Answer:
-80 ; 2 ; - 15 ; - 15
Step-by-step explanation:
Given that:
1.)
A withdrawal of $80, will cause reduction in the initial value, hence, negative
= - 80
2.)
A 2 - inch rise in water level, indicates increase from initial level, hence, positive
= + 2
3.)
A lose of 15 pounds indicates reduction in weight, hence, negative
= - 15
4.)
Draining 15 gallons of water from a fish tank indicates reduction Hence, negative
= - 15
The volume of a rectangular prism is 7/x-3/5x. If it has a width of 2/x and a height of 4/x, find the length of the prism?
a. 4/5
b. 32x²/40x
c. 4
d. 4x/5
The length of the rectangular prism is L = 4x/5
What is the volume of a prism?A three-dimensional solid object called a prism has two identical ends. It consists of equal cross-sections, flat faces, and identical bases. Without bases, the prism's faces are parallelograms or rectangles.
The volume of a prism is the product of its base area and height
Volume of Prism = B x h
where B = base area of prism
h = height of prism
Given data ,
The formula for the volume of a rectangular prism is V = lwh, where l, w, and h are the length, width, and height of the prism, respectively.
In this problem, we are given that the volume of the prism is 7/(x - 3/5x) and the width and height are 2/x and 4/x, respectively.
So we can substitute these values into the formula for the volume and solve for the length:
V = lwh
7/(x - 3/5x) = l * (2/x) * (4/x)
Multiplying both sides by (x - 3/5x), we get:
7 = l * 8/(5x² - 3x)
Simplifying, we get:
l = 56x²/(5x² - 3x)
Now we need to check if this solution satisfies the condition that the width is 2/x and the height is 4/x:
w = 2/x, h = 4/x
V = lwh = (56x²/(5x² - 3x)) * (2/x) * (4/x) = 7/(x - 3/5x)
So the solution is correct.
Hence , the length of the prism is 56x²/(5x² - 3x), which can be simplified to 32x²/40x or 4x/5
To learn more about volume of prism click :
https://brainly.com/question/11336446
#SPJ2
Which set of ordered pairs does not represent a function? Delta math
Answer:
The first set of ordered pairs is a function, because no two ordered pairs have the same first coordinates with different second coordinates. The second example is not a function, because it contains the ordered pairs (1,2) and (1,5). These have the same first coordinate and different second coordinates
5x < -10
I cant find the answer
Answer:
x<-2
Step-by-step explanation:
5x<-10 (divide both sides by 5)
5x÷5<-10÷5 (divide)
solution: x<-2
hope this helps!
What is the slope of the line
Graph the system of inequalities presented here on your own paper, then use your graph to answer the following questions:
y > 3x + 10
y < -3/4x - 1
Part A: Describe the graph of the system, including shading and the type of lines graphed. Provide a description of the solution area.
Part B: Is the point (8, 10) included in the solution area for the system? Justify your answer mathematically.
Answer:
Part A:
I have attached the graph of this system of inequalities.
Part B:
Plug in (8,10) into both equations
10 > 3(8) + 10
10 > 24 + 10
10 > 34
This is false!
10 < (-3/4)(8) - 1
10 < (-3)(2) - 1
10 < -6 - 1
10 < -7
This is also false!
So, (8,10) is not included in the solution area for the system.
Step-by-step explanation:
1 point
3.) Jamal then says that there are other types of trends in the periodic
table and tells Nic about Atomic Radius. He looks at the same four elements
and points to the element with the largest atomic radius. Which should he
point to?
F
Ci
Br
I
Answer:
the largest one is f or francium.
14. Higher Order Thinking: Lauren can drive her car 320 miles on 10 gallons of gasoline. Melissa can drive her car 280 miles on 8 gallons of gasoline. Who can drive farther on 40 gallons of gasoline? Complete the ratio tables to justify your solution.
Lauren can drive farther on 40 gallons of gasoline than Melissa because her car is more fuel efficient.
What is miles?
Miles are a unit of measurement used to measure distances, typically between two points. Miles are typically used to measure the length of a journey, such as how many miles it is from one city to another. Miles can also be used to measure the length of a route or the total distance that a person has traveled. In the United States, a mile is equal to 5,280 feet or 1.61 kilometers.
Lauren:
10 gallons : 320 miles
40 gallons : x miles
x = 1280 miles
Melissa:
8 gallons : 280 miles
40 gallons : y miles
y = 1120 miles
Since Lauren can drive 1280 miles on 40 gallons of gasoline, she can drive farther than Melissa, who can only drive 1120 miles on the same amount of gasoline. This is because Lauren’s car has higher fuel efficiency, meaning it uses less gasoline for the same distance.
In conclusion, Lauren can drive farther on 40 gallons of gasoline than Melissa because her car is more fuel efficient. This difference in fuel efficiency can be seen in the ratio tables, which show that Lauren can travel 160 miles farther than Melissa on the same amount of gasoline.
To know more about miles click-
brainly.com/question/25631156
#SPJ1
Which of the following is the solution to the inequality?
y>4x-3
(-1,1)
(0,0)
(3,2)
Answer:
[tex]y > 4x - 3 = y + 3 > 4x \\ let \: take \: (0.0) \\ 0 + 4 > 4 \times 0 \\ 4 > 0 \\ solution = (0.0)[/tex]
Tim and Ollie share some money in the ratio 2:5
Tim gets £80
Work out how much Ollie gets.
Answer:
£200
Step-by-step explanation:
The ratio is 2:5
we then have
80:x
Because one side of the ratio was multiplied by 40 we have to do the same to the other
20*5=200
therefore our new ratio is
80:200
Ollie gets £200
hi
can you answer this and explain please
Answer:
B
Step-by-step explanation:
Inequalities of the type | x | ≤ a, have solution of the form
- a ≤ x ≤ a , so
| x | ≤ 4
- 4 ≤ x ≤ 4
The values of x are between - 4 and + 4, but can equal - 4 and 4 since the symbol is ' less than or equal to '
This is indicated on a number line by solid circles, where not equal to are denoted by open circles.
Thus the solution is Graph B
Which of the following is not a function?
Question 2 options:
{(1,2)(0,9)(3,4)(5,6)}
{(1,2)(3,4)(5,6)(7,8)}
{(1,5)(2,5)(3,5)(4,5)}
{(7,1)(2,4)(7,5)(8,3)}
Answer:D
Step-by-step explanation:
D, the X values repeat for 7.
Write the fraction 36/27 in simplest form
Answer:
Step-by-step explanation:
9/13.5
HELP PLS!!
A landscaper wants to create a rectangular patio in a backyard. He wants it to have a total area of 148 square feet and it should be 8 feet longer than it is wide. What dimensions should he use for the patio? Round to the nearest tenth of a foot if necessary
Answer:
L=16.8
w = 8.8
Step-by-step explanation:
L = x +8
w = x
x(x+8) = 148
x^2 + 8x = 148
x^2 + 8x - 148 =0
a = 1
b = 8
c = - 148
x = [tex]\frac{-8 +/- \sqrt{8^2 + 4*1*(-148)} }{2}[/tex]
(x - 8.8)(x + 16.8) = 0
(x + 16.8) is an extraneous root.
x = 8.8 which is the width
L = 16.8
how do i solve 9/10 y = -36
Answer:
-40
Step-by-step explanation:
Multiply both sides by the reciprocal of 9/10 to get rid of the fraction
[tex]\frac{10}{9}[/tex]×[tex]\frac{9}{10}[/tex]×y=-36 ×[tex]\frac{10}{9}[/tex]
y=-36×[tex]\frac{10}{9}[/tex]
y=[tex]\frac{-360}{9}[/tex]
y=-40
Rewrite the equation y - 4= 2(x + 4) in slope-intercept form.
First distribute the 2 through the parenthses on the right side.
So we have y - 4 = 2x + 8.
In slope-intercept form, the y is by itself on the left side.
So we add 4 to isolate the y on the left to get y = 2x + 12.
So in slope-intercept form, our equation is y = 2x + 12.
HELP PLEASE
Consider the line y = 6x-7. Find the equation of the line that is perpendicular to this line and passes through the point (8, 3). Find the equation of the line that is parallel to this line and passes through the point (8, 3).
Answer:
perpendicular line: y = -¹/₆ x + 4¹/₃ parallel line: y = 6x - 45Step-by-step explanation:
y=m₁x+b₁ ⊥ y=m₂x+b₂ ⇔ m₁×m₂ = -1
{Two lines are perpendicular if the product of theirs slopes is equal -1}
y = 6x - 7 ⇒ m₁=6
6×m₂ = -1 ⇒ m₂ = -¹/₆
The line y=-¹/₆ x+b passes through point (8, 3) so the equation:
3 = -¹/₆ ×8 + b must be true
3 = -⁴/₃ + b
b = 4¹/₃
Therefore equation in slope-intercept form:
y = -¹/₆ x + 4¹/₃
y=m₁x+b₁ ║ y=m₂x+b₂ ⇔ m₁ = m₂
{Two lines are parallel if their slopes are equal}
y = 6x - 7 ⇒ m₁=6 ⇒ m₂=6
The line y=6x+b passes through point (8, 3) so the equation:
3 = 6×8 + b must be true
3 = 48 + b
b = -45
Therefore equation in slope-intercept form:
y = 6x - 45
In a survey of 2,400 people who owned a certain type of car, 1,200 said they would
buy that type of car again. What percent of the people surveyed were satisfied with the car?
Answer:
50%
Step-by-step explanation:
2,400divied by 1,200 =50%
Brainiest plz ?
PLEASE HELP thank u (:
Which of the following theorems cannot be used to prove two lines are
parallel?
Answer:
Option H
Step-by-step explanation:
Option F
If two lines are cut by a transversal so that a pair of corresponding angles are congruent, then the lines are parallel.
True.
Option G
If two lines are cut by a transversal so that a pair of alternate exterior angles are congruent, then the lines are parallel.
True
Option H
If two line are cut by a transversal so that a pair of vertical angles are congruent, then the lines are parallel.
Since, vertical angles don't prove the lines cut by a transversal are parallel.
So the statement is False.
Option J
If two lines are are cut by a transversal so that a pair of same side interior angles are supplementary, then the lines are parallel.
True.
solve -3x + 12 < 18
help-
Answer:
x>−2
Step-by-step explanation:
−3x+12−12<18−12
−3x<6
Step 2: Divide both sides by -3.
−3x
−3
<
6
−3
please answer for 20 points
Answer:
C
Step-by-step explanation:
whenever you see a (as in ax^2 + bx+c) as a number other than 1, you should see if you can factor that out
2(6x^2 -x -1)
= 2(3x+1) (2x-1)
Answer:
2\(3x+1)(2x-1\)
Step-by-step explanation:
Write the equation of the line parallel to the line 3x + 5y = 7 and passes through the point (-1, 3) in standard form. Please help
Answer:
3x + 5y = 12Step-by-step explanation:
3x + 5y = 7 {subtract 3x from both sides}
5y = -3x + 7 {divide both sides by 5}
y = -³/₅x + ⁷/₅ ← slope-intercept form
y=m₁x+b₁ ║ y=m₂x+b₂ ⇔ m₁ = m₂
{Two lines are parallel if their slopes are equal}
y = -³/₅x + ⁷/₅ ⇒ m₁ = -³/₅ ⇒ m₂ = -³/₅
(-1, 3) ⇒ x₁ = -1, y₁ = 3
The point-slope form:
y - 3 = -³/₅(x - (-1))
y - 3 = -³/₅(x + 1) {myltiply both sides by 5}
5y - 15 = -3x - 3 {add 3x to both sides}
3x + 5y - 15 = - 3 {add 15 to both sides}
3x + 5y = 12
Which of the following best describes the equation below?
y = -2x + 5
A.
relation only
В.
function only
C.
both a relation and a function
D
neither a relation nor a function
Answer:
it most likely is the answer B
I need help with question 2 and 3
Answer:
2. Carbon-Dioxide and Nitrogen
3.After the Earth's surface had cooled to a temperature below the boiling point of water, rain began to fall for centuries. As the water drained into the great hollows and gaps in the Earth's surface, the primeval ocean came into existence.
Step-by-step explanation:
The forces of gravity prevented the water from leaving the planet.
RSTis graphed on a coordinate plane below. The triangle undergoes two
transformations and the new vertices are R"(4,2), S"(8,2), and T"(8,-6). Determine
the transformations and the order in which they were applied.
A. 90° counter-clockwise rotation, then reflected across the y-axis
B. Reflected across the y-axis, then a 90° counter-clockwise rotation
C. 90° counter-clockwise rotation, then reflected across the x-axis
D. Reflected across the y=x, then a 90° counter-clockwise rotation
Answer:C
Step-by-step explanation:
Transformation involves changing the position of a shape
The transformations and the order in which they were applied are:
A. 90° counter-clockwise rotation, then reflected across the y-axis
From the figure, the coordinate of RST is:
[tex]R= (2,4)[/tex]
[tex]S = (2,8)[/tex]
[tex]T =(-6,8)[/tex]
Using R to illustrate the transformation.
We have
[tex]R= (2,4)[/tex]
First, R is rotated 90 degrees counterclockwise
The rule of this transformation is:
[tex](x,y) \to (-y,x)[/tex]
So, we have:
[tex](2,4) \to (-4,2)[/tex]
Next, the point is reflected across the y-axis.
The rule of this transformation is:
[tex](x,y) \to (-x,y)[/tex]
So, we have:
[tex](-4,2) \to (4,2)[/tex]
From the question, we have the coordinate of R" to be;
[tex]R: =(4,2)[/tex] --- same as the result of the above sequence
Hence, option (A) is correct
Read more about transformations at:
https://brainly.com/question/13801312
Select the correct shapes.
Select the shapes that are similar to shape A.
Answer: Its the pink one and the green one
hope that was helpful!
Step-by-step explanation:
Answer:
pink, dark blue, and red
Step-by-step explanation:
2m² + 10 for m = -6
Help please
Answer:
82
Step-by-step explanation:
2×m²+10
m²= -6×-6=36
36×2=72+10=82
Hey there!
• If m = –6 then substitute it in the equation where m is at!
2(–6)² + 10
(–6)² = (–6)(–6) = 36
2(36) + 10 =
72 + 10 = 82
Answer: 82 ☑️
Good luck on your assignment and enjoy your day!
~LoveYourselfFirst:)
Happy Paws charges $21.00 plus $2.50 per hour to keep a dog
during the day.
Woof Watchers charges $10.00 plus $3.75 per hour to keep a
dog during the day.
Use the variable x to represent the number of hours. Write an
equation and solve for x to find out how many hours the total
cost of the services is equal. (Write your final answer as a
decimal.)
Answer:
8.8 hours
Step-by-step explanation:
happy paws charges $21 in addition to $2.5 per hour -- we can write this as
21 + 2.5 per hour -- since the number of hours is x, this is equal to
21 + 2.5 (x)
similarly, woof watchers is
10 + 3.75 (x)
we must find when the services are equal --
21 + 2.5x = 10+3.75x
subtract 10 from both sides
11 + 2.5x = 3.75x
subtract 2.5x from both sides
11 = 1.25
divide both sides by 1.25
x = 8.8
Is the number 61 a prime or composite number
Answer: 61 is a prime number :3
Answer:
Composite.
Step-by-step explanation:
Composite numbers are basically odd numbers. Prime numbers are all even.
A group of students went on a field trip. There were 3 boys for every 4 girls inthe group. If there were 20 girls, how many students in all went on the field trip? 10 points
Answer:
15 boys
Step-by-step explanation:
start by dividing 20 by 4
you get 5
5 times 3 next
now you have 15
Answer:
25 girls and boys
Step-by-step explanation:
There are 3 boys for every 4 girls
To find the rate we must
Divide 20 by 4 then multiply that by 3
20 divided by 4 is 5
5 times 3 is 15
15 boys went on the field trip
20 girls went on the field trip
The total number of students is 25 girls and boys