12. If f(5) = 20.58 and f(6)= 2.94

f(7) = __. f(8) = Recursive Function:

Answer:  703

Step-by-step explanation:

This situation is the same as,

7,030 / 10  = 703

Answer:

[tex]x=15/2=7.5[/tex]

Step-by-step explanation:

So we have the function:

[tex]f(x)=2x+1[/tex]

And we want to find x such that:

[tex]f(x)=16[/tex]

To do so, substitute 16 for f(x):

[tex]f(x)=2x+1\\16=2x+1[/tex]

Subtract 1 from both sides. The right side cancels:

[tex](16)-1=(2x+1)-1\\2x=15[/tex]

Divide both sides by 2. The left side cancels:

[tex](2x)/2=(15)/2\\x=15/2=7.5[/tex]

The value of x is 7.5

Answer:

[tex]x=\frac{15}{2}[/tex]

Step-by-step explanation:

We are given the value of f(x). Insert this value into the original equation:

[tex]f(x)=16\\\\16=2x+1[/tex]

Solve for x. Subtract 1 from both sides:

[tex]16-1=2x+1-1\\\\15=2x[/tex]

Divide both sides by 2 to isolate x:

[tex]\frac{15}{2} =\frac{2x}{2} \\\\\frac{15}{2}=x[/tex]

When f(x) equals 16, x is equal to [tex]\frac{15}{2}[/tex]

Answer:

x = 1

y = 1

Step-by-step explanation:

Given:

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

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

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]

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:

113 square feet

Step-by-step explanation:

Since the shape of the mosaic that the architect would be using is circular is shape, the formula to apply to solve this question is area of a circle.

The formula for the area of a circle = πr²

In the above question,Area if a circle = πr²

radius of the circle = r = 6 feet

πr² = π × 6²

113.09733553 square feet

Approximately to the next whole number ≈ 113 square feet.

Therefore, the number in square feet of tiles needed for the mosaic is 113 square feet

Answer:

x-y=-2.

4x+y=2.

Answer is x=4/3 or 1.333333333.

Substitute x into eqtn I.

4/3-y=-2.

y=4/3+2.

y=10/3=3.333333333.~3.33

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:

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

Answer:

8x+40

Step-by-step explanation:

8*x=8x

8*5=40

=8x+40

Hope This Helped!!!

Answer: 8x+40

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:

The sum of a number and 7 multiplied by 2 is increased by 10

Step-by-step explanation:

Answer:

Total cost is 2,800

Step-by-step explanation:

The given ratio 5:7:13 represents profit to cost of materials to labour.

However it is stated that cost of materials is Le 840 more than that of labour

Cost of material - 840 = labour

Cost of material = labour - 840

Let

Cost of material be x, and labour be y

x ÷ y = 7 ÷ 13 (equation 1)

x = y - 840 (equation 2)

Substitute x from equation 1 in equation 2

(y - 840) ÷ y = 7 ÷ 13

13 (y -840) = 7y

y = 1,820

Substitute value of y in equation 2

x = 1820 - 840

x = 980

So total cost is cost of material plus cost of labour = 980 + 1820 = 2,800

This will satisfy the ratio of 5:7:13 representing profit to cost of materials to labour

Answer:

A: Domain: {9, 8, 7, -5} Range: {1, -3, 5, 3}

Step-by-step explanation:

C = {(9, 1) (8, -3) (7, 5) (-5, 3)}

The domain is the inputs

Domain: { -5,7,8,9}

The range is the output

Range{ -3,1,3,5}

This is a functions since there is no input that goes to multiple outputs

Step-by-step explanation:

Given that,

The area of a blackboard is [tex]1\dfrac{1}{3}=\dfrac{4}{3}\ \text{yards}^2[/tex]

The area of poster is [tex]\dfrac{8}{9}\ \text{yards}^2[/tex]

We need to find the unit rate of the blackboard's area to the poster's area. So, it can be calcualted by dividing blackboard's area to the poster's area.

So,

[tex]\dfrac{\dfrac{4}{3}}{\dfrac{8}{9}}=\dfrac{4}{3}\times \dfrac{9}{8}\\\\=1.5[/tex]

So, the rate of [tex]1.5\ \text{yard}^2[/tex].

Answer:

A, B, E

Step-by-step explanation:

Three or more points are said to be collinear, if they lie on a single straight line

Answer:

[tex]\boxed{y=-\frac{1}{2}x+2}[/tex]

Step-by-step explanation:

[tex]2x+4y=8\\\\2x-2x+4y=8-2x\\\\4y=8-2x\\\\\frac{4y=8-2x}{4}\\\\y=2-\frac{2}{4}x\\\\ y=2-\frac{1}{2}x\\\\\boxed{y=-\frac{1}{2}x+2}[/tex]

Hope this helps.

Answer:

y=4-x/2

Step-by-step explanation:

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:

Truck can safely carry 2310 pounds of cargo.

Step-by-step explanation:

Given the safety limit of weight to cross the bridge safely is 4 tons.

1 ton is equal to 2000 pounds.

so, 4 tons are equal to 2000 [tex]\times[/tex] 4 = 8000 pounds

Now, given that

weight of empty truck and driver = 5690 pounds

To find:

Weight of cargo that the truck can safely carry ?

Solution:

Total weight of the truck is actually the combined weight of the empty truck, the drive and the cargo carried in it.

So, Total Weight allowed = 8000 pounds = 5690 pounds + Weight of Cargo

Weight of Cargo = 8000 - 5690 pounds

Weight of Cargo = 2310 pounds

Truck can safely carry 2310 pounds of cargo.

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

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

Explanation:

55 is close to 50

99 is close to 100

55/99 is close to 50/100 = 1/2

Using a calculator, 55/99 = 0.556 approximately which rounds to 0.5 = 1/2

[tex]2x+2(3x-8)=32\\2x+6x-16=32\\8x=48\\x=6[/tex]distribute and collect like-terms

to make sure of the answer:

[tex]2x+2(3x-8)=32\\2(6)+2(3(6)-8)=32\\12+2(18-8)=32\\12+36-16=32\\12+20=32\\32=32[/tex]

Answer:

Step-by-step explanation:

Area of rectangle = Length ×Breadth

[tex]Length =8x+1\\Breadth = 3x-2\\\\A =\left(8x+1\right)\left(3x-2\right)\\\\=8x\times\:3x+8x\left(-2\right)+1\times\:3x+1\times\left(-2\right)\\\\=8\times\:3xx-8\times \:2x+1\times \:3x-1\times\:2\\\\=24x^2-13x-2[/tex]

Answer:

Putting the value in x = 2 , y =4 in 2x - 2y we get,

2 × 2 - 4× 2= 4-8 = -4

Putting the value in z = 3 in z - 5 we get,

z - 5 = 3 - 5 = -2

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:

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:

Answer: 13 + 12i

Step-by-step explanation:

Answer:

-13+4i

Step-by-step explanation:

(-8+8i)-(5+4i)

(-8+8i)-5-4i

-8+8i-5-4i

-8-5+8i-4i

-13+4i

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

Answer:

B. 50 times greater

Step-by-step explanation:

Given;

size of phytoplankton = 2 × 10⁻⁶ in

size of sand grain = 1 × 10⁻⁴ in

Determine how many times longer the grain of sand is than the phytoplankton.

Divide the sand size by the phytoplankton size, to find out how much greater the sand is.

This can be done by equating it as follows;

2 × 10⁻⁶ (y)  = 1 × 10⁻⁴

[tex]y = \frac{1*10^{-4}}{2*10^{-6}} \\\\y = 50[/tex]

Therefore, the grain of sand is 50 times greater than the phytoplankton

B. 50 times greater

Answer:

D. X=2

Step-by-step explanation:

Answer:

X=2

Step-by-step explanation:

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