Solve x² + 8x - 3 = 0 using the completing-the-square method.
Ox=4± √3
Ox=4+√3
Ox=4±√19
Ox=4±√19
Answers
The sοlutiοns tο x² + 8x - 3 = 0 using the cοmpleting-the-square methοd are x = -4 ± √19.
What is square?A square is a geοmetric shape with fοur equal sides and fοur equal angles. In algebra, the term "square" is οften used tο refer tο raising a number tο the pοwer οf 2, οr multiplying a number by itself.
Tο sοlve the quadratic equatiοn x² + 8x - 3 = 0 using the cοmpleting-the-square methοd, we fοllοw these steps:
Mοve the cοnstant term tο the right-hand side οf the equatiοn:
x² + 8x = 3
Cοmplete the square by adding the square οf half the cοefficient οf x tο bοth sides οf the equatiοn:
x² + 8x + (8/2)² = 3 + (8/2)²
x² + 8x + 16 = 25
Rewrite the left-hand side οf the equatiοn as the square οf a binοmial:
(x + 4)² = 25
Take the square rοοt οf bοth sides οf the equatiοn, remembering tο cοnsider bοth the pοsitive and negative square rοοts:
x + 4 = ±5
Sοlve fοr x by subtracting 4 frοm bοth sides οf each equatiοn:
x = -4 ±5
Sο, the sοlutiοns tο the equatiοn x² + 8x - 3 = 0 are:
x = -4 + 5 = 1
x = -4 - 5 = -9
Therefοre, the sοlutiοns tο the equatiοn are x = 1 and x = -9.
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Related Questions
In the figure, BC=26, EF=22. Find OD. Round to the nearest hundredth.
Answers
Check the picture below.
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2 \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{13}\\ a=\stackrel{adjacent}{OD}\\ o=\stackrel{opposite}{11} \end{cases} \\\\\\ (13)^2= (OD)^2 + (11)^2\implies 13^2-11^2=OD^2\implies 48=OD^2 \\\\\\ \sqrt{48}=OD\implies 6.93\approx OD[/tex]
Round 453, 605 to the nearest 10,000
Answers
Answer:450,000
Step-by-step explanation:It becomes 450,000 thousand because anything under 5 in the ten thousands place becomes a zero and anything in front of it which is the 4 will stay the same.
if i'm given a list of values and asked to graph the average and standard deviation, what kind of graph should i use
Answers
To graph the average and standard deviation of a given list of values, you should use a bar graph or a histogram.
1. Calculate the average (mean) of the given list of values.
2. Calculate the standard deviation of the given list of values.
3. Create a bar graph or histogram with two bars.
4. Label the first bar as "Average" and set its height to the calculated average value.
5. Label the second bar as "Standard Deviation" and set its height to the calculated standard deviation value.
This graph will visually represent the average and standard deviation of the given list of values.
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a right conical tank with the point oriented down, a height of 14 feet, and a radius of 6 feet has sprung a leak. how fast does the depth of water change when the water is 2 feet high if the cone leaks water at a rate of 13 cubic feet per minute?
Answers
The depth of water changes at a rate of -13/72π feet per minute when the water is 2 feet high.
To begin, we must use the formula for the volume of a cone, which is given as:
V = 1/3πr2hwhere V represents the volume, π represents the constant pi, r represents the radius, and h represents the height.
Substituting the given values into the formula, we get:
V = 1/3π (6 ft)2(14 ft)V = 1/3π (36 ft2) (14 ft)V = 1/3π (504 ft3)V = 168π ft^3
Now, we must determine the rate at which water is leaking. It is given that the cone leaks water at a rate of 13 cubic feet per minute. This implies that the volume of the water reduces by 13 cubic feet every minute. Therefore, the rate of change of the volume of water is -13 cubic feet per minute. Here, the negative sign indicates a decrease in the volume of water.
Now, we must find how fast the depth of water changes when the water is 2 feet high. Let d represent the depth of water. Then, the volume of water is given as:
V = 1/3πr^2d
We know that when d = 2 ft, V = 1/3π(6 ft)2(2 ft)
V = 8π ft^3
Now, we must determine how fast the volume of water is changing with respect to time when d = 2 ft. We differentiate the expression for V with respect to time to get:
dV/dt = (d/dt)[1/3πr2d]
dV/dt = 1/3πr^2(d/dt)[d]
dV/dt = 1/3πr^2(d/dt)[2]
dV/dt = 2/3πr^2
The rate of change of the volume of water with respect to time is given as -13 cubic feet per minute. Therefore, substituting this into the expression above, we get:
-13 = 2/3π(6 ft)2(d/dt)
When we simplify the above equation, we get:
d/dt = -13/72π
Therefore, when the water is 2 feet high, the depth of the water changes at a rate of -13/72π feet per minute.
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Which postulate proves the two triangles are congruent?
A. none
B. HL
C. SAS
D. AAS
Answers
Answer:
AAS
Step-by-step explanation:
They share the same side, and the 2 angles are the same as well and match
Who invented the number zero?
Answers
Aryabhata, the famous Indian mathematician discovered 0.
What is an Integer?Integers include all whole numbers and negative numbers. This means if we include negative numbers along with whole numbers, we form a set of integers.
The concept of zero was first developed by ancient Indian mathematicians as early as the 5th or 6th century CE. However, the actual symbol for zero (a small circle) was invented by the Indian astronomer and mathematician Brahmagupta in 628 CE.
Aryabhatta, the famous Indian mathematician discovered 'zero'. Grutsamad discovered the process of writing zeroes after figures.
Hence, Aryabhata, the famous Indian mathematician discovered 0.
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The area of a rectangle is 6x^2 + 9x, and its width is 3x. What is the length of the rectangle?
Answers
Answer:
L=2x-3
Step-by-step explanation:
A =L×W
Given,
A=6x²-9x
W=3x
Substituting into the main equation
6x²-9x=L×(3x)
3x(2x-3)=L×(3x)
divide both sides by 3x
2x-3=L
L=2x-3
On a map, the distance between two towns is 4.25 inches. The map scale is 1 inch = 16 miles. What is the actual distance between the towns?
Answers
Step-by-step explanation:
4.25 inches * 16 miles / 1 inch = 68 miles
For each of the values a=1, a=2,a=4, and a=6
Answers
The number of minutes, m, that it takes to
print a batch of newspapers is inversely
proportional to the number of printers used,
n.
The equation of proportionality is m =
100
n
Calculate how long it will take to print a
batch of newspapers if 20 printers are
used.
If your answer is a decimal, give it to 1 d. p.
Answers
It will take 5 minutes to print a batch of newspapers if 20 printers are used.
What is proportionality?
Proportionality is a mathematical relationship between two variables, where one variable is a constant multiple of the other. In other words, two quantities are proportional if they maintain a constant ratio to each other, meaning that as one quantity increases or decreases, the other quantity changes in the same proportion.
We are given that the time it takes to print a batch of newspapers, m, is inversely proportional to the number of printers used, n, and the equation of proportionality is:
m = k/n
where k is a constant of proportionality. We are also given that when k = 100, the equation is satisfied. So we can substitute k = 100 into the equation to get:
m = 100/n
To find the time it will take to print a batch of newspapers if 20 printers are used, we can substitute n = 20 into the equation:
m = 100/20 = 5
So it will take 5 minutes to print a batch of newspapers if 20 printers are used. Rounded to 1 decimal place, the answer is 5.0 minutes.
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Graph the function y = 2/x-2 +1
**Please use dotted lines to indicate the vertical and horizontal asymptotes. **Please clearly indicate at least 3 (three) points on your graph. **No computer-generated graphs will be accepted
Answers
Answer:
Step-by-step explanation:
Domain: D=R-{2}
Asymptote vertical: x=2
Asymptote horizontal: y=1
Hey, I tried to graph this function, I hope you understand something here...
a sphere has a radius of 2.7cm what is its volume to the nearest cubic centimeter
Answers
Answer:
around 82.45 cubic cm
Step-by-step explanation:
The formula for the volume of a sphere is (4/3) * pi * r^3.
Since the radius is 2.7, we can plug this into the formula to get (4/3) * pi * 19.683.
This simplifies to 26.244pi, which is around 82.45 cubic cm.
Use the figure below to answer the following questions. NOT TO SCALE!
10
2
12
6
6
a. Give the perimeter of the figure.
b. Give the area of the figure.
Junits2
c. If the figure above was a yard measured in feet, and sod cost $2.99 per square foot, how much would it cost to sod the yard.
units
d. If the figure above was a garden measured in feet, and you wanted to put up edging that cost $8.87 per 6 foot piece, how much would it cost to
edge the garden? (you cannot by part of a piece) S
Answers
Perimeter of the figure is 56 units.
Area of figure is 100sq. units²
Cost to sold the yard is $299
For edging, total cost is $82.8
Define perimeter and areaPerimeter and area are two important measurements used in geometry to describe the size and shape of two-dimensional figures.
Perimeter is the measurement of the distance around the outside of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape.
Area is the measurement of the space inside a two-dimensional shape. It is the amount of surface that the shape covers. For example, the area of a rectangle can be calculated by multiplying the length of the rectangle by its width.
Perimeter of the figure=sum of all sides of the figure
=10+4+2+12+6+6+2+4+6+4=56 units.
Area of figure=10×4+6×6+4×6
=40+36+24
=100sq. units²
Cost to sold the yard=area× cost per square foot
=100×2.99
=$299
Given: edging costs $8.87 per 6 foot piece
For edging, total cost =total perimeter/no.of foot piece×$8.87
=(56/6)×8.87
=496.72/6
=$82.78≈$82.8
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Angela, the head of the office party planning committee, sent two coworkers, Kevin and Dwight, to the party store to purchase party hats and party whistles. Kevin purchased four packs of party hats and three packs of party whistles, and paid a total of $15.53. Dwight purchased three packs of party hats and four packs of party whistles, and paid a total of $13.73. When they returned to the office, Angela informed them that they were supposed to buy a total of four packs of party hats and four packs of party whistles and sent them back to the store to straighten things out. How much should they be refunded?
Answers
The owner of the Jazz has given out 10 signed basketballs at a pre-season event. Their goal is to give out 3 basketballs each week during the season. Function b gives the total number of basketballs as a function of the number of weeks since the pre-season event.
Answers
describe four right that individuals in relationships have when they stay together
Find the probability of rolling a 6-sided dice and getting a number that is a divisor of 20.
Answers
Answer:
The divisors of 20 are 1, 2, 4, 5, 10, and 20. A 6-sided dice has the numbers 1 to 6 on its faces. The probability of rolling a number that is a divisor of 20 is the number of favorable outcomes divided by the number of possible outcomes. There are four favorable outcomes (1, 2, 4, and 5) and six possible outcomes (1 to 6). Therefore, the probability is 4/6 or 2/3 or about 0.67.
using diagonals from a common vertex, how many triangles could be formed from a 14-gon?
Answers
Using diagonals from a common vertex of a 14-gon, a total of 11 triangles can be formed.
To see why, we can apply the formula for the number of triangles formed by drawing all the diagonals from a single vertex of a polygon, which is (number of sides - 2). For a 14-gon, the formula gives us:
number of triangles = (14 - 2) = 12
However, we need to subtract one from the total because the vertex where the diagonals are drawn from is not included in any of the triangles. Therefore, the number of triangles formed by drawing diagonals from a common vertex of a 14-gon is:
number of triangles = 12 - 1 = 11
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Answer: 14-2=12
Step-by-step explanation:
Question
Solve the equation. Check your solutions.
∣x−7∣=∣2x−8∣
Answers
Answer:
x = 1, x = 5
Step-by-step explanation:
You want the solutions to the absolute value equation ...
|x -7| = |2x -8|
Piecewise equationEach of the absolute value functions is equivalent to a piecewise-defined function. The boundary for the pieces is the turning point of the absolute value function, where its argument is zero.
The turning points are ...
x -7 = 0 ⇒ x = 7
2x -8 = 0 ⇒ x = 8/2 = 4
This means the equivalent piecewise equation will have 3 pieces. We know the absolute value function is defined as ...
[tex]|x|=\begin{cases}-x&\text{for }x < 0\\x&\text{for }x\ge0\end{cases}[/tex]
If we write the equation in the form |x -7| - |2x -8| = 0, we have ...
[tex]0=\begin{cases}-(x-7)-(-(2x-8))&\text{for }x < 4\\-(x-7)-(2x-8)&\text{for }4\le x < 7\\(x-7)-(2x-8)&\text{for }7\le x\end{cases}[/tex]
x < 4The equation simplifies to ...
-x +7 +2x -8 = 0
x -1 = 0 . . . . collect terms
x = 1 . . . . . . a value in the domain. This is one solution.
4 ≤ x < 7The equation simplifies to ...
-x +7 -2x +8 = 0
15 = 3x . . . . . . . . . . add 3x
5 = x . . . . . . . . a value in the domain. This is another solution
7 ≤ xThe equation simplifies to
x -7 -2x +8 = 0
-x +1 = 0
x = 1 . . . . . . . . . not in the domain 7 ≤ x, so not a solution
The solutions are x = 1 and x = 5.
__
Check
|1 -7| = |2·1 -8| ⇒ |-6| = |-6| . . . . true
|5 -7| = |2·5 -8| ⇒ |-2| = |2| . . . . true
Both solutions check in the original equation.
Write a recursive sequence that represents the sequence defined by the following
explicit formula:
an = -2-4(n − 1)
Answers
an = -2-4(n-1)
To write a recursive sequence that represents this sequence, we need to find a formula for the nth term in terms of the (n-1)th term. We can do this by substituting (n-1) for n in the explicit formula:
a(n-1) = -2-4((n-1)-1)
a(n-1) = -2-4(n-2)
We can simplify this expression to get:
a(n-1) = -2-4n+8
a(n-1) = 6-4n
Therefore, the recursive formula for the sequence is:
a1 = -2 (the first term is given)
an = 6-4(n-1) for n > 1
We can check that this recursive formula generates the same sequence as the explicit formula by calculating the first few terms:
a1 = -2
a2 = 6-4(2-1) = 2
a3 = 6-4(3-1) = -2
a4 = 6-4(4-1) = -6
a5 = 6-4(5-1) = -10
We can see that these are the same values as we would get from the explicit formula.
Using v^2 - u^2 =2as, find " v " when s = 21, u = 4 and a = 2.
Answers
Answer:
v = 10
Step-by-step explanation:
[tex] \dashrightarrow \: { \sf{ {v}^{2} - {u}^{2} = 2as}} \: \: \: \\ \\ \dashrightarrow \: { \sf{ {v}^{2} = {u}^{2} + 2as }} \: \: \: \\ \\ \dashrightarrow \: { \sf{v = \sqrt{ {u}^{2} + 2as} }} \\ \\ \: \: \: \: \: \: \: { \colorbox{lightblue}{substitute \: variables}} \\ \\ \dashrightarrow \: { \sf{v = \sqrt{ {4}^{2} + 2(2 \times 21) } }} \\ \\ \dashrightarrow \: { \sf{v = \sqrt{16 + 84} }} \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\\dashrightarrow \: { \sf{v = \sqrt{100} }} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \dashrightarrow \: { \sf{v = 10}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
find the circumference of 80 cm using π ² = 3.14
Answers
Answer:
....
Step-by-step explanation:
can you provide an image if the question instead...
1. What is the vertex of the parabola?
Answers
Answer:
Step-by-step explanation: frost add the vertical and horizontal axis to find your nearest angle
Explanation: it looks about right
Mr. Hesch has 4 stations set up in his classroom. Each station is labeled with a color: blue, purple, green, or yellow. As each student enters the classroom, they spin the spinner to decide at which station they will start. What is the probability a student spins purple?
Answers
The probability of spinning purple on the spinner is 1/4 or 25%.
What is permutation and combination?Calculating the variety of ways to select or arrange a collection of items is a key component of the probability theory concepts of permutation and combination. The key distinction between combination and permutation is whether or not order matters. Contrarily, combination refers to the variety of ways to choose a smaller subset of items from a larger collection, where the order of the items is irrelevant. For instance, there are three potential two-letter combinations if you have the letters A, B, and C: AB, AC, and BC.
Given there are 4 stations, thus he spinner is equally likely to land on any of the four colors.
The probability of spinning purple is 1/4 or 25%.
Hence, the probability of spinning purple on the spinner is 1/4 or 25%.
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Determine the value of k such that the points whose coordinates are given lie on the same line. (k, 2), (0, −2), (10, −7)
Answers
The value of k that makes the three points lie on the same line is -8.
To determine the value of k such that the given points lie on the same line, we can use the slope-intercept form of the equation of a line, which is:
y = mx + b
where m is the slope of the line, and b is the y-intercept.
First, we can find the slope of the line passing through the two points (0, -2) and (10, -7):
m = (y2 - y1) / (x2 - x1)
m = (-7 - (-2)) / (10 - 0)
m = -5 / 10
m = -1/2
Now, we can use the slope-intercept form with the point (0, -2) to find the value of b:
-2 = (-1/2)(0) + b
b = -2
So the equation of the line passing through the two points (0, -2) and (10, -7) is:
y = (-1/2)x - 2
To check if the point (k, 2) lies on this line, we can substitute k for x and 2 for y in the equation:
2 = (-1/2)k - 2
4 = (-1/2)k
k = -8
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your recipe calls for 7 ounces of granulated sugar, but your kitchen scale only measures weight in grams. how many grams of granulated sugar will you need to measure to equal 7 ounces?
Answers
Answer:198.447
Step-by-step explanation:
just search 7 ounces to grams
Consider the following square pyramid:
Calculate the Volume of the pyramid.
Volume = _____ m3
Answers
The Volume of the pyramid.
Volume = 288.67 m³
As the volume of the pyramid is the amount of space enclosed inside the pyramid, the formula to find the volume of a square pyramid is given as;
Volume = (1/3) × base area × height.
Where: Base area (B) = s²
Where; s = length of the square pyramid side
And, Height (h) = perpendicular height to the base.
Substituting the given values in the formula we get;
Volume = (1/3) × s² × h
Given, s = 8.5m and h = 12m
Therefore, Volume = (1/3) × 8.5² × 12
= (1/3) × 72.25 × 12
= 288.67 m³
Thus, the volume of the given square pyramid is 288.67 m³, to the nearest hundredth of a cubic meter.
The volume of any pyramid is a measure of the total amount of space enclosed within the pyramid. If you have a pyramid of a specific shape and size, you can calculate its volume by using an appropriate formula. In this case, we have been given the length of the square pyramid side (s) and the perpendicular height (h) of the pyramid to the base. We can use the formula to calculate the volume of the pyramid.
The formula is Volume = (1/3) × base area × height.
For a square pyramid, the base area is the area of the square that forms the base. Since all four sides of the square are of equal length, the area is given as the square of the length of one of the sides. Thus, Base area (B) = s².
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c) (-1,2) m = -4
What is the equation of the line?
Answers
Answer:
Point-slope form:
[tex]y - 2 = - 4(x + 1)[/tex]
Slope-intercept form:
[tex]y = - 4x - 2[/tex]
Standard form:
[tex]4x + y = - 2[/tex]
Step-by-step explanation:
[tex]y - 2 = - 4(x + 1)[/tex]
[tex]y - 2 = - 4x - 4[/tex]
[tex]y = - 4x - 2[/tex]
[tex]4x + y = - 2[/tex]
Pls help right away asap 20 point question!!
Answers
The answer of the given question is , the predicted average retail price of a car in 2003 is $9860.40.and the car will be worth $814 in the year 2010.
What is Regression Equation?A regression equation is a mathematical formula that is used to describe the relationship between two or more variables. It is typically used in statistical analysis to model the relationship between a dependent variable and one or more independent variables.In simple linear regression, there is only one independent variable, and the regression equation takes the form of a straight line. In multiple regression, there are two or more independent variables, and the regression equation takes the form of a more complex mathematical function.
Using a calculator, we can input the data points into a regression equation to find the line of best fit. Using the given data, we get the regression equation:
y = -1357.4x + 18003.8
where y represents the retail price of a car and x corresponds to the year, with x = 1 representing 1998.
To predict the average retail price of a car in 2003, we need to substitute x = 6 (since 2003 corresponds to x = 6) into the regression equation:
y = -1357.4(6) + 18003.8
y = -8144.4 + 18003.8
y = 9860.4
So, the predicted average retail price of a car in 2003 is $9860.40.
To determine the year when the car will be worth $814, we need to substitute y = 814 into the regression equation and solve for x:
814 = -1357.4x + 18003.8
Simplifying, we get:
-1357.4x = -17189.8
x = 12.65
Rounding up to the nearest whole number, we get x = 13, which corresponds to the year 2010. Therefore, the car will be worth $814 in the year 2010.
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How to solve a system of equations by graphing
Answers
According to the solution we have come to find that, Write the two equations in the form y = mx + b, where m is the slope and b is the y-intercept.
What is graph?In mathematics, a graph is a collection of vertices or nodes and edges, where each edge connects a pair of nodes.
To solve a system of equations by graphing, follow these steps:
Write the two equations in the form y = mx + b, where m is the slope and b is the y-intercept.
Plot the y-intercept of each equation on the y-axis.
Use the slope of each equation to find one or two more points on the line, and plot these points.
Draw a line through the plotted points for each equation.
Look for the point where the two lines intersect. This point represents the solution to the system of equations.
Check the solution by plugging in the coordinates of the intersection point into both equations. If the coordinates satisfy both equations, then the point is the correct solution.
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Differentiate y = 7x^4.
Answers
Therefore, the derivative of y = 7x⁴ with respect to x is dy/dx = 28x³.
What is differentiation?Differentiation is a mathematical concept that refers to the process of finding the derivative of a function. The derivative of a function is the rate at which the function changes with respect to its independent variable. In other words, it measures how quickly the output of the function is changing as the input value is changing.
The derivative of a function can be used to determine many properties of the function, such as its slope, maximum and minimum values, and whether it is increasing or decreasing. It is an important tool in calculus and is used in many fields, including physics, engineering, economics, and finance.
The process of differentiation involves applying specific rules to a given function to determine its derivative. The most common method of differentiation is using the power rule, which states that the derivative of a function raised to a power is equal to the product of the power and the function raised to the power minus one. Other rules include the product rule, the quotient rule, and the chain rule, which are used to differentiate more complex functions.
by the question.
To differentiate y = 7x⁴, we need to use the power rule of differentiation, which states that if [tex]y = kx^{n}[/tex], where k is a constant and n is a non-negative integer, then the derivative of y with respect to x is dy/dx = [tex]\frac{dy}{dx} = nkx^{(n-1)}[/tex].
Using this rule, we can differentiate y = 7x⁴ as follows:
dy/dx = 47[tex]x^{4-1}[/tex] [applying the power rule]
dy/dx = 28x³
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