MATHEMATICS HIGH SCHOOL

F(13) = -3x+ 7
What’s the answer?

Answers

Answer 1
Answer:

Answer:

3.3

Step-by-step explanation:

7-7=0

-3+-7=-10

10 divided by 3 is 3.3

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What is the final amount if 1885 is increased by 5% followed by a further 18% increase
Mara carried water bottles to the field to share with her team at halftime. The water bottles weighed a total of 60x2 + 48x + 24 ounces. Which factorization could represent the number of water bottles and weight of each water bottle? 6(10x^2 + 8x + 2) 12(5x^2 + 4x + 2) 6x(10x^2 + 8x + 2) 12x(5x^2 + 4x + 2)
i cant find my answer. You should really give your people the answer they are looking fo instead of giving sujestions.
How do you solve -8+3x <-17x+17 for graphing?

Find the equation of all tangent lines having slope of -1 that are tangent to the curve y=(9)/(x+1)

Answers

Answer: y = -x + 5   and    y = -x - 7     (see attached graph)

Step-by-step explanation:

y = (9)/(x + 1)

  = 9(x + 1)⁻¹

Use the product rule to find the derivative

a = 9           a' = 0

b = (x + 1)⁻¹   b' = -(x + 1)⁻²

 ab' + a'b

= 9[-(x + 1)⁻²] + 0[(x + 1)⁻¹ ]

= (-9)/((x + 1)^(2))

Set the derivative equal to the desired slope of -1 to solve for x

-1 = (-9)/((x + 1)^(2))

-(x + 1)² = -9

 (x + 1)² = 9

 √(x + 1)² = √9  

    x + 1 = +/- 3

x + 1 = 3      x + 1 = -3

     x = 2          x = -4

Plug those values into the original equation to solve for y:

y = (9)/(x + 1)

  = (9)/(2 + 1)

  = 3

(2, 3)

y = (9)/(x + 1)

  = (9)/(-4 + 1)

  = -3

(-4, -3)

Next, plug in the given slope (-1) and the coordinates above into the Point-Slope formula y - y₁ = m(x - x₁) to find the equations:

m = -1, (x₁ y₁) = (2, 3)                             m = -1, (x₁ y₁) = (-4, -3)

y - 3 = -1(x - 2)                                       y + 3 = -1(x + 4)

y - 3 = -x + 2                                          y + 3 = -x - 4

    y = -x + 5                                                y = -x - 7

Answer:

f(x)=\frac9{x+1}\n f'(x)=-\frac9{(x+1)^2}\n f'(x)=-1\ \iff\ -\frac9{(x+1)^2}=-1\ \to \ \frac9{(x+1)^2}=1\ \to \ (x+1)^2=9\n |x+1|=3\ \to \ x+1=3\ \vee\ x+1=-3\n x_1=2\ \vee\ x_2=-4\n f(x_1)=f(2)=\frac9{2+1}=3\n f(x_2)=f(-4)=\frac9{-4+1}=-3

First tangent line:

y=f'(x_1)\cdot (x-x_1)+f(x_1)\ \to \ y=-1(x-2)+3\ \to \ y=-x+5

Second tangent line:

y=f'(x_2)\cdot (x-x_2)+f(x_2)\ \to \ y=-1(x+4)-3\ \to \ y=-x-7


Notice: slope of -1 means that both f'(x_1), \ f'(x_2) are equal to -1, so f'(x_1)=-1 \ and \ f'(x_2)=-1

mike drove to a frineds house at the rage of 40 mph. he returned hoke by the dsne route at 45 mph the driving time for the round trip was four hours how long did it take mike to get home

Answers

Let the distance be x miles

Time = Distance / speed

Time taken by Mike to go to his friend's house = x / 40 hours

Time taken by him to return = x / 45 hours

Total time = x / 40 + x / 45 = 4 hours

= 9x + 8x = 1440 miles

17x = 1440

= x = 1440 ÷ 7

= x = 84.706

Time taken to return home = 84.706 /45= 1.882 hours .

Therefore , Mike took1.882hoursto reach home .

a weight hangs from a rope 20 feet long. It swings through an angle of 27 degrees each second. how far does the weight travel each second? round to the nearest 0.1 foot

Answers

Answer:

S=9.42 feet

Step-by-step explanation:

Since, the length of the rope is 20 feet and it swings through an angle of 27° each second, let s be the distance traveled by the weight, then

using the formula, S=\frac{{\theta}}{360^{{\circ}}}{*}2{\pi}r

Placing the given values, we get

S=\frac{27^{{\circ}}}{360^{{\circ}}}{*}2{*}(22)/(7){*}20

=0.075{*}(44)/(7){*}20

=9.42 feet

If three bags of birdseed cost $14.16, how much will 14 bags cost? A. $33.71
B. $66.08
C. $30.34
D. $70.80

Answers

All the information's required for solving this problem is already given in the question.
The cost of 3 bags of birdseed = 14.16 dollars
Then
The cost of 1 bag of birdseed = (14.16/3) dollars
So
The cost of 14 bags of birdseed = (14.16/3) * 14 dollars
                                                    = 198.24/3 dollars
                                                    = 66.08 dollars
So from the above deduction we can see that the correct option is option "B". The cost of 14 bags of birdseed is $66.08. I hope the procedure is clear enough for you to understand.
the correct cost would have to be b. $66.08. You have to divide $14.16 by 3, then multiply by 14.

The trees at a national park have been increasing in numbers. There were 1,000 trees in the first year that the park started tracking them. Since then, there have been as many new trees each year. Create the sigma notation showing the infinite growth of the trees and find the sum, if possible. Year New trees 1 1000 2 200 3 40

Answers

Answer:

Step-by-step explanation:

There were 1000 trees in the first year and every year new trees are getting added.

The sequence formed for the new trees every year is

Year                1           2           3

New trees   1000      200      40

We see a geometric sequence has been formed by the new trees added

Ratio of the second year and 1st year trees added = (200)/(1000)=(1)/(5)

Similarly ratio of trees added in 3rd year to 2nd year = (40)/(200)=(1)/(5)

So there is a common ratio of (1)/(5)

Explicit formula of a geometric sequence representing growth of the trees by

T_(n)=a(r)^(n-1)

where a = number of trees grown first year

r = common ratio

n = number of years

Explicit formula showing the growth of the trees using sigma notation will be

\sum_(n=1)^(\infty)1000((1)/(5))^(n-1)

And Formula for number of trees every year will be

\sum_(n=1)^(\infty)1000+1000((1)/(5))^(n-1)

\sum_(n=1)^(\infty)1000[1+((1)/(5))^(n-1)]

Sum of the trees will be

S=(a)/(1-r)

        = (2000)/(1-(1)/(5))

        = (2000)/((4)/(5) )

        = (2000* 5)/(4)

        = 2500

For each sentence below, use the drop-down menu to select a symbol that correctly indicates the relationship.Three is less than a number. 3 < x
One more than a number is at least seven. x + 1 > 7
The maximum value of a number is 29. x < 29
The difference of a number and ten is at least 91. x - 10 > 91

Answers

Answer:

3 < x

  x + 1 \geq 7

 x \leq 29

x - 10 \geq 91

Step-by-step explanation:

Let the unknown number be x

Three is less than a number: for less than we use < symbol

3 < a number becomes 3 < x

One more than a number is at least seven: Number atleast 7 means 7 or more than 7. So we use ≥ 7. One more than a number is x+1

           x + 1 \geq 7

The maximum value of a number is 29: maximum value of x is 29 , so 29 or less than 29. Use ≤ symbol

            x \leq 29

The difference of a number and ten is at least 91: The difference of a number and 10 is x-10. For at least we use ≥ because 91 is included.

           x - 10 \geq 91
Three is less than a number.
3 < x

One more than a number is at least seven.
x + 1 ≥ 7

The maximum value of a number is 29.
x ≤ 29

The difference of a number and ten is at least 91.
x - 10 ≥ 91
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