The quadratic equation x^2 - 4x + 4 = 0 has one real number solution, x = 2, which is a repeated solution since the discriminant of the equation is zero.
To determine the number of real number solutions for the equation x2
- 4x + 4 = 0, we can use the discriminant method. The discriminant D of a quadratic equation ax2 + bx + c = 0 is given by b2 - 4ac. For our equation, a = 1, b = -4, and c = 4.
Calculating the discriminant gives us D = (-4)2 - 4(1)(4) = 16 - 16 = 0. Since the discriminant is equal to zero, it indicates that there is exactly one real number solution, which means the quadratic has a perfect square trinomial, or the two real solutions are identical.
In this case, the solution to the equation can be found by factoring the quadratic as (x - 2)2 = 0, which implies that x = 2. Therefore, the equation x2 - 4x + 4 = 0 has one real solution, x = 2, which is repeated.
A used car dealership buys a car for $2800 and then sells it for $4500 what is the percent increase?
The percentage is the indicating hundredth of any change in quantity thus the percentage increase of cars from $2800 to $4500 is 60.72%.
What is the percentage?The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
As per the given question,
Buying cost of car = $2800
Selling cost of car = $4500
Percentage change = (change/original) × 100
Percentage change = [(4500 - 2800)/(2800)] × 100
Percentage change = [(1700)/2800] × 100
Percentage change = 0.607 × 100
⇒ 60.72%
Hence "The percentage is the indicating hundredth of any change in quantity thus the percentage increase of cars from $2800 to $4500 is 60.72%".
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Converting improper fractions to mixed numbers questions
√(-3) is negative, positive, undefined, or an integer
The area of a triangle is 27 square feet its height is three times the length of its base find the height and base of the triangle
p: If two out of five people use the subway every day, then the probability of a person using the subway is 0.4.
2 divided by 5 = 0.4
so that statement is true.
1. Find a counterexample.
If two angles are complementary, then they are not congruent.
Dan has a flower shop. Each day he displays 24 roses. He gives away 10 and sells the rest. Each day he displays 36 carnations. He gives away 12 and sells the rest. What expression can you use to find out how many roses and carnations Dan sells in in a week.
evaluate the expression to find out how many roses and carnations dan sells in a week
what is the solution to the inequality 2n+5 > 1
The solution to the inequality 2n + 5 > 1 is n > -2 after isolating the variable n and simplifying the equation.
Explanation:The solution to the inequality 2n + 5 > 1 involves some basic algebra. First, we should isolate the variable, n, on one side of the inequality. This is accomplished by subtracting 5 from both sides of the inequality which gives us: 2n > 1 - 5.
Simplifying the right side gives us 2n > -4. Then, we need to divide every term by 2 which gives us n > -4/2. Simplifying further, we find that the solution to the inequality 2n + 5 > 1 is n > -2.
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2 angles, angle A and angle B, form a linear pair. Angle B is an obtuse angle. What type of angle is angle A
Nina can ride her bike 63,360 feet in 3,400 seconds, and Sophia can ride her bike 10 miles in 1 hour. What is Nina's rate in miles per hour if there are 5,280 feet in a mile?
Which girl bikes faster?
3400/60 = 56.6666 minutes/60 = 0.94 hours
63360/5280 = 12 miles
12/0.94 = 12.76 miles per hour for Nina
Nina is faster
Jamir spent $15 on Halloween candy. If each bag of candy costs $2.50, how many bags of candy did he buy?
To find out how many bags of candy Jamir bought with $15, divide the total spent by the cost per bag, which is $2.50. This calculation is similar to finding total spend on fruits by multiplying the quantity by price per unit. Jamir was able to buy 6 bags of candy.
Explanation:To answer the question of how many bags of candy Jamir bought, we need to perform a basic division operation.
The total amount Jamir spent on Halloween candy is $15, and he purchased each bag for $2.50.
Therefore, to find the total number of bags of candy that Jamir bought, we divide the total amount spent by the cost per bag.
Drawing a comparison to similar calculations, if we look at other examples such as spending on fruits, we can see a consistent method of calculation:
10 apples at 50 cents each results in $5.00 spent on apples.
12 bananas at 20 cents each gives us a total of $2.40 spent on bananas.
Similarly, 2 bunches of grapes at 65 cents per bunch would equal a spend of $1.30.
Lastly, if we purchase 1 pint of raspberries at $2 each, we spend $2.00 on raspberries.
The same concept applies to Jamir's Halloween candy purchase. By dividing $15 by $2.50, we get the number of bags he was able to buy, which is 6 bags of candy.
Therefore, Jamir bought 6 bags of Halloween candy with his $15.
Final answer:
Jamir was able to buy 6 bags of Halloween candy for $15, given each bag's price of $2.50.
Explanation:
Jamir spent $15 on Halloween candy, with each bag costing $2.50. To find out how many bags of candy Jamir could buy, we divide the total amount spent by the cost per bag of candy.
The calculation would be as follows:
Divide the total amount spent, $15, by the cost per bag, $2.50.
$15 ÷ $2.50 = 6.
Therefore, Jamir bought 6 bags of Halloween candy.
Cynthia besch wants to buy a rug for a room that is 1313 ft wide and 2222 ft long. she wants to leave a uniform strip of floor around the rug. she can afford to buy 112112 square feet of carpeting. what dimensions should the rug have?
Suppose a number from 1 to 100 is selected at random. what is the probability that a multiple of 4 or 5 is chosen?
The probability that a multiple of 4 or 5 is chosen is 2/5.
The range 1-100 is 100 numbers, divide by 4 and 5 to find the number of multiples.
100/4 = 25
100/5 = 20
The probability of choosing a multiple of 4
25/100 = 1/4
The probability of choosing a multiple of 5
20/100 = 1/5
The probabilities are not mutually exclusive because there are duplicate numbers, (overlap) multiples of both 4 and 5 being counted twice.
5/100 = 1/20
20, 40, 60, 80, 100
When or is used, add the probabilities, and subtract the duplicates.
1/4 + 15 - 1/20
=5/20 + 4/20 - 1/20
= 8/20
= 2/5
The probability that a multiple of 4 or 5 is chosen is 2/5.
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Which fraction represents the decimal .12 repeating
The answer is c.) 4/33
Determine the slope of a line perpendicular to the line with equation 6x-4y= 30
Write a real world description to fit the expression -59/5
A debt of $59 dollars owed by five (5) ladies and will also be divided among them. They borrow $59 dollars to buy the materials for their science project because 3 out of 5 ladies do not have money to spend to their science project.
If the polynomial x5 − 105 can be split as the product of the polynomials x − 10 and a, what is a?
Answer:
Value of a is:
[tex]x^4+10x^3+100x^2+1000x+10000[/tex]
Step-by-step explanation:
we know that:
[tex]x^n-a^n=(x-a)(x^{n-1}+ax^{n-2}+a^2x^{n-3}+...+a^{n-2}x+a^{n-1})[/tex]
Here, a=10 and n=5
[tex]x^5-10^5=(x-10)(x^4+10x^3+100x^2+1000x+10000)[/tex]
[tex]x^5-10^5=(x-10)a[/tex]
⇒ [tex]a=x^4+10x^3+100x^2+1000x+10000[/tex]
Hence,Value of a is:
[tex]x^4+10x^3+100x^2+1000x+10000[/tex]
Convert the equation (y + 2) = –1/3(x – 4) to the point-slope form. Then fill in the blanks below to describe how to graph the equation.
Plot the point _______, move _______ unit(s) down, and _______ unit(s) over to find the next point on the line.
Which diagram shows the most useful positioning and accurate labeling of an isosceles trapezoid in the coordinate plane?
The third image contains the labels (a,b), (c,d), (-a,b), and (-c,d).
The diagram that shows the most useful positioning and accurate labeling of an isosceles trapezoid in the coordinate plane is the first figure.
Because it tells you the lengths of the trapezoid's bases and height.
For example, the base lengths are as follows:
a - (-a) = a + a = 2a
c - (- c) = c + c = 2c
height: b-d
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The third image contains the labels (a,b), (c,d), (-a,b), and (-c,d).
An isosceles trapezoid is a type of trapezoid (a quadrilateral with at least one pair of parallel sides) where the non-parallel sides are congruent (have the same length). The base angles, formed by the intersection of the non-parallel sides and the parallel sides, are also congruent in an isosceles trapezoid.
The diagram that shows the most useful positioning and accurate labeling of an isosceles trapezoid in the coordinate plane is the first figure.
Because it tells you the lengths of the trapezoid's bases and height.
For example, the base lengths are as follows:
a - (-a) = a + a = 2a
c - (- c) = c + c = 2c
height: b-d
What is the best first step for solving the given system using substitution while avoiding fractions?
2x+6y=7
6x+18y=24
a. Solve for x in the first equation.
b. Solve for y in the first equation.
c. Solve for x in the second equation.
d. Solve for y in the second equation.
Find a number whose product with 9 is the same as its sum with 56
Final answer:
The requested number is 7, which when multiplied by 9 or added to 56, gives the same result of 63.
Explanation:
To find a number whose product with 9 is the same as its sum with 56, we set up the equation x * 9 = x + 56. Solving for x, we first distribute the 9 to the x, resulting in 9x = x + 56. Next, we subtract x from both sides to get 8x = 56. Finally, we divide both sides by 8 to find that x = 7. Hence, 7 is the number we are looking for, as 7 * 9 = 63 and 7 + 56 = 63, confirming that the product and the sum yield the same result.
Is this a function?
Kira and ahmad walk around a track. Kira walks each lap in 10 minutes.Ahmad walks each lap in 12 minutes. The two of them begin at the starting line at the same time.They walks until they meet again at the starting line. How much times does it take for them to meet again at the starting line? How many laps did kira complete? How many laps did ahmad complete Plz help <3
I need help with number 8,please.
Noah wants to put $1,000 in a savings account with a 1.5% annual interest rate. How much more money will he have after one year if it is compounded monthly versus no compounding
A:$0.10
B:$15.00
C:$1015.00
D:$1015.10
explain too
1.Evaluate the expression.
[(24÷12)⋅6]+3⋅8÷2
2.Evaluate the expression.
(26÷13)⋅(−7)+14−4
3.Simplify this expression.
9 + 3 × 2
15
21
24
48
4.What is the value of this expression?
6⋅[(32−8)÷4+2]
5.Simplify.
6y+5z+8y−3z
11y + 5z
14y +2z
14y + 8z
16yz
During the month of February, Fabulous Feet Shoe Mart sold 30 pairs of red loafers. After an ad campaign to boost sales, they sold 39 pairs in March. Find the percent of increase in sales.
35%
30%
23%
18%
How many different 7-place license plates are possible if the first 3 places are to be occupied by letters?
A science teacher needs to choose 4 students from a class of 20 to go to the library to do some research. How many different groups can he select?
The number of groups the science teacher can make is 5.
What are arithmetic operations?The arithmetic operations are the fundamentals of all mathematical operations. The example of these operators are addition, subtraction, multiplication and division.
The total number of students is 20.
And, the number of students in one group is 4.
Now, the number of groups can be found using the following operation as,
Number of group = Total students ÷ Number for each group
⇒ 20 ÷ 4 = 5.
Hence, the total number of groups can be obtained as 5.
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HELP PLEASE The Appalachian Mountains had what effect on the people of the thirteen original colonies? A) they acted as a barrier to further settlement to the west B) they provided protection to the colonists from invading Indians C) they provided protection to the colonists from Spanish conquistadors D) animals lived there and were an important food source to major cities in the East
the answer is...