8w+5=4(2w+1) How many solutions does it have?

The height of Atlas V rocket used for space lifts was 205 feet. What is the height of a model of Atlas V rocket if the scale fac

KengaRu [80]

Answer: 6.4 feet

Step-by-step explanation:

Height of Atlas V rocket = 205 feet

Ratio of the model = 1:32 = 1/32

Model / Real = 1/32

Since Real height = 205, we put it into the equation and this will be:

Model / Real = 1/32

Model / 205 = 1/32

Model × 32 = 205 × 1

Model = 205/32

Model = 6.4 feet

The height of the model is 6.4 feet.

7 0

3 years ago

PLEASE HELP ASAP

vovikov84 [41]

Answer:

Third option

Step-by-step explanation:

$x^{2}$ -10x+25=0 is the correct answer. 100% sure

7 0

3 years ago

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A CLOSER LOOK AT Compound Inequalities We previously learned that compound inequalities are two inequalities joined by the word

alex41 [277]

Answer:

The sign at the ticket booth should read "Guests that are under 3 years old or over 62 years old get free admission!"

Step-by-step explanation:

Compound inequalities are the combination of two inequalities by the words "or" or "and".

In the given example, the compound inequality is,

Guests that are under 3 years old and over 62 years old get free admission!

The given inequality can be broken into two individual inequalities as,

Inequality 1: Guests that are under 3 years old get free admission

Inequality 2: Guests that are over 62 years old get free admission

The above two inequalities are combined by "and" in the given compound inequality.

Now, "and" signifies that both the conditions or inequalities should be fulfilled at the same time. But a guest can either be under 3 years old or he/she should be older than 62. Both the conditions cannot be fulfilled at the same time and hence, the sign doesn't make any sense.

To correct the sign, "and" should be replaced with "or".

Therefore, the corrected sign at the ticked booth should read "Guests that are under 3 years old or over 62 years old get free admission!".

For more details, refer to the link:

brainly.com/question/20296065?referrer=searchResults

3 0

3 years ago

Giving 100 points.

Nitella [24]

Answer:

1. Cost per customer: 10 + x

Average number of customers: 16 - 2x

$\textsf{2.} \quad -2x^2-4x+160\geq 130$

3. $10, $11, $12 and $13

Step-by-step explanation:

Given information:

$10 = cost of buffet per customer
16 customers choose the buffet per hour
Every $1 increase in the cost of the buffet = loss of 2 customers per hour
$130 = minimum revenue needed per hour

Let x = the number of $1 increases in the cost of the buffet

Part 1

Cost per customer: 10 + x

Average number of customers: 16 - 2x

Part 2

The cost per customer multiplied by the number of customers needs to be at least $130. Therefore, we can use the expressions found in part 1 to write the inequality:

$(10 + x)(16 - 2x)\geq 130$

$\implies 160-20x+16x-2x^2\geq 130$

$\implies -2x^2-4x+160\geq 130$

Part 3

To determine the possible buffet prices that Noah could charge and still maintain the restaurant owner's revenue requirements, solve the inequality:

$\implies -2x^2-4x+160\geq 130$

$\implies -2x^2-4x+30\geq 0$

$\implies -2(x^2+2x-15)\geq 0$

$\implies x^2+2x-15\leq 0$

$\implies (x-3)(x+5)\leq 0$

Find the roots by equating to zero:

$\implies (x-3)(x+5)=0$

$x-3=0 \implies x=3$

$x+5=0 \implies x=-5$

Therefore, the roots are x = 3 and x = -5.

Test the roots by choosing a value between the roots and substituting it into the original inequality:

$\textsf{At }x=2: \quad -2(2)^2-4(2)+160=144$

As 144 ≥ 130, the solution to the inequality is between the roots:

-5 ≤ x ≤ 3

To find the range of possible buffet prices Noah could charge and still maintain a minimum revenue of $130, substitute x = 0 and x = 3 into the expression for "cost per customer.

[Please note that we cannot use the negative values of the possible values of x since the question only tells us information about the change in average customers per hour considering an increase in cost. It does not confirm that if the cost is reduced (less than $10) the number of customers increases per hour.]

Cost per customer:

$x =0 \implies 10 + 0=\$10$

$x=3 \implies 10+3=\$13$

Therefore, the possible buffet prices Noah could charge are:

$10, $11, $12 and $13.

8 0

2 years ago

Use triangle ABC below to answer the question that follows:

AnnyKZ [126]

Answer: Choice 1) The sum of the angles A and B are supplementary to angle C

Why is this the answer? Because we'll use facts 2 through 4 to help prove the triangles similar. If fact 2 is true, then fact 3 leads to helping set up the congruent corresponding angles (either A = D or C = E). Fact 4 is true because all angles are congruent to themselves, and this fact is the other angle pair we need to prove the triangles similar.

We don't use fact 1 even though it's a true statement. The fact that A+B+C = 180 isn't really useful to compare across two triangles.

3 0

3 years ago

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