Q: A is 8km due north of phone mast B. C is 9.5km due west of phone mast B. Calculate the distance AC

Answer:

Simplifying  the expression: [tex]2(\frac{3}{5}x+\frac{2}{3}y-\frac{1}{4}x-1\frac{1}{2}y +3)[/tex] we get [tex]\mathbf{42x-100y-360}[/tex]

Step-by-step explanation:

We need to simplify the expression: [tex]2(\frac{3}{5}x+\frac{2}{3}y-\frac{1}{4}x-1\frac{1}{2}y +3)[/tex]

First we will solve terms inside the bracket

[tex]2(\frac{3}{5}x+\frac{2}{3}y-\frac{1}{4}x-1\frac{1}{2}y +3)[/tex]

Converting mixed fraction [tex]1\frac{1}{2} y[/tex] into improper fraction, we get: [tex]\frac{3}{2}y[/tex]

Replacing the term:

[tex]2(\frac{3}{5}x+\frac{2}{3}y-\frac{1}{4}x-\frac{3}{2}y +3)[/tex]

Now, taking LCM of: 5,3,4,2 we get 60

Now multiply 60 with each term inside the bracket

[tex]2(\frac{3}{5}x\times60+\frac{2}{3}y\times60-\frac{1}{4}x\times60-\frac{3}{2}y\times60 +3\times60)\\2(3x\times12+2y\times20-1x\times15-3x\times30-3\times60)\\2(36x+40y-15x-90y-180)[/tex]

Now, combine like terms

[tex]2(36x-15x-90y+40y-180)\\2(21x-50y-180)[/tex]

Now, multiply all terms with 2

[tex]42x-100y-360[/tex]

So, Simplifying  the expression: [tex]2(\frac{3}{5}x+\frac{2}{3}y-\frac{1}{4}x-1\frac{1}{2}y +3)[/tex] we get [tex]\mathbf{42x-100y-360}[/tex]

Answer:

Saturday 3 9/10 hours = 60/10 = 6, 6 X 9 =54

3 hours 54 mins

Sunday 5 1/6 hours = 60/6 = 10, 10 X 1 = 10

5 hours 10 mins

3 hrs 54 mins + 5 hrs 10mins = 9 hrs 4 mins

Answer:9 4/10

Step-by-step explanation:

Answer:use math(way

Step-by-step explanation

It help

Answer: 2 miles per hour

Step-by-step explanation: Reduce the common factor which would be 5 and then you divide and you get 2

Answer: A) y = 1/3x − 4

Step-by-step explanation:

Find the Equation Using Point-Slope Formula

slope: 1/3

point: (6, −2)

Use the slope 1 and a given point (6, −2) to substitute for [tex]x_1[/tex]  and [tex]y_1[/tex]  in the point-slope form  

y - [tex]y_1[/tex] = m(x - [tex]x_1[/tex]), which is derived from the slope equation m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

  y − (−2) = 1/3 ⋅ (x − (6))

Simplify the equation and keep it in point-slope form.

  y + 2 = 1/3 ⋅ (x − 6)

Solve for y.  

  1/3 ⋅ (x − 6).

Apply the distributive property.

  y + 2 =  1 /3 x +  1 /3 ⋅ − 6

Combine 1/3 and x.

  y + 2 =  x/3 +1/3 ⋅ −6

Cancel the common factor of 3.

  y + 2 =  x /3 − 2

Move all terms not containing y to the right side of the equation.

Subtract 2 from both sides of the equation.

  y = x/3 − 2 − 2

Subtract 2 from −2. x

  y = x/3 − 4

Reorder terms.

  y = 1/3x − 4

List the equation in different forms.

Slope-intercept form:  

y = 1/3x − 4

Point-slope form:

y + 2 = 1/3 ⋅ (x − 6)

Answer:

3 years

Step-by-step explanation:

540 = 4000 x 0.045x

540 = 180x

x = 3

1. 74 tens

2. 3, 7, 11

3. 4 2 5

4. 23

5. 560

6.440

7. Sum

8. 1 dollar and 40 cents

9. 84 cents

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Answer:

1. 74

2. 3, 7, and 11

3. 4, 2, and 5

4. 20.2307692308

5. 560

6. 440

7. sum

8.  Chloe

9. 84 cents

Step-by-step explanation:

We have 5x + 4y = 87 and x + y = 20.

=> 5x + 4y = 87 and 4x + 4y = 80.

5x + 4y = 87

- (4x + 4y = 80)

=> x = 7

Therefore (7) + y = 20, y = 13.

The answers are x = 7 and y = 13.

Answer:

B ($905)

Step-by-step explanation:

Plug in $17 for the h value in the equation, and you get this:

c = 50 (17) + 55

c = 850 + 55

c = 905

So the answer is $905 for 17 hours of work (plus the service fee)

Answer:

[tex]81.2\:\mathrm{ft}[/tex]

Step-by-step explanation:

We can form a right triangle and use basic trig for a right triangle to solve this problem:

[tex]\tan33^{\circ}=\frac{h}{125}[/tex], where [tex]h[/tex] is the height of the tree.

Solving, we get:

[tex]h=125\cdot \tan 33^{\circ},\\h\approx \fbox{$81.2\:\mathrm{ft}$}[/tex].

Answer:

(6a + 18)+(-4 +12a)

6a +12a + 18 -4 = 18a + 14

18a +14 = 0

18a = -14

a = -0/7 ~ -0/8

Answer:

A

Step-by-step explanation:

Answer:

b is the answer

Step-by-step explanation:

4 1/2 divided by 1 1/4 = 3 3/5

The distance Ben jogged in one hour is 3 3/5 miles. The correct option is B. 3 3/5 miles

From the question, we are to determine how far Ben jogged in one hour. That is, how far he jogged per hour.

This means we should determine the rate

Using the formula,

Rate = Distance / Time

From the given information,

Distance = 4 1/2 miles

Time = 1 1/4 hours

∴ Rate = 4 1/2 ÷ 1 1/4

Rate = 3 3/5  miles/hour

Hence, the distance Ben jogged in one hour is 3 3/5 miles. The correct option is B. 3 3/5 miles

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Answer:

10 times

Step-by-step explanation:

After signing up she received 75 points, so the number of points he needs to get a free ticket : 140 - 75 = 65

If she earns 6.5 points or each visit, she would have to visit 65/6.5 times to get a free ticket

65/6.5 = 10

Answer:

10 times bud.

Step-by-step explanation:

Hope this helps!

Answer: 126, 126, 152

or

100, 126, 126

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

V = pie x r*2 x h

Answer:

17 right

Step-by-step explanation:

68 percent of 25 is 17

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Answer: That would be 15ft

Answer:

the total amount that should be paid back at the end of 10 years is £10,200

Step-by-step explanation:

The total amount that should be paid back at the end of 10 years is shown below:

= Borrowed amount + simple interest

= £6000 + (£6000 × 0.07 × 10)

= £6000 + £4,200

= £10,200

Hence, the total amount that should be paid back at the end of 10 years is £10,200

Answer:

Perimeter: [tex]48\sqrt{2} \: \mathrm{inches}[/tex]

Area: [tex]288\mathrm \: \mathrm{square \: inches}[/tex]

Step-by-step explanation:

If the diagonal of the square is 24 inches, the side length of the square is [tex]12\sqrt{2}[/tex] inches ([tex]2x^2=24^2[/tex]). The perimeter of this square is then [tex]4 \cdot 12\sqrt{2}=\fbox{$48\sqrt{2}\: \mathrm{in}$}[/tex] and the area [tex](12\sqrt{2})^2=\fbox{$288\: \mathrm{in^2}$}[/tex].

The area of the square is 288 in.² and the perimeter is 48√2 in.

Given to us,

Diagonal of the square = 24 in.

We know that for a square,

[tex]\bold{(Diagonal)^2 = 2\times (side)^2}[/tex]

substituting the values,

[tex]{(Diagonal)^2 = 2\times (side)^2}\\24^2 = 2\times (side)^2}\\side = 12\sqrt {2}[/tex]

Also, the area of a square is given by (side)², and, perimeter by (4 x side).

[tex]\bold{Area = (12\sqrt2)^2 = 288 in.^2}[/tex]

[tex]\bold{Perimeter= (4\times 12\sqrt2) = 48\sqrt 2 in.}[/tex]

Hence, the area of the square is 288 in.² and the perimeter is 48√2 in.

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Answer:

It is an unknown number but add 16 + 32 degrees and you get 48x degrees then multiply 48 X 72 degrees and you get 336 degrees.

Step-by-step explanation:

Answer:

20 bolts per bookcase

Step-by-step explanation:

Answer:

I think B.Reflexive property

The property best describes the congruence statement is

Symmetric property.

Congruent means same shape and same size. So congruent has to do with comparing two figures, and equivalent means two expressions are equal. So to say two line segments are congruent relates to the measures of the two lines are equal.

We know,

The Symmetric Property states that for all real numbers

if x = y then y=x

and, Transitive Property

The Transitive Property states that for all real numbers

if x = y and y = z then z=x.

and, Reflexive Property

for any x, x = x.

Here, the property used is Symmetric.

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Answer:

2x - 3y = 24

Step-by-step explanation:

You use the formula Ax ± By = C.

This is the standard linear equation form.