Zina solves a system of linear equations by elimination and finds a solution of (2, 2). One of the equations is a + b = 4. What is the other equation?

Answers

Answer 1

Answer: a - b = 0 <=== ur other equation

check...
a + b = 4
a - b = 0
--------------add
2a = 4
a = 4/2
a = 2

a - b = 0
2 - b = 0
-b = 0 - 2
-b = -2
b = 2

solution is (2,2)

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Let f(x)=√4x and g(x)=x+6, whats the smallest number that is the domain of f^o g?

Answers

f(x) = √(4x)
g(x) = x + 6

(f ο g)(x) = f(g(x))
(f ο g)(x) = √(4(x + 6))
(f ο g)(x) = 2√(x + 6)

The smallest number that is the domain of (f ο g)(x) is -6.

Find three consecutive integers such that the sum of twice the smallest and 3 times the largest is 126.

Answers

The addition is one of the four fundamental mathematical operations. The three consecutive terms are 24, 25, 26.

What is Addition?

The addition is one of the four fundamental mathematical operations, the others being subtraction, multiplication, and division. When two whole numbers are added together, the total quantity or sum of those values is obtained.

Let the first integer be represented by x. Then the other two integers will be (x+1) and (x+2).

Since it is given that the sum of twice the smallest and 3 times the largest is 126. Therefore we can write,

2x + 3(x+2) = 126

2x + 3x + 6 = 126

5x = 126 - 6

5x = 120

x = 120/5

x = 24

Thus, the three consecutive terms are,

x = 24

x + 1 = 25

x + 2 = 26

Hence, the three consecutive terms are 24, 25, and 26.

Learn more about Addition here:

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#SPJ2

x-smallest
y middle
z largest

x+1=y
y+1=z
2x+3z=126

2x+ 3(y+1)=126
2x+3y+3=126
2x+3(x+1)=123
5x=120
x=24

y=25

z=26

the following table shows the revenue for a company generates based on the increases in the price of the product. What is the y-value of the Vertex of the parabola that models the date?

Answers

Answer:

The y-value of the Vertex of the parabola that models the data is 1125.

Step-by-step explanation:

Let the function of parabola is

$f(x)=ax^2+bx+c$

From the given that it is noticed that the parabolic function passing through the points (1,1045), (3,1105) and (5,1125). It means the function must be satisfied by these points.

$1045=a(1)^2+b(1)+c$

$1045=a+b+c$ ....(1)

$1105=a(3)^2+b(3)+c$

$1105=9a+3b+c$ ....(2)

$1125=a(5)^2+b(5)+c$

$1125=25a+5b+c$ ....(3)

On solving (1), (2) and (3) we get,

$a=-5$

$b=50$

$c=1000$

Therefore the equation of parabola is

$f(x)=-5x^2+50x+1000$

The vertex of the parabola is

$((-b)/(2a),f((-b)/(2a)))$

$(-b)/(2a)=-(50)/(2(-5))=5$

$f(5)=1125$

Therefore the vertex is (5,1125) and y-value of the Vertex of the parabola that models the data is 1125.

The vertexes of the parabola are, (5, 1125).

Explanation

The table given to us in the problem are the data points that will lie on the parabola, therefore,

Point 1 = (1, 1045)

Point 2 = (3, 1105)

Point 3 = (5, 1125)

Point 4 = (3, 1105)

Point 5 = (1, 1045)

Equation of a Parabola,

We know that the equation of a parabola is given as,

$y = ax^2 +bx+c$

For point 1,

Point 1 = (1, 1045)

Substituting the value in the equation of a parabola,

$1045 = a(1)^2 +(1)b+c\n\n1045 = a+b+c$ ..... equation 1,

For point 2,

Point 2 = (3, 1105)

Substituting the value in the equation of a parabola,

$1105 = a(3)^2 +(3)b+c\n\n1105= 9a+3b+c$ ..... equation 2,

For point 3,

Point 3 = (5, 1125)

Substituting the value in the equation of a parabola,

$1125= a(5)^2 +(5)b+c\n\n1125= 25a+5b+c$ ..... equation 3,

Solving the three equations we get,

a = -5,

b = 50,

c = 1000

Substitute the values in the equation of a parabola,

$y=f(x) = -5x^2 +50x +1000$

How to find Vertexes of a parabola?

To find the vertex of a parabolic equation we bring the equation into the form,

$y = a(x-h)+k\n$ , where h and k are the vertexes of the parabola.

Vertexes of the parabola

Vertex of the Parabola,

$y=f(x) = -5x^2 +50x +1000\n\ny = -5x^2 +50x +1000\n\ny =-5(x^2 -10x)+1000\n\ny =-5(x^2 -10x+25-25)+1000\n\ny =-5(x^2 -10x+25)+ (-5* -25)+1000\n\ny =-5(x^2 -10x +25)+125+1000\n\ny =-5(x^2 -5)^2+1125$

Comparing it to the equation, $y = a(x-h)+k\n$ ,

the vertexes of the parabola are,

(5, 1125)

Learn more about the Equation of a Parabola:

brainly.com/question/4443998

20 hundreds equal how many thousands

Answers

The answer you want is 2

20 hundreds = 2000 or 2 thousands

How to solve it:

20 * 100 = 2000

And:

2000 = 2 thousands

Hope it helped,

BioTeacher101

In a right triangle, the measure of one acute is double the measure of the other acute angle. If the length of the short leg of the triangle is 3cm , find the length of the hypotenuse.

Answers

An right angle has a 90 degree angle , plus it's acute right triangle so it's degrees are 30-60-90 . So to find the hypotenuse you multiply the short leg by two . So your hypotenuse is 6

Answer:

you answer is for your hypotenuse witch would be 6

Help please thank you!

Answers

Answer:

yes

Step-by-step explanation:

good

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Could someone show me the work for the answer?