If:
JK = 6x + 2,
KL=7+4, and
JL= 45,
Find KL.
J
K
L

We know that,

[tex]\dag\bf\:sin^2A=\dfrac{1-cos2A}{2}[/tex]

[tex]\dag\bf\:sin2A=2sinA\:cosA[/tex]

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Now, Let's solve !

[tex]\leadsto\:\bf\dfrac{sin^2A-sin^2B}{sinA\:cosA-sinB\:cosB}[/tex]

[tex]\leadsto\:\sf\dfrac{\frac{1-cos2A}{2}-\frac{1-cos2B}{2}}{\frac{2sinA\:cosA}{2}-\frac{2sinB\:cosB}{2}}[/tex]

[tex]\leadsto\:\sf\dfrac{1-cos2A-1+cos2B}{sin2A-sin2B}[/tex]

[tex]\leadsto\:\sf\dfrac{2sin\frac{2A+2B}{2}\:sin\frac{2A-2B}{2}}{2sin\frac{2A-2B}{2}\:cos\frac{2A+2B}{2}}[/tex]

[tex]\leadsto\:\sf\dfrac{sin(A+B)}{cos(A+B)}[/tex]

[tex]\leadsto\:\bf{tan(A+B)}[/tex]

Answer:  see proof below

Step-by-step explanation:

Use the Power Reducing Identity:  sin² Ф = (1 - cos 2Ф)/2

Use the Double Angle Identity:  sin 2Ф = 2 sin Ф · cos Ф

Use the following Sum to Product Identities:

[tex]\sin x - \sin y = 2\cos \bigg(\dfrac{x+y}{2}\bigg)\sin \bigg(\dfrac{x-y}{2}\bigg)\\\\\\\cos x - \cos y = -2\sin \bigg(\dfrac{x+y}{2}\bigg)\sin \bigg(\dfrac{x-y}{2}\bigg)[/tex]

Proof LHS →  RHS

[tex]\text{LHS:}\qquad \qquad \qquad \dfrac{\sin^2A-\sin^2B}{\sin A\cos A-\sin B \cos B}[/tex]

[tex]\text{Power Reducing:}\qquad \dfrac{\bigg(\dfrac{1-\cos 2A}{2}\bigg)-\bigg(\dfrac{1-\cos 2B}{2}\bigg)}{\sin A \cos A-\sin B\cos B}[/tex]

[tex]\text{Half-Angle:}\qquad \qquad \dfrac{\bigg(\dfrac{1-\cos 2A}{2}\bigg)-\bigg(\dfrac{1-\cos 2B}{2}\bigg)}{\dfrac{1}{2}\bigg(\sin 2A-\sin 2B\bigg)}[/tex]

[tex]\text{Simplify:}\qquad \qquad \dfrac{1-\cos 2A-1+\cos 2B}{\sin 2A-\sin 2B}\\\\\\.\qquad \qquad \qquad =\dfrac{-\cos 2A+\cos 2B}{\sin 2A - \sin 2B}\\\\\\.\qquad \qquad \qquad =\dfrac{\cos 2B-\cos 2A}{\sin 2A-\sin 2B}[/tex]

[tex]\text{Sum to Product:}\qquad \qquad \dfrac{-2\sin \bigg(\dfrac{2B+2A}{2}\bigg)\sin \bigg(\dfrac{2B-2A}{2}\bigg)}{2\cos \bigg(\dfrac{2A+2B}{2}\bigg)\sin \bigg(\dfrac{2A-2B}{2}\bigg)}[/tex]

[tex]\text{Simplify:}\qquad \qquad \dfrac{-2\sin (A + B)\cdot \sin (-[A - B])}{2\cos (A + B) \cdot \sin (A - B)}[/tex]

[tex]\text{Co-function:}\qquad \qquad \dfrac{2\sin (A + B)\cdot \sin (A - B)}{2\cos (A + B) \cdot \sin (A - B)}[/tex]

[tex]\text{Simplify:}\qquad \qquad \quad \dfrac{\cos (A+B)}{\sin (A+B)}\\\\\\.\qquad \qquad \qquad \quad =\tan (A+B)[/tex]

LHS = RHS:    tan (A + B) = tan (A + B)    [tex]\checkmark[/tex]

Answer:

708480

Step-by-step explanation:

You follow the order of BEDMAS. There are brackets in this equation, meaning we have to focus on what is inside the brackets first. The next step is Exponents. So you multiply 2.05 by 10^5.

This would give you 205000.

You then multiply this number by the number on the outside of the brackets which is 3.456.

This would give you 708480. (You can get these answers by using a calculator).

Don't forgot to follow the order of BEDMAS or whatever law of operations you were taught (BIDMAS/BIMDAS etc)

Answer:

[tex]x\le \:-\frac{20}{21}[/tex]

Step-by-step explanation:

[tex]-3\left(9x+20\right)\ge \:15x-20\\\\\mathrm{Expand\:}-3\left(9x+20\right):\quad -27x-60\\-27x-60\ge \:15x-20\\\\\mathrm{Add\:}60\mathrm{\:to\:both\:sides}\\-27x-60+60\ge \:15x-20+60\\\\\mathrm{Simplify}\\-27x\ge \:15x+40\\\\\mathrm{Subtract\:}15x\mathrm{\:from\:both\:sides}\\-27x-15x\ge \:15x+40-15x\\\\\mathrm{Simplify}\\-42x\ge \:40\\\\\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}\\\left(-42x\right)\left(-1\right)\le \:40\left(-1\right)[/tex]

[tex]Simplify\\42x\le \:-40\\\\\mathrm{Divide\:both\:sides\:by\:}42\\\frac{42x}{42}\le \frac{-40}{42}\\\\Simplify\\x\le \:-\frac{20}{21}[/tex]

Answer:

multiplication property

Step-by-step explanation:

The multiplication property states that the product of any number and zero is zero. It doesn't matter what the number is, when you multiply it to zero, you get zero as the answer. So: 2 x 0 = 0.

Answer:

j=4

Step-by-step explanation:

5j+15=12j-13

Answer: j = 4

Step-by-step explanation:

5j + 15 = 12j - 13

5j = 12j - 28                  Subtract 15 from both sides        

-7j = -28                        Subtract 12j from both sides

j = 4                               Divide -7 from both sides

Step-by-step explanation:

Let the first part be x. Then,

the second part will be (10000-x).

So, According to question,

(10% of x) + { 7% of (10000-x)} = 805

(10/100*x) +{7/100*(10000-x)} = 805

(x/10) + (70000-7x/100) = 805

Then,

We will take the lcm of 10 and 100 which is 100 and then add both the fractions.

Solution:

10x + 70000-7x/ 100 = 805

3x + 70000/100 = 805

3x + 70000 = 805*100

3x + 70000 = 80500

3x = 80500-70000

3x = 10500

x = 10500/3

x = 3500

So the first part is 3500.Then,

the second part will be (10000-3500)

= 6500

HOPE IT WILL HELP YÔÛ.♥️♥️

Answer:

  -24

Step-by-step explanation:

The integer in "elevation of -24 meters" is -24.

Answer:

[tex]y=8[/tex]

[tex]RS=77, ST=31[/tex]

Step-by-step explanation:

Note that the entire segment RT is the combined lengths of RS and ST. So:

[tex]RT=RS+ST[/tex]

We know that RT is 108, RS is (9y+5), and ST is (3y+7). Substitute:

[tex]108=(9y+5)+(3y+7)[/tex]

On the right, combine like terms:

[tex]108=(9y+3y)+(5+7)[/tex]

Add:

[tex]108=12y+12[/tex]

Subtract 12 from both sides. The right cancels:

[tex]96=12y[/tex]

Divide both sides by 12:

[tex]y=8[/tex]

So, the value of y is 8.

To find RS and ST, substitute 8 for y. So:

[tex]RS=9y+5[/tex]

Substitute 8 for y:

[tex]RS=9(8)+5[/tex]

Multiply:

[tex]RS=72+5[/tex]

Add:

[tex]RS=77[/tex]

Do the same for ST:

[tex]ST=3y+7[/tex]

Substitute 8 for y:

[tex]ST=3(8)+7[/tex]

Multiply:

[tex]ST=24+7[/tex]

Add:

[tex]ST=31[/tex]

Area=[tex]\pi[/tex] [tex]r^{2}[/tex]

divide diameter with 2 to get radius 13/2= 6.5

area= pi 6.5x6.5

=[tex]\pi[/tex]42.25

answer= 42.25[tex]\pi[/tex]

Area of a circle is equal to [tex]\boldsymbol{132.8}[/tex] square inches.

A circle is a collection of all the points that are at the fixed distance (radius) from a fixed point (center).

Diameter of a circle [tex]=\boldsymbol{13}[/tex] centimeter

Radius of a circle is half of the diameter.

So,

Radius of a circle [tex]=\frac{13}{2}[/tex] centimeter

Area of a circle [tex]=\boldsymbol{\pi r^2}[/tex] where [tex]r[/tex] denotes radius of a circle.

                         [tex]=\frac{22}{7}\times \left ( \frac{13}{2} \right )^{2}\\=132.7857[/tex]

                         [tex]\boldsymbol{\approx 132.8}[/tex] square inches

So, area of a circle is equal to [tex]\boldsymbol{132.8}[/tex] square inches.

Find out more information about circle here:

https://brainly.com/question/11833983?referrer=searchResults

Answer:

2x+1= 8

2x= 8-1

2x= 7

x= 7/2

x= 3.5

hope this helps uh

Answer:

t = -1

Step-by-step explanation:

[tex]2t + 1 = 3t - 1 + 3[/tex]

Collect like terms and simplify

[tex]2t - 3t = - 1 + 3 - 1 \\ - t = 1[/tex]

Divide through by -1

[tex] \frac{ - t}{ - 1} = \frac{ 1}{ - 1} \\ t = - 1[/tex]

Answer:

t = - 2

Step-by-step explanation:

[tex]\frac{2t + 1}{3} = \frac{(3t-1) + 3}{4}[/tex]

First we need to cross multiply to get rid of the division to make it easier to solve.

Multiply 2t+1 by 4 and (3t-1) + 3 by 3

4 ( 2t + 1 ) = 3 ( ( 3t - 1 ) + 3 ) On the right we need to combine terms.

4 ( 2t + 1 ) = 3 ( 3t - 1 + 3 )

4 ( 2t + 1 ) = 3 ( 3t + 2 )   Multiply

4 * 2t + 4 * 1 = 3 * 3t + 3 * 2     Remember order of operations. Multiplication comes before addition and subtraction.

4 * 2t + 4 * 1 = 3 * 3t + 3 * 2

8t + 4 = 9t + 6      Subtract 8t from each side

8t - 8t + 4 = 9t - 8t + 6

4 = t + 6       Subtract 6 from each side

4 - 6 = t + 6 - 6

4 - 6 = t

- 2 = t

Answer:

C

Step-by-step explanation:

it says that if he makes an a, he will take advanced math, and if he does that he'll join the math team, so since henry made an a, he is gonna take advanced math and join the team.

Answer:

The answer is A) Henry will take Calculus

Step-by-step explanation:

If he made an A in math class, then he would take advanced math next year, which would be Calculus. then he will join the math team, which would be next.

Hope this helps :)

Answer:

1.3 cups

Step-by-step explanation:

if 3/4 cups of sugar are needed for every 2 1/4 cups of flour then for 4 cups of flour: (3/4*4)/(9/4) =1.3 cups of sugar

if 1 cup of sugar for every 3 cups of flour then

x=4/3=1.3

Answer:

i dunno

Step-by-step explanation:

somebody help

Answer:

Step-by-step explanation:

[tex]a+c=23\\a+d=20\\e+c=21\\b+e=24\\d+b=22\\[/tex]

...

Answer: 49 degrees

Step-by-step explanation:

Answer:

-47

Step-by-step explanation:

[tex]-(5-6) x (2-7^{2})\\[/tex]

[tex]-(-1) x (2-49)[/tex]

1 x (-47)

= -47

Answer: Subtract

Step-by-step explanation: Make your denominator equal using the concept of LCM, then subtract the numerators accordingly. Rewrite each fraction to its equivilent fraction with a denominator equal to the LCM=30, then you need to subtract the numberators, but make sure to reduce your answer to the lowest possible term. I hope this helps.

Answer:

when you find the common denominators you find the LCM.

Step-by-step explanation:

A withdrawal is taking money out which is a negative value.

She took $18 out so it would be written as -18.

The answer is:

A number line going from negative 20 to positive 20. A point is at negative 18.

Answer:

Carly withdraws $18 from her bank account.

We assume that Carly has $x in her account. She withdraws $18 from her bank account.

So we have to subtract $18 from $x amount.

Which is $x - 18.

So we are subtracting $18 from her account.

It should be represented by an integer -18.

Now we have to identify the which number line represents -18.

It is D)

Step-by-step explanation:

There are 24 hours in a day and so 15 hours is 15÷24=58 of a day. Since the rig drills 60 feet underground in a day, in 58 of a day it will drill

(58 days)×(60feetday)=3008 feet.

So the rig will have drilled 3008=37.5 feet underground in 15 hours.

The rig drills 60 feet underground per day so to find how long it has been running to go 143.6 feet underground, we need to calculate

(143.6 feet)÷(60feetday)=143.660 days.

This is about 2.4 days. Alternatively, it is 57.44 hours

We know that the rig drills at a constant rate, so there is a proportional relationship between the two quantities d, the height to which the drill has dug, and t, the number of days the drill runs. It drills at -60 feet per day, so we can represent this relationship with the equation:

–60t=d

Since 15 hours is 1524=58 days, we can use the equation to find d:  

–60⋅58=d

Since the depth is the same whether we think of it as a positive depth below the surface or a negative height above the surface, we can find this value by multiplying 60⋅58=37.5  and then noting that the sign must be negative if we are representing positions below the surface of the earth by negative numbers. So d=–37.5 and the drill will be at height -37.5 feet after 15 hours.

Likewise, if we know the drill has dug to -143.6 feet, we can use the equation again, this time to find t:  

−60t=−143.6

so t=(−143.6)÷(−60). Since the amount of time would be the same if we were working with positive feet below the surface of the earth and a drill rate of 60 feet per day below the earth surface, we can find this value by dividing 143.6÷60, which is about 2.4 days.

Answer:

Translation of MATH to M'A'T'H' by 5 units to the left.

Step-by-step explanation:

From the figure attached,

Quadrilateral MATH has been transformed to the image M'A'T'H'.

Shape and size of MATH is not altered in this transformation, only translation has been done.

We take a point A(4, 3) which has been translated to A'(-1, 3).

Rule followed for the translation,

(x, y) → (x-5, y)

Translation by 5 units to the left.

Answer:

lol the number of comments got maxed out

Step-by-step explanation:

Answer:

6 1/10

Step-by-step explanation:

0.1 is 1/10 of 100. So the answer is 6 1/10

Hope This Helps :)

Question

Which list of integers is in order from greatest to least?

a) -11, -18, -33, 9, 24

b) -33, 24, -18, -11, 9

c) 24, 9, -33, -24, -11

d) 24, 9, -11, -24, -33

Answer:

d) 24, 9, -11, -24, -33

Step-by-step explanation:

The question asked us which list of integers is in order from greatest to least. This means, we should arrange the integers in descending order from the highest to the least or lowest number.

24< 9< -11< -24 < -33

Hence, from the greatest to the least =

24, 9, -11, -24, -33

Option d), is correct.

1073.4 centimeters = 1.073 decameters

Answer:

107.34 decimeter

Step-by-step explanation:

Answer:

the paper is 54.79 cm .

Step-by-step explanation:

34.85 * 2 = 69.7 ( two pieces of paper altogether )

69.7 - 14.91 = 54.79 ( when got cut )

Answer:

x = - 26

Step-by-step explanation:

Let the number be x.

According to the question,

[tex]\frac{x+5}{x-2} = \frac{3}{4}\\[/tex]

Cross multiplying 4 & 3 gives :-

[tex]4(x+5)=3(x-2)[/tex]

And solving this eqn. gives :-

[tex]4(x+5)=3(x-2)\\=> 4x+20=3x-6\\=>4x-3x=-20-6\\=>x=-26[/tex]

Verification :-

(putting the value of x = -26 )

[tex]\frac{x+5}{x-2} \\\\=>\frac{-26+5}{-26-2} \\\\=> \frac{-21}{-28} \\\\=>\frac{21}{28}[/tex]

Reducing  [tex]\frac{21}{28}[/tex]  by 7 gives  [tex]\frac{3}{4}[/tex] .

3x and 4x are like terms. Add them together and you get 7x.

2 and -1 are like terms. Add them together and you get 1.

3x+2+4x-1

7x+1 is your final answer

Answer:

Sjhdhdnjsuemshusushdj

Step-by-step explanation:

now yte don't do this because then you will be reported and people really want to learn and STEAL THESE ANSWERS pop it's time for my class brb but don't do this if you don't know the answer don't put it in or you will, be reported. Time for P.E and sorry.

Answer:

Las reglas para escribir un número en forma estándar es que primero escribes un número entre 1 y 10, luego escribes × 10 (a la potencia de un número). En una calculadora, generalmente ingresa un número en forma estándar de la siguiente manera: Escriba el primer número (el que está entre 1 y 10). Presione EXP

Step-by-step explanation:

Answer:0.32

Step-by-step explanation: