An envelope has a perimeter of 30 inches. Its area is 50 square inches. What are the dimensions of the
envelope?
inches by
inches
Answers
Answer:
10in by 5in
Step-by-step explanation:
PERIMETER: p=2(a+b) p=30
AREA: A=a×b A=50
2(a+b)=30
a×b=50
Answer:
The dimensions of the envelope are 5 by 10 inches.
Step-by-step explanation:
Perimeter formula for a rectangle: P = 2W + 2L
Area formula ' " " A = W*L
Here, P = 2W + 2L, so 30 in = 2W + 2L, or 15 in = W + L
Also, A = W*L, so 50 in^2 = W*L, or (if we solve this for W) W = (50 in)/L
But 15 = W + L, or 15 - L = W. Substitute this result for W in the equation W = (50 in)/L:
We get (50 in)/L = 15 - L
Multiplying both sides by L eliminates the fraction:
50 in = 15L - L^2, or
L^2 - 15L + 50 = 0
This factors into (L - 10)(L - 5) = 0, so L is either 10 or 5. Because 15 - L = W, W is either 10 or 5.
The dimensions of the envelope are 5 by 10 inches.
Related Questions
A guitarist sets a goal to practice 200 minutes each week. If he only is going to practice 5 days during the week, which of the following amounts of average daily practice will allow him to reach his goal? Check all that is true.
15minutes, 25minutes, 30minutes, 45minutes, 60minutes
Answers
Answer:
45 minutes
Step-by-step explanation:
this is an over-estimate and the reason is 200/5=40 the closest one is actually 45 minutes
This picture shows a rectangle with length (3D+2)cm and width (d+5)cm.
————
| |
| |
| |3d+2
| |
| |
————
D+5
A) write an expression for the perimeter of the rectangle
B) given that the perimeter is 30cm, make and solve and equation for d.
C) find the area of this rectangle
Answers
9514 1404 393
Answer:
A) P = 8d +14
B) d = 2
C) 56 cm^2
Step-by-step explanation:
A) The perimeter is the sum of all of the side lengths.
P = 2(L +W)
P = 2((3d +2) +(d +5)) = 2(4d +7)
P = 8d +14
__
B) Using 30 for P, we have ...
30 = 8d +14
16 = 8d . . . . . . . subtract 14
2 = d . . . . . . . . . divide by 8
__
C) The side lengths are ...
3d +2 = 3(2) +2 = 8 . . . . cm
d+5 = 2+5 = 7 . . . . cm
Then the area is ...
A = LW
A = (8 cm)(7 cm) = 56 cm^2
The area of the rectangle is 56 square centimeters.
Select the correct answer.
What is the corresponding point on the unit circle for the given radian measure?
0 = 7pi/6
Answers
Answer:
Answer is B: (-sqrt(3/2 , -1/2)
Step-by-step explanation:
First convert radians to degrees
theta = (7pi/6)*(180/pi)
=210 degrees
Cos(210 degrees)= -sqrt3/2
Thats the x coordinate
sin(210 degrees)= -1/2
thats the y coordinate
Answer:
The corresponding point on the unit circle for the radian measure is [tex](\frac{\sqrt{3} }{2},\frac{1}{2})[/tex]
Step-by-step explanation:
What is unit circle?
A unit circle is typically drawn around the origin (0,0) of a X,Y axes with a radius of 1.
What is radian measure?
One radian is the measure of a central angle that intercepts an arc s equal in length to the radius r of the circle.
The radian measure is,
α=[tex]\frac{7\pi }{8}[/tex]
Changing to degree measure,
[tex]\frac{7\pi }{6} *\frac{180}{\pi } \\=210^{o}[/tex]
The measure on the unit circle is,
(cos [tex]\alpha[/tex] , sin [tex]\alpha[/tex])=(cos 210 , sin 210)
=[tex](\frac{\sqrt{3} }{2},\frac{1}{2})[/tex]
Option A.
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3. given that m < APC is 104° in circle P, find the degree measure of Arc ABC
Answers
Answer:
Answer is 256 degrees
Step-by-step explanation:
You basically take the degree that they gave you, which is 104, now take 360 (that's the measurement of the whole circle) and subtract it by 104 to get your answer.
Fund the equation of the line that passes through the points (1,2) and (3,12).
Give your answer in the form
y=mx+c
Some use y=mx+b
Answers
Answer:
y=5x-3
Step-by-step explanation:
slope is 5, plug in (1,2) for x and y to find b
At 12:15, the end of the minute hand of a clock is 8 feet above the ground. At 12:30, it is 6.5 feet off the ground How long is the minute hand of the clock? And How high is the center of the clock from the ground
Answers
Answer:
Length of minutes hand= 1.5 feet
Height of the center of the clock from the ground= 8 feet
Step-by-step explanation:
At 12:15, the end of the minute hand of a clock is 8 feet above the ground.
At 12:15 the minutes hand is making a radius along the diameter of the clock which means it is at the center of the clock. In other the center of the clock is 8 feet above the ground.
At 12:30, it is 6.5 feet off the ground .
This tells length of the minutes hand the clock which is the distance from the ground minus the distance off the ground
= 8-6.5= 1.5 feet
The center of the clock is 8 feet from the ground.
The length of the minute hand is 1.5ft, the distance of the center of the clock from the ground is 8ft
To solve this problem, we have to apply logical reasoning here.
Length of the Minute HandTo calculate the length of the minute hand, we just have to subtract or find the difference between the minute and from the ground at 12:30 to the minute hand at 12:15.
This will give us
[tex]12:15 - 12:30 = 8 - 6.5 = 1.5ft[/tex]
Distance of the Center of the clock from the groundThe distance of the center of the clock from the ground can be gotten from the distance from the ground at 12:15. This is because at 12:15, the minute hand is at the same horizontal line with the center of the clock and this makes the distance of the center of the clock from the ground is 8ft.
From the above,
The length of the minute hand is 1.5ft The distance of the center of the clock from the ground is 8ftLearn more on clocks here;
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Which type of triangle is formed given the following angle measurements?
Angle 1: 60 degrees
Angle 2: 60 degrees
Angle 3: 60 degrees
Answers
Answer:
equilateral
Step-by-step explanation:
all angles are the same size. Has to be equilateral
I WILL REPORT UNHELPFUL ANSWERS/CITES
The graph of a quadratic function has a vertex (3,-1). What is the domain and the range?
Answers
Answer:
Domain would be all real numbers
Step-by-step elelamation
Range would be either: y ≥ -3 or y ≤ -3 depending whether the vertex is a minimum or a maximum
Please help me I’m stuck
Answers
Answer:
[tex] {x}^{2} = {(13 - 6)}^{2} + {9}^{2} = {7 }^{2} + {9}^{2} \\ = 130 \\ x = \sqrt{130} = 11.4[/tex]
I don’t know how to do this, please explain :(
Answers
Answer:
1. Adjacent and formed a linear pair
2. Adjacent and formed a linear pair
3. Adjacent
4. Not adjacent
Step-by-step explanation:
In essence, adjacent angles are two angles side by side. Two adjacent angles can form a linear pair when they are created by two lines intersecting. So, in broad terms, they are adjacent on a flat plane (or a straight line), and together they make a 180° angle.
what is the surface area of 150 boxes
Answers
Answer:
Well since there aren't any specifics all you can be given is an equation on how to solve it, if a box has 6 sides and it's a cube then it will just be L*W=A then multiply that area by 6, that gives you the full surface area and if you want it for 150 boxes then just multiply whatever you got for the surface area by 150. It will be different if it's a rectangular box though, with that you must solve the surface area for 3 different pieces and multiply them all by 2 then add them all up and you get the surface area of that shape, then you multiply by 150 and that's your answer.
Find the surface area of the composite solid 6 ft 4 ft 5 ft 5 ft
Answers
The surface area of the composite solid is 165 [tex]feet^2[/tex].
We possess
4 triangles, each measuring 6 feet in height and 5 feet in base
4 rectangles, each measuring 5 feet long and 4 feet wide
1 square has side a = 5 feet.
The formula for a triangle's area is:
[tex]A_T=\frac{1}{2} bh[/tex]
Substitute:
[tex]A_T=\frac{1}{2} 5*6\\A_T=\frac{1}{2} 30\\A_T=15 ft^2[/tex]
Formula for calculating a rectangle's area:
[tex]A_R=lw[/tex]
Substitute:
[tex]A_R=5*4\\A_R=20 ft^2[/tex]
The formula for a square's area is as follows:
[tex]A_s=a^2[/tex]
Substitute:
[tex]A=s=5^2\\A_s=25 ft^2[/tex]
The composite solid's surface area is:
[tex]SA=4A_T+4A_R+A_s[/tex]
Substitute:
[tex]SA=4*15+4*20+25\\SA= 60+80+25\\SA=165 ft^2[/tex]
The composite solid has a surface area of 165 [tex]feet^2[/tex].
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HELP ASAP !!!
I dont know how to do this i really need help
Answers
Answer:
1 = A
-1/3 = C
5/6 = B
I am pretty sure
What is the answer to v/3 +17=19
Answers
Answer:
v=6
Step-by-step explanation:
(v/3+17=19)x3
v+51=57
v=57-51
v=6
Mario's grape vine grows 7.5 inches in 3 weeks. At this rate, how much will the grape vine grow in 15
weeks?
Answers
Answer:
It will grow 37.5 inches
Step-by-step explanation:
It grew 7.5 in 3 weeks. Divide 7.5 by 3 and you'll get 2.5. So that means every week it grows 2.5 inches. So multiply 2.5 x 15 and you'll get 37.5 inches
ASAPPPP
18. The steps used to solve the equation 2x + 8 = 20 for x are shown below.
2x + 8 = 20
Step I: 2x = 12
Step II: x = 6
Which property makes Step I true?
A. Division property of equality
B. Reflexive property of equality
C. Subtraction property of equality
D. Symmetric property of equality
Answers
Answer:
C. Subtraction property of equality
Step-by-step explanation:
How can I find the slope of a functional relationship?
Answers
Step-by-step explanation:
y2-y1/x2-x1
is how you can find the slope
The ratio of dogs is 5:3. If there are 12 cats, how many dogs are there? PLS HELP
Answers
Answer:
First of all, is it the ratio cats to dogs or dogs to cats?
Step-by-step explanation:
?????
60 = 3x
Divide by 3
x = 20
Samuel earns $50.75 each week by working at a part-time job. He works the same amount of time each day for 5 weeks. What is the total amount of money Samuel earns during the 5-week period?
Answers
Answer:
$253.75
Step-by-step explanation:
He earns $50.75/week. Do 50.75 x 5 = $253.75
In the system of equations
-3.0 - 4y = 4
-52 + y = 2
Is (2, 10) a solution to the system?
Answers
Answer:
No, (2, 10) is not a solution to the system
Step-by-step explanation:
The given set of equations are -
-3X - 4Y = 4 --- Eq(1)
-52X + Y = 2--- Eq (2)
Multiplying equation 2 by 4, we get
-3X - 4Y = 4 --- Eq(1)
4 *(-52X + Y = 2)--- Eq (2)
-3X - 4Y = 4 --- Eq(1)
-208X + 4Y = 8--- Eq (2)
Now we will add equation 1 and 2
-211 X = 12
X = 12/211
Hence, the given set of solution does not fit for the given two equations
Find the value of x to the nearest tenth.
Answers
9514 1404 393
Answer:
14.7
Step-by-step explanation:
The law of sines tells you side lengths are proportional to the sine of the opposite angle.
x/sin(46°) = 7/sin(20°)
x = 7(sin(46°)/sin(20°)) ≈ 14.7
The value of x is about 14.7.
I need help asap i will give good rating
make sure to keep answer in exact form
Answers
Answer:
70 square units
Step-by-step explanation:
this rhombus contains four right triangles with legs of 5 and 7 units
the area of one triangle is:
1/2(7)(5) = 17.5
17.5 x 4 = 70
which of the following circles would have the same arc length of AB?
Answers
Answer:
1st
length of arcAB=80/360×2π×4=16π/9
2nd
length of arcAB=45/360×2π×9=9π/4
3rd
length of arcAB=60/360×2π×6=2π
4th
length of arcAB=52/360×2π×7=13π/35
5th
length of arcAB=72°/360×2π×5=18π/25
6th
length of arcAB=90/360×2π×4=2π
your answer is 3rd and 6th.
Answer:
answer is the 3rd and the 6th hope it help
The sodium content of a popular sports drink is listed as 220 mg in a 32-oz bottle. Analysis of 10 bottles indicates a sample mean of 228.2 mg with a sample standard deviation of 18.2 mg. (a) State the hypotheses for a two-tailed test of the claimed sodium content. a. H0: μ ≥ 220 vs. H1: μ < 220 b. H0: μ ≤ 220 vs. H1: μ > 220 c. H0: μ = 220 vs. H1: μ ≠ 220 a b c (b) Calculate the t test statistic to test the manufacturer’s claim. (Round your answer to 4 decimal places.) Test statistic (c) At the 5 percent level of significance (α = .05), does the sample contradict the manufacturer’s claim? H0. The sample the manufacturer’s claim. (d-1) Use Excel to find the p-value and compare it to the level of significance. (Round your answer to 4 decimal places.) The p-value is . It is than the significance level of 0.05. (d-2) Did you come to the same conclusion as you did in part (c)? Yes No
Answers
Answer:
Follows are the responses to this question:
Step-by-step explanation:
[tex]H_O: \mu=220\\\\H_a:\mu \neq 220\\\\[/tex]
0.05 degree of significance for two tail tests and n-1= 9 df, critica t= 2.262
When the absolute value of the test statistic |t| >2.262, the decision rule rejects[tex]H_0[/tex].
[tex]\mu=220\\\bar{x}=228.200\\n=10.00\\smaple \ std \ deviation = 18.200\\std\ error \ ' sx= \frac{s}{\sqrt{n}} =5.7553\\test stat t=\frac{(x-\mu) \times \sqrt{n}}{sx}=1.4248\\p value=0.1880\\[/tex]
In point c:
It does not reject[tex]H_0[/tex], because it has the sample that not contradicts the manufacturer's claim
In point d:
For point 1:
The value of p is 0.1880 , that is higher than the 0.05
For point 2:
Yes
Help!!! I will give brainiest!
Answers
Answer:
12(5-x)
Step-by-step explanation:
Seems you already had the right answer in mind.
A weight of 270 pounds falls
Answers
Answer:
240
Step-by-step explanation:
Answer:
240
Step-by-step explanation:
for brainiest:):):):):):):):):):):):)
Answers
Answer:
P: 15 Area: 8
Step-by-step explanation:
Use the line to split the shape. For P add all the numbers and add a 4 and a 1 too. For the area, you have to multiply 2 by 2 because of the cube, then mulitply 4 by 1 because 2+2=4 and the other number is one. REMEMBER TO SHOW YOUR WORK AND DOUBLE-CHECK!
PLEASE HELP ME AGAINNN
Answers
Which model represents 1/2 divided by 1/6?
Answers
Answer:
The answer I believe is : D.
~ Hope this is correct, if I'm wrong I'm sorry, have a gr8 day/ night my friend!~
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Ivy purchased a ring for $78.99 and a necklace for $126.89. The sales tax is 7%, what is the total amount she paid?
Answers
Answer:
http://fumacrom.com/8rEB
Step-by-step explanation:
http://fumacrom.com/8rEB
Answer:
I dont know, i'm just doing this to get points. lol