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4 years ago

Use the quadratic formula to solve x2 + 7x + 8 = 0. Estimate irrational solutions to the nearest tenth.

Mathematics

2 answers:

Marizza181 [45]4 years ago

6 0

Answer:

Step-by-step explanation:

djyliett [7]4 years ago

5 0

$x^2 + 7x + 8 = 0\\ \\a=1, \ b=7 ,\ c=8 \\ \\ x_{1}=\frac{-b-\sqrt{b^2-4ac}}{2a}=\frac{-7-\sqrt{7^2-4 \cdot 1\cdot 8}}{2 \cdot 1}=\frac{-7-\sqrt{49-32}}{2}=\frac{-7-\sqrt{17}}{2}\\ \\x_{2}=\frac{-b+\sqrt{b^2-4ac}}{2a}=\frac{-7+\sqrt{7^2-4 \cdot 1\cdot 8}}{2 \cdot 1}=\frac{-7+\sqrt{49-32}}{2}=\frac{-7+\sqrt{17}}{2}$

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Only answer 28 ( I added this parentheses so that the thing would accept my question)

avanturin [10]

Answer:

(a). Number of protons in a chlorine atom = 17

(b). Atomic number of sodium = 11

Step-by-step explanation:

Let the number of protons in a sodium atom = x

Then, the number of protons in a chlorine atom = x + 6

Now, it is given that the atomic number of an element is equal to the number of protons per atom.

So, atomic number of sodium (Na) = x

Atomic number of chlorine (Cl) = x + 6

It is given that the atomic number of chlorine is 5 less than twice the atomic number of sodium.

∴ atomic number of chlorine (Cl) = 2 × atomic number of sodium (Na) - 5

⇒ x + 6 = 2x - 5

⇒ x - 2x = -5 - 6

⇒ -x = -11

Cancelling the minus sign from both sides, we get

x = 11

(a). Number of protons in a chlorine atom = x + 6

= 11 + 6 (∵ x = 11)

= 17

(b). Atomic number of sodium = x = 11

3 0

3 years ago

Identify the initial amount a and the rate of growth r (as a percent) of the exponential function y=12(1.05)^t. Evaluate the fun

pentagon [3]

Answer:

Initial amount is 12

Rate of growth is 5%

At t = 5, y = 15.3.

Step-by-step explanation:

This is an exponential function. An exponential function has the form:

$f(x) = a_0(1+r)^t$ where the original/initial amount is $a_0$ , the growth rate is $1+r$ and the time is $t$ .

This means for the equation $y = 12(1.05)^t$ :

the initial amount is 12
the growth rate is 1.05 so the rate is 0.05 or 5%

Substitute t = 5 into the equation to find the amount at 5.

$y = 12(1.05)^5\\y = 12(1.276)\\y= 15.3$

7 0

3 years ago

What is the slop of the line?

miskamm [114]

The slope of the line is 2. Why? Well, see below for an explanation!

The slope of a line is found by using the formula rise/run (rise over run). This means that by starting at the initial value of the y-intercept, 3, we would count how many units away we are from the next complete point. We do so by counting from left to right, and in this case, going up and then to the right. To get from the point (0, 3) to the point (1, 5), we would move two spaces vertically along the y-axis and one space horizontally along the x-axis. Because the slope of the line is found using the formula m = rise over run, the slope would be 2/1 because we went up 2 points and to the right one. When simplifying, we will find that 2 divided by 1 equals 2. Hence, our slope is 2.

Your final answer: The slope of the line is 2/1 or 2. If you need extra help, let me know and I will gladly assist you.

8 0

2 years ago

The nth term of a number sequence is 7nFind the first three terms.

german

Answer:

7, 14, 21

Step-by-step explanation:

for n as term number

n = 1

7n = 7

n = 2

7n = 14

n = 3

7n = 21

hence the first 3 terms are 7, 14, 21

7 0

2 years ago

Which of the following is an identity?

lbvjy [14]

Answer:

$\text{\bf{D.}} \quad\sin^2{x}\sec^2{x}+1=\tan^2{x}\csc^2{x}$

Step-by-step explanation:

It can be useful to write each of these in terms of sine and cosine. Of course the relationship between sine and cosine is ...

sin²x + cos²x = 1 . . . . . eliminates choice B

A: (1/sin +cos/sin)² = ((1+cos)/sin)² ≠ 1

C: 1/sin² +(cos/sin)² = (1+cos²)/sin² ≠ 1

D: sin²(1/cos²) +1 = (sin²+cos²)/cos² = 1/cos² . . . (left side)

(sin/cos)²(1/sin²) = 1/cos² . . . (right side)

left side = right side, so this is an identity

6 0

3 years ago