4t+2<10

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Answers

Answer 1

Answer:

Answer:

= t<2t is less than 2$t<2$

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A zoo has 15 emperor penguins. The emperor penguins make up 30%, percent of all the penguins at the zoo. How many penguins live at the zoo?

Factorize 16x^2 + 16xy + 4y^2. A) (4x + 2y)^2 B) (4x - 2y)^2 C) 4(x + y)^2 D) 4(x - y)^2

Answers

Answer:

Step-by-step explanation:

given

16x² + 16xy + 4y²

an expression factorised as a perfect square has the form

(ax + by)²

= a²x² + 2abxy + b²y²

16x² + 16xy + 4y² ← is in this form

with a² = 16 , b² = 4

so a = $√(16)$ = 4 and b = $√(4)$ = 2

then 2ab = 2(4)(2) = 16

Thus

16x² + 16xy + 4y² = (4x + 2y)² ← in factorised form

barista alex is crafting a new coffee blend. he combines two coffee beans: bean a, which has a bitterness level of 25%, and bean b, which has a bitterness level of 75%. to create his signature blend, he wants a 1000g batch with a bitterness level of 40%. how much of each coffee bean should he use?

Answers

Answer:

Barista Alex should use 700g of bean A (with 25% bitterness) and 300g of bean B (with 75% bitterness) to create his 1000g batch with a bitterness level of 40%.

Step-by-step explanation:

To create a 1000g batch of coffee blend with a bitterness level of 40%, you can use a weighted average based on the bitterness levels of the two beans, bean A (25%) and bean B (75%).

Let x be the amount of bean A (with 25% bitterness) and y be the amount of bean B (with 75% bitterness) in the blend. You want the total batch to be 1000g, so we have:

x + y = 1000

Now, to achieve the desired bitterness level of 40%, you can set up the following equation based on the weighted average:

(25% * x + 75% * y) = 40% * 1000

Now, let's convert the percentages to decimal values (divide by 100):

(0.25x + 0.75y) = 0.40 * 1000

Simplify:

0.25x + 0.75y = 400

Now you have a system of two equations:

x + y = 1000

0.25x + 0.75y = 400

You can solve this system of equations. Let's use the substitution method. Solve equation (1) for x:

x = 1000 - y

Now, substitute this expression for x into equation (2):

0.25(1000 - y) + 0.75y = 400

Now, solve for y:

0.25 * 1000 - 0.25y + 0.75y = 400

0.75y - 0.25y = 400 - 250

0.5y = 150

y = 150 / 0.5

y = 300

So, he should use 300g of bean B (with 75% bitterness). Now, you can find the amount of bean A by using the first equation:

x + 300 = 1000

x = 1000 - 300

x = 700

Therefore, Barista Alex should use 700g of bean A (with 25% bitterness) and 300g of bean B (with 75% bitterness) to create his 1000g batch with a bitterness level of 40%.

Jayne stopped to get gas before going on a road trip. The tank already had 4 gallons of gas in it. Which of the statements below best describes why the graph relating the total amount of gasoline in the tank, y, to the number of gallons that she added to it, x, will be continuous or discrete? A. The graph will be continuous because the amount of gas that she added to the tank does not need to be an integer amount. B. The graph will be continuous because we are not told a maximum value for the amount of gas. C. The graph will be discrete because there are already exactly 4 gallons of gas in the tank.

Answers

A. The graph will be continuous because the amount of gas that she added to the tank does not need to be an integer amount.

"The graph will be continuous because the amount of gas that she added to the tank does not need to be an integer amount" is the statement that best describes why the graph relating the total amount of gasoline in the tank, y, to the number of gallons that she added to it, x, will be continuous or discrete. The correct option is option "A".

It's not a really a question but how to solve these types of questionsLet f(x) = 9x − 2 and g(x) = −x + 3. Find f(g(x)).

Let f(x) = 2x + 2. Solve f−1(x) when x = 4.

Let f(x) = x + 8 and g(x) = x2 − 6x − 7. Find f(g(2)).

Let f(x) = x2 − 8x + 5. Find f(−1).

Answers

Answer:

Part 1) $f(x) = 9x- 2$ and $g(x) = -x + 3$

Find f(g(x)).

$f(x) = 9x- 2$

Substitute value of g(x) in place of x

$f(g(x)) = 9(-x+3)- 2$

$f(g(x)) = -9x+27- 2$

$f(g(x)) = -9x+25$

So, $f(g(x)) = -9x+25$

Part 2) $f(x) = 2x + 2$

$y = 2x + 2$

Replace y with x and x with y

$x = 2y + 2$

Find y

$(x-2)/(2) = y$

So, $f^(-1)(x)=(x-2)/(2)$

Substitute x = 4

$f^(-1)(4)=(4-2)/(2)$

$f^(-1)(4)=1$

Part 3) $f(x) = x + 8$ and $g(x) = x^2- 6x-7$

$f(x) = x + 8$

Substitute value of g(x) in place of x

$f(g(x)) =x^2- 6x-7 + 8$

$f(g(x)) =x^2- 6x+1$

Substitute x = 2

$f(g(x)) =2^2- 6(2)+1$

$f(g(x)) =4- 12+1$

$f(g(x)) =-7$

Part 4) $f(x) = x^2-8x + 5$

Substitute x = -1

$f(-1) = (-1)^2-8(-1) + 5$

$f(-1) =14$

1. 9(-x+3) - 2
3.[ (2)2 - 6(2) - 7] + 8
4.(-1)2 - 8(-1) + 5

00:00Lara and her brothers are painting a wall. Lara paints 2/8 of the wall.
Chuck and Max each 3/8 paint of the wall. How much of the wall do they paint all together?
Enter your answer in the box.

of the wall