The solution to the quadratic equation x² - 6x + 7 = 0 is found by modifying the equation to the form (x - h)² = k, adding 9 to each side, and then taking the square root of each side to solve for x, resulting in x = 3 ± √2.
Explanation:To complete the square and solve the quadratic equation x² - 6x + 7 = 0, we need to perform a few steps.
First, we need to modify the equation to the form (x - h)² = k by manipulating the x² - 6x part of the equation. By taking half of the coefficient of x (which is -6) and squaring it, we will get 9. Adding 9 to both sides of the equation will give us (x - 3)² = 2. Finally, to solve for x, we take the square root of each side, resulting in x - 3 = ±√2. Solving for x, we find that the solutions of the quadratic equation are x = 3 ± √2. Learn more about Solving Quadratic Equation here:
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Your friend Zoe is very earnest about the benefits of her special diet. She believes that having kale for breakfast every day will lower your cholesterol.
4a. What's the best method for testing Zoe's claim: a survey, an observational study, or an experiment? Give at least one reason to support your answer. (4 points)
4b. Describe how you would set up a test to determine how much truth there is to Zoe's claims. In particular, what steps would you take to make sure the results were unbiased and valid?
Help please i can’t figure this out
Which of the values in the set {2, 3, 4, 5} is a solution to the equation 2x + 4 = 10?
A. 2
B. 3
C. 4
D. 5
Answer:
Your answer would be B!
Step-by-step explanation:
I took the test myself just now and got it right <3
Ken's cafe serves hot cocoa.each serving has 9 grams of chocolate.how many grams of chocolate are in 8 servings of hot cocoa?
the school cafeteria served 125.6 liters of milk on Monday and 5.34 more liters of milk on Tuesday than on monday.how many total liters of milk were served on Monday and Tuesday
what's the radius of a circle with an area of 64 square feet?
If a function is odd, then which statement is true?
Cindy has a jar of mixed nuts. There are two pecans, three peanuts, and one cashew in the jar. Cindy grabs two nuts and gives them to her friend, Paul, and he eats them. What is the probability of Paul eating a cashew and a pecan?
A. 1/18
B. 1/15
C. 2/11
D. 1/4
A single , standard number cube is tossed. What is the probability of getting a 4 or 5 ?
1. 1
2. 1 / 5
3. 1 / 3
4. 1 / 6
[tex] |\Omega|=6\\
|A|=2\\\\
P(A)=\dfrac{2}{6}=\dfrac{1}{3}\approx33\% [/tex]
Math Financial Literacy HELP
For the equation, y= -x - 4, tell whether it’s graph passes through the first quadrant. Explain how you know.
A.) No; for x<0 the y-values are negative.
B.) Yes; for x>0 some y-values are positive.
C.) No; for x>0 the y-values are negative.
D.) Yes; for x<0 some y-values are positive.
The graph of the equation y = -x - 4 does not pass through the first quadrant because for x < 0, the y-values are negative.
Explanation:The given equation is y = -x - 4. To determine whether its graph passes through the first quadrant, we need to assess the values for x and y. In the first quadrant, both x and y values are positive.
If we substitute any positive value for x into the equation, we will obtain a negative value for y. Therefore, the graph does not pass through the first quadrant. Hence, the correct answer is option A.
A bag contains 10 identical balls numbered from 1 to 10. What is the probability that a person reaches into the bag and randomly selects a ball with a number that is even?
A dice is rolled and a marble is selected at random from a bag with 2 red marbles, 2 green marbles, 2 yellow marbles, 1 purple marble and 1 blue marble. Find the P(odd and not green).
Parker bought 4 times as many marbles as Molly.Cole bought 5 fewer marbles than Parker. If Molly bought p marbles how many did Cole buy?
Pedro’s Father is building a shed how many square feet of wood are needed
7÷10p^3 ÷ 2÷ 8p^2 please help
Sharon is paving a rectangular concrete driveway on the side of her house. The area of the driveway is 5x^2 + 43x - 18, and the length of the driveway is x + 9.
Additionally, Sharon plans to install a carport over a small portion of the driveway. The volume that the carport can enclose is 48x^3 + 68x^2 - 8x - 3, and the area of driveway beneath the carport is 8x^2 + 10x - 3.
Determine the width of the entire driveway and height of the carport in terms of x. Replace the values of m and b to complete the expression that represents the width of the entire driveway on the first line, and then replace the values of m and b to complete the expression that represents the height of the carport on the second line.
You have to type the answer in mx+b
im just trying to graduate....
Answer:
Width: 5x-2
Height: 6x+1
Step-by-step explanation:
write and solve an inequality to represent the situation
The diameter of a DVD is 12 centimeters. The hole in the center of a DVD has a diameter of 1.5 centimeters. Find the area of the DVD. Round to the nearest hundredth if necessary.
The area of the circular DVD is given by A = 111.33 cm²
What is a Circle?A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The circumference of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle.
The equation of circle is ( x - h )² + ( y - k )² = r²
For a unit circle , the radius r = 1
x² + y² = r² be equation (1)
Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )
Given data ,
Let the area of the circular DVD be A
Let the diameter of the DVD = 12 cm
So , the radius of the DVD = 6 cm
Now , the diameter of the hole = 1.5 cm
So , the radius of the hole = 0.75 cm
And , area of the circular DVD be A = π [ ( 6 )² - ( 0.75 )² ]
On simplifying , we get
The area of circular DVD is A = π ( 36 - 0.5625 )
The area of circular DVD is A = π ( 35.4375 )
The area of circular DVD is A = 111.33 cm²
Hence , the area of the circular DVD is 111.33 cm²
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At a fair, each person can spin two wheels of chance. The fist wheel has numbers 1,2, and 3. The second wheel has the letters A and B. (A) list all the possible outcomes of the computed event. (B) if you spin both wheels, what is the probability that you get either a 1 or an A? Explain.
(a) There are 3 numbers on the fist well and 2 letters on the second, so number of possible outcomes = 3*2 = 6 possible outcomes
The possible outcomes are 1A, 2A, 3A, 1B, 2B, 3B
So in total there are 6 possible outcomes as shown above if a person can spin the two wheels
(b) From possible outcomes A or 1 can appear four times namely: 1A,2A,3A and 1B
So probability is number of successes/ total number = 4/6
Simplify the expression. (3.14×107)×(1.3×10−3)÷0.2
Scientific notation PLS!
Jade is making a square birthday card and she's going to put a ribbon borders on each of the 4 equal sides piece of ribbon that is 33 inches long do you have all of the ribbon how many inches of ribbon conget put on all
equals side
Final answer:
Jade can use 8.25 inches of ribbon on each side of her square birthday card by dividing the total ribbon length of 33 inches by the number of sides, which is 4.
Explanation:
Jade is making a square birthday card and wants to put ribbon borders on each of the 4 equal sides using a piece of ribbon that is 33 inches long. To determine how much ribbon can be put on each side, we divide the total length of the ribbon by the number of sides of the square. Since a square has four sides, we divide 33 inches by 4.
33 inches ÷ 4 sides = 8.25 inches per side
Therefore, Jade can put 8.25 inches of ribbon on each side of the birthday card.
If the mean of a symmetrical distribution is 42, which of these values could be the median of the distribution?
Answer:
42
Step-by-step explanation:
The median of a distribution is the exact center of the distribution, you start taking out numbers equally from the outside to the center, and eventually you will find the median, in a symmetrical distribution that means that there are the same number of values to the sides of the median, and the mean of a symmetrical distribution is always going to be equal to the median, so in this case the median and the mean would be the same, 42.
-6 < -3; Divide both sides by -3
a rectangular box has a volume of 480 cubic inches. The height of the box is 5 inches. The ratio of the length of the box to the width of the box is 3 to 2. What is the measure of the width of the box?
picking a month of the year in the day of the week (fundamental counting principle)
Using the fundamental counting principle to pick a month of the year in the day of a week would give 84 combinations.
How to find the number of combinations ?
The Fundamental Counting Principle is a concept in combinatorics that helps you calculate the total number of possible outcomes when you have multiple independent choices or events.
Choices for the Month: There are 12 months in a year. So, you have 12 choices for the month.
Choices for the Day of the Week: There are 7 days in a week
To find the total number of possible combinations of a month and a day of the week, you simply multiply the number of choices for each event:
Total Number of Combinations = Number of Choices for Month x Number of Choices for Day of the Week
Total Number of Combinations = 12 months x 7 days
= 84 combinations
In conclusion, there are 84 different combinations of selecting a month of the year and a day of the week using the Fundamental Counting Principle.
convert: 7 tons 500 lb to lb
Final answer:
7 tons and 500 pounds equals 14,500 pounds, which is calculated by converting tons to pounds and adding the additional pounds.
Explanation:
To convert 7 tons and 500 pounds to pounds only, follow these two steps:
Convert tons to pounds. Since 1 ton is equal to 2,000 pounds, you multiply the number of tons by 2,000. For 7 tons, it would be 7 × 2,000 = 14,000 pounds.
Add the additional pounds to the converted weight. So, you would add 500 pounds to 14,000 pounds, resulting in 14,500 pounds.
Therefore, 7 tons and 500 pounds is equivalent to 14,500 pounds.
which types of triangles can be formed by taking the cross section of a cube
The coordinate plane represents a map. Each grid unit represents 20 miles. A retail company has a warehouse at N(40, 60). A store is located at P(40, −30). How long will it take a truck driving at 50 miles per hour to drive from warehouse N to this store?
The truck will take 36 hours to travel from warehouse N to store P.
To calculate the time it will take for a truck to travel from warehouse N to store P, we need to first determine the distance between the two points in the coordinate plane. Since each grid unit represents 20 miles, we will use the coordinates of N(40, 60) and P(40, -30) to calculate the distance in grid units and then convert that into miles. The two points share the same x-coordinate, so the truck is only traveling in the north-south direction. By subtracting the y-coordinate of P from that of N, we find that the two points are 90 grid units apart in the y-direction (60 - (-30) = 90). After converting the grid units into miles by multiplying by 20, the total distance is 90
20 miles = 1800 miles.
The truck drives at a speed of 50 miles per hour, so we divide the total distance by the truck's speed to find the time it takes to travel from N to P:
1800 miles / 50 miles per hour = 36 hours.
A rhombus has diagonals 500 yd and 800 yd in length. Find the area in square miles.