Find two consecutive integers(with the least sum) whose sum is at least 107

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.

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

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

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

40

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

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!

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.

Answer:

division property of equality.

Step-by-step explanation:

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

Step-by-step explanation:

this is solutions of your questions

Answer:  703

Step-by-step explanation:

This situation is the same as,

7,030 / 10  = 703

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

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:

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

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

gronala bars:18

energy drinks:9

Step-by-step explanation:

$0.50 •18= $9

$2.00•9=$18

$9+$18=$27

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!

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

Answer:

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

The answer is 3b + 6 in Khan Accademy

Answer:

D. X=2

Step-by-step explanation:

Answer:

X=2

Step-by-step explanation:

Answer:

-2(3v - 6) = 0

-6v + 12 = 0

-6v = -12

v = -12/-6

v = 2 answer

Step-by-step explanation:

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.

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

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

Answer:

x = 15

Step-by-step explanation:

4x - 3 ( x - 2 ) = 21

Distribute

4x -3x +6 = 21

Combine like terms

x+6 = 21

Subtract 6 from each side

x+6-6=21-6

x = 15

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)

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.

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:

Answer:

x=13

Step-by-step explanation:

Q is the midpoint of PR

PQ + QR = PR

PQ= QR

PQ+QR = PR

QF + QR = PR

2QR = PR

2*43 = 9x-31

86 = 9x-31

Add 31 to each side

86+31 = 9x-31+31

117 = 9x

Divide each side by 9

117/9 = 9x/9

13 =x

Answer:

x = 13

Step-by-step explanation:

since Q is the midpoint of PR and QR is 43, then

PR = QR * 2 ⇒ 43 * 2 = 86

PR = 9x - 31

⇒ 9x - 31 = 86

⇒ 9x = 86 + 31

⇒ 9x = 117

Divide both sides by 9 ⇒ [tex]\frac{9x}{9} = \frac{117}{9}[/tex]

⇒ x = 13

Answer:

y=-2x-3

Step-by-step explanation:

y-y1=m(x-x1)