Pat and Rich drove to the beach
last weekend. It took them twice as
long to get back as it did to drive
there. If they spent 9 hours traveling
to and from the beach, how long
did it take them to drive each way?

Answer:

x = 4  rounded to the nearest whole number (actually 4.0801)

Step-by-step explanation:

The triangle formed by the sides of length 0.9x, 2.8x and 12 form a right triangle with the side of length 12 as they hypotenuse

By the Pythagorean theorem

c² = a² + b² where c = hypotenuse, a and b being the other two sides

Plugging in values we get

12² = (0.9x)² + (2.8x)²

144 = 0.81x² + 7.84x² = 8.65x²

Switching sides:

8.65x²= 144

x² = 144/8.65 = 16.6473

x = √16.6473= 4.0801

Rounded to the nearest integer, x = 4

Answer: y=5x+2

Step-by-step explanation: I answered this question already, I believe.

The solution is in the attachment!!

Angles in a triangle add to [tex]180^{\circ}[/tex].

[tex]\angle B=180^{\circ}-115.5^{\circ}-27.2^{\circ} \longrightarrow \boxed{\angle B=37.3^{\circ}}[/tex]

Using the Law of Sines:

[tex]\frac{AC}{\sin 37.3^{\circ}}=\frac{76.0}{\sin 115.5^{\circ}}\\\\\boxed{AC=\frac{76\sin 37.3^{\circ}}{\sin 115.5^{\circ}} \text{ ft}}[/tex]

[tex]\frac{BC}{\sin 27.2^{\circ}}=\frac{76.0}{\sin 115.5^{\circ}}\\\\\boxed{BC=\frac{76\sin 27.2^{\circ}}{\sin 115.5^{\circ}} \text{ ft}}[/tex]

sin(A) / a = sin(B) / b = sin(C) / c

where A, B, and C are the angles of the triangle, and a, b, and c are the lengths of the sides opposite those angles.

the maximum number of caps she can order is 162.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

Given, Laura is the fundraising manager for a local charity she is ordering caps for an upcoming charity walk.

Let "x" be the number of caps she ordered.

Since, manufacturing cost for a cap = $6

shipping charges for the lot = $25

Thus,

Total price she paid for x caps = 6*x + 25

Since she had only 1000$

So,

6x + 25 ≤ 1000

6x ≤ 975

x ≤ 975/6

x ≤ 162.5

therefore, the maximum number of caps she can order is 162.

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Hey  there!

[tex]\huge\textbf{Assuming:}[/tex]

[tex]\mathsf{f(x) = x^2 + 3x - 5}[/tex]

[tex]\mathsf{f(x) = 3^2 + 3(3) - 5}[/tex]

[tex]\mathsf{f(x) = 3 \times 3 + 9 - 5}[/tex]

[tex]\mathsf{f(x) = 9 + 9 - 5}[/tex]

[tex]\mathsf{f(x) = 18 - 5}[/tex]

[tex]\mathsf{f(x) = 13}[/tex]

[tex]\huge\text{Therefore your answer should be:}[/tex]

[tex]\mathsf{f(x) = 13}[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The value of x is 30°

Angle geometry is a branch of mathematics that deals with the study of angles and their properties in two-dimensional figures such as circles, triangles, and polygons.

(5w+20)° + 3w° = 180° (sum of angles on a straight line is 180° )

5w +20 + 3w = 180

8w + 20 = 180

8w = 180 - 20

8w = 160

w = 160/8

w = 20°

3w° + 4x°  = 180° (sum of angles on a straight line is 180° )

3w + 4x  = 180

Put w = 20 and solve for x:

3(20) + 4x  = 180

60 + 4x  = 180

4x = 180 - 60

4x = 120

x = 120/4

x = 30°

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The converse of the statement  x⇒y is y⇒ x, So correct option is A.

A converse statement is a type of logical statement in mathematics that takes a conditional statement and switches its hypothesis and conclusion. The converse of a statement is formed by interchanging the hypothesis and conclusion of the original statement. In other words, the converse of a statement takes the form "If B, then A," whereas the original statement takes the form "If A, then B."

For example, consider the statement "If it rains, then the roads are wet." The converse of this statement would be "If the roads are wet, then it rains." It's important to note that the converse of a statement may not always be true, even if the original statement is true.

In mathematical proofs, a converse statement can sometimes be used to support a proof, but it is not always reliable on its own. This is because the converse of a statement only establishes a logical relationship between two statements if both the original statement and its converse are true. If either the original statement or its converse is false, then the converse cannot be used to make a conclusion about the relationship between the two statements.

In conclusion, a converse statement is a type of logical statement that takes a conditional statement and switches its hypothesis and conclusion. It's important to note that the converse of a statement may not always be true, and its validity depends on the validity of both the original statement and its converse.

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Answer:1.28

Step-by-step explanation:

The amplification of the sinusoidal function will be 4 times.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The graph of the sinusoidal function is shown below.

The amplification of the function is given as,

A = Range / 2

A = (1 - (-7)) / 2

A = 8 / 2

A = 4

The amplification of the sinusoidal function will be 4 times.

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The expression √6 (4√3 + 2√6)​ is multiplied and simplified to get 12√2 + 12

From the problem we have the expression

√6 (4√3 + 2√6)​

The problem is solved multiplying first

=√6 (4√3 + 2√6)​

= √6 * 4√3 + √6 * 2√6

Using the distributive property, we can simplify each term:

√6 * 4√3 = 4 * √(6 * 3) = 4 * √18 = 4 * 3√2

√6 * 2√6 = 2 * √(6 * 6) = 2 * √36 = 2 * 6

Adding the two simplified terms, we get:

4 * 3√2 + 2 * 6 = 12√2 + 12

So, the expression √6 (4√3 + 2√6) simplified to 12√2 + 12.

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Answer:

Step-by-step explanation:

y=mx + b where b= y intercept(when x=0) and m= slope(rise/run)

so there is a slope of 4 and a y intercept of 9

so starting from 9, you go up 4, and to the right 1. and that just repeats till you're satisfied.

The required statements are true or false, are below in the solution part.

A square is defined as a polygon that has four sides and is a closed, two-dimensional (2D) object. A square has equal and parallel sides on all four sides.

a) True. If a quadrilateral is a square, then it has four equal sides and four right angles. By definition, a rectangle also has four right angles, so a square is also a rectangle.

b) False. A counterexample is a parallelogram, which has a pair of parallel sides but does not have a pair of opposite sides that are congruent.

c) False. A counterexample is a rectangle, which has perpendicular diagonals but is not a rhombus, which is defined as a quadrilateral with four equal sides.

d) False. A counterexample is an isosceles trapezoid, which has one right angle but not all angles are right angles.

e) Converse of a) - If a quadrilateral is a rectangle, then it is a square. This is false, as there are rectangles that are not squares.

The converse of b) - If a quadrilateral has a pair of opposite sides that are congruent, then it must have a pair of parallel sides. This is true.

The converse of c) - If a quadrilateral is a rhombus, then its diagonals are perpendicular to each other. This is true.

The converse of d) - If all angles of a quadrilateral are right angles, then it has one right angle. This is false, as a square has four right angles but only one of them can be considered "one right angle".

f) Contrapositive of a) - If a quadrilateral is not a square, then it is not a rectangle. This is true.

The contrapositive of b) - If a quadrilateral does not have a pair of parallel sides, then it does not have a pair of opposite sides that are congruent. This is true.

The contrapositive of c) - If a quadrilateral's diagonals are not perpendicular to each other, then it is not a rhombus. This is true.

The contrapositive of d) - If a quadrilateral does not have one right angle, then all of its angles must not be right angles. This is true.

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Answer: 1.+900

2. -24

3.  -5

4. +10

Step-by-step explanation:

Answer: the mean will increase but the median will be unchanged

Step-by-step explanation: (I used desmos. Plugging all values in and using functions --> statistics ----> mean/median)

before values:

median- 82

mean- 80.81

After values:

median- 82

mean- 81.76

The sample space for rolling a fair seven-sided die is the one on the first option.

S= {1, 2, 3, 4, 5, 6, 7}

For any experiments with some given outputs, the sample space is the set of the possible outputs.

For example, for a coin with two outputs (heads and tails) the sample space is just {head, tails}

Particularly, for a fair seven-sided die we have 7 possible outputs, which are all the whole numbers from 1 to 7, then the sample space for that die is:

S= {1, 2, 3, 4, 5, 6, 7}

So the correct optionis the first one.

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Answer:

The sample space for rolling a fair seven-sided die is the one on the first option.S= {1, 2, 3, 4, 5, 6, 7}

Step-by-step explanation:

that's it simple

Answer:

Step-by-step explanation:

Answer:

they each download 36 songs

Answer:

[tex]a_n = (-4)^{n - 1}; a_1 = -1.5[/tex]

Step-by-step explanation:

[tex] a_1 = a_1 [/tex]

[tex] a_2 = a_1 \times r [/tex]

[tex] a_3 = a_1 \times r^2 [/tex]

[tex] a_4 = a_1 \times r^3 [/tex]

[tex] a_5 = a_1 \times r^4 [/tex]

[tex] a_1 \times r = 6 [/tex]

[tex] a_1 \times r^4 = -384 [/tex]

[tex] r = \dfrac{6}{a_1} [/tex]

[tex] a_1 \times (\dfrac{6}{a_1})^4 = -384 [/tex]

[tex] r = \dfrac{6}{a_1} [/tex]

[tex] \dfrac{1296}{a_1}^3} = -384 [/tex]

[tex] r = \dfrac{6}{a_1} [/tex]

[tex] \dfrac{1}{a_1}^3} = -\dfrac{384}{1296} [/tex]

[tex] r = \dfrac{6}{a_1} [/tex]

[tex] a_1^3 = -\dfrac{27}{8} [/tex]

[tex] r = \dfrac{6}{a_1} [/tex]

[tex] a_1 = -1.5 [/tex]

[tex] r = \dfrac{6}{-1.5} [/tex]

[tex] a_1 = -1.5 [/tex]

[tex] r = -4 [/tex]

[tex] a_1 = -1.5 [/tex]

[tex]a_n = (-4)^{n - 1}; a_1 = -1.5[/tex]

Answer:

130 minutes

Step-by-step explanation:

We know

They watch 50% of the movie and take a break; they watch the remaining 65 minutes later.

So, to find it, we take

65 x 2 = 130 minutes

So, the movie was 130 minutes long.

Answer:  $41

Step-by-step explanation: $82 all total. 2 days. 82/2=41. He made $41 on Saturday

The function table representing the numerical values is given below.

An function in mathematics defines a relationship between one variable (the independent variable, x)  and another variable (the dependent variable, y). Example -

y = f{x} = ax + b

Given is a function as -

h = -5t² + 14t + 3

We can write the complete table as -

time {sec}                                                          height {m}

-2                                                                 - 5 x 4 + 14 x - 2 + 3 = - 45

-1                                                                  - 5 x 1 + 14 x - 1 + 3 = - 16

-0                                                                 - 5 x 0 + 14 x 0 + 3 = 3

1                                                                   - 5 x 1 + 14 x 1 + 3 = 12

2                                                                  - 5 x 4 + 14 x 2 + 3 = 11

3                                                                  - 5 x 9 + 14 x 3 + 3 = 0

4                                                                  - 5 x 16 + 14 x 4 + 3 = - 21

-5                                                                 - 5 x 25 + 14 x 5 + 3 = - 52

Therefore, the function table representing the numerical values is given above.

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The slope for the first piece of the tax function is given as follows:

0.1.

The slope for the second piece of the tax function is given as follows:

0.2.

It tells that for smaller salaries, the tax rate is of 10%, while for salaries on a second range, the tax rate is of 20%.

The slope of a linear function represents the rate of change of the output variable relative to the input variable.

For the first piece, when x increases by 5000, the output increases by 500, hence the slope m is given as follows:

m = 500/5000

m = 0.1.

For the second piece, when x increases by 5000, the output increases by 1000, hence the slope m is given as follows:

m = 1000/5000

m = 0.2.

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The maximum height attained by the ball is 311 feet and it takes approximately 1.5 seconds to get there

To find the time at which the ball reaches its maximum height, we need to find when its velocity is equal to 0. We can find the velocity at any time by taking the derivative of the height function, f(x). So, f'(x) = -32x + 48. Setting f'(x) = 0, we get:

f'(x) = -32x + 48 = 0

32x = 48

x = 1.5

So it takes 1.5 seconds for the ball to reach its maximum height.

b. To find the maximum height, we substitute t = 1.5 back into the height function, f(x):

f(1.5) = -16(1.5)^2 + 48(1.5) + 275

f(1.5) = -16(2.25) + 72 + 275

f(1.5) = -36 + 72 + 275

f(1.5) = 36 + 275

f(1.5) = 311 ft

Therefore, the maximum height the ball reaches is 311 feet.

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The equation y = 15x + 20 means that the registration fee is $20 and $15 is charged per month

An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.

The standard form of a linear equation is:

y = mx + b

Where m is the rate of change and b is the y intercept

Let y represent the total cost of an amusement park membership for x number of months

Given that:

y = 15x + 20

Therefore the rate of change is $15 per month and the initial fee is $20. This means that the registration fee is $20 and $15 is charged per month

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All the equations are direct variation equations

A relationship between two variables is said to be a direct variation if one of the variables is proportional to the other, meaning that their ratio is always constant.

Using the above as a guide, we have the following:

y = -5x:

Direct variation

Constant of variation = -5

2y = x

Direct variation

Constant of variation = 1/2

y/x = 12

Direct variation

Constant of variation = 12

x/y = 4

Direct variation

Constant of variation = 1/4

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The instantaneous rate of change of the daily receipts on day 42 is approximately -0.542 million dollars day-1.

Rate of change is a major of house quickly one quantity change in relation to another.it is parisu of the changing the changing another quantity over specified time period.

The instantaneous rate of change of the daily receipts on day 42 can be estimated by taking the difference in receipts between day 28 and day 42 and dividing it by the difference in time between them. Since day 28 and day 42 are 14 days apart, the instantaneous rate of change of the daily receipts on day 42 can be calculated as:

Rate of change = (5.587 - 14.666) / 14 = -0.542 million dollars day-1.

Therefore, the instantaneous rate of change of the daily receipts on day 42 is approximately -0.542 million dollars day-1.

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Answer:

Let x be the price per ream in dollars. Then, the manufacturer's profit per ream sold is (x - $2).

The manufacturer estimates that for each $1 increase in the price, 400 fewer reams will be sold each month. Thus, the number of reams sold can be expressed as 4000 - 400(x - $5) reams per month.

The manufacturer's total monthly profit is given by the product of the number of reams sold and the profit per ream, so it can be expressed as:

P(x) = (4000 - 400(x - $5)) * (x - $2)

So the monthly profit as a function of the price per ream is:

P(x) = 4000x - 8000 - 400x^2 + 2000x + 8000

This is a quadratic equation and its maximum value can be found using techniques from algebra or calculus.

Step-by-step explanation:

ABOVE