Town Hall is located 4. 3 miles directly east of the middle school. The fire station is located 1. 7 miles directly north of Town Hall.


Part A


What is the length of a straight line between the school and the fire station? Round to the nearest tenth. Enter your answer in the box.



Part B


The hospital is 3. 1 miles west of the fire station. What is the length of a straight line between the school and the hospital? Round to the nearest


tenth. Enter your answer in the box.

Answer:

\(\displaystyle 1\frac{2}{5}=\frac{7}{5}\)

Step-by-step explanation:

\(\displaystyle a\frac{b}{c}=\frac{ac+b}{c}\\\\1\frac{2}{5}=\frac{(1)(5)+2}{5}=\frac{5+2}{5}=\frac{7}{5}\)

Answer:

Yes i do the answer is C

Step-by-step explanation:

Have a good day:))))

Answer:

i think it would be 1550?

Step-by-step explanation:

im pretty sure you add teh weight of the three people and convert it to one ton

The algebraic expression in question b can be simplified to give (x² - 5x)/5.

Simplification of an algebraic expressions is the process of writing an expression in the most efficient and compact way, that is in their simplest form, without changing the value of the original expression.

2x²(x - 5)/10x = 2x × x(x - 5)/ 2x × 5

2x is a common factor to both the numerator and denominator, hence can cancel out

2x²(x - 5)/10x = x(x - 5)/5

opening bracket we have;

2x²(x - 5)/10x = (x² - 5x)/5

Therefore, (x² - 5x)/5 is the result after simplifying the algebraic expression 2x²(x - 5)/10x

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Answer:

40 is ur answer

Step-by-step explanation:

144-105=39

39 written as a percentage is 39%

39% rounded to nearest tenth is 40

Answer:

dhchdhduc

Step-by-step explanation:

Answer:

Width of the 12 ipads and 8 kindles is 4.98 inches

so I think it C

Step-by-step explanation:

IT C  i hink but I'm not fully sure but i did the math and that what i got

There are 120 five digit numbers that can be created

The digits are given as:

2, 3, 5, 7 and 8

Since there are no conditions, and the digits cannot be repeated.

Then the number of digits is:

Digits = 5!

Expand

Digits = 5 * 4 * 3 * 2 * 1

Evaluate

Digits = 120

Hence, there are 120 five digit numbers that can be created

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The width of pool deck is 7 ft and new dimensions of pool and deck are 21 ft and 35 ft .

In the given question we have,

Area of whole background ( pool + deck) = 1176 ft²------(1)

Area is a two dimensions quantity . so, we work here in 2-D.

length of pool = 28 ft , width of pool= 14 ft

let the width of deck be x ft . Now, the new dimensions are following

length of pool and deck = 28 + x + x = (28+2x ) ft

width of pool and deck = 14 + x + x = (14+ 2x) ft

here, 2x include in lenth and width for surronding deck.

total area of pool and deck ( backyard ) = lenth × width = 1176 ft² ( from (1) )

(28+2x) ( 14+2x) = 1176 ----(2)

Now, we shall solve above equation (2) and find out value of x

28×14 + 56x + 28x + 4x^2 = 1176

=> 4x²+ 84x + 392 - 1176 = 0

=> 4x² + 84x - 784=0 => x² + 21x - 196 = 0

=> x²+ 28x - 7x - 196 = 0 => x(x+ 28) - 7(x+28)=0

=> (x+28) (x-7) = 0

either x + 28= 0 or x - 7 = 0 =>either x= -28 or x= 7

but width can't be negative value so, discard

x= -28.

Hence, the width of pool deck is 7 ft.

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Step-by-step explanation:

hope it helps.

Answer:

Below

Step-by-step explanation:

√(18*49)

= √882

= 29.70 to nearest hundredth.

The numerical value of each expression,

a. cosh(ln(5)) = 2.50258.

b. cosh(5) = 74.20995.

(a) Using the identity cosh(x) = (\(e^x\) + \(e^{(-x)}\))/2 and substituting x = ln(5), we get:

To find cosh(ln(5)), we first evaluate ln(5) which is approximately equal to 1.60944.

cosh(ln(5)) = (\(e^{(ln(5)}\)) + \(e^{(-ln(5)}\)))/2

= (5 + 1/5)/2

= 2.50258

Therefore, cosh(ln(5)) = 2.50258 (rounded to five decimal places).

(b) Using the identity cosh(x) = (\(e^x\) + \(e^{(-x)}\))/2 and substituting x = 5, we get:

cosh(5) = (\(e^5\) + \(e^{(-5)}\))/2

= (148.41316 + 0.00674)/2

= 74.20995

Therefore, cosh(5) = 74.20995 (rounded to five decimal places).

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Answer:

x = 1

Step-by-step explanation:

Since all the fractions have a common denominator of 3, you can multiply both sides by 3 to get rid of the denominator. (Make sure you distribute)

\(\frac{7}{3}x+\frac{1}{3}x=1+\frac{5}{3}x\)

\(3(\frac{7}{3}x+\frac{1}{3}x)=3(1+\frac{5}{3}x )\)

7x + x = 3 + 5x

8x = 3 + 5x

8x - 5x = 3 + 5x - 5x

3x = 3

x = 3/3

x = 1

Answer: 151/14

Step-by-step explanation:

6x+13+4x+16+4x=180

14x + 29 = 180

14x = 151

x = 151/14

Answer:

It has 1 solution in different forms.

Step-by-step explanation:

In the exact form it is: -83/8

In the decimal form it is: -10.375

In the mixed number form it is: -10 \(3/8\)

Hope this helps:)

The vector orthogonal to the plane through the points P, Q, and R is (8, -8, 12), and the area of triangle PQR is \($\sqrt{301}$\).

For part (a), we can find a nonzero vector orthogonal to the plane through the points P, Q, and R by constructing a normal vector to the plane using the cross product of two vectors in the plane. The two vectors in the plane are \($\vec{PQ} = (1- (-2), 0-1, 1-3) = (3, -1, -2)$\) and \($\vec{PR} = (1-4, 0-2, 1-5) = (-3, -2, -4)$\). Taking the cross product of the two vectors gives us the normal vector to the plane, \($\vec{n} = \vec{PQ} \times \vec{PR} = (8, -8, 12)$\). Therefore, the vector orthogonal to the plane is \($\vec{n} = (8, -8, 12)$.\)

For part (b), the area of triangle PQR can be found using the formula for Heron's Formula, which states that the area of a triangle with sides a, b,and c is given by

\($A = \sqrt{s(s-a)(s-b)(s-c)}$\)

where \($s = \frac{a+b+c}{2}$\) . In this case, the sides are \($a = \|\vec{PQ}\| = \sqrt{3^2 + (-1)^2 + (-2)^2} = \sqrt{14}$, $b = \|\vec{QR}\| = \sqrt{(-2-4)^2 + (1-2)^2 + (3-5)^2} = \sqrt{14}$\), and\($c = \|\vec{PR}\| = \sqrt{(-3)^2 + (-2)^2 + (-4)^2} = \sqrt{29}$\). Plugging these values into the formula, we get

\(= \sqrt{s(s-a)(s-b)(s-c)} = \sqrt{\frac{7(7-\sqrt{14})(7-\sqrt{14})(7-\sqrt{29})}{4}} = \sqrt{7(7-\sqrt{14})^2(7-\sqrt{29})} = \sqrt{7(7-\sqrt{14})^2(\sqrt{14}+\sqrt{29})} = \sqrt{7(7-\sqrt{14})^2\sqrt{43}} = \sqrt{301}$\)Therefore, the area of triangle PQR is \($\sqrt{301}$\)

The vector orthogonal to the plane through the points P, Q, and R is (8, -8, 12), and the area of triangle PQR is \($\sqrt{301}$\).

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Answer:

324

Step-by-step explanation:

Answer:

24=10

Step-by-step explanation:

The value of y when  x = 10 is 5/4

If y varies directly as x, this is expressed as:

\(y \alpha x\\y = kx\\\)

where

k is the constant of proportionality

If y = 3 when x = 24, then:

3 = 24k

k = 3/24

k = 1/8

In order to get the value of x when y = 10

Recall that y = kx

y = 1/8 * 10

x = 10/8

y = 5/4

Hence the value of y when  x = 10 is 5/4

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A: The height of the street sign is obtained by indirect measurement method as 15 feet.

B: The two proportions Betsy can use is 5/1.5 = x/4.5 and 5/.x = 1.5/4.5

C: Using both the proportions height of the street sign is obtained as 15 feet.

What is indirect measurement?

A mathematical technique called as an indirect measurement is used to discover unknown measures of items that are challenging to measure. A direct measurement is something that can easily be measured, like a toddler's height.

The height of Betsy is h = 5 feet.

The shadow of Betsy is h' = 1.5 feet.

The height of the street sign is H = x feet.

The height of the shadow of street sign is H' = 4.5 feet.

The two proportions are -

h/h' = H/H' and h/H = h'/H'

These two can be used to find the measurement of the street sign.

To find the height of the street sign use the method of indirect measurement -

h/h' = H/H'     h/H = h'/H'

Substitute the values in the given equation -

5/1.5 = x/4.5            5/x = 1.5/4.5  

1.5 × x = 5 × 4.5      5 × 4.5 = 1.5 × x

1.5x = 22.5              22.5 = 1.5x

Simplify the equation further -

x = 22.5/1.5             x = 22.5/1.5

x = 15                       x = 15

Therefore, the value of the x is obtained as 15 feet.

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The z-score with probability 0.225 to the right is 0.15 and the z-score with probability 0.900 to the left is -1.28. This can be calculated using the Z-score table for a standard normal distribution.

(a) Probability 0.225 to the right is equal to z-score 0.15.

This can be calculated using the Z-score table for a standard normal distribution.

The probability to the right of z-score is equal to the cumulative probability of the z-score.

The cumulative probability of 0.15 is 0.225, which is the probability to the right.

(b) Probability 0.900 to the left is equal to z-score -1.28.

This can be calculated using the Z-score table for a standard normal distribution.

The probability to the left of z-score is equal to the cumulative probability of the z-score.

The cumulative probability of -1.28 is 0.900, which is the probability to the left.

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The company's cost of preferred stock is 9.08%, which means the correct answer is B) 9.08%. The cost of a service may be determined by the amount of time and expertise required to provide it. In general, cost is an important factor in determining the feasibility and profitability of a project or business venture.

Cost refers to the amount of money that is required to purchase or produce something. For example, the cost of a product may be determined by the amount of materials and labor that went into producing it, as well as any other expenses associated with bringing it to market.

To calculate the company's cost of preferred stock, we need to use the following formula:

Cost of preferred stock = annual dividend / price per share - flotation cost

In this case, the annual dividend is $8.50, the price per share is $97.50, and the flotation cost is 4.00% of the price paid by investors. Plugging these values into the formula, we get:

Cost of preferred stock = $8.50 / $97.50 - 4.00% = $8.50 / $97.50 * (1 - 0.04) = $8.50 / $93.80 = 0.0908

Therefore, the company's cost of preferred stock is 9.08%, which means the correct answer is B) 9.08%.

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Answer:

Put it in your calculator then you will get the right answer.

Step-by-step explanation:

The value of the base in the given triangle is 22.96.

Three edges and three vertices make up the three sides of a triangle, which is a three-sided polygon in geometry. The fact that a triangle's internal angles can be added up to equal 180 degrees is its most significant characteristic. Triangle's angle sum property is what this characteristic is known as.

We have given to find m, we will use cosine rule

cos ∅ = base/hypotenuse

Here ∅ = 35°

Base = m

Hypotenuse = 28

lets substitute the values and we get,

⇒ cos 35° = m/28

⇒ m = cos 35°  × 28

⇒ m = 0.82 × 28                   ( cos 35° = 0.82)

⇒ m = 22.96

Thus, the value of the base in the given triangle is 22.96.

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Answer:

6

Step-by-step explanation:

A=hbb/2

9·6/2

=27

Answer:

3) 9x² - 5x - 9

Step-by-step explanation:

Combine like terms

5x² - 9x + 3 + 4x² + 4x - 12 = 5x² + 4x²  - 9x + 4x    + 3 - 12

                                           = 9x² - 5x - 9

Answer:

Step-by-step explanation:

z/8 -5/8= (z-5)/8

it can not be simplified more than this

Answer:

z-5/8

Step-by-step explanation:

change it to a single fraction

Answer:

D. 29 I just know the awnser sorry

To find the value of f(−2), we substitute −2 for x in the function f(x):

f(−2) = 4(-2)^2 − 3(-2) + 7

= 4(4) − 3(2) + 7

= 16 − 6 + 7

= 11

Therefore, f(−2) = 11.

Using the graph, it is found that the average rate of change of the function over the interval 0 ≤ x ≤ 20 is of 1.

The average rate of change of a function f(x) over an interval [a,b] is given by:

\(A = \frac{f(b) - f(a)}{b - a}\)

In the interval for this problem, we have that:

Hence:

\(A = \frac{24 - 4}{20 - 0} = 1\)

The average rate of change of the function over the interval 0 ≤ x ≤ 20 is of 1.

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Answer:

6^7

Step-by-step explanation:

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 6 from 13 to get 7.

​

Answer:

6^7

Step-by-step explanation:

6^13/6^6 = 6^7

A 11.544 acre-feet of this ice field will melt from the beginning of day 1 (t = 0) to the beginning of day 4 (t = 3). So, correct option is C.

To solve the problem, we need to integrate the given rate of melting with respect to time over the interval [0,3] to find the total amount of ice that melts during this time.

First, we can simplify the given rate of melting by using the identity: sin³(t) = (3sin(t) - sin(3t))/4

So, M(t) = 4 - (3sin(t) - sin(3t))/4 = 16/4 - 3sin(t)/4 + sin(3t)/4 = 4 - 0.75sin(t) + 0.25sin(3t)

Integrating this expression with respect to t over the interval [0,3], we get:

\(\int\limits^3_0\) M(t) dt = \(\int\limits^3_0\) (4 - 0.75sin(t) + 0.25sin(3t)) dt

= [4t + 0.75cos(t) - (1/3)cos(3t)]|[0,3]

= (12 + 0.75cos(3) - (1/3)cos(9)) - (0 + 0.75cos(0) - (1/3)cos(0))

= 11.544

Therefore, the answer is (C) 11.544.

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