He typically work each day for 10 hours.
According to the question, the expression can be written as:
The time taken to stretch the fingers = (1/2)t
Similarly, the time taken to smashed toes = (1/5)t
Total time = 7 hours
Now, the final expression can be written as:
(1/2)t + (1/5)t = (7)
(7/10)t = 7
t = 10 hours
Hence, he typically work each day for 10 hours.
What is time and work?
The time and work represents the problems deals with the time either with the individual or the group of the people to complete the piece of work. And the efficiency taken by each individual.
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Solve each system by elimination.
2r + s = 3 , 4r - s = 9
By elimination, the solution of the system of equations, 2r + s = 3 and 4r - s = 9, is (r , s) = (2 , -1).
A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.
There are three methods that can be used to solve system of equations.
1. Elimination
2. Substitution
3. Graphing
Using the elimination method, given two equations in r and s, a variable should be eliminated by adding/subtracting the two equations.
Adding the two equations will eliminate the variable s.
2r + s = 3 (equation 1)
4r - s = 9 (equation 2)
6r = 12
r = 2
Substitute the value of r to any of the two equations and solve for s.
2r + s = 3 (equation 1)
2(2) + s = 3
s = 3 - 4
s = -1
Hence, the solution of the system of equations is (r , s) = (2 , -1).
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The phones continue to be made with the
correct working part, so the percentage
continues to increase.
What percent is reached if (round answers to the nearest tent
The next 50 phones are working?
%
The next 100 phones are working?
The next 500 phones are working?
DONE
%
%
Answer:
The next 50 phones are working? ---> 88.3%
The next 100 phones are working? ---> 93.6%
The next 500 phones are working? ---> 98.6%
Step-by-step explanation:
I hope this helps
b. If y² varies directly with x², does that mean y must vary directly with x ? Explain.
No, If y² varies directly with x², it does not that mean y must vary directly with x
Let's say y² = 16 and x² = 4
Now if y² = 16
Then y = 4 or -4 and same for x = 2 or -2
As the square root can be either negative or positive, if y² varies directly with x², it does not that mean y must vary directly with x .
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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If the area of the triangle is 12, what is the value of x?
Answer:
X = 3 and -7
Step-by-step explanation:
area of a triangle is = ½ ×base × height
Margo earns
$13.50 per hour as
earn approximately $300 per week? lifeguard. How many hours per week must she work if she
wants to
Earn approximately $300 per week
Margo works 23 hour per week to earn approximately $300 per week .
The unitary technique could be a technique within which you discover the worth of a unit so the worth of a needed range of units.For simplification, continually write the items to be calculated on the right-hand facet and things best-known on the left-hand facet.It is given that Margo earns $13.50 per hour .
Using unitary method , we get
To get his weekly financial gain, we have a tendency to multiply his hourly wage by the quantity of hours he worked.
Pay = hourly rate × variety of hours worked
300 = 13.50 × number of hours worked
number of hours worked = 300 /13.50
= 22.22
On rounding off , we get the hour = 23 hours
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Find the next two terms in each sequence. Write a formula for the n th term. Identify each formula as explicit or recursive. 21,13,5,-3, ......
The formula for nth term of the given sequence is [tex]T_{n+1} = T_{n} - 8[/tex].
According to the given question.
We have a sequence, 21,13,5,-3, .......
Since, the first term of the given sequence is 21.
The second term of the given sequence is 13.
Here we can see that, each term is less than 8 to the previous term. It means the common ratio of the given sequece is -8 and it is an arithmetic sequence.
Therefore, the formula for nth term of the given sequence is given by
[tex]T_{n+1} = T_{n} - 8[/tex]
Where, n is the number of term.
Hence, the formula for nth term of the given sequence is [tex]T_{n+1} = T_{n} - 8[/tex].
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Find the vertex, focus, and the directrix of each parabola. x= 1/16 y²
The vertex, focus and directrix of the parabola y = x²/4 are:
v = (0,0)f = (4, 0)d = y = -4What is a parabola?The parabola is a geometric shape that is formed from the intersection of a vertical plane in a cone.
The parabola is a quadratic function, it is composed of a vertex, or inflection point, a focus and a directrix.
In this case we have an expression given by:
x = y²/16
We must find the canonical equation:
(y - 0)² = 16 (x - 0)
has the form
(y - k)² = 4p(x - h)
This means that the vertex of this parabola is
v = (h, k)
v = (0,0)
To know the focus we must know the value of "p".
4p = 16p = 4f = (0 + 4, 0)
f = (4, 0)
Directrixd = y = 0 - 4
d = y = -4
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The ratio of dogs to cats in the shelter is 10 to 8. If there are 20 cats, how many dogs are in the shelter?
A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.The ratio of dogs to in the shelter is 10 to 8. If there are 20 cats, then 25 dogs are in the shelter.
What is ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
The ratio of dogs to cats in the shelter is 10 to 8. i.e 10/8
If there are 20 cats then we need to find number of dogs.
Let the number of dogs be x when there are 20 cats.
10/8=x/20
Apply cross Multiplication.
200=8x
Divide both sides by 8.
x=25.
Therefore there are 25 dogs in the shelter if the number of cats are 20.
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Evaluate each logarithm.
log₅ 5√5
Answer:
well done...I hope it's helpful
Rewrite the following polynomial in standard form.
x+9-7x³ x4
Answer:
-7x³+ 4x²+x+9
Step-by-step explanation:
Line k contains points at (4,1) and (-5,-5). Find the distance between line k and point F(-4,0).
F. 3.3 units
G. 3.6 units
H. 4.0 units
J. 4.2 units
The distance between line k and point F(-4,0) is 3.6 units
The correct answer is an option (G) 3.6 units
We know that for a line l: ax + by + c = 0 and a point P(x1, y1), the distance between the line line 'l' and a point P is:
[tex]d=\frac{|ax_1+by_1+c|}{\sqrt{a^{2} +b^{2} } }[/tex]
In this question we have been given a line k contains points at (4,1) and (-5,-5).
Also, we have been given a point F(-4, 0)
We need to find the distance between line k and point F(-4,0).
First we find the equation of line k.
[tex]\frac{y-1}{-5-1} =\frac{x-4}{-5-4} \\\\\frac{y-1}{-6} =\frac{x-4}{-9} \\\\-9y+9=-6x+24\\\\6x-9y+9-24=0\\\\6x-9y-15=0[/tex]
So, the equation of line k is 6x - 9y - 15 = 0
Now we find the distance between line k and point F(-4, 0).
Using above formula the distance between line k and point F(-4,0) would be,
[tex]d=\frac{|6(-4) - 9(0) - 15|}{\sqrt{6^{2} +(-9)^{2} } } \\\\d=\frac{|-24-0-15|}{\sqrt{36+81} }\\\\ d=\frac{|-39|}{\sqrt{117} } \\\\d=\frac{39}{10.82}\\\\ d=3.6[/tex]
Therefore, the distance between line k and point F(-4,0) is 3.6 units
The correct answer is an option (G) 3.6 units
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3. Name a line that contains point e.
4. Name all points contained on line n.
5. What are two other names for line p?
6. Name the plane containing lines n and p.
7. Name a line that point B is on in six different ways.
8. How many lines does plane G contain? Name the lines.
B
9. Draw and label a figure with a plane, a line, and a line segment.
Answer:
3. Line q
4. Point B and Point A
5. Line DC or Line CD
6. Plane G
7. Line n, Line q, Line AB, Line BA, Line BE, Line EB
8. Line N, and Line Q
Step-by-step explanation:
What is the inverse of f(x) = (x+4)^3
Answer:
C
Step-by-step explanation:
[tex]Answer:\ f^{-1}(x)=\sqrt[3]{x} -4[/tex]
Step-by-step explanation:
[tex]f(x)=(x+4)^3[/tex]
Extract the cube root from both parts of the equations:
[tex]\sqrt[3]{f(x)} =x+4\\\sqrt[3]{f(x)}-4=x+4-4\\ \sqrt[3]{f(x)} -4=x[/tex]
Redefine the variables:
[tex]f^{-1}(x)=\sqrt[3]{x} -4[/tex]
Jose and Nancy take care of animals when their owners are away. Jose charges $15 plus $2 per animal and Nancy charges $5 plus $3 per animal. For how many animals do they charge the same amount?
For 10 animals do Jose and Nancy charge the same amount.
What is defined by the linear equation?A linear equation would be an algebraic equation with only a constant and the first-order (linear) term of the form y = mx+b, in which m is the slope and b is the y-intercept. The above is sometimes referred to as a "linear equation of 2 variables," where x and y are the variables.For, the given question;
Let there be 'x' number of animals.
Jose charges $15 plus $2 per animal.
15 + 2x
And, Nancy charges $5 plus $3 per animal.
5 + 3x
Then,
For the same amount, equate both equations.
15 + 2x = 5 + 3x
On solving;
x = 10
Thus, for 10 animals, their total charge will be equal.
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Suppose y varies directly with x , and y=15 when x=10 . What is y when x=22 ?
So, from the question statement, we can conclude that the y and x axes are directly proportional. In order to show it in the equation form, we can write,
Y=kx (directly proportional)
y=k x
The values that are given in the question are
y = 15
and,
x = 10
Now we will put these individual values in the above relation equation of x and y,
y=k x
15=10k
k=15/10
k=1.5
So, we found the unknown factor by putting the values of the available terms. Now in order to find the new value of y, when the new values of x are given and is,
x=22
We will simply modify the relation equation,
y=k x
By putting the known terms in the above equation,
x=22, k=1.5
y=1.5 * 22
y = 33.
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Determine whether each list is a sequence or a series and finite or infinite. -0.5-0.25-0.125- . . . . . .
The numbers that are given:
-0.5-0.25-0.125- . . . . . .
They are part of an infinite series
What is a series?A series is the summation of a set of numbers or sequences.
What are sequences?A sequence is an order of elements that are governed by a pattern, that is, it has variations between each element that remain constant and allow us to determine values before or after the known elements.
A sequence maintains an order, and this numerical order can be finite or infinite, in the given case we have the following list:
-0.5-0.25-0.125- . . . . . .
If we analyze the variation between each term we have the form:
(-1/2ⁿ)
-1/2¹ = -0.5-1/2² = -0.25-1/2² = -0.125(-1/2ⁿ)
In this series we have the initial value of the same, but we do not know the final value, although we know its behavior, we can say that this series has no end, it is an infinite serie.
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For what amounts of sales do you earn more in the first year with Job Offer A? with Job Offer B?
Job Offer A
Base salary
Commission
$46,975
4.5% of sales
Job Offer B
Base salary
Commission
Sign-on bonus
$42,550
6.5% of sales
$2500
Using linear functions, it is found that until $77,000 in sales, Job B pays more, and for more than than, Job A pays more.
What is a linear function in slope-intercept form?A linear function is modeled according to the following rule:
y = mx + b
In which:
m is the slope of the function, called the rate of change of the function, and is given by the change in y divided by the change in x.b is the y-intercept of the function, which is given by the the value of y when the function crosses the x-axis(x = 0).For this problem, the earnings are modeled by linear functions, in which:
The slope is given by the commission percentage.The intercept is given by the sum of the base salaries and the sign-on bonus.Hence the earnings for sales of x are given as follows:
A(x) = 46975 + 0.045x.B(x) = (42550 + 2500) + 0.065x = 45050 + 0.065x.Due to the higher intercept, until they are equal, A(x) is greater, and after that B(x) is greater, hence we have to find when they are equal as follows:
A(x) = B(x)
45050 + 0.065x = 46975 + 0.045x
0.025x = 1925ntil $77,000 in sales, Job B pays more, and for more than than, Job A pays more.
x = 1925/0.025
x = 77000.
Hence:
Until $77,000 in sales, Job B pays more, and for more than than, Job A pays more.
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Adam has RM500. He keeps 30% of his money in the bank. Calculate the balance of the money he has with him.
Answer:
RM350
Step-by-step explanation:
calculate 30% of RM500
= [tex]\frac{30}{100}[/tex] × 500 = 0.3 × 500 = 150
RM150 is left in the bank
and 500 - 150 = RM350 is the money he has with him
What's the next fraction in the sequence?
1/3, 7/15, 3/5, 11/15
Answer:
13/15
Step-by-step explanation:
If we give all of these fractions a common denominator, this problem will be much easier. We see that a common denominator can be 15.
We can take 1/3 and multiply both the numerator and denominator by 5, getting 5/15. 7/15 already has a denominator of 15. Now if we multiply the numerator and denominator by 3, we get 9/15. Then we have 11/15.
Now the pattern is 5/15, 7/15, 9/15, 11/15. The numerator increases by 2 each time, so the next fraction should be 13/15.
Quadrilateral RSTU is circumscribed about ®j . If the perimeter is 18 units, find x .
The value of x is 1.5 units
Given that a quadrilateral RSTU is circumscribed about [tex]\odot J[/tex].
Also given that the perimeter of the quadrilateral is 18 units.
Then the the sides ST, TU, UV and RS are tangents to the circle at points A, B, C and D respectively.
Then we have,
AT = BT
BU = UC
RC = RD
SD = SA
Given that AT = UC = x and RC = RD = SD = SA = 3 units
Therefore, BT = BU = x
We need to find 'x'.
Perimeter = 18 units
i.e., ST + TU + UV + RS = 18 units
⇒ AT + BT + BU + UC + RC + RD + SD + SA = 18 units
⇒ x + x + x + x + 3 + 3 + 3 + 3 = 18
⇒ 4x + 12 = 18
⇒4x = 6
⇒ x = 6/4 = 3/2
⇒ x = 1.5 units
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What is the equation of each line in slope-intercept form?
b. the line perpendicular to y = (2/3)x - 1 through (0,6)
The slope-intercept form is y = 3/2x - 6 for line perpendicular to y = (2/3)x - 1 through (0,6)
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
In an equation, perpendicular lines have the opposite reciprocal slope. In other words, if a line's slope is a positive fraction, its reciprocal slope is negative.
Here given that y = (2/3)x - 1
Here 2/3 is the slope and 1 is the y-intercept
To find a perpendicular line to the following equation, use the opposite reciprocal slope and point, then solve using the point-slope formula.
y - y₁ = m(x - x₁)
We have, m = 3/2, x₁ = 0 and y₁ = 6
y - 6 = 3/2(x - 0)
y - 6 = 3/2x - 0
y = 3/2x - 6
We have the slope-intercept form y = 3/2x - 6 of a line perpendicular to y = (2/3)x - 1 through (0,6)
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r
(b)
Page 7
Children go to a Rodeo camp during the Easter holiday. Ms Rekha buys bananas and oranges
for the children at the camp.
(i)
Bananas cost $3.85 per kilogram. Ms Rekha buys 25 kg of bananas and receives a
discount of 12%. How much money does she spend on bananas?
Answer:
84.7
Step-by-step explanation:
first you multiply 3.85 x 25 =96.25 then you need to determin the percent of 12 which is 11.55 the lasly you subtract 96.25-11.55=84.7 btw 84.7 for bannas is a scam for real
PLEASE HELP ME NOW ASAP RIGHT ANSWERS ONLY
Slope from graph
What is the slope of the line?
Answer: Slope: 3/2
Step-by-step explanation:
Coordinates: (1, -3), (3, 0)
Slope formula: m=(y2-y1)/(x2-x1)
m=(0-(-3))/(3-1)
m=(0+3)/2
m=3/2 ==> Slope: 3/2
Fireworks are shot from a barge in a river There is an explosion circle inside which all n the fireworks will explode. Spectators sit outside â safety circle 800 feet from the center of the fireworks display.
b. If the safety circle is 200 to 300 feet farther from the center than the explosion circle, find the range of values for the radius of the explosion circle.
The range of values for the radius of the explosion circle is found to be 500-600 ft.
What exactly is a circle?A circle is a shape founded by all locus in a plane at a fixed distance from its centre.
It is the path traced by a moving point in a plane to ensure that its distance from a specified place remains constant.The radius of a circle is the distance between two locations on the circle and the center.The radius must usually be a positive number.A circle to r = 0 is a degenerate case.Now, according to the stated question;
Evaluate the circumference by the formula;
Formula: 2πr
Radius = 800 feet
Substitute the value in the formula;
C = 2πr
C = 2π800
C = 5026.54825 feet
Therefore, radius of the explosion circle will range from 500 to 600 feet.
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solve by elimination
steps plssss
Answer:
(x, y, z) = (1, 1, 0)
Step-by-step explanation:
You want to solve the given system of equations by elimination.
SolutionThere are a couple of nice choices for variables to eliminate.
The last equation has an x-coefficient that is the opposite of the x-coefficient in the other two equations. Adding that equation to those will eliminate the x-variable:
(-2x +2y +3z) +(2x +3y +3z) = (0) +(5) ⇒ 5y +6z = 5 . . . . add eqns 1, 3
(-2x -y +z) +(2x +3y +3z) = (-3) +(5) ⇒ 2y +4z = 2 . . . . add eqns 2, 3
The second of these equations can be divided by 2 to give ...
y +2z = 1
Three times this equation can be subtracted from the first of the reduced equations to eliminate z:
(5y +6z) -3(y +2z) = (5) -3(1) ⇒ 2y = 2
y = 1 . . . . divide by 2
SubstitutionNow, we can substitute this value into the previous equation to find the other variables.
y +2z = 1 = 1 +2z ⇒ 0 = 2z ⇒ z = 0
-2x -y +z = -3 = -2x -(1) +(0) ⇒ -2 = -2x ⇒ x = 1
The solution is (x, y, z) = (1, 1, 0).
__
Additional comment
The attachment shows a calculator solution to the system of equations by reducing the augmented matrix to "reduced row-echelon form." In general, that is a process of elimination. Each equation ends up with one variable having a coefficient of 1, so we have x = 1, y = 1, z = 0.
You could also start by eliminating the y-variables. Adding twice the second equation to the first will do that, as will adding 3 times the second equation to the third. The result of these operations is two equations in x and z.
Determine the volume
Answer:
2000.18
Step-by-step explanation:
Volume=V=(3.14)r^2h=3.14·7^2·13=2000.18.
Hope this helps.
solve for x
3/2 x−4= 1/2 x−3
please help this is so confusing
Answer:
x=1
Step-by-step explanation:
Ok, this is a two step equation, so the first step you will do is get the regular numbers (-4 and -3) on one side of the equation, like this:
3/2x-4=1/2x-3
+4 +4
3/2x=1/2x+1
Next, you need to get the variables on one side of the equation, so you will minus 1/2x like this.
3/2x=1/2x+1
-1/2x -1/2x
2/2x=1
Simplify
x=1
Answer:
x = 1
Step-by-step explanation:
[tex]\frac{3}{2} x-4 = \frac{1}{2} x-3[/tex]
[tex]x - 4 = -3[/tex]
x = 1
100 POINTS I will report all bad answers. I have over 2.5k points so I can easily repost if I have too. ONLY LEGIT ANSWERS. --
Given the linear functions f(x) = x − 3 and g(x) = −2x + 4, determine (f ⋅ g)(x).
(f ⋅ g)(x) = −2x − 12
(f ⋅ g)(x) = −2x^2 − 12
(f ⋅ g)(x) = −2x^2 − 2x − 12
(f ⋅ g)(x) = −2x^2 + 10x − 12
The product of the two linear functions f(x) = x − 3 and g(x) = −2x + 4 is -2x² + 10x - 12
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the linear functions f(x) = x − 3 and g(x) = −2x + 4, hence:
(f.g)(x) is the product of the two functions:
(f . g)(x) = (x - 3)(-2x + 4)
(f . g)(x) = -2x² + 6x + 4x - 12 = -2x² + 10x - 12
The product of the two linear functions f(x) = x − 3 and g(x) = −2x + 4 is -2x² + 10x - 12
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WORTH 20 POINTS THX FOR HELP
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The formula for a three-dimensional
midpoint is
dimension, north as the y-dimension, and above as the z-dimension.
+3+3+1+2). Use this formula to solve the following problem, using west as the x-
Two airplanes are circling a small airport. Airplane 1 has a position 2000 feet West, 600 feet North, and 3000 feet above the air traffic control tower.
Airplane 2 has a position 1000 feet East, 1400 feet North, and 2200 feet above the air traffic control tower. Relative to the tower, what is the location of the
point directly between the two airplanes?
Enter the correct coordinates in the boxes.
Assume the air traffic control tower to be at the three-dimensional coordinate (0, 0, 0).
5 of 5
The location of the point directly between the two airplanes is (1,500 1,000, 2,600), relative to the tower.
Showing hint 1 of 2
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9:37
Using the midpoint concept, the location of the point directly between the two airplanes is (-500, 1000, 2600).
What is the midpoint concept?The midpoint between two points is the halfway point between them, and is found using the mean of the coordinates.
For this problem, the coordinates are given as follows:
Airplane 1: (-2000, 600, 3000).Airplane 2: (1000, 1400, 2200).Hence the coordinates of the midpoint are given as follows:
x: (-2000 + 1000)/2 = -500.y: (600 + 1400)/2 = 1000.z: (3000 + 2200)/2 = 2600.The location is (-500, 1000, 2600).
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