Jose left the White House and drove toward the recycling plant at an average speed of 40 km/h. Rob left some time later driving in the same direction at an average speed of 48 kn/h. After driving for five hours Rob caught up with Jose. How long did Jose drive before Rob caught up?

Answer:

[tex](-7x^2+3)(x-3)[/tex]

Step-by-step explanation:

We can take "common" from first 2 terms and common from next 2 terms. Shown below:

[tex]-7x^3+21x^2+3x-9\\-7x^2(x-3)+3(x-3)\\(-7x^2+3)(x-3)[/tex]

That's how we do it. We can't simplify, or factor, any further.

Answer:

No correlation

Step-by-step explanation:

With the information provided, we have to conclude there is no correlation, since there is no apparent link between the two information.

It would be a positive correlation for example if we knew that the more apples Juan eats, the more he sleeps (or vice-versa).

It could be a negative correlation if we found that the more apples he eats, the less hours of sleep he has (or vice-versa).

But in this instance, we don't have any data indicating there is any form of correlation between those two numbers.

Answer: Option B

2 is NOT in the domain of f ° g

Step-by-step explanation:

First we must perform the composition of both functions:

If [tex]g(x) = \sqrt{x-9}[/tex] and not [tex]\sqrt{x} -9[/tex]

[tex]f (x) = 4x + 3\\\\g (x) = \sqrt{x-9}\\\\f (g (x)) = 4 (\sqrt{x-9}) + 3[/tex]

The domain of the composite function will be all real numbers for which the term that is inside the root is greater than zero. When x equals 2, the expression within the root is less than zero

[tex]f (g (x)) = 4 (\sqrt{2-9}) + 3\\\\f (g (x)) = 4 (\sqrt{-7}) + 3[/tex]

The root of -7 does not exist in real numbers, therefore 2 does not belong to the domain of f ° g

The answer is Option B.

Note. If   [tex]g(x) = \sqrt{x}-9[/tex]

So

[tex]f(g(x)) = 4(\sqrt{x})-36 + 3[/tex]   And  2 belongs to the domain of the function

ANSWER

C

E

F

EXPLANATION

The result of the synthetic division is :

3 -1 0

The last number is the remainder which is 0

The first two numbers are the coefficients of the quotient.

Therefore the quotient is 3x -1

Since the remainder is 0, x-4 is a factor of

[tex]f(x) = 3 {x}^{2} - 13x + 4[/tex]

This also means that:

[tex](3 {x}^{2} - 13x + 4) \div (x - 4) = 3x - 1[/tex]

This again means that x=4 is a root of

[tex]f(x) = 3 {x}^{2} - 13x + 4[/tex]

The correct choices are C,E and F.

Answer:

The amplitude  of the given sinusoidal function is 3.5

Step-by-step explanation:

The given sinusoidal function is

[tex]m(x)=-3.5\cos x[/tex]

This function is of the form:

[tex]m(x)=a\cos bx[/tex]

where

a=|-3.5|=3.5 is the amplitude.

Therefore the amplitude of the given sinusoidal function is 3.5

Answer:

Step-by-step explanation:

[tex]\text{De}\text{finition of logarithm:}\\\\\log_ab=c\iff a^c=b\\\\\text{where}\ a>0\ \wedge\ a\neq1\ \wedge\ b>0\ \wedge\ c\in\mathbb{R}\\===========================\\\\\log_2n=4\iff n=2^4\\\\n=16[/tex]

Answer:

I don't know what answers you were given to your problem but I think the answer is

D) log n =4log2

Sorry if I got it wrong.

Answer:

3n+21

Step-by-step explanation:

3 × n =3n

3 × (+7) = +21

Answer:

Use distributive property.

3(n+7),

3*n + 3*7=

3n + 21

Hope this helps and have a great day!

I believe I did this correctly. Comment to tell me if I didn't.

__________________________________

I got infinite solutions.

For the second problem, I subtracted 9 from both sides. Then I divided them all by -1. They are the same equations.

ANSWER

b) infinite solutions

EXPLANATION

The given system is:

x=3y+9 ...(1)

9-x=-3y...(2)

Put equation (1) into equation (2)

This implies that,

9-(3y+9)=-3y

Expand the parenthesis,

9-3y-9=-3y

-3y=-3y

1=1

This implies that, that the system has infinitely many solutions.

Answer:

C. 9P6

Step-by-step explanation:

Given choices are :

A. 8P5

B. 9P1

C. 9P6

D.8P1

Now we need to find about which below is largest when evaluated.

So let's evaluate them using formula:

[tex]nPr=\frac{n!}{\left(n-r\right)!}[/tex]

[tex]8P5=\frac{8!}{\left(8-5\right)!}=\frac{8!}{\left(3\right)!}=6720[/tex]

[tex]9P1=\frac{9!}{\left(9-1\right)!}=\frac{9!}{\left(8\right)!}=9[/tex]

[tex]9P6=\frac{9!}{\left(9-6\right)!}=\frac{9!}{\left(3\right)!}=60480[/tex]

[tex]8P1=\frac{8!}{\left(8-1\right)!}=\frac{8!}{\left(7\right)!}=8[/tex]

Largest value among those numbers is 60480.

Hence correct choice is C. 9P6

Answer:wazz up

Step-by-step explanation:

yooo what’s up dude

Answer:

The variation equation is

[tex] f = \frac{k.m_1.m_2}{ {r}^{2} } [/tex]

step-by-step explanation:

From the question, the two masses are

[tex]m_1 \: and \: m_2[/tex]

This implies that the product of the two masses

[tex] = m_1 \times m_2 = m_1.m_2[/tex]

Moreover, the force,f varies directly with the products of the two masses

[tex] \implies \: f\propto m_1.m_2....eqn.1[/tex]

Also, the force varies inversely with the square of the distance,r

[tex] \implies \: f\propto \frac{1}{ {r}^{2} }.......eqn.2[/tex]

Joining equation 1 and 2, we got

[tex] \implies \: f\propto \frac{1}{ {r}^{2}} \times m_1.m_2[/tex]

[tex] \implies \: f \propto\frac{m_1.m_2}{ {r}^{2}}[/tex]

But the constant of variation is k

Multiplying the right hand side of the equation by k, we got

[tex] \implies \:f=\frac{k.m_1.m_2}{ {r}^{2}}[/tex]

Answer:

[tex]96\ basketballs[/tex]

Step-by-step explanation:

step 1

Find the volume of the cylinder (hollow drum)

The volume is equal to

[tex]V=\pi r^{2} h[/tex]

we have

[tex]h=48\ in[/tex]

[tex]r=24\ in[/tex]

substitute

[tex]V=\pi (24)^{2} (48)[/tex]

[tex]V=27,648\pi\ in^{3}[/tex]

step 2

Find the volume of one basketball

The volume of the sphere is equal to

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

we have

[tex]r=6\ in[/tex]

substitute

[tex]V=\frac{4}{3}\pi (6)^{3}[/tex]

[tex]V=288\pi\ in^{3}[/tex]

step 3

Find the maximum number of basketballs that the cylindrical drum contains

so

Divide the volume of the cylinder by the volume of one basketball

[tex]27,648\pi/288\pi=96\ basketballs[/tex]

The area of the square is 36 squared inches, because it is a square with a side of 6 inches.

The two semicircles have a radius of 3 inches. If we subtract their areas from the area of the square, we have

[tex]36-2\left(\dfrac{\pi\cdot 3^2}{2}\right) = 36-9\pi[/tex]

The shaded region is half of this area, so the answer is

[tex]\dfrac{36-9\pi}{2} \approx 7.7[/tex]

36 minus 9 multiplied by Pi . Then divide that answer by 2 to get 7.7

None.

Distribute the 3 to the (x + 4) to get 3x + 12.

Subtract 3x from both sides to get 12 = 4.

This is not true, so there are no solutions.

Where is 'the following'?

(I'll Answer in comments just give detail)

Answer:

range

Step-by-step explanation:

this is because it is asking the not central which is range.

Answer:

Option B f(x) = x + 1

Step-by-step explanation:

The given points are

x        y        Relationship (x & y)

-2      -1        -2 + 1 = -1      

0        1         0 + 1 = 1    

1        2          1 + 1 = 2    

3       4          3 + 1 = 4    

5       6          5 + 1 = 6

As we can see the difference in x and y values of each ordered pairs is one

Therefore, relationship between x & y that can be represented by y = x + 1

Option B f(x) = x + 1 is the answer.

Answer: Second option.

Step-by-step explanation:

The square root of a number "x" is a number "b" that multiplied by itself is "x":

[tex]b*b=x[/tex]

We know that the square root of 16 is 4 ([tex]\sqrt{16}=4[/tex]) because:

[tex]4*4=16[/tex]

Then [tex]\sqrt{13}[/tex] should be less than 4.

We know that the square root of 9 is 3 ([tex]\sqrt{9}=3[/tex]) because:

[tex]3*3=9[/tex]

Then [tex]\sqrt{13}[/tex] should be greater than 3.

Therefore, the value of  [tex]\sqrt{13}[/tex] is between 3 and 4.

This matches with the second option.

Hello Brainly Student! Your answer is 3 and 4! Hope this helped!!

Answer:

A) −13

Step-by-step explanation:

(x + 6)^2 = 49

Take the square root of each side

sqrt((x + 6)^2) = ±sqrt(49)

x+6 = ±7

Subtract 6 from each side

x+6-6 = -6  ±7

x =-6  ±7

Separating into 2 parts

x = -6+7          x = -6-7

x = 1               x = -13

Answer:

A. 6

Step-by-step explanation:

f(x) = x² − 12x + 7

To complete the square, we first factor the leading coefficient to make it 1 (which it already is).

Then, we take half the second coefficient, square it, and then add to both sides.  So (-12/2)² = (-6)² = 36.

f(x) + 36 = x² − 12x + 36  + 7

Then we factor the perfect square:

f(x) + 36 = (x − 6)² + 7

Then solve for f(x) by subtracting and simplifying:

f(x) = (x − 6)² + 7 − 36

f(x) = (x − 6)² − 29

So the value of a is 6.

Answer:

-6 I think

Step-by-step explanation:

r1 = -12 and r2 = 12

[tex]\bf 40\pi =\cfrac{5}{18}\pi r^2\implies 40\pi =\cfrac{5\pi r^2}{18}\implies 720\pi =5\pi r^2\implies \cfrac{720\pi }{5\pi }=r^2 \\\\\\ 144=r^2\implies \sqrt{144}=r\implies 12=r[/tex]

T o find the median if there are two numbers in between find the mean or the average. To do that add up the 2 middle numbers then divide by 2 that's your median

Answer:

C

Step-by-step explanation:

[tex] \frac{ - 1}{3} \times a = -1[/tex]

then

[tex]a = 3 \: where \: a \: is \: our \: line \: slope[/tex]

Answer:

[tex]\boxed{\text{C. } y - 2 = 3(x - 6)}[/tex]

Step-by-step explanation:

The slope of the perpendicular line m₂ must  be the negative reciprocal of the slope m₁ of the first line.

[tex]m_{2} = -\dfrac{1}{m_{1}} = -\dfrac{1}{-\frac{1}{3}} = 3[/tex]

The only equation with m = 3 is  

[tex]\boxed{\textbf{C. } y - 2 = 3(x - 6)}[/tex]

This is the point slope form of the equation for a straight line through (6, 2) with slope = 3.

Answer:

113.09733552923 in2

Step-by-step explanation:

The leash is basically the radius. If the radius is 6...

If you find the area of the circle using the formula πr square. π=3.14. you can do the rest.

Answer:

n = 4, m = 1

Step-by-step explanation:

Given the 2 equations

3m + n = 7 → (1)

m + 2n = 9 → (2)

Rearrange (2) expressing m in terms of n, by subtracting 2n from both sides

m = 9 - 2n → (3)

Substitute m = 9 - 2n into (1)

3(9 - 2n) + n = 7 ← distribute left side

27 - 6n + n = 7 ← simplify left side

27 - 5n = 7 ( subtract 27 from both sides )

- 5n = - 20 ( divide both sides by - 5 )

n = 4

Substitute n = 4 into (3) for corresponding value of m

m = 9 - (2 × 4) = 9 - 8 = 1

Thus m = 1 and n = 4

All triangles equal 180 degrees.

The answer is 180 degrees.

The value of the expression for 121 is 11

Answer:

$36.75

Step-by-step explanation:

Answer: the sales tax alone is $36.75

the above ground pool with the sales tax is 561.75

Step-by-step explanation:

525x.07 =36.75

525x1.07=561.75 or another way you could do it is 525+36.75=561.75

Answer:

B

Step-by-step explanation:

Corresponding angles are not always congruent

Corresponding angles are congruent.

Answer is B.

Answer:

the answer is 2.9 x 10^0 and 3.2 x 10^-2

Step-by-step explanation:

10^0 is equal to 1 so 2.9 x 10^0 is really 2.9 times 1 which is less than 3

if i could get brainliest answer that would be great!

10^-2 is a exponential that makes a number go down so 3.2 going down is less than 3

Answer:

C and D

Step-by-step explanation:

A.   2.9 × 10¹ = 2.9 × 10     = 29

B.  3.2 × 10³ = 3.2 × 1000 = 3000

C.  2.9 × 10⁰ = 2.9  × 1      = 2.9

D. 3.2 × 10⁻² = 3.2 × 0.01 = 0.032

Both C and D have values less than 3.