31. the minimum perimeter of the rectangle is ( 38 ) inches.
32.the maximum perimeter is ( 170 ) inches.
To find the minimum and maximum perimeter of the rectangle, we need to consider all possible combinations of length and width that yield an area of 84 square inches.
Given that the area of the rectangle is 84 square inches, we can find all the pairs of factors of 84. These pairs will represent the possible combinations of length and width.
The pairs of factors of 84 are:
1. [tex]\( 1 \times 84 \)[/tex]
2. [tex]\( 2 \times 42 \)[/tex]
3. [tex]\( 3 \times 28 \)[/tex]
4. [tex]\( 4 \times 21 \)[/tex]
5. [tex]\( 6 \times 14 \)[/tex]
6. [tex]\( 7 \times 12 \)[/tex]
Now, we calculate the perimeter for each pair:
1. [tex]\( \text{Perimeter} = 2 \times (1 + 84) = 2 \times 85 = 170 \)[/tex]
2. [tex]\( \text{Perimeter} = 2 \times (2 + 42) = 2 \times 44 = 88 \)[/tex]
3. [tex]\( \text{Perimeter} = 2 \times (3 + 28) = 2 \times 31 = 62 \)[/tex]
4.[tex]\( \text{Perimeter} = 2 \times (4 + 21) = 2 \times 25 = 50 \)[/tex]
5.[tex]\( \text{Perimeter} = 2 \times (6 + 14) = 2 \times 20 = 40 \)[/tex]
6.[tex]\( \text{Perimeter} = 2 \times (7 + 12) = 2 \times 19 = 38 \)[/tex]
Therefore, the minimum perimeter of the rectangle is ( 38 ) inches, and the maximum perimeter is ( 170 ) inches.
PLEASE HELP ASAP The set of all numbers greater than -10 and less than -3
Answer:
(-10, -3)
Step-by-step explanation:
() excludes -10 and -3 so it only includes the numbers in between.
The set builder notation is {x: x ∈ Z⁻, -10 < x < -3} and the set is {-9, -8, -7, -6, -5, -4}
Set-builder notation The set notation consists of symbols like ': - such that', '∈ - belongs to', ' <, >, ≤, ≥', and all these are enclosed in flower braces. The Capital letter that is used in this represents the category or the set to which the given values are related. A variable is used for representing the given set of data values.Set-builder notation is a mathematical notation for describing a set by representing its elements or explaining the properties that its members must satisfy.
It is given the set of numbers that are greater than -10 and less than -3.
Since they are negative integers, so all the required numbers also belong to the same category of numbers.
So, it is represented by Z⁻
Then, the set builder notation is
{x: x ∈ Z⁻, -10 < x < -3} and
The set is {-9, -8, -7, -6, -5, -4}
To learn more about Set-builder notation refer to:
https://brainly.com/question/11676827
#SPJ2
If the point G(–4, 6) was moved horizontally 4 units to the left, which of the following is the correct mapping to define the translation? (x, y) Right-arrow (x, y + 4) (x, y) Right-arrow(x + 4, y) (x, y) Right-arrow (x, y – 4) (x, y) Right-arrow (x – 4, y)
Answer:
(x, y ) → (x - 4, y )
Step-by-step explanation:
A horizontal move of 4 to the left means subtract 4 from the x- coordinate, leaving the y- coordinate unchanged, thus
(x, y ) → (x - 4, y ) ← translation rule
Answer:
(x, y) Right-arrow (x – 4, y)
Step-by-step explanation:
just did it
A cylinder-shaped kid's pool has a diameter of 12 feet and a height of 2 feet. If each cubic footholds 7.48 gallons of water, about how many gallons of water can the kid's pool hold?
Answer:
About 1691.886 gallons.
Step-by-step explanation:
The firs step is to find the volume of the pool in cubic feet. The formula for the volume of a cylinder is [tex]\pi r^2 h[/tex], which in this case is [tex]\pi \cdot 6^2 \cdot 2\approx 226.188[/tex] cubic feet. Multiplying this by 7.48, you get a total of about 1691.886 gallons of water. Hope this helps!
A region with a 15 mile diameter has a population density of about 5000 people per square mile. Find the number of people who live in the region.
Answer:
55 of people
A circle in the xy-plane has its center at (-2/3,-3/4)
and radius 5. Which of the following is an
equation of the circle?
Answer:
(x + 2/3)^2 + (y + 3/4)^2 = 5^2
Step-by-step explanation:
Apply the general formula for a circle: (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius. Since the center is (-2/3, -3/4), and r = 5, we get:
(x + 2/3)^2 + (y + 3/4)^2 = 5^2
6-2/3 doubled would be?
Answer:
10.6
Step-by-step explanation:
1. 2(6-2/3)
a. 2(5.33)
b. 10.6
Answer:
32/3, 10 2/3, 10.67
Step-by-step explanation:
First, we can set up the expression.
2(6-2/3)
Use the distributive property.
12-4/3
Get a common denominator.
12*3/3=36/3
36/3-4/3
32/3
or
10 2/3
or
10.66 (repeated)
Round it to 10.67
I kinda know the answer but want to make sure 14 points!
Answer:
Second
Step-by-step explanation:
This question is asking for the largest magnitude. The second is of so. The deeper you go the more negative the number gets as thats how far you are off sea-level.
Answer:
the second one
Explanation: If you got this you are right
Solve each equation. Check your solution. 4x - 8= 5x
Answer:
x= -8
Step-by-step explanation:
Answer:
x= -8
Step-by-step explanation:
Principal = $800
Interest Rate = 3.5%
Time = 6 months
Find the interest earnedi
The interest earned is $14.
To find the interest earned, we can use the formula for simple interest:
[tex]\[ \text{Simple Interest} = \frac{P \times R \times T}{100} \][/tex]
Where:
- [tex]\( P \)[/tex]is the principal amount (the initial amount of money) [tex]= $800[/tex]
-[tex]\( R \)[/tex]is the interest rate per period (in decimal form) [tex]= 3.5% = 0.035[/tex]
-[tex]\( T \)[/tex] is the time the money is invested for (in years)[tex]= 6 months = 0.5 years[/tex]
Now, plug in the values:
[tex]\[ \text{Simple Interest} = \frac{800 \times 3.5 \times 0.5}{100} \][/tex]
[tex]\[ \text{Simple Interest} = \frac{800 \times 3.5 \times 0.5}{100} \][/tex]
[tex]\[ \text{Simple Interest} = \frac{800 \times 1.75}{100} \][/tex]
[tex]\[ \text{Simple Interest} = \frac{1400}{100} \][/tex]
[tex]\[ \text{Simple Interest} = \[14 \][/tex]
Complete correct question:
Principal = $800
Interest Rate = 3.5%
Time = 6 months
Find the interest earnedi
Rob is a high school student taking both algebra and geometry. Last night he had 27 homework problems combined from the two classes, and he took a total of 90 minutes to do them. If each algebra problem took him 2 minutes and each geometry problem took him 5 minutes, how many algebra problems did he have for homework?
2
5
12
15
Answer:
15
Step-by-step explanation:
Let x represent the number of algebra problems. Then the number of geometry problems was 27-x and the total working time was ...
2x +5(27 -x) = 90
-3x = 90 -135 . . . . subtract 135
x = -45/-3 = 15 . . . divide by -3
Rob had 15 algebra problems for homework.
Answer:
15 problems
Step-by-step explanation:
All I need is the answer if your right you will be marked brainzileient
Answer:
C; E
Step-by-step explanation:
They are the only 2 equivalent expressions
Answer:
C & E is the correct answer.
The volume of the prism is 90 cubic meters. Find the value of x
.
The value of [tex]\( x \)[/tex] in a prism with volume [tex]\( 90 \)[/tex] cubic meters is approximately [tex]\( 2.466 \)[/tex] meters.
To find the value of [tex]\( x \)[/tex], knowing the volume [tex]\( V \)[/tex] of the prism, use the formula:
[tex]\[ V = l \times w \times h \][/tex]
Given [tex]\( V = 90 \)[/tex] cubic meters, if we assume the length [tex]\( l = 3x \)[/tex], width [tex]\( w = 2x \)[/tex], and height [tex]\( h = x \)[/tex], then:
[tex]\[ 90 = (3x) \times (2x) \times (x) \][/tex]
[tex]\[ 90 = 6x^3 \][/tex]
[tex]\[ x^3 = \frac{90}{6} \][/tex]
[tex]\[ x^3 = 15 \][/tex]
[tex]\[ x = \sqrt[3]{15} \][/tex]
[tex]\[ x \approx 2.466 \] meters.[/tex]
Based on the scale drawing, what is the length, in feet, of the actual parking lot? On the drawing they have the width 12.8 cm and the length is 3.2 cm.
Answer:
The width of 48 feet is represented by 12.8cm; the length represented by 1cm is 48/12.8 = 15/4 = 3.75 feet.
The length on the drawing is 3.2cm, which is exactly 1/4 of the width of 12.8cm; therefore the length of the actual parking lot is 48/4 = 12 feet.
To find the actual length of a parking lot based on a scale drawing, you need the scale, which is often given as a ratio like '1 cm : 10 ft'. You would multiply the length on the drawing by the scale value to get the actual length. However, without the scale, a definitive answer cannot be provided.
Explanation:To find the actual length of the parking lot, you need to know the scale of the drawing, which is not provided in the current question. The scale is usually expressed as a ratio, essentially representing a conversion factor. An example could be '1 cm : 10 ft', meaning every one centimeter on the drawing represents ten feet in real life.
Let's say the scale is '1 cm : 10 ft' as an example. You would then multiply the scale value (10 ft) by the length of the parking lot on the drawing (3.2 cm). So: 3.2 cm * 10 ft/cm = 32 ft. Hence, in this example, the actual length of the parking lot would be 32 feet. However, without the scale, we cannot provide a definitive answer.
Learn more about Scale Conversion here:https://brainly.com/question/33515865
#SPJ2
David has 56 baseball card I wish he sells three cars per week write an equation representing the number of cards n he has left at the end of any given week W
Answer:
56-3=N
Step-by-step explanation:
David starts with 56 baseball cards and sells 3 per week, so the equation representing the cards remaining after W weeks is n = 56 - 3W.
The equation that represents the number of baseball cards David has left at the end of any given week W is n = 56 - 3W. Here, 'n' stands for the number of cards he has left, '56' is the initial number of cards, '3' is the number of cards he sells each week, and 'W' is the number of weeks that have passed.
For example, at the end of week 1 (when W = 1), David will have:
n = 56 - 3(1) = 56 - 3 = 53 cards left.
At the end of week 2 (when W = 2), it would be:
n = 56 - 3(2) = 56 - 6 = 50 cards remaining.
This pattern continues as more weeks pass.
HELLO? Can anyone answer my question PLS!!! HELP!!!
Write the explicit equation
for the sequence
9, 5, 1, -3, -7…
Answer:
13-4n
Step-by-step explanation:
The generic formula to calculate this is. a+(n-1) d
“a” is the first term and “d” is the difference in our case “a” is 9 and “d” is -4
9+(n-1)(-4)
9-4n+4
13-4n
Answer:
[tex]a_{n}[/tex] = 13 - 4n
Step-by-step explanation:
Note the common difference d between consecutive terms, that is
d = 5 - 9 = 1 - 5 = - 3 - 1 = - 7 - (- 3) = - 4
This indicates the sequence is arithmetic with n th term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 9 and d = - 4, thus
[tex]a_{n}[/tex] = 9 - 4(n - 1) = 9 - 4n + 4 = 13 - 4n ← explicit equation
HELP !
BEST ANSWER GETS MARKED BRAINLIEST !
Answer:
I think u=11
Step-by-step explanation:
A=6a^2
726 divided by 6= 121
square root of 121=11
answer=11
Right Triangle Trig.
The values are vx = [tex]\frac{14\sqrt{3} }{\sqrt{2} }[/tex], vw = [tex]\frac{14\sqrt{3} }{\sqrt{2} }[/tex] and m∠x = 45°, for the given right angle diagram.
Step-by-step explanation:
The given is,
Right angled triangle XVW,
XW = 14[tex]\sqrt{3}[/tex]
m∠V = 90°
m∠W = 45°
Step:1
Given diagram is right angle triangle,
Trigonometric ratios for right angle is,
[tex]sin[/tex] ∅ [tex]=\frac{Opp}{Hyp}[/tex]............................(1)
[tex]cos[/tex] ∅ [tex]= \frac{Adj}{Hyp}[/tex] .........................(2)
[tex]tan[/tex] ∅ [tex]= \frac{Opp}{Hyp}[/tex]..........................(3)
Step:2
For the value of VX,
[tex]sin[/tex] ∅ [tex]=\frac{VX}{XW}[/tex]
From given,
∅ = 45°
XW = 14[tex]\sqrt{3}[/tex]
Above equation becomes,
[tex]sin[/tex] 45 [tex]=\frac{VX}{14\sqrt{3} }[/tex]
Where, Sin 45 = [tex]\frac{1}{\sqrt{2} }[/tex],
[tex]\frac{1}{\sqrt{2} } = \frac{VX}{14\sqrt{3} }[/tex]
[tex]VX = \frac{14\sqrt{3} }{\sqrt{2} }[/tex]
Step:3
For the value of VW,
[tex]cos[/tex] ∅ [tex]=\frac{VW}{XW}[/tex]
From given,
∅ = 45°
XW = 14[tex]\sqrt{3}[/tex]
Above equation becomes,
[tex]cos[/tex] 45 [tex]=\frac{VW}{14\sqrt{3} }[/tex]
Where, cos 45 = [tex]\frac{1}{\sqrt{2} }[/tex],
[tex]\frac{1}{\sqrt{2} } = \frac{VW}{14\sqrt{3} }[/tex]
[tex]VW = \frac{14\sqrt{3} }{\sqrt{2} }[/tex]
Step:4
For the value m∠x = a,
[tex]tan[/tex] a [tex]=\frac{VX}{VW}[/tex]
From given,
VX = [tex]\frac{14\sqrt{3} }{\sqrt{2} }[/tex]
VW = [tex]\frac{14\sqrt{3} }{\sqrt{2} }[/tex]
Above equation becomes,
[tex]tan[/tex] a [tex]=\frac{\frac{14\sqrt{3} }{\sqrt{2} } } {\frac{14\sqrt{3} }{\sqrt{2} } }[/tex]
[tex]tan[/tex] a = 1
a = [tex]tan^{-1}[/tex] (1)
a = 45°
m∠x = a = 45°
Step:5
Check for solution,
m∠v = m∠w + m∠x
= 45° + 45°
90° = 90°
Result:
The values are vx = [tex]\frac{14\sqrt{3} }{\sqrt{2} }[/tex], vw = [tex]\frac{14\sqrt{3} }{\sqrt{2} }[/tex] and m∠x = 45°, for the given right angle diagram.
Which describes a uniform probability model?
A) drawing a red or black card from a deck of cards
B) selecting a ball from 2 red balls and 3 yellow balls
C) selecting a sock from 5 black socks and 10 white socks
D) equally divided five section spinner with three colors
Answer:a
Step-by-step explanation:
One week, Huey worked 7 hours less than Dewey,
and Louie worked twice as long as Huey. Together
they worked 87 hours. Find the number of hours
worked by each.
Answer:
Number of hour worked by Dewey = 27 hours
Number of hour worked by Huey = 20hours
Number of hours worked by Louie = 40 hours
Step-by-step explanation:
Let x be number of hours worked by Dewey
Number of hour worked by Huey = x - 7
Number of hours worked by Louie = 2*(x-7) = 2*x -2*7 = 2x- 14
Together they worked 87 hours
x + x-7 + 2x-14 = 87
4x - 21 = 87
4x = 87 +21
4x = 108
x = 108/4
x = 27 hours
Number of hour worked by Dewey = 27 hours
Number of hour worked by Huey = x - 7 = 27 - 7 = 20hours
Number of hours worked by Louie = 2x - 14 = 2*27 - 14 = 54 - 14 = 40 hours
1. Find the height of a cylinder with a volume of 30 in) and a radius of 1 in.
Answer:
9.55
Step-by-step explanation:
with a radius of 1 and a volume of 30 the height should be around 9.55
The height of the cylinder is 9.549 in with a volume of 30 cubics in and a radius of 1 in.
It is given that the volume of a cylinder is 30 cubic in and the radius is 1 in.
It is required to find the height of the cylinder.
What is volume?It is defined as a three-dimensional space enclosed by an object or thing.
We know the volume of a cylinder:
[tex]\rm V = \pi r^2 h[/tex]
Where r is the radius of a cylinder and h is the height of the cylinder.
Here V = 30 cubic in and r = 1 in
[tex]\rm 30 = \pi\times 1^2\times h[/tex] or
πh = 30
h = 9.549 in
Thus, the height of the cylinder is 9.549 in with a volume of 30 cubics in and a radius of 1 in.
Learn more about the volume here:
https://brainly.com/question/16788902
What is the solution to the system of equations shown in the graph?
A) (0, 5) C) (0, -1)
B) (-2, 1) D) (1, -2)
Answer:
B) (-2,1)
Step-by-step explanation:
The solution is where the two lines intersect, in this case at (-2,1)
Hope this helps! :)
Answer:
B) (-2, 1)
Step-by-step explanation:
2 units left from the origin
So x = -2
1 unit up
So y = 1
Which graph shows the solution set for 2 x + 3 greater-than negative 9?
A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the left of the circle is shaded.
A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the right of the circle is shaded.
A number line going from negative 8 to positive 2. An open circle is at negative 6. Everything to the left of the circle is shaded.
A number line going from negative 8 to positive 2. An open circle is at negative 6. Everything to the right of the circle is shaded.
Correct option is D) A number line going from negative 8 to positive 2. An open circle is at negative 6. Everything to the right of the circle is shaded.
Step-by-step explanation:
We have following inequality :2 x + 3 greater-than negative 9 or ,
⇒ [tex]2x+3>-9[/tex]
Let's solve this :
⇒ [tex]2x+3>-9[/tex]
⇒ [tex](2x+3)+9>-9+9[/tex]
⇒ [tex]2x+12>0[/tex]
⇒ [tex](2x+12)-12>0-12[/tex]
⇒ [tex]2x>-12[/tex]
⇒ [tex]x>-6[/tex]
So , the value of x is greater then -6 . So , Correct option is D) A number line going from negative 8 to positive 2. An open circle is at negative 6. Everything to the right of the circle is shaded.
Answer:
The person in the comments said...
The answer is c. When your dividing by a negative number the arrow is turned around.
Step-by-step explanation:
Hi, have a great day/night whichever one, stay safe and always be kind ^w^
p.s. i'm giving all the credit to the person in the comments
Pythagorean theorem (picture provided)
Answer:
12
Step-by-step explanation:
To solve for a side using pythag:
[tex]\sqrt{37^2-35^2}[/tex]
Highlight the ordered pair that is a the solution. Show your work to justify your answer.
To determine the ordered pair that is a solution, we need an equation or a system of equations.
Explanation:The question asks to highlight the ordered pair that is a solution. To do this, you would need an equation or a system of equations to solve. Without the equation(s), it is not possible to determine the ordered pair that is a solution. Please provide the equation(s) so we can help you further.
Learn more about ordered pair solutions here:https://brainly.com/question/33579562
#SPJ1
The surface area of this square prism is
A) 45 ft2.
B) 69 ft2.
C) 78 ft2.
D) 245 ft2.
Answer:
C) 78 ft2
step-by-step explanation:
(1) volume: V = a²h(2) surface area: S = 2a(a+2h)(2) is the one you want to find out.
Volume= 45 ft2
Surface area= 78 ft2
Alex has trained his puppy, Popper, to jump through a ring. According to Alex's measurements and calculations, the ring has a diameter of 3.5 feet. What is the ring's circumference (use 3.14 for pi)?
Answer:
11 ft
Step-by-step explanation:
The ring takes circular shape and for a circle, circumference is given by
[tex]C=\pi d[/tex]
Where C represent circumference and d is the diameter.
Taking use 3.14 for pi as instructed and substituting 3.5 ft for diameter d then
C=3.14*3.5=10.99 ft
Rounding off, this is approximately 11 ft
Answer:
10.99 ft
Step-by-step explanation:
Given: The ring has a diameter of 3.5 feet
To find: The ring's circumference
Formula: [tex]C = 2\pi r[/tex]
Solution: To calculate the circumference of a circle, multiply the diameter of the circle with π (pi). The circumference can also be calculated by multiplying 2 × radius with pi (π = 3.14).
C = pi × 2r
C = pi × diameter (3.5)
C = 3.14 × 3.5 = 10.99
Hence, the ring's circumference is 10.99 ft
8.888194417 to one decimal place first one gets brainlist
Which equation can be used to find the surface area of the cylinder?
Answer:
the first option
Step-by-step explanation:
the formula to find the surface area of a cylinder is
2πrh+2πr²
Answer:
A=2πrh+2πr2=2·π·4·16+2·π·42≈502.65482
Step-by-step explanation:
up there
What is the variable equal to?
x 7 = 14
Answer:
Varible x equals 2
Step-by-step explanation:
7x = 14
Dividing both sides by 7, we will have
x = 14/7
x = 2
Find the area of the figure to the nearest tenth.