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Gnesinka [82]
3 years ago
12

Express the equation y= x² + 10x +30 in the form y= a(x - h)² +k

Mathematics
1 answer:
nikklg [1K]3 years ago
3 0

Answer:

\large \boxed{\sf \ \ y=(x+5)^2+5 \ \ }

Step-by-step explanation:

Hello, please find my work below.

y=x^2+10x+30\\\\\text{*** We can notice that ***}\\\\\text{***  } x^2+10x = x^2+2\cdot 5 \cdot x=(x+5)^2-5^2=(x+5)^2-25\\\\y=x^2+10x+30=(x+5)^2-25+30=(x+5)^2+5\\\\

a = 1

h = -5

k = 5

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

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If the lines are parallel with angle a measuring 5x + 8 and angle b measuring 8x - 7, the measure of angle a would be ___ degree
Mandarinka [93]

The value of angle a will be 33°.

It should be noted that when we've parallel lines, then the angles will be equal. In this case, the value of angle a will be equal to that of angle b and this will be:

5x + 8 = 8x - 7.

Collect like terms .

8x - 5x = 8 + 7

3x = 15

Divide both side by 3

3x/3 = 15/3

x = 5

Therefore, the value of angle a will be:

= 5x + 8

= 5(5) + 8

= 25° + 8°

= 33°

The measure of angle a is 33°.

Read related link on:

brainly.com/question/24576134

7 0
3 years ago
The yearly expenses for the Glenn family are represented in the circle graph. The Glenn’s have just purchased a new car. A new c
tiny-mole [99]

Answer:

Car: 18.4% Other: 4.9%

Step-by-step explanation:

Glenn family yearly total expenses are

\$8,600+\$4,800+\$5,400+\$2,400+\$7,000+\$1,800=\$30,000

Other expenses are $7,000.

The payments for the new car are: $375.00 per month and the insurance for the new car $85.00 per month, in total, $460 per month. Yearly expenses for car are

\$460\cdot 12=\$5,520

Now, the expenses for the following two categories are

Car - $5,520

Other - $7,000 - $5,520 = $1,480

Percentage:

Car:

\dfrac{5,520}{30,000}\cdot 100\%=18.4\%

Other

\dfrac{1,480}{30,000}\cdot 100\%\approx 4.93\%

4 0
3 years ago
Or the past 100 years, the average high temperature on october 1 is 78° with a standard deviation of 5°. what is the probability
valina [46]

Answer:

The probability is 0.683

Step-by-step explanation:

To calculate this, we shall be needing to calculate the z-scores of both temperatures

mathematically;

z-score = (x-mean)/SD

From the question mean = 78 and SD = 5

For 73

z-score = (73-78)/5 = -5/5 = -1

For 83

z-score = (83-78)/5 = 5/5 = 1

So the probability we want to calculate is within the following range of z-scores;

P(-1 <z <1 )

Mathematically, this is same as ;

P(z<1) - P(z<-1)

Using the normal distribution table;

P(-1<z<1) = 0.68269 which is approximately 0.683

3 0
4 years ago
What are the values of each Halloween icon? (Math Logic Puzzles) (78 POINTS)
Mekhanik [1.2K]

Answer:

is there anything else i can use to help me? besides a bunch of icons?

4 0
3 years ago
David’s family is driving from New York to Florida. They know the distance they will travel is about 1100 miles. If a map has a
zaharov [31]

Answer:

Step-by-step explanation:

do the proportion ...

1 inch/ 80 miles =x inch/ 1100 miles

1100= 80x

x=1100/80=13.75

The trip would be about 13.75 inches on the map

hope this will help u

3 0
4 years ago
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