On a map, the distance from Langhorne to Tannersville measures 2 centimeters. What is the actual distance if the scale of the map shows that 1 centimeter is equal to 30 kilometers?

Step-by-step explanation:

From Pythagorean theorem, one of the sides can be determined as x^2 + y^2 =8^2

or y = (8^2 - x^2)^(1/2)

we can write the perimeter P as

P = 2x + 2y ---> 20 = 2x + 2(8^2 - x^2)^(1/2)

Dividing by 2, we get

10 = x + (8^2 - x^2)^(1/2)

Move the x to the other side,

10 - x = (8^2 - x^2)^(1/2)

Take the square of both sides to get rid of the radical sign:

(10 - x)^2 = 8^2 - x^2

Move everything to the left and expand the quantity inside the parenthesis:

x^2 + (100 - 20x + x^2) - 64 = 0

2x^2 - 20x + 64 = 0

or

x^2 - 10x + 32 = 0

Now we can see that a = -10 and b = 32

Answer:

a = -10, b = 18

Step-by-step explanation:

The Pythagorean Theorem is, indeed, involved.  Use it to find an expression (you won't get a number!) for the height of the rectangle.

Using the right triangle, one leg has length  x  and hypotenuse length 8.  for a moment, label the height  h.  Then

[tex]x^2+h^2=8^3\\\\h^2=64-x^2\\\\h=\sqrt{64-x^2}[/tex]

This expression tells the height of the rectangle, so it is the length of the two vertical sides.  The top and bottom sides each have length x.

Perimeter = 20 says that the total length of all the sides is 20.  Set that up and do a heap of algebra!

[tex]x+x+\sqrt{64-x^2}+\sqrt{64-x^2}=20\\\\2x+2\sqrt{64-x^2}=20[/tex]

Divide by 2 (to simplify a bit).

[tex]x +\sqrt{64-x^2}=10[/tex]

Subtract x to get the square root by itself (you'll see why in the next step).

[tex]\sqrt{64-x^2}=10-x[/tex]

Square both sides of the equation.

[tex](\sqrt{64-x^2})^2=(10-x)^2\\\\\\64-x^2=100-20x+x^2\\\\64=100-20x+2x^2\\\\0=36-20x+2x^2[/tex]

Divide by 2 again (because you can)

[tex]0=18-10x+x^2[/tex]

Rearrange terms to match the order in the question.

[tex]x^2-10x+18=0[/tex]

The coefficient of  x  is  a = -10.  The constant is  b = 18.

The correct option is (a) 48.

In algebra, an equation is a statement of equality between two expressions. These expressions can be numbers, variables, or a combination of both.

In the equation:

b/4 = 12, the variable b is on one side of the equation and the value 12 is on the other side.

To find the value of b that makes the equation true, we need to isolate the variable b on one side of the equation.

In this case, we can do this by multiplying both sides of the equation by 4.

This cancels out the denominator of the fraction on the left side, and we get,

b = 12*4= 48.

This means that when b is equal to 48, the equation b/4 = 12 is true.

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The surface area of a regular square pyramid is 332.64 square cm

We know that the surface area of pyramid is nothing but the sum of the areas of its lateral faces and its base.

surface area of pyramid

= areas of lateral faces of pyramid + area of base of pyramid

We know that the formula for the lateral surface area of regular pyramid is:

A = ½ × P × l

where P is the perimeter of the base and l is slant height

Here, a base of regular square pyramid with has sides of 13. 2 cm

a = 13.2 cm and slant height of 6 cm i.e., l = 6 cm

Using the formula of area of square, the base area of pyramid would be,

B = (13.2)²

B = 174.24 sq.cm.

the perimeter of base is:

P = 4 × 13.2

P = 52.8 cm

So, using the above formula of lateral surface area of pyramid the lateral surface area would be

A1 = 1/2 ×  52.8 × 6

A1 = 158.4 sq. cm.

So, the surface area of the pyramid is:

A = A1 + B

A =  158.4 + 174.24

A = 332.64 square cm

Therefore, the surface area of the pyramid = 332.64 square cm

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Answer: 3

Step-by-step explanation:

Given

The dimension of the small block is

[tex]\dfrac{1}{3}\times 1\times 1[/tex]

The Volume of the cube having unit length is

[tex]V=1\times 1\times 1\\V=1\ unit^3[/tex]

The number of blocks that can be in the unit cube is the division of the volume of the unit cube and block.

[tex]\Rightarrow \dfrac{1\times 1\times 1}{\dfrac{1}{3}\times 1\times 1}\\\\\Rightarrow \dfrac{3}{1}=3[/tex]

Answer:3

Step-by-step explanation:

Answer:

12.56 yards

Area of Triangle: [tex]\pi r^2[/tex]

So, [tex]\pi[/tex][tex]2^2[/tex]

Finally, 3.14*4 = 12.56

Step-by-step explanation:

the answer is x>3

this is the answer becuase x-3 cannot be 0 because tou cant divide by zero and it cant be negative because it is in the square root notation which cant be negative without the use of inaginary numbers

The equation that relates x and y for the given data is y = (3/4)x.

The relationship between the number of shutters (x) and the number of hours (y) is an inverse variation because as the number of shutters increases, the number of hours required to paint them decreases and vice versa.

An inverse variation is a relationship between two variables in which their product is always equal to a constant value. Mathematically, it can be represented by the equation: y = k/x where k is a constant and x and y are the variables in question.

Hence, the equation that relates x and y can be found using the information given:

y = (9 hours) / (12 shutters) * x shutters

y = (3/4)x is the required equation.

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Answer:

0.6420758

Step-by-step explanation:

x = 275 ; n = 400

Phat = x / n = 275 / 400 = 0.6875

Z at 95% = 1.96

Confidence interval = phat ± margin of error

Margin of Error :

Z * √phat(1 - phat) / n

1.96 * √0.6875(0.3125) / 400

1.96 * 0.0231756

= 0.0454242

Lower boundary :

Phat - margin of error

0.6875 - 0.0454242

= 0.6420758

Answer:

the city at a lower altitude would have a colder climate

The median of the distinct positive values of all of the fractions less then or equal to 1 with positive integer denominators less than or equal to 5 is 11/20.

In the statistics, the median is the value in the middle of a data set. It means that 50% of data points have a value smaller or equal to the median and 50% of data points have a value higher or equal to the median. The middle number is found by ordering all data points and picking out the one in the middle or if there are two middle numbers, taking the mean of those two numbers. We have to arrange data values from lowest to highest value. The median is the data value in the middle of the set. If there are 2 data values in the middle the median is the mean of those 2 values.

The set of numbers are,

1 /5, 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 1

we have to take the average of middle two .

The middle of the set are 1/2 and 3/5. and the average of these two is 11/20.

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Answer: 1 x 10^3

Step-by-step explanation:

Answer:

yv1dzybazu ai zai is zie

Step-by-step explanation:

side zue auebaiw ai was wiz

Answer:

it looks like a reflection or translation but my gut is saying translation

Answer:

i can see

Step-by-step explanation:

UKDIAMOND is a great place for the people of sentence to get it 4out in a sense that you are a very

Answer:

b = 99°

Step-by-step explanation:

XY is a line segment and so it is a straight line which means that it is a straight angle - 180°

a = 28°

c = 53°

b = ?

=> a + b + c = 180°

=> 28° + b + 53° = 180°

=> b = 180° - (53 + 28)°

=> b = 180° - 81°

=> b = 99°

Therefore b = 99°

Hope it helps :)

Answer:

B.

Step-by-step explanation:

Answer:

x = 90

Step-by-step explanation:

The diagram shows that angles 1 and 4 correspond with each other. Given that the two lines should be parallel, corresponding angles have the same answer. When corresponding angles cross at the same relative location (known as the junction), they will have the same angle measure.

So, set the 1st and 4th angles equal to each other.

3x-160 = x+20

2x = 180

x=90

Answer:x=90

Step-by-step explanation:Angles 1 and 4 must be equal to each other, as they are corresponding angles, so you set 3x-160 equal to x+20 and after solving, you get x is equal to 90.

Answer:

Step-by-step explanation:

Use formula for continuous interest:

If A = 3P, and r = 0.085 then the equation is:

The formula for compounded continuously is A = Pe^rt where A if the final amount, P is the initial value, r is the rate and t is the length of time.

E is the constant for continuous interest.

Using the information from the problem $20 tripled would be 20x3 = $60

Now you have 60 = 20e^0.085(t)

We need to solve for t:

Divide both sides by 20:

e^0.085(t) =3

Apply the exponent rule:

0.085(t) = ln(3)

Solve for t:

T = ln(3)/0.085

T = 12.92 years. (Round off as needed)

Answer:

2x^2 + 5x - 8

Step-by-step explanation:

   6x^2 + 3x - 5

- (4x^2 - 2x + 3)

--------------------------

2x^2 + 5x - 8

Answer: I think it's 6816606.576

Step-by-step explanation: Hope this helps?

Answer: 750

Step-by-step explanation:

3000/4= 750

750

The value of tan 3° is 0.0524.

tangent is the trigonometric ratio.

we can find out the value of tangent by taking perpendicular of the triangle divided by base of the triangle.

tan Q = perpendicular of the triangle  /base of the triangle.

sine theta divided by cos theta gives the value of tan theta.

tan Q = sin Q/ cos Q.

some formula of the tan Q are as follows,

1- tan Q = sin Q/cos Q

2- tan Q= 1 /cot Q

3-tan^2 Q =sec^2 Q -1

4- tan(90 - Q)=cot Q

5- tan (Q+π) = tan Q

6- tan (π-Q) = -tan Q

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Answer:

12

Step-by-step explanation:

Answer:12

feet

Step-by-step explanation:

Answer:

The two answers would be 0 and ln (7)

Step-by-step explanation:

Hope it helps:)

Answer:

[tex] = \sqrt{ {40}^{2} + {9}^{2} } \\ = \sqrt{1681} \\ = 41 \: mi[/tex]

Step-by-step explanation:

i. AD = BC= 6cm (each two opposite sides are equal in length in parallelogram)

ii.DC=AB=9cm (each two opposite sides are equal in length in parallelogram)

iii.DCB=60 ,, bec DC and AB are parallel so their interior angles are supplementary their sum equals 180°

so DCB = 180-120=60°

iv.ADC=ABC = 120° because each two opposite angles are equal in measure in parallelogram

v. DAB=DCB =60° because each two opposite angles are equal in measure in parallelogram

vi. OC=AO =7cm because the diagonals of parallelogram bisect each other

vii. OB=DO=5cm because the diagonals of parallelogram bisect each other

viii . DAB=60° ,, CDA= 120 °

DAB+CDA =180°

or you could simply say that because DC and AB are parallel their interior angles are supplementary their sum is 180°

Answer:

o

Step-by-step explanation: