Which equivalent equation results when completing the square to solve x^2-8x+7=0?

Which Equivalent Equation Results When Completing The Square To Solve X^2-8x+7=0?

Answers

Answer 1
\((x-4)^2\text{ = 9 (option D)}\)Explanation:\(x^2\text{ - 8x + 7 = 0}\)

Using complete the square method:

\(\begin{gathered} x^2\text{ - 8x + 7 = 0} \\ x^2\text{ - 8x = -7} \\ \text{Add half the square of the coefficient of x to both sides:} \\ \text{half the coefficient = -8/2 = -4} \\ \text{square half the coefficient = (-4)}^2 \end{gathered}\)\(\begin{gathered} x^2-8x+(-4)^2=-7+(-4)^2 \\ \text{making it a p}\operatorname{erf}ect\text{ square:} \\ (x-4)^2\text{ = -7 }+(-4)^2 \end{gathered}\)\(\begin{gathered} (x-4)^2\text{ = -7 + 16} \\ (x-4)^2\text{ = 9 (option D)} \end{gathered}\)


Related Questions

What is 6x3-69+12x4-7x(9x3)+7-1?

Answers

Answer:

44

Step-by-step explanation:

6 times 3 is 18 so.. 18 minus 69 would be -36 plus 12 is a positive 1 times 14 would be 14 minus 7 would be 7 7 times 27 would 38 plus 7 would be  45 minus one would be 44

Answer:

-186

Step-by-step explanation:

6x3-69+12x4-7(27)+7-1

18-69+48-189+7-1

-51+48-189+7-1

-3-189+7-1

-192+7-1

-185-1

-186

-2,6,-18,54, what is the common ratio of the sequence

Answers

Answer:

2

Step-by-step explanation:

Answer:

Common Ratio=-3

Step-by-step explanation:

To find any common ratio in a sequence, always take the second number in the sequence and divide it by the first number. However, you must be careful because the common ratio should only be negative if the values in the sequence are alternating between negative and positive. Therefore, if the sequence of numbers is simply decreasing in value, this does not mean that the common ratio is negative. The common ratio would still be positive. If the sequence is decreasing in value, this means that the common ratio would be a fraction or a decimal less than one.

Round 3,389
to the
nearest 100

Answers

Answer:

3400, If it's a decimal version then, 3.39

Step-by-step explanation:

3,389

The 8 is after the 3/the hundreds place. So you round the 8 because the 8 is greater then 5 and then you get 3,400. Decimal version: 3.34, the hundreds place in the decimal is the second digit to the right of the period. 3.389 = 3.34 9 is greater then 5. Your welcome :)

Which of the values satisfy the following in equality? 5M +1 is greater than or equal to four choose all answers that apply

Which of the values satisfy the following in equality? 5M +1 is greater than or equal to four choose

Answers

Solution:

Given the inequality:

\(5m+1\leq4\)

To evaluate the values of m that satisfies the inequality, we have

\(\begin{gathered} 5m+1\leq4 \\ add\text{ -1 to both sides} \\ 5m+1-1\leq4-1 \\ \Rightarrow5m\leq3 \\ divide\text{ both sides by the coefficient of m, which is 5} \\ \frac{5m}{5}\leq\frac{3}{5} \\ \Rightarrow m\leq0.6 \end{gathered}\)

Hence, the value(s) of m that apply to the inequality in the given options is

\(m=0\)

The correct option is

Which of the values satisfy the following in equality? 5M +1 is greater than or equal to four choose

Jenna walked to the
store in 15.4 minutes. She
bought Band-Aids for
$0.55, gauze for $1.29,
and suntan lotion for
$2.89. She gave the
clerk a $10 bill. She left
the store at 3:45 a.m. It
took her 18.4 minutes to
walk home. How much
longer did it take her to
walk home than it took
to walk to the store?

Answers

Answer: 3.0 minutes

Step-by-step explanation:

Factor out the greatest common factor 6x^2 - 14xy

Answers

6x² - 14xy

The greatest common factor is 2x, so we will factor out 2x

Hence;

6x² - 14xy = 2x ( 3x - 7y)

what does a discrete quantitative variable mean?

Answers

Answer:

A discrete quantitative variable is one that can only take specific numeric values (rather than any value in an interval)

Step-by-step explanation:

A discrete quantitative variable is one that can only take specific numeric values (rather than any value in an interval), but those numeric values have a clear quantitative interpretation. Examples of discrete quantitative variables are number of needle punctures, number of pregnancies and number of hospitalizations.

What is the correct formula for calculating kinetic energy?

Answers

Answer:

K.E = 1/2mv²

Kinetic energy

Isolate the variable by adding a constant to each side of the equation 4(x-5)=25

Answers

Answer:

ummm I think u want the answer x= 11 1/4

Answer:

x = 45/4

Step-by-step explanation:

4(x - 5) = 25

4x - 20 = 25

4x - 20 + 20 = 25 + 20

4x = 45

4x/4 = 45/4

x = 45/4

Given the graph of the quadratic function, identify the solutions.

Given the graph of the quadratic function, identify the solutions.

Answers

Answer:  -6 and 0

Explanation:

The solutions, or roots, are the x intercepts of the graph. This is where the curve crosses or touches the x axis. In this case, the two x intercepts are -6 and 0.

How many whole numbers are there between 32 and 96?

Answers

Answer:

there are 20 while numbers between 32 and 96

Step-by-step explanation:

hope it helps and give me a brainliest

The number of whole numbers that come between 32 and 96 will be 64.

What is Algebra?

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The number of whole numbers that come between 32 and 96 is given as,

⇒ 96 - 32

⇒ 64

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You are running a fuel economy study. One of the cars you find is blue. It can travel
45 1/2 miles on 1 1/4 gallons
of gasoline. Another car is red. It can travel
24 4/5 on 4/5 gallons
of gasoline. What is the unit rate for miles per gallon for each​ car? Which car could travel the greater distance on 1 gallon of​ gasoline?

Answers

The unit rate for miles per gallon for eachcar will be 36.4 and 31. And the blue car can travel greater distances on 1 gallon of​ gasoline.

What is the rate?

The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.

You are running an efficiency study. One of the vehicles you find is blue. It can travel 45 ¹/₂ miles on 1 ¹/₄ gallon of fuel. Another vehicle is red. It can travel 24 ⁴/₅ on ⁴/₅ gallons of fuel.

The rate of blue cars is given as,

⇒ (45 ¹/₂) / (1 ¹/₄)

⇒ 45.5 / 1.25

⇒ 36.4 miles per gallon

The rate of red cars is given as,

⇒ (24 ⁴/₅) / (⁴/₅)

⇒ 24.8 / 0.8

⇒ 31 miles per hour

The unit rate for miles per gallon for eachcar will be 36.4 and 31. And the blue car can travel greater distances on 1 gallon of​ gasoline.

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Sally used 8.74 inches of a ribbon to make a bow for her hairband and another 12.32 inches to make a bow for her hat. Determine the total length of ribbon used to make the bows

Answers

Answer:

21.06

Hope this helps

Step-by-step explanation:

Answer is 21.06 inches

A cake shop can make 240 boxes of cakes for 8 days. How many cakes can the shop make in 12 days?​

Answers

Answer:

360 cakes

Step-by-step explanation:

soln:onecake =240\8=30then 12 cakes =30×12=360

Answer:

360

Step-by-step explanation:

240÷8days=30

30×12days=360

Given f(x) = 2x² + 8x - 4 and g(x) = 5x +6, find 3f(x) – 2g(x).

Answers

Step-by-step explanation:

When the problem says 3f(x), it means that you are multiplying f(x) by 3. The same goes for 2g(x).

\(3(2x^2+8x-4)= 6x^2+24x-12\)

\(2(5x+6) = 10x+12\)

Now, we subtract f(x) from g(x) after being multiplied.

\((6x^2+24x-12)-(10x+12)\)

\(6x^2+14x-24\)

How do you solve this equation?

-4=-8+n/2

Answers

Answer:

n = 8

Step-by-step explanation:

-4 + 8 = n/2

4 = n/2

4 x 2 = n

8 = n

2. Which set of numbers have a least common
multiple of 80?
A. 4 and 20
B. 8 and 10
C. 16 and 20
D. 12 and 40

Answers

Answer:

C.

Step-by-step explanation:

Multiples of 16:

16, 32, 48, 64, 80

Multiples of 20:

20, 40, 60, 80, 100.

Here are the options verified:

A. 4 and 20. Incorrect. It takes a while to get to 80 by 4's.B. 8 and 10. Incorrect. Same thing goes with A, but with 8's.C. 16 and 20. Correct.D. 12 and 40. Incorrect. 12 is not a multiple of 80.

Option C is your answer.

write equation that has base of 3 stretched vertically by factor of 2/3 reflected in y axis, asymptote of y=2 and passes through point (0,3,5)

Answers

The exponential equation is \(y = \frac23(3)^{-x+0.74} + 2\)

How to determine the equation?

An exponential function is represented as:

\(y = b^x\)

The base is 3.

So, we have:

\(y = 3^x\)

It is stretched vertically by 2/3.

So, we have:

\(y = \frac23(3)^x\)

When reflected over the y-axis, we have:

\(y = \frac23(3)^{-x}\)

An asymptote of y = 2, makes the function becomes

\(y = \frac23(3)^{-x} + 2\)

Lastly, it passes through the point (0, 3.5).

So, we have:

\(y = \frac23(3)^{-x+h} + 2\)

This gives

\(3.5 = \frac23(3)^{-0+h} + 2\)

\(3.5 = \frac23(3)^{h} + 2\)

Subtract 2 from both sides

\(1.5 = \frac23(3)^{h}\)

Multiply by 3/2

\(2.25 = (3)^{h}\)

Take the logarithm of both sides

log(2.25) = h * log(3)

Solve for h

h = 0.74

Substitute h = 0.74 in \(y = \frac23(3)^{-x+h} + 2\)

\(y = \frac23(3)^{-x+0.74} + 2\)

Hence, the exponential equation is \(y = \frac23(3)^{-x+0.74} + 2\)

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Two mechanics worked on a car. The first mechanic charged $45 per hour, and the second mechanic charged $115 per hour. The mechanics worked for a
combined total of 35 hours, and together they charged a total of $2625. How long did each mechanic work?

Answers

Answer:

The answer to this question is 17.5 hours due to dividing

Step-by-step explanation:

35÷2=17.5

Need help with question

Need help with question
Need help with question

Answers

Answer:

f(2) = 1

x = 0

Step-by-step explanation:

f(2) = 1 since y=1 when x=2.

f(0) = -3 since x=0 when y=-3

What is the diameter of a sphere with a volume of 18174 ft 3 , 18174 ft 3 , to the nearest tenth of a foot?

Answers

Answer

The diameter of the sphere is 32.6ft.

Step-by-step explanation:

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What is the diameter of a sphere with a volume of 18174 ft 3 , 18174 ft 3 , to the nearest tenth of a

Are the 2 triangles congruent?

Are the 2 triangles congruent?

Answers

Answer:

ya they r

Step-by-step explanation:

Yes they are hope this helps :)

how to turn NSQ to SQ statistical problem

Answers

NSQ can be turned into SQ through hypothesis testing and statistical analysis to determine significant relationships and patterns in the data.


To turn a non-statistical question (NSQ) into a statistical question (SQ), we need to rephrase it in a way that allows for statistical analysis. A statistical question is one that can be answered by collecting and analyzing data. Here is an example of how to turn an NSQ into an SQ:

This is a non-statistical question because it cannot be answered by collecting and analyzing data. It is purely a matter of personal preference and cannot be measured quantitatively. However, we can turn it into a statistical question by rephrasing it as:

To answer this question, we would need to collect data from a sample of the population and analyze it statistically. For example, we could conduct a survey of 1000 people and ask them which beverage they prefer. We would then calculate the percentage of respondents who prefer tea over coffee and use statistical methods to estimate the margin of error and confidence interval.

By turning the non-statistical question into a statistical question, we have made it possible to collect and analyze data to answer it. This approach is useful in many fields, including market research, social sciences, and healthcare, where data-driven decisions are increasingly important.

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Harry is training for a cross-country track event. The table shows the proportional relationship between his distance and time. Distance (miles) 0.7 1.4 ? Time (minutes) 7.7 15.4 28.6 How many miles can Harry run in 28.6 minutes? 2.6 miles 2.4 miles 2.1 miles 3 miles

Answers

With respect to the proportional relationship table, Harry can run 2.6 miles in 28.6 minutes

What is the proportional relationship?

If all of the ratios of the variables are equal, then there is a proportional link between the two variables. In a proportional relationship, one variable is, in other words, always a constant value multiplied by the other variable. In other words, a relationship is proportional if it can be explained by multiplying each pair of data values by a certain amount.

Solution Explained:

A/Q, the table shows the proportional relationship between distance and time.

Given,

Distance                   Time
0.7                             7.7
1.4                              15.4
x                                 28.6

We know, the ratios are equivalent in a proportional relationship
If we divide, 0.7 and 7.7, we get 11
so taking 11 as the constant of proportionality, we get

x X 11 = 28.6
x = 28.6 / 11
x = 2.6

Therefore, Harry can run 2.6 miles in 28.6 minutes.

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Answer:

Harry can run 2.6 miles in 28.6 minutes

Step-by-step explanation:

A/Q, the table shows the proportional relationship between distance and time.

Given,

Distance                   Time

0.7                             7.7

1.4                              15.4

x                                 28.6

We know, the ratios are equivalent in a proportional relationship

If we divide, 0.7 and 7.7, we get 11

so taking 11 as the constant of proportionality, we get

x X 11 = 28.6

x = 28.6 / 11

x = 2.6

Therefore, Harry can run 2.6 miles in 28.6 minutes.

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what are the zeros of the functions f(x)=x(x-2)/(x+3)(x-5)??

Answers

\(~~~~~~~\dfrac{x(x-2)}{(x+3)(x-5)}=0\\\\\\\implies x(x-2) = 0\\\\\\\implies x = 0,~ x =2\\\\\text{The zeroes are}~ 0~ \text{and}~ 2.\)

The table shows the weight of bunches of bananas and the price of each bunch

Answers

Wow good to know. But I’m not seeing a picture

Laat season Ria's football team scored 50 goals in 20 matches. This season they scored 60 goals in 25 matches. work out the mean number of goals per match for each season.​

Answers

The last season they scored 2.5 goals per match: 50/20=2.5
This season they scored 2.4 goals per match : 60/25=2.4

6. Write an equation for a line that passes through (6, 12) and (10, 20).

Answers

Answer:

Step-by-step explanation:

Y = mx +b        / Slope intercept form

  mx - y = -b      / Standard form

6m -2 = -b   / Plug in ( 6,2)

-9m -10 = -b / Plug in  ( -9, 10)

 Solve the system of equation for m and b.

 6m -2 = -9m -10  , then   15m = -8      m = -8/15

     b = -6m +2     ,then         b= -6 ( -8/ 15) +2 = 78/15

    -8/15 X -  y = - 78/15

     8X +15y = 78  / Equation of in standard form

Note: This is a different methods of solving this problem. All methods find their roots coming from the basic premises.

Equation of a line in the slope intersect form is

   Y = mx +b

   To convert to standard form of ax + by =c

      Simply move over the parameters

       mx - y = -b        where a = m , and c = -b

      Then we feed coordinates of 2 points in there

       make a 2 equation with 2 unknown( m,b) to

       solve.

EXER 1. Evaluate the following (a) 28-{15 (3+2)​

Answers

The value of the expression 28 - {15 (3+2)} is -47.

To evaluate the expression 28 - {15 (3+2)}, we need to follow the order of operations (also known as PEMDAS/BODMAS) which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Let's break down the expression step by step:

First, we solve the expression inside the parentheses:

3 + 2 = 5

Now, we substitute the result back into the original expression:

28 - {15 * 5}

Next, we perform the multiplication:

15 * 5 = 75

Now, we substitute the result back into the expression:

28 - 75

Finally, we perform the subtraction:

28 - 75 = -47

Therefore, the value of the expression 28 - {15 (3+2)} is -47.

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it cost 13.80 for 5 tickets how much would it cost for 3 tickets

Answers

Answer:

$8.28

Step-by-step explanation:

So, first we must find the price per ticket so we do

13.80/5 = 2.76

So the $2.76 per ticket

So now all we do to find the price of three tickets we times the price per ticket by 3

2.76 x 3 = $8.28

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