Use synthetic division to solve (4x-3x+5x+6)/(x+6). What is the quotient?

What's 65-70 days in weeks

dusya [7]

Answer:

About 9-10 weeks

Step-by-step explanation:

70/7= 10

4 0

3 years ago

Read 2 more answers

Since 2010, when 102390 Cases were reported, each year the number of new flu cases decrease to 85% of the prior year. Predict th

BaLLatris [955]

Answer:

20,158 cases

Step-by-step explanation:

Let $t=0$ represent year 2010.

We have been given that since 2010, when 102390 Cases were reported, each year the number of new flu cases decrease to 85% of the prior year.

Since the flu cases decrease to 85% of the prior year, so the flu cases for every next year will be 85% of last year and decay rate is 15%.

We can represent this information in an exponential decay function as:

$F(t)=102,390(1-0.15)^t$

$F(t)=102,390(0.85)^t$

To find number of cases in 2020, we will substitute $t=10$ in our decay function as:

$F(10)=102,390(0.85)^{10}$

$F(10)=102,390(0.1968744043407227)$

$F(10)=20,157.970260446597\approx 20,158$

Therefore, 20,158 cases will be reported in 2020.

3 0

3 years ago

Give the properties for the equation -2x 2 - y + 10x - 7 = 0.

Sladkaya [172]

Given:

The quadratic equation is

$-2x^2-y+10x-7=0$

To find:

The vertex of the given quadratic equation.

Solution:

If a quadratic function is $f(x)=ax^2+bx+c$ , then

$Vertex=\left(\dfrac{-b}{2a},f(\dfrac{-b}{2a})\right)$

We have,

$-2x^2-y+10x-7=0$

It can be written as

$-2x^2+10x-7=y$

$y=-2x^2+10x-7$ ...(i)

Here, $a=-2,b=10,c=-7$ .

$\dfrac{-b}{2a}=\dfrac{-10}{2(-2)}$

$\dfrac{-b}{2a}=\dfrac{-10}{-4}$

$\dfrac{-b}{2a}=\dfrac{5}{2}$

Putting $x=\dfrac{5}{2}$ in (i), we get

$y=-2(\dfrac{5}{2})^2+10(\dfrac{5}{2})-7$

$y=-2(\dfrac{25}{4})+\dfrac{50}{2}-7$

$y=\dfrac{-50}{4}+25-7$

$y=\dfrac{-25}{2}+18$

On further simplification, we get

$y=\dfrac{-25+36}{2}$

$y=\dfrac{11}{2}$

So, the vertex of the given quadratic equation is $\left(\dfrac{5}{2},\dfrac{11}{2}\right)$ .

Therefore, the correct option is A.

3 0

3 years ago

Find the quadratic function that has a vertex at (3,4) and goes through the point (0,13).

vladimir2022 [97]

Answer:

f

(

x

)

=

−

1

2

x

2

+

3

x

−

1

2

Explanation:

A quadratic function can be written in vertex form as:

f

(

x

)

=

a

(

x

−

h

)

2

+

k

where

(

h

,

k

)

is the vertex and

a

is a constant multiplier.

In our example the vertex

(

h

,

k

)

is

(

3

,

4

)

, so we can write:

f

(

x

)

=

a

(

x

−

3

)

2

+

4

Given that this passes through the point

(

1

,

2

)

, we must have:

2

=

a

(

1

−

3

)

2

+

4

=

4

a

+

4

Subtract

4

from both ends to get:

−

2

=

4

a

Divide both sides by

4

and transpose to find:

a

=

−

1

2

So our quadratic function can be written in vertex form as:

f

(

x

)

=

−

1

2

(

x

−

3

)

2

+

4

We can multiply this out and simplify as follows:

f

(

x

)

=

−

1

2

(

x

−

3

)

2

+

4

f

(

x

)

=

−

1

2

(

x

2

−

6

x

+

9

)

+

4

f

(

x

)

=

−

1

2

x

2

+

3

x

−

9

2

+

4

f

(

x

)

=

−

1

2

x

2

+

3

x

−

1

2

Step-by-step explanation:

PLZ MARK ME BRAINLYIST

4 0

3 years ago

Lane is making accessories for the soccer team. He uses 759.46 inches of fabric on headbands for 44 players and 2 coaches. He al

madam [21]

Answer:

Fabric used by each each player for headband is 16.51 inches and fabric used for wristband is 1.99 inches

Step-by-step explanation:

In first case it is given that there are players and 2 coaches

So total number = 44+2 = 46

It is given that 759.46 inches of fabric is used on headbands for 44 players and 2 coaches

So fabric used by each player $=\frac{759.46}{46}=16.51inches$

Now in second 87.64 inches fabric is used for 44 players

So fabric used by each players $=\frac{387.64}{44}=1.99inches$

So fabric used by wristband is 1.99 inches

4 0

3 years ago