A heavy box is pulled across a wooden floor with a rope. The rope forms an angle of 60.0° with the floor. A tension of 80.0 N is maintained on the rope. What are the horizontal and vertical components of the force?

If the sum of an integer and 6 times the next consecutive integer is 61, the the value of lesser integer is 7

Consider the first odd integer as x

Then the next consecutive odd integer = x+2

The 6 times the second integer=  6(x+2)

= 6x+12

Sum of an integer and 6 times the next consecutive odd integer is 61

Then the equation will be

x + 6x+12 = 61

Add the like terms in the equation

(1+6)x + 12 = 61

7x +12 = 61

Move 12 to the right hand side of the equation

7x = 61-12

7x = 49

x = 49/7

x = 7

The second number is

x+2 = 7+2

= 9

Hence, if the sum of an integer and 6 times the next consecutive integer is 61, the the value of lesser integer is 7

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Based on the temperature at 6:00 am and the temperature at 6:00pm, the change in temperature can be shown by the formula D. |–5 – 7| = |–12| = 12°F.

To find the change in temperature, you need to subtract the temperature at 6: 00 pm from the temperature at 6: 00 am.

The change in temperature is therefore:

= | temperature at 6 am - temperature at 6pm |

= | -5 - 7 |

= | - 12 °F|

The absolute value of - 12 °F is 12 °F which was therefore the change in temperature.

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Answer: You have to use a calculator

Step-by-step explanation:

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The probability that a student walks to school is 7/15

The tree diagram represents the given parameter

From the tree diagram, we have the following parameters

P(Rain) = 2/5

P(Rain and walk) = 1/6

P(No rain) = 3/5

P(No rain and walk) = 2/3

The probability of walking to school is then calculated as

P = P(Rain) x P(Rain and walk) + P(No rain) x P(No rain and walk)

Substitute the known values in the above equation

So, we have

P = 2/5 x1/6 + 3/5 x 2/3

Evaluate the products

P = 1/15 + 6/15

Evaluate the sum

P = 7/15

Hence, the probability is 7/15

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We will solve as follows:

The measure of the angles are 56.25° and 33.75°.

The value in a complementary angle is equal to 90°.

Let the first angle = x

The second angle will be: 1 - (40% × x) = 1 - 0.4x = 0.6x

Therefore, they'll be added together as follows:

x + 0.6x = 90°

1.6x = 90°

Divide

x = 90/1.6

x = 56.25

The second angle will be:

= 0.6x

Since x = 56.25, this will be used in the illustration below.

= 0.6x

= 0.6 × 56.25

x = 33.75

Therefore, the second angle is 33.75.

This illustrates the concept of complimentary angles.

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Since the algae grow exponentially with doubling time of 4 days, then the population will be quadruple in size in 8 days and will be triple in size in  6.34 days.

The easiest way is to consider the situation as a geometric sequence. If the population doubles its size in 4 days, then it will be quadruple in:

2 x 4 days = 8 days.

In general, we can use the growth formula:

P(t) = Po . 2^(t/Td)

Where:

P(t) = population at time t

Po = initial population

Td = doubling time

Parameters given:

Td = 4 days

P(t) = 3Po

Plug those parameters into the formula:

3 Po = Po . 2^(t/4)

3 = 2^(t/4)

log 3 = (t/4) log 2

t = 4 . log 3 / log 2 = 6.34 days.

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Step-by-step explanation:

12/4 = x/8

1st: cross multiply

96 = 4x

2nd: divide both sides by 4

96/4 = 4x/4

therefore x = 24

Solution

- The question would like us to solve the following

- The solution is outlined below:

Final Answer

The answer is x < 33

Multiply by the decimal form of the percentage,

60 * 0.18 = 1.08

So the discount is for $1.08 off,

60 - 1.08 = 58.92

Giving a total of $58.92 after the discount is applied

Answer:

A

Step-by-step explanation:

The range is the y values.  The y value is as low as -10 and as high as 8.

9x + 6 - 4x - 2x + 1 - 15

9x - 4 x- 2x = (9-4-4)x = 3x

6 +1 -15 = -8

____________

Answer

3x -8

______________

Please tell me if you can see the updates

ok

________________

The perimeter of triangle ABC that is congruent to triangle XYZ is: 36 cm.

Triangles that are congruent to each other have corresponding side lengths that have the same lengths that are equal to each other.

The sum of all the three sides of a triangle is equal to the perimeter of the triangle.

Since triangle ABC is congruent to triangle XYZ, their corresponding side lengths will also be congruent to each other. That is, they will have the same lengths.

Therefore:

Side AB = side XY = 12 cm [corresponding congruent sides]

Side AC = side XZ = 14 cm [corresponding congruent sides]

Side BC = side YZ = 10 cm [corresponding congruent sides]

Find the perimeter of triangle ABC by adding all three triangles together.

Perimeter of triangle ABC = side AB + side AC + side BC

Perimeter of triangle ABC = 12 + 14 + 10

Perimeter of triangle ABC = 36 cm

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Law of Cosines

Given two side lengths a and b of a triangle and the angle included by them θ, the length of the third side can be calculated as:

We have a = 14, b = 9, θ = 71°. Substituting:

The length of CD is 13.96

By application of the combination formula, there are 210 ways for distributing 10 indistinguishable candies among 4 children.

Combination is the arrangement of objects in which order is not taken into account.

The applicable formula is:

n combination r = n!/[(n - r)!r!]

where n is the number of indistinguishable items (10 candies), and r is the possible number of recipients (4 kids).

Hence;

10 combination 4 = 10!/[(10 - 4)!4!] ways

10 combination 4 = 10!/(6! × 4!) ways

10 combination 4 = (10 × 9 × 8 × 7 × 6!)/(6! × 4 × 3 × 2 × 1) ways

10 combination 4 = 10 × 3 × 7 ways

10 combination 4 = 210 ways

Therefore, there are 210 ways for the 10 indistinguishable candies to be distributed among the 4 children by with the application of combination formula.

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The values of the vectors obtained from the vector diagram are;

[tex]\overrightarrow{AB} = - a + b[/tex]

[tex]\overrightarrow{MN} = ( -2\cdot a + 0.5 \cdot b)[/tex]

[tex]\overrightarrow{MP} = ( -0.5\cdot b + a+ K \cdot ( - a + b)[/tex]

K = 2.5

A vector can be expressed as a line segment that has a direction.

The given parameters are;

The straight lines are; OAN, OMB, APB, and MPN

AN = 3•OA

The midpoint of OB = M

The vectors

[tex] \overrightarrow{OA} = a[/tex]

[tex] \overrightarrow{OB} = b[/tex]

[tex]\overrightarrow{AP} = K \cdot \overrightarrow{AB} [/tex]

From the question diagram, we have;

[tex]\overrightarrow{AB} = - a + b[/tex]

[tex]\overrightarrow{AP} = K \cdot ( - a + b)[/tex]

[tex]\overrightarrow{MN} = ( -2\cdot a + 0.5 \cdot b)[/tex]

[tex]\overrightarrow{AN} [/tex] = 2•a

[tex]\overrightarrow{NP} = \overrightarrow{AP} - \overrightarrow{AN} [/tex]

[tex]\overrightarrow{NP} = -2\cdot a + K \cdot ( - a + b)[/tex]

[tex] \overrightarrow{MB} = 0.5 \cdot b[/tex]

[tex]\overrightarrow{PB} = -a + b - K \cdot ( - a + b)[/tex]

[tex]\overrightarrow{MP} =0.5 \cdot b - -a + b - K \cdot ( - a + b) = ( -0.5\cdot b + a+ K \cdot ( - a + b)[/tex]

[tex]\overrightarrow{MP} = ( -0.5\cdot b + a+ K \cdot ( - a + b)[/tex]

Given that we can write;

[tex]x \cdot \overrightarrow{NP} = \overrightarrow{NM}[/tex]

x × (-2•a + k•(-a + b)) = -3•a + 0.5•b

-2•x•a - k•x•a + x•k•b = -3•a + 0.5•b

Which gives;

-2•x - k•x = -3...(1), and x•k = 0.5...(2)

From (2), x = 0.5÷k

From (1), -2×(0.5÷k) - k×(0.5÷k) = 3

-k - 0.5 = -3

-k = -3 + 0.5 = -2.5

k = 2.5

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The value of f¹(x) = x/5

What is function?

A function in maths is a special relationship among the inputs (i.e. the domain) and their outputs (known as the codomain) where each input has exactly one output, and the output can be traced back to its input.

We are given f(x) = 5x

and we are to find inverse of f(x).

Replace f(x) by y.

So,

y = 5x

Isolate x

x = y/5

Replace x by f'(y)

So,

f'(y) = y/5

Replace all occurrences of y by x.

So,

f'(x) = x/5

Therefore, the inverse of function f(x) = 5x is f'(x) = x/5

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The length will then be L = 18(41/19) = 738/19 cm.

As a check, the area should be A = LW = (738/19)(41/19) = 30258 cm2

sorry if this isn't much help but i had a similar problem once and i used the same steps for your question

The value of the unknown angle in the triangle is as follows;

The exterior angle theorem states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.

In other words,  an exterior angle of a triangle is equal to the sum of the two opposite interior angles.

The external angle is ∠JRS.

Therefore, m∠S can be found as follows:

∠JRS = m∠S + m∠T

Hence,

m∠S  = 3x + 4

m∠T = 8x + 4

∠JRS = 140°

Hence,

140 = 3x + 4 + 8x + 4

140 = 3x + 8x + 4 + 4

140 = 11x + 8

140 - 8 = 11x

132 = 11x

x = 132 / 11

x = 12

Therefore,

m∠S  = 3(12) + 4 = 40 degrees.

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Answer:

x = 11.2 cms.

Step-by-step explanation:

I infer that the units are in centimeters.

8-3 = 5

One side = 5 cm

Other side = 10 cm

By the Pythagorean Theorem:

x² = 5² + 10²

x² = 25 + 100

x² = 125

√x² = √125

x = 11.18 cms

To the nearest tenth:

x = 11.2 cms

Answer:

y=x+1

Step-by-step explanation:

y-y1=m(x-x1)

y-2=1(x+3)

y-2=x+3

y=x+1

Answer: [tex]-10 < x < 0, x > 12[/tex]

Step-by-step explanation:

[tex]f(x) < g(x)[/tex] when the graph of [tex]f(x)[/tex] is below the graph of [tex]g(x)[/tex].

sSlope means the inclination of the line

Intercept is the point where the line touches the Y axis.

The line that is perpendicular to the equation of a line given is y = -2x + 3

The equation of a perpendicular line can be found using the slope of the line first and then applying the points through which the line passes through.

For the given question, the equation of the line is y = 1/2x + 11 and the point is (6, -9).

To find an equation of a line;

The equation of the line can be modified into y - y₁ = m(x - x₁)

substituting the values into the equation above gives y = -2x + 3

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The average before training with new trainer is 20 mph.

Let the average speed with old trainer be x. Forming the equation as per given information- Average speed with new trainer = 5% × Average speed with old trainer + Average speed with old trainer

Keep the values in formula to find the average speed with old trainer.

21 = 5/100x + x

Multiplying the equation with 100

2100 = 5x + 100x

Performing addition

105x = 2100

Shifting 105 to Right Hand Side of the equation

x = 2100 ÷ 105

Performing division on Right Hand Side of the equation

x = 20

Thus, average speed with old trainer was 20 mph.

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A

1) Since the sum of the interior angles of any triangle is 180º, and this is an isosceles triangle

2) Then the other angle, has the same measure 50º since this is an isosceles triangle, at least two congruent sides, and two congruent angles.

We can finally write

x+88 +50 +50 = 180

x +188 =180 subtract 188 from both sides

x= 180-188

x= -8

3) So x=-8 is the answer.

The statement p is: Saturn is a planet.

The statement q is: Hong Kong is a city.

Now the first part of our composite proposition is:

This means that we have to negate the statement q, this would be: Hong Kong is not a city.

Now we make the disjunction between the statement p and the negation of q, then we have:

The second part of our composite porposition is:

This means that we have to negate the statement p, then we have: Saturn is not a planet. Then we make the conjunction between the negation of p and q, then we have:

Finally we make the disjunction between the statements discussed so far, hence the statament

means:

Saturs is a planet or Hon kong is not a city OR Saturn is not a planet and Hong Kong is not a city.

Now, to determine the truth value of the composite proposition we have to remember that a disjunction is TRUE if one of the statements that make it is true and that the conjunction is TRUE only if both stataments that make it are true.

The first statement is: Saturn is a planet or Hong kong is not a city. Since this is a disjunction and the statement Saturn is a planet is TRUE, then the proposition is true.

The second statement is: Saturn is not a planet and Hong Kong is not a city. Since this is a conjunction and the statement Saturs is not a planet is FALSE, the the second statement is FALSE.

Now since the composite statemtent is made of a TRUE and a FALSE statement and it is a disjunction we conclude that the truth value of the statement given is TRUE.

Answer:

4 * ( 2 + 3 * 2) = 32

Step-by-step explanation:

The strategy I used in this question is generally trial and error. The most important thing here to remember is to follow the order of operations. If you think a little out of the box, then you will see the answer. To solve, first multiply 3*2, then add two, which should result in 8. 4*8 is 32, which makes the equation true.

Given that the backyard is rectangular and the length is 56 feet while the area is 1400 square feet. Recall that the area A of a rectangle is the product of the length L and the width B.

A = L * B

Hence the width B may be found from

1400 = 56 * B

B = 1400/56

B = 25 feet

b. If the fencing cost $10 per foot then because a rectangle has two lengths and two widths,

the total cost to fence the backyard will be

= $10 * 2(56 + 25)

= $1,620