The two numbers whose sum is 2 and product is -24 are 6 and -4
What is a quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x
a[tex]x^{2}[/tex]+bx+c=0
with a ≠ 0 . Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
Let the two numbers be x and y
so that
x + y = 2 ----------------1
xy = -24 -----------------2
from equation 1 make x the subject of the equation, so that it becomes
x = 2 - y ---------------3
substitute x in equation 3 in equation 2
y(2-y) = - 24
multiply out the bracket
2y - [tex]y^{2}[/tex] = -24
taking all terms to one side of the equation, it becomes
[tex]y^{2}[/tex] -2y -24 = 0
factorizing the equation
[tex]y^{2}[/tex] -6y + 4y - 24 = 0
y(y - 6) +4(y - 6) = 0
taking the terms outside bracket and putting them in a new bracket we have
(y + 4) (y - 6) = 0
so y + 4 = 0 or y - 6 = 0
y = -4 or y = 6
using y = -4 and substituting in equation 3
x = 2 - - 4
x = 6
In conclusion the two numbers are 6 and -4
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f(x)=0.145x^2
The function above models f, the kinetic energy, in joules, of a baseball traveling at a speed of x meters per second. Based on the function, what is the kinetic energy, in joules, of a baseball traveling at a speed of 40meters per second?
A) 5.8
B) 58
C) 232
D) 2,320
Answer: A) 5.8
Step-by-step explanation: Hard guess
Lauren is going to a carnival that has games and rides. Each game costs $2 and each ride costs $4.75. Lauren spent $50 altogether at the carnival and the number of rides she went on is 2 more than the number of games she played. Write a system of equations that could be used to determine the number of games Lauren played and the number of rides Lauren went on. Define the variables that you use to write the system.
Taking into account the definition of a system of linear equations, the system of equations to be solved is
r= g+2
2g + 4.75r= 50
where "g" is the number of games Lauren played and "r" is the number of rides Lauren went on.
System of linear equationsA system of linear equations is a set of two or more first degree equations, in which two or more unknowns are related and it is desired to find their value.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. Thit is, the values of the unknowns must be find, and when the are replacing, they must give the solution proposed in both equations.
This caseIn this case, a system of linear equations must be proposed taking into account that:
"g" is the number of games Lauren played."r" is the number of rides Lauren went on.You know:
Each game costs $2 and each ride costs $4.75.Lauren spent $50 altogether at the carnival.The number of rides Lauren went on is 2 more than the number of games she played.The system of equations to be solved is
r= g+2
2g + 4.75r= 50
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This is 100% correct. Just got it right.
"g" is the number of games.
"r" is the number of rides.
System of equations
r = g + 2
2g + 4.75r = 50
ANSWER ASAP 8TH GRADE MATH EASY
Answer:
It is the first option
Step-by-step explanation:
A rock is dropped from a height of 100 feet. Calculate the time between when the rock was dropped and when it landed. If we choose “down” as positive and ignore air friction, the function is h(t)=25t^2-81
The time between when the rock was dropped and when it landed is 2.7 seconds.
What is function?
A function is a procedure or a relation that links each element of a non-empty set A, at least one element of another non-empty set B, to another element of the first non-empty set A. In mathematics, a function is defined as a relation f between a set A (the function's domain) and a set B (its co-domain). For any a A and b B, f = (a,b)| .Every element of set A must have exactly one image in set B for a relation to be considered a function. A relation from a non-empty set B is called a function if it has the property that no two separate ordered pairs in f have the same first element.
Here the given height h(t) = 100 feet
Now the given function is,
=> h(t)=25[tex]t^2[/tex]-81 .
Put h(t)=100 then ,
=> 100= 25[tex]t^2[/tex]-81 .
=> 100+81=25[tex]t^2[/tex]
=>[tex]t^2[/tex]= 181/25
=> t = 2.69=2.7 sec.
Hence the time between when the rock was dropped and when it landed is 2.7 seconds.
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Please help me, please
Answer:
m∠1 = 88°
m∠2 = 42°
m∠3 = 113°
Step-by-step explanation:
All of the angles in a triangle add up to 180°. This knowledge can be used to find angle 3, which I will rename c to make writing an equation easier.
[tex]180=25+42+c\\180=67+c\\113=c[/tex]
Angle 3 is 113°
Two angles on either side of the intersection of two straight lines are equal, therefore angle 2, or b:
[tex]b=42[/tex]
Angle 2 is 42°
Now that two angles are known in the leftmost triangle, we can solve for the last one: Angle 1, or a:
[tex]180=50+42+a\\180=92+a\\88=a[/tex]
Angle 1 is 88°
need help for this question dhsjwiqibdbsns
Answer:
130°
Step-by-step explanation:
Triangle JKL is an isosceles triangle and leg angles are equal :
m<J = m<L
The sum of interior angles in a triangle is equal to 180.
m<J + m<L + m<K = 180
25 + 25 + m<K = 180
50 + m<K = 180 subtract 50 from both sides
m<K = 130°
a manager of a clothing store always orders 2 small T-shirts and 3 large t-shirts for every 4 medium T-shirts.The manager plans to order 24 medium T-shirts. How many small T-shirts and large T-shirts should the manager order? show your work.
Answer: 12 small t-shirts and 18 large t-shirts
Step-by-step explanation:
24÷4=6
2×6=12 small t-shirts
3×6=18 large t-shirts
Use front-end estimation to place the decimal point in each answer. a) 32.47 6.75 2 5 7 2 b) 118.234 19.287 1 3 7 5 2 1 c) 17.9 0.8 1 7 1
Using front end estimation, the correct decimal solutions to the given problems are;
1) 25.72
2) 137.521
3) 17.1
How to use front end estimation?Front end estimation is defined as one way to round numbers in such a manner that an approximate answer can be easily found.
1) 32.47 - 6.75
First of all, deal with the whole numbers portion to get;
32 - 6 = 26
Next step is to handle the decimal part to get;
0.47 is approximately equal to 0.5 while 0.75 is approximately equal to 0.8. Thus;
0.5 - 0.8 = - 0.3
Therefore, we have;
26 + (-0.3) = 25.70
Therefore, the correct decimal solution can be written as; 25.72
2) 118.234 + 19.287
First of all, deal with the whole numbers portion to get;
118 + 19 = 137
Next step is to handle the decimal part to get;
0.234 is approximately equal to 0.2 while 0.287 is approximately equal to 0.3. Thus;
0.2 + 0.3 =0.5
Therefore, we have;
137 + 0.5 = 137.5
Therefore, the correct decimal solution can be written as; 137.521
C) 17.9 - 0.8
First of all, deal with the whole numbers portion to get;
17 - 0 = 17
Next step is to handle the decimal part to get;
0.9 - 0.8 = 0.1
Therefore, we have;
17 + 0.1 = 17.1
Therefore, the correct decimal solution can be written as; 17.1
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company x has 50 employees and company y has 60 employees. both companies have the same number of full-time employees, but company y has 3 more than twice the number of part-time employees that company x has. how many part-time employees does company y have?
Using the simplification, company y has 17 number of part-time employees.
In the given question we have to find how many part-time employees does company y have.
From the question, company x has 50 employees and company y has 60 employees.
Both companies have the same number of full-time employees, but company y has 3 more than twice the number of part-time employees that company x has.
Let company x has A number of part-time employees.
According the given statement
Company y has number of part-time employees = 2A+3
Let company X and Y have B number of full-time employees.
So the total number of employees in company x;
A+B = 50....................(1)
The total number of employees in company x;
2A+3+B = 60
Subtract 3 on both side we get
2A+B=57....................(2)
Subtract Equation 2 and 1
2A+B-(A+B)=57-50
2A+B-A-B=57-50
A=7
Now putting the value of A in equation 1
7+B=50
Subtract 7 on both side we get
B=43
As, Company y has number of part-time employees = 2A+3
Company y has number of part-time employees = 2×7+3
Company y has number of part-time employees = 14+3
Company y has number of part-time employees = 17
Hence, company y has 17 number of part-time employees.
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Find the measure of the that is supplementary to in the diagram below. Enter only the number.
Image showing line A B and line C D that intersect at point E. The angle A E D is labeled 65 degrees.
Answer: 115
Step-by-step explanation: trust me bro free lee
Two angles are supplementary if their sum is 180° thus the angle supplementary to angles m∠AED are m∠DEB and m∠AEC and their measure is 115° both.
What is an angle?The angle is the measurement of the angular distance for example for linear motion we have a meter inch but for angular rotation, we don't have the measurement so the angle is useful to measure the angular rotation.
As per the given lines, AB intersect CD at E has been drawn below,
m∠AED = 65° (given)
m∠AED + m∠DEB = 180° (supplementary)
m∠DEB = 180° - 65° = 115°.
m∠AED + m∠AEC = 180° (supplementary)
m∠AEC = 180° - 65° = 115°.
Hence "Two angles are supplementary if their sum is 180° thus the angle supplementary to angles m∠AED are m∠DEB and m∠AEC and their measure is 115° both".
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Please help I’m really confused on this. Thanks!
Answer:
[tex]y=\frac{1}{2}x-8[/tex]
Step-by-step explanation:
Perpendicular lines have the same slope. So, the slope of the line we need to find is 1/2.
Thus, the equation is
[tex]y+5=\frac{1}{2}(x-6) \\ \\ y+5=\frac{1}{2}x-3 \\ \\ y=\frac{1}{2}x-8[/tex]
each side of a square is increasing at a rate of 8 cm/s. at what rate (in cm2/s) is the area of the square increasing when the area of the square is 16 cm2? incorrect: your answer is incorrect. cm2/s
The rate of the square increasing when the area is 16 cm² is 64 cm²/s. The result is obtained by using basic derivative rules.
How to count the rate of a square increasing?The rate of a square increasing can be counted by the derivative of the area of the square as a function of time.
dA/dt = 2s ds/dt
Where s is side length.
If each side of a square is increasing at a rate of 8 cm/s, what is the rate of the square increasing when the area is 16 cm²?
We have the side of the square as the function of time.
ds/dt = 8 cm/s
When the area is 16 cm², the side length is
A = s²
16 = s²
s = √16
s = 4 cm
The rate of the square increasing is
dA/dt = 2s ds/dt
dA/dt = 2 × 4 × 8
dA/dt = 64 cm²/s
Hence, the rate of the square increasing when the area is 16 cm² is 64 cm²/s.
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Anna wants to take fitness classes. She compares two gyms to determine which would be the best deal for her. Fit fast charges a set fee per class. Stepping up charges a monthly fee, plus an additional fee per class. What is the system of equations representing these costs? y = 5. 5x and y = 7. 5x + 10 y = 7. 5x and y = 5. 5x y = 7. 5x and y = 5. 5x + 10 y = 7. 5x + 10 and y = 5. 5x + 10.
The system of equations representing these costs is y = 7.5x and y = 5..5x + 10
Given,
Anna desires to enroll in fitness courses. She contrasts two gyms to see which offers the best value. Each class at Fit Fast costs a specified amount. Stepping up costs a monthly fee as well as a price for each lesson.
We have to find the system of equations representing these costs;
Fit Fast: a certain number of feet per class = y = Ax
Stepping Up: a monthly charge plus a cost for each additional class = h = Bx + C
The second and fourth systems can be ignored since they lack the form that is implied by the statement.
Given that it reflects a choice that is always preferable to the alternative, the first system produces an obvious result. There is no need to compare because, for any positive value of x, 5.5x will be less than 7.5x + 10,
The third system is
It is necessary to solve the equations y = 7.5x and y = 5.5x + 10 to decide when one rate is more practical than the other.
That is,
The system of equations representing these costs is y = 7.5x and y = 5..5x + 10
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Determine the equation of the line that is perpendicular to the given line, through the given point
y=x-1; (-6,2)
Answer:
y = -x - 4
Step-by-step explanation:
Given line: y = x - 1
Slope of given line = 1
The slopes of perpendicular lines are negative reciprocals, so the slope of the perpendicular line is -1.
slope = -1
point: (-6, 2)
y = mx + b
y = -x + b
2 = -(-6) + b
2 = 6 + b
b = -4
Equation:
y = -x - 4
what is 0.675 as a percent
Answer:
67.5
Step-by-step explanation:
Answer:67.5
Step-by-step explanation:0.675*100=67.5
Simplify: |2-5|-(6 divided 2+1)^2
After simplification of |2-5|-(6/2+1)², the resultant answer is (A) -13.
What is simplification?To simplify simply means to make anything easier.
In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler.
Calculations and problem-solving techniques simplify the issue.
Substitute "of" for "multiplication," and "/" for "division."
Always carry out operations in accordance with "BODMAS."
Division and multiplication are equally important (Start from left) Both addition and subtraction are equally important.
So, simplify |2-5|-(6/2+1)² as follows:
|2-5|-(6/2+1)²
|-3| - (6/2 + 1)²
We know that : |-3| = 3 and (6/2 + 1)² = 16
Then, we have:
3 - 16
- 13
Therefore, after simplification of |2-5|-(6/2+1)², the resultant answer is (A) -13.
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The given lengths are two sides of a right triangle. All three sides of the triangle form a Pythagorean Triple. Find the length of the third side and tell whether it is a leg or the hypotenuse. 9 and 41
Answer:
40, leg
Step-by-step explanation:
The triangle has side lengths of 9, 40, and 41.
41 is the hypotenuse, so 40 is a leg.
In order to combine exponents with the multiplication or division properties, the terms must have the same?
Answer:
To multiply terms containing exponents, the terms must have the same base and/or the same power. To multiply terms with the same base, keep the same base and add the powers together. To multiply terms with different bases but the same power, raise the product of the bases to the power.
Step-by-step explanation:
is y=7-3x linear? if it is than why?
Yes y = 7 - 3x is a linear function
What is linear function ?A linear function consists of functions where the variables has exponents of 1.
The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
Definition of variables of a linear function
y = output variable
m = slope
x = input variable
c = y intercept
In comparison to the question asked
y = 7-3x
m = slope = -3
x = input variable
c = 7
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3 tons of topsoil cost 2,520.00. What is the price per pound?
Answer:
$0.42
Step-by-step explanation:
3ton=6000pounds
2,520/6000=$0.42
Juan is learning about like terms in his math class. He must check all the combinations below that are like terms. Which ones should he check? 3x and x and 0.5 4 ✔ -m and 8m ✓ -xy² and 2xy² * y and y² * 4xy and -5x²y * m and n ✔ -7 and 6
the answers are 1,2,3,4,8 i just took it rn
From given set, 3x and x; 1/4 and 0.5; –m and 8m; –xy² and 2xy²; –7 and 6 are the like terms combinations
Like and unlike terms in algebraic expression:In algebraic terms, the terms that contain the same variable and the same power or degree are called like terms, In algebraic like terms, the numerical coefficients can vary but are not variables.
Here are some examples of like terms and unlike terms,
4x and 9x are like terms
3x²y and 10x²y are like terms
2xy and 10yx are like terms
3x and 19y are unlike terms [ ∵ variable is different ]
2xyz and 2xy are unlike terms [ ∵ variables is missing in 2nd term ]
Here we have a set of algebraic terms that can be classified as given below
=> 3x and x - like terms
=> 1/4 and 0.5 - like terms
=> –m and 8m - like terms
=> –xy² and 2xy² - like terms
=> y and y² - unlike terms [ ∵ powers are not same ]
=> 4xy and –5x²y - unlike term [ ∵ powers are not same ]
=> m and n - unlike term [ ∵ variables are not same ]
=> –7 and 6 like terms
Therefore,
From given set, 3x and x; 1/4 and 0.5; –m and 8m; –xy² and 2xy²; –7 and 6 are the like terms combinations
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The complete Question
Juan is learning about like terms in his math class. He must check all the combinations below that are like terms. Which ones should he check? Choose all that apply.
=> 3x and x
=> 1/4 and 0.5
=> –m and 8m
=> –xy² and 2xy²
=> y and y²
=> 4xy and –5x²y
=> m and n
=> –7 and 6
I need help please please
Hallar centro, radio y longitud de los siguientes intervalos
a) [3, 8]
b) [-5,2]
c) [0, 12]
d) [-9,0]
A continuación, se resume el centro, el radio y la longitud de cada intervalo:
Caso A: Centro: 5.5, Radio: 2.5, Longitud: 5
Caso B: Centro: - 1.5, Radio: 3.5, Longitud: 7
Caso C: Centro: 6, Radio: 6, Longitud: 12
Caso D: Centro: - 4.5, Radio: 4.5, Longitud: 9
¿Cómo hallar el centro, el radio y la longitud de un intervalo?
En este problema tenemos cuatro casos de intervalos de números reales sobre una recta numérica. Los números reales representan un conjunto continuo, no discreto, lo cual significa que existe un número infinito de puntos dentro de la distribución lineal.
El centro es igual al punto medio del intervalo, el radio es la distancia entre el punto medio y cualesquiera de los extremos y la longitud es el doble del radio del intervalo.
Centro:
C = 0.5 · (m + M)
Radio
R = C - m
Longitud
L = 2 · R
Donde:
m - Límite inferior del intervalo.M - Límite superior del intervalo.A continuación, determinamos el centro, el radio y la longitud de cada intervalo:
Caso A
C = 0.5 · (3 + 8) = 0.5 · 11 = 5.5
R = 5.5 - 3 = 2.5
L = 2 · 2.5 = 5
Caso B
C = 0.5 · [(- 5) + 2] = 0.5 · (- 3) = - 1.5
R = - 1.5 - (- 5) = - 1.5 + 5 = 3.5
L = 2 · 3.5 = 7
Caso C
C = 0.5 · (0 + 12) = 6
R = 6 - 0 = 6
L = 2 · 6 = 12
Caso D
C = 0.5 · [(- 9) + 0] = - 4.5
R = - 4.5 - (- 9) = 4.5
L = 2 · 4.5 = 9
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The line crossing the point (2,-2) and with the slope = -6.
What is the solution to the system of equations? y = –5x + 3 y = 1 (0. 4, 1) (0. 8, 1) (1, 0. 4) (1, 0. 8).
The solution to the system of equations (0.4, 1).
Given equations according to the question,
y = -5x+3
y = 1
Now we can use y = 1 and substitute the value of y in y = -5x+3
After substituting we get, the value of y we get,
= 1 = -5x+3
Now given points according to the questions are
(0.4, 1) , (0.8, 1), (1, 0.4), (1, 0.8).
We substitute these points in the equation to see which points satisfy the equation, the point satisfying the equation is our point.
First, we will use (0.4, 1)
= 1 = -5x+3
= 1 = -5×0.4 + 3
= 1 = -2+3
= 1 = 1
Hence (0.4, 1) is our first solution of the equation.
Then we will use (0.8 ,1)
= 1 = -5x+3
= 1 = -5×0.8 + 3
= 1 = -4+3
= 1 = -1
Hence (0.8, 1) is not out the solution to the equation.
Then we will use (1,0.4)
= 1 = -5x+3
= 1 = -5×1 + 3
= 1 = -5+3
= 1 = -2
Hence (1, 0.4) is not the solution to the equation.
Then we will use (1,0.8)
= 1 = -5x+3
= 1 = -5×1 + 3
= 1 = -5+3
= 1 = -2
Hence (1, 0.8) is not the solution to the equation.
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write an equation for the line in the slope-intercept form.
slope= 8/9, y-intercept=-4
A) f(x) = 9/8x +9/2
B) f(x) = -8/9x - 4
C) f(x) = 8/9x - 4
D) f(x) = -8/9x + 4
Answer:
the answer is c.
Step-by-step explanation:
the slope will always have an x behind it and the y intercept is exactly as written
Assume that louisa carried an average balance of $1,000 from her credit card purchases over the past year. The a. P. R. On her credit card for the past year was 19. 99%. Approximately how much interest would louisa have paid over the course of the year?.
It would have cost Louisa $200 in interest charges.
The simple interest amount is calculated as follows;
SI = P*I*t
That is where we have
The balance is P.
The interest rate is I.
The time is t.
Regarding this issue;
Balance of $1,000, 19.99% APR, and 1 year.
She will pay the following sum;
SI = 1000 *0.199*1
SI = 199.9
SI ≅ 200
Louisa would have had to pay $200 in interest fees.
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A bag containing 5 red and 7 green marbles.Two marbles are drawn consecutively without replacing them. Calculate the probability that both marbles are off the same color by using a tree diagram.
The probability that both marbles are of the same color is 31/66
What is probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Here, we have
5 red and 7 green marbles.
We have to calculate the probability of two marbles being drawn consecutively without replacing them.
The first is that if we define events R to be two red marbles, and G to be two green marbles, then we can verify that:
P(R) = (5/12)(4/11)
P(G) = (7/12)(6/11)
Then, P(R ∪ G) = P(R) + P(G)
= (5/12)(4/11) + (7/12)(6/11)
= 5/33 + 7/22
= 31/66
Hence, the probability that both marbles are of the same color is 31/66
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naomi osaka plays tennis regularly with a friend, and from past experience, she believes that the outcome of each match is independent. for any given match she has a probability of 0.6 of winning. the probability that she wins the next two matches is:
The probability that she wins the next two matches is 36% or 0.36
How to calculate the probability of two matches?
Given,
She believes that the outcome of each match is independent. So, the outcome of next match does not depend on the previous match, is called independent event.
The probability of winning one match is 0.6
Since the outcome of each match is independent, we easily get the probability of she winning the next two matches by multiplying the probability of she winning per match. So,
Probability she wins the next two matches = 0.6 x 0.6
= 0.36 or 36%
Thus, the probability that she wins the next two matches is 36% or 0.36
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Is it possible that creating a Boxplot could show outliers but z-scores show no outlier?
No, Is it not possible that creating a Boxplot could show outliers but z-scores show no outlier. This is because Any z-score that is either higher than +3 or lower than -3 is viewed as an issue.
When there isn't an anomaly, what does that mean?When you declare a data point to be an outlier and reject it, you are indicating that even if you have already observed the point, it is unlikely to happen again.
Z scores make it easier to determine whether a data value is larger or less than the mean and how far from the mean it is. The Z score precisely indicates the number of standard deviations a data point deviates from the mean.
So, Outliers can be highlighted using scatterplots, histograms, and boxplots. Asterisks or other symbols are displayed on the graph in boxplots to plainly show the presence of outliers in a dataset.
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