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VARVARA [1.3K]
3 years ago
6

Solve the following quadratic. `x^{2}\ +\ 4x\ +\ 1\ =\ 6`

Mathematics
1 answer:
Flauer [41]3 years ago
7 0

Answer:

x = -5 and 1

Step-by-step explanation:

1. Subtract 6 from both sides to get x²+4x-5=0

2. Factor the quadratic equation. Find two numbers that have a sum of 4 and a product of (-5). The numbers 5 and (-1) add to 4 and multiply to get -5

3. The factored equation is (x+5)(x-1)=0

4. Set each factor to equal zero and solve for x.

x+5=0 ... x=-5

x-1=0 ... x=1

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What is the answer to this question?
Vlad [161]

The question:

Mr. Green orders some cookies from a local youth group. Using his order form shown below, complete the last column to find the total to be paid.

Quantity

Description

Unit Price

Total of Line

2

Krispy Kosmos

$2.89

1

Chewy Chocos

$3.19

1

Gooey Globs

$2.99

Total

5.8% tax

Total to be paid

a.

$9.60

b.

$11.96

c.

$12.65

d.

$18.90

Answer:

First, we are going to find the total cost of the groceries before tax:

We know from our table that he bought 2 Krispy Kosmos for $2.89, so the cost of the the 2 Krispy Kosmos was 2($2.89) = $5.78

We also know that he bought only one of the the other two items (Chewy Chocos and Gooey Globs), so to find the total cost of the groceries, we just need to add their respective value to the total value of the 2 Kispy Kosmos:

Total = $3.19+$2.99+$5.78 = $11.96

Now the only thing left is add the sale tax . To do it, we are going to calculate the cost of the tax, and then we'll add that cost to the total.

To calculate the cost of the tax, we need to find 5.8% of $11.96. To do it we are going to convert the tax from percentage to decimal and multiply the resulting decimal by $11.96:

To convert the tax from percentage to decimal, we are going to divide it by 100%: tax=\frac{5.8}{100} =0.058.

Since we have our tax expressed as a decimal, we can find the cost of the tax:

(0.058)($11.96) = $0.69

Now we just need to add the cost of the tax to the total:

Total to be paid = $11.96 + $0.69 = $12.65

We can conclude that the correct answer is c. $12.65

3 0
3 years ago
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One of the roots of the equation x^2 + kx -6 = 0 is 3, and k is constant
Aleks [24]
In order to solve this problem, we need to use the factor and remainder theorem. Suppose we have a quadratic equation of Q(x) and a binomial x-a=0, where a is a constant such that x=a. When you substitute x=a to the quadratic equation, you use the answer as basis. Whatever the answer is, is the remainder. If the answer is zero, that means that x=a is a factor. 

In this case, we substitute x=3 to the quadratic equation and equate to zero to find k.

Q(x) = x²+kx-6
Q(3) = 3²+k(3)-6 = 0
k = -1

The value of k is -1.
8 0
3 years ago
The supplement and twice the complement of an angle differ by 35 degrees. Find the angle. (Show all work)
polet [3.4K]
The angle is 35 degrees

(180 - x) = 2(90 - x) + 35
180 - x = 180 - 2x + 35
180 - x = 215 - 2x
180 + x = 215
x = 35

Check:
180 - 35 = 145 supplement
90 - 35 = 55 complement
55*2 = 110 twice the complement
110 + 35 = 145 :)
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3 years ago
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Zigmanuir [339]
12 because 36÷3= 12
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What is the negative square root of 0.25?
Annette [7]

Answer:

-0.5

Step-by-step explanation:

7 0
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