Which equivalent equation results when completing the square to solve x^2-8x+7=0?
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Using complete the square method:
[tex]\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}[/tex][tex]\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}[/tex][tex]\begin{gathered} (x-4)^2\text{ = -7 + 16} \\ (x-4)^2\text{ = 9 (option D)} \end{gathered}[/tex]Related Questions
Question
Refer to section 1.3.2, Credit scores, beginning on page 22 of the report.
Arrange the five tiers of credit scores in order, starting with the lowest tier of credit scores.
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The five credit score tiers are listed in ascending order, starting with the lowest tier:
Deep Subprime < Subprime < near prime < prime < super prime
A consumer's credit score may have a big impact on their ability to receive credit. These interactive infographics show how lending practices have changed for borrowers with various credit score profiles.
We focus on the five credit score levels that are commercially available.
The range of subprime credit scores is 580 to 619.
The range of Prime's credit score is from 660 to 719.
Deep subprime credit scores fall below 580.
Near prime credit scores range from 620 to 659.
Super prime credit is defined as having a score of 720 or higher.
The following are the five credit scores, listed from lowest to highest:
Deep Subprime < Subprime < near prime < prime < super prime
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And if you can step by step on how to do it
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The radius of the cylinder is r=3 cm.
The height of the cylinder is h=7 cm.
The expression for the volume of the cylinder is,
[tex]V=\pi r^2h[/tex]Substituting the given values in the above equation,
[tex]\begin{gathered} V=\pi(3\operatorname{cm})^2(7\operatorname{cm}) \\ =\frac{22}{7}\times9cm^2\times7\operatorname{cm} \\ =198cm^3 \end{gathered}[/tex]Thus, option (C) is the correct solution.
Write the coordinates of the vertices after a reflection over the line y=-x
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The coordinates of the vertices after a reflection over the line y=-x are (y, -x)
How to determine the coordinates?From the question, the transformation rule is given as
Reflection over the line y=-x
There are four types of transformation,
These transformations are
DilationRotationReflectionTranslationEach of these transformations have their rule, and they are represented as
Reflection: reflection across linesDilation: k(x, y)Rotation: rotation by anglesTranslation: (x + h, y + k)So, we have
Reflection over the line y=-x
When represented as a coordinate, the coordinate is
(x, y) = (y, -x)
Hence, the coordinates are (y, -x)
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Match the following reasons to the statements given.Given:ABEF isEBDCProve:ACDF is
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Solution
For this case we can do the following:
2. Part of lines FE and AB
4. Transitive
1. Given
5. Definition of parallelogram
3. Opposite sides of a parallelogram are II
Seventh grade > X.9 Reflections over the x- and y-axes: find the coordinates TF8 You have prizes to reveal The point D(-5, -3) is reflected over the y-axis. What are the coordinates of the resulting point, D'?
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Answer
The coordinates of the resulting point, D' = (5, -3)
Explanation
When a given point with coordinates A (x, y) is reflected over the y-axis, the y-coordinate remains the same and the x-coordinate takes up a negative in front of it. That is, A (x, y) changes after being reflected across the y-axis in this way
A (x, y) = A' (-x, y)
So, for this question where the coordinate is D (-5, -3). it changes in the manner,
D (-5, -3) = D' (-(-5), -3) = D' (5, -3)
Hope this Helps!!!
AcuveDetermining If a Number Is a SolutionQUICK CHECKWhich values are solutions to the inequality -3x – 4< 2? Check all of the boxes that apply.-4-2OOO03DONE
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We have the next inequality given:
[tex]-3x-4<2[/tex]Solve the x variable:
Add both sides 4
[tex]\begin{gathered} -3x-4+4<2+4 \\ -3x<6 \end{gathered}[/tex]Divide both sides by 3
[tex]\begin{gathered} \frac{-3}{3}x<\frac{6}{3} \\ -x<2 \end{gathered}[/tex]Finally, multiply both sides by -1:
[tex]\begin{gathered} (-1)(-x)<2(-1) \\ x>-2 \end{gathered}[/tex]Hence, x can take any value greater than -2.
So, the solutions that apply are 0 and 3.
Write vector h= 8i – 11j in vector component form.
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Solution:
Given the vector h;
[tex]h=8i-11j[/tex]The vector in component form is;
[tex]h=<(8,-11)>[/tex]A small company produces baseball and racquetball by the function B(x)=-6x^2+2,556x-106,878. The profit made from the racquetball products can be represented by the function R(x)=-x^2+293x-16,770. If x is the total number of products made, which function best describes P(x), the profit the company makes from these two products?
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profit made from the baseball products
[tex]B(x)=-6x^2+2556x-106878[/tex]Profit made from the racquetball products
[tex]R(x)=-x^2+293x-16770[/tex]Profit made from those 2 products is
[tex]\begin{gathered} P(x)=-6x^2-x^2+2556x+293x-106878-16770 \\ P(x)=-7x^2+2849x-123648 \end{gathered}[/tex]2/5m = 1/2 what is the m stand for ?
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we can interpret m as a constant of proportionality.
Zach can buy a dozen pencils for $1.89, 24 pencils for $3.60, or 36 pencils for $5.49. What is the best buy?
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To know which one is the best option we have to divide the cost in the number of pencils so:
[tex]\frac{1.89}{12}=0.16[/tex]the second option is:
[tex]\frac{3.60}{24}=0.15[/tex]the thert option is:
[tex]\frac{5.49}{36}=1.16[/tex]So the best option is the second option
A focus group of 12 people is to be chosen randomly from among 24 right-handed people and 5 left-handed people. In order to find the probability that 3 of the people chosen are right-handed, you should use
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Let 1 and 2 mean that a person is right-handed or left-handed, respectively.
Consider the probability space as the different groups of 12 people that can be formed with the 29 total people. {(1,1,1,1,1,...1),(2,1,1,1,1,...,1),...}
We need to use the binomial distribution in order to find the answer.
Consider X to be the number of right-handed people in the group.
The probability of X=3 is then:
[tex]Pr(X=3)=\text{ binomial coefficien(}12,3\text{)}(\frac{24}{29})^3(1-\frac{24}{29})^{12-3}[/tex]We used the formula
[tex]\begin{gathered} Pr(X=k)=\text{ binomial coefficient(n,k)}\cdot p^k(1-p)^{n-k} \\ \text{where } \\ k=3 \\ n=12 \\ p=\frac{24}{29} \end{gathered}[/tex]Finally, we need to simplify the expression, as shown below
[tex]\Rightarrow P(X=3)=220(\frac{24}{29})^3(\frac{5}{29})^9=0.0000167[/tex]This is the answer one obtains using the binomial distribution; nevertheless, the actual probability is equal to zero because it is not possible to form a group of 12 people that only contains 3 right-handed people as there are only 5 left-handed people (3+5=8).
76. A company has hired 10 new employees, I men and 3 women. The company mustassign 5 of them to the morning shift, 3 of them to the swing shift, and the restof them to the graveyard shift.(a) (2 points) Find the prob that at least one man is assigned to the swing shift?
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Answer:
[tex]\frac{2519}{2520}[/tex]Explanation:
Here, we want to get the probability that at least one man is assigned to the swing shift
From the question, 3 of the employees are assigned to the swing shift
Thus we have to calculate the probability of:
1 man , 2 men or 3 men
Mathematically, we have that as:
1 - p(all of the swing shift employees are women)
For the swing shift, for all them to be women, we will be selecting 3 out of 3 so the combination here is 3 C 3 which is 1
We now calculate the probability by dividing this value by the total number of possible ways
Mathematically, we have that as follows:
[tex]\frac{1}{10\text{ C 5 }\times\text{ 5 C 3 }^\times\text{ 1}}\text{ = }\frac{1}{2520}[/tex]This is the probability of placing all of the women on the swing shift
So, the probability that at least 1 man is assigned will be:
[tex]1-\text{ }\frac{1}{2520}\text{ = }\frac{2519}{2520}[/tex]Jan 10, 7:17:08 PM Which equation represents a line which is perpendicular to the line x - 2y = -14? Oy= -27 -1 Oy= 2x + 8 Submit Answer Oy=x+4 Oy = -x + 2
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You need to determine which line is perpendicular to the line
[tex]x-2y=-14[/tex]For two lines to be considered perpendicular their slopes must be the inverse positive, that is, if, for example, you have the lines
[tex]y_1=mx_1+b[/tex][tex]y_2=nx_2+c[/tex]For them to be perpendicular one slope must be the inverse negative of the other such as
[tex]n=-\frac{1}{m}[/tex]The first step is to write the given line in slope-intercept form:
1) Pass the x term to the right side of the equal sign
[tex]\begin{gathered} x-2y=-14 \\ x-x-2y=-14-x \\ -2y=-x-14 \end{gathered}[/tex]2) Divide both sides of the expression by "-2"
[tex]\begin{gathered} -\frac{2y}{-2}=-\frac{x}{-2}-\frac{14}{-2} \\ y=\frac{1}{2}x+7 \end{gathered}[/tex]The slope of the line is
[tex]m=\frac{1}{2}[/tex]So the slope of a line perpendicular to it will be the inverse negative of it
[tex]\begin{gathered} n=-(\frac{1}{\frac{1}{2}}) \\ n=-2 \\ \end{gathered}[/tex]The correct option is the one that has slope -2
Draw the graph of the line that is parallel to Y -3 = 1/3(x+2) and goes through the point (1, 7)
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Explanation:
We are required to draw the graph of the line that is parallel to y-3=1/3(x+2) and goes through the point (1, 7).
Given the equation of the line:
[tex]y-3=\frac{1}{3}(x+2)[/tex]Compare the equation with the slope-point form of a line:
[tex]$$y-y_1=m(x-x_1)$$[/tex]• The slope of the line, m=1/3
,• In addition, the line goes through the point (1,7)
Substitute these values into the point-slope form given above:
[tex]y-7=\frac{1}{3}(x-1)[/tex]Finally, graph the line by looking for another point in addition to point (1,7):
When x=-2
[tex]\begin{gathered} y-7=\frac{1}{3}(x-1) \\ y-7=\frac{1}{3}(-2-1) \\ y-7=\frac{1}{3}(-3) \\ y-7=-1 \\ y=-1+7 \\ y=6 \\ \implies(-2,6) \end{gathered}[/tex]Join the points (1, 7) and (-2, 6) to plot the line.
Answer:
The graph showing the two points is attached below:
Note:
For comparison purposes and to show that the two lines are parallel, the other graph is added below:
absolute value of v-5>3
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Answer: v=8
Step-by-step explanation:
-5+5=0
3+5=8
v=8
Find ca^2+b^2=c^2 3^2+2^2=c^29+4=13
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Substituting with a = 3 and b = 2, we get:
[tex]\begin{gathered} 3^2+2^2=c^2 \\ 9+4=c^2 \\ 13=c^2 \\ \sqrt[]{13}=c \\ 3.6\approx c \end{gathered}[/tex]Can I get help w this pleaseThe dimensions of a rectangular prism are quadrupled.if the original surface area was 225ft^2 was is the new surface area?
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Answer:
Concept:
Doubling the dimensions of a prism will increase the new area by 4 times the original area
Tripling the the dimensions of the prism will increase the new area by 9 times the original area
Quadrupling will increase the new area by 16 times the original area
Given that the original area given is
[tex]=225ft^2[/tex]The new area therefore will be
[tex]\begin{gathered} 16\times225 \\ =3600ft^2 \end{gathered}[/tex]Hence,
The final answer will be
[tex]\rightarrow3600ft^2[/tex]which calculation does not show the surface area of the cube?
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Given: A cube with side 6.5 cm
Required: Which calculation does not show the surface area of the cube.
Explanation:
Surface area of cube with side a is 6a².
So here the surface area of cube is
[tex]6(6.5)^2[/tex]Oprion 2, 3 and 4 reflects the calculation correctly.
But option A is actually the volume of the cube, it is not a correct way to show surface area of the cube.
Final Answer: option A is correct.
Convert each angle in radians to degrees 3π/4
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we have only to change pi by 180, and solve the multiplication
[tex]\frac{3\pi}{4}\rightarrow3\cdot\frac{180}{4}=135^{\circ}[/tex]Classwork Area of Algebra Tiles 1 An If the side lengths of a tile can be measured exactly, then the area of the tile can be calculated by multiplying these two lengths together. The area is measured in square units. For example, the tile at right measures 1 unit by 5 units, so it has an area of 5 square units. 1 The next tile at right has one side length that is exactly one unit long. If the other side length cannot have a numerical value, what can it be called? ?
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The other side of a tile can be called as width of hte tile
Hello I will send a picture of my equation I need help on.
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Answer:
p = -5
Explanation:
Given the expression
p + 5p - 2p + 4p = -40
6p - 2p + 4p = -40
6p + 2p = -40
8p = -40
Divide both sides by 8
8p/8 = -40/8
p = -5
Hence the value of p is -5
In a middle school with 300 students, there are 40% boys, 1/3 of the students wear glasses, and 15% of the girls wear glasses. What is the probability (= how many percent is it) that a randomly selected student does not wears glasses? (Round the percentage to the nearest hundredth) *
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We know that
• There are 300 students.
,• 40% are boys (this means 60% are girls).
,• 1/3 of the students wear glasses.
If 1/3 of the students wear glasses, then 2/3 of the students don't wear glasses. Let's find 2/3 of 300.
[tex]\frac{2}{3}\cdot300=\frac{600}{3}=200[/tex]Therefore, 200 students don't wear glasses.
Then, we divide to find the probability.
[tex]P=\frac{200}{300}=0.6667[/tex]Then, we multiply by 100.
[tex]0.6667\cdot100=66.67[/tex]Therefore, the probability is 66.67%.A company produces 11 times as many rings on shift 1+ shift to if I total of 12,000 rings were produced how many were produced on each shift
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Shift 1 produced 11000 rings and Shift 2 produced 1000 rings.
What does "parent company" mean and how Do Parent Companies Work?
A single firm that owns a majority stake in another company or groups of companies is known as a parent company.
Parent corporations are created through acquisition, merger, spin-off, or carving out of subsidiaries.
A parent company is a business that controls a significant portion of another business, giving it operational authority over that business.
Given :-
Production of Shift 1 = 11 times of Production of Shift 2
total production = 12,000 rings
production of ( Shift 1 + Shift 2 ) = Total production
on solving we get,
Production of Shift 1 = 11,000 rings
Production of Shift 2 = 1,000 rings
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Which transformations can be used to carry ABCD onto itself? The point ofrotation is (3,2). Check all that apply.у5DС321АВ012345
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The point of rotation is (3, 2). We would subtract this origin from each vertex. Let us consider vertex D(1, 3). Subtracting, we have (1 - 3, 3 - 2) = (- 2, 1).
if we rotate it 180 degrees, we have (- - 2, - 1) = (2, - 1). If we add the vertex again, it becomes (- 2 + 3, 1 + 2) = (1, 3). If we reflect it over the line, y = 2, we have (3, 2)
The correct options are
B. Rotate 180 degrees
D) reflection over the line, y = 2
solving rational equations 1[tex] \frac{9x}{x - 2} = 6[/tex]2[tex] \frac{7}{x + 2} + \frac{5}{x - 2} = \frac{10x - 2}{x {}^2{ - 4} } [/tex]3[tex] \frac{ x - 1}{2x - 4} = \frac{2x - 2}{3x} [/tex]step by step instructions please thank you
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the given expression is.,
[tex]\frac{9x}{x-2}=6[/tex][tex]\begin{gathered} 9x=6x-12 \\ 9x-6x=-12 \\ 3x=-12 \\ x=-\frac{12}{3} \\ x=-4 \end{gathered}[/tex]also, the given expression is,
[tex]\frac{7}{x+2}+\frac{5}{x-2}=\frac{10x-2}{x^2-4}[/tex][tex]\begin{gathered} \frac{7x-14+5x+10}{x^2-4}=\frac{10x-2}{x^2-4} \\ 12x-4=10x-2 \\ 12x-10x=4-2 \\ 2x=2 \\ x=\frac{2}{2}=1 \\ x=1 \end{gathered}[/tex]a. Solve for c: E = mc^2
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ANSWER
[tex]\text{c = }\sqrt[]{\frac{E}{m}}[/tex]EXPLANATION
We want to solve for c in:
[tex]E=mc^2[/tex]To do that, we will make c the subject of the formula:
[tex]\begin{gathered} E=mc^2 \\ \Rightarrow\text{ }\frac{E}{m}=c^2 \\ Find\text{ the square root of both sides:} \\ \Rightarrow\text{ c = }\sqrt[]{\frac{E}{m}} \end{gathered}[/tex]We have solved for c.
- What is the closed linear form of the sequence 3, 4,5, 6, 7, ...?
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Solve the system using the elimination method:2x - y + z = -26x + 3y - 4z = 8-3x + 2y + 3z = -6
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multiply 2x - y + z = - 2 for 3
[tex]6x-3y+3z=-6[/tex]then sunstract the equation 1 and 2
[tex]\begin{gathered} 6x+3y-4z=8 \\ 6x-3y+3z=-6 \\ 6y-7z=14 \end{gathered}[/tex]multiply -3x+2y+3z=-6 for 2
[tex]-6x+4y+6z=-12[/tex]adding
[tex]\begin{gathered} -6x+4y+6z=-12 \\ \underline{6x-3y+3z=-6} \\ y+9z=-18 \end{gathered}[/tex]multiply y+9z=-18 for 6
[tex]6y+54z=-108[/tex]Subtracting
[tex]\begin{gathered} 6y+54z=-108 \\ \underline{6y-7z=14} \\ 61z=-122 \end{gathered}[/tex]then solve
[tex]\begin{gathered} 61z=-122 \\ \frac{61z}{61}=\frac{-122}{61} \\ z=-2 \end{gathered}[/tex][tex]\begin{gathered} 6y-7\mleft(-2\mright)=14 \\ 6y+14=14 \\ 6y+14-14=14-14 \\ 6y=0 \\ y=0 \end{gathered}[/tex][tex]\begin{gathered} 6x-3\cdot\: 0+3\mleft(-2\mright)=-6 \\ 6x-6=-6 \\ 6x-6+6=-6+6 \\ 6x=0 \\ x=0 \end{gathered}[/tex]answer is: x = 0, y = 0 and z = - 2
Nathan loved learning about earthquakes in science class. He told his brother that up until a 7.8-magnitude earthquake hit Nepal in 2015, Mount Everest had been moving northeast at a rate of 7.7×10^-6 centimeters per minute. What would be the most appropriate unit for Nathan to use instead of centimeters per minute?
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The most appropriate unit for Nathan to use instead of centimeters per minute is centimeters per year.
What is an earthquake?An earthquake simply means a rapid motion of the solid layer of the Earth.
In this case, Nathan told his brother that up until a 7.8-magnitude earthquake hit Nepal in 2015, Mount Everest had been moving northeast at a rate of 7.7×10^-6 centimeters per minute.
Since the year is being discussed, the unit should be based on the year.
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Use the graph of y = f (x) to find the following value of f. f(2) =
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Answer:
f(2)=4
Explanation:
Consider the graph below:
When x=2, the value of f(x) = 4 (the poiny circled in blue above).
Therefore:
[tex]f(2)=4[/tex]The value of f(2) is 4.