(4 pts) Henry walks out of his hall and proceeds to walk 200 feet due north. He then turns left (west) and walks 190 more feet. Finally, he turns 45∘ left and walks 260 feet. How many feet is Henry from his starting point

Answers

Answer 1

Answer:

Answer:

Henry is approximately 276 feet from his starting point.

Step-by-step explanation:

To find how many feet Henry is from his starting point, you can use the Pythagorean theorem because he walked in both the north and west directions, creating a right triangle. Here's the calculation:

1. The distance he walked north is 200 feet.

2. The distance he walked west is 190 feet.

3. The 45-degree angle forms a right triangle.

Now, use the Pythagorean theorem:

a² + b² = c²

Where:

a = 200 feet (north)

b = 190 feet (west)

a² + b² = c²

(200)² + (190)² = c²

40000 + 36100 = c²

76100 = c²

Now, find the square root of 76100:

c = √76100 ≈ 276 feet

So, Henry is approximately 276 feet from his starting point.

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Admission to a baseball game is $4.50 for general admission and $6.00 for reserved seats. The receipts were $4210.50 for 845 paid admissions. how many of each ticket were sold?

Answers

Let's solve this problem using a system of equations. Let's assume the number of general admission tickets sold is represented by 'x' and the number of reserved seats sold is represented by 'y'.

We know that the total number of paid admissions is 845, so we can write the equation:

x + y = 845 (Equation 1)

We also know that the total receipts from ticket sales is $4210.50. Since the price for general admission is $4.50 and the price for reserved seats is $6.00, we can write the equation:

4.50x + 6.00y = 4210.50 (Equation 2)

Now, we can solve this system of equations to find the values of 'x' and 'y'.

From Equation 1, we can rewrite it as:

x = 845 - y

Substituting this value of 'x' into Equation 2, we get:

4.50(845 - y) + 6.00y = 4210.50

Expanding and simplifying:

3802.50 - 4.50y + 6.00y = 4210.50

Combine like terms:

1.50y = 408.00

Divide both sides by 1.50:

y = 272

Substituting this value of 'y' back into Equation 1, we can solve for 'x':

x + 272 = 845

x = 573

Therefore, 573 general admission tickets and 272 reserved seats were sold.

find the lateral area and surface area of a right cone with radius 6 in. and height 8 in. give your answers in terms of pie

Answers

$r=6in\n\nH=8in\n\nA=\pi rl\n\nPythagoras\ theorem:\n\nr^2+H^2=l^2\n\nl^2=6^2+8^2\n\nl^2=36+64\n\nl^2=100\n\nl=√(100)\n\nl=10\ (in)$

$A=\pi\cdot6\cdot10=60\pi\ (in^2)$

Solve the equation. If necessary, round your answer to the nearest tenth.x2 = 196

A.

14

B.
–14, 14

C.

98

D.
–98, 98

Answers

x^2 =196
x^2 -196=0
(x-14)*(x+14)=0
so (x-14)=0 && (x+14)=0
x=14 , -14
the answer is B

Answer:

14, -14

Step-by-step explanation:

x^2 = 196

x = $√(196)$

x = $√(4 * 49)$

x = $√(4)$ * $√(49)$

x = 2 * 7

x = 14

Hope this helps >.<

How to write 25/4% as a decimal

Answers

First let's reduce 25/4

25/4 = 6 1/4

Now we can convert 1/4 to hundredths

6 1/4 = 6 25/100

Now just rewrite 25/100 according to place value (twenty-five hundredths is .25)

6 25/100 = 6.25

Now don't forget we are still in percentage (25/4% = 6.25%)

convert to decimal by dividing by 100 ( move decimal 2 places to the left).

6.25% = .0625

To write 25/4 as a decimal you have to divide numerator by the denominator of the fraction.
We divide now 25 by 4 what we write down as 25/4 and we get 6.25
And finally we have:
25/4 as a decimal equals 6.25

which are the roots of the quadratic function f(b) = b2 – 75? check all that apply. b = 5 square root of 3 b = -5 square root of 3 b = 3 square root of 5 b = -3 square root of 5 b = 25 square root of 3 b = -25 square root of 3

Answers

The answers are b = 5 square root of 3; b = -5 square root of 3. f(b) = b^2 – 75. If f(b) = 0, then b^2 – 75 ) 0. b^2 = 75. b = √75. b = √(25 * 3). b = √25 * √3. b = √(5^2) * √3. Since √x is either -x or x, then √25 = √(5^2) is either -5 or 5. Therefore. b = -5√3 or b = 5√3.

Answer:

$b=5√(3)$ and $b=-5√(3)$ are the roots of given quadratic equation.

Step-by-step explanation:

Given quadratic equation is $f(b)=b^2-75$

We have to check all the given options.

If the value of f(b) gives 0 when put the value of b in above equation then only that b value is the root of quadratic equation.

$b=5√(3): (5√(3))^(2)-75=75-75=0$

$b=-5√(3): (-5√(3))^(2)-75=75-75=0$

$b=3√(5): (3√(5))^(2)-75=45-75=30\neq 0$

$b=-3√(5): (-3√(5))^(2)-75=45-75=30\neq 0$

$b=25√(3): (25√(3))^(2)-75=1875-75=1800\neq 0$

$b=-25√(3): (-25√(3))^(2)-75=1875-75=1800\neq 0$

hence, only first two values $b=5√(3),-5√(3)$ gives the value of f(b)=0 .

⇒ $b=5√(3)$ and $b=-5√(3)$ are the roots of given quadratic equation.

What is the product of 32/3 and 142/5

Answers

remember that
$(x)/(y)$ times $(z)/(t)$ = $(x times z)/(y times t)$
so we have
$(32)/(3)$ times $(142)/(5)$
that equals
$(32 times 142)/(3 times 5)$ = $(4544)/(15)$ =302 and 14/15

$(32)/(3) * (142)/(5) =(32*142)/(3*5)=(4544)/(15)=\boxed{\bf{302(14)/(15)=302.933333}}$

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