The length of a rectangular birthday party invitation is 1 inch less than twice its width. The area of the invitation is 15 square inches.
Answers
The length of a rectangular birthday party invitation is 9 inch.
The length of a rectangular birthday party invitation is 1 inch less than twice its width.
Area of the invitation 15 square inches.
what is the area of the rectangle?
A=length× width
That is,the area of a rectangle is length times width.
let x be the width rectangle
width = x
length = 2x - 1
\(Area= 15 square inches\)
Using these variables, set up the equation for area.
x(2x - 1) = 15
Solve the equation for x.
\(2x^{2} - x = 15\)
Subtract 21 on both sides of the equation.
\(2x^{2} - x - 15=0\)
Which method we use to factor the polynomial?
FOIL method
Factor using FOIL, if possible.
(2x +5)(x - 5) = 0
Set the factors equal to zero and solve for x.
2x = -5 and x - 5 = 0
x =- 5/2 or x = 5
x =- 2.5 or x=5
Since we cannot accept a negative value for dimensions, we accept the positive value of x:
x = 5
Therefore,
Length = 2(5) - 1
Length = 10-1
Length = 9
Therefore we get the length is 9 inch
To learn more about the length visit:
https://brainly.com/question/2005046
Related Questions
What is the sum of 1.57 and 6.88?
Answers
Answer:
8.45
Step-by-step explanation:
Find the sum by adding the two numbers together:
1.57 + 6.88
= 8.45
So, the sum is 8.45
in the figure, four long straigfht wires are perpendicular to the page, and their corss sections form a square edge length a. what is the magnitude of the net magnetic field at the square's center?
Answers
The magnitude of the net magnetic field at the square's center is \(= (7.94 * 10^{-4}N/m)i+(-7.94 * 10^{-4}N/m)j\).
Using \(dB=\frac{u_0i}{4\pi} \frac{sin\theta}{r^2}\) the force on say, wire 1 (the wire at the upper left of the figure) is along the diagonal (pointing toward wire 3, which is at the lower right). Only the forces (or their components) along the diagonal direction contribute. With θ=45°, we find the force per unit meter on wire 1 to be
\(f_1 = |F_{12}+F_{13}+F_{14}|\\\\= 2F_{12}cos\theta+f_{13}\\\\=2(\frac{u_0i^2}{2\pi a} )cos45^0+\frac{u_0i^2}{2\sqrt{2}\pi a }\)
\(=\frac{3}{2\sqrt{2}\pi }(\frac{u_0i^2}{0})\\\\=\frac{3}{2\sqrt{2}\pi } \frac{(4\pi*10^{-7}T.m/A)(15.0A)^2} {(8.50*10^{-2}m)}\)
\(= 1.12 * 10^{-3}N/m\)
The direction of F1 is along r^=(i^=j^)/sqrt2. In unit-vector notation, we have
\(F_1 = \frac{(1.12 * 10^{-3}N/m)}{\sqrt{2} }(i - j) \\\\= (7.94 * 10^{-4}N/m)i+(-7.94 * 10^{-4}N/m)j\)
Hence the answer is the magnitude of the net magnetic field at the square's center is \(= (7.94 * 10^{-4}N/m)i+(-7.94 * 10^{-4}N/m)j\).
To learn more about perpendicular click here https://brainly.com/question/28063031
#SPJ4
At one store, you can purchase 7 apples for $5. 46. At another store, you canget 5 apples $3. 95. Which is the better deal.
Answers
As long as N is significanly less than K, logistic growth is indistinguishable from exponential O True O False if dN/dt > 0, then N O equals to zero O decreases O remains stable O increases
Answers
The statement "As long as N is significantly less than K, logistic growth is indistinguishable from exponential" is false. If dN/dt > 0, then N increases.
The statement "As long as N is significantly less than K, logistic growth is indistinguishable from exponential" is false. Logistic growth takes into account the carrying capacity of the environment, represented by K, which limits the growth of a population as it approaches this limit. In contrast, exponential growth assumes an unlimited supply of resources and no constraints on population growth. Therefore, as N approaches K, logistic growth begins to level off, while exponential growth continues to increase indefinitely.
If dN/dt > 0, then N increases. This means that the population size is growing at a positive rate. If dN/dt is equal to zero, then N remains stable, indicating that the population size is not changing. Finally, if dN/dt is negative, then N decreases, indicating that the population size is shrinking. Therefore, the correct answer to this question is "increases."
for more questions on logistic growth
https://brainly.com/question/2102628
#SPJ11
How many sheets of standard notebook paper (8.5 in x 11 in) would it take to cover a football field (50 yards x 120 yards)?
Answers
By using metric conversion concept, it can be concluded that it would take approximately 83,084 sheets of standard notebook paper to cover a football field.
Metric Conversion refers to the conversion of the given units to desired units for any quantity to be measured.
For example, to convert 5 meters to centimeters, a conversion factor is required. Thus, the conversion factor is “multiplying by 100”.
To determine the number of sheets of standard notebook paper it would take to cover a football field, we need to use measurement to calculate the area of both the football field and the notebook paper.
First, let's calculate the area of the football field:
The area of the football field = 50 x 120
= 6,000 square yards.
Next, we need to convert the measurement of the notebook paper from inches to yards, where the length in yards is equal to the inches divided by 36.
8.5 in = 0.236 yard
11 in = 0.306 yard
The area of the notebook paper = 0.236 x 0.306
= 0.072216 square yards.
Finally, we can divide the area of the football field by the area of the notebook paper to determine the number of sheets it would take to cover the field to get the number of sheets of notebook paper:
Number of sheets of notebook paper = 6,000 / 0.072216
= 83,084.08 sheets of notebook paper.
Therefore, it would take approximately 83,084 sheets of standard notebook paper to cover a football field.
To learn more about metric conversion, click here: https://brainly.com/question/30360455
#SPJ11
help appreciated thanks
Answers
Answer:
No
Step-by-step explanation:
x=(b-5)/c≠(5-b)/c
supposedly
b=6
c=1
x=6-5/1=1
x=5-6/1= -1
1≠ -1
Answer:
No
Step-by-step explanation:
x = b - 5 / L equal to - (5 - b) / L
How to graph something
Answers
Answer:
plot x and y co-ordinates after drawing axis
Can someone please help rq
Answers
Answer:
19
Step-by-step explanation:
zót95zktTkzktzktzltl
\(\frac{2x-5}{3}=11 \ \ /\cdot3\\\\2x-5=33 \ \ /+5\\\\2x=38 \ \ /:2\\\\\huge\boxed{x=19}\)
The points a(-3,6), b(2,1) and c(-3,1) are the corners of a triangle. what type of triangle is it
Answers
The triangle formed by the points A(-3, 6), B(2, 1), and C(-3, 1) is an isosceles triangle.
To determine the type of triangle formed by these points, we can analyze the lengths of the sides.
The distance between points A and B can be calculated using the distance formula: √((x2 - x1)^2 + (y2 - y1)^2). In this case, the distance between A(-3, 6) and B(2, 1) is √((2 - (-3))^2 + (1 - 6)^2) = √(25 + 25) = √50.
The distance between points B and C is √(((-3) - 2)^2 + (1 - 1)^2) = √((-5)^2 + 0) = 5.The distance between points C and A is √((-3 - (-3))^2 + (1 - 6)^2) = √(0 + 25) = √25 = 5.Comparing the lengths of the sides, we can see that all three sides have the same length: √50 = 5.
An isosceles triangle is a triangle that has two sides of equal length. Since the triangle formed by the points A, B, and C has two sides with a length of 5 units, it is classified as an isosceles triangle.Therefore, the triangle formed by the points A(-3, 6), B(2, 1), and C(-3, 1) is an isosceles triangle.
Learn more about triangle here:
https://brainly.com/question/2773823
#SPJ11
solve by using the quadratic formula
Answers
Answer:
H =
\(x = \frac{7 + - i \sqrt{71} }{10} \)
I =
\(x = \frac{ - 1 + - i \sqrt{35} }{6} \)
Quadratic Formula
x = -b +- sqrt{b^2 - 4ac}/(2a)
For question H, subtract 4 from 10 and equate to 0. We now let a = 5, b = -7 and c = 6.
Plug into the formula and do the math..
For question I, subtract 7 from 13 and equate to 0. We know let a = 6, b = 2 and c = 6.
Plug into the formula and do the math.
In a series of transformations, which transformation would make two figures similar as opposed to congruent?dilationreflectionrotationtranslation
Answers
Answer:
A dilation would make them similar. Similar is the same shape, but not necessarily the same size. A dilation is a transformation that can make figures shrink or expand. The other forms of transformations are rigid. They do not change the size.
Step-by-step explanation:
What is the answer please…
Answers
Answer:
answer is T 25............
Make a table of solutions for y = 16x + 4 using values x = 1, 2, 3, and 4.
Answers
X Y
1, 20
2, 36
3, 52
4, 68
The solution table for the given expression:
X Y
1, 20
2, 36
3, 52
4, 68
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given the equation is y = 16x + 4. The value of y will be calculated as,
y = 16x + 4
y = 16 x 1 + 4 = 20
y = 16x + 4
y = 16 x 2 + 4 = 32 + 4 = 36
y = 16x + 4
y = 16 x 3 + 4 = 48 + 4 = 52
y = 16x + 4
y = 16 x 4 + 4 = 64 + 4 = 68
To know more about an expression follow
https://brainly.com/question/723406
#SPJ2
write the equation of the line that passes through the point (-2,4) and (5,8). Put your answer in fully reduced point slope form, unless it is a vertical or horizontal line.
Answers
Answer:
y-4=4(x+2)/7
Step-by-step explanation:
slope(m) = (8-4)/(5-(-2)) =4/7
b = 4-(4/7)×(-2) = 36/7
y = mx+b
y = 4x/7+36/7
in point-slope form,
y-4=4(x+2)/7
Air flows into the duct of air-conditioner at 101kPa and 10∘C at a rate of 17 m^3 /min. The diameter of the duct is 23 cm and heat is transferred to the air in the duct by the air-conditioner at a rate of 5 kW. 5. The speed (rounded to two decimal places) of the air as it enters the duct is equal to: (a) 7,36 m/s (b) 6,40 m/s (c) 4,86 m/s (d) 6,82 m/s (e) 10,11 m/s 6. The temperature (rounded to two decimal places) of the air as it exits the duct is equal to: (a) 23,72∘C (b) 23,94∘C (c) 23,65∘C (d) 24,08∘C (e) 24,37∘C
Answers
The correct answer is the speed of the air as it enters the duct is approximately 6.79 m/s.the temperature of the air as it exits the duct is approximately 24.19°C.
To find the speed of the air as it enters the duct, we can use the continuity equation, which states that the mass flow rate of a fluid is constant along a flow path. The equation is given as:
A1v1 = A2v2,
where A1 and A2 are the cross-sectional areas of the duct at the entrance and exit respectively, and v1 and v2 are the speeds of the air at the entrance and exit respectively.
Given:
A1 = π(\(0.23/2)^2 = 0.04173 m^2\) (convert diameter to radius)
A2 = A1 (since the duct diameter remains constant)
v1 = ? (to be determined)
v2 = ? (to be determined)
We also know that the volume flow rate (Q) is given as:
Q = A1v1 = 17 m^3/min = 0.2833 m^3/s (convert minutes to seconds)
Now we can rearrange the equation to solve for v1:
v1 = Q / A1 = 0.2833 m^3/s / 0.04173 m^2
v1 ≈ 6.79 m/s (rounded to two decimal places)
Therefore, the speed of the air as it enters the duct is approximately 6.79 m/s.
To determine the temperature of the air as it exits the duct, we can use the first law of thermodynamics, which states that the rate of heat transfer (Q) is equal to the mass flow rate (ṁ) times the specific heat capacity (Cp) times the change in temperature (ΔT):
Q = ṁ * Cp * ΔT,
where Q is given as 5 kW, ṁ is the mass flow rate (which remains constant), Cp is the specific heat capacity of air at constant pressure, and ΔT is the change in temperature.
Given:
Q = 5 kW = 5000 W
ṁ = ρ * Q = ρ * A2 * v2 (mass flow rate equation, assuming constant density)
Cp = specific heat capacity of air = 1005 J/(kg⋅K) (approximately)
ΔT = ? (to be determined)
We need the density (ρ) of the air to calculate ṁ. Using the ideal gas law:
PV = nRT,
where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
We know:
P = 101 kPa = 101000 Pa
V = Q = 0.2833 m^3/s
R = 8.314 J/(mol⋅K) (ideal gas constant)
T = 10°C = 283.15 K (convert Celsius to Kelvin)
Rearranging the ideal gas law equation and solving for n:
n = PV / RT = (101000 Pa * 0.2833 m^3/s) / (8.314 J/(mol⋅K) * 283.15 K)
n ≈ 12.102 mol (rounded to three decimal places)
Since the molar mass of air is approximately 28.97 g/mol, the mass flow rate (ṁ) can be calculated:
ṁ = n * molar mass of air = 12.102 mol * 28.97 g/mol / 1000 (convert grams to kilograms)
ṁ ≈ 0.350 kg/s (rounded to three decimal places)
Now we can calculate ΔT:
Q = ṁ * Cp * ΔT
5000 W = 0.350 kg/s * 1005 J/(kg⋅K) * ΔTSolving for ΔT:
ΔT = 5000 W / (0.350 kg/s * 1005 J/(kg⋅K))
ΔT ≈ 14.19 K (rounded to two decimal places)
Therefore, the temperature of the air as it exits the duct is approximately 10°C + 14.19 K = 24.19°C (rounded to two decimal places).
The answers to the questions are:
5. The speed of the air as it enters the duct is approximately 6.79 m/s.
The temperature of the air as it exits the duct is approximately 24.19°C.
Learn more about speed here:
https://brainly.com/question/13771725
#SPJ11
A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 40 pounds each, and the small boxes weigh 20 pounds each. There
are 125 boxes in all. If the truck is carrying a total of 3900 pounds in boxes, how many of each type of box is it carrying?
Answers
x+y=125
40x+20y=3900
y=125-x
40x+20(125-x)=3900
40x+2500-20x=3900
20x=1400
x=70
125-70=y
y=55
true or false 4-10 if you don’t mind
Answers
Answer:
Step-by-step explanation:
4). False
5). False
6). True
7). True
8). False
9). False
10). True
x² - 10 - 3 x² + 5×-8
hello please solve and give a solution thankyou!!
Answers
Answer:
-2x2 - 50
Step-by-step explanation:
First, you collect the like terms:
x2 - 3x2 + 5 x -8 -10
Do multiplication first:
x2 - 3x2 + (-40) - 10
Combine the terms:
-2x2 - 50
Answer:
5 star of you
Step-by-step explanation:
you are cool dictator
Cypress Middle School wants to have a fundraiser to buy art supplies. Fundraiser A will give the school $1.50 for each order placed plus $75 as a bonus. Fundraiser B will give the school $3.00 for each order placed, but no bonus. How many orders must be placed in order for the total amount of money earned by each fundraiser to be the same? a 150 b.5 c.17 d.50
Answers
Answer:
50
Step-by-step explanation:
Let the number of orders required be x
Fund raiser A , 1.50 for each other plus bonus of 75
for x orders, we have 1.50 * x = 1.50x
Add the bonus = 1.50x + 75
Fund raiser B, $3 for each other , no bonus
Total from fund raiser B is 3 * x = 3x
So to make them equal, we ensure that e equate both values;
3x = 1.5x + 75
3x -1.5x = 75
1.5x = 75
x = 75/1.5
x = 50
50 orders will make both funds equal
The following situation applies to questions 2-5.
Lincoln Middle School plans to collect more than 2,000 cans of food in a food drive. So far, 668 cans have been collected. Write and solve an inequality to
find numbers of cans the school can collect on each of the final 7 days of the drive to meet this goal.
Which two-step inequality represents this situation?
7 + 668 > 2000
7c + 668 < 2000
O +668 > 2000
70 +668 > 2000
Answers
Answer:
7c + 668 > 2000
Step-by-step explanation:
Given that :
Target = more than. 2000 food cans
Amount already collected = 668 food cans
Food can remaining to collect per day within 7 days = 2000 - 668
Let number of cans left to collect per day with 7 days = c
7 * c + cans already collected > target
7c + 668 > 2000
At a bank, the tellers on average take 17 minutes per customer, with a standard deviation of 8 minutes. What is the coefficient of variation of the service time? (Write the answer as a decimal fraction, not a percentage. Provi de two decimal places)
Answers
The coefficient of variation of the service time at the bank is approximately 47.06%.
To find the coefficient of variation of the service time at the bank, we need to divide the standard deviation by the mean and then multiply by 100 to express it as a percentage.
Mean (µ) = 17 minutes
Standard Deviation (σ) = 8 minutes
To calculate the coefficient of variation:
Coefficient of Variation = (Standard Deviation / Mean) * 100
Coefficient of Variation = (8 / 17) * 100
Now, let's calculate it:
Coefficient of Variation = 0.470588 * 100
Therefore, the coefficient of variation of the service time at the bank is approximately 47.06%.
To learn more about variation from the below link
https://brainly.com/question/13293164
#SPJ11
Solve 1/2 cot(x) >= over 0 <= x <= 2pi
Answers
Answer: answer is b on edg
Step-by-step explanation:
Roberto earns $6.50 per hour. He worked 32 hours at the regular rate, 8 hours at a time and a half, and 8 at double time. How much did he earn?
Answers
Answer $390
Step-by-step explanation:
Answer:
$390
Step-by-step explanation:
First Roberto works 32 hours at 6.50 per hour. At that time, he earn 32*6.5 = $208. Then he works 8 hours at a time and a half. This means that his pay rate is 50% more, or 6.5*1.5 = $9.75 per hour. Since he worked 8 hours at this pay rate, he earns 8*9.75 = $78. And then he works 8 hours double time. This means his pay rate was doubled during that duration. 6.5*2 = 13, 13*8 = $104.
Total: 208 + 78 + 104 = $390
18. What is the y-intercept of the line BC?
O A-2
B) -3
C) -2.3
OD 2
Answers
Answer:
18. What is the y-intercept of the line BC?
b) -3
Answer:
C
Step-by-step explanation:
It intercepts the horizontal line between -2 and -3, so that means that it is not a whole number. Therefore, the only answer possible is -2.3.
simplify 12e^5 divided 3e^3
Answers
The division of 12e⁵ by 3e³ will be 4e².
What is the arithmetic operation?In mathematics, the arithmetic operation has four main operators such as addition, subtraction, multiplication, and division.
The symbol of + represents the addition
The symbol of ÷ represents the division
The symbol of - represents subtraction
The symbol of × represents multiplication
Given the division,
12e⁵ by 3e³
⇒ 12e⁵ / 3e³
⇒ 12/3 × e⁵/e³
⇒ 4e²
Hence "The division of 12e⁵ by 3e³ will be 4e²".
To learn more about the arithmetic operators,
brainly.com/question/25834626
#SPJ1
Which of the following is not a property of the normal distribution? The tails asymptotically approach the horizontal axis The area undemeath the curve and to the right of the mean is 1 It has a bell shape The mean, median, and mode are all equal
Answers
The property that is not true for the normal distribution among the given options is: "The mean, median, and mode are all equal."
The normal distribution is characterized by several key properties. It has a bell shape, meaning it is symmetric around its mean. The tails of the distribution asymptotically approach the horizontal axis, which means they gradually decrease in height as they extend toward positive and negative infinity. The area underneath the curve and to the right of the mean is equal to 0.5, not 1. This is because the total area under the curve represents the probability of all possible outcomes and must sum up to 1. Lastly, the mean, median, and mode of the normal distribution are all equal to each other, making them measures of central tendency that coincide.
Therefore, the property that does not hold for the normal distribution is that the area underneath the curve and to the right of the mean is 1, as it is actually 0.5.
Learn more about normal distribution here: https://brainly.com/question/30390016
#SPJ11
2. Find the general relation of the equation cos3A+cos5A=0
Answers
\(A=\frac{\pi}{8}+\frac{n\pi}{4}or\ A=\frac{\pi}{2}+n\pi\)
Step-by-step explanation:Find angles\(cos3A+cos5A=0\)
________________________________________________________
Transform the expression using the sum-to-product formula\(2cos(\frac{3A+5A}{2})cos(\frac{3A-5A}{2})=0\)
________________________________________________________
Combine like terms\(2cos(\frac{8A}{2})cos(\frac{3A-5A}{2})=0\\\\ 2cos(\frac{8A}{2})cos(\frac{-2A}{2})=0\)
________________________________________________________
Divide both sides of the equation by the coefficient of variable\(cos(\frac{8A}{2})cos(\frac{-2A}{2})=0\)
________________________________________________________
Apply zero product property that at least one factor is zero\(cos(\frac{8A}{2})=0\ or\ cos(\frac{-2A}{2})=0\)
________________________________________________________
Cos (8A/2) = 0:Cross out the common factor\(cos\ 4A=0\)
________________________________________________________
Solve the trigonometric equation to find a particular solution\(4A=\frac{\pi}{2}or\ 4A=\frac{3\pi}{2}\)
________________________________________________________
Solve the trigonometric equation to find a general solution\(4A=\frac{\pi}{2}+2n\pi \ or\\ \\ 4A=\frac{3 \pi}{2}+2n \pi\\ \\A=\frac{\pi}{8}+\frac{n \pi}{4\\}\)
________________________________________________________
cos(-2A/2) = 0Reduce the fraction\(cos(-A)=0\)
________________________________________________________
Simplify the expression using the symmetry of trigonometric function\(cosA=0\)
________________________________________________________
Solve the trigonometric equation to find a particular solution\(A=\frac{\pi }{2}\ or\ A=\frac{3 \pi}{2}\)
________________________________________________________
Solve the trigonometric equation to find a general solution\(A=\frac{\pi}{2}+2n\pi\ or\ A=\frac{3\pi}{2}+2n\pi,n\in\ Z\)
________________________________________________________
Find the union of solution sets\(A=\frac{\pi}{2}+n\pi\)
________________________________________________________
A = π/8 + nπ/4 or A = π/2 + nπ, n ∈ ZFind the union of solution sets\(A=\frac{\pi}{8}+\frac{n\pi}{4}\ or\ A=\frac{\pi}{2}+n\pi ,n\in Z\)
I hope this helps you
:)
Find the value of x in the triangle shown below.
Answers
Answer:
x=13
Step-by-step explanation:
Use Pythagorean theorem
a^2+b^2=c^2, where c is this case is your x.
5^2+12^2=c^2
169=c^2
c=13
Answer:
13
Step-by-step explanation:
Pythagorean theorem
a^2+b^2=c^2
5^2+12^2=c^2
25+144=c^
169=c^2
13=c
WILL GIVE BRAINLIEST!!!! What is the solution to the equation1 over the square root of 8 = 4(m + 3)? (1 point)
m = − 15 over 4
m = − 11 over 4
m = 5 over 4
m = 9 over 4
Answers
Answer:
A
Step-by-step explanation:
Plug in -15/4 in your calculator and you will see that it is equal to \(\frac{1}{\sqrt{8} }\)
0.35355339059
what is 4x-3 i need a 6th grade explanation
Answers
Answer:
-12?
Step-by-step explanation: