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kumpel [21]
2 years ago
13

How many positive 3-digit numbers have property that the first digit is at least three times the second digit?

Mathematics
1 answer:
ss7ja [257]2 years ago
3 0

The number of positive 3-digit numbers have a property that the first digit is at least three times the second digit is 285.

<h3>How to get the number?</h3>

Since restriction is set to the first digit, all you have to think is about the last two digits e.g if the first digit is one, the last two digits can only be zeros.

Thus, by the principle of multiplication, 1×1=1 way. If the first digit is 2, then the last digits can be either 1 or 0. You have 2×2=4 ways

For first digit 3, the last two digits can be 0,1 or 2. 3x3=9, there is a succinct pattern. Therefore, 1+4+9+16+25+36+49+64+81=285.

Learn more about numbers on:

brainly.com/question/251701

#SPJ1

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For the given pair of equations, give the slopes of the lines, and then determine whether the two lines are parallel, perpendicu
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Answer/Step-by-step explanation:

Given,

10x - 3y = 3

3x + 10y = 30

Rewrite both equation in slope-intercept form, y = mx + b.

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Thus,

✔️10x - 3y = 3

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y = 10/3x - 1

Slope of this line would be 10/3

✔️3x + 10y = 30

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y = -3/10x + 3

The slope of this line is -³/10.

✔️The two lines are pendivukar to each other because the slope of one is the negative reciprocal of the other.

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3 years ago
Question 7
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Answer:

Step-by-step explanation:

New height to initial height=

10/4=2.5

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4 0
3 years ago
There is a 4-foot fence that surrounds your backyard. The fence casts a shadow that is 5 feet long. If you are 6 feet tall and s
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My shadow would be 7 feet tall.

Since I am standing next to the fence, then whatever difference its actual height and its shadow has, will be the same difference of my shadow to my actual height.

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me    : Actual height - 6 ft : Shadow height - ?   ; difference - 1ft

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3 0
3 years ago
Angela and Jayden were at track practice. The track is 2/5 kilometers around. Angela ran 1 lap in 2 Minutes. Jayden ran 3 laps i
I am Lyosha [343]

Answer:

Step-by-step explanation:

Angel ran 1 lap in 2 minutes.

Jayden ran 3 laps in 5 minutes.

How many minutes does it take Angel to run one kilometer? What about Jayden?

How far does Angel run in one minute? What about Jayden?

Who is running faster? Explain your reasoning.

IM Commentary

Parts (a) and (b) of the task ask students to find the unit rates that one can compute in this context. Part (b) does not specify whether the units should be laps or km, so answers can be expressed using either one.

The purpose of part (c) is to give students an opportunity to make use of the unit rates that they found in parts (a) and (b). While it is possible for students to solve part (c) in other ways, the solution shown represents the kind of reasoning with unit rates that 7th graders should be able to do. It is important to note that the answer can be determined using different unit rates as long as the reasoning behind it is correct.

Solution

We can create a table that shows how far each person runs for a certain number of laps:

Number of laps Number of km

1 25

2 45

3 65

We can see from the table that 1 km is exactly half way between 2 and 3 laps. So it will take 2.5 laps to run 1 km.

Since it takes Angel 2 minutes to run 1 lap, she will take

2.5 laps1 km⋅2 minutes1 lap=5 minutes1 km.

So it takes Angel 5 minutes to run 1 km.

Since it takes Jayden 5 minutes to runs 3 laps, she runs 1 lap in 53 minutes. Thus, it takes Jayden

2.5 laps1 km⋅5 minutes3 laps=52⋅53 minutes/km=256 minutes/km=416 minutes/km.

So it takes Jayden 416 minutes to run 1 km.

Angel runs 1 lap in 2 minutes so she runs 12 lap in 1 minute. Since 1 lap is 25 km, 12 lap is 15 km. So she also runs 15 km in one minute.

Since Jayden runs 1 lap in 53 minutes, she will run 35 laps in 1 minute. Since Jayden runs 1 km in 256 minutes, she will run 625 km in 1 minute.

Jayden runs the same distance in less time than Angel (alternatively, Jayden runs farther in the same time than Angel), so Jayden is running faster than Angel.

4 0
2 years ago
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