Let Length of each Plan A workout be [tex] a[/tex]
and Length of each Plan B workout be $b$
on Wednesday,
$5a+3b=7$
$2a+12b=19$
multiply equation one by $4$ and subtract equation two from it
to get,
$18a=9$ or $a=\frac12$
substitute $a$ in eq 2. to get $b$, $12b=18\implies b=\frac32$
what is the answer to (x+1)(3x+2)
2. The ratio of
the profit, cost of
materials and labour
in the production of
an article is 5:7:13
respectively. If the
cost of materials is Le
840 more than that of
labour, find the total
cost of producing the
article
Answer:
3500Step-by-step explanation:
Given the ratio of the profit, cost of materials and labour in the production of
an article to be 5:7:13 respectively, total ratio = 5+7+13 = 25
If the cost of labour is x, the cost of material will be 840+x (since the cost of materials is Le 840 more than that of labour) .
Let the total cost of producing the article be y.
Cost of labour = 13/25 * y = x
Cost of labour = 13y/25 = x.................... 1
Cost of material = 7/25*y = 840+x
Cost of material = 7y/25 = 840+x ..................... 2
From 1, 13y = 25x
x = 13y/25 ................... 3
Substituting equation 3 into 2:
7y/25 = 840+x
7y/25 = 840+13y/25
collect the like terms:
7y/25 - 13y/25 = 840
-6y/25 = 840
-6y = 25*840
y = 25*840/6
y = 3,500
Hence the total cost of producing the article is 3500
Why do you think that when subtracting a negative
number, in reality you are adding it? (For example: 1-
(-1) = 1+1=2)
Answer:
See explanation
Step-by-step explanation:
When we have a positive number and a negative number, let's imagine it with a number line.
<-----------0----------->
If we have the positive number 1:
<-----------0--1-------->
And we want to subtract 1 from it, the number would move to the left
1 - 1 = 0
<-----------0----------->
However, if we were to subtract a negative number, they are opposites. It can't move to the left because that's what a positive number does. The only other way to go: right.
1 + -1 = 2
<-----------0--1--2----->
Hope this helped!
Someone please help! Thank you
Answer:
Hey there!
We can write a equations here:
3x+y=180
Also, since all of the angles have 3x on the outside, then y must be constant.
3y=180
y=60
Thus, for x, we have 3x+60=180, 3x=120, x=40.
2x+6y
2(40)+6(60)
80+360
440.
Let me know if this helps :)
A bus travels from Station A to Station B, and a truck travels from Station B to Station A on the same road. The speed of the bus is 54 km/h, and the speed of the truck is 48 km/h. After they pass each other, they continue drive to the destinations. Once they reach the destination, they turn around to continue travel along the same road. When they meet again, the bus travels 216 km more than the truck. What is the distance between the two stations in kilometers?
Answer:
The distance between the two train stations is 1728 km
Step-by-step explanation:
The speed of the bus = 54 km/h
The speed of the truck = 48 km/h
When the bus and truck meet again, the distance covered by the bus = 216 km more than he distance traveled by the truck
Let the distance between the two train stations = x
Let the location where they first meet be y from station A we have;
The location where they meet again = y - 216 km
Therefore, we have;
Location where they
The time for the truck and the bus to meet again = t
Therefore, 54 × t - 48 × t = 216 km
6·t = 216 km
t = 36 hours
Therefore, the time for the bus to travel x + 216 km = 36 hours
54 × 36 = 1944 = x + 216
x = 1944 - 216 = 1728 km
The distance between the two train stations = 1728 km.
What is the center of a circle with the equation (x - 6)2 + (y + 2)2 = 9?
A)
(6,2)
B)
(6,-2)
0)
(-6, 2)
D)
(-6, -2)
Answer:
B. (6,-2)
Step-by-step explanation:
The equation of a circle is (x-h)^2+(y-k)^2=r^2
The center of the circle is (h,k)
So, in this problem, h is 6 and k is -2, so the center of this circle is (6,-2).
Prime factors of 2601
Answer:
The prime factors are: 3 x 3 x 17 x 17. or also written as { 3, 3, 17, 17 }
Step-by-step explanation:
Person above agrees
Four witches are making a brew.Patricia puts in x frogs legs.sheila puts in five more than patricia.Anne puts double the amount that Sheila adds,and Winifred adds three times the number Sheila adds.
write down an algebraic expression for:
Sheila. Anne. Winifred
Answer:
see explanation
Step-by-step explanation:
Given Patricia puts in x frogs legs, then
Sheila puts in x + 5 ( 5 more than Patricia )
Anne puts in 2(x + 5) ( double the amount of Anne )
Winifred puts in 3(x + 5) ( three times the number of Sheila )
(I) Factorice completely
x³- 6x² + 11x-6
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
Factor [tex]x^3 - 6x^2 + 11x - 6[/tex]
[tex]x^3 - 6x^2 + 11x - 6[/tex]
= [tex]( x - 1) ( x - 2) ( x - 3)[/tex]
So you would be : [tex]( x - 1) ( x - 2) ( x - 3)[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
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If this helped you, could you maybe give brainliest..?
Also Have a great day/night!
❀*May*❀
A sprinter run 400 meter in 54 second.what about s the runner's average running rate in meter per second?round to the nearest tenth
Answer:
7.4
Step-by-step explanation:
400 ÷ 54 =7.407407...
7.407407... rounded to the nearest tenth is 7.4
I hope this helps... and plz mark me brainliest!!!
If a population grows 3.5% per year, how much does it grow per decade? A. 35% B. 41.1% C. 38% D. 27.6%
Answer: 35%
Step-by-step explanation: It grows 3.5% every year. A decade is 10 years. 10 x 3.5% = 35% because you move the decimal one point to the right.
The population grows 41.1% per decade. Therefore, option B is the correct answer.
What is population growth and population decrease formula?If a constant rate of growth be R% per annum, then population after n years = P(1+R/100)ⁿ.
Given that, a population grows 3.5% per year.
Now, D(n)=P(1+R/100)ⁿ
Let P=1
So, D(1)=1(1+0.035)¹
D(1)=1.035
Similarly per 10 years with the same rate
D(10)=1(1+0.035)¹⁰
= (1.035)¹⁰
= 1.41059
= 1.411-1 (Initial population is 1)
= 0.411
= 0.411×100
= 41.1%
The population grows 41.1% per decade. Therefore, option B is the correct answer.
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Simplify
(3x + 14) + (19x - 35)
Answer:
22x -21
Step-by-step explanation:
(3x + 14) + (19x - 35)
Combine like terms
3x+19x + 14-35
22x -21
Simplify 7.5 + n + 9.63.
Answer: Hi!
The only thing we're able to do to simplify this equation is combine our like terms. We have two like terms in the equation: 7.5 and 9.63.
7.5 + 9.63 = 17.13
Our equation now looks like this:
n + 17.13
We have nothing left to simplify, so we're done!
Hope this helps!
I got this wrong please help me get the right answer in the first little box marked in red. thx
Answer:
The inverse is 1/2x +2
Step-by-step explanation:
f(x) = 2x-4
y= 2x-4
To find the inverse
Exchange x and y
x = 2y-4
Solve for y
Add 4 to each side
x+4 = 2y
Divide by 2
x/2 + 4/2 = 2y/2
1/2x +2 = y
The inverse is 1/2x +2
What is the area of the trapezoid shown below?
Answer:
180 units
Step-by-step explanation:
In order to solve this, we need to find the length of the missing side of the triangle using the Pythagorean theorem.
a²+b²=c²
a= 7
b=x
c= 25
7²+x²=25²
49+x²=625
Subtract 49 from both sides
x²=576
x=24
The length of the missing side of the triangle is 24, which is also the base of the triangle. We need to find the area of the triangle so we use the formula for the area of a triangle, A=1/2bh.
A= 1/2 (24 x 7)
A=84
Now, we need to find the area of the rectangle.
Formula for area of rectangle: A= bh
A= bh
A= 4 x 24
A= 96
Next, we add the areas of both shapes to get the area of the entire figure.
96+84=180
Area of figure= 180
Answer:
area = 180
Step-by-step explanation:
will make it simple and short
area of a trapezoid = (a + b) h/2
h = sqrt(25² - 7²) = 24
Area = (4 + 11) * 24/2
area = 180
You have this information about ΔABC, ΔFDE, and ΔGIH:
AB = DF
AB = GI
BC = HI
DE = HI
m∠B = m∠D = m∠I
Which triangles must be congruent?
The triangle ABC, triangle FDE, and triangle GIH are congruent with each other.
What is a triangle?Three sides and three internal angles define a triangle, a basic shape. The symbol is used to represent one of the geometric shapes in which the three corners are connected to one another. Triangles are categorized according to their sides into numerous different forms.
As per the given data in the question,
Sides AB = DF, AB = GI, BC = HI, and DE = HI are equal to each other.
Also, the angles, m∠B = m∠D = m∠I are equal.
Then by the property of the side angle side all the triangles are congruent with each other.
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Answer:
A. ΔABC, ΔFDE, and ΔGIH
Question 9(Multiple Choice Worth 4 points)
(02.05 LC)
Which of the following statements best describes the effect of replacing the
graph of y = f(x) with the graph of y = f(x - 9)?
The graph of y = f(x) will shift up 9 units.
The graph of y = f(x) will shift down 9 units.
The graph of y = f(x) will shift left 9 units.
The graph of y = f(x) will shift right 9 units.
Answer: D) right 9 units
Step-by-step explanation:
The Vertex form of a quadratic equation is: y = a(x - h)² + k where
a is the vertical stretch or shrink(x, h) is the vertex→ h is the horizontal shift (+ is right, - is left)
→ k is the vertical shift (+ is up, - is down)
y = f(x - 9)
↓
h=9
Since h is positive, the graph moves 9 units to the RIGHT
Answer:
The graph of y = f(x) will shift right 9 units.
Step-by-step explanation:
If the -9 is inside the parenthesis, the graph g(x) shifts 9 points to the right.
the product 9f 2 numbers is 16/9 . if one number is 5 /2 find the other number
Answer:
The answer is 32/45Step-by-step explanation:
Let the number be x
The product of two numbers is 16/9
That's
x × y = 16/9
One of the numbers is 5/2
That's
y = 5/2
So we have
[tex] \frac{5}{2} x = \frac{16}{9} [/tex]
Multiply through by the LCM
The LCM of 2 and 9 is 18
That's
[tex]18 \times \frac{5}{2} x = \frac{16}{9} \times 18[/tex]
9 × 5x = 16 × 2
45x = 32
Divide both sides by 45
we have the final answer as
[tex]x = \frac{32}{45} [/tex]
Hope this helps you
4x3+ 13x2 + 5x- 4 is divided by x+ 1?
Answer:
The quotient to this equation is 4x² + 13x + 1
Step-by-step explanation:
When we divide exponents, we subtract the exponential numbers.
4x³ + 13x² + 5x - 4 / x + 1
Now, we divide. For this problem, we are only dividing the like terms of x because anything divided by 1 will equal to itself.
4x² + 13x + 5 - 4
Now, we combine like terms.
4x² + 13x + 1
A carpenter has a 10 1/2 foot wood plank. He cuts off 4 1/4 feet to replace a deck board as well as 3 2/3 feet to repair a step. He uses the rest of the plank for a shelf. How many feet of wood does the carpenter have for the shelf? PLEASE SHOW YOUR WORK AND EXPLAIN HOW YOU GOT THE ANSWER PLEASE I WILL MARK YOU BRAINIEST.
Answer:
The carpenter used 2 7/4 feet of plank for the shelf
Step-by-step explanation:
Total length of plank =10 1/2 foot
He used
For Deck board=4 1/4 feet
Step=3 2/3 feet
Shelf=x feet
Total plank=deck board + step + shelf
10 1/2 = 4 1/4 + 3 2/3 + x
Change the fractions
21/2 = 17/4 + 11/3 + x
Add 17/4 + 11/3
21/2 =51+44/12 + x
21/2= 95/12 + x
Collect like terms
21/2 - 95/12 =x
126-95/12 = x
31/12=x
2 7/12 =x
Therefore, the carpenter used 2 7/4 feet of plank for the shelf
Answer:
Step-by-step explanation:
Total length of plank =10 1/2 foot
He used
For Deck board=4 1/4
Step=3 2/3
Shelf=x
Total plank=deck board + step + shelf
10 1/2 = 4 1/4 + 3 2/3 + x
While sailing, Jacob is 150 feet from a lighthouse. The angle of elevation from his feet on the boat (at sea level) to the top of the lighthouse is 48°
What can you conclude about the height of the lighthouse, with respect to Jacob's distance from the lighthouse? Explain your answer.
Answer:
The height of the lighthouse is approximately 166.6 feet.
Step-by-step explanation:
Let the height of the lighthouse be represented by s, then;
Tan 48° = (opposite) ÷ (adjacent)
Tan 48° = s ÷ 150
⇒ s = 150 × Tan 48°
= 150 × 1.1106
= 166.59
s ≅ 166.6 feet
Therefore, the height of the lighthouse is approximately 166.6 feet.
Answer:
The height of the lighthouse is approximately 42.
Step-by-step explanation:
This situation forms a right triangle so the angles would be 90 and 48
90+48+x=180
138+x=180
x=180-138
x=42
A soccer team has 18 players. 5 of the players have scored at least 4 goals this season. Approximately what percent of the players have scored
at least 4 goals?
Select the best answer from the choices provided.
O A. 1596
OB.
30%
Ос.
6096
D
7596
Answer:30%
Step-by-step explanation:you divide 18 by 100 and then multiply that by 30 and it gives you 5.4 which is close to 5 players. So 30% is the answer
What’s the value of X in this triangle
Answer:
x = 69.4
Step-by-step explanation:
law of sines
sine x/4 = sine 55/3.5
x = ( sine(55) * 4 ) / 3.5
x = inv sine (0.936)
x = 69.4
The citizens of a certain community were asked to choose their favorite pet. The pie chart below shows the distribution of the citizens' answers. If there are 140,000 citizens in the community, how many chose Fish or Cats?
Incomplete Question:
The content of the pie chart is as follows:
Hamsters = 9% ; Snakes = 10% ; Cats = 23%
Birds = 21% ; Dogs = 26% ; Fish = 11%
Answer:
The number of citizens who chose cat or fish is 47,600
Step-by-step explanation:
Given
Number of citizens = 140,000
Required
Determine the number of those that chose fish or cats
First, we need to calculate the percentage of those whose pets are either cats or fish
[tex]Percentage = Cat + Fish[/tex]
Substitute 23% for cat and 11% for fish
[tex]Percentage = 23\% + 11\%[/tex]
[tex]Percentage = 34\%[/tex]
Next, is to multiply the calculated percentage by the number of citizens
[tex]Cat\ or\ Fish = Percentage * Number\ of\ Citizens[/tex]
[tex]Cat\ or\ Fish = 34\% * 140000[/tex]
[tex]Cat\ or\ fish = 47600[/tex]
Hence, the number of citizens who chose cat or fish is 47,600
the number of citizens who chose cat or fish is 47,600
The calculation is as follows;= Number of citizens × total percentage
[tex]= 140,000 \times (23\% + 11\%)\\\\= 140,000 \times 34\%[/tex]
= 47,600
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please i really need help The line plot below displays the fraction of incoming calls answered before the second ring by a group of employees. What fraction of employees answered less than of their incoming calls before the second ring?
Answer:
B
Step-by-step explanation:
If we count the number of points we find out that there are 36 employees
so the fraction must go like x/36
x is the numbers of dots that are less than a 1/2 which are 1/8, 1/4 and 3/8
so x=6
6/36
1/6
so option B
daniel thinks of a number and subtracts 2
from it. He divides 32 by the result. If
his answer is 4, what number does he
think of
Answer:
the number is 126
Step-by-step explanation:
1) multiply each side by 32: (n-2) / 32 = 4
2) subtract 2 from each side: n-2 = 128
3) n = 126
Answer:
130
Step-by-step explanation:
So basically this number, minus 2, divided by 32 is 4, so lets write the unknown number as x.
So, (x-2)/32 = 4.
First multiply both sides by 32 to get rid of the denominator.
(32)(x-2)/32 = 4(32) x-2 = 128
Now the -2 remains to figure out x, so you add 2 to both sides to get rid of the -2.
So, x-2+2 = 128+2, -2 +2 is 0, and 128 +2 is 130, so you have x = 130.
how many are 9 raised to 2 ???
Answer:
[tex]\boxed{81}[/tex]
Step-by-step explanation:
9 raised to 2 is
=> [tex]9^2[/tex]
=> 9 * 9
=> 81
Tuition for one year at the University of Atlantis costs $12,000 per year. Rachel would like to attend this university and will save money each month for the next 3 years. Her parents will contribute $3,000 for her first year's tuition. How much money will Rachel need to save each month to have enough money for the first year of college at the University of Atlantis?
Answer:
250 dollars per month.
Step-by-step explanation:
We first need to subtract the amount of money her parents are giving her.
12000-3000=9000.
Since she is saving money every month for 3 years we have to multiply 3×12=36 months.
We than need to divide how much money she needs by the amount of months she has to get it.
9000÷36=250
Please help I did the first 2 already.
The answer to C is 1.5 or 3/2
Since we know that 2x is equal to 3 because the solution is three and 3+3=6 then we divide 3 by 2 to get 3/2
if the mean of 3 2 x 11 13 14 is 8 find the value of x
Answer:
x=5
Step-by-step explanation:
To find the mean, add up all the numbers and then divide by the number of numbers
(3+ 2+x+ 11+ 13+14)/6 = 8
Multiply each side by 6
(3+ 2+x+ 11+ 13+14) = 48
Combine like terms
43+x = 48
Subtract 43 from each side
x =5
Answer:
[tex]\huge \boxed{{x=5}}[/tex]
Step-by-step explanation:
The mean is the average value of a data set.
[tex]\displaystyle \sf mean = \frac{sum \ of \ terms}{number \ of \ terms}[/tex]
The mean is given solve for x.
[tex]\displaystyle 8 = \frac{3+2+x+11+13+14}{6}[/tex]
Multiply both sides by 6.
[tex]\displaystyle 8(6) = \frac{3+2+x+11+13+14}{6} \times (6)[/tex]
[tex]48=3+2+x+11+13+14[/tex]
Combine the numbers on the right side of the equation.
[tex]48=x+43[/tex]
Subtract 43 from both sides.
[tex]48-43=x+43-43[/tex]
[tex]5=x[/tex]
