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3 years ago

14

Given the equation f(x) = (x + 3)2 – 8, fill in the blanks:

1 answer:

Neko [114]3 years ago

4 0

Quadratic f(x) = (x -h)² +k has vertex (h, k) and axis of symmetry x=h. When k is negative, the number of real solutions is 2, because both branches of the function cross the x-axis.

In your equation, h = -3 and k = -8.

Axis of symmetry: x = -3
Vertex: (-3, -8)
Number of real solutions: 2

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On a number line, show all points whose coordinates satisfy the following inequalities: |x−20|<5

VLD [36.1K]

Answer:

On the number line integers from 16 to 24 is the answer.

4 0

3 years ago

Read 2 more answers

In 1998, Cathy's age is equal to the sum of the four digits in the year of her birthday, then how old was Cathy in 1998?

ycow [4]

Answer:

<em>Cathy was born in 1980 and she was 18 years old in 1998</em>

Step-by-step explanation:

<u>Equations</u>

This is a special type of equations where all the unknowns must be integers and limited to a range [0,9] because they are the digits of a number.

Let's say Cathy was born in the year x formed by the ordered digits abcd. A number expressed by its digits can be calculated as

$x=1000a+100b+10c+d$

In 1998, Cathy's age was

$1998-(1000a+100b+10c+d)$

And it must be equal to the sum of the four digits

$1998-(1000a+100b+10c+d)=a+b+c+d$

Rearranging

$1998=1001a+101b+11c+2d$

We are sure a=1, b=9 because Cathy's age is limited to having been born in the same century and millennium. Thus

$1998=1001+909+11c+2d$

Operating

$88=11c+2d$

If now we try some values for c we notice there is only one possible valid combination, since c and d must be integers in the range [0,9]

c=8, d=0

Thus, Cathy was born in 1980 and she was 18 years old in 1998. Note that 1+9+8+0=18

5 0

4 years ago

X + 3/ 5 = 2<br> -5<br> -3<br> 7<br> 13

ahrayia [7]

X 3/5 =2x+15=2x=15-2x=13

answer 13

4 0

3 years ago

Trey evaluated 12/15 + 1/10 and got the answer of 13/25. which statement is true about this answer?

Ganezh [65]

Answer:

Option C. His answer is not correct, because the same can not be less than either attend

Step-by-step explanation:

we have

$\frac{12}{15}+\frac{1}{10} =\frac{13}{25}$

we know that

$\frac{12}{15}=0.8$

$\frac{1}{10}=0.10$

$\frac{13}{25}=0.52$

substitute

$0.80+0.10=0.52$ ----> is not true

therefore

His answer is not correct, because the same can not be less than either attend

6 0

3 years ago

Hey can you please help me with this

Tasya [4]

x=-11

Hope this helps :T

8 0

3 years ago