Answer: 3 hours
Let john take x hours to finish the work
Let nelly take y hours to finish the work
given, y =x+3
Portion of work done by john alone in one hour = 1/x
Portion of work done by Nelly alone in one hour = 1/y
∴Portion of work done by both john and nelly in one hour = 1/x + 1/y
[tex]= \frac{1}{x} + \frac{1}{x+3}\\=\frac{x+3+x}{x*(x+3)}\\=\frac{2x+3}{x^2+3x}[/tex]
Total time taken by John and nelly to finish the work = 2 hours
[tex]\therefore [2(2x+3)]/[x^2 + 3x] = 1\\= > 4x + 6 = x^2 + 3x\\= > x^2 -x -6 =0\\= > x^2 - 3x + 2x -6 =0\\= > x(x-3) + 2(x-3)=0\\= > (x+2)(x-3)=0[/tex]
Hence either x = -2 or x = 3
Since x is time taken, it cannot be negative, hence x = 3
∴Time taken by john to finish the work = 3 hours
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Manvita deposits Rs. 5000 in her bank account after two days. She withdraws Rs.
3748 from it. If the amount deposited is a positive integer. How will you represent
the amount withdrawn and also find the balance amount in the account?
If the amount deposited is a positive integer , so the amount withdrawn is represented by -3748 and the balance amount in the Manvita's account is Rs 1252 .
In the question ,
it is given that
Money deposited by Manvita = Rs 5000 .
Money withdrawn by Manvita = Rs 3748 .
Since , amount deposited is a positive integer ,
So, the amount withdrawn will be a negative integer
Balance in Manvita's account = Money deposited + Money Withdrawn
Substituting the values , we get
Balance in Manvita's account = 5000 + (-3748)
= 5000 - 3748
= 1252
Therefore , if the amount deposited is a positive integer , so the amount withdrawn is represented by -3748 and the balance amount in the Manvita's account is Rs 1252 .
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The perimeter of AMUD is 38cm.
m/D=
MD=
14cm
360
Blank 1:
Blank 2:
cm
M
D
The side MD measures 10 cm and ∠D=72° for the given triangle.
What is triangle?
A shape with corners and three vertices is called a triangle. It is one of the most fundamental geometric shapes. Triangle ABC is the designation for a triangle containing vertices A, B, & C. In Euclidean geometry, all three points that are not collinear produce a singular triangle and a singular plane.The perimeter of ΔMUD= 38cm
MU=DU=14cm
∠U=36°
⇒∠M=∠D=x
Applying Angle sum property,
36°+x+x=180°
2x=180°-36°
x=72°
∴∠D=72°
Perimeter of triangle=14+14+MD
38=28+MD
⇒MD=10cm.
The side MD measures 10 cm and ∠D=72° for the given triangle.
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Simplify The answer please
Answer:
-18/35
Step-by-step explanation:
Three consecutive intergers are such that four times the least integer is three times the greatest . What is the greatest of this integers? A-16, B-8, C-10, D-12, E-14
If we call the middle number in the sequence [tex]x[/tex], the numerical values of the other terms will be [tex]x-1[/tex] and [tex]x+1[/tex], respectively, since they are consecutive.
We are told that [tex]4[/tex] times the smallest number is equal to [tex]3[/tex] times the largest number. Let us write our equality.
[tex]4(x-1)=3(x+1)[/tex][tex]4x-4=3x+3[/tex][tex]4x-3x=4+3[/tex][tex]x=7[/tex]We found our number in the middle. Since it wants the value of our largest number, let's add 1 to the middle number.
[tex]x+1=7+1=8[/tex]The answer is B.
Graph the image of rectangle CDEF after a translation 4 units left and 9 units up.
The graph of the image of rectangle CDEF after a translation 4 units left and 9 units up is as shown below.
In this question, we have been given the image of rectangle CDEF.
The coordinates of rectangle CDEF are:
C = (-6, -6)D = (-2, -6)E = (-2, 0)F = (-6, 0)
The rectangle CDEF is a translated 4 units left and 9 units up.
When rectangle CDEF is a translated 4 units left then the coordinates of rectangle would be,
C' = (-10, -6)
D' = (-6, -6)
E' = (-6, 0)
F' = (-10, 0)
Then rectangle C'D'E'F' is translated 9 units up then the coordinates of rectangle would be,
C'' = (-10, 3)D'' = (-6, 3)E'' = (-6, 9)F'' = (-10, 9)
The graph of the image of rectangle CDEF after a translation 4 units left and 9 units up is as shown below.
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Model with Mathematics
The owner of a frozen yogurt stand considers different pricing options for a serving of yogurt plus toppings. For what number of toppings do the two options give the same price?
A. Define the variables.
B. Write a system of equations that models this situation.
C. Graph the system. What is the intersection point?
D. What is the solution of the problem?
E. Is the solution reasonable for this situation? Explain.
Answer:
Step-by-step explanation:
A, B: Define the Variables and Write Equations
Let T be the number of toppings.
Option 1: $3 + $0.75*T
Option 2: $4 + $0.50*T
C. Graph the System
See the attached graph. The intersection point is (4,6). This means that 4 toppings will result in a cost of $6 for both yogurt options.
D. Solution to the Problem
The solution is given above, but we can also solve using equations, instead of graphing. We want the value of T that will make these expressions equal:
$3 + $0.75*T = $4 + $0.50*T
$0.25*T = $1
T = 4 toppings
=============
CHECK:
For 4 toppings:
Option 1: $3 + $0.75*T
$3 + $0.75*(4)
$3 + $3 = $6
Option 2: $4 + $0.50*T
$4 + $0.50*(4)
$4 + $2 = $6
Four toppings will make both options equal in cost.
E: Is the solution reasonable?
Yes. The cheaper option ($3) has a more expensive topping, so at some point (at 4 toppings) it will be the same price as the second option, with a higher initial price, but with cheaper toppings.
Monique built a wooden frame woth dimensions 0.8m by0.5m.how much wood will be left from a 3.4m length of timber
Answer: 0.8 m
Step-by-step explanation:
1. The perimeter P of the wooden frame is equal to:
P=2(0.8+0.5)
P=2(1.3)
P=2.6 m
2. The remaining length of wood is equal to:
3.4-2.6=
0.8 m
41.4 is what percent of 92?
Answer: 45
41.4 is 45 percent of 92
Answer: 45%
Step-by-step explanation:
Solution for 41.4 is what percent of 92:
41.4:92*100 =
(41.4*100):92 =
4140:92 = 45
Now we have: 41.4 is what percent of 92 = 45
Question: 41.4 is what percent of 92?
Percentage solution with steps:
Step 1: We make the assumption that 92 is 100% since it is our output value.
Step 2: We next represent the value we seek with x.
Step 3: 100%=92.
Step 4: In the same vein, x%=41.4.
Step 5: This gives us a pair of simple equations:
$100%=92(1).
$x%=41.4(2).
Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS
(left hand side) of both equations have the same unit (%); we have
100%/x%= 92/41.4
Step 7: Taking the inverse (or reciprocal) of both sides yields
x%/100% = 41.4/92
-> x=45%
Therefore, 41.4 is 45% of 92.
If pH = -log [H+], find the pH of a substance that has a hydrogen concentration [H+] = 5.7 X 10-4.Round your answer to the nearest ten thousandth (4 decimals).
[H+] = -1.7243
Explanation:
Since [H+] = 5.7 * 10 - 4, in the function -log[H+] representing pH, replace H+
pH = -log [5.7 *10 - 4]
pH = -log[53]
pH = -1.7243
NB:
This number is rounded up from -1.72427.....
Trevon left home and traveled toward the recycling plant. Mike left one hour later traveling 14 mph faster in an effort to catch up to him. After four hours Mike finally caught up. Find Trevon's average speed.
The most appropriate choice for speed will be given by-
Average speed of Trevon is 56 mph
What is speed?
The distance travelled by the body per unit time is called speed of the body.
If d is the distance travelled by the body and t is the time taken, then
speed = [tex]\frac{d}{t}[/tex]
Speed is a scalar quantity as the direction is not taken into account.
Here,
Let the average speed of Trevon be [tex]x[/tex] mph
Average speed of Mike = [tex](x + 14)[/tex] mph
Time for which Trevon driven = [tex](4 + 1)[/tex] h
= [tex]5[/tex] h
Time for which Mike driven = [tex]4[/tex] h
By the problem,
[tex]5 \times x = 4 \times (x+14)[/tex]
[tex]5x = 4x+56[/tex]
[tex]5x-4x=56[/tex]
[tex]x =56[/tex] mph
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How do u solve this?
Answer:
See below
Step-by-step explanation:
the two angles add to a total of 360 °
5x - 40 + `150 = 360
x = 50°
What is the value of (−14)3 when evaluated? −2,744 −196 42 2,744
The value of (-14) 3 when evaluated is -42.
Given,
The expression = (-14) 3
We have to evaluate this and find the value.
Evaluating an expression:
Finding the value of an algebraic expression when a specified integer is used to replace a variable is known as evaluating the expression. When evaluating an expression, we change the variable in the expression to the given number and then use the order of operations to simplify the expression.
That is,
(-14) 3 = -14 × 3 = -42
Therefore, the value of (-14) 3 when evaluated is -42
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what expression is equivalent to 1.2y + 4.5 - 3.4y - 6.3
The expression is equivalent to the given expression by combining like terms is -2.2[tex]y[/tex]-1.8 .
What is a expression?An expression is a set of terms combined using the operations +, -, x or ÷
and the variables. Number, symbols and operators are grouped to form an expression . An expression can be simplified by combining like terms.
Given that,
1.2y + 4.5 - 3.4y - 6.3
The terms that has same variables are like terms Combine like terms by adding or subtracting the terms.
-1.2[tex]y[/tex]-3.4[tex]y[/tex]+4.5-6.3
-2.2[tex]y[/tex]-1.8
Hence, The expression is equivalent to the given expression by combining like terms is -2.2[tex]y[/tex]-1.8 .
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Can someone help with questions 3,4 and 5? THANK YOUUU ^^ I did questions 1 and 2
Answer:
Question 3.
[tex]y = \frac{2}{7} x - 3[/tex]
question 4
[tex]y = - 4x - 1[/tex]
question 5
[tex]y = 5x + 3[/tex]
Step-by-step explanation:
Question 3
1.Write down what is given in equation form
[tex]y = \frac{2}{7} x + c[/tex]
2. Insert the given point to work out c
[tex] - 5 = \frac{2}{7} ( - 7) + c[/tex]
[tex]c = - 3[/tex]
3. answer
[tex]y = \frac{2}{7} x - 3[/tex]
Question 4
1 write what was given in an equation
[tex]y = - 4x + c[/tex]
2. insert given point (-1;3) to work out c
[tex]3 = - 4( - 1) + c[/tex]
[tex]c = - 1[/tex]
3. final answer
[tex]y = - 4x - 1[/tex]
question 5
1.with what was given write it in equation form
[tex]y = 5x + c[/tex]
2. substitute the given point (-2;-7) to work out c
[tex] - 7 = 5( - 2) + c[/tex]
[tex]c = 3[/tex]
3.final answer
[tex]y = 5x + 3[/tex]
with show work. trigonometry
Gabriel bought 12 donuts and fritters from the
bakery. Donuts cost $1.00 and fritters cost
$2.00. Gabriel spent a total of $17.00. How
many donuts (d) and how many fritters (f) did
he buy?
d+f=12
1d + 2f = 17
[?] donuts [?] fritters
Answer:
Gabriel spent $12 in just Donuts. If fritters are $2 a piece, he could buy 2 fritters at max. Perhaps he bought an extra donut to equal $17.
Step-by-step explanation:
Answer:
7 donuts and 5 fritters
Step-by-step explanation:
If you partition a line segment in a ratio of 4:1, what is the fraction?
Answer:
Your answer would be 4 over 1
How can you rewrite -8 -10 as an addition problem?
Answer:
-8 + (-10)
Hope this help!
a soccer club has 120 members this year, compared to 85 members last year. find the percent increase or decrease
The number of members that the club had last year was 85
The number of members that the club has this year is 120.
The number by which it increased is
120 - 85 = 35
Percentage is expressed in terms of 100. Thus, the percentage increase is
35/85 * 100
= 41.2%
The percentage isncrease is 41.2%
what is −2x+y=15? i cant undestand
Step-by-step explanation:
it is a linear equation
Normally two if them are given together to solve
hope it helps
Need ASAP!! Please solve the equation and include steps if you're able to :). Best answer with steps gets Branliest
Answer:
I couldn't do the second question but I did the first and third
1. x=125
3. 11.84
Step-by-step explanation:
2x+6x= 1,000 Set up equation
8x=1,000 Add the like terms-so, 2x and 6x
x=1,000/8 Isolate the x by taking the 8 to the other side to divide
x=125
-2.3x-4.2x=-66.3 Equation
-5.6x= -66.3 Add -2.3 and -4.2 because both r negative
x=-66.3/-5.6 isolate x bu dividing
x= 11.84 Rounded answer
A particular bacterium population is found to double the in 20 minutes. If a laboratory culture
begins with a population of P=340 of this bacteria and there is no change in the growth rate, how
many bacteria will be present in t=37 minutes?
Hint: Use equation P = Poekt, where k is the relative growth. Round to two decimal places.
The bacteria present at t=37 minutes is found to be 8.40, with no change in growth rate.
What does population growth exponentially mean?When a population's per capita growth rate remains constant, regardless of population size, exponential growth occurs, causing the population to grow exponentially as the population increases.
Given:
P = 340
It has been discovered that a specific bacterial population doubles in 20 minutes.
k = 2/20 = 0.1
t = 37 minutes
We know that,
P = P₀[tex]e^{kt}[/tex]
340 = P₀([tex]e^{0.1*37}[/tex])
340 =P₀(40.44)
P₀ = 8.40
As a result, the bacteria that will be present in t=37 minutes is found to be 8.40 with no change in growth rate.
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Marsha used a graphing calculator to graph an expense and a revenue function for her family’s printing business. The graph looked like the one below.
The break-even points for her graph are given approximately as follows:
C. 15 and 47.
Expense, revenue and break-even pointThe expenses and the revenue are defined as follows:
Expenses: amount spent by the person/company to develop each unit of the product, that is, the cost of the product.Revenue: amount earned by the person/company for each unit of the product sold.The break-even points are the points in which the expenses and the revenue are equal.
In the context of this problem, the functions are given as follows:
Revenue: given by the parabola.Expenses: Given by the line.The break-even point is given by the intersection of the two curves, which happen around x = 15 and x = 47, hence option C is the correct option.
Missing informationThe problem is given by the image at the end of the answer.
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what is the highest in order from least to greatest
Answer:
Least to greatest: 1. International finance center
2. Petronas towers
3. Zifeng towers
4. Burj Khalifa
Why do visit the zoo on cold days
Answer:
How is this math?
Step-by-step explanation:
Answer:
Visiting the zoo on cold days limits the number of people there and it isn't too hot so you don't stand in the sweltering heat. Besides, on cold days, the animals may be in a better mood, but be cautioned, remember to bring a jacket just in case.
Step-by-step explanation:
In survey, 9 out of 11 doctors recommended a certain medicine. If 88 doctors were surveyed, how many doctors recommended the medicine? please answer this asap
Answer:
72 doctors recommended the medicine
Step-by-step explanation:
9 out of 11 doctors recommended the medicine, making it 9/11 there are 88 doctors in total 9/11 doctors out of 88 doctors recommended the medicineso, this becomes multiplication. 9/11*88/1 you get 72What is the answer to this
|-0.4| ?
Answer:
0.4
Step-by-step explanation:
The absolute value is just the number in the line things but positive.
The absolute value is the distance between a number and zero. The distance between − 0.4 and 0 is 0.4
if |-0.4| is all that is in the question it is 0.4
3×(9-4)³ - 46×3
A) 1
B) 237
C) 711
D) 987
Answer:
237
Step-by-step explanation:
3×(9-4)³ - 46×3
subtract 4 from 9 to get 5
3x5³-46x3
calculate 5 to the power of 3 and get 125
3x125-46x3
multiply 3 and 125 to get 375.
375-46x3
Multiply 46 and 3 to get 138
375-138
subtract 138 from 375 to get 237.
And there's your answer
You can follow the rule of BODMAS.
BODMAS stands for Bracket, Of, Division, Multiplication, Addition, Subtraction
By following the rule of BODMAS, the solution will be like this:
3×(5)³ - 46×3
= 3×125 - 46×3
= 375 - 138
= 237
I hope my explanation has helped you.
You can do well to declare this answer as the Brainiest Answer.
Thanks so much
satisfy this equation x + |y| = y + |x|
IF -10 ≤ x ≤ 10 and -10 ≤ y ≤ 10
The equation x + |y| = y + |x| that contains the absolute values of x and y, is satisfied when the values of x and y are given by the iniquities;
0 ≤ x ≤ 10 and 0 ≤ y ≤ 10What is an absolute value?The absolute value or modulus of a real number gives its non negative value irrespective of the sign (positive or negative) of the number.
The given equation is presented as follows;
x + |y| = y + |x|
The possible values of x and y are;
-10 ≤ x ≤ 10 and -10 ≤ y ≤ 10
Collecting the absolute values of the equation on one side gives;
|y| - |x| = y - x, which gives;
+y - +x = y - x
The equation is therefore satisfied when both x and y are larger than zero.
Therefore, x + |y| = y + |x|, gives;
0 ≤ x ≤ 10, and 0 ≤ y ≤ 10
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What is -3 times 4??
Answer:
-12
Step-by-step explanation:
hope it helps
have a nice evening