How does the figure help verify the triangle inequality theorem?

The line is drawn from a length of 15,  two lines constructing a triangle and intersecting the arc from a length of the lines 7, 4
A.
by showing that a triangle cannot be formed when the sum of the lengths of two sides is less than the length of the third side
B.
by showing that only one triangle can be formed when the sum of the lengths of two sides equals the length of the third
C.
by showing that only one triangle can be formed when the sum of the lengths of two sides is less than the length of the third
D.
by showing that a triangle cannot be formed when the sum of the lengths of two sides equals the length of the third

Answer:

Step-by-step explanation:

1)  The equation of circle  having center at origin:

       x² + y² = r²

Where 'r' is the radius.

diameter = 36

r = 36 ÷ 2 = 18

  Equation of circle :

      x² + y² = 18²

       x² + y² = 324

Option d.

2) Find the discriminant D.

 If  D > 0, then the quadratic equation has two distinct real roots.

  If  D= 0, then the quadratic equation has two identical real roots.

  If  D < 0, then the quadratic equation has no real roots.

  D = b² - 4ac

 x² - 6x + 9 = 0

a = 1  ; b = -6 ; c = 9

D = (-6)² - 4*1*9

  = 36 - 36

D = 0

As D = 0, the quadratic equation has two identical real roots

Option a.

3) The axis of symmetry of a parabola is the vertical line passing through the vertex. It will be middle of the x-intercepts.

X- intercepts are -8 , 2

 ( -8 + 2 ) ÷ 2 = -6 ÷ 2  =  -3

x = - 3

Option d.

Answer:

a = 2

b = 11

c = 11

d = -2

Step-by-step explanation:

[tex]\sf \left[\begin{array}{cc}a&b\\c&d \end{array}\right] *\left[\begin{array}{ccc} 22&11&7\\ 6&-9&-15 \end{array}\right] =\left[\begin{array}{ccc} 22a+6b&11a-9b&7a-15b\\22c+6d&11c-9d&7c-15d \end{array}\right][/tex]

   [tex]\sf \left[\begin{array}{ccc} 22a+6b&11a-9b&7a-15b\\22c+6d&11c-9d&7c-15d \\ \end{array}\right] =\left[\begin{array}{ccc} 110&-77&-151\\230&139&107 \\ \end{array}\right][/tex]  

On comparing to right side, we get,

 22a + 6b = 110

Divide the entire equation by 2

   11a + 3b = 55  ------------(I)

 11a   - 9b  = -77  -------------(II)

Subtract equation (II) from (I)

       11a + 3b = 55

       11a - 9b = -77

      -      +        +     {Now subtract}

               12b = 132

                 b = 132/12

[tex]\sf \boxed{\bf \ b = 11}[/tex]

Substitute the value of b in eqaution (I)

  11a + 3*11 = 55

  11a + 33   = 55

             11a = 55 - 33

             11a = 22

               a = 22/11

      [tex]\sf \boxed{\bf \ a = 2}[/tex]

           22c + 6d = 230

Divide by 2

           11c + 3d = 115  -----------------(III)

           11c - 9d  = -139 ------------------(IV)

Subtract (IV) from (III)

           11c + 3d  = 115

           11c - 9d  = 139

           -     +         -      

                  12d  =  -24

                      d = -24/12

                     [tex]\sf \boxed{\bf \ d = -2}[/tex]

Plugin d = - 2 in equation (III)

    11c + 3*(-2) = 115

     11c  - 6      = 115

                11c  = 115 + 6

               11c = 121

                  c = 121/11

                 [tex]\sf \boxed{\bf \ c = 11}[/tex]

Answer: 1. an = n + 4,   2. ( 3 1/2, 3.5, 5),   3. 6 1/12,   4. 97,   5. 0.2 meters,    6. 4.52,   7. 3 1/18

Step-by-step explanation:

The rate of change is also known as the slope. The formula to find the slope of a line is (y2 - y1) / (x2 - x1).

You can use any two points, as long as both are on the line.

Point 1 = (2, 55)

Point 2 = (8, 220)

slope = (220 - 55) / (8 - 2)

slope = 165 / 6

slope = 55 / 2 = 27.5 / 1

Lavaughn earns $27.50 for working one hour.

Hope this helps!

Answer:

K = 17

Based on the given conditions, formulate: 

51 / 3 = k

Swap the sides : k = 51 / 3

Cross out the common factor: k = 17

The figure which is like a long oval can be decomposed to two semicircles and a rectangle so as to find the area.

Given a long oval and two lines are drawn where the sides are straight to form right angles.

We are required to find the way how we can decompose the composite figure to determine its area.

Area means the amount of space occupied by a two dimensional shape or object. The area of a figure can be decomposed to smaller figures so as to find the area.

The composed figure can be decomposed to two semicircles and a rectangle so as to find the area.

Hence the composite figure can be decomposed to two semicircles and a rectangle so as to find the area.

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Answer:

a

Step-by-step explanation:

1. The average rate of change in a riders height between 1 and 3 seconds -30 ft/s

2. The average rate of change in a riders height between 0 and 5 seconds -24 ft/s

3. Another word for rate of change in this situation is speed

Speed is defined as the rate of change of the distance travelled with time. Mathematically, it can be expressed as:

Speed = distance / time

With the above idea, we can obtain the answers to the question given above.

Rate = Change in height / change in time

Rate = -60 / 2

Rate = -30 ft/s

Rate = Change in height / change in time

Rate = -120 / 5

Rate = -24 ft/s

From the definition of speed given above, we can say that: another word for rate of change is speed

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The odds in favor of winning $5 or more is 3 : 13

The odds of winning $5 or more can be determined by finding the ratio of the total value of tickets that have a value of $5 or greater to the total value of tickets.

Total number  of the tickets that have a value of $5 or more = 25 + 5 = 30

Total number of ticket  = 25 + 5 + 100 = 130

Ratio : 30 : 130

3 ; 13

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Answer:

Cookies = 44

Step-by-step explanation:

universal U=60

let the number of cookies be C,

n(C)=(3*b)-4

and the number of brownies be b,

n(b)=?

n(buc)=60

b+c=60

then, c=60-b

substitute for c=60-b.

60-b=3b-4

60+4=3b+b

64=4b

b=16

c=60-b

c= 60-16

c=44

n/3n - 2.

The denominator of the given simplified expression is

The given expression is ( 2n/6n + 4 ) ( 3n + 2/ 3n - 2 )

To find the denominator of the simplified expression :

First, simplify the given expression as below ;

( 2n/6n + 4 ) ( 3n + 2/ 3n - 2 )

( 2n/2₍₃ₙ ₊ ₂₎ ( 3n + 2/ 3n - 2 )  ( here by taking the common term 2 outside the factor )

= (n/1) ( 1/ 3n - 2 ) ( here by simplifying the factors )

= n/3n - 2.

Therefore, ( 2n/6n + 4 ) ( 3n + 2/ 3n - 2 ) = n/3n - 2

Therefore the result of the given simplified expression is = n/3n - 2.

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Let [tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex] be the nonzero rows of [tex]$R$[/tex] starting from the 1st row to the [tex]k[/tex]th row.

Step 1: We want to show that

R(R)= span [tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex]

For any vector [tex]v $$\in \mathcal{R}(R)$$[/tex], We may write

v= [tex]$$c_{1} \boldsymbol{r}_{1}+c_{2} \boldsymbol{r}_{2}+\cdots+c_{k} \boldsymbol{r}_{k}+c_{k+1} \mathbf{0}+\cdots+c_{m} \mathbf{0}$$[/tex]

Then v= [tex]$$c_{1} r_{1}+c_{2} r_{2}+\cdots+c_{k} r_{k}$$[/tex]

So [tex]v[/tex] belongs to span{ [tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex]}

Thus R(R)[tex]\leq[/tex] Span [tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex]

But trivially,

span [tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex]≤ span{[tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex], 0, . . . , 0} = R(R),

span [tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex]=R(R)

Step 2: We want to show that  [tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex]are linearly independent. Suppose otherwise,

then we can write

[tex]$$c_{1} \boldsymbol{r}_{i_{1}}+\cdots+c_{\ell} \boldsymbol{r}_{i_{\ell}}=\mathbf{0}$$[/tex]

From Steps 1 and 2, we have proven that the nonzero rows of R form a basis for the row space.

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Answer:

A' (-15, -5)

B' (10, -10)

C' (-5, -20)

Answer:

A ' (-15, -5)

B ' (10, -10)

C ' (-5, -20)

Step-by-step explanation:

The scale factor is [tex]K=5[/tex]. This tells us to multiply each coordinate, of each point, by the scale factor (5) to get the dilated points.

Point A is at [tex](-3,-1)[/tex] and moves to [tex]A ' (-15, -5)[/tex] after multiplying the x and y coordinates by 5. The same applies to points B and C as well.

Point B moves from [tex](2,-2)[/tex] to [tex]B' (10,-10)[/tex] because [tex]2*5=10[/tex] and [tex]-2*5=-10[/tex]. This also means that Point C moves from [tex](-1,-4)[/tex] to [tex]C' (-5,-20)[/tex] because  [tex]-1*5=-5[/tex] and [tex]-4*5=-20[/tex].

The dilation rule can be written as [tex](x, y)[/tex] → [tex](5x, 5y)[/tex]

As a result of the dilation, triangle A'B'C' has sides that are 5 times longer compared to the corresponding sides of triangle ABC.

The surface area of the shape is 168 square cm

The surface area of a figure is the area of the faces of the given figure.

For the given figure, the area will be the sum of area of 2 triangles and 3 rectangles.

Area = (6*3) +(10*6)+(6+10) +(10*3)

Surface area = 18 + 120 + 30

Surface area = 168 square cm

Hence the surface area of the shape is 168 square cm

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The length of an edge of a cube is 5 feet.

In Geometry, a Cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges.

Total surface area of a cube = 6[tex]l^{2}[/tex]

Given that,

Total surface area of a cube = 150 square feet

Total surface area of a cube = 6[tex]l^{2}[/tex]

[tex]\Rightarrow[/tex]                                  150 = 6[tex]l^{2}[/tex]

[tex]\Rightarrow[/tex]                                     [tex]l^{2}[/tex] =  [tex]\frac{150}{6}[/tex]

[tex]\Rightarrow[/tex]                                     [tex]l^{2}[/tex] = 25

[tex]\Rightarrow[/tex]                                    l [tex]=\sqrt{25}[/tex]

[tex]\Rightarrow[/tex]                                    l = 5 feet

Hence, the length of an edge of a cube is 5 feet.

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For birthday events 33/100 gifts were packed by the music boosters at the mall.

Total number of gift items = 100

For the wedding purpose,out of 100 gifts, 3/10 number of gifts were boxed = 3/10*100 = 30

For the baby shower, out of 100 gifts, 37/100 gifts were packed = 37

The rest amount of the gift = 100-( wedding + baby shower)

= 100-(30+37) = 33

So, according to the question, these 33 numbers gift was for a birthday.

When it is expressed as a fraction,

The fraction should be = 33/100

Therefore, it is concluded that 33/100 gifts were packed for birthday occasions.

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The two cars lying on one side of the plane are 50 meters apart.

An equation is an expression that shows the relationship between two or more numbers and variables.

let us assume that the height is 100 m. Let d represent the horizontal distance. For depression of 38°, Ф = 90 - 38 = 52°, hence:

tan(52°) = d / 100

d = 128 m

For depression of 52°, Ф = 90 - 52 = 38°, hence:

tan(38°) = d / 100

d = 78 m

Distance apart = 128 - 78 = 50 m.

The two cars lying on one side of the plane are 50 meters apart.

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The correct option is C.

The formula that could be used to represent a  function w is

= w(x)=v(x-7)+7

A polynomial divided by another polynomial can be used to represent a rational function. Since polynomials are defined everywhere, the set of all numbers excluding the zeros in the denominator constitutes the domain of a rational function.

Example 1. x = f(x) (x - 3). The denominator, x = 3, only contains one zero. When the denominator is zero, rational functions are no longer defined.

According to the given Information:

Rational functions whose point of discontinuity is at x=7.

When a point of discontinuity exists for a rational function,

It occurs when:

q(x) = r(x-a),  x=a

In this instance, we are required to notice the following relationship, which is a union of a parent rational function and a vertical translation:[tex]w(x)=v(x-a)+k\\ \forall k \in \mathbb{R}[/tex], (2)

If we are aware of a=7 and k=7 .

The equation that could be used to represent a  function w is. w(x)=v(x-7)+7

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I understand that the question you are looking for is:

Rational functions v and w both have a point of discontinuity at x = 7. Which equation could represent function w?

A. w(x)=v(x-7)

B. w(x)=v(x+7)

C. w(x)=v(x-7)+7

D. w(x)=v(x)+7

The extreme drop can be said to most likely represent: b. A reflection of the migratory nature of the birds at the lake.

Bird migration is a natural process which can be described as a the movement of different birds by flight across thousands of kilometers in search of ecological conditions and habitats that favors breeding, feeding, and raising of their young.

Migratory birds have well built physiology and morphology that make them better equip to fly fast and across long distances in search of the best ecological conditions, which is dependent on seasons.

Like in the graph given, like we see that at the beginning of January, number of birds were few in the lake until sudden increase occurred. It can be said that during those period of increase, the ecological conditions favored the survival of the bird until November and December. This extreme drop can be said to most likely represent: b. A reflection of the migratory nature of the birds at the lake.

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Rule 1:

1, 3, 7, 15, 31, 63, 127, 255, 511, 1023 etc

Rule 2:

40, 24, 16, 12, 10, 9, 8.5, 8.25, 8.125, 8.0625 etc

Hope this helps!

The perimeter of the mat is 4m and the area of the mat is [tex]m^{2}[/tex].

The complete length of a square's boundary is referred to as its perimeter. To get the perimeter of a square, we must add all of its sides.

Perimeter of square = sum of the length  of all 4 sides.

In the question side of the mat is m.

Perimeter of the mat = m + m + m + m

                                   = 4m.

Therefore, the perimeter of the mat is 4m.
What is the area of the square?

The total number of unit squares in a square's shape is used to calculate its area.

Area = (Side x Side)

Since, side of the mat is m.

Area of the mat = m x m

                           = [tex]m^{2}[/tex]

Therefore, the area of the mat is [tex]m^{2}[/tex].

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Answer:

1.) The slope is 2

2.) The y-intercept is (0,1)

3.) y = 2x + 1

Step-by-step explanation:

1.) you can either use rise over run or the slope formula. rise over run is quicker, but here's the formula:

you can use any two points on the line, i chose (2, 5) and (1, 3)

[tex]\frac{(y_{2}-y_{1})}{(x_{2}-x_{1})} \\[/tex]

[tex]\frac{3-5}{1-2} \\\\\frac{-2}{-1} \\\\\frac{2}{1} \\\\2[/tex]

2.) for the y-intercept, you just look for the point where the graph crosses the y-axis and x = 0

3.) using the formula y = mx + b, m being the slope and b being the y-intercept, you take the information above and plug it in to get y = 2x + 1

i hope this helped!

Answer:

[tex]d=\frac{t}{12}+\frac{4}{3}[/tex]

Step-by-step explanation:

The average rate of change is (10-6)/(104-56) = 1/12.

So, the equation is of the form d = t/12 + c for some constant c.

Substituting in d=6 and t=56 gives that c=4/3.

So, the equation is

[tex]d=\frac{t}{12}+\frac{4}{3}[/tex]

They form supplementary angles when they are added together.

Reason for Being Called Supplementary Angles

It is given that the angle made by the wall in one room is 36° and the angle formed by the same wall in the other room is 144°.

This implies that,

∠1 = 36°

∠2 = 144°

∠1 and ∠2 are adjacent angles and,

∠1 + ∠2 = 36° + 144°

⇒ ∠1 + ∠2 = 180°

Hence, these two adjacent angles make a straight-line angle. Hence, they are supplementary angles.

What are supplementary angles?

Two angles that form a straight line angle, that is, angle equal to 180°, when they are added together are said to be a pair of supplementary angles.

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Answer:

p = 21.4 cm

∠P = 44°

Step-by-step explanation:

Apply the Pythagorean Theorem to solve for the length of p.

Now, take the inverse sine function to find angle P :

Answer:

  a) 21.4 cm

  b) 45.6°

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relationships between trig functions and sides of a right triangle. Here, two relevant function are ...

  Cos = Adjacent/Hypotenuse

  Tan = Opposite/Adjacent

The hypotenuse of the triangle, and the side adjacent to angle P are given, so we have ...

  cos(P) = (21 cm)/(30 cm)

The angle value can be found using the inverse cosine function:

  P = arccos(21/30)

  P ≈ 45.6°

Now, we know angle P and the side adjacent to it. We want to find the measure of side p, which is opposite the angle. This can be done using either the sine function or the tangent function. Here, we choose to use the tangent function.

  tan(P) = p/21

  p = 21×tan(P) = 21·tan(45.573°)

  p ≈ 21.4 . . . . cm

__

Additional comment

In the attached, part of the calculator keypad is shown so you can see that the inverse cosine function is the 2ND function of the Cos key. The calculator mode is set to DEG (lower left of display) so that angles are in units appropriate to this problem.

Of course, you can always use the Pythagorean theorem to find the length of side p. More calculations are involved, so we used trig functions instead. Note that the angle P must be found first using the approach here, and its value must be retained with enough significant digits to ensure accuracy in the 'p' calculation.

The possible outcomes are WH, BH, BH, BH, RH, RH, WL, BL, BL, BL, RL, RL

The given parameters are:

Coin = Head (H) and Tail (T)

Marble = W, B, B, B, R, R

See attachment for the tree diagram

From the tree diagram, we have the following possible outcomes

WH, BH, BH, BH, RH, RH, WL, BL, BL, BL, RL, RL

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Nani could purchase her pineapple from stores A, D, and E.

Given Information

It is given that Nani needs to purchase  8 cups of pineapple.

The unit prices of pineapple at each store is as follows,

Store A : 0.49

Store B : 0.51

Store C : 0.55

Store D : 0.48

Store E : 0.45

Amount that Nani has = $4

Reason Behind Purchasing From Either A, D, or E

Since Nani has amount of $4, she can purchase pineapple only from the stores where the total cost of 8 pineapple cups adds up to less than $4. The purchase of 8 pineapple cups at each store would be given as,

Store A : 0.49(8) = $3.92

Store B : 0.51(8) = $4.08

Store C : 0.55(8) = $4.40

Store D : 0.48(8) = $3.84

Store E : 0.45(8) = $3.60

As it can be seen, Nani can purchase from the store A, D, and E as it falls within her budget of $4.

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Answer: x² + 4x +3=0

Step-by-step explanation:

Add 4x to both sides.

Answer:

Step-by-step explanation:

A = 4 ft

B = 10 ft

C = 8 ft

D = 6 ft

b) Area of rectangle = length * width

Area of 2 triangle = base * height

Area of right triangular prism = area of 2 triangles +area of left rectangle + area of middle rectangle + area of right rectangle

  = 6 * 8  + 4* 6 + 4 * 10 + 4 * 8

  = 48 + 24 + 40 + 32

  = 144 ft²

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Formulas:}[/tex]

[tex]\huge\text{Area of rectangle is: }\huge\boxed{\rm{\bold{w}idth \times \bold{h}eight = \bold{a}rea}}[/tex]

[tex]\huge\text{Area of triangle is: }\huge\boxed{\rm{\dfrac{1}{2} \times \bold{b}ase \times \bold{h}eight = \bold{a}rea}}[/tex]

[tex]\huge\textbf{Now, that we have that out of the}\\\\\huge\textbf{way, we can label your given equation:}[/tex]

[tex]\rm{A \rightarrow 4\ \boxed{\rm{ft}}}\\\\\rm{B \rightarrow 10\ \boxed{\rm{ft}}}\\\\\rm{C \rightarrow 8 \ \boxed{\rm{ft}}}\\\\\rm{D \rightarrow 6\ \boxed{\rm{ft}}}[/tex]

[tex]\huge\textbf{What should your equation look like?}[/tex]

[tex]\rm{6\times 8 + 4\times 6 + 4 \times 10 + 4 \times 8}[/tex]

[tex]\huge\textbf{What should it look like when we're}\\\huge\textbf{solving for the answer?}[/tex]

[tex]\rm{6\times 8 + 4\times 6 + 4 \times 10 + 4 \times 8}[/tex]

[tex]\rm{= 48 + 4\times6 + 4\times10 + 4\times8}[/tex]

[tex]\rm{= 48 + 24 + 4 \times 10 + 4\times8}[/tex]

[tex]\rm{= 72 + 4\times 10 + 4\times8}[/tex]

[tex]\rm{= 72 + 40 + 4\times8}[/tex]

[tex]\rm{= 112 + 4\times8}[/tex]

[tex]\rm{= 112 + 32}[/tex]

[tex]\rm{= 144}[/tex]

[tex]\huge\textbf{What is the answer?}[/tex]

[tex]\huge\boxed{\textsf{Answer: }\boxed{\frak{144\ ft^2}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

$600

Step-by-step explanation:

For 8 hours she makes $120

For 1 hour she makes $120÷8 = $15

For 40 hours she makes $15 × 40 = $600

Our final answer is $600

Hope this helped and have a good day