please help with all the questions

Given :

Three points ,  P(4, 3, 4), Q(2, 1, 3), R(2, 7, 0) .

To Find :

The length of sides .

Given :

We know , length of two points P(x,y ,z) and Q(a,b,c) is given by :

[tex]L=\sqrt{(x-a)^2+(y-b)^2+(z-c)^2}[/tex]

Length of PQ :

[tex]PQ=\sqrt{(4-2)^2+(3-1)^2+(4-3)^2}\\\\PQ=\sqrt{4+4+1}=\sqrt{9}\\\\PQ=3[/tex]

Length of QR :

[tex]QR=\sqrt{(2-2)^2+(1-7)^2+(3-0)^2}\\\\QR=\sqrt{0+6^2+3^2}\\\\QR=\sqrt{36+9}\\\\QR=\sqrt{45}\\\\QR=3\sqrt{5}[/tex] :

Length of RP :

[tex]RP=\sqrt{(2-4)^2+(7-3)^2+(0-4)^2}\\\\RP=\sqrt{2^2+4^2+4^2}\\\\RP=\sqrt{4+16+16}\\\\RP=\sqrt{36}\\\\RP=6[/tex]

Hence , this is the required solution .

Answer:

[tex]\dfrac{\pi}{6}, \dfrac{5\pi}{6}, \dfrac{3\pi}{2}[/tex]

Step-by-step explanation:

Given the quadratic equation as:

[tex]2sin^2x+sinx=1\\OR\\2sin^2x+sinx-1=0[/tex]

Let us put [tex]sinx=y[/tex] for simplicity of the equation:

Now, the equation becomes:

[tex]2y^2+y-1=0[/tex]

Now, let us try to solve the quadratic equation:

[tex]\Rightarrow 2y^2+2y-y-1=0\\\Rightarrow 2y(y+1)-1(y+1)=0\\\Rightarrow (2y-1)(y+1)=0\\\Rightarrow 2y-1 = 0, y+1 = 0\\\Rightarrow y = \dfrac{1}{2}, y = -1[/tex]

So, the solution to the given trigonometric quadratic equation is:

[tex]sinx = \dfrac{1}{2}[/tex]

and

[tex]sinx=-1[/tex]

Let us try to find the values of [tex]x[/tex] in the interval [tex][0, 2\pi)[/tex].

[tex]sin\theta[/tex] can have a value equal to [tex]\frac{1}{2}[/tex] in 1st and 2nd quadrant.

So, [tex]x[/tex] can be

[tex]30^\circ, 150^\circ\\OR\\\dfrac{\pi}{6}, \dfrac{5\pi}{6}[/tex]

For [tex]sinx=-1[/tex],

[tex]x = 270^\circ\ or\ \dfrac{3 \pi}{2}[/tex]

So, the answer is:

[tex]\dfrac{\pi}{6}, \dfrac{5\pi}{6}, \dfrac{3\pi}{2}[/tex]

Answer:

[tex]\frac{xy^{3}}{25}[/tex]

Step-by-step explanation:

Given

[tex]\frac{5x^6y^6}{125x^5y^3}[/tex]

Required

Simplify the given expression

[tex]\frac{5x^6y^6}{125x^5y^3}[/tex]

Start by applying law of indices

[tex]\frac{5x^{6-5}y^{6-3}}{125}[/tex]

[tex]\frac{5xy^{3}}{125}[/tex]

Divide numerator and denominator by 5

[tex]\frac{xy^{3}}{25}[/tex]

Hence; the expression is equivalent to [tex]\frac{xy^{3}}{25}[/tex]

Answer:

no solution

Step-by-step explanation:

|f-6| = |f+8|

solve absolute values

f-6 = f+8

add 6 to 8

f = f+14

subtract f from f

0=14

not true; no solution

Answer:

Step-by-step explanation:

F(x) = 3x - 7

g(x) = -2x - 6

To find (f o g)(4) we must first find (f o g)(x)

To find (f o g)(x) substitute g(x) into f(x) that's for every x in f (x) replace it with

g (x).

We have

(f o g)(x) = 3( - 2x - 6) - 7

= - 6x - 18 - 7

We have

(f o g)(x) = - 6x - 25

To find (f o g)(4), substitute the value of x that's 4 into (f o g)(x)

We have

(f o g)(4) = - 6(4) - 25

= - 24 - 25

We have the final answer as

Hope this helps you

Answer:

84 cm²

Step-by-step explanation:

Surface are of the net = sum of the area of each section

Area of the 2 right triangles:

base (b) = 4cm, height (h) = 3 cm

Area = 2(½*b*h) = 2(½*4*3) = 4*3 = 12 cm²

Area of rectangle with the following dimensions:

length (L) = 6 cm, width (W) = 4 cm

Area = L*W = 6*4 = 24 cm²

Area of rectangle with the following dimensions:

length (L) = 6 cm, width (W) = 5 cm

Area = L*W = 6*5 = 30 cm²

Area of rectangle with the following dimensions:

length (L) = 6 cm, width (W) = 3 cm

Area = L*W = 6*3 = 18 cm²

Surface area of the net = 12 + 24 + 30 + 18 = 84 cm²

Answer: equation of the tangent plane is z = 1

Step-by-step explanation:

Given equation

z = e^(-x²-y²) at point (0,0,1)

now let z = f(x,y)

Δf(x,y) = [ fx, fy ]

= (-2xe^(-x²-y²)), (-2ye^(-x²-y²))

now

Δf (0,0) = [ 0, 0 ] = [ a, b ]

equation of the tangent plane therefore will be

z - z₀ = a(x-x₀) + b(y-y₀)

z - 1 = 0(x-0) + 0(y-0)

z - 1 = 0 + 0

z = 1

Therefore equation of the tangent plane is z = 1

Answer:

45

Step-by-step explanation:

Answer:

Distributive Property

Step-by-step explanation:

5y + 2 + 6 + 2y

= 5y + 2(y + 3) + 2 This is the distributive property of multiplication w.r.t. addition

= 6y − y + 2y + 10 − 4 + 2

The distributive property of multiplication with respect to addition  is the one  which separates each term by using multiplication and then addition.

So we see that 2 is multiplied with y and 3 and then added with the like terms. If there was a minus sign the property would be distributive over subtraction.

answer.next time out the graph

Step-by-step explanation:

Answer:

It's A, an odd function

Answer : -Idenify the slope, and the y-intercept, then graph.

-Find the x - and y - intercept and then graph.

Step-by-step explanation:

Options (C) identify the slope and y - intercept and then graph and (D) find the x and y intercepts and then graph are the correct answers.

A line graph is a graph formed by segments of straight lines that join the plotted points that represent given data. The line graph is used to solve changing conditions, often over a certain time interval.

For the given situation,

The line graph consists of a horizontal x-axis and a vertical y-axis.

Methods to graph a line are

Hence we can conclude that options (C) identify the slope and y - intercept and then graph and (D) find the x and y intercepts and then graph are the correct answers.

Learn more about line graph here

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Answer:

16

Step-by-step explanation:

Answer:

The average is:

105 cm

Step-by-step explanation:

1 m = 100cm

2m = 2*100 = 200cm

then:

(200 + 20 + 95)/3 = 315/3 = 105cm

Answer : 4.5 × 10⁴ square inches can be washed per hour.

Step-by-step explanation :

As we are given that an area can be washed at a rate of 4,900 cm²/min. Now we have to determine the square inches can be washed per hour.

Given conversions are:

1 cm = 0.39 in    and    1 hr = 60 min

As, 1 cm² = (0.39)² in²    and    1 min = 1/60 hr

So, [tex]1cm^2/min=(0.39)^2\times 60in^2/hr[/tex]

[tex]1cm^2/min=9.126in^2/hr[/tex]

Now we have to determine the square inches can be washed per hour.

As, [tex]1cm^2/min=9.126in^2/hr[/tex]

So, [tex]4900cm^2/min=\frac{4900cm^2/min}{1cm^2/min}\times 9.126in^2/hr=44717.4in^2/hr=4.5\times 10^4in^2/hr[/tex]

Therefore, 4.5 × 10⁴ square inches can be washed per hour.

Answer:

1) x = ln(7) -1

2) x = [tex]\frac12(3+e^5)[/tex]

Step-by-step explanation:

In the first one, take the ln left and right and isolate x.

In the second one, take the e power left and right and isolate x.

Answer:

-1<x<9

(I think you notated it wrong, it should be |x-4|-2<3)

Answer:

d

Step-by-step explanation:

Answer:

A. 15%

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

1. Start by substituting 3 for every h, so it looks like 3^2-3(3)+2

2. Do the exponent first 9-3(3)+2

3. Multiply 3(3) to get 9-9+2

4. Subtract 9-9, 0+2

5. Add 0 and 2 to get 2

Answer:

The loss is $4600.

Step-by-step explanation:

The par value of the bonds = $210400

The carrying value of the bonds or the actual value of bonds = $218600

The company calls the bonds at the price = $214000

Now have to find the gain or loss from the given information. Thus, below is the calculation to find the gain or loss.  

Loss or gain on retirement = $214,000 - $218,600 = -$4,600

Thus the loss on retirement is $4600.

Answer:

8

Step-by-step explanation:

The angle above the y is 90 degrees ( shown by the little square)

The 3 inside angles of a triangle need to equal 180.

Y = 180 - 90 - 48

Y = 42

Answer: y = 42°

Step-by-step explanation:

Triangle Sum Theorem states the sum of the angles of a triangle is 180°

y + 48° + 90° = 180°

y + 138° = 180°

y = 42°

Answer:

[tex]\huge\boxed{\mathrm{Yes.}}[/tex]

Step-by-step explanation:

If the two lines are perpendicular, Multiplying their slopes must give the result of -1.

=> [tex]\sf -\frac{2}{9} * \frac{9}{2}[/tex]

=> -1

Since, the result of multiplying these slopes give -1, So, the two lines are perpendicular.

Answer:

0.943125.

Step-by-step explanation:

I used an website which is Desmos.com. it works great and is very helpful. you should give it a try.

Answer:

24x^7 y^4 √7y

Step-by-step explanation:

The value of expression would be 24x⁷y⁴√7y  which is determined by simplification of the given expression  8 √63x¹⁴y⁹.

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

We have been the given expression as :

8 √63x¹⁴y⁹

We can simplify as:

⇒ 8 √63x¹⁴y⁹

The square root of a number is a number that can be multiplied by itself and gives the actual number.

⇒ 8 √[3×3×7( x⁷)²x (y⁴)² y]

Assume x and y are nonnegative.

⇒ 24x⁷y⁴√7y

Hence, the value of expression would be 24x⁷y⁴√7y.

Learn more about the algebraic expression here :

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Answer:

7

Step-by-step explanation:

For any real number x, if x > 0 then |x| = x and if x < 0 then |x| = -x. In this case, x < 0 so |-7| = -(-7) = 7.

Answer:

answer is 7

Step-by-step explanation:

if its a negative, its always the positive of that number....if that makes sense

LCM = 30

15 = 3×5

2 = 2¹

10 = 2×5

LCM = 2×3×5 = 30