1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
iragen [17]
1 year ago
12

Maths functions question

Mathematics
1 answer:
yarga [219]1 year ago
5 0

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

You might be interested in
How to find slope of any given line segment?
aniked [119]

 Best Answer:<span>  </span><span>I'll make one up and explain how to do it. 

Lets say your two points are (2,6) and (-4,7) 

To start with you need to use the point-slope formula which is y2-y1/x2-x1 

Remember (x,y), Thus we have 

7-6/-4-2 = 1/-6; So out slope is -1/6 

Now lets use the following equation y = mx+b to solve for b which is the y-intercept. By substitution of either order pair we can solve for b 

6 = 2(-1/6)+b; distribute the 2 
6 = -2/6+b; add 2/6 to each side to isolate b 
6+2/6 = b; put 6 over 1 
6/1+2/6 = b; get a common denominator between 6/1 and 2/6 which is 6 
6(6/1)+2/6 = b ; distribute 
36/6+2/6 = b; add these up 
38/6 = b; reduce to lowest terms by dividing by 2 to each 
19/3 = b 

So our final equation is y = -1/6x+19/3 </span>
5 0
3 years ago
124 / 74152<br> What is the answer
GalinKa [24]
The correct answer is 598
6 0
2 years ago
Read 2 more answers
Inverse of y=14x2 show derivations
Rudik [331]
<h2>Answer:</h2>

f^{-1}  (x)=\sqrt{\frac{x}{14}}.

<h2>Step-by-step explanation:</h2>

<h3>1. Write the expression.</h3>

y=14x^2

<h3>2. Substitute y for x, and x for y.</h3>

x=14y^{2}

<h3>3. Solve for y.</h3>

14y^{2}=x\\ \\y^{2} =\frac{x}{14} \\ \\y=\sqrt{\frac{x}{14}}

<h3>4. Express your result.</h3>

f^{-1}  (x)=\sqrt{\frac{x}{14}}.

4 0
1 year ago
Help me, save me!!!!!!!!
Anni [7]

Answer:

D

Step-by-step explanation:

Open circle means less than or greater than, and the dot is on -5, so the answer is greater than -5

5 0
3 years ago
Read 2 more answers
!!!!!!!!! PLEASE HELP !!!!!!!!!!<br><br><br> Solve x² - 6x - 7 = 0
sesenic [268]

Answer:

x = 7, -1

Step-by-step explanation:

4 0
2 years ago
Other questions:
  • (4x3 + 5)(2x3 + 3) = 8x6 + tx3 + 15<br> What value of t makes the statement true?
    14·1 answer
  • At the local gas station, gasoline costs $2.75 per gallon and diesel fuel costs $3.02 per gallon. Gabriel needs to purchase 15.2
    7·1 answer
  • Answer gets BRAINLIEST If q varies inversely as r, and g = 10 when r = 2.5, find the equation that connects a
    5·1 answer
  • Decrease £19060 by 9%<br> Give your answer rounded to 2 DP.
    12·1 answer
  • 5(x+3)-7x I need help
    13·2 answers
  • Which consumer uses the most water in the United States each year?
    11·2 answers
  • PLEASE HELP ME ASAP!!!
    8·1 answer
  • Round 1.33 to the nearest tenth.
    9·2 answers
  • Why won't anyone help me :(​
    6·1 answer
  • 5. Write the following inequality in slope-intercept form. −8x + 4y ≥ −52 y ≤ 2x − 13 y ≥ 2x − 13 y ≤ 2x + 13 y ≥ 2x + 13
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!