A-
1 box --- 6 minutes
y boxes --- 1 minute
y = 1/6
B-
1 box --- 9 minutes
t boxes --- 1 minute
t = 1/9
So...
r - used time
r(1/9 + 1/6)=100
r=(100.18)/5
r= 360 minutes
1/6 . 360 = 60 boxes
answer: 60 boxes
In total, machine A filled 66 boxes, and machine B filled 66 boxes, resulting in a total of 100 boxes filled.
Let's use the concept of the rate of work to solve this problem. The rate of work is the amount of work done per unit of time.
Machine A's rate of work is 1 box of nails every 6 minutes.
Machine B's rate of work is 1 box of nails every 9 minutes.
Let's assume that machine A filled x boxes, and machine B filled y boxes. Since they worked for the same amount of time, the total number of boxes filled by both machines is 100.
So, the equation representing the total work is:
x (boxes filled by A) + y (boxes filled by B) = 100
Now, let's use their rates of work to form two more equations:
Rate of work of A = 1 box every 6 minutes
Rate of work of B = 1 box every 9 minutes
Since work = rate × time, we can write two equations:
x (boxes filled by A) = (1/6) * t (time in minutes)
y (boxes filled by B) = (1/9) * t (time in minutes)
Since they both worked for the same time, we can set the time for both machines as equal:
t = t
Now, we have a system of equations:
x + y = 100
x/6 = y/9
t = t
Let's solve the system of equations. We can start by substituting the value of y from the second equation into the first equation:
x + (x/6)*3 = 100
x + (x/2) = 100
Multiply both sides by 2 to eliminate the fraction:
2x + x = 200
3x = 200
x = 200/3
Now, let's find the value of y using the second equation:
y = (x/6)*3
y = (200/3)/6 * 3
y = 200/3
So, machine A filled 200/3 boxes of nails, which is approximately 66.67 boxes.
Machine B filled 200/3 boxes of nails, which is also approximately 66.67 boxes.
Since they cannot fill a fraction of a box, we can distribute the remaining 2/3 box between machine A and machine B, giving one extra box to each.
In total, machine A filled 66 boxes, and machine B filled 66 boxes, resulting in a total of 100 boxes filled.
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Help
Find the lateral area of this cone.
Round to the nearest tenth.
Answer:
233.5 in²
Step-by-step explanation:
First we have to find the slant height.
5²+14²=c²
25+196=c²
221=c²
c=14.866
Now we can find the lateral area.
[tex]\pi[/tex]rl
[tex]\pi[/tex](5)(14.866)
=233.51566
To the nearest tenth=
233.5 in²
PLEASE ANSWER THESE QUESTIONS WITH A HOW TO PLEASE I DONT UNDERSTAND:
1) 0.01 divided by 1000
2) 0.012 divided by 100
3) 0.000851 divided by 10
Answer:
1) 0.00001
2) 0.00012
3)0.0000851
Step-by-step explanation:
Move the decimal place the amount of times being the same as the amount of zeros. Move it to make the number smaller because you are dividing.
1) move the decimal point to the right 3 times (because there are 3 zeros in 1000)
Hope that helped!!! k
Woah woah, no need to panic! I’ve got this taken care of for you!
1. 0.01 divided by 1,000= 100,000.000
Change the divisor 0.01 to a whole number by moving the decimal point 2 places to the right. Then move the decimal point in the dividend the same, 2 places to the right.
We then have the equations:
100000 ÷ 1 = 100,000.000
and therefore:
1,000 ÷ 0.01 = 100,000.000
Both calculated to 3 decimal places.
2. 0.012 divided by 100= 8,333.333
Change the divisor 0.012 to a whole number by moving the decimal point 3 places to the right. Then move the decimal point in the dividend the same, 3 places to the right.
We then have the equations:
100000 ÷ 12 = 8,333.333
and therefore:
100 ÷ 0.012 = 8,333.333
Both calculated to 3 decimal places.
3. 0.000851 divided by 10= 11,750.881
Change the divisor 0.000851 to a whole number by moving the decimal point 6 places to the right. Then move the decimal point in the dividend the same, 6 places to the right.
We then have the equations:
10000000 ÷ 851 = 11,750.881
and therefore:
10 ÷ 0.000851 = 11,750.881
Both calculated to 3 decimal places.
I hope this helped! <3
- ʕ•ᴥ•ʔ
A furniture shop refinishes cabinets. Employees use one of two methods to refinish each cabinet Method I takes 1 hour and the material costs $6. Method II takes 2 hours, and the material costs $5. Next week, they plan to spend 260 hours in labor and $986 in material for refinishing cabinets. How many cabinets should they plan to refinish with each method?
Answer:
They should refinish 96 tables using method 1
They should refinish 82 tables using method 2
Step-by-step explanation:
Let
a = number of tables refinished using method 1
b = number of tables refinished using method 2
Time equation
a+2b=260 (1)
Cost equation
6a+5b=986 (2)
a+2b=260 (1)
6a+5b=986 (2)
Multiply (1) by 5 and (2) by 2
5a+10b=1,300 (3)
12a+10b=1,972 (4)
Subtract (3) from (4)
7a=672
Divide both sides by 7
a=96
Recall,
a+2b=260
96+2b=260
2b=260-96
2b=164
Divide both sides by 2
b=164/2
=82
They should refinish 96 tables using method 1
They should refinish 82 tables using method 2
can somewon help me plz i want help
Answer:
5 * 10^10.
Step-by-step explanation:
(9 * 10^10) - (4 * 10^10) = (9 - 4) * 10^10 = 5 * 10^10.
Hope this helps!
Answer:
5*10^10
Step-by-step explanation:
9 times ten is 9^10, and 4 Times 10^10 is 4^10 so 9^10 minus 4^10 is 50000000000 which is also called 5^10 which is also 5 x 10^10 I think. pls correct me if im wrong
Follow the process of completing the square to solve x^2 - 10x + 8 = 0. What is the value of the constant that will be isolated on the right side of the equation in step 3? A.-8 B.-12 C.-32
Answer:
A. -8
Step-by-step explanation:
[tex]x^2-10x+8=0[/tex]
then we subtract 8 from both sides
[tex]x^2-10x+8-8=0-8[/tex]
[tex]x^2-10x=-8[/tex]
The value on the right side is -8 in the process of completing the square.
Answer:
A. -8
Step-by-step explanation:
Find the lateral area of the following cone.
Leave your answer in terms of pi
Answer:
The lateral surface area of cone is A = π×r×l where r represents radius and l is slant height.
The formula to find slant height is l = √(h²+r²) where h represents height.
The lateral surface area of the cone is 65[tex]\pi[/tex] square cm.
Given,
The height is 12 cm and the radius is 5 cm.
We are to find the lateral surface area of a cone.
What is the lateral surface area of a cone?The lateral surface area of a cone:
A = [tex]\pi[/tex] x r x l
where r = radius and l = slant height.
The slant height:
l = √(h²+r²) where h =height.
We have,
h = 12 cm and r = 5 cm
l =√(h²+r²)
l = √(12^2 + 5^2)
l = √(144 + 25)
l = √169
l = 13 cm
Now,
l = 13 cm and r = 5 cm
A = [tex]\pi[/tex] x r x l
A = [tex]\pi[/tex] x 13 x 5 = 65[tex]\pi[/tex] square cm
Thus lateral surface area of the cone is 65[tex]\pi[/tex] square cm.
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the graph of y=f(x) is shown below. find all the values of x where f(x)=1
When you substitute the value of x = 3, you get f(x) = 1.
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
What is Parabola?A parabola is a U-shaped curve this is drawn for a quadratic function,
f(x) = ax² + b x + c. The graph of the parabola is downward (or opens down), when the price of a is much less than 0, a < 0. The graph of the parabola is upward (or opens up) when the value of a is more than 0, a > 0.
parabola, open curve, a conic segment produced via the intersection of a proper circular cone and a plane parallel to an element of the cone.
Here the given graph of y = f(x) is shown.
When you substitute the value of x = 3, you get f(x) = 1.
Hence, you can get f(x) = 1 by substituting the value of x = 3
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Find the m∠DCA A. 10 B. 29 C. 116 D. 40
Hence, the m∠DCA is 59.2
What is an angle?An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs, and sometimes the arms of the angle.
How to solve?m∠DCB = (4x) + (6x-58) = 90
10x = 148
x = 14.8
m∠DCA = 4x
= 4(14.8)
= 59.2
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In the figure below MNOP is a parallelogram. Which of the following statements can be used to
explain why the shaded triangles are congruent?
Answer:
ΔNXO is the result of reflecting ΔPXM across a line parallel to line MP and through point X.ΔNXO is the result of rotating ΔPXM 180° clockwise about point X.Step-by-step explanation:
According to the choices given, only statements 1 and 3 are correct!
The true statement about the shaded triangles is; ΔNXO is the result of rotating ΔPXM 180° clockwise about point X.
How to solve congruency problems?The correct statement about the shaded triangles to explain the congruency is;
ΔNXO is the result of rotating ΔPXM 180° clockwise about point X.
This is because when we rotate ΔPXM 180° clockwise about point X, the corresponding parts of both triangles will be congruent based on Congruency proofs.
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Graph the function. h ( x ) = 8 ⋅ ( 3 4 ) x h(x)=8⋅( 4 3 )
answer....
Step-by-step explanation:
h
(
x
)
=
3
x
+
8
HELP MEH HELP MEH PLZ
Answer:
[2×10*(-3) × (4×10*(4)] = 80
Step-by-step explanation:
First of all 0.002 is 10*(-3) and not 10(-2) , so you can eliminate the first 2 answers.
Second of all, according to the calculator the left equation is correct, while the right one isn't... so there you go
Glad to help :)
please help me find the nth term of this sequence 0, 3, 8, 15, 24
Answer:
80
Step-by-step explanation:
0, 3, 8, 15, 24, 35, 48, 63, 80 which is the nth term
first step you have to find how many steps the sequence was going with.
examples= from 0 to 3 the steps were 3
=from 3 to 8 the steps were 5
= from 8 to 15 the steps were 7
you will recognize that the steps the sequence is going with is odd numbers.
so you will use the odd numbers until you find what you need. which leads you to 80 which is the nth number in the sequence.
Answer:
80
Step-by-step explanation:
You weigh six packages and find the weights to be 34, 24, 74, 29, 69, and 64 ounces. If you include a package that weighs 154 ounces, which will increase more, the median or the mean? A. The median and the mean will stay the same. B. The median and mean are affected the same amount. C. The mean increases more. D. The median increases more.
Answer:
C. the mean increases more
Step-by-step explanation:
the mean is more affected by outliers because it is an average of all the numbers.
Answer:
C. the mean increases more
Step-by-step explanation:
Jack is building a square garden. Each side length measures 777 meters. Jack multiplies 7\times77×77, times, 7 to find the amount of space in his garden is equal to 494949 square meters. Which measurement does 494949 square meters represent?
Which expression can be used to find the surface area of the following triangular prism? *picture of triangular prism* Choose 1 answer: (Choice A) 24+24+ 120+160+20024+24+120+160+20024, plus, 24, plus, 120, plus, 160, plus, 200 (Choice B) 24+20024+20024, plus, 200 (Choice C) 24+24+200+120+12024+24+200+120+12024, plus, 24, plus, 200, plus, 120, plus, 120 (Choice D) 48+48+120+160+20048+48+120+160+200
Answer:
A) 24+24+120+160+200
Step-by-step explanation:
The two ends are 24 (1/2bh= 1/2(8*6)).
One side (the back) is 6x20=120
One side (the bottom) is 8x20=160
One side (the top) is 10x20=200
So the equation is 24+24+120+160+200
Solve the equation 14=7(2x-4) using two different methods. Show your work. Which method do you prefer? Explain. need help thanks
Answer:
x=3
Step-by-step explanation:
14=7(2x-4)
14/7=2x-4
2=2x-4
2x=2+4
2x=6
x=6/2
x=3
------------
14=7(2x-4)
14=14x-28
14x=14+28
14x=42
x=42/14
x=3
The equation 14 = 7(2x - 4) can be solved using two different methods: the distributive property method and the inverse operations method. Both methods yield the same solution, which is x = 3. The preference between the two methods depends on personal preference and the specific equation being solved.
Distributive Property Method:
We'll distribute the 7 to the terms inside the parentheses:
14 = 7(2x - 4)
14 = 14x - 28
Next, we'll isolate the variable term:
14x = 14 + 28
14x = 42
Finally, we'll solve for x by dividing both sides of the equation by 14:
x = 42/14
x = 3
So the solution to the equation is x = 3.
Inverse Operations Method:
We'll use inverse operations to solve the equation step by step:
14 = 7(2x - 4)
Divide both sides of the equation by 7 to isolate the term in parentheses:
14/7 = 7(2x - 4)/7
2 = 2x - 4
Add 4 to both sides of the equation to isolate the variable term:
2 + 4 = 2x - 4 + 4
6 = 2x
Divide both sides of the equation by 2 to solve for x:
6/2 = 2x/2
3 = x
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If f(x) = x2 – 2x and g(x) = 6x + 4, for which value of x does (f+g)(x) = 0?
O -4
O-2
O 2
O 4
Answer:
x = -2
Step-by-step explanation:
If you have any questions about the way I solved it, don't hesitate to ask ;)
The value of the function (f+ g)(x) = 0 then x = -2.
What is Function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Given:
f(x) = x² - 2x and g(x) = 6x + 4
As, (f+g)(x) = 0
x² - 2x + 6x + 4 = 0
x² + 4x + 4 =0
x² + 2x + 2x + 4 = 0
x(x+2) + 2 (x +2 )= 0
(x + 2)(x+2) = 0
(x+ 2)²= 0
x+ 2= 0
x = -2
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A state highway department uses a salt storage enclosure that is in the shape of a cone, as shown above. If the volume of the storage enclosure is 48π m3, then what is the diameter of the base of the cone, in meters?
Answer:
Diameter of the base of the cone = 8 meters
Step-by-step explanation:
State highway department uses a salt storage enclosure which is in the shape of a cone.
Height of the storage in conical shape = 9 meters
Volume of the storage = 48π m³
Let the radius of this conical storage = r meters
Formula to get the volume of a cone = [tex]\frac{1}{3}\pi r^{2}h[/tex]
Here 'r' is the radius of the base of the cone and 'h' is the height of the cone.
Therefore, Volume = [tex]\frac{1}{3}(\pi ) r^{2}(9)[/tex]
[tex]48\pi=3\pi r^{2}[/tex]
r² = [tex]\frac{48\pi }{3\pi }[/tex]
r = [tex]\sqrt{16}[/tex]
r = 4 meters
Since, diameter = 2r
= 2(4)
= 8 meters
Therefore, diameter of the base of the cone = 8 metres
Find the measure of the remote exterior angle. m∠x=(197−5n)°m∠y=(6n+22)°m∠z=(n+7)°
A. 14
B. 91
C. 21
D. 127
Answer:
D. 127°
Step-by-step explanation:
The exterior angle (x) is the sum of the remote interior angles (y, z).
Setupx = y +z
(197 -5n) = (6n +22) +(n +7) . . . . . substituting the given expressions
SolutionEliminating parentheses and collecting terms, we have ...
197 -5n = 7n +29
168 = 12n . . . . . . . . . add 5n-29
14 = n . . . . . . . . . . divide by 12
Then the measure of remote exterior angle x is ...
m∠x = (197 -5(14))° = (197 -70)°
m∠x = 127°
The tee for the fifth hole on a golf course is 355 yards from the tee. On that hole, Marsha hooked her ball to the left, as sketched below. Find the distance between Marsha’s ball and the hole to the nearest tenth of a yard.
Answer:
184
Step-by-step explanation:
what is the domain of the function shown in the graph below?
answer type: interval, all real numbers, all values except one, all values except two
interval:
Answer:
All numbers except 1
Step-by-step explanation:
The graph has an asymptote at 1.
So the function will grow toward but without reaching it.
The equation of the asymptote is x=1
So the domain is all real numbers except 1.
(07.05 LC)
Which statement is true for the equation 4n − 3 = 4n − 2?
It has no solution.
It has one solution.
It has two solutions.
It has infinitely many solutions.
Answer:
The answer is (A); there is no solution.
Step-by-step explanation:
It doesn't require any calculations, really, just logic. Look, 4n = 4n wil be equal because they are the same numbers multiplied by the same variable - no matter the variable's value. However, if you subtract both values by different numbers, you won't get the same number:
Let's say n = 5
4n = 4n
= 4(5) = 4(5)
= 20 = 20
Now,
4n - 3 = 4n - 2
= 4(5) - 3 = 4(5) - 2
= 20 - 3 = 20 -2
= 17 ≠ 18
Hope this helps! Tell me if I was wrong!
Answer:
It has no solution.
Step-by-step explanation:
If we try and solve it we end up with nonsense, so it has no solutions:
4n - 3 = 4n - 2
4n - 4n = - 2 + 3
0 = 1
- which is, of course, absurd.
Also, just by looking at the equation we can see that the term 4n -3 cannot in any way be equal to 4n - 2.
Translate to an expression. How far have I travelled if I biked at 10mph for hhrs, I walked at 3mph for twice as long as I biked, and ran at 10mph for one quarter as long as I walked?
Answer:
10*h+3*2*10
Step-by-step explanation:
What effect will replacing x with (x−3) have on the graph of the equation y=x2 y = x 2 ? A. slides the graph 3 units down B. slides the graph 3 units right C. shrinks the graph by a factor of 3 D. slides the graph 3 units left
Answer:
B. slides the graph 3 units right
Step-by-step explanation:
Replacing x with x-h moves the graph 'h' units to the right. In this case, the graph is moved 3 units right by replacing x with x-3.
a box has a square base of side 9cm. calculate the volume of the box if it is 10cm high
Answer:
810 cubic centimetres
Step-by-step explanation:
If the box has a square base, the length and breadth of the box are the same. In this case, it's 9cm
The formula for the area of a rectangular prism is
A = lbh
where
l = length
b = breadth
h = height
Therefore the area is 9x9x10 = 810cm³
Answer:
V = 810 cm³
Step-by-step explanation:
V = Ab × h
Ab = s² = (9cm)² = 81 cm²
V = 81cm²×10cm = 810 cm³
Find the distance between the points X and Y shown. Question 5 options: A. 29−−√ B. 21−−√ C. 21 D. 5–√
Answer:
A
Step-by-step explanation:
From the graph we can notice that the coordinates of the poinrs x and y are:
● x(-2,0)
● y(3,-2)
There are many methods to find the distance between x and y. We will use the distance formula.
Let d be the distance between x and y.
● d = √[(-2-3)^2 + (0-(-2))^2]
● d = √[(-5)^2 + 2^2]
● d = √(25+ 4)
● d = √(29)
The other method was using the pythagorian theorem. d is the hypotenus.
Complete each congruency statement and name the rule used. If you cannot show the triangles are congruent from the given information, leave the triangle's name blank and write CNBD for "Cannot be determined" in place of the rule. ∆ANT ≅ ∆_____ by _____
Answer:
The correct answer is;
ΔANT ≅ ΔFLE by the SIde-Side-Side (SSS) rule of congruency
Step-by-step explanation:
The given information are;
Segment TN is congruent ts segment EL
Segment TA is congruent ts segment EF
Segment AN is congruent ts segment FL
Therefore, triangle ΔANT is congruent to ΔFLE by the Side-Side-Side (SSS) rule of congruency
One of the rule used to serve as proof that two or more triangles are congruent, is the Side-Side-Side (SSS) rule of congruency. The Side-Side-Side rule of congruency states that if the dimensions of the three sides of one triangle are equal to the dimensions of the three sides of another triangle, the two triangles are congruent.
Therefore, the correct option is ΔANT ≅ ΔFLE by the Side-Side-Side (SSS) rule of congruency
Answer: cannot be determined
Step-by-step explanation:
there isnt a rule SSS
DONT ANSWER!! am i right? 20 points!
Answer:
yes
Step-by-step explanation:
Step-by-step explanation:
Hi, there!!!
It's so simple,
so, let's simply work with it;
Here, the given equation is;
4d-4 = 5d-8
so, let's take "4d" to right side and -8 to left side. we get,
-4+8 = 5d-4d
or, 4 = d
Therefore, the value of d is 4.
{here, we simply simplified to get answer}
YOU ARE ABSOLUTELY RIGHT...
Hope it helps....
h(x+1)=x^2-4 evaluate function by substuting x+1
Answer:
h(x + 1) = (x+3)(x-1)
Step-by-step explanation:
Simply plug the value of x+1 into the equation for x.
h(x) = x^2 - 4
h(x + 1) = (x + 1)^2 - 4
h(x + 1) = x^2 + 2x + 1 - 4
h(x + 1) = x^2 + 2x - 3
h(x + 1) = (x+3)(x-1)
Cheers.
Answer:
h(t)= t² - 2t -3
Step-by-step explanation:
h(x+1)= x²-4 is the given function
We can write it x²-4 as:
(x+2)(x-2)= (x+1+1)(x+1 - 3)Substituting x+1 with t. Then function is:
h(t)= (t+1)(t-3)= t² - 2t -3or
h(t)= t² - 2t -3Of a group of boys and girls at Central Middle School’s after-school party, 15 girls left early to play in a volleyball game. The ratio of boys to girls then remaining was 2 to 1. Later, 45 boys left for a football game. The ratio of girls to boys was then 5 to 1. How many students attended the party?
Answer:
90
Step-by-step explanation:
Let g and b represent the number of girls and boys attending, respectively.
After 15 girls left, the ratio of boys to girls was ...
b/(g -15) = 2/1
b = 2g -30 . . . . . multiply by (g-15)
__
After 45 boys left, the ratio of girls to boys was ...
(g -15)/(b -45) = 5/1
g -15 = 5b -225 . . . . . . multiply by (b-45)
g = 5b -210
Using the latter to substitute into the former, we have ...
b = 2(5b -210) -30
450 = 9b . . . . . add 450-b
50 = b . . . . . . 50 boys attended
g = 5(50) -210 = 40 . . . . . 40 girls attended
The number of students who attended the party was 50 +40 = 90.
_____
Check
After 15 girls left, the ratio of boys to girls was 50/25 = 2/1.
After 45 boys left, the ratio of girls to boys was 25/5 = 5/1.
Answer:
let b = original number of boys
let g = original number of girls
:
Of a group of boys and girls at Central Middle School's after-school party, 15 girls left early to play in a volleyball game.
The ratio of boys to girls then remaining was 2 to 1.
b%2F%28%28g-15%29%29 = 2%2F1
Cross multiply
b = 2(g-15)
b = 2g - 30
:
Later, 45 boys left for a football game. The ratio of girls to boys was then 5 to 1.
%28%28g-15%29%29%2F%28%28b-45%29%29 = 5%2F1
cross multiply
g - 15 = 5(b-45)
g - 15 = 5b - 225
g = 5b - 225 + 15
g = 5b - 210
Replace b with (2g-30)
g = 5(2g-30) - 210
g = 10g - 150 - 210
g = 10g - 360
360 = 10g - g
360 = 9g
g = 360/9
g = 40 girls originally
find b
b = 2(40) - 30
b = 50 boys originally
" How many students attended the party?"
40 + 50 = 90 students
