Write 4–6 sentences explaining why it is important to have precise definitions
in mathematics. Choose five terms, some from geometry and some from other
areas of mathematics, and give a precise definition of each. Then change each
of those definitions so that it still describes the term but not precisely enough to avoid ambiguity. formulate counter examples, with sketches when feasible, that show how things could satisfy the less precise definitions but not match the intended terms.
pleaseeee help asap !
avoid ambiguity. Formulate counterexamples, with sketches when feasible, that
show how things could satisfy the less precise definitions but not match the
intended terms.

Answer:

[tex]x=-3, y=5, z=6[/tex]

Step-by-step explanation:

1. Divide by 2 both sides in the second equation:

2. From the third equation find z in terms of x:

3. Add up the first and new second equations and find y in terms of x:

4. Put new alternatives instead of y and z in the first equation:

5. Now we can easily find other two unknowns by using their equations by means of x:

Answer:

Step-by-step explanation:

2x + 6y - 2z = 12

12x - 6y + 6z = -30

14x + 4z = -18

6x + z = -12

14x + 4z = -18

-24x - 4z = 48

-10x = 30

x = -3

6(-3) + z = -12

-18 + z = -12

z = 6

-3 + 3y - 6 = 6

-9 + 3y = 6

3y = 15

y = 5

x = -3, y = 5, z = 6

Answer:

7

Step-by-step explanation:

5x-x=28  The dad is 5 times as old and the difference in their ages is 28years.

4x=28 Simplify and divide.

x=7

Answer:

30 seconds.

Step-by-step explanation:

That will be the Lowest Common Multiple of 5 and 6.

This is 5 *6 = 30.

Answer:

11325.

Step-by-step explanation:

Step 1: address the formula, input parameters & values.

Input parameters & values:

The number series 1, 2, 3, 4, . . . . , 149, 150.

The first term a = 1

The common difference d = 1

Total number of terms n = 150

Step 2: apply the input parameter values in the formula

Sum = n/2 x (a + Tn)

= 150/2 x (1 + 150)

= 22650/2

1 + 2 + 3 + 4 + . . . . + 149 + 150 = 11325

Therefore, 11325 is the sum of positive integers up to 150.

The sum of the first 150 odd positive integers is 11325.

The number series 1, 2, 3, 4, . . . . , 149, 150.

The first term a = 1

The common difference d = 1

Total number of terms n = 150

Sum = n/2 x (a + Tn)

= 150/2 x (1 + 150)

= 22650/2

1 + 2 + 3 + 4 + . . . . + 149 + 150 = 11325

: An integer is positive if it is greater than zero. Example 1, 2, 3 . . . Negative Integers: An integer is negative if it is less than zero. Example -1, -2, -3 . . .

The definition of a positive integer is a whole number greater than zero. The set of positive integers includes all counting numbers (that is, the natural numbers).

Odd numbers are the numbers that cannot be divided by 2 evenly. It cannot be divided into two separate integers evenly. If we divide an odd number by 2, then it will leave a remainder. Examples of odd numbers are 1, 3, 5, 7, etc.

Learn more about odd numbers here:https://brainly.com/question/2263958

#SPJ2

Answer:

5

Step-by-step explanation:

The slope of a line is always rise over run.

We need to make the rise over run equivalent to 2 to find the value of y.

Looking at the x-coordinates, 2 and 6, we can see there is an increase in 4.

Now we ask: What number, times 2, will equal 4?

That is 2.

So we have to make the increase in the y coordinates 2.

If we have the original point 3, an increase in 2 is 5.

So y is 5.

Hope this helped!

Answer:

11 = y

Step-by-step explanation:

Using the slope formula

m = (y2-y1)/(x2-x1)

2 = (y-3)/(6-2)

2 = (y-3)/4

Multiply each side by 4

2*4 = y-3

8 = y-3

Add 3  to each side

8+3 = y-3+3

11 = y

Answer:

Step-by-step explanation:

Given the expression written by Elizabeth as  3.3 - 0.21= 1.2, to check if Elizabeth expression is reasonable or not, we need to check if her answer is close to or equal to the answer of the diiferebce between 3.3 - 0.21.

Converting 3.3 and 0.21 to fraction

3.3 = 33/10

0.21 = 21/100

Taking the difference of both fractions

[tex]= \dfrac{33}{10} -\dfrac{21}{100} \\\\= \dfrac{330-21}{100} \\\\= \dfrac{309}{100} \\\\= 3.09\\[/tex]

Hence 3.3 - 0.21 = 3.09 ≈ 3.0 (to nearest whole number). Comparing Elizabeth answer which is 1.2 to the answer f=gotten, it can be seen that her answer is far from the right answer with a difference of about 1.8 (3.0-1.2). This large difference makes Elizabeth answer unreasonable.

D.

The estimate would be 30

3​, so her answer is not reasonable

Answer:

6/8

Step-by-step explanation:

6 bags and 8 friends which is less than one or .75 or 6/8

Answer:

[tex]x=13[/tex]

Step-by-step explanation:

So we have:

[tex]\frac{x}{11}=\frac{13}{11}[/tex]

To solve for x, multiply both sides by 11.

[tex](11)\frac{x}{11}=(11)\frac{13}{11}[/tex]

Both the left and the right cancel. Thus:

[tex]x=13[/tex]

Our answer is 13 :)

Answer:

Hey there!

x=13

The denominator is the same for both sides, so to make the equation equal, x has to be 13.

Hope this helps :)

Answer:

its very simple you just need to collect like terms...

which is 4x-6x+6+9 which is

-2x+15.

This is my answer I hope it helps you.

Answer:

i think its -2x+15

Step-by-step explanation:

you do 4x-6x (-6 cuz it has a neg. in front) which gives you -2x then 9+6 and it gives you 15

Answer:

B, You can build your credit history

Step-by-step explanation:

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{6 \: \% \: }}}}}[/tex]

Step-by-step explanation:

Given

Principal ( P ) = N 245

Interest ( I ) = N 117.60

Time ( T ) = 8 years

Rate = ?

Finding the rate percent :

[tex] \boxed{ \sf{rate = \frac{interest \: \times 100}{principal \times time} }}[/tex]

plug the values

⇒[tex] \sf{ \frac{117.60 \times 100}{245 \times 8} }[/tex]

Calculate

⇒[tex] \sf{ \frac{11760}{1960} }[/tex]

⇒[tex] \sf{6 \: \%}[/tex]

Hope I helped!

Best regards!!

Answer:

5x - 1 or x>−1

Step-by-step explanation:

Just combine like terms: 13,-14

Combine like terms: 6,10

Divide by -4:-4x/-4<4/-4

Answer:

  A. 0

  B. -66

  C. 4

  D. 998

  E. -12

Step-by-step explanation:

A. By definition, the sum of anything and its additive inverse is zero.

__

B. If you have trouble with sums, your calculator can help.

  -22 + (-44) = -22 -44 = -66

__

C. -36/x = -9 can be solved by multiplying by x and dividing by -9:

  -36 = -9x

  -36/-9 = x = 4

Since the product of the divisor and quotient is the dividend, dividing the dividend by either gives the other. Here, your dividend is -36 and your quotient is -9. To find the divisor, you can divide -36 by -9, as we did.

__

D. The absolute value function changes the sign of negative numbers to positive:

  |-998| = 998

__

E. If you have trouble with sums, your calculator can help.

  (−2)−[(−3)−(−7)−(−6)]

  = -2 -(-3 +7 +6) = -2 -10 = -12

==============================================

Work Shown:

g(x) = x^2-2

g(-2) = (-2)^2-2

g(-2) = 2

Saying (-2, g(-2)) is the same as saying (-2, 2)

---------------

g(x) = x^2-2

g(1) = 1^2 - 2

g(1) = -1

Saying (1, g(1)) is the same as saying (1, -1)

---------------

Let's find the slope of the line through (-2,2) and (1,-1)

m = (y2 - y1)/(x2 - x1)

m = (-1-2)/(1-(-2))

m = (-1-2)/(1+2)

m = -3/3

m = -1

Now turn to point slope form to find the equation

y - y1 = m(x - x1)

y - 2 = -1(x - (-2))

y - 2 = -(x + 2)

y - 2 = -x - 2

y-2+2 = -x-2+2 ... add 2 to both sides

y = -x

You could use the other point (1,-1) and you'd get the same answer. The slope m = -1 is the same each time.

Answer:

[tex] \boxed{ \bold{ \boxed{ \sf{15 \: cookies}}}}[/tex]

Step-by-step explanation:

Total cookies = 150

percentage of cookies that she ate = 10 %

To find : Number of cookies that she ate

[tex] \sf{10\% \: of \: 150}[/tex]

To convert percent into fraction, divide it by 100 and remove the % symbol.

⇒[tex] \sf{ \frac{10}{100} \times 150}[/tex]

⇒[tex] \sf{15 \: cookies}[/tex]

Thus, She ate 15 cookies.

Hope I helped!

Best regards!!

Answer:

x < -3

Step-by-step explanation:

Order of Operations: BPEMDAS

Step 1: Write out equation

5 - 9(8 - 2x) < 2x - 115

Step 2: Distribute parenthesis

5 - 72 + 18x < 2x - 115

Step 3: Combine like terms

-67 + 18x < 2x - 115

Step 4: Add 67 on both sides

18x < 2x - 48

Step 5: Subtract 2x on both sides

16x < -48

Step 6: Divide both sides by 16

x < -3

And we have our answer!

Answer:

x<-3

Step-by-step explanation:

5−9(8−2x)<2x−115

Use the distributive property to multiply −9 by 8−2x.

5−72+18x<2x−115

Subtract 72 from 5 to get −67.

−67+18x<2x−115

Subtract 2x from both sides.

−67+18x−2x<−115

Combine 18x and −2x to get 16x.

−67+16x<−115

Add 67 to both sides.

16x<−115+67

Add −115 and 67 to get −48.

16x<−48

Divide both sides by 16. Since 16 is >0, the inequality direction remains the same.

x<-48/16

Divide −48 by 16

x<−3

Answer:

Las cosas que se pueden contar (i.e. Contar y clasificar frutas) así como cosas que se pueden dividir se pueden medir en fracciones (i.e. Cortar un pastel), mientras que las cosas que no se pueden contar, de naturaleza no discreta, así como cosas que no se pueden dividir (i.e. Líquidos, material granulado) se pueden medir en decimales.

Step-by-step explanation:

Las cosas que se pueden contar (i.e. Contar y clasificar frutas) así como cosas que se pueden dividir se pueden medir en fracciones (i.e. Cortar un pastel), mientras que las cosas que no se pueden contar, de naturaleza no discreta, así como cosas que no se pueden dividir (i.e. Líquidos, material granulado) se pueden medir en decimales.

Answer:

50000 m

Step-by-step explanation:

50km/h

It means that 1 hour can travelling 50 km

1km=1000m

50km=50000m

So 1hour can travel 50000m

 Answer:  m=4

Step-by-step explanation:

5(m-2) - 10 = 6 + 2(1 - m)  Apply the distributive property on both sides

5m -10 -10 = 6 + 2-2m         Now combine like terms on both sides

5m -20 = 8- 2m     Now add 2m to both sides

+2m              +2m

7m  - 20= 8    Add 20 to both sides

        +20  +20

7m = 28      Divide both sides by  7

m = 4  

Answer:

x=2y-3

Step-by-step explanation:

x=Jan's age

y=Tritt's age

Answer:

m = 3/5

Step-by-step explanation:

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Step 1: Find 2 coordinates

(0, 80)

(-50, 50)

Step 2: Find slope m

m = (50 - 80)/(-50 - 0)

m = -30/-50

m = 3/5

Answer:

chart.

Step-by-step explanation:

ah yes chart.

Answer:

X=6

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

15=7x+3−5x

15=7x+3+−5x

15=(7x+−5x)+(3)(Combine Like Terms)

15=2x+3

15=2x+3

Step 2: Flip the equation.

2x+3=15

Step 3: Subtract 3 from both sides.

2x+3−3=15−3

2x=12

Step 4: Divide both sides by 2.

2x2=122

x=6

Answer:

x=6

500 because 80% of 500 is 100

Answer:

7/100

Step-by-step explanation:

We want to write .07 as a fraction

7/100  were a = 7 and b = 100

Answer:

seven hundredths

Answer:  England

Step-by-step explanation:

England: 1.35 euro/liter

[tex]\text{U.S:}\quad \dfrac{\$3.39}{gallon}\times \dfrac{0.705\ euro}{\$1.50}\times \dfrac{1\ gallon}{3.785\ liter}=\dfrac{0.42\ euro}{liter}[/tex]

     1.35 > 0.42

England > US

Answer:

For larger measurements, we use larger unit while for smaller measurement we use smaller unit.

Step-by-step explanation:

Normally, For larger distances we make use of larger units while for smaller distances we make use of smaller units.

For example, if we consider the distance travelled by a person in some days;

For 15000 units distance; We can represent this value as 15 Kilometers

For 800 units distance; Rather than using kilometers, it would be better to represent it in meters as 8 meters.

Also, For 70 units distance; Instead of kilometers or meters, 70 cm would be a better unit of representation.

Likewise, If we consider some 3 dimensional shapes holding some substances,

For 7000 units, best unit of weight representation would be 7 Kg

For 600 units, instead of in kg, best unit of weight representation would be 600 grams

For 50 units, best unit of weight representation would be 50 grams

So, looking at the examples given in both weight and distances, we will conclude that for larger measurements, we use larger unit while for smaller measurement we use smaller unit.

Answer:c

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Sonia: 19.6 (3/5 = 0.6)

Cesar: 19.7

Stacy: 19.75

Roberto: 19.5 (1/2 = 0.5)