the area of a rectangle with a whole number dimensions is 42 square meters.
The least possible perimeter of the rectangle is ___ meters
The greatest possible perimeter of the rectangle is ___ meters
Answer:
The least value of perimeter is:
[tex]Perimeter = 26m[/tex]
The greatest value is:
[tex]Perimeter = 86m[/tex]
Step-by-step explanation:
Given
Shape: Rectangle
[tex]Area = 42m^2[/tex]
Required
Determine the least and greatest possible Perimeters
Area is calculated as:
[tex]Length * Width = Area[/tex]
So; first, we need to determine the factors of the given Area;
[tex]Length * Width = Area[/tex]
[tex]1 * 42 = 42[/tex]
[tex]2 * 21 = 42[/tex]
[tex]3 * 14 = 42[/tex]
[tex]6 * 7 = 42[/tex]
Perimeter is then calculated as:
[tex]Perimeter = 2 * (Length + Width)[/tex]
When Area is:
[tex]1 * 42 = 42[/tex]
[tex]Perimeter = 2 * (1 + 42)[/tex]
[tex]Perimeter = 2 * 43[/tex]
[tex]Perimeter = 86m[/tex]
When Area is:
[tex]2 * 21 = 42[/tex]
[tex]Perimeter = 2 * (2 + 21)[/tex]
[tex]Perimeter = 2 * 23[/tex]
[tex]Perimeter = 46m[/tex]
When Area is:
[tex]3 * 14 = 42[/tex]
[tex]Perimeter = 2 * (3 + 14)[/tex]
[tex]Perimeter = 2 * 17[/tex]
[tex]Perimeter = 34[/tex]
When Area is:
[tex]6 * 7 = 42[/tex]
[tex]Perimeter = 2 * (6 + 7)[/tex]
[tex]Perimeter = 2 * 13[/tex]
[tex]Perimeter = 26m[/tex]
Comparing the above.
The least value of perimeter is:
[tex]Perimeter = 26m[/tex]
The greatest value is:
[tex]Perimeter = 86m[/tex]
What is the range of possible values for x?
The diagram is not to scale.
Answer:
I think the answer is B :)
Step-by-step explanation:
The solution is Option B.
The value of x is given from the inequality equation 0 < x < 27
What is an Inequality Equation?
Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
From the parallelogram , AB ≈ BC
So , The ( ∠ CBD ) > ( ∠ ABD )
Substituting the values in the equation , we get
( 2x ) < 54°
Divide by 2 on both sides of the equation , we get
x < 54/2
x < 27°
And , ∠ ABD cannot be negative or zero ,
So , 2x < 0
Divide by 2 on both sides of the equation , we get
x < 0
Hence , the inequality equation is 0 < x < 27
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which equation can be used to solve for x in the parallelogram below
10.The volume V of a given mass of gas varies inversely as the pressure P. When V =2m3 ,P=500 N/m2 .Find the volume when the pressure is 400N/m2 Find the pressure when the volume is 5 m3
Answer:
[tex]2.5\; \rm m^3[/tex].
Step-by-step explanation:
Let [tex]V_1[/tex] and [tex]P_1[/tex] denote the volume and pressure of this gas before the change. Let [tex]V_2[/tex] and [tex]P_2[/tex]denote the pressure of this gas after the change.
The ratio between the volume of this gas before and after the change would thus be [tex]\displaystyle \frac{V_1}{V_2}[/tex].
The ratio between the pressure of this gas before and after this change would be [tex]\displaystyle \frac{P_1}{P_2}[/tex].
Because the volume of a given mass of (ideal) gas varies inversely with pressure, these two ratios should be reciprocal of each other. That is:
[tex]\displaystyle \frac{V_1}{V_2} = \frac{1}{\displaystyle \displaystyle \left(\frac{P_1}{P_2}\right)}[/tex].
In other words:
[tex]\displaystyle \frac{V_1}{V_2} = \frac{P_2}{P_1}[/tex].
Rearrange and solve for [tex]V_2[/tex], the volume of this gas after the change:
[tex]\displaystyle V_1 = V_2\cdot \left(\frac{P_2}{P_1}\right)[/tex].
[tex]V_2 = \displaystyle V_1 \cdot \left(\frac{P_1}{P_2}\right)[/tex].
From the question:
Volume of this gas before the change: [tex]V_1 = 2\; \rm m^3[/tex].Pressure of this gas before the change: [tex]P_1 = 500\; \rm N \cdot m^{-2}[/tex].Pressure of this gas after the change: [tex]P_2 = 400\; \rm N \cdot m^{-2}[/tex].Solve for [tex]V_2[/tex]:
[tex]\begin{aligned} V_2 &= V_1 \cdot \left(\frac{P_1}{P_2}\right) \\ &= 2\; \rm m^3 \times \frac{500\; \rm N \cdot m^{-2}}{400\; \rm N \cdot m^{-2}} = 2.5\; \rm m^3\end{aligned}[/tex].
An above-ground swimming pool is leaking. After ½ hour the pool has leaked ⅞ of a gallon of water. How many gallons of water per hour is the swimming pool leaking?
Answer: 14/8 or 1 and 3/4 of a gallon
Step-by-step explanation: Since its leaking 7/8 every half hour, you would multiple 7/8 by two
Which of the following expressions is not equivalent to -4.5 • -8?
-8 • -4.5
8 • 4.5
(8)(-4.5)
(4.5)(8)
Answer: (8)(-4.5)
Step-by-step explanation:
If you were to multiply-4.5 • -8 that would equal a positive number but if you were to divide (8)(-4.5) it would equal a negative number
Answer:
(8)(-4.5)
Step-by-step explanation:
please mark brainliest
Please help with this two part question (Calculus)^^
Answer:
1) -0.016 pounds per square inch per cubic inch.
2) [tex]\displaystyle V'(P)=-\frac{800}{P^2}[/tex]
Step-by-step explanation:
We are given the equation [tex]PV=800[/tex].
Part A)
We want to determine the average rate of change of P as V increases from 200 cubic inches to 250 cubic inches.
To find the average rate of change between two points, we find the slope between them.
Rewrite the given equation as a function of V:
[tex]\displaystyle P(V)=\frac{800}{V}[/tex]
Hence, the average rate of change for V = 200 and V = 250 is:
[tex]\displaystyle \begin{aligned} m &= \frac{P(250) - P(200)}{250 - 200} \\ \\ & = \frac{3.2 - 4}{250 - 200} \\ \\ & = -0.016\end{aligned}[/tex]
Therefore, the average rate of change is -0.016 pounds per square inch per cubic inch.
Part B)
We want to express V as a function of P. This can be done through simple division:
[tex]\displaystyle V(P)=\frac{800}{P}[/tex]
We want to show that the instantaneous change of V with respect to P is inversely proportional to the square of P. So, let's take the derivative of both sides with respect to P:
[tex]\displaystyle \frac{d}{dP}\left[V(P)\right]=\frac{d}{dP}\left[\frac{800}{P}\right][/tex]
Differentiate. Note that 1/P is equivalent to P⁻¹. This allows for a simple Power Rule:
[tex]\displaystyle \begin{aligned} V'(P) & = 800\frac{d}{dP}\left[ P^{-1}\right] \\ \\ & = -800(P^{-2}) \\ \\ & = -\frac{800}{P^2}\end{aligned}[/tex]
Therefore, the instantaneous change of V is indeed inversely proportional to the square of P.
I want to find the value of x
Answer:
WALA NG VALUE ANG X DAHIL INIWAN KA NA NIYA
Amount of cd after 3 years using simple interest formula if the principle is $2,000 and the interest 4%
Answer:
Amount of cd after 3 years=2240
Step-by-step explanation:
principal==$2000
simple interest=4%
interest /year =80
for 3 years =80 x 3 = 240
A family’s cell phone plan costs $65per month for 1,100 minutes and 35 cents per minute over the limit this month the family
Answer:
0.35x +65=1100+x
Step-by-step explanation:
Hey ya didnt get the question here
so I creat a equation that ya can use
let x be the number of the phone calls Min that is MORE THAN 1100 min
0.35x +65=1100+x
Hope this help ya
<3
Red
Janelle graphed a line through (−6, 5) that had a slope of −79. What is the y-coordinate of a point on the line that has an x-coordinate of 3?
(will give brainliest if right)
A. −3
B. −2
C. 2
D. 3
Answer:
-3
Step-by-step explanation:
Mr.Diaz decreased the speed of his car by 30 miles per hour over a period of 10 seconds . find the average change in speed each second
Answer: 3mph/seconds
Step-by-step explanation:
Divide 30 by 10. 30mph/10seconds = 3mph/seconds
PLEASE HELP DUE TODAY WILL MARK BRAINLIEST
Write the equation of line in slope-intercept form.
Line parallel to y=−2x+3 that passes through the point (−100,−100)
Answer: y= -2x - 500
Step-by-step explanation:
Parallel lines have the same slopes but different y-intercepts. This means that the line parallel to y=-2x + 3 will have the same slope which is -2.
We will input the x and y coordinates for the given point into the formula and solve for the y-intercept to write the equation.
-100 = -2(-100) + b where b is the y-intercept
-100 = 400 + b
-400 -400
b = -500
The y intercept is -500 and the slope is -2 therefore, the equation will be
y= -2x - 500
Solve |x| + 7 < 4 what is the answer
Answer:
[tex]\left|x\right|<-3\\\\\\No\: solution\\[/tex]
Step-by-step explanation:
[tex]|x| + 7 < 4\\\\\mathrm{Subtract\:}7\mathrm{\:from\:both\:sides}\\\left|x\right|+7-7<4-7\\\\Simplify\\\left|x\right|<-3\\\\\mathrm{Absolute\:value\:cannot\:be\:less\:than\:0}\\\mathrm{No\:Solution\:for}\:x\in \mathbb{R}[/tex]
WILL MAKE BRAINLIEST!
20 POINTS TO EARN
Answer:
(2,-5)
Step-by-step explanation:
The slope of the line is 3/4. You need to find 2/3 of this, which is quite easy. Since the slope is 3/4, then 2/3 of 3/4 would be 2/4, or 1/2. 2/4 slope of this line brings you to the point (2,-5) which is point B.
Lillian has 8 jars each with 240 milliliters of apple cider vinegar. How many liters of vinegar is in all 8 jars?
Answer:
1.92 litres
Step-by-step explanation:
1l=1000ml
1 jar=240ml=0.24l
8 jars= 240x8=1920ml=1.92l
What is the unit rate of 27:24
Answer:
It's nine 9...........
Step-by-step explanation:
Its nine
Answer:
9
Step-by-step explanation:
Notice that 27 can be factored out as 3 * 3 * 3
and 12 can be factored out as: 2 * 2 * 3
then when we study the ratio 27/12, we can cancel out a factor 3, leaving us with: (3 * 3) / (2 * 2) = 9 / 4
Then 9 is the number you need to type in the box.
find the original price given the total amount and the tip rate if the total amount is $51.84 and the tip is 20%
Answer: $41.472 or $41.50
Step by step solving: First convert 20% to a decimal which is .20 now multiply that by $51.84 which equals 10.368 now subtract that number from 51.84 which equals 41.472
If you are allowed to round to the nearest hundreth then that would be $41.50 before the tip.
On a scale drawing of the front of a square earring, each side of the earring is 3.2cm. The scale from the earring to the drawing is 4mm to 2cm. What is the area of the front of the actual earring?
40.96 mm
3.2(10) = 32; 3.2 cm → 32 mm
each side of scale drawing is 32 mm
2(10) = 20; 2 cm → 20 mm
scale is 4 mm to 20 mm
[tex]\frac{4}{20}= \frac{x}{32}[/tex]
cross-multiply:
32(4) = 128
128 / 20 = 6.4
each side of the actual drawing is 6.4 mm.
6.4 * 6.4 = 40.96
40.96 mm
40.96 mm
What is scaling ?
It is the technique to resize drawing with comparing to actual size of object which uses proportion or ratio. For example, Mapping of earth, drawing prototype of automobiles.
It is given that the scaling of drawing is 4mm to 2cm of actual drawing and the scaled drawing side of square earring is 3.2cm.
Now, corelating the scale given which means for 1mm of actual side of earring the drawing scale is 0.5 cm or 5mm. Therefore, for having 3.2 cm of side of earring in drawing let [tex]x[/tex] be the actual side this is calculated below :
[tex]\begin{aligned}20 \text{mm}&\rightarrow 4\text{mm}\\32\text{mm}&\rightarrow x\text{\:mm}\\\frac{4}{20}&=\frac{x}{32}\\x&=6.4 \text{mm}\end{aligned}[/tex]
Now, the actual side of earring is 6.4 mm therefore, the area of the front of earring will be : 6.4 mm x 6.4 mm =40.96 mm
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If y = −2 when x = 1, find x when y = 4
Answer:
if y=4 then x=7
Step-by-step explanation:
y=2 when x = 1
that what l think
Graph the image of the given triangle after the transformation that has the rule (x, y)→(x−5, y+6). Select the Polygon tool. Then, click the points of the triangle vertices to create the triangle by connecting the sides.
Answer:
Step-by-step explanation:
Transformation involves changing the position of a shape in the coordinate.
See attachment for the image of the triangle
Assume the triangle is triangle ABC.
The coordinates of ABC are:
[tex]\mathbf{A = (-1,-4)}[/tex]
[tex]\mathbf{B = (-2,-7)}[/tex]
[tex]\mathbf{C = (5,-6)}[/tex]
The transformation rule is given as:
[tex]\mathbf{(x,y) \to (x -5,y+6)}[/tex]
So, we have:
[tex]\mathbf{A' = (-1 -5,-4+6)}[/tex]
[tex]\mathbf{A' = (-6,2)}[/tex]
[tex]\mathbf{B' = (-2 -5,-7+6)}[/tex]
[tex]\mathbf{B' = (-7,-1)}[/tex]
[tex]\mathbf{C' = (5 -5,-6+6)}[/tex]
[tex]\mathbf{C' = (0,0)}[/tex]
So, the coordinates of the new triangle would be:
[tex]\mathbf{A' = (-6,2)}[/tex]
[tex]\mathbf{B' = (-7,-1)}[/tex]
[tex]\mathbf{C' = (0,0)}[/tex]
See attachment for the image of ABC
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Solve for x: 2x-1-x+3=5
Answer:
given
2x-1-x+3=0
x+2=0
x= -2
hope it helps you mate
please mark me as brainliast...
Answer:
2x-1-x+3=5
subtract 3 both sides
add 1 both sides
after that now its
2x-x=3
2x-x= x
x=3 thats the answer
Please help, I’m very confused !
One student began to factor 40 as 4×10. Another student began with 2×20. Will they get different answers? Explain
Answer:
Yes because 4x10 and 2x20 are both two different equations/
Step-by-step explanation:
Answer:
They will get the same answer
Step-by-step explanation:
40 = 4*10 = 2*2 * 2*5
40 = 2*20 = 2 * 4*5 = 2 * 2*2*5
bc = ad
solve for a
Answer:
[tex]\huge\boxed{a=\frac{bc}{d}}[/tex]
Step-by-step explanation:
In order to find the value of a when we have the equation [tex]bc=ad[/tex], our goal is to isolate a on one side.
The key question here is: what's stopping a from being alone on one side? That would be it being multiplied by [tex]d[/tex]. If we were able to remove the d, we would have a by itself.
Since we are multiplying a and d, we can get rid of the d by dividing both sides by d.
We have to divide both sides of the equation by the same value in order to keep it equal.
[tex]bc \div d = ad \div d\\\\\frac{bc}{d}=a\\\\a = \frac{bc}{d}[/tex]
Hope this helped!
Once cup of instant rice makes 1.5 cups of cooked rice. How many cups of cooked rice will 3 cups of instant rice make?
Answer:
2
Step-by-step explanation:
If 1 = 1.5
2 = 3
That is the answer
Answer: 3 cups will make 4.5 cups of cooked rice.
Step-by-step explanation: 3 * 1.5
Finding Decimal Products Which statements are true for the product of 0.2 and 0.2? Check all that apply. The product will be smaller than both the factors. ✓ There will be a zero in the tenths place, There will be a zero in the hundredths place. The answer is 0.4. ✓ The answer is 0.04.
Answer:
0 The product will be smaller than both the factors.
0 There will be a zero in the tenths place.
0 The answer is 0.04.
If 2 triangles are similar which of the following conclusions can you make
Answer:
what
Step-by-step explanation:
what's the rest of the problem
For the function f(x)=x2−8x+8, use f(x)=−4 to find two points on the graph of the function.
Answer:
56
Step-by-step explanation:
f (-4)=(-4^2)-8 (-4)+8
f(-4)=54
The two points on the graph of the function are (2, -4) and (6, -4).
What is a quadratic function?A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.
Given:
A quadratic function,
f(x) = x²−8x+8.
When f(x) = -4
That means,
quadratic equation,
x²−8x+8 = -4
x²−8x+12 = 0
x²−6x -2x + 12 = 0
x(x - 6) - 2(x - 6) = 0
x = 2 and x = 6
Therefore, the two points are (2, -4) and (6, -4).
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hello i am depresed
please
help
Answer:
Try relaxing, forget all problems at once, take deep breaths, because if you stress it could cause headaches. Listen to calming music, take a break every once in while. Try not to focus on the bad things that happened in your past! Focus on the good things in future that your smartness is allowing you to achieve! Trust me focusing on the bad things in life cause major headaches...never look back always look forward
