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Answer:

103mm or 53mm

Step-by-step explanation:

--A------B------C--

AB=78mm BC=25mm AC=AB+BC=103mm

--A----C---B---

AB=78mm BC=25mm AC=AB-BC=53mm

-B---A---C-

is impossible because BA<BC but 78mm>25mm

Answer:

(x,y)—>(6,2)

Step-by-step explanation:

Add both equations to eliminate y

9x=54

x=6

plug x=6 into either equation

2(6)+6y=24

6y=24-12

y=12/6=2

Answer:

1 : 4

Step-by-step explanation:

3.5 : 14 ( divide both parts by 3.5 )

= 1 : 4

The limit of the nth term of a sequence does not exist option (D) is correct.

A limit is a value at which a function approaches the output for the given values in mathematics. Limits are used to determine integrals, derivatives, and continuity in calculus and mathematics.

We have an expression:

[tex]= \rm \dfrac{2n^5+25n^2+32n-15}{6n^4+2n^3-11n^2-2n+17}[/tex]

Applying limit:

[tex]= \lim_{n \to \infty} \rm \dfrac{2n^5+25n^2+32n-15}{6n^4+2n^3-11n^2-2n+17}[/tex]

[tex]=\lim _{n\to \infty \:} n \left(\dfrac{2+\dfrac{25}{n^3}+\dfrac{32}{n^4}-\dfrac{15}{n^5}}{6+\dfrac{2}{n}-\dfrac{11}{n^2}-\dfrac{2}{n^3}+\dfrac{17}{n^4}}\right)[/tex]

= ∞ = The limit does not exist

Thus, the limit of the nth term of a sequence does not exist option (D) is correct.

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Answer:

2ab(b + 4a​)

Step-by-step explanation:

2ab² + 8a²b​

Factor Out the 2:

2(ab² + 4a²b​)

Factor Out the a:

2a(b² + 4ab​)

Factor Out the b:

2ab(b + 4a​)

Answer:

16.5 meters

Step-by-step explanation:

The length of an arc of a circle = 2πr(C/360°) ;where:

C is the central angle of the arc,

R is the radius of the arc

Length of the arc = 2π(7)(135/360)

= 16.493

= 16.5 metres (approx.)

Answer:

Arc Length: 5.25π or [tex]\frac{21}{4} \pi[/tex]

Explanation:

An arc is the part of the circumference of a circle.

Formula:

[tex]\sf Arc \ Length = \dfrac{\theta}{360} \ \times \ 2\pi \ \times radius[/tex]

If applied:

[tex]\sf Arc \ Length = \dfrac{135}{360} \ \times \ 2\pi \ \times 7[/tex]

[tex]\sf Arc \ Length = \dfrac{3}{8} \ \times \ 14\pi[/tex]

[tex]\sf Arc \ Length = \dfrac{21}{4} \pi[/tex]

[tex]\sf Arc \ Length = 5.25 \pi[/tex]

Answer:

g(x) = -5x²

(option B)

Step-by-step explanation:

we know that our original graph, f(x) = x² is a parabola.

So, we can consider what happens when we adjust the function/equation of a parabola.

when we "vertically stretch" a parabola, we are increasing the value of x.

 think of it this way: the steepness of a slope is rise over run. If we rise ten, and run one, that's going be a lot more steep than if we rise 1, run 1.

Let's say our x = 5

if f(x)=x²

f(5) = 25

> y value / steepness is 25

f(x) = 3x²

f(5) = 75

 > y value / steepness is 75

So, we are looking for an equation with an increase in x present.

When a parabola has been flipped over the x-axis, we know that the original equation now includes a negative

suppose that x = 1

if y = x² ; y = 1² = 1

if y = -(x²) ; y = -(1²) ; y = -1

So, when we set x to be negative, we make our y-values end up as negative also (which makes the graph look as if it has been flipped upside-down)

This means that we are looking for a function with a negative x value.

So, we are looking for a negative x-value that is multiplied by a number >1

The graph that fits our requirements is g(x) = -5x²

hope this helps!!

Answer:

This would shift the equation to the right by 5

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

consider X  = Damon's age

3x + 8 = 2x

x = 8

so Damon will be 16 in 8 years ( 8+8)

Answer:

16

Step-by-step explanation:

24/3 8

24+8=32

8+8=16

16/32=1/2

The correct answer is option A [tex](\dfrac{x-2}{3})^2+(\dfrac{y+1}{2})^2=1[/tex] it will be an ellipse.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Let's consider the following trigonometric identity:

Sin²[tex]\theta[/tex] + Cos²[tex]\theta[/tex] = 1

Each trigonometric function is cleared respectively in given parametric equations:

[tex]Cos \theta = \dfrac{x-2}{3}[/tex] and  [tex]Sin\theta =\dfrac{y+1}{2}[/tex]

The equivalent expression in rectangular form is:

[tex](\dfrac{x-2}{3})^2+(\dfrac{y+1}{2}^)^2 = 1[/tex]

Therefore the correct answer is option A [tex](\dfrac{x-2}{3})^2+(\dfrac{y+1}{2})^2=1[/tex] it will be an ellipse.

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Answer:

The sum of the interior angles of any quadrilateral is 360°.

Answer:

Step-by-step explanation:

A quadrilateral is a polygon which has 4 vertices and 4 sides enclosing 4 angles and the sum of all the angles is 360°.

I'll give you an example with the square, it has 4 right angles, so the sum is 360 ° as in all quadrilaterals.

Answer: Choice [B]

Step-by-step explanation:

Hii, I'd love to help you out! (:

This particular problem is all about finding inverse functions.

This can be done in 3 easy steps, which are shown below.

The process is shown below.

[tex]\multimap\quad \tt f(x)=3x+5 \\ y=3x+5\\ x=3y+5\\Solve\;for\;y[/tex]

[tex]\multimap\quad \tt x=3y+5\\x-5=3y\\\cfrac{x-5}{3}=y[/tex]

Why doesn't our answer show up among the answer choices? Has all of our hardwork been in vain?

Ofc not! There's just one more thing that can be done to simplify our answer.

[tex]\tt \cfrac{x}{5}-\cfrac{5}{3}[/tex]

We're getting closer!

[tex]\tt \cfrac{1}{3}x-\cfrac{5}{3}[/tex]

Voila! There's our answer, cheers! (;

________________

Hope I helped!

Best wishes.

Reach far.

Aim high.

Dream big.

______________

Monica win 2 games.

In maths, an expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.)

According to the question,

First we  look from the perspective of one player.

How many games does this person play? 5.

Now, each or the 6 people in the tournament played 5 games,

SO,  

[tex]^{6} C_{2} = \frac{6!}{2! * 4!} = \frac{6*5}{2} = 15[/tex]

Therefore,

We know that there were a total of 15 games played.

This means, there were 15 losses, and more importantly, 15 wins.

Not counting Monica, there were:

4 + 3 + 2 + 2 + 2 = 13 wins.

This leaves,

15 − 13 = 2 wins for Monica.

Hence, 2 games won by monica in a tournament.

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Answer:

×=11

Step-by-step explanation:

2×-4×+27-5=0

-2×+22=0

-2×=-22

×=11

Answer:

[tex]\boxed {cot T = -\frac{5}{12}}[/tex]

Step-by-step explanation:

Finding the missing side :

Taking the cot value :

Answer:

csc T =13/12

(cot T)^2=csc^2T -1

Cot T)^2=(13/12)^2-1

(cot. T )^2=169/144-1

(cot T)^2=169-144/144

(cot T)^2=25/144

cot T =√ 25/144

cot T=5/12

where cot is negative in WE

so Cot T=-5/12

Step-by-step explanation:

please mark me as brainlest

The value of x would be 30 degrees.

The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.

Let's consider an angle CAD be t.

In a triangle ABD

x + 90 + t = 180

t = 180 -x - 90

t = 90 - x ( by angle sum property)

Now, we know that the sum of the corresponding angle on a transversal is 180

So,

Angle A + angle D = 180

2x + t + x + x = 180

substitute the t value

2x + 90 - x + 2x = 180

3x + 90 = 180

3x = 90

x = 30 degree

Hence, the value of x would be 30 degrees.

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Step-by-step explanation:

if it is cloudy, then it is snowing. False.  This is obviously not true since sometimes it's just cloudy and it's also cloudy when it rains.

all quadrilaterals are rectangles. False. A quadrilateral has four straight sides which don't have to be parallel to each other unlike a rectangle which has four straight sides with all four sides being parallel to one other side.

All chocolates like students? False? Not sure if I'm writing the converse correctly for this one but if I am this isn't true because chocolate doesn't have feelings...

All triangles with two or more congruent angles are a right triangle. False. This is only true when those two congruent angles add up to 90 which is when they're both 45. But they could also both be 30, 29, 28, etc... which won't result in a right triangle.

Answer:

If it is cloudy, then it is snowing.

   Counter-argument: It can be cloudy in the summer.

If a figure is a quadrilateral, then it is a rectangle.

   Counter-argument: Trapezoids are not rectangles.

If someone likes chocolate, then they are a student.

    Counter-argument: many people like chocolate who are not students.

If a triangle has 2 or more congruent angles, then it is a right triangle.

    Counter-argument: Equilateral tr6iangles have 3 congruent angles.

    None are right angles.

Step-by-step explanation:

Converse statements reverse the If Then in the original.

Answer: x = 2

Step-by-step explanation:

First, let's take the root of 256 to find the length of each side before the addition of x.

[tex]\sqrt{256} = 16[/tex]

This means 16 cm is the length of each side before the addition of x.

Then increase each side by X to get

[tex](16 + x)(16 + x) = 324[/tex]

[tex]256 + 16x + 16x + x^2=324[/tex]

[tex]x^2+32x -68=0[/tex]

[tex]x=2[/tex]  or   [tex]x=-34[/tex]

The value cannot be negative so x has to be 2

The value of the give expression is  [tex]\frac{313}{748845}[/tex] OR 4.18 × 10⁻⁴

From the question, we are to determine the value of

2(5+34-67/45*43)^2

This can be written as

[tex]2 (\frac{5+34-67}{45 \times 43 })^{2}[/tex]

First, we will simplify the bracket

[tex]2 (\frac{-28}{1935 })^{2}[/tex]

Then, we get

[tex]2 \times \frac{-28}{1935 }\times \frac{-28}{1935 }[/tex]

= [tex]\frac{1568}{3744225}[/tex]

= [tex]\frac{313}{748845}[/tex] OR 4.18 × 10⁻⁴

Hence, the value of the give expression is  [tex]\frac{313}{748845}[/tex] OR 4.18 × 10⁻⁴

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The bearing of B from C based on the information given will be 40°.

A bearing is an angle measured from the North direction clockwise. Notice that the bearing of B from C is 40° because according to the problem, all four points are on level ground, which means they are coplanar, and the angle between the plane and the North is 40°.

The bearing of A from C is also 110° because it's the bearing of C from A and A from C are same-side internal angles between parallels which must sum 180°.

The bearing of D from C is 40° too because that setup is parallel to the bearing of B from C.

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Answer:

Number of Days he can feed Pickles from a 15-cup bag of Hungry Hound  =  5 Days

Step-by-step explanation:

this is question based on simple algebraic equations

Simple Algebraic equations -  An algebraic equation can be defined as a mathematical statement in which two expressions are set equal to each other. The algebraic equation usually consists of a variable, coefficients and constants. we can apply many operations on algebraic equations like addition, subtraction, multiplication, division and raising to a power, and extraction of a root.

so in the question algebraic operation used to solve is simple division.

therefore, according to the question -

Total cups of Hungry Hound dog food pickles eats each day are - 3 cups

Total number of cups of Hungry Hound Terrence have = 15 cups

Number of days Terrence can feed pickles from these cups are =    

15/3 =  5 days

so the correct answer is = 5 Days

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The two equivalent equations are d₁= 2a/d₂ and d₂= 2a/d₁ , Option 2 and 5 is the right answer.

Rhombus is a quadrilateral with all the sides equal to each other.

It is given that d₁ and d₂ are the lengths of the diagonals.

and Area = a

a = (1/2) d₁ * d₂

       d₁ * d₂ = 2a

       It can be written as

        d₁= 2a/d₂

a = (1/2) d₁ * d₂

        d₂= 2a/d₁

Therefore Option 2 and 5 are the correct answer.

The options of this question are:

1.  d₁=2Ad₂

2. d₁= 2A/d₂

3. d₂= d₁/2A

4. d₁= 2A/d₂

5. d₂= 2A/d₁

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Answer:

38.667°

Step-by-step explanation:

the total sum of 3 angles in a triangle is 180

in triangle PQR this means:

P+Q+R = 180

so:

64+x+2x=180

64+3x=180

3x=116

x=116/3=38.667

So Q=X=38.667

Answer:

14a+2

Step-by-step explanation:

Perimeter of a rectangle: P=2(l+w) where l=length and w=width.

So P=2[(4a-1)+(3a+2)]=2(4a-1+3a+2)=2(4a+3a-1+2)=2(7a+1)=14a+2.

The expression to find the perimeter of the rectangle is 14a + 2.

Perimeter of a straight sided figures or objects is the total length of it's boundary.

Given that,

Sides of a rectangle is represented as 4a - 1 and 3a + 2.

Perimeter of a rectangle is represented as,

Perimeter = 2 (l + w)

Here l is the length and w is the width.

Substituting,

Perimeter = 2 (4a - 1 + 3a + 2)

                = 2(7a + 1)

                = 14a + 2

Hence the expression to find the perimeter is 14a + 2.

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Answer:

Given that A cereal manufacturer decides to offer a new family-sized box based on the regular-sized box. They want the volume of the family-sized box to be three times the volume of the regular-sized box. However, they want the length of the family-sized box to be the same as the regular-sized box.

If original dimensions are l,w and h then volume = lwh

Volume of new box is= 3lwh

But here w becomes 2w and l remains the same.  Let h' be the new height

Then we have

So by 1.5 factor height should be dilated.

Step-by-step explanation:

7h-15h+40=-72

40+72=15h-7h

112=8h

h=14

Answer:

8 units

Step-by-step explanation:

ratios  

(x-3) /( x+1)  = (x-2)/(x+3)     cross multiply

x^2 -x -2 = x^2 - 9

  -x - 2 + 9 = 0

    x = 7          

           so TS = x + 1 = 8 units

Answer:

2,

Step-by-step explanation:

The vertex is the very highest or very lowest point. X coordinates are listed first, then Y.