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3 years ago

One-third of a number added to itself equals 3 times the difference of the number and seven.

Mathematics

1 answer:

olya-2409 [2.1K]3 years ago

3 0

Answer:

Step-by-step explanation:

Do this step by step.

Let the number = x

1/3 of a number = 1/3 x

Added to itself 1/3x + x

3*(x - 7)

So the equation is

1/3x + x = 3(x - 7) Remove the brackets. Collect 1/3x and x

4/3 x = 3x - 21 Multiply both sides by 3.

4x = 3*(3x - 21) Remove the brackets again

4x = 9x - 63 Subtract 9x from both sides

-5x = -63 Divide by -5

x = -63/-5

x = 12.6

You might be interested in

A DVD player is regularly priced at 79.95 and is on sale for 30% off. What is the discount?

evablogger [386]

Answer:

$2.40 or $77.55

Step-by-step explanation:

I don't know if you are asking for how much off or what, so I'm doing both

First, we have to find how much we have to take off or what is 30% of 79.95 so our equation is:

79.95 x 0.03 = 2.40

So 30% of 79.95 is $2.40

To find how much our new price sale is, we have to take that $2.40 off so our equation is:

79.95 - 2.4 = 77.55

So our discount price is $77.55

hope this helps:)

7 0

3 years ago

Triangle ABC is to be dilated through point P with a scale factor of 3. How many units away from point A along ray PA will A’ be

drek231 [11]

Answer:

A' will be located 10 units from point A along ray PA

Step-by-step explanation:

we know that

The scale factor is equal to 3

To obtain PA', multiply PA by the scale factor

PA'=PA*3

PA=5 units

substitute

PA'=(5)*3=15 units

AA'=PA'-PA=15-5=10 units

therefore

A' will be located 10 units from point A along ray PA

3 0

3 years ago

Read 2 more answers

What is the value of 106 ?

Artemon [7]

Is that meant to be 10 to the power of 6?
Assuming it is it would be 10×10×10×10×10×10.
This equals 1,000,000 so the answer is C.

7 0

3 years ago

Read 2 more answers

rotation of 90 degrees counterclockwise about the origin, point O, then a reflection across the x-axis reflection across the y-a

SpyIntel [72]

Answer:

The point O can be (x,y) or (-x,y) or (-x,-y) or ( x,-y) reason being that you haven't given point O lies in which quadrant.

Rotation through 90° counter clockwise

(x,y) = (-y,x)

(-x,y)=(-y,-x)

(-x,-y)=(y,-x)

(x,-y) =(y,x)

Then Reflection across X axis has taken place.

(-y,x) = (-y,-x)

(-y,-x)=(-y,x)

(y,-x)=(y,x)

(y,x)=(y,-x)

Then a reflection across the y-axis has taken place.

(-y,-x)=(y,-x)

(-y,x) = (y,x)

(y,x) =(-y,x)

(y,-x)=(-y,-x)

Then a translation a units to the right and b units up has taken place.

(y,-x)=(y+a,-x+b)

(y,x) =(y+a, x+b)

(-y,x) =(-y+a,x+b)

(-y,-x)=(-y+a,-x+b)

Then a rotation of 180 degrees counterclockwise about the origin has taken place.

(y+a,-x+b)=[-(y+a),-(-x+b)]

(y+a, x+b)=[- (y+a), -(x+b)]

(-y+a,x+b)=[-(-y+a),-(x+b)]

(-y+a,-x+b) =[-(-y+a),-(-x+b)]

Now Again a reflection across the Y axis has taken place.

[-(y+a),-(-x+b)]=[(y+a),-(-x+b)]

[-(y+a),-(x+b)]=[(y+a),-(-x+b)]

[-(-y+a),-(x+b)]=[(-y+a),-(x+b)]

[-(-y+a),-(-x+b)]=[(-y+a),-(-x+b)]

Totally depends on value of a and b on which quadrant these point lies.

7 0

3 years ago

In a group of college students, the ratio of men to women is 3:1 (i.e., 3 to 1). In a recent survey, 40% of the men in this grou

katovenus [111]

Answer:

0.3875

Step-by-step explanation:

Given that in a group of college students, the ratio of men to women is 3:1 (i.e., 3 to 1). In a recent survey, 40% of the men in this group selected hiking as their favorite outdoor activity whereas 35% of the women in the group selected hiking as their favorite outdoor activity

From the above information we find that

P(Men) = 0.75 and P(women) = 0.25 (since men:women = 3:1)

Out of men prob for not selecting hiking as their favorite outdoor activity

$=1-0.6 = 0.4$

Out of women prob for not selecting hiking as their favorite outdoor activity

$=1-0.35 = 0.65$

Prob for a randomly selected person that hiking is not his/her favorite outdoor activity = Prob (man and not selected activitiy) + P(women and not selected activity) (since men and women are mutually exclusive and exhaustive)

= $0.75(0.4)+0.25(0.35)\\= 0.30+0.0875\\\\=0.3875$

6 0

3 years ago