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IrinaK [193]
2 years ago
14

A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is

the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation. x + y = 24 3x + 5y = 100 What does the solution of this system indicate about the questions on the test? The test contains 4 three-point questions and 20 five-point questions. The test contains 10 three-point questions and 14 five-point questions. The test contains 14 three-point questions and 10 five-point questions. The test contains 20 three-point questions and 8 five-point questions.
Mathematics
1 answer:
nadezda [96]2 years ago
7 0

Answer:

Let x be the number of 3- point questions and y be the number of 5-points questions.

Step-by-step explanation:

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Tomtit [17]

Answer: a\cdot b= 7

Step-by-step explanation:

We are given

a=3\hat{i}+2\hat{j}-\hat{k}

b=4\hat{i}+5\hat{k}

They can be written as

a=3\hat{i}+2\hat{j}+(-1)\hat{k}

b=4\hat{i}+0.\hat{j}+5\hat{k}

Now , the dot product of and b is given by :-

\Rightarrow\ a\cdot b= (3\hat{i}+2\hat{j}+(-1)\hat{k})\cdot(4\hat{i}+0.\hat{j}+5\hat{k})

\Rightarrow\ a\cdot b=3\cdot 4 \cdot\hat{i}\cdot\hat{i}+2\cdot0\cdot\hat{j} \cdot\hat{j}+ (-1)\cdot 5 \cdot \hat{k}\cdot \hat{k}

\Rightarrow\ a\cdot b=12 \cdot\hat{i}^2+0-5 \cdot \hat{k}^2

\Rightarrow\ a\cdot b=12 \cdot(1)+0-5 \cdot (1)[Since \hat{i}^2=\hat{k}^2=1]

\Rightarrow\ a\cdot b=12 -5=7  

Therefore , the value of the dot product a\cdot b= 7

5 0
3 years ago
If Frances can paint 1/3 of a wall in 20 minutes, how long will it take her to paint a room with 4 walls.
charle [14.2K]

Answer:

1/3 is 20

4 is x

C

Step-by-step explanation:

6 0
3 years ago
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from the top of an 800 foot tall car talk tower, tom sees a plane; the angle of elevation is 67 degrees. at the same instant tay
AlekseyPX

Answer:

Height of plane = 25971.7 meters

Step-by-step explanation:

let H =height of plane

Let x = distance ray to the point under the plane

800 foot = 245meters

1 mile = 1609meters.

Tan 81 = \frac{H}{1609+x}    -----------------------(1)

Tan 67 = \frac{H-245}{x}    -----------------------(2)

6.3134  = \frac{H}{1609+x}   ------------------------(3)

2.3556 =  \frac{H-245}{x}    -----------------------(4)

from (3) and (4)

H = 10158.26 + 6.3134x  ---------------(a)

H = 245 + 2.2336x ---------------(b)

equating both (a) and (b) we have:

9913.26 = 3.9576x

x = 2504.74

Subst. x = 2504.74 into (a)

H = 25971.7meters

8 0
3 years ago
After reading a book for English class, 100 students were asked wether or not they enjoyed it. Nine twenty-fifths of the class d
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Answer: 64 students

Step-by-step explanation:

What you already know : Total students in English class= 100

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Therefore, the number of students like the book =Total students- students did not like the book

=100-36=64 students.

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The length of a rectangle is 6m longer than its width. If the perimeter of the rectangle is 52m, find its area
sveticcg [70]
If length is x, then width is 6+x 
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<span>Area = length*width = 10*(6+10) </span>
<span>Area = 10*16 = 160 meter square</span>
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