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9 days ago

which inequality represents the following situation 3/5 times 5 less than a number is no more than 27

Mathematics

1 answer:

AnnZ [11.9K]9 days ago

6 0

The solution is $\frac{3}{5}(x-5) \leq 27$

Let's develop the expression incrementally, converting phrases into mathematical equations:

"3/5 of..." $\to \frac{3}{5} \times \ldots$

"5 less than a certain number..." $\to x-5 \ldots$

Thus, the initial segment becomes

"3/5 of 5 less than a certain number..." $\to \frac{3}{5}(x-5) \ldots$

"...is at most 27" $\ldots \leq 27$

Hence, combining all parts leads to the solution

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The bus routes in a city run on average every 15 minutes. The route times can vary by three minutes. Which absolute value equati

AnnZ [11930]

Response:

$Max = 18\ mins$

$Min = 12\ mins$

Step-by-step explanation:

Information given:

$Time = 15\ mins$

$Variation = 3\ mins$

Objective:

Calculate the maximum and minimum values

The max value is found as follows:

$Max = Time + Variation$

$Max = 15\ mins + 3\ mins$

$Max = 18\ mins$

The min value is identified as follows:

$Min = Time - Variation$

$Min = 15\ mins - 3\ mins$

$Min = 12\ mins$

3 0

1 month ago

What is the value of the product (4 – 2i)(6 + 2i)? 20 – 4i 20 + 16i 28 + 16i 28 – 4i

Zina [11999]

(4 – 2i)(6 + 2i)

Use FOIL

First: 4 multiplied by 6 equals 24

Outer: 4 times 2i gives 8i

Inner: -2i times 6 results in -12i

Last: -2i times 2i equals -4i², which simplifies to 4

Combine the results

24 + 8i - 12i + 4

Final result: 28 - 4i

The answer is: 28 - 4i

8 0

1 month ago

Read 2 more answers

A father lifts a toddler 1.5 m up in the air. The child gains 187.5 J of energy in her gravitational potential energy store as a

Svet_ta [12294]

The toddler weighs 12.5 kg.

In-depth explanation:

The formula for gravitational potential energy is Ep=mgh where;

Ep=gravitational potential energy

m=mass of an object

g=gravitational field strength

h=height in meters

Given that; h= 1.5m, Ep=187.5J, g=10 N/kg then finding m;

Ep=mgh

187.5=m*10*1.5

187.5=15m

187.5/15 =15m/15

m=12.5 kg

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5 0

19 days ago

You have 80 pieces of fabric to make a wall hanging. Each piece of fabric is a square with a side length of 5 inches. You use as

tester [11911]

The area would amount to 25

and we could create 3 squares. This would leave 75

5 inches remaining.

8 0

14 days ago

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Alice and Briana each participate in a 5 kilometer race. Alice's distance covered, in kilometers, after t minutes can be modeled

PIT_PIT [11932]

Answer:

a. Alice

b. Briana

c. 0.51 minutes

Step-by-step explanation:

a. Alice's formula is applicable for any t > 0 minutes, while Briana’s is only applicable when

2t - 1 > 0

2t > 1

t > 1/2 minutes

b. They complete the race when their total distance equals 5 kilometers. For Alice:

t/4 = 5

t = 20 minutes

For Briana:

√(2t - 1) = 5

2t - 1 = 25

2t = 26

t = 13 minutes

c. They reach the same point when they have traveled the same distance, expressed as:

t/4 = √(2t - 1)

(t/4)² = 2t - 1

t²/16 = 2t - 1

t² = 16(2t - 1)

t² = 32t - 16

t² - 32t + 16 = 0

Using the quadratic formula:

$t = \frac{-b \pm \sqrt{b^2 - 4(a)(c)}}{2(a)}$

$t = \frac{32 \pm \sqrt{-32^2 - 4(1)(16)}}{2(1)}$

$t = \frac{32 \pm 30.98}{2}$

$t_1 = \frac{32 + 30.98}{2}$

$t_1 = 31.49$

$t_2 = \frac{32 - 30.98}{2}$

$t_2 = 0.51$

Only the second solution fits this scenario because the race concluded before they took 31.49 minutes.

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1 month ago

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