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.
To know more about machine:
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PLEASE HELP!! I WILL GIVE BRAINLIEST AND 16 POINTS!!
Complete the equation of the line through (3,-1) and (4,7). Use exact numbers. What does "y" equal?
Answer:
lets start with finding the slope
m=7-(-1)/4-3
m=8
now we can choose either of the 2 points given and the slope and plug that into the point slope form
y-7=8(x-4)
y-7=8x-32
y=8x-25
and that is your equation
Answer:
y = 8x - 25
Step-by-step explanation:
The equation of a line is y = mx + b
To find the slope use y2-y1/x2-x1
When you plug it in it will be 7 + 1/4 - 3 (8)
Now it is y = 8x + b
Lastly you need to plug in a coordinate to the equation to find b
7 = 8(4) + b (-25)
write the slope- intercept form of the equation for the line.
Y=2x-1
Y=1/2x-1
y=-2x-1
y=1/2x+1
Answer:
The answer will be y=2x-1
Step-by-step explanation:
With the graph we are able to use the formula rise/run, which means we count down from the top point, and then over, and then divide.
Going down is 4 points, and over is 2.
4/2 is 2.
This leaves us with two answers. With this information, we look at the direction the graph is going, it is going upwards, making it positive. Which means that your answer is the first one. Plus the line goes through -1.
Thank you, if you need any more help let me know.
Find the reference angle of the following angles:405°, 750°, ‒ 210°, 495° ‒660°, 480°
Answer:
Step-by-step explanation:
405÷180=2×180+45,45°
750=180×4+30,30°
-210+180=-30,30°
495÷180=2×180+135,180-135=45°
-660°+360=-300°+360=60,60°
480-360=120,180-120=60,60°
Find the area of the figure at the right in square feet. The figure can be separated into a rectangle and a trapezoid. Find the area of each. (image attached)
Answer:
Shape 1: Trapezoid
A= h(a+b/2)
A=32
Shape 2: rectangle
A=lw
A=96
32+96=128
Let me know if this helps!
5.
A leaky faucet is losing water and is filling a 7-gallon bucket every 21 hours. At that rate, how many
gallons of water will the faucet leak in 30 hours?
(2-Point Holistic Rubric)
Show your work.
Answer:
10 gallons.
Step-by-step explanation:
A leaky faucet is losing water and;
filling a 7-gallon bucket every 21 hrs.
So 7 gallons of water are leaked in 21 hrs
We are to find the number of gallons that will be leaked in 30 hrs.
Cross-multiplying this gives;
[tex]\frac{30 * 7}{21}[/tex] = 10 gallons.
Write as an inequality. "Four more than half a number is at most sixteen"
1/2 + 4 ≤ 16
four more = +4
half a number = 1/2
at most means less or greater which is ≤
Answer:
0.5n + 4 ≤ 16
Step-by-step explanation:
add 4 to half of the unknown number (n). It is at most 16 (less than or equal to).
0.5n + 4 ≤ 16
please help with this math question
Answer:
E H
F F
G E
I hope I helped.
apples are on sale for $3 and 12 per kilogram is the total cost of the apples proportional to the total yes or no
Answer:
yes the apples are porportinal
Step-by-step explanation:
Answer:
apple is proportional
Step-by-step explanation:
4. EF is the median of trapezoid ABCD.
B
X +12
с
E
4x-18
F
3x-4
A
Part I: Solve for x. Show your work. (4 points)
Answer:
x = 11
BC = 23
AD = 29
EF = 26
Step-by-step explanation:
Given:
Trapezoid ABCD, having,
median = EF = 4x - 18
base BC = x + 12
base AD = 3x - 4
Required:
Part I: value of x
Part II: Length of BC, AD, and EF.
Solution:
Part I: Value of X
The median length of a trapezoid is said to be the ½ of the sum of the 2 bases of the trapezoid.
Therefore, EF = ½(BC + AD)
4x - 18 = ½((x + 12) + (3x - 4)
4x - 18 = ½(x + 12 + 3x - 4)
4x - 18 = ½(x + 3x +12 - 4)
4x - 18 = ½(4x + 8)
Multiply 2 by both sides
2(4x - 18) = 4x + 8
8x - 36 = 4x + 8
Add 36 to both sides
8x - 36 + 36 = 4x + 8 + 36
8x = 4x + 44
Subtract 4x from both sides
8x - 4x = 4x + 44 - 4x
4x = 44
Divide both sides by 4
x = 11
Part II:
BC = x + 12 = 11 + 12 = 23
AD = 3x - 4 = 3(11) - 4 = 33 - 4 = 29
EF = 4x - 18 = 4(11) - 18 = 44 - 18 = 26
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 values except one (-2)
Step-by-step explanation:
The function heads off toward infinity at x=-2, so it is not defined there. The function is defined for all values except one.
Which data set could be represented by the box plot shown below?
Answer:
Step-by-step explanation:22
Translate the following into an algebraic expression: The number that is 40% more than five more than a number a.
Answer:
1.4a > 5+a
Step-by-step explanation:
If the number is increased by 40% of that number, then it multiplies by 1.4. So, the left side of the equation is 1.4a.
On the right side of the equation, if the number is increased by 5, then the equation is a + 5.
Since the left side of the equation is more than the right side of the equation, we add a greater than sign. So the expression is 1.4a > 5+a
Solve. 4x - 2 ——— = -7 2
Answer:
x = -3
Step-by-step explanation:
Dividing by 2 is the same as multiplying by 1/2. The distributive property applies.
[tex]\dfrac{4x-2}{2}=-7\\\\2x-1=-7\quad\text{simplify}\\\\2x=-6\quad\text{add 1}\\\\\boxed{x=-3}\quad\text{divide by 2}[/tex]
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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can someone answer this
Answer:
3-5: 3+(-5) and -5+3
5-3: 5+(-3) and -3+5
Step-by-step explanation:
3+(-5) is 3 plus -5 which is simplified into 3-5
-5+3 can be rearranged to make 3-5
5+(-3) is 5 plus -3 which is simplified into 5-3
-3+5 can be rearranged to make 5-3
The frequency table categorizes winners of a prestigious award from.1990-2012 by their age at the time they received the award.
Answer:
is there an image of the frequency table attached? whats the question
Step-by-step explanation:
A park is mapped on a coordinate plane, where C1, C2, C3, and C4 represent chairs and SW1, SW2, and SW3 represent swings. How far is C2 from SW1? A. 89−−√ units B. 145−−−√ units C. 97−−√ units D. 41−−√ units
Answer:
Option (B)
Step-by-step explanation:
To calculate the distance between C2 and SW1 we will use the formula of distance between two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].
d = [tex]\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^2 }[/tex]
Coordinates representing positions of C2 and SW1 are (2, 2) and (-6, -7) respectively.
By substituting these coordinates in the formula,
Distance between these points = [tex]\sqrt{(-6-2)^2+(-7-2)^2}[/tex]
= [tex]\sqrt{(64)+(81)}[/tex]
= [tex]\sqrt{145}[/tex] units
Therefore, Option (B) will be the correct option.
Sally’s house is located at (5, −1) and her school is located at (−9, 7). Her best friend Molly lives at
the midpoint of Sally’s house and school. What coordinate represents Molly’s house?
A. (2, −3) B. (−2, 3) C. (3, −2) D. (−3, 2)
Answer:
B. (−2, 3)
Step-by-step explanation:
To find the midpoint of a segment, add the x-coordinates of the endpoints and divide by 2. Add the y-coordinates of the segments and divide by 2.
x: (5 + (-9))/2 = -2
y: (-1 + 7)/2 = 3
Midpoint: (-2, 3)
Answer: B. (−2, 3)
Answer:
b
Step-by-step explanation:
-9+5=-4÷2=-2
-1+7=6÷2=3
a grandfather purchased a brand new car in 1958 for $2500.the car depreciated $325 a year. what would the car be worth 4 years after it was bought?
Answer:
$1200
Step-by-step explanation:
Since the value of the car depreciates $325 a year.
After 4 years it would be 1300, becuase $325 × 4 = $1300.
So, $2500 - $1300 = $1200
Iy
What is the domain of the function f(x) = 3|x + 4[ + 1?
ca
4+
3
-2-
1+
O all real numbers
O all real numbers less than or equal to -4
O all real numbers greater than or equal to 1
O all real numbers greater than or equal to -4
-7-5-5
3-2-11
5.6
X
2.
2Y
16
Answer:
all real numbers
Step-by-step explanation:
The function f(x) = 3|x +4| +1 is defined for all values of x. Its domain is all real numbers.
I got b = 5 but I wanted to make sure from you beautiful ppl <3
10 = -2b + 4b [find the value of b]
Answer:
b=5
Step-by-step explanation:
10 = -2b + 4b
Combine like terms
10 = 2b
Divide each side by 2
10/2 = 2b/2
5 = b
[tex]\huge\boxed{\underline{\bf \: Answer}}[/tex]
[tex] \sf \: 10 = - 2b + 4b \\ \sf \: 10 = 2b \\ \sf \: \frac{10}{2} = b \\ \sf \: 5 = b[/tex]
The value of b is [tex]\boxed{\underline{\bf \: 5}}[/tex]
Hope it helps.
RainbowSalt2222
find the surface area of the composite figure. answer asap please :)
Answer:
144
Step-by-step explanation:
An architect maps two buildings, which are located on a piece of land, onto a coordinate plane. He wants to build a wall at the diagonal AC to divide the piece of land into two parts. What will be the length of the wall? A. 65–√ units B. 6 units C. 237−−√ units D. 2 units
Answer:
[tex] 6\sqrt{5} units [/tex]
Step-by-step Explanation:
The length of the wall = diagonal AC = distance between point A (-6, -2) and point C (6, 4).
Distance formula between two points on a graph (d) = [tex] \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
Where,
[tex] A(-6, -2) = (x_1, y_1) [/tex]
[tex] C(6, 4) = (x_2, y_2) [/tex]
[tex] d = \sqrt{(6 - (-6))^2 + (4 -(-2))^2} [/tex]
[tex] d = \sqrt{(6 + 6)^2 + (4 + 2)^2} [/tex]
[tex] d = \sqrt{(12)^2 + (6)^2} [/tex]
[tex] d = \sqrt{144 + 36} [/tex]
[tex] d = \sqrt{180} [/tex]
[tex] d = \sqrt{36*5} [/tex]
[tex] d = 6\sqrt{5} [/tex]
The length of the wall = [tex] 6\sqrt{5} units [/tex]
Quick guys! I appreciate the help!!
Home depot provides truck rental services. Tom goes to Homedepot to rent a truck for his move. They
charge a flat rate of $50 dollars for renting services and $10 per hour the truck is out. Tom returned the
truck after 6.5 hours. What is the entire cost for the rental service?
Y=x($10)+$50
Y=cost to rent truck
X=how many hours rented
Here is our equation: y = 10x + 50
Where x represents the hours that Tom rented the truck, and y represents the amount that Tom will spend to rent the truck.
We want to find out how much it will cost if Tom rented the truck for 6.5 hours. So, we are looking and solving for y in this case, because we know that Tom rented the truck for 6.5 hours, or the x value. To solve, all we have to do is plug in 6.5 for x into our equation and solve for y.
y = 10(6.5) + 50
y = 65 + 50
y = 110
The entire cost for the rental service is $110.
Hope this helps! :)
Answer:
The answer is $110.
Step-by-step explanation:
To start, you should write out the information you know in an equation. You know that Home Depot charges a flat rate of $50, so this is your constant (which means it doesn't change throughout the problem). You also know that it cost $10 per hour to rent the truck. Using this information, you can write out your formula of y=10x+50.
Next, you are trying to figure out the total cost, y, when Tom rents the truck for 6.5 hours. To do this, all you have to do is plug in 6.5 for x. This will give you y=10(6.5)+50. When you simplify this, you get y=65+50, so y=$110.
If the sin of angle x is four fifths and the triangle was dilated to be two times as big as the original, what would be the value of the sin of x for the dilated triangle? Clue: Use the slash symbol ( / ) to represent the fraction bar, and enter the fraction with no spaces.
Hey there! I'm happy to help!
Sine is a trigonometric ratio. It is the ratio of the opposite side of the angle to the hypotenuse. Since it is a ratio, it does matter how big or small the triangle is as long as the sides remain in proportion. If the opposite side is 4 and the hypotenuse is 5, the sine of x will be the same as it would be if the opposite were 16 and the hypotenuse were 20 because they simplify to the same ratio (4/5).
The sine (or any trigonometric ratio) of any number stays the same even if the triangle is dilated because the proportion between the sides stays the same no matter how big or small. So, they told us the answer at the beginning. The sine of angle x is 4/5.
Have a wonderful day! :D
Answer: 4/5
Step-by-step explanation: Took the test and got it right. I assumed it was the same because angles do not change after being dilated.
I need help... please help me through this trigonometry. I need full answer.
Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identities
tan(x + y) = [tex]\frac{tanx+tany}{1-tanxtany}[/tex] , tan(x - y) = [tex]\frac{tanx-tany}{1+tanxtany}[/tex], tan [tex]\frac{\pi }{4}[/tex] = 1
tan2x = [tex]\frac{2tanx}{1-tan^2x}[/tex]
Consider the left side
tan([tex]\frac{\pi }{4}[/tex] + Θ ) - tan([tex]\frac{\pi }{4}[/tex] - Θ )
= [tex]\frac{tan\frac{\pi }{4}+tan0 }{1-tan\frac{\pi }{4}tan0 }[/tex] - [tex]\frac{tan\frac{\pi }{4}-tan0 }{1+tan\frac{\pi }{4}tan0 }[/tex]
= [tex]\frac{1+tan0}{1-tan0}[/tex] - [tex]\frac{1-tan0}{1+tan0}[/tex]
= [tex]\frac{(1+tan0)^2-(1-tan0)^2}{(1-tan0)(1+tan0)}[/tex]
= [tex]\frac{1+2tan0+tan^20-1+2tan0-tan^20}{1-tan^20}[/tex]
= [tex]\frac{4tan0}{1-tan^20}[/tex]
= 2 [tex]\frac{2tan0}{1-tan^20}[/tex]
= 2 tan2Θ = right side
help me plx can somewon help me
Move the decimal so that there is one non-zero digit on the left of the decimal point. (The number of decimal spaces you move = exponent on 10) Since the decimal is moving to the left, we know the exponent is positive.
2 + 7 = 9
Answer: 9 * 10^16
Which set below is the domain of
{(2, -3),(-1,0), (0,4),(-1,5),(4, -2)}?
(AD {-3, 0, 4, 5, -2} (CD, {2,-1,4}
(3) -3,4,5,-2) (D) {2,-1,0,4}
Answer:
Domain { -1,0,2,4}
Step-by-step explanation:
{(2, -3),(-1,0), (0,4),(-1,5),(4, -2)}
The domain is the input values
Domain { 2,-1,0,-1,4}
We normally write them in order from smallest to largest and no repeating
Domain { -1,0,2,4}
Answer:
[tex]\large \boxed{\sf D. \ \{2,-1,0,4\}}[/tex]
Step-by-step explanation:
The domain are all possible values of x.
[tex]\{(2, -3),(-1,0), (0,4),(-1,5),(4, -2)\}[/tex]
The x values are 2, -1, 0, -1, and 4.
The domain of the set is {2,-1,0,4}.
Find the length of MK¯¯¯¯¯¯ A. 7 B. 47 C. 19 D. 34
Answer:
19
Step-by-step explanation:
JH = 47 (70 - 23)
HM = 23
MK = 19 (42 - 23)
KU = 34 (81 - 47)
UC = 7 (47 - 40)
CN = 40
Answer:
19
Step-by-step explanation:
HM + MK = HK
23 + MK = 42
Subtract 23
MK = 42-23
MK =19
HELLLLLLPPOP HELPPPP
Part a
60h ≤ 438
Part b
7.3 hours
Must click thanks and mark brainliest