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3 years ago

The table below represents a linear function f(x) and the equation represents a function g(x):

1 answer:

4 0

Slope of f(x)

Slope of g(x)

PART A)
The slopes of f(x) and g(x) are the same.

PART B)
The equation for line f(x)
y = 4x + b
-1 = 4(0) + b
-1 = b

y = 4x - 1

The function G(x) has a bigger y-intercept. The y-intercept of g(x) is 3, while the y-intercept of f(x) is -1.

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Which decimal has the LEAST value? O 32.12 O 32.14 O 32.1 O 31.00

MArishka [77]

Answer:

32.1. It has the least values in the decimal place. Overall, it's 31.00, but the least decimal value is 32.1

Step-by-step explanation:

6 0

3 years ago

Complete the square for 5x2 – 30x = 5.

Tresset [83]

C is the answer because (5x-3)

6 0

3 years ago

A dog weighs two pounds less than three times the weight of a cat. The dog also weights twenty-two more pounds than the cat. Wri

8090 [49]

Answer:

Weight of dog: 34 pounds,

Weight of cat: 12 pounds.

Step-by-step explanation:

Let d represent weight of dog and c represent weight of cat.

We have been given that a dog weighs two pounds less than three times the weight of a cat.

3 times weight of cat: $3c$

We can represent the given information in an equation as:

$d=3c-2...(1)$

We are also told that the dog also weights twenty-two more pounds than the cat. We can represent the given information in an equation as:

$d=c+22...(2)$

Equate both equations:

$3c-2=c+22$

$3c-c-2=c-c+22$

$2c-2=22$

$2c-2+2=22+2$

$2c=24$

$\frac{2c}{2}=\frac{24}{2}$

$c=12$

Therefore, the weight of cat is 12 pounds.

Substitute $c=12$ in equation (2)

$d=c+22$

$d=12+22$

$d=34$

Therefore, the weight of dog is 34 pounds.

4 0

3 years ago

Write this statement in your own words: ∃x ∈ ℕ, y ∈ ℤ|x² = y² Rewrite this using the appropriate mathematical notation: Even num

Serga [27]

Answer:

See below.

Step-by-step explanation:

So we have:

$\exists x\in\mathbb{N},y\in\mathbb{Z}|x^2=y^2$

This can be interpreted as:

"There exists a natural number x and an integer y such that x² is equal to y²."

So we want even numbers are in the set of integers.

$\{2n:n\in\mathbb{Z}\}\in\mathbb{Z}$

This is interpreted as:

"The set of even numbers (2n such that n is an integer) is in the set of integers"

6 0

3 years ago

a guy wire for a tree is 20 ft long, making a 21 angle with the ground. How far is the base of the tree from a stake anchoring t

evablogger [386]

Answer:

18.7 feet far

Step-by-step explanation:

Based on the information given we can conclude that our set up will be a Right triangle (i.e. one angle is 90°), where the hypotenuse will be denoted by the guy wire of $20ft$ and angle of 21° is the angle formed between then hypotenuse and the base (i.e. ground).

Thus we want to find the base length (lets call it $x$ ) of this triangle, so we can use trigonometry as we have one angle and the hypotenuse, as follow:

$cos(21)=\frac{adjacent side}{hypotenuse}=\frac{baselength}{guywire}\\\\ cos(21)=\frac{x}{20} \\x=20cos(21)\\x=18.671\\x=18.7ft$

So the base is approximately 18.7 feet far from the tree of the anchored wire.

8 0

3 years ago