Answer:
y=-5x+9
m=-5
b=9
y=5x-4
m=5
b= -4
y=8
m=0
b=8
Step-by-step explanation:
Answer:
1) 15x + 3y = 27 in slope-intercept form.
→y=-5x+9
→m =-5
→b =(0,9)
2) 15x − 3y = 12 in slope-intercept form.
→y =5x-4
→m =5
→b =(0,-4)
3) 2y = 16 in slope-intercept form.
→y =8
→m =0
→b =(0,8)
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 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.
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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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
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:
How do you do this please explain!
Largest prime factor of 35 x the smallest prime factor of 15
Answer:
7x3=21 ... i think
Step-by-step explanation:
the factor of 35 is 1,5,7 and 35 but 7 is the largest prime number like the factors of 15 is 1,3,5 and 15 but 3 is the smallest prime number according to the question the answer is 7x3+21
You plan to run 2 miles, but you only make it \frac{3}{4}
4
3
of the way. How many miles did you run in total?
Answer:
1.5 miles
Step-by-step explanation:
What is the equation for
7x - 4/y =10
in the form y = mx + b?
Answer:
Step-by-step explanation:
assume the equation is (7x-4)/y=10
10y= 7x-4 didvide both sides by 10
y= (7/10)*x - (2/5)
m=7/10
b=-2/5
The equation for 7x - 4/y =10 in the form y = mx + b . The equation in the form
[tex]\(y = mx + b\) is: \[y = \frac{4}{7x - 10}\][/tex]
To rewrite the equation in the form we need to [tex]\(y = mx + b\),[/tex] isolate the term involving y on one side of the equation. Here's the step-by-step process:
Step 1: Add [tex]\(\frac{4}{y}\)[/tex] to both sides of the equation to isolate the 7x term on the left side:
[tex]\[7x = 10 + \frac{4}{y}\][/tex]
Step 2: Get rid of the fraction by multiplying both sides of the equation by y:
[tex]\[7xy = 10y + 4\][/tex]
Step 3: Now, we want to express y alone on one side. To do this, subtract 10y from both sides:
[tex]\[7xy = 10y + 4\][/tex]
Step 4: Factor out y on the left side:
[tex]\[y(7x - 10) = 4\][/tex]
Step 5: Finally, divide both sides by to solve for [tex]\((7x - 10)\)[/tex]
[tex]\[y = \frac{4}{7x - 10}\][/tex]
Now, the equation is in the form where [tex]\(y = mx + b\), \(m\)[/tex] is the coefficient of x and b is the constant term. In this case,[tex]\(m = \frac{4}{7x - 10}\) and \(b\)[/tex] is equal to 0.
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Help please here is a picture:
Answer:
2 1/3, 2 1/4, 2 3/7
Step-by-step explanation:
Mixed Fractions
Mixed fractions are made of an integer part followed by a proper fraction.
Some examples of mixed fractions are:
3 1/2, -4 5/8, 2 2/3
Between two consecutive integers a and a+1, there are infinitely many fractions. The centered number is a 1/2. Any number with its improper fraction part less than 1/2 is closer to a than to a+1.
In our problem, Jayne bought between 2 and 3 pounds of granola. We need to provide a mixed number that is closer to 2 pounds than to 3 pounds.
We can select any number with integer part 2 and a proper fraction less than 1/2.
Examples could be :
2 1/3, 2 1/4, 2 3/7
All of them are less than 2.5
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.
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]
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
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
:)
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.
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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Wayne raked 30 bags of leaves in 3 hours. If he raked the same number of bags each hour, how many bags of leaves did he rake in 1 hour?
Answer:
he raked 10 bags each hour
30/3 = 10
using the arithmetic sequence 7 10 13 16 find the 6th term of the sequence
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:
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]
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
CAN SOMEBODY PLEASE HELO ME!?!?!?
The radius of the unit circle is equal to_____.
•2π
•1
•2
•π
Answer:
r =1
Step-by-step explanation:
The radius of unit circle is 1
Answer:
1
Step-by-step explanation:
is y=-2x proportional
Answer:
no
Step-by-step explanation:
Answer:
Yes, if you are referring to proportionality in general. No if you are referring to a direct proportionality.
Step-by-step explanation:
y = -2x is negatively proportional so it is not directly proportional because y or one quantity decreases when x or another quantity increases. In a directly proportional relationship, as one quantity increases another quantity must increase at the same rate, in other words both must increase thus be positive. When something is proportional it has a constant ratio, and relation.
Direct proportionality or variation is represented by y ∝ x, where ∝ is the symbol used to represent proportionality.
y = kx where k is the constant of proportionality.
Where k = y/x.
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
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
What value of y makes the equation below true?
2y – 25 = 19
44
A
B
22
C
с
-3
oo
D
-6
Please hurry
Answer:
b
Step-by-step explanation:
2*22 = 44
44-25 = 19
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
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? :)
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
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