1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
damaskus [11]
3 years ago
7

7 • (6 • t) and (7 • 6) •t

Mathematics
2 answers:
xenn [34]3 years ago
6 0
The answer to this question is 42t.
maxonik [38]3 years ago
5 0
7*(6*t)=42
Hope this helped
You might be interested in
Can someone solve this problem for me? Show me your steps to solve this problem as well.
AveGali [126]
\bf 3^x=81\qquad 
\begin{cases}
81=3\cdot 3\cdot 3\cdot 3\\
\qquad 3^4
\end{cases}\implies 3^x=3^4\implies x=4

if their base is the same, the exponents must also be the same for the equation to be true.
5 0
3 years ago
Naeem weighs different salad takeout containers. The containers respectively weigh 4.5 ounces, 5.01 ounces, 5.3 ounces, 4.75 oun
shusha [124]
But your answer would be 25 ounces i hope this helps
7 0
2 years ago
Factor.<br> 4z² – 8z - 5
Nataly [62]

Answer: z = -1/2 = -0.500

z = 5/2 = 2.500

Step-by-step explanation:

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 (22z2 -  8z) -  5  = 0  

Step  2  :

Trying to factor by splitting the middle term

2.1     Factoring  4z2-8z-5  

The first term is,  4z2  its coefficient is  4 .

The middle term is,  -8z  its coefficient is  -8 .

The last term, "the constant", is  -5  

Step-1 : Multiply the coefficient of the first term by the constant   4 • -5 = -20  

Step-2 : Find two factors of  -20  whose sum equals the coefficient of the middle term, which is   -8 .

     -20    +    1    =    -19  

     -10    +    2    =    -8    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -10  and  2  

                    4z2 - 10z + 2z - 5

Step-4 : Add up the first 2 terms, pulling out like factors :

                   2z • (2z-5)

             Add up the last 2 terms, pulling out common factors :

                    1 • (2z-5)

Step-5 : Add up the four terms of step 4 :

                   (2z+1)  •  (2z-5)

            Which is the desired factorization

Equation at the end of step  2  :

 (2z - 5) • (2z + 1)  = 0  

Step  3  :

Theory - Roots of a product :

3.1    A product of several terms equals zero.  

When a product of two or more terms equals zero, then at least one of the terms must be zero.  

We shall now solve each term = 0 separately  

In other words, we are going to solve as many equations as there are terms in the product  

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

3.2      Solve  :    2z-5 = 0  

Add  5  to both sides of the equation :  

                     2z = 5

Divide both sides of the equation by 2:

                    z = 5/2 = 2.500

Solving a Single Variable Equation :

3.3      Solve  :    2z+1 = 0  

Subtract  1  from both sides of the equation :  

                     2z = -1

Divide both sides of the equation by 2:

                    z = -1/2 = -0.500

Supplement : Solving Quadratic Equation Directly

Solving    4z2-8z-5  = 0   directly  

Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

Parabola, Finding the Vertex :

4.1      Find the Vertex of   y = 4z2-8z-5

For any parabola,Az2+Bz+C,the  z -coordinate of the vertex is given by  -B/(2A) . In our case the  z  coordinate is   1.0000  

Plugging into the parabola formula   1.0000  for  z  we can calculate the  y -coordinate :  

 y = 4.0 * 1.00 * 1.00 - 8.0 * 1.00 - 5.0

or   y = -9.000

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = 4z2-8z-5

Axis of Symmetry (dashed)  {z}={ 1.00}  

Vertex at  {z,y} = { 1.00,-9.00}  

z -Intercepts (Roots) :

Root 1 at  {z,y} = {-0.50, 0.00}  

Root 2 at  {z,y} = { 2.50, 0.00}  

Solve Quadratic Equation by Completing The Square

4.2     Solving   4z2-8z-5 = 0 by Completing The Square .

Divide both sides of the equation by  4  to have 1 as the coefficient of the first term :

  z2-2z-(5/4) = 0

Add  5/4  to both side of the equation :

  z2-2z = 5/4

Now the clever bit: Take the coefficient of  z , which is  2 , divide by two, giving  1 , and finally square it giving  1  

Add  1  to both sides of the equation :

 On the right hand side we have :

  5/4  +  1    or,  (5/4)+(1/1)  

 The common denominator of the two fractions is  4   Adding  (5/4)+(4/4)  gives  9/4  

 So adding to both sides we finally get :

  z2-2z+1 = 9/4

Adding  1  has completed the left hand side into a perfect square :

  z2-2z+1  =

  (z-1) • (z-1)  =

 (z-1)2

Things which are equal to the same thing are also equal to one another. Since

  z2-2z+1 = 9/4 and

  z2-2z+1 = (z-1)2

then, according to the law of transitivity,

  (z-1)2 = 9/4

We'll refer to this Equation as  Eq. #4.2.1  

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

  (z-1)2   is

  (z-1)2/2 =

 (z-1)1 =

  z-1

Now, applying the Square Root Principle to  Eq. #4.2.1  we get:

  z-1 = √ 9/4

Add  1  to both sides to obtain:

  z = 1 + √ 9/4

Since a square root has two values, one positive and the other negative

  z2 - 2z - (5/4) = 0

  has two solutions:

 z = 1 + √ 9/4

  or

 z = 1 - √ 9/4

Note that  √ 9/4 can be written as

 √ 9  / √ 4   which is 3 / 2

Solve Quadratic Equation using the Quadratic Formula

4.3     Solving    4z2-8z-5 = 0 by the Quadratic Formula .

According to the Quadratic Formula,  z  , the solution for   Az2+Bz+C  = 0  , where  A, B  and  C  are numbers, often called coefficients, is given by :

                                     

           - B  ±  √ B2-4AC

 z =   ————————

                     2A

 In our case,  A   =     4

                     B   =    -8

                     C   =   -5

Accordingly,  B2  -  4AC   =

                    64 - (-80) =

                    144

Applying the quadratic formula :

              8 ± √ 144

  z  =    —————

                   8

Can  √ 144 be simplified ?

Yes!   The prime factorization of  144   is

  2•2•2•2•3•3  

To be able to remove something from under the radical, there have to be  2  instances of it (because we are taking a square i.e. second root).

√ 144   =  √ 2•2•2•2•3•3   =2•2•3•√ 1   =

               ±  12 • √ 1   =

               ±  12

So now we are looking at:

          z  =  ( 8 ± 12) / 8

Two real solutions:

z =(8+√144)/8=1+3/2= 2.500

or:

z =(8-√144)/8=1-3/2= -0.500

Two solutions were found :

z = -1/2 = -0.500

z = 5/2 = 2.500

3 0
3 years ago
Read 2 more answers
A school purchsed basketball for $20 each and footballs for $15 each. they a brought a total of 28 for $480 how many of each typ
satela [25.4K]

Answer:

i in total spent : 480

Step-by-step explanation:

he bought 12 basketballs = 240

he bought 16 football = 240

you can decide how to make your system

4 0
3 years ago
Simplify c x d x 4 =
White raven [17]

Answer:

Ya the person above me is right 4cd

3 0
2 years ago
Other questions:
  • What is the value represented by the letter A on the box plot of the data?
    14·1 answer
  • During his workout Allen spent 28% of the time on the treadmill what fraction of his workout was on the treadmill
    10·1 answer
  • Order the following from greatest to least -0.4,0.8
    15·1 answer
  • What is the solution of mc016-1.jpg? \frac{x^2-1}{x^2+5x+4}&lt;0
    10·2 answers
  • F(-3) if f(x)= -8x + 2
    6·2 answers
  • Find -2 2/5 + 4/5 need help please
    10·1 answer
  • Sue baked 5 pies and cut each one into sixth. how much money would she make if she sold each slice for $0.75 ​
    5·2 answers
  • Solve for x. 206-x= 133​
    8·2 answers
  • Dawson baked one pie in 7/12 of an hour. How long will it take Dawson to bake 9 pies
    14·1 answer
  • Helpp me with this.. answer this
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!