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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:

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

You might be interested in

Find the volume of a right circular cone that has a height of 12.7 m and a base with a circumference of 18.9 m. Round your answe

DochEvi [55]

Step-by-step explanation:

We have,

Height of cone, h = 12.7 m

Circumference of base, C = 18.9 m

The base of a circular cone is circular. The circumference of circle is given by :

$C=2\pi r$

r is radius

$r=\dfrac{C}{2\pi}\\\\r=\dfrac{18.9 }{2\pi}\\\\r=3\ m$

The volume of a right circular cone is given by the formula as :

$V=\dfrac{1}{3}\pi r^2h$

$V=\dfrac{1}{3}\times 3.14 \times 3^2\times 12.7\\\\V=119.634\ m^3$

7 0

2 years ago

Ariana and Emily are both standing in line at Papa Joe’s Pizza. Ariana orders 4 large cheese pizzas and 1 order of breadsticks.

Eva8 [605]

The cost of 1 large pizza is $7.99 and cost of one breadstick is $2.50

Elimination method was used.

Step-by-step explanation:

Let,

Cost of one large pizza = x

Cost of one breadstick = y

According to given statement;

4x+y=34.46 Eqn 1

2x+y=18.48 Eqn 2

Subtracting Eqn 2 from Eqn 1

$(4x+y)-(2x+y)=34.46-18.48\\4x+y-2x-y=15.98\\2x=15.98$

Dividing both sides by 2

$\frac{2x}{2}=\frac{15.98}\\x=7.99$

Putting x=7.99 in Eqn 2

$4(7.99)+y=34.46\\31.96+y=34.46\\y=34.46-31.96\\y=2.50$

The cost of 1 large pizza is $7.99 and cost of one breadstick is $2.50

Elimination method was used.

Keywords: linear equation, elimination method

Learn more about elimination method at:

#LearnwithBrainly

6 0

2 years ago

What are the dimensions of the rectangle shown below? Remember to use the axes on the coordinate grid to help you.

miskamm [114]

Keep in mind its been a while since i did this type of work lol.....

did you try to draw it out on a grid paper....what will be helpful is if you got the coordinates and put the points down and then if you connect the dots you get your shape now you will count the unis in which the width and length is timed. so like if you had grid and it gave you coordinates and you did all that now you will count how many units is in the width and how many in the length.
but your best answer might be 14 units x 4 units

3 0

2 years ago

Jack was so frustrated with his slow laptop that he threw it out of his second story window. The height, h, of the laptop at tim

jeyben [28]

Answer:

The domain of the function is the interval [0,2.23]

see the explanation

Step-by-step explanation:

Let

t ----> the time in seconds

h(t) ----> the height of the laptop in units

we have

$h(t)=-16t^{2}+28t+17$

we know that

When the laptop hits the ground, the value of h(t) is equal to zero

For h(t)=0

$-16t^{2}+28t+17=0$

Solve the quadratic equation

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$-16t^{2}+28t+17=0$

$a=-16\\b=28\\c=17$

substitute in the formula

$x=\frac{-28(+/-)\sqrt{28^{2}-4(-16)(17)}} {2(-16)}$

$x=\frac{-28(+/-)\sqrt{1,872}} {-32}$

$x=\frac{-28(+/-)12\sqrt{13}} {-32}$

$x_1=\frac{-28(+)12\sqrt{13}} {-32}=-0.477$

$x_1=\frac{28(-)12\sqrt{13}} {32}=-0.477$ ---> is not a solution

$x_2=\frac{-28(-)12\sqrt{13}} {-32}$

$x_2=\frac{28(+)12\sqrt{13}} {32}=2.23\ sec$

therefore

The domain of the function is the interval [0,2.23]

All real numbers greater than or equal to 0 seconds and less than or equal to 2.23 seconds

$0\ sec \leq x \leq 2.23\ sec$

5 0

2 years ago

Freddy the frog is climbing up a well. Every day he climbs up 3 m but some nights he falls asleep and slips back 4m at the start

Anarel [89]

Answer: The frog fell asleep for 4 nights.

Step-by-step explanation: First, he climbs up 3m every night. there are 16 nights before he gets to 29m. He has not climbed up for the 16th day so 15*3= 45. 45-29= 16. 16/4=4. The frog slept for 4 nights.

7 0

2 years ago