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Citrus2011 [14]

3 years ago

6

Tim worked twenty hours during the last five days assuming that he worked the same amount of hours each day, how long did he wor

k each day

1 answer:

algol [13]3 years ago

5 0

Answer:

he worked 4 hours each day

Step-by-step explanation:

You might be interested in

Maths functions question

yarga [219]

Answer:

a) OA = 1 unit

b) OB = 3 units

c) AB = √10 units

Step-by-step explanation:

<u>Given function</u>:

$g(x)=2^x$

<h3><u>Part (a)</u></h3>

Point A is the y-intercept of the exponential curve (so when x = 0).

To find the y-value of Point A, substitute x = 0 into the function:

$\implies g(0)=2^0=1$

Therefore, A (0, 1) so OA = 1 unit.

<h3><u>Part (b)</u></h3>

If BC = 8 units then the y-value of Point C is 8.

The find the x-value of Point C, set the function to 8 and solve for x:

$\begin{aligned}f(x) & = 8 \\\implies 2^x & = 8\\2^x & = 2^3\\\implies x &= 3\end{aligned}$

Therefore, C (3, 8) so Point B is (3, 0). Therefore, OB = 3 units.

<h3><u>Part (c)</u></h3>

From parts (a) and (b):

A = (0, 1)
B = (3, 0)

To find the length of AB, use the distance between two points formula:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$\textsf{where }(x_1,y_1) \textsf{ and }(x_2,y_2)\:\textsf{are the two points.}$

Therefore:

$\implies \sf AB=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}$

$\implies \sf AB=\sqrt{(3-0)^2+(0-1)^2}$

$\implies \sf AB=\sqrt{(3)^2+(-1)^2}$

$\implies \sf AB=\sqrt{9+1}$

$\implies \sf AB=\sqrt{10}\:\:units$

5 0

2 years ago

Denice buys 7 movies. each movie cost $9. what is the total cost of 7 movies?

Lapatulllka [165]

Answer:

$63

Step-by-step explanation:

$7 \times 9$

5 0

4 years ago

Read 2 more answers

Let f (x) = 3x - 4. Determine the equation of f 1 (2)

LenKa [72]

Answer:

2

Step-by-step explanation:

f(2)=3(2)-4

hope this helps :)

7 0

3 years ago

Elena has $225 in her bank account. She takes out $20 each week for weeks. After weeks she has d dollars left in her bank accoun

leonid [27]

Answer:

the equation to use would be D (255-20(5) = ?). To solve, first multiply 20 and 5 and you would get 100 so the equation would be 255 - 100 = ? Then you would subtract 100 from the 255 to get $155 left. To solve for 7 weeks you would replace the 5 in the equation with 7 so your equation would be 255 - 20(7) = ? Next you would multiply 20 and 7 to get 140. the equation would then be 255 - 140 = ? Subtract 140 from 255 and you would get 115. So after 7 weeks she would have $115 left in her account.

7 0

3 years ago

I have two questions. Please try to answer both!

OlgaM077 [116]

Answer:

(a)59

(b) $d=\dfrac{1}{2}$

Step-by-step explanation:

<u>Part A</u>

The nth term of an arithmetic sequence, $T_n=a+(n-1)d$

Let the first angle of the triangle =a

Let the common difference = d.

Since the measures of the angles are in an arithmetic progression

We have:

a + (a + d) + (a + 2d) = 180

3a+3d=180

a+d=60

Since a or d cannot be equal to zero, the minimum possible values of a and d is 1 and the maximum possible values of a and d is 59.

Therefore, there are 59 non-similar triangles.

<u>Part B</u>

In an arithmetic sequence

$a_7 -2a_4 = 1, a_3 = 0.$

$2a_4=a_7-1\\a_4=\dfrac{a_7-1}{2}$

Common difference,

$d=a_4-a_3\\=\dfrac{a_7-1}{2}-0\\d=\dfrac{a_7-1}{2}$

$a_7=a_4+3d\\=\dfrac{a_7-1}{2}+3(\dfrac{a_7-1}{2})\\=\dfrac{a_7-1}{2}+\dfrac{3a_7-3}{2}\\=\dfrac{a_7-1+3a_7-3}{2}\\a_7=\dfrac{4a_7-4}{2}\\$Cross multiply\\2a_7=4a_7-4\\2a_7-4a_7=-4\\-2a_7=-4\\a_7=2$

Therefore:

$d=\dfrac{2-1}{2}\\d=\dfrac{1}{2}$

7 0

4 years ago