Answer:
Step-by-step explanation:
Fraction :x/y
numerator x = y - 2
Now the fraction can be written as: (y-2)/y
3 is added to both denominator and numerator.
After adding 3, the new fraction = [tex]\frac{y-2 +3 }{y + 3 } = \frac{y+ 1 }{y +3}[/tex]
The sum of the new fraction and the original fraction is 53/35
[tex]\frac{y+1}{y+3} + \frac{y-2}{y} = \frac{53}{35}\\\\\frac{(y+1)*y}{(y+3)*y}+\frac{(y-2)*(y+3)}{y(y+3)}=\frac{53}{35}\\\\\frac{y^{2}+y}{y^{2}+3y}+\frac{y^{2}+y-6}{y^{2}+3y}=\frac{53}{35}\\\\\frac{y^{2}+y+y^{2}+y-6}{y^{2}+3y}=\frac{53}{35}\\\\\frac{2y^{2} + 2y - 6}{y^{2}+3y}=\frac{53}{35}\\\\[/tex]
35*(2y² + 2y - 6) = 53 *(y² + 3y)
35*2y² + 2y * 35 - 6*35 = 53 *y² + 53*3y
70y² + 70y - 210 = 53y² + 159y
70y² + 70y - 210 - 53y² - 159y = 0
70y² - 53y² + 70y - 159y - 210 = 0
17y² - 89y - 210 = 0
Answer:
17y^2 - 89y - 210 = 0
Step-by-step explanation:
Original fraction: x/y
The numerator is 2 les than the denominator, x = y - 2
Original fraction: (y - 2)/y
New fraction:
Add 3 to the numerator and denominator of the original fraction:
(y - 2 + 3)/(y + 3) = (y + 1)/(y + 3)
Add the new fraction and old fraction and get 53/35.
(y - 2)/y + (y + 1)/(y + 3) = 53/35
35y(y + 3)[(y - 2)/y] + 35y(y + 3)[(y + 1)/(y + 3)] = 35y(y + 3)(53/35)
35(y + 3)(y - 2) + 35y(y + 1) = 53(y^2 + 3y)
35(y^2 + y - 6) + 35(y^2 + y) = 53y^2 + 159y
17y^2 - 89y - 210 = 0
You have a budget of $1,900 per week for employees. Employees are pald $11 per hour and work 40 hours per week.
Ignoring overhead, how many employees can you hire ?
[tex]\boldsymbol{4}[/tex] employees were hired by the company.
Define unit method.Amount of total budget [tex]=\$1,900[/tex]
Amount paid to an employee per hour [tex]=\$11[/tex]
Number of hours for which an employee worked per week [tex]=40[/tex]
So,
Total amount paid to an employee [tex]=11\times 40[/tex]
[tex]=\$440[/tex]
Number of employees hired [tex]=4.3[/tex]
[tex]\approx 4[/tex]
So, [tex]\boldsymbol{4}[/tex] employees were hired by the company.
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Ignoring overhead, you can hire 4 employees.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
You have a budget of $1,900 per week for employees.
Employees are paid $11 per hour and work 40 hours per week.
That means,
11 x 40 = $440 per week.
The number of employees = 1900/440
= 4.3
≈ 4
Therefore, 4 number of employees.
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The perimeter of a rectanglar field is 334 yards. If the widths the field is 78 yards, what is its length
Answer:
The length of rectangular field is 129 yards.
Step-by-step explanation:
Given that
Perimeter = P = 334 yards
Width = w = 78 yards
Length = l = ??
We will use the perimeter of the formula to find the length of rectangle.
The perimeter of a rectangle is given by:
[tex]P = 2(l+w)[/tex]
Putting the values of perimeter and width
[tex]334 = 2(l+38)\\334 = 2l+76\\334-76 = 2l+76-76\\258 = 2l\\\frac{2l}{2} = \frac{258}{2}\\l = 129[/tex]
Hence,
The length of rectangular field is 129 yards.
If m ≤ f(x) ≤ M for a ≤ x ≤ b, where m is the absolute minimum and M is the absolute maximum of f on the interval [a, b], then
m(b − a) ≤
b
f(x) dx
a
≤ M(b − a).
Use this property to estimate the value of the integral.
2
3
1 + x2
dx
0
Answer:
smaller value is 1.2
larger value is 6
Step-by-step explanation:
[tex]f(x)=\frac{3}{1+x^{2} }[/tex]
when x=a=0, one has
[tex]f(0)=\frac{3}{1+0^{2} } \\f(0)=3[/tex]
now, when x=b=2, one has
[tex]f(2)=\frac{3}{1+2^{2} } \\f(2)=\frac{3}{5}[/tex]
Therefore, the absolute minumun is
[tex]m=\frac{3}{5}[/tex]
and the absolute maximun is
[tex]M=3[/tex]
The approximation to the integral is
[tex]\frac{3}{5}(2-0)\leq \int\limits^2_0 {f(x)} \, dx \leq 3(2-0)[/tex]
hence
[tex]\frac{3}{5}(2)\leq \int\limits^2_0 {f(x)} \, dx \leq 3(2)\\\frac{6}{5} \leq \int\limits^2_0 {f(x)} \, dx \leq 6\\1.2 \leq \int\limits^2_0 {f(x)} \, dx \leq 6[/tex]
Help please! I’ll give brainliest!
Answer:
Corresponding
congruent interior
equation 9x+8=4x+18
angle measure 26
Explanation:
9x+8=4x+18
-4x = -4x
5x+8=18
-8 = -8
5x=10
x=10/5
x=2
---
so... now plug in 9(2)+8 = 18+8=26degrees
to confirm the angle should be the same for the next one
4x+18=26
solve for x
26-18=4x
8=4x
8/4=x
2=x
find the value of x of this question
perpendicular=p=8cm
Hypontenuse =h =10cm
We need to find base=bAccording to Pythagoras thereon
[tex]{\boxed{\sf b^2=h^2-p^2}}[/tex]
Substitutethe values[tex]\longrightarrow[/tex][tex]\sf b^2=10^2-p^2[/tex]
[tex]\longrightarrow[/tex][tex]\sf b={\sqrt {10^2-8^2}}[/tex]
[tex]\longrightarrow[/tex][tex]\sf b={\sqrt{100-64}}[/tex]
[tex]\longrightarrow[/tex][tex]\bf b={\sqrt {36}}[/tex]
[tex]\longrightarrow[/tex][tex]\sf b=6[/tex]
[tex]\therefore[/tex][tex]\overline{BC}=6cm[/tex]
BD=BC+CD
[tex]\longrightarrow[/tex][tex]BD=9+6[/tex]
[tex]\longrightarrow[/tex][tex]BD=15cm [/tex]
Now in [tex]\triangle ABD [/tex]Perpendicular=p=8cm
Base =b=15cm
We need to find Hypontenuse =AD(x)According to Pythagoras thereon
[tex]{\boxed {\sf h^2=p^2+b^2}}[/tex]
Substitute the values[tex]\longrightarrow[/tex][tex]\sf h^2=8^2+15^2 [/tex]
[tex]\longrightarrow[/tex][tex]\sf h={\sqrt {8^2+15^2}}[/tex]
[tex]\longrightarrow[/tex][tex]\sf h={\sqrt {64+225}}[/tex]
[tex]\longrightarrow[/tex][tex]\sf h={\sqrt {289}}[/tex]
[tex]\longrightarrow[/tex][tex]\sf h=17cm [/tex]
[tex]\therefore[/tex][tex]{\underline{\boxed{\bf x=17cm}}}[/tex]
Hypotenuse a =?; b =40; c=50
a² = b² + c²
a² = 40² + 50²
a² = 1600 + 2500
a² = 4100
a = √4100
a = 64.03
A storage company designs a rectangular box with an open top that has a volume of 220 in3. Each box has a length that is three times its width. Calculate the minimum surface area of one of these boxes. Round your answer to three decimal places.
Answer:
191.016 in²
Step-by-step explanation:
Let the volume of the cube be V = lwh where l = length of box, w = width of box and h = height of box.
Now l = 3w.
So, V = lwh = (3w)wh = 3w²h
h = V/3w²
Since the rectangular box is open at the top, its total surface area is A = lw + 2lh + 2wh
substituting l = 3w, we have
= (3w)w + 2h(l + w)
= 3w + 2h(3w + w)
= 3w² + 2h(4w)
= 3w² + 8wh
substituting h = V/3w²
= 3w² + 8w(V/3w²)
A = 3w² + 8V/3w
Differentiating A with respect to w and equating it to zero, we have
dA/dw = d[3w² + 8V/3w]dw
dA/dw = d3w²/dw + d(8V/3w)/dw
dA/dw = 6w - 8V/3w²
dA/dw = 0
6w - 8V/3w² = 0
6w = 8V/3w²
6w³ = 8V/3
w³ = 8V/(3 × 6)
w³ = 4V/9
w = ∛(4V/9)
substituting V = 220 in³, we find the minimum value for the width
w = ∛(4 × 220 in³/9)
w = ∛97.7778
w = 4.607 in
To determine if this is a minimum value of width which gives minimum area, we take the second derivative of A. So,
d²A/dw² = d(6w - 8V/3w²)/dw
= 6 + 16V/3w³
substituting w³ = 4V/9, we have
d²A/dw² = 6 + 16V/3(4V/9)
= 6 + (16 × 9)/(3 × 4)
= 6 + 4 × 3
= 6 + 12
= 18
Since d²A/dw² = 18 > 0 , w = ∛(4V/9) = 4.607 in gives a minimum for the surface area.
So, we calculate this area by substituting w = 4.608 in. So,
A = 3w² + 8V/3w
= 3 × (4.607 in)² + (8 × 220 in³)/(3 × 4.607 in)
= 63.6733 in² + 1,760 in³/13.821 in
= 63.6733 in² + 127.3424 in²
= 191.0157 in²
≅ 191.016 in² to three decimal places.
The height of a cylinder with a fixed radius of 6 cm is increasing at the rate of 3 cm/min. Find the rate of change of the volume of the cylinder (with respect to
time) when the height is 20 cm.
A. 36Pi
B. 108pi
C. 360pi
D. None of these
Answer:
108π cm^3/min
Step-by-step explanation:
At a time of t min, let the height be h cm
The volume of a cylinder;
V = π r^2 h
= 36π h
differentiating both sides with respect to t;
dV/dt = 36π dh/dt
but dh/dt = 3 cm/min
dV/dt = 36π(3) = 108π cm^3/min
In how many ways can a president, vice president, and secretary be chosen from a class of 20 girls and 30 boys if the president must be a girl and the vice president a boy?
Given:
Number of girls = 20
Number of boys = 30
The president must be a girl and the vice president a boy
To find:
Number of ways to choose a president, vice president, and secretary.
Solution:
The president must be a girl and the vice president a boy. So, out of three students 1 is girl and 1 is boy. Third student can be a girl or a boy.
Total number of ways = Selecting 2 boys and 1 girl + Selecting 1 boy and 2 girls
[tex]=^{30}C_2\times ^{20}C_1+^{30}C_1\times ^{20}C_2[/tex]
[tex]=\dfrac{30!}{2!(30-2)!}\times \dfrac{20!}{1!(20-1)!}+\dfrac{30!}{1!(30-1)!}\times \dfrac{20!}{2!(20-2)!}[/tex]
[tex]=\dfrac{30\times 29\times 28!}{2\times 1\times 28!}\times \dfrac{20\times 19!}{19!}+\dfrac{30\times 29!}{29!}\times \dfrac{20\times 19\times 18!}{2\times 1\times 18!}[/tex]
[tex]=\dfrac{30\times 29}{2}\times 20+20\times \dfrac{20\times 19}{2}[/tex]
[tex]=8700+3800[/tex]
[tex]=12500[/tex]
Therefore, the required number of ways is 12500.
The three graphs represent the types of solutions that are possible for a system of equations. Which graph represents a system of equations with no solution? On a coordinate plane, 2 lines have a positive slope. On a coordinate plane, 2 lines are parallel to each other. On a coordinate plane, 2 lines have a positive slope.
Answer:
the second one
Step-by-step explanation:
Answer:
The answer is B.) The second graph
Step-by-step explanation:
I just did he instruction on edge and got it right
Which statement is false? All points with an x-value of 3 are located in Quadrant I. There is only one point on the coordinate plane that is on both the x- and y-axes. All points with an x-value of 0 are located on the y-axis. There is only one point on the coordinate plane with an x-value of 2 and a y-value of 2.
Answer: Choice A) All points with an x-value of 3 are located in Quadrant I.
We can show it is false through the use of a counter example. For instance, the point (3, -5) is not in quadrant 1, but rather in quadrant 4.
We would need to say "all points with x value 3 and positive y value" to ensure the point is in quadrant 1.
The false statement:
All points with an x-value of 3 are located in Quadrant I.
What are coordinates?Coordinates are a pair of integers (Cartesian coordinates), or occasionally a letter and a number, that identify a certain place on a grid, often referred to as a coordinate plane.
From the given choices:
Let the statement is true.
All points with an x-value of 3 are located in Quadrant I.
Let the coordinate point (3, -7)
This point lies in the fourth quadrant.
Which is contradiction.
Therefore, the statement is false.
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PLS HELP ME I ADDED SCREENSHOT i made sure to add it this time
Answer:
-(400/9)
Step-by-step explanation:
-44(4/9)
answer A
Please answer this question (the photo attached)! I will give brainliest to the correct answer!
using the arithmetic sequence 7 10 13 16 find the 6th term of the sequence
If the radius of the circle is 7 cm, find its area, rounded to 2 decimal places.
A= _______ cm2
Answer:
153.94
Step-by-step explanation:
The formula for area is pi*radius^2
the radius is 7, so we do pi7^2 which is 49pi
49pi is 153.93804 which is 153.94 rounded to two decimal places
simply 8×4³+2×4⁴ giving you answer in the form of 4^b
Answer:
4^5
Step-by-step explanation:
8×4³+2×4⁴
4×2×4^3+2×4^4
4^4×2+2×4^4
4^4(2+2)
4^4×4
4^5
So answer is 4^5
Find the value of 2y if 2x - y = 5 and
x + y = 4.
Answer:
the value of 2y would be 2
Step-by-step explanation: 3+1=4 so you would plug the 3 in for x and the 1 in for y to get 5
PLEASSSSEEE SOMEONEE HELPPP ILL DO ANYTHING
Answer:
[tex]m=\frac{1}{4}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Point (0, 1)
Point (4, 2)
Step 2: Find slope m
Substitute: [tex]m=\frac{2-1}{4-0}[/tex]Subtract: [tex]m=\frac{1}{4}[/tex]PLEASE HELP! WILL GIVE BRAINLIEST!
1. for a party, the family bought 24 pizzas for $12.50 each and 36 bottles of soda for $1.20 each. how much did the family spend on pizza? fill in the blank with the numerical answer only. the family spent $_______ on pizza.
2. for a party, the family bought 24 pizzas for $12.50 each and 36 bottles of soda for $1.20 each. how much did the family spend on soda? fill in the blank with the numerical answer only. the family spent $_______ on soda.
3. for a party, the family bought 24 pizzas for $12.50 each and 36 bottles of soda for $1.20 each. how much did the family spend in all? fill in the blank with the numerical answer only. the family spent $_______ in all.
Answer:
Step-by-step explanation: for a party, the family bought 24 pizzas for $12.50 each and 36 bottles of soda for $1.20 each. how much did the family spend on pizza? fill in the blank with the numerical answer only. the family spent $_______ on pizza.
The family spent 300$ on pizza
Answer:
Answer
Step-by-step explanation:
for pizza: $300.00
for soda: $43.20
In all: 343.20
Write an equation of the line that passes through a pair of points (2,3),(4,-2)
Answer:
y=-5/2x+13
Step-by-step explanation:
m=(-2)-3/4-2
m=-5/2
y-y=m(x-x1)
y-3=-5/2(x-2)
y-3=-5/2x+10
+3 +3
y=-5/2x+13
Find the slope (0,0) and (4.16)
Find the slope (0,0) and (4,8)
Answer:
first one is 4
second is 2
Step-by-step explanation:
let me know if you need to show work
Answer:
first one is 4, 2nd one is 2
Step-by-step explanation:
Make a fraction become a decimal
1. 55/300
2. 1 1/2
3.5/9
4. 2 3/4
5. 9/11
6. 4 1/9
Answer:
1. 0.18333333333
2. 1.5
3. 0.55555556
4. 2.75
5. 0.81818181818
6. 4.1111111111
Have a nice day, brainliest Please? :)
A man buys furniture that has a list price of $255. He is allowed a discount of 12%
but must pay a sales tax of 3% on the cost. Which of the following is the amount he
actually pays for the furniture:
(A) $217.67
(B) $231.13 (C) $224.40 (D) $232.50 (E)
none of these.
Answer:
Option B. $231.13 is the correct answer.
Step-by-step explanation:
Given that
Listed price of furniture = P = $255
Discount = d = 12%
Sales tax = s = 3%
First of all, we have to find the discounted price by calculating the discount first
So,
[tex]Discount = 12\%\ of\ P\\= 0.12*255\\= 30.6[/tex]
Discounted Price:
[tex]= Listed\ Price - Discount\\= 255 - 30.6\\= 224.4[/tex]
The sales tax will be calculated on the discounted price
So,
[tex]Sales\ tax = 3\%\ of\ Discounted\ price\\= 0.03 * 224.4\\= 6.732[/tex]
Now,
[tex]Final\ price\ of\ furniture = Discounted\ price + Sales\ tax\\= 224.4 + 6.732\\=231.132[/tex]
He will actually pay $231.132 for the furniture.
Hence,
Option B. $231.13 is the correct answer.
the floor of a shed has an area of 77 square feet the floor is in the shape of a rectangle whose lenght is 3 ft. less than twice the width find the lenght and the width of the floor of the shed use formula area= lenght *width the width of thee floor of the shed is how many feet ft.
Answer:
x=40
Step-by-step explanation:
2−3=77
2−3+3=77+3
2=77+3
2x=80
2x/2=80/2
x=80/2
x=40
Is 518 decimal number
Answer:
no
Step-by-step explanation:
because there is supposed to be a decimal point for example 5.18 there needs to be a period
Answer:
what do you mean there is not decimal in the number you could make it a decimal tho
it would be 5.18 as a decimal
Step-by-step explanation:
What is the value of x in the equation 3x-15=-18
Answer:
x = -1
Step-by-step explanation:
3x - 15 = -18
Add 15 to both sides;
3x = -3
Divide both sides by 3;
x = -1
Answer:
X=-1
Step-by-step explanation:
3x-15=-18
+15 +15
3x=-3
x=-1
what is 9k + 1 = ─9 + 7k solved for the variable???
Answer:
k = -5
Step-by-step explanation:
The variable is k
9k + 1 = -9 + 7k
-7k -1
2k = -10
2k/2 -10/2
k = -5
:)
At the store,Finlay bought 48 ounces of cand for $4.How many ounces could he buy for $1?
Answer:
12
Step-by-step explanation:
Answer:
12 ounces
Step-by-step explanation:
48÷4 = 12 ounces
the longer diagonal is 4 more than the shorter diagonal of a kite. The area is 5 times the shorter diagonal. If the shorter side is 6 cm. Find the longer diagonal and the area.
Write the equation of a line PERPENDICULAR to y = 4x + 3 that passes through the point (4, 1)
Answer:
y = 1/4x
Step-by-step explanation:
The slope changes from 4 to 1/4
so,
y = 1/4x + b
Then, plug in (4,1) into the equation
1 = 1/4(4) + b
1 = 1 + b
b = 0
y = 1/4x + 0
y = 1/4x