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Mice21 [21]
2 years ago
7

Find the length of UX

Mathematics
1 answer:
Dahasolnce [82]2 years ago
4 0

Answer:

\dfrac{8}{\sin(6^\circ)} \approx 76.53

Step-by-step explanation:

UX \sin(6^\circ) = 8 \Rightarrow \boxed{UX = \dfrac{8}{\sin(6^\circ)} \approx 76.53}

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Which is the more reasonable measure for the length of a car?<br> 50m<br> 5cm<br> 5m<br><br> Thanks
Roman55 [17]

Answer:

5m

Step-by-step explanation:

8 0
2 years ago
The Johnson twins were born five years after their older sister. This​ year, the product of the three​ siblings' ages is exactly
Mamont248 [21]

Answer:

13 years.

Step-by-step explanation:

Suppose, today, the Johnson twins' age is x years. Then the age of their elder sister will be (x + 5) years old. It is given that product of the three​ siblings' ages is exactly 2998 more than the sum of their ages. Therefore:

x + x + x + 5 + 2998 = (x)(x)(x + 5).

3x + 3003 = x^3 + 5x^2.

x^3 + 5x^2 - 3x - 3003 = 0.

To solve the question, factor theorem will be used. It states if any number c satisfies the equation f(c) = 0, then c is the factor of f(x). By observation, it can be seen that x = 13 can be a possible candidate for the factor of f(x). To verify, check f(13).

f(13) = 13^3 + 5(13^2) - 3(13) - 3003 = 2197 + 845 - 39 - 3003 = 0.

Since f(13) = 0, therefore x = 13 is the factor of f(x).

Now applying synthetic division:

Column 1       2       3       4            5

     13    |         1       5      -3        -3003  (Row 1)

______|______<u>  _13__234___3003</u>   (Row 2)

            |         1       18      231          0    (Row 3)

The method requires to write the coefficients of all the powers in the Row 1 on the right hand side of the table. Put the factor x = 13 on the left hand side of the table (Row 1 Column 1). The first step involves the second column elements to be added. Since there is only 1, thus there will be 1 below the line. Next step involves multiplying 1 with the factor (which is 13) and this will be the element for row 2 column 3. The add the elements of the column 3. The answer comes out to be -3. Repeat the above steps for the columns 4 and 5. The sum of the column 5 (the last column) should be 0, which is the case. The elements of the last row are actually the coefficients of the quadratic equation which is resultant from dividing f(x) by (x - 13). Thus:

x^2 + 18x + 231 = 0.

Using completing the square:

x^2 + 18 = -231.

(x)^2 + 2*(x)*(9) + (9)^2 = -231 + (9)^2.

(x + 9)^2 = -231 + 81.

(x + 9)^2 = -150.

Taking square root on both sides shows that rest of the 2 answers of this polynomial will be complex roots since square root of -150 does not exist in real numbers. Therefore, since the age is a real quantity and not a complex quantity, the age of the twins is 13 years!!!

8 0
3 years ago
11. Delila is multiplying three negative numbers and determines that the solution will be negative. Is she correct or incorrect?
Gre4nikov [31]

Answer: CORRECT

Step-by-step explanation: Because any negative number will be positive when multiplied together but since there are 3 negative number the 3rd negative will always negate the positive so therefore Delila is correct

8 0
2 years ago
What are the domain and range of the relation
tia_tia [17]
The answer to the question

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3 years ago
Ann's car can go 238 miles on 7 gallons of gas. During a drive last weekend, Ann used 4 gallons of gas. How far did she drive? E
Andru [333]

Answer:

its c 320+56

Step-by-step explanation:

4 0
3 years ago
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