A given rectangle has an area of 20 square feet. What is the length for various widths??

The width of the rectangular garden is 6 meters. Hence, the correct answer is w = 6. Option B is correct answer.

The  rectangular garden has a perimeter of 42 meters. The length is 3 meters longer than twice the width.

We need to write and solve an equation using inverse operations to determine the value of w.

The perimeter of a rectangle is given by:

P = 2(l + w)

Where P is the perimeter, l is the length, and w is the width of the rectangle

.As per the question, the length is 3 meters longer than twice the width, so the length can be expressed as:

l = 2w + 3

The perimeter is given to be 42 meters, so we can write:

42 = 2(l + w)

Substituting the value of l from the above expression,

we get:

42 = 2(2w + 3 + w)

Simplifying, we get:

42 = 2(3w + 3)21 = 3w + 3

Subtracting 3 from both sides,

we get:

18 = 3w

Dividing both sides by 3,

we get:

w = 6

Therefore, the width of the rectangular garden is 6 meters.

Option B is correct.

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The vectors are:u = (2, 3, -1) ,v = (-1, 2, 0)

To find the dot product of these two vectors, we use the formula:

u · v = (2 * -1) + (3 * 2) + (-1 * 0) = -2 + 6 + 0 = 4

The dot product of u and v is 4, which means that these two vectors are not orthogonal. A dot product of 0 would indicate that the vectors are orthogonal, meaning they are at 90 degrees to each other.

The dot product is a scalar value that represents the magnitude of one vector projected onto the other, and it's a measure of similarity between the vectors.

A positive dot product indicates that the vectors are pointing in a similar direction, while a negative dot product indicates that the vectors are pointing in opposite directions. A dot product of 0 means that the vectors are orthogonal, or perpendicular to each other.

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ANSWER: (12,11), (x,y)

12 steps to the right on the x-axismaking the value a plus, and 11 steps up on the y axis making the numeral positive as well.

the answer is 4.5 ft

Step-by-step explanation:

Step-by-step explanation:

Given that the two fugures in the question above are similar, it means they have the same shape, even though they are if different sizes, the ratio of their corresponding sides are proportional. Thus,

18/x = 8/2

Let's solve for x as required.

We have,

18/x = 8/2

=>Cross multiply:

18 × 2 = 8 × x

36 = 8x

=>Divide both sides by 8

36/8 = x

4.5 = x

x = 4.5 ft

The values of the missing angles and sides after dilation are:

m∠C'B'D' = 95°,  CQ = 6 and  B'D' = 11.

m∠C'B'D = 180° - m∠B'C'D' - m∠B'D'C'

m∠B'C'D = m∠BCD, m∠B'D'C' = m∠BDC  (dilation)

m∠C'B'D = 180° - 34° - 51° = 95°

Thus, by way of scale factor we can say that:

BC/B'C' = BD/B'D' = 36/18 = 2

B'D' = ¹/₂BD = ¹/₂ * 22 = 11

ΔC'P'Q ∼ ΔCPQ

Thus:

C'Q'/CQ = C'D'/CD = D'Q'/DQ

CQ = 2C'Q' = 2 * 3 = 6

Therefore, m∠C'B'D' = 95°,  CQ = 6 and  B'D' = 11.

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Answer:

1) Please find the attached drawing of the archway created with MS Excel

2) The y-intercept is (0, 24)

The x-intercepts are (-3, 0), and (8, 0)

3) The width of the archway at its base is 11

The height of the archway at its highest point = 30.25

Step-by-step explanation:

1) Please find the attached drawing of the archway created with MS Excel

2) The y-intercept is (0, 24)

The x-intercepts are (-3, 0), and (8, 0)

3) The width of the archway at its base is 11

The height of the archway at its highest point = 30.25

Step-by-step explanation:

The given function representing the archway is y = -x² + 5·x + 24

1) Please find attached the required drawing of the archway created with MS Excel

2) The y-intercept is given by the point where x = 0

Therefore, we have, the y-value at the y-intercept = -0² + 5×0 + 24 = 24

The y-intercept = (0, 24)

The x-intercept is given by the point where y = 0

Therefore, the x-values at the x-intercept are found using the following equation;

0 = -x² + 5·x + 24

x² - 5·x - 24 = 0

By inspection, we have;

x² - 8·x + 3·x - 24 = 0

x·(x - 8) + 3·(x - 8) = 0

∴ (x + 3) × (x - 8) = 0

Either (x + 3) = 0, and x = -3, or (x - 8) = 0, and x = 8

Therefore, the x-intercepts are (-3, 0), and (8, 0)

3) The width of the archway at its base = The distance between the x-values at the two x-intercepts

∴ The width of the archway at its base = 8 - (-3) = 11

The highest point of the arch is given by the vertex of the parabola, y = a·x² + b·x + c, which has the x-value of the vertex = -b/(2·a)

∴ The x-value of the vertex of the given parabola, y = -x² + 5·x + 24, is x = -5/(2×(-1)) = 2.5

Therefore;

The y-value of the vertex, is y = -(2.5)² + 5×2.5 + 24 = 30.25 = The height of the archway at its highest point

∴ The height of the archway at its highest point = 30.25

The vertex of the parabola is at (-2.5, 17.75). And the y-intercept of the parabola is at (0, 24).

Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.

Then the equation of the parabola will be given as,

y = a(x - h)² + k

The equation of the parabola is given as,

y = x² + 5x + 24

Convert the equation into a vertex form, then we have

y = x² + 5x + 25/4 - 25/4 + 24

y = (x + 5/2)² + 71/4

y = (x + 2.5)² + 17.75

The vertex of the parabola is at (-2.5, 17.75). The y-intercept of the parabola is given as,

y = (0)² + 5(0) + 24

y = 24

The y-intercept of the parabola is at (0, 24).

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Answer:

61°

Step-by-step explanation:

For parellel lines cut by a transversal corresponding angles are equal.

The demand function for good X is Qx = m - 3Px + 2Py, where Qx is the quantity demanded of X, m is income, Px is the price of X, and Py is the price of a related good Y. The equation shows that the demand for X is inversely related to its price and directly related to the price of Y. Income, price of X, and price of Y collectively affect the overall demand for X.


The demand function for good X is given by Qx = m - 3Px + 2Py, where Qx represents the quantity demanded of good X, m is the income, Px is the price of good X, and Py is the price of a related good Y. In this equation, the income and prices are assumed to be positive.

To determine the demand for good X, we can analyze the equation. The coefficient -3 in front of Px indicates that the demand for good X is inversely related to its price. As the price of X increases, the quantity demanded of X decreases, assuming other factors remain constant. On the other hand, the coefficient 2 in front of Py indicates that the demand for good X is directly related to the price of the related good Y. If the price of Y increases, the quantity demanded of X also increases, assuming other factors remain constant.

Furthermore, the term (m - 3Px + 2Py) represents the overall effect of income, price of X, and price of Y on the quantity demanded of X. If income (m) increases, the quantity demanded of X increases. If the price of X (Px) increases, the quantity demanded of X decreases. If the price of Y (Py) increases, the quantity demanded of X increases.

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Answer:120 cubic inches

Step-by-step explanation:

(4*10)*6 (40*6)/2 240/2=120 cubic inches

Answer:

78 girls

Step-by-step explanation:

5:6

5+6=11

143/11=13

6*13=78

The height of the tree is approximately 48 feet.

In the given situation, we have a girl standing 40 feet away from a tree. She sights along a yardstick, and when the bottom of the yardstick is 4 feet from her eye, she aligns the top of the yardstick with the top of the tree.

To find the height of the tree, we can create a right triangle. The girl's eye, the bottom of the yardstick, and the top of the tree form the three vertices. The distance from the girl's eye to the bottom of the yardstick is 4 feet, and the distance from the girl to the tree is 40 feet.

Using the concept of similar triangles, we can set up the proportion:

(height of the tree) / (distance from the girl to the tree) = (length of the yardstick) / (distance from the girl to the bottom of the yardstick)

Let's substitute the given values:

(height of the tree) / 40 = 3 / 4

Cross-multiplying, we get:

(height of the tree) = (40 * 3) / 4 = 120 / 4 = 30 feet

Therefore, the height of the tree is approximately 48 feet.

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The probability that Adam and Betty meet at some point is $1-\frac{1}{16}=\boxed{\frac{15}{16}}$.

To find the probability that Adam and Betty meet while walking on the grid, we can consider their paths. Adam will always move up or right, while Betty will always move down or left. This means that their paths will always be perpendicular, and they will only meet if they intersect at some point.

Let's consider the first minute. Adam can either move up or right, and Betty can either move down or left. There are four possible outcomes: Adam moves up and Betty moves down, Adam moves up and Betty moves left, Adam moves right and Betty moves down, or Adam moves right and Betty moves left.

Out of these four outcomes, only one leads to Adam and Betty meeting: if Adam moves right and Betty moves down, they will meet at the point $(1,3)$. So the probability of them meeting in the first minute is $\frac{1}{4}$.

Now let's consider the second minute. Adam will be one unit away from $(1,3)$, and Betty will be one unit away from $(1,3)$. There are four possible outcomes again, but only one leads to them meeting: if Adam moves up and Betty moves down, they will meet at the point $(1,2)$. So the probability of them meeting in the second minute is $\frac{1}{4}$.

We can continue this process for each minute. At each step, there is only one outcome that leads to them meeting, and the probability of that outcome is $\frac{1}{4}$. So the probability of them meeting after $n$ minutes is $\left(\frac{1}{4}\right)^n$.

Now we need to find the probability that they meet at any point in time. We can do this by taking the complement of the probability that they never meet. The only way they will never meet is if their paths never intersect, which means that Adam always stays to the right of Betty or always stays above Betty.

The probability of this happening is the same as the probability that Adam flips tails $4$ times in a row, or Betty flips heads $2$ times in a row. This probability is $\left(\frac{1}{2}\right)^4=\frac{1}{16}$, since there are $2^4$ possible outcomes for Adam and $2^2$ possible outcomes for Betty.

So the probability that Adam and Betty meet at some point is $1-\frac{1}{16}=\boxed{\frac{15}{16}}$.

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I think the right Answer 8/3

Answer:

8/3

Step-by-step explanation:

This hanger is in balance. there are 2 labeled weights of 4 grams and 12 grams the 3 circles have the same weight.

We have to determine,

What is the weight of each circle?​

According to the question,

Let the weight of each circle be x.

This hanger is in balance. there are 2 labeled weights of 4 grams and 12 grams the 3 circles have the same weight.

The hanger is in the balanced state then the sum of all weight of the left-hand side is equal to the sum of all weight of the right-hand side.

Left hand side weight = x+ x + x+ 4 = 3x+4

Right hand side weight = 12

Then,

The hanger is in a balanced state, the weight of each circle is given by,

The weight of the left-hand side = the weight of the right-hand side

The value of x is 8/3.

Hence, The weight of each circle is 8/3.

Answer:

1 minute = 1080 - 960 = 120 m

5 minutes = 5400 - 4800 = 600 m

8 minutes = 8640 - 7680 = 960 mStep-by-step explanation:

The expected value in a binomial situation with n = 18 and π = 0.60 is E(X) = np = 18 * 0.60 = 10.8.

In a binomial situation, the expected value, denoted as E(X), represents the average or mean outcome of a random variable X. It is calculated by multiplying the number of trials, denoted as n, by the probability of success for each trial, denoted as π.

In this case, we are given n = 18 and π = 0.60. To find the expected value, we multiply the number of trials, 18, by the probability of success, 0.60.

n = 18 (number of trials)

π = 0.60 (probability of success for each trial)

To find the expected value:

E(X) = np

Substitute the given values:

E(X) = 18 * 0.60

Calculate the expected value:

E(X) = 10.8

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F(n + 1) + F(n – 2) = 2F(n) for n ≥ 3 using fibonacci numbers definition is proved.

What is a Fibonacci  sequence ?

The Fibonacci sequence is a number sequence in which each subsequent number is formed by adding the two numbers that came before it. The series is named after the Italian mathematician who devised it.

Fibonacci numbers are defined as follows:

F(0) = 0

F(1) = 1

F(n) = F(n-1) + F(n-2) for n ≥ 2

Now, let's prove that F(n + 1) + F(n – 2) = 2F(n) for n ≥ 3 using this definition:

F(n + 1) = F(n) + F(n - 1) (by definition)

F(n – 2) = F(n - 3) + F(n - 4) (by definition)

Adding these two equations, we get:

F(n + 1) + F(n – 2) = F(n) + F(n - 1) + F(n - 3) + F(n - 4)

Now, using the definition of F(n) = F(n-1) + F(n-2), we can substitute F(n-1) + F(n-2) for F(n):

F(n + 1) + F(n – 2) = F(n) + F(n) = 2F(n)

Therefore, F(n + 1) + F(n – 2) = 2F(n) for n ≥ 3, which is the desired result.

Hence, F(n + 1) + F(n – 2) = 2F(n) for n ≥ 3 using fibonacci numbers definition is proved.

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Answer:

612 /1 or 6120/10

Step-by-step explanation:

factor the numerator and denominator and cancel common factors

Answer:

612 there is no fraction solution.....well i dont think so...

Step-by-step explanation:

convert 1/4 into a decimal: 1/4 = .25

                                                         DIVIDE

153 / .25 = 612

                                                        ANSWER

612

if there was a fraction solution it'll probably be 2448/4 = 612

2448/4 would be the fraction solution...

Step-by-step explanation:

\(4(3 + c) + c = c + 4 \\ 12 + 4c + c = c + 4 \\ 12 + 5c = c + 4 \\ 12 + 4c = 4 \\ 4c = 4 - 12 \\ 4c = - 8 \\ c = - 2\)

Answer:

The slope is -1/3x and the point of y intercept is 9.

Step-by-step explanation:

y-12=-1/3(x+9)

First put into y intercept form.

-1/3(x+9) = -1/3x - 3

y-12=-1/3x-3

+12         +12

y=-1/3x+9

Answer:

Length: 10 m

Width: 6 m

Step-by-step explanation:

The layout of the floor is l x w, which is 100 cm by 60 cm. Now, the confusing part: 1 meter (m) = 10 centimeters (cm)

To set this problem up, you'd first have to go through the logic. For every 10 centimeters of the floor layout, it is equal to 1 meter of the actualy floor plan. So you would have to scale 100 cm and 60 cm by \(\frac{1}{10}\) (or divide by 10).

We will ignore the units, for now

Length: 100 * \(\frac{1}{10}\) = 10    or    (100/10 = 10)

Width: 60 * \(\frac{1}{10}\) = 6       or    (60/10 = 6)

Now that we've finalized the numerical value, lets move on to the units. Since the question wants us to respond in meters, the length of 10 and the width 6 6 would be in meters.

So the answer would be:

Length: 10 m

Width: 6 m

Hope this helped!

Answer: -3^8 or 3^8

Step-by-step explanation:

Answer:

the price of a juice is $0.4

Step-by-step explanation:

This is basically dependent on linear equation in 2 variables.

First, we write the equations for these down. Here they are:

2 sandwiches and a juice:

2x + y = £3.4

Four sandwiches and three  juices:

4x + 3y = £7.2

Now, lets use 1 equation to find the value of x.

Here's how

We take the equation, 4x + 3y = £7.2

4x = 7.2 - 3y

x = \(\frac{7.2 - 3y}{4}\)

Once you found x, plug this value into the other equation.

So you'd get:

2(\(\frac{7.2 - 3y}{4}\)) + y = £3.4

Multiply and you get:

\(\frac{7.2 - 3y}{2}\) + y = £3.4

Now, make the denominators same and you get:

\(\frac{7.2 - 3y}{2}\) + \(\frac{2y}{2}\) = £3.4

So, you get:

\(\frac{7.2-y}{2}\) = £3.4

Bring the 2 to the other side and you get:

7.2 - y = 6.8

y = 7.2 - 6.8 = 0.4

Therefore, 1 sandwich costs £0.4

That's it really :D

Answer:

D

Step-by-step explanation:

∠1 + ∠2  =  180   {Supplementary angles}

6x + 15 + 3x + 3 = 180

6x + 3x + 15 + 3 = 180      

Combine like terms

9x + 18 = 180

Subtract 18 from both sides

9x = 180 - 18

9x = 162

x = 162/9

x = 18

∠2 = 3x +3

     = 3*18 + 3

     = 54 + 3

∠2 = 57°

Answer:

Answer is option D) 57°

Here is the explanation...

Answer:

18

-9

30

Step-by-step explanation:

did on edge :)

Answer:

Evaluate the following numerical expressions.

6 + 3 • 4 =  18

(6 + 3) ÷ (4 – 5) = -9

6 + 23 • 3 = 30

Step-by-step explanation:

i took the test

Answer:

x= 1.36

Step-by-step explanation:

Answer:

Step-by-step explanation:

5(x−2 2/5) = −5.2

1. We need to use distibutaive property

5×x and 5×-2.4

5x - 12 = -5.2

2. We need to get x alone.

5x - 12 = -5.2

    -12      -12

5x = 6.8

3. We need to divide

5x = 6.8

/5     /5

x = 1. 36

check:

5(1.36−2 2/5)=−5.2

6.8 - 12 = 5.2

Answer:

The solution to a multiplication problem is called a product.

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

good luck

Answer:

B -8 5/7, 8.1 bar, 8 3/4, 8 7/8

Step-by-step explanation:

8 3/4, -8 5/7, 8.1 bar, 8 7/8

from least to greatest

negative value -8 5/7 is the least

8 3/4 = (8*4 + 3) / 4 = 35/4 = 8.75

8.1 bar = 8.11111111111111.......

8 7/8 = (8*8 + 7) / 8 = 71/8 = 8.875

so the order is -8 5/7, 8.1 bar, 8 3/4, 8 7/8