Answer:True
Step-by-step explanation:
Answer:
The sum of the exterior angles of a polygon is always 180 degrees.
Step-by-step explanation:
Please mark brainliest and have a great day!
Identify an equation in point-slope form for the line perpendicular to y = -1/3x - 6 that passes through (-1, 5).
A. y + 1 = 3(x - 5)
B. y + 5 = 1/3(x - 1)
C. y - 5 = -1/3(x + 1)
D. y - 5 =3(x + 1)
Answer:
D. y - 5 =3(x + 1)
Step-by-step explanation:
y = -1/3x -6
The slope is -1/3
Take the negative reciprocal to find the slope of the line that is perpendicular
- (-3) = 3
The slope would be 3
We have the slope and a point
Using point slope form
y-y1 = m(x-x21)
y-5 = 3(x--1)
y-5 = 3(x+1)
Answer:
D. y - 5 =3(x + 1)
Step-by-step explanation:
Given equation of line:
[tex]y = -\frac{1}{3}x-6[/tex]
Comparing it with the standard form of equation of line
y=mx+b
m = -1/3
Let m1 be the slope of line perpendicular to the given line.
We know that the product of slopes of two perpendicular lines is -1.
[tex]m*m_1 = -1\\-\frac{1}{3} * m_1 = -1\\ m_1 = -1 * -\frac{3}{1}\\ m_1 = 3[/tex]
The equation of line in point slope form is:
[tex]y-y_1 = m(x-x_1)[/tex]
where x_1 and y_1 is the point from which the line passes.
So, putting the values of slope and point,
[tex]y-5 = 3[x-(-1)]\\y-5=3(x+1)[/tex]
Option D is correct ..
Which statement about this figure is true?
It has rotational symmetry with an angle of rotation of 30°.
It has no reflectional symmetry.
It has no rotational symmetry.
It has reflectional symmetry with 6 lines of symmetry.
Answer:
b and d
Step-by-step explanation:
The figure has 12 peaks. A full circle has 360 degrees.
(360 degrees)/12 = 30 degrees.
b. It has rotational symmetry with an angle of rotation of 30 deg.
If you draw a line between each pair of opposite peaks, that line is an axis of reflectional symmetry. Since there are 12 peaks, there are 6 such lines.
d. It has reflectional symmetry with 6 lines of symmetry.
Answer:
It has rotational symmetry with an angle of rotation of 30°.
Step-by-step explanation:
A shape is said to possess rotational symmetry, when it still looks the same after some rotation.
We can see, that the given shape looks the same from every angle and every side.
So, the correct answer is: It has rotational symmetry with an angle of rotation of 30°.
30 degrees because it has 12 angles and [tex]360/12=30[/tex] degrees.
A student needs at least 80% of all points on the tests in a class to get a B. There are three
100-point tests and a 250-point final. The student's test scores are 72%, 85%, and 78% for
the 100 point tests. What is the least score the student can make on the final and still get a B?
How many points are there total? (3*100)+250 = 550
So far, he has 72 + 85 + 78, or 235
He needs 0.80 * 550 for a B, or 440 points
440 - 235 = 205 points on the final to get a B
Percentage-wise, he needs 205/250, or 0.82
34x+5−12x=3 what is the value of x?
Answer:
[tex]\large\boxed{x=-\dfrac{1}{11}}[/tex]
Step-by-step explanation:
[tex]34x+5-12x=3\qquad\text{subtraxct 5 from both sides}\\\\34x-12x=3-5\\\\22x=-2\qquad\text{divide both sides by 22}\\\\x=\dfrac{-2}{22}\\\\x=-\dfrac{2:2}{22:2}\\\\x=-\dfrac{1}{11}[/tex]
To solve the equation 34x+5−12x=3, we combine like terms to get 22x+5=3, then isolate x to find that x=-1/11.
The student's question, 34x+5−12x=3, presents a linear equation where we need to find the value of x.
To solve for x, we shall first consolidate like terms on the left side of the equation.
We have:
34x - 12x + 5 = 3
22x + 5 = 3
22x = 3 - 5
22x = -2
x = -2/22
x = -1/11
The value of x in this equation is -1/11.
Jeremy looked at this table of prices and said the cost for renting a bike is $7.00 per hour. What mistake may jeremy have made?explain
Answer:
Answer will be: Jeremy is looking at the rate for renting a bike for 2 hours. To find the rate for one hour divide 7 by 2. The rate for renting a bike for one hour is $3.50.
The mistake that jeremy made is that the cost renting is not $7.00 for hour, it is $7.00 for two hours.
What is Unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value
Given:
The table is attached below
Jeremy said the cost bike renting for an hour is $7.00. But looking at the table the difference between two consecutive cost is $7.00 not in the gap of 1 hour in fact in gap of 2 hours.
It means that the the cost of bike renting $7.00 is for 2 hours.
For an hour the cost for renting bike will be,
=7/2
=3.5 hours.
Hence, the cost of bike renting is 3.5 hours per hour.
Learn more about unitary method here:
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What is the slope of the line
Answer:
-1/2 b
Step-by-step explanation:
Which equation represents a line that passes through (-9,-3) amd has a slope of -6
Answer:
Step-by-step explanation:
Point slope form is y-y1=m(x-x1)
(x1,y1) is (-9,-3)
m is -6
Plug in!
y-(-3)=(-6)(x-(-9)) The answer could look like this.
y+3=-6(x+9) Or this.
y=-6(x+9)-3 Or this
y=-6x-54-3 Even this but unlikely...
y=-6x-57 Or this.
I will change my answer after choices are posted.
Answer:
y+3 = -6(x+9) point slope form
y = -6x-57 slope intercept form
Step-by-step explanation:
We can use the point slope equation of a line
y-y1 = m(x-x1)
y--3 = -6(x--9)
y+3 = -6(x+9)
If we want the equation in point slope form
Distribute the -6
y+3 = -6x -54
Subtract 3 from each side
y+3-3 = -5x-54 -3
y = -6x-57
what is the value of k
Answer: We need a picture or a description of how we need to find the value ok k.
Step-by-step explanation:
28,32,47,16,40,35,38,54 what is the MAD of the data
Answer:
Mean Absolute Deviation (MAD): 8.5
Step-by-step explanation:
Xmean = (28 + 32 + 47 + 16 + 40 + 35 + 38 + 54)/8 = 290/8
Xmean = 36.25
MAD =
(28 - 36.25) + (32 - 36.25) + (47 - 36.25) + (16 - 36.25) + (40 - 36.25) + (35 - 36.25) + (38 - 36.25) + (54 - 36.25) divided by 8
a break down of each ( )
(8.25) + (4.25) + (10.75) + (20.25) + (3.75) + (1.25) + (1.75) + (17.75) divided by 8 = 68
then you take 68/8 = Mean Absolute Deviation 8.5
Answer:
Mean Absolute Deviation (M.A.D): 8.5
Step-by-step explanation:
1. To find the mean absolute deviation of the data, start by finding the mean of the data set.
2. Find the sum of the data values, and divide the sum by the number of data values.
3. Find the absolute value of the difference between each data value and the mean: |data value – mean|.
4. Find the sum of the absolute values of the differences.
5. Divide the sum of the absolute values of the differences by the number of data values.
Hope that helped! :)
If the measure of a central angle is 124°, then what is the measure of the arc it creates? 248° 62° 31° 124°
PLEASE HELP!!!!!!!!!!!
Answer:
The measure of the arc it creates from the central angle is 124°
Step-by-step explanation:
Remember that a central angle's vertex is located on the center of the circle. The measure of the arc, is the same as the measure of the central angle. If it's an inscribed angle, the measure of the arc is two times the measure of the inscribed angle.
Answer:
124
Step-by-step explanation:
If the diagonal path is 750 feet long and the width of the park is 450 feet, what is the length, in feet, of the park?
A. 675 ft.
B. 550 ft.
C. 600 ft.
D. 650 ft.
Answer:
600 feet
Step-by-step explanation:
I am assuming that the park is rectangular, and the together, the length, with and diagonal form a right triangle.
In this case, we are given
Diagonal = 750 ft = hypotenuse
Width = 450 feet
Find length L
Using the Pythagorean theorem,
L² + 450² = 750²
L² = 750² - 450² = 360,000
L= √360,000 = 600 feet
Answer:
C, 600 ft.
Step-by-step explanation:
a^2+b^2=c^2
C is always the hypotenuse/diagonal. Let A represent length and B represent width.
A^2+450^2=750^2
A^2+202500=562500
562500-202500=360000=A^2
take the square root of both sides to solve for A and the value of A is 600.
Tori examined the pattern of exponents in the table.
Based on the pattern, which statements are true? Check all that apply.
Answer:
Option B and C are correct.
Step-by-step explanation:
We need to find the pattern of the values in the table and find the values of a and b.
6³ = 216
216/6 = 36
6² = 36
36/6 = 6
6¹ = 6
6/6 = 1
6⁰ = 1
1/6 = 1/6
6⁻¹ = 1/6
1/6*1/6 = 1/36
6⁻² = 1/36
So, value of a = 1/6
and value of b = 1/36
And we have seen as the exponent is decreasing, each previous value is divided by 6.
So, Option B and C are correct.
Answer: The correct options are
(B) the value of b is [tex]\dfrac{1}{36}.[/tex]
(C) As the value of the exponent decreases, each previous value is divided by 6.
Step-by-step explanation: We are given that Tori examined the pattern of exponents in the following table :
[tex]\textup{power of 6}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\textup{value}\\\\6^3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~216\\\\6^2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~36\\\\6^1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~6\\\\6^0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~1\\\\6^{-1}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a\\\\6^{-2}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~b[/tex]
We are to select the true statements based on the above pattern.
We will be using the following property of exponents :
[tex]x^{-y}=\dfrac{1}{x^y}.[/tex]
Therefore, we get
[tex]a=6^{-1}=\dfrac{1}{6^1}=\dfrac{1}{6}.[/tex]
and
[tex]b=6^{-2}=\dfrac{1}{6^2}=\dfrac{1}{36}.[/tex]
Also, the value of the exponent is decreasing and we see that
[tex]\dfrac{216}{36}=\dfrac{36}{6}=\dfrac{6}{1}=\dfrac{1}{\frac{1}{6}}=\dfrac{\frac{1}{6}}{\frac{1}{36}}=6.[/tex]
So, each previous value is divided by 6.
Thus, the correct options are
(B) the value of b is [tex]\dfrac{1}{36}.[/tex]
(C) As the value of the exponent decreases, each previous value is divided by 6.
Write [tex]\frac{4}{50}[/tex] as a percentage
Answer:
8%
Step-by-step explanation:
[tex]4 \div 50 \times 100 \: = \: 8[/tex]
Hello There!
[tex]\frac{4}{50}[/tex] as a percentage is 8%
You can first reduce this fraction by dividing both the numerator and denominator by the Greatest Common Factor of 4 and 50 using 2.
4 ÷ 2 ≈ 2
50 ÷ 2 ≈ 25
We now have a fraction [tex]\frac{2}{25}[/tex]
We now divide 2 by 25 and we get a quotient of 0.08
Finally we multiply 0.08 by 100 and we get 8 so 4/50 as a percentage is 8%
Find the length of arc ED
Answer:
ED = 5π/6
Step-by-step explanation:
First convert angles into radians by using formula 1° = π/180 rad
So, 50° becomes 5π/18.
Now using formula,
angle = length of arc / radius of circle
we get,
5π/18 = length of arc / 3
Hence , length of arc = 5π/6
Answer:
ED ≈ 2.62 in
Step-by-step explanation:
The length of the arc ED is calculated as
ED = circumference × fraction of circle
= 2πr × [tex]\frac{50}{360}[/tex]
= 2π × 3 × [tex]\frac{5}{36}[/tex]
= 6π × [tex]\frac{5}{36}[/tex]
= [tex]\frac{5\pi }{6}[/tex] ≈ 2.62 in ( to 2 dec. places )
Which best describes the graph of the function f(x) = 4(1.5)"?
The graph passes through the point (0,4), and for each increase of 1 in the x-values, the y-values increase by 1.5.
The graph passes through the point (0,4), and for each increase of 1 in the x-values, the y-values increase by a factor of
1.5.
The graph passes through the point (0, 1.5), and for each increase of 1 in the x-values, the y-values increase by 4.
The graph passes through the point (0, 1.5), and for each increase of 1 in the x-values, the y-values increase by a factor of
Answer:
2nd one
Step-by-step explanation:
I think I'm understanding your function to be f(x)=4(1.5)^x.
It goes through (0,4) becuase when x=0, you have y=4(1.5)^0=4(1)=4.
It also increases by a factor of 1.5 each time x goes up by 1.
Example: When x=1, you have 4(1.5)^1=4(1.5)
Another example: When x=2, you have 4(1.5)^2=4(1.5)(1.5).
Those are called factors because the operation is multiplication.
Answer:
b
Step-by-step explanation:
3.
Clara goes miniature golfing. She pays $7.50
for an admission ticket and $6.25 for each
round she golfs. The total amount Clara pays
for admission and the number of rounds she
golfs is $26.25. Which equation can be used to
determine the number of rounds, x, that Clara
golfs?
A 6.25 x + 7.50 = 26.25
B 6.25x - 7.50 = 26.25
C 7.50x + 6.25 = 26.25
D 7.50x - 6.25 = 26.25
Answer:
[tex]6.25x+7.50=26.25[/tex]
Clara played 3 rounds of golf.
Step-by-step explanation:
The admission fee is = $7.50
Let the number of rounds be = x
Each round costs = $6.25
Total money Clara paid = $26.25
We can denote this in equation form as:
[tex]6.25x+7.50=26.25[/tex]
Now we will solve for x
[tex]6.25x=26.25-7.50[/tex]
=> [tex]6.25x=18.75[/tex]
=> x = 3
Hence, Clara played 3 rounds of golf.
The equation used to determine the number of rounds, x, that Clara golfs is 6.25x + 7.50 = 26.25
Equation
An equation is an expression that is used to show the relationship between two or more variables and numbers.
Let x represent the number of rounds that Clara golfs.
The total amount Clara pays for admission and the number of rounds she golfs is $26.25, hence this is given by:
6.25x + 7.50 = 26.25The equation used to determine the number of rounds, x, that Clara golfs is 6.25x + 7.50 = 26.25
Find out more on equation at: https://brainly.com/question/13763238
functions need help fast
Konichiwa~! My name is Zalgo and I am here to help you out on this beautiful day. The answer is -7x-1. When you input it into the equation, you should get f (-7x-1) = -8.
Samantha swam upstream for some distance in one hour. She then swam downstream the same river for the same distance in only 12 minutes. If the river flows at 4 mph, how fast can Samantha swim in still water?
recall your d = rt, distance = rate * time.
s = Samantha's speed rate
one thing to bear in mind is that, when Samantha is going upstream, she's not really going "s" mph fast, because she's going against the current, and the current's rate is 4 mph and subtracting speed from her, then she's really going "s - 4" fast.
Likewise, when she's going downstream because she's going with the current, the current is adding speed to her, so she's going "s + 4" fast.
Now, let's say the distance she covered both ways was the same "d" miles.
Let's recall that since there are 60 minutes in 1 hour, 12 minutes is 12/60 = 1/5 of an hour.
[tex]\bf \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ Upstream&d&s-4&1\\ Downstream&d&s+4&\frac{1}{5} \end{array}\qquad \implies \begin{cases} d=(s-4)(1)\\ d=(s+4)\left( \frac{1}{5} \right) \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \stackrel{\textit{from 1st equation}}{\boxed{d}=s-4}\qquad \qquad \stackrel{\textit{substituting on the 2nd equation}~\hfill }{\boxed{s-4}=\cfrac{s+4}{5}\implies 5s-20=s+4} \\\\\\ 4s-20=4\implies 4s=24\implies s=\cfrac{24}{4}\implies s=6[/tex]
Answer:
6 mph
Step-by-step explanation:
Let the the total distance is D and the speed of Samantha's speed in still water is x ( in mph ),
Here, speed of stream = 4 mph,
Thus, the speed in upstream = (x - 4) mph,
Speed in downstream = (x + 4) mph,
We know that,
[tex]Speed =\frac{Distance}{Time}\implies Time =\frac{Distance}{Speed}[/tex]
∴ Time taken in upstream = [tex]\frac{D}{x-4}[/tex]
And, time taken in downstream = [tex]\frac{D}{x+4}[/tex]
According to the question,
[tex]\frac{D}{x-4}=1\implies D = x-4-----(1)[/tex]
[tex]\frac{D}{x+4}=\frac{12}{60}\implies \frac{D}{x+4}=\frac{1}{5}\implies 5D=x+4----(2)[/tex]
Equation (1) - 5 equation (2),
0 = x + 4 - 5x + 20
0 = -4x + 24
4x = 24
⇒ x = 6 mph.
Hence, Samantha swims with the speed 6 mph.
A high school is having a pancake breakfast fundraiser. They have 4 packages of pancake mix that each feed 120 people. The function
N(p) = 120p represents the number of people, N(p), that p packages of pancake mix feed.
Write the domain and range as compound inequalities.
Final answer:
The domain of the pancake mix function N(p) is 0 <= p <= 4 and the range is 0 <= N(p) <= 480, assuming the school has 4 packages and each package feeds 120 people.
Explanation:
The high school pancake breakfast fundraiser question deals with writing the domain and range for a given function. Our function is N(p) = 120p, where N(p) represents the number of people fed by p packages of pancake mix, and each package feeds 120 people. Since the school has 4 packages of pancake mix, the domain, which is the set of all possible values of p (packages), would be 0 <= p <= 4, as they cannot use negative packages and have only 4 packages available. The corresponding range would be the number of people that can be fed, which is from 0 to 4 times 120, so 0 <= N(p) <= 480.
If 2x+b = y + 2b what is b^2 in terms of x and y
Answer:
b² = 2bx - 2by
Step-by-step explanation:
2x + b = y + 2b
b = 2x - y
b² = (2x - y)²
b² = (2x - y)(2x - y)
b² = 4x² - 2xy - 2xy + y²
b² = 4x² - 4xy + y²
NEED HELP 50 POINTS!! WILL MARK BRAINLIEST ANSWER. Find the lengths of all the sides and the measures of the angles.
Answer:
Part 1) ∠ABD=23.9°
Part 2) ∠ADB=119.1°
Part 3) AB=506.7 ft
Part 4) ∠BDE=60.9°
Part 5) ∠BED=77.1°
Part 6) DE=239.6 ft
Part 7) BE=312.8 ft
Part 8) ∠BEC=102.9°
Part 9) ∠EBC=36.1°
Step-by-step explanation:
Let
A-----> Zebra house
B ----> Entrance
C ----> Tiger house
D ---> Giraffe house
E ----> Hippo house
see the attached figure with letters to better understand the problem
step 1
In the triangle ABD
Find the measure of angle ABD
Applying the law of sines
sin(37°)/349=sin(ABD)/235
sin(ABD)=235*sin(37°)/349
sin(ABD)=0.4052
∠ABD=arcsin(0.4052)=23.9°
step 2
In the triangle ABD
Find the measure of angle ADB
Remember that the sum of the internal angles of a triangle must be equal to 180 degrees
so
∠ADB+23.9°+37°=180°
∠ADB+23.9°+37°=180°-60.9°
∠ADB=119.1°
step 3
In the triangle ABD
Find the measure of side AB
Applying the law of sines
sin(37°)/349=sin(119.1°)/AB
AB=349*sin(119.1°)/sin(37°)
AB=506.7 ft
step 4
In the triangle BDE
Find the measure of angle BDE
we have
∠BDE+∠ADB=180° ----> by supplementary angles
∠ADB=119.1°
substitute
∠BDE+119.1°=180°
∠BDE=180°-119.1°
∠BDE=60.9°
step 5
In the triangle BDE
Find the measure of angle BED
Remember that the sum of the internal angles of a triangle must be equal to 180 degrees
so
∠BED+60.9°+42°=180°
∠BED=180°-102.9°
∠BED=77.1°
step 6
In the triangle BDE
Find the measure of side DE
Applying the law of sines
sin(77.1°)/349=sin(42°)/DE
DE=349*sin(42°)/sin(77.1°)
DE=239.6 ft
step 7
In the triangle BDE
Find the measure of side BE
Applying the law of sines
sin(77.1°)/349=sin(60.9°)/DE
BE=349*sin(60.9°)/sin(77.1°)
BE=312.8 ft
step 8
In the triangle BEC
Find the measure of angle BEC
we have
∠BEC+∠BED=180° ----> by supplementary angles
∠BED=77.1°
substitute
∠BEC+77.1°=180°
∠BEC=180°-77.1°
∠BEC=102.9°
step 9
In the triangle BEC
Find the measure of angle EBC
Remember that the sum of the internal angles of a triangle must be equal to 180 degrees
so
∠EBC+102.9°+41°=180°
∠EBC=180°-143.9°
∠EBC=36.1°
what substitution should be used to rewrite 6(x+5)^2+5(x+5)-4=0 as a quadratic equation
Step-by-step explanation:
6 (x+5 )^2 +5(x+5)-4=0
let x+5= y
6y^2 + 5y - 4=0
6y^2 + 8y - 3y-4 =0
2y (3y+4) - 1 (3y+4)=0
(2y-1)(3y+4)=0
2y-1=0 or 3y+4=0
y=1/3 or -4/3
Recall that x+5=y
When y=1/3
x+5=1/3
x= -14/3
when y= -4/3
x+5=-4/3
x = -11/3
Answer:
u=(x+5)
Step-by-step explanation:
The means and mean absolute deviations of the individual times of members on two 4x400-meter relay track teams are
shown in the table below.
Means and Mean Absolute Deviations of
Individual Times of Members of 4x400-meter Relay Track Teams
Team A
Team B
Mean
59.32 s
59.1 s
Mean Absolute Deviation
1.5 s
245
What percent of Team B's mean absolute deviation is the difference in the means?
9%
15%
25%
65%
Answer:
9%
Step-by-step explanation:
To find the percentage of Team B's mean absolute deviation difference in the means, you have to subtract the two means, 59.32-59.1.
After this, divide your answer the the mean absolute deviation of Team B, or you could put it all in the calculator or paper like this:
[tex]\frac{59.32-59.1}{2.4}[/tex]
You'd then end with the decimal: .0916, which you would multiply by 100 to get about 9%
Answer:
A
Step-by-step explanation:
What would y=
4.6
13.9
21.6
Answer:
13.9 is the right answer :)
Step-by-step explanation:
For this case we have to define trigonometric relations of rectangular triangles, that the tangent of an angle is given by the leg opposite the angle on the leg adjacent to the angle.
Then, according to the figure we have:
[tex]tg (60) = \frac {y} {8}\\y = 8 * tg (60)\\y = 8 * 1.73205081\\y = 13,85640648[/tex]
Rounding the value we have that [tex]y = 13.9[/tex]
ANswer:
Option B
How many total roots are must there be in this function explain how you know
H(x)=x3-7x2-x+7
Final answer:
The total number of roots in the function H(x) = x³ - 7x² - x + 7 is 3, with 2 real roots and 1 complex root.
Explanation:
The function H(x) = x³ - 7x² - x + 7 is a cubic function, meaning it is a polynomial of degree 3. The total number of roots for a cubic function is always 3. This is because the highest power of x in the function is 3.
To determine the number of real roots, we can use the rule of signs. We count the number of sign changes in the coefficients of the function. In this case, we have two sign changes from positive to negative. Therefore, there are either 2 or 0 real roots.
To find the number of complex roots, we subtract the number of real roots from the total number of roots. So, in this case, there must be 3 - 2 = 1 complex root.
The number of roots that the function H(x) has is: a total of 3 roots
What is the number of roots of the Polynomial?
The function H(x) = x³ - 7x² - x + 7 is a polynomial of degree 3.
According to the fundamental theorem of algebra, a polynomial of degree n has exactly n roots, counting multiplicities.
In this case, the function has 3 roots, which may be real or complex, taking into account their multiplicities. The number of roots is determined by the degree of the polynomial, and the roots are the values of x for which the polynomial is equal to zero. Therefore, the function H(x) has a total of 3 roots
simplify(x^5/8)^2/3
Answer:
[tex]x^{5/12}[/tex]
Step-by-step explanation:
Having a power to a power means that you multiply them:
[tex]x^{5/8 * 2/3} = x^{(5 * 2)/ (8 * 3)} = x^{10/24} = x^{5/12}[/tex]
The simplified expression is [tex]x^{(\frac{5}{12} )[/tex].
Given that an expression [tex](x^{\frac{5}{8}} )^\frac{2}{3}[/tex], we need to simply it.
To simplify the expression, first, we raise the fraction to the power of 2/3:
Step 1: [tex](x^{\frac{5}{8}} )^\frac{2}{3}[/tex]
Now, when raising a power to another power, we multiply the exponents:
Step 2: [tex]x^{\frac{5}{8} \times \frac{2}{3}[/tex]
To simplify further, we multiply the fractions:
Step 3: [tex]x^{\frac{10}{24}[/tex]
Now, we can simplify the exponent by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 2 in this case:
Step 4: [tex]x^{(\frac{5}{12} )[/tex]
So, the simplified expression is [tex]x^{(\frac{5}{12} )[/tex].
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Given that y varies directly to the square root of (x + 1), and that y = 1 when x = 8,
(a)
express y in terms of .x,
(b)
find the value of y when x = 3,
(c)
find the value of x when y = 5.
Answer:
a) y=1/3 sqrt(x+1)
b) 2/3
c) 224
Step-by-step explanation:
a) y varies directly to sqrt(x+1)
means there is some constant k such that y=ksqrt(x+1)
y=1 when x=8 (plug this in and find k) 1=ksqrt(8+1)
1=ksqrt(9)
1=k(3)
1/3=k
So the equation is y=1/3 * sqrt(x+1)
a) y=1/3 *sqrt(x+1)
b) what is y when x=3 if you have y=1/3 * sqrt(x+1)
Plug in 3 for x
y=1/3 *sqrt(3+1)
y=1/3 *sqrt(4)
y=1/3 *2
y=2/3
b) 2/3
c) what is x when y=5
Plug in 5 for y
5=1/3 *sqrt(x+1)
multiply both sides by 3
15=sqrt(x+1)
square both sides
225=x+1
subtract 1 on both sides
224=x
c) 224
what is the sum ? 2x
Answer: Third option.
Step-by-step explanation:
Given the expression [tex]\frac{2x+4}{x+1}+\frac{-x+5}{x+1}[/tex] you need to make the addition indicated.
First, it is important to remember the multiplication of signs:
[tex](+)(+)=+\\(-)(-)=+\\(-)(+)=-[/tex]
Therefore, since both fractions have equal denominator, you can rewrite the same denominator and add the numerators. Then you get that the sum is:
[tex]\frac{2x+4}{x+1}+\frac{-x+5}{x+1}=[/tex][tex]\frac{(2x+4)+(-x+5)}{x+1}=\frac{2x+4-x+5}{x+1}=\frac{x+9}{x+1}[/tex]
Answer:
The correct answer is third option
(x + 9)/(x + 1)
Step-by-step explanation:
It is given an expression,
(2x + 4)/(x + 1) + (-x + 5)/(x + 1)
To find the sum
The given expression shows the sum of two fractions,
The denominators are same
(2x + 4)/(x + 1) + (-x + 5)/(x + 1)
= [2x + 4 + -x + 5]/(x + 1)
= (x + 9)/(x + 1)
Therefore the correct answer is third option
(x + 9)/(x + 1)
-11 - (-5)
————
2 x 3
Is an example of
A.) an algebraic expression
B.) A numerical equation
C) A numerical equation
D.) An algebraic equation
Answer:
A.) an algebraic expression
Step-by-step explanation:
Note that there are only integers (whole numbers) and the usage of algebraic operations. Also note that there is no "equal" sign (which would make it an equation), making the problem a expression.
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* PLZ ANSWER QUICK* The correlation coefficient between two quantitative variables is approximately 0.6. What does the value of this correlation coefficient indicate about how well the model fits the data? ANSWER CHOICE'S
A.
The model is not a good fit.
B.
The model is a good fit.
C.
The correlation coefficient is not within the correct range.
D.
No conclusion can be drawn regarding how well the model fits the data.
Answer:
A.
The model is not a good fit.
Step-by-step explanation:
The correlation coefficient is a measure of the degree of association between two quantitative variables , such as weight and height.
On the other hand, the quantity R-squared is an indicator of the predictive power of a model. It is an indicator of how well the model fits the data. R-squared is the coefficient of determination.
R-squared = the square of the correlation coefficient
= 0.6 * 0.6
= 0.36
Therefore, only 36% of the variations in the dependent variable can be explained by the model. More than 50% can thus not be explained by the model. The model is thus not a good fit.
Answer:
A the model is not good
Step-by-step explanation: