All categories

3 years ago

Which inequality represents all values of x for which the product below is defined ?

Mathematics

2 answers:

IRISSAK [1]3 years ago

8 0

Answer:

x ≥6

Step-by-step explanation:

Given the product:

√(x-6)*√(x+3)

The function has to be defined if x ≥0

Hence;

√(x-6)*√(x+3)≥0

Find the product

√(x-6)(x+3)≥0

Square both sides

(x-6)(x+3)≥0

x-6≥0 and x+3≥0

x≥0+6 and x ≥0 - 3

x ≥6 and x ≥-3

Hence the required inequality is x ≥6

Step2247 [10]3 years ago

4 0

Answer:

B. x>/ 6

Step-by-step explanation:

A P E X

You might be interested in

128,32,8 what is the next term of the geometric sequence

pochemuha

Given:

The given geometric sequence is 128, 32, 8

We need to determine the next term of the geometric sequence.

Common ratio:

Since, it is given that the sequence is a geometric sequence, then the common ratio is given by

$r=\frac{32}{128}$

$r=\frac{1}{4}$

Thus, the common ratio is $r=\frac{1}{4}$

Next term:

The next term of the sequence can be determined by multiplying the previous term with the common ratio.

Thus, we have;

Next term = $8\times (\frac{1}{4})$

= 2

Thus, the next term is 2.

Hence, the next term of the geometric sequence is 2.

4 0

4 years ago

Select all expressions that represent a correct solution to the equation 6(x+4)=20. copied for free from openupresources.Org Sel

baherus [9]

Option D: $20 \div 6-4$ is the correct solution to the equation $6(x+4)=20$

Option E: $\frac{1}{6} (20-24)$ is the correct solution to the equation $6(x+4)=20$

Option F: $(20-24) \div 6$ is the correct solution to the equation $6(x+4)=20$

Explanation:

The expression is $6(x+4)=20$

Let us find the value of x.

$\begin{aligned}6(x+4) &=20 \\6 x+24 &=20 \\6 x &=-4 \\x &=-\frac{2}{3}\end{aligned}$

Now, we shall find the expression that is equivalent to the value $x=-\frac{2}{3}$

Option A: $(20-4) \div 6$

Simplifying the expression, we have,

$\frac{16}{6}=\frac{8}{3}$

Since, $\frac{8}{3}$ is not equivalent to $x=-\frac{2}{3}$ , the expression $(20-4) \div 6$ is not equivalent to the equation $6(x+4)=20$

Hence, Option A is not the correct answer.

Option B: $16(20-4)$

Simplifying the expression, we have,

$16(16)=256$

Since, 256 is not equivalent to $x=-\frac{2}{3}$ , the expression $16(20-4)$ is not equivalent to the equation $6(x+4)=20$

Hence, Option B is not the correct answer.

Option C: $20-6-4$

Simplifying the expression, we have,

$20-10=10$

Since, 10 is not equivalent to $x=-\frac{2}{3}$ , the expression $20-6-4$ is not equivalent to the equation $6(x+4)=20$

Hence, Option C is not the correct answer.

Option D: $20 \div 6-4$

Using PEMDAS and simplifying the expression, we have,

$\begin{aligned}(20 \div 6)-4 &=\frac{10}{3}-4 \\ &=\frac{10-12}{3} \\ &=-\frac{2}{3} \end{aligned}$

Thus, $-\frac{2}{3}$ is equivalent to $x=-\frac{2}{3}$ , the expression $20 \div 6-4$ is equivalent to the equation $6(x+4)=20$

Hence, Option D is the correct answer.

Option E: $\frac{1}{6} (20-24)$

Simplifying the expression, we have,

$\begin{aligned} \frac{1}{6}(20-24) &=\frac{1}{6}(-4) \\ &=-\frac{4}{6} \\ &=-\frac{2}{3} \end{aligned}$

Thus, $-\frac{2}{3}$ is equivalent to $x=-\frac{2}{3}$ , the expression $\frac{1}{6} (20-24)$ is equivalent to the equation $6(x+4)=20$

Hence, Option E is the correct answer.

Option F: $(20-24) \div 6$

Simplifying the expression, we have,

$\begin{aligned}(20-24) \div 6 &=-\frac{4}{6} \\ &=-\frac{2}{3} \end{aligned}$

Thus, $-\frac{2}{3}$ is equivalent to $x=-\frac{2}{3}$ , the expression $(20-24) \div 6$ is equivalent to the equation $6(x+4)=20$

Hence, Option F is the correct answer.

6 0

4 years ago

A shopkeeper marks his goods at 40% above cost (the price he pays for the goods) and then offers a 25% discount. If a jacket cos

Ierofanga [76]

A shopkeeper marks:
$200 * 1.4 = $280
With a discount of 25%:
$280 * 0.75 = $210

4 0

3 years ago

(5 – 3x)4 – 2Please I need help. Show steps im so confused

guapka [62]

hello

to solve this problem, let's open the bracket and simplify

8 0

1 year ago

Graph the equation y = -1/4x + 2

valkas [14]

Answer:

y - intercept: 2 slope: down 1(-1), right 4(40

Step-by-step explanation:

5 0

3 years ago