describe a rule for each pattern. 35,70,105,140​

Answers

Answer 1

Answer:

A linear sequence

Step-by-step explanation:

In this sequence, the difference between the first two terms is  70−35=35 , we can check this is correct by finding the difference between the 2nd and 3rd terms, which is  105−70=35 . This means the first difference is 35.

The first difference gives us the number we multiply  n  by, or the quotient of n.

This means we get the nth term as  35n+c .

To get  c , we check the difference between the first term and the number we get when we multiply  n  by  35 , when  n=1 .

This gives us:

35n+c=35  

c=35−35n  

c=35−35(1)  

c=35−35  

c=0  

Once we have  c , we get the nth term of  35,70,105  to be  35n .


Related Questions

Wakaba buys some granola bars at $0.50 each and energy drinks at $2 each for a group hike. She buys twice as many granola bars as energy drinks. If she spends $27 in total, how many granola bars and energy drinks does she buy?

Answers

gronala bars:18

energy drinks:9

Step-by-step explanation:

$0.50 •18= $9

$2.00•9=$18

$9+$18=$27

sᴏʟᴠᴇ ɪᴛ ʙʏ sᴜʙsᴛɪᴛᴜᴛɪᴏɴ ᴍᴇᴛʜᴏᴅ​

Answers

Answer:

x = 1

y = 1

Step-by-step explanation:

Given:

x/a + y/b = 1/a + 1/bx/a - y/b = 1/a - 1/b

Add up the two equations side-by-side, this will cancel y/b and 1/b:

x/a+x/a = 1/a+1/a2x/a=2/ax = 1

Subtract the  two equations side-by-side, this will cancel x/a and 1/a:

y/b+y/b = 1/b+1/b2y/b=2/by=1

Answer:

x = 1, y = 1

Step-by-step explanation:

[tex] \frac{x}{a} + \frac{y}{b} = \frac{1}{a} + \frac{1}{b} .....(1) \\ \frac{x}{a} - \frac{y}{b} = \frac{1}{a} - \frac{1}{b} .....(2) \\ \\ let \: \: \frac{1}{a} = m, \:\:\&\: \: \frac{1}{b} = n \\ so \: equatin \: (1) \: reduces \: to: \: \\ \\ so \: equatin \: (1) \: reduces \: to: \: \\ mx + ny = m + n....(3)\\ and \: equatin \: (2) \: reduces \: to: \: \\ mx - ny = m - n....(4) \\ adding \: equations \: (3) \: (4) \\ mx + ny = m + n \\ mx - ny = m - n \\ - - - - - - - - - - \\ 2mx = 2m \\ x = \frac{2m}{2m} \\ \huge \red{ \boxed{x = 1}} \\ substituting \: x = 1 \: in \: equatin \: (3) \\ m \times 1 + ny \: = m + n \\ m + ny \: = m + n \\ ny = m + n - m \\ ny = n \\ y = \frac{n}{n} \\ \huge \purple{ \boxed{y = 1}}[/tex]

if
[tex] \frac{ {a}^{2x} }{ {a}^{(x - y)} } =a [/tex]
then y =​

Answers

Answer:

y= 1-x

Step-by-step explanation:

● (a^2x)/a^(x-y) = a

This means that:

● 2x-(x-y) = 1

● 2x - x +y = 1

● x + y = 1

Substract x from both sides

● x+y -x = 1-x

● y = 1-x

which property of equality was used to solve this equation
[tex]9x = 88 \\ \frac{9x}{9} = \frac{88}{9} \\ x = 9 \frac{7}{9} [/tex]
A. addition property of equality
B. subtraction property of equality
C. multiplication property of equality
D. division property of equality

Answers

Answer:

division property of equality.

Step-by-step explanation:

Angle RST is a right angle. Angle RSU has a measure of 25°. Lines R S and S T connect to form a right angle. Another line extends from point S to point U. Angle R S U is 25 degrees. What is the measure of angle TSU? 25° 45° 65° 75°

Answers

Answer:

The measure of ∠TSU = 65°

Step-by-step explanation:

Since RST is a right-angled triangle and RS and ST connect to form a right angle, ∠RST = 90°. Also, since RS and ST connect to form a right angle, ∠RST = ∠RSU + ∠TSU.

We make ∠TSU subject of the formula. So,

∠TSU = ∠RST - ∠RSU

Given that angle ∠RSU = 25° and ∠RST = 90°, substituting these values into he expression for ∠TSU, we have

∠TSU = ∠RST - ∠RSU

∠TSU = 90° - 25°

∠TSU = 65°

So, ∠TSU = 65°

The measure of ∠TSU = 65°

Answer:

65

Step-by-step explanation:

you know it forms a right angle because of the marking on it

so take 90 because thats the degree of a right angle, and subtract 25 from it and you will get your other side

90-25=x

65=x

check by adding both angles

65+25=90

2 + 10 = 24
3 + 6 = 27
7 + 2 = 63
5 + 3 = ????​

Answers

Answer:

40

Step-by-step explanation:

2 + 10 = 24

2(2 + 10) = 2×12 = 24

3 + 6 = 27

3(3 + 6) = 3×9 = 27

7 + 2 = 63

7(7 + 2) = 7×9 = 63

5 + 3 = 40

5(5 + 3) = 5×8 = 40

Preston adopted a cat from a rescue shelter. He needs to buy some cat litter, so he compares prices at different stores. He finds the best deal at Fluffy Felines Pet Shop, which sells a 20-pound jug of cat litter for $8.60. How much does the cat litter cost per pound?

Answers

Answer:

$0.43

Step-by-step explanation:

Preston adopted a cat from a rescue shelter

He needs to buy food for his new cat so he compared the price of cat litter at different stores

Preston gets the best deal at fluffy felines pet shop

They sell 20 pound jug litter for $8.60

Therefore the cost of the cat litter per pound can be calculated as follows

= 8.60/20

= 0.43

Hence the cost of the cat litter per pound is $0.43

I have a rectangular prism with a height of 30cm, a length of 15cm, and a width of 10cm. What is the volume of my prism? V= Bh B= area of the base of the rectangular prism a= L x W

Answers

Answer: V = 4500 cubic units or units^3

Step-by-step explanation:

So far, we know that the givens are:

a height of 30cm, a length of 15cm, and a width of 10cm

So we have to find the volume. The formula for volume is just V = lwh which means that the volume equals the length times the width times the height.

V  = (l)(w)(h)

Now, all you have to do is to substitute the given numbers into the equation:

V = (15)(10)(30)

Simplify that:

V = 4500

Put it in the terms:

V = 4500 cubic units or units^3

Hence your answer!

v=4500 cubic units or units^3

Inga knows that the radius of a certain cone is 4 cm and its volume is about 134 cubic centimeters. Which is the best estimate of the cone's height?

Answers

Answer:

h=8cm

Step-by-step explanation:

V= πr^2h/3

Where

V=volume of a cone

π=pi= 3.14

r= radius=4cm

h= height = ?

V= πr^2h/3

134= 3.14*4*4*h/3

134= 50.24h/3

Divide both sides by 50.24

h/3= 134 / 50.24

h/3= 2.67

Cross product

h= 2.67*3

h= 8.01

Approximately h= 8cm

The best estimate of the cone's height is 8cm

simplify : -2(3v - 6) ( WITH STEPS TOO)

please and thank you!!

Answers

Answer:

-2(3v - 6) = 0

-6v + 12 = 0

-6v = -12

v = -12/-6

v = 2 answer

Step-by-step explanation:

-2(3v - 6)

Multiply the terms in parentheses by -2

(You get this) -2 x 3v - 2 x (-6)

Calculate the product

-6v - 2 x (-6) then multiply the numbers

Finished product is -6v + 12

Hope this helps you ♥︎

solve for x using zeros of function method
-x³+2x²+x-2=0​

Answers

Answer:

x = - 1, x = 1, x = 2

Step-by-step explanation:

The coefficients of the polynomial sum to zero, that is

- 1 + 2 + 1 - 2 = 0

This indicates that x = 1 is a zero

let x = - 1, then

- (- 1)³ + 2(- 1)² + (- 1) - 2 = 1 + 2 - 1 - 2 = 0

Thus x = - 1 is a zero

let x = 2

- (2)³ + 2(2)² + 2 - 2 = - 8 + 8 + 2 - 2 = 0

Thus x = 2 is a zero

The 3 zeros are x = - 1, x = 1, x = 2

Fuad’s model racing car drives at an average speed of 3 feet per second. Fuad records the distances and times in a table like the one shown below. Speed of Model Race Car Distance (ft.) 3 Time (s) 1 At this rate, how long will it take the car to travel 21 feet?

Answers

Answer:

7.0 seconds

Step-by-step explanation:

i did the test but how i know this is bc 3 divided by 21 is 7

NOT 9

DON'T USE 9 AS THE ANSWER

Answer:

7.0 seconds

Step-by-step explanation:

Solve for x: the quantity of x plus 16 all over 3 = 3x (1 point) a x = −7 b x = −13 c x = 8 d x = 2

Answers

Answer:

D. X=2

Step-by-step explanation:

Answer:

X=2

Step-by-step explanation:

A rectangular athletic field is twice as long as it is wide. If the perimeter of the athletic field is 72 yards, what are its dimensions?
what is the width? in yards​

Answers

Answer:

Width= 12 yards

Length= 24 yards

Step-by-step explanation:

Perimeter of a rectangle= 2(length + width)

Let

w= width

Twice as long as it is wide

Length= 2w

Perimeter of the rectangle= 72 yards

Perimeter of a rectangle= 2(length + width)

72 = 2(2w + w)

72 = 4w + 2w

72 = 6w

Divide both sides by 6

72/6 = w

12= w

w=12

Therefore,

Width= 12 yards

Length= 2w

=2(12)

=24 yards

Solve x^3 = 8/729 please answer

Answers

Answer:

x=2/9

Step-by-step explanation:

x^3=8/729

Hence,

x= cube root of (8/729)

x=cube root of 8

  cube root of 729

x=2

   9

Answer: decimal form : x=0.10475656

Step-by-step explanation:

Take roots of both sides and solve

VW is the bisector of AY , and they intersect at E. If EY = 3.5, what is AY?

Answers

Step-by-step explanation:

this is solutions of your questions

Tyler can swim 1/2 mile in 1/3 hour at a constant speed how fast does Tyler swim in miles per hour

Answers

Answer:

[tex]Speed = \frac{3}{2}[/tex]mph

Step-by-step explanation:

Given

Distance = [tex]\frac{1}{2}[/tex] mile

Time = [tex]\frac{1}{3}[/tex] hour

Required

Determine the speed

To do this, we simply divide distance by time

[tex]Speed= \frac{Distance}{Time}[/tex]

[tex]Speed = \frac{1}{2} / \frac{1}{3}[/tex]

[tex]Speed = \frac{1}{2} * \frac{3}{1}[/tex]

[tex]Speed = \frac{3}{2}[/tex]

Hence, the speed is [tex]\frac{3}{2}[/tex] mile per hour

Tyler's speed is 1.5 miles per hour.

The formula for speed is:

= Distance / Time

Distance = 1/2 miles

Time = 1/3 hours

Tyler's speed is therefore:

= 1/2 ÷ 1/3

= 1 / 2 x 3/1

= 3/2 miles per hour or.

= 1.5 miles per hour

Tyler's speed is therefore 1.5 miles per hour.

Find out more at https://brainly.com/question/10722020.

(7 thousands 3 tens) ÷ 10 =

Answers

Answer:  703

Step-by-step explanation:

This situation is the same as,

7,030 / 10  = 703

The answer is 703 like the person above me


How can I solve question b). ?

Answers

Answer:

It was not my intention to post that answer, as it does not solve the question, but hope it helps somehow.  

Step-by-step explanation:

[tex]$\text{b)} \frac{\sin(a)}{\sin(a)-\cos(a)} - \frac{\cos(a)}{\cos(a)-\sin(a)} = \frac{1+\cot^2 (a)}{1-\cot^2 (a)} $[/tex]

You want to verify this identity.

[tex]$\frac{\sin(a)(\cos(a)-\sin(a))}{(\sin(a)-\cos(a))(\cos(a)-\sin(a))} - \frac{\cos(a)(\sin(a)-\cos(a))}{(\sin(a)-\cos(a))(\cos(a)-\sin(a))} = \frac{1+\cot^2 (a)}{1-\cot^2 (a)} $[/tex]

The common denominator is

[tex](\sin(a)-\cos(a))(\cos(a)-\sin(a))= \boxed{2\cos (a)\sin(a)-\cos ^2(a)-\sin ^2(a)}[/tex]

Solving the first and second numerator:

[tex]\sin(a)(\cos(a)-\sin(a))=\sin(a)\cos(a)-\sin^2(a)[/tex]

[tex]\cos(a)(\sin(a)-\cos(a))= \cos(a)\sin(a)-\cos^2(a)[/tex]

Now we have

[tex]$\frac{ \sin(a)\cos(a)-\sin^2(a) -(\cos(a)\sin(a)-\cos^2(a))}{2\cos (a)\sin(a)-\cos ^2(a)-\sin ^2(a)}$[/tex]

[tex]$\frac{ -\sin^2(a) +\cos^2(a)}{2\cos (a)\sin(a)-\cos ^2(a)-\sin ^2(a)}$[/tex]

Once

[tex]-\sin^2(a) +\cos^2(a) = \cos(2a)[/tex]

[tex]2\cos (a)\sin(a) = \sin(2a)[/tex]

Also, consider the identity:

[tex]\boxed{\sin^2(a)+\cos^2(a)=1}[/tex]

[tex]$\frac{ -\sin^2(a) +\cos^2(a)}{2\cos (a)\sin(a)-\cos ^2(a)-\sin ^2(a)}=\boxed{\frac{ \cos(2a)}{\sin(2a)-1}}$[/tex]

That last claim is true.

Find the value of X. I greatly appreciate your help

Answers

Answer:

x = 14

Step-by-step explanation:

comp = add up to be 90

3x + 14 + 2x + 6 = 90

5x + 20 = 90

5x = 70

x = 14

explain about herb some lines​

Answers

Answer:

Herbs are small plants that have a fleshy or juicy stem when they are young. The stems of some herbs develop hard, woody tissue when they grow old. Most herbs are perennials. This means that the tops of the plants die each growing season, but the roots remain alive and produce new plants year after year.

Step-by-step explanation:

Jack had 3 bags of golf balls with bbb balls in each bag; then his friend gave him 6 more golf balls.
How many golf balls does Jack have now?
Write your answer as an expression.

Answers

Answer:

y=3b + 6 ................ . ..

The answer is 3b + 6 in Khan Accademy

Multiplying two functions results in h(x) = 10x2 + 12x – 16, while adding the same functions results in j(x) = 7x. Which statements describe f(x) and g(x), the original functions? Select two options. Both functions must be linear. Both functions must be quadratic. Both functions must have a y-intercept of 0. The rate of change of either f(x) or g(x) must be 0. The y-intercepts of f(x) and g(x) must be opposites.

Answers

Answer:

Both functions must be linear. The y-intercepts of f(x) and g(x) must be opposites.

Step-by-step explanation:

First we need to solve.

h(x) = 10[tex]x^{2}[/tex] + 12[tex]x[/tex] - 16

It seems tricky at first but we know a couple things. When we add the factors of h(x) together we get j(x) = 7[tex]x[/tex] so we know that when we multiply 2 numbers together it should equal 10 but add up to 7.

Lets write the possible combinations of 10:

1 x 10 = 10

2 x 5 = 10

5 x 2 = 10

10 x 1 = 10

Now which combination will add or subtract to 7?

1 - 10 = 9    1 + 10 = 11  

2 - 5 = -7    2 + 5 = 7   We can stop here!

2 and 5 are in our factor, so let's write it down.

(2x      ) (5x        )     We know there will one + and one - because the -16. If we had two + it would be positive 16, and is we had two - it would also be positive 16 because a    - x - = +

Now the last number is 16. Let's find the possible combinations of 16.

1 x 16 = 16

2 x 8 = 16

4 x 4 = 16  We will stop here because we end up repeating posibilities.

Here is where we think critically. Whichever combination we choose has to be multiplied by 2 and 5 and end up equaling 12. I think 16 is too high so let's try 2 and 8.

2x * 2 = 4x     5x * 8 = 40x    Now one is positive and the other is negative. Let's try each combination.

4x - 40x = -36x   -4x + 40x = 36x     Neither of those are 12x. So let's Try 4 and 4.

2x * 4 = 8x       5x * 4 = 20x  One will be positive and the other will be negative. Let's try each combination.

8x - 20x = -12x    -8x + 20x = 12x There is our combination!  Remeber when you mutiply together you have to multiply the opposite factor. Here are the combinations:

(Ax + B )(Cx + D) = (Ax*Cx) + (Ax*D) + (B*Cx) + (B*D)

(Ax - B )(Cx + D) = (Ax*Cx) + (Ax*D) - (B*Cx) - (B*D)

(Ax + B )(Cx - D) = (Ax*Cx) - (Ax*D) + (B*Cx) - (B*D)

(Ax - B )(Cx - D) = (Ax*Cx) - (Ax*D) - (B*Cx) + (B*D)

So we have:

(2x + 4) (5x - 4)

Let's prove is and multiply it back out.

2x*5x - 2x*4 + 4*5x - 4*4

10[tex]x^{2}[/tex] - 8[tex]x[/tex] + 20

10[tex]x^{2}[/tex] + 12[tex]x[/tex] - 16  So we got it right!

Now let's see if they really add up to 7x.

(2x + 4) (5x - 4)  which we now need to add together

2x + 4 + 5x - 4   Rearrange

2x + 5x + 4 - 4   Combine like terms

7x + 0  or 7x  It works!

So our original functions are f(x) = 2x + 4   and g(x) = 5x - 4

Now to answer the question. Select 2 options.

Both functions must be linear. Yes, because an equation with only an [tex]x[/tex] will be a straight line, if we graph both functions they are both straight lines.

Both functions must be quadratic. No, because a quadratic equation is any equation that can be rearranged in standard form as [tex]ax^{2} + bx +c = 0[/tex] Neither f(x) or g(x) can be rearranged to fit that.

Both functions must have a y-intercept of 0. No, to find the y intercept we set x to 0 and solve for y.

2x + 4 = y                    5x - 4 = y

2(0) + 4 = y                  5(0) - 4 = y

0 + 4 = y                        0 - 4 = y

y = 4                                y = -4

Neither are 0.  

The rate of change of either f(x) or g(x) must be 0. Let's find the rate of change for each equation.

We need an interval so we have to find one. Let's use 1 and 2 for x, but we have to solve for y to get the coordinate.

f(x[tex]_{1}[/tex]) = 2x + 4       f(x[tex]_{2}[/tex]) = 2x + 4         g(x1) = 5x - 4        g(x2) = 5x - 4

x[tex]_{1}[/tex] = 1                     x[tex]_{2}[/tex] = 2                      x

y[tex]_{1}[/tex] = 2(1) + 4           y[tex]_{2}[/tex] = 2(2) + 4           y

y[tex]_{1}[/tex] = 2 + 4              y[tex]_{2}[/tex] = 4 + 4                y

y[tex]_{1}[/tex] = 6                    y[tex]_{2}[/tex] = 8                      y

( 1 , 6 )                  ( 2 , 8 )                     ( 1 , 1 )                   ( 2 , 6 )

Rate of change formula is:

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

Now we just plug in for each function.

f(x) = 2x + 4                                      g(x) = 5x - 4

[tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex] = [tex]\frac{8 - 6}{2 - 1}[/tex] = [tex]\frac{2}{1}[/tex] = 2                            

You can see the rate of change is not 0 for either function.

The y-intercepts of f(x) and g(x) must be opposites. Yes, we solved for the y intercepts earlier.

To find the y intercept we set x to 0 and solve for y.

2x + 4 = y                    5x - 4 = y

2(0) + 4 = y                  5(0) - 4 = y

0 + 4 = y                      0 - 4 = y

y = 4                             y = - 4

4 and - 4 are opposites, so this statement is also true.

please help im am timed​

Answers

Answer:

________________________

I believe that it's 114 degrees.

________________________

Answer:

114

Step-by-step explanation:

angle Bcd=180-66=114 degrees

the two angles are supplementary equal to 180 degrees

evaluate the expression

Answers

Answer:

-5

Step-by-step explanation:

We are given the expression:

[tex]\frac{1}{4} [-5+5(-3)][/tex]

and asked to evaluate.

We must solve this expression according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition and Subtraction.

Solve inside the brackets first. Multiply 5 and -3.

5 * -3= -15

[tex]\frac{1}{4} [-5+-15][/tex]

Add -5 and -15.

-5+-15= -20

[tex]\frac{1}{4} [-20][/tex]

Finally, multiply 1/4 and -20, or divide -20 by 4.

1/4 * -20 = -5      OR       -20/4= -5

[tex]-5[/tex]

When evaluated, the expression 1/4 [ -5 +5(-3)] is equal to -5.

the answer is -5

first you multiply 5 and -3 to get -15.

next you add -5 and -15 to get -20.

the final step is to multiply 1/4 and -20 to get -20/4 which can be simplified to -5.

hope this helped!!

50 points pls answer I will give Brainlyist

Answers

Answer:

point A: 2

point B: -3

your friend is incorrect

Step-by-step explanation:

Answer:

point A: 2

point B: -3

your friend is incorrect

Step-by-step explanation:

prove tan^2 theta - tan^2 phi = (sin^2 theta- sin^2 phi) /cos^2 theta cos^2phi

Answers

Answer:

tan^2 theta - tan^2 phi = (sin^2 theta- sin^2 phi) /(cos^2 theta cos^2phi) (identity has been verified)

Step-by-step explanation:

Verify the following identity:

tan(θ)^2 - tan(ϕ)^2 = (sin(θ)^2 - sin(ϕ)^2)/(cos(θ)^2 cos(ϕ)^2)

Hint: | Eliminate the denominator on the right hand side.

Multiply both sides by cos(θ)^2 cos(ϕ)^2:

cos(θ)^2 cos(ϕ)^2 (tan(θ)^2 - tan(ϕ)^2) = ^?sin(θ)^2 - sin(ϕ)^2

Hint: | Express the left hand side in terms of sine and cosine.

Write tangent as sine/cosine:

cos(θ)^2 cos(ϕ)^2 ((sin(θ)/cos(θ))^2 - (sin(ϕ)/cos(ϕ))^2) = ^?sin(θ)^2 - sin(ϕ)^2

Hint: | Simplify the left hand side.

cos(θ)^2 cos(ϕ)^2 ((sin(θ)/cos(θ))^2 - (sin(ϕ)/cos(ϕ))^2) = cos(θ)^2 cos(ϕ)^2 ((sin(θ)^2)/(cos(θ)^2) - (sin(ϕ)^2)/(cos(ϕ)^2)):

cos(θ)^2 cos(ϕ)^2 (sin(θ)^2/cos(θ)^2 - sin(ϕ)^2/cos(ϕ)^2) = ^?sin(θ)^2 - sin(ϕ)^2

Hint: | Put the fractions in sin(θ)^2/cos(θ)^2 - sin(ϕ)^2/cos(ϕ)^2 over a common denominator.

Put sin(θ)^2/cos(θ)^2 - sin(ϕ)^2/cos(ϕ)^2 over the common denominator cos(θ)^2 cos(ϕ)^2: sin(θ)^2/cos(θ)^2 - sin(ϕ)^2/cos(ϕ)^2 = (cos(ϕ)^2 sin(θ)^2 - cos(θ)^2 sin(ϕ)^2)/(cos(θ)^2 cos(ϕ)^2):

cos(θ)^2 cos(ϕ)^2 (cos(ϕ)^2 sin(θ)^2 - cos(θ)^2 sin(ϕ)^2)/(cos(θ)^2 cos(ϕ)^2) = ^?sin(θ)^2 - sin(ϕ)^2

Hint: | Cancel down (cos(θ)^2 cos(ϕ)^2 (cos(ϕ)^2 sin(θ)^2 - cos(θ)^2 sin(ϕ)^2))/(cos(θ)^2 cos(ϕ)^2).

Cancel cos(θ)^2 cos(ϕ)^2 from the numerator and denominator. (cos(θ)^2 cos(ϕ)^2 (cos(ϕ)^2 sin(θ)^2 - cos(θ)^2 sin(ϕ)^2))/(cos(θ)^2 cos(ϕ)^2) = (cos(θ)^2 cos(ϕ)^2 (cos(ϕ)^2 sin(θ)^2 - cos(θ)^2 sin(ϕ)^2))/(cos(θ)^2 cos(ϕ)^2) = cos(ϕ)^2 sin(θ)^2 - cos(θ)^2 sin(ϕ)^2:

cos(ϕ)^2 sin(θ)^2 - cos(θ)^2 sin(ϕ)^2 = ^?sin(θ)^2 - sin(ϕ)^2

Hint: | Express cos(ϕ)^2 in terms of sine via the Pythagorean identity.

cos(ϕ)^2 = 1 - sin(ϕ)^2:

1 - sin(ϕ)^2 sin(θ)^2 - cos(θ)^2 sin(ϕ)^2 = ^?sin(θ)^2 - sin(ϕ)^2

Hint: | Express cos(θ)^2 in terms of sine via the Pythagorean identity.

cos(θ)^2 = 1 - sin(θ)^2:

sin(θ)^2 (1 - sin(ϕ)^2) - 1 - sin(θ)^2 sin(ϕ)^2 = ^?sin(θ)^2 - sin(ϕ)^2

Hint: | Expand (1 - sin(ϕ)^2) sin(θ)^2.

(1 - sin(ϕ)^2) sin(θ)^2 = sin(θ)^2 - sin(θ)^2 sin(ϕ)^2:

sin(θ)^2 - sin(θ)^2 sin(ϕ)^2 - sin(ϕ)^2 (1 - sin(θ)^2) = ^?sin(θ)^2 - sin(ϕ)^2

Hint: | Expand -(1 - sin(θ)^2) sin(ϕ)^2.

-(1 - sin(θ)^2) sin(ϕ)^2 = sin(θ)^2 sin(ϕ)^2 - sin(ϕ)^2:

sin(θ)^2 - sin(θ)^2 sin(ϕ)^2 + sin(θ)^2 sin(ϕ)^2 - sin(ϕ)^2 = ^?sin(θ)^2 - sin(ϕ)^2

Hint: | Evaluate sin(θ)^2 - sin(θ)^2 sin(ϕ)^2 - sin(ϕ)^2 + sin(θ)^2 sin(ϕ)^2.

sin(θ)^2 - sin(θ)^2 sin(ϕ)^2 - sin(ϕ)^2 + sin(θ)^2 sin(ϕ)^2 = sin(θ)^2 - sin(ϕ)^2:

sin(θ)^2 - sin(ϕ)^2 = ^?sin(θ)^2 - sin(ϕ)^2

Hint: | Come to a conclusion.

The left hand side and right hand side are identical:

Answer: (identity has been verified)

Write the slope intercept form of the equation of the line through (-4,5) and a slope of -2

Answers

Answer:

y=-2x-3

Step-by-step explanation:

y-y1=m(x-x1)

Seven more than twice a number x is forty-seven

Answers

Step-by-step explanation:

Seven more than twice a number is 47. Let's break down this sentence into numbers so you can see what's going on.

"Seven more than twice a number" - This tells you that there is a number, let's call it y, that is 7 more than twice a different number, lets call this x. So in equation form this is y = 7 + 2x. Hmm this seems a little tricky, how do we find the answer? Well if we keep reading, it tells you that the number that is 7 more than twice another number is 47, so we now know that y = 47. So let's redo our equation by substituting y for the number 47:

47 = 7 + 2x

Now we have a workable equation. We need to solve for x. So let's rewrite this equation without changing it, just putting it in different order. Now we have 2x + 7 = 47. So how do we solve for x? First, we subtract 7 from both sides. Remember, when solving for x, anything you do to one side you must do to the other. So now we get this:

2x + 7 = 47 simplifies to 2x = 40

Now if we divide both sides by 2 to get x all by itself, we get x = 20. That is your answer. You can check it by substituting 20 for s in your original equation of 2x + 7 = 47, then you get 2(20) + 7 = 47. It works! Hope this helps!

Please help I will give out brainliest

Answers

Answer:

a.  L.B. = 20.5

b.  U.B. = 21.5

Step-by-step explanation:

Length is measured 21 cm correct to 2 significant figures

a.  Lower bound of 21

  =  20.5 < 21

  = 20.5

b. Upper bound of 21

   = 21 < 21.5

   = 21.5

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