which of the following statements must be true abut this diagram. check all that apply

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: x=-1 and y=-2

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]

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

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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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:

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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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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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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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: 8/15, 15/8

Step-by-step explanation:

By the Pythagorean theorem, the length of the unknown side is

[tex]\sqrt{17^{2}-8^{2}}=15[/tex]

So, the tangents of the acute angles are [tex]\boxed{\frac{8}{15}, \frac{15}{8}}[/tex]

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 :)

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.

Step-by-step explanation:

6+8-90+90008-70000000

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

Answer:

40 total students

Explanation:

Total students: 100%

Let the number of total students be x.

Solving stepwise:

7.5% : 100% --> 3 : x

[tex]\rightarrow \sf \dfrac{7.5}{100} = \dfrac{3}{x}[/tex]

[tex]\rightarrow \sf 7.5x = 3(100)[/tex]

[tex]\rightarrow \sf 7.5x = 300[/tex]

[tex]\rightarrow \sf x =40[/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.

-10 belongs to the set of negative integers and rational numbers and also belongs to the set of real numbers.

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

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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El cuadrado completo es:

[tex]\left[\begin{array}{ccc}0.048&0.056&0.016\\0.008&0.04&0.072\\0.064&0.024&0.032\end{array}\right][/tex]

Tenemos el cuadrado:

[tex]\left[\begin{array}{ccc}0.048&a&0.016\\b&c&0.072\\0.064&e&f\end{array}\right][/tex]

Y queremos encontrar los valores de las letras, tal que cada suma de columna, fila y de cada diagonal de 0.12,

Entonces tenemos:

0.048 + b + 0.064 = 0.12

b = 0.12 - 0.048 - 0.064 = 0.008

0.016 + 0.072 + f = 0.12

f = 0.12 - 0.016 - 0.072 = 0.032

Tambien las diagonales deben dar 0.12, entonces:

0.064 + c + 0.016 = 0.12

c = 0.12 - 0.016 - 0.064 = 0.04

Reemplazando esos valores obtenemos:

[tex]\left[\begin{array}{ccc}0.048&a&0.016\\0.008&0.04&0.072\\0.064&e&0.032\end{array}\right][/tex]

Ahora las filas tambien deben dar 0.12:

0.048 + a + 0.016 = 0.12

a = 0.12 - 0.048 - 0.016 = 0.056

0.064 + e + 0.032 = 0.12

e = 0.12 - 0.064 - 0.032 = 0.024

El cuadrado completo es:

[tex]\left[\begin{array}{ccc}0.048&0.056&0.016\\0.008&0.04&0.072\\0.064&0.024&0.032\end{array}\right][/tex]

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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

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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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 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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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.

The surface area of the cylinder is 244. 92 inches²

surface area of a cylinder = 2πr(r + h)

where

Therefore,

r = 6 / 2 = 3 inches

h = 10 inches

surface area of a cylinder =  2 × 3.14 × 3(3 + 10)

surface area of a cylinder = 18.84(13)

surface area of a cylinder = 244.92

surface area of a cylinder = 244. 92 inches²

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Using the arc length formula, the length of ST in the circle is: 15 units.

Arc length of a circle = ∅/360 × 2πr.

In the image given, we have:

∅ = m∠TSU = 72º

Arc length TU = 6π

r = ST

Plug in the values

6π = 72/360 × 2π(ST)

6π = 0.2 × 2π(ST)

6π/2π = 0.2 × ST

3 = 0.2(ST)

3/0.2 = ST

ST = 15 units.

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Answer:

50 points

Step-by-step explanation:

Let the total points scored by the team = x

30% of x = 15 points

     [tex]\sf \dfrac{30}{100}*x = 15\\\\[/tex]

              [tex]\sf x = 15* \dfrac{100}{30}\\\\ x = 50[/tex]

The team scored 50 points.