Mr. Jackson has just finished building his treehouse and still needs to buy a ladder to be attached to the ledge of the treehouse and anchored at a point on the ground, as modeled below. Mr. Jackson is standing 1.3 meters from the stilt supporting the treehouse. This is the point on the ground where he has decided to anchor the ladder. The angle of elevation from his eye level to the bottom of the treehouse is 56 degrees. Mr. Jackson's eye level is 1.5 meters above the ground. Determine and state the minimum length of a ladder, to the nearest tenth of a meter, that Mr. Jackson will need to buy for his treehouse. (do not round until the very end)

Congruence theorem can be used to prove WXS = YZS is  ASA.

What is Congruence theorem ?

If two triangles are identical in size and shape, they are said to be congruent. Corresponding sides (sides in the same location) and corresponding angles (angles in the same position) are congruent when triangles are congruent (equal).

Point S makes the two connected angles the same. They both have right angles.

And one side of each is congruent.

This means you know 2 angles are the same and one side is the same.

You would use ASA (Angle, Side, Angle).

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Answer:

D. Line symmetry

Step-by-step explanation:

I am pretty sure it is Line symmetry because it has a line pass through the vertex and divides the graph into two equal halves. If I am wrong, I am sorry!

The equation describes a line that contains the point (4, -3) is y = ( -1/25 )x - 71/25 .

Given :

The point (4, -3) and is perpendicular to the line represented by the equation y = 25x +3 .

Here slope m = 25

Perpendicular slope = -1 / m

= -1 / 25

The line equation is y = mx + c

Substitute m and ( 4 , -3 ) we get

-3 = -1/25 * 4 + c

-75 = -4 + 25c

-71 = 25c

c = -71/25

y = mx + c

y = ( -1/25 )x - 71/25

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Answer:

3

Step-by-step explanation:

She's got 315 total pictures. if she uses one page for 6 pictures then she will fix 52 and a half pages. if only half the page is filled you have 3 photos left

The number of pictures leftover in the scrapbooks is A = 3

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

The total number of pictures = 315

The number of pictures in each page = 6

Since Anne can only fill complete pages, she will use 52 pages. The remaining pictures will be:

The remaining pictures = total pictures - (pictures per page x pages used)

On simplifying the equation , we get

The remaining pictures A = 315 - (6 * 52)

The remaining pictures A = 315 - 312

The remaining pictures A = 3

Hence , Anne will have 3 pictures left over.

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Lines that have the same slope are said to be parallel, and if the slope of one line is equal to the negative reciprocal of the slope of the other, the two lines are said to be perpendicular; otherwise, they are merely intersecting lines.

A line's slope is defined as the ratio of the change in the y coordinate to the change in the x coordinate.

Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by Δy and Δx, respectively. and

m = Δy/Δx = dy/dx = change in y/change in x

where "m" represents a line's slope.

Additionally, the slope of the line may be shown as

tan θ = Δy/Δx

A line's slope often indicates the steepness and direction of the line.

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Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by Δy and Δx, respectively. and

m = Δy/Δx = dy/dx = change in y/change in x

where "m" represents a line's slope.

Additionally, the slope of the line may be shown as

tan θ = Δy/Δx

“5 more than a number” written as an algebraic expression is “x+5”.

In a formula or equation involving mathematical operations, the representation of numbers by alphabet is referred to as algebra. Similar to how a statement explains the link between certain words, algebraic equations describe the connection between unknown variables. 

We are given a mathematical statement and have to convert it into an algebraic expression using the information above.

Let there be a number “x”.

A number 5 more than this number is obtained after adding 5 to the given number.

So a number 5 more than x is equal to x+5.

Hence “5 more than a number” written as an algebraic expression is “x+5”.

Complete question: How do you write 5 more than a number?

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The sum of the geometric sequence is 88,573.

The formula for the sum of a geometric sequence is

S = a₁(1 - rⁿ)/(1-r),

where a₁ is the first term of the sequence, r is the common ratio between terms, and n is the number of terms in the sequence. In this case, the first term is a₁ = 1, the common ratio between terms is r = 3, and the number of terms is n = 10. Inserting these values into the formula,

we get S = 1(1 - 3⁹)/(1-3) = 1(1 - 19,683)/(-2) = -9,841.5.

Therefore, the sum of the geometric sequence is 88,573.

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The price of the two pencils is Rs.100 (expensive) and Rs.60 (cheaper).

Let the price of the expensive pencil be = x

And the price of the cheaper one be = y.

According to the question:

The difference between the price of 2 = 40

Therefore,

x- y =40

Total amount = 1800.

The number of Expensive pencils that can be bought = 1800/x.

The number of Expensive pencils that can be bought = 1800/y.

According to the question,

1800/y -1800/x = 15 (the number of extra pencils)

= (1800x -1800y)/xy = 15

= 1800x -1800y =15xy

= 1800 (x-y) =15xy

Substituting x-y as 40

1800 x 40 =15xy

xy = 4800.

We know that x-y =40

Therefore, x = y+ 40

xy = 4800

(y+40) y = 4800

[tex]y^{2}[/tex] + 40 y = 4800

Using the quadratic equation formula,

y = 52.111 or y = -92.111

Thus, the cost of the cheaper pencil (y)= Rs. 52.111

The cost of the expensive pencil (x) = 52.111 + 40 = Rs 92.111

Therefore the cost of two pencils is =   Rs. 52.111 and Rs 92.111.

The two expressions equal to the area of the figure are (6×10) + (6×6) + (6×10) square centimeters and (6×4) + (18×6) + (6×4) square centimeters. Select these options

Consider the images I attached:

First image:

The area of the figure = area of rectangle A + area of rectangle B + area of rectangle C

The area of the figure = (6×10) + (6×6) + (6×10)

Second image:

The area of the figure = area of rectangle D + area of rectangle E + area of rectangle F

The area of the figure = (6×4) + (18×6) + (6×4)

Thus, (6×10) + (6×6) + (6×10) square centimeters and (6×4) + (18×6) + (6×4) square centimeters are the two expressions equal to the area of this figure

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TRUE: The ratio of 6 and 8 is equivalent to 3/4.

Remember that the ratio is the same when you multiply both sides of a fraction by a number.

= 3/4

= 3*2 / 4*2

= 6/8

= 6:8

Thus, the ratio of 6 and 8 is equivalent to 3/4.

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Is 6:8 equals 3/4 ? Is it true or false and why?

A one-dimensional array is the simplest type of array in which the elements are stored linearly and can be accessed individually by determining the index value of each element stored in the array.

A one-dimensional array is the simplest type of array in which the elements are stored linearly and can be accessed individually by determining the index value of each element stored in the array.

One Dimensional Arrays are used to implement other data structures such as stacks, queues, heaps, graphs.

A typical advantage of one Dimensional Arrays is that they help in accessing elements easily using the index number.

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Answer:

False

Step-by-step explanation:

Vertical angles are always congruent regardless of if the lines are parallel.

The mean deviation of the data 8,9,12,15,16,20,24,30,32,34​ is 8

Given data: 8,9,12,15,16,20,24,30,32,34

The formula for the mean (x bar) =  sum of observations /no. of observations

Mean (x bar) = 8+9+12+15+16+20+24+30+32+34/ 10

Mean = 200/10

∴ Mean = 20

Now, we find the mean deviation using mean

Mean deviation using mean = 1/n Σ|x- x bar|

where n= number of observations = 10

x= each observation in the data

x bar= mean of the data= 20

Mean deviation using mean

= 1/10 x [(20-8)+(20-9)+(20-12)+(20-15)+(20-16)+(20-20)+(24-20)+(30-20)+           (32-20)+(34-20)]

= 1/10 x [12+11+8+5+4+0+4+10+12+14]

= 1/10 x (80)

= 80/10

Mean deviation = 8

Thus the mean deviation is 8.

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Answer:

The graph of given function is shown below.

Step-by-step explanation:

The absolute parent function is g(x)=|x|. The graph of parent function is a V-shape d and vertex of the function is origin.

The given function is

             .... (1)

The vertex from of an absolute function is

         .... (2)

where, a is a constant and (h,k) is vertex of the function.

From (1) and (2) we get

The value of a is -1. The value of a is negative it means the graph of parent function reflect across x-axis.

The vertex of the function is (0,-2). It means the graph of parent function shifts 2 units down.

Answer:

A. It is an increase in assets.

Step-by-step explanation:

The Debit section shows what the business purchased which is $12,000 worth of equipment. Hence, the business gained equipment worth $12,000 which is an increase in assets.

Answer:

A. It is an increase in assets.

Step-by-step explanation:

The entry "Equipment 12,000" is listed as a debit in the T-account because it is an increase in assets.

A T-account is a visual representation used in accounting to track and display the balances of a specific account, with the "debit" side showing increases and the "credit" side showing decreases.

When office equipment is purchased, it represents an increase in the company's assets. An increase in assets (or a decrease in liabilities) is recorded as a debit on a company's balance sheet.

In this case, the business is acquiring equipment, which is considered an asset, and therefore, it is debited to reflect the increase in the asset account.

Answer: 49/ 16

Step-by-step explanation:

-3.5 or -35/ 10 = - 7/2

-7/8 times -7/2 = 49/ 16

Negative time negative will be positive!

The joint relative frequency of students using mobile devices in traditional classes, is

The joint relative frequency of students that use mobile devices in the setting of a traditional class is :
= Number of students using mobile devices in traditional class / Number of total students accessing courses

Number of students using mobile devices in traditional class =  46 students

Number of total students accessing courses = 200

The  joint relative frequency of students using mobile devices in traditional classes :

= 46 / 200

= 23 %

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The simplified equation for finding the inverse of y = 2x² is x = 2y².

It is worth noting that the inverse of y = 2x² is √x/2 = y.

x = 2y²

Make the subject of the formula 'y²'.

x/2 = y²

Make 'y' the subject of the equation by taking the square root of both sides.

√x/2 = √y²

The square root cancels out the square.

√x/2 = y

Thus, the simplified equation for finding the inverse of y = 2x² is,

x = 2y².

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Solving and graphing of inequality can be done by following rules of simplification and graphing accordingly.

The horizontal straight lines in mathematics known as number lines are where integers are arranged in equal intervals. A number line can be used to represent every number in a sequence. The endpoints of this line go on forever. Integers are arranged on a number line in the image above.

On the number line, find the first number. To add, take as many steps to the right as the second number. Move as far to the right as the second number in order to subtract. The solution is the number you finally select.

When resolving an inequality, you can do one of the following: • Add the same amount to each side; • Subtract the same amount from each side; • Multiply or divide each side by the same positive amount. You must flip the inequality sign if you multiply or divide each side by a negative number.

To represent an inequality on a number line, such as x>3, first draw a circle around the number (e.g., 3). Fill in the circle if the sign also says equal to (). Leave the circle blank if the sign doesn't include equal to (> or <).

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Therefore , the 4 year old children can able to count to 1 to 100 counting by making them learn.

Mathematicians can add numbers using the counting-on technique. When using this method, a learner begins by adding the larger number, then "counts on" with the other addends to get the sum. The student will recognize 4 as the higher number and add three more numbers, such as integers "4... 5, 6, 7," if the number sentence is 4 + 3.

Here,

Children develop and learn on an individual basis, however many

4 year old are able to learn their numbers between 1 and 100 and can count over 10.

They could be prepared to practice counting by fives or other skip counting techniques (5, 10, 15, 20, and so on).

Start working on number recognition with your kid as soon as you can.

Therefore , the 4 year old children can able to count to 1 to 100 counting by making them learn.

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The value of x is 20 units.

The correct answer is 20 units .

According to the triangle,

ST = 9, TQ = 16 and RQ = x

From similar triangles,

Δ SRQ ⩭ Δ STR ------(1)

{∵ RT 丄 Hypotenuse SQ}

Δ SRQ ⩭ Δ RTQ ------(2)

{∵ Δ SRQ, Δ STR and Δ RTQ are similar triangles}

⇒ SR/ST = SQ/SR = RQ/TR

⇒ SR/9 = 25/SR = x/TR

⇒ SR2 = 25 × 9

⇒ SR = 5 × 3 = 15

[tex]SR^2[/tex] + [tex]RQ^2[/tex] = [tex]SQ^2[/tex]

[tex]RQ^2 = SQ^2 - SR^2[/tex]

[tex]RQ^2 = 25^2 - 15^2[/tex]

RQ = x = √(625 - 225) = √400

x = 20 units.

Hence, The value of x is 20 units.

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The complete question is this:

What is the value of x?

12 units, 15 units, 20 units, 24 units

Answer:

A = 5 + 3t

B = 7 + 2t

2 hours

Step-by-step explanation:

7 + 2t > 5 +3t

                      (subtract 2t from both sides)

7         > 5 + t

                      (subtract 5 from both sides)

2         > t

therefore in 2 hours, the parking would be cheaper in Garage A than B

You may use three triangle-specific theorems to quickly distinguish similar triangles.

There are three theorems that may be used to determine whether two triangles are similar: Angle - Angle (AA), Side - Angle - Side (SAS), and Side - Side - Side (SSS).

SSS, which stands for "side, side, side," denotes that there are two triangles with identical angles on all three sides. The triangles are congruent if their third sides are the same as those of another triangle.

That is what the SAS regulation says. The triangles are congruent if the two sides and included angle of one triangle are the same as the two sides and included angle of another triangle. Any angle that is created by two specified sides is an included angle.

According to the AA postulate of Euclidean geometry, two triangles are similar if their two corresponding angles are congruent. The fact that the sum of a triangle's internal angles is always equal to 180° leads to the AA postulate.

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The equations of the asymptotes are y = 2 and x = -1, respectively

The equation of the function is given as

f(x) = 2x² + 7x - 4/x² + 5x + 4

Introduce bracket, to differentiate the numerator and the denominator

So, we have

f(x) = (2x² + 7x - 4)/(x² + 5x + 4)

Next, we plot the graph of the function (see attachment)

The asymptotes are the points on the graph is a line that acts as the limit of another line or curve

From the graph, we have the asymptotes to be

x = -1 and y = 2

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Complete question

What is the equation of the asymptote?

f(x) = 2x² + 7x - 4/x² + 5x + 4

Answer:

y ≈ 76.4°

Step-by-step explanation:

To solve for the angle a trigonometric function is being used on, we have to use the inverse of the trigonometric function.

Inverse of tan(y°) = 4.12:

[tex]tan^-1(4.12) = y[/tex]

Next, I used a scientific calculator to find the angle measure of y.

[tex]76.4 = y[/tex]

"It's pouring if the grass is wet." Our inverse sentence would be, "If it is NOT raining, then it is NOT wet on the grass."

Given,

Inverse Sentence;

Each of the original statements is presupposed to be false in an inverted statement. "If it is not snowing" would be the polar opposite of "If it is snowing." "Then it is not chilly" would be the polar opposite of "then it is cold."

Example of inverse sentence;

Now, we can construct the three other statements using the concepts we established before. If anything, we would say the opposite: "If the grass is wet, it's pouring." "If it is NOT raining, then the grass is NOT wet," would be our inverse claim.

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Students are pushed by reform mathematics curricula to make sense of novel mathematical concepts through investigations and projects, frequently in practical settings.

A point, line, or geometric object can be changed in four different ways that are all collectively referred to as transformations. The pre-image is the shape of the object as it was originally, and the transformed shape of the object is termed the image.

Students are pushed by reform mathematics curricula to make sense of novel mathematical concepts through investigations and projects, frequently in practical settings. Writing and speaking clearly, cooperating in groups, and drawing connections between ideas and representations are all stressed in reform textbooks.

Translation, rotation, reflection, and expansion are the four different types of transformation. Each change must be carried out, and you must be able to tell which transformations have been carried out.

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Answer:

A. M1+ M2 + M3

Step-by-step explanation:

M1 is the money supply that makes it easy to convert assets/items into currency.

M2 is the deposits and money market funds.

Add M1, M2, and M3 to calculate the entire money supply of all the money in the economy.

Answer:

A. M1+ M2 + M3

M3 consists of all currency notes held by the public, all demand deposits with the bank, deposits of all the banks with the RBI and the net Time Deposits of all the banks in the country. So M3 = M1 + time deposits of banks.

Step-by-step explanation:

The square root of some number 'X' is a number which, when you multiply it by itself, the answer is 'X'.

The square root of a number is the factor that we can multiply by itself to get that number. The symbol for square root is [tex]\sqrt{x}[/tex] . Finding the square root of a number is the opposite of squaring a number.

In mathematics, a square root of a number x is a number y such that y² = x; in other words, a number y whose square (the result of multiplying the number by itself, or y ⋅ y) is x.[1] For example, 4 and −4 are square roots of 16, because 4² = (−4)² = 16.

Thus , the square root of some number 'X' is a number which, when you multiply it by itself, the answer is 'X'.

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