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raketka [301]
3 years ago
15

Alicia answered 20 out of 25 problems correctly on a test. What percent did she get correct?

Mathematics
2 answers:
Likurg_2 [28]3 years ago
7 0
20/25 = 0.8...the " / " means divide....to find the percent, multiply by 100
0.8 * 100 = 80%
DedPeter [7]3 years ago
3 0
80% of the problems correct.
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Which correctly describes how the graph of the inequality 6y − 3x > 9 is shaded? -Above the solid line
baherus [9]

The statement which correctly describes the shaded region for the inequality is \fbox{\begin\\\ Above the dashed line\\\end{minispace}}

Further explanation:

In the question it is given that the inequality is 6y-3x>9.  

The equation corresponding to the inequality 6y-3x>9 is 6y-3x=9.

The equation 6y-3x=9 represents a line and the inequality 6y-3x>9 represents the region which lies either above or below the line 6y-3x=9.

Transform the equation 6y-3x=9 in its slope intercept form as y=mx+c, where m represents the slope of the line and c represents the y-intercept.  

y-intercept is the point at which the line intersects the y-axis.  

In order to convert the equation 6y-3x=9 in its slope intercept form add 3x to equation 6y-3x=9.  

6y-3x+3x=9+3x

6y=9+3x

Now, divide the above equation by 6.  

\fbox{\begin\\\math{y=\dfrac{x}{2}+\dfrac{1}{2}}\\\end{minispace}}

Compare the above final equation with the general form of the slope intercept form \fbox{\begin\\\math{y=mx+c}\\\end{minispace}}.  

It is observed that the value of m is \dfrac{1}{2} and the value of c is \dfrac{3}{2}.

This implies that the y-intercept of the line is \dfrac{3}{2} so, it can be said that the line passes through the point \fbox{\begin\\\ \left(0,\dfrac{3}{2}\right)\\\end{minispace}}.

To draw a line we require at least two points through which the line passes so, in order to obtain the other point substitute 0 for y in 6y=9+3x.  

0=9+3x

3x=-9

\fbox{\begin\\\math{x=-3}\\\end{minispace}}  

This implies that the line passes through the point \fbox{\begin\\\ (-3,0)\\\end{minispace}}.  

Now plot the points (-3,0) and \left(0,\dfrac{3}{2}\right) in the Cartesian plane and join the points to obtain the graph of the line 6y-3x=9.  

Figure 1 shows the graph of the equation 6y-3x=9.

Now to obtain the region of the inequality 6y-3x>9 consider any point which lies below the line 6y-3x=9.  

Consider (0,0) to check if it satisfies the inequality 6y-3x>9.  

Substitute x=0 and y=0 in 6y-3x>9.  

(6\times0)-(3\times0)>9  

0>9

The above result obtain is not true as 0 is not greater than 9 so, the point (0,0) does not satisfies the inequality 6y-3x>9.  

Now consider (-2,2) to check if it satisfies the inequality 6y-3x>9.  

Substitute x=-2 and y=2 in the inequality 6y-3x>9.  

(6\times2)-(3\times(-2))>9  

12+6>9  

18>9  

The result obtain is true as 18 is greater than 9 so, the point (-2,2) satisfies the inequality 6y-3x>9.  

The point (-2,2) lies above the line so, the region for the inequality 6y-3x>9 is the region above the line 6y-3x=9.  

The region the for the inequality 6y-3x>9 does not include the points on the line 6y-3x=9 because in the given inequality the inequality sign used is >.

Figure 2 shows the region for the inequality \fbox{\begin\\\math{6y-3x>9}\\\end{minispace}}.

Therefore, the statement which correctly describes the shaded region for the inequality is \fbox{\begin\\\ Above the dashed line\\\end{minispace}}

Learn more:  

  1. A problem to determine the range of a function brainly.com/question/3852778
  2. A problem to determine the vertex of a curve brainly.com/question/1286775
  3. A problem to convert degree into radians brainly.com/question/3161884

Answer details:

Grade: High school

Subject: Mathematics  

Chapter: Linear inequality

Keywords: Linear, equality, inequality, linear inequality, region, shaded region, common region, above the dashed line, graph, graph of inequality, slope, intercepts, y-intercept, 6y-3x=9, 6y-3x>9, slope intercept form.

4 0
3 years ago
Read 2 more answers
You are a mechanic. You have been given an engine job time of 0.7 hour about how many minutes should you allow for the job
vitfil [10]
I would allow 42 minutes for the job
6 0
3 years ago
Explain a strategy u could use to compare 2/6 and 5/8.
Schach [20]
Try to get the fractions with same denominators. Use the LCD system to find equal factors to a common denominator. Then just simply compare it. 

*Note: Larger fraction is the greater numerator.*

Hoped this helped.

~Bob Ross® 
6 0
3 years ago
Where v is the final velocity (in m/s), u is the initial velocity (in m/s), a is the acceleration (in m/s²) and s is the distanc
Anna11 [10]

Answer:

The final velocity v is 21.74 m/s.

Step-by-step explanation:

Given:

\textrm{initial velocity} = u = 9\ m/s\\\textrm{acceleration} = a = 7\ m/s^{2}\\\textrm{distance} = s = 28\ m

To find:

\textrm{final velocity} = v = ?

Solution:

As we know the third equation of motion is represented as

v^{2} = u^{2} + 2\times a\times s\\

Substituting the values u, a and s in the above equation we get

v^{2} = 9^{2} + 2\times 7\times 28\\ =81 + 392\\=473\\

v =\±\sqrt{473} \\v =\sqrt{473} \ \textrm{as acceleration is positive v is also positive}\\v = 21.74\ m/s

7 0
3 years ago
What is the length of the hypotenuse?
gayaneshka [121]

Answer:

Hello! answer: 5

Step-by-step explanation:

What you do to find the answer for these is do a^2+b^2=c^2 Basically meaning 4 × 4 + 3 × 3 will equal a number that you then find the suare root of square root just meaning a number multiplied by itself to equals that number so...

4 × 4 = 16

3 × 3 = 9

16 + 9 = 25

√25 = 5

5 × 5 = 25 therefore c = 5 hope that helps!

5 0
3 years ago
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