What is the value of h when the function is converted to vertex form?
g(x) = x^2 – 6x + 14

Answers

Answer 1

Answer: Hello,

g(x)=x²-6x+14=x²-2*3x+9+14-9=(x-3)²+5
h=3, k=5

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Firewood is stacked in a pile. The bottom row has 20 logs, and the top row was 14 logs. Each row has one more log than the row above it. How many logs are in the pile?

The pair of points (6,y) and (10,-1) lie on a line with a slope 1(over)4. What is the value of y?

Answers

The formula for Slope is m = $(y_2 - y_1)/(x_2 - x_1)$ where m is the slope and the x's and y's are your given coordinates. So, plug the given information into the formula and solve for y.

m = $(y_2 - y_1)/(x_2 - x_1)$ Plug in the given values
$(1)/(4)$ = $(-1 - y)/(10 - 6)$ Cross multiply
10 - 6 = -4 - 4y Subtract
4 = -4 - 4y Add 4 to both sides
8 = -4y Divide both sides by -4
-2 = y Swich the sides to make it easier to read
y = -2

Check your answer by plugging -2 back into the equation with the other values.

[tex] \frac{1}{4} [/tex] = $(-1 - (-2))/(10 - 6)$ Simplify the double negative
$(1)/(4)$ = $(-1 + 2)/(10 - 6)$ Simplify the numerator and denominator
$(1)/(4)$ = $(1)/(4)$

Since both sides equal each other, y = -2.

Use the formula to find the slope which is m= y2-y1 over x2-x2. The equation would look like 1/4= -1 -y over 10-6. First, you do the subtraction in the denominator and you get 4. The equation would look like 1/4=-1-y over 4.

Then, you multiply the 4 to both side in order to get rid of the fraction from the equation. You would then have 1=-1-y. You add -1 to both side and you would have 2=-y. Since the variable cannot be negative, you divide -1 from both side and get -2=y. Therefore the answer is y=-2.

Hope this helps.

Ranger says the expression is not in its simplest form. He thinks the two terms need to be combined. Is Ranger right that 8x − 20 can be simplified further?

Answers

Yes, Ranger was right that expression 8x-20 can be simplified further as 4(2x-5).

The given expression is 8x-20.

Ranger says the expression is not in its simplest form. He thinks the two terms need to be combined.

Yes Ranger is correct, the given expression can simplified further.

That is, 8x-20

Factors of 8x and 20 are

8x=2×2×2×x

20=2×2×5

So, the common term is 4

Now, 8x-20=4(2x-5)

Yes, Ranger was right that expression 8x-20 can be simplified further as 4(2x-5).

To learn more about an expression visit;

brainly.com/question/28170201.

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4•(2x-5y) is the furthest it will go

Multiply and simplify
(5a + 2bc) (5a - 2bc)

Answers

One of the tools that's great to keep in your algebra toolbox for the rest of your life is:

The product of (sum of 2 things) (difference of 2 things) = (difference in their squares).

For example: (x + y) (x - y) = (x² - y²)

When you're trying to factor algebra expressions, it's always good to keep your
eyes open for the difference of two squares, and remember that it's going to be
(sum) x (difference) of the things that they're squares of.

Here you have (a sum) x (a difference) of the same 2 things:

(5a + 2bc) (5a - 2bc)

You can multiply them out, or just use the little tool above:

(5a)² = 25a²

(2bc)² = 4b²c²

So (their sum) x (their difference) is (25a² - 4b²c²) .

⇒ (a + b)(a - b) = a² - b²

Multiply and simplify :

$(5a + 2bc) (5a - 2bc) \n =25a^2+10abc-10abc-4bc^2 \n =25a^2-4b^2c^2$

1. A rectangular picture 6cm by 8cm is enclosed by a frame 1/2cm wide. Calculate the area of the frame. A.15sq cm B. 20 sq cm C. 13 sq cm D. 16 sq cm E. 17

Answers

Answer:

The area of 1/2 cm wide frame = 48 - 35 = 13 cm²

Step-by-step explanation:

Length of rectangular picture frame = 6 cm

Width of rectangular picture frame = 8 cm

Area of rectangular picture frame = 6×8 cm² = 48 cm²

Length, excluding 1/2 cm wide frame of rectangular picture = (6–1/2-1/2) = 5 cm

Width, excluding 1/2 cm wide frame of rectangular picture = (8–1/2-1/2) = 7 cm

Area, excluding 1/2 cm wide frame of rectangular picture = 5×7 cm² = 35 cm²

Area of 1/2 cm wide frame = 48 - 35 = 13 cm²

Therefore, the area of 1/2 cm wide frame = 48 - 35 = 13 cm²

Uh, I need help with this question (10 points)

Answers

Answer:

2 cups

Step-by-step explanation:

When dividing 878 by 31, a student finds a quotient of 28 with a remainder of 11. Check the students work, and use the check to find the error in the solution

Answers

The solution of the student work is wrong

The remainder number should be 10

Further explanation

The division operation is one of the basic arithmetic operations

Common signs used are $\boxed{:}}$ or $\boxed{\slash}$

The division is written by placing the numerator above the denominator with a horizontal line between them or use a slash with the numerator's position and the denominator is parallel

The division is actually an iterative subtraction operation (as many as the number of divisors)

Division is the opposite of multiplying

The general form of division can be stated by: