To approximate the length of a lake, a surveyor starts at one end of the lake and walks 245 yards. He then turns 110 and walks 270 yards until he arrives at the other end of the lake. Approximately how long is the lake?

Hello!

Answer:

21.6

Steps:

7.20 increase 200% =

7.20 × (1 + 200%) = 7.20 × (1 + 2) = 21.6

Answer:

Step-by-step explanation:

By Pythagoras:

d^2 = (3.5)^2 + (4.5)^2

d^2 = 12.25 + 20.25 = 32.5

d = √32.5

Answer:

11th term is 0

Step-by-step explanation:

30, 27 , 24 ,......0

a = first term = 30

Common difference = second term - first term = 27 - 30 = -3

nth term = a+(n-1)*d

a + (n-1)d = 0

30 + (n - 1) *(-3) = 0

30 + n*(-3) -1*(-3) = 0

30 - 3n + 3 = 0

      -3n + 33 = 0

               -3n = -33

                   n = -33/-3

n = 11

Answer:

AAS

Step-by-step explanation:

I'm pretty sure its this, but im sorry if im wrong!

transverse s at angle 135°

180° - 135° = 45°

Angle 2 is congruent to 45° because they're alternate exterior angles.

transverse t at angle 120°

180° - 120° = 60°

Angle 3 is congruent to 60° because they're alternate exterior angles.

One rule for exterior angles in triangles is that the exterior angle is equal to the sum of the two angles adjacent to the opposite angle of the exterior angle.

135° = angle 1 + 60°

angle 1 = 75°

120° = angle 1 + 45°

angle 1 = 75°

Therefore angle 1 is 75°,angle 2 is 45° and angle 3 is 60°

Answer:

m∠1 = 75° m∠2 =45° m∠3 = 60°

Step-by-step explanation:

m∠1 = 180 - { (180 - 135) + (180 - 120) }

m∠1 = 180 - { 45 + 60 }

m∠1 = 75°

The angle between 1 and 3, lets call it x,  is vertically opposite to ∠2, so we must find it first to be able to get ∠2

Since a ║b

Therefore ∠x and ∠135 are co-interior angles

Therefore ∠x = 180-135

m∠x = 45°

∠2 = ∠x (Vertically opposite angles)

∠2 = 45°

Between ∠2 and ∠3 there is an angle, let's call it z.

∠z = ∠1 (Vertically opposite angles)

∠z = 75°

Since the sum of  ∠2, ∠z and ∠3 = 180° (Straight angle)

Therefore m∠3 = 180 - (∠2 + ∠z)

m∠3 = 180 - (45 + 75)

m∠3 = 60°

Or in a different way

∠2 + ∠z + ∠3 = 180

45 + 75 + ∠3 = 180

120 + ∠3 = 180

∠3 = 180 - 120

∠3 = 60°

Hope it helps

The number of overtime hours Bolton will need at his new position in other to make the same monthly income ls 10 hours per week.

New position :

Let the number of overtime hours required weekly = t

Hence,

(14.90 × 40) + 22.35t = 820

596 + 22.35t = 820

22.35t = 820 - 596

22.35t = 224

t = 224 / 22.35

t = 10

Therefore, he'll need 10 hours of overtime.

Learn more : https://brainly.com/question/18112348

Answer: [tex]\frac{17}{4}[/tex]

Step-by-step explanation:

Simply convert 3/1 into 12/4, then add it to 5/4, to get 17/4.

Hope it helps :) and let me know if you want me to elaborate.

Answer:

What subject is this

Step-by-step explanation:

Answer:

-2/3x+4

Step-by-step explanation:

the reason is that if we take 2 point from the graph for example;

0,4 and 6,0

1) to get the gradient it is y2-y1/x2-x1

sub 0,4 and 6,0 into the equation from 1

4-0/0-6 which is 4/-6

4/-6 = 2/-3 and +4 because as seen in the graph it's hits the y-axis at +4

so it is 2/-3x + 4

Answer:

9

Step-by-step explanation:

Since 12 divided by 4 is 3, that is the constant. So 3 times 3 is 9

Answer:

even

Step-by-step explanation:

because a is not and odd number its even

The requried two words that describe A² are "Odd" and "Positive".

Odd numbers are integers that cannot be divided evenly by 2, which means they have a remainder of 1 when divided by 2. They can be represented as 2n + 1, where n is an integer. Examples of odd numbers include 1, 3, 5, 7, 9, and so on. The opposite of odd numbers are even numbers, which can be divided evenly by 2.

The square of any negative or positive number is always positive. Thus, the first two options "Negative" and "Positive" do not apply to A². As for "Even", it describes a number that is divisible by 2, while "Odd" describes a number that is not divisible by 2. Since A is an odd number, A² will also be odd, as it is the product of an odd number multiplied by itself.

Therefore, the two words that describe A² are "Odd" and "Positive".

Learn more about odd numbers here:

https://brainly.com/question/29635088

#SPJ2

Answer:

Step-by-step explanation:

Staring point = 2 o'clock

The travel is 1/4 of 12 hour full revolution:

Point to stop is the start point plus the travel:

refer to the attachment

Answer:

HCF(12, 48, 60) = 12

Step-by-step explanation:

HCF of 12, 48, 60 is 12 since 12 is largest number which exactly divides all the numbers

Highest common factor (HCF) of 12, 48, 60 is 12.

Hope this helped you- have a good day bro cya)

Data can be represented in tables, charts, and graphs.

Answer:

A, C, E

Step-by-step explanation:

Substitute the x- coordinate of the points into the equation and if the result is equal to the y- coordinate of the point then it is a solution.

A (- 2, 5 )

y = 2² + 1 = 4 + 1 = 5 → (- 2, 5 ) is a solution

B (- 1, 0 )

y = (- 1)² + 1 = 1 + 1 = 2 ≠ 0 ← not a solution

C (1, 2 )

y = 1² + 1 = 1 + 1 = 2 → (1, 2 ) is a solution

D (2, 4 )

y = 2² + 1 = 4 + 1 = 5 ≠ 4 ← not a solution

E (3, 10 )

y = 3² + 1 = 9 + 1 = 10 → (3, 10 ) is a solution

Answer:

a,6. b, 6 c, -4.5. d, -9

Step-by-step explanation:

a, -3*-2

3*2. b/c of -ve * -ve is positive the answer comes 6

b, same as a

c, -3*1.5

- 4.5

d, -3*3

- 9

Answer: The actual distance is 68 miles.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

It’s b

Answer:

-3/7

Step-by-step explanation:

1. The formula to find the slope of a line given two points is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex].

Therefore, the answer is -3/7.

Answer:

Step-by-step explanation:

2.  Should be 500

8.  Should be 290

The rest are correct

Answer:

1. 100 good job

2. 500 round to the nearest hundred either 400 or 500. 500 is closer.

3. 9,000 good job

4. 7,800 good job

5. 250 good job

6. 4,000 good job

7. 6,800 good job

8. 290 round to the nearest 10 either 290 or 300 290 is closer

9. 400 good job

10. 8,000 good job

Step-by-step explanation:

Rounding to the nearest number is up at 5 and below for 4 and less. The same concept applies to larger numbers.

Work Shown:

45.40 - 40 = 5.40

She made $5.40 in profit. Divide this over the original price to find the percentage profit

(5.40)/(40) = 0.135 = 13.5%

Answer:

Step-by-step explanation:

[tex]\dfrac{x}{2}=\dfrac{y}{3}\\\\[/tex]

Cross multiply,

3x = 2y    ------------(I)

[tex]\dfrac{y}{4}=\dfrac{z}{4}\\\\4*\dfrac{y}{4}=\dfrac{z}{4}*4\\\\y=z[/tex]

y = z --------------(II)

Plugin y =z in (I)

3x = 2z

3x/2 = z  ----------------(III)

x + 2y - z = 10

From (I) and (III)

[tex]x + 3x - \dfrac{3x}{2}=10\\\\4x - \dfrac{3x}{2}=10\\\\Multiply \ the \ entire \ equation \ by \ 2\\\\2*4x - 2*\dfrac{3x}{2}=10*2\\\\8x - 3x = 20\\\\5x = 20[/tex]

Divide both sides by 5

x = 20/5

x = 4

Plugin x = 4 in (I)

3*4=2y

12 = 2y

2y = 12

y = 12/2

y  = 6

z = y

z = 6

Answer:

-16x, and 3(x−28)

Step-by-step explanation:

-8x^2+3=-16,

Multiply 2 times −8.

which should get you −16x^2−1

Subtract 1 from 2, then you have −16x^1. For any term t, t ^1=t. so then it is -16x.

−9 ^2+3x−3

Calculate 9 to the power of 2 and get 81.

−81+3x−3

Subtract 3 from −81 to get −84.

=−84+3x

and if you need help with algebra  https://mathsolver.microsoft.com/ will help!

Answer:

Step-by-step explanation:

1.Consider the quadratic relation y = x^2 – 6x – 16.

a) Factor this equation using the Trinomial Method (find two numbers that multiply to 'c' and add to 'b'; the factored form has 2 pairs of brackets).

[y = x^2 – 6x – 16 : Two numbers when multiplied = -16, but when added = -6, would be: -8 and 2. [-8+2 = -6, and -8*2 = -16] This would lead to (x+2)(x-8) as the two factors.

b) Find the x-intercepts (zeroes) of the relation. Remember to let y = 0 then solve for each x separately.

(x+2)=0; x= -2

(x-8)=0; x = 8

2. Consider the quadratic relation y = 2x^2 + 6x – 80.

a) Factor this equation by:

1. Determining the greatest common factor (GCF).

The GCF is 2: 2*(x^2 + 3x - 40)

2. Factoring the equation using common factoring.

2*(x^2 + 3x - 40): Two numbers that when multiplied = -40, but added = 3, would be 8 and -5. So we can factor:

2*(x + 8)(x - 5)

3. Factor the expression inside the brackets using the Trinomial Method (find two numbers that multiply to 'c' and add to 'b'; the factored form has 2 pairs of brackets).

2*(x + 8)(x - 5)

b) Find the x-intercepts (zeroes) of the relation. Remember to let y = 0 then solve for each x separately.

0 = (x + 8) and 0=(x - 5); x = -8, and x=5

Answer:

c

Step-by-step explanation:

Answer:

f(m) = -9

Step-by-step explanation:

We replace m with 5 in the function.

f(m) = 1 - 4(m/2) becomes f(5) = 1 - 4(5/2)

then we solve the numbers in the parenthesis first

= 1 - 4 (5/2)

= 1 - 4 (2.5)

= 1 - 10

= -9