Answer:
1,440
Step-by-step explanation:
1.5 percent of 96k
What is the sum of The square root of negative 2 and the square root of negative 18
Answer:
[tex]\large\boxed{\sqrt{-2}+\sqrt{-18}=4\sqrt2\ i}[/tex]
Step-by-step explanation:
[tex]\sqrt{-1}=i\\\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\===================\\\\\sqrt{-2}+\sqrt{-18}=\sqrt{(2)(-1)}+\sqrt{(9)(2)(-1)}\\\\=\sqrt2\cdot\sqrt{-1}+\sqrt9\cdot\sqrt2\cdot\sqrt{-1}\\\\=\sqrt2\cdot i+3\cdot\sqrt2\cdot i\\\\=i\sqrt2+3i\sqrt2=4i\sqrt2[/tex]
The sum of √-2 and √-18 is 4√2i.
What is the square root of -1?The square root of -1 is an imaginary number which is represented by i.
√-1=i
Here we have to calculate √-2+√-18
√-2+√-18
=√(-1).2+√(-1).18
=√(-1).√2+√(-1).√18
=i√2+i√18 (as √-1=i where i is imaginary number)
But √18=√(9*2)=√9*√2=3√2
(as √(ab)=√a.√b)
=i√2+i3√2
=√2(i+3i)
=√2*4i
=4√2i
Therefore the sum of √-2 and √-18 is 4√2i.
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Which best describes the graph of the function f(x)=4x ?
Answer:
F
Step-by-step explanation:
The equation of a line in slope-intercept form is
y = mx + b
where m = slope, and b = y-intercept.
This line has equation
y = 4x
When we compare y = 4x with y = mx + b, we see that m = 4, and b = 0.
This line intersects the y-axis (the y-intercept) at y = 0, which is the origin. The slope is positive, so it slopes up to the right.
Answer: F
The function f(x) = 4x is a linear function, and when graphed, it will produce a straight line with a slope of 4. The graph demonstrates the dependence of y on x and it's an example of a line graph.
Explanation:The question asks for a description of the graph of the function f(x) = 4x.
The function f(x) = 4x is a linear function, which means it creates a straight line when graphed. The number 4 in the function is the slope of the line. This value indicates that for each increase by 1 in the x value, the y value will increase by 4.
This demonstrates the dependence of y on x. So, a graph of this function would be a straight line that slopes upward from left to right, starting at the origin (0,0) and increasing by 4 in the y direction for each step of 1 in the x direction. This is a typical representation of a linear function demonstrating the relationship between two variables on a line graph.
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What happens when you reflect a shape over the x-axis and then the y-axis. What is the one transformation that could have been performed to achieve the same result? A degree rotation.
Reflecting a shape over the x-axis and then the y-axis is equivalent to a 180-degree rotation around the origin.
When a shape is reflected over the x-axis, any point (x, y) on the shape will have its y-coordinate inverted, becoming (x, -y). If this reflected shape is then reflected over the y-axis, the x-coordinate is inverted, so (x, -y) becomes (-x, -y). The same final position of the shape could have been achieved by a single transformation: rotating the shape 180 degrees around the origin.
Mathematically, the combination of these two reflections can be represented by matrices and is equivalent to the composition of two reflection transformations. The reflection across the x-axis can be represented by a matrix that inverts the sign of the y-coordinate and reflection across the y-axis can be represented by a matrix inverting the x-coordinate. Together, these operations are equivalent to a 180-degree rotation around the origin.
which set of three numbers could be the side lengths of an triangle 3,5,9 2,4,6 2,4,8 3,5,7
Answer:
3,5,7
Step-by-step explanation:
to find which set it is you have to add the first too like this
3+5 >7 if greater than 7 move on too this
5+7>3 if greater move on to this
3+7>5 if greater that means it is a set you can use
3,5,7 is the set of three numbers that could be the side lengths of a triangle. This can be obtained by using the triangle inequality theorem.
What is triangle inequality theorem?Triangle inequality theorem: The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
If ΔABC is a triangle with sides a, b and c, then it should satisfy the following conditions, a+b>c
b+c>a
a+c>b
Which is the required set of three numbers?
Use the triangle inequality theorem in each set,
Set 1: 3,5,93+5=8<9, does not satisfy the theorem
Set 2: 2,4,62+4=6, does not satisfy the theorem
Set 3: 2,4,82+4=6<8, does not satisfy the theorem
Set 4: 3,5,73+5=8>7
3+7=10>5
5+7=12>3, this set satisfies the theorem
Hence 3,5,7 is the set of three numbers that could be the side lengths of a triangle.
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ANY HELP WOULD REALLY HELP ME :)
White shapes and black shapes are used in a game some of the shapes ae circles all the other shapes are squares.
The ratio of the number of white shapes to the number of black shapes is 5:11 the ratio of the number of white circles to the number of white squares 3:7
The ratio of the number of black circles to the number of black squares is 3:8 work out what fraction of all the shapes are circles.
Answer:
6/11
Step-by-step explanation:
3 white circles, 3 black circles, so six circles out of the total 11 peices
complete the solution of the equation find the value of Y when X equals -8.
4x+9y=-14
Answer:
[tex]\large\boxed{y=2}[/tex]
Step-by-step explanation:
In this question, we're going to solve the equation.
What we would do is plug in the given information in the right variable. In this case, we would plugin -8 to x, since x = -8
We are solving for y, so we would nee to find how much y = ?
Your equation should look like this:
[tex]4(-8)+9y=-14[/tex]
Lets solve:
[tex]4(-8)+9y=-14\\\\\text{Multiply}\, 4(-8)\\\\-32+9y=-14\\\\\text{Add 32 to both sides}\\\\9y=18\\\\\text{Divide}\\\\y=2[/tex]
When you're done solving, you should get y = 2
This means that y = 2
I hope this helped you out.Good luck on your academics.Have a fantastic day!In a triangle, the measure of the first angle is 24 degrees more than the measure of the second angle. The measure of the third angle is four times the measure of the second angle. If the total number of degrees in a triangle is 180, what is the measure of the largest angle?
Answer:
First angle = 50, second angle = 26 and the third angle = 104 degrees.
Largest angle is 104 degrees.
Step-by-step explanation:
Let the second angle be x degrees, the the first will be x + 24 and the third is
4x degrees.
x + x+ 24 + 4x = 180
6x = 180 - 24
6x = 156
x = 26
so the other 2 angles are 26 + 24 = 50 and 4*26 = 104 degrees.
Triangle is the polygon with three edges, three vertices and three angle. The total number of degrees in a triangle is always 180 degrees. The value of the largest angle in the given triangle is 104 degrees.
Given-
Let The measure of the second angle is x degrees.
The measure of the first angle is 24 degrees more than the measure of the second angle. Thus first angle is (24+x) degrees.
The third angle is four times the measure of the second angle. Thus the measure of the third angle is 4x.
What is triangle?Triangle is the polygon with three edges, three vertices and three angle. The total number of degrees in a triangle is always 180 degrees.
As we know that the sum of the all the three angle in the triangle is 180 degrees. Therefore,
[tex](24+x)+x+4x=180[/tex]
[tex]6x=124-48[/tex]
[tex]6x=156[/tex]
[tex]x=\dfrac{156}{6}[/tex]
[tex]x=26[/tex]
Hence the the measure of the second angle is 26 degrees. Now The measure of the first angle is 24 degrees more than the measure of the second angle. Thus,
[tex]=24+26[/tex]
[tex]=50[/tex]
Hence measure of the first angle is 50 degrees. Now the third angle is four times the measure of the second angle. Thus,
[tex]=4\times 26=104[/tex]
Hence, the measure of the third angle is 104 degrees.
Thus the value of the largest angle in the given triangle is 104 degrees.
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Trisha has $22.50 to spend at the movies . Her ticket is $11.50, and she gets a large popcorn and soda. If the popcorn and soda each cost the same amount and she spends all her money , how much was the popcorn?
Answer:
The popcorn was $5.50
Answer:
$5.50
Step-by-step explanation:
22.50 - 11.50 = 11
divide 11 by 2 and you get 5.5
Hope this helps!
Given WXYZ what is the measure of Z
Answer: 35
Step-by-step explanation:
The measure of ∠Z is 35°
The correct answer is an option (D)
What is parallelogram?"It is a quadrilateral in which opposite sides are parallel and equal in length.""The opposite angles of parallelogram are equal.""The adjacent angles of the parallelogram are supplementary."For given question,
We have been given a parallelogram WXYZ.
The measure of angle X is 35°
We know that, the opposite angles of parallelogram are equal.
⇒ ∠X = ∠Z
⇒ ∠Z = 35°
Therefore, the measure of ∠Z is 35°
The correct answer is an option (D)
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Helppppppppppping me please
Answer:
8. D) 2x + 89. C) 6x + 32 = 15810. 50 ftStep-by-step explanation:
Look at the picture.
9. The perimeter of the rectangle l × w:
P = 2l + 2w
Substitute l = 2x + 8 and w = x + 8:
P = 2(2x + 8) + 2(x + 8) use the distributive property
P = (2)(2x) + (2)(8) + (2)(x) + (2)(8)
P = 4x + 16 + 2x + 16 combine like terms
P = (4x + 2x) + (16 + 16)
P = 6x + 32
10. Solve the equation:
6x + 32 = 158 subtract 32 from both sides
6x = 126 divide both sides by 6
x = 21
Put the value of x to the expression 2x + 8:
2(21) + 8 = 42 + 8 = 50
Which statement is true about the factorization of 30x2 +40xy+51y2
Answer:
prime
not factorable over the reals
Step-by-step explanation:
30x^2+40xy+51y^2 is not factorable (also know as prime)
because the discriminant is negative.
That is when I computed b^2-4ac, in this case 40^2-4(30)(51)=-4520.
If the discriminant is negative, then it isn't factorable over the reals.
You have 2 jugs(and only 2 jugs), one can hold 3 gallons of water and the other can hold 5. You need exactly 4 gallons of water. Assume the jugs have no markings, you have no measuring equipment, and you have infinite water.
Answer:
See below.
Step-by-step explanation:
You fill the 5 gallon up to the top then you pour 3 gallons into the 3 gallon jug, leaving 2 gallons in the bigger jug.
You throw the contents of the 3 gallon jug away then transfer the 2 gallons from the bigger jug into the 3 gallon jug. So you have 2 gallons in the 3 gallon jug.
You then fill the 5 gallon jug and pour 1 gallon into the 3 gallon jug, so you are left with 4 gallons of water in the 5 gallon jug.
d/dx (28000-50x²-400x)
Answer:
[tex]-100x - 400[/tex]
Step-by-step explanation:
The derivative of a sum is the sum of the derivatives by the sum rule, and this also extends to differences by the constant multiple rule
[tex]\dfrac{d}{dx}(28000 - 50x^2 - 400x) = \dfrac{d}{dx}(28000) - \dfrac{d}{dx}(50x^2) - \dfrac{d}{dx}(400x)[/tex]
By the constant multiple rule, we have
[tex]= \dfrac{d}{dx}(28000) - 50\dfrac{d}{dx}(x^2) - 400\dfrac{d}{dx}(x)[/tex]
The derivative of any constant is 0.
The power rule says that for any real number [tex]n[/tex], [tex]\frac{d}{dx} x^n = nx^{n-1}[/tex]. And note that [tex]x = x^1[/tex]. Thus we have
[tex]= 0 - 50(2)x - 400(1)x^0 = -100x - 400[/tex]
since [tex]x^0 = 1[/tex]
Which system is equivalent to y = -2x , y = x-2 ?
The given system of equation can be solved if x = 2/3 and y = -4/3.
So we need to find another system which can be solved by these values.
From the given 4 options lets find out which can be solved by x = 3/2 and y = -4/3
1.
y = -2y^2 -2 , x = y - 2
lets put the value of y here
y = -2(16/9)-2 = -32/9-2= -50/ 9
So not an equivalent equation.
2.
y = -2y^2 + 2 , x = y + 2
y = -2(16/9)+2=-32/9+2=-14/9
So not an equivalent system.
3.
y = -2y^2 - 8y - 8 , x = y + 2
y = -2(16/9)-8(-4/3)-8 = -32/9+32/3-8=64/9-8=-8/9
So not an equivalent system.
4.
y = -2y^2 + 8y - 8 , x = y -2
y = -2(16/9)+8(-4/3)-8=-32/9-32/3-8=-128/9-8=-22.22
So this is not an equivalent equation too
Answer:
C. [tex]\left \{ {{y=-2y^{2}-8y-8 } \atop {x=y+2}} \right.[/tex]
Step-by-step explanation:
Edge 2020
The paragraphs below come from the rental agreement signed by a customer when they set up an account at Super Video.
“All rentals are due back by midnight of the due date as printed on the transaction receipt. Any rental not received by midnight on the day it is due is subject to a late charge of $1.50 for each day it is late. Any rental not returned by the fifth day after the due date will be transferred to a sale. The Customer will then be required to pay the purchase price of the item in addition to five (5) days of late fees. The Customer will not be required to return the product once the total balance is paid.”
According the rental agreement, which of the following is not a responsibility of the customer?
a.
Pay a $1.50 late fee per movie per day past the due date.
b.
Get his or her rentals back by midnight the day they are due.
c.
Return a rental item kept out thirteen days past the due date.
d.
Pay the purchase price and five days of late fees for any item kept more than five days past the due date.
Answer:
Option C
Step-by-step explanation:
As per the contract:
"Any rental not received by midnight on the day it is due is subject to a late charge of $1.50 for each day it is late."
this makes option a: "Pay a $1.50 late fee per movie per day past the due date" responsibility of customer
"All rentals are due back by midnight of the due date as printed on the transaction receipt."
this makes option b: "Get his or her rentals back by midnight the day they are due." responsibility of customer
"Any rental not returned by the fifth day after the due date will be transferred to a sale. The Customer will then be required to pay the purchase price of the item in addition to five (5) days of late fees. "
this makes option d: "Pay the purchase price and five days of late fees for any item kept more than five days past the due date." responsibility of customer
Hence option C is correct: Return a rental item kept out thirteen days past the due date!
The option that is not the responsibility of the customer is Return a rental item kept out thirteen days past the due date.
What are the duties of the customer? The responsibilities of the customer include:Return the rentals back by midnight the day they are due.Pay a $1.50 late fee per movie per day past the due date.Pay the purchase price and five days of late fees for any item kept more than five days past the due date.To learn more about contracts, please check: https://brainly.com/question/984979
Solve 16t2 - 96t + 48 = 0.
Answer:
the question is not written correctly 16t2 can't be used in the equation
Step-by-step explanation:
do it it correctly you need to combine the like numbers, subtract the 48 from both sides and then divide the number with the t to both sides.
We get the value of t as:
[tex]t=3+\sqrt{6}\ and\ t=3-\sqrt{6}[/tex]
Step-by-step explanation:We are asked to solve the given equation for t.
The quadratic equation in terms of the variable t is given by:
[tex]16t^2-96t+48=0[/tex]
On dividing both side of the equation by 16 we get:
[tex]t^2-6t+3=0[/tex]
Now, we know that any quadratic equation of the type:
[tex]at^2+bt+c=0[/tex] has solution as :
[tex]t=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Here,
[tex]a=1,\ b=-6\ and\ c=3[/tex]
i.e.
[tex]t=\dfrac{-(-6)\pm \sqrt{(-6)^2-4\times 1\times 3}}{2\times 1}\\\\t=\dfrac{6\pm \sqrt{36-12}}{2}\\\\t=\dfrac{6\pm \sqrt{24}}{2}\\\\t=\dfrac{6\pm 2\sqrt{6}}{2}\\\\t=3\pm \sqrt{6}[/tex]
i.e.
[tex]t=3+\sqrt{6}\ and\ t=3-\sqrt{6}[/tex]
A ball has a surface area of 26.87 square feet. To the nearest tenth of a foot, what is the radius of the ball? Use π = 3.14.
Answer:
about 1.5 feet
Step-by-step explanation:
First we need to note the equation to find the surface area of a sphere. This is 4πr^2.
4πr^2=Surface Area
4πr^2=26.87
4(3.14)r^2=26.87 Substitute
r^2=26.87/(4*3.14) Divide
r^2=26.87/12.56 Simplify
r=√(26.87/12.56) Find square root of both sides
r≈1.5 Do the calculations
So the radius of the ball is about 1.5 feet.
Answer:1.5 ft
Step-by-step explanation:
Given
Surface area of ball=[tex]26.87 ft^2 [/tex]
And we know surface area of ball is =[tex]4\pi r^2[/tex]
Equating
[tex]26.87=4\times 3.14\times r^2 [/tex]
[tex]r^2=2.1393[/tex]
[tex]r=1.4626\approx 1.5 [/tex]
6 1/4% interest on $150 is how much money?
$9.38
0.0625×150=$9.38
Have a good day
BEDE
Which of the following equations represents a line that is perpendicular to
Y = -4x+9 and passes through the point, (4, 5)?
A. y =1/4×+6
B. y = 3x+4
C. y = 1/4×+5
D. y = -4x+ 4
Answer:
[tex]\large\boxed{y=\dfrac{1}{4}x+4}[/tex]
Step-by-step explanation:
[tex]Let:\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\============================\\\\\text{We have the equation of the line:}\ y=-4x+9\to m_1=-4.\\\\\text{Therefore}\ m_2=-\dfrac{1}{-4}=\dfrac{1}{4}.\\\\\text{Put the value of the slope and the coodrdinates of the given point (4, 5)}\\\text{to the equation of a line}\ y=mx+b:\\\\5=\dfrac{1}{4}(4)+b\\\\5=1+b\qquad\text{subtract 1 from both sides}\\\\4=b\to b=4\\\\\text{Finally:}\\\\y=\dfrac{1}{4}x+4[/tex]
A 10 kg ball is traveling at the same speed as a 1 kg ball. Compared to the 10 kg ball, the 1 kg ball has...
Answer: The 1-kg ball has 1/10 as much kinetic energy as the 10-kg ball.
Step-by-step explanation:
Option (a) - "less momentum" - accurately describes the relationship between the momentum of the 1 kg ball compared to the 10 kg ball.
The momentum of an object is directly proportional to its mass. When comparing a 10 kg ball to a 1 kg ball traveling at the same speed, the 10 kg ball has more momentum due to its greater mass. Since momentum is determined by both mass and velocity, and the velocity is the same for both balls, the difference in momentum is solely due to the difference in mass. The 10 kg ball has ten times the mass of the 1 kg ball. Therefore, the 1 kg ball has less momentum compared to the 10 kg ball. In fact, it has one-tenth of the momentum of the 10 kg ball.
Complete question: A 10 kg ball is traveling at the same speed as a 1 kg ball. Compared with the 10 kg ball, the 1 kg ball has
a-less momentum.
b-twice momentum.
c-five times the momentum.
d-the same momentum.
Page 1:
(MC 02.03)
What set of reflections and rotations would carry rectangle ABCD onto itself?
(4 points)
1) Rotate 180°, reflect over the x-axis, reflect over the line yox
2) Reflect over the x-axis, rotate 180°, reflect over the x-axis
3) Rotate 180°, reflect over the y-axis, reflect over the line y=x
4) Reflect over the y-axis, reflect over the x-axis, rotate 180°
Answer:
4) Reflect over the y-axis, reflect over the x-axis, rotate 180°
Step-by-step explanation:
Since, the rule of 180° rotation,
[tex](x,y)\rightarrow (-x,-y)[/tex]
Rule of reflection over x-axis,
[tex](x,y)\rightarrow (x,-y)[/tex]
Rule of reflection over y-axis,
[tex](x,y)\rightarrow (-x,y)[/tex]
Rule of reflection over line y = x,
[tex](x,y)\rightarrow (y,x)[/tex]
∵ In the set of reflection,
Rotate 180°, reflect over the x-axis, reflect over the line y=x,
[tex](x,y)\rightarrow (-x,-y)\rightarrow (-x,y)\rightarrow (y,-x)[/tex]
Reflect over the x-axis, rotate 180°, reflect over the x-axis,
[tex](x,y)\rightarrow (x,-y)\rightarrow (-x,y)\rightarrow (-x,-y)[/tex]
Rotate 180°, reflect over the y-axis, reflect over the line y=x,
[tex](x,y)\rightarrow (-x,-y)\rightarrow (x,-y)\rightarrow (-y,x)[/tex]
Reflect over the y-axis, reflect over the x-axis, rotate 180°,
[tex](x,y)\rightarrow (-x,y)\rightarrow (-x,-y)\rightarrow (x,y)[/tex]
Hence, the set of reflections and rotations that would carry rectangle ABCD onto itself is,
Reflect over the y-axis, reflect over the x-axis, rotate 180°.
Option '4' is correct.
Answer:
Reflect over the y-axis, reflect over the x‒axis, rotate 180°
Step-by-step explanation:
6.
What is the product of the expression below?
(2x - 5)(2x - 3)
A 4x² + 16x + 15
B 4x2 - 16x - 15
c 4x2 + 16x - 15
D 4x2 - 16x + 15
I’m not exactly sure what to do... please help (25 points)
Answer:
Choice A
Step-by-step explanation:
Use the F. O. L. D method while solving
Explain how to model the multiplication of –6 and 3 on a number line
Answer:
Multiplication is basically repeating addition
Step-by-step explanation:
So, on a numberline, start at 0 then add -6 three times (since you are multiplying it by three) and you should get -18
A square has an area of 25 square inches. How long are its sides?
Answer:
5
Step-by-step explanation:
[tex]A_{s} = l^2[/tex], where l - is a side
[tex]l = \sqrt{A_s}[/tex]
[tex]l = \sqrt{25} = 5[/tex]
Which equations represent the line that is parallel to 3x − 4y = 7 and passes through the point (−4, −2)? Select two options.
Options:
1. y= -3/4x+1
2. 3x-4y=-4
3.4x-3y=-3
4. y-2=-3/4(x-4)
5. y+ 2 = 3/4(x + 4)
Please help ASAP thank you ! :)
Answer:
2 and 5
Step-by-step explanation:
The slope-intercept form of a line is y=mx-b where m is slope and b is y-intercept.
The point-slope form of a line is y-y1=m(x-x1) where m is the slope and (x1,y1) is a point on the line.
The standard form a line is ax+by=c.
So anyways parallel lines have the same slope.
So if we are looking for a line parallel to 3x-4y=7 then we need to know the slope of this line so we can find the slope of our parallel line.
3x-4y=7
Goal: Put into slope-intercept form
3x-4y=7
Subtract 3x on both sides:
-4y=-3x+7
Divide both sides by -4:
[tex]y=\frac{-3}{-4}x+\frac{7}{-4}[/tex]
Simplify:
[tex]y=\frac{3}{4}x+\frac{-7}{4}[/tex]
So the slope of this line is 3/4. So our line that is parallel to this one will have this same slope.
So we know our line should be in the form of [tex]y=\frac{3}{4}x+b[/tex].
To find b we will use the point that is suppose to be on our new line here which is (x,y)=(-4,-2).
So plugging this in to solve for b now:
[tex]-2=\frac{3}{4}(-4)+b[/tex]
[tex]-2=-3+b[/tex]
[tex]3-2=b[/tex]
[tex]b=1[/tex]
so the equation of our line in slope-intercept form is [tex]y=\frac{3}{4}x+1[/tex]
So that isn't option 1 because the slope is different. That was the only option that was in slope-intercept form.
The standard form of a line is ax+by=c and we have 2 options that look like that.
So let's rearrange the line that we just found into that form.
[tex]y=\frac{3}{4}x+1[/tex]
Clear the fractions because we only want integer coefficients by multiplying both sides by 4.
This gives us:
[tex]4y=3x+4[/tex]
Subtract 3x on both sides:
[tex]-3x+4y=4[/tex]
I don't see this option either.
Multiply both sides by -1:
[tex]3x-4y=-4[/tex]
I do see this as a option. So far the only option that works is 2.
Let's look at point slope form now.
We had the point that our line went through was (x1,y1)=(-4,-2) and the slope,m, was 3/4 (we found this earlier).
y-y1=m(x-x1)
Plug in like so:
y-(-2)=3/4(x-(-4))
y+2=3/4 (x+4)
So option 5 looks good too.
Answer:
OPTION 2.
OPTION 5.
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope and "b" is the y-intercept.
Given the line [tex]3x - 4y = 7[/tex], solve for "y":
[tex]3x - 4y = 7\\\\-4y=-3x+7\\\\y=\frac{3}{4}x-\frac{7}{4}[/tex]
The slope of this line is:
[tex]m=\frac{3}{4}[/tex]
Since the slopes of parallel lines are equal, the slope of the other line is:
[tex]m=\frac{3}{4}[/tex]
Substitute the slope and the given point into [tex]y=mx+b[/tex] and solve for "b":
[tex]-2=\frac{3}{4}(-4)+b\\\\-2+3=b\\\\b=1[/tex]
Then, the equation of this line in Slope-Intercept form is:
[tex]y=\frac{3}{4}x+1[/tex]
The equation of the line in Standard form is:
[tex]Ax+By=C[/tex]
Then, manipulating the equation [tex]y=\frac{3}{4}x+1[/tex] algebraically, we get:
[tex]y-1=\frac{3}{4}x\\\\4(y-1)=3x\\\\4y-4=3x\\\\-4=3x-4y\\\\3x-4y=-4[/tex]
What is the vertex form of Y = x2 - 6x + 6?
Answer:
[tex]\large\boxed{y=(x-3)^2-3}[/tex]
Step-by-step explanation:
The vertex form of a quadratic equation y = ax² + bx + c:
y = a(x - h)² + k
(h, k) - coordinates of a vertex
We have the equation y = x² - 6x + 6.
Convert to the vertex form:
[tex]y=x^2-2(x)(3)+6\\\\y=\underbrace{x^2-2(x)(3)+3^2}_{(*)}-3^2+6\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\qquad(*)\\\\y=(x-3)^2-9+6\\\\y=(x-3)^2-3\to h=3,\ k=-3[/tex]
What is the factored form of the polynomial?
x2 − 15x + 36
(x − 4)(x − 9)
(x − 3)(x − 12)
(x + 4)(x + 9)
(x + 3)(x + 12)
Answer:
(x - 3)(x - 12)
Step-by-step explanation:
Given
x² - 15x + 36
Consider the factors of the constant term (+ 36) which sum to give the coefficient of the x- term (- 15)
The factors are - 3 and - 12, since
- 3 × - 12 = + 36 and - 3 - 12 = - 15, hence
x² - 15x + 36 = (x - 3)(x - 12) ← in factored form
The factored form of the polynomial x² − 15x + 36 is (x − 3)(x − 12). This can be obtained by using the steps of splitting the middle term method.
Find the factored form using splitting the middle term:Given the polynomial, x² − 15x + 36
Step 1:First we should multiply first term and last term, x²×36=36x²Step 2:This product ,that is 36x², should be slit such that the factors sum is the middle term, -15x.(-3x)×(-12x)=36x² and (-3x)+(-12x)= - 15x
-3x and -12x are the required factors of 36x²
Step 3:Substitute the factors in the place of middle term,x² - 3x - 12x+36
Step 4:Take common terms from the first two terms and last two terms,x² - 3x - 12x+36 = x(x - 3) - 12(x - 3)
=(x - 3)(x - 12)
Hence the factored form of the polynomial x² − 15x + 36 is (x − 3)(x − 12).
Learn more about factorisation of polynomial here:
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f(x) = x^2-5
g(x) = 4x - 4
Find (f-g) (5)
Answer:
The correct answer option is: 4.
Step-by-step explanation:
We are given the following two functions and we are to find the value of [tex] ( f - g ) ( 5 ) [/tex]:
[tex]f(x) = x^2 - 5[/tex]
[tex]g(x) = 4x - 4[/tex]
Finding [tex] ( f - g ) ( x ) [/tex]:
[tex] ( f - g ) ( x ) [/tex] [tex]= (x^2-5)-(4x-4) = x^2-4x-5+4[/tex]
[tex]( f - g ) ( x ) = x^2-4x-1[/tex]
So, [tex]( f - g ) ( 5 ) = (5)^2-4(5)-1 = 4[/tex]
The functions f(x) and g(x) are defined below. f(x)=sq. root x^2+12x+36 g(x)=x^3-12 Which expression is equal to f(x) · g(x)?
Answer: [tex]\bold{x^4+6x^3-12x-72}[/tex]
Step-by-step explanation:
[tex]f(x) = \sqrt{x^2+12x+36} \implies f(x)=\sqrt{(x+6)^2}\implies f(x) = x+6\\\\\\f(x)\cdot g(x)=(x+6)(x^3-12)\\.\qquad \qquad =x(x^3-12)+6(x^3-12)\\.\qquad \qquad =x^4-12x +6x^3-72\\.\qquad \qquad =\large\boxed{x^4+6x^3-12x-72}[/tex]
The expression equal to f(x)·g(x) is [tex]x^{4} + 6x^{3} - 12x - 72[/tex] .
What is the equivalent expression of f(x)·g(x) after simplification ?The expressions given are f(x) = [tex]\sqrt{x^{2}+12x+36}[/tex] and g(x) = [tex]x^{3} - 12[/tex] .
Thus we have
⇒ f(X) = [tex]\sqrt{x^{2}+12x+36}[/tex]
⇒ f(x) = [tex]\sqrt{(x+6)^{2} }[/tex]
⇒ f(x) = x + 6 .
Therefore the expression of multiplication of f(x)·g(x) is =
= [tex](x^{3} - 12)*(x + 6)[/tex]
= [tex]x^{4} + 6x^{3} - 12x - 72[/tex]
Thus, the expression equal to f(x)·g(x) is [tex]x^{4} + 6x^{3} - 12x - 72[/tex] .
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If tan^3(theta) -1/tan(theta)-1 - sec^2(theta) + 1 = 0 find cot(theta)
[tex]\tan^3\theta-\dfrac1{\tan\theta-1}-\sec^2\theta+1=0[/tex]
Recall that [tex]\tan^2\theta+1=\sec^2\theta[/tex], so we can write everything in terms of [tex]\tan\theta[/tex]:
[tex]\tan^3\theta-\dfrac1{\tan\theta-1}-\tan^2\theta=0[/tex]
Let [tex]x=\tan\theta[/tex], so that
[tex]x^3-\dfrac1{x-1}-x^2=0[/tex]
With some rewriting we get
[tex]x^3-x^2-\dfrac1{x-1}=0[/tex]
[tex]x^2(x-1)-\dfrac1{x-1}=0[/tex]
[tex]\dfrac{x^2(x-1)^2-1}{x-1}=0[/tex]
Clearly we cannot have [tex]x=1[/tex], or [tex]\tan\theta=1[/tex].
The numerator determines when the expression on the left reduces to 0:
[tex]x^2(x-1)^2-1=0[/tex]
[tex]x^2(x-1)^2=1[/tex]
[tex]\sqrt{x^2(x-1)^2}=\sqrt1[/tex]
[tex]|x(x-1)|=1[/tex]
[tex]x(x-1)=1\text{ or }x(x-1)=-1[/tex]
Completing the square gives
[tex]x(x-1)=x^2-x=x^2-x+\dfrac14-\dfrac14=\left(x-\dfrac12\right)^2-\dfrac14[/tex]
so that
[tex]\left(x-\dfrac12\right)^2=\dfrac54\text{ or }\left(x-\dfrac12\right)^2=-\dfrac34[/tex]
The second equation gives no real-valued solutions because squaring any real number gives a positive real number. (I'm assuming we don't care about complex solutions.) So we're left with only
[tex]\left(x-\dfrac12\right)^2=\dfrac54[/tex]
[tex]\sqrt{\left(x-\dfrac12\right)^2}=\sqrt{\dfrac54}[/tex]
[tex]\left|x-\dfrac12\right|=\dfrac{\sqrt5}2[/tex]
which again gives two cases,
[tex]x-\dfrac12=\dfrac{\sqrt5}2\text{ or }x-\dfrac12=-\dfrac{\sqrt5}2[/tex]
[tex]x=\dfrac{1+\sqrt5}2\text{ or }x=\dfrac{1-\sqrt5}2[/tex]
Then when [tex]x=\tan\theta[/tex], we can find [tex]\cot\theta[/tex] by taking the reciprocal, so we get
[tex]\boxed{\cot\theta=\dfrac2{1+\sqrt5}\text{ or }\cot\theta=\dfrac2{1-\sqrt5}}[/tex]
Answer: A. -1
Step-by-step explanation:
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