The value of r is 6+ 2[tex]\sqrt{14}[/tex]
What is quadratic equation ?Algebraic equation in x that has a second degree. The quadratic equation in its conventional form is Ax2 + bx + c = 0 where a and b are the coefficients, x is the variable, and c is the constant term. To qualify as a quadratic equation, an equation must contain a non-zero term (a 0) for the coefficient of x2. In order to create a quadratic equation in standard form, the x2 term, the x term, and the constant term must be written first, second, and third, respectively. As opposed to fractions or decimals, integral values are typically used to express the numerical values of letters a, b, and c.
[tex]r^{2}-12r=51-31\\ r^{2}-12r-20=0\\ \frac{b^{2} }{4a} \\ =[/tex]
=36
= do ±36 in equation
=[tex]r^{2}-12r +36 -36 = 20\\ (r-6)^{2}=56[/tex]
=(r-6) = ±[tex]\sqrt{56}[/tex]
r = 6 ±[tex]\sqrt{56}[/tex]
r= 6+ 2[tex]\sqrt{14}[/tex]
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seth bouth pencils 1/2 are red and 1/6 are blue how many are blue or red
Answer:
3 red and 1 blue 3 of another color
Step-by-step explanation:
well you can converte the fraction 1/2 to 3/6 so ye i believe this is correct :) atleast i hope :)
B.E.S.T. TEST PREP Which of the following values of x and y make the relation a function? Select all that apply.
( − 3, 7), ( – 2, 3), (0, 8), (1, − 1), (x,y)
O x=-4, y = 0
0
x = 1, y = -2
O x = 5, y = -1
O x=2, y = 8
G
The x and y values that makes the relation a function are x = -4, y = 0, x = 5, y = -1 and x = 2, y = 8
How to determine the values of x and y?The ordered pairs are given as
(− 3, 7), (–2, 3), (0, 8), (1, − 1), (x,y)
For a list of ordered pairs to represent a function, the following must be true
The x values must have exactly one y value
Using the above as a guide, we can see that x = -4, y = 0, x = 5, y = -1 and x = 2, y = 8 fits the above description
Hence, the values of x and y are x = -4, y = 0, x = 5, y = -1 and x = 2, y = 8
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Evalúe the limit. Show steps
After evaluating the limit we have came to find that the limit of [tex]\lim_{x\rightarrow \infty }-\frac{3x^2}{x^2\ +4}[/tex] as x approaches ∞ is -3
What is limit?A limit is the value that a function, sequence, or index approaches as an input or index approaches a specified value in mathematics. Limits are required in the definitions of continuity, derivatives, and integrals, which are essential in calculus and mathematical analysis.
The notion of a limit of a sequence is further generalized to include the notion of a limit of a topological network, in addition to being closely related to the concepts of limit & direct limit in category theory.
A limit of a function is typically expressed in formulas as
[tex]{\displaystyle \lim _{x\to c}f(x)=L,}[/tex]
To find the limit we will use L'Hôpital's Rule
Find the derivative
⇒ [tex]\lim_{x\rightarrow \infty }-\frac{3x^2}{x^2\ +4}[/tex]
⇒ [tex]\lim_{x\rightarrow \infty }-\frac{6x}{2x + 0}[/tex]
⇒ [tex]\lim_{x\rightarrow -\infty }\frac{-6x}{2x }[/tex]
Evalúe ∞ as x
⇒ [tex]\frac{-6(\infty)}{2(\infty)} }[/tex]
⇒ -3
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The table represents a quadratic function. Write an equation of the function in
standard form.
X- -3,-2,-1,0
f(x)-6,0,-2,0
An equation of the quadratic function in standard form is equal to -2x² - 7x - 6 = 0.
What is a quadratic function?A quadratic function can be defined as a mathematical expression (equation) that can be used to define and represent the relationship that exists between two or more variable on a graph.
In Mathematics, the standard form of a quadratic equation is given by;
ax² + bx + c = 0
y = f(x) = ax² + bx + c
Next, we would formulate a system of equations from the data contained in the table above:
-6 = a(-3)² + b(-3) + c ⇒ -6 = 9a - 3b + c .......equation 1.
0 = a(-2)² + b(-2) + c ⇒ 0 = 4a - 2b + c .......equation 2.
-2 = a(-1)² + b(-1) + c ⇒ -2 = a - b + c .......equation 3.
From eqn. 2, we have:
c = -4a + 2b .....equation 4.
Substituting eqn. 4 into eqn. 1 and 3, we have:
-2 = a - b - 4a + 2b ⇒ -2 = -3a + b
-6 = 9a - 3b - 4a + 2b ⇒ -6 = 5a - b
By using the elimination method, we have:
-8 = 2a
a = -4
For the value of b, we have:
-2 = -3a + b
b = -2 + 3a
b = -2 + 3(-4)
b = -2 - 12
b = -14
For the value of c, we have:
c = -4a + 2b
c = -4(-4) + 2(-14)
c = 16 - 28
c = -12.
Substituting the values of a, b and c into the standard form of a quadratic equation:
ax² + bx + c = 0
-4x² - 14x - 12 = 0
-2x² - 7x - 6 = 0
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I can send the other options? I just need this explained?
The standard equation of a circle is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle.
For:
[tex]\begin{gathered} (x+3)^2+(y+1)^2=16 \\ \end{gathered}[/tex]Rewrite the equation as:
[tex]\begin{gathered} (x-(-3))^2+(y-(-1))^2=4^2 \\ so\colon \\ h=-3 \\ k=-1 \\ r=4 \end{gathered}[/tex]We can conclude it is a circle with center at (-3,-1) and radius of 4
Answers:A.(a,-2b)B.(-a,2b)C.(-a,-2b)D.(a,2b)
Midpoint formula
[tex](x_m,y_m)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]where (x1, y1) and (x2, y2) are two points and (xm, ym) are the coordinates of the midpoint between (x1, y1) and (x2, y2).
In this case, we want to find the coordinates of the midpoint between Y(0, -4b) and Z(-2a, 0). Substituting into the above formula:
[tex]\begin{gathered} (x_m,y_m)=(\frac{0+(-2a)}{2},\frac{-4b+0}{2}) \\ (x_m,y_m)=(\frac{-2a}{2},\frac{-4b}{2}) \\ (x_m,y_m)=(-a,-2b) \end{gathered}[/tex]On a roll. Suppose that you roll a fair, 6-sided die 10 times. What's the probability that
you get at least one 6?
Tyne a responro
?
MATH WIZARDS HELP PLEASE!!!!
Equation: h(t) = 96t - 16t²
This equation will form a parabolaThe zeros of the parabola will indicate the start time and height (0,0) and the end time and height (x, 0)The maximum point will be the maximum height the ball will reachThe maximum point will be the halfway point between the two zerosStep-by-Steph(t) = 96t - 16[tex]t^{2}[/tex]
Find the zeros of the given equation:
Factor out the greatest common factor (GCF)
h(t) = 8t (12 - 2t)
The two factors are:
0 = 8t
0 = 12 - 2t
For both factors, solve for t
8t = 0
8t/8 = 0/8
t = 0
12 - 2t = 0
-2t = -12
t = 6
Now we have the x-values (t) of our zeros:
t = 0
(0, 0)
t = 6
(6, 0)
The ball will land on the ground at 6 seconds
Recall that the maximum point of the graph is halfway between the two zeros:
6 + 0 = 6
6 ÷ 2 = 3
The ball will reach its maximum height in 3 seconds
To find this height, substitute t for 3 in the given equation, and solve for h:
t = 3
h(3) = 96(3) - 16(3)²
= 288 - 16(9)
= 288 - 144
= 144
The maximum height the ball will reach is 144 feet
***Refer to the graph below to check your answer:
=======================================================
Explanation:
I'll use x in place of t
And use y in place of h(t)
The equation we have is y = 96x - 16x^2
This rearranges to y = -16x^2 + 96x
Compare this to y = ax^2+bx+c to find that
a = -16b = 96c = 0The x coordinate of the vertex is
h = -b/(2a)
h = -96/(2*(-16))
h = 3
Then plug this into the equation to find the value of y
y = -16x^2 + 96x
y = -16(3)^2 + 96(3)
y = 144
The y coordinate of the vertex is k = 144
The vertex is located at (h,k) = (3, 144) to represent the highest point of the parabola.
The max height of 144 feet occurs when the ball is in the air for 3 seconds.
Help me solve this please it’s the last question
Answer:
32?
Step-by-step explanation:
????????tell me if it is correct??
I need help with a geometry problem, but I cannot type it out i will need to send a picture of it
From the triangle given, we are required to solve for x and y.
Since they are similar triangles, let's find x and y below.
For x:
[tex]\frac{5}{8}=\frac{5+x}{10}[/tex]Let's find x, from the equation above.
Cross multiply:
[tex]\begin{gathered} 8(5+x)=10(5) \\ \\ 40+8x=50 \\ \\ \text{Subtract 40 from both sides:} \\ 40-40+8x=50-40 \\ \\ 8x=10 \end{gathered}[/tex]Divide both sides by 8:
[tex]\begin{gathered} \frac{8x}{8}=\frac{10}{8} \\ \\ x=1.25 \end{gathered}[/tex]For y:
[tex]\begin{gathered} \frac{7}{8}=\frac{7+y}{10} \\ \\ 8(7+y)=7(10) \\ \\ 56+8y=70 \\ \\ 8y=70-56 \\ \\ 8y=14 \\ \\ \frac{8y}{8}=\frac{14}{8} \\ \\ y=1.75 \end{gathered}[/tex]ANSWER:
x = 1.25, y = 1.75
Solve the following system of equations:
x -2y = 18
4x + 3y = -16
What's the (x,y) coordinates
Step-by-step explanation:
Solve for X for one equation then input that value into the other equation.
x+2y=9
x=9-2y
x-y=3
(9-2y)-y=3
9-3y=3
6=3y
y=2
x=5
The value of the y-coordinate of the system of equations is y=2.
I hope it help
The height of a triangle is 5 centimeters greater than the base. The area of the triangle is 63 square centimeters. Find the length of the base and the height of the triangle.
The base and height of the triangle are 9 cm and 14 cm respectively.
How to find the side of a triangle?The height of the triangle is 5 centimetres greater than the base.
The area of the triangle is 63 cm².
Therefore,
area of a triangle = 1 / 2 bh
where
b = baseh = heightTherefore,
h = 5 + b
Hence,
area of a triangle = 1 / 2 × b × (5 + b)
area of a triangle = 1 / 2 × 5b + b²
63 = 5b + b² / 2
cross multiply
126 = 5b + b²
b² + 5b - 126 = 0
b² + 14b - 9b - 126 = 0
b(b + 14) - 9(b + 14) = 0
(b + 14)(b - 9) = 0
b = -14 or b = 9
Therefore, the base can only be positive .
Hence,
Base of the triangle = 9 cm
height of the triangle = 9 + 5 = 14 cm
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what's the difference AAA,ASA and SSS
There are three main distinctions between AAA, ASA, and SSS:
AAA: A triangle is said to be comparable to another if any two of its three angles are equal to any two of its three angles.
ASA: According to the ASA rule, two triangles are said to be congruent if any two angles and the side located between the angles of one triangle are equal to the corresponding two angles and the side located between the angles of the second triangle.
SSS: According to the SSS rule, two triangles are considered to be congruent if all three sides of one triangle are comparable to the corresponding three sides of the other triangle.
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Riders for the Kiddie Koaster at the State Fair must be no more than 48 inches tall. Which inequality best expresses the height of the riders?
[tex]x \leqslant 48[/tex]
In a classroom of 28 students 75% of the students have met their reading goal. Label the double number line.How many students met their reading goal?What fraction of 28 students met their reading goal? Explain.
Explanation:
Total number of students = 28
75% of 28 = 75% × 28
= 0.75 × 28 = 21
This means 21 students have met their reading goal
Fraction of 28 students that met their reading goal = 21/28
Divide numerator and denominator by 7
3/4
Attaching the label:
I omitted the first label on both lines: it should be 0 and 0% respectively
28/4 = 7
100%/4 = 25%
Each demacation represent 7 units on the first line
Each dividing line represent 25% on the second line
a cycle wheel does 2096 full turns in 8 minutes work out the number of full turns per minute
So basically you do 2096 divided by 8
Answer : 262 Minutes is alr i got u bro
Factor the following expression. x^2+17x+60
nswer:
[tex](x+12)(x+5)[/tex]Explanation:
iven the below expression;
[tex]x^2+17x+60[/tex]We'll follow the below steps to factor the given expression;
tep 1: L
The factors are 12 and 5. We'll go ahead and replace the middle term 17x with these factors as seen below;
[tex]x^2+12x+5x+60[/tex]tep 2: GG
[tex](x^2+12x)+(5x+60)[/tex]tep 3: F
[tex]x(x+12)+5(x+12)[/tex]tep 4: FW
[tex](x+12)(x+5)[/tex]which sets of ordered pairs are functions and which are not functions? 1. { (1,5),(2,5),(3,5),(4,5) } 2. { (1,5),(1,6),(1,7),(1,8) } 3. { (1,6),(2,5),(2,3),(4,8) } 4. { (1,5),(3,7),(4,8),(4,9) }
Number 2 is not a function, because we have more that one value of x that is the same
Number 3 is also not a function, we have more than one value of x that is the same
Number 4 is also not a function
Therefore, only number 1 is a function
Is 10.6 x 10^14 scientific notation
Is 2.019 x 10^12 scientific notation
is 9.5 x 10^-7 scientific notation
0.526 x 10^-2 scientific notation
Answer:
The top and the bottom numbers are not in scientific notation; the other two are in scientific notation.
Of all the people who attended the school
play, 65% were parents of children in the
play. If the total attendance was 500 people,
how many were parents of children in the
play?
Answer:
Step-by-step explanation:
Total attendance = 500 people
Parents of children in play = 65% of 500
=>0.65 * 500
=> 325
325 were the parents of children in the play.
Assume that 40% of a country's population has had Covid and that 55% of the country's population has been vaccinated. There is some overlap between the two groups, and 25% of the country's population has both had Covid and has also been vaccinated. Either having Covid or being vaccinated gives some protection against getting Covid. Based on these assumptions, if you choose a resident of this country at random what is the probability that the person has either had Covid or has been vaccinated and therefore has some protection against Covid?
The probability that the person has either had Covid or has been vaccinated and therefore has some protection against Covid is 45%
Data obtained from the questionFrom the question given, the following data were obtained:
40% of a country's population has had Covid55% of the country's population has been vaccinated25% of the country's population has both had Covid and has also been vaccinatedHow to determine the required probabilityThe probability that the person has either had Covid or has been vaccinated and therefore has some protection against Covid can be obtained as follows:
The percentage of person that had Covid and not vaccinated
= 40% - 25%
= 15%
The percentage of person that has been vaccinated and never had Covid
= 55% - 25%
= 30%
The probability that the person has either had Covid or has been vaccinated
= 15% + 30%
= 45%
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Anders discovered an old pay statement from 12 years ago. His monthly salary at the time was $2800 versus his current salary of $4970 per month. At what (equivalent) compound annual rate has his salary grown during the period
The (equivalent) compound annual rate at which Anders' salary has grown during the 12 years is 4.9%.
What does the compound annual rate signify?The compound annual rate is the equivalent rate of interest at which the present value of money grows to attain a future value.
At a 4.9% compound annual rate, Anders' salary has been growing by adding the growth amount to the initial salary and compounding both the principal and subsequent interest amounts until 12 years.
N (# of periods) = 12 years
PV (Present Value) = $2,800
PMT (Periodic Payment) = $0
FV = $-4,971.23
Results:
I/Y (Interest per year) = 4.9%
Total Interest = $2,171.23
Thus, using the online finance calculator, we can determine that Anders' salary has been compounded at 4.9% annually.
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Write the vector shown by the image below:
the vectors are : (i+5j) , (5i+j)
Here a vector is an object that has both a magnitude and a direction. Geometrically, able to picture a vector as a coordinated line fragment, whose length is the magnitude of the vector, and with an arrow demonstrating the direction. The direction of a vector is from its tail towards its head. Two vectors are the same on the off chance that they have the same magnitude and direction. We signify vectors utilizing boldface as in a or b. In the given graph we can see, for the vector T, it is 1 unit on the x-axis and 5 units on the y-axis, whereas for the vector S its 5 units on the x-axis and 1 unit on the y-axis. Since the unit vectors for the x-axis and y-axis are i and j,
So, the vectors will i+5j and 5i+j
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write an expression with a value that is twice as much as 236+912
The sum of two numbers is 50 the smaller number is 16 less than the larger number
The larger number is 33 and the smaller number is 17.
Let the larger number be x
Then, the smaller number will be x-16
According to the question,
Larger number + smaller number = 50
So,
x+(x-16) = 50
2x = 50+16
2x = 66
x = 66÷2
x = 33
Hence,
Larger number = x = 33
Smaller number = x-16 = 33-16 = 17
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Solve the following inequalities,express the solution in interval notation and graph it 4.a)
The inequality is given to be:
[tex]\mleft|x-6\mright|\ge2[/tex]Recall the Absolute Rule:
[tex]\mathrm{If}\: |u|\: \ge\: a,\: a\: >\: 0\: \mathrm{then}\: u\: \le\: -a\: \quad \mathrm{or}\quad \: u\: \ge\: a[/tex]Applying this to the inequality, we have:
[tex]\begin{gathered} x-6\ge2 \\ x\ge2+6 \\ x\ge8 \end{gathered}[/tex]or
[tex]\begin{gathered} x-6\le-2 \\ x\le-2+6 \\ x\le4 \end{gathered}[/tex]Therefore, the solution to the inequality is:
[tex]x\le\: 4\quad \mathrm{or}\quad \: x\ge\: 8[/tex]Determine the MOST precise bane for quadrilateral PQRS
Solution:
Given:
To get the precise name of the quadrilateral PQRS, using the coordinates of the points given;
The distance between points P and Q, and points Q and R are the same.
Also the distance between points P and S, and points R and S are also the same.
This means;
[tex]\begin{gathered} PQ\cong QR \\ PS\cong RS \end{gathered}[/tex]Hence, the image is as shown;
By the property of a kite, which says that two pairs of consecutive sides are congruent sides.
Hence, the most precise name for the quadrilateral PQRS is a KITE.
100 POINTS TO WHOEVER RESPONDS FIRST!!!!
The domain and range of the given inequality graph are; Domain: {x | -2 ≤ x ≤ 2} and Range: {x | -6 ≤ x ≤ 6}
What is the Domain and Range of the Function?The domain of a function is the set of all possible input values that make a function possible. Meanwhile the range of a function is the set of all possible output values that make a function possible.
Now, when dealing with an inequality graph, it is pertinent to note that a shaded dot implies less than or equal to (≤) or greater than or equal to (≥) while unshaded means less than or greater than.
Now. the range of the graph is closed from y = -6 to y = 6. Thus, the range is; {y| -6 ≤ y ≤ 6}
Meanwhile the domain of the graph is closed from x = -2 to x = 2. Thus, the domain of the graph is;
{x | -2 ≤ x ≤ 2}
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slove system of equations x+y=4 -x + y = 2
The solution for the equations x = 1 and y = 3
How to determine the solution to the system?A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
x + y=4
-x + y = 2
Add the equations
So, we have
2y = 6
Divide both sides by 2
y = 3
Substitute y = 3 in x + y = 4
x + 3 = 4
Evaluate
x = 1
Hence, the solution for the system of linear equations x + y=4 and -x + y = 2 are x = 1 and y = 3
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How do I convert 65 mi/hr to centimeters per minute
In the metric system, centimeters per minute (cpm) represents speed or velocity. It counts the centimeters that are covered in a minute.
65 mi/hr to 174346 centimeters per minute.
How to convert Miles Per Hour to Centimeters Per Minute (mi/h to cm/min ?$1 mi/h = 2682.2346355307 cm/ min.
65 × 2682.2346355307 cm/min = 174345.2513095 Centimeters Per Minute.
Always check the results; rounding errors may occur.
The base unit of [speed] (meters per second), 1 Miles Per Hour (mi/h) exists equivalent to
0.44704 meters-per-second,
while 1 Centimeters Per Minute (cm/min) = 0.000166667 meters-per-second.
65 Miles Per Hour to common speed units
65 mi/ h = 65 miles per hour (mi/h)
65 mi/h = 1.0833333333333 miles per minute (mi/m)
65 mi/h = 174346 centimeters per minute
Therefore, the correct answer is 174346 centimeters per minute.
The base unit for speed is meters per second (Non-SI Unit)
[Miles Per Hour] symbol/abbreviation: (mi/h)
[Centimeters Per Minute] symbol/abbreviation: (cm/min)
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