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Pavlova-9 [17]
2 years ago
9

Emma's sister is nine years older then Emma. Their combined ages add up to 49. How old is Emma

Mathematics
1 answer:
miss Akunina [59]2 years ago
3 0

Answer:

emma is 20 because 49-9/2=40/2 which is 20

Step-by-step explanation:

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Lupita rides a taxi that charges a flat rate of $6.75 plus $3.20 per mile. If the taxi charges Lupita $40.03 in total for her tr
yaroslaw [1]

Answer:

10.4 miles

Step-by-step explanation:

Write an equation for the total cost paid as a function of the # of miles driven:

L(x) = $6.75 + ($3.20/mile)x

and set this equal to $40.03 to determine the # of miles Lupita rode:

L(x) = $6.75 + ($3.20/mile)x = $40.03

Isolate the x term by subtracting $6.75 from both sides:

($3.20/mile)x = $40.03 - $6.75 = $33.28

Finally, divide both sides by  ($3.20/mile):

x = $33.28 /  ($3.20/mile)

  =  10.4 miles

Lupita rode 10.4 miles in the taxi.

4 0
3 years ago
F⃗ (x,y)=−yi⃗ +xj⃗ f→(x,y)=−yi→+xj→ and cc is the line segment from point p=(5,0)p=(5,0) to q=(0,2)q=(0,2). (a) find a vector pa
DerKrebs [107]

a. Parameterize C by

\vec r(t)=(1-t)(5\,\vec\imath)+t(2\,\vec\jmath)=(5-5t)\,\vec\imath+2t\,\vec\jmath

with 0\le t\le1.

b/c. The line integral of \vec F(x,y)=-y\,\vec\imath+x\,\vec\jmath over C is

\displaystyle\int_C\vec F(x,y)\cdot\mathrm d\vec r=\int_0^1\vec F(x(t),y(t))\cdot\frac{\mathrm d\vec r(t)}{\mathrm dt}\,\mathrm dt

=\displaystyle\int_0^1(-2t\,\vec\imath+(5-5t)\,\vec\jmath)\cdot(-5\,\vec\imath+2\,\vec\jmath)\,\mathrm dt

=\displaystyle\int_0^1(10t+(10-10t))\,\mathrm dt

=\displaystyle10\int_0^1\mathrm dt=\boxed{10}

d. Notice that we can write the line integral as

\displaystyle\int_C\vecF\cdot\mathrm d\vec r=\int_C(-y\,\mathrm dx+x\,\mathrm dy)

By Green's theorem, the line integral is equivalent to

\displaystyle\iint_D\left(\frac{\partial x}{\partial x}-\frac{\partial(-y)}{\partial y}\right)\,\mathrm dx\,\mathrm dy=2\iint_D\mathrm dx\,\mathrm dy

where D is the triangle bounded by C, and this integral is simply twice the area of D. D is a right triangle with legs 2 and 5, so its area is 5 and the integral's value is 10.

4 0
3 years ago
Find the area of a parallelogram with sides of 6 and 12 and an angle of 60°.
Anna007 [38]

ANSWER

36√3 square units.

EXPLANATION

The area of a parallelogram is obtained by multiplying the base by the height.

We use the sine ratio to obtain the height.

\sin(60 \degree)  =  \frac{h}{6}

h = 6 \sin(60 \degree)

h = 3 \sqrt{3}

The area becomes:

12 \times 3 \sqrt{3}  = 36 \sqrt{3} {units}^{2}

4 0
3 years ago
Solve this inequality j/4 - 8 < 4
zubka84 [21]
J/4 - 8 < 4
<u>    + 8   + 8  </u>   *add 8 to both sides to cancel -8.
j/4      < 12
<u>*4/1       *4/1   </u>   *multiply 4/1 to both sides to cancel 1/4
j         < 48

j should be less than 48 to make the inequality true.

example: j = 47
j/4       - 8 < 4
47/4   - 8 < 4
11.75 - 8 < 4
       3.75 < 4  

Any number below 48 will end up with an answer less than 4. if j is 48 and above, the inequality is false because the answer arrived at will be equal to or greater than 4.
5 0
3 years ago
Really really need help on ONE math graph question.
Nat2105 [25]
The answer is      -3.5, 0.5
7 0
3 years ago
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