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const2013 [10]
3 years ago
14

The function f(x) = -x2 - 4x + 5 is shown on the graph. Which statement about the function is true? V 14 2 (-2.9) 10 8+ O The do

main of the function is all real numbers less than or equal to -2. O The domain of the function is all real numbers less than or equal to 9. O The range of the function is all real numbers less than or equal to -2. 0 The range of the function is all real numbers less than or equal to 9. 64 ON --} -6 15 4 -3 -2 -12 12 3 4 5 -124​
Mathematics
1 answer:
ikadub [295]3 years ago
3 0

Answer:

we have

using a graph tool

see the attached figure

the domain of the function is all real numbers------> the interval is (-∞,∞)

the range of the function is --------------------------------> the interval (-∞,9]

therefore

the answer is

The range of the function is all real numbers less than or equal to 9

Step-by-step explanation:

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The average age of 4 children is 15 yrs . if the ages of their parents are added , their average age is 25 .find the age of thei
WITCHER [35]

The age of the father is 57 years old

<h3>Calculating mean of a population</h3>

Total age = Average age x Population

Average of the four children = 15

Population = 4

Total age of the four children = 15 x 4

Total age of the four children = 60 years

If the parents are added:

Population = 6

Average age = 25

Total age = 25 x 6

Total age = 150 years

Total age of the parents = 150 - 60

Total age of the parents = 110 years

The father is 4 years older than his wife

Let the age of the father be x

The age of the wife = x - 4

x + x - 4 = 110

2x = 114

x = 114/2

x = 57

Therefore, the age of the father is 57 years old

Learn more on The mean of numbers here: brainly.com/question/20118982

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6 0
2 years ago
If a°, 30° and 2a° are the angle of triangle find a°​
valina [46]

Answer:

a=50

Step-by-step explanation:

a + 2a + 30 = 180

3a + 30 = 180

(-150 from both sides)

3a = 150

(Divide by 3 from both sides)

a = 50

8 0
3 years ago
Match the parabolas represented by the equations with their vertices. y = x2 + 6x + 8 y = 2x2 + 16x + 28 y = -x2 + 5x + 14 y = -
GaryK [48]

Consider all parabolas:

1.

y = x^2 + 6x + 8,\\y=x^2+6x+9-9+8,\\y=(x^2+6x+9)-1,\\y=(x+3)^2-1.

When x=-3, y=-1, then the point (-3,-1) is vertex of this first parabola.

2.

y = 2x^2 + 16x + 28=2(x^2+8x+14),\\y=2(x^2+8x+16-16+14),\\y=2((x^2+8x+16)-16+14),\\y=2((x+4)^2-2)=2(x+4)^2-4.

When x=-4, y=-4, then the point (-4,-4) is vertex of this second parabola.

3.

y =-x^2 + 5x + 14=-(x^2-5x-14),\\y=-(x^2-5x+\dfrac{25}{4}-\dfrac{25}{4}-14),\\y=-((x^2-5x+\dfrac{25}{4})-\dfrac{25}{4}-14),\\y=-((x-\dfrac{5}{2})^2-\dfrac{81}{4})=-(x-\dfrac{5}{2})^2+\dfrac{81}{4}.

When x=2.5, y=20.25, then the point (2.5,20.25) is vertex of this third parabola.

4.

y =-x^2 + 7x + 7=-(x^2-7x-7),\\y=-(x^2-7x+\dfrac{49}{4}-\dfrac{49}{4}-7),\\y=-((x^2-7x+\dfrac{49}{4})-\dfrac{49}{4}-7),\\y=-((x-\dfrac{7}{2})^2-\dfrac{77}{4})=-(x-\dfrac{7}{2})^2+\dfrac{77}{4}.

When x=3.5, y=19.25, then the point (3.5,19.25) is vertex of this fourth parabola.

5.

y =2x^2 + 7x +5=2(x^2+\dfrac{7}{2}x+\dfrac{5}{2}),\\y=2(x^2+\dfrac{7}{2}x+\dfrac{49}{16}-\dfrac{49}{16}+\dfrac{5}{2}),\\y=2((x^2+\dfrac{7}{2}x+\dfrac{49}{16})-\dfrac{49}{16}+\dfrac{5}{2}),\\y=2((x+\dfrac{7}{4})^2-\dfrac{9}{16})=2(x+\dfrac{7}{4})^2-\dfrac{9}{8}.

When x=-1.75, y=-1.125, then the point (-1.75,-1.125) is vertex of this fifth parabola.

6.

y =-2x^2 + 8x +5=-2(x^2-4x-\dfrac{5}{2}),\\y=-2(x^2-4x+4-4-\dfrac{5}{2}),\\y=-2((x^2-4x+4)-4-\dfrac{5}{2}),\\y=-2((x-2)^2-\dfrac{13}{2})=-2(x-2)^2+13.

When x=2, y=13, then the point (2,13) is vertex of this sixth parabola.

3 0
3 years ago
One-half of the sum of a number and 12 is less than 27.  What is the number?  Write as an inequality.  ​
kirill115 [55]

Answer:

Call the number we need to find a.

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<=> 12 + a < 54

<=> a < 54 - 12

<=> a < 42

3 0
3 years ago
How many 2/3 pounds are in a sixth of a pound?
mote1985 [20]
None. ⅔ is greater than 1/6 but ⅔ equals 2 x (1/6).
Basically one half of ⅔ equals 1/6
6 0
3 years ago
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