Answer:
1.05660377358 or 1.06 rounded
Step-by-step explanation:
If it needs to be rounded, use 1.06 or 1.057. If not, the exact answer is 1.05660377358.
Answer:
1.056603774
Step-by-step explanation:
What is the equation of a parabola that has a vertical axis, passes through the point (–1, 3), and has its vertex at (3, 2)?
= –216+616–4116
= –216+616–4116
=216–616+4116
=216–616+4116
Answer: y= x^2/16-6x/16+41/16
Step-by-step explanation:
The equation of a parabola will be; y = x^2/16 - 6x/16 + 41/16
What is vertex form of a quadratic equation?If a quadratic equation is written in the form
y=a(x-h)^2 + k
then it is called to be in vertex form. It is called so because when you plot this equation's graph, you will see vertex point(peak point) is on (h,k)
Otherwise, we had to use calculus to get critical points, then second derivative of functions to find the character of critical points as minima or maxima or saddle etc to get the location of vertex point.
This point (h,k) is called the vertex of the parabola that quadratic equation represents.
WE need to find the equation of a parabola that has a vertical axis, passes through the point (–1, 3), and has its vertex at (3, 2)
Thus, the equation of a parabola will be;
y = x^2/16 - 6x/16 + 41/16
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Write an equation of a circle given the center (-4,4) and radius r=5
Answer:
Step-by-step explanation:
Equation of circle: (x - h)² + (y - k)² = r² where (h,k) is the center.
Center( -4 , 4) and r = 5
(x -[-4])² + (y - 4)²= 5²
(x + 4)² + (y-4)² = 25
x² + 2*4*x +4² + y² - 2*y*4 + 4² = 25
x² +8x + 16 + y² - 8y + 16 = 25
x² + 8x + y² - 8y + 16 + 16 -25 = 0
x² + 8x + y² - 8y +7 = 0
We have that the an equation of a circle given the center (-4,4) and radius r=5 is mathematically given as
(x-4)^2+(y-4)^2=5^2
Equation of a circle
Question Parameters:
Given the center (-4,4) and radius r=5
Generally the equation for the Equation of a circle is mathematically given as
(x-x')^2+(y-y')^2=r^2
Therefore, The resultant equation will be
(x-x')^2+(y-y')^2=r^2
(x-4)^2+(y-4)^2=5^2
Hence,an equation of a circle given the center (-4,4) and radius r=5 is
(x-4)^2+(y-4)^2=5^2
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SOMEONE PLEASE HELP ME OUT THIS IS DUE In 20 MINUTES (PICTURE)
y = –2x2 - 4x – 6 has how many real roots?
Answer:
Step-by-step explanation:
None
They are both imaginary or complex. You can check that out by calculating the discriminate. If you get a minus answer, then there are no real roots. Let's try it.
a = - 2
b = - 4
c = - 6
D = sqrt(b^2 - 4*a * c)
D = sqrt( (-4)^2 - 4*(-2)(-6) )
D = sqrt( 16 - 48)
D = sqrt(-32) which is negative and there are no real roots.
Cho 6 số thỏa mãn: xa+yb=c ,xb+yc=a, xc+ya=b; abc khác 0
Tính P= [tex]$\frac{a^{2}}{bc}$ + $\frac{b^{2}}{ca}$ + $\frac{c^{2}}{ab}$[/tex]
Answer:
Step-by-step explanation:
xa+yb=c
xb+yc=a
xc+ya=b
add
x(a+b+c)+y(a+b+c)=a+b+c
x+y=1 ... (1)
xac+ybc=c²
xab+yac=a²
xbc+yab=b²
add
x(ab+bc+ca)+y(ab+bc+ca)=a²+b²+c²
[tex]x+y=\frac{a^2+b^2+c^2}{ab+bc+ca} \\\frac{a^2+b^2+c^2}{ab+bc+ca} =1\\a^2+b^2+c^2=ab+bc+ca\\a^2+b^2+c^2-ab-bc-ca=0\\a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-bc-ca)=(a+b+c)(0)=0\\a^3+b^3+c^3=3abc\\\frac{a^3}{abc} +\frac{b^3}{abc} +\frac{c^3}{abc} =3\\\frac{a^2}{bc} +\frac{b^2}{ca} +\frac{c^2}{ab} =3[/tex]
In Exercises 51−56, the letters a, b, and c represent nonzero constants. Solve the equation for x
x + a = ¾
Answer:
x = ¾-a
Step-by-step explanation:
x + a = ¾
Subtract a from each side
x + a -a= ¾-a
x = ¾-a
▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓
[tex]x+a=\dfrac{3}{4}\\\\x=\dfrac{3}{4}-a\\\\x=\dfrac{3-4a}{4}[/tex]
▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓
√25x+75 +3√x-2 =2+4√x-3 +√9x-18
Answer: No solutions
Step-by-step explanation:
[tex]\large \bf \boldsymbol{ \boxed{\sqrt{a}\cdot \sqrt{b}=\sqrt{a\cdot b} }} \\\\\\ \sqrt{25x+75} +3\sqrt{x-2} =2+4\sqrt{x-3} +\sqrt{9x-18} \\\\ \sqrt{25} \cdot \sqrt{x+3}+3\sqrt{x-2} =2+4\sqrt{x-3} +\sqrt{9}\cdot \sqrt{x-2} \\\\5\sqrt{x+3} +3\sqrt{x-2} \!\!\!\!\!\!\!\!\!\!\bigg{/} \ \ =2 +4\sqrt{x-3} +3\sqrt{x-2} \!\!\!\!\!\!\!\!\!\!\bigg{/} \\\\(5\sqrt{x+3})^2 =(2+4\sqrt{x-3} )^2 \\\\ \ \ \ let \ \ t=x+3 \ \ ; \ \ \ t-6=x-3 \\\\ \big(5\sqrt{t} \ \big)^2=(2+\sqrt{t-6} )^2 \\\\[/tex] [tex]\large \boldsymbol{} \bf 25t=4+16\sqrt{t-6} +16(t-6) \\\\(9t+92)^2=(16\sqrt{t-6} )^2 \\\\81t^2+1656t+8464=256(t-6)\\\\81t^2+1400t+10000=0 \\\\ D=1400^2-324000=-128000=> \\\\D<0 \ \ no \ \ solutions[/tex]
if n(u) = 800. n(a) = 400. n(b) = 300 n(āūb) = 200 what is n(anb) and n(a)
A number is raised to the 4 th power, then divided by half the of the original number, and finally increased by 141/2. If the result is 100, what was the orginal number
Answer:
the number is 2.45
Step-by-step explanation:
let the original number = n
[tex]\frac{n^4}{n/2} = \frac{2n^4}{n} = 2n^3\\\\2n^3 + \frac{141}{2} = 100\\\\4n^3 + 141= 200\\\\4n^3 = 200 - 141\\\\4n^3 = 59\\\\n^3 = \frac{59}{4} \\\\n^3 = 14.75\\\\n = \sqrt[3]{14.75} \\\\n = 2.45[/tex]
Therefore, the number is 2.45
The sine of angle θ is 0.3.
What is cos(θ)?
The answer:
[tex]\sqrt{9}1 /10[/tex]
Explanation to your question:
Since the sin of theta is 0.3, we can reasonably deduct that the opposite side to theta has a ration of 3 to 10 to that of the hypotenuse. Thus, the adjacent side to theta, using the pythagorean theorem, will be root91. Therefore, since the cosine of theta is the adjacent/hypotenuse, we get root 91/10
Instructions: Use the ratio of a 30-60-90 triangle to solve for the variables. Leave your
answers as radicals in simplest form.
Answer:
x =10
y = 10 sqrt(3)/ 3
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp / hyp
sin 60 = 5 sqrt(3) / x
x sin 60 = 5 sqrt(3)
x = 5 sqrt(3)/sin 60
x = 5 sqrt(3) / sqrt(3)/2
x = 5*2
x =10
tan theta = opp /adj
tan 60 = x/y
ytan 60 = 10
y = x/ tan 60
y = 10/ sqrt(3)
y = 10/ sqrt(3) * sqrt(3)/ sqrt(3)
y = 10 sqrt(3)/ 3
convert 100110 base two to a number in base three
Convert to base 10:
10 0110₂ = 2⁵ + 2² + 2¹ = 38
Convert to base 3:
38 = 27 + 11 = 27 + 9 + 2 = 3³ + 3² + 2×3⁰ = 1102₃
Jeremy is buying a new car. The total cost, including tax, is $18275. If the tax rate is 7.5% , what is the sticker price of the car?
Answer:
$17000
Step-by-step explanation:
Given
[tex]Total = 18275[/tex]
[tex]Tax = 7.5\%[/tex]
Required
The original price
This is calculated using:
[tex]Price(1 + Tax) = Total[/tex]
Make Price the subject
[tex]Price = \frac{Total}{(1 + Tax)}[/tex]
So, we have:
[tex]Price = \frac{18275}{(1 + 7.5\%)}[/tex]
[tex]Price = \frac{18275}{1.075}[/tex]
[tex]Price = 17000[/tex]
I need help solving
What is the possible answer?
Standard form of a quadratic equation: ax^2 + bx + c = 0
3x - 4 = -x^2
x^2 + 3x - 4 = 0
Hope this helps!
At Tubman Middle School, there are 6 English teachers and 5 science teachers. If each
student takes one English class and one science class how many possible combinations of
teachers are there?
There are 30 possible combinations of teachers.
Given that at Tubman Middle School, there are 6 English teachers and 5 science teachers, to determine, if each student takes one English class and one science class, how many possible combinations of teachers are there, the following calculation must be performed:
To calculate possible combinations, the number of options A must be multiplied by the number of options B. Thus, the calculation would be as follows.
6 x 5 = X30 = XTherefore, there are 30 possible combinations of teachers.
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Find m angle AFE.
Please I need help badly
The measure of the angle AFE or m∠AFE is 173 degrees option (B) 173 is correct if the angle AFB = 25 degrees, Angle BFC = 57 degrees, Angle CFD = 34 degrees, and Angle DFE = 57 degrees.
What is an angle?When two lines or rays converge at the same point, the measurement between them is called a "Angle."
We have angles shown in the picture.
Angle AFB = 25 degrees
Angle BFC = 57 degrees
Angle CFD = 34 degrees
Angle DFE = 57 degrees
Angle AFE is the sum of the angle AFB, Angle BFC, Angle CFD, and Angle DFE.
Angle AFE = Angle AFB + Angle BFC + Angle CFD + Angle DFE
Angle AFE = 25 + 57 + 34 + 57
Angle AFE = 173 degrees
Thus, the measure of the angle AFE or m∠AFE is 173 degrees option (B) 173 is correct if the angle AFB = 25 degrees, Angle BFC = 57 degrees, Angle CFD = 34 degrees, and Angle DFE = 57 degrees.
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Given the a center (-1, -2) and a radius r = 2. Identify the circle.
Answer:
1st option
1st graph has the centre on (-1,-2) and the distance of the circumference from the centre is 2
Answered by GAUTHMATH
work out the area of a semicircle take pi to be 3.142 11cm
Answer:
if the diameter is 11, them the answer is 47.52275cm
Solve the system of equations and choose the correct ordered pair.
4x - 2y = -2
6x + 3y = 27
A. (2,5)
B. (3,7)
C. (0, -1)
D. (0,9)
Answer:
(2,5)
Step-by-step explanation:
4x - 2y = -2
6x + 3y = 27
Divide the first equation by 2 and the second equation by 3
2x - y = -1
2x + y = 9
Add the equations together
2x - y = -1
2x + y = 9
-------------------
4x = 8
Divide by 4
4x/4 = 8/2
x =2
2x+y = 9
2(2) +y = 9
4+u = 9
y = 9-4
y=5
(2,5)
e Reasons Y...
SIVARI Leaming su...
Solve for 2. Round to the nearest tenth, if necessary.
х
K
J
63°
I
PLS HELP
Answer:
x = .5
Step-by-step explanation:
Since we have a right triangle, we can use trig functions
tan theta = opp / adj
tan 63 = 1/x
x tan 63 = 1
x = 1/ tan 63
x=0.50952
Rounding to the nearest tenth
x = .5
x.(9x-1).(x+2)-x(3x-1).(3x+1)
Answer:
=17x²-x
Step-by-step explanation:
=x.(9x²+18x-x-2)-x.(9x²-1)
=x.(9x²+17x-2-9x²+1)
=x.(17x-1)
=17x²-x
Find the product (x - 10) ( x - 5)
꙰ Hello there mohammedsaquibali45 ! My Name is ⚝Tobie⚝ and I'm glad you asked! Let me walk you step by step in order to comprehend the question better! ꙰
i
{x}^{2}-5x-10x+50
x
2
−5x−10x+50
ii Collect like terms.
{x}^{2}+(-5x-10x)+50
x
2
+(−5x−10x)+50
iii Simplify.
{x}^{2}-15x+50
x
2
−15x+50
(x - 10)(x - 5) = ...
= x^2 + (-10 + (-5))x + (-10•(-5))
= x^2 - 15x + 50
Can anyone help pls :)? Thank you
Answer:
It's D:5.3
Step-by-step explanation:
√28 =5.29
Round off therefore is 5.3
Could someone please help? I’ve done this lesson so many times and still struggle.
Nice job on getting problem 1 correct.
=================================================
Problem 2
The double stem and leaf plot says we have the following data set for the men's side
53,54,57 60,61,62,63,63,64,64,66,67,67,68,69 70,70,70,70,70,73,76,77,77,77,77,79 81,82,85,86,88,88 90,92,93,98Be careful to read the stem first, followed by the leaf (even though the leaf values are listed on the left side of the stem).
Notice how each row is a different stem (in this case, tens digit) to help make things more readable.
If we were to add up all of those values I listed above, then we should get the sum 2707. Divide this over n = 37 to get 2707/n = 2707/37 = 73.162 approximately. This rounds to 73 since your teacher wants you to round to the nearest whole point.
The average score for the men is 73.You'll do the same thing for the women's side. That data set is
55,59 60,60,62,62,63,64,65,66,66,67 70,71,71,72,73,74,75,76,79,79 80,81,82,83,83,84,89 90,92,92,93,93,95,98 100Again, it's handy to break the scores up by stem or else you'll have a long string of scores to get lost in (or it's easier to get lost in).
Adding up those 37 scores should get you 2824 which then leads to a mean of 2824/n = 2824/37 = 76.324 approximately. This rounds to 76
The average score for the women is 76.=================================================
Problem 3
The range for the men is max - min = 98 - 53 = 45
The range for the women is max - min = 100 - 55 = 45
Both groups have the same range (which is 45)==================================================
Problem 4
It's strongly recommended to use a spreadsheet here. Let's focus on the men's data set.
The idea is to subtract each data value from the mean 73.162, and then square the result. So each term is of the form (x-mu)^2 where mu is the mean.
For example, the data value x = 53 on the men's side will lead to
(x-mu)^2 = (53 - 73.162)^2 = 406.506
We consider this a squared error value.
You'll do this with the remaining 36 other values in the men's data set.
After doing this, you'll add up the 37 items in this new column and you should get roughly 4711.027, and this is the sum of the squared errors (SSE).
Divide this over n = 37 and we get 4711.027/37 = 127.325
Lastly, apply the square root and we arrive at sqrt(127.325) = 11.284 which rounds to 11.28
The steps for the women's standard deviation will be the same. You should get 12.30
-------------
Answers:Men's standard deviation = 11.28Women's standard deviation = 12.30These are population standard deviation values. If you don't want to use a spreadsheet, a much better option is to use online calculators that specialize in population standard deviation.
1) The men's and women's team each played 37 games.
2) the mean score of men's and women's team is 73 and 76 approximately.
3) the range of men's and women's score is 45.
4)the standard deviation of men and women team 11 and 12 approximately.
Number of observations can be found by counting the observations.
Mean is the average of all observations. It is the sum product of observations divided by the number of observations.
The range of observations is the measure of spread. It is the highest value minus the lowest value.
The standard deviation is another measure of variability. It is the square root of variance, where variance is the sumproduct of observations minus the mean, divided by the number of observations.
The data set is given by:
Men's team
53,54,5760,61,62,63,63,64,64,66,67,67,68,6970,70,70,70,70,73,76,77,77,77,77,7981,82,85,86,88,8890,92,93,98Women's team
55,5960,60,62,62,63,64,65,66,66,6770,71,71,72,73,74,75,76,79,7980,81,82,83,83,84,8990,92,92,93,93,95,981001) Number of games each team played :
men's team = 37
women's team = 37
2)mean = [tex]\frac{sum \ of \ observations}{number \ of \ observations}[/tex]
men's team = [tex]\frac{2707}{37}[/tex] = = 73.162
women's team = [tex]\frac{2824}{37}[/tex] = = 76.324
3)range = highest observation - lowest observation
men's team = 98 - 53 = 45
women's team = 100 - 55 = 45
4)population standard deviation = [tex]\sqrt{ \frac{\sum (x-\bar x)^2}{n}}[/tex]
On using the formula :
men's team = [tex]\sqrt{\frac{4711.027}{37} } = \sqrt{127.325} = 11.284[/tex]
women's team = [tex]\sqrt{151.29}[/tex] = 12.3
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Round off all these
1) 378811,
2) 267988,
3) 250260,
4) 196596,
5) 193171
to the nearest ten thousand
Answer:
1. 380,0002. 270,0003. 250,0004. 200,0005. 190,000[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
Describe the steps to dividing imaginary numbers and complex numbers with two terms in the denominator?
Answer:
Let be a rational complex number of the form [tex]z = \frac{a + i\,b}{c + i\,d}[/tex], we proceed to show the procedure of resolution by algebraic means:
1) [tex]\frac{a + i\,b}{c + i\,d}[/tex] Given.
2) [tex]\frac{a + i\,b}{c + i\,d} \cdot 1[/tex] Modulative property.
3) [tex]\left(\frac{a+i\,b}{c + i\,d} \right)\cdot \left(\frac{c-i\,d}{c-i\,d} \right)[/tex] Existence of additive inverse/Definition of division.
4) [tex]\frac{(a+i\,b)\cdot (c - i\,d)}{(c+i\,d)\cdot (c - i\,d)}[/tex] [tex]\frac{x}{y}\cdot \frac{w}{z} = \frac{x\cdot w}{y\cdot z}[/tex]
5) [tex]\frac{a\cdot (c-i\,d) + (i\,b)\cdot (c-i\,d)}{c\cdot (c-i\,d)+(i\,d)\cdot (c-i\,d)}[/tex] Distributive and commutative properties.
6) [tex]\frac{a\cdot c + a\cdot (-i\,d) + (i\,b)\cdot c +(i\,b) \cdot (-i\,d)}{c^{2}-c\cdot (i\,d)+(i\,d)\cdot c+(i\,d)\cdot (-i\,d)}[/tex] Distributive property.
7) [tex]\frac{a\cdot c +i\,(-a\cdot d) + i\,(b\cdot c) +(-i^{2})\cdot (b\cdot d)}{c^{2}+i\,(c\cdot d)+[-i\,(c\cdot d)] +(-i^{2})\cdot d^{2}}[/tex] Definition of power/Associative and commutative properties/[tex]x\cdot (-y) = -x\cdot y[/tex]/Definition of subtraction.
8) [tex]\frac{(a\cdot c + b\cdot d) +i\cdot (b\cdot c -a\cdot d)}{c^{2}+d^{2}}[/tex] Definition of imaginary number/[tex]x\cdot (-y) = -x\cdot y[/tex]/Definition of subtraction/Distributive, commutative, modulative and associative properties/Existence of additive inverse/Result.
Step-by-step explanation:
Let be a rational complex number of the form [tex]z = \frac{a + i\,b}{c + i\,d}[/tex], we proceed to show the procedure of resolution by algebraic means:
1) [tex]\frac{a + i\,b}{c + i\,d}[/tex] Given.
2) [tex]\frac{a + i\,b}{c + i\,d} \cdot 1[/tex] Modulative property.
3) [tex]\left(\frac{a+i\,b}{c + i\,d} \right)\cdot \left(\frac{c-i\,d}{c-i\,d} \right)[/tex] Existence of additive inverse/Definition of division.
4) [tex]\frac{(a+i\,b)\cdot (c - i\,d)}{(c+i\,d)\cdot (c - i\,d)}[/tex] [tex]\frac{x}{y}\cdot \frac{w}{z} = \frac{x\cdot w}{y\cdot z}[/tex]
5) [tex]\frac{a\cdot (c-i\,d) + (i\,b)\cdot (c-i\,d)}{c\cdot (c-i\,d)+(i\,d)\cdot (c-i\,d)}[/tex] Distributive and commutative properties.
6) [tex]\frac{a\cdot c + a\cdot (-i\,d) + (i\,b)\cdot c +(i\,b) \cdot (-i\,d)}{c^{2}-c\cdot (i\,d)+(i\,d)\cdot c+(i\,d)\cdot (-i\,d)}[/tex] Distributive property.
7) [tex]\frac{a\cdot c +i\,(-a\cdot d) + i\,(b\cdot c) +(-i^{2})\cdot (b\cdot d)}{c^{2}+i\,(c\cdot d)+[-i\,(c\cdot d)] +(-i^{2})\cdot d^{2}}[/tex] Definition of power/Associative and commutative properties/[tex]x\cdot (-y) = -x\cdot y[/tex]/Definition of subtraction.
8) [tex]\frac{(a\cdot c + b\cdot d) +i\cdot (b\cdot c -a\cdot d)}{c^{2}+d^{2}}[/tex] Definition of imaginary number/[tex]x\cdot (-y) = -x\cdot y[/tex]/Definition of subtraction/Distributive, commutative, modulative and associative properties/Existence of additive inverse/Result.
In a sports club of 150 members, 88 play golf, 63 play bowls, and 45 play golf and bowls. Find the probability that:
a) a member plays golf only.
b) a member doesn't play golf or bowls.
pls explain too if u could. thanks!
Answer:
a) .287
b) .293
Step-by-step explanation:
The answers are boxed in red in the picture.
First I found how many people only golfed. Then I did the same for the people that only bowled. Next I found how many members didn't golf or bowl.
From there I found the probabilities by dividing
a.) # of members that only golf / total # of members
b.) # of members that don't bowl or golf / total # of members
please help!!!! i need it in this instant!!!
Answer: 14
Step-by-step explanation:
If they hit the ball 4/8 times, that equals 1/2, so we just multiply 1/2 (or 0.5) by 28 and you get 14 :)
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. Match each set of vertices with the type of quadrilateral they form.
I'm sorry but there's not enough info
Step-by-step explanation:
Answer:
The triangle with vertices A (2 , 0) , B (3 , 2) , C (5 , 1) is isosceles right Δ
The triangle with vertices A (-3 , 1) , B (-3 , 4) , C (-1 , 1) is right Δ
The triangle with vertices A (-5 , 2) , B (-4 , 4) , C (-2 , 2) is acute scalene Δ
The triangle with vertices A (-4 , 2) , B (-2 , 4) , C (-1 , 4) is obtuse scalene Δ