The roots of the equation [tex]x^{2}[/tex]-15x +2 =0 are 14.865 and 0.135
What is completing the square method?Completing the square method is one of the methods to find the roots of the given quadratic equation.
Given equation is:
[tex]x^{2}[/tex]-15x +2 =0
Using Completing the Square method we have
[tex]x^{2}[/tex]-15x +2 + [tex](\frac{15}{2})^{2}[/tex] - [tex](\frac{15}{2})^{2}[/tex] =0
Now,
[tex]x^{2}[/tex]-15x + [tex](\frac{15}{2})^{2}[/tex] - [tex](\frac{15}{2})^{2}[/tex] +2=0
or, [tex][x-(\frac{15}{2})]^{2}[/tex] - 225/4 +2 =0
or, [tex][x-(\frac{15}{2})]^{2}[/tex] -217*4 =0
or, [tex][x-(\frac{15}{2})]^{2}[/tex] = 217/4
or, [tex]x[/tex] = [tex]\pm \frac{14.73}{2} + \frac{15}{2}[/tex]
or, [tex]x_1[/tex]= 14.865, [tex]x_2[/tex]= 0.135
Thus, the roots of the quadratic equation are: 14.865 and 0.135
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A ball is projected up into the air from the surface of a platform to the ground below. The height
of the ball above the ground, in feet, is modeled by the function f(t) = -16t2 + 96t + 112, where
t is the time, in seconds, after the ball is projected.
State the coordinates of the vertex. Explain what it means in the context of the problem
The vertex of the quadratic function is of (3,256), which means that a maximum height of 256 feet is obtained after 3 seconds.
What is the vertex of a quadratic equation?A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The vertex is given by:
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex][tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]Considering the coefficient a, we have that:
If a < 0, the vertex is a maximum point.If a > 0, the vertex is a minimum point.In this problem, the height of the ball is given by:
f(t) = -16t² + 96t + 112.
Hence the coefficients are a = -16 < 0, b = 96, c = 112, and the coordinates of the vertex are:
[tex]x_v = -\frac{96}{2(-16)} = 3[/tex][tex]y_v = -\frac{96^2 - 4(-16)(112)}{4(-16)} = 256[/tex]The vertex of the quadratic function is of (3,256), which means that a maximum height of 256 feet is obtained after 3 seconds.
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Consider this cone. a cone. point a is the vertex, b is the height, c is the radius, and d is the diameter. identify the parts of the cone. which letter indicates the height? which letter indicates the radius? which letter indicates the diameter? which letter indicates the vertex?
The parts of the cone can be explained as;
The height is ABThe radius is CBThe diameter is CDThe vertex is AWhat is a cone ?A cone can be regarded as a three-dimensional shape which has a vertex at the top of it.
Considering a cone as described in the question, we could see that the distance from point A to B will gives us the height which is the vertical length.
Therefore, Vertex is at the top of the cone which is point A.
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Answer:
b
c
d
a
Step-by-step explanation:
;)
When are two triangles similar? Select all that apply.
All three of their corresponding angles have the same measure.
Two of their corresponding angles are the same angle measure.
Only one of their angles match.
All ratios of corresponding sides are proportional.
Two of their corresponding sides are in the same ratio.
Two triangles are said to be similar when; two of their corresponding angles are the same angle measure.
What is a triangle?A triangle is a polygon with three sides and three angles.
Types of triangles
Equilateral triangleScalene triangleIsosceles triangleTwo triangles are said to be similar if two pairs of their corresponding angles are congruent. This is because if two pairs of angle are the equal, then the third pair must also be equal.
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subtract the quotient of 15 divided by 3 from the sum of 33 and 7
Answer:
(33+7)-(15/3) = 35
Step-by-step explanation:
35
Step-by-step explanation:
fancy way of saying (33+7) - (15/3)
33 + 7 = 40
15 / 3 = 5
40 - 5 = 35
What is the eighth term of the sequence below?
5, 9, 13, 17, …
A. 33
B. 30
C. 29
D. 34
Answer:
A. 33
Step-by-step explanation:
Add 4 to each number
1. 5 is your first number
2. 5+4= 9 is your second number
3. 9+4= 13 is your third number
4. 13+4= 17 ...
5. 17+4= 21 ...
6. 21+4= 25 ...
7.25+4= 29 ...
8.29+ 4= 33 is your eight number
Pls solve 3c for me.will mark branliest a
.
Step-by-step explanation:
if you could solve 3a and 3b, you can also solve 3c. it is the same principle.
x-intercepts means y = 0.
remember, a square root has always 2 results : a positive and a negative one.
3c
0 = -(x - 3)² + 25
(x - 3)² = 25
x - 3 = ±5
x1 = +5 + 3 = 8
x2 = -5 + 3 = -2
3a
0 = (x + 1)² - 4
4 = (x + 1)²
±2 = x + 1
x1 = +2 - 1 = 1
x2 = -2 - 1 = -3
3b
0 = (x + 2)² - 9
9 = (x + 2)²
±3 = x + 2
x1 = +3 - 2 = 1
x2 = -3 - 2 = -5
A car starts from an office building, which is 5 miles east and 2 miles south of the town center. The car travels 6 miles north, makes a left turn and then travels 8 miles. What is the car’s final position? What single translation vector moves the car from its starting position to its final position?
Answer:
[tex]\displaystyle \binom{-8}{6}[/tex]
Step-by-step explanation:
The car's starting position is 2 miles south of the town center. If it travels 6 miles north, then it will be 4 miles north of the town center.
The car's starting position is 5 miles east of the town center. If it travels 8 miles west, it will be 3 miles west of the town center.
Therefore, its final position is 4 miles north and 3 miles west of the town center.
If the car travels 6 miles north from it's starting position, the y-value of the vector will be 6, as the car is moving in a positive direction along the y-axis.
If the car travels 8 miles left, the x-value of the vector will be -8, as the car is moving in a negative direction along the x-axis.
Therefore, the single translation vector that moves the car from its starting position to its final position is:
[tex]\displaystyle \binom{x}{y}=\binom{-8}{6}[/tex]
A sector whose central angle measures 72º has an area of 16.211 square feet. What is the radius of the circle?
Answer:
81.055 ft²
Step-by-step explanation:
A full circle has a central angle of 360°.
A sector with a central angle is 72° is 72/360 = 1/5 of a circle.
A full circle has 5 times the area of a sector with a 72° central angle.
A = 5 × 16.211 ft²
A = 81.055 ft²
find the solution to the system of equations. Y=2x+2
Answer:
[tex](0, 2)[/tex]
Step-by-step explanation:
From the image (or by just looking at the equations and know what each part represents) you can tell the solution is (0;2)
Analitically, you already have them in a [tex]y=\square[/tex] form, so let's compare the two RHSs: [tex]2x+2=-x+2 \rightarrow 3x=0 \rightarrow x=0[/tex]. Let's replace the value in either to find [tex]y=0[/tex]
If two supplementary angles are in the ratio of 7: 8 ,find them.
Answer:
84° and 96°Step-by-step explanation :
Given :
Two supplementary angles are in the ratio of 7: 8To Find :
The two anglesSolution :
Let the angles be 7x and 8x respectively
As We know that, Sum of supplementary angles is always 180°
So, Adding Both the angles,
→ 7x + 8x = 180°
→ 15x = 180°
→ x = 180/15
→ x = 12
Hence,
7x = 7(12) = 84° 8x = 8(12) = 96°Therefore,
The required angles are 84° and 96°do the math please. i need it nowwwwww
Using algebraic expressions, the value of x in the diagram given is calculated as: x = 4
What is an Algebraic Equation?An algebraic equation is an equation that has an unknown variable (i.e. x) and digits, which can be used to solve a problem.
Algebraic expression for Mat A is: 4x + 3
Algebraic expression for Mat B is: 2x + 11
We would have the following algebraic equation:
4x + 3 = 2x = 11
Solve for the value of x
4x - 2x = 11 - 3
2x = 8
x = 8/2
x = 4
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Construct a confidence interval using a sample of size 15, with a sample standard deviation of 1.45, a sample mean of 5.3, and a confidence level of 90%. Write your answer EXACTLY as is given by Excel. Do not round.
A confidence interval is the mean of the estimate plus and minus the variation in that estimate.
How to depict the confidence interval?
From the excel, Confidence.T(0.10,1.45,15)
Margin of error = 0.659414066
Lower limit will be;
= mean-0.659414066
= 5.3 - 0.659414066
= 4.640585934
Upper limit will be:
= mean+0.659414066
= 5.3+0.659414066
= 5.959414066
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Enter the values for the highlighted variables that show how to subtract the rational expressions correctly: startfraction 2 over x squared minus 36 endfraction minus startfraction 1 over x squared 6 x endfraction = startfraction 2 over (x 6) (x minus 6) endfraction minus startfraction 1 over x (x a) endfraction. = startfraction b x over (x 6) (x minus 6) x endfraction minus startfraction x minus c over (x 6) (x minus 6) x endfraction. = startfraction d x minus x e over (x 6) (x minus 6) x endfraction. = startfraction x f over (x 6) (x minus 6) x endfraction. = startfraction g over x (x minus 6) endfraction a = b = c = d = e = f = g =
The values for the highlighted variables that show how to subtract the rational expressions correctly are a = 6, x^2 + 6x is equal to x(x+6), and b=2.
How to explain rational expressions?From the informaation, the denominator and numerator of the first term are multiplied by x.
The second term is multiplied by (x-6)/(x-6).
Now that they have the same denominator, the two terms are combined. 2 is the coefficient of the first term. In the same way as d is carried over from b, e is carried over from c.
We factor out the (x+6) from the numerator and denominator.
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the distance lesley walks from home to school is 120 meters and 80 meters when he goes to church from home. gusion estimates that the distance lesley walks when he goes directly to church. coming frim school is 180 meters. guinevere's estimation is 210 meters which etimation is feasible? make a map of lesley ways from home to school and church justify.
Find the coordinates of the midpoint of the line segment with endpoints at ( 6, -7) and (-3,5)
Answer:
Coordinates of the midpoint are ( 9/2 , -6 )
Renting Cars Floppy Jalopy Rent-a-Car has 25 cars available for
rental-20 big bombs and 5 midsize cars. If two cars are selected at
random, what is the probability that both are big bombs?
The probability that both are big bombs is 19/30 or 0.63 if the renting Car's Floppy Jalopy Rent-a-Car has 25 cars available for rental-20 big bombs and 5 midsize cars. If two cars are selected at random.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have:
Renting Cars Floppy Jalopy Rent-a-Car has 25 cars available for rental-20 big bombs and 5 midsize cars. If two cars are selected at random.
Total number of outcomes = C(25, 2) = 300
Total number of favorable outcomes = C(20, 2) = 190
Probability = 190/300 = 19/30 or
= 0.63
Thus, the probability that both are big bombs is 19/30 or 0.63 if the renting Car's Floppy Jalopy Rent-a-Car has 25 cars available for rental-20 big bombs and 5 midsize cars. If two cars are selected at random.
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please answer this!!!
Step-by-step explanation:
sin60 =opp/hyp
0.86=y/20
y=17.2
cos60=adj/hyp
0.5=x/20
x=10
sin57=y/15
0.83=y/15
y=12.45
VW has a midpoint at M(12, 0.5). Point V is at (10, -18). Find the coordinates of point W. Write the coordinates as decimals or integers.
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ V(\stackrel{x_1}{10}~,~\stackrel{y_1}{-18})\qquad W(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x +10}{2}~~~ ,~~~ \cfrac{ y -18}{2} \right)~~ = ~~\stackrel{M}{(12~~,~~0.5)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x +10}{2}=12\implies x+10=24\implies \boxed{x=14} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y -18}{2}=0.5\implies y-18=1\implies \boxed{y=19}[/tex]
Robert climbed 125 steps in five minutes at this rate how many steps did he average per minute
The solution is 62. We have to multiply the mixed number by the whole number. 12 1/2 is 25/2 so we now multiply by flipping the 25/2 to 2/25 and when you multiply you get 1550/25, which is 62
Percentage:
A shop has 150 gaming pc. They sold 30.
Find the percentage of the PC that they have not sold.
A certain ore contains 9 percent gold. How much ore (in tons) is needed to obtain 126 tons of gold
Answer:
251,991 tons of ore are need to obtain 126 tons of gold.
Step-by-step explanation:
I need help with part 2 on this question (Screenshot)
Somebody please explain how to solve this by formula or theorem
[tex]\text{It is an equilateral triangle, so all angles are equal to}~ 60^{\circ}\\\\~~~~~~m\angle 2 = x+72\\\\\implies 60 = x+72\\\\\implies x = 60-72\\\\\implies x = -12[/tex]
Solve This please!
Divide twice the variable x by the summation of z and y.
Answer:
2x/z+y
Step-by-step explanation:
Which expression is equal to -4-9?
Answer:
-4+(-9)
Step-by-step explanation:
if you have two negatives in an equation next to each other like -4-9 then it is basically adding the two but will just equal a negative sum
In the past month, Joe rented 5 video games and 4 DVDs. The rental price for each video game was $2.60. The rental price for each DVD was $3.30. What is
the total amount that Joe spent on video game and DVD rentals in the past month?
Answer:
$26.2
Step-by-step explanation:
5*2.50 is 13 for video games
4*3.30 is 13.2 for DVD
Sum them up and you get 26.2
A goat race is 325 meters long. An ant race is 75 centimeters long.
How much longer is the goat race than the ant race in meters?
Step 1: To compare the distances, they must both be in meters or both be in centimeters. Change 75 centimeters to meters.
Question 2
Step 2: Determine how much longer the goat race is than the ant race in meters.
The goat race is 324.25 meters longer than the ant race .
How to find the distance differences?
The goat race is 325 meters long. The ant race is 75 centimetres long.
The goat race is in meters while the ant race is in centimetres.
Let's convert the ant race to meters.
Hence,
1 cm = 0.01 m
75 = ?
cross multiply
Ant race = 0.75 meters
Therefore, let's find the difference between the goat race and the ant race.
325 - 0.75 = 324.25 meters.
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Answer: Step 1: To compare the distances, they must both be in meters or both be in centimeters. Change 75 centimeters to meters.
So=75 cm ÷ 100 = 0.75 m
Step-by-step explanation:
Step 2: Determine how much longer the goat race is than the ant race in meters.
o get the correct answer, subtract the length of the ant race in meters from the length of the goat race.
Remember to line up the decimal points and add zeros as plac
eholders. The difference of 325 and 0.75 is 324.25.
The goat race is 324.25 meters longer than the ant race.
what is the circumference of a circle that has a diameter of 12 feet
Answer:
i think it's 37.7
Step-by-step explanation:
triple the sum of x and 5
Answer:
The expression becomes 3(x+5) = 3x+15
please slove question 5
Answer:
2,160 mm³
Step-by-step explanation:
Q5
V = 1/2 × lwhV = 1/2 × 24 × 10 × 18V = 12 x 10 x 18V = 216 x 10V = 2,160 mm³