the probability that 2 randomly selected points from Q,R,S,T and W are noncollinear is

Answer:

The expression in factored form is (3x - 7)(3x + 7)

Step-by-step explanation:

Here in this question, we are interested in using the difference of two squares to factor the given expression.

Mathematically, supposed we have two squares a^2 and b^2, and we are told to factorize a^2-b^2.

By using the difference of two squares;

a^2-b^2 can thus be written as;

(a-b)(a + b)

Now, we can apply same approach to the problem at hand.

9x^2 - 49

kindly note that 9x^2 can be written as ((3x)^2 and 49 can be written as 7^2

So applying what we have said earlier about difference of two squares;

9x^2 - 49 will be ;

(3x-7)(3x + 7)

Answer:

The answer is (3x - 7) (3x +7)

Step-by-step explanation:

Answer:

(-2, 4, 2)

Where x = -2, y = 4, and z = 2.

Step-by-step explanation:

We are given the system of three equations:

[tex]\displaystyle \left\{ \begin{array}{l} 4x -y -2z = -8 \\ -2x + 4z = -4 \\ x + 2y = 6 \end{array}[/tex]

And we want to find the value of each variable.

Note that both the second and third equations have an x.

Therefore, we can isolate the variables for the second and third equation and then substitute them into the first equation to make the first equation all one variable.

Solve the second equation for z:

[tex]\displaystyle \begin{aligned} -2x+4z&=-4 \\ x - 2 &= 2z \\ z&= \frac{x-2}{2}\end{aligned}[/tex]

Likewise, solve the third equation for y:

[tex]\displaystyle \begin{aligned} x+2y &= 6\\ 2y &= 6-x \\ y &= \frac{6-x}{2} \end{aligned}[/tex]

Substitute the above equations into the first:

[tex]\displaystyle 4x - \left(\frac{6-x}{2}\right) - 2\left(\frac{x-2}{2}\right)=-8[/tex]

And solve for x:

[tex]\displaystyle \begin{aligned} 4x+\left(\frac{x-6}{2}\right)+(2-x) &= -8 \\ \\ 8x +(x-6) +(4-2x) &= -16 \\ \\ 7x-2 &= -16 \\ \\ 7x &= -14 \\ \\ x &= -2\end{aligned}[/tex]

Hence, x = -2.

Find z and y using their respective equations:

Second equation:

[tex]\displaystyle \begin{aligned} z&=\frac{x-2}{2} \\ &= \frac{(-2)-2}{2} \\ &= \frac{-4}{2} \\ &= -2\end{aligned}[/tex]

Third equation:

[tex]\displaystyle \begin{aligned} y &= \frac{6-x}{2}\\ &= \frac{6-(-2)}{2}\\ &= \frac{8}{2}\\ &=4\end{aligned}[/tex]

In conclusion, the solution is (-2, 4, -2)

Answer:

x = -2

y =4

z=-2

Step-by-step explanation:

4x−y−2z=−8

−2x+4z=−4

x+2y=6

Solve the second equation for x

x = 6 -2y

Substitute into the first two equations

4x−y−2z=−8

4(6-2y) -y -2 = 8  

24 -8y-y -2z = 8

-9y -2z = -32

−2(6-2y)+4z=−4

-12 +4y +4z = -4

4y+4z = 8

Divide by 4

y+z = 2

z =2-y

Substitute this into -9y -2z = -32

-9y -2(2-y) = -32

-9y -4 +2y = -32

-7y -4 = -32

-7y =-28

y =4

Now find z

z = 2-y

z = 2-4

z = -2

Now find x

x = 6 -2y

x = 6 -2(4)

x =6-8

x = -2

Answer:

The word problem is "How many $25 are there in $125?"

Step-by-step explanation:

Given

[tex]n(\$25) = \$125[/tex]

Required

Write a word problem for the expression

We start by solving the given equation

[tex]n(\$25) = \$125[/tex]

Divide both sides by $25

[tex]\frac{n(\$25)}{\$25} = \frac{\$125}{\$25}[/tex]

[tex]n = \frac{\$125}{\$25}[/tex]

[tex]n = 5[/tex]

This implies that there are 5, $25 in $125

Hence; The word problem is "How many $25 are there in $125?"

Answer:

[tex]\huge\boxed{9,40,46}[/tex]

Step-by-step explanation:

Let's check it using Pythagorean Theorem:

[tex]c^2 = a^2 + b^2[/tex]

Where c is the longest sides, a and b are rest of the 2 sides

1) 9 , 40 , 46

=> [tex]c^2 = a^2 + b^2[/tex]

=> [tex]46^2 = 9^2 + 40^2[/tex]

=> 2116 = 81 + 1600

=> 2116 ≠ 1681

So, this is not a Pythagorean Triplet

2) 16, 30 and 34

=> [tex]c^2 = a^2 + b^2[/tex]

=> [tex]34^2 = 16^2 + 30^2[/tex]

=> 1156 = 256 + 900

=> 1156 = 1156

No need to check more as we've found the one which is not a Pythagorean Triplet.

Answer:

Option A is the correct option.

Step-by-step explanation:

1. Let h , p and b are the hypotenuse , perpendicular and base of a right - angled triangle respectively.

From Pythagoras theorem,

[tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex]

Here, we know that the hypotenuse is always greater than perpendicular and base,

h = 46 , p = 40 , b = 9

⇒[tex] \sf{ {46}^{2} = {40}^{2} + {9}^{2} }[/tex]

⇒[tex]2116 = 1600 + 81[/tex]

⇒[tex] \sf{2116  ≠ 1681}[/tex]

Thus , the relation [tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex] is not satisfied by h = 46 , p = 40 , b = 9

So, The set of numbers 9 , 40 , 46 is not Pythagorean triple.

------------------------------------------------------

2. 16 , 30 , 34

h = 34 , p = 30 , b = 16

[tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex]

⇒[tex] \sf{ {34}^{2} = {30}^{2} + {16}^{2} }[/tex]

⇒[tex] \sf{1156 = 900 + 256}[/tex]

⇒[tex] \sf{1156 = 1156}[/tex]

The relation [tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex] is satisfied by the particular values of h , p and b i.e h = 34 , p = 30 , b = 16

So, the set of numbers 16 , 30 , 34 is a Pythagorean triple.

------------------------------------------------------

3. 10, 24 , 26

h = 26 , p = 24 , b = 10

[tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex]

⇒[tex] \sf{ {26}^{2} = {24}^{2} + {10}^{2} }[/tex]

⇒[tex] \sf{676 = 576 + 100}[/tex]

⇒[tex] \sf{676 = 676}[/tex]

The relation [tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex] is satisfied by the particular values of h , p and h i.e h = 26 , p = 24 , b = 10

So, the set of numbers 10, 24 , 26 is the Pythagorean triple.

-----------------------------------------------------

4. 50 , 120 , 130

h = 130 , p = 120 , b = 50

[tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex]

⇒[tex] \sf{ {130}^{2} = {120}^{2} + {50}^{2} }[/tex]

⇒[tex] \sf{16900 = 14400 + 2500}[/tex]

⇒[tex] \sf{16900 = 16900}[/tex]

The relation [tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex] is satisfied by the particular values of h , p and b i.e h = 130 , p = 120 , b = 50

So, the set of numbers 50, 120 , 130 is the Pythagorean triple.

-----------------------------------------------------

In this way, to satisfy the Pythagoras Theorem , the hypotenuse ( h ) , perpendicular ( p ) and the base ( b ) of a right - angles triangle should have the particular values in order. These values of h , p and b are called Pythagorean triple.

Hope I helped!

Best regards!!

Answer:

Step 1: Isolate the absolute value expression.

Step2: Set the quantity inside the absolute value notation equal to + and - the quantity on the other side of the equation.

Step 3: Solve for the unknown in both equations.

Step 4: Check your answer analytically or graphically.

Step-by-step explanation:

Answer:

Rewrite the absolute value equation as two separate equations, one positive and the other negative

Solve each equation separately

After solving, substitute your answers back into original equation to verify that you solutions are valid

Write out the final solution or graph it as needed

Step-by-step explanation:

Answer:

75 cm

Step-by-step explanation:

∅=90° , r = 21 cm

Arc length= (2πr∅)/360

=(2π×21×90)/360

=33 cm

Perimeter= arc length + 2(radius)

=33+2(21)

=33 + 42

= 75 cm

Answer:

I hope this will help!

Step-by-step explanation:

Answer:

It is reduced to the equation of the Theorem of Pythagoras.

Step-by-step explanation:

Any triangle can be modelled by this formula under the Law of Cosine:

[tex]b = \sqrt{a^{2}+c^{2}-2\cdot a\cdot c\cdot \cos B}[/tex]

Where:

[tex]a[/tex], [tex]b[/tex], [tex]c[/tex] - Side lengths, dimensionless.

[tex]B[/tex] - Angle opposed to the side [tex]b[/tex], measured in sexagesimal degrees.

Now, let suppose that angle B is a right angle (90º), so that b is a hypotenuse and a and c are legs. Hence:

[tex]\cos B = 0[/tex]

And the equation is reduced to the form of the Theorem of Pythagoras, that is to say:

[tex]b = \sqrt{a^{2}+c^{2}}[/tex]

Answer & Step-by-step explanation:

For this problem, we have two inequalities to solve for x.

3x - 91 > -87

17x - 16 > 18

Now that we know what our inequalities are, we will solve them as if we are solving for the value of x.

3x - 91 > -87

Add 91 on both sides.

3x > 4

The solution for the first inequality is 3x > 4

Now let's do the second inequality.

17x - 16 > 18

Add 16 on both sides.

17x > 34

Divide by 17 on both sides.

x > 2

The soultion for the second inequality is x > 2

Answer:

The answer is x>2

Step-by-step explanation:

Answer: $10

Step-by-step explanation:

let x = the price of green fabric, then x+2 = blue fabric price

8x+5(x+2)=62

8x+5x+10=62

    13x+10=62

          13x=52

              x=4

price of green fabric=$4

price of blue fabric=$6

4+6=$10

Answer:

[tex]\huge \boxed{\mathrm{-1}}[/tex]

Step-by-step explanation:

[tex](5xe^2 - 3x) - (5xe^2 - 3x+1)[/tex]

Distribute negative sign.

[tex]5xe^2 - 3x- 5xe^2 +3x-1[/tex]

Combine like terms.

[tex]0xe^2 +0x-1[/tex]

[tex]0-1=-1[/tex]

-5,3,-2,1 on a number line

<-|----|----|----|----|----|----|----|----|->

-5 -2 0 1 3

Answer:

The decimal value of the volume already given= 1885.2 unit³

For radius 11 unit height 12 unit

Volume= 484π unit³

Volume= 1520.73 unit ³

For radius 4 unit height 6 unit

Volume= 32π unit³

Volume= 100.544 unit³

For radius 20 unit height 15 unit

Volume= 2000π unit³

Volume= 6284 unit³

Step-by-step explanation:

The decimal value of the volume already given= 600π

The decimal value of the volume already given= 600*3.142

The decimal value of the volume already given= 1885.2 unit³

For radius 11 unit height 12 unit

Volume= πr²h/3

Volume= 11²*12/3 *π

Volume= 484π unit³

Volume= 1520.73 unit ³

For radius 4 unit height 6 unit

Volume = πr²h/3

Volume= 4²*6/3(π)

Volume= 32π unit³

Volume= 100.544 unit³

For radius 20 unit height 15 unit

Volume= πr²h/3

Volume= 20²*15/3(π)

Volume= 2000π unit³

Volume= 6284 unit³

Here's the right answer.

distance of a point [tex](x,y)[/tex] from origin is $\sqrt{x^2+y^2}$

so distance is $\sqrt{(-15)^2+(8)^2}=\sqrt{225+64}=\sqrt{289}=17$

Answer:

Distance=17 units

Step-by-step explanation:

Coordinates of the origin: (0, 0)

Coordinates of the point in question: (-15, 8)

Distance formula for any two points [tex](x_1,y_1), (x_2,y_2)[/tex] on the plane:

[tex]distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\distance=\sqrt{(-15-0)^2+(8-0)^2}\\distance=\sqrt{(15)^2+(8)^2}\\distance=\sqrt{225+64} \\distance=\sqrt{289} \\distance=17[/tex]

Answer:

−5 < x < 10

Step-by-step explanation:

−6 < x − 1 < 9

Add 1 to all sides

−6+1 < x − 1+1 < 9+1

−5 < x < 10

Answer:

B

Step-by-step explanation:

Add one to everything

-5 < x < 10

Best of Luck!

Answer:

y  = 0.45X + 39  

hope it helps.I was reading the same chapter

Answer:

900 outfits

Step-by-step explanation:

You just have to multiply them all together :)

a)

X + Y = 5

2X - Y = 9      

X + 2X + Y - Y = 5 + 9

3X = 14

Para Y, basta substituir o valor de X em qualquer uma das 2 equacoes - arbitrariamente. Escolhendo a primeira:

X+ Y = 5

14/3 + Y = 5

Y = 5 - 14/3

.........................

b)

3X - Y = 10

X + Y = 18        

3X + X - Y + Y = 10 + 18

4X = 28

Para Y, basta substituir o valor de X em qualquer uma das 2 equacoes - arbitrariamente. Escolhendo a segunda:

X + Y = 18

7 + Y = 18

Y = 18 - 7

Answer:

3x+11y-3

Step-by-step explanation:

Hey! So here is what you do to solve the problem-

Combine like terms:

(x) 5x-2x=3x

(y) 3y+8y=11y

(#) 7-10 =-3

So....

3x+11y-3 is your answer!

Hope this helps!:)

[tex](-3+5,10-7)=(2,3)[/tex]

Sandy got 350 out of 2400.

Her portion is 350/2400 which can be reduced to:

35/240 = 7/48

The portion is 7/48

Answer:

[tex]\large \boxed{1296}[/tex]

Step-by-step explanation:

6 raised to 4 indicates that the base 6 has an exponent or power of 4.

[tex]6^4[/tex]

6 is multiplied by itself 4 times.

[tex]6 \times 6 \times 6 \times 6[/tex]

[tex]=1296[/tex]

Answer:

Step-by-step explanation:

When the quadratic is written in vertex form:

  x = a(y -k)^2 +h

the vertex is (x, y) = (h, k), and the length of the latus rectum is 1/a.

For your given equation, ...

  x = (1/2)(y -5)^2 +7

you have a=1/2, k = 5, h = 7, so ...

  the vertex is (7, 5)

  the length of the latus rectum is 1/(1/2) = 2

Answer:

as ratio of two type of fabric is different .

hence, the relationship between the number of square yards and the cost

is not proportional between the two types of fabric

Step-by-step explanation:

For a relation to be proportional

a:b = c:d

in other form

a/b = c/d

______________________________________________

Ratio for first type of fabric

cost of fabric/ area of fabric = 31.25/5 = 6.25

Ratio for other type of fabric

cost of fabric/ area of fabric = 71.50/11 = 6.5

as ratio of two type of fabric is different .

hence, the relationship between the number of square yards and the cost

is not proportional between the two types of fabric

Answer:

JK = 6.86

Step-by-step explanation:

The parameters given are;

LJ = 14

JM = 48

LM = 50

[tex]tan(\angle JML )= \dfrac{Opposite \ leg \ length}{Adjacent \ leg \ length} = \dfrac{LK}{JM} = \dfrac{14}{48} = \dfrac{7}{24}[/tex]

[tex]tan \left( \dfrac{7}{24} \right)= 16.26 ^{\circ }[/tex]

∠JML = 16.26°

Given that ∠JML is bisected by KM, we apply the angle bisector theorem which states that a ray that bisects an interior angle of a triangle bisects the opposite (bisected angle facing side) in the proportion of the ration of the other two sides of the triangle.

From the angle bisector theorem, we have;

LM/JM = LK/JK

50/48 = LK/JK................(1)

LK + KJ = 14.....................(2)

From equation (1), we have;

LK = 25/24×JK

25/24×KJ + JK = 14

JK×(25/24 + 1) = 14

JK × 49/24 = 14

JK = 14×24/49 = 48/7. = 6.86.

JK = 6.86

Answer:

1) B. The differences are normally distributed or the sample size is large

C. The  sample size mus be large

E. The sampling method results in an independent sample

2) The null hypothesis H₀:  [tex]\bar x_1[/tex] =  [tex]\bar x_2[/tex]

The alternative hypothesis Hₐ: [tex]\bar x_1[/tex] <  [tex]\bar x_2[/tex]

Test statistic, t = -0.00693

p- value = 0.498

Do not reject Upper H₀ because, the P-value is greater than the level of significance. There is sufficient evidence to conclude that sons are the same height as their fathers  at 0.10 level of significance

Step-by-step explanation:

1) B. The differences are normally distributed or the sample size is large

C. The  sample size mus be large

E. The sampling method results in an independent sample

2) The null hypothesis H₀:  [tex]\bar x_1[/tex] =  [tex]\bar x_2[/tex]

The alternative hypothesis Hₐ: [tex]\bar x_1[/tex] <  [tex]\bar x_2[/tex]

The test statistic for t test is;

[tex]t=\dfrac{(\bar{x}_1-\bar{x}_2)}{\sqrt{\dfrac{s_{1}^{2} }{n_{1}}-\dfrac{s _{2}^{2}}{n_{2}}}}[/tex]

The mean

Height of Father, h₁,  Height of Son h₂

72.4,      77.5

70.6,      74.1

73.1,       75.6

69.9,      71.7

69.4,      70.5

69.4,      69.9

68.1,       68.2

68.9,      68.2

70.5,       69.3

69.4,       67.7

69.5,       67

67.2,       63.7

70.4,       65.5

[tex]\bar x_1[/tex]  = 69.6      

s₁ = 1.58

[tex]\bar x_2[/tex] = 69.9

s₂ = 3.97

n₁ = 13

n₂ = 13

[tex]t=\dfrac{(69.908-69.915)}{\sqrt{\dfrac{3.97^{2}}{13}-\dfrac{1.58^{2} }{13}}}[/tex]

(We reversed the values in the square root of the denominator therefore, the sign reversal)

t = -0.00693

p- value = 0.498 by graphing calculator function

P-value > α Therefore, we do not reject the null hypothesis

Do not reject Upper H₀ because, the P-value is greater than the level of significance. There is sufficient evidence to conclude that sons are the same height as their fathers  at 0.10 lvel of significance

Answer:

Given the information above, the area of the square is 361 cm²

Step-by-step explanation:

A square is a shape with four equal sides. So, in order to find the area of the square, we must find the length of each individual side. We can do this by dividing the perimeter by 4 because a square has 4 equal sides meaning they have the same lengths.

The perimeter of the square is 76. So, let's divide 76 by 4.

76 ÷ 4 = 19

So, the lengths of each sides in the square is 19cm.

In order to find the area, we must multiply the length and the width together. Since a square has equal sides, then we will multiply 19 by 19 to get the area.

19 × 19 = 361

So, the area of the square is 361 cm²

Answer:

361 cm^2

Step-by-step explanation:

The area of a square can be found by squaring the side length.

[tex]A=s^2[/tex]

A square has four equal sides. The perimeter is the sum of all four sides added together. Therefore, we can find one side length by dividing the perimeter by 4.

[tex]s=\frac{p}{4}[/tex]

The perimeter is 76 centimeters.

[tex]s=\frac{76 cm}{4}[/tex]

Divide 76 by 4.

[tex]s=19 cm[/tex]

The side length is 19 centimeters.

Now we know the side length and can plug it into the area formula.

[tex]A=s^2\\s=19cm[/tex]

[tex]A= (19 cm)^2[/tex]

Evaluate the exponent.

(19cm)^2= 19 cm* 19cm=361 cm^2

[tex]A= 361 cm^2[/tex]

The area of the square is 361 square centimeters.

Answer:

The volume of the pyramid is 867 inch^3

Step-by-step explanation:

Here in this question, we are interested in calculating the volume of a square based pyramid.

Mathematically, we can use the formula below to calculate the volume V of a square based pyramid.

V = a^2h/3

where a represents the length of the side of the square and h is the height of the pyramid

From the question, the length of the side of the square is 17 in while the height is 9 in

Plugging these values, we have ;

V = (17^2 * 9)/3 = 17^2 * 3 = 867 cubic inch

Answer:

4ny²+4n²-4n-8+y⁴-2y²