Is the statement true or false? If false, give a counterexample.

For all real numbers a, b and c, a(b + c) = ab + bc.

A. true
B. false; a(b + c) = ab − ac
C. false; if a = b = c = 1, then 1(1 + 1) ≠ 1(1) + 1(1)
D. false; if a = 1, b = 2, and c = 3, then 1(2 + 3) ≠ 1(2) + 2(3)

Answers

Answer 1

Answer:

D. false; if a = 1, b = 2, and c = 3, then 1(2 + 3) ≠ 1(2) + 2(3)

Step-by-step explanation:

A is false, because the a is being distributed/ being multiplied to all terms inside the parenthesis, and not the term b.

B is also false. There is no indicated negative signs.

C is also false because 1(1 + 1) is EQUAL to 1(1) + 1(1)

D is true.


Related Questions

An iscosceles right angled triangle is shown

Answers

Answer : x = 4

Step-by-step explanation:

Area = 1/2 × base × height

Area= 200cm²

base = 5x

height = 5x

200cm² = 1/2 × base × height

200 = 1/2 × 5x × 5x

200 = 1/2 × 25x²

2( 200) = 25x²

400 = 25x²

16 = x²

4 = x

Answer:  " x = 4 " .

______________________________________

Step-by-step explanation:

______________________________________

The formula for the area of a triangle:

             Area, "A" = (1/2) * base * height;

          that is:   A = (1/2) * b * h ;

From our given problem and image/diagram:

    A = 200 cm² ;

          b = 5x ;

          h = 5x ;

We are asked to find the value for "x" ;

 A = (1/2) * b * h ;

Plug in our known values:

 200 cm² = (1/2) * 5x * 5x ;

Simplify:

 200 cm²  = (1/2)*(25x²) ;

 200 cm² = (12.5)x² ;

⇔  (12.5)x² = 200 cm² ;

Divide each side by:  " (12.5)" ;

     (12.5)x² / (12.5)  = (200 cm²)/(12.5) ;

to get:   x² = 16 ;

Take the positive square root of each side of the equation; to get the value for "x" ;

   ⁺ [tex]\sqrt{x^{2} } =[/tex] ⁺ [tex]\sqrt{16}[/tex] ;

to get:

  x = 4 .

________________________

Good luck to you in your academic endeavors!

________________________

Helpppo I’ll name you the brainliest

Answers

X - intercept is 2 or (2,0) of line A

x intercept of line b is 6 or (6,0)

Which expression is equivalent to [4h^7k^2]^4?

Answers

Answer:

614656h²⁸k⁸

Step-by-step explanation:

Exponent Power Rule: [tex](b^m)^n=b^{mn}[/tex]

Step 1: Write expression

[4h⁷7k²]⁴

Step 2: Distribute power 4 to each term

4⁴h⁷⁽⁴⁾7⁴k²⁽⁴⁾

Step 3: Simplify

256h⁷⁽⁴⁾2401k²⁽⁴⁾

614656h⁷⁽⁴⁾k²⁽⁴⁾

Step 4: Use Exponent Rule

614656h²⁸k⁸

7. The width, w, of a bolt is supposed to be 2 cm, but it may have a 0.01-cm margin of error.
Solve the inequality lw - 2 30.01. What does the solution mean in this context?
PLEASE HELP

Answers

Answer:

to be honest.....I HAVE NO FRINKIN CLUE, i just answered to say that you have a cute name if thats your real name

Step-by-step explanation:

Congrats, you have reach the worlds biggest idiot

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PLEASE HELP ME GIVING Brainliest!!!
Keyleanis and her friend both started a part-time job at McDonnald earning $14 per hour. Claudia worked 38 ½ hours her first week. Keyleanis agreed to pay her friend 1/5 of her salary for reimbursement off gas and food. How much money did Keyleanis pay her friend for gas?

Answers

Answer:

107 and 4/5 or 107.8

Step-by-step explanation:

14 times 38.5 is 539.

539 times 1/5 is 107 and 4/5 or 107.8

Answer:

$106.73

Step-by-step explanation:

14 x 38 ½ = 533.68

533.68 ÷ 5 = 106.73.   Keyleanis paid Claudia $106.73

Please answer quickly!

Answers

Sorry I think the picture is blocked so I can't see it

Graph the linear function f(x)=3−6x

Answers

Answer:

(-1,9) (0,3), (1,-3), (2,-9)

Step-by-step explanation:

y intercept is -3

slope is -6, so you would go down by 6 and right by 1.

Answer:

The coordinates to graph this would be (-1,9) (0,3) (1,-3) (2,-9)

Find a counterexample for the given conjecture.
The difference of two odd numbers is always an odd number.

Answers

Answer:

The difference of two odd number is always even as seen below.

Step-by-step explanation:

First odd number = x

Second odd number = x + 2

Third odd number = x + 4

Therefore

(x + 4) - (x + 2) = x

Where x is any odd number

Using 1 :

(1 + 4) - (1+2)

5 - 3 = 2

2 is not an odd number

We can say the difference of two odd number is always even

HELP ASAP: Can you draw a quadrilateral that's not a parallelogram with only one pair of congruent angles? Explain why one pair of congruent angles isn't enough information to prove that a quadrilateral is a parallelogram.

Answers

Yes it is possible. We could draw a trapezoid that has 2 right angles as shown below. A trapezoid has only one pair of parallel sides. A parallelogram needs both pairs of opposite sides to be parallel.

Yes, it is conceivable. As shown below, we could draw a trapezoid with two right angles.

What is quadrilateral?

A quadrilateral is a four-sided polygon with four edges and four corners in geometry. A trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are known as the trapezoid's bases.

Yes, it is conceivable. As shown below, we could draw a trapezoid with two right angles. A trapezoid has only one parallel pair of sides. Both pairs of opposite sides of a parallelogram must be parallel.

The shape of the required quadrilateral is attached with the answer below.

To know more about quadrilaterals follow

https://brainly.com/question/16691874

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Does this graph show the set of all solutions for 7x +2y = -14?

Answers

Answer:

yes

Step-by-step explanation:

y= -7/2x -7

Worth 30 points.

Show all work to solve the equation for x. If a solution is extraneous, be sure to identify it in your final answer.

the square root of x minus 3 plus five equals x.

Picture of question and equation attached.

Answers

Answer:

x=7 valid solution

x=4 extraneous solution

Step-by-step explanation:

sqrt( x-3) +5 = x

Subtract 5 from each side

sqrt( x-3) +5 -5= x-5

sqrt( x-3)  = x-5

Square each side

(sqrt( x-3))^2 = (x-5)^2

Foil the right side ( x-5)(x-5) =x^2 -5x-5x+25 = x^2 -10x+25

x-3 = x^2 -10x+25

Subtract x from each side

-3 = x^2 -10x -x+25

Add 3 to each side

0 = x^2 -11x +25 +3

0 = x^2 -11x+28

Factor

0 = (x-7)(x-4)

Using the zero product property

x-7 =0  x-4=0

x=7  x=4

Check the solutions

sqrt( x-3) +5 = x

x=7

sqrt( 7-3) +5 = 7

sqrt(4) +5 = 7

2 +5 = 7  valid solution

x=4

sqrt( 4-3) +5 = 4

sqrt(1) +5 = 4

1 +5 = 4    not true   extraneous solution

if the centroid of the triangle formed by (x,0), (5.2) and (-8.y) is at (-2,1) then (x,y) is equal to
only proper people will be given this mark...or else will fire u from brainly...​

Answers

Answer: Hola, ila munkililakum ghithishalan fee mabruk ilal habeebi

Help me please I need to answer this

Answers

Answer:

three shirts an hour

Step-by-step explanation:

A stack of 3 books weighs 7.8 kilogramh book weighs the s. If eacsame amount, how much does each book weigh?

Answers

Answer:

they each way 2.6 kilograms

What is the length of side A, in centimeters, on the enlarged trapezoid?
4
6
12
20

Answers

Answer:

C

Step-by-step explanation:

given the fact that the other side measures all multiply by 4 when they are enlarged in the second shape, we know that the scale factor is 4. 3 enlarged by a scale factor of 4 = 12

Since all of the other sides were multiplied by four, therefore you’d multiply side A by four as well.

So,

The length of side A is 4 centimeters.

Evaluate each expression.
2(5) + 3(4+ 3) =

Answers

Answer:

Step-by-step explanation:

10 + 3(7)

10 + 21

= 31

Answer:

31

Step-by-step explanation:

You can use BODMAS rule here to Simplify an expression and do not have to worry about which to do first multiply or addition.

B- bracketsO- ofD- DivisionM- multiplicationA- additionS- subtraction

2(5) + 3(4+3)

= 10 + 3(7)

= 10 + 21

=31

An ice cream shop sells five sundaes for every six cones. Yesterday the shop sold 60 sundaes. How many cones were sold?

Answers

Answer:

50

Step-by-step explanation:

To get each sundae come from sold, you divide sold by for every x cones, then multiply by how many sundaes

Answer:

72

Step-by-step explanation:

60÷5=12

6×12=72 cones

Dom and Riley both want to find the change from the 6 AM temperature to the new 12 PM temperature. Dom says that you can use a number line and add the distances from 0 to the 6 AM temperature and from 0 to the new 12 PM temperature. Riley says that you can subtract -1.4 from the 12 PM temperature. Is either Dom or Riley correct? Explain your reasoning and find the change in temperature.

Answers

Answer:

Neither Dom or Riley is correct

Step-by-step explanation:

The change in temperature between 12PM and 6AM can be obtained by subtracting the 12PM temperature from the 6AM temperature because temperature increases as the hours of the day go by.

To carry out this subtraction on the number line, the following steps should be taken;

(i) Mark the numbers corresponding to 6AM and 12PM temperatures on same number line.

(ii) From the number corresponding to the 12 PM temperature, find out how many steps that are needed to reach the position of the number corresponding to the 6AM temperature.

This number of steps represents the temperature change between the 12PM temperature and the 6 AM temperature.

8. The length of an actual road is
1,000 miles. If 1 inch represents
100 miles, what is the length of
the road on the map?

Answers

Answer:

It's A.

Step-by-step explanation:

Answer:

10 inches

Step-by-step explanation:

1,000 / 100 = 10

Triangle ABC has vertices A (1,1) B (7,1) C (4,9) (A)Find the perimeter of triangle ABC. (B) Find the area of triangle ABC​

Answers

9514 1404 393

Answer:

perimeter = 6+2√73 ≈ 23.09 unitsarea = 24 units²

Step-by-step explanation:

It can help to draw a figure.

The altitude of this isosceles triangle is 8 units, and it splits the base into equal lengths of 3 units. Using the Pythagorean theorem, we find the length of a side to be ...

  BC = AC = √(3² +8²) = √73

The perimeter is the sum of the lengths of those two sides and the base:

  P = 2(√73) +6 ≈ 23.088 . . . units

The area is given by the formula ...

  A = 1/2bh

  A = (1/2)(6 units)(8 untis) = 24 units²

__

The perimeter is 6+2√73 ≈ 23.09 units.

The area is 24 units².

Forensic specialists can estimate the height of a deceased person from the lengths of the person's bones. These lengths are substituted into mathematical inequalities. For instance, an inequality that relates the height h, in centimeters, of an adult female and the length f, in centimeters, of her femur is |h − (2.47f + 54.10)| ≤ 3.72. Use this inequality to estimate the possible range of heights, rounded to the nearest 0.1 centimeter, for an adult female whose femur measures 32.25 centimeters.

Answers

Answer:

[tex]130.2845\leq h\leq 137.7245[/tex]

Step-by-step explanation:

Given an inequality that relates the height h, in centimeters, of an adult female and the length f, in centimeters, of her femur by the equation

[tex]|h - (2.47f + 54.10)| \leq 3.72[/tex]

If an adult female measures her femur as 32.25 centimeters, we can determine the possible range of her height by plugging f = 32.25cm into the modelled equation as shown:

[tex]|h - (2.47(32.25) + 54.10)| \leq 3.72\\|h - (79.9045 + 54.10)| \leq 3.72\\|h - (134.0045)| \leq 3.72\\[/tex]

If the modulus function is positive then:

[tex]h - 134.0045 \leq 3.72\\h \leq 3.71+134.0045\\h\leq 137.7245[/tex]

If the modulus function is negative then:

[tex]-(h - 134.0045) \leq 3.72\\-h+134.0045 \leq 3.72\\-h\leq 3.72-134.0045\\-h\leq -130.2845\\[/tex]

multiply through by -1

[tex]-(-h)\geq -(-130.2845)\\h\geq 130.2845\\130.2845\leq h[/tex]

combining the resulting inequalities, the estimate of the possible range of heights will be [tex]130.2845\leq h\leq 137.7245[/tex]

8800000 in scientific notation

Answers

Answer:

8.8 x 10 to the power of 6

Step-by-step explanation:

Which pair of functions are inverses of each other?

Answers

Answer:

A

Step-by-step explanation:

Inverse means that the function is reversed from the original function, f(x).

To find the inverse function of f(x)=5x-11, add 11 to x, then divide the expression by 5.

This would be (x+11)/5.

So, you know that A is true.

Try the other selections too.

B: [tex]g(x)=x^3/2[/tex]       The x should be tripled before being divided by 2; FALSE

C: [tex]g(x)=7/(x+9)[/tex]     7 should by in the numerator; FALSE

D: [tex]g(x)=6(x+8)[/tex]    8 should be added before being multiplied by 6; FALSE

I hope this helps!!!

Using composite functions, it is found that the pair of functions that are inverse of each other is given by:

A. [tex]f(x) = 5x - 11[/tex] and [tex]g(x) = \frac{x + 11}{5}[/tex]

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

The composite of functions f and g is given by:

[tex](f \circ g)(x) = f(g(x))[/tex]

Two functions f and g are inverse of each other if:

[tex]f(g(x)) = g(f(x)) = x[/tex]

Item a:

[tex]f(x) = 5x - 11[/tex]

[tex]g(x) = \frac{x + 11}{5}[/tex]

[tex]f(g(x)) = f(\frac{x + 11}{5}) = 5(\frac{x + 11}{5}) - 11 = x + 11 - 11 = x[/tex]

[tex]g(f(x)) = g(5x - 11) = \frac{5x - 11 + 11}{5} = \frac{5x}{5} = x[/tex]

Since [tex]f(g(x)) = g(f(x)) = x[/tex], these functions are inverse of each other.

A similar problem is given at https://brainly.com/question/23458455

Find the value of 5x+6 when x=-2

Answers

Answer:

-4

Step-by-step explanation:

5 times negative -2 is -10 and you just add 6 so the answer is -4

The value of 5x + 6 when x = -2 will be -4.

What is Expression?

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given is the following expression -

5x + 6

Given is the following expression -

5x + 6

At x = -2, we can evaluate the expression as -

5x + 6

5 x -2 + 6

-10 + 6

-4

Therefore, the value of 5x + 6 when x = -2 will be -4.

To solve more questions on Evaluating expression, visit the link below-

https://brainly.com/question/13589173

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How many four-digit numbers can you make with these three integers?
0, 1, 2

Answers

Answer:

I would think 2222

Step-by-step explanation:

Between the three numbers, that four-digit number is the greatest.

(Apologies if not correct)

a) (x^2 + 1/2)^2

using the formula:
(a+b)^2= a^2+2ab+b^2​

Answers

Step-by-step explanation:

(x^2+1/2)^2=(x^2)^2+2*x^2*1/2+(1/2)^2=

x^4+(2x^2)/2+1/4=

x^4+x^2+1/4

Answer:

x^4 + x^2 + 1/4

Step-by-step explanation:

[tex] {( {x}^{2} + \frac{1}{2} })^{2}[/tex]

a = x^2

b = 1/2

[tex] {a}^{2} + 2ab + {b}^{2} [/tex]

[tex] ({x {}^{2}) }^{2} + 2( {x}^{2} )( \frac{1}{2} ) + { \frac{1}{2} }^{2} [/tex]

[tex] {x}^{4} + {x}^{2} + \frac{1}{4} [/tex]

Marcellus is making a deposit that will leave him with a balance of $381. He noticed that if he added $54 to the amount he started with in his account and then tripled the sum, he would get the new amount. How much did Marcellus originally have in his account? Which equation represents the situation?

Answers

Answer:

Step-by-step explanation:

Let the initial money deposited in the account be x:

If he added $54 to the amount he started with in his account, the expression will become:

x+54

If the sum is tripled, we will have:

3(x+54)

Since the balance an-mount is $381, the final equation will give:

3(x+54) = 381

The equation that represents the situation is 3(x+54) = 381

Next is to calculate x:

3(x+54) = 381

open the parenthesis

3x+162 = 381

3x = 381 - 162

3x = 219

x = 219/3

x = 73

Hence the original amount in his account is $73

PLEASE HELP ME OUT IF YOU CAN

Answers

Answer:

D

Step-by-step explanation:

find the missing angle in the image below?

Answers

Answer:

? = 40°

Step-by-step explanation:

100° = 60° + ? (The exterior angle property of triangles)

100° - 60° = ? (By the law of transposition)

40° = ?

If my answer helped, kindly mark me as the brainliest!

Thank You!

Answer:

the missing angle is 40

Step-by-step explanation:

let the missing angle be x

then x+ 60 = 100 using (exterior angle property)

so x= 100-60 which is equal to 40.  

hope this helps u buddy..

What is the square root of 51.84​

Answers

The square root of 51.84 is 7.2
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