For less than 6 hours, Hank's Movers charge less.
For what lengths of time does it cost less to hire Hank's Movers?Acme movers charge $210 plus $20 per hour, so if they work for x hours they charge:
A(x) = $210 + $20*x
Hank's movers only charge $55 per hour, so here the linear equation is:
H(x) = $55*x
They charge the same amount when:
A(x) = H(x)
$210 + $20*x = $55*x
Now we can solve that to get:
$210 + $20*x = $55*x
$210 = $55*x - $20*x = $35*x
$210/$35 = x = 6
So, for 6 hours, both companies charge the same amount.
For less than 6 hours, Hank's Movers charge less.
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Combine like terms to create an equivalent expression.
Enter any coefficients as simplified proper or improper fractions or integers.
6
W
1
34
Answer:
3w - 4 1/2
Step-by-step explanation:
6(1/2w- 3/4)
distributing gives you
6/2w- 18/4
simplifying it gives you
3w-4 1/2
How you do this someone please help????
Answer:
a. Explicit: f(x) = 2x² +3. Recursive: f(-3) = 21; f(x) = f(x -1) +4x -2
b. Explicit: g(x) = 3x² -2x. Recursive: g(5) = 65; g(x) = g(x -1) +6x -5
Step-by-step explanation:
Given two tables of values, you want to find the explicit and recursive formulas for those values.
General approachWhen the x-values are consecutive integers, as they are in these tables, it is usually useful to look at the first difference of the y-values. If those are constant, the table represents a linear function.
When the first differences are not constant, the exercise can be repeated. If the second differences are constant (as here), then the explicit formula will be a second-degree polynomial. The coefficients of the polynomial can be found different ways. We will describe one way here.
2nd degree explicit formulaThe constant second differences are double the leading coefficient of the quadratic that describes the relation between x and y. Knowing this, we can see how well the 2nd degree term by itself represents the relation. To that end, we have added to the table columns for the difference between the y-value and the 2nd degree term (y1 -ax^2), and the difference of those differences (diff).
Explicit formula, Table AThe attachment shows the first second difference of the values of Table A is 4. That means our first approximation of the sequence will be (4/2)x². The next column shows us this is always 3 less than the value of y, so our explicit formula can be ...
f(x) = 2x² +3
Explicit formula, Table BThe attachment shows the first second difference of the values of Table B is 6. That means our first approximation of the sequence will be (6/2)x². Subtracting this from the value of y, we find an arithmetic sequence that has a common difference of -2, and a value of -10 when x=5.
The explicit formula for an arithmetic sequence with a first term a1 and a common difference d is ...
an = a1 +d(n -1) . . . . . . where 1 is the x-value of the first term
Our sequence of differences doesn't start with x=1, but with x=5. This means our explicit formula will be ...
g(x) = 3x² +(-10 +(-2)(x -5))
g(x) = 3x² -2x
2nd degree recursive formulaA recursive formula is one that expresses a given term as a function of previous terms of the sequence. When the sequence is 2nd degree, as here, we know the difference from one term to the next is an arithmetic sequence. Thus we can write the formula for a term as the sum of the previous term and a value that depends on the term number.
The explicit formula for the arithmetic sequence of differences has the form shown above. For the purpose here, the difference from the previous term is shown on the line above the x-value.
Recursive formula, Table AThe applicable sequence of first differences has first term -10 and common difference 4. The first of the differences of consequence corresponds to x=-2, so can be written ...
d(x) = -10 +4(x -(-2)) = 4x -2
Then the recursion relation is
f(x) = f(x -1) +d(x) = f(x -1) +4x -2
And the recursive formula is ...
f(-3) = 21; f(x) = f(x -1) +4x -2
Recursive formula, Table BThe applicable sequence of first differences has first term 31 and common difference 6. The first of the differences of consequence corresponds to x=6, so can be written ...
d(x) = 31 +6(x -6) = 6x -5
Then the recursive formula is ...
g(5) = 65; g(x) = g(x -1) +6x -5
convert gallons to cups
Answer:
There are 16 cups in a gallon.
Step-by-step explanation:
Not sure what you're asking but there are 16 cups in a gallon.
Find the greatest common factor of 60y^8, 40y^4, 20y^5 and 80y^5.
Answer:
20
Step-by-step explanation:
The common factors for 60,40,20,80 60 , 40 , 20 , 80 are 1,2,4,5,10,20 1 , 2 , 4 , 5 , 10 , 20 . The GCF for the numerical part is 20 .
x/6 - 7 = -4 helpppppppp
Answer:
x = 18
Step-by-step explanation:
x/6 - 7 = -4
x/6 = -4 + 7
x/6 = 3
x = 6*3
x = 18
Check:
18/6 - 7 = -4
3 - 7 = -4
Grady's father is building a 15-meter fence with the start of the fence at coordinates(8,5) and the midpoint of the fence at coordinates (3.5,-1) . What are the coordinates of the other end of the fence?
Using proportions, it is found that the coordinates of the other end of the fence are (-1,-7) when the start point is (8, 5) and the mid point is (3.5, -1).
A proportion refers to the fraction of the total amount, and the measures are related using a rule of three.
The midpoint of a segment refer to the mean of the coordinates of the endpoints, so we get that:
3.5 = (x + 8) / 2
x + 8 = 7
x = 7 - 8
x = - 1
-1 = (y + 5) / 2
y + 5 = -2
y = -2 - 5
y = - 7.
End point =- (-1, -7)
Therefore, using proportions, it is found that the coordinates of the other end of the fence are (-1,-7) when the start point is (8, 5) and the mid point is (3.5, -1).
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what is the solution to |2x-8|<6 ?
Answer:
1 < x < 7
Step-by-step explanation:
Hello!
There are two cases for this equation:
2x - 8 < 62x - 8 > -6Solve for x in each case.
Solve for x2x - 8 < 6The solution set is 1 < x < 7.
How does a flow proof show logical steps in the proof of a conditional statement?
The way a flow proof shows logical steps in the proof of a conditional statement is; A flow proof organizes statements in logical order, starting with the given statements. Each statement has its reason written below it and arrows are used to indicate the order of the statements.
What is a Flow Proof?
A flow proof uses a diagram to show each statement leading to the conclusion. Arrows are drawn to represent the sequence of the proof. The layout of the diagram is not important, but the arrows should clearly show how one statement leads to the next. The explanation for each statement is written below the statement.
A flow proof organizes statements in logical order, starting with the given statements. Each statement has its reason written below it and arrows are used to indicate the order of the statements.
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The triangles are similar. Find the missing side, angle or value of the variable.
∠B
a = 7 cm
b = 59°
59°
30°
91°
7 cm
Using the fact that both triangles are similar, we will conclude that the measure of angle B is 59°.
How to find the measure of angle B?
First, two figures are similar if the figures have the same shape, then the interior angles are all the same in both figures.
Here we know that the two triangles are similar and thus, the internal correspondent angles of the two triangles are equal in measure.
First, there is a common vertex at C, so the angle there is the same for both triangles. We also can see that angles A and D have the same measure, then the angles B and b will also have the same measure.
And we know that the measure of angle b is 59°, then we can conclude that the measure of angle B will also be 59°, so the correct option is the first one.
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1. Find the perimeter of the rectangle.
4in w 7in L
O11 in.
O22 in.
O28 in.
O56 in.
Answer:
(b) 22 in
Step-by-step explanation:
You want the perimeter of a rectangle with side lengths 4 inches and 7 inches.
PerimeterThe perimeter of a rectangle is the sum of the lengths of its sides. Your rectangle has two sides that are 4 inches, and two sides that are 7 inches. The perimeter is the sum of these lengths:
P = 4 in + 4 in + 7 in + 7 in
P = 22 in
The perimeter of the rectangle is 22 inches.
__
Additional comment
We can save a math operation by recognizing the sum can be arranged to ...
P = (4 in +7 in) +(4 in +7 in) = 2(4 in +7 in)
This is evaluated using one sum and one product, rather than the three sums we need if we simply add the lengths of the four sides.
This is why the usual formula for the perimeter of a rectangle is ...
P = 2(L +W)
Determine whether the statement is True or False.
Answer:
1. True
2. True
3. True
4. False
5. False
6. False
7. True
8. False
9. True
10. False
Step-by-step explanation:
∈ means "is an element of"
⊂ means "only contains some, but not all, the elements of"
⊆ means "only contains some, possibly all, the elements of"
If one of those symbols is strickenthrough, it simply means the opposite, e.g. "it's not true that it's an element of" or "it's not true that it only contains some, (...) the elements of"
∅ is an empty set
{ something } is a set containing everything inside the curly brackets. Thus, { } is an empty set.
Let's rewrite the statements:
1. 5 is an element of {1, 3, 5, 7, 9}
TRUE
2. 4 is not an element of {1, 3, 9}
TRUE
3. {5, 6, 7} only contains some, possibly all, the elements of {5, 6, 7}
TRUE
4. {1, 2, 3} only contains some, but not all, the elements of {1, 2, 3}
FALSE (it contains all)
5. it's not true that {9} only contains some, possibly all, the elements of {9, 10}
FALSE (it does only contain elements of {9, 10} )
6. it's not true that 8 is an element of {2,4,6,8,10}
FALSE (because it is an element of that set)
7. empty set only contains some, possibly all, the elements of empty set
TRUE (it contains only elements of empty set - all of them, namely none)
8. 0 is an element of empty set
FALSE (empty set is empty, so it cannot contain 0)
9. {13, 11} only contains some, but not all, the elements of {11, 12, 13}
TRUE (order is irrelevant)
10. {7, 8} only contains some, possibly all, the elements of {8}
FALSE (7 is not an element of {8} )
graph the line in the image please
The equation shows that the slope of the line is 3 and the y-intercept is 4 that is the line will pass through the point (0, 4)
Graphing linear equation
The standard linear equation is expressed as y = mx + b where;
m is the slope
b is the y-intercept
Given the linear equation (y-1) = 3(x+3)
Expand
y-1 = 3x + 3
y-3x = 3 + 1
y-3x = 4
y = 3x + 4
The equation shows that the slope of the line is 3 and the y-intercept is 4 that is the line will pass through the point (0, 4)
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square with a perimeter of 240 inches is dilated by a scale factor of 1.5. what is the area of the dilated image of the square?
the awnser: is 960 inches
Determine whether the rule represents an exponential function. Explain why or why not.
y=-11.x4
Answer:
Hello!
for 11 we can put in values
x = 0
y = 12 * 0^2
y=0
One point is (0,0)
x=1
y=12*1^2
y=12
Another point is (1,12)
x=-1
y = 12 * -1^2
y=12
A third point is (-1,12)
This tells us that this is not exponential since an exponential function as a steep curve on one side not two.
You can think of an exponential function as a half parabola if it helps.
13. We can plug in numbers again here.
x=0
y=7(0)+3
y=3
So the first point is (0,3)
x=1
y=7(1)+3
y=10
The second point is (1,10)
x=-1
y=7(-1)+3
y=-4
so the third point is (-1,-4)
This shows that the graph is not exponential it is linear since it goes in a straight line.
15. We just plug in -2 for t so
g(-2) = 2*0.4^-2
0.4^2 is 0.16 * 2 is 0.32 which is the answer
17. We can put 18 for w
h(18) = -0.5*4^18
This is where there is a issue because 4^18 is a extremely small number (6.9 * in scientific notation-
But we can multiply that by -0.5 to get
-3.4 *
which I believe is -0.000000034
Step-by-step explanation:
Subtract.
3−11−(−6)
whats the answer im confused
Answer:
-2
Step-by-step explanation:
3−11−(−6)=
3-11= -8
-8-(-6)
the two minus become plus so
-8+6= -2
the difference between any two consecutive numbers in the list a,b,c,d,e is the same . If b = 5.5 and e = 10, what is the value of a
The value of a based on the information is 4.
How to calculate the value?It should be noted that b = 5.5
It should be noted that e = 10
There are three alphabets in between them. This means the difference will be:
= (10 - 5.5)/3
= 4.5/3
= 1.5
Therefore, the value of a will be:
= 5.5 - 1.5
= 4
The value of a is 4.
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The value of a based on the information is 4.
How to calculate the value?
It should be noted that b = 5.5
It should be noted that e = 10
There are three alphabets in between them. This means the difference will be:
= (10 - 5.5)/3
= 4.5/3
= 1.5
Therefore, the value of a will be:
= 5.5 - 1.5
= 4
The value of a is 4.
Which describes the intersection of line m and line n?
point W
point X
point Y
point Z
Answer:
Option A on edge
Step-by-step explanation:
Its point W.
You collect coins. One of your favorite coins is a silver-colored coin showing a man's portrait. The radius of the coin is 12 millimeters. What is the diameter of the coin? What is the circumference of the coin? What is the area of the coin?
The circumference is 150.72 millimeters and the area is 1808.64 square millimeters
What is the diameter of the coin?The radius of the coin is given as
r = 12 millimeters
The diameter of the coin is calculated as
Diameter = 2 * r
So, we have
Diameter = 2 * 12 millimeters
Evaluate
Diameter = 24 millimeters
What is the circumference of the coin?The circumference of the coin is calculated as
C = 2πr
So, we have
C = 2 * 3.14 * 24
Evaluate
C = 150.72 millimeters
What is the area of the coin?The area of the coin is calculated as
A = πr²
So, we have
A = 3.14 * 24²
Evaluate
A = 1808.64 square millimeters
Hence, the circumference is 150.72 millimeters and the area is 1808.64 square millimeters
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How many boards 5 1/6 in. wide will it take to cover a floor 248in. wide?
The number of boards it would take to cover the floor is 48
Calculating amountFrom the question, we are to determine how many boards it would take to cover the floor
From the given information,
The width of the floor is 248 in.
and
The width of the board is 5 1/6 in.
Thus,
The number of boards it would take to cover the floor is
248 ÷ 5 1/6
= 248 ÷ 31/6
= 248 × 6/31
= 1488/31
= 48
Hence, the number of boards it would take to cover the floor is 48
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1. In a conditional statement, where do you find the hypothesis?
Answer: A conditional statement (also called an if-then statement) is a statement with a hypothesis followed by a conclusion. The hypothesis is the first, or “if,” part of a conditional statement. The conclusion is the second, or “then,” part of a conditional statement.
Step-by-step explanation:
What value of a makes the equation an identity? 3a(x-4) = 8x-16
We can conclude that no value of 'a' will make the equation an identity.
What exactly are equations?In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal.3x + 5 = 14, for example, is an equation in which the expressions 3x + 5 and 14 are separated by a 'equal' sign.The equation is an identity if solving it results in a true statement such as 0 = 0.So, to get 0 = 0 to make the equation an identity, we have to get such a value of a that makes the LHS 8x - 16 which will be similar to RHS 8x - 16.
If we take a = 1 then the LHS will be less than the RHS as:
3(1)(x-4) = 8x-163x - 12 ≠ 8x-16If we take a = 2 then:
3(2)(x-4) = 8x-166x - 24 ≠ 8x-16If we take a = 3 then the LHS will be greater than the RHS as:
3(3)(x-4) = 8x-169x - 36 ≠ 8x-16So, we can conclude that no value of 'a' will make the equation an identity.
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678876590* 34567845678
Answer:
ano yan ang tanong mo
Step-by-step explanation:
ano yan
Which expression is equivalent to 9(4+2x)?
evaluate 7 to the negative 2nd power
Answer:
exact form= 1/49
and the decimal form= 0.02040816
Step-by-step explanation:
{-415%, -√17, -4.1, -4.08} THE ORDER SET OF NUMBERS FROM LEAST TO GREATEST
The order of set of numbers {-415%, -√17, -4.1, -4.08} from least to greatest is {-415% < -√17 < -4.1 < -4.08}
Order of set of numbers:
Numerical order is a way of arranging a group of numbers into a sequence. This could be ascending or descending.
When we arrange numbers in ascending order, we arrange them from small to big, and when we arrange numbers from big to small, it is called descending order.
Given,
=> {-415%, -√17, -4.1, -4.08}
Here we need to convert the numbers into decimal for to arrange it,
First, we have to convert the value -415% into decimal,
=> -415%
=> -415/100
=> -4.15
Next, √17 is equal to,
=> -√17
=> -4.12
How we have to arrange them in order,
=> { -4.15< -4.12 < -4.1 < -4.08}
Which is equal to,
=> {-415% < -√17 < -4.1 < -4.08}
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What is the value of the expression below when x = 3
7x + 2
If a fraction between 0 and 1 is multiplied by another fl fraction between 0 and 1, the product is greater than 1
Answer: False
Step-by-step explanation: If you multiply a fraction between 0 and 1 by another fraction between 0 and 1, the result would be smaller than 1.
For example, [tex]\frac{3}{5} * \frac{1}{2} = \frac{3}{10}[/tex]
ill give lots of points if you help
The simplified fraction is -2 1/4
FractionsFrom the question, we are to evaluate the given fractions
The given fraction is
[tex]-1\frac{4}{5} + (-\frac{1}{4}) + (- \frac{1}{5} )[/tex]
Evaluating the fraction
[tex]-1\frac{4}{5} + (-\frac{1}{4}) + (- \frac{1}{5} )[/tex]
First, convert the mixed fraction to an improper fraction
[tex]-\frac{9}{5} + (-\frac{1}{4}) + (- \frac{1}{5} )[/tex]
Now, clear the parentheses
[tex]-\frac{9}{5} -\frac{1}{4}- \frac{1}{5}[/tex]
Find the LCM of the denominators
The LCM is 20
Thus,
[tex]\frac{-36 - 5 - 4}{20}[/tex]
= [tex]\frac{-45}{20}[/tex]
= [tex]-2\frac{5}{20}[/tex]
= [tex]-2\frac{1}{4}[/tex]
Hence, the simplified fraction is - 2 1/4
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PLEASE HELP
Solve the following system algebraically. y = x^2 + 11 and y = –12x
Answer:
x^2+12x=-11
Step-by-step explanation:
Answer:
(-1, 12) and (-11, 132)
Step-by-step explanation:
I
A tree casts a shadow 42 feet long. At the same time, a person 5 feet tall casts a shadow 7 feet
long. What is the height of the tree?
x
11
59 ft
30 ft
5 ft
xft
7ft
Answer:
The tree is 30 feet
Step-by-step explanation:
Set up a proportion
[tex]\frac{height}{shadow}[/tex] = [tex]\frac{height}{shadow}[/tex] Fill in what you know
[tex]\frac{x}{42}[/tex] = [tex]\frac{5}{7}[/tex] Cross multiply
7x = 210 Divide both sides by 7
x = 30