1. the smallest composite number is ________

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

If geometry symbol represented as small triangle with three sides. abc geometry congruent symbol represented as two small horizo

n200080 [17]

The value of x in the congruent triangles abc and dec is 1

<h3>How to determine the value x?</h3>

The question implies that the triangles abc and dec are congruent triangles.

The congruent sides are:

ab = de

bc = ce = 4

ac = cd = 5

The congruent side ab = de implies that:

4x - 1 = x + 2

Collect like terms

4x - x = 2 + 1

Evaluate the like terms

3x = 3

Divide through by 3

x = 1

Hence, the value of x is 1

Read more about congruent triangles at:

brainly.com/question/12413243

#SPJ1

<u>Complete question</u>

Two triangles, abc and cde, share a common vertex c on a grid. in triangle abc, side ab is 4x - 1, side bc is 4, side ac is 5. in triangle cde, side cd is 5, side de is x + 2, side ce is 4. If Δabc ≅ Δdec, what is the value of x? a. x = 8 b. x = 5 c. x = 4 d. x = 1 e. x = 2

3 0

2 years ago

If x^(3/5) = 1.84, then x^2 = ?<br> Show Work.<br> A.) 7.63<br> B.) 10.40<br> C.) 21.15

svetlana [45]

X^(3/5) = 1.84

x^(3/5) = (1.84)

Raise both sides of the equation to (5/3).

This is so that on the side with x, 3/5 * 5/3 = 1.

(x^3/5 )^5/3 = (1.84)^(5/3)

x^(3/5 * 5/3) = 1.84^(5/3)

x^1 = 1.84^(5/3)

x = 1.84^(5/3)

But remember we are solving for x^2.

x = 1.84^(5/3)

x^2 = (1.84^(5/3))^2

x^2 = 1.84^(5/3 *2 )

x^2 = 1.84^(10/3)

Use a calculator here.

x^2 = 1.84^(10/3) ≈ 7.63

Option A.

Cheers!

5 0

3 years ago

The Ferrer family is taking a vacation. During their vacation they will drive a total of 686 miles at an average speed of 65 mil

aleksklad [387]

Answer:

A- m= 686 - 65h

B- h = 686 + 65m

C- m = 686 + 65h

D- h = 686 - 65m

step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Write an expression to describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for t

ollegr [7]

Answer:

<u>The expression to describe this sequence is Aₙ = (n - 1) * 1 - 6</u>

Step-by-step explanation:

1. Let's write an expression to describe the sequence which first four terms are as follows:

- 6, -5, -4, - 3.....

Aₙ = (n - 1) * 1 - 6; A₁ = - 6

A₁ = (n - 1) * 1 - 6 = (1 - 1) * 1 - 6 = 0 * 1 - 6 ⇒A₁ = - 6

A₂ = (n - 1) * 1 - 6 = (2 - 1) * 1 - 6 = 1 * 1 - 6⇒ A₁ = - 5

A₃ = (n - 1) * 1 - 6 = (3 - 1) * 1 - 6 = 2 * 1 - 6⇒ A₁ = - 4

A₄ = (n - 1) * 1 - 6 = (4 - 1) * 1 - 6 = 3 * 1 - 6⇒ A₁ = - 3

A₅ = (n - 1) * 1 - 6 = (5 - 1) * 1 - 6 = 4 * 1 - 6⇒ A₁ = - 2

A₆ = (n - 1) * 1 - 6 = (6 - 1) * 1 - 6 = 5 * 1 - 6⇒ A₁ = - 1

A₇ = (n - 1) * 1 - 6 = (7 - 1) * 1 - 6 = 6 * 1 - 6⇒ A₁ = 0

5 0

3 years ago

1. the smallest composite number is _________​

1. the smallest composite number is _________