The sum of a number w is more than -12 becomes w > -12
What is a solution set to an inequality or an equation?If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality.
We have been given that the sum of a number w is more than -12.
Now the sum of a number = w
It is more than -12 means the inequality form as;
w > -12
Therefore, the overall expression becomes w > -12
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a farmer wants to make a rectangular field with a total area of 2000 square meters. it is surrounded by a fence. it is divided into 4 equal areas by fences. what is the shortest total length of fence this can be done with?
The shortest total length of fence this can be done with will be 440 m as the total area is 2000 m².
What is perimeter?The length of a shape's outline is its perimeter. You must add the lengths of all four sides of a rectangle or square to determine its perimeter. In this instance, x represents the rectangle's length and y its width. The distance around an object is called the perimeter. For instance, the yard of your home is fenced in. The fence's length serves as the perimeter. Your fence is 200 feet long if the yard is 50 feet by 50 feet.
Here,
The area=2000 m²
xy=2000
x=2000/y
p=4x+2y
p=4*(2000/y)+2y
=8000/y+2y
p'=-8000/y²+2
-8000/y²+2=0
2y²-8000=0
y²-4000=
y²=4000
y= 20 m
p=8000/20+2*20
p=400+40=440 m
Given that the total area is 2000 m², the shortest total length of fence that can be used is 440 m.
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Two complementary angles have measures of x and y. If y is 9 less than twice x, write a system of linear equations that can be used to determine the measure of each angle. Find the measure of each angle.
Using system of linear equation, the complementary angles (x, y) are 27 and 63 degrees respectively.
Complementary AnglesWhen the sum of two angles is equal to 90 degrees, they are called complementary angles. For example, 30 degrees and 60 degrees are complementary angles. However, when the sum of the two angles is equal to 180 degrees, the angles are supplementary angles
In this case, we have two angles x, y which are complimentary to one another.
We can represent this with system of equations;
x + y = 90 ...eq(i)y - 9 = 2x ... eq(ii)solving equation (i) and (ii)
The value of x and y are 27 and 63
The complementary angles are 27 and 63
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To pay for a home improvement project that totals $16,000, Genesis is choosing between taking out a simple interest bank loan at 8% for 3 years or paying with a credit card that compounds monthly at an annual rate of 15% for 7 years. Which plan would give Genesis the lowest monthly payment?
A) The monthly credit card payment would be $511.11, which is lower than the monthly payment on the bank loan.
B) The monthly payment on a bank loan would be $480, which is lower than the monthly credit card payment.
C) The monthly payment on a bank loan would be $551.11, which is lower than the monthly credit card payment.
D) The monthly credit card payment would be $540.78, which is lower than the monthly payment on the bank loan.
Any explanation would be greatly appreciated as well! <3
The plan that would give Genesis the lowest monthly payment is D. The monthly credit card payment would be $540.78, which is lower than the monthly payment on the bank loan.
How to calculate the payment?From the information, the home improvement project that totals $16,000, and Genesis is choosing between taking out a simple interest bank loan at 8% for 3 years.
The simple interest earned will be:
= Principal × Rate × Time / 100
= (16000 × 8 × 3)/100
= $551.11
The compound interest will be:
A = P(1 + r/n)^nt
A = accumulated amount
P = amount deposited
r = rate
n = times of compound per year
t = years
This will be:
A = 16000(1 + 0.15/12)^(12×7)
A = $540.78
Therefore the correct option is D.
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can anyone please help with this! it’s so confusing! 100 points to whoever can help me with all of them! and please show how u did it not just answers!! tysm
Answer:
Step-by-step explanation:
(a is in the file)
B. An add 3 inches to height would affect the surface area more than 3 inches to weight because if the same number was multiplied to 0.13 and 0.08… 0.13 would have the greater outcome.
c. a number more than 10 but less than 11 is 10.5
The height is 50 so plug those two numbers into the equation
10.5=0.08W+(0.13)50-1.03
10.5=0.08W+ 6.5-1.03
10.5=0.08W+5.47
Subtract 5.47 from both sides
5.3=0.08
Divide by 0.08 on both sides
= 62.87lbs in one possibility for the value of W
D. a number between 12 and 13 is 12.5
12.5= 0.08w+ 0.13H-1.03
Subtract 1.03 on both sides
11.47= 0.08w+ 0.13H
Divide 11.47 in 2 so that weight and height can be added up to equal 11.47 in the end
5.73=0.08 5.73=0.13
71.68=W 44.07=H
J is the midpoint of segment CT.
CJ = 9x + 1
JT = 2x + 15
Find CT.
The length CT of the line segment is 38 units
How to determine the length of CT?From the question, we have the following parameters
CJ = 9x + 1
JT = 2x + 15
Also, we understand that:
Point J is the midpoint of segment CT.
This means that
CJ = CT
So, we have
9x + 1 = 2x + 15
Evaluate the like terms
7x = 14
So, we have
x = 2
Length CT is calculated as
CT = 9x + 1 + 2x + 15
So, we have
CT = 9 x 2 + 1 + 2 x 2 + 15
Evaluate
CT = 38
Hence, the length is 38 units
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There are 1,459 children registered for camp. There is enough room for 18 campers to sleep in
each cabin. What is the least number of cabins needed for all the registered campers?
Answer:
82 rooms
Step-by-step explanation:
1459/18=81.05
so 82 rooms
Please mark as brainliest
Answer:
82
Step-by-step explanation:
1459/18
[tex]1459 \div 18[/tex]
for each cabin there 18 And there are 1459
81.05 \times 48=159
since you can't have a half a cabinet the answer is 82
The average mass of a man is 84 kg and of a woman is 70 kg
a lift can safely carry 620 kg
work out the maximum number of people the lift can safely carry
The maximum number of people the lift can safely carry is 8 people.
Given that, the average mass of a man is 84 kg and of a woman is 70 kg.
What is the average?In maths, the average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values. When we need to find the average of a set of data, we add up all the values and then divide this total by the number of values.
Now, average = (84+72)/2
= 156/2
= 78
Let the number of people in the left be n.
So, 78n≤620
Divide 78 to both the sides of the inequality
78n/78≤620/78
⇒ n≤7.9
⇒ n≤8
Therefore, the maximum number of people the lift can safely carry is 8 people.
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13. What is the length of the missing side, x?
40 in.
51°
35 in.
49 in.
74°
55°
X
For the given triangles the length of the missing side x is 56in.
As given in the question,
Two triangles are given ,
Let the triangle with measurement 40in. and 35in. be A and another is B.
In triangle A,
Let missing angle be α
Sum of all the angles in the interior of a triangle is equal to 180°
51°+ 74° + α = 180°
⇒α = 55°
In triangle B.
Let missing angle be β,
74° + 55° + β = 180°
⇒β= 51°
By AAA both the triangles are similar.
Length of corresponding sides are in proportion.
40: x = 35 : 49
⇒x = ( 40×49)/35
⇒x= 56in.
Therefore, for the given triangles the length of the missing side x=56in.
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the count in a bacteria culture was 800 after 20 minutes and 1700 after 40 minutes. assuming the count grows exponentially, what was the initial size of the culture?
The culture starts out with 39 members.
Given that;
After 20 minutes and 40 minutes, a bacteria culture had an 800 and 1700 count, respectively.
To get exponential growth;
We can get growth with an exponential function,
F(t) = A₀[tex]e^k^t[/tex]
Here, k is the growth constant and A₀ is the initial amount of bacteria.
Let;
800 = A₀[tex]e^2^0^k[/tex] → (I)
1700 = A₀[tex]e^4^0^k[/tex] → (II)
From (I) and (II);
1700 / 800 = A₀[tex]e^4^0^k[/tex] / A₀[tex]e^2^0^k[/tex]
17/8 = [tex]e^2^0^k[/tex]
For the above equation take the natural log on both sides;
ln(17/8) = ln [tex]e^2^0^k[/tex]
ln(17/8) = 20k
k = ln(17/8) / 20
To get the initial size of the culture;
From (I),
800 = A₀[tex]e^2^0^k[/tex]
800 = A₀e⁰°⁰³⁷⁶ ˣ ²⁰
A₀ = 800 / 20.76
A₀ = 38.53 ≅ 39
Therefore, the initial size of the culture is 39.
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Waukee railroad is considering the purchase of a powerful, high-speed wheel grinder to replace a standard wheel grinder now in use. selected information on the two machines follows: standard wheel grinder high-speed wheel grinder original cost/new cost $ 45,000 $ 67,500 accumulated depreciation to date $ 18,000 $ 0 current salvage value $ 11,750 $ 0 estimated cost per year to operate $ 26,250 $ 16,250 remaining years of useful life 5 years 5 years required: compute the net advantage or disadvantage of purchasing the high-speed wheel grinder covering the five-year period. use only relevant costs in your analysis. ignore tax effects.
The net disadvantage of purchasing the high-speed wheel grinder is $ 5,750
What is net advantage or disadvantage?
Net advantage or disadvantage is the total of potentially monetary savings from action of a business choosing to purchasing or lease an asset.
First, we calculate the net advantage in year 0
= current salvage value of standard - Original cost of high-speed
= $ 11,750 - $ 67,500
= - $ 55,750
Next we calculate the net advantage in year 5
= net advantage in year 0 + cost saving in 5 years
= - $ 55,750 + ($ 26,750 - $ 11,750) * 5
= - $ 55,750 + $ 50,000
= - $ 5,750
Thus, the net disadvantage of purchasing the high-speed wheel grinder is $ 5,750
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Jane paints a 2 1/3 wall with 2/3 can of paint joe paints 3 1/4 walls with 3/4 can of paint who paints a wall at a faster rate
Answer:
Jane paints faster if I may be correct
What is the surface area of the cuboid below? Remember to give the correct units.
Answer:
surface area=2(lb+lh+bh)
surface area=2(9)(4)+(9)(12)+(4)(12)
surface area=384cm2
4. (02.08 MC)
Let
f(x) = 2x²5x - 7
and
g(x) = x² - 2.
Find f(g(x)). Show each step of your work. (10 points)
Answer:
Step-by-step explanation:
[tex]f(x) = 2x^{2} + 5x - 7\\\\g(x) = x^{2} -2\\ \\f(g(x)) = 2(x^{2}-2) + 5(x^{2} -2) - 7\\ \\= 2x^{2} - 4 +5x^{2} -10 - 7\\= 2x^{2} + 5x^{2} -4-10-7\\\\\\f(g(x)) = 7x^{2} -21[/tex]
the probability that a new microwave oven will stop working in less than 2 years is 0.05. the probability that a new microwave oven is damaged during delivery and stops working in less than 2 years is 0.04. the probability that a new microwave oven is damaged during delivery is 0.10. given that a new microwave oven is damaged during delivery, what is the probability that it stops working in less than 2 years? responses 0.05 0.05 0.06 0.06 0.10 0.10 0.40 0.40 0.50
Option D is the right choice.
It is discovered through the use of conditional probability that there is a 0.4 = 40% chance that it will stop working in less than 2 years.
Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.
Conditional Probability:
P (B / A) = P (A∩B) / P (A)
Here:
P(B / A) is the likelihood that event B will occur in the absence of event A.
P (A∩B) is the likelihood that both A and B will occur.
P(A) denotes the likelihood that A will occur.
As per the question:
Event A: Delivery was harmed.
Event B: Fails to function after less than two years.
P (A) = 0.1 due to the probability of being damaged during delivery being 0.1.
P (A∩B) = 0.04 because there is a 0.04 likelihood that it will be damaged during the delivery and stop working.
The likelihood under the condition is:
P (B / A) = P (A∩B) / P (A) = 0.04 / 0.1 = 0.4
0.4 = 40% chance that it will stop working in under two years.
Therefore, option D is correct.
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The functions f(x)=−34x+2 and g(x)=(14)x+1 are shown in the graph. What are the solutions to −34x+2=(14)x+1? Select each correct answer. Responses −1 negative 1 0 0 1 1 2 2 3
A solution to −34x+2=(14)x+1 is x = 1/48
In this question, we have been given functions f(x) = -34x + 2 and g(x) =(14)x + 1
We need to find the solutions to −34x + 2 = (14)x + 1
i.e., we need to find the solution to f(x) = g(x)
Consider, f(x) = g(x)
-34x + 2 = (14)x + 1
-34x + 2 - 14x = 14x + 1 - 14x
-48x + 2 = 1
-48x = -1
x = 1/48
Therefore, a solution to −34x+2=(14)x+1 is x = 1/48
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750 people go on a coach trip
each coach can hold 50 people
How many coaches are needed
Answer:
15 coaches
Step-by-step explanation:
750 people go on a coach trip each coach can hold 50 people How many coaches are needed?
750/50 = 15 coaches
Answer:
Answer:750÷50 = 15
The answer is 15.
Because 750 people are going in a coach trip and each coaches can hold 50 people.
Juan always saves 30% of all his earnings. Last month he saved $141. How much did he earn last month?
Answer:
$470
Step-by-step explanation:
%30 of 470 = $141
Answer: $470
I hope it help
Which rule describes rotating 90° counterclockwise?
(x,y)→(-y,x)
(x,y)→(y, -x)
(x,y)→(x,y)
(x,y)-(-x,-y)
when x = -2, y = []
when x = 0, y = []
when x = 2, y = []
when x = 4, y = []
The values of y respective to x values are when x = -2 then y = 12 when x = 0 then y = 2 when x = 2 then y = -8, & when x = 4 then y = -18.
What is a function rule?
The equation-based relationship between the dependent and independent variables is known as a function rule. In simple words, a function is an association between inputs in which each input is connected to precisely one output.
Given, y = -5x + 2
when x= -2, y = (-5)* (-2) + 2 = 10 + 2 = 12, y = 12
when x= 0, y = (-5)* (0) + 2 = 0 + 2 = 2, y = 2
when x= 2, y = (-5)* (2) + 2 = -10 + 2 = -8, y = -8
when x= 4, y = (-5)* (4) + 2 = -20 + 2 = -18, y = -18
Hence, these are the required values of y to the respective input value of x.
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Factorise fully
12m + 8m²
Answer:
Step-by-step explanation:
3.4.m+2.4.m.m
4m(3+2m)
I'm having trouble with this, which one is it?
The information illustrated regarding the numbers shows that it's a C. Direct variation.
What is a direct variation?A direct variation means the variation that has a constant of proportionality.
In this case, when x is 256, y is 32. The constant is 32/256 = 1/8
When y = 6, x = 48. The constant is also 6/48 = 1/8.
Therefore, it's a direct variation.
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Higher Order Thinking You use a garden hose to fill a
vading pool. If the water level rises 11 centimeters every
minutes and you record the data point of (10, y), what is
he value of y? Use slope to justify your answer
The value of y = 110.
What is slope intercept form?
The graph of the linear equation y = mx + c is a line with m as slope, m and c as the y-intercept. This form of the linear equation is called the slope-intercept form, and the values of m and c are real numbers.
Rise of the water = 11
run = 1 min
slope m = 11/1 = 11.
The slope intercept form is
y = mx +b
after substituting the values, we get
m = 11,
x = 10and y = ?
y = 10 (11)
y = 110.
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help pls thank you ( i need 2 answers )
Answer:
a. 111.5 / 100
b. 1.15 feet
Step-by-step explanation:
a. if Eloise's statue is 1/100th of the height, it means that for every 100 cm of height of the actual statue, Eloise will have 1cm on hers.
Therefore the division problem 111.5 / 100 can be used to calculate the height of her statue in feet.
b. 111.5 feet / 100 = 1.15 feet
The l of a rectangular field is 5 metres longer than its width. if the perimeter is 150 metres , find the width
Answer:
width = 35 m
Step-by-step explanation:
w is the width, then l = w + 5
Perimeter P = 2(l + w)
=> 150 =2(w + 5 + w)
75 = 2w + 5
2w = 70
w = 35
I need help. How is this possible ?This is an exterior angle
Answer:
x = 36
The measure of the exterior angle is 114°
The remote interior angles are 24° and 90°.
Step-by-step explanation:
The angle marked 3x + 6 is the exterior angle. The other two marked angles are called "remote interior angles"
The two remote interior angles added together equals the exterior angle.
3x+6 = 24° + 2x + 18
Combine like terms.
3x + 6 = 2x + 42
Subtract 2x from both sides.
x + 6 = 42
Subtract 6 from both sides.
x = 36
If required, use the x=36 to find the measure of the exterior angle.
3(36) + 6
= 108 + 6
= 114°
Or find the measures of the remote interior angles.
2(36) + 18
= 72 + 18
= 90°
The remote interior angles are 24° and 90°.
1/4(8x+12)=-15 ''solve''
After solving the value of x in the equation is x [tex]=[/tex] -9 .
In the question ,
it is given that ,
the equation is 1/4(8x+12) = -15
Applying the associative property of multiplication ,
we get ,
8x/4 + 12/4 = -15
cancelling out the common factor 2 from numerator and denominator ,
we get ,
2x + 3 = -15
Subtracting the number 3 from both sides of the equation ,
we get ,
2x = -15 - 3
2x = -18
Dividing both sides of the equation above by the number 2 ,
we get ,
x = -18/2
x = -9
Therefore , After solving the value of x in the equation is x [tex]=[/tex] -9 .
The given question is incomplete , the complete question is
Solve the given equation for x ?
1/4(8x+12)= -15
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URGENT PLEASEEE!
What is an equation of the line that passes through the points (2, -8) and (-6, 0)
Answer:
It should be y=2x-1
Step-by-step explanation:
lupita rides a taxi that charges a flate rate of $6.75 plus $3.20 per mile . if the taxi charges lupita $40.03 in total for her trip , how many miles is her ride ?
50 miles because of the miles
Find the x- and y-intercepts of the graph of 2x+8y=122x+8y=12. State each answer as an integer or an improper fraction in simplest form.
Answer:
x,y [tex]( \frac{2}{61})(\frac{91}{61} )[/tex]
The kinetic energy of an object is directly proportional to the square of its
velocity.
An airplane with velocity 220 m/s has a kinetic energy of 10,890 megajoules.
What is the kinetic energy of the same airplane when its velocity is 300 m/s?
By using the concept of kinetic energy, it is obtained that
Kinetic energy of the airplane when its velocity is 300 m/s is 20250 megajoule
What is Kinetic energy?
Kinetic energy is the energy possessed by the body by virtue of its motion
If m is the mass of the body and v is the velocity of the body, then kinetic energy is given by the formula
Kinetic energy = [tex]\frac{1}{2} \times m \times v^2[/tex]
Let the mass of the airplane be m kg
Velocity = 220 m/s
Kinetic energy = [tex]\frac{1}{2} \times m \times (220)^2[/tex]
By the problem,
[tex]\frac{1}{2} \times m \times (220)^2 = 10890\times 10^6[/tex]
[tex]m = \frac{10890\times 10^6\times 2}{220\times 220}[/tex]
m = [tex]0.45 \times 10^6[/tex] kg
Now,
Velocity = 300 m/s
Kinetic energy = [tex]\frac{1}{2} \times 0.45 \times 10^6 \times 300 \times 300[/tex]
= [tex]20250 \times 10^6[/tex] J
= 20250 mega joules
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