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kotykmax [81]
3 years ago
8

There are 3 consecutive integers. The third integer subtracted from the sum of the first two integers equals 9. What is the midd

le integer ?
Mathematics
1 answer:
Alexus [3.1K]3 years ago
3 0

Answer:

The middle integer is 11.

Step-by-step explanation:

Hi there!

Let <em>x</em> be the smallest of the three consecutive integers.

Let <em>x</em>+1 and <em>x</em>+2 be the next consecutive integers. This makes <em>x</em>+1 the middle integer.

We're given that the third integer subtracted from the sum of the first two integers equals 9. We can use this to construct an equation:

(x)+(x+1)-(x+2)=9

Combine like terms:

x+x+1-x-2=9\\x+x-x+1-2=9\\x-1=9\\x=10

Therefore, the smallest integer is 10.

Because the middle integer is <em>x</em>+1, the middle integer is 11.

I hope this helps!

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Find a quadratic function that includes the set of values below.
Mariana [72]

Answer:

f(x) = -3x^2 + 10x + 3

Step-by-step explanation:

(0,3) (2,11)(3,6)

Using the form ax^2 + bx + c = y

From the first set we know that c = 3

Write an equation for the last two sets

x=2; y=11

a(2^2) + b(2) + 3 = 11

4a + 2b = 11 - 3

4a + 2b = 8

simplify divide by 2

2a + b = 4

and

x=3, y=6

9a + 3b + 3 = 6

9a + 3b = 6 - 3

9a + 3b = 3

simplify divide by 3

3a + b = 1

:

Use elimination to find a

3a + b = 1

2a + b = 4

--------------subtracting eliminate b

a = -3

Find b using the equation 2a + b = 4

2(-3) + b = 4

b = 4 + 6

b = 10

:

The equation: f(x) = -3x^2 + 10x + 3

8 0
3 years ago
An electrician charges Mr. Speer $300 before sales tax, for wiring his home. (a) What is the amount of sales tax that Mr. Speer
PilotLPTM [1.2K]

Answer: See explanation

Step-by-step explanation:

Your question isn't complete as you didn't give the sales tax percent. In order to solve the question, let's assume that the sales tax is 6%.

(a) What is the amount of sales tax that Mr. Speer has to pay?

This will be:

= Sales tax percent × Amount charged

= 6% × $300

= 6/100 × $300

= 0.06 × $300

= $18

The sale tax is $18

(b) What is the total amount Mr. Speer has to pay?.

The total amount will be the addition of the amount charged and the sales tax. This will be:

= $300 + $18

= $318

4 0
3 years ago
What is the type of association between variables x and y?
Molodets [167]

Answer:

strong negative correlation

Step-by-step explanation:

if x goes up y goes down and if y goes up x comes down

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3 years ago
On a motor trip, Mr. Williams covered 2/6 of his total trip distance by driving 388 miles. The total distance to be covered in m
Reptile [31]

Answer:

B

Step-by-step explanation:

2/6  x  d   = 388

d = 388 x 6/2 = 1164 m

3 0
2 years ago
Read 2 more answers
Lizette wanted to see if it would be possible to use a little less materials in a tea infuser but still not be required to be at
Oksi-84 [34.3K]

Considering the volume of a rectangular prism, since the new volume is greater than the filled volume, the new dimensions would work, and 90.29% of the infuser would be filled.

<h3>What is the volume of a rectangular prism?</h3>


The volume of a rectangular prism of length l, width w and height h is given by:

V = lwh.

The original dimensions are:

h = 7.9 cm, l = 3 cm, w = 1.5.

Hence the volume in cm³ was:

V = 7.9 x 3 x 1.5 = 35.55 cm³.

The infuser was filled to 80% capacity, hence:

Vf = 0.8 x 35.55 = 28.44 cm³.

For the new dimensions, we have that h = 7 cm, hence the volume is:

Vn = 7 x 3 x 1.5 = 31.5 cm³.

28.44/31.5 x 100% = 90.29%.

Since the new volume is greater than the filled volume, the new dimensions would work, and 90.29% of the infuser would be filled.

More can be learned about the volume of a rectangular prism at brainly.com/question/17223528

#SPJ1

4 0
2 years ago
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