The length of a rectangle is 1 inch shorter than twice the width (x).Which is the width (x) when the area (y) = 3321 square inches?
Answers
the width (x) of the rectangle = 41 inches
Explanation:
let the width = x
twice the width = 2x
The length of a rectangle is 1 inch shorter than twice the width (x) = 2x - 1
length = 2x -1
Area of rectangle = length × breadth
area (y) = 3321 square inches
y = x × 2x - 1 = x(2x - 1)
3321 = 2x² - x
2x² - x - 3321 = 0
We use factorisation to find x:
a = 2, b = -1, c = -3321
a × c = 2(-3321) = -6642
The factors which gives -1 when we sum together but gives -6642 when we multiply together are -82 and +81
2x² -82x + 81x - 3321 = 0
2x(x - 41) + 81(x - 41) = 0
(2x + 81) (x - 41) = 0
(2x + 81) = 0 or (x - 41) = 0
2x + 81 = 0
2x = -81
x = -81/2 inches
(x - 41) = 0
x - 41 = 0
x = 41 inches
Since we can't have a negative number as the width, the width (x) of the rectangle = 41 inches
Related Questions
Consider the quadratic function.What are the x-intercepts and y-intercept?What is the equation of the axis of symmetry?What are the coordinates of the vertex?Graph the function on the coordinate plane. Include the axis of symmetry.
Answers
Kindly check below
1) Let's do it in parts.
a) We can find the x-intercepts by using the factor zero property from each factor. Like this:
[tex]\begin{gathered} -(x+4)=0\Rightarrow-x-4=0\Rightarrow-x=4\Rightarrow x=-4 \\ (x-1)=0\Rightarrow x=1 \end{gathered}[/tex]The best way to find the y-intercept with this factored form is by plugging into that equation x=0
[tex]\begin{gathered} f(x)=-\left(x+4\right)\left(x-1\right) \\ y=-\left(x+4\right)\left(x-1\right) \\ y=-(0+4)(0-1) \\ y=-(4)(-1) \\ y=4 \end{gathered}[/tex]b) Expanding those factors by distributing them (FOIL) we can find this:
[tex]\begin{gathered} f(x)=-\left(x+4\right)\left(x-1\right) \\ f(x)=-\left(xx+x\left(-1\right)+4x+4\left(-1\right)\right) \\ f(x)=-x^2-3x+4 \end{gathered}[/tex]So now, let's find the x-coordinate of the vertex V(h,k):
[tex]\begin{gathered} h=\frac{-b}{2a}=\frac{-(-3)}{2(-1)}=\frac{3}{-2}=-\frac{3}{2} \\ Axis\:of\:symmetry:x=-3/2 \end{gathered}[/tex]c) The coordinates of the vertex can be found by plugging the x-coordinate into the quadratic function. This way:
[tex]\begin{gathered} f(x)=-\left(x+4\right)\left(x-1\right) \\ f(-\frac{3}{2})=-(-\frac{3}{2}+4)(-\frac{3}{2}-1)=\frac{25}{4} \\ \\ V(-\frac{3}{2},\frac{25}{4}) \end{gathered}[/tex]d) Finally, we can plot that function by setting a table:
So plotting these points (-2,6),(-1,6), (0,4), (1,0),(2,-6) and opening down the parabola for a is -1 we can plot this:
Solve the following system of linear equations by addition. Indicate whether the given system of linear equations has one solution, hasno solution, or has an infinite number of solutions. If the system has one solution, find the solution.7x + 7y = 281 4x + 4y = 16
Answers
Infinite number of solutions
Explanation:The given system of equations:
7x + 7y = 28........(1)
4x + 4y = 16.........(2)
Multiply equation (1) by 4
28x + 28y = 112..............(3)
Multiply equation (2) by -7
-28x - 28y = -112...............(4)
Add equations (3) and (4) together
0x + 0y = 0....................(5)
Since the right hand and left hand sides of equation (5) are equal, the equation has infinite number of solutions
How do you use the distance formula to figure out the area of the triangle. I don't really know how to solve this problem or use distance formula
Answers
The Area of a Right Triangle
The area of any triangle of base B and height H is:
[tex]A=\frac{B\cdot H}{2}[/tex]The base and the height must be perpendicular, i.e, the angle between them must be 90°.
The trick here is to prove the triangle is right at the point (15, 5).
If two lines are perpendicular, the product of their slopes is -1.
Calculate the slope of the line that joins the vertices at (5, 15) and (15, 5):
[tex]\begin{gathered} m_1=\frac{5-15}{15-5} \\ m_1=-\frac{10}{10} \\ m_1=-1 \end{gathered}[/tex]Calculate the slope of the line that joins the vertices at (20, 10) and (15, 5);
[tex]\begin{gathered} m_2=\frac{5-10}{15-20} \\ m_2=\frac{-5}{-5} \\ m_2=1 \end{gathered}[/tex]It can be verified that m1 * m2 = -1, thus the lines are perpendicular and we can use the formula given above to compute the area.
Find the length of both lines with the formula of the distance:
[tex]\begin{gathered} L_1=\sqrt[]{(5-15)^2+(15-5)^2} \\ \text{Calculating:} \\ L_1=\sqrt[]{200} \end{gathered}[/tex][tex]\begin{gathered} L_2=\sqrt[]{(5-10)^2+(15-20)^2} \\ L_2=\sqrt[]{50} \end{gathered}[/tex]Apply the formula of the area:
[tex]\begin{gathered} A=\frac{\sqrt[]{200}\cdot\sqrt[]{50}}{2} \\ A=\frac{\sqrt[]{10000}}{2} \\ A=\frac{100}{2}=50 \end{gathered}[/tex]The area is 50 square units
Simple calculator test - determine the angle, θ, to the nearest whole degree from each of the following:A. cos(θ) = 0.2079B. tan(θ) = 0.2126C. sin(θ) = 0.5446
Answers
Step 1
Find the value of θ using the inverse sign of all the functions.
A)
[tex]\begin{gathered} cos(\theta)=0.2079 \\ \theta=\cos^{-1}(0.2079) \\ \theta\approx78^{\circ} \end{gathered}[/tex]B)
[tex]\begin{gathered} tan(\theta)=0.2126 \\ \theta=\tan^{-1}(0.2126) \\ \theta\approx12^{\circ} \end{gathered}[/tex]C)
[tex]\begin{gathered} sin(\theta)=0.5446 \\ \theta=\sin^{-1}(0.5446) \\ \theta\approx33^{\circ} \end{gathered}[/tex]- 16m’n-(-25m’n)+(-7m’n)Which of the following is equivalent to the expression above?
Answers
As a rule , - times - = + and - times + = -
[tex]\begin{gathered} -16m^2n-(-25m^2n)+(-7m^2n\text{ ) } \\ =-16m^2n+25m^2n-7m^2n\text{ ( based on the rule above )} \\ =+9m^2n-7m^2n\text{ ( -16 + 25 = + 9 )} \\ =+2m^2n \end{gathered}[/tex]Therefore the correct answer to the question is 2m squared n
points reflected over an axis graphically
Answers
The coordinate of the point N is (-6,2).
The point on reflection about x axis, the x -coordinate remain same and sign of y-coordinate changes.
Determine the coordinate of point N'.
[tex]N^{\prime}(-6,-1\cdot2)\rightarrow N^{\prime}(-6,-2)[/tex]Plot the point on the graph.
24 2. Which two teams have equivalent ratios of wins to losses? Team Wins Losses Leopards 15 10 Pirates 12 8 Knights 14 7 Lions 18 10
Answers
The ratio wins to losses of each team are:
[tex]\begin{gathered} \text{Leopards:}\frac{15}{10}=\frac{3}{2} \\ \text{ Pirates:}\frac{12}{8}=\frac{3}{2} \\ \text{Knights:}\frac{14}{7}=2 \\ \text{Lions:}\frac{18}{10}=\frac{9}{5} \end{gathered}[/tex]Then, Leopards and Pirates have the same ratio
SaveSubmitD23567*9TO111213Which point represents the approximate location of V28?esApoint AB)point BpointD)point DHelp me almost done and tried
Answers
Thus, the point which represent square root of 28 should lie between 5 and 6 which is point B.
Thus, option (B) is correct.
A file that is 289 megabytes is being downloaded. If the download is 18.6% complete, how many megabytes have been downloaded? Round your answer to thenearest tenth.
Answers
Given:
289 megabytes
and 18.6% = 0.186
Therefore:
[tex]289\times0.186=53.754[/tex]Round to the nearest tenth: 53.8
Answer: 53.8 megabytes
Thinking: Two students were having a discussion. They stated:“Since we factored f(x) = 2x2 + 3x + 1 into (2x+1)(x+1) we could say this:If we let h(x) = 2x + 1 and g(x) = x + 1, then we can say f(x) = h(x)g(x)” Howmight you verify their statement?
Answers
Given:
If we let h(x) = 2x + 1 and g(x) = x + 1 and
[tex]f(x)=2x^2+3x+1[/tex]Required:
How might you verify their statement?
Explanation:
We have h(x) and g(x)
[tex]\begin{gathered} =h(x)g(x) \\ =(2x+1)(x+1) \\ =2x^2+2x+x+1 \\ 2x^2+3x+1=f(x) \\ f(x)=h(x)g(x) \end{gathered}[/tex]Answer:
Hence, verified the statement.
How to round off 18,600 to the nearest 10,000
Answers
Answer:
The nearest 10,000 is;
[tex]20,000[/tex]Explanation:
We want to round off the given number to the nearest 10,000.
[tex]18,600[/tex]We will find the closest ten thousand to the given number;
[tex]18,600\rightarrow20,000[/tex]Therefore, the nearest 10,000 is;
[tex]20,000[/tex]
Han spent a total of $221.76, before tax, on bags of chips for the basketball team, and each bag cost $3.52. What is the total number of bags of chips that Han bought?
Answers
Given:
a.) Han spent a total of $221.76, before tax, on bags of chips for the basketball team.
b.) Each bag cost $3.52.
Let's determine the number of bags of chips bought.
[tex]\text{ No. of bags of chips bought = }\frac{\text{ Total cost}}{\text{ Price of each bag}}[/tex][tex]\text{ = }\frac{\text{ 221.76}}{\text{ 3.52}}[/tex][tex]\text{ = 63}[/tex]Therefore, Han bought 63 bags of chips for the basketball team.
The answer is 63.
The points scored on a test for a sample of 39 students are summarized in the following table
Answers
the mean score of the test for sample of 39 students is 76.92.
The data is given as:
Number of students Score of each student Total score
07 90 630
17 80 1360
11 70 770
04 60 240
The total number of students = 7 + 17 + 11 + 4
n = 39
Total scores = 630 + 1360 + 770 + 240
T = 3000
Mean score = T / n
M = 3000 / 39
M = 1000 / 13
M = 76.92
Therefore, the mean score of the test for sample of 39 students is 76.92.
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whats the variance and the standard deviation of the data set 6,9,2,5,4,10,3,12,2,7,7,8
Answers
Given:
6,9,2,5,4,10,3,12,2,7,7,8
Required:
To find the variation and standard deviation of the given data set.
Explanation:
Now variation is
[tex]s^2=\frac{\sum_{i\mathop{=}1}^n(x_i-x)^2}{n-1}[/tex]The numerator in the above is sum of the square of the given data.
Therefore,
[tex]\begin{gathered} =(6-6.25)^2+(9-6.25)^2+(2-6.25)^2+(5-6.25)^2+(4-6.25)^2+(10-6.25)^2+ \\ (3-6.25)^2+(12-6.25)^2+(2-6.25)^2+(7-6.25)^2+(7-6.25)^2+(8-6.25)^2 \end{gathered}[/tex][tex]\begin{gathered} s^2=\frac{112.25}{12-1} \\ \\ =\frac{112.25}{11} \\ \\ =10.2045 \end{gathered}[/tex]Final Answer:
[tex]10.2045[/tex]what scale factor or multiplier of the dilation below
Answers
Given:
The triangle ABC is similar to the triangle A'B'C'
So, the corresponding sides are proportions
So, the factor of dilation will be:
[tex]\frac{A^{\prime}B^{\prime}}{AB}=\frac{8}{12}=\frac{2}{3}[/tex]so, the answer will be 2/3
write an extended proportion to indicate the proportional corresponding sides of the triangles
Answers
The correct extended proportion is:
[tex]\frac{MN}{RS}=\frac{MP}{RT}=\frac{NP}{ST}[/tex]Since the other two options have some non-correspondant proportions.
Alice fills up the gas tank of her car before going for a long drive . The equation below models the amount of gas , g , in gallons , in Alice's car when she has driven m miles . What is the meaning of 32 in the equation ?
Answers
Solution
For this case we have the following equation given:
[tex]g=15-\frac{m}{32}[/tex]We want to know what represent the 32 value
So then the answer is:
Total of miles that can cover the car with 15 gallons of gas
The ratio of the length of an airplane wing to its width is 9 to 1. If the length of a wing is 43.9 metérs, how wide must it be? The airplane wing must be ____ meters wide. (Round to the nearest hundredth.)
Answers
To compute the width of the wing, we can use the next proportion
[tex]\frac{9\text{ meters long}}{43.9\text{ meters long}}=\frac{1\text{ meter wide}}{x\text{ meters wide}}[/tex]Solving for x,
[tex]\begin{gathered} 9\cdot x=1\cdot43.9 \\ x=\frac{43.9}{9} \\ x=4.88 \end{gathered}[/tex]The airplane wing must be 4.88 meters wide.
Which values has three significant figures?14001001101.22310
Answers
a) 1400 has 2 significant figures, zeros are no consider as significant figures
b) 1001 has 4 significant figures, zeros in between two nonzero numbers are significant figures
c) 101.2 has 4 significant figures, zeros in between two nonzero numbers are significant figures. Nonzero number are significant figures
d) 2310 has three significant figures. 2,3 and 1 are significant figures.
The probability that VSU and KSU both win a basketball game in the same week is 47%. Theprobability that VSU wins is 50%. What is the probability that KSU will win given that VSUhas already won?
Answers
EXPLANATION
Let the probability that KSU will win a game be Pr(A), and let the probability that VSU wins be Pr(B). Therefore;
[tex]\begin{gathered} Pr(A\cap B)=0.47 \\ Pr(B)=0.5 \end{gathered}[/tex]We can then use the conditional probability formula below.
[tex]Pr(A|B)=\frac{Pr(A\cap B)}{Pr(B)}[/tex]Therefore, the probability that KSU will win given that VSU has already won becomes
[tex]Pr(A|B)=\frac{0.47}{0.50}=0.94[/tex]Answer: 0.94
what is the value of x would make lines l and m parrallel
Answers
We know that if l and m are parallel there might be some angles that are equal to others:
Alternate interior angles
The angles closed by a blue circle are alternate interior angles, then they should be equal if l||m.
Vertcial angles
The angles closed by an orange circle are vertical angles, because they are opposite to each other on two crossed lines.
Now, we know two angles of the triangle of the middle:
We know that the addition of all the inner angles of a triangle is 180º. This is:
50º + 55º + xº = 180º
↓
105º + xº = 180º
Now, we can find x:
105º + xº = 180º
↓
xº = 180º - 105º
xº = 75º
Answer: xº = 75ºpredict adjusted wages in 1998 does this prediction require interpolation or extrapolating
Answers
The required interpolation in adjusted 2020 is 0.50
Explanation:We find the interpolation using the formula:
[tex]y=y_1+\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Let us choose these points as follows:
[tex]\begin{gathered} x_1=7.69 \\ x_2=7.87 \\ y_1=3.80 \\ y_2=5.15 \end{gathered}[/tex]So,
[tex]\begin{gathered} y=3.80+\frac{5.15-3.80}{7.87-7.69}(x-7.69) \\ \\ =3.80+\frac{1.35}{0.18}(x-7.69) \\ \\ =3.80+7.5(x-7.69) \\ y=7.5x-53.875 \end{gathered}[/tex]In adjusted 2020, we have x = 7.25, using this, we have:
[tex]\begin{gathered} y=7.5(7.25)-53.875 \\ =54.375-53.875 \\ =0.50 \end{gathered}[/tex]the sum of 2 numbers is 75. the second number is 3 less than twice the first. find the numbers
Answers
SOLUTION
Let one of the numbers be x
Using the statement: The second number is 3 less than twice the first
Then the second number is
[tex]2x-3[/tex]Since, the sum of 2 numbers is 75
It follows:
[tex]x+2x-3=75[/tex]Solve for x
[tex]\begin{gathered} 3x=75+3 \\ 3x=78 \\ x=\frac{78}{3} \\ x=26 \end{gathered}[/tex]Therefore the first number is 24
The second number is
[tex]\begin{gathered} 2(26)-3 \\ =49 \end{gathered}[/tex]therefore the numbers are 49 and 26.
Example 10 in. 20 in. A carpenter builds the table shown. If the floor is level, how likely is it that a ball placed on the table will roll off? 20 in. 10 in.
Answers
According to the given image, the table has a flat surface, whcih means the ball would not roll off because there's no slope or inclination. Also, assuming that there's no other forces being applied, the ball should not roll off.
Not ConnectedThunde...lt BridgeNot Connected2 (07.01 HC)answer the following question. Find the value of sin x and cosy. What relationship do the ratios of sin x® and cos yº share?
Answers
The given triangle is a right-angled triangle.
Consider PO is Hypotenuse.
By using the Pythagoras formula, we get
[tex]PO^2=8^2+6^2[/tex][tex]PO^2=64+36[/tex][tex]PO^2=100=10^2[/tex][tex]PO=10[/tex]Consider the angle x:
Recall the sine formula
[tex]\sin \theta=\frac{Opposite\text{ side}}{\text{Hypotenuse}}[/tex]Substitute Opposite side =6 and Hypotenuse=10, we get
[tex]\sin x^o=\frac{6}{10}[/tex][tex]\sin x^o=\frac{3}{5}[/tex][tex]\text{Use sin }36.869=\frac{3}{5}[/tex][tex]\sin x^o=\sin 36.869[/tex][tex]x^o=37[/tex]Consider the angle y:
Recall the sine formula
[tex]\sin \theta=\frac{Opposite\text{ side}}{\text{Hypotenuse}}[/tex]Substitute Opposite side =8 and Hypotenuse=10, we get
[tex]\sin y^o=\frac{8}{10}[/tex][tex]\sin y^o=\frac{4}{5}[/tex][tex]\text{Use }\sin 53.13^{}=\frac{4}{5}[/tex][tex]\sin y^o=\sin \text{ 53.13}[/tex][tex]y^o=53^{}[/tex]Hence the required values are
[tex]x^o=37^o[/tex][tex]y^o=53^o[/tex].
A culture of bacteria has an initial population of 220 bacteria and doubles every 8
hours. Using the formula Pt = Po · 2a, where P is the population after t hours, Po
is the initial population, t is the time in hours and d is the doubling time, what is the
population of bacteria in the culture after 11 hours, to the nearest whole number?
Answers
The population of bacteria in the culture after 11 hours is 581 using the exponential decay formula.
What is meant by population?The total number of people living in a particular area, such as a city or town, region, country, continent, or the entire world, is typically referred to as the population. Governments frequently conduct censuses to estimate the number of residents living within their jurisdiction. A census is a process for gathering, analyzing, compiling, and releasing statistics regarding a population.
A culture of bacteria has an initial population of 220 bacteria, which doubles every eight hours, according to the information provided.
By applying the formula,
P(t)=P₀.[tex]2^{t/d}[/tex]
P(t) is the population at the end of t hours.
P0 is the starting populace.
d is the doubling time, while t is the time in hours.
After 11 hours, we are asked to determine the bacteria population.
First, we will enter the following values in the doubling life formula as substitutes:
P(t)=220([tex]2^{t/8}[/tex])
Now we will substitute t=11 in our formula to find the population of bacteria after 11 hours as follows:
P(11)=220([tex]2^{17/8}[/tex])
P(11)=220([tex]2^{1.4}[/tex])
P(11)=220(2.639015822)
P(11)=580.5834807≈581
P(11)=581
Consequently, after 11 hours, there will be 581 bacteria.
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Gaby's piggy bank contains quarters and nickels worth $7.50. If she has 58 coins in all, howmany of each does she have?
Answers
let the number of quarters = x , and the number of nickels = y
quarter = $0.25 and nickel = $0.05
So, x + y = 58
x = 58 - y
and 0.25 x + 0.05 y = 7.5
so,
0.25 (58 - y) + 0.05 = 7.5
14.5 - 0.25 y + 0.05 y = 7.5
-0.2 y = -7
y = -7/-0.2 = 35
x = 58 - 35 = 23
So, the number of quarters = 23 and the number of nickels = 35
Gifty works out that the material for a dress cost R dollar per meter and 3 meters are required for the dress. Acessories cost $50.00. what is the total amount of money Gifty will need to spend on the dress in terms of R? If Gifty has $4000 to spend on her dress including accessories, what is the maximum value of R?
Answers
We are given that
Cost of dress per meter = $R
Total cost of dress = $ 3R
Cost of Acessories = $50
We want to find:
Part A
The total amount of money Gifty will need to spend on the dress in terms of R
To find the total amount, we just add up
Let T denotes the total amount of money
[tex]\begin{gathered} T=3R+50 \\ \end{gathered}[/tex]Thus, the total amount is $ (3R + 50)
Part B
If Gifty has $4000 to spend on her dress including accessories, what is the maximum value of R?
We only need to equate T to 4000 and solve for R
[tex]\begin{gathered} T=4000 \\ 3R+50=4000 \\ 3R=4000-50 \\ 3R=3950 \\ R=\frac{3950}{3} \\ R=1316.666667 \\ R=1316.67\text{ (to 2 decimal places)} \end{gathered}[/tex]Thus, the maximum value of R is $1316.67
Which mathematical property is demonstrated?5 • 7 • 4 = 5 • 4 • 7commutative property of additioncommutative property of multiplicationassociative property of additionassociative property of multiplication
Answers
What we can observe in equality is the commutative property of multiplication.
The answer would be Commutative Property of Multiplication
What are the coordinates of point P on the directed line segment from R to Q such that 5 Pis 6 the length of the line segment from R to Q? Round to the nearest tenth, if necessary. A (-3.5, 2.3 ) B. (3.5, -2.3 ) C. (-3, 2) D. (3, 2)
Answers
Answer
Option A is correct.
P(x, y) = (-3.5, 2.3)
Explanation
Mathematically, if a point P(x, y) divides the coordinates R(x₁, y₁) and Q(x₂, y₂) internally in the ratio m:n then point P(x, y) is given as
x = [(mx₂ + nx₁)/(m + n)]
y = [(my₂ + ny₁)/(m + n)]
For this question,
R(x₁, y₁) and Q(x₂, y₂) = R (4, -1) and Q (-5, 3)
m:n = 5:1 (5/6 of a distance divides the two parts of the distance into 5/6 and 1/6, hence, the ratio is 5:1)
x₂ = -5
x₁ = 4
y₂ = 3
y₁ = -1
m = 5
n = 1
x = [(mx₂ + nx₁)/(m + n)]
x = [(5×-5 + 1×4)/(5 + 1)]
x = [(-25 + 4)/(5 + 1)]
x = (-21/6)
x = -3.5
y = [(my₂ + ny₁)/(m + n)]
y = [(5×3 + 1×-1)/(5 + 1)]
y = [(15 - 1)/(5 + 1)]
y = (14/6)
y = 2.3
P(x, y) = (-3.5, 2.3)
Hope this Helps!!!