Which strategy uses place value to correctly solve for 321 x 4?

Show your solution follow the steps need an answer, please need an answer, please.

STatiana [176]

Answer:

Step-by-step explanation:

27 ) 2x² - x - 1 = 0

2x² - 2x + x - 1 = 0

2x ( x - 1) + (x - 1) = 0

(x - 1)(2x + 1) = 0

x - 1 = 0 ; 2x + 1 = 0

x = 1 ; 2x = -1

x = -1/2

x = 1 ; -1/2

Option b

28) Area of a rectangle = 24 cm²

length * width = 24

(3x +2 )(2x -1) = 24

3x(2x -1) + 2(2x - 1) = 24

3x *2x - 3x *1 + 2*2x - 2*1 = 24

6x² -3x + 4x - 2= 24

6x² + x - 2 -24 = 0

6x² + x - 26 = 0

6x² -12x + 13x - 26 = 0

6x(x - 2) + 13(x - 2) = 0

(x -2)(6x +13) = 0

x = 2 {Ignore 6x + 13 as it gives negative value}

length = 3x + 2 = 3*2 + 2 = 6 + 2 = 8 cm

Width = 2x - 1 = 2*2 - 1 = 4 - 1 = 3 cm

29) Area of square = 900 cm²

Side² = 900

(5x)² = 900

25x² = 900

x² = 900/25

x² = 36

x = √36 = √6*6

x = 6 cm

30) base = b cm

height = b + 2

Area of triangle = 24 cm²

$\dfrac{1}{2}base*height = 24\\\\\dfrac{1}{2}*b*(b+2) = 24\\$

b(b + 2) = 24*2

b² + 2b = 48

b² + 2b - 48 = 0

b² - 6b + 8b - 48 = 0

b(b - 6) + 8(b - 6) = 0

(b - 6) (b + 8) = 0

b - 6 = 0 {Ignore b +8 = 0 as it gives negative value}

b = 6 cm

height = 6+ 2 = 8 cm

5 0

3 years ago

HELLER HELLPPPP MEHHHH

ivolga24 [154]

Answer:

I think the answer is D.

Step-by-step explanation:

Five plus two times a number means 5 + 2n vice versa.

4 0

2 years ago

Read 2 more answers

Suppose that the dollar cost of producing x radios is c(x) = 400 + 20x - 0.2x 2. Find the marginal cost when 30 radios are produ

My name is Ann [436]

C(x) = 400 + 20x - 0.2x²

c(30) = 400 + 20(30) - 0.2(30)²

= 400 + 600 - 0.2(900)
= 1000 - 180
= 820

It costs $820 when 30 radios are produced.

Marginal cost is how much it would cost to make one MORE of the same product so now we find how much it costs to produce 31 radios and compare the two.

c(31) = 400 + 20(31) - 0.2(31)²

= 400 + 620 - 0.2(961)
= 1020 - 192.2
= 827.8 or ≈828.

Now we find the difference which means we subtract the two.

828 - 820 = 8.

Your marginal cost is $8.

To compare we can also do 29 radios.

c(29) = 400 + 20(29) - 0.2(29)² = 811.8 or ≈812

820 - 812 = 8.

7 0

3 years ago

The sum of three consecutive even integers is 258. write an equation ad solve to find the integers

slavikrds [6]

The consecutive integers are 85,86,87

Explanation:

n

:

the first number

n

+

1

:

the second number

n

+

2

:

the third number

n

+

(

n

+

1

)

+

(

n

+

2

)

=

258

3

n

+

3

=

258

3

n

=

258

−

3

n

=

255

n

=

255

3

n

=

85

n

+

1

=

85

+

1

=

86

n

+

2

=

85

+

2

=

87

8 0

3 years ago

Read 2 more answers

Solve the following quadratics. State the FACTORS AND SOLUTIONS. 1. 2x^2 - 7x + 3 2. 3x^2 + 7x +2

tekilochka [14]

Answer:

1. x = 3, 1/2 (solutions); (x - 3)(2x - 1) (factors)

2. x = -1/3, -2 (solutions); (3x + 1)(x + 2) (factors)

Step-by-step explanation:

1. 2x^2 - 7x + 3

To solve problem 1, you will need to identify your a, b, and c values in this quadratic function.

Since this problem is in standard form, it will be easy to identify these values. The standard form of a quadratic function is ax^2 + bx + c.

The a value is 2, the b value is -7, and the c value is 3 if we use our standard form and see which numbers are plugged into it.

Since we know that

a = 2
b = -7
c = 3

we can use the quadratic formula: $x = \frac{-b~\pm~\sqrt{b^2~-~4ac} }{2a}$

Substitute the a, b, and c values into the quadratic formula: $x=\frac{-(-7)\pm\sqrt{(-7)^2-4(2)(3)} }{2(2)}$

Now simplify using the laws of pemdas: $x=\frac{7\pm\sqrt{(49)-(24)} }{4}$

Simplify even further: $x=\frac{7\pm\sqrt{(25)} }{4} \rightarrow x=\frac{7\pm (5) }{4}$

Now split this equation into two equations to solve for x: $x=\frac{12 }{4} ~~and~~ x=\frac{2 }{4}$

12/4 can be simplified to 3, and 2/4 can be simplified to 1/2.

This means your solutions to problem 1 is 3, 1/2.

$\boxed {x=3,\frac{1}{2} }$

There is also another way to solve for the quadratic functions, and this was by factoring.

If you factor 2x^2 - 7x + 3 using the bottoms-up method, you will get (x - 3)(2x - 1).

After factoring, solving for the solutions is simple because all you have to do is set each factor to 0.

x - 3 = 0
2x - 1 = 0

After solving for x by adding 3 to both sides, or by adding 1 to both sides then dividing by 2, you will end up with the same solutions: x = 3 and x = 1/2.

2. 3x^2 + 7x + 2

To save time I'll be using the bottoms-up factoring method, but remember to refer back to problem 1 (quadratic formula) if you prefer that method.

Factor this quadratic function using the bottoms-up method. After factoring you will have (3x + 1)(x + 2). These are your factors.

Now to solve for x and find the solutions of the quadratic function, you will set both factors equal to 0.

3x + 1 = 0
x + 2 = 0

Solve.

First factor: 3x + 1 = 0

Subtract 1 from both sides.

3x = -1

Divide both sides by 3.

x = -1/3

Second factor: x + 2 = 0

Subtract 2 from both sides.

x = -2

Your solutions are x = -1/3 and x = -2.

$\boxed {x = -\frac{1}{3} , -2}$

7 0

3 years ago