Two Ships leave port at the same time. Ship X is heading due north andShip y is heading due east. Thirteen hours later they are 650 milesapart. If Ship X had traveled 520 miles from the port, how many mileshad Ship y traveled?

After calculation we get

11) d. m/JML = 90 degrees, a. m/GMH = 45 degrees, b. mLH = 90 degrees, c. m/LKH = 45 degrees

12) a. AGKH is an isosceles triangle, b. Another triangle formed by two radii is an equilateral triangle.

13) a. m/GKH = 33.4 degrees, c. m/KHJ = 33.4 degrees, e. mJL66.8 degrees, b. m/KGH = 66.8 degrees, d. m/JKL = 113.2 degrees

A quadrilateral is a geometric shape with four straight sides and four angles. Examples of quadrilaterals include squares, rectangles, parallelograms, trapezoids, and kites.

According to the given information:

a. Since m/LGH and m/GHJ are both 45°, GH is a bisector of ∠JGL. Therefore, m/GMH = 90° - 45° = 45°.

b. Since GH is a bisector of ∠JGL, m/LGH = m/HGL = 45°. Also, since LH is a straight line, m/LGH + mLH + m/HGL = 180°. Thus, mLH = 90° - 45° = 45°.

c. Since GH is a bisector of ∠LJK, m/GHK = m/JHK = 45°. Also, since LK is a straight line, m/LKH + m/JHK + m/LJK = 180°. Thus, m/LKH = m/LJK = (180° - 2*45°)/2 = 45°.

d. Since GH is a bisector of ∠JGL and JML is a straight line, m/JML = m/JGH + m/HGL = 45° + 45° = 90°.

a. AGKH is a quadrilateral with two sides that are radii of the circle. Since all radii of a circle are equal, AGKH is a kite. Furthermore, since the two radii AG and KH are perpendicular to each other, AGKH is also a rectangle.

b. Another triangle formed by two radii is AKJ, where AK and AJ are radii of the circle and KJ is a chord.

a. Since GH is a diameter of the circle and GKH is a right triangle with ∠GHK = 90°, m/GKH = 180° - 90° = 90°.

b. Since GH is a diameter of the circle and KJ is a chord, m/KGH = m/KJ = 1/2 * m/KHJ = 1/2 * (180° - 113.2°) = 33.4°.

c. Since GH is a diameter of the circle and KHJ is a right triangle with ∠KHJ = 90°, m/KHJ = 180° - m/GKH = 180° - 90° = 90°.

d. Since GH is a diameter of the circle and JKL is a right triangle with ∠JKL = 90°, m/JKL = 180° - m/KJ - m/JKH = 180° - 33.4° - 45° = 101.6°.

e. Since JL is a chord of the circle and ∠JGL is an inscribed angle that intercepts it, m/JGL = 1/2 * m/JL = 1/2 * (180° - m/JKL) = 1/2 * (180° - 101.6°) = 39.2°. Also, since GH is a diameter of the circle and GJL is a right triangle with ∠GJL = 90°, m/GJL = 90° - m/GHL = 90° - 45° = 45°. Therefore, m/JLH = m/JGL - m/GLH = 39.2° - 45° = -5.8°. Note that the negative value indicates that ∠JLH is a reflex angle.

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Answer:

25

Step-by-step explanation:

20*1.25=25

Answer:

\((-\infty,2)\)

Step-by-step explanation:

Since \(-3x+6\nless 0\), then \(x\ngtr 2\), therefore, the domain of the function is \((-\infty,2)\).

Answer: 10 / 5 = 2

Step-by-step explanation:

Answer:

The answer is

Step-by-step explanation:

To find an equation of a line in point slope form when given the slope and a point we use the formula

\(y - y_1 = m(x - x_1)\)

where

m is the slope

( x1 , y1) is the point

From the question the point is (-7,1)

and slope/m=3

The equation of the line is

\(y - 1 = 3(x + 7)\)

Hope this helps you

Answer:

Step-by-step explanation:

The first thing you need to do, is find the total amount of gorillas.
to do this, you are going to use the equation:

24 + g = 7g

Both sides are equal, since the wallabies and the buffalo are equal. This makes the equation true.
you subtract g from 7g, and you should get:

24= 6g

Divide by six:

4 = g  

That is the # of gorillas.

Now, if you add 24 + 4

You get the # of buffalo.

Which is: 28

Since the buffalo and wallabies are the same, the # of wallabies is also 28.
if you want to check, multiply 4x7 to get the amount of wallabies.

The value of the quadratic equation given as x^2 = 25 is 5

Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

The quadratic equation is given as

x2 = 25

Rewrite the equation properly

So, we have

x^2 = 25

Take the square roots of both sides

x = 5

Hence, the solution of the equation is 5

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If the equation be 7p = 14 then the unknown factor p be 1.75.

Since dividing is the inverse of multiplying and factor times factor equals product, we may state: Product / Factor = Missing Factor.

An unknown is referred to as a variable. You must isolate the variable in order to determine the equation's answer. A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.

Any amount can be the unknown. It's an unknown if you don't know it. The unknown in any particular circumstance is referred to as a variable, and it is symbolized by a letter, typically x or y.

Let the equation be Product / Factor = Missing Factor.

Given: 7p = 14

substitute the values in the above equation, we get

then p = 7/4 = 1.75

Therefore, the value of  p be 1.75.

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Answer:

Step-by-step explanation:

1st you solve the triangle by L x W then round it by x 10, hope this helps!

The intervals in which the function is decreasing. \([-\pi , -\frac{\pi }{3} ], [\frac{\pi }{3}, \pi ]\). Option 3

We're given a function f(x) = 2 sin x - x, which describes a curve on a graph. We want to find the intervals where this curve is decreasing (going down) within the range of -π to π.

To find when the function is decreasing, we look at its slope. The slope tells us if the curve is going up or down. We find the slope by taking the first derivative of the function: f'(x) = 2 cos x - 1.

We now have an equation for the slope, f'(x) = 2 cos x - 1. A negative slope means the function is decreasing. So, we want to find where f'(x) is less than 0 (negative).

We set up the inequality: 2 cos x - 1 < 0. We solve it to find the x-values where the slope is negative. The solution is cos x < 1/2.

From the inequality cos x < 1/2, we find the intervals within the range of -π to π where the function is decreasing. These intervals are [-π, -π/3] and [π/3, π].

The above answer is in response to the question below as seen in the picture.

Determine the interval(s) in \([-\pi, \pi ]\) on

which f(x) =  2 sin x - x

is decreasing.

1. \([-\frac{\pi }{3}, \frac{\pi }{3} ]\)

2. \([-\frac{\pi }{6}, \frac{\pi }{6} ]\)

3. \([-\pi , -\frac{\pi }{3} ], [\frac{\pi }{3}, \pi ]\)

4. \([-\pi , -\frac{-2\pi }{3} ], [\frac{2\pi }{3}, \pi ]\)

5. \([-\pi , - \frac{5x}{6} ], [\frac{\pi }{6}, \pi ]\)

6. \([-\frac{\pi }{6}, \frac{5\pi }{6} ]\)

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Answer: 5 weeks

Explanation:

To find out when both siblings will have the same amount of money in their savings accounts, we need to solve the system of equations:

y = 10x + 25

y = 5x + 50

We can set the two equations equal to each other and solve for x:

10x + 25 = 5x + 50

5x = 25

x = 5

Therefore, after 5 weeks, both siblings will have the same amount of money in their savings accounts. So the answer is 5 weeks.

Answer:

z > -4/5

Step-by-step explanation:

-9 - (2z - 7) > -2z - 6 - 5z

Get rid of the parenthesis

-9 - 2z + 7 > -2z - 6 - 5z

Combine like terms:

       -2 - 2z > -7z - 6

       +2       >       +2

Add 2 to both sides.

 -2z > -7z - 4

 +7z > +7z

Add 7 to both sides.

5z > -4

Divide both sides by 5 to get z.

z > -4/5

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

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The y-intercept of the line representing Beatrice's monthly music is 20

From the question, we have the following parameters that can be used in our computation:

y = -.95x + 20

To calculate the y-intercept of the line, we set x = 0

So, we have

y = -.95 * 0 + 20

Evaluate

y = 20

Hence, the y-intercept of the line representing Beatrice's monthly music is 20

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Question

What is the y-intercept of the line representing Beatrice's monthly music subscription bill as a function of the number of songs she downloaded?

The equation is y = -.95x + 20

Answer:

60

Step-by-step explanation:

With compound interest of 6% paid semiannually, a deposit of $900 would result in $1,191.02 after 5 years, while simple interest would earn $270, resulting in a total of $1,170.

To calculate the future value of an investment with compound interest, we can use the following formula:

FV =\(PV * (1 + r/n)^{(n*t)}\)

where FV, PV, r, n and t is the future value, present value, annual interest rate, number of compounding periods per year and number of years respectively.

In this case, the present value (PV) is $900, the annual interest rate (r) is 6%, and the interest is compounded semiannually, so there are 2 compounding periods per year (n=2). The period (t) of investment  is 5 years.

Using these values, we can calculate the future value (FV) as follows:

FV = \(\$900 * (1 + 0.06/2)^{(2*5)\)

= \(\$900 * (1.03)^{10\)

= $1,191.02

Therefore, the future value of the investment after 5 years with compound interest would be $1,191.02.

If the interest were simple interest instead of compound interest, the calculation would be simpler. Simple interest is calculated as follows:

I = P x r x t

where I is the interest, P is the principal or present value, r is the interest rate, and t is the time period.

In this case, the interest rate is still 6% and the investment period is still 5 years, but the interest is calculated only on the principal amount of $900. Therefore, the interest earned would be:

I = $900 x 0.06 x 5

= $270

Therefore, the total amount after 5 years with simple interest would be the sum of the principal and the interest earned, which is:

Total = $900 + $270

= $1,170

Therefore, if the interest were simple interest instead of compound interest, the total amount after 5 years would be $1,170, and the interest earned would be $270.

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Answer:

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Teaching and learning fractions can be relatively easy or challenging depending on various factors such as the grade level of the learner, the teaching methods used, the learning environment, and the learner's prior knowledge. However, with effective teaching strategies and consistent practice, fractions can be easily taught and learned.

Here are some factors that make fractions easy or challenging to teach and learn:

1. Conceptual Understanding: Fractions are easier to learn when students have a solid conceptual understanding of the concept. They need to understand that fractions represent a part of a whole or a quantity and that fractions can be expressed as decimals or percentages. Teachers can use visual aids such as fraction circles, number lines, and charts to help students grasp the concept.

2. Age and Grade Level: Teaching and learning fractions is easier at lower grade levels when students are introduced to fractions in a concrete way, such as dividing objects into equal parts. As students progress to higher grade levels, fractions become more abstract and complex, making them more challenging to learn.

3. Instructional Methods: Effective teaching methods that make use of real-world examples, hands-on activities, and interactive learning strategies help to make fractions more accessible and understandable. Teachers can also use online resources and educational apps to support student learning.

4. Learning Environment: A positive and supportive learning environment can make a significant difference in how easily students learn fractions. Teachers can create an environment that encourages participation and risk-taking, provides opportunities for students to work collaboratively, and celebrates student success.

In summary, teaching and learning fractions can be easy or challenging depending on various factors, including conceptual understanding, age and grade level, instructional methods, and learning environment. However, with effective teaching strategies and consistent practice, fractions can be easily taught and learned.

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Therefore,  one of the rectangle braces measures 137.3 cm to the closest tenth of a centimetre.

A rectangle is a rectangle with four perpendicularly in the Euclidean plane. It is also known as an apparent equal-sided rectangle or an equiangular parallelogram. Another option for the trapezoid is a straight angle. A square has four edges that are the same length. Quadrilaterals that are rectangular have four identical sides and 4 90° edges. As a result, it is sometimes referred to as a "rectangular trapezoid".

Here,

the vertical brace serves as the hypotenuse of a right triangle, which has the bookcase's sides serving as its legs. The diagonal brace's length can be determined as follows:

length of diagonal brace

=> √(length² + height²)

When we enter the numbers from the problem, we obtain:

length of diagonal brace

= >√(115² + 76²) ≈ 137.3 cm

Using the closest tenth of a centimetre as a guide, we obtain:

diagonal brace length: 137.3 centimetres

As a result, one of the braces measures 137.3 cm to the closest tenth of a centimetre.

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The probability that Aakesh will select a blue marble from each bag is 4/45.

To find the probability that Aakesh will select a blue marble from each bag, we need to calculate the probability of selecting a blue marble from each bag and then multiply those probabilities together.

Let's start with the first bag, which contains 5 marbles: 2 red marbles, 2 blue marbles, and 1 green marble. The probability of selecting a blue marble from the first bag is:

P(Blue from first bag) = Number of blue marbles / Total number of marbles in the first bag

P(Blue from first bag) = 2 / 5

Now, let's move on to the second bag, which contains 9 marbles: 3 red marbles, 2 blue marbles, and 4 green marbles. The probability of selecting a blue marble from the second bag is:

P(Blue from second bag) = Number of blue marbles / Total number of marbles in the second bag

P(Blue from second bag) = 2 / 9

To find the probability of both events happening (selecting a blue marble from each bag), we multiply the individual probabilities together:

P(Blue from both bags) = P(Blue from first bag) * P(Blue from second bag)

P(Blue from both bags) = (2 / 5) * (2 / 9)

P(Blue from both bags) = 4 / 45.

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The solution for the given expression is 16.

There are different power rules, see some them:

1. Multiplication with the same base: you should repeat the base and  add the exponents.

2. Division with the same base: you should repeat the base and  subctract the exponents.

3.Power. For this rule, you should repeat the base and multiply the exponents.

4. Zero Exponent. When you have an exponent equals to zero, the result must be 1.

First, you apply the Power Rules - Power for  \((\frac{2^2x^2y}{xy^3} )^2}\). For this rule, you should repeat the base and multiply the exponents. Thus, the result will be:\(\frac{16x^4y^2}{x^2y^6}\).

After that, you should apply the  Power Rules - Division . For this rule, you should repeat the base and  subctract the exponents. Thus, the result will be:\(\frac{16x^2}{y^4}\).

Now, you should replace the variable x by 4 and the variable y by 2. Thus, the result will be:\(\frac{16*4^2}{2^4}=\frac{16*16}{16} =16*1=16\)

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Let the pathway be x meters wide

The pathway is 3.5 metres wide.

Answer:

Step-by-step explanation:

side of square=√(2²+2²)=√8

perimeter of square=4√8=4×2√2=8√2≈11.31 units

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.

Match the change in the position of the minute hand with the angle made by the change.

π/3 → The minute hand moves from 4 to 6.

2π/3 → The minute hand moves from 3 to 7.

5π/6 → The minute hand moves from 5 to 10.

7π/6 → The minute hand moves from 2 to 9.

The required change in angle is given by 7π/6,  4π/6, π/2, 5π/6.

Match the change in the position of the minute hand with the angle made by the change.

Minute hand is tip in the clocks that shows the minutes of time.

Here,
60 min = 360 x π /180
1 min = π /30
A) The minute hand moves from 2 to 9 = 7 x5 x π /30 = 7π/6.
B) The minute hand moves from 3 to 7 = 4 x 5 x π /30 = 4π/6.
C) The minute hand moves from 1 to 4. = 3 x 5 x π /30 =  π/2.
D) The minute hand moves from 5 to 10 = 5 x 5 x π /30 = 5π/6.

Thus, the required change in angle is given by 7π/6,  4π/6, π/2, 5π/6.

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The polynomial equation is:

We want to find the value of a knowing that the points (-2,0), (1,0), (3, 0) and (0, -18) satisfy the equation.

The three first points are the roots of the polynomial, so we can easily say:

Now we can use this values and the last point to find the value of a: