Given that y = 12 cm and 0 = 45°, work
out a rounded to 1 DP.

The diagram is not drawn accurately.
X
cm

ABC is a right angle

ABCD is a parallelogram

Opposite sides of a parallelogram are equal

So

Opposite angles are equal

<B=<D

Hence

∆ABC and ∆CDB are congruent by SAS

Answer:

16

Step-by-step explanation:

Referring to the diagram, we can use Pythagoras' Theorem to find ZY. (which is the distance from Point Y to WX)

By Pythagoras' Theorem,

[tex]c^{2} =a^{2} +b^{2} \\WY^{2} =WZ^{2} +ZY^{2} \\(16\sqrt{2}) ^{2} =16^{2} +ZY^{2} \\ZY^{2} = (16\sqrt{2}) ^{2} -16^{2} \\ZY^{2} =512-256\\ZY^{2} =256\\ZY=\sqrt{256} \\ZY=16[/tex]

[tex]\Large\maltese\underline{\textsf{Our problem:}}[/tex]

When [tex]\bf{p^2-4p}[/tex] is subtracted from[tex]\bf{p^2+p-6}[/tex], the result is...?

[tex]\Large\maltese\underline{\textsf{This problem has been solved!}}[/tex]

[tex]\bf{Subtract:}[/tex]

[tex]\bf{p^2+p-6-p^2-4p}[/tex]. | combine like terms

[tex]\bf{p^2-p^2+p-4p-6}[/tex] | simplify

[tex]\bf{0p^2-3p-6}[/tex] | simplify

[tex]\bf{-3p-6}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\bf{Result:}[/tex]

                   [tex]\bf{-3p-6}[/tex]

[tex]\boxed{\bf{aesthetic \not101}}[/tex]

Answer:

5p - 6

Step-by-step explanation:

p² + p - 6 - (p² - 4p) ← distribute parenthesis by - 1

= p² + p - 6 - p² + 4p ← collect like terms

= 5p - 6

Step-by-step explanation:

6+8-90+90008-70000000

Answer:

Step-by-step explanation:

h² means h * h

We can start with a number like "10". 10*10 = 100, so we have to guess a bit higher.

12*12 = 144.

However, it can also be -12 * -12 since the two negative signs will cancel each other out.

So, h can be 12 or -12

Answer: +12 or -12

Step-by-step explanation:

h^2=144

taking sqrt root on both sides

h=±12

so answer is +12 or-12

There are 31 possible lengths for the third side.

Unknown Side +  16 > 21

Unknown Side >  5

16 + 21  > Unknown Side

37 > Unknown Side      

Unknown Side  <  37

So, the possible integer lengths range from

6 -  36  

=   36 - 6 + 1  

= 31 possible lengths

The length of the third side of a triangle has to continually be among (but not equal to) the sum and the distinction among the alternative facets. As an instance, take the example of two, 6, and seven. and consequently, the 0.33 facet length has to be extra than four and less than eight.

The regulation of Cosines to calculate the unknown aspect, then use the Law of Sines to find the smaller of the opposite angles and then use the 3 angles add to 180° to find the final attitude.

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A horizontal translation of the function by 4 units and a vertical translation down by 3 units

The parent function of the given function is g(x) = |x|. The resulting function (x) = | 2x − 4 | − 3 shows the following translations

A vertical stretch of the graph by 2 units

A horizontal translation of the function by 4 units and a vertical translation down by 3 units

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Step-by-step explanation:

so when you want to rationalize the denominator when it's in the form [tex](a-\sqrt{b})[/tex] you multiply by the conjugate which is [tex](a+\sqrt{b})[/tex] which is where the sign is the opposite. This is because it's using the difference of squares to get rid of the square root. Because [tex](a-b)(a+b) = a^2-b^2[/tex] this will remove the square root since it's going to become square and the ab - ab will cancel so there will be no square root

Multiply by conjugate

[tex]\frac{5\sqrt3}{4-\sqrt6} * \frac{4+\sqrt6}{4+\sqrt6}\\[/tex]

Simplify:

[tex]\frac{20\sqrt{3} + 5\sqrt{6 * 3}}{16-6}[/tex]

Simplify radical

[tex]\frac{20\sqrt{3} + 15\sqrt{2}}{10}\\[/tex]

You could go further and do

[tex]2\sqrt{3} + 1.5\sqrt{2}[/tex]

Answer:

The given lines are un-related.

Step-by-step explanation:

In the question two functions are given as h(t)=3t-4 and j(t)=5-t.

It is required to find whether these lines are perpendicular, parallel or neither.

Step 1 of 1

Find the slope of two lines by comparing these to the standard form.

y=mx+b

Then, [tex]$m_{1}[/tex]=3

And [tex]$m_{2}[/tex]=-1

Since, both slopes are neither equal nor reciprocal of each other.

Therefore, the lines are un-related.

The values of x and y by the descriptions in the task content are; 7.5 and 9 respectively.

It follows from the task content that the description in the task content registers the bottom right angle measure of the second intersection as equal to 10y.

Hence, it follows that; 10y = 90 and; y = 9.

From the first intersection; 6x + 5y = 90;

6x + 5(9) = 90

6x + 45 = 90

6x = 45

x = 45/6 = 7.5

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Answer:

horizontal asymptote of y = -7

Step-by-step explanation:

The parent function is shown on the coordinate plane. The graph of the parent function has a horizontal asymptote (an imaginary line that the graph approaches, but never touches or intersects) of y = 0.

Since the function of g(x) = e^x - 7 is the graph of the parent function translated 7 units down, the function would have a horizontal asymptote of y = -7.

Answer:

x = 108°

y = 72°

z = 36°

Step-by-step explanation:

   If all sides are equal in a pentagon, then it is a regular pentagon.

n = the number of sides = 5

Sum of all angles in a pentagon = (n -2) * 180

                                                     = (5 - 2)* 180

                                                     = 3 *180

                                                     = 540°

Sum of each angle of regular pentagon = 540 ÷ 5

                                                                  = 108°

  [tex]\sf \boxed{\bf x= 108^\circ}[/tex]

Linear pair: If the non common arm of adjacent angles form a straight line, then the adjacent angles are called linear pair and they add up to 180°

∠DCB + y = 180 °   {Linear pair}

  108  + y = 180

            y = 180 - 108

            [tex]\sf \boxed{\bf y = 72^\circ}[/tex]

Exterior angle property of triangle: The exterior angle equals the sum of opposite interior angles.

In Δ BCF ,

  x = y + z

Now, substitute the values of x and y , and we can find the value of z.

      108° = 72 + z

108  - 72 = z

     [tex]\sf \boxed{\bf z = 36^\circ}[/tex]

The cost to drive 325 miles is $152.75.

Given: Initial cost = $39

Per mile cost= $0.35

To find: To find the total cost for 325 miles

Concept: Multiplication is the method of finding the product of two or more numbers. It is a primary arithmetic operation that is used quite often in real life.

The cost to drive 325 miles without adding the initial cost = $0.35*325 = $ 113.75

The cost to drive 325 miles while adding the initial cost = $ 113.75 +39 = $  152.75

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The new number in the sequence is found to be 7.

In mathematics, a sequence is a list of components, usually numbers, where the components' order is important. Here, everything fits into a predetermined pattern.

A sequence can be arranged in either ascending or descending order.

There are certain unique sequences, including the triangular number series, square number sequence, cube number sequence, geometric sequence, Fibonacci sequence, and harmonic sequence.

According to the question, the sequence follows the pattern:

Next number=2(Previous number)-2

On substituting the values,

48=2(Previous number)-2

50=2(Previous number)

Previous number=[tex]\frac{50}{2}[/tex]=25

New number=sum of digits of the previous number in the sequence

                     =2+5

                     =7

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If we know the concepts of transformations and horizontal translation and that f(x) = √x and k = - 2, then the transformed function is g(x) = √(x + 2).

The transformation of functions are operations which modify the relationship between input and outputs in a function. The parent function represents a canonical square root function and the transformed function is the consequence of applying a horizontal translation.

This kind of transformation is defined by the following expression:

g(x) = f(x - k)     (1)

Where k represents a rightward translation for k > 0.

If we know that f(x) = √x and k = - 2, then the transformed function is g(x) = √(x + 2).

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Answer: 36

Step-by-step explanation:

[tex]\overline{AB} \cong \overline{BC}[/tex] (Triangle ABC is isosceles)

[tex]m\angle CAB=m\angle CBA=30^{\circ}[/tex] (base angles of an isosceles triangle are congruent)

[tex]\angle MCB=90^{\circ}[/tex] (In triangle CMB, angles in a triangle add to 180 degrees)

[tex]\angle ACM=30^{\circ}[/tex] (triangle sum theorem)

[tex]MB=24[/tex] (30-60-90 triangle CMB)

[tex]AB=12[/tex] (sides opposite congruent angles in a triangle are congruent)

[tex]AB=36[/tex] (segment addition postulate)

The value of AB = 36

An isosceles triangle is a triangle with base angles equal with any two sides equal.

Analysis:

∠ACB = 120

ABC is isosceles, so ∠CAB = ∠CBA = x

x + x + 120 = 180 ( sum of angles in Δ ABC)

2x = 60

x = 30

∠AMC = 180 - ∠BMC( angles on a straight line)

           = 180 - 60 = 120

∠ACM = 180 - (30 + 120) = 180 - 150 = 30°

∠MCB = 90°

using sine rule,

12/sin 30 = AM/ sin 30

AM = 12

MB/sin 90 = 12/sin30

MB sin 30 = 12 sin 90

MB = 12/sin 30 = 12/0.5 = 24

AB = MB + AM = 24 + 12 = 36

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Answer:

1 9/20x or 29/20x

Step-by-step explanation:

Reorder so it can be seen better

5x-4x+1/5x+1/4x

Combine like terms

x+1/5x+1/4x

Common multiple

x+4/20x+5/20x

Combine like terms

9/20x+x

Finalize

29/20x

Simplified

1 9/20x

Answer: -1/20x

Step-by-step explanation:

got all 5 correct this one was one of my five

The sampling distribution is illustrated below.

Based on the information given, the population is illustrated as 1, 4, 7. The sample without replacement will be:

Sample Mean

1 and 4. 2.5

1 and 7. 4

4 and 7. 5.5

The population mean will be:

= (1 + 4 + 7)/3

= 4

The sample mean is an unbiased estimator of the population mean.

The sampling with replacement illustrates that the mean will be:

= 36/9 = 4

Also, when n = 3, the number of samples will be:

= 3³ = 27

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When writing an informative essay about an event in history, you should:

To avoid finding it difficult to find information on your topics, pick a topic that has been well researched and has several sources of information on it. European history is well researched.

In the introduction, talk about why you think this topic is significant and include a thesis statement that would be the main logic you are producing details about.

Then divide this thesis into several points and talk about each point in a different paragraph. Use sentences that are not too long so that people don't lose interest.

Use primary and secondary information sources but make sure you reference these sources in the required format.

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Answer: 140°

Step-by-step explanation:

- all straight lines are 180°

- since ACD and DCB help to create the straight line they must equal 180° when combined

- so 180 - 40 = 140

- therefore, ACD is 40° and DCB is 140°

hope this helps :)

The difference of squares is 4m^2 - 20mn + 25n^2

Its a perfect square trinomial.

A perfect square trinomial is the square of a binomial. It follows a pattern when it is factored, so that the first and last terms are perfect squares of monomials and the middle term is twice their product. If the pattern does not fit for a particular trinomial, it is not a perfect square trinomial.

(-2m + 5n)^2

(-2m + 5n)(-2m + 5n)

4m^2-10mn-10mn+25n^2

4m^2 - 20mn + 25n^2

Thus, the difference of squares is 4m^2 - 20mn + 25n^2

Its a perfect square trinomial.

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The area of the deck is 413 square feet

Start by calculating the area of the outer rectangle using:

Area = Length * Width

This gives

Area1 = (18 + 12) * (16 + 8)

Area1 = 720

Next, calculate the area of the inner rectangle using:

Area = Length * Width

This gives

Area2 = 16 * (18 + 8)

Area2 = 416

Subtract these areas

A1 = Area1 - Area2

A1 = 720 - 416

A1 = 304

Next, calculate the area of the outer semicircle using:

Area = 0.5πR²

This gives

Area1 = 0.5 * 3 * (12-1)²

Area1 = 181.5

Next, calculate the area of the inner semicircle using:

Area = 0.5πr²

This gives

Area2 = 0.5 * 3 * (7)²

Area2 = 73.5

Subtract these areas

A2 = Area1 - Area2

A2 = 181.5 - 73.5

A2 = 108

Add A1 and A2

A = 304 + 108

Evaluate the sum

A = 412

Hence, the area of the deck is 413 square feet

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Answer: x+y=

Step-by-step explanation:

you would just write it out step by step explaining wht u need to do to solve the question

Using the distance formula, the area of the rectangle is: 16 units².

Area of a rectangle = (length)(width).

Given the vertices:

Area = (AB)(BC)

Apply the distance formula, [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex], to find AB and BC:

AB = √[(1−(−3))² + (3−(−1))²]

AB = √[(4)² + (4)²]

AB = √32

BC = √[(1−3)² + (3−1)²]

BC = √[(−2)² + (2)²]

BC = √8

Area = (√32)(√8) = √256

Area = 16 units²

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The amount of waste is 22 oz

The weights of the 3 rainbow trouts are:

3 Ib 5 oz, 2 Ib 12 oz, and 3 Ib 8 oz.

The total weight is:

Total = 3 Ib 5 oz + 2 Ib 12 oz + 3 Ib 8 oz

Evaluate the sum

Total = 8 Ib 25 oz

The amount she was left with is 8 Ib 2 oz

Subtract this amount from the total

Waste = 8 Ib 25 oz - 8 Ib 2 oz

Evaluate

Waste = 22 oz

Hence, the amount of waste is 22 oz

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Answer:

to find domain just take the first values of each ordered pairs

to find the range just take the second values of each ordered pairs.

The missing statement in the proof is; AB/BD = CB/EB

Similar triangles have the same corresponding angle measures and proportional side lengths.

The given proof is the triangle proportionality theorem which states that the segments formed by side DE are proportional.

The two column proof is presented as follows;

Statement                                           Reason

1. DE || AC                                             1. Given

2. ∠CAB ≅ ∠EDB        2. Corresponding angles formed between ║ lines

3. ΔABC ~ ΔDBE                  3. AA criterion for similarity

4. AB/BD = CB/EB                4. Corr. sides of similar Δs are prop.

5. AB = AD + DB                   5. Segment addition CB = CE + EB

6. (AD + DB)/(DB) = (CE + EB)/(EB)        6. Substitution Property of Equality

7. (AD)/(DB) + 1 = (CE)/(EB) + 1               7. Division

8. (AD)/(DB) = (CE)/(EB)                          8. Subtraction Property of Equality

Hence, the missing statement in the proof is; AB/BD = CB/EB

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Hello,

[tex]g(x) = 2x - 2[/tex]

[tex]g(-3) = 2 \times (- 3) - 2 = -6 - 2 = -8[/tex]

Answer: g(-3) = -8

Given that:

To find g(-3), insert (x = -3):

⇒ g(-3) = 2(-3) - 2

⇒ g(-3) = -6 - 2

⇒ g(-3) = -8

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The distance from the center of dilation, P, to.the image vertice S' is; 6 units.

It follows from the task content that the center of dilation of the triangle QRS is point P and the length of segment PS in the pre-image is; 8 units.

Ultimately, since the dilation factor is; three-fourths, it therefore follows that the distance of point P to S' in the image is; (3/4) × 8 = 6 units.

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Answer: OPTION C

Step-by-step explanation: