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3 years ago

Write the solution to the given inequality in interval notation.

Mathematics

1 answer:

melomori [17]3 years ago

8 0

The answer is [4,6) because a square bracket (closed) denotes that the lower bound is inclusive, and the parenthesis (open) denotes that the upper bound is exclusive.

As you can see on the number line, there is a closed dot on 4 and an open dot on 6.

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Select the correct answer. Consider the following system of equations. Use this graph of the system to approximate its solution.

vesna_86 [32]

The approximate solution to the given system of equations, considering the graph, is given as follows:

D. $\left(-\frac{13}{4}, \frac{5}{2}\right)$ .

<h3>What is a system of equations?</h3>

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

On a graph, the solution of a system of equations is given by the intersection between the curves. In this graph, the intersection of the two curves happen close to x = -3.25, y = 2.5, hence the solution is approximated by:

D. $\left(-\frac{13}{4}, \frac{5}{2}\right)$

More can be learned about a system of equations at brainly.com/question/24342899

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7 0

2 years ago

Last month 4,861 books were checked out from the Library.this month 3,278 books were checked out.how many more books were checke

ludmilkaskok [199]

Answer:

1,583

Step-by-step explanation:

4,861 - 3278 = 1,583. All you have to do is subtract each amount of books from both months.

6 0

3 years ago

Marina has 2.5 lb of cashews. she puts 6 oz in a bag and gives the bag to her brother. what weight of cashews does marina have l

faust18 [17]

2.5/x = 1/16
cross mutiply
x = 40 oz

40 oz - 6oz = 34 oz
She has 34 oz or 2 1/8 pounds

4 0

4 years ago

A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed of 31 ft/s. (a) A

julsineya [31]

Answer:

a) -13.9 ft/s

b) 13.9 ft/s

Step-by-step explanation:

a) The rate of his distance from the second base when he is halfway to first base can be found by differentiating the following Pythagorean theorem equation respect t:

$D^{2} = (90 - x)^{2} + 90^{2}$ (1)

$\frac{d(D^{2})}{dt} = \frac{d(90 - x)^{2} + 90^{2})}{dt}$

$2D\frac{d(D)}{dt} = \frac{d((90 - x)^{2})}{dt}$

$D\frac{d(D)}{dt} = -(90 - x) \frac{dx}{dt}$ (2)

Since:

$D = \sqrt{(90 -x)^{2} + 90^{2}}$

When x = 45 (the batter is halfway to first base), D is:

$D = \sqrt{(90 - 45)^{2} + 90^{2}} = 100. 62$

Now, by introducing D = 100.62, x = 45 and dx/dt = 31 into equation (2) we have:

$100.62 \frac{d(D)}{dt} = -(90 - 45)*31$

$\frac{d(D)}{dt} = -\frac{(90 - 45)*31}{100.62} = -13.9 ft/s$

Hence, the rate of his distance from second base decreasing when he is halfway to first base is -13.9 ft/s.

b) The rate of his distance from third base increasing at the same moment is given by differentiating the folowing Pythagorean theorem equation respect t:

$D^{2} = 90^{2} + x^{2}$