Answer: [tex]\bold{\dfrac{19}{3}}[/tex]
Step-by-step explanation:
[tex]\dfrac{7b-2}{-a+1}\\\\\\=\dfrac{7(3)-2}{-(-2)+1}\\\\\\=\dfrac{21-2}{2+1}\\\\\\=\dfrac{19}{3}[/tex]
For which nonnegative value of x is the expression 5+x
———
25-x^2
undefined?
please explain steps and what the question means!
Answer:
x = 5
Step-by-step explanation:
the expression is "undefined" when the denominator is equal to zero
[tex]\frac{\left(5+x\right)}{25-x^2\:} \\[/tex]denominator = 25 - x²
Values of x where the equation is "undefined"
0 = 25 - x²
x² = 25
√x² = √25
x = ± 5
Nonnegative value of x where the equation is "undefined"
x = 5
An expression is said to be undefined, if it has 0 as its denominator. For [tex]\frac{5 + x}{25 - x^2}[/tex] to be undefined, x must be 5.
Given that:
[tex]\frac{5 + x}{25 - x^2}[/tex]
For the expression to be undefined, the denominator must equal 0.
i.e.
[tex]25 - x^2 = 0[/tex]
Collect like terms
[tex]-x^2 = 0 - 25[/tex]
[tex]-x^2 = - 25[/tex]
Cancel out negatives
[tex]x^2 = 25[/tex]
Take positive square root
[tex]x = 5[/tex]
This means that when [tex]x = 5[/tex], [tex]\frac{5 + x}{25 - x^2}[/tex] is undefined.
Read more about undefined expressions at:
https://brainly.com/question/13464119
a plain takes off at an angel of 20 degree. assuming a constant speed and trajectory, by the time it has travelled 25 kilo meter horizontally, how h8gh it will be fly
Answer:
9.10 km to the nearest hundredth.
Step-by-step explanation:
We have a triangle whose adjacent side is 25 km and angle 20 degrees.
If h is the height we have the equation:
tan 20 = h / 25
h = 25 tan 20
= 9.099 km.
a rectange has a width of 9 units and a length of 40 unit. what is the length in diagonal
Answer:
41 units
Step-by-step explanation:
The diagonal forms a right triangle with the sides, so we can use Pythagorean theorem.
c² = a² + b²
d² = 9² + 40²
d = 41
The diagonal is 41 units long.
410 in 8 Hours At A Unit Rate !
Answer:
12 miles per hour
Step-by-step explanation:
flock of birds is flying south, toward the equator, at an hourly rate. A scientist created the function f(x)=−60x+1320 to represent how many miles away from the equator the birds are after a given number of hours.
Which of the answers are true of the scenario represented by this function?
There is more than one correct answer. Select all answers that apply.
The birds began 1320 miles from the equator.
It will take the birds 1320 hours to reach the equator.
The birds began 60 miles from the equator.
It takes the birds 60 hours to fly x miles.
The birds are flying toward the equator at a rate of 1320 mph.
The birds are flying toward the equator at a rate of 60 mph.
Answer: First and last option
The birds began 1320 miles from the equator.
The birds are flying toward the equator at a rate of 60 mph.
Step-by-step explanation:
Note that the function f(x) is a linear function.
[tex]f (x) = - 60x + 1320[/tex]
If x represents the number of hours and f(x) represents the distance from the equator, then x = 0 means that the first hour has not yet elapsed.
When x = 0 then:
[tex]f (0) = -60 * 0 +1320\\f (0) = 1320[/tex].
This means that the initial distance at which the birds of the equator are located is 1320 miles.
Then when x = 1 then:
[tex]f (x) = -60 * 1 + 1320\\f (x) = -60 +1320[/tex]
When x = 2 then:
[tex]f (x) = -60 * 2 + 1320\\f (x) = -120 +1320[/tex]
As x increases by one unit then the distance of the birds to the equator decreases by 60 miles. This means that birds travel at a speed of 60 miles per hour
Answer:
The birds began 1320 miles from the equator.
The birds are flying toward the equator at a rate of 60 mph.
Step-by-step explanation:
Find the slope of the line that passes through the given points.
Finding the slope using two points:
The formula for slope is
[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
In this case...
[tex]y_{2} =-7\\y_{1} =2\\x_{2} =4\\x_{1} =-3[/tex]
^^^Plug these numbers into the formula for slope...
[tex]\frac{-7 - 2}{4 - (-3)}[/tex]
[tex]\frac{-9}{6}[/tex]
^^^Reduce this fraction
[tex]\frac{-3}{2}[/tex]
^^^This is your slope
Hope this helped!
~Just a girl in love with Shawn Mendes
Please help??
The equation of a standard pitcher’s mound in baseball is (x+5)^2+(y+7)^2=81. The diameter of the pitcher’s mound is____ units
The equation (x+5)^2 + (y+7)^2=81 is a variation of a circles standard formula (x - h)^2 + (y - k)^2 = r^2
To find the diameter you must first know the radius.
In this question the radius is 9.
9^2 = 81
The diameter is composed of the length of two radii, this means that the equation to find the diameter when the radius is known is (let diameter be D and radius be r): D = 2r
D = 9 * 2
D = 18
The diameter is 18 units
Hope this helped!
~Just a girl in love with Shawn Mendes
In the diagram below, Pis circumscribed about quadrilateral ABCD. What is
the value of x?
A. 60°
B. 100°
C. 80°
D. 120°
Answer:
c
Step-by-step explanation:
x=180-100=80
The value of x is [tex]80^{o}[/tex].
What are the opposite angle of a quadrilateral?The opposite angles in a quadrilateral are those angles that are located diagonally opposite to each other.
What is the sum of the opposite angles of a quadrilateral?The sum of the opposite angles of a cyclic quadrilateral is 180 degrees.
According to the given question.
We have a quadrilateral ABCD which is inscribed in a circle.
Also, m ∠ABC = 100 degrees
Since, we know that the sum of the opposite angles of a cyclic quadrilateral is 180 degrees.
Therefore,
[tex]m\angle ABC +m\angle CDA = 180^{o} \\\implies 100^{o} + x = 180^{o} \\\implies x = 180^{o} -100^{o} \\\implies x = 80^{o}[/tex]
Hence, the value of x is [tex]80^{o}[/tex].
Find out more information about sum of the opposite angles of a cyclic quadrilateral here:
https://brainly.com/question/16900958
#SPJ2
Which are the solutions of the quadratic equation?
x2=7X+4
-7-165 -7 + 165
-7.0
7- 165 7+ / 65
7,0
For this case we must find the roots of the following equation:
[tex]x ^ 2-7x-4 = 0[/tex]
We have to:
[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}[/tex]
Where:
[tex]a = 1\\b = -7\\c = -4[/tex]
Substituting the values:
[tex]x = \frac {- (- 7) \pm \sqrt {(- 7) ^ 2-4 (1) (- 4)}} {2 (1)}\\x = \frac {7 \pm \sqrt {49 + 16}} {2}\\x = \frac {7\pm\sqrt {65}} {2}[/tex]
We have two roots:
[tex]x_ {1} = \frac {7+ \sqrt {65}} {2} = 7.53\\x_ {2} = \frac {7- \sqrt {65}} {2} = - 0.53[/tex]
Answer:
[tex]x_ {1} = \frac {7+ \sqrt {65}} {2} = 7.53\\x_ {2} = \frac {7- \sqrt {65}} {2} = - 0.53[/tex]
Answer:
(C)
Step-by-step explanation:
♥☺
Which of these statements being true would show that x-10 is a factor of the polynomial p(x)
P(10)=0
p(0)=10
p(0)=-10
p(-10)=0
PLEASE HELP ASAP ALGEBRA 2
Answer:
P(10)=0
Step-by-step explanation:
As per factor theorem:
If x-10 is factor of polynomial p(x), then the remainder after division by x-10 should be zero. i.e. If we synthetic-divide a p(x) by x = 10 and get zero remainder as following
P(10)=0
it is reverse of remainder theorem!
which of the following is a trinomial with a constant term?
A nominal has three terms.
Only B and D have three terms.
A constant term would be a number without a variable.
All the terms in B have variables ( x , y are part of each term).
The last term in D is the number 12, with no variable associated with it.
The answer would be D.
Answer:
it's d y^5+13x+12. you feel me you gon get it right
A flight from Seattle to New York takes 5 1/4 hours. We have traveled 5/8 of the way. How many hours until we land in New York?
Answer:
1.97 hours to land in New York
Step-by-step explanation:
We know that the number of hours it takes to complete the flight is: 5 [tex]\frac{1}{4}[/tex] hours
This is the same as [tex]5 + \frac{1}{4} = 5.25\ hours[/tex]
If we have traveled [tex]\frac{5}{8}[/tex] of the way, then [tex]\frac{3}{8}[/tex] more of the way to get to New York is missing, therefore the number of hours remaining is:
[tex]\frac{3}{8}*5.25\ hours = 1.97\ hours[/tex]
1.97 hours to land in New York
The time left for the flight from Seattle to New York, after travelling 5/8 of the way, is approximately 2 hours.
Explanation:The flight from Seattle to New York takes 5 1/4 hours. If you've travelled 5/8 of the way, it means you've covered a significant portion of the total flight time. Here's how you would figure out how much time you have left:
First, convert the total flight time to a straight decimal for simplicity. 5 1/4 hours is equivalent to 5.25 hours.Next, multiply that total flight time by the fraction of the flight completed, which is 5/8. This gives you how many hours you've already flown. So, 5.25 * 5/8 = approximately 3.28 hours.Finally, to find out how much longer you have to fly, subtract the time already flown from the total flight time. So, 5.25 – 3.28 = approximately 1.97 hours, or about 2 hours left.Learn more about Flight Time Calculation here:
https://brainly.com/question/23345050
#SPJ12
If Kevin makes c toys in m minutes, how many toys can he make per hour?
Answer:
The number of toys that Kevin can make per hour is equal to [tex]60\frac{c}{m}\ toys[/tex]
Step-by-step explanation:
we know that
Kevin makes c toys in m minutes
Remember that
1 hour=60 minutes
so
Using proportion find out how many toys can be make in 60 minutes (one hour)
Let
x -----> the number of toys that Kevin can make per hour
so
[tex]\frac{c}{m}=\frac{x}{60}\\ \\x=60\frac{c}{m}\ toys[/tex]
therefore
The number of toys that Kevin can make per hour is equal to [tex]60\frac{c}{m}\ toys[/tex]
g(x) = x4 − 3x2 + 4x − 5
Let's solve for g.
gx=x4−3x2+4x−5
Step 1: Divide both sides by x.
gx
x
=
x4−3x2+4x−5
x
g=
x4−3x2+4x−5
x
Answer:
g=
x4−3x2+4x−5
x
DeMarco has the following coins in his
pocket: 5 nickels, 3 dimes, and 2 quarters.
What percent of one dollar does DeMarco
have in nickels?
Answer:
5=.25, 3=.30, 2=.50
Step-by-step explanation:
5×5=.25
Answer: 25%
Step-by-step explanation: A nickel is worth 5 cents. There are 5 nickels. Multiply 5 by 5. 5 x 5 = 25. You have 25 cents in nickels. There are 100 cents in a dollar, so divide 25 by 100. 25/100 = 0.25. To get the percent, multiply 0.25 by 100. 0.25 x 100 = 25%.
In graphing the equation y<2x -5, the line is dotted and shaded below the line drawn.
True
False
Answer:
True.
Step-by-step explanation:
This is 'less than' so the area below the line is shaded.
It is a dotted line because the solution does not contain points on the line as the inequality sign is < NOT ≤.
Answer:
First option: True.
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope of the line and "b" is the y-intercept.
Given this inequality:
[tex]y<2x -5[/tex]
We know that the line is:
[tex]y=2x -5[/tex]
Whose slope is 2 and the y-intercept is -5
The symbol "<" provided in the inequalty, indicates that the shaded region must be below the line and the line must be dotted. Therefore, the answer is: TRUE.
Consider this square pyramid. Recall the volume can be found using the formula V = 1/3Bh.
What is the volume of the pyramid after dilating by a scale factor of 1/4? Describe the effects.
A.) 16 m³. The volume of the new pyramid is the volume of the original pyramid times 1/64.
B.) 64 m³. The volume of the new pyramid is the volume of the original pyramid times 1/16.
C.) 256 m³. The volume of the new pyramid is the volume of the original pyramid times 1/4.
D.) 1,024 m³. The volume of the new pyramid is equal to the volume of the original pyramid.
Answer:
Option A.) 16 m³. The volume of the new pyramid is the volume of the original pyramid times 1/64.
Step-by-step explanation:
step 1
Find the volume of the original pyramid
The volume of the pyramid is equal to
[tex]V=\frac{1}{3}Bh[/tex]
where
B is the area of the base
h is the height of the pyramid
we have
[tex]B=16^{2}=256\ m^{2}[/tex] ----> is the area of a square
[tex]h=12\ m[/tex]
substitute
[tex]V=\frac{1}{3}(256)(12)[/tex]
[tex]V=1,024\ m^{3}[/tex]
step 2
Find the volume of the new pyramid
we know that
If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube
so
Let
z -------> the scale factor
x ------> the volume of the new pyramid
y -----> the volume of the original pyramid
[tex]z^{3}=\frac{x}{y}[/tex]
we have
[tex]z=\frac{1}{4}[/tex]
[tex]y=1,024\ m^{3}[/tex]
substitute and solve for x
[tex](\frac{1}{4})^{3}=\frac{x}{1,024}[/tex]
[tex]x=(1,024)\frac{1}{64}=16\ m^{3}[/tex]
therefore
The volume of the new pyramid is the volume of the original pyramid times 1/64
Answer:
The answer is A
Step-by-step explanation:
Find the domain of the graphed function.
-10
The domain is the X values.
There are two dots located at x = -4 and x = 9
The answer would be: D -4 < x < 9
The domain of the graphed function is - 4 ≤ x ≤ 9, that is option D. This can be obtained by finding all the x-values.
What is the domain of the graph?⇒Domain is all x-values of a function.
From the graph, we can say that the graph start from (-4,-4) to (8,9).
Thus x-values are from -4 to 9.
Since the endpoints are closed circles the points -4 and 9 are included.
∴The required domain is - 4 ≤ x ≤ 9
Hence the domain of the graphed function is - 4 ≤ x ≤ 9, that is option D.
Learn more about graphed functions here:
brainly.com/question/2709928
#SPJ2
The coordinate plane below represents a city.
Points A through F are schools in the city. graph of coordinate plane. Point A is at negative 3, negative 4. Point B is at negative 4, 3. Point C is at 2, 2. Point D is at
The coordinate plane is below
Part A: Using the graph above, create a system of inequalities that only contain points C and F in the overlapping shaded regions. Explain how the lines will be graphed and shaded on the coordinate grid above.
Part B: Explain how to verify that the points C and F are solutions to the system of inequalities created in Part A.
Part C: Natalie can only attend a school in her designated zone. Natalie's zone is defined by y < −2x + 2. Explain how you can identify the schools that Natalie is allowed to attend.
Answer:
Part A) The system of inequalities is
[tex]x\geq2[/tex] and [tex]y\geq2[/tex]
Part B) In the procedure
Part C) The schools that Natalie is allowed to attend are A,B and D
Step-by-step explanation:
Part A: Using the graph above, create a system of inequalities that only contain points C and F in the overlapping shaded regions
we have
Points C(2,2), F(3,4)
The system of inequalities could be
[tex]x\geq2[/tex] -----> inequality A
The solution of the inequality A is the shaded area at the right of the solid line x=2
[tex]y\geq2[/tex] -----> inequality B
The solution of the inequality B is the shaded area above of the solid line y=2
see the attached figure N 1
Part B: Explain how to verify that the points C and F are solutions to the system of inequalities created in Part A
we know that
If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities
Verify point C
C(2,2)
Inequality A
[tex]x\geq2[/tex] -----> [tex]2\geq2[/tex] ----> is true
Inequality B
[tex]y\geq2[/tex] ------> [tex]2\geq2[/tex] ----> is true
therefore
Point C is a solution of the system of inequalities
Verify point D
F(3,4)
Inequality A
[tex]x\geq2[/tex] -----> [tex]3\geq2[/tex] ----> is true
Inequality B
[tex]y\geq2[/tex] ------> [tex]4\geq2[/tex] ----> is true
therefore
Point D is a solution of the system of inequalities
Part C: Natalie can only attend a school in her designated zone. Natalie's zone is defined by y < −2x + 2. Explain how you can identify the schools that Natalie is allowed to attend.
we have
[tex]y < -2x+2[/tex]
The solution of the inequality is the shaded area below the dotted line [tex]y=-2x+2[/tex]
The y-intercept of the dotted line is the point (0,2)
The x-intercept of the dotted line is the point (1,0)
To graph the inequality, plot the intercepts and shade the area below the dotted line
see the attached figure N 2
therefore
The schools that Natalie is allowed to attend are A,B and D
How to constructed a square polygon
Answer:
Construct a square of side length 4 cm
Step-by-step explanation:
* Lets explain how to construct a square polygon with side length 4 cm
- Use your straightedge to draw a horizontal line
- Measure on the horizontal line a segment of 4 cm
- Label its endpoints by A and B (AB = 4 cm)
- Open your compass at a distance greater then half AB (3 cm)
- Put the pin of the compass at point B and draw an arc intersects AB
at point E and the horizontal line at point F
- Open the compass at a distance greater than the length of the side
of the square (6 cm) and put its pin on the point E and draw an arc
- Put the pin of the compass on the point F without changing the open
of the compass and draw another arc
- The two arcs intersect each other at point G
- Join BG and measure 4 cm from point B and label the end point of
the 4 cm by C
- Open your compass at a distance 4 cm and put the pin on point C
and draw an arc and put it on point A with the same distance 4 cm
and draw another arc, the two arc intersect each other at point D
∴ ABCD is a square of side length 4 cm
# Look to the attached figure to more understand
15. Which table correctly lists the x- and y-values for the equation 5x + y = 14?
A.
x
–1
0
1
y
21
28
7
B.
x
–1
0
1
y
19
14
9
C.
x
–1
0
1
y
9
14
19
D.
x
–1
0
1
y
–5
0
5
Answer:
B
Step-by-step explanation:
Given
5x + y = 14 ( subtract 5x from both sides )
y = 14 - 5x
Substituting values of x into the right side allows the corresponding value of y to be found.
x = - 1 : y = 14 - 5( - 1) = 14 + 5 = 19
x = 0 : y = 14 - 5(0) = 14 - 0 = 14
x = 1 : y = 14 - 5(1) = 14 - 5 = 9
Hence the corresponding values of x and y are
x y
- 1 19
0 14
1 9
GCF of 32ab cubed and 40a squared
Answer:
8a.
Step-by-step explanation:
32 = 2*2*2*2*2
40 = 2*2*2* 5
Thus the GCF of 32 and 40 is 2*2*2 = 8.
The GCF of a and ab = a.
For this case we must find the GCF of the following expressions:
[tex]32ab ^ 3\\40a ^ 2[/tex]
By definition, the GCF is given by the largest factor that divides both numbers without leaving residue.
We look for the factors of 32 and 40:
32: 1,2,4,8,16
40: 1,2,4,5,8,10,20
Thus, the GCF is 8.
On the other hand, the GCF of [tex]ab ^ 3[/tex]and [tex]a ^ 2[/tex] is a.
Finally, the GFC of the expressions is:
[tex]8a[/tex]
Answer:
[tex]8a[/tex]
The curved part of this figure is a semicircle. What is the best approximation for the area of this figure? 18+12.125π units² 36+24.25π units² 36+12.125π units² 18+24.25π units²
Answer:
18+12.125π units²
Step-by-step explanation:
The diameter of the semicircle can be found by the use Pythagoras theorem.
Δx²+Δy²=d²
Δx=3--1=4
Δy=3--6=9
d²=4²+9²
d=√(16+81)
Area=πr²/2
=π×(√(16+81)/2)²÷2
=[π×(97)/4]/2
=97π/8
=18+12.125π units²
97π/8 is equivalent to 18+12.125π units²
Answer:
18+12.125π units²
I tooked the test (●'◡'●)
Step-by-step explanation:
348,0 19.57 which digit is in the ten thousands place
Answer:
4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
See attached reference
Calculating cos-1 ( help is gladly appreciated :) )
Answer:
[tex]\frac{3\pi}{4}[/tex]
(Assuming you want your answer in radians)
If you want the answer in degrees just multiply your answer in radians by [tex]\frac{180^\circ}{\pi}[/tex] giving you:
[tex]\frac{3\pi}{4} \cdot \frac{180^\circ}{\pi}=\frac{3(180)}{4}=135^{\circ}[/tex].
We can do this since [tex]\pi \text{ rad }=180^\circ[/tex] (half the circumference of the unit circle is equivalent to 180 degree rotation).
Step-by-step explanation:
[tex]\cos^{-1}(x)[/tex] is going to output an angle measurement in [tex][0,\pi][/tex].
So we are looking to solve the following equation in that interval:
[tex]\cos(x)=-\frac{\sqrt{2}}{2}[/tex].
This happens in the second quadrant on the given interval.
The solution to the equation is [tex]\frac{3\pi}{4}[/tex].
So we are saying that [tex]\cos(\frac{3\pi}{4})=\frac{-\sqrt{2}}{2}[/tex] implies [tex]\cos^{-1}(\frac{-\sqrt{2}}{2})=\frac{3\pi}{4}[/tex] since [tex]\frac{3\pi}{4} \in [0,\pi][/tex].
Answer is [tex]\frac{3\pi}{4}[/tex].
A simple random sample of 60 is drawn from a normally distributed population, and the mean is found to be 28, with a standard deviation of 5. Which of the following values is within the 95% confidence interval (z-score = 1.96) for the population mean? Remember, the margin of error, ME, can be determined using the formula ME=z*s/square root n. The value of 26, because it’s not greater than 26.7 and less than 29.3. The value of 27, because it’s greater than 26.7 and less than 29.3. The value of 32, because it’s greater than 23 and less than 33. The value of 34, because it’s not greater than 23 and less than 33.
Answer:
The value of 27, because it’s greater than 26.7 and less than 29.3.
Step-by-step explanation:
You should find the confidence Interval at 95%
The formula to apply is;
C.I= x±z*δ/√n
where C.I is the confidence interval, x is the mean of the sample, z is the z* value from the standard normal distribution for 95% confidence interval, δ is the standard deviation and n is the sample size
Substitute values in the formula
[tex]z*=1.96\\\\[/tex]
Find δ/√n
[tex]=\frac{5}{\sqrt{60} } =0.64549722436\\\\\\[/tex]
Calculate z*δ/√n
[tex]=1.96*0.64549722436=1.2652\\\\\\[/tex]
C.I= 28±1.2652
Upper limit is = 28+1.2652=29.2625
Lower limit is =28-1.2652=26.7348
Solution
The value 27 is within 95% confidence interval because it is greater than 26.7 and less than 29.3
Answer:
B.The value of 27, because it’s greater than 26.7 and less than 29.3.Step-by-step explanation:
What is the measure of angle B
As you can see from the image in the picture all the sides of the triangle are equal to each other (25). This means that this is an equilateral triangle.
The definition of an equilateral triangle is:
A triangle that has all sides equal to each other. The angles are also equal to each other. Since it is known that the sum of all the angles of a triangle equals 180, one angle of an equilateral triangle is always 60 degrees ( 180 / 3 = 60).
That means angle B has the measure of 60 degrees
Hope this helped!
~Just a girl in love with Shawn Mendes
What is the measure of arc ABC?
Answer: A
Step-by-step explanation:
360°-50°=310°
Answer:it’s actually 260
Step-by-step explanation:
I just did the test
Match each expression to its equivalent standard form.
Answer:
(x+1+i)(x+1-i) goes with x^2+2x+2
(x+2i)(x-2i) goes with x^2+4
(x-2+2i)(x-2-2i) goes with x^2-4x+8
Step-by-step explanation:
(x+1+i)(x+1-i)
(x+[1+i])(x+[1-i])
Use foil.
First: x(x)=x^2
Outer: x(1+i)=x+ix
Inner: x(1-i)=x-ix
Last: (1+i)(1-i)=1-i^2 since 1+i and 1-i are conjugates
__Add together to get: x^2+2x+1-i^2
We can actually simplify this because i^2=-1
So x^2+2x+1-i^2=x^2+2x+1-(-1)=x^2+2x+2
(x+2i)(x-2i)
These are conjugates so just do first and last of foil.
First: x(x)=x^2
Last: 2i(-2i)=-4i^2=-4(-1)=4
==Adding together gives x^2+4
(x-2+2i)(x-2-2i)
(x+[-2+2i])(x+[-2-2i])
This is similar to first.
Foil time!
First: x(x)=x^2
Outer: x(-2-2i)=-2x-2ix
Inner: x(-2+2i)=-2x+2ix
Last: (-2-2i)(-2+2i)=4-4i^2 (multiplying conjugates again)
==Add together giving us x^2-4x+4-4i^2
This can be simplified since i^2=-1.
So applying this gives us x^2-4x+4-4(-1)
=x^2-4x+4+4
=x^2-4x+8
Answer:
1. The first expression is equivalent to [tex]x^2+2x+2[/tex].
2. The second expression is equivalent to [tex]x^2+4[/tex].
3. The third expression is equivalent to [tex]x^2-4x+8[/tex].
Step-by-step explanation:
(1).
The given expression is
[tex](x+1+i)(x+1-i)[/tex]
[tex][(x+1)+i][(x+1)-i][/tex]
Using the algebraic properties, we get
[tex](x+1)^2-(i)^2[/tex] [tex][\because a^2-b^2=(a-b)(a+b)][/tex]
[tex]x^2+2x+1-(i)^2[/tex] [tex][\because (a+b)^2=a^2+2ab+b^2][/tex]
[tex]x^2+2x+1-(-1)[/tex] [tex][\because i^2=-1][/tex]
[tex]x^2+2x+2[/tex]
Therefore the first expression is equivalent to [tex]x^2+2x+2[/tex].
(2).
The given expression is
[tex](x+2i)(x-2i)[/tex]
Using the algebraic properties, we get
[tex](x)^2-(2i)^2[/tex] [tex][\because a^2-b^2=(a-b)(a+b)][/tex]
[tex]x^2-4i^2[/tex]
[tex]x^2-4(-1)[/tex] [tex][\because i^2=-1][/tex
[tex]x^2+4[/tex]
Therefore the second expression is equivalent to
[tex]x^2+4[/tex].
(3)
The given expression is
[tex](x-2+2i)(x-2-2i)[/tex]
[tex][(x-2)+2i][(x-2)-2i][/tex]
Using the algebraic properties, we get
[tex](x-2)^2-(2i)^2[/tex] [tex][\because a^2-b^2=(a-b)(a+b)][/tex]
[tex]x^2-4x+4-4i^2[/tex] [tex][\because (a-b)^2=a^2-2ab+b^2][/tex]
[tex]x^2-4x+4-4(-1)[/tex] [tex][\because i^2=-1][/tex]
[tex]x^2-4x+4+4[/tex]
[tex]x^2-4x+8[/tex]
Therefore the third expression is equivalent to [tex]x^2-4x+8[/tex].
A triangle has vertices at F (−7, 3), G (2, 6), and H (3, 5). What are the coordinates of each vertex if the triangle is reflected over the x axis?
Answer:
F(-7,3) -> F'(-7,-3)
G(2,6) -> G'(2,-6)
H(3,5) ->H'(3,-5)
Step-by-step explanation:
If you are taking point (a,b) and reflecting it across the x-axis (the horizontal axis), your x value is going to stay the same because you want the point on the same vertical line as (a,b). The y-coordinate is going to be opposite because you want a reflection and the opposite of b will this give you the same distance from the x-axis as b.
So the transformation is this: (a,b) -> (a,-b).
All this means is leave x the same and take the opposite of y.
F(-7,3) -> F'(-7,-3)
G(2,6) -> G'(2,-6)
H(3,5) ->H'(3,-5)
The coordinates of each vertex if the triangle is reflected over the x-axis are [tex]F'(-7,-3),G'(2,-6),H'(3,-5)[/tex].
Given:
The vertices of a triangle are [tex]F(-7,3),G(2,6),H(3,5)[/tex].
To find:
The coordinates of each vertex if the triangle is reflected over the x-axis.
Explanation:
If a triangle is reflected over the x-axis, then the rule of reflection is defined as:
[tex](x,y)\to (x,-y)[/tex]
Using this rule, we get
[tex]F(-7,3)\to F'(-7,-3)[/tex]
[tex]G(2,6)\to G'(2,-6)[/tex]
[tex]H(3,5)\to H'(3,-5)[/tex]
Therefore, the coordinates of each vertex if the triangle is reflected over the x-axis are [tex]F'(-7,-3),G'(2,-6),H'(3,-5)[/tex].
Learn more:
https://brainly.com/question/974424