x - inf - 8 1/5 + inf
x+8 - 0 + +
5x-1 - - 0 +
result + 0 - ║ +
x+8/(5x-1) > 0 if x € ] -inf ; - 8[ U ] 1/5 ; + inf [
=> x < - 8 and x > 1/5
The solution to the inequality (x + 8)/(5x - 1) ≤ 0 is:
x ∈ (-∞, -8] ∪ [1/5, ∞)
We have,
To solve the inequality (x + 8)/(5x - 1) ≤ 0,
We can use the following steps:
Step 1:
Find the critical values of x where the expression (x + 8)/(5x - 1) is equal to zero or undefined.
The expression is undefined when the denominator is equal to zero:
5x - 1 = 0
x = 1/5
The expression is equal to zero when the numerator is equal to zero:
x + 8 = 0
x = -8
Therefore,
The critical values are x = -8 and x = 1/5.
Step 2:
Create a sign chart to determine the sign of the expression (x + 8)/(5x - 1) for each interval between the critical values.
On the interval (-∞, -8), the expression (x + 8)/(5x - 1) is negative if x + 8 is negative, which means x < -8.
On the interval (-8, 1/5), the expression (x + 8)/(5x - 1) is positive if both the numerator and denominator are negative, or if both are positive.
The numerator is negative on this interval, so the expression is positive if the denominator is negative, which means x < 1/5.
On the interval (1/5, ∞), the expression (x + 8)/(5x - 1) is negative if the numerator is negative and the denominator is positive, which means x > 1/5.
Step 3:
Write the solution in interval notation.
Therefore,
The solution to the inequality (x + 8)/(5x - 1) ≤ 0 is:
x ∈ (-∞, -8] ∪ [1/5, ∞)
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Use a diagram to show that (3x+1)(x+2) is equivalent to 3x2+7x+2.
The circumference of a circle is 15pi centimeters. What is the area of the circle in terms of pi?
Answer: [tex]56.25\pi[/tex]
Step-by-step explanation:
The circumference of a circle can be found using [tex]d\pi[/tex], where d is the diameter. In this case, we can clearly see the diameter is 15.
Next, we must find the radius as the formula for the area of a circle is [tex]\pi r^2[/tex]
The radius is half of the diameter. [tex]\frac{15}{2} =7.5[/tex]
Now sub in this value for the formula of the area of a circle
[tex]\pi r^2\\\\\pi (7.5)^2\\\\56.25\pi[/tex]
Answer:
56.25[tex]\pi[/tex]
Step-by-step explanation:
circumference=2[tex]\pi r[/tex]
15[tex]\pi[/tex]=2[tex]\pi r[/tex]
r=7.5
Area=[tex]\pi r^{2}[/tex]
=[tex]\pi * 7.5^{2}[/tex]
= 56.25[tex]\pi[/tex]
the first day of shooting a movie, a director uses 30% of a film reel. The strip of
film used was 90 meters long.
What is the standard length on a film reel?
Answer:
27
Step-by-step explanation:
30% of 90 can be written as 30% × 90
= 30/100 × 90
= 27
please help
The table below shows the number of hours that a
scientist has been observing bacteria in a petri dish
Answer:
In the beginning there were 20 bacterias in the petri dish.
How many nickels to make 20
Answer:
if you're talking 20 cents, then 4, if you're talking dollars, then 400.
tell me pls if you want an explanation.
Answer:
400 nickels
Step-by-step explanation:
How many nickels to make $20?
1 nickel = 5 cents ($0.05)
? nickels = $20
How many nickels make $1?
0.05x = 1
/0.05 /0.05
x = 20 <== 20 nickels make $1
How many nickels make $20?
20x = $20
20(20) = $20
400 = $20
This means that 400 nickels make $20
Hope this helps!
After eating at the restaurant, Tom, Mary, and
Sara decided to divide the bill evenly. If each
person paid 42 dollars, what was the total of the
bill?
Answer:
$126
Step-by-step explanation:
since they divided it evenly therefore everyone paid $42 you just times that by the amount of people. there is tom, mary and sara therefore 3. 42*3=126
Answer:
total bill was $126
Step-by-step explanation:
3 people ate: Tom, Mary and Sara
if they split the bill evenly, they would all pay the same amount
if each person paid 42 dollars, you just multiply that amount by the number of people
42 x 3 = 126
A cube has a surface area of 600 square centimeters. What is the side length?
Answer:
10 cm
Step-by-step explanation:
The formula for finding the surface area of a cube is 6 x (side length)^2.
Since the surface area equals 600, you can divide the surface area by 6 (because a cube has 6 faces) so that becomes 100. The square root of 100 is 10, so the side length is equal 10 cm.
15. If y varies directly as x and y = 540 when x = 10, find x when y = 1080
[tex]\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\stackrel{\textit{"y" varies directly as "x"}}{y = kx}\qquad \textit{we also know that} \begin{cases} y = 540\\ x = 10 \end{cases}\implies 540=k(10) \\\\\\ \cfrac{540}{10}=k\implies 54=k~\hfill \boxed{y=54x} \\\\\\ \textit{when y = 1080, what is "x"?}\qquad 1080=540x\implies \cfrac{1080}{540}=x\implies 2=x[/tex]
The value of x when y = 1080 for the condition when its given that y varies directly as x and that y = 540 when x = 10, is found to be x = 20
Let there are two variables p and q
Then, p and q are said to be directly proportional to each other if
[tex]p = kq[/tex]
where k is some constant number called constant of proportionality.
This directly proportional relationship between p and q is written as
[tex]p \propto q[/tex] where that middle sign is the sign of proportionality.
In a directly proportional relationship, increasing one variable will increase another.
Now let m and n are two variables.
Then m and n are said to be inversely proportional to each other if
[tex]m = \dfrac{c}{n} \\\\ \text{or} \\\\ n = \dfrac{c}{m}[/tex]
(both are equal)
where c is a constant number called constant of proportionality.
This inversely proportional relationship is denoted by
[tex]m \propto \dfrac{1}{n} \\\\ \text{or} \\\\n \propto \dfrac{1}{m}[/tex]
As visible, increasing one variable will decrease the other variable if both are inversely proportional.
For this case, it is specified that y varies directly as x.
That means
[tex]y \propto x\\or\\y = kx[/tex]
At x = 10, y is 540. Putting these values in the equation y = kx as they're related, we get:
[tex]540 = k \times 10\\\\\text{Dividing both the sides by 10}\\\\\dfrac{540}{10} = k\\\\k = 54[/tex]
Thus, the relationship between x and y is: y = 54x
Now, when y = 1080, we get:
[tex]1080 = 54x\\\\\text{Dividing both the sides by 54}\\\\\dfrac{1080}{54} = x\\\\x = 20[/tex]
Thus, the value of x when y = 1080 for this condition is when x = 20.
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write -5 as a logarithim with a base of 4
Answer:
[tex]log_4(\frac{1}{4^5}) = -5[/tex]
Step-by-step explanation:
[tex]log_b(a) = c[/tex] ↔ [tex]b^c = a[/tex]
You are given [tex]b[/tex] = 4
You re also given [tex]c[/tex] = -5
To find a, use the exponential form:
[tex]b^c = a[/tex]
[tex]= (4)^{-5} = \frac{1}{4^5} = a[/tex]
Then you can convert into a logarithm.
[tex]log_4(\frac{1}{4^5}) = -5[/tex]
Answer:
There are multiple ways of writing this:
[tex]\sf -5log_4(4)=log_4(4^{-5})=log_4\left(\dfrac{1}{4^5}\right)=log_4\left(\dfrac{1}{1024}\right)[/tex]
Step-by-step explanation:
Log rule: [tex]\sf log_a(a)=1[/tex]
[tex]\sf \implies log_4(4)=1[/tex]
[tex]\sf \implies -5log_4(4)=-5[/tex]
Log rule: [tex]\sf c \cdot log_ab=log_a(b^c)[/tex]
[tex]\sf \implies -5log_4(4)=log_4(4^{-5})[/tex]
[tex]\sf = log_4\left(\dfrac{1}{4^5}\right)[/tex]
[tex]\sf = log_4\left(\dfrac{1}{1024}\right)[/tex]
please answer . thanks in advance
Answer:
Step-by-step explanation:
If they are the same, the ratio of length to width when reduced to the lowest terms are
Large rectangle L/w = 36/24 = 3/2
Small triangle L/w = 24/18 = 4/3
Answer: The ratios are not the same. The rectangles are not similar.
Please help I will give brainliest.
Given that the measure of 2x is 45°, and the measure of zy is 499, find the
measure of z
Answer:
86 degrees
Step-by-step explanation:
The angles of a triangle all add up to 180.
x is 45 degrees
y is 49 degrees
49 + 45 = 94
180 - 94 = 86
The last angle of the triangle is 86 degrees. Since z is on the opposite side of it, it is equal to 86
-4x + 3y = 29
5x + y = -3
solve by substitution
Step-by-step explanation:
please mark me as brainlest
Answer:
y = 7x = -2Explanation:
-4x + 3y = 29 __ equation 15x + y = -3make x the subject in equation 2,
5x + y = -3
y = -3 - 5x __ equation 2
using substitution method,
-4x + 3(-3 - 5x) = 29
-4x -9 -15x = 29
-19x = 38
x = -2
Find y,
y = -3 - 5x
y = -3 - 5(-2)
y = 7
Liam buys three identical plastic
containers that are right rectangular
prisms. one face of each container
measures 4 and 1/2 in. by 2 in. the total
volume of the three containers is
135 in.. how many of these containers
can liam set on a shelf that is 24 in. long
with the 4and 1/2in-by-2 in. faces touching?
The number of rectangular prism container that would be set on the shelf is: 4.
What is the Volume of a Rectangular Prism?Volume of rectangular prism = length × width ×height
Given the following:
Volume of three containers = 135 in.³Volume of each rectangular prism container = 135/3 = 45 in.³One face = width × height = 4.5 × 2 = 9 in.Find the length of one rectangular prism using the volume formula since volume for one prism = 45 in.³
45 = length × 9
length = 5 in.
Each rectangular prism container is 5 in. long, therefore, the number of the containers that can be set on the shelf that is 24 in. long, if the 4.5 in by 2 in. face touches each other = 24/5 = 4.8.
The fifth container won't fit in. Therefore, the number of rectangular prism container that would be set on the shelf is: 4.
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A bag contains 40 red and green marbles. The number of green marbles, g, is 9 times the number of red marbles, r.
How many red marbles are in the bag?
Answer:
4 red marbles
Step-by-step explanation:
green marbles = 9r
red marbles = r
9r + r = 40
10r = 40
r = 4 = red marbles
Use the information given to answer the question.
which two inequalities represent the constraints for the art studio classes
per week?
an art studio offers classes for painting and pottery. each painting class is 1
2+ y = 40
hour long. each pottery class is 1.5 hours long. the art studio is only open
0 2 +1.5y = 40
for classes a maximum of 40 hours per week, and only one class is offered at
o +1.5y > 40
35(2 + y) < 1,000
a time. each class costs $35,and the art studio earns a minimum of $1,000
35(x + y) > 1,000
per week from all classes. let be the number of painting classes offered per
calculator
week, and let y be the number of pottery classes offered per week.
The two inequalities that represents the constraints for the art studio classes per week are:
x + 1.5y = 40
35(x + y) > 1,000
What two inequalities represent the constraints?Here are inequalities signs and what they mean:
> means greater than
< means less than
≥ means greater than or equal to
≤ less than or equal to
= means equal to
The inequality that represents the total hoursthe art studio is open would be an equal to sign. This is because the store is open for a maximum of 40 hours.
The inequality that represents the total earnings would be represented with a greater than sign because the studio earns more than $1000 weekly.
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What is the length of a diagonal of rectangle EFGH?
Answer:
[tex]\sqrt{53}[/tex]
Step-by-step explanation:
First, we find out the length of EH, which is 7. And then, we find the length of GH, which is 3. If we square both the numbers and add them, we get 53. And then we square root that to get [tex]\sqrt{53}[/tex]
Hope this helps <:)
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American Eagle is having a 60 % clearance sale on all summer merchandise. The consumer purchased $342.57 of the summer merchandise. What is the final cost to the consumer? Sales tax is 5%.
Answer:
$143.88
Step-by-step explanation:
Look at image above...
I did not add this to the picture but to get the new total of $137.03, you need to subtract $205.54 (the 60% off) from the original total.
Margaret is building storage boxes. each box will have a length of 8 feet, a width of 512 feet, and a height of 412 feet. a pint of paint covers 50 square feet. how many pints of paint does margaret need to buy in order to paint 3 boxes? 7 pints 10 pints 12 pints 13 pints
The surface area of a cuboid is the area of all the six faces of a cuboid. The Paint that is required to paint 3 boxes is 13 pints.
What is the surface area of a cuboid?The surface area of a cuboid is the area of all the six faces of a cuboid. It is given by the formula,
[tex]\rm \text{Surface area of the box}= 2[(Length \times width)+(Width \times Height)+(Length \times height)][/tex]
As it is given the dimensions of the storage box are a length of 8 feet, a width of 5 1/2 feet(5.5 feet), and a height of 4 1/2 feet(4.5 feet). Therefore, the surface area of the box can be written as,
[tex]\rm \text{Surface area of the box}= 2[(Length \times width)+(Width \times Height)+(Length \times height)][/tex]
[tex]\rm \text{Surface area of the box}= 2[(8\times 5.5)+(5.5\times 4.5)+(8 \times 4.5)] = 209.5\ ft^2[/tex]
As it is given that the surface area that can be covered with a pint of paint is 50 square feet, therefore, the paint that will be required to paint 209 square feet is,
[tex]\text{Paint Required} = \dfrac{\text{Total area that is needed to be paint}}{\text{Area covered in a pint of paint}}[/tex]
[tex]\rm \text{Paint Required} = \dfrac{209.5}{50} = 4.19\ pints[/tex]
Now, we know that the surface area of the box is 209 square feet, while the paint required to paint a complete box is 4.19, therefore, the paint that will be required to paint 3 boxes will be,
[tex]\text{Paint required to paint 3 boxes} = 3 \times 4.19 = 12.57 \approx 13[/tex]
Hence, the Paint that is required to paint 3 boxes is 13 pints.
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PLEASE HELP!!! I am stuck!!
How do I get question c)
Answer:
When the actual temperature is -14 degrees Celsius, the wind chill equivalent temperature would be -22.2 degrees Celsius.
When the actual temperature is 3 degrees Celsius, the wind chill equivalent temperature would be 0.6 degrees Celsius.
Step-by-step explanation:
There is a + 1.2 pattern going right. So each time you increase the actual temperature by 1, you increase the wind chill equivalent temperature by 1.2
please help with angle addition
Answer:
m∠1 = 89°
Step-by-step explanation:
Since m∠2 is a part of ∠GFH, he can do the following.
∠GFH - m∠2 = m∠1
133° - 44° = 89°
There was a bottle of milk at home. After the brother drank 1.94L of it, there were 0.56L left. How many litres of milk was there at the beginning?
Answer:
add the 1.94+0.56 to get 2.5 liter
Step-by-step explanation:
wow, he drank almost 2 liters of milk more or less in one turn ? he might spend quite some time in the bathroom ...
anyway, x = original amount of milk.
x - 1.94 = 0.56 now we add 1.94 to both sides
x = 2.5 L
solve for x:
-3(x-2)^2+17=0
round your answer to the nearest hundredth
Answer:
-3(x-2)×2+17=0
-3x+6×2+17=0-3x+12+17=0-3x+29=0-3x=0-29=-29-3x=-2929÷3=9.700 to the nearest hundredthwhat's another way to say a+a
A. a^2
B. a+2
C. a-a
D. 2a
Answer:
[tex]\boxed{\sf{2a}}[/tex]Step-by-step explanation:
In order to solve this problem, you need to add their similar elements together.
First, add similar to elements.
[tex]\sf{a+a=\boxed{\sf{2a}}[/tex]
So, the correct answer is D. 2a.I hope this helps you! Let me know if my answer is wrong or not.
Line n goes through points A and B. What is the slope of line n?
Point A;(4,7)
Point B:(18,17)
Answer:
The slope is 5/7.
Step-by-step explanation:
Use a slope formula.
Slope:
[tex]\sf{\dfrac{y_2-y_1}{x_2-x_1} }[/tex]
y₂ = (17)
y₁ = (7)
x₂ = (18)
x₁ = (4)
Rewrite the problem down.
[tex]\sf{\dfrac{17-7}{18-4}=\dfrac{10}{14}={\dfrac{10\div2}{14\div2}=\boxed{\sf{\dfrac{5}{7}}}[/tex]
Therefore, the slope is 5/7.
I hope this helps! Let me know if my answer is wrong or not.
Answer:
5/7
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(17-7)/(18-4)
m=10/14
simplify
m=5/7
apter 13
4. The base rate for workers' compensation insurance for roolers
in one state is $16.95 per $100 paid to employees. The total
monthly payroll for Certified Roofing is $15,738.00. What is the
monthly premium for workers' compensation insurance?
Answer:
$2,667.59
Step-by-step explanation:
The insurance premium is found by multiplying the payroll amount by the premium rate.
($15,738) × $16.95/$100 = $15,738 × 0.1695 ≈ $2,667.59
The monthly workers' compensation insurance premium is $2,667.59.
_____
Additional comment
The roofers in that state must have an exceptionally high rate of accident, injury, or illness. Many places, the average rate of workers' comp insurance is less than $2 per $100.
Answer:
The roofers in that state must have an exceptionally high rate of accident, injury, or illness. Many places, the average rate of workers' comp insurance is less than $2 per $100.
Step-by-step explanation:
i need help cause is due at 11:59 est
Answer:
Matt used diameter of the ball instead of Radius
Step-by-step explanation:
The volume of a sphere is given as:
4/3πr³⇒ Matt made an error in his calculation by failing to covert the value of the diameter given to Radius.
⇒ By dividing the diameter by 2 = 15 / 2 = 7.5, we obtain the Radius, which is what Billy did in her own calculation.
Hey, need to solve for x
2(x-3)=9x+8
Answer:
x = -2
Step-by-step explanation:
2x-6 = 9x+8
-7x = 14
x = -2
PLEASE RATE!! I hope this helps!!
Which number is the smallest?
A. 817.9
B. 871.003
C. 817.1
D. 817.099
Answer:
D.
Step-by-step explanation:
817.099 is the smallest
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The small cylinder can fill the big cylinder to a height of 5cm. Work out the radius if the big cylinder