The cross product of a = 8, 0, −2 and b = 0, 9, 0 is 18, 0, 72.
The cross product of two vectors a and b is given by:
a × b = |a| |b| sinθ n
where |a| and |b| are the magnitudes of vectors a and b, θ is the angle between them, and n is a unit vector perpendicular to both a and b in the direction given by the right-hand rule.
Given a = 8, 0, −2 and b = 0, 9, 0, we have:
|a| = √(8² + 0² + (-2)²) = √68 = 2√17
|b| = √(0² + 9² + 0²) = 3√2
The angle between a and b is 90 degrees since they are perpendicular.
So, sinθ = sin(90°) = 1
A unit vector n in the direction of a × b can be found by:
n = (a × b) / |a × b|
where |a × b| is the magnitude of a × b.
Now, we can find a × b:
a × b = |a| |b| sinθ n
= (2√17)(3√2)(1) n
= 6√34 n
To find n, we first need to find a × b in component form:
a × b = (a₂b₃ - a₃b₂)i - (a₁b₃ - a₃b₁)j + (a₁b₂ - a₂b₁)k
= (-18)i - (-16)j + 0k
= -18i + 16j
The magnitude of a × b is:
|a × b| = √((-18)² + 16²) = 2√170
Therefore, a unit vector n in the direction of a × b is:
n = (a × b) / |a × b|
= (-18i + 16j) / (2√170)
= (-9/√170)i + (8/√170)j
Thus, we have:
a × b = 6√34 (-9/√170)i + 6√34 (8/√170)j
= -54/17 i + 48/17 j
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brain liest for who ever does all (NOTE: this is not a test!! ) thanks :D
I can't see what you posted it's blocked off but I could probably answer it if I knew what the questions were
The following integration can be solved by using the technique, where we have x= and dx= , to get ∫zx2−1dx= (Choose the correct letter). A. x2−2+sec−1(2x)+c B. x2−4−2sec−12x+c C. 2x2+4+sec−12x+c D. x2−4+2sec−1x+c E. None of these are correct
The correct option is (D) x2−4+2sec−1x+c because it has secθ which is equal to √(x2−1) where x is given in the above expression.
Given integral is,∫zx2−1dx
This integration can be solved by the trigonometric substitution technique, where x = secθ and dx = secθtanθ dθ.Now let us convert the given integral using the above trigonometric substitution;
∫zx2−1dx= ∫secθ(sec2θ - 1)
secθtanθ dθ= ∫secθ( tan2θ)
dθ= ∫tanθ( tanθsecθ)
dθ= ∫tanθ(d secθ)
= ln|secθ + tanθ| + C
Now we need to find the answer by substituting back x = secθ in the above expression.
We know that tanθ = √(sec2θ - 1)
Therefore, x = secθ = √(tan2θ + 1)
The correct option from the given alternatives is (D) x2−4+2sec−1x+c because it has secθ which is equal to √(x2−1) where x is given in the above expression.
Therefore, ln|√(x2−1) + x| + C is the final answer.
Therefore, the given integration can be solved by using the trigonometric substitution technique.
We substitute x = secθ and dx = secθtanθ dθ, which transforms the given integral into
∫zx2−1dx = ∫secθ(sec2θ - 1)secθtanθ dθ
= ∫secθ( tan2θ) dθ
= ∫tanθ( tanθsecθ) dθ
= ∫tanθ(d secθ)
After solving the above integral, we get ln|secθ + tanθ| + C.
Now we need to substitute x = secθ in the final answer to get the solution of the given integral.
Therefore, x = secθ = √(tan2θ + 1).
Therefore, ln|√(x2−1) + x| + C is the final answer.
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Solve the equation for x.
5x = -60
Answer:
x=-12
Step-by-step explanation:
5x/5=1x = -60/5=-12
x=-12
Answer:
-12
Step-by-step explanation:
5x=-60
Divide both sides by 5 to isolate
X=-12
please prove it
(full steps required)
(No spam answers)
Answer:
Step-by-step explanation:
It's given in the question,
\(2^x=3^y=12^z\)
\(2^x=12^z\)
\(\text{log}2^x}=\text{log}12^z}\)
\(x\text{log2}=z\text{log12}\)
\(x=\frac{z\text{log}12}{\text{log2}}\)
\(3^y=12^z\)
\(\text{log}3^y}=\text{log}12^z}\)
\(y\text{log}3}=z\text{log}12}\)
\(y=\frac{z\text{log12}}{\text{log}3}\)
Now substitute the values in the equation,
\(\frac{1}{y}+\frac{2}{y} =\frac{1}{\frac{z\text{log12}}{\text{log}3}}+\frac{2}{\frac{z\text{log}12}{\text{log2}}}\)
\(=\frac{\text{log}3}{z\text{log}12}+\frac{2\text{log}2}{z\text{log}12}\)
\(=\frac{\text{log}3+\text{log}2^2}{z\text{log}12}\)
\(=\frac{\text{log}(3\times 2^2)}{z\text{log}12}\)
\(=\frac{\text{log}(12)}{z\text{log}12}\)
\(=\frac{1}{z}\)
Hence proved.
Solve-3(z-6) ≥ 2z-2 for z
Answer: Z<4
Step-by-step explanation:
Rearrange the equation
-3(z-6) - (2z-2)>0
-3z+18-2z+2>0
-5z +20>0
-5(z-4)>0
divide both side by -5
z-4<0
z<4
A quilter wants to make the design shown at left using the Golden Ratio. Specifically, he wants the ratio of the triangle heights
The quilter wants to make a design using the Golden Ratio, specifically focusing on the ratio of triangle heights. To find the height ratio, we can use the properties of the Golden Ratio.
The Golden Ratio is a mathematical concept where two quantities are in proportion if their ratio is equal to the ratio of their sum to the larger of the two quantities. Mathematically, it can be represented as (a + b) / a = a / b, where a is the larger quantity and b is the smaller quantity.
In this case, the quilter wants to find the ratio of triangle heights. Let's assume the height of the larger triangle is a and the height of the smaller triangle is b. According to the Golden Ratio, we have (a + b) / a = a / b.
To solve for the height ratio, we can cross-multiply and simplify the equation. We get a^2 + ab = a^2, which simplifies to ab = a^2 - a^2, or ab = 0.
Since ab = 0, we can conclude that the height ratio of the triangles is 0. This means that the height of the smaller triangle is 0, while the height of the larger triangle can be any positive value.
In summary, when using the Golden Ratio to determine the ratio of triangle heights, the ratio is 0.
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A count went from 605 to 203. What was the approximate percent decrease? Round the numbers to find an estimate of the percent decrease.
Answer:
66 %
Step-by-step explanation:
it is 66% because 203 is less than half of 605 .So, you would add together .
203+203=406 Thats not even close to 605 so now you add almost half so that would be about 66%
IT'S D
HOPE THIS HELPED MARK ME BRAINLIST PLS
A physics class has 40 students. of these, 15 students are physics majors and 16 students are female. of the physics majors, six are females. find the probability that a randomly selected student is female or a physics major
The probability that the randomly selected student is female or Physics major is 0.625.
Given Information
Total number of students = 40
Number of Physics major out of the total students, P = 15
Number of females in the class, F = 16
Number of females that are Physics major, (P∩F) = 6
We have to find the probability P(P∪F).
Calculating the Probability
Probability of Physics major students, P(P) = 15/40
= 0.375
Probability of female students, P(F) = 16/40
= 0.4
Probability of female students who are Physics major, P(P∩F) = 6/40
= 0.15
Since, we know that,
P(P∪F) = P(P) + P(F) - P(P∩F)
∴ P(P∪F) = 0.375 + 0.4 - 0.15
P(P∪F) = 0.625
Thus, the probability that the randomly selected student will be a Physics major or a female is 0.625
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Julissa wants to find the perimeter of her bedroom that is similar to her brother's. If her brother's bedroom is 12 ft long and 10 ft wide and her bedroom is 10 feet long, what is the perimeter of her room? What is the perimeter of her room? (Round to the nearest tenth).
A card is selected to from a standard deck of 52 card what are the odds of selecting a red 9
The odds of selecting a red 9 is 1/26.
Probability of an event E is represented by P(E) can be defined as (the number of favorable outcomes) / (Total number of outcomes).
Given the total number of cards in a standard deck = 52
there can be only two red9 as one 9 from heart and one red from diamond.
So the number of outcome for red 9 =2
the probability of odds of selecting red 9 is \(\frac{2}{52}\) which can be further simplified into \(\frac{1}{26}\).
Therefore , The odds of selecting a red 9 is 1/26.
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it takes 222 wooden sticks and 1.51.51, point, 5 square feet of paper to make a kite, and it takes 121212 wooden sticks and 888 square feet of paper to make a lamp.
To make a kite, you need 222 wooden sticks and 1.5 square feet of paper. For a lamp, you need 12 wooden sticks and 88 square feet of paper.
Now, let's calculate the number of wooden sticks and square feet of paper needed for the kite and the lamp separately.
For the kite:
- Number of wooden sticks: 222
- Square feet of paper: 1.5
For the lamp:
- Number of wooden sticks: 12
- Square feet of paper: 88
it takes 222 wooden sticks and 1.5 square feet of paper to make a kite, while it takes 12 wooden sticks and 88 square feet of paper to make a lamp.
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A truck driver is trying to decide between two jobs offers. Driving company A offers pay for $600 per week, plus $0.15 per mile driven. Driving company B offers $700 per week, plus $0.10 per mile driven. The truck diver wants to know how many miles would they need to drive in a week to be making the same amount between the 2 companies.
Answer:
$1,202
Step-by-step explanation:
There ya go
First rewrite into exponential form. Then use properties of exponents to simplify each expression. Leave your answer in exponential form.
Explanation:
Question 2
To answer the question, we will use the exponential laws
\(\begin{gathered} a^{\frac{1}{b}}=\sqrt[b]{a} \\ a^{-1}=\frac{1}{a} \\ a^{\frac{b}{c}}=\sqrt[c]{a^b} \\ a^b\times a^c=a^{b+c} \\ a^b\div a^c=a^{b-c} \end{gathered}\)Applying these laws
Question 2a
\(\sqrt[4]{(mn)^{12}}=(mn)^{\frac{12}{4}}\)\(\sqrt[4]{(mn)^{12}}=(mn)^{\frac{12}{4}}=(mn)^3\)Question 2b
\(\sqrt{x}.\sqrt[7]{x}\)we will rewrite it as
\(x^{\frac{1}{2}}\times x^{\frac{1}{7}}=x^{\frac{1}{2}+\frac{1}{7}}=x^{\frac{9}{14}}\)Question 2c
\(\frac{\sqrt[6]{x}}{\sqrt[4]{x}}=\frac{x^{\frac{1}{6}}}{x^{\frac{1}{4}}}\)Then
\(\frac{x^{\frac{1}{6}}}{x^{\frac{1}{4}}}=x^{\frac{1}{6}-\frac{1}{4}}=x^{-\frac{1}{12}}=\frac{1}{x^{12}}\)Question 2d
\(\sqrt[6]{\frac{r^6}{s^{18}}}=(\frac{r^6}{s^{18}})^{\frac{1}{6}}\)Simplifying further
\(\frac{r^{\frac{6}{6}}}{s^{\frac{18}{6}}}=\frac{r}{s^3}\)Question 2e
\(\sqrt[3]{x^6q^9}=(x^6q^9)^{\frac{1}{3}}\)Simplifying further
\((x^6q^9)^{\frac{1}{3}}=x^{\frac{6}{3}}q^{\frac{9}{3}}=x^2q^3\)Question 2f
\(\sqrt{49x^5}=(49x^5)^{\frac{1}{2}}\)Simplifying further
\(49^{\frac{1}{2}}x^{\frac{5}{2}}=7x^{\frac{5}{2}}\)what's the most likely slope
Answer:
Undefined.
Step-by-step explanation:
Slope is the Rise/Run of a straight line. Run is the change in the value of y for a change in x. The graph shows all values are possible for y even when there is zero change in x. All Values/0 = Undefined.
PLS HELP MEH PLLLSSSSSSSSSS
Write an inequality and solve each problem.
Oct 07, 1:28:22 PM
What is the equation of the line that passes through the point (-4, 4) and has a slope of 3/4
Answer:
y=3/4x+7
Step-by-step explanation:
You want to find the equation for a line that passes through the point (-4,4) and has a slope of 3/4.
First of all, remember what the equation of a line is:
y = mx+b
Where:
m is the slope, and
b is the y-intercept
To start, you know what m is; it's just the slope, which you said was 3/4. So you can right away fill in the equation for a line somewhat to read:
y=3/4x+b.
Now, what about b, the y-intercept?
To find b, think about what your (x,y) point means:
(-4,4). When x of the line is -4, y of the line must be 4.
Because you said the line passes through this point, right?
Now, look at our line's equation so far: . b is what we want, the 3/4 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the the point (-4,4).
So, why not plug in for x the number -4 and for y the number 4? This will allow us to solve for b for the particular line that passes through the point you gave!.
(-4,4). y=mx+b or 4=3/4 × -4+b, or solving for b: b=4-(3/4)(-4). b=7.
hope this answers your question sorry it's soo long i just like writing long stuff have a great day!!
Your grandmother has been putting $5,000 into a savings account on every birthday since your first that is, when you turned one). The account pays an interest rate of 7% How much money will be in the account medialty after your grandmother makes the deposit on your 18th birthday The amount in the account upon your 18th birthday is (Round to the nearest dollar)
After your grandmother makes a $5,000 deposit on your 18th birthday, the amount in the savings account can be calculated using compound interest. Assuming the account pays an interest rate of 7%, the amount in the account immediately after the deposit can be determined by applying the compound interest formula.
To calculate the amount in the savings account after the deposit on your 18th birthday, we can use the compound interest formula: A = P(1 + r/n)^(nt), where A represents the final amount, P is the principal (initial deposit), r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.
In this case, the initial deposit is $5,000, the interest rate is 7% (or 0.07 as a decimal), and the deposit is made on your 18th birthday, which means the time is 17 years. Since no information is given about the compounding frequency, let's assume it is compounded annually (n = 1).
Plugging in the values into the compound interest formula, we have A = 5000(1 + 0.07/1)^(1*17) = 5000(1.07)^17 ≈ $15,128.
Therefore, the amount in the savings account immediately after your grandmother makes the deposit on your 18th birthday is approximately $15,128, rounded to the nearest dollar.
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Carmen and Josh shared a meal for lunch. Josh paid 3/5 of the $30 bill and Carmen paid the rest. How much did they each pay?
Answer:
Josh 18
Carmen 12
Step-by-step explanation:
3/5 of 30 means multiply
3/5 * 30
3 * 30 = 90
90/5 = 18
Josh paid 18
Carmen paid the rest
30-18 = 12
Carmen paid 12
Answer:
See below!
Step-by-step explanation:
Total bill = $30
Josh paid:
= 3/5 of 30
Key: "of" means "to multiply"
= (3 x 30)/5
= 90/5
= $18So, Josh paid $18 of the bill.
Carmen paid:
= Total - Josh paid
= 30 - 18
= $12\(\rule[225]{225}{2}\)
A student randomly selects 10 CDs at a store. The mean is $8.75 with a standard deviation of $1.50. Construct a 95% confidence interval for the population standard deviation, $$\sigma.$$ Assume the data are normally distributed.
To construct a confidence interval for the population standard deviation, we can use the chi-square distribution.
The formula for the chi-square distribution is: (X - n*σ^2)/σ^2 ~ χ^2(n-1)
where X is the sample variance, n is the sample size, σ is the population standard deviation, and χ^2(n-1) is the chi-square distribution with n-1 degrees of freedom.
We can rearrange this formula to get a confidence interval for σ:(X/χ^2(a/2, n-1), X/χ^2(1-a/2, n-1))
where X is the sample variance, n is the sample size, a is the level of significance (1 - confidence level), and χ^2(a/2, n-1) and χ^2(1-a/2, n-1) are the chi-square values with n-1 degrees of freedom that correspond to the lower and upper bounds of the confidence interval, respectively.
First, we need to calculate X, the sample variance:s^2 = (1/n) * Σ(xi - x)^2
where s is the sample standard deviation, n is the sample size, xi is the value of the i-th observation, and x is the sample mean.
Substituting the given values, we get:s = $1.50
n = 10
x = $8.75
s^2 = (1/10) * Σ(xi - x)^2
s^2 = (1/10) * [(xi - x)^2 + ... + (xi - x)^2]
s^2 = (1/10) * [(xi - 8.75)^2 + ... + (xi - 8.75)^2]
s^2 = (1/10) * [(54.76) + ... + (0.06)]
s^2 = 5.47
Next, we need to find the chi-square values for the 95% confidence interval:a = 0.05
χ^2(0.025, 9) = 2.700
χ^2(0.975, 9) = 19.023
Finally, we can calculate the confidence interval for σ:(X/χ^2(0.975, 9), X/χ^2(0.025, 9))
(5.47/19.023, 5.47/2.700)
($0.32, $2.02)
Therefore, we can say with 95% confidence that the population standard deviation is between $0.32 and $2.02.
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Find the difference.
(k^3-7k+2)-(k^2-12)=
The difference between the two expressions is:
(k³-7k+2)-(k²-12) = k³ - k² - 7k + 14
What is an expression?
We can begin by simplifying the left side of the equation:
(k³ - 7k + 2) - (k² - 12)
= k³ - 7k + 2 - k² + 12 // Distribution of the negative sign
= k³ - k² - 7k + 14 // Combining like terms
So the difference between the two expressions is:
k³ - k² - 7k + 14
An expression is a combination of one or more values, variables, and operators that can be evaluated to produce a result. Expressions can be as simple as a single number or variable, or they can be complex, combining multiple operators and functions.
What are variables?
A variable is a symbol or a named memory location that can hold a value. It is used to store and manipulate data during the execution of a program. Variables can be assigned different types of values, such as numbers, text, or Boolean (true/false) values. The value of a variable can change during the execution of a program, and it can be used in expressions and statements to perform calculations, make decisions, or control the flow of the program.
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Complete question is: (k³-7k+2)-(k²-12) = k³ - k² - 7k + 14
How many servings are in an 8lb bag of French fries?
There are 16 ounces in a pound.
The proper serving size of french fries is reportedly only 12 to 15 fries.
consider the quadratic function y equals short dash x squared plus 6 x minus 5. what do we know about the graph of this quadratic equation, based on its formula?
Based on the formula of the quadratic function y=-x^2+6x-5, we know that its graph is a downward-facing parabola that opens wide, with a vertex at (3,-14), and an axis of symmetry at x=3.
Based on the formula of the quadratic function y=-x^2+6x-5, we can determine several properties of its graph, including its shape, vertex, and axis of symmetry.
First, the negative coefficient of the x-squared term (-1) tells us that the graph will be a downward-facing parabola. The leading coefficient also tells us whether the parabola is narrow or wide. Since the coefficient is -1, the parabola will be wide.
Next, we can find the vertex using the formula:
Vertex = (-b/2a, f(-b/2a))
where a is the coefficient of the x-squared term, b is the coefficient of the x term, and f(x) is the quadratic function. Plugging in the values for our function, we get:
Vertex = (-b/2a, f(-b/2a))
= (-6/(2*-1), f(6/(2*-1)))
= (3, -14)
So the vertex of the parabola is at the point (3,-14).
Finally, we know that the axis of symmetry is a vertical line passing through the vertex. In this case, it is the line x=3.
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Dennis has a credit card with an APR of 13.09% and a billing cycle of 30 days. The following table shows his transactions with that credit card in the month of November.
If the finance charge for November is $4.93, which method of calculating the finance charge does Dennis’s credit card company use?
Answer:
previous questions have been asked using this same question
Step-by-step explanation:
A.) adjusted balance method
lean draws a square with an area that is greater than the area of rentangle B what are the two possible side length of lena square
METHOD
\(\begin{gathered} \text{Area of a square = L}^2 \\ \text{Area of a rectangle = L x W = LW} \end{gathered}\)Next
\(\begin{gathered} \text{Area of square - area of rectangle }>\text{ 0} \\ L^2\text{ - LW }>\text{ 0} \\ \text{next, factor L out} \\ L(L\text{ - W) > 0} \\ L\text{ > 0 or L - W > 0} \\ L\text{ > 0 or L > w} \end{gathered}\)The two possible side length of Lena square
is
L > 0 or L > W
The baseball bat question
the seventh inning stretch company has created a new baseball that will improve your chances of hitting a home run.
the 36-inch bat is only available online. to protect the bat, it must be shipped so the handle of the bat is in one corner
of the box and the top portion of the bat touches the opposite diagonal corner.
a. the shipping box has a length of 30 inches and a height of 6 inches. how wide should the box be to fit
the 36-inch bat?
show and explain your work.
Using the 3D Pythagorean theorem, we need the length of the diagonal to be 36 inches.
Let the width of the box be \(w\). Then,
\(\sqrt{30^2 +6^2+w^2}=36\\\\30^2+6^2+w^2=36^2\\\\w^2=36^2-30^2-6^2\\ \\ w=\sqrt{36^2-30^2-6^2}\\\\w=6\sqrt{10} \text{ in}\)
What is the inverse of f(x)=3x^2
Answer:
f^-1 (x)=sqrt(x/3), -sqrt(x/3).
Step-by-step explanation:
f(x)=3x^2
y=3x^2
x=3y^2
y^2=x/3
y=sqrt(x/3), -sqrt(x/3).
Answer:
\(y=3x^2\)
\(y=3x^2\)
Step-by-step explanation:
There is no step-by-step explanation because it's a graph. Well, it's how I did it. Therefore, the graph in the picture that I'm about to post will be your answer.
can someone explain this to me thank u :)
Answer:
1/4
Step-by-step explanation:
It is really weird that this answer is not on there but here is my explanation.
We can consider this question in two different ways.
First, we could list the possible outcomes.
HHH
HHT
HTH
HTT
THH
THT
TTH
TTT
In total 8 possibilities, 2 of which are either all heads or all tails. So the probability is 2/8 which is 1/4.
Alternatively, we could look at each of the three independent events in turn.
We toss the first coin. We don’t mind whether it lands head or tail, but we need to note the result. The probability of getting any result is 1.
We toss the second coin and there is a probability of 1/2 that the result matches the first toss.
We now toss the third coin and again there is a probability of 1/2 that the result matches the first toss.
So the probability of getting all heads or all tails is the probability of getting any result from the first toss (1) multiplied by the probability of a matching result for the second toss (1/2) multiplied by the probability of a matching result for the third toss (1/2).
So that’s 1 * (1/2) * (1/2), which is 1/4.
Directions:Find the unknown measurements.(Square)Area: Side:2.6m
Answer:
Area = 6. 76 square cm
Explanation
Each side of the square = 2.6 cm
Area of a square = s^2
Where s = 2.6cm
Area = 2.6^2
Area = 6.76 square cm
Therefore, the area of the square is 6. 76 square cm
A plot of land for sale has a width of x ft. and a length that is 8 ft. less than its width. A farmer will only purchase the land if it measures 240 ft^2. Create an equation in terms of w that models this situation.
Given:
a.) A plot of land for sale has a width of x ft. and a length that is 8 ft. less than its width.
b.) A farmer will only purchase the land if it measures 240 ft.
From the given description of the measurement of the land, we generate the following equations:
Width = w
Length = w - 8
Area of the Land = 240 ft.^2
Area = Width x Length
240 = (w)(w - 8)
240 = w^2 - 8w
w^2 - 8w - 240 = 0
Question 1: Create an equation in terms of w that models this situation.
Answer: 240 = w^2 - 8w
Factoring out 240 = w^2 - 8w, we get:
240 = w^2 - 8w
w^2 - 8w - 240 = 0
w^2 - 8w - 240 = 0 → (w - 20)(w + 12) = 0
First possible measure of the width,
w - 20 = 0
w = 20 ft.
Second possible measure of the width,
w + 12 = 0
w = -12 ft.
A dimension must never be a negative value, therefore, the width must be equal to 20 ft.
Let's determine the length,
Length = w - 8
= 20 - 8
Length = 12 ft.
Summary:
The equation that models the situation: 240 = w^2 - 8w or w^2 - 8w = 240
The measure of the length = 12 ft.
The measure of the width = 20 ft.
Which number line best shows how to solve -8 - (-6)? (5 points)
Question 3 options:
1)
2)
3)
4)
Question 4 (5 points)
Answer:
its 3 solve -6
Step-by-step explanation:
Answer:
Where are the pictures
Step-by-step explanation: