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2 years ago

17 less than 12 times a certain number (m) IS 23 less than six times the same

Mathematics

1 answer:

REY [17]2 years ago

3 0

Answer:

m = -1

Step-by-step explanation:

12 times the number is 12m

17 less than that is 12m -17.

23 less than 6 times the number is 6m-23.

These expressions are said to be the same:

12m -17 = 6m -23

6m -17 = -23 . . . . . . . . subtract 6m from both sides

6m = -6 . . . . . . . . . . add 17 to both sides

m = -1 . . . . . . . . . divide both sides by 6

The value of m is -1.

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Triangle L M Q is cut by perpendicular bisector L N. Angle N L Q is 32 degrees and angle L M N is 58 degrees.

Serga [27]

Answer:

Yes

Step-by-step explanation:

ΔMNL ≅ ΔQNL by ASA or AAS

by ASA

Proof:

∠ LNM = ∠LNQ =90

LN = LN {Common}

∠MLN = ∠QLN {LN bisects ∠ L}

By AAS

∠Q + ∠QLN + ∠LNQ = 180 {Angle sum property of triangle}

∠Q + 32 + 90 = 180

∠Q + 122 = 180

∠Q = 180 -122 =

∠Q = 58

∠Q = ∠M

∠MNL =∠QNL = 90

LN = LN {common side}

8 0

3 years ago

Is the sum of two rational numbers rational

Advocard [28]

Answer:

no they are irrational

6 0

2 years ago

If tatianna works 3hrs a day on school days and make $123.75 a week what is her hourly rate?

madreJ [45]

Answer:

Her hourly rate is $8.25

Explanation:

Tatianna works 3 hours a day on school days and makes a total of $123.75 in a week

We know that:

There are 5 school days in a week

We are given that:

She works for 3 hours a day each of those days

Therefore:

Total number of hours worked = hours worked daily * number of days

Total number of hours worked = 3 * 5 = 15 hours in a week

The equation used to calculate Tatianna's earnings is:

Amount she makes in a week = Total number of hours worked * hourly rate

Now, we substitute with the givens to get the hourly rate as follows:

Amount she makes in a week = Total number of hours worked * hourly rate

123.75 = 15 * hourly rate

Hourly rate = $8.25

6 0

3 years ago

Step 1: 12x – 15 – 12x = 7x + 20

stealth61 [152]

Step-by-step explanation:

step 1. 12x - 15 - 12x = 7x + 20

step 2. 12x - 12x - 15 = 7x + 20 (grouping of terms)

step 3. -15 = 7x + 20 (adding like terms)

step 4. -35 = 7x (subtract 20 from both sides)

step 5. this step is incorrect.

step 6. -5 = x ( divide both sides by 7)

step 7. x = -5 (put the variable first).

5 0

3 years ago

Find four consecutive even integers such that seven times the first exceeds their sum by 18.

Ganezh [65]

Answer:

10, 12, 14, 16

Step-by-step explanation:

Given: Four consecutive even integers such that seven times the first exceeds their sum by 18.

Lets assume the first number be "x".

As it is even integers

∴ Second consecutive number will be $(x+2)$

Third consecutive number will be $(x+4)$

Fourth consecutive number will be $(x+6)$

Now, as given seven times the first exceeds their sum by 18.

∴ $[x+(x+2)+(x+4)+(x+6)]+18 = 7x$

solving the equation to find the number.

⇒ $[x+(x+2)+(x+4)+(x+6)]+18 = 7x$

Opening parenthesis

$x+x+2+x+4+x+6+18 = 7x$

⇒ $4x+30= 7x$

subtracting both side by 4x

⇒ $30= 3x$

Dividing both side by 3

∴ x= 10.

Hence, subtituting the value x to find four consecutive even integers.

First number is 10

Second consecutive number will be $(10+2)$ = 12

Third consecutive number will be $(10+4)$ = 14

Fourth consecutive number will be $(10+6)$ = 16

∴ Four consecutive even integers are 10,12,14,16.

8 0

3 years ago