MATHEMATICS HIGH SCHOOL

The model represents x2 – 9x + 14.Which is a factor of x2 – 9x + 14?

A. x – 9
B. x – 2
C. x + 5
D. x + 7

Answers

Answer 1
Answer:

Factorize the quadratic trinomial x^2 - 9x + 14 by the rule:

ax^2+bx+c=a(x-x_1)(x-x_2), \text{ where } x_1,\ x_2 \text{ are its roots. }

1. Find the roots:

2. Factorize the polynomial:

x^2 - 9x + 14=(x-2)(x-7).

3. Only factor x-2 is given in options, then the correct choice is B.
Answer 2
Answer:

The factor of the given polynomial expression is (x - 2). So, option B.

Using variables and coefficients, polynomials are algebraic expressions. The word indeterminates is sometimes used to describe variables.

For polynomial expressions, addition, subtraction, multiplication, and positive integer exponents are all mathematical operations that are possible, however division by variables is not one of them.

The given polynomial expression is,

x²- 9x + 14

So, we can write that,

(x - a) (x - b) = x²- 9x + 14

So, we can write two equations,

ab = 14

a + b = 9

Therefore, we can say that,

a = 2 and b = 7

Therefore, the factors of the given polynomial expression is,

(x - 2) (x - 7) = x²- 9x + 14

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Share $420 in the ratio 2:1:4​

Answers

Answer:

120:60:240

Step-by-step explanation:

2+1+4=7

420/7=60

2*60:1*60:4*60

=120:60:240

Check my work:

120+60+240=420

Can someone help me? Plzzzzz :c I need it for tmw I'll be soo happy if someone help me

Mike purchased 3 DVD's and 14 video games for $203. Nick went to the same store and brought 11 DVD's and 11 video games for $220. How much is each video game and each DVD?

Answers

x-cost\ of\ DVD\ny-cost\ of\ video\ game\n\n \left \{ {{3x+14y=203\ \ \ } \atop {11x+11y=220\ \ } \right. \n\n From\ first\ second:\n11x=220-11y\ \ \ \ |:11\nx=20-y\n\nSubstitute\ to\ first:\n3(20-y)+14y=203\n60-3y+14y=203\n-3y+14y=203-60\n11y=143\ \ \ \ |:11\ny=13\n\nx=20-13=7\n\n \left \{ {{y=13} \atop {x=7}} \right.
3D+14G=203(11)    use elimination      33D+154G=2233
11D+11G=220(-14)   to cancel G   -154D-154G=-3080
                                      
                                     -121D=-847   divide by -121 on both sides
                                         D=7     plug back into equation
11(7)+11G=220
77+11G=220   subtract 77 from both sides
11G=143 divide by 11 on both sides
G=13

5x^2+19x+12 factor the polynomial

Answers

Δ = 19^2 - 4*5*12 => Δ = 121 => √(delta) = 11;
x1 = -0.8; x2 = -3;
5x^2+19x+12 = 5( x + 0.8)( x + 3) = ( 5x + 4)( x + 3);

Answer:

( x − 3 )( 5x − 4 )

Step-by-step explanation:

In an equation or inequality, you want to get the variable.

Answers

To solve for [variable] in the equation [equation], apply inverse operations to isolate [variable]. For inequalities, follow the same steps, but note the direction of the inequality sign to find valid values.

To solve for a variable in an equation, one must follow a systematic process. First, identify the equation's form, whether linear, quadratic, or another type. Then, apply appropriate operations to isolate the variable. For example, in linear equations, perform addition, subtraction, multiplication, or division to isolate the variable on one side of the equation. For quadratic equations, use factoring, completing the square, or the quadratic formula.

When dealing with inequalities, the same principles apply, but one must also consider the direction of the inequality sign (>, <, ≥, ≤). When multiplying or dividing by a negative number, the inequality sign must be reversed.

In both cases, it's crucial to perform the same operation on both sides of the equation or inequality to maintain balance and equivalence. Lastly, check the solution by substituting it back into the original equation or inequality to ensure its validity.

This systematic approach ensures that we can accurately solve for variables in equations and find the values that satisfy inequalities while maintaining mathematical integrity.

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Complete question below:

"How do you solve for [variable] in the equation [equation]?""What are the steps to find the values of [variable] that satisfy the inequality [inequality]?"
What you want to do is get the variable x on the left side by itself (just like you would if this were an equation). Be sure to perform the same operations on both sides of the inequality until x is all by itself on the left side.

an open rectangular box with square ends is fitted with an overlapping lid that covers the top and front face determine the maximum volume of the box if 1square meter of metal is used in its construction

Answers

Volume is a three-dimensional scalar quantity. The maximum volume of the box is 0.8m³.

What is volume?

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

Surface area of the box = 2x² + 3xy

Surface area of lid = 2xy

Total area = 2x² + 5xy = 6

y = (6-2x²)/5x

Volume of the box, V = x²y

V = x²[(6-2x²)/5x] = (6x/5)-(2x³/5)

Now, for the volume to be the maximum,

dV/dx = 0

(6/5)-(6x²/5) = 0

x² = 1

x = ±1

y = 4/5

Thus, the maximum volume of the box = x²y = (1)²×(4/5) = 0.8 m³

Hence, the maximum volume of the box is 0.8m³.

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so would it be 8 meters because it has 8 sides 

Write an expression that is equivalent to three over four (5z+ 16).

Answers

an expression that is equivalent to three over four (5z+ 16).
3/ (20z + 64)

…would be equivalent
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