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-BARSIC- [3]
3 years ago
6

Cousin Hector drove 1,851 miles to the reunion. He lives in Mexico and drove 747 miles through that country to the United States

border. How many miles did he drive in the United States?
Mathematics
1 answer:
Sonja [21]3 years ago
3 0

Answer:

1104 miles

Step-by-step explanation:

Say he lives in a place in Mexico which is at a distance of <em>a </em>miles from the Mexico-America border point and the reunion is at <em>b </em>miles from the same border point, in America.

So the total distance travelled is ( a + b ) miles

( this is just sum of distance travelled in Mexico + that in America )

Given , a=747 and a+b=1851

that implies:

747 + b = 1851

So, b = 1104 miles.

Therefore he has travelled 1104 miles in America,

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Is The polar form of a complex number is unique?
Pie

Answer:

  no

Step-by-step explanation:

The angle in the polar form of a complex number can have any multiple of 2π radians added to it, and the number will be the same number. That is, there are an infinite number of representations of a complex number in polar form.

6 0
3 years ago
Philip made a total of 9 bracelets and necklaces from 120 inches of cord. He used 8 inches of cord for each bracelet and 20 inch
Viktor [21]

Answer:

So Philip made 5 bracelets and 4 necklaces.

Step-by-step explanation:

Let x = number of bracelets and y = number of necklaces.

Since we have a total of 9 bracelets and necklaces,

x + y = 9 (1)

Also, we have 8 inches of cord for each bracelet and 20 inches of cord for each necklace, then the total length for the bracelet is 8x and that for the necklace is 20y.

So, the total length for both is 8x + 20y. Since the total length of cord used is 120 inches,

8x + 20y = 120 (2)

Simplifying it we have

2x + 5y = 30  (3).

Writing equations (1) and (3) in matrix form, we have

\left[\begin{array}{ccc}1&1\\2&5\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}9\\30\end{array}\right]

Using Cramer's rule to solve for x and y,

x = det \left[\begin{array}{ccc}9&1\\30&5\end{array}\right] /det \left[\begin{array}{ccc}1&1\\2&5\end{array}\right] \\

x = (9 × 5 - 30 × 1) ÷ (1 × 5 - 1 × 2)

x = (45 - 30) ÷ (5 - 2)

x = 15 ÷ 3

x = 5

y = det \left[\begin{array}{ccc}1&9\\2&30\end{array}\right] /det \left[\begin{array}{ccc}1&1\\2&5\end{array}\right] \\

y = (30 × 1 - 9 × 2) ÷ (1 × 5 - 1 × 2)

y = (30 - 18) ÷ (5 - 2)

y = 12 ÷ 3

y = 4

So Philip made 5 bracelets and 4 necklaces.

3 0
3 years ago
Consider the quadratic function:
MrRissso [65]

Answer: the vertex would be (4,-25)

Step-by-step explanation:

id suggest using desmos. its an app/website and is super helpful.

8 0
3 years ago
Can you help me to solve this​
Ber [7]

Answer:

\frac{4a-2}{2a+1}

Step-by-step explanation:

Factorise the numerator and denominator

8a² - 2 ← factor out 2 from each term

= 2(4a² - 1) ← 4a² - 1 is a difference of squares

= 2(2a - 1)(2a + 1)

4a² + 4a + 1 ← is a perfect square

= (2a + 1)²

Thus

\frac{8a^2-2}{4a^2+4a+1}

= \frac{2(2a-1)(2a+1)}{(2a+1)(2a+1)} ← cancel (2a + 1) on numerator/ denominator

= \frac{2(2a-1)}{2a+1}

= \frac{4a-2}{2a+1}

3 0
3 years ago
Read 2 more answers
Help me, cause I'm tuck
r-ruslan [8.4K]

Answer:

The answer would be 1.33 x 10^{4}

Step-by-step

1.28 x 10^{4} = 12800

5 x 10^{2} = 500

12800 + 500 = 13300

13300 = 1.33 x 10^{4} in scientific notation

Hope this helps:)

Sorry, I got the wrong answer earlier but I fixed it:)

8 0
3 years ago
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