Answer:
7 1/2 days
Step-by-step explanation:
The carpenter can do 1/5 of the work in 1 day. The assistant, who takes 'a' days to do the work, can do 1/a of the work in 1 day. Together, they can do 1/3 of the work in 1 day:
1/5 + 1/a = 1/3
1/a = 1/3 -1/5 = 2/15
a = 1/(2/15) = 15/2 = 7.5
The assistant takes 7.5 days to do the work alone.
8 times of the eight term of an arithmetic progression is equal to 12 times of the twelfth term. find its first term if the common difference is -2 .
Answer:
38
Step-by-step explanation:
We can express the 8th term as x and the 12th term as y.
This would mean that 8x=12y
Because the common difference between terms is -2 and term 8 and term 12 are 4 terms apart, this means that the 12th term is 8 less than the 8th term, so x-8=y
Now we can use this to substitute y with x in the first equation. This would give us:
8x=12(x-8)
Which we can expand and solve:
8x=12x-96
-4x=-96
Therefore x=24
This means the 8th term is 24 and the 12th term is 16 (24-8).
To test if this is correct we can do:
8x24=12x16
Which indeed are equal, both sides multiply to 192.
Now that we have our 8th term, we can find the 1st term, which is 7 terms away, therefore we just add 14 to the 8th term 24. (7x2=14)
24+14=38.
The first term is 38.
Hope this helped!
Question 24
The Sugar Sweet Company is going to transport its sugar to market. It will cost $4500 to rent trucks, and it will cost an additional $250 for each ton of sugar
transported.
Let C represent the total cost (in dollars), and let S represent the amount of sugar (in tons) transported. Write an equation relating C to S. Then use this
equation to find the total cost to transport 17 tons of sugar.
Answer: C=250S+4500
C=250(17) + 4500
C=4250+4500
C=8750
Step-by-step explanation:
As an equation, 250 would be the slope because it is multiplying by the ton and 4500 is the y intercept. If you substitute in 17 for S, then multiply 17 by 250, you get 4250 then add the 4500 and you get 8750 so if S=17, C=8750
The cost of transporting 17 tons of sugar is $8750.
What is an equation?An equation is written in the form of variables and constants separated by the operation of multiplication and division,
An equation states that terms in different forms on both sides of the equality sign are equal.
Multiplication and division do not separate the terms of an equation.
The given information can be related as,
C = 250S + 4500.
Now, when tons of sugar is 17 we'll simply replace S with 17.
∴ C = 250(17) + 4500.
C = 4250 + 4500.
C = 8750.
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Multiply the polynomials. (x2 – 4) (x2 + 3x – 5)
Answer:
[tex] \boxed{ \bold{ \boxed{ \sf{ {x}^{4} + 3 {x}^{3} - 9 {x}^{2} - 12x + 20}}}}[/tex]
Step-by-step explanation:
[tex] \sf{( {x}^{2} - 4)( {x}^{2} + 3x - 5)}[/tex]
Use distributive property
[tex] \dashrightarrow{ \sf{ {x}^{2} ( {x}^{2} + 3x - 5) - 4( {x}^{2} + 3x - 5)}}[/tex]
[tex] \dashrightarrow{ \sf{ {x}^{4} + 3 {x}^{3} - 5 {x}^{2} - 4 {x}^{2} - 12x + 20}}[/tex]
Collect like terms
[tex] \dashrightarrow{ \sf{ {x}^{4} +3 {x}^{3} - 9 {x}^{2} - 12x + 20}}[/tex]
Hope I helped!
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What value of x would result in the numerical value of zero in the expression 7+x+(−10) ?
Answer:
3
Step-by-step explanation:
7 plus three is 10, adding -10 to that equals zero.
The value of x would result in the numerical value of zero in the expression 7+x+(−10) is 3.
Based on the information given, we simply have to find the value of x. Therefore, the value of x from the equation will be:
7 + x + (-10) = 0
Collect like terms
x = 10 - 7
x = 3
Therefore, the value of x would result in the numerical value of zero in the expression 7+x+(−10) will be 3.
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How many signs can be made from a piece of
sheet metal that is 4 feet long and 8 feet wide?
A dolphin was swimming 28 meters below the ocean's surface. It changed its depth to avoid a predator and ended up 21 meters below the surface.
What was the change in the dolphin's depth?
Answer:
7 meters
Step-by-step explanation:
Now write an equation that represents the situation. You want to find the change in the dolphin's depth, so subtract its beginning depth from its final depth.
The change in the dolphin's depth is negative 7 meters.
What is Subtraction?Subtraction of two or more numbers or algebraic expressions is the method of taking away a certain value from a number. This operation is also called difference of numbers.
Subtraction is one of the basic operations in mathematics along with division, multiplication and addition.
Initial depth that Dolphin was swimming = 28 meters
Then the Dolphin changed it's depth to avoid predator.
Final depth that Dolphin was swimming = 21 meters
Change in depth = Final depth - Initial depth
= 21 - 28
= -7 meters
This implies that depth of the Dolphin decreases with -7 meters.
Hence the change in the Dolphin's depth is -7 meters if the initial depth was 28 meters and final depth was 21 meters.
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Find the intersection of the two sets.
{2,3,4,5,7} n{2,4, 6, 8, 10}
{2,4, 10)
{2,4}
{2,3,4,5,6,7,8, 10)
Answer:
{2, 4}
Step-by-step explanation:
Intersection of given sets would be {2,4}.
Answer:
C) {2,4}
Step-by-step explanation:
C) {2,4}
The union would be all of them. The intersection are the ones they have in common.
COMPETE
Answer as a dec
2.8+7.22
DONE
Answer:
Hi, there my name is 1frogaroni and I will be helping you out today!
Step-by-step explanation:
The answer to your question is 10.02.
2.8+7.22
=2.8+7.22
=10.02
You must simplify. if this helped I would be happy to get brainliest in order for me to rank up.
Have a great day!
What percent is represented by the shaded area?
Answer:
1.91%
Step-by-step explanation:
URGENT: how many integers have an absolute value less than 10π
Answer:
Step-by-step explanation:
Let's calculate 10 pi.
1 pi is about 3.14.
10 pi should be about 31.4.
-31 to -1 is 31 integers.
1 to 31 is 31 more integers.
0 is 1 integer.
31 + 31 = 62
62 + 1 = 63
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Which of the following numbers can be classified as a whole number, natural number, integer, and rational number? 0.4. -78 15 0
Answer:
0.4 since the number is non terminating and non repeating therefore it is irrational number.
-78 A rational number is a number that can be expressed as a fraction where both the numerator and the denominator in the fraction are integers. The denominator in a rational number cannot be zero
15 The number 15 is a rational number. It is an integer and all integers are rational numbers.
0 Yes zero is a rational number. Thus, 0 can be written as, where a/b = 0, where a = 0 and b is any non-zero integer.
Whats 855000 in scientific notation?
Answer:
8.55x10^5 in scientific notation
Answer:
8.55 × 10^5
Step-by-step explanation:
855000 = 855 × 10³
8.55 × 10² × 10³
8.55 × 10²+³
8.55 × 10^5
Point B is on line segment AC. Given AB = 2x + 10, BC = x, and AC = 5x,
determine the numerical length of AC.
Answer:
Step-by-step explanation:
the answer is 25 not 5
The numeric value of x will be 25 for the given line segment.
What is a line segment?A line section that can connect two places is referred to as a segment.
In other words, a line segment is just part of a big line that is straight and going unlimited in both directions.
The line is here! It extends endlessly in both directions and has no beginning or conclusion.
Given the line segment AC
AC = AB + BC
Given,
AB = 2x + 10, BC = x, and AC = 5x,
So,
5x = 2x + 10 + x
5x = 3x + 10
2x = 10
x = 5
So,
AC = 5x
AC = 5(5) = 25 units.
Hence, The numeric value of x will be 25 for the given line segment.
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Which function describes this table of values?
Answer:
y = 4/5x
Step-by-step explanation:
We know it's not y = x - 2 because if you plug x into the equation, it works for the first one, but not the second one. Ex: 10 - 2 = 8 but 5 - 2 = 3 not 4.
We also know that it can't be y = -5/4x because if you plug x into that equation, it does not equal y.
y = 4/5x because when you plug x into the equation it works.
TLDR basically you just plug x into the equations.
How many seconds are in 4.98 minutes? Round your answer to the nearest tenth (to one decimal point)
Answer: 298.8 seconds
Step-by-step explanation: 4.98*60=298.8
Answer:
298.8
Step-by-step explanation:
4.98x60=298.8 so you have been understand
The tempature at 5pm is 20°F. The tempature at 10pm is -5°F. How many degrees did the tempature fall?
Answer:
25 degrees
Step-by-step explanation:
20 - (-5)
negatives cancel out
20+5 = 25
:D
The quotient of 24 and x equals 14 minus 2 times x
Answer:
x = 3, x = 4
Step-by-step explanation:
Given
[tex]\frac{24}{x}[/tex] = 14 - 2x ( multiply through by x , x ≠ 0 )
24 = 14x - 2x² ( subtract 14x - 2x² from both sides )
2x² - 14x + 24 = 0 ( divide through by 2 )
x² - 7x + 12 = 0 ← in standard form
(x - 3)(x - 4) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 3 = 0 ⇒ x = 3
x - 4 = 0 ⇒ x = 4
Danny wants to sell his house. He would like to receive $136,000 after deducting the 6% commission due to the real estate agent. What should the selling price for the house be to the nearest dollar?
Answer:
The selling price of the house is $144,681
Step-by-step explanation:
The computation of the selling price of the house is shown below:
Let us assume the selling price be x
So, the commission would be 0.06x
Now the danny would received
= x - 0.06x
= 0.94x
And, the amount received is $136,000
So equate this value
Like this
0.94x = $136,000
x = [tex]\frac{\$134,000}{0.94}[/tex]
= $144,681
Hence, the selling price of the house is $144,681
Jillian said √25 is irrational because it is a square root. Why is she wrong
Answer:
She is wrong because the answer is 5 and that is rational
Step-by-step explanation:
the quotient of 100 and w
Answer:
[tex]\frac{100}{w}[/tex]
Step-by-step explanation:
When it asks for the quotient you are dividing/ putting it in a fraction.
Please help me solve this thanks
Answer:
A
Step-by-step explanation:
let r represent rate and d distance.
Given that r varies directly as d² then the equation relating them is
r = kd² ← k is the constant of variation
To find k use the condition r = 4 when d = 15, then
4 = k × 15² = 225k ( divide both sides by 225 )
k = [tex]\frac{4}{225}[/tex]
r = [tex]\frac{4}{225}[/tex] d² ← equation of variation
When r = 9, then
9 = [tex]\frac{4}{225}[/tex]d² ( multiply both sides by 225 )
2025 = 4d² ( divide both sides by 4 )
506.25 = d² ( take the square root of both sides )
d = [tex]\sqrt{506.25}[/tex] = 22.5 = 22 [tex]\frac{1}{2}[/tex] → A
At midnight, the temperature was 15°C. Over the next six hours, the temperature dropped 3 degrees each hour. By noon, the temperature increased 12 degrees. A. What was the temperature at 6 a.m.? B. Then what was the temperature at noon?
Answer:
a)3C b)27C
Step-by-step explanation:
a) 6hours*3degrees=18 degrees
15-18=3C
b)15+12=27C
In the given diagram, which of the following can you use to prove that triangle ABC is an isosceles triangle? Show the slopes of AB and CD are negative reciprocals. Show that D is the midpoint of AB. Show that CD = AD = DB.
Answer:
I’ll tell you that the answer is NOT l, ll, and lll
Step-by-step explanation:
Which expression is equivalent to 5(x - 7)?
Answer:
5x - 35
Step-by-step explanation:
Apply the distributive property. That means to multiply the number on the outside of the perenthesis with each of the numbers inside the perenthesis.
Solve the following equation 2/3x+6=1/2x+1/4x
Answer:
x = -72/17
Step-by-step explanation:
(2/3)*x+(1/2)*x+(1/4)*x+6 = 0
17/12*x+6 = 0 // - 6
17/12*x = -6 // : 17/12
x = -6/17/12
x = -72/17
x = -72/17
zelly works 30 hours a week at a food market for $8.50 an hour she takes home $7.65 an hour after deductions. what is her rate for deductions? use an equation to model the problem and solve it. use r to represent the rate for her deductions.
Answer:
Her deduction is 10%, or 0.85
Step-by-step explanation:
help please thank you
Answer:
a) n/4 - 8
Step-by-step explanation:
A quotient is an answer to a division equation, in this case, is n/4
A delivery person uses a service elevator to bring boxes of books up to an office. The delivery person weighs 150lb and each box of books weighs 40lb. The maximum capacity of the elevator is 1140lb. How many boxes of books can the delivery person bring up at one time?
Answer:
24
Step-by-step explanation:
The delivery person can take 24 boxes of books up the elevator at one time. This was my process:
(1140-150) / 40
990 / 40
24.75
But you cannot have three quarters of a box so the final answer would be 24.
Which of the following transformations will not produce a congruent image?
A.
rotation
B.
translation
C.
dilation
D.
reflection
Answer:
Translation, rotation and reflection
Step-by-step explanation:
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