What number must you add to the polynomial below to complete the square?x^2-x
A. 1/4
B. 1/2
C. 2
D. 1

Answers

Answer 1

Answer: (-1/2)^2 = 1/4

So you have to add 1/4 to complete the square.

Answer is A.

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Critical thinking. Make a conjecture about the relationship between three consecutive whole numbers based on this relationship illustrated by the numbers 7, 8, and 9: 7+9/2=8. Can you find a counterexample?

Answers

I need help with that too. :,-(

Solve :
8-(4c-5)=11

Answers

8−(4c−5)=11
8+−1(4c−5)=11
8+−1(4c)+(−1)(−5)=11
8+−4c+5=11
(−4c)+(8+5)=11
−4c+13=11

−4c+13−13=11−13
−4c=−2
−4c divided by−4 = −2 divided by −4
c=1/2

Find the coordinates of the points of intersection of the graphs without building them: 5x–4y=16 and x–2y=6

Answers

we have that
equation 1
5x–4y=16
and
equation 2
x–2y=6

we know that

Part A) the x-intercept is when y=0
equation 1
5x–4y=16
for y=0
5x=16--------> x=16/5---> x=3.2
the point is (3.2,0)

equation 2
x–2y=6
for y=0
x=6
the point is (6,0)

Part B) the y-intercept is when x=0
equation 1
5x–4y=16
for x=0
-4y=16-------> y=-4
the point is (0,-4)

equation 2
x–2y=6
for x=0
-2y=6------> y=-3
the point is (0,-3)

the answer is
the coordinates of the points of intersection are
equation 1
5x–4y=16
(3.2,0) and (0,-4)

equation 2
x–2y=6
(6,0) and (0,-3)

Final answer:

To find the coordinates of the points of intersection of two graphs without building them, solve the given system of equations. The coordinates of the points of intersection of the graphs 5x - 4y = 16 and x - 2y = 6 are approximately (-8.67, -2.33).

Explanation:

To find the coordinates of the points of intersection of the graphs without building them, we can solve the given system of equations: 5x - 4y = 16 and x - 2y = 6.

Step 1: We can solve the second equation for x: x = 6 + 2y.

Step 2: Substitute the value of x from Step 1 into the first equation: 5(6 + 2y) - 4y = 16.

Step 3: Simplify and solve for y: 30 + 10y - 4y = 16. Combine like terms: 6y = -14. Divide by 6: y = -7/3.

Step 4: Substitute the value of y from Step 3 into the second equation to find x: x - 2(-7/3) = 6. Simplify: x + 14/3 = 6. Subtract 14/3 from both sides: x = -26/3.

Therefore, the coordinates of the points of intersection are (-26/3, -7/3) or approximately (-8.67, -2.33).

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An animal shelter spends $2.35 per day to care for each cat and $5.50 per day to care for eachdog. Pat noticed that the shelter spent $89.50 caring for cats and dogs on Wednesday.
Write an equation to represent the possible numbers of cats and dogs that could have been at the
shelter on Wednesday.
Pat said that there might have been 8 cats and 14 dogs at the shelter on Wednesday. Are Pat’s
numbers possible? Use your equation to justify your answer.
Later, Pat found a record showing that there were a total of 22 cats and dogs at the shelter on
Wednesday. How many cats were at the shelter on Wednesday?

Answers

Equation:
89.50=2.35c+5.50d

If theres 22 dogs and cats in total you can plug in number less than 22 for c(# of cats) and d(# of dogs).

So we try pats numbers 8 cats and 14 dogs so

89.50=2.35(8)+5.50(14)

89.50=18.8+77

89.50=95.8

So pats numbers were wrong so we try different numbers

So i started pluging in numbers from under 22 so i got c is 10 and d is 12 lets try it with the equation

89.50=2.35(10)+5.50(12)

89.50=23.5+66

89.50=89.50 so it works the answer to how many number of dogs and cats is 12 dogs and 10 cats

Final answer:

The equation representing the costs to care for the animals is 2.35c + 5.5d = $89.50. Pat's proposal of 8 cats and 14 dogs does not match the costs. Upon using additional information of the total number of animals being 22, we can solve the system of equations to find that there were 16 cats and 6 dogs at the shelter on Wednesday.

Explanation:

Let's denote the number of cats as c and the number of dogs as d. We know from the cost of care per day per animal that 2.35c + 5.5d = $89.50. This is the equation representing the possible number of cats and dogs at the shelter in terms of costs. For Pat's numbers, we can substitute c=8 and d=14 into the equation and check if they are possible. That is, substitute and check if 2.35(8) + 5.5(14) equals to 89.5. In this case, it does not since the total here comes to more than $89.50. So, Pat's numbers were not possible.

Regarding the total number of animals, we know that c + d = 22. With this equation, we can solve the system of equations to find out the actual number of cats and dogs at the shelter on Wednesday. Solving these two equations, we will find that 16 cats and 6 dogs were present at the shelter on Wednesday.

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The sum of 3 consecutive integers is -27. what are the numbers?

Answers

Call x the smallest of the three numbers, then:

x + (x+1) +(x+2) = -27

x + x + 1 + x + 2 = -27

3x+3 =-27
3x = -27 -3
3x = -30
x = -30/3 = -10

The three numbers are: -10, -9 and -8.

Input the equation for the following line in standard form Ax + By =c. Reduce all fractional answers to lowest terms. A line with y-intercept of 2 that is parallel to 2x + y = -5.
Given two points on the line, input the equation of the line in standard form Ax + By =
c. Reduce all fractional answers to lowest terms. (7, -3), (4, -8)
A line that passes through the origin and is parallel to x + y = 6.