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
Ulleksa [173]
3 years ago
13

If

Mathematics
1 answer:
dsp733 years ago
8 0

Answer:

\large\boxed{Q1.\ q(x)=\dfrac{1}{2}x+\dfrac{7}{2},\ q(2)=\dfrac{9}{2}}\\\boxed{Q2.\ t(x)=\dfrac{1}{2}x+\dfrac{7}{2},\ t(0)=\dfrac{7}{2}}

Step-by-step explanation:

\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\\\\\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\text{We have}\\\\q(-1)=3\to(-1,\ 3)\\q(3)=5\to(3,\ 5)

\text{Calculate the slope:}\\\\m=\dfrac{5-3}{3-(-1)}=\dfrac{2}{4}=\dfrac{2:2}{4:2}=\dfrac{1}{2}\\\\\text{We have the equation:}\\\\y=\dfrac{1}{2}x+b\\\\\text{Put the coordinates of the point (-1, 3) to the equation:}\\\\3=\dfrac{1}{2}(-1)+b\\\\3=-\dfrac{1}{2}+b\qquad\text{add}\ \dfrac{1}{2}\ \text{to both sides}\\\\3\dfrac{1}{2}=b\to b=3\dfrac{1}{2}=\dfrac{7}{2}

q(x)=\dfrac{1}{2}x+\dfrac{7}{2}\\\\q(2)-\text{put x = 2 to the equation:}\\\\q(2)=\dfrac{1}{2}(2)+\dfrac{7}{2}=\dfrac{2}{2}+\dfrac{7}{2}=\dfrac{9}{2}

t(-4)=3\to(-4,\ 3)\\t(4)=4\to(4,\ 4)\\\\m=\dfrac{4-3}{4-(-4)}=\dfrac{1}{8}\\\\y=\dfrac{1}{8}x+b\\\\\text{put the coordinates of the point (4,\ 4):}\\\\4=\dfrac{1}{8}(4)+b\\\\4=\dfrac{1}{2}+b\qquad\text{subtract}\ \dfrac{1}{2}\ \text{from both sides}\\\\3\dfrac{1}{2}=b\to b=3\dfrac{1}{2}=\dfrac{7}{2}\\\\t(x)=\dfrac{1}{2}x+\dfrac{7}{2}\\\\t(0)=\dfrac{1}{2}(0)+\dfrac{7}{2}=0+\dfrac{7}{2}=\dfrac{7}{2}

You might be interested in
Which expression is equivalent to x³ - x² - 14x + 24?
serg [7]

Answer:

<h3>A. ( x - 2 )( x - 3 )(x + 4 )</h3>

<h3>Step-by-step explanation:</h3>

<h3>x³ - x² - 14x + 24</h3>

<h3>1. Use the rational root theorem</h3>

= (x  - 2) \frac{x ^{3}  -x^{2}  - 14x + 24}{x - 2}

<h3>2. \frac{  {x}^{3} - {x}^{2}  - 14x + 24 }{x - 2}  =  {x}^{2}  + x - 12</h3><h3 />

= ( x - 2 )( x² + x - 12 )

<h3>3. Factor x² + x - 12 : ( x -3 )( x + 4)</h3>

= ( x - 2 )( x - 3 )(x + 4 )

<h3>Solution : </h3>

<h3>= ( x - 2 )( x - 3 )(x + 4 )</h3>
3 0
1 year ago
What is the volume of a rectangular prism<br> 8 inches long, 5 inches wide, and 2 inches high?
Ivahew [28]

Answer:

132 Cubic Inches, Search up how to find the the surface area for rectangular prism it helps!

5 0
3 years ago
Divide write the answer in simplest form
Rom4ik [11]

Answer:

3 is the answer

1/3*9/1=9/3=3

Step-by-step explanation:

6 0
2 years ago
The angle measurement in the diagram are represented by the following expressions.
8_murik_8 [283]

Answer:

x = 9 and ∠ B = 40°

Step-by-step explanation:

See the diagram given with the question first.

Here we have ∠ A = ∠ B {They are corresponding angles}

Now, it is given that ∠ A = 5x - 5 and ∠ B = 3x + 13

Hence, 5x - 5 = 3x + 13

⇒ 2x = 18

⇒ x = 9

Therefore, ∠ B = 3x + 13 = 3(9) + 13 = 40° (Answer)

5 0
3 years ago
1. The chart below represents the percentage of Americans traveling to each destination.
lidiya [134]
B 23%
6100 planned to travel to the united states mid west
7 0
3 years ago
Other questions:
  • Difference of a number and -3 is 6. what is the number
    5·1 answer
  • Can you guys Divide and check using Multiplication for these 2 Problems? 1st: 326 Divided by 53. And 192 Divided by 38
    8·1 answer
  • I have 5 questions
    11·1 answer
  • How do you solve this question both​
    7·1 answer
  • Line l is parallel to line m. The slope of line l is 2/7
    5·1 answer
  • The exponential function g, represented in the table, can be written as g(x)=a times b^x x g, left parenthesis, x, right parenth
    5·2 answers
  • A car travels 355 miles in 5 hours. How many miles did they travel per hour?
    8·2 answers
  • Hanna simplified the following math statement. What did she do wrong? Show the correct answer and explain your reasoning.
    9·1 answer
  • PLEASE HELP. Select the correct shapes.<br> Select the shapes that are similar to shape A.
    12·1 answer
  • Which expression is equivalent to 144 superscript three-halves?
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!