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Lelu [443]
3 years ago
6

The product of two consecutive negative integers is 1122. What are the numbers? The product of two consecutive negative integers

is 1122. What are the numbers? @Mathematics
Mathematics
1 answer:
saw5 [17]3 years ago
4 0
Let the two numbers be -x and -x - 1, then
-x(-x - 1) = 1,122
x^2 + x = 1,122
x^2 + x + 1/4 = 1,122 + 1/4
(x + 1/2)^2 = 4,489/4
x + 1/2 = sqrt(4,489/4) = + or -67/2
x = 67/2 - 1/2 = 66/2 = 33

Therefore, the two numbers are -33 and -34
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A paint mixture was formed by mixing exactly 3 colors of paint. By volume, the mixture was x% blue paint, y% green paint, and z%
sergeinik [125]

Answer:

Both statements are sufficient to answer the question

Step-by-step explanation:

Given:

- The paint mixture has following proportions:

 Total volume of paint = T

 Blue:  x*T / 100

 Green: y*T/100

 Red: z*T/100

Find:

Statement 1: x = y

Statement: z = 60

Which of the above statement is sufficient to calculate the amount of green paint used

Solution:

Statement 1:

- The amount of blue paint used is:

                    1 gallon = x*T / 100

- x = y,

                    1 gallon = y*T / 100

Hence,

                    Amount of green paint used is 1 gallon

- The statement is sufficient

Statement 2:

- The amount of red paint used is:

                    3 gallon = z*T / 100

                    T = 300 / z = 300 / 60 = 5 gallons

                    T = R + B + G

                    G = T - R - B

                    G = 5 - 3 - 1

                    G = 1 gallons

Hence,

                    Amount of green paint used is 1 gallon

- The statement is sufficient

5 0
3 years ago
Look at the graph below and answer the following.
bearhunter [10]

Answer:

Part 1) The graph has three (3) x-intercepts and  has one (1) y-intercept

Part 2) The y-value of the minimum point is -3

Part 3) f(4)=3

Part 4) f(0)=3

Part 5) f(5)=1.5

Part 6) x=-6

Part 7) The horizontal line y=-1 intersects the graph three times

Part 8) The value of the function for f(6) is equal to zero

Part 9) The function is increasing on the interval (-6,-2) and (8,11) and the function is decreasing on the interval (2,8)

Part 10) The function is positive on the interval (-3,6) and (10,11) and is negative on the interval (-6,-3) and (6,10)

Step-by-step explanation:

Part 1) Find the number of x-intercepts and y-intercepts of the graph

we know that

The<u> x-intercepts</u> are the values of x when the value of y (the function) is equal to zero

Look at the graph

The graph has 3 x-intercepts

The x-intercepts are the points (-3,0), (6,0) and (10,0)

The<u> y-intercepts</u> are the values of y when the value of x is equal to zero

Look at the graph            

The graph has 1 y-intercept

The y-intercept is the point (0,3)

Part 2) The y value of the minimum point on the graph is?

we know that

Look at the picture

The minimum point is (-6,-3)

therefore

The y-value of the minimum point is -3

Part 3)  f(4) is equal to?

we know that

f(4) is the value of the function when the value of x is equal to 4

Look at the graph

For x=4

The value of the function is equal to y=3

therefore

f(4)=3

Part 4) f(0) is equal to?

we know that

f(0) is the value of the function when the value of x is equal to 0

Look at the graph

For x=0

The value of the function is equal to y=3

therefore

f(0)=3

Part 5) f(5) is equal to?

we know that

f(5) is the value of the function when the value of x is equal to 5

Look at the graph

For x=5

The value of the function is about y=1.5  (see the attached figure)

therefore

f(5)=1.5

Part 6) The value of x when f(x)= -3 is?

Look at the graph

we have the point (-6,-3)

when the value of f(x)=-3

the value of x is equal to x=-6

Part 7) The horizontal line y = -1 intersects the graph _____ times?

Look at the graph

The horizontal line y=-1 intersects the graph three times (see the attached figure)

Part 8) f(6) is positive or negative?

Look at the graph

we have the point (6,0)

For x=6

The value of the function is equal to zero

Part 9) Is the graph increasing or decreasing on the interval -6?

Look at the graph

The function is increasing on the interval (-6,-2) and (8,11) and the function is decreasing on the interval (2,8)

Part 10) Is the graph positive or negative on the interval 6

Look at the graph

The function is positive (f(x) > 0) on the interval (-3,6) and (10,11) and is negative (f(x) < 0) on the interval (-6,-3) and (6,10)

4 0
3 years ago
Choose the correct answer for each of the following questions Find the y-intercept for following equation F(X)=-(X+1)^21- -12- -
devlian [24]

Solution

Find the y-intercept for following equation:

f(x)=-(x+1)^2

Using the slope equation formular:

\begin{gathered} y=mx+c \\ f(x)=-(x+1)^2 \\ f(x)=-x^2-2x-1 \end{gathered}

The value of y when x = 0

\begin{gathered} f(0)=-0^2-2(0)-1 \\ y=-1 \end{gathered}

Hence the answer is - 1

7 0
1 year ago
This is the 4th question
gavmur [86]

Answer:

a) There are 9 outcomes.

b) **i have attached the tree diagram**

c) 1/9

d) 1/9

Step-by-step explanation:

Both events (choosing a shirt and choosing pants) are not mutually exclusive (disjoint). Meaning that both events can occur at the same time.

a) For a sequence of two events in which the first event can occur <em>m</em> ways and the second event can occur <em>n</em> ways, the events together can occur a total of <em>m</em> • <em>n</em> ways. So for this problem, you would do 3 • 3 which equals 9.

b) **tree diagram is attached**

c) Because there are two different events occurring (choosing a shirt and choosing pants) you need to multiply using the Multiplication Rule for Independent Events : P(A and B) = P(A) * P(B)

The probability of event A occurring (choosing a red shirt) is 1/3 and the probability of event B occurring (choosing brown pants) is also 1/3.

1/3 * 1/3 = 1/9

d) You would do the same thing here as part c.

The probability of event A occurring (choosing a blue shirt) is 1/3 and the probability of event B occurring (choosing blue pants) is again 1/3.

1/3 * 1/3 = 1/9

I hope this was helpful!! :)

4 0
2 years ago
Y = x² + 6x + 3
olganol [36]

Vertex<em> </em>is at \left(-3,-6\right)

<em>y-intercept</em> is 3.

The parabola <em>opens up</em>.

Step-by-step explanation:

The graph of the equation is hereby attached in the answer area.

Vertex is the point on the parabola where the graph crosses its axis of symmetry. The axis of symmetry here(x =-3), is shown with the dotted line in the graph attached.

<em>y-intercept </em>is defined as the value of y where the graph crosses the y-axis. In other words, when x=0. Putting

And, the graph opens up as shown the graph figure as well. It is also evident from the co-efficient of x in the given equation y =x^{2} + 6x + 3. Here, co-efficient of

So, vertex<em> </em>is at \left(-3,-6\right)

<em>y-intercept</em> is 3.

The parabola <em>opens up</em>.

7 0
2 years ago
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