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dem82 [27]
3 years ago
15

Express the product in the simplest form

Mathematics
1 answer:
KatRina [158]3 years ago
4 0

Answer:

21

Step-by-step explanation:

Set it up as 7/4 x 12/1.  Multiply the numerators and denominators.  That equals 84/4 which simplifies to 21.

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Find the area of a rectangle that has a length of (x - 5) and a width of (3x + 1).
avanturin [10]

Answer:

A=3x^2 -14x -5

Step-by-step explanation:

(x-5)(3x+1)

3x^2 +x -15x -5

3x^2 -14x -5

5 0
3 years ago
Sonia opened a savings account and then added the same amount to the savings account eyery week. After 5 weeks, her savings acco
Goryan [66]

Answer:

since Sonia saved 45$ in 5 weeks and 70$ in 10 weeks. we are to find the amount she saved up in x weeks.

let's make the amount y

so x= y

5 = 45 cross multiplying the values

we then have 45x= 5y

y= 7x

x=y

10=70

10x = 70y

y= 7x = y=5x+ 20, y = 20x+5

7 0
3 years ago
The height h of a projectile is a function of the time t it is in the air. the height in feet for t seconds is given by the func
alexgriva [62]

Domain means the values of independent variable(input) which will give defined output to the function.

Given:

The height h of a projectile is a function of the time t it is in the air. The height in feet for t seconds is given by the function

h(t)=-16t^2 + 96t

Solution:

To get defined output, the height h(t) need to be greater than or equal to zero. We need to set up an inequality and solve it to find the domain values.

To \; find \; domain:\\\\h(t) \geq0\\\\-16t^2+96t \geq  0\\Factoring \; -16t \; in \; the \; left \; side \; of \; the \; inequality\\\\-16t(t-6) \geq  0\\Step \; 1: Find \; Boundary \; Points \; by \; setting \; up \; above \; inequality \; to \; zero.\\\\t(t-6)=0\\Use \; zero \; factor \; property \; to \; solve\\\\t=0 \; (or) \; t = 6\\\\Step \; 2: \; List \; the \; possible  \; solution \; interval \; using \; boundary \; points\\(- \infty,0], \; [0, 6], \& [6, \infty)

Step \; 3:Pick \; test \; point \; from \; each \; interval \; to \; check \; whether \\\; makes \; the \; inequality \; TRUE \; or \; FALSE\\\\When \; t = -1\\-16(-1)(-1-6) \geq  0\\-112 \geq  0 \; FALSE\\(-\infty, 0] \; is \; not \; solution\\Also \; Logically \; time \; t \; cannot \; be \; negative\\\\When \; t = 1\\-16(1)(1-6) \geq  0\\80 \geq  0 \; TRUE\\ \; [0, 6] \; is \; a \; solution\\\\When \; t = 7\\-16(7)(7-6) \geq  0\\-112 \geq  0 \; FALSE\\ \; [6, -\infty) \; is \; not \; solution

Conclusion:

The domain of the function is the time in between 0 to 6 seconds

0 \leq  t \leq  6

The height will be positive in the above interval.

7 0
3 years ago
Read 2 more answers
Solve this system by substitution. y = 3 y = -3x + 6 *Remember to write your answer as a coordinate point (x, y). I​
DochEvi [55]

Answer:

(1, 3)

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Equality Properties

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtraction Property of Equality

<u>Algebra I</u>

  • Coordinates (x, y)
  • Solving systems of equations using substitution/elimination

Step-by-step explanation:

<u>Step 1: Define Systems</u>

y = 3

y = -3x + 6

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Substitute in <em>y</em>:                                                                                                 3 = -3x + 6
  2. [Subtraction Property of Equality] Subtract 6 on both sides:                      -3 = -3x
  3. [Division Property of Equality] Divide -3 on both sides:                                1 = x
  4. Rewrite/Rearrange:                                                                                        x = 1

<u>Step 3: Solve for </u><em><u>y</u></em>

  1. Define original equation:                                                                               y = -3(1) + 6
  2. Multiply:                                                                                                           y = -3 + 6
  3. Add:                                                                                                                 y = 3
6 0
2 years ago
What is the value for x?
Nataly [62]
The value of x would be: 5
8 0
2 years ago
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