1/3x + a= 1/2b for x

Find three consecutive odd integers such that the sum of the smallest number and twice the largest number is equal to fifteen mo

inn [45]

Answer:

The three consecutive odd integers are: -11, -13 and -15.

Step-by-step explanation:

Let the smallest number be represented by x. then the three consecutive odd integers are: x, (x + 2) and (x = 4).

The sum of the smallest number and twice the larges number = x + 2(x + 4)

Fifteen more than four times the middle number = 4(x + 2) + 15

So that;

x + 2(x + 4) = 4(x + 2) + 15

x + 2x + 8 = 4x + 8 + 15

3x + 8 = 4x + 23

3x - 4x = 23 - 8

-1x = 15

⇒ x = -15

(x + 2) = (-15 + 2) = -13

(x + 4) = (-15 + 4) = -11

The three consecutive odd integers are: -11, -13 and -15.

7 0

4 years ago

Which of the following is the graph of y = 3x2 + 6?

natali 33 [55]

Answer:

what are the graphs?

Step-by-step explanation:

4 0

3 years ago

Lily's basketball team won 4/5 of their games. Lily scored points 2/3 of the games her team won. In waht fraction of her team's

igor_vitrenko [27]

$\huge\fcolorbox{blue}{aqua}{Answer:}$

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Lily's basketball team won 4/5 of their games. Lily scored points 2/3 of the games her team won. In waht fraction of her team's winning games did Lily score points?

Answer: =D. $\frac{5}{6}$

Solution:

$\frac{ 2 }{ 3 } \div \frac{ 4 }{ 5 } =$

$\frac{2}{3}\times \left(\frac{5}{4}\right)$

$\frac{2\times 5}{3\times 4}$

$\frac{10}{12}$

= $\frac{5}{6}$

I reduced the fraction $\frac{10}{12}$ into the Lowest terms by doing extracting and cancelling out the $2$

= $\frac{5}{6}$

So the answer is letter D. $\frac{5}{6}$

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Explanation:

#Carry on learning

4 0

3 years ago

A cell phone company charges a basic rate of $19.99 per month for 300 minutes of local usage. Any local usage over 300 minutes i

Lera25 [3.4K]

total = 19.99 + 0.10(x-300) + 0.25y

x = 375

y=54

total = 19.99 +0.10(375-300) +0.25(54)

total = 19.99 + 0.10(75) + 0.25(54)

total = 19.99 + 7.50 + 13.50

total = $40.99

8 0

3 years ago

This graph represents a quadratic function. What is the function’s equation written in factored form and in vertex form?

creativ13 [48]

Answer:

Part a) The function’s equation written in vertex form is

$f(x)=2(x-2)^2-8$

Part b) The function’s equation written in factored form is equal to

$f(x)=2x(x-4)$

Step-by-step explanation:

Part a) What is the function’s equation written in vertex form?

we know that

The equation of a vertical parabola written in vertex form is equal to

$f(x)=a(x-h)^2+k$

where

a is a coefficient

(h,k) is the vertex

Looking at the graph

The vertex is the point (2,-8)

substitute

$f(x)=a(x-2)^2-8$

Find the value of the coefficient a

take one point from the graph

(0,0)

substitute in the equation

$0=a(0-2)^2-8\\0=4a-8\\4a=8\\a=2$

therefore

The function’s equation written in vertex form is

$f(x)=2(x-2)^2-8$

Part b) What is the function’s equation written in factored form?

we know that

The equation of a vertical parabola written in factored form is equal to

$f(x)=a(x-x_1)(x-x_2)$

where

a is a coefficient

x_1 and x_2 are the zeros or x-intercepts of the function

Remember that the x-intercept is the value of x when the value of the function is equal to zero

Looking at the graph

The zeros or x-intercepts of the function are

x=0 and x=4

so

$f(x)=a(x-0)(x-4)$

$f(x)=ax(x-4)$

Find the value of the coefficient a

take one point from the graph

(2,-8)

substitute

$-8=a(2)(2-4)\\-8=-4a\\a=2$

therefore

The function’s equation written in factored form is equal to

$f(x)=2x(x-4)$

4 0

4 years ago