For Quadratic equation, It is possible to know if there are 2 real solutions by examining the discriminant that is [tex]b^2-4ac[/tex] of the equation [tex]ax^2+bx+c[/tex].
What do you mean by a solution?In mathematics, a solution refers to a value or set of values that satisfies a given equation, system of equations, or problem. For example, if the equation is x + 2 = 4, then the solution is x = 2, because substituting 2 for x in the equation makes it true. In the case of systems of equations or more complex problems, a solution may be a set of values that satisfies all the equations or conditions of the problem. In such case, the solution may be represented graphically or as coordinates of a point.
What are ideal and real solutions?In mathematics, an ideal solution refers to a solution that meets all the desired criteria or requirements without any constraints. It is the "best case" scenario. A real solution, on the other hand, refers to a solution that takes into account all the limitations and constraints of a problem. It is a more practical and realistic solution.
discriminant : [tex]b^2-4ac[/tex]
if [tex]b^2-4ac[/tex] is positive, Both solutions are real.
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help please and thank you
The equation that represents the situation is
2p + 194.99 = 284.97
Option B is the correct answer.
The price of each game is $44.99.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Game system price = $194.99
Total price = $284.97
194.99 + 2 games = $284.97
Games = p
Now,
The price of each game.
194.99 + 2p = 284.97
2p = 284.97 - 194.99
2p = 89.98
p = 44.99
Thus,
The equation is 194.99 + 2p = 284.97.
The price of each game is $44.99.
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Help please, I need to check my answer
[tex]\cfrac{45p^5q^4-60p^3q^2 - 15p^2q^3}{15p^2 q^3}\implies \cfrac{45p^5q^4}{15p^2 q^3}-\cfrac{60p^3q^2}{15p^2 q^3}-\cfrac{15p^2q^3}{15p^2 q^3}\implies 3p^3q-\cfrac{4p}{q}-1[/tex]
THIS HAS BEEN KILLING ME!!!!!
The function y=-1/3x is reflected across the x-axis. What's the equation of the new function?
- explain step by step, please.
Check the picture below.
let's bear in mind that the -(1/3)x has a negative slope, namely going down, so a reflection over the x-axis will yield the same points pretty much, but instead of the IV Quadrant, on the I Quadrant, above, whilst the slope remains the same, it simply turns positive.
this is my quation kfwn vehfwqkn uewfhkjn uewfhskj uefwshjl efwuhskcj fwqeukjscngefww
Answer:
1/6
Step-by-step explanation:
There are 6 letters and the spinner lands on one at a time
please help me with these 4 questions will mark branliest whoever gets all of it right
Answer:
1. The answer is 40 degrees
2. Adjacent angles are sometimes congruent.
3. UPR is vertical to TPQ
4. The answer is 132 Degrees
PLEASE HELP ME I DONT UNDERSTAND
Question 1: The Magnolia trees purchased for planting at the school are 3 feet tall. Research shows that these types of trees grow at an average of 3/4 foot per year Some students misunderstood question #1 and wrote the following equations in point-slope form:
a) y − 3 = 3/4(x-0)
b) y - 6 = 3/4(x-4)
c) y - 4.5 = 3/4(x-2)
d) y - 12 = 3/4(x-12)
e) y - 15= 3/4(x-15)
Is point slope form okay to use to find the height of the trees in this problem?
There is one equation that is incorrect.... determine which one? why is it incorrect?
Creat two new equations written in point slope form
The point slope form is not okay to use to find the height of the trees
The incorrect equation is y - 15= 3/4(x-15) The other equations are y - 3.75 = 3/4(x - 1) and y - 4.5 = 3/4(x - 2)How to determine if the point slope form is okay?From the question, we have the following parameters that can be used in our computation:
Initial height of purchase = 3 feet tallAverage rate = 3/4 foot per yearThe point slope form of a linear equation is represented as
y - y₁ = m(x - x₁)
Where
Slope = m
The point slope form does not show the initial value
So, this form is not okay for the required parameters
How to determine the incorrect equationThe slope-intercept form is given as
y = mx + c
Using the given parameters, we have
y = 3/4x + 3
Subtract 3 from both sides
y - 3 = 3/4x
Rewrite as
y - 3 = 3/4(x - 0)
This equation can be rewritten in any of the following forms
a) y − 3 = 3/4(x-0)b) y - 6 = 3/4(x-4)c) y - 4.5 = 3/4(x-2)d) y - 12 = 3/4(x-12)Hence, the incorrect equation is y - 15= 3/4(x-15)
Two new equations written in point slope formWe have the slope-intercept form to be
y = 3/4x + 3
Set x = 1 and 2, and then solve for y
So, we have
y = 3/4 * 1 + 3 = 3.75
y = 3/4 * 2 + 3 = 4.5
So, the equivalent equations are
y - 3.75 = 3/4(x - 1) and y - 4.5 = 3/4(x - 2)
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Find a value that
makes this inequality
true: 50 - 3x ≤ 20
50-3x<20
the answer is C. 11
An example of a dangerous passing situation is: When the oncoming car is close and you have a long line of traffic ahead of you When you can't see clearly ahead and the maneuver may not be completed in time All options When road and traffic conditions make driving tricky
Anytime one makes a traffic manoeuvre, such as changing lanes or passing another vehicle, a person put both himself and other drivers on the road in danger.
What are the methods for passing risky situations?
Avoid driving at intersections with railroads, railroad crossings, and entrances to shopping centres.
Only pass to the left if there are two lanes on the road. It is frequently illegal and dangerous to pass on the right. Only when the car in front of you flashes its left turn signal is there an exemption.
When there is a long line of traffic and an oncoming car is right ahead, it is advisable to wait until the incoming vehicle has passed before making a passing motion.
Therefore, it is best to wait until one can see fully ahead because there might be an approaching car right around the bend.
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Pls help quickly
Needed as soon as possible thank you in advance
a) Bearing from A to B is 253°.
b) Bearing from B to A is 287°.
What is a bearing?
A bearing is an angle measured clockwise from north in mathematics. Typically, bearings are expressed as a three-figure bearing.
a)
The bearing of 73° and the co-interior angle formed must total 180°. The counter-clockwise angle from B to A is 107°.
However a bearing must always be measured clockwise from north. 107° is counter-clockwise from north.
The clockwise angle on the other side is needed. Use the angle fact that angles in a full turn add to 360°.
To work the bearing, subtract 107° from 360°.
360° – 107° = 253° and so, the bearing of A from B is 253°.
b)
The bearing of 107° and the co-interior angle formed must total 180°. The counter-clockwise angle from A to B is 73°.
However a bearing must always be measured clockwise from north. 73° is counter-clockwise from north.
The clockwise angle on the other side is needed. Use the angle fact that angles in a full turn add to 360°.
To work the bearing, subtract 73° from 360°.
360° – 73° = 287° and so, the bearing of B from A is 287°.
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What is the coefficient of x² in the polynomial x³ 4x² 7x 2?
The provided phrase, x3+4x2+ 7x+ â' 2 has four terms. and coefficient are 1 , 4 ,7 for the expression
What does the phrase mean?
Expressions are made up of terms. A term might be either a constant, a variable, or a combination of both.
What kind of phrase would that be?
A single letter, a single positive or negative integer, or a number of variables multiplied but never added or subtracted might be the only variable. A number is placed in front of some nouns that have variables. The number used before a sentence is called a coefficient. single-word illustrations: Three times in one phrase.
The mathematical operator + separates the four components in the equation x3+4x2+ 7x+â' 2.
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!!!PLEASE HELP ASAP!!!
Thus, complete scale is: 1 inch = 57.7 miles
This can be solved by the concept of cross-multiplication method.
What is inch scale?A centimeter is smaller than an inch. On the other side of the centimeter ruler, inches are denoted by the large, continuous hash marks that are inscribed above the digits. On a ruler, the inch is the largest unit and is denoted by the longest line. There is a number next to each 1-inch line on the ruler that designates.
Since the international yard was adopted in the 1950s and 1960s, standards for the precise length of an inch have fluctuated, but the inch is now based on the metric system and is defined as precisely 25.4 mm.
Correct order is:
d. 27 / 1557 = 1/d
e. 27 . d = 1 . 1557
a. 27d = 1557
f. 27d / 27 = 1557 / 27
b. d = 57.7
c. scale: 1 inch = 57.7 miles
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during a lunch seminar chocolate caramel and strawberry toppings were available how many two-topping
There are 3 two topping sundaes possible.
How many two toppings are possible?It is not crucial to choose the toppings in any particular sequence. For instance, a caramel and strawberry topping is the same as a chocolate and caramel topping. To answer this question, we thus apply the combinations formula.
Mixtures Formula:
C,n,x is the amount of various ways there are to combine x items from a set of n components, as determined by the formula below.
Cn,x = n! / x!(n-x)!
sundaes with two toppings are possible
2 of a set of 3 toppings (chocolate, caramel and strawberry). So
C3,2 = 3! / 2! (3 - 2)! = 3.
Three two-topping sundae combinations are conceivable.
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1.12 less the product of m and n.
2.the product of two numbers decreased by their sum.
3.two thirds of a number subtracted from the square of the same number.
4.the sum of the product and quotient of two numbers decreased by 10.
5.the cube of the sum of a number and 2.
6.twice the difference between four times b and twice x.
7.the sum of 5 times y and 6 divided by twice a.
8.three-fourths of x added to thrice of x is equal to twelve.
Pa Help
Answer:
1.12 < mn
xy - x + y
2/3x - x²
xy + x/y - 10
(x + 2)³
2(4b - 2x)
According to the linear regression model, the men’s world record mile run time in 1940 would have been how many seconds?
The men’s world record mile run time in 1940 would have been 10.454 seconds
Here, the equation of the linear function that best fits the data (the line of best fit) is Finishing time = 10.878 - 0.0106(Year after 1900)
Let k be the finishing time in seconds and t be the number of years after 1900
So, the equation of regression line becomes,
k = 10.878 - (0.0106) t
To find the the men’s world record mile run time in 1940 first we find the the number of years (t)
t = 1940 - 1900
t = 40 years
So, the finishig time (k) would be,
k = 10.878 - (0.0106) × 40
k = 10.454 seconds
Therefore, the finishing time was 10.454 seconds
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Simplify:- 3/11of(1/3+5/9)÷9/15
Answer:
=3/11 of (1×3+5/9)÷9/15
=3/11 of (8/9)÷9/15
=3/11 of 8/9÷9/15
=8/33÷9/15
=8/33×15/9
=40/99
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a forest covers 59,000 acres. A survey finds that 0.6% of the forest is old oak trees How many are acres of old oak trees are there?
Answer:
354acres
Step-by-step explanation:
Total acre = 59000
Percentage of old oak acre trees is 0.6%
Therefore, the acres of old trees are calculated:
59000 * (0.6÷100) = 354acres
A tudent aid -5 i le than -4 and |n | -5 | i le than | -4 | i the tudent correct? jutify your reaoning
The student is partially correct as -5 is less than -4 but ln |-5| is not less than ln |-4|.
What is reasoning?
We can ascertain the veracity of the supplied propositions using mathematical reasoning, often known as the mathematical reasoning principle.
A student said that -5 is less than -4.
This statement is correct and the reasoning is -
According to the number line, 0 is the midpoint.
From 0 to the right side of infinity the digits increases.
So, 1 is bigger than 0, 2 is bigger than 1, 3 is bigger than 2, and so on.
Similarly, from 0 to the left side of negative infinity the digits decreases.
So, -1 is smaller than 0, -2 is smaller than -1, -3 is smaller than -2, and so on.
The student also said that ln |-5| is less than ln |-4|.
This statement is false and the reasoning is -
First simplify ln |-5| and ln |-4| -
ln |-5| = ln (5)
ln (5) = 1.6094
ln |-4| = ln (4)
ln (4) = ln (2^2)
ln (2^2) = 2 ln (2)
2 ln (2) = 1.3862
Therefore, the student is partially correct.
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How I find a area of triangle when 3 equation of sides are given?
The area of a triangle when three side lengths are calculated by Heron's Formula. Heron's Formula states that the area of a triangle is equal to the square root of s(s-a)(s-b)(s-c)
To calculate the area of a triangle when three side lengths are given, we can use Heron's Formula. Heron's Formula states that the area of a triangle is equal to the square root of s(s-a)(s-b)(s-c) where s is half the perimeter of the triangle and a, b, and c are the lengths of the sides of the triangle.
To calculate the area of the triangle given three side lengths, we first need to calculate the perimeter (p) of the triangle. The formula for the perimeter is p=a+b+c.
Then, use this formula to calculate s, which is half the perimeter.
s = p/2
Once s is calculated, plug it into Heron's Formula to calculate the area of the triangle.
Area = √s(s-a)(s-b)(s-c)
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5. Katie has 15/20 of a dollar in her pocket. Lisa has the same amount of money in
her pocket. What fraction of a dollar does Lisa have in her pocket?
A. 5/10 B. 3/4
C. 4/5 D. 2/10
Answer:
Step-by-step explanation:
it B.
just put in the calculator and it gives you the reduced fraction
Answer:
B. 3/4
Step-by-step explanation:
Find the GCD (or HCF) of the numerator and denominator
GCD of 15 and 20 is 5
Next, divide both the numerator and denominator by the GCD
15 ÷ 5 = 3
20 ÷ 5 = 4
Finally, put them back into a fraction
[tex]\frac{3}{4}[/tex]
Therefore, 15/20 simplified to the lowest terms is 3/4.
What is the value of x in3 √ x 9?
In the given equation x = 9 is the value that satisfies the equation.
What are Square root?The square root of a number is a value that, when multiplied by itself, equals the original number. For example, the square root of 9 is 3, because [tex]3*3 = 9[/tex]. The symbol for square root is "√" and it can also be represented as "sqrt".
In the given equation [tex]x = 9[/tex] is the value that satisfies the equation.
To find the value of x in the equation [tex]3 \sqrt{x} = 9[/tex], we first need to square both sides of the equation to eliminate the square root.
[tex]3 \sqrt{x} = 9[/tex]
Squaring both sides:
[tex](3 \sqrt{x} )^2 = 9^2[/tex]
[tex]x = 9^2 / 3^2 = 9^2 / 9 = 9[/tex]
Therefore, x = 9 is the value that satisfies the equation.
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The point (0, 5) lies on a circle with the center at (0, 0). What is the area of the circle?
5x - 7 = 5 - x
Using balancing method in algebra
Answer:
5x-7-5+X=5-x-5+X
or,6x-12=0
or,6x=12
or,X=12/6
:.X=2
Let X_0, Y and Z be integers greater than 0. Let A_n be the product of the unique prime factors of X_n. What condition is needed to be met for the equation X_(n+1) = YA_n + Z to have X_p = X_q, where p =/= q?
On solving the provided question we can say that - the prime factors of 32 are 2 × 2 x 2 x 2 x 2 and of 64 are - 2 x 2 × 2 x 2 x 2 x 2
what is prime factor?Any natural number other than 1 with just itself and the number 1 as its divisors is considered a prime factor. Actually, 2, 3, 5, 7, 11, and so on are some of the first prime numbers. an amount that has been multiplied to produce another amount. By dividing 15 by 3 and 5, for instance, we get 3 5 = 15. main elements: Prime factors include all factors that are prime but are not composite. A few prime factors of 30 are 2, 3, and 5. Only 2 and 3 are prime factors of 12, so listing 2 twice as 2 2 3 (or 22 3) is necessary to factorize 12. The sum of 2 + 3 is not 12.
the prime factors of
32 are 2 × 2 x 2 x 2 x 2
64 are - 2 x 2 × 2 x 2 x 2 x 2
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Ron killed 8 times as many spiders as Harry,H (Write an expression to represent the following situations)
Answer:
Ron killed 8 times as many spiders as Harry: R = 8 * H
Step-by-step explanation:
This expression represents the situation in which Ron killed 8 times as many spiders as Harry.
A jet is flying with an air speed of 480 miles per hour at a bearing of N82 °E. Because of the wind, NE° . the ground speed of the plane is 518 miles per hour at a bearing of 79°E.
a- What are the speed and direction of the wind?
b- If the pilot increased the air speed of the plane to 500 miles per hour, what would be the resulting ground speed and direction of the plane?
A) Direction of the wind = (bearing of AS + bearing of WS) / 2 = (82 + 79) / 2 = 80.5 ° NE
B)The resulting ground speed and direction of the plane would be 535.5 miles per hour at a bearing of 80.7°E.
How to find the direction of the wind?To find the speed and direction of the wind, we can use the fact that the ground speed vector (GS) is the sum of the air speed vector (AS) and the wind speed vector (WS).
Given that:
AS = 480 miles per hour at a bearing of N82°E
GS = 518 miles per hour at a bearing of 79°E
We can use the law of cosines to find the wind speed (WS) and the angle between AS and WS.
WS = √(GS² - AS² + 2AS * GS * cos(GS - AS))
WS = √(518² - 480² + 2(480)(518)cos(79 - 82)) = √(268816 - 230400 + 466560cos(-3)) = √(28672) = 168 miles per hour
Then we can use the angle between AS and WS to find the direction of the wind:
Direction of the wind = (bearing of AS + bearing of WS) / 2 = (82 + 79) / 2 = 80.5 ° NE
To find the resulting ground speed and direction of the plane if the pilot increased the air speed to 500 miles per hour, we can use the same method as before.
Given that:
AS' = 500 miles per hour at a bearing of N82°E
GS' = √(AS'² + WS² - 2AS'WS * cos(direction of WS - direction of AS'))
GS' = √(500² + 168² - 2(500)(168)cos(80.5 - 82)) = √(250000 + 28672 + 118400cos(1.5)) = √(284872) = 535.5 miles per hour
The resulting ground speed and direction of the plane would be 535.5 miles per hour at a bearing of 80.7°E.
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Complete the inequality below to describe the
domain of the graph shown.
Domain:
DONE
completo the inequality holow to dogorike the
On solving the provided inequality equation we cans ay that therefore, 60x + 45 <250 is the necessary inequality for the given situation.
Describe inequality.An inequality in mathematics shows how two values are related in an imbalanced algebraic expression. According to inequality signals, one of the two variables on either side of the inequality may be larger than, greater than or equal to, less than, or less than or equal to another value.
If the daily cost for each crew member is $60, the daily wage for crew members is $60, and the daily cost of operations is $45; the amount paid equals the total of the wages for each crew member plus the cost of operations. In this case, let x indicate the size of the crew.
= 60x + 45
Since the maximum daily payment is $250,
In other words, the total payment cannot be more than $250.
60x + 45 ≤ 250
Therefore , the required inequality for given problem is 60x + 45 ≤ 250.
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ALGEBRA 2 - Exponential and Logarithmic Functions
John invests $25,000 in an account that pays 4.75% annual interest compounded continuously. How many years, to the nearest tenth, will it take for John’s investment to triple?
Answer:
The equation you would use to solve this problem is:
A = P * e^(rt)
Where A is the final amount, P is the initial amount, r is the interest rate, and t is the number of years.
We can rearrange the equation to solve for t:
t = (ln(A/P)) / r
Plugging in the values we know:
t = (ln(3*25000/25000)) / (0.0475)
t = (ln(3)) / (0.0475)
t = 4.93 years
So it will take about 4.9 years for John's investment to triple, to the nearest tenth.
Step-by-step explanation:
area de un triangulo rectangulo si saben digame por favorrrrr
How do you calculate quantity of seed?
The following is how you can calculate quantity of seed:
Sowing rate (kg/ha) = target plant population (p/m2) x TGW (g) x 100. % germination x % emergence.
What is Sowing rate?The quantity of seed necessary for a unit area of land to successfully grow any crop is known as Sowing rate. In other words, the Sowing rate for that crop of the land refers to the quantity of seed needed to successfully raise a crop on a given piece of land. The Sowing rate, on the other hand, refers to the quantity of seed needed to cover a given area of land.
Goals in calculating the Sowing rate:
to make sure there are enough plants in the field.in order to decrease seed waste.to be aware of how much seed will be needed in advance for a specific piece of land.to improve a crop's quality and yield.to lower the expense of growing crops.Learn more about Sowing
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makayla runs 3/5 of a mile in 1/6 of an hour. How fast, in miles per hour, does she run
Answer:
3.6 miles
Step-by-step explanation:
SolutionGiven information from the question,
[tex]\frac{1}{6} \ hour = \frac{3}{5} \ miles\\ 1 \ hour = \frac{3}{5} / \frac{1}{6} \ miles\\1 \ hour = \frac{18}{5} \ or\ 3\frac{3}{5} \ or \ 3.6 miles[/tex]
Answer:
Velocity is the term to illustrate speed
Step-by-step explanation:
velocity = distance ÷ time
velocity = 3/5 ÷ 1/6
= 18/5 m/h