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3 years ago

Write an equation in which the quadratic expression 4x^2-26x+42 equals 0. Must show all work to receive credit.

Mathematics

2 answers:

Masteriza [31]3 years ago

8 0

Answer:

(a) (x + 3)(2x + 7) = 0

(b) These solutions mean that for these two x values, f(x) is equal to 0. It's also where the graph of f(x) crosses the x-axis.

Step-by-step explanation:

(a) We set 4x² -26x + 42 equal to 0:

4x² -26x + 42 = 0

Let's divide both sides by 2 to simplify this a bit:

2x² - 13x + 21 = 0

Now, we need factors a and b of 2 and c and d of 21 such that ac + bd = -13. The factors of 2 are: 1 and 2, so let's say a = 1 and b = 2. The factors of 21 are: (1, 21), (3, 7), (-1, -21), and (-3, -7). We see that if c = -7 and d = -3, this works:

ac + bd = 1 * (-7) + 2 * (-3) = -7 - 6 = -13

So, the factored form is:

(x - (-3))(2x - (-7)) = 0

(x + 3)(2x + 7) = 0

(b) So now we need to solve this. Set each of the two parenthetical expressions equal to 0:

x + 3 = 0

x = -3

AND

2x + 7 = 0

x = -7/2

These solutions mean that for these two x values, f(x) is equal to 0. It's also where the graph of f(x) crosses the x-axis.

Ksju [112]3 years ago

7 0

Answer:

a) 2(x - 3)(2x - 7) = 0

b) function is 0 when x = 3 or 7/2

Step-by-step explanation:

4x² - 26x + 42 = 0

2(2x² - 13x + 21) = 0

2[2x² - 6x - 7x + 21] = 0

2[2x(x - 3) - 7(x - 3)] = 0

2(x - 3)(2x - 7) = 0

Solutions:.

x = 3, 7/2

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Eva8 [605]

A tessellation that uses only one type of regular polygon.

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When we cover a surface with a pattern of a flat geometric shapes such that there should have no overlaps or gaps, then the surface is called a tessellation.

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Hence, A is the correct option.

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2 years ago

a farmer uses 1/3 of his land to plant cassava 3/5 of the remaining land to plant Maize and the rest vegetables if vegetables co

Rzqust [24]

Answer:

37.5 acres.

Step-by-step explanation:

Fraction of his land where vegetables are grown

= 1 - 1/3 - 2/3 *3/5

(after taking away 1/3 we get 2/3 and the farmer uses 3/5 of this 2/3 to grow Maize.

= 1 - 1/3 - 6/15 LCD of 3 and 15= 15 so we write:

= 1 - 5/15 - 6/15

= 1 - (5+6)/16

= 1 - 11/15

= 4/15.

4 /15 is equivalent to 10 acres

so total area (= 1) = 10 / 4/15 Invert the 4/15 and multiply:

= 10 * 15/4

= 150/4

= 37.5 acres.

3 0

3 years ago

The perimeter of a rectangle is 42 inches, and its area is 110 square inches. find the length and width of the rectangle.

lorasvet [3.4K]

$p = 2w + 2l$ $p = 42$
$a = l * w$ $a = 108$

You want to make either the length or width variable (I chose the width variable to be by itself. It doesn't matter) by itself by:

Divide both sides by 2.
(p) ÷ 2 = (2w + 2l) ÷ 2
$2's$ $cancel$ $out$
$\frac{p}{2} = w + l$

Subtract both sides by either length or width depending on what variable you chose to make by itself (in this case I subtracted the length variable because I wanted the width variable by itself).
$\frac{p}{2} - l = w + l - l$
$l's$ $cancel$ $out$
p/2 - l = w

$a = l * w$

You replace w with the equation above p/2 - l = w
$a = l( \frac{p}{2} - l)$

Multiply out the L.
$a = \frac{p}{2}l - l^{2}$

Plug in all your numbers a = 110 and p = 42
$110 = \frac{42}{2}l - l^{2}$
$110 = 21l - l^{2$

Move everything to the left side so $l^{2}$ would be positive (makes the equation easier when $l^{2}$ is positive).
$l^{2} - 21l + 110 = 0$

Factor.
$(l -10)(l-11) = 0$

Make each parenthesis set equal to 0.
$l-11=0$ $l-10=0$

Add.
$l = 11$ $l = 10$

By doing this you solve for both the width and length so the answer is:
w = 11 L = 10

8 0

3 years ago

team has a 75% chance to win each of the 3 games they will play this week. Clare simulates the week of games by putting 4 pieces

kaheart [24]

Answer: 88

Step-by-step explanation:

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