All categories

3 years ago

Write an expression to represent each of the following sketches. Then give the value of each sketch.

Mathematics

1 answer:

zysi [14]3 years ago

4 0

The sketches are illustrations of inequalities

The first sketch is: $-2 \le x \le 5$ .
The second sketch is: $3 \ge x \ge -4$

Sketch A

In sketch A, we have the following observations:

The arrow faces left (this implies less than)
The dots on -2 and -5 are closed dots (this implies less than or equal to).

Hence, the inequality is:

$-2 \le x \le 5$

Sketch B

In sketch B, we have the following observations:

The arrow faces right (this implies greater than)
The dots on -4 and 3 are closed dots (this implies greater than or equal to).

Hence, the inequality is:

$3 \ge x \ge -4$

You might be interested in

3n - 5 = -8(6 + 5n) what does n equal?

Mariana [72]

3n - 5 = -8(6 + 5n)

3n - 5 = -48 - 40n

3n + 40n = -48 + 5

43n = -43

n = -1

8 0

3 years ago

Read 2 more answers

In this exercise, we consider strings made from uppercase letters in the English alphabet and decimal digits.

Yuri [45]

Answer:

a) $26^2 36^8$

b) $21\cdot10\cdot36^7$

c) $5^3 31^7$

d) $10\cdot 9\cdot 8 \cdot 7 \cdot 26^6$

Step-by-step explanation:

We will use the product rule from combinatorics.

a) There are 26 letters in the English alphabet, so there are 26 possible choices for the first character and 26 possible choices for the last one. Each one of the remaining eight characters of the string has 36 choices (letters or digits). By the product rule, there are $26\cdot36\cdot 36\cdots 36\cdot 26=26^2 36^8$ strings.

b) We have 5 possible choices for the first character, it must be some vowel a,e,i,o,u. The second character can be chosen in 21 ways, selecting some consonant. There are 10 possibilities for the last character because only of the digits are allowed. The other seven characters have no restrictions, so each one can be chosen in 36 ways. By the product rule there are $21\cdot 10\cdot 36^7$ strings.

c) The third character has 5 possibilities. Repetition of vowels is allowed, so the sixth and eighth characters have each one 5 possible choices. There are seven characters left. None of them are a vowel, but they are allowed to take any other letter or digit, so each one of them can be chosen in 36-5=31 ways. Therefore there are $5^3 31^7$ strings.

d) Remember that the binomial coefficient $\binom{n}{k}$ is the number of ways of choosing k elements from a set of n elements. In this case, to count all the possible strings, we first need to count in how many ways we can select the four positions that will have the digits. This can be done in $\binom{10}{4}$ ways, since we are choosing four elements from the set of the ten positions of the string. Now, for the first position, we can choose any digit so it has 10 possibilities. The second position has 9 possibilities, because we can't repeat the digit used on the first position. Similarly, there are 8 choices for the third position and there are 7 choices for the fourth. Now, these are the only digits on the string, so the remaining 6 characters must be letters, then each one of them has 26 possibilities. By the product rule, there are $10\cdot 9\cdot 8 \cdot 7 \cdot 26^6$ strings.

3 0

3 years ago

HELP ASAP ILL GIVE U BRAINLIEST PLS HELP ASAPP

lakkis [162]

Answer: 70.56 miles

Step-by-step explanation:

d = 5/6 sqrt(h)

7 = 5/6 sqrt(h)

42/5 = sqrt(h)

h = (42/5)^2 = 1,764/25 = 70.56 miles

8 0

2 years ago

Read 2 more answers

Hurry, I'll mark brainliest!!! Write the sentence as an equation. The product of q and 321 is the same as z

iVinArrow [24]

Answer: 321q = z

This is the same as z = 321q

The term "product" means "result of multiplying two or more values"

For example, the product of 2 and 3 is 2*3 = 6

Writing 321q is the same as 321*q, but we often leave out the multiplication sign. You could say q*321, but convention usually has the number come first then the variable second. The 321 is the coefficient.

6 0

3 years ago

What is the volume of a box that is 5 feet long, 6 feet wide and 10 feet tall

WITCHER [35]

Answer:

The volume is 300 square feet.

Step-by-step explanation:

Volume is calculated by multiplying as such:

$l \times w \times h$