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Jill has a collection of bugs. Her collection contains butterflies and tarantulas. She has 47 bugs and counts 320 total legs. (N

prisoha [69]

Answer:

The solution to this system of equations is:

B = 28
T = 19

Step-by-step explanation:

We are given that Jill has 47 bugs and counts a total 320 legs.

We can concur that by adding the total number of butterflies and the total number of tarantulas, we will get 47 bugs.

$\text{tarantulas + butterflies} = 47$

We are also told that T is tarantulas and B is butterflies.

$T + B = 47$

Then, we also know that butterflies have 6 legs and tarantulas have 8 legs. So, for every tarantula, we get a multiple of 8 and for butterflies, we get a multiple of 6. This gives us a new equation:

$6B + 8T = 320$

Now, we can set up a system of equation.

$\displaystyle \left \{ {{B + T = 47} \atop {6B + 8T = 320}} \right.$

Using the first equation, we can solve for B.

$\displaystyle B + T = 47\\\\B + T - T = 47 - T\\\\B = 47 - T$

Then, we can substitute this value of B into the second equation and solve for T.

$\displaystyle 6(47-T)+8T=320\\\\282 - 6T + 8T = 320\\\\282 + 2T = 320\\\\2T + 282 = 320\\\\2T + 282 - 282 = 320 -282\\\\2T = 38\\\\\frac{2T}{2}=\frac{38}{2}\\\\T = 19$

Finally, we can substitute this value of T into the first equation to solve for B.

$B + 19 = 47\\\\B + 19 - 19 = 47 - 19\\\\B = 28$

Therefore, the solution to this system of equations is:

B = 28
T = 19

7 0

3 years ago

PLEASE HELP WHAT IS THE ANSWER SHOW WORK PLEASE !!!

Mrac [35]

Answer:

d = 6.1m

n = 7km

Step-by-step explanation:

To find the variables, use tan

⇒ tan = $\frac{opposite}{adjacent}$

finding d:

⇒tan 63 = $\frac{d}{3.1}$

tan of 63 is 1.963

⇒ 1.963 = $\frac{d}{3.1}$

multiply 3.1 on both sides

⇒ 1.963 x 3.1 = $\frac{d}{3.1}$ x 3.1

⇒ 6.0853 = d

round to the nearest tenth:

⇒ 6.0853 = 6.1

finding n:

⇒ tan 45 = $\frac{7}{n}$

tan of 45 is 1

⇒ 1 = $\frac{7}{n}$

multiply 7 on both sides:

⇒ 1 x 7 = $\frac{7}{n}$ x 7

7 = n

7 0

3 years ago

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What value of a is a solution to this equation?<br> 1=3+a<br> 4

Romashka-Z-Leto [24]

Answer:

1=a4+3

Step 1: Subtract a^4+3 from both sides.

1−(a4+3)=a4+3−(a4+3)

−a4−2=0

Step 2: Add 2 to both sides.

−a4−2+2=0+2

−a4=2

Step 3: Divide both sides by -1.

−a4

−1

=

2

−1

a4=−2

Step 4: Take root.

a=±(−2)(

1

4

)

Answer:

No real solutions.

6 0

3 years ago

NEED HELP ASAP PLS DUE TODAY !!!

S_A_V [24]

Answer:

with what do you need help? if you took a picture i cant see it at all

Step-by-step explanation:

6 0

3 years ago

Bryan took a taxi home from the opera. The taxi fare was $2.50 per mile, and he gave the driver a tip of $3. Bryan paid a total

7nadin3 [17]

It is 13 miles between the Opera House and Bryan's home.

7 0

3 years ago

Read 2 more answers