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2 years ago

Solve the inequality 6h−5(h−1)≤7h−11 and write the solution in interval notation. Use improper fractions if necessary.

Mathematics

1 answer:

Kobotan [32]2 years ago

6 0

Answer:

$h \geq 2\frac{2}[3}$

Step-by-step explanation:

We solve the inequality similarly to how we would solve an equalitu.

$6h - 5(h-1) \leq 7h - 11$

$6h - 5h + 5 \leq 7h - 11$

$h - 7h \leq -11 - 5/$

$-6h \leq -16$

Multiplying everything by -1

$6h \geq 16$

Simplifying by 2

$3h \geq 8$

$h \geq \frac{8}{3}$

8 divided by 3 is 2 with rest two. So as a improper fraction, the answer is:

$h \geq 2\frac{2}[3}$

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The school is 3.2 blocks from someone’s house. how many blocks does the person walk to go to and from school?

DENIUS [597]

The answer is: " 6.4 blocks " .

________________________________________________________

3.2 blocks (one way), PLUS: 3.2 blocks the other way:

3.2 + 3.2 = 6.4 blocks .

or: (3.2) * 2 = 6.4 blocks .

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3 years ago

Imaginen que un maratonista corre toda una carrera a una velocidad constante. Después de dos horas lleva recorridos 22 km

saw5 [17]

For this case we have:

If after 2 hours the marathon runner has traveled 22 kilometers we have:

2h -----------> 22km

Applying a rule of three, we can know the time it takes to run 42km. So, we have:

2h -----------> 22km

x -------------> 42km

Where "x" is the time it takes to travel 42km. Resolving we have:

$x = \frac {(42 * 2)} {22}$

$x = \frac {84} {22}$

$x = \frac {42} {11}$

$x = 3.82 hours$

Thus, after 3.82 hours the marathon runner will travel 42km.

Answer:

3.82 hours

6 0

2 years ago

Three students, Matthew, Thompson and Amos shared #15000 in the ratio of 5:2:x respectively. If Matthew's share is 7500, calcula

jasenka [17]

Answer:

The value of x is 3.

Step-by-step explanation:

Matthew earned 7500 of 15000, which is exactly half the total amount, meaning that the fraction corresponding to his earnings is 1/2.

Rate of 5:2:x, with number 5 corresponding to Matthew, mean that his fraction of the earnings, in function of x is given by:

$\frac{5}{5 + 2 + x} = \frac{5}{7 + x}$

Both fractions are equal, so:

$\frac{5}{7 + x} = \frac{1}{2}$

Applying cross multiplication:

$7 + x = 10$

$x = 10 - 7$

$x = 3$

The value of x is 3.

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2 years ago

What is the answer to <img src="https://tex.z-dn.net/?f=%5Cfrac%7Bz-5%7D%7Bz%2B1%7D%3D%5Cfrac%7B3%7D%7B2%7D" id="TexFormula1" ti

rusak2 [61]

The correct answer is Z=-13

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2 years ago

Read 2 more answers

a theater is designed with 15 seats in the first row, 19 in the second, 23 in the third, and so on. if this seating pattern cont

marusya05 [52]

Answer:

<u>131 seats</u> are in the 30th row.

Step-by-step explanation:

The theater is designed with the first row there are 15 seats, in second row 19 seats and in the third row there are 23 seats.

Now, to find the number of seats in the 30th row.

So, we get the common difference( $d$ ) from the arithmetic sequence first:

$19-15=4.$

Thus, $d=4.$

So, the first tem $a(1)$ = 15.

The number of last row ( $n$ ) = 30.

Now, to get the number of seat in the 30th row we put formula:

$a(n) = a(1) + d(n-1)$

$a(30)=15+4(30-1)$

$a(30)=15+4\times 29$

$a(30)=15+116$

$a(30)=131$

Therefore, 131 seats are in the 30th row.

4 0

3 years ago