By applying the concept of discriminant, the discriminant of the quadratic equation 2 · x² - 9 · x + 2 = - 1 is equal to 57.
How to determine the discriminant of a quadratic equation
For a quadratic equation of the form a · x² + b · x + c = 0, the discriminant is equal to d = b² - 4 · a · c. In this problem we must transform the polynomial into the canonical form and calculate the discriminant:
2 · x² - 9 · x + 2 = - 1
2 · x² - 9 · x + 3 = 0
d = (-9)² - 4 · (2) · (3)
d = 81 - 24
d = 57
By applying the concept of discriminant, the discriminant of the quadratic equation 2 · x² - 9 · x + 2 = - 1 is equal to 57.
To learn more on quadratic equations: https://brainly.com/question/2263981
#SPJ1
Find the equation of the line that passes through (1,3) and is perpendicular to y = 1 − 2 x . Leave your answer in the form y = m x + c
Answer:
[tex]y = \frac{1}{2} x + \frac{5}{2} [/tex]
Step-by-step explanation:
Since the line with equation y = 1 - 2x has slope -2, we need to find the equation of the line with slope 1/2.
[tex]3 = \frac{1}{2} (1) + b[/tex]
[tex]3 = \frac{1}{2} + b[/tex]
[tex]b = \frac{5}{2} [/tex]
[tex]y = \frac{1}{2}x + \frac{5}{2} [/tex]
An urn contains two red and three yellow balls. Two balls are selected randomly without replacement. What is the probability that both are yellow
The probability that both are yellow is 3/10.
Using the probability method, we get
P(y1 and y2) = P(y1) P(y2|y1)
= 3/5 x 2/4
= 6 / 20
= 3 / 10
The probability that both are yellow is 3/10.
Probability is sincerely how in all likelihood something is to manifest. each time we're uncertain approximately the final results of an occasion, we will speak about the possibilities of sure effects—how probably they're. The analysis of activities ruled by using possibility is known as statistics.
A series of actions where the outcomes are continually unsure. The tossing of a coin, selecting a card from a deck of playing cards, throwing a dice. occasion. It is a single final result of an experiment.
Learn more about probability here: https://brainly.com/question/251701
#SPJ4
(please answer quick, i'm timed!!)
What is the simplest form of StartRoot 1,764 EndRoot?
A] 21
B] 42
C] 3^2(7^2)
D]2^2(3^2)(7^2)
Squares are the results of multiplying a value by itself. The correct option is B.
What is square root?Squares are the results of multiplying a value by itself. Whereas the square root of a number is a value that when multiplied by itself yields the original value. As a result, both are vice versa approaches. For example, the square of 2 is 4 and the square root of 4 is 2.
The number 1764 in the form of prime factors can be written as,
1764 = 2×2×3×3×7×7×1
Therefore,
√1764 = 2×3×7 = 42
Hence, the correct option is B.
Learn more about Square Root:
https://brainly.com/question/3120622
#SPJ1
Answer: d}2^2(3^2)(7^2)
Step-by-step explanation: I did the quiz
A model of a ship is built to scale of 1 cm:5 meters.The length of the model ship is 30 cm. What is the actual length of the ship?
Answer:
The actual length of the ship is 150 meters.
Step-by-step explanation:
The scale of the model is 1 cm:5 meters, which means that every 1 cm on the model represents 5 meters on the ship. Since the model ship is 30 cm long, that means it represents 150 meters on the real ship.
What term best describes 3x + 5?
Answer:
algebric expression
Answer:
Binomial
Step-by-step explanation:
Comment
Answer: Two terms make up the expression you are given (3x + 5) ).
When two terms are on either side of an isolated plus (or minus) sign, then the expression is called a Binomial.
Tara makes donut topping by mixing sugar and 12 g of cinnamon. The tape diagram shows the ratio of sugar to
cinnamon.
Complete the table.
Here is the completed table:
Original Ratio Amount (g)
Sugar 3 18
Cinnamon 2 12
Total topping 5 30
How should the table be filled?Original ratio of Cinnamon = total topping - original ratio of sugar
5 - 3 = 2
Amount of Sugar = (12 x 3) / 2 =18g
Total toppings = 18 + 12 = 30g
Please find attached the complete question. To learn more about ratios, please check: https://brainly.com/question/9194979
#SPJ1
prime factorization of 90
Jim has 10 used books and 12 used DVD's to sell at a garage sale for $1.50 and $5.00 each respectively.
Let x be the number of books and y be the number of DVD's Jim ends up selling.
Which of the following systems of linear inequalities represents this situation if Jim wants to make at least $40.00?
a.)
x ≥ 10
y ≥ 12
1.5x + 5y ≥ 40
b.)
x ≤ 10
y ≤ 12
1.5x + 5y ≥ 40
c.)
x ≥ 1.5
y ≥ 5
10x + 12y ≥ 40
d.)
x ≤ 1.5
y ≤ 5
10x + 12y ≥ 40
Answer:
The correct system of inequalities is b.
A certain test is designed to measure the satisfaction of an individual with his/her relationship. Suppose that the scores on this test are approximately normally distributed with a mean of 60 and a standard deviation of 8. An individual with a score of 50 or less is considered dissatisfied with his/her relationship. According to this criterion, what proportion of people in relationships are dissatisfied? Round your answer to at least four decimal places.
The probability that an individual will score of 50 or less is 0.06.
Given mean of 60 and standard deviation of 8.
We have to find the probability that individual will score 50or less.
Probability is the chance of happening an event among all the events possible. The probability lies between 0 and 1. The formula to calculate probability is as under:
Probability = number of items/total items.
We have to first find the z value from 50 to 60 which can be found as under:
z value=(50-60)/60
=-0.167
P value from 50 to 60 is 0.44
probability that the individual will score 50 or less is 0.5-0.44
=0.06
Hence the probability that the individual will score 50 or less is 0.06.
Learn more about probability at https://brainly.com/question/24756209
#SPJ4
In the rhombus below, if NL = 7 and KM = 8 find JL.
Answer:
JL = 14
Step-by-step explanation:
N represents the center of the rhombus
Then
N is the midpoint of the diagonal (line segment) JL
Then
JL = 2 × NL
= 2 × 7
= 14
On a coordinate plane, a curved line with a minimum value of (negative 1.25, negative 3.25) and a maximum value of (0.25, negative 1.75), crosses the x-axis at (negative 2.25, 0), and crosses the y-axis at (0, negative 2). The line exits the plane at (negative 2.75, 6) and (1.5, 6).
Which statement is true about the end behavior of the graphed function?
As the x-values go to positive infinity, the function's values go to negative infinity.
As the x-values go to zero, the function's values go to positive infinity.
As the x-values go to negative infinity, the function's values are equal to zero.
As the x-values go to positive infinity, the function's values go to positive infinity.
The statement which is true about the end behavior of the graphed function is third option that is as the x-values go to negative infinity, the function's values are equal to zero.
A coordinate plane is a two dimensional plane formed by the intersection of two number lines . One of these number lines is a horizontal number lines called the x-axis and the other number line is a vertical number line called the y-axis.
The exact answer is third option that is as the x-values go to negative infinity, the function's values are equal to zero.
Step by step explanation:
Minimum value (negative 1.25, negative 3.25)
Maximum value of (0.25, negative 1.75)
The x intercepts where the graph crosses the x axis.
Value of x when y=0 crosses x axis at (negative 2.25, 0)
The y intercept are where the graph crosses the y axis.
Value of y when x=0 crosses y axis at (0, negative 2)
The line exits the plane at (negative 2.75, 6) and (1.5, 6).
It can be seen from the coordinates that as the x-values go to negative infinity, the function's values are equal to zero, the coordinates of y approaches zero.
Learn more about coordinates from:
https://brainly.com/question/17206319
#SPJ10
Answer:
D
Step-by-step explanation:
Jon's bathtub is rectangular and its base is 16 ft2. How fast is the water level rising if Jon is filling the tub at a rate of 0.5 ft3/min
Jon is filling the tub at a rate of 0.5 ft3/min is 0.3125 ft/min.
If we take a look at a rectangular bathtub, the volume of the bathtub can be expressed as:
Volume (V) = length × breadth × height
where;
the base = length × breadth = 16ft²
∴ the volume of the rectangular bathtub = 16h --- (1)
Using differentiation to differentiate 16h with respect to t implicitly, then:
dV/ dT = 16 dH /dT
When the rate of rising of the volume is 0.5 ft³/min
Then:
0.5 = 16 dH /dT
dH /dT = 1 / 16 * 0.5
dH /dT = 0.3125.
Jon is filling the tub at a rate of 0.5 ft3/min is 0.3125 ft/min.
Learn more about differentiation here: https://brainly.com/question/25081524
#SPJ4
If
1 ƒ (x) = 3x + 5/x, what is f(a + 2)?
Answer: [tex]3a+6+\frac{5}[a+2}[/tex]
Step-by-step explanation:
[tex]f(a+2)=3(a+2)+\frac{5}{a+2}=3a+6+\frac{5}[a+2}[/tex]
A bag contains 75 marbles some red some blue the ratio of red marbles to blue marbles is 3 to 2 how many red marbles are there
Answer: 45 red marbles
Step-by-step explanation:
Using the ratios, we can create a fraction for the number of marbles.
3/5 of the bag would be red marbles, and 2/5 of the bag would be blue marbles.
(you get the 5 from adding 3+2 together)
If you take 3/5 of 75, you would get 45 red marbles.
It is claimed that the mean age of bus drivers in chicago is 50. 2 years. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?.
The result to reject the null hypothesis can be interpreted as follows,
There is sufficient evidence to disprove the claim μ = 50.2
What is a null hypothesis?
A statistical hypothesis known as a null hypothesis asserts that no statistical significance can be found in a collection of provided observations. Using sample data, hypothesis testing is performed to judge a theory' veracity. It is sometimes referred to as just "the null," and its symbol is H0.
To determine if a theory regarding markets, investing methods, or economies is correct or wrong, quantitative analysts perform a hypothesis testing and employ the null hypothesis, often known as the conjecture. Any variation between the selected attributes that you observe in a collection of data is thought to be the result of chance, according to the null hypothesis.
Learn more about null hypothesis here:
https://brainly.com/question/19263925
#SPJ4
A 20-ft ladder leans against a building so that the angle between the ground and the ladder is 72 degrees. How high does the ladder reach on the building?
The height of the building is 19.02 feet, for a 20-ft ladder to lean against the building at an angle of 72 degrees.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Trigonometric ratio is used to show the relationship between the sides and angles of a right angle triangle.
Let h represent the height of the building, hence:
sin(72) = h/20
h = 19.02 feet
The height of the building is 19.02 feet, for a 20-ft ladder to lean against the building at an angle of 72 degrees.
Find out more on equation at: https://brainly.com/question/13763238
#SPJ1
The height reached by the ladder of height 20-ft. inclined at 72° is approximately 19.02-ft.
How can the height reached by the ladder be found?Length of the ladder = 20 feet
Angle between the ground and ladder = 72°
Height reached by the ladder = Required
Solution:
From the definition of the sine of an angle, we have;
[tex]sin (\theta) = \mathbf{ \frac{opposite \: side}{hypotenuse}} [/tex]
The length of the ladder = The hypotenuse side = 20 ft.
The opposite side to the angle 72° = The height reached by the ladder
Which gives;
[tex]sin (72 ^ {\circ})= \frac{height \: reached}{20} [/tex]
Height = 20 × sin(72°) = 19.02
The height reached by the ladder on the building ≈ 19.02-ft.Learn more about the sine of angles here:
https://brainly.com/question/2920412
#SPJ1
A moving company sells boxes for packing items. the large box has a volume of 6x^2+2x+3 cubic units. the medium box has a volume of 2x^2-5 cubic units. a customer purchases two large boxes and one medium box. what is the total volume of the purchased boxes?
The total volume of the purchased boxes is 14x^2+4x+1
Sum of polynomialsGiven the following parameters
Volume of a large box = 6x^2+2x+3 cubic units
Volume of medium = 2x^2-5 cubic units.
If a customer purchases two large boxes and one medium box, the total volume is expressed as:
Total volume = 2(6x^2+2x+3) + 2x^2-5
Expand
Total volume = 12x^2+4x+6+2x^2-5
Total volume = 14x^2+4x+1
Hence the total volume of the purchased boxes is 14x^2+4x+1
Learn more on sum of polynomial here: https://brainly.com/question/26147255
#SPJ1
4. Verbal
Explain how to find a line parallel to a linear function that passes through a given point.
Answer:
The required line can be found by substituting the slope and the given point in the slope intercept form of a line and is given by y=mx+c, where m is the slope and c is the y intercept.
Step-by-step explanation:
In the given question, it is given that a linear function passes through a given point.It is required to find a line parallel to the function.When two functions are parallel, their slopes are equal.Thus, substitute the slope and the given point in the slope intercept form of a line and is given by y=mx+c, where m is the slope and c is the y intercept.The equation of a parallel line to a linear function that passes through a point can be explained using the examples below.
We have,
The parallel line to a linear function that passes through a point can be explained using the examples below.
Example:
Let's find a line parallel to the linear function y = 3x - 2 that passes through the point (2, 5).
Step 1: Given linear function and point
Linear function: y = 3x - 2
Point: (2, 5)
Step 2: Determine the slope of the given linear function
The slope (m) of the given function y = 3x - 2 is 3.
Step 3: Use the slope to find the equation of the parallel line
Since the parallel line has the same slope (3), its equation will be
y = 3x + b, where "b" is the y-intercept that we need to find.
Step 4: Substitute the coordinates of the given point into the equation of the parallel line
Using the coordinates (2, 5) of the given point, we can solve for "b":
5 = 3(2) + b
5 = 6 + b
b = 5 - 6
b = -1
So, the equation of the line parallel to y = 3x - 2 and passing through the point (2, 5) is:
y = 3x - 1.
Thus,
The equation of a parallel line to a linear function that passes through a point can be explained using the examples above.
Learn more about equation of a line here:
https://brainly.com/question/23087740
#SPJ7
identify the domain of the function shown in the graph
0
x is all real numbers
Using it's concept, the domain of the square root function shown in the graph is:
[tex]x \geq 0[/tex]
What is the domain of a function?The domain of a function is the set that contains all possible input values for the function. In a graph, the domain is the set that contains the values of x.
Researching the problem on the internet, the graph is of the square root function, defined for [tex]x \geq 0[/tex], which is the domain of the function.
More can be learned about the domain of a function at https://brainly.com/question/10891721
#SPJ1
Hey guys- need help in this one
Answer:
c
Step-by-step explanation:
[tex]x=5+i\sqrt{7} , y = 5-i\sqrt{7}\\ x^2-2xy+y^2=(x-y)^2\\ (x-y)^2=(2i\sqrt{7} )^2\\4.i^2.7\\-28[/tex]
Answer:
c
Step-by-step explanation:
given x = 5 + i[tex]\sqrt{7}[/tex] then y = 5 - i[tex]\sqrt{7}[/tex]
x² - 2xy + y² ← is a perfect square
= (x - y)² ← substitute values for x and y
= (5 + i[tex]\sqrt{7}[/tex] - (5 - i[tex]\sqrt{7}[/tex] )²
= (5 + i[tex]\sqrt{7}[/tex] - 5 + i[tex]\sqrt{7}[/tex] )²
= (2i[tex]\sqrt{7}[/tex] )²
= 2² × i² × ([tex]\sqrt{7}[/tex] )²
= 4 × - 1 × 7
= - 28
Find the slope of the line on the graph.
Write your answer as a fraction or a whole
number, not a mixed number or decimal.
Answer:
-3
Step-by-step explanation:
Define two points on the line:
[tex]\textsf{let}\:(x_1,y_1)=(0,4)[/tex][tex]\textsf{let}\:(x_2,y_2)=(2,-2)[/tex]Substitute the defined points into the slope formula and solve for m:
[tex]\begin{aligned} \textsf{slope}\:(m) & = \dfrac{y_2-y_1}{x_2-x_1}\\\\ \implies m & =\dfrac{-2-4}{2-0}\\\\ & =\dfrac{-6}{2}\\\\ & =-3\end{aligned}[/tex]
Therefore the slope of the given line is -3.
Hi! having a bit of trouble with this one problem that I can't seem to solve correctly. This is an exponential and logarithmic equation problem, but I keep getting 1.74036... and apparently that isn't the answer. I'd appreciate the help!
The value of x from the given expression is 0.7558
Solving exponential equationsThe standard exponential equation is expressed as y = ab^x
Given the equation below
10^x +5 = 60
Subtract 5 from both sides
10^x = 60 - 5
10^x = 55
Take the log of both sides
log10^x = log55
x = log55/log10
x = 0.7558
Hence the value of x from the given expression is 0.7558
Learn more on exponential equation here: https://brainly.com/question/2456547
#SPJ1
Can someone help please
Answer:
35.3
Step-by-step explanation:
please mark brainliest
Answer:
35.3
Step-by-step explanation:
can someone please help me
Answer: A
Step-by-step explanation:
Answer:
A
I solved on paper it took me 45 mins
what would be 12% of 40
Hello,
Answer:
4,8
Step-by-step explanation:
what would be 12% of 40 ?
12% × 40 = 12/100 × 40 = 0,12 × 40 = 4,8
Angelica Reardon received a 4-year non-subsidized student loan of $17,000 at an annual interest rate of 6.1%. What are Angelica's monthly loan payments for this loan after she graduates in 4 years? (Round your answer to the nearest cent.) $
Answer:
$1503.08 per month
Step-by-step explanation:
simplify \sqrt{50} for maths please quick
Hello,
[tex] \sqrt{50} = \sqrt{2 \times 25} = \sqrt{2 \times 5 {}^{2} } = 5 \sqrt{2} [/tex]
How long should the ladder be if they want to use all the cable they have? Use the law of sines to find the length
Answer:
Step-by-step explanation:
I need the answer please work out this tough question for me
Answer:
56
Step-by-step explanation:
Let N be the total number of spins.
Probability of A on Red and B on Red = 0.5 x 0 .6 = 0.3 (top branch of tree)
Therefore with N spins, the estimated number of times spinner A and spinner B land on red is 0.3N and we are given this as 84
So 0.3N = 84
N = 84/0/3 = 280
The probability of spinner A on blue and spinner B on blue is 0.5 x 0.4 = 0.2 (lowest branch of tree)
For 280 spins, the estimated number of times that both spinners land on blue is given by 0.2 x 280 = 56
47. A car travels at a constant speed of 50 miles per hour.
The distance the car travels in miles is a function of
time, t, in hours given by d(t) = 50t. Find the inverse
function by expressing the time of travel in terms of
the distance traveled. Call this function t(d). Find
t(180) and interpret its meaning.
Answer:
The inverse of the given function is [tex]$t(d)=\frac{d}{50}$[/tex]. The time taken to travel 180 miles is 3.6 hours.
Step-by-step explanation:
It is given that a car travels at a constant speed of 50 miles per hour. A function for distance traveled is also given as d(t)=50t.
It is required to find the inverse of the function by expressing the time travel in terms of distance traveled and also find t(180).
To find the inverse, express time traveled in terms of distance traveled using normal algebraic methods and then substitute 180 for t and explain its results.
Step 1 of 2
The given function is d(t)=50t.
Consider d(t) as d and t as t(d) and rewrite the equation.
The rewritten function is d=50 t(d)
Divide by 50 on both sides of the equation.
[tex]$$\begin{aligned}&d=50 t(d) \\&\frac{d}{50}=\frac{50 t(d)}{50} \\&t(d)=\frac{d}{50}\end{aligned}$$[/tex]
Step 2 of 2
Substitute 180 for $t$ in the simplified expression and interpret the results.
[tex]$$\begin{aligned}&t(d)=\frac{d}{50} \\&t(d)=\frac{180}{50} \\&t(d)=3.6\end{aligned}$$[/tex]
The time taken to travel 180 miles is 3.6 hours.