c = 5
Since, Quadratic formula is,
x = - b ± √b² - 4ac / 2a
Hence, Substituting all the values of a, b and c in quadratic formula we get;
x = - (-4) ± √(-4)² - 4*2*5 / 2*2
x = 4 ± √16 - 40 / 4
x = 4 ± √-24 / 4
x = 4 ± 2√-6 / 4 ( Since, i = √-1 )
x = 4 + 2√6 i / 4 and x = 4 - 2√6 i / 4
So, The solution by using the quadratic formula is,
x = 4 + 2√6 i / 4 and x = 4 - 2√6 i / 4
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hello can someone please explain?
Find the value of x and y.
Answer:
x = 36
y = 15
Step-by-step explanation:
127 - 52 = 75
75 / 5 = 15
2x + 3 = 5(15)
2x + 3 = 75
2x = 72
x = 36
Solve showing all work and simplify completely:
7/15 + 1/3
Answer: 4/5
Step-by-step explanation:
7/15 + 1/3
(7/15 x 1/1) (1/3 x 5/5) = ?
7/15 + 5/15 = ?
7+5/15 = 12/15
12/15 both sides divided by 3 = 4/5
therefore
7/15 + 1/3 = 4/5
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{\dfrac{7}{15} + \dfrac{1}{3}}[/tex]
[tex]\mathsf{= \dfrac{7}{15} + \dfrac{1\times5}{3\times5}}[/tex]
[tex]\mathsf{= \dfrac{7}{15} + \dfrac{5}{15}}[/tex]
[tex]\mathsf{= \dfrac{7 + 5}{15 - 0}}[/tex]
[tex]\mathsf{= \dfrac{12}{15}}[/tex]
[tex]\mathsf{= \dfrac{12\div3}{15\div 3}}[/tex]
[tex]\mathsf{= \dfrac{4}{5}}[/tex]
[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{\dfrac{4}{5}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]