Which of these is a unit of density?

A. km/m³
B. kg/m²
C. kg/m³
D. kg/m
​

Answer:

Step-by-step explanation:

To graph an exponential function f(x) = [tex]2^{x-1}[/tex],

Step - 1 :

Find the value of x that makes the exponent 0.

x - 1 = 0

x = 1

f(1) = 2⁰ = 1

Similarly, for other input values (x- values),

For x = 2,

f(2) = [tex]2^{2-1}[/tex]

     = 2¹

     = 2

For x = 3

f(3) = [tex]2^{3-1}[/tex]

     = 2²

     = 4

For x = 4

f(4) = [tex]2^{4-1}[/tex]  

     = 2³

     = 8

Therefore, table for input - output values will be,

x        1            2            3          4

f(x)     1            2            4          8

Answer:

:>

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

........

Answer:

42

Step-by-step explanation:

Area= 1/2(bh)

Area=1/2(12)(7)

Area=1/2)(84)

Area=42

Answer:

x = 135

Step-by-step explanation:

Use the right triangle altitude theorem and similar triangles.

x/81 = 225/x

x^2 = 81 * 225

x = 9 * 15

x = 135

Answer:

135

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

To answer this question, set the equation equal to 100 and solve for x. Thus:

[tex]100=50(1.03)^x[/tex]

[tex]2=(1.03)^x[/tex]

[tex]x=\log_{1.03}2\approx23.45\approx23[/tex]

Therefore, 23 years after 2000, the population will reach 100 million.

Hence, our answer is B, at the year 2023.

Answer:

B

Step-by-step explanation:

Answer:

40% spent. 60% left.

Step-by-step explanation:

To find the percentage spent, divide the two values, then multiply by 100.

$32 / $80 = 0.40    0.40 x 100 = 40% spent.

To find the percentage of money left, subtract the two values.

$80 -$32 = $48

Then, divide the two values and multiply by 100.

$48 / $80 = 0.60   0.60 x 100 = 60% left.

Answer:

B. 120°

Step-by-step explanation:

If two tangents intersect in the exterior of a circle, then the measure of the angle formed is one half the difference of the measures of the intercepted arcs.

m∠A° = 1/2(300 - 60)

m∠A° = 1/2(240)

m∠A° = 120

Answer:

2.4

Step-by-step explanation:

The first decimal place is 3, the digit after that is 7 which is more or equal to 5. So add +1 to the 3, followed by zeros.

2.37 ⇒ 2.40

Answer: [tex]x^2-17x+30=0[/tex]

Step-by-step explanation:

Let x = Time taken (in days) by Jean to do the job.

Then, Time taken by Kate to do the job = x-5

Then, together they will take time (t) as

 [tex]\dfrac{1}{t}=\dfrac{1}{x}+\dfrac{1}{x-5}[/tex]

[tex]=\dfrac{x-5+x}{x(x-5)}=\dfrac{2x-5}{x(x-5)}[/tex].

[tex]\Rightarrow\ t=\dfrac{x(x-5)}{2x-5}[/tex]

Since it is given that Kate and Jean paint a house together in 6 days.

i.e.

[tex]6=\dfrac{x(x-5)}{2x-5}\\\\\Rightarrow 6(2x-5)=x^2-5x\\\\\Rightarrow\ 12x-30=x^2-5x\\\\\Rightarrow\ x^2-5x-12x+30=0\\\\\Rightarrow\ x^2-17x+30=0[/tex]

So, the equation represents the time it takes Kate to paint the house by herself is [tex]x^2-17x+30=0[/tex] .

Answer:

x^2 − 7x − 30 = 0 

Step-by-step explanation:

Answer: A

Step-by-step explanation:

The domain of a function is the minimum and maximum value of independent variable (x).

The domain of the function according to the given graph will be the starting point of the line of best fit to the end point of the line.

Trace the starting point and the end point to the x - axis.

If you do so, the starting point is 2 and the end point is 10.

The domain is therefore, 2< = x <= 10. The correct answer is A

Answer:

see below

Step-by-step explanation:

2x^2-3x+

Factor out 2

2( x^2 -3/2x)

Take the coefficient of x

-3/2

Divide by 2

-3/4

Square it

(-3/4) ^2 = 9/16

This is the number inside the square

2( x^2 -3/2x + 9/16)

Multiply by 2 since that is factored on the outside

9/16 *2 = 9/8

Add to the equation

2x^2-3x+9/8

Answer:

[tex](x+10)^2-186[/tex]

Step-by-step explanation:

Answer:

=434.86

Step-by-step explanation:

The radius = 4.7cm

this means that using the equation that is given (V=4/

3πr^3)

add the radius where it says r

it also says you are allowed to use a calculator so put the equation into your calculator to give you the answer.

i hope this helped :)

Answer:

volume of sphere is 4 thirds pie r squared. Google it!

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Answer:

[tex]2(x + 4)(x - 5)[/tex]

Step-by-step explanation:

Given

[tex]2x^2 - 2x - 40[/tex]

Required

Factorize

[tex]2x^2 - 2x - 40[/tex]

Start by expanding the above expression

[tex]2x^2 - 10x + 8x- 40[/tex]

Then, split the expanded expression into two

[tex](2x^2 - 10x) + (8x- 40)[/tex]

Factorize the split expression:

[tex]2x(x - 5) + 8(x- 5)[/tex]

[tex](2x + 8)(x - 5)[/tex]

Expand the expression in the first bracket

[tex](2x + 2*4)(x - 5)[/tex]

Then take out common factor

[tex]2(x + 4)(x - 5)[/tex]

From the list of given options, option A is correct

Answer:

A

Step-by-step explanation:

I took the test.

Answer:

C.

Step-by-step explanation:

add up all of the angles correct ft im not sure but i think its C.

Answer: The number one occurs 300 times while writing the numbers from 1 to 999.

Step-by-step explanation:

Answer:

Question 8 should be 25.6 hours

Step-by-step explanation:

Since time = distance/speed.

We just replace the words with the appropriate numbers.

time =

[tex] \frac{ 3.84 \times {10}^{5} }{1.5 \times {10}^{4} } [/tex]

which equals 25.6

Answer: parallel

Step-by-step explanation:  If two parallel planes are cut by a third plane, then the lines of intersection are parallel. Parallel lines are defined as lines that have only one point in common. Skew lines are parallel.

Answer:

The graph of the function f( (1/2)x ) will expand across x-axis

Step-by-step explanation:

We have been given the function:

f(x) = x⁴

If we substitute x = (1/2)x into the given equation, we get:

f((1/2)x) = ( (1/2)x )⁴

We can simplify the equation

f((1/2)x) = = (1/2)⁴ x⁴

f((1/2)x) = = (1/16) x⁴

Graph of both of the functions is shown below. We can clearly see that that the graph of the function f((1/2)x) = = (1/16) x⁴ expands horizontally on x-axis as compared to the graph of f(x) = x⁴

Answer:

Step-by-step explanation:

Total number of cards = 48

Red cards/black cards = 1/1

(so, 24 each of read and black cards)

8 red cards are removed.

Now, there will be (24-8) number of cards left in the pack which equals to 16 cards.

So, now the number of red cards in the pack= 16

Number of black cards = 24

Ratio of red card/ black card

[tex] = \frac{16}{24} [/tex]

[tex] = \frac{2}{3} [/tex]

Hope this helps...

Good luck on your assignment...

Answer: 0, −5, 4

Step-by-step explanation:

The given function is

[tex]f(x)=x^3+x^2-20x[/tex]

One of the zero of the given polynomial function is x=0.

To find other zeroes put f(x)=0

[tex]x^3 + x^2 - 20x=0\\\\\Rightarrow\ x(x^2+x-20)=0\ \ \ [\text{Taking x as common}][/tex]

That is

[tex]x^2+x-20=0[/tex] or [tex]x=0[/tex]

if [tex]x^2+x-20=0[/tex]

then [tex]x^2+5x-4x-20=0\ \ \ [\text{By using middle term splitting method}][/tex]

[tex]\Rightarrow\ x(x+5)-4(x+5)=0\\\\\Rightarrow\ (x+5)(x-4)=0\\\\\Rightarrow\ x=-5, 4[/tex]

So, the zeroes of f(x) are 0, −5, 4 .

Hence, the correct option is 0, −5, 4.

Answer:

Leftmost box: Graph, because it has zero x intercepts

Middle box: Function f with a vertex at 2, 0

Rightmost box: g(x)=x^2+x-2

Answer:

g(x)=x^2+x-2

Step-by-step explanation:

Answer:

last three questions are statistical question

Answer:

The last three questions

Step-by-step explanation:

Answer:

1. a. His new texting speed after one month is 2 + 1/2 = 2.5 characters per second.

b. After two months it will be 2 + (1/2) * 2 = 3 characters / second.

c. Answer is 2 + 1/2 * 3 = 3.5 characters/second/.

2. The answer is s = 1/2m + 2

3. To solve for m we write 8 = 1/2m + 2 → 6 = 1/2m → m = 12 months.

4. 10r + 4 = 8 → 10r = 4 → r = 0.4

5. The variable r represents the rate she must increase her texting speed by per month.

6. A scenario could be "Allison has 37 marbles in a jar. She took out 5 from the jar and wants to divide the remaining amount equally among her 8 friends. How many marbles does each friend get?".

Answer:

So your answer is  d = -1/4 = -0.250

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    6*d-11/2-(2*d-13/2)=0

           13

Simplify   ——

           2

        11            13

 (6d -  ——) -  (2d -  ——)  = 0

        2             2

2.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  2  as the denominator :

          2d     2d • 2

    2d =  ——  =  ——————

          1        2  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

2.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

2d • 2 - (13)     4d - 13

—————————————  =  ———————

      2              2  

        11     (4d - 13)

 (6d -  ——) -  —————————  = 0

        2          2    

           11

Simplify   ——

           2

4.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  2  as the denominator :

          6d     6d • 2

    6d =  ——  =  ——————

          1        2  

4.2       Adding up the two equivalent fractions

6d • 2 - (11)     12d - 11

—————————————  =  ————————

      2              2    

5.1       Adding fractions which have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

(12d-11) - ((4d-13))     8d + 2

————————————————————  =  ——————

         2                 2  

6.1     Pull out like factors :

  8d + 2  =   2 • (4d + 1)

 4d + 1  = 0

 4d + 1  = 0

7.1      Solve  :    4d+1 = 0

Subtract  1  from both sides of the equation :

                     4d = -1

Divide both sides of the equation by 4:

                    d = -1/4 = -0.250

Answer:

d = -1/4 = -0.250

Step-by-step explanation:

Answer:   £ 81.38

Step-by-step explanation:

Given: On Monday,

5 builders took [tex]3\dfrac{1}{2}[/tex] hours  ( i.e. [tex]\dfrac{7}{2}[/tex] hours )  to build a wall.

On Tuesday, only 2 builders were available.

As workers are inversely proportional to the time if the job remains constant.

Inverse variation equation : [tex]x_1y_1=x_2y_2[/tex]

Let x be the time taken by 2 builders, then

[tex]2\times x =5\times \dfrac{7}{2}[/tex]

[tex]\Rightarrow\ x=\dfrac{35}{2}\times\dfrac{1}{2}=\dfrac{35}{4}=8.75[/tex]

So, 2 builders will take 8.75 hours.

Each paid  £9.30 for each hour.

Then, each builder will be paid for the work completed on Tuesday = £9.30 x  8.75

≈ £ 81.38

Hence, each builder will be paid £ 81.38 for the work completed on Tuesday .

Answer:

300 degrees

Step-by-step explanation:

we know that [tex]\pi = 360 degrees[/tex][tex]\pi = 360 \ degrees[/tex]

we have to find value of [tex]5\pi /6[/tex]

for that we have to multiply 5/6 to [tex]\pi[/tex] and 360 degrees

[tex]\pi = 360 \ degrees\\5\pi /6 = 5/6 *360 = 300[/tex]

Thus,  [tex]5\pi /6[/tex] = 300 degrees.

Answer:

150

Step-by-step explanation:

Answer:

3 1/2 (in fraction form but 11.2... something) hope this helps

Step-by-step explanation:

(i) AB and DC are parallel, so the lines containing these sides have the same slope.

The line containing AB has slope (2 - (-1))/(10 - 4) = 3/6 = 1/2.

Use the point-slope formula to find the equation of the line containing CD:

[tex]y-8=\dfrac12(x-12)\implies y=\dfrac x2+2\implies\boxed{2y=x+4}[/tex]

AP is perpendicular to both AB and CD, and perpendicular lines have slopes that are negative reciprocals of one another. This means the line containing AP has slope -1/(1/2) = -2. Using the point-slope formula again, the equation of the line containing AP is

[tex]y-(-1) = -2(x-4)\implies \boxed{y=-2x+7}[/tex]

(ii) D lies on the x axis, so its y-coordinate is 0. Find the x-coordinate by plugging y = 0 into the equation for the line containing CD:

[tex]2\cdot0=x+4\implies x=-4[/tex]

So D is the point (-4, 0).

P is the intersection of the lines containing CD and AP, so set them equal and solve for x and y :

[tex]y=\dfrac x2+2\text{ and }y=-2x+7[/tex]

[tex]\implies\dfrac x2+2=-2x+7\implies 5x=10\implies x=2[/tex]

[tex]\implies y=-2\cdot2+7\implies y=3[/tex]

So P is the point (2, 3).

(iii) For ASBC to be a parallelogram, we need to find the coordinates of S such that the line containing AS is parallel to the line containing BC, and the line containing SC is parallel to the line containing AB.

BC has slope (8 - 2)/(12 - 10) = 6/2 = 3. Then the line containing AS has equation

[tex]y-(-1)=3(x-4)\implies y=3x-13[/tex]

We already know AB has slope 1/2. Then the line containing SC has equation

[tex]y-8=\dfrac12(x-12)\implies y=\dfrac x2+2[/tex]

S is the intersection of these two lines:

[tex]3x-13=\dfrac x2+2\implies\dfrac{5x}2=15\implies5x=30\implies x=6[/tex]

[tex]\implies y=3\cdot6-13\implies y=5[/tex]

So S is the point (6, 5), and *not* (2, -7) as the answer key suggests. In fact, (2, -7) is located lower than the point A and slightly to the left; if you draw that point and connect it to the other three, there's no way to get a parallelogram.

(iv) Find the lengths of AB, CD, and AP. Then the area is (AB + CD)*AP/2.

[tex]AB=\sqrt{(4-10)^2+(-1-2)^2}=3\sqrt5[/tex]

[tex]CD=\sqrt{(12-(-4))^2+(8-0)^2}=8\sqrt5[/tex]

[tex]AP=\sqrt{(4-2)^2+(-1-3)^2}=2\sqrt5[/tex]

so the area is

[tex]\dfrac{(3\sqrt5+8\sqrt5)2\sqrt5}2=\boxed{55}[/tex]