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1 year ago

Which inequality in standard form represents the shaded region?

Mathematics

1 answer:

Lubov Fominskaja [6]1 year ago

5 0

The figure is represented by the inequality y ≥ 5 · x² - 40 · x - 45. (Correct choice: C)

<h3>What inequality represents the figure</h3>

In accordance with the figure, we have an inequation of the form y ≥ f(x). Now we proceed to find the quadratic equation of the parabola:

f(x) = a · (x + 1) · (x - 9)

- 125 = a · (4 + 1) · (4 - 9)

- 125 = a · 5 · (- 5)

- 125 = - 25 · a

a = - 5

f(x) = 5 · (x + 1) · (x - 9)

f(x) = 5 · (x² - 8 · x - 9)

f(x) = 5 · x² - 40 · x - 45

The figure is represented by the inequality y ≥ 5 · x² - 40 · x - 45. (Correct choice: C)

To learn more on inequalities: brainly.com/question/17675534

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You might be interested in

What is the conjugate? √x + 2√b

Llana [10]

The correct answer is: " √x − 2√b " .
_________________________________________________________

The "conjugate" of " √x + 2√b " is: " √x − 2√b " .
_________________________________________________________

Explanation:
_________________________________________________________
In an expression with 2 (TWO) terms; that is, in a "binomial expression",
the "conjugate" of that expression refers to that very expression — with the "sign" in between those two terms—"reverse" (e.g. "minus" becomes "plus" ; or, "plus" becomes "minus" .) .
_________________________________________________________

→ So: We are given: " √x + 2√b " .

 → Note that this is a "binomial expression" ;

→ that is, there are 2 (TWO) terms: " √x " ; and: " 2√b " .
_________________________________________________________

To find the "conjugate" of the given binomial expression:

→ " √x + 2√b " ;

→ We simply change the "+" {plus sign} to a "−" {minus sign} ; and rewrite:
___________________________________________________________

→ " √x − 2√b " ;

→ which is the "conjugate" ; and is the correct answer:
___________________________________________________________
→ " √x − 2√b " ; is the "conjugate" of the expression: " √x + 2√b " .
___________________________________________________________
→ {that is: " √x − 2√b " ; is the conjugate.}.
___________________________________________________________

7 0

3 years ago

Amy gets a new kennel for her dog. A sketch of the kennel is shown here. If the roof is in the shape of a triangular prism (bott

SpyIntel [72]

Answer:

Surface area of the roof of the kennel, including the bottom face is 58.96 ft^2

Step-by-step explanation:

The image is attached below

For the triangular sides of the roof, area is

A = $\frac{1}{2}bh$

where b is the base = 4 ft

h is the vertical height = 2.24 ft

A = $\frac{1}{2}*4*2.24 =$ 4.48 ft^2

for the two faces we have 2 x 4.48 ft^2 = 8.96 ft^2

For the rectangular sections of the roof, area is

A = $lh$

where $l$ is the length of the rectangle = 5 ft

h is the height of the rectangle = 3 ft

A = 5 x 3 = 15 ft^2

For the two rectangular faces, we have 2 x 15 ft^2 = 30 ft^2

For the bottom face, area is

A = $lw$

where $l$ is the length of the house = 5 ft

w is the width of the house = 4 ft

A = 5 x 4 = 20 ft^2

Surface area of the roof of the dog kennel is

8.96 ft^2 + 30 ft^2 + 20 ft^2 = 58.96 ft^2

4 0

2 years ago

Choose the algebraic description that maps the image ΔABC onto ΔA′B′C′.

murzikaleks [220]

The algebraic description that maps the image ΔABC onto ΔA′B′C′ is (x, y) ⇒ (x + 7, y - 4)

<h3>What is transformation?</h3>

Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, rotation, translation and dilation.

Translation is the movement of a point either up, left, right or down in the coordinate plane.

The algebraic description that maps the image ΔABC onto ΔA′B′C′ is (x, y) ⇒ (x + 7, y - 4)

Find out more on transformation at: brainly.com/question/4289712

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7 0

1 year ago

In physics, if a moving object has a starting position at so, an initial velocity of vo, and a constant acceleration a, the

emmasim [6.3K]

Answer:

$a=\frac{2S -2v_ot-2s_o}{t^2}$

Step-by-step explanation:

We have the equation of the position of the object

$S = \frac{1}{2}at ^2 + v_ot+s_o$

We need to solve the equation for the variable a

$S = \frac{1}{2}at ^2 + v_ot+s_o$

Subtract $s_0$ and $v_0t$ on both sides of the equality

$S -v_ot-s_o = \frac{1}{2}at ^2 + v_ot+s_o - v_ot- s_o$

$S -v_ot-s_o = \frac{1}{2}at ^2$

multiply by 2 on both sides of equality

$2S -2v_ot-2s_o = 2*\frac{1}{2}at ^2$

$2S -2v_ot-2s_o =at ^2$

Divide between $t ^ 2$ on both sides of the equation

$\frac{2S -2v_ot-2s_o}{t^2} =a\frac{t^2}{t^2}$

Finally

$a=\frac{2S -2v_ot-2s_o}{t^2}$

5 0

3 years ago

In 1995, Hazel was 25 years older than her son Gary. In 2022, Hazel's age will be 150% of Gary's age. How old were they in 1995?

Kitty [74]

So find the difference between 1995 and 2022 to make it easier
2022-1995=27

so the rephrased question is
when hazel was x years old, she was 25 years older than son gary who was y old at that time (equation is x is 25 more than y or x=25+y)
in 27 years, (this means x+27 and y+27) hazel's age will be 150% of gary's age (x+27= 150% of y+27)
percent means parts out of 100 so 150%=150/100=15/10=1.5
'of' in math means multiply so
the equations are
x=25+y
x+27=1.5(y+27)
subsitute 25+y for x in second euation
25+y+27=1.5(y+27)
add like terms
y+52=1.5(y+27)
I personally dislike decimals to multiply both sides by 2 to make 2 0.5's or 1 (you are technically supposed to distribute or divide both sides by 1.5) so
2y+104=3(y+27)
distribute
2y+104=3y+81
subtract 2y from both sides
104=y+81
subtract 81 from both sides
23=y
subsitute
x=25+y
x=25+23
x=48

Hazel was 48 and Gary was 23 in the year of 1995

5 0

2 years ago