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3 years ago

11

Kareem has a collect of dimes and quarters. He can tell that he has more quarters than dimes, and he knows that he has at most $

2.
Write the system of inequalities to represent this.

1 answer:

Mariulka [41]3 years ago

8 0

Answer:

D<Q≤2 Or D<Q Q+D≤2

Step-by-step explanation:

I'm pretty sure this is the answer but it's been a while since I've done system of inequalities. Essentially the value and number of dimes is less than the value and number of quarters. And the value of both is less than or equal to 2 dollars

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Find the next two terms in the given sequence, then write it in recursive form. A.) {7,12,17,22,27,...} B.) { 3,7,15,31,63,...}

iren [92.7K]

Answer:

A) a_n = 5n + 2

B) a_n = (2^(n + 1)) - 1

Step-by-step explanation:

A) The sequence is given as;

{7,12,17,22,27,...}

The differences are:

5,5,5,5.

This is an arithmetic sequence following the formula;

a_n = a_1 + (n - 1)d

d is 5

Thus;

a_n = a_1 + (n - 1)5

Now, a_1 = 7. Thus;

a_n = 7 + 5n - 5

a_n = 5n + 2

B) The sequence is given as;

{ 3,7,15,31,63,...}

Now, let's write out the differences of this sequence:

Differences are:

4, 8, 16, 32

This shows that it is a geometric sequence with a common ratio of 2.

In the given sequence, a_1 = 3 and a_2 = 7 and a_3 = 15

Thus, a_2 = 2a_1 + 1

Also, a_(2 + 1) = 2a_2 + 1

Combining both equations, we can deduce that: a_(n + 1) = 2a_n + 1

Thus; a_n can be expressed as:

a_n = (2^(n + 1)) - 1

7 0

3 years ago

Find the absolute maximum and minimum values of f(x,y)=xy−4x in the region bounded by the x-axis and the parabola y=16−x2.

skad [1K]

Answer:

The absolute maximum and minimum is $20\; \text{and} -20.$

Step-by-step explanation:

We first check the critical points on the interior of the domain using the

first derivative test.

$f_x=y-4=0$

$f_y=x=0$

The only solution to this system of equations is the point (0, 4), which lies in the domain.

$f_{xx}=0, \;f_{yy}=0\; \text{and}\; f_{xy}=-1$

$\Rightarrow f_{xx}f_{yy}-f_{xy}=o-1=-1$

$\therefore (0,4)$ is a saddle point.

Boundary points - $(4,0), (-4,0), (0,16)$

Along boundary $y=16-x^2$

$f=x(16-x^2)-4x$

$=16x-x^3-4x$

$\Rightarrow f^'=16-3x^2-4=0$

$\Rightarrow 3x^2=12$

$\Rightarrow x=\pm2,\;\;y=14$

Values of f(x) at these points.

$\begin{array}{}(4,0)=-16\\(-4,0)=16\\(0,16)=0\\(2,14)=20\\(-2,14)=-20\end{array}$

Therefore, the absolute maximum and minimum is $20\; \text{and} -20.$

6 0

3 years ago

Which coordinate pairs make the equation x-9y=12 true?

asambeis [7]

Answer:

(12,0) and (3, -1) and (0,-4/3)

Step-by-step explanation:

To find if a point makes an equation true, just substitute its x and y values in in the equation and simplify.

1) Let's test the point (12,0). Substitute 12 for x and 0 for y in the equation:

$x-9y=12\\(12)-9(0)=12\\12-0=12\\12=12$

12 does equal 12, so (12,0) makes the equation true.

2) Let's test the point (0, 12). Substitute 0 for x and 12 for y in the equation:

$x-9y=12\\(0)-9(12) = 12\\0-108 = 12\\-108 = 12$

However, -108 does not equal 12, so (0,12) does not make the equation true.

3) Let's test the point (3, -1). Substitute 3 for x and -1 for y in the equation:

$x-9y=12\\(3)-9(-1) = 12\\3 + 9 = 12\\12 = 12$

12 does equal 12, so (3, -1) makes the equation true.

4) Let's test the point (0, -4/3). Substitute 0 for x and -4/3 for y in the equation:

$(0) -9(-\frac{4}{3} ) = 12\\0 + \frac{36}{3} = 12\\0 + 12 = 12 \\12 = 12$

12 does equal 12, so (0, -4/3) makes the equation true.

8 0

3 years ago

The area of a triangle is 36 4/5 units squared and the height of the triangle 9 1/5 what is the length of the triangles base

den301095 [7]

Answer:

Height = 8 units

Step-by-step explanation:

Area of a triangle = $36\frac{4}{5}$ square units

= $\frac{184}{5}$ square units

Height of the triangle = $9\frac{1}{5}$ units

= $\frac{46}{5}$ units

Formula to calculate the area of a triangle is,

Area = $\frac{1}{2}(\text{Base})(\text{Height})$

$\frac{184}{5}= \frac{1}{2}\times (\frac{46}{5})\times (\text{Height})$

$\frac{184}{5}= (\frac{46}{10})\times (\text{Height})$

Height = $\frac{184}{5}\times \frac{10}{46}$

= $\frac{368}{46}$

= 8 units

Therefore, height of the given triangle is 8 units.

6 0

2 years ago

Read 2 more answers

How can you tell if an inequality will have a solid line

Virty [35]

Answer:

b. the symbol has or equal to

Step-by-step explanation:

Required

When does an inequality have a solid line

The question is pretty straightforward and the answer is (b) which means that when the symbol has or equal to.

This implies that, the symbol could be:

> or = i.e. $\ge$

and it could also be:

< or = i.e. $\le$

Take for instance:

$x + 1 \ge 2$ and $y- 5\le 10$

<em>The above expressions will have a solid line</em>

6 0

2 years ago