The slope of the line which is perpendicular to the given line 3x+18y=108 is (6).
What is the slope?The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.
We already know the equation of a line in slope intercept form y = mx + b and we also know that perpendicular lines that have slopes which are negative reciprocals of each other.
Given a line 13x + 18y=108, this slope intercept form can be written as,
3x + 18y = 108
18y = 108 - 3x
y = (108 /18) - (3/18)x.
y = (6) - 1x/6.
y = -(1/6)x + 6.
∴ The slope of the given line is (-1/6), thus the slope of the line which is perpendicular is (6).
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help me please
help me :>
Based on the graphs and equations given, the simultaneous equations can be solved to give x = 1.5 and y = 5.5.
How to solve the simultaneous equation?To solve the simultaneous equation, come up with the values of y using values of x in the given formulas:
For y = 3x + 1: the values of y will be:
When x = 1, then y will be:
= 3(1) + 1
= 4
When x = 2, then y will be:
= 3(2) + 1
= 7
When x = 3, then y will be:
= 3(3) + 1
= 9
For the equation, x + y = 7:
When x = 1, then y will be:
y = 7 - 1
= 6
When x = 2, then y will be:
= 7 - 2
= 5
When x = 3, then y will be:
= 7 - 3
= 4
When these are plotted on a graph, we find that the value of x is 1.5 and the value of y is 5.5. This is the point where the lines intersect.
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Which system of linear inequalities is represented by the graph? O y=x-2 and x-2y 4 O y=x + 2 and x + 2y = 4 O y=x-2 and x + 2y = 4 O y =x-2 and x + 2y =-4
The two inequalities are (option c) y > x - 2 and2y + x < 4
Given,
Let's start by locating the red-hued area.
If the shadow is visible to be over the line, then the situation will be as follows:
y > ax + b
Hence the equation for the line is ax + b.
The slope is a, and the y-intercept is b.
The line in the graph intersects the y-axis at y = -2, which results in:
b = -2
Two points on the line are required to determine the slope; these points are (0, -2), and (2, 0)
We are aware of the slope for a line passing through the points (x1, y1) and (x2, y2) as follows:
a = (y2 - y1)/(x2 - x1) (x2 - x1)
The slope for this line will then be:
a = (0 - (-2))/(2 - 0) = 2/2 = 1
Then this line's equation is:
1x - 2
And here's the inequality:
y > x - 2.
The shaded area of the blue one is below the line, thus we will have:
y < ax + b
The y-intercept in this situation is y = 2.
This line crosses through the points (0, 2) and, as can be seen (4, 0)
The slope is then:
a = (0 - 2)/(4 - 0) (4 - 0) = -2/4 = -1/2
This inequality is then:
y < (-1/2)x + 2
If we rewrite this using the choices, we get the following:
y < (-1/2)x + 2
2y < -x + 2 ×2
2y + x < 4
The two inequalities are (option c) y > x - 2 and2y + x < 4
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Answer: C
Step-by-step explanation:
Given: angle CDE congruent to angle CED,
Angle A = angle B
Prove: DE || AB
Please explain the statement and reasoning
Ex: AB is congruent (the sign) to DE. Given
Ill reward brainliest to the one who explains it best ty
1) [tex]\angle CDE \cong \angle CED, \angle A \cong \angle B[/tex] (given)
2) [tex]m\angle CDE=m\angle CED, m\angle A=m\angle B[/tex] (definition of congruent angles)
3) [tex]m\angle C+m\angle CDE+m\angle CED=180^{\circ}, m\angle C+m\angle A+m\angle B=180^{\circ}[/tex] (sum of angles in a triangle)
4) [tex]m\angle C+2m\angle CDE=180^{\circ}, m\angle C+2m\angle A=180^{\circ}[/tex] (substitution)
5) [tex]m\angle C=180^{\circ}-2m \angle CDE, m\angle C=180^{\circ}-2m\angle A[/tex] (subtraction)
6) [tex]180^{\circ}-2m \angle CDE=180^{\circ}-2m \angle A[/tex] (transitive)
7) [tex]-2m\angle CDE=-2m\angle A[/tex] (subtraction)
8) [tex]m\angle CDE=m\angle A[/tex] (division)
9) [tex]\angle CDE \cong \angle A[/tex] (definition of congruent angles)
10) [tex]\overline{DE} \parallel \overline{AB}[/tex] (converse of corresponding angles theorem)
find the derivative:f(x)= -3/ x^4
Given the function f(x), we can write it like this:
[tex]\begin{gathered} f(x)=-\frac{3}{x^4} \\ \Rightarrow f(x)=-3x^{-4} \end{gathered}[/tex]Using the formula for polynomial derivatives, we get:
[tex]\begin{gathered} f(x)=-3x^{-4} \\ \Rightarrow f^{\prime}(x)=-3\cdot(-4)x^{-4-1}=12x^{-5} \\ f(x)=\frac{12}{x^5} \end{gathered}[/tex]Therefore, the derivative f'(x) is 12/x^5
Find the mean and population standar deviation for each data set.
Hours slept
Mean of given set is 7.8
Define mean.The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency. The most typical or average value among a group of numbers is called the mean. It is a statistical measure of a probability distribution's central tendency along the median and mode. It also goes by the name "anticipated value." It is a statistical idea with significant financial implications.
Given,
Mean:
Formula:
Sum = 118.25
Total = 15
[tex]\frac{sum}{total}[/tex]
[tex]\frac{6.75 + 6.5 + 7 +8 +7+8.75+7.25+5.75+9.25+7.75+7+7.5+8+7.5+8+6.25}{15}[/tex]
= [tex]\frac{118.25}{15}[/tex]
= 7.8
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The standard height from the floor to the bull's-eye at which a standard dartboard is hung is 5 feet 8 inches. A standard dartboard is 18 inches in diameter.
Suppose a standard dartboard is hung at standard height so that the bull's-eye is 12 feet from a wall to its left.
Brian throws a dart at the dartboard that lands at a point 11.5 feet from the left wall and 5 feet above the floor.
Does Brian's dart land on the dartboard?
Drag the choices into the boxes to correctly complete the statements.
Considering the equation of a circle, it is found that:
The equation of the circle that represents the dartboard is [tex](x - 12)^2 + \left(y - \frac{17}{3}\right)^2 = 81[/tex], where the origin is the lower left corner of the room and the unit of the radius is in inches;The position of Brian's dart is represented by the coordinates (11.5, 5). Brian's dart does land on the dartboard.What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given as follows:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
In the context of this problem, we have that:
The radius of the circle is of 9 inches, as the diameter is of 18 inches and the radius is half the diameter.The height is of 5 feet 8 inches = 5 feet and 2/3 feet = 17/3 feet, which is the y-coordinate of the center.The bull's-eye is 12 feet from a wall to its left, hence the x-coordinate of the center is of 12.Hence the equation of the circle is given by:
[tex](x - 12)^2 + \left(y - \frac{17}{3}\right)^2 = 81[/tex]
Brian's dart lands at the following position:
(11.5, 5)
All the points that land on the dartboard respect the following equation:
[tex](x - 12)^2 + \left(y - \frac{17}{3}\right)^2 \leq 81[/tex]
For the coordinate where the dart landed, we have that:
(11.5 - 12)² + (5 - 17/3)² = 0.7 < 81, meaning that Brian's dart lands on the dartboard.
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7/5 convert improper fractions
Answer:
1 2/5
Step-by-step explanation:
Improper Fraction - A fraction that has a numerator that is larger than the denominator
Mixed Fraction - A fraction with a whole number, or a quotient with its remainder
In order to convert improper fractions to mixed fractions, you must divide the numerator by the denominator.
So, 7/5 = 7 ÷ 5 = 1 2/5
The quotient being 1, and the remainder being 2/5 because there is 2 left out of the 5.
Solve the trig equation on the interval [tex]0 \leqslant theta \: \ \textless \ 2\pi[/tex][tex]3 sec \: \: theta \: - 2 \sqrt{3 } = 0[/tex]
Answer:
pi/6 and 11pi/6
Explanation
Given the trigonometry equation:
[tex]\begin{gathered} 3\text{sec}\theta\text{ - 2}\sqrt[]{3}=0 \\ \end{gathered}[/tex]Add 2\sqrt[3] to both sides as shown;
[tex]\begin{gathered} 3\sec \theta-2\sqrt[]{3}=0+2\sqrt[]{3} \\ 3\sec \theta\text{ = 2}\sqrt[]{3} \\ \sec \text{ }\theta\text{ = }\frac{2\sqrt[]{3}}{3} \\ \frac{1}{\cos \theta}=\frac{2\sqrt[]{3}}{3} \\ \cos \theta\text{ =}\frac{3}{2\sqrt[]{3}} \\ \cos \text{ }\theta\text{ = }\frac{3\sqrt[]{3}}{2\cdot3} \\ \cos \text{ }\theta\text{ = }\frac{\sqrt[]{3}}{2} \\ \end{gathered}[/tex]Take the cos inverse of both sides
[tex]\begin{gathered} \cos ^{-1}(\cos \theta)=cos^{-1}\frac{\sqrt[]{3}}{2} \\ \theta=cos^{-1}\frac{\sqrt[]{3}}{2} \\ \theta=30^0 \end{gathered}[/tex]Since theta is between 0 and 2pi
theta = 360 - 30
theta = 330^0
Convert to radians
180^0 = pi rad
30^0 = x
180x = 30pi
x = 30pi/180
x = pi/6
Similarly;
180^0 = pi rad
330^0 = x
180x = 330pi
x = 330pi/180
x = 11pi/6
Hence the value of thets between 0 and 2pi are pi/6 and 11pi/6
complete the two-column proof.
pleasee
∠2 ≅ ∠4 and m∠2 = 110°, and proved m<3 = 70⁰.
The answers of the blank lines are:
A . Vertically opposite angle.
B . Linear angle .
C . Hence proved .
Solution:Given ,
∠2 ≅ ∠4 and m∠2 = 110°.
We have to prove
m<3 = 70⁰
Here ,
m<2 = m<4 => They are vertically opposite angles.
And here ,
m<3 and m<4 are supplementary angles.
m∠3 + m∠4 = 180° => linear angle .
m<4 = 110⁰ => since m<2 = m<4
By substituting m∠4 we get,
m∠3 + m∠4 = 180°
= m∠3 + 110 = 180
= 180 - 110
m∠3 = 70°
Hence proved.
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A farm is being divided so that each section of land has equal access
to the canal running through the property for watering crops. If the road on the
opposite side of the property runs parallel to the canal, explain how this can be
done.
The best way to divide the land having canal and road parallel, is divide land with the line perpendicular to the road and canal.
What is parallel and perpendicular?
In simple geometry, two geometric objects cross at a right angle (90 degrees or /2 radians) if they are perpendicular to one another. The perpendicular symbol,⟂, can be used to graphically depict the condition of perpendicularity. It can be defined between two planes, between two lines (or line segments), and between two lines.
In geometry, parallel lines are coplanar, straight lines that never intersect. Any parallel planes in the same three-dimensional space are those that never intersect. Parallel curves are those that have a predetermined minimum separation between them and do not touch or intersect.
We need to give equal access of canal to each section of land so, the best way to divide land is divide land perpendicularly to canal and the road.
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Past due I don't really understand, what's the answer??
Answer:
$50.16
Step-by-step explanation:
id.k if it's actually right but i believe the tip would be $8.36 if it's 20% so adding it together is $50.16
Please help asap
this is an assignment due today please help real quick
no fake answers
Answer:
where???????????????
a department store chain is expanding into a new market, and is considering 16 different sites on which to locate 7 stores. assuming that each site is equally likely to be chosen, in how many ways can the sites for the new stores be selected?
A department store chain that is entering a new area is looking at 16 possible locations for the placement of its 7 outlets. There are 57657600 many possible ways to the sites for the new stores.
Given that,
A department store chain that is entering a new area is looking at 16 possibility locations for the placement of its 7 outlets.
We have to find how many different possibility are there to choose the locations for the new businesses, provided that each site has an equal chance of being chosen.
By multiplying the number of possibilities each store has, we may determine the total number of ways.
It can be put on 16 sites for store 1. 15 locations can accommodate Store 2 (since store 1 is already on site 1). Up until shop 7, which has 10 sites, store 3 can be situated on 14 sites.
The quantity of ways is thus:
= 16 × 15 × 14 × 13 × 12 × 11 × 10
= 57657600
Therefore, there are 57657600 many possible ways to the sites for the new stores.
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Solve 4(3m + 1) − 2m = −16. m = −0.83 m equals negative 20 over 12 m equals negative 17 over 10 m = −2.
The solution to the equation given as 4(3m + 1) − 2m = −16 is m = -2
How to determine the solution to the equation?The equation is given as
4(3m + 1) − 2m = −16
Open the brackets in the above equation
So, we have
12m + 4 − 2m = −16
Collect the like terms in the above equation
So, we have the following equation
12m − 2m = −16 -4
Evaluate the like terms in the above equation
So, we have the following equation
10m = −20
Divide both sides by 10
m = -2
Hence, the soluton is m = -2
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A circle passes through (-2, 6) , (2, 8) , and (5, -1) Using the general form of a circle and the points above, fill in missing numbers to create the system of equations. (-2, 6) creates D + E + 1F = (2, 8) creates D + E + 1F = (5, -1) creates D + E + 1F = Solve the system of equations that you created, and write the equation for the circle by filling in the values for D, E, and F.
The equation of the circle passing through points (-2, 6) , (2, 8) , and (5, -1) is given as follows:
(x - 2)² + (y - 3)² = 25.
Equation of a circleThe equation of a circle with center (x*, y*) and radius r is given according to the following rule:
(x - x*)² + (y - y*)² = r².
The circle passes through point (-2,6), hence the first equation of the system is given as follows:
(-2 - x*) + (6 - y*)² = r².
r² = x*² + 4x* + 4 + y*² - 12y* + 36.
The circle also passes through point (2,8), hence the second equation of the system is given as follows:
(2 - x*) + (8 - y*)² = r².
r² = x*² - 4x* + 4 + y*² - 16y* + 64.
The final point is point (5,-1), meaning that the third equation is:
(5 - x*) + (-1 - y*)² = r².
r² = x*² - 10x* + 25 + y*² + 2y* + 1.
The system of equations to find the coordinates of the center and the radius is given as follows:
x*² + y*² + 4x* - 12y* + 40 - r² = 0.x*² + y*² - 4x* - 16y* + 68 - r² = 0.x*² + y*² - 10x* + 2y* + 26 - r² = 0.The solution to the system is given as follows:
x* = 2, y* = 3, r² = 25.
Hence the equation of the circle is:
(x - 2)² + (y - 3)² = 25.
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Find the range, the standard deviation, and the variance for the given samples. Round non-integer results to the nearest tenth.−10, −16, −21, −24, −4, −30, −32 range ________standard deviation __________variance __________
From the given values, we can see that the lowest values is -32 and the highest value ie -4. Since the range is the difference betwwwn the highest and the lowest value, the range is
[tex]\begin{gathered} \text{Range}=-4-(-32) \\ \text{Range}=28 \end{gathered}[/tex]On the other hand, the sample variance formula is
[tex]S^2=\sqrt[]{\frac{\sum ^7_{n\mathop=1}(x-\bar{x})^2}{n-1}}[/tex]where x^bar is the mean and n is the total number of sample elements. In our case, n=7 and the mean is
[tex]\begin{gathered} \bar{x}=\frac{-10-16-21-24-4-30-32}{7} \\ \bar{x}=-\frac{137}{7} \\ \bar{x}=-19.5714 \end{gathered}[/tex]Then, the sample variance is given by
[tex]\begin{gathered} S^2=\frac{(-10-19.57)^2+(-16-19.57)^2+(-21-19.57)^2+\cdot\cdot\cdot+(-32-19.57)^2}{6} \\ S^2=105.2857 \end{gathered}[/tex]Since the standard deviation is the square root of the sample variance, we have
[tex]\begin{gathered} S=\sqrt[]{105.2857} \\ S=10.26088 \end{gathered}[/tex]By rounding the solutions to the nearest tenth, the answers are:
[tex]\begin{gathered} \text{Range}=28 \\ \text{Variance}=105.3 \\ \text{ Standard deviation = 10.3} \end{gathered}[/tex]PLEASE HELP! this is probably easy, THANK YOU!
Answer:
The percent change in attendance from the 2014 to 2015 school year is a 11.5385% decrease, or 12% when rounded.
Make sure to mark as Brainliest if this is correct so others know that this is the correct answer.
Answer:
r u cheating or just need "HELP"
Step-by-step explanation:
Determine the number of terms in the arithmetic sequence below:-70, -69, -68, ..., 37, 38, 39, 40
Number of terms of sequence N
Difference D = -1
Then there are here
In negative part, 70 numbers
In positive x line, 40 numbers
And add also zero
Then, ANSWER IS
N= 70 + 40 + 1
. = 111
There are 111 numbers
The table below shows the average annual cost of health insurance for a single individual, from 1999 to 2019, according to the Kaiser Family Foundation.YearCost1999$2,1962000$2,4712001$2,6892002$3,0832003$3,3832004$3,6952005$4,0242006$4,2422007$4,4792008$4,7042009$4,8242010$5,0492011$5,4292012$5,6152013$5,8842014$6,0252015$6,2512016$6,1962017$6,4352017$6,8962019$7,186(a) Using only the data from the first and last years, build a linear model to describe the cost of individual health insurance from 1999 onward. Use t to represent years after 1999 (treating 1999 as year 0).Pt = (b) Using this linear model, predict the cost of insurance in 2030.$ (c) = According to this model, when do you expect the cost of individual insurance to reach $12,000? Give your answer as a calendar year (ex: 2020).During the year (d) Using a calculator or spreadsheet program, build a linear regression model to describe the cost of individual insurance from 1999 onward. Use t to represent years after 1999 (treating 1999 as year 0), and round the values of P0 and d to the nearest dollar.Pt= (e) Using the regression model, predict the cost of insurance in 2030.$ (f) According to the regression model, when do you expect the cost of individual insurance to reach $12,000? Give your answer as a calendar year (ex: 2020).During the year
Part (a) Using only the data from the first and last years, build a linear model to describe the cost of individual health insurance from 1999 onward. Use t to represent years after 1999 (treating 1999 as year 0).
we have the ordered pairs
(1999, 2,196) -------> (0,2,196)
(2019,7,186) -------> (20,7,196)
Find out the slope
where
t -----> is the number of years since 1999
P ----> the cost
m=(7,196-2,196)/(20-0)
m=5,000/20
m=250
Find the equation of the linear model in slope-intercept form
P=mt+b
we have
m=250
point (0,2,196)
substitute and solve for b
2,196=250(0)+b
b=2,196
therefore
P=250t+2,196
Part b
Using this linear model, predict the cost of insurance in 2030
For t=2030=2030-1999=31 years
substitute
P=250(31)+2,196
P=$9,946
Part c
According to this model, when do you expect the cost of individual insurance to reach $12,000? Give your answer as a calendar year (ex: 2020).
For P=$12,000
substitute in the linear model
12,000=250t+2,196
250t=12,000-2,196
250t=9,804
t=39 years
therefore
1999+39=year 2038
Part d
Using a calculator or spreadsheet program, build a linear regression model to describe the cost of individual insurance from 1999 onward. Use t to represent years after 1999 (treating 1999 as year 0), and round the values of
P0 and d to the nearest dollar
using a regression calculator
the equation is
ŷ = 239.15065X + 2406.39827
y=239x+2,406
Part e
Using the regression model, predict the cost of insurance in 2030
For t=2030-1999=31 years
P=239(31)+2,406
P=$9,815
Part f
According to the regression model, when do you expect the cost of individual insurance to reach $12,000? Give your answer as a calendar year (ex: 2020).
For P=$12,000
substitute
12,000=239x+2,406
239x=12,000-2,406
239x=9,594
t=40 years
year=1999+40=2039
What is the slope of the line shown?
Answer:
-11/6
Step-by-step explanation:
you can use rise over run to find your answer
A ride sharing company offers two options: riding in small cars that can carry up to 3 passengers each, or riding in large vans that can carry up to 6 passengers each. A group of 27 people is going to use the ride sharing service to take a trip. The trip in a small car costs $10 and the trip in a large van costs $15. The group ends up spending $80 total.What do x and y represent?
Answer:
x = no of people in a small car
y = number of people in a van
Explanation:
The relevant information in the problem is that the total number of people is 27 and that the small car costs $10 and the large van $15.
If we call x the number of people in a small car, and y the number in the large van then the following equations can be obtained
[tex]\begin{gathered} x+y=27 \\ 10x+15y=80 \end{gathered}[/tex]The first equation simply says that the total number of people is 27 and the second equation says that the total cost of the trip is $80.
Hence,
x = no of people in a small car
y = number of people in a van
Evaluate log2 10 using the change of base formula. Round your answer to the nearest thousandth.
Take into account the following property:
[tex]\log _ab=\frac{\log b}{\log a}[/tex]Then, for the given expression you have:
[tex]\log _210=\frac{\log10}{\log2}=\frac{1}{\log }\approx3.322[/tex]Hence, the answer is approximately 3.322
3. Arrange the like terms in columns and add them. - a) 2x³ - 7x⁴ + 7x⁵ and 11x³ - 4x⁴ – x b) -2p - 3p² and 1 - 5p + 8p²
The required solution of the expressions is (a) 7x⁵ + 13³ - 11x⁴ - x, (b) 5p² - 7p + 1.
Given that,
To arrange the like terms in columns and add them. - a) 2x³ - 7x⁴ + 7x⁵ and 11x³ - 4x⁴ – x b) -2p - 3p² and 1 - 5p + 8p².
The algebraic expression consists of constant and variable. eg x, y, z, etc.
Here,
(a)
= 2x³ - 7x⁴ + 7x⁵ + 11x³ - 4x⁴ – x
= 7x⁵ - 7x⁴ - 4x⁴+ 2x³ + 11x³– x
= 7x⁵ + 13³ - 11x⁴ - x,
(b)
= -2p - 3p² + 1 - 5p + 8p²
= 1 -2p - 5p -3p² + 8p²
= 1 - 5p + 8p²
Thus, the required solution of the expressions is (a) 7x⁵ + 13³ - 11x⁴ - x, (b) 5p² - 7p + 1.
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The required solutions to the given polynomials are 13x³- 11x⁴+ 7x⁵ – x and - 7p + 5p²+ 1.
What is a polynomial?A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers.
The polynomials are given in the question :
2x³ - 7x⁴ + 7x⁵, and 11x³ - 4x⁴ – x
-2p - 3p² and,1 - 5p + 8p²
According to the question,
⇒ 2x³ - 7x⁴ + 7x⁵ + 11x³ - 4x⁴ – x
Rearrange the terms and apply the arithmetic operation,
⇒ 2x³ + 11x³- 7x⁴- 4x⁴ + 7x⁵ – x
⇒ 13x³- 11x⁴+ 7x⁵ – x
⇒ -2p - 3p² + 1 - 5p + 8p²
Rearrange the terms and apply the arithmetic operation,
⇒ -2p - 5p - 3p² + 8p²+ 1
⇒ - 7p + 5p²+ 1
Thus, the required solutions to the given polynomials are 13x³- 11x⁴+ 7x⁵ – x and - 7p + 5p²+ 1.
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How many students age 15 and above take a car to school? Show work
A. 18
B. 38
C. 87
im pretty sure its B or most likeley C
Please help!
2|x-1| >2
5
Answer: 6, -4
Step-by-step explanation:
[tex]\frac{2}{5}|x-1| \geq 2\\\\|x-1| \geq 5\\\\x-1 \leq -5, x-1 \geq 5\\\\x \leq -4, x \geq 6[/tex]
Select the correct answer.
Which of the following represents a function?
A. The first graph
B. The second graph
C. {(0,1), (3,2), (-8,3), (-7,2), (3,4)}
D.
x -5 -1 9 8 -1
y 1 7 23 17 1
Answer:
The answer is to the question A
Answer:
Its B 100%
i took the test and got it right
k bye :):):):):):):)
Step-by-step explanation:
12 is 150% of what number
To get 150% of a given number x, we multiply it by 1.5
This way, we'll have that:
[tex]1.5x=12[/tex]Solving for x,
[tex]1.5x=12\rightarrow x=\frac{12}{1.5}\rightarrow x=8[/tex]Therefore, we can conclude that 12 is 150% of 8
Apply the laws of exponents to evaluate the expression.
(0.5) (0.5) 4
(0.5)²
After evaluation using the exponential laws, the expression "(0.5)∧(0.5)∧4 + (0.5)²" is evaluated as 2(0.5)².
What are exponents?Exponentiation is a mathematical operation that involves the base b and the exponent or power n. It is written as bn and is pronounced as "b to the n." There are four different types of exponents: positive, negative, zero, and rational/fractional. By interpreting the exponent as the total number of times the base number must be multiplied by the same base, one can determine the value of the number. Exponents laws: Keep the base constant when multiplying like bases and add the exponents. Keep the base constant and multiply the exponents when raising a base with power to another power. When dividing with like bases, keep the base constant and deduct the exponents of the numerator and denominator.So, evaluate "(0.5)∧(0.5)∧4 + (0.5)²" using laws of exponents:
Then,
(0.5)∧(0.5)∧4 + (0.5)By law: Power of power rule
(0.5)∧(0.5)×4 + (0.5)(0.5)²+ (0.5)²2(0.5)²Therefore, after evaluation using the exponential laws, the expression "(0.5)∧(0.5)∧4 + (0.5)²" is evaluated as 2(0.5)².
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The correct question is given below:
Apply the laws of exponents to evaluate the expression.
(0.5)∧(0.5)∧4 + (0.5)²
Write a verbal sentence to represent each equation.
9.3n-3579
10. 2(n³ + 3n²) = 4n
11.
5n
n+3
-=n-8
The expression's variables can be represented by a different symbol than the conventional x and y.
A mathematical assertion represented in English is known as a verbal expression.What does an algebraic verbal model mean?Talking Model is a formula utilizing the terms found in the problem. Labels matching variables or numerical values to the linguistic model Equational Expression Modification of the Verbal Model by the substitution of mathematical values and variables.How to Convert Algebraic Expressions to Verbal Expressions.
Step 1: Recognize the algebraic operations—such as addition, subtraction, multiplication, and division—used in the expression.Step 2: Write a statement in which a vocabulary word is combined with the numbers to represent each of these processes.Therefore, the expression's variables can be represented by a different symbol than the conventional x and y.
A mathematical assertion represented in English is known as a verbal expression.To learn more about Verbal Expression refer to:
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What is the equation, in slope-intercept form, of the line that is perpendicular to the given line and passes through the point (2, −1)? y = Negative one-thirdx − One-third y = Negative one-thirdx − Five-thirds y = 3x − 3 y = 3x − 7
1st , 3rd & 5th choices
Step-by-step explanation:
perpendicular line would have a slope that is a
negative reciprocal
so if the slope is 3 then a perpendicular line would have a slope of -1/3
y - 1 = 1/3 (x + 2)
make the line look like y = mx + b
y = 1/3 (x + 2) + 1
y = 1/3 (x + 2) + 3/3
y = 1/3x + 2/3 + 3/3
y = 1/3x + 5/3
m = 1/3
perpendicular line has a slope of
m = -3