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The angle does a 3.8 meter ladder make with the ground if it reaches 2.1 meter up the wall is 33.54 degrees and the distance between the foot of the ladder and the wall is 3.16 meters

The length of the ladder = 3.8 meter

The length of wall = 2.1 meter

Draw the figure using the measurements

We have to use the trigonometric function

The angle that a ladder make with the ground

sin θ = Opposite side / Hypotenuse

sin θ = 2.1/3.8

θ = 33.54 degrees

The distance from the foot of the ladder from the wall

cos θ = Adjacent side / Hypotenuse

cos 33.54 = Adjacent side / 3.8

Adjacent side = 3.8 × cos 33.54

= 3.16 meters

Hence, the angle does a 3.8 meter ladder make with the ground if it reaches 2.1 meter up the wall is 33.54 degrees and the distance between the foot of the ladder and the wall is 3.16 meters

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Answer:

√6(x−11)/6

Step-by-step explanation:

f^−1(x)=√6(x−11)/6

Answer:

a) Yes, the graph is proportional.  It is linear and it goes through the point (0,0)

b) No shells cost no dollars

c)  3 shells cost 1.20

Step-by-step explanation:

To graph this, you only need 2 points.  You have the points (0,0).  You can put a point at (0,0) and at the point ( (3, 1.20) and then draw a line through those 2 points.

1) According to the exponent's law, any exponent whose base is 1, that yields 1. For example

2) The same does not happen to 0.1

Since 0.1 is a fraction, we'll raise to the 4th power 1 and 10 simultaneously, as a ratio.

3) So the answer is

Answer:

Angle 1: 159

Angle 2: 21

Angle 4: 21

Step-by-step explanation:

The amount to be paid after paying interest of 7% for 10 years is 10,2000

The amount to be borrowed from the bank = 6000

Interest rate for the amount per year = 7%

The total time period of the loan = 10 years

Thus , the final amount can be calculated by using the formula

                    A = P(1 + rt)

where A is the final amount

          P is the principal amount to be borrowed

          r is the rate of interest

          t is the time period

Now, let us substitute the known values in the above equation , we get

             A = 6000 ( 1 + 0.07 x 10)

                 = 6000 (1 + 0.7)

                 = 6000 (1.7)

             A = 10,200

Therefore , the final amount to be paid is 10,200

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To solve the exercise you can rewrite the fractions in decimal form and then we order.

To write them in decimal form divide the numerator by the denominator, then we have

The box plot that matches the data is a box and whisker plot is shown above a number line that extends from 0 to 20 with 1-unit markings. The box extends from 4 to 8, with the median at 5. There is also a point marked at 7. The whisker on the left extends from 2 to 4. The whisker on the right extends from 8 to 12.

A box and whisker plot is a graph that is made up of two lines and a box. The two lines are known as whiskers. The end of the first whisker is the minimum value and the end of the second whisker is the maximum value.

On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.

The data : 2, 3, 4, 4, 5, 5, 7, 8, 9, 12

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If Sarah is 148 centimeters tall. Sarah's height in inches is 58.27 inches

Information given in the question include

Sarah is 148 centimeters tall

Round to the nearest tenth inch

Sarah's height in inches is is determined using conversion from centimeters to inches

centimeters = cm

inches = in

The unit conversion factor is given as

1 centimeter = 0.393701 inches

148 cm = ?

cross multiplying gives

? * 1 = 148 * 0.393701

? = 58.2677 in

? = 58.27 in ( to the nearest tenth of inch )

Therefore Sarah's height when converted form cm to inches is 58.27 in

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Answer:58.3 inches

Before rounding:58.2677

According to the given graph, the given angles are alternate interior angles that are always equivalent.

Having said that, we can express the following equation.-

Solving for x, we have

Answer:

In the graph, the coordinate point (4,-9) is a vertex

In the graph, the coordinate point (1,0) is an x-intercept

In the graph, the coordinate point (7,0) is an x-intercept

In the graph, the coordinate point (4,0) is on the line of symmetry.

Explanation:

The x-intercepts are the points where the parabola crosses the x-axis, so the coordinates of the x-intercepts are (1, 0) and (7, 0)

The y-intercept is the point where the parabola crosses the y-axis, so the y-intercept is (0, 7)

The vertex is the minimum point of the parabola, in this case, (4, -9).

The line of symmetry depends on the first coordinate of the vertex, so the line of symmetry is x = 4. It means that any point with a first coordinate equal to 4 is on the line of symmetry.

Then, the answers are:

In the graph, the coordinate point (4,-9) is a vertex

In the graph, the coordinate point (1,0) is an x-intercept

In the graph, the coordinate point (7,0) is an x-intercept

in the graph, the coordinate point (4,0) is on the line of symmetry.

Step-by-step explanation:

Deshaun is going to rent a truck for one day. There are two companies he can choose from, and they have the following prices. Company A charges $84 and allows unlimited mileage. Company B has an initial fee of $75 and charges an additional $0.60 for every mile driven. For what mileages will Company A charge less than Company B? (Use m for the number of miles driven, and solve your inequality for m.)

inequality: 0.6m + 75 < 84

subtract 75 from both sides:

0.6m + 75 - 75 < 84 - 75

0.6m  < 9

divide both sides by 0.6:

0.6m/0.6 < 9/0.6

m < 15

SO:

For anything less than 15 miles, Company A charges less than Company B.

Answer:

II. 8

III. 2

Step-by-step explanation:

Solving an inequality

9 ≤ 3x +4

Subtract 4 from each side

9-4 ≤ 3x +4-4

5 ≤ 3x

Divide each side by 3

5/3 ≤ 3x/3

5/3 ≤ x

x must be greater than or equal to 5/3

I. - 7  this is not greater than or equal to 5/3

II. 8   this is  greater than or equal to 5/3

III. 2 this is  greater than or equal to 5/3

The outer perimeter of the no-slip surface is 78 feet if the swimming pool has a 3-ft-wide no-slip surface around it.

The outer perimeter of an area or land can be described as the whole of its outer edge or can be described as the sum total of the outside edge lengths.

We can find the outer perimeter of this swimming pool by adding 3 feet twice to all the sides of this rectangular swimming pool followed by the addition of these sides together.

As the swimming pool is 12-ft-by-15-ft, this represents that two sides of this rectangular swimming pool are 15 feet and the other two sides are 12 feet, therefore;

12 + 6 = 18

15 + 6 = 21

Now we can find the perimeter by the addition of all the sides as follows;

18 + 18 + 21 + 21 = 78 feet

Therefore, the outer perimeter of the no-slip surface is found to be equal to 78 feet.

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The equation that represent the relationship model that will reach $0 in the same number of days as the scenario gave is: y = -2x + 12

To solve this problem, we have to state the equation using the information of the problem.

Information about the problem:

Writing the equation according to the information gave, we have:

y = -2x + 12

Where:

So that (y) equals zero, the number of days (x) should be = 6

y = -2x + 12

0 = -2*6 + 12

0 = -12 + 12

0 = 0

The "y" variable is the dependent variable, because it will change according to the number of days passed (x).

The "x" variable is the independent variable, because it doesn't depend on any other value, just the number of days passed.

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

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Answer:

12

Step-by-step explanation:

In a case whereby the the shortest side of a right triangle measures 6, and the longest side measures 10 the measurement of the unknown side is 8.

We can use this expression from trigonometry to know the third side of the triangle as:

a^2 + b^2 = c^2

Then since the longest side measures 10 which is the c side of the triangle then the unknown side can be calculated as :

10^2 - 6^2

The we can simplify as

100-36=64

Then [tex]\sqrt{64}[/tex] = 8.

Therefore, the second option is correct.

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For the given points B(-1, -10) is reflected over the line y = x , the coordinates of B' is given by ( -10 , -1).

As given in the question,

Given points :

B (-1, -10)

Reflected over the line y = x

Reflected represents the transformation which shows the movement of original points to the new location. There are different types of transformation such as reflection, rotation, dilation , and translation.

Reflection represents the flipping of the points over the line y =x.

B(x, y) and B'(y, x).

For the given points B (x, y) = (-1,-10) is reflected over the line y =x , the coordinates of B'(y, x) = ( -10 , -1).

Therefore, for the given points B(-1, -10) is reflected over the line y = x , the coordinates of B' is given by ( -10 , -1).

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The prices for jeans and shirts are $6 and $6

Given that:

3 pairs of jeans and 7 shirts for $60.

And 2 pairs of jeans and 3 shirts for $30.

Let jeans be x

Let shirts be y

3x + 7y = 60.... eq 1

2x + 3y = 30...... eq 2

Let us make x the subject formula from equation 2

2x = 30-3y

x= (30-3y)/2..... eq 3

Put the value of x into equation 1

3 * (30-3y)/2 + 7y = 60

(90- 9y)/2 + 7y = 60

45 - 4.5y + 7y = 60

2.5y =15

y = 6

Then, put the value of y into eq 3

x= (30-3(6))/2

x= 15 - 9

x= 6

Hence, we can see that the values of x and y are 6 apiece.

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Answer:

yeah it's correct , very much well

DE will be equal to AB, then DE=8

A 20-ounce bottle of lotion costs $3.95 then each of the ounce of the bottle will cost 0.173 ounce.

we were told that the cost of the 20-ounce bottle of lotion is  $3.95

then we can know the value cost of just one of the bottle of notion by using the expression below

X = the cost of each of the  bottle of lotion

then X=  $3.95 / 20-ounce bottle= 0.173 ounce

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Answer:-1a+2

Step-by-step explanation:

add like terms

Hey there!

(2a - 5) - (3a + 5)

= 2a - 5 - 3a + 5

COMBINE the LIKE TERMS

= (2a - 3a) + (-5 + 3)

= 2a - 3a + (-5) + 3

= -1a - 2

Therefore, your answer should be:

-1a - 2

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The numbers from greatest to least is - 1 2/3, -1 5/6, -2.1 and -2.2.

Based on the information, we want to arrange the numbers from the greatest to the least.

In this case, it will be illustrated thus:

-2.1

-1 5/6 = -1.83

-1 2/3 = -1.67

-2.2

This will be arranged as - 1 2/3, -1 5/6, -2.1 and -2.2. In this case, it can be deduced that - 1 2/3 is the greatest and the least number is -2.2. This shows the concept of descending numbers.

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As per the angle sum property, the value of x is 125°

Angle sum property:

According to the angle sum property, the sum of interior angles of a triangle is 180°.

Given,

In the given diagram, PQR and SQT are straight line.

Now we need to find the value of x.

As per the angle sum property, we know that the sum of all the angles of the triangle is 180 degrees.

While we equate the given values within this property, we get.

x° + 55° = 180°

x° = 180° - 55°

x° = 125°

Therefore, the value of x is 125°.

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The exact value of cos(A - B) is -2√5 /25.

Therefore,

sin A = 0.3

sin B = (1/√5)

cos A = 0.7

cos B = (-1/√5)

cos(A-B) = cos a cos b + sin a sin b

⇒ cos(A-B) = 0.7(-1/√5) + 0.3((1/√5))

⇒ cos(A-B) = -0.7/√5 + 0.3/√5

⇒ cos(A-B) = -0.4/√5

On multiplying, √5 on the numerator and denominator,

⇒ cos(A-B) = -0.4 x √5 / 5

⇒ cos(A-B) = -2√5 /25

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The population mean, exists even comprehended as the average or mean of all values in a population, exist determined by summing all population values and dividing that total by the number of population values.

The population mean can be determined by dividing the total number of values in the given data/population by the sum of all values in the data/population. The whole sum of the numbers is referred to as summation. The sign μ stands for the population mean.

The population mean, also known as the average or mean of all values in a population, is determined by summing all population values (represented by the symbol X) and dividing that total by the number of population values (represented by the symbol N).

Therefore, the correct answer is option a. less than the population mean.

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Answer:

Explanation:

Here, we want to write the equation of a line in point-slope form

Mathematically, we have that as:

where m, which is the slope is -2/3 and (x1,y1) which is the point is (-3,2)

Substituting the values, we have it that:

In the images, we are given an exercise which is solved by taking T as the midpoint of SU. This is the