Answer:
Step-by-step explanation:
[tex]\[\frac{1+2\sqrt{-3} }{1+\sqrt{-3} } =\frac{1+2\sqrt{-3} }{1+\sqrt{-3} } \times \frac{1-\sqrt{-3} }{1-\sqrt{-3} } =\frac{(1+2\sqrt{-3})(1-\sqrt{-3} ) }{1^{2}-(\sqrt{-3})^{2} } =\frac{1+2\sqrt{-3}-\sqrt{-3}-2(\sqrt{-3} )^{2} }{4} =\frac{1+\sqrt{-3}+6 }{4} =\frac{7+\sqrt{-3} }{4} \][/tex]
Need help please and thank you
Answer:
The answer is B.
Graphs. I dont understand. Please. Thank you!
ANSWER
D. G(x)=(x+1)²
EXPLANATION
The equation of the red graph is
[tex]F(x) = {x}^{2} [/tex]
This function has its vertex at the origin.
The blue graph is obtained by shifting the red graph 1 unit to the left.
The vertex will now be at (-1,0)
The equation of the new function in the vertex form is
[tex]G(x)= {(x + 1)}^{2} [/tex]
The correct choice is D.
Which point is a reflection of T(-6.5, 1) across the x-axis and the y-axis?
A. point U
B. point V
C. point W
D. point X
Answer:
V
Step-by-step explanation:
Under a reflection in the x- axis
a point (x, y) → (x, - y)
Under a reflection in the y- axis
a point (x, y) → (- x, y)
Hence
U(- 6.5, 1 ) → W(- 6.5, - 1) ← reflection in x- axis
W(- 6.5, 1) → V(6.5, -1) ← reflection in y- axis
Answer:
i think its v
Step-by-step explanation:
i hope this is right
is the following function even, odd or neither? f(x)=x^3 +4x
- even f(x) = f(-x)
- both
- odd f(-x) = -f(x)
- neither
Answer:
D, neither
Step-by-step explanation:
to determine whether a function is even, odd or neither, we need to know what it means
an even function is symmetric with respect to the y-axis
an odd function is symmetric with respect to the origin
to solve an equation to see if its even or odd, we would need to substitute x in the equation for -x.
in an even function when we substitute f(-x), it should be equal to to f(x)
in an odd function when we substitute f(-x), it should be equal to -f(x)
so lets test the function given to see if its even
f(x) = x³ + 4x
f(-x) = (-x)³ + 4(-x)
f(-x) = x³ - 4x
f(-x) = x³ - 4x ≠ f(x) = x³ + 4x
comparing this to the orignal function, we see that f(-x) = x³ - 4x is not even as we did not get the same output as the original function
now we should test to see if its odd. we have already seen what f(-x) is, now lets try -f(x) and compare it to f(-x) and f(x)
-f(x) = -(x³ + 4x) -->
-f(x) = -x³ - 4x ≠ f(-x) = x³ - 4x
f(-x) = x³ - 4x ≠ f(x) = x³ + 4x
comparing this to f(x) and f(-x), we see that it not odd as we did not get the same output
so the answer is D, neither even nor odd
Determine the domain of the function. f as a function of x is equal to the square root of x plus one divided by x plus four times x minus six.
answers:
a) x ≥ -1, x ≠ 6
b) All real numbers except -4 and 6
c) All real numbers
d) x ≥ 0
Answer:
a) x ≥ -1 , x ≠ 6
Step-by-step explanation:
To quickly solve this problem, we can use a graphing tool or a calculator to plot the equation.
Please see the attached images below, to find more information about the graph
The correct answer is option
a) x ≥ -1 , x ≠ 6
Answer:
a) [tex]x\geq -1,x\neq 6[/tex]
Step-by-step explanation:
We have been given a function [tex]f(x)=\frac{\sqrt{x+1}}{(x+4)(x-6)}[/tex]. We are asked to find the domain of our given function.
We can see that our given function is a rational function and numerator of our given function is a square root.
To find the domain of our given function, we will find the number that will make our denominator 0 and the domain of square root function will be the values of x that will make our numerator non-negative.
Undefined points for our given function:
[tex](x+4)(x-6)=0[/tex]
[tex]x+4=0\text{ or }x-6=0[/tex]
[tex]x=-4\text{ or }x=6[/tex]
The domain of denominator is all values of x, where x is not equal to negative 4 and positive 6.
Non negative values for radical:
[tex]x+1\geq 0[/tex]
[tex]x+1-1\geq 0-1[/tex]
[tex]x\geq -1[/tex]
The domain of numerator is all value of x greater than or equal to negative
Upon combining real regions and undefined points for our given function, the domain of our given function will be all values of x greater than or equal to negative 1, where x is not defined for 6.
Therefore, domain of our given function is [tex]x\geq -1,x\neq 6[/tex].
Part A: Factor 2x2y2 + 6xy2 + 18x2y2. Show your work.
Part B: Factor x2 + 10x + 25. Show your work.
Part C: Factor x2 − 36. Show your work.
Answer:
A.
[tex]2xy^2(10x+3)[/tex]
B.
[tex](x+5)^2[/tex]
C.
[tex](x-6)(x+6)[/tex]
Step-by-step explanation:
Part A. The expression [tex]2x^2y^2+6xy^2+18x^2y^2[/tex] consists of three terms: [tex]2x^2y^2,\ \ 6xy^2,\ \ 18x^2y^2[/tex] The first and the last terms are like terms, we can add them:
[tex]2x^2y^2+18x^2y^2=20x^2y^2[/tex]
Now,
[tex]20x^2y^2=2xy^2\cdot 10x\\ \\6xy^2=2xy^2\cdot 3[/tex]
So,
[tex]2x^2y^2+6xy^2+18x^2y^2=2xy^2(10x+3)[/tex]
Part B. The expression [tex]x^2+10x+25[/tex] is a square of [tex]x+5,[/tex] so
[tex]x^2+10x+25=(x+5)^2[/tex]
Part C. Use the difference of squares formula:
[tex]x^2-36=x^2-6^2=(x-6)(x+6)[/tex]
solve this system of two linear equations using substitution
y=3x-5,3y-x+1
Answer:
y=3/2
x=13/6
Step-by-step explanation:
y=3x-5 → -3x +y = -5
3y-x+1 → -x +3y = -1
Multiply the 2nd eq by -3 and add to 1st one and replace it
-3x +y = -5 → -8y =-6
3x -9y = -1 3x -9y = -1
→ y =3/2=1.5 . Replace this value in any eq -3x + 3/2 = -5 → x =13/6
- On Tuesday, Elena completed 20 items of her math homework in 36 minutes. At that same rate, how long (
will it take her to complete 35 items for Wednesday's math homework?
Answer:
Step-by-step explanation
20=36
1=x
Then cross multiply
20x=36
x=1.8
If it takes her 1.8 minutes to complete 1 item then:
1=1.8
35=x
x=63
It takes her 63 minutes
Graph the exponential model !!! Help needed !!!
Answer:
i think its the 2
Step-by-step explanation:
for sure❤
Answer:
Point (1 , 0.75) lies on the graph of the function ⇒ last answer
Step-by-step explanation:
* Lets revise the exponential function
- An exponential function with base b is defined by f (x) = ab^x
where a ≠0, b > 0 , b ≠1, and x is any real number.
- The base, b, is constant and the exponent, x, is a variable.
- The graph of it in the attached figure
- Features (for this graph):
• The domain is all Real numbers.
• The range is all positive real numbers (not zero).
• The y-intercept at (0 , 1.5). Remember any number to
the power of zero is 1.
• Because 0 < b < 1, the graph decreases (b = 1/2)
* Now lets check which point lies on the graph
- Substitute the value of x of the point, in the function
- If the answer is the same as y, then the point lies on the graph of
the function
∵ y = 1.5(1/2)^x
∵ x = -3
∴ y = 1.5(1/2)^(-3) = 187.5 ≠ 1
∴ Point (-3 , 1) does not lie on the graph of the function
∵ x = 2
∴ y = 1.5(1/2)² = 3/8 ≠ 5
∴ Point (2 , 5) does not lie on the graph of the function
∵ x = -2
∴ y = 1.5(1/2)^-2 = 6 ≠ 3
∴ Point (-2 , 3) does not lie on the graph of the function
∵ x = 1
∴ y = 1.5(1/2)^1 = 0.75
∴ Point (1 , 0.75) lies on the graph of the function
Which expression is equivalent to 13x-2(3x+6)?
answer
7x-12
explanation
13x -2(3x+6)
13x -6x-12
7x-12
Answer:
7x+12
Step-by-step explanation:
i just took a test and that was the answer
good ?
Find the missing length of the right triangle: a=6,b=8, c=?
Final answer:
The missing length of the hypotenuse (c) in the right triangle with legs a=6 and b=8 is found using the Pythagorean theorem. By squaring both a and b, adding those squares together, and then taking the square root, we determine that c equals 10 units.
Explanation:
To find the missing length of the hypotenuse (c) of the right triangle when given the lengths of the other two sides (a and b), we can use the Pythagorean theorem. The theorem states that for a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). In mathematical terms, this is represented as a² + b² = c².
Given that side a is 6 and side b is 8, we can substitute these values into the theorem's formula:
Calculate the square of a: 6² = 36.Calculate the square of b: 8² = 64.Add the squares of a and b: 36 + 64 = 100.Take the square root of the sum to find c: √100.c = 10.Therefore, the length of the hypotenuse (c) is 10 units.
Can anyone else please
Since 308 people can visit each day, and there's 8 shows each day, we just multiply 308 by 8.
308*8 = 2464 people.
Volume of prisms and cylinders
Answer:
7)V=16257.74
8)V= 226.19
9)V=12.56
10)V=6283.18
11)r=6.631
12)h=69.05
13)V=35328.78
Step-by-step explanation:
Volume of cylinder is given by formula:
V=πr^2h
where r is radius and h is height of cylinder
7)
r=15
h=23
Putting values in formula:
V= π(15)^2(23)
=5175π
=16257.74
8)
diameter=6
r=d/2=3
height =?
Finding height by pythagoras theorem:
h^2= 10^2-6^2
=100-36
=64
h=8
Putting values in formula:
V=π(3)^2(8)
= 72π
= 226.19
9)
r= 2
h=1
Putting values in formula:
V=π(2)^2(1)
=4π
= 12.56
10)
diameter =20
r=d/2=10
h=20
Putting values in formula:
V=π(10)^2(20)
=2000π
=6283.18
Now finding the missing measures:
11)
Given V=210π
h = 15
r=?
Putting values in formula:
210π=π(r)^2(15)
r^2= 210π/15
=14π
r= 6.631
12)
V=197.82
r=3
h=?
Putting values in formula:
197.82=π(3)^2(h)
h= 197.82/9π
= 69.05
13)
r=21
h=25.5
Putting values in formula:
V= π(21)^2(25.5)
=11245.5π
=35328.78 !
The value of the calculated volume and height of the cylinders are
7) 16,259.9 mm³
8) 904.9 yd³
9) 12.6 ft³
10) 25136.0 ft³
11) 6.8 m
12) 7.0 m
13) 35333.4 in³
How to determine volume and height of a cylinderThe volume of a cylinder is given by = πr²h
where
r is the radius
h is the vertical height
7) h = 23 mm, r = 15 mm
V = π(15)²(23)
=5175*π
= 16,259.9 mm³
8) r = 6 yd, slant height = 10 yd
Use Pythagorean theorem to find the height
10² = 6² + h²
h² = 100-36
= 64
h = √64 = 8 yd
V = π(6)²(8)
= 288*π
= 904.9 yd³
9) r = 2 ft, h = 1 ft
V = π(2)²(1)
= 4π
= 12.6 ft³
10) r = 20 ft, h = 20 ft
V = π(20)²(20)
= 8000*π
= 25136.0 ft³
11) V = 210 ft³, h = 15 ft
1 foot = 0.3048 m
15 ft = 0.3048*15
= 4.572 m
210π = πr²(4.572)
r² = 210/4.572
= 45.9317
r = √{45.9317}
= 6.8 m
12) V = 197.82 m³, r = 3 m
197.82 = π(3)²x
197.82 = 3.142*9*x
197.82 = 28.278x
x =197.82/28.278
= 7.0 m
13) r = 21 inches, h = 25.5 inches
V = π(21)²(25.5)
= 11245.5*π
= 35333.4 in³
learn more about cylinder here
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What is a reflection image of P (0, 0) after two reflections, first across X= -3 and then cross Y= -3?
Answer:
(-6,-7)
Step-by-step explanation:
What is the equation of A-16=3
Answer:
Equation: a - 16 = 3
Answer: a = 19
PLEASE HELP 25 POINTS
The lcd would be 10x^3y^3
Answer:
The LCM will be: [tex]10x^3y^3[/tex]
and The Solution will be: [tex]\frac{12y^2-5x}{10x^3y^3}[/tex]
Step-by-step explanation:
We need to solve the problem
[tex]\frac{6}{5x^3y}-\frac{1}{2x^2y^3}[/tex]
Since there is minus sign, so we take LCM of 5x^3y and 2x^2y^3
The LCM will be: [tex]10x^3y^3[/tex]
Our equation will become after taking LCM
[tex]=\frac{12y^2}{10x^3y^3}-\frac{5x}{10x^3y^3}\\=\frac{12y^2-5x}{10x^3y^3}[/tex]
There are 24 muffins in a bakery.If 3/8 of the muffins are blueberry,how many muffins are blueberry?
Answer:
There are 9 blueberry muffins.
Step-by-step explanation:
In order to find this amount, we need to multiply the fraction that represents blueberry muffins by the total number of muffins.
24 * 3/8 = 9
Answer:
9
Step-by-step explanation:
24/8=3
3x3=9, so there are 9 muffins
Total/denominator, then that number times the numerator.
sin(-180° + θ) = ________
Answer:
[tex]\sin\left(-180^o+\theta\right)=-\sin\left(\theta\right)[/tex]
Step-by-step explanation:
We need to find the value of [tex]\sin(-180^o+ \theta)[/tex]
So let's apply formula
[tex]\sin\left(A+B\right)=\sin\left(A\right)\cos\left(B\right)+\sin\left(B\right)\cos\left(A\right)[/tex]
[tex]\sin\left(-180^o+\theta\right)=\sin\left(-180^o\right)\cos\left(\theta\right)+\sin\left(\theta\right)\cos\left(-180^o\right)[/tex]
[tex]\sin\left(-180^o+\theta\right)=0\cdot\cos\left(\theta\right)+\sin\left(\theta\right)\cdot\left(-1\right)[/tex]
[tex]\sin\left(-180^o+\theta\right)=0-\sin\left(\theta\right)[/tex]
[tex]\sin\left(-180^o+\theta\right)=-\sin\left(\theta\right)[/tex]
Put the correct graph to each category
Answer:
First one is a slope between 0 and 1
second one is a slope lower than 0
third one is a slop higher than 1
last one is a slope higher than 1 (technically undefined)
Step-by-step explanation:
if tan=-4/3 in quadrent 2 what is cos
Answer:
-3/5
Step-by-step explanation:
Answer:
[tex]-\frac{3}{5}[/tex]
Step-by-step explanation:
Remember that the tangent trigonometric ratio is the opposite side of right triangle divided by the adjacent side:
[tex]tan(\alpha )=\frac{opposite-side}{adjacent-side}[/tex]
[tex]tan(\alpha )=-\frac{4}{3}[/tex]
Comparing the equations we can infer that:
opposite side = 4
adjacent side = 3
Now we can use Pythagoras to find the hypotenuse of our right triangle:
[tex]hypotenuse^2=side^2+side^2[/tex]
[tex]hypotenuse^2=4^2+3^2[/tex]
[tex]hypotenuse^2=25[/tex]
[tex]hypotenuse=\sqrt{25}[/tex]
[tex]hypotenuse=5[/tex]
Remember that the cosine trigonometric ratio is the adjacent side divided by the hypotenuse; in other words:
[tex]cos(\alpha)=\frac{adjacent-side}{hypotenuse}[/tex]
We know that adjacent side = 3 and hypotenuse = 5.
Replacing values:
[tex]cos(\alpha )=\frac{3}{5}[/tex]
Now, remember that cosine means x and sine means y. In Quadrant 2 x is negative, which means that cosine is negative.
So, if [tex]tan(\alpha )=-\frac{4}{3}[/tex] in quadrant 2, then [tex]cos(\alpha )=-\frac{3}{5}[/tex]
Kamari spent $74.92 on Christmas present for her four cousin's if she spends the same amount on each how much did she spend on each cousin?
Explanation please.
D.
Because... You have four cousins, that means you're gonna divide 74.92 by 4.
Need help ASAP!
20 POINTS
In New York State, 48% of all teenagers own a skateboard and 39% of all teenagers own a skateboard and roller blades. What is the probability that a teenager owns roller blades given that the teenager owns a skateboard? Enter your answer in decimal form rounded to two decimal places. Hint Change the percentages to decimals before plugging them into the conditional probability formula.
Answer:0.81
Step-by-step explanation:
A: Given teenager owns a skateboard. P(A) = 0.48
B: Given teenager owns roller blades. P(B) = ? - we dont know and dont need
AB: Given teenager owns a skateboard and roller blades. P(AB) = 0.39
P(B/A) = P(AB)/P(A) = 0.39/0.48 = 0.8125
Answer:
0.81
Step-by-step explanation:
Just divide them and write as a decimal.
Tracy is running a lemonade stand. She expects to make $126 for the day, but ends up making 364% of that amount. How much money did Tracy make that day?
Answer:
Tracy made $458.64 that day
The surface area of a sphere is 275.56 1 cm? What is the approximate volume of the sphere?
A. 2,287.15 pi cm3
B. 762.38 pi cm3
C. 6,099.06 pi cm3
D. 381.19cm3
Answer:
[tex]V=430.19\ cm^3[/tex] or [tex]V=136.93\pi\ cm^3[/tex]
Step-by-step explanation:
The surface area of a sphere is:
[tex]A_s=4\pi r^2[/tex]
Where r is the radius of the sphere
In this case we know that [tex]A_s = 275.561\ cm^2[/tex]
So
[tex]4\pi r^2=275.561[/tex]
We solve the equation for r
[tex]4\pi r^2=275.561\\r^2 = \frac{275.561}{4\pi}\\\\r=\sqrt{ \frac{275.561}{4\pi}}\\\\r=4.683\ cm[/tex]
Now we know the radius of the sphere.
The volume of a sphere is:
[tex]V=\frac{4}{3}\pi r^3[/tex]
We substitute the value of the radius in the formula
[tex]V=\frac{4}{3}\pi (4.683)^3[/tex]
[tex]V=430.19\ cm^3[/tex]
Determine the measure of angle FGC.
A. 22°
B. 70°
C. 110°
D.120°
Answer:
Option C. [tex]110\°[/tex]
Step-by-step explanation:
step 1
Determine the measure of angle AGC
we know that
The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.
so
[tex]m<AGC=\frac{1}{2}[81\°+59\°][/tex]
[tex]m<AGC=\frac{1}{2}[140\°][/tex]
[tex]m<AGC=70\°[/tex]
step 2
Determine the measure of angle FGC
we know that
[tex]m<AGC+m<FGC=180\°[/tex] ----> by supplementary angles
so
[tex]70\°+m<FGC=180\°[/tex]
[tex]m<FGC=180\°-70\°=110\°[/tex]
which expression is the factored form of x^2 -7+10
Answer:
(x -5) * (x -2) = x^2 -7 +10
Step-by-step explanation:
find the area of the path 3m wide runs around the circular feild of radius 7m.
The area of the path is ².
Area of Bigger Circle:Radius = 7m + 3m = 10m Area of circle= πr²3.14×10×10
= 314m²
Area of smaller Circle:-Radius = 7m Area of circle=πr²3.14×7×7
= 154m²
Area of circular pathArea of bigger circle - area of smaller circle
= (314 - 154) m²
= 160m²
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I have been on this question for so long if anyone can help me I would greatly appreciate it. Thank you
Answer:
Step-by-step explanation:
let x be the number
2(x+8)=-4x+4
2x+16=-4x+4
6x=-12
x=-2
Answer:
x=-2
Step-by-step explanation:
2(x+8)=-4x+4
2x+16=-4x+4
6x=-12
x=-2
Which net folds into the rectangular prism above?
Answer:
the answer is Z
Step-by-step explanation:
What is the ratio of the perimeter of the smaller triangle to the perimeter of the larger triangle?
Answer:
Option C. [tex]\frac{5}{6}[/tex]
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its perimeters is equal to the scale factor
and
The scale factor is equal to the ratio of its corresponding sides
Let
z-----> the scale factor
[tex]z=\frac{15}{18}[/tex]
simplify
[tex]z=\frac{5}{6}[/tex]