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2 years ago

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How do I do number 7 please help me with

1 answer:

riadik2000 [5.3K]2 years ago

3 0

There is a Khana Academy video that explains everything you have to do and it’s the same page that you’re on

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Consider this enlargement. 2 trapezoids. Side A corresponds to 20 centimeters, side B corresponds to 25 centimeters, and a side

DIA [1.3K]

Answer:

the answer is 10

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Problems 2.21, 2.22, 2.23

RoseWind [281]

Statements can be proved by contrapositive, contradiction or by induction.

<em>2.21 and 2.23 are proved by contrapositive</em>
<em>2.22 is proved by induction</em>

<u />

<u />

<u>2.21: If </u> $n^3$ <u> is even, then n is even (By contrapositive)</u>

The contrapositive of the above statement is that:

<em>If n is odd, then </em> $n^3$ <em> is odd</em>

Represent the value of n as:

$n = 2k + 1$ , where $k \ge 0$

Take the cube of both sides

$n^3 = (2k + 1)^3$

Expand

$n^3 = 8k^3 + 6k^2 + 6k + 1$

Group

$n^3 =[ 8k^3 + 6k^2 + 6k] + 1$

Factor out 2

$n^3 =2[4k^3 + 3k^2 + 3k] + 1$

Assume w is an integer; where:

$w =4k^3 + 3k^2 + 3k$

So, we have:

$n^3 =2w + 1$

The constant term (i.e. 1) means that $n^3$ is odd.

Hence, the statement has been proved by contrapositive.

<em>i.e. If n is odd, then </em> $n^3$ <em> is odd</em>

<u />

<u>2.22 </u> $3n + 4$ <u> is even, if and only if n is even</u>

We have: $3n + 4$ <u />

<u />

Assume that: $n = 2k + 2$ for $k \ge 0$

So, we have:

$3n + 4 = 3(2k + 2) + 4$

Open bracket

$3n + 4 = 6k + 6 + 4$

$3n + 4 = 6k + 10$

Factorize

$3n + 4 = 2(3k + 5)$

The factor of 2 means that $3n + 4$ is even.

<em>Hence, </em> $3n + 4$ <em> is even, if and only if n is even </em>

<em />

<u />

<u>2.22: </u> $s \ne -1$ <u> and </u> $t \ne -1$ <u>, then </u> $s + t + st \ne -1$ <u />

To do this, we prove by contrapositive.

The contrapositive of the above statement is:

If $s = -1$ and $t=-1$ , then $s + t + st = -1$

We have:

$s + t + st = -1$

Substitute the values of s and t in: $s + t + st = -1$

$-1 -1 -1 \times -1 = -1$

$-1 -1 + 1 = -1$

$-1 = -1$

Hence, by contrapositive:

If $s = -1$ and $t=-1$ , then $s + t + st = -1$

Read more about proofs at:

brainly.com/question/19643658

7 0

3 years ago

Kamila [148]

Answer:

y coordinate of the solution to the system is -5

7 0

3 years ago

A standard deck of 52 cards has four queens. two cards are randomly drawn in succession, without replacement, from a standard de

AnnyKZ [126]

There are a total of 4 queens in a standard deck of 52 cards. The probability that the 2 consecutive draws are queen is:

Probability = (4 / 52) * (3 / 51)

<span>Probability = 12 / 2652 = 0.004</span>

3 0

3 years ago

Read 2 more answers

A sphere and a cylinder have the same radius and height. The volume of the cylinder is 21m. what is the volume of the sphere.

Goshia [24]

Answer:

The volume of the sphere is 14m³

Step-by-step explanation:

Given

Volume of the cylinder = $21m^3$

Required

Volume of the sphere

Given that the volume of the cylinder is 21, the first step is to solve for the radius of the cylinder;

<em>Using the volume formula of a cylinder</em>

The formula goes thus

$V = \pi r^2h$

Substitute 21 for V; this gives

$21 = \pi r^2h$

Divide both sides by h

$\frac{21}{h} = \frac{\pi r^2h}{h}$

$\frac{21}{h} = \pi r^2$

The next step is to solve for the volume of the sphere using the following formula;

$V = \frac{4}{3}\pi r^3$

Divide both sides by r

$\frac{V}{r} = \frac{4}{3r}\pi r^3$

Expand Expression

$\frac{V}{r} = \frac{4}{3}\pi r^2$

Substitute $\frac{21}{h} = \pi r^2$

$\frac{V}{r} = \frac{4}{3} * \frac{21}{h}$

$\frac{V}{r} = \frac{84}{3h}$

$\frac{V}{r} = \frac{28}{h}$

Multiply both sided by r

$r * \frac{V}{r} = \frac{28}{h} * r$

$V = \frac{28r}{h}$ ------ equation 1

From the question, we were given that the height of the cylinder and the sphere have equal value;

This implies that the height of the cylinder equals the diameter of the sphere. In other words

$h = D$ , where D represents diameter of the sphere

Recall that $D = 2r$

So, $h = D = 2r$

$h = 2r$

Substitute 2r for h in equation 1

$V = \frac{28r}{2r}$

$V = \frac{28}{2}$

$V = 14$

Hence, the volume of the sphere is 14m³

4 0

3 years ago

Read 2 more answers