Line a is parallel to line b. If the
measure of Z2 is 78°, what is the
measure of Z8?
78° =21
314
615
718
b

The distance between the fire and station B is 10.7miles

The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.

The angle at A = 90- 35

= 55°

The angle at B = 90-49

= 41°

Angle at the fire = 180-(41+55)

= 180-96 = 84°

Using sine rule

sin84/13 = sin55/x

xsin84 = 13sin55

0.995x = 10.65

x = 10.65/0.995

x = 10.7 miles

Therefore the distance between the fire and station B is 10.7 miles.

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Step-by-step explanation:

Just use the Law of Indices.

Answer:

2

Step-by-step explanation:

the same as...

(2) is the answer

If the population is highly skewed, the sample size needed for the central limit theorem to apply usually has to be the same as that when the population is not highly skewed.

The central limit theorem states in probability theory that, in many instances, when independent random variables are added together, their correctly normalized sum tends toward a normal distribution, even if the original variables are not normally distributed.

If the population is highly skewed, the sample size needed for the central limit theorem to apply usually has to be the same as that when the population is not highly skewed.

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Answer:

Step-by-step explanation:

A

Answer:

Step-by-step explanation:

Answer:

1.1892

Step-by-step explanation:

view the attached picture to see how i got that answer :)

Answer:

From the looks of it, 70 is the correct answer, or answer B.

Step-by-step explanation:

Answer:

Your right it is 70 angles it’s b

Step-by-step explanation:

Answer:

Development is necessary because without development a country cannot be developed and people cannot get enough raw materials.More people will suffer from poverty, health facilities and drinking water.

Answer:

$25.50

Step-by-step explanation:

8 tickets cost $204.

$204 ÷ 8 = $25.50

This is the remainder when the polynomial p(x) is divided by (x-1)(x-3).

remainder = 5/2(x-1) - 3/2(x-3)

To find the remainder when the polynomial p(x) is divided by (x-1)(x-3),

we can use the Chinese Remainder Theorem.
Step 1: Given remainders and divisors
When p(x) is divided by (x-1), remainder is 3.
When p(x) is divided by (x-3), remainder is 5.
Step 2: Find the constants
Let's call the constants A and B.

We need to find A and B such that:
A(x-1) + B(x-3) = remainder
Step 3: Use given remainders to find the constants
For (x-1), the remainder is 3.

So when x=1,
A(1-1) + B(1-3) = 3
0 + B(-2) = 3
B = -3/2
For (x-3), the remainder is 5.

So when x=3,
A(3-1) + B(3-3) = 5
A(2) + 0 = 5
A = 5/2
Step 4: Write the remainder using the constants
remainder = 5/2(x-1) - 3/2(x-3)
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Answer:

Well having the given information

2 pm is when the first trian leaves or (a)

5 pm is when the second train leaves (b) since 3 hours later

Now train a travels 50mph

Whilst train b travels 60 mph

Train b is 3 hours behind so a is already at the 150 miles mark.

Now we just find when train B catches up with A

60, 120, 180, 240, 300, 360, 420, 480, 540, 600

150, 200, 250, 300, 350, 400, 450, 500, 550, 600

Well 600  when they meet up at the same time

So in this scenario it’s starting 5pm and there are 10 hours

Now we just add 10 hours to 5pm

3am

Answer:

-20x

Step-by-step explanation:

Let the number be x.

The product of -4 and this number is -4x.

5 times this is 5(-4x), which simplfiies to -20x.

The orthogonal projection of vector v onto vector w in R^3 is (-54/14, -159/70, -159/35).

To find the orthogonal projection of v onto w, we need to calculate the scalar projection of v onto w and multiply it by the unit vector of w. The scalar projection of v onto w is given by the formula:

proj_w(v) = (v⋅w) / (w⋅w) * w

where ⋅ denotes the dot product.

Calculating the dot product of v and w:

v⋅w = (-7)(-5) + (6)(-3) + (-6)(-6) = 35 + (-18) + 36 = 53

Calculating the dot product of w with itself:

w⋅w = (-5)(-5) + (-3)(-3) + (-6)(-6) = 25 + 9 + 36 = 70

Now, substituting these values into the formula, we have:

proj_w(v) = (53/70) * (-5,-3,-6) = (-54/14, -159/70, -159/35)

Therefore, the orthogonal projection of v onto w is (-54/14, -159/70, -159/35).

In simpler terms, the orthogonal projection of v onto w can be thought of as the vector that represents the shadow of v when it is cast onto the line defined by w. It is calculated by finding the component of v that aligns with w and multiplying it by the direction of w. The resulting vector (-54/14, -159/70, -159/35) lies on the line defined by w and represents the closest point to v along that line.

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the absolute value function written as a piecewise function is:

f(x) = x + 8      if     x ≥ -8

f(x) = -(x + 8)     if    x + < -8

The absolute value function:

y = |x|

works as follows:

That is a piecewise function.

Now, in our case:

f(x) = |x + 8| can be rewritten to:

f(x) = x + 8      if     (x + 8) ≥ 0

f(x) = -(x + 8)     if    (x + 8) < 0.

Now we should simplify the inequalities, so we get:

f(x) = x + 8      if     x ≥ -8

f(x) = -(x + 8)     if    x + < -8

Here we have the absolute value function written as a piecewise function.

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Answer:

18,646

Step-by-step explanation:

>you can graph the equation on a calculator and see that the minimum is at the point (250, 18646) , so the minimum unit cost is 18,646

>you can use the first derivative to find the minimum

c'(x) = (0.2x²-100x+31,146)' = .4x -100

.4x-100= 0 , so x= 250

c(x=250) = 0.2(250)² -100*250 +31,146 =18,646

Answer: 260 gallons

Step-by-step explanation:

We can use a proportion to solve this problem. We know that a family used 15 gallons of milk every 3 weeks. Since the problem asks for how much they will need for a year, we can gather that a year is 52 weeks. We can come up with the following proportion.

\(\frac{15}{3} =\frac{x}{52}\)          [cross multiply]

\(3x=780\)       [divide both sides by 3]

\(x=260\)

Therefore, they will need to purchare 260 gallons.

3(2a - 2) = 2(3a - 3)

6a - 6 = 6a - 6

6a - 6a = -6 + 6

0 = 0

Answer: all reel numbers are solutions

\(\\ \sf\longmapsto 3(2a-2)=2(3a-3)\)

\(\\ \sf\longmapsto 6a-6=6a-6\)

\(\\ \sf\longmapsto 6a-6-6a+6=0\)

\(\\ \sf\longmapsto 0=0\)

Hence

\(\\ \sf\longmapsto a\epsilon R\)

Answer:

(b) 5.5 × 10^-6

Step-by-step explanation:

hope if helps

1) The area of a circle circumscribed about a square is 307.7 cm².

2.a.) The angle ACB is 39 degrees.°.

2b.) The value of x is 5.42.

We shall find the radius to determine the area of a circle.

First,  find the side length of the square:

Since the perimeter of the square = 56 cm, then, each side of the square is 56 cm / 4 = 14 cm.

Next, find the diagonal of the square, using the Pythagorean theorem:

Diagonal = the diameter of the circumscribed circle.

Diagonal² = side length² + side length²

= 14 cm² + 14 cm²

= 196 cm² + 196 cm²

= 392 cm²

Take the square root of both sides:

Diagonal = √392 cm ≈ 19.80 cm (rounded to two decimal places)

Then, the radius of the circle which is half the diagonal:

Radius = Diagonal / 2 ≈ 19.80 cm / 2 ≈ 9.90 cm (rounded to two decimal places)

Finally, compute the area of the circle using the formula:

Area = π * Radius²

Area = 3.14 * (9.90 cm)²

Area ≈ 307.7 cm² (rounded to two decimal places)

Therefore, the area of the circle that is circumscribed about a square with a perimeter of 56 cm is 307.7 cm².

2. a) We use the property of angles in a circle to solve for angle ACB: an angle inscribed in a circle is half the measure of its intercepted arc.

Given that arc AB has a measure of 78°, we can find angle ACB as follows:

Angle ACB = 1/2 * arc AB

= 1/2 * 78°

= 39°

Therefore, the angle ACB is 39 degrees.

2b.) To solve for the value of x, we use the information that the angle ADB =  (3x - 12)⁴.

Given that angle ADB is (3x - 12)⁴, we can equate it to the measure of the intercepted arc AB, which is 78°:

(3x - 12)⁴ = 78

Solve the equation for x, by taking the fourth root of both sides:

∛∛((3x - 12)⁴) = ∛∛78

Simplify,

3x - 12 = ∛(78)

Isolate x by adding 12 to both sides:

3x - 12 + 12 = ∛(78) + 12

3x = ∛(78) + 12

Finally, divide both sides by 3:

x = (∛(78) + 12) / 3

x = (4.27 +12) / 3

x = 5.42

So, x is 5.42

Therefore,

1) The area of the circle is 154 cm².

2a.) Angle ACB is equal to 102°.

2b.) The value of x is 5.42

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The answer is x = 3 y=3. This can be solved by reorganising the equation 2x + 3y = 15, x-y=0.

This property is true for all real numbers, including integers, fractions, decimals, and any other real number. The Multiplication Zero Property states that the product of any number and zero is equal to zero.

Reorganising the equation:

2x + 3y = 15

x-y=0

To find the solution, multiply both parts of the equation by a multiplier, as in 2x+3y=15.

2(x-y)=0 x 2

Utilize the multiplicative distributional rule.

2x+3y=15

2x-2y=0 x 2

Application of the Multiplication Zero Property

2x+3y=15

2x-2y=0

Separate the two formulas: 2x+3y-(2x-2y)=15-0

2x+3y-2x+2y=15

Take the parentheses off

3+2=15

Expressions combined: 5y=5

Multiply both sides of the equation by the value of the variable: y = 15/5

Take out the joining piece. y=3

Substitute 0 for 2x-2x-2x in one of the computations.

2x-6=0 is used to determine the product.

In the calculation, 6 should be shifted to the left: 2x=6

Add the variable's value to both ends of the equation, then subtract it:

x = 6/2

Take out the intermediary: 2 = 3

The  answer is x = 3 y=3.

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Answer:

b

Step-by-step explanation:

Answer: 17

Step-by-step explanation:

Answer:

y-4=3/2(x+4)

Step-by-step explanation:

If you plug the numbers into the equation (y-y1=m(x-x1)), you get y-4=3/2(x+4).

HOPE THIS HELPS

Answer:

Step-by-step explanation:

cos A = \(\frac{\sqrt{8} }{3}\)

Answer:

I don't know what are you saying bro

Answer:

\( \boxed{\sf Area \ of \ rectangle = 10x^3} \)

Given:

Length of rectangle = 5x²

Width of rectangle = 2x

To Find:

Area of rectangle

Step-by-step explanation:

\(\sf Area \ of \ rectangle = Length \times Width\)

\( \sf = 5 {x}^{2} \times 2x\)

\( \sf = 5 \times 2 {x}^{2 + 1} \)

\( \sf = 5 \times 2 {x}^{3} \)

\( \sf = 10 {x}^{3} \)

Answer:

\(\huge\boxed{Area\ of\ Rectangle = 10x\³}\)

Step-by-step explanation:

Area of Rectangle = Length * Width

Where Length = 2x and Width = 5x²

Area of Rectangle = (2x)(5x²)

Area of Rectangle = 10x³

Let's say the side length of square A is x, which means the side length of square B is 2x.

Then, the area of square A can be written as , and the area of square B can be written as .

There's no diagram here with shaded region, so I'll just find the area of square A as a percentage of the area of square B:

= 1/4 = 25%

So, the answer is 25% (note this is the answer to the question: "express the area of square A as a percentage of the area of square B; there is no diagram showing me where the shaded area is, so I cannot answer the original question

I think the answer is A and C!

Answer:

B) Keeping A constant and decreasing B

C) Increasing A and keeping B constant

Step-by-step explanation:

I did it on Khan Academy :)

Answer:

A and D

Step-by-step explanation: