y2-y1
m =
X2-X1
Find the slope of the line that passes
through these two points.
Simplify completely.
(1,5)
(4,6)
m =
[?]

[tex]\text{L.H.S}\\\\=(\tan q + \sec q)^2\\\\\\=\left(\dfrac{\sin q}{ \cos q} + \dfrac 1{ \cos q} \right)^2\\\\\\=\left( \dfrac{1+ \sin q}{\cos q}\right)^2\\\\\\=\dfrac{(1+ \sin q)^2}{\cos^2 q}\\\\\\=\dfrac{(1+ \sin q)^2}{1-\sin^2 q}\\\\\\=\dfrac{(1 + \sin q)(1 + \sin q)}{(1+ \sin q)(1 - \sin q)}\\\\\\=\dfrac{1+ \sin q}{1- \sin q}\\\\=\text{R.H.S}\\\\\text{Proved.}[/tex]

Answer:

35 is the least common denominator

Step-by-step explanation:

35 is the least (smallest) common (same) multiple of 5 and 7. We use the smallest number that both 5 and 7 go into, because its supposed to be easier to use smaller numbers.

4/5 becomes 28/35 and 5/7 becomes 25/35. And now that they have the same denominator, you could add or subtract them.

Answer:

6+2x >32

2x>32-6

2x>26

divide both sides by 2

therefore, x>13

Step-by-step explanation:

this is because x don't has a negative sign or is on the other side

Answer:

θ = 0°

θ = 30°

θ = 150°

θ = 180°

Step-by-step explanation:

2sin² θ = sin θ

Then

2sin² θ - sin θ = 0

Then

sin θ (2sin θ - 1) = 0

Then

sin θ = 0  or  2sin θ - 1 = 0

Then

sin θ = 0  or  sin θ = 1/2

…………………………………………

We have sin θ = 0 and - 270° ≤ θ ≤180°

Then

θ = 0 or θ = π = 180°

On the other hand,

sin θ = 1/2 and - 270° ≤ θ ≤180°

Then

θ = π÷6 or θ = 5π÷6

π÷6 = 30° and 5π÷6 = 150°

sometimes

Step-by-step explanation:

irrational numbers are numbers that cannot be expressed as a quotient of 2 numbers

rational numbers are numbers that can be expressed as a fraction.

for example let's take these examples of iirational numbers:

[tex] \sqrt{2} \times \sqrt{2} = 2[/tex]

[tex]\pi \times \pi = 9.86960....[/tex]

the 1st product (2) can be written as a fraction but the second one cannot be written as a fraction

answer:

4nd rank

Step-by-step explanation:

I'm not sure btw.

Answer:

  65.9 ft

Step-by-step explanation:

The Law of Sines tells us the relationship between an angle and the opposite side. We are given the angle opposite the given side, but we need the angle opposite the side of interest.

__

The sum of angles in a triangle is 180°, so the measure of the angle at the balloon is ...

  angle C = 180° -75° -60° = 45°

Then the distance between Amaya and Rochelle (c) is ...

  c/sin(C) = r/sin(R)

  c = r×sin(C)/sin(R) = (90 ft)×sin(45°)/sin(75°)

  c ≈ 65.8846

Amaya and Rochelle are about 65.9 feet apart.

Answer:

see below

Step-by-step explanation:

I would use the sine function for the info given

 in a right triangle    sine = opp leg / hypotenuse

        so  sin 57 =  10.8/x  

           then x =  10.8 / sin 57 = 12.87

Answer:

the answer is 8200

Step-by-step explanation:

8200+8200=16400

If Kara rollerblades at given average speed, in 15 minutes, she will rollerblade a distance of 3.5kilometers or 3500meters.

Note that, speed is distance traveled per unit time.

Mathematically, Speed = Distance ÷ time.

Hence, Distance = Speed × time

Given that;

Distance = Speed × time

Distance = 14km/hr × 0.25hr

Distance = 3.5km or (3.5×1000)m

Distance = 3.5km or 3500m

Therefore, if Kara rollerblades at given average speed, in 15 minutes, she will rollerblade a distance of 3.5kilometers or 3500meters.

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For 90 degrees coordinate will be swapped and the position of the coordinate is in the third quadrant. Then the location of point q will be at (–4, –3).

A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.

A rectangle is transformed according to the rule 90º.

The rectangle has vertices located at r'(–4, 4), s'(–4, 1), p'(–3, 1), and q'(–3, 4).

Then the location of q will be

For 90 degrees coordinate will be swapped and the position of the coordinate is in the third quadrant. Then the location of point q will be at (–4, –3).

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Answer:

Step-by-step explanation:

We can set up two equations:  one for each sister:

Let C and D be the prices for a Candy bag and and Drink.  

Sister 1:  3C + 1D = 3.20  [The total spent by sister 1 is the sum of 3 candy bags(C) and 1 drink (D), which comes to $3.20.]

Sister 2:  2C + 4D = 6.30  [The total spent by sister 2 is the sum of 2 candy bags(C) and 4 drinks (D), which comes to $6.30.]

We have two unknowns, C and D, BUT we have 2 equations.  Therefore, we're likely going to be able to solve for C and D if we rearrange one of the equations to isolate one of the unknowns, and then use that expression in the other equation.  Seems unlikely, but it always works.

I'll pick Sister 1's equation and solve for D, the price of a drink:

3C + 1D = 3.20

1D = 3.20 - 3C  [This tells us the price of a drink is 3.20 - 3C]

Use this definition of 1D in Sister 2's equation:

2C + 4D = 6.30

2C + 4(3.20 - 3C) = 6.30

2C + 12.80 - 12C = 6.30

-10C = - 6.5

C = $0.65

One candy bag, C, is $0.65.

Use this value of C in any equation to find D, the cost of 1 drink.  I'll pick The expression we derived above:

1D = 3.20 - 3C

1D = 3.20 - 3(0.65)

1D = 3.20 - 1.95

1D = $1.25

One drink, D, is $1.25.

===================

Check the values:

Candy Bags = $0.65 each    Drinks = $1.25 each

             Reported    

Sister         1      2      1       2  

Candy bags    3  2       $1.95   $1.30  

Drinks         1  4          $1.25   $5.00  

                $3.20   $6.30 Calculated

                 $3.20    $6.30 Reported

T

Answer:

2018 I believe.

Step-by-step explanation:

He'll be two times his age in 2032 which is 28 years old. Subtract 28 from 2032 and you get 2018.

Answer:

2018

Step-by-step explanation:

in 2032 he will be 28 years old because he is 2 times older than 14, 2032-14=2018, because 14 years have passed since he was 14

B. The square root function is the quadratic function reflected across

the line y = x, with a limited domain.

graph y=x^2 and y=√x and y=x

graph is attached

gathmath

Answer:

x = 10

Step-by-step explanation:

The sum of the angles of a quadrilateral is 360°

(4x + 23) + (7x - 3) + (6x - 5) + (16x + 15) = 360°

4x + 23 + 7x - 3 + 6x - 5 + 16x + 15 = 360°

Add like terms

33x + 30 = 360°

Subtract 30 from both sides

33x = 330°

x = 10

Answer:

10

Step-by-step explanation:

we should note that the sum of angles of a quadrilateral is equal 360°

therefore,

(4x+23)+(16x+15)+(6x-5)+(7x-3)=360

30 +33x= 360

33x= 360-30

33x= 330

dividing through by 33

x= 330/33

x= 10

These following translations happened to transform f(x) into g(x):

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, the functions are as follows:

The changes were as follows:

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Answer:

B (2,6,10,14)

Step-by-step explanation:

I think C and D are imposible to be the answer.

A and B are 50% to be the answer.

But I choose B.

Answer:

y = 9

Step-by-step explanation:

y = (2)^2 + 5

y = 4 + 5

y = 9

The length of the support wire on the pole is 27 feet

The given parameters are:

The length (L) of the support wire is then calculated using the following cosine function

cos(x) = b/L

This gives

cos(68) = 10/L

Make L the subject

L = 10/cos(68)

Evaluate

L = 27

Hence, the length of the support wire is 27 feet

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Answer: [tex]R_{C, 180^{\circ}} \circ r_{m}[/tex]

Step-by-step explanation:

The sequence is a reflection over line m followed by a rotation 180 degrees about point C.

Among all the options give the last option that is,

⇒ r m0 Rc180° , is the right answer.

A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

Now, In the given figure ABCDE is transformed to figure A”B”C”D”E.

Hence, When a figure is reflected along a line  the reflected image is at the same distance to the line as the original figure was.

The figure ABCDE is first reflected through the line m to get the figure A'B'C'D'E'.

When a figure is rotated by 180 degrees the x and y coordinates change its place and y sign is reversed.

A'B'C'D'E' is  rotated by 180 degrees to come to figure A"B"C"D"E".

Hence, Among all the options give the last option that is,

⇒ r m0 Rc180° , is the right answer.

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No, it does not make any sense to say that the density of helium is  0.1785 kilograms per square meter.

No, it does not make any sense to say that the density of helium is  0.1785 kilograms per square meter.

The reason why it doesn't make sense is because density of helium, and all the rest of the chemical elements are calculated as;

Density = mass/volume

where;

mass is measured in kilograms.

volume is measured in cubic meter.

Thus, the density of the helium should be expressed as 0.1785 kilograms per cubic meter.

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3x - 5 = -26​

step 1:

subtract +5 on each side because you have to do the inverse operation

step 2:

3x= -21

step 3:

now divide 3 on each side

the answer is -7

Hope this helped!

TheOneAndOnlyLara~

Answer:

x=-7.

Step-by-step explanation:

Hi student! Let me help you out.

_________________

First, add 5 to both sides.

[tex]\sf 3x=-26+5[/tex]. Upon simplifying, we obtain this.

[tex]\sf 3x=-21[/tex].

                                           ↪

Now divide both sides, by 3.

[tex]\sf x=-7[/tex]

[tex]\therefore,\sf the \quad value \quad of \quad x \quad is \quad -7[/tex]. Which is our final answer.

⇨Hope that this helped! have a great day ahead! ⇦

Best Wishes!

[tex]\star\bigstar\underline{\overline{\overline{\textsf{Reach far. Aim high. Dream big.}}}}[/tex]

◆◆-Greetings!-◈◈

__________________________

Part (a)

There are 3 face cards (jack, queen, king) in any given suit. We have 4 suits. That gives 3*4 = 12 face cards total.

12/52 = 3/13 is the probability of getting a face card on any random selection. This probably does not change for any future selection because we put the current card back. In other words, the deck has not changed. Contrast this with part (b) where the probabilities will change since the card counts decrease each time (since we don't put the card back).

The probability of getting 3 face cards in a row, with replacement, is:

(3/13)*(3/13)*(3/13) = 0.012289 approximately

This converts to the percentage 1.2289% after moving the decimal point two spots to the right. This is the same as multiplying by 100.

Lastly, round that to one decimal place to get 1.2%

The percent sign is already taken care of, so you'll just input the number only.

=============================================================

Part (b)

Like mentioned earlier, the probability of a face card is 12/52

I won't reduce that fraction, as you'll see why below.

After that first card is not put back, the 12 decreases to 12-1 = 11 and we have 52-1 = 51 cards left over.

11/51 is the probability of getting another face card, where we have no replacement going on.

Then 10/50 is the probability of getting a third face card. Again, with no replacement.

Therefore,

(12/52)*(11/51)*(10/50) = 0.009955

is the approximate probability of getting 3 face cards in a row with no replacement. Notice the count down 12,11,10 in the numerators. There's also the countdown 52, 51, 50 in the denominators. This nice pattern only happens if we don't reduce the reducible fractions. This is why I didn't reduce.

Anyways 0.009955 converts to 0.9955% which rounds to 1.0% or simply 1%

Answer:

<

Step-by-step explanation:

5.62x10^4=56200, 4.7x10^5=470000, so it is <.

Answer:

Step-by-step explanation:

By the inscribed angle theorem, [tex]a=21, b=42[/tex]

So, since angles in a triangle add to 180 degrees, the angle vertical to c is [tex]180-21-42=117[/tex], and thus [tex]c=117[/tex]

Answer:

what subject of math? Anything to do with calc is a tough area but I can try.

Step-by-step explanation:

The given quadratic equation [tex]y = x^2 + 3x - 10[/tex] Hence, the correct option is D one real root.

Let the quadratic equation given be of the form ax^2 + bx + c = 0, then

The quantity [tex]b^2 - 4ac[/tex] is called its discriminant.

The solution contains the term [tex]\sqrt{b^2 - 4ac}[/tex] which will be:

Real and distinct if the discriminant is positive

Real and equal if the discriminant is 0

Non-real and distinct roots if the discriminant is negative

The given quadratic equation

[tex]y = x^2 + 3x - 10[/tex]

a = 1

b = 3

c = -10

The discriminant

[tex]b^2 - 4ac[/tex]

= 9 - 4(1)(-10)

= 9- 40

= - 31

Thus, Non-real and distinct roots if the discriminant is negative.

Hence, the correct option is D one real root.

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Answer:

(4, 3) , (4, 0) , (6, 0)

Step-by-step explanation:

M (1, 4)

M ' ( 1 + 3, 4 - 1)

namely M ' (4, 3)

N (1, 1)

N ' ( 1 + 3 , 1 - 1)                       ((x, y) 3 squares right and 1 square down means

namely n" (4, 0)                         ( x + 3, y - 1))

p (3, 1)

p ' ( 3 + 3 , 1 - 1)

namely p' (6, 0)        

Step-by-step explanation:

(3,4) not that sure about the coordinates are right

The length of r if AB is tangent to circle C, forming a right triangle is 8 units.

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

From the diagram, using Pythagoras theorem:

BC² = AC² + AB²

17² = 15² + r²

r = 8 units

The length of r if AB is tangent to circle C, forming a right triangle is 8 units.

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