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3 years ago

Using the completing-the-square method, rewrite f(x) = x2 - 8x + 3 in vertex form.

Mathematics

1 answer:

Leto [7]3 years ago

5 0

Answer:

Step-by-step explanation:

Given

f(x) = x² - 8x + 3

To complete the square

add/subtract ( half the coefficient of the x- term )² to x² - 8x

x² + 2(- 4)x + 16 - 16 + 3

(x - 4)² - 13 ← in vertex form → B

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If F, G, and H are the midpoints of the sides of triangle JKL , FG = 37, KL = 48, and GH = 30 find each measure

seraphim [82]

Answer:

The measure of JK is 60

Step-by-step explanation:

It is given that the points F, G, and H are the midpoints of the sides of triangle JKL , FG = 37, KL = 48, and GH = 30.

The point F is midpoint of JK, point G is midpoint of KL and the point H is midpoint of LJ as shown in figure .

According to the midpoint theorem, the line connecting the midpoints of two sides is parallel to the third and its length is half of the third si

8 0

2 years ago

Read 2 more answers

Which group of three squares will form a right triangle when joined at their vertices?

Ilia_Sergeevich [38]

Answer:

Option ?) 17 cm, 15 cm, 8 cm

The assignment should have four options to choose from, but there is only a picture of two.

Step-by-step explanation:

None of the squares shown form a right triangle. To determine if sides form a right triangle, you use this formula:

a²+b²=c²

We are given two options in the picture.

Option A) 18, 10, and 8.

Option B) 12, 9, and 6.

So, now we need to apply the formula:

Option A)

║8² + 10² = 18²

↓

║64 + 100 = 324

↓

║FALSE

Option B)

║6² + 9² = 12²

↓

║36 + 81 = 144

↓

║FALSE

Both of these options are false. But, I decided to look up this assignment to check my answer. It turns out, there are 4 options, and you only had a picture of two. So, what's the answer?

There is an answer choice that shows 3 squares with the lengths of 17 cm, 15 cm, and 8 cm. This is the correct answer.

For proof, let's apply the formula:

Option ?)

║8² + 15² = 17²

↓

║64 + 225 = 289

↓

║TRUE

[Since the option isn't shown, I'll put a '?' so there is no confusion]

8 0

3 years ago

Delicious Candy markets a two-pound box of assorted chocolates. Because of imperfec- tions in the candy making equipment, the ac

saveliy_v [14]

Answer:

The required probability is 0.533.

Step-by-step explanation:

Consider the provided information.

The actual weight of the chocolate has a uniform distribution ranging from 31 to 32.5 ounces.

Let x is the random variable for the actual weight of chocolate.

According to PDF function.

$P(a\leq x\leq b)=\int\limits^b_a {f(x)} \, dx$

Where $f(x)=\left\{\begin{matrix}\frac{1}{b-a} & a$

It is given that ranging from 31 to 32.5 ounces.

Substitute a=31 and b=32.5 in above function.

$f(x)=\left\{\begin{matrix}\frac{1}{32.5-31} & 31$

$f(x)=\left\{\begin{matrix}\frac{1}{1.5} & 31$

We need to find the probability that a box weighs less than 31.8 ounces

Now according to PDF:

$P(x$

Hence, the required probability is 0.533.

6 0

3 years ago

Which point below is a solution to the equation y = 2x + 3?

Anastasy [175]

Answer:

C (37, 77)

Step-by-step explanation:

<h3>Option A:</h3>

$291=2(145)+3\\\\291=290+3\\\\\boxed{291\neq 293}$

Option A is not a solution.

<h3>Option B:</h3>

$163=2(78)+3\\\\163=156+3\\\\\boxed{163\neq 159}$

Option B is not a solution.

<h3>Option C:</h3>

$77=2(37)+3\\\\77=74+3\\\\\boxed{77=77}$

Option C is a solution.

Hope this helps.

6 0

3 years ago

Read 2 more answers

What is a composite number that is less than 5?

babunello [35]

I believe 4, because two times two equals four

4 0

3 years ago

Read 2 more answers