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3 years ago

13

1285 students went on a field trip six buses were filled with the same number of students and seven other student travel in coll

ege how many students are in each bus

2 answers:

Mademuasel [1]3 years ago

6 0

213 students were in each bus

Dmitry [639]3 years ago

3 0

Answer:

213

Step-by-step explanation:

1285 students -7 students travel : 1278

1287 students / 6 buses= 1278/6=213

213 students

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The sum of a whole number and twice the square of the number is 10. Find the number.

sveticcg [70]

Answer:

x = $\frac{10}{1 + 2x}$

Step-by-step explanation:

Let the number be x

x + 2x² = 10

Factorize x + 2x²

x(1 + 2x) = 10

Divide both sides by (1 + 2x)

x = $\frac{10}{1 + 2x}$

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4 years ago

Sixteen students went on

amid [387]

Answer:

Step-by-step explanation:

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4 years ago

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2. Jolie manages an annual film festival in her town. Every year, one movie from every genre is chosen as a finalist to win best

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Answer:

Step-by-step explanation:

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4 0

3 years ago

I’m confused on this one

dedylja [7]

It's a parallelogram so if one angle is 90 degrees they all will be because of transverse angles and all that good stuff.

So we're given the diagonal of a rectangle and one side and we're asked to find the other. The diagonal of a rectangle is the hypotenuse of the right triangle whose legs are the sides of the rectangle. So this is a Pythagorean Theorem question in disguise:

$AB^2 + AD^2 = BD^2$

$AD^2 = BD^2 - AB^2$

$AD = \sqrt{ BD^2 - AB^2 }$

$AD = \sqrt{149^2 - 51^2} = \sqrt{19400} = 140$

Answer: 140 cm

I don't recall seeing this Pythagorean Triple before.

3 0

3 years ago

Find number a and k so that x-2 is afactor<br>OF F(x)=x4-2ax tax-<br>X+k and F(-1)=3

Slav-nsk [51]

Question:

Find numbers a and k so that x-2 is a factor of

$f(x)=x^4-2ax^3+ax^2- x+k$

and

$f(-1)=3$

Answer:

$k = -2$ and $a=1$

Step-by-step explanation:

Given

$f(x)=x^4-2ax^3+ax^2- x+k$

$Factor:\ x - 4$

$f(-1)=3$

Required

Find a and k

For $f(-1)=3$

Substitute -1 for x

$f(x)=x^4-2ax^3+ax^2- x+k$

$f(-1) = (-1)^4 - 2a *(-1)^3 + a*(-1)^2 - (-1) + k$

$f(-1) = 1 - 2a *-1 + a*1 +1 + k$

$f(-1) = 1 +2a + a +1 + k$

$f(-1) = 2 +3a + k$

Substitute 3 for f(-1)

$3 = 2 +3a + k$

Collect Like Terms

$3 - 2 = 3a + k$

$1 = 3a + k$

Also:

If $x - 2$ is a factor, then

$f(2) = 0$

Substitute 2 for x and 0 for f(x)

$f(x)=x^4-2ax^3+ax^2- x+k$

$0 = 2^4 - 2a * 2^3 + a * 2^2 - 2 + k$

$0 = 16 - 2a * 8 + a * 4 - 2 + k$

$0 = 16 - 16a + 4a - 2 + k$

$0 = 16 - 12a - 2 + k$

Collect Like Terms

$2 - 16 = - 12a + k$

$-14 = k - 12a$

$k = 12a - 14$

Substitute 12a - 14 for k in $1 = 3a + k$

$1 = 3a + 12a - 14$

$1 = 15a - 14$

Collect Like Terms

$15a = 1 + 14$

$15a = 15$

Solve for a

$a = \frac{15}{15}$

$a=1$

Substitute 1 for a in $k = 12a - 14$

$k = 12 * 1 - 14$

$k = 12 - 14$

$k = -2$

3 0

3 years ago