The coordinates of the vertices for rectangle ABCD are A (2,4), B (6,10), C (9,8) and D (5,2). What
is the length of a diagonal (AC or BD) of the rectangle?

A √13

B √52

C √60

D √65

Answer: 71.429 miles

Step-by-step explanation:

The charge for the rental truck can be represented by the equation: y= 0.28m+80

m is the miles driven

y is the total cost

Plug in 100 for y because that’s how much you have to spend

100=0.28m+80

-80 -80

20=0.28m. Divide both sides by 0.28

71.429 miles

You can round it again if you want

71.43 or 71.4 or 71

Answer:

$1865

The gold calculator is a gold melt value calculator which can be used to determine the value of gold metal inside an item with a known weight and gold purity. These items may include gold jewelry (such as, bangles, bracelets, chains, earrings, necklaces, pendants, and rings), gold bullion and gold coins.

The gold calculator is designed to calculate the gold metal value for one item at a time. If you would like to calculate the gold metal value for multiple items simultaneously consider using the scrap gold calculator for scrap gold, the gold bullion calculator for gold bullion bars and coins, and the gold coin calculator for gold coins.

The prairie dog population in 1991 was estimated to be 0.8 million. This is calculated using the equation , where P is the prairie dog population in millions, t is the number of years after 1975, and r is the growth rate, which is 6%. In 1991, t = 16, so P = 0.3 * (1.06)^16 = 0.8.

The equation P = 0.3 * (1.06)^t models the prairie dog population as a geometric sequence. The first term is 0.3, the common ratio is 1.06, and the number of terms is t. The population in 1991 is calculated by substituting t = 16 into the equation. The answer is rounded to the nearest tenth.

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Answer:

4.802 x 10^7

Step-by-step explanation:

Hope this helps! :)

If this wasn't what you were looking for please don't hesitate to comment again. Have a nice day/night! :)

Answer:

4.802 x 10 power of 7

Step-by-step explanation:

i did this so i know

At the instant when x=4 and y=3, (dx/dt) ≈ 0.143.  We are given the rates of change of z and x with respect to t, and a relationship between x and y, but we are not given the rate of change of y with respect to t.

However, we can use the relationship between x, y, and z to find an expression for (dy)/(dt).

From the hint, we have:

z^2 = x^2 + y^2

Differentiating both sides with respect to t, we get:

2z(dz/dt) = 2x(dx/dt) + 2y(dy/dt)

Simplifying and dividing by 2, we get:

z(dz/dt) = x(dx/dt) + y(dy/dt)

Substituting the given values of (dz)/(dt) and (dx)/(dt), we have:

z = sqrt(x^2 + y^2)

(dz/dt) = 1

(dx/dt) = (3(dy/dt))/t

At the instant when x=4 and y=3, we have:

z = sqrt(4^2 + 3^2) = 5

(dx/dt) = (3(dy/dt))/t

To find (dy/dt), we substitute into the expression we derived earlier:

z(dz/dt) = x(dx/dt) + y(dy/dt)

5(1) = 4(3(dy/dt))/t + 3(dy/dt)

5 = (12/t + 3)(dy/dt)

(dy/dt) = 5/(12/t + 3) = 5t/(12t + 36) = (5/12)(t/(t + 3))

Substituting this into the expression for (dx/dt), we get:

(dx/dt) = (3(dy/dt))/t = (3/12)(t/(t + 3)) = (1/4)(t/(t + 3))

At the instant when x=4 and y=3, we have:

(dx/dt) = (1/4)(4/(4 + 3)) = 1/7

Therefore, at the instant when x=4 and y=3, (dx/dt) ≈ 0.143.

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The number of electrons flowing per second is known as as electric current, Option (c) is correct.

The Current represents the flow of electric charge in a circuit and is measured in Amperes (A). It is a fundamental quantity that indicates the rate at which electrons pass through a specific point in a conductor.

The Voltage (potential difference), is the driving force that pushes the electrons through the circuit. The Resistance, on the other hand, opposes the flow of current. Power, measured in Watts (W), is the rate at which electrical energy is consumed or produced in a circuit.

Therefore, the correct option is (c).

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When A'B'C' is reflecting in origin, A" (4, 1), B" (0, -7), and C" are the coordinates of the vertices' pictures (-2, -5).

The vertices of ABC are A (4, -1), B (0, 7), and C (-2, 5), respectively.

The coordinates of the points for ABC will be A' (-4, -1), B' (0, 7), and C' after reflecting in the y-axis (2, 5).

Once more, when "A'B'C" is reflecting in origin, "A" will be at (4, 1), "B" will be at (0, -7), and "C" will be at (4, 1). (-2, -5).

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A discrete variable is a variable whose value is obtained by counting while a continuous variable is a variable whose value is obtained by measuring.

From the question,

The number of cars a car dealer sells in a day is a discrete variable.

The time it takes to have a medical physical exam is a continuous variable.

Given:

Consider \(AB\parallel DE\) in triangle ABC and \(AD=8,DC=3.2,BE=9\).

To find:

The length of BC.

Solution:

Basic proportionality theorem (BPT): If a line intersect the two sides of triangle and parallel to the third side, then that line intersects the other two sides proportionally.

Using Basic proportionality theorem, we get

\(\dfrac{AD}{DC}=\dfrac{BE}{EC}\)

\(\dfrac{8}{3.2}=\dfrac{9}{EC}\)

On cross multiplication, we get

\(8\times EC=9\times 3.2\)

\(EC=\dfrac{28.8}{8}\)

\(EC=3.6\)

Now,

\(BC=BE+EC\)

\(BC=9+3.6\)

\(BC=12.6\)

Therefore, the length of side BC is 12.6 units.

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The vendor sold 172 sodas and 58 hotdogs at the hockey game.

An equation of degree one is known as a linear equation.

A linear equation of two variables can be represented by ax + by = c.

let, the number of soda cans be 'x' and the number of hot dogs be 'y'.

So, From the given information x = 3y and the vendor sold a total of 232.

Therefore, x + y = 232.

3y + y = 232.

4y = 232.

y = 232/4.

y = 58.

So, He sold 58 hot dogs and 3×58 = 172 soda cans.

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a) Since the triangles are congruent, and ΔABC is congruent to ΔDEF, segments AB and DE have the same value. Therefore, you can use algebra to solve for x when using the knowledge that (12 - 4x) is equal to (15 - 3x).

To solve:

12 - 4x = 15 - 3x

12 = 15 + x

-3 = x

Therefore, x is equal to -3.

b) To find the value of AB, plug in the value of x found in part a).

12 - 4x

12 - 4(-3)

12 - (-12)

12 + 12 = 24

Thus, segment AB is equal to 24.

c) As shown in part b), plug in the value of x found in part a) to find the value of segment DE.

15 - 3x

15 - 3(-3)

15 - (-9)

15 + 9 = 24

Thus, segment DE is also equal to 24.

We can confirm the knowledge of the equal side lengths because the triangle are congruent. This means that all the side lengths in the triangle are the same, which is confirmed when algebraically plugging in the value of x to solve for the values of the segments AB and DE.

I hope this helps!

Answer:

Slope is 2

Step-by-step explanation:

To find the slope of a line, pick two points and do y1-y and x1-x

The two points I picked is (2,3) and (5,9)

y1=9

y=3

----------

x1=5

x=2

Subtract, then put it as a fraction.

6/3 or 2.

The pick-up rate in this scenario would be 80%. This is calculated by dividing the number of rooms occupied (160) by the number of rooms reserved (200), and then multiplying by 100 to get a percentage. So, (160/200) x 100 = 80%. This means that 80% of the reserved rooms were ultimately occupied.

It's important to note that a pick-up rate of 80% is generally considered to be a good result in the hospitality industry. It indicates that the hotel was able to accurately predict the number of rooms that would be needed by the groups, and that the groups themselves followed through on their reservations. A lower pick-up rate could suggest that the hotel overestimated demand, or that some of the groups cancelled their bookings at the last minute. On the other hand, a higher pick-up rate could indicate that the hotel was too conservative in its initial estimates, or that some of the groups requested additional rooms after the initial reservation was made. Ultimately, the pick-up rate is a useful metric for assessing the accuracy of a hotel's forecasting and planning processes.

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To compute a basis of the eigen space corresponding to eigen value -2, we need to find the null space of the matrix A + 2I, where A is the 3x3 matrix and I is the identity matrix.

The null space will give us the basis vectors of the eigen space

To find the eigen space corresponding to the eigen value -2, we start by constructing the matrix A + 2I, where A is the given 3x3 matrix and I is the 3x3 identity matrix. Next, we solve the homogeneous system of linear equations (A + 2I)x = 0, where x is a vector. The solutions to this system form the null space of the matrix A + 2I.

By finding a basis for this null space, we can obtain the basis vectors of the eigen space corresponding to the eigen value -2.

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Answer:

she has 13 dollars left

Step-by-step explanation:

simple math of subtraction. 45 - 32 = 13

13 goes into her account after paying her debt to the bank

The length of the unknown leg is 8 yd in the given right triangle.

The Pythagoras theorem states that a right-angled triangle's hypotenuse square (90 degrees) equals the sum of the squares of its other two sides.

Let the three legs of the right triangle be a, b and c where a is the altitude, b is the base and c is hypotenuse of the given right angled triangle.

Here, a = \(\sqrt{23}\) yd, b = ? and c = \(\sqrt{87}\)

According to the Pythagoras theorem,

Hypotenuse² = Base² + Altitude²

c² = b² + a²

\((\sqrt{87})^{2}\) = b² + \((\sqrt{23})^{2}\)

87 = b² + 23

Subtracting 23 from both sides of the equation.

87 - 23 = b²

b² = 64

Taking square root of the both sides.

b = ± 8

Since the value of length can't be negative so the value of b = - 8 is rejected.

Therefore, the value of b = 8 yd.

As we have calculated above, the length of the unknown leg is 8 yd.

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The fraction 4/6 + 8/6 is added to give 2

The addition of fraction is done as follows

check if the denominator of the both fraction are equal. In this case they are equal with a value of 6

4/6 + 8/6

the addition requires adding the numerators

= (4 + 8) / 6

= 12 / 6

= 2

adding the fractions gives a value of 2

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In order to check if the new industrial product is profitable, we need to determine if the mean of the advance orders (4 units) is greater than or equal to the required number of units per customer (4.2 units).

Industrial products are physical goods or services produced by industries. These products are used in the production of other goods or services.

We can use a one-sample t-test to determine if the difference in means is statistically significant at the 1% level. The null hypothesis for this test is that the mean of the sample is equal to the required number of units per customer (4.2 units).

The one-sample t-test yields a p-value of 0.73, which is greater than the 1% level. Therefore, we cannot reject the null hypothesis and conclude that the mean of the sample is not significantly different from the required number of units per customer. As such, the new industrial product is likely to be profitable.

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Answer:

the coordinate of the vertex is going to be (-3,-1) and it's concave up

Step-by-step explanation:

1.notice this function is in graphing form (x-h)^2+k, where (h,k) is your coordinate of the vertex, hence in this problem it's going to be (-3,-1)

2. notice that this function have a parent function of x^2, where it's a parabola that is concave up which in this case is basiclly the same shape it's also concave up

In calculus, we can proof it by finding the first derivatives and find the critical points, then take the second derivative at that critical points to see if that's negative or positive in this case it's positive

The first five coefficients, we have: f(x) = e⁻² + e⁻²(x + 2) + (e⁻²/2)(x + 2)² + (e⁻²/6)(x + 2)³ + (e⁻²/24)(x + 2)⁴ + ..

To find the Taylor series for the function f(x) = eˣ about x = -2, we can use the general formula for the Taylor series expansion:

f(x) = ∑n=0^∞ c_n(x - a)ⁿ

where c_n represents the nth coefficient, (x - a)^n is the term raised to the nth power, and a is the point about which we are expanding the series.

In this case, we want to find the Taylor series for f(x) = eˣ about x = -2. So, a = -2.

To find the coefficients c_n, we can use the formula:

c_n = (1/n!) * fⁿᵃ

where f^(n)(a) denotes the nth derivative of f evaluated at x = a.

Let's find the first five coefficients:

Step 1: Find f(x) and its derivatives:

f(x) = eˣ

f'(x) = eˣ

f''(x) = eˣ

f'''(x) = eˣ

f''''(x) = eˣ

Step 2: Evaluate the derivatives at x = -2:

f(-2) = e⁻²

f'(-2) = e⁻²

f''(-2) = e⁻²

f'''(-2) = e⁻²

f''''(-2) = e⁻²

Step 3: Calculate the coefficients:

c_0 = f(-2)/0! = e⁻²/1 = e⁻²

c_1 = f'(-2)/1! = e⁻²/1 = e⁻²

c_2 = f''(-2)/2! = e⁻²/2 = e⁻²/2

c_3 = f'''(-2)/3! = e⁻²/6 = e⁻²/6

c_4 = f''''(-2)/4! = e⁻²/24 = e⁻²/24

Therefore, the first five coefficients for the Taylor series expansion of f(x) = eˣ about x = -2 are:

c_0 = e⁻²

c_1 = e⁻²

c_2 = e⁻²/2

c_3 = e⁻²/6

c_4 = e⁻²/24

The Taylor series for f(x) = e^x about x = -2 can be written as:

f(x) = ∑n=0^∞ c_n(x + 2)ⁿ

Substituting the first five coefficients, we have: f(x) = e⁻² + e⁻²(x + 2) + (e⁻²/2)(x + 2)² + (e⁻²/6)(x + 2)³ + (e⁻²/24)(x + 2)⁴ + ..

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there are 55 red marbles in the jar

Answer:

There are 55 red marbles in the jar.

Step-by-step explanation:

Green marbles = 125 x 2/100 = 2.5

Blue marbles = 125 x 54/100 = 67.5

Red marbles = 125 - 67.5 - 2.5 = 55

7/6 already has a denominator of 6. 1/3=2/6

7/6-2/6=5/6

So the answer is 5/6

---

hope it helps

Answer:

The answer is 250 meters from the lodge

Answer: 40

Step-by-step explanation:

38+ 52=90

230-90=40

Reflection across the y-axis requires changing the sign of the x-coordinate while keeping the y-coordinate the same. This can be seen in Physics with the reflection of light rays off symmetrical mirrors. The transformed coordinates, after a y-axis reflection, of a point A with original coordinates (3, 4) would be (-3, 4).

A reflection across the y-axis in Mathematics involves changing the sign of the x-coordinate and keeping the y-coordinate intact. If the original coordinates of the vertex, point A, were (x, y), then following the reflection, the new coordinates of A would be (-x, y).

This concept is similar to the reflection of light seen in Physics. For instance, if a ray of light hits the vertex of a symmetrical mirror, it is reflected symmetrically about the optical axis of the mirror. This helps us understand how images are formed by reflection in mirrors.

Suppose within our example, point A had coordinates (3, 4). Following reflection across the y-axis, point A would be mapped to the coordinates (-3, 4).

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Answer:

doesnt this count as plagirism

Step-by-step explanation: