Answer:
4
Step-by-step explanation:
Given expression:
[tex](3^{8} \cdot 2^{-5} \cdot 9^{0})^{-2} \cdot \left(\dfrac{2^{-2}}{3^{3}}\right)^{4} \cdot 3^{28}[/tex]
Any number to the power of zero is 1:
[tex]\implies (3^{8} \cdot 2^{-5} \cdot 1)^{-2} \cdot \left(\dfrac{2^{-2}}{3^{3}}\right)^{4} \cdot 3^{28}[/tex]
[tex]\implies (3^{8} \cdot 2^{-5})^{-2} \cdot \left(\dfrac{2^{-2}}{3^{3}}\right)^{4} \cdot 3^{28}[/tex]
[tex]\textsf{Apply the exponent rule} \quad (a^b \cdot c^d)^p=a^{bp}\cdot c^{dp}:[/tex]
[tex]\implies 3^{(8 \cdot -2)} \cdot 2^{(-5 \cdot -2)} \cdot \left(\dfrac{2^{-2}}{3^{3}}\right)^{4} \cdot 3^{28}[/tex]
[tex]\implies 3^{-16} \cdot 2^{10} \cdot \left(\dfrac{2^{-2}}{3^{3}}\right)^{4} \cdot 3^{28}[/tex]
[tex]\textsf{Apply the exponent rule} \quad \left(\dfrac{a}{b}\right)^c=\dfrac{a^c}{b^c}:[/tex]
[tex]\implies 3^{-16} \cdot 2^{10} \cdot \dfrac{\left(2^{-2}\right)^{4} }{\left(3^{3}\right)^{4} } \cdot 3^{28}[/tex]
[tex]\textsf{Apply the exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies 3^{-16} \cdot 2^{10} \cdot \dfrac{2^{(-2 \cdot 4)}}{3^{(3\cdot 4)}} \cdot 3^{28}[/tex]
[tex]\implies 3^{-16} \cdot 2^{10} \cdot \dfrac{2^{-8}}{3^{12}} \cdot 3^{28}[/tex]
[tex]\textsf{Apply the exponent rule} \quad \dfrac{1}{a^n}=a^{-n}[/tex]
[tex]\implies 3^{-16} \cdot 2^{10} \cdot 2^{-8} \cdot 3^{-12} \cdot 3^{28}[/tex]
Gather like terms:
[tex]\implies 2^{10} \cdot 2^{-8} \cdot3^{-16} \cdot 3^{-12} \cdot 3^{28}[/tex]
[tex]\textsf{Apply the exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]
[tex]\implies 2^{(10-8)}\cdot3^{(-16-12+28)}[/tex]
[tex]\implies 2^{2}\cdot3^{0}[/tex]
Any number to the power of zero is 1:
[tex]\implies 2^{2}\cdot 1[/tex]
[tex]\implies 2^2[/tex]
Therefore, the solution is:
[tex]\implies 2^2=2 \times 2=4[/tex]
Item 3What type of transformation takes the graph of f(x)=|x| to the graph of g(x)=|4+x|? horizontal translation of 4 units rightvertical translation of 4 units upvertical translation of 4 units downhorizontal translation of 4 units left
As given by the question
There are given that the function
[tex]f(x)=|4+x|[/tex]Now,
According to the concept,
x+4 means, horizontal translation of 4 units left.
Hence, the correct option is D.
A distribution of values is normal with a mean of 198 and a standard deviation of 74.5.
Find P10, which is the score separating the bottom 10% from the top 90%.
P10 =
Enter your answer as a number accurate to 1 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
The probability P10 for a data with mean of 198 and standard deviation of 74.5 is P10 = 25.15%
As per the question statement, a distribution of values is normal with a mean of 198 and a standard deviation of 74.5 and we are supposed to find P(10), which is the score separating the bottom 10% from the top 90%.
Given mean (µ) = 48.5 , SD(σ) = 18.2
z = (X - μ) / σ, where X = data
X = 216.74
z = (216.74 - 198) / 74.5 = 0.2515 or 25.15%
Hence the probability P10 for a data with mean of 198 and standard deviation of 74.5 is P10 = 25.15%
Probability: The chance of happening of any event is its probability.Mean: The average of any given set of data is called mean and is calculated by dividing the sum of all observations by the total number of observations.Standard deviation: A number calculated to depict the degree of variation across the board for a group.To learn more about Probability, click on the link given below:
https://brainly.com/question/11234923
#SPJ1
how to solve a given fraction by multiplying the denominators, not by factoring
In the picture there is a problem which is incomplete. There are two terms with the numerator and denominator. The fraction is [tex]\frac{a-b}{2a^{2}-ab-3b^{2} } -\frac{a+b}{2a^{2}-5ab+3b^{2}}=0[/tex]
Given that,
In the picture there is a problem which is incomplete.
We have to complete the fractions by solving.
There are two terms with the numerator and denominator.
There are only variable not numbers.
We have,
=[tex]\frac{a-b}{2a^{2}-ab-3b^{2} } -\frac{a+b}{2a^{2}-5ab+3b^{2}}[/tex]
We have to take an LCM.
[tex]\frac{(a-b)(2a^{2}-ab-3b^{2})- (a+b)(2a^{2}-5ab+3b^{2})}{(2a^{2}-ab-3b^{2})(2a^{2}-5ab+3b^{2})}[/tex]
Now,
Just take the numerator term and solve it
[tex](a-b)(2a^{2}-ab-3b^{2})- (a+b)(2a^{2}-5ab+3b^{2})[/tex]
Separate each term with multiplication
a(2a²-ab-3b²)-b(2a²-ab-3b²)-a(2a²-5ab+3b²)-b(2a²-5ab+3b²)
Multiply the terms
2a³-a²b-3ab²-2a²b+ab²+3b³-2a³+5a²b-3ab²-2a²b+5ab²-3b³
Arrange the terms to get calculation easy
2a³-2a³-a²b-2a²b+5a²b-2a²b-3ab²+ab²-3ab²+5ab²+3b³-3b³
Subtract the terms
2a³-2a³=0
-a²b-2a²b+5a²b-2a²b=-5a²b+5a²b=0
-3ab²+ab²-3ab²+5ab²=-6ab²+6ab²=0
3b³-3b³=0
Now, We get the numerator as 0.
So, If numerator is 0 then the whole term is 0.
Because, any term divides by 0 is 0.
Therefore, The fraction is [tex]\frac{a-b}{2a^{2}-ab-3b^{2} } -\frac{a+b}{2a^{2}-5ab+3b^{2}}=0[/tex]
To learn more about fraction visit: https://brainly.com/question/10354322
#SPJ1
The general equation of a horizontal line is?
Solution
Explanation:
The equation of a horizontal line passing through a point (a, b) is y = b, where 'b' is constant because in the equation y = mx + b, where 'b' is the y-intercept, there is no change in the value of y on the horizontal line and the slope is zero, therefore, the equation of a horizontal line is y = b.
Answer:
The general equation of a horizontal line is y = b where b is constant.
Kamal drew a scale drawing of a theater. He used the scale 6 inches = 10 feet. What scale factor does the drawing use?Simplify your answer and write it as a ratio, using a colon.
Given:
Kamal drew a scale drawing of a theater.
He used the scale 6 inches = 10 feet.
The scale factor will take the form:
[tex]inches\colon feet=x\colon y[/tex]Where (x) is the number of inches that corresponding to the number of feet (y)
So, x = 6, y = 10
So, the scale factor =
[tex]inches\colon feet=6\colon10[/tex]Simplifying the ratio, so the answer will be:
[tex]inches\colon feet=3\colon5[/tex]The area of a rectangle is 3/5 square m² the width is 2/5 m a what is the area of the rectangle write your answer as a fraction in simplest form the length of the rectangle is meters how many times greater is the length than the rest write your answer in simplest form the length is times greater than the width
The length of the rectangle based on the information is 6/25 meters.
The length is 3/5 times more than the width.
How to calculate the length?From the information, the area of a rectangle is 3/5 square m² and the width is 2/5m. It should be noted that the length will be:
Length = Area / Width
Length = 3/5 ÷ 2/5
Length = 3/5 × 2/5
Length = 6/25
The length will s 6/25 meters.
The number of times that the length is more than the width will be:
= 6/25 ÷ 2/5
= 6/25 × 5/2
= 3/5 time.
Learn more about area on:
brainly.com/question/25292087
#SPJ1
A right triangle has a hypotenuse of length 10 units and includes a 40° angle. What are the length of the other two size
1) Let's sketch this out to better grasp it:
2) Since the sum of the interior angles is 180º, we can write out the following to find the missing angle:
[tex]\begin{gathered} 40+90+\alpha=180 \\ 130+\alpha=180 \\ \alpha=180-130 \\ \alpha=50 \end{gathered}[/tex]3) We can find the lengths by using trigonometric ratios (sine, cosine, tangent).
[tex]\begin{gathered} \sin (40)=\frac{opposite\text{ leg}}{hypotenuse}=\frac{b}{10} \\ \sin (40)=\frac{b}{10} \\ b=10\cdot\sin (40) \\ b\approx6.43 \\ \\ \sin (50)=\frac{c}{10} \\ c=10\cdot\sin (50) \\ c=7.66 \end{gathered}[/tex]If you multiply three negative integers, will
the product always, sometimes, or never
be negative.
Find an equation for the perpendicular bisector of the line segment whose endpoints are (1,4)and(-9,-6)
The endpoints are (1,4) and (-9,-6). The equation for the perpendicular bisector of the line segments with given end points is x-y+3=0.
Given that,
The endpoints are (1,4) and (-9,-6).
We have to find the equation of the perpendicular bisector of the line segments with given end points.
First we have to find
The slope of the line m= [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
m=(-6-4)/(-9-1)
m=-10/-10
m=1
Now,
The equation of the line is y-y₁=m(x-x₁)
Taking point (1,4)
y-4=1(x-1)
y-4=x-1
x-y+4-1=0
x-y+3=0
Therefore, the equation for the perpendicular bisector of the line segments with given end points is x-y+3=0.
To learn more about equation visit: https://brainly.com/question/10413253
#SPJ1
I need help please!!! I need the answer please!!
A 2.7 meter ladder leans against a house forming a 30° angle with the house. Exactly how far is the base of the ladder from the house?
Given the information, we have the following right triangle:
notice that x represents the distance from the base of the ladder to the house.
Then, using the trigonometric function sine we have the following:
[tex]\begin{gathered} \sin (30)=\frac{\text{opposite side}}{hypotenuse}=\frac{x}{2.7} \\ \Rightarrow\frac{1}{2}=\frac{x}{2.7} \\ \Rightarrow x=2.7\cdot\frac{1}{2}=1.35 \\ x=1.35 \end{gathered}[/tex]thus, the base of the ladder is 1.35m from the house
in one hour thirty two cars pass through a particular intersection at the same rate how long would it take for 96 cars to pass through the intersection
In one hour number of cars pass a pparticular intersection is 32.
The number of hours to pass 96 cars is three times the hours to pass the 32 cars.
Determine the number of hours to pass 96 cars from a particular intersection.
[tex]3\cdot1=3[/tex]Answer: 3 hours
Right and solve any quality which can be used to determine v , The number of visits Nolan can make to his first free movie ticket.
Answer:
20 + 2.5v ≥ 40
v ≥ 8
Step-by-step explanation:
Nolan receives:
- fixed value: 20
- vari
Given, 115=1+6(5r+4), what is the value of 9r?
Answer:
9r=27
Step-by-step explanation:
you first are gonna multiply 6 into the 5r+4 then you are gonna have this: 115=1+30r+24then u add the 24 and 1 togetheryou get 115=30r+25then you subbtract 25 from both sidesyou get 90=30rthen you didvide 30 by both sidesyou get 3=rso now we multiply 9 cause we need the value of 9r and r=33*9=27write the answer in standard form(-3x^4+x^6-9x^5+2x^2-7)-(-2x^5+x-4x^2-x^4+12)
Let's make the operation:
[tex]\begin{gathered} (-3x^4+x^6-9x^5+2x^2-7)-(-2x^5+x-4x^2-x^4+12) \\ =-3x^4+x^6-9x^5+2x^2-7+2x^5-x+4x^2+x^4-12 \\ =x^6-7x^5-2x^4+6x^2-x-19 \end{gathered}[/tex]Therefore the answer is:
[tex]x^6-7x^5-2x^4+6x^2-x-19[/tex]If an absolute value expression is greater than a negative number, there is no solution. O True O False
Absolute value inequalities are defined by the following properties:
[tex]\begin{gathered} |x|a\rightarrow x<-b,or,x>b \end{gathered}[/tex]Notice that when the absolute value expression is greater than real numbers, the solution is defined.
Therefore, the given statement is false because there's a solution in such a case.Elias incorrectly finds the measure of
Answer:
105 degrees
Elias' mistake was that he added m
Explanation:
To be able to determine the measure of AFB, we have to 1st of all find the value of x.
Let's go ahead and solve for x as shown below;
[tex]m\angle AFD=m\angle\text{BFC (vertically opposite angles are equal)}[/tex][tex]\begin{gathered} 3x+3=2x+27 \\ 3x-2x=27-3 \\ x=24 \end{gathered}[/tex]Since we know the value of x, let's go ahead and solve for [tex]\begin{gathered} (3x+3)+m\angle\text{AFB}=180\text{ (sum of angles on a straight line)} \\ 3(24)+3+m\angle AFB=180 \\ 75+m\angle AFB=180 \\ m\angle AFB=180-75 \\ m\angle AFB=105^{\circ} \end{gathered}[/tex]
solve x and graph solution on number line, 10th grade
Solution:
Given the inequality;
[tex]-10x>-90[/tex]Divide both sides of the inequality by -10 and change the sign;
[tex]\begin{gathered} \frac{-10x}{-10}<\frac{-90}{-10} \\ \\ x<9 \end{gathered}[/tex]Thus, the solution on the number line is;
Find the distance
d(P1.P₂) between
the given points P1
and P2.
P1 = (0,0)
P2 = (6,5)
Simplify your answer, use radicals as needed.
The distance between the two points P1 and P2 is d = √61.
What is the distance?Distance is a measurement of how far apart two objects or points are, either numerically or occasionally qualitatively. The distance can refer to a physical length in physics or to an estimate based on other factors in common usage. Length is measured in distance. For instance, the length of a road is its distance. The most popular units of measurement for distance in the metric system are millimeters, centimeters, meters, and kilometers.So, the distance between points P1 and P2:
Where, P1 = (0,0) and P2 = (6,5).The distance formula: d = √(x₂-x₁)²+(y₂-y₁)²Now, substitute the values in the formula as follows:
d = √(x₂-x₁)²+(y₂-y₁)²d = √(6-0)²+(5-0)²d = √36+25d = √61Therefore, the distance between the two points P1 and P2 is d = √61.
Know more about distance here:
https://brainly.com/question/26046491
#SPJ9
What percent of last semesters college cost was spent on books
Okay, here we have this:
Considering the provided information, we obtain the following equation:
3. Given AB with coordinates A(-4,5) and B(12,13). Find the horizontal distance and the vertical
distance from A to B, stated in that order.
The required distance would be 17.88 units coordinates A(-4,5) and B(12,13) and the horizontal distance is 16 units and the vertical distance is 8 units from A to B which are determined by the graphing method.
What is the distance between two points?The distance between two points is defined as the length of the line segment between two places representing their distance.
Given AB with coordinates A(-4,5) and B(12,13).
The formula of the distance between two points is A(x₁, y₁) and B(x₂, y₂) is given by: d (A, B) = √ (x₂ – x₁)² + (y₂ – y₁) ².
x₁ = -4, y₁ = 5
x₂ = 12, y₂ = 13
distance = √ (12 – (-4))² + (13 – 5)²
distance = √ (12 + 4)² + (8)²
distance = √ (16)² + (8)²
distance = √ (256 + 64)
distance = √320
distance = 17.88 units
The horizontal distance is 16 units and the vertical distance is 8 units from A to B which are determined by the graphing method.
Learn more about the distance between two points here:
brainly.com/question/15958176
#SPJ1
Look at the construction being preformed in this diagram below
When we draw a perpendicular bisector, we are also:
1. Bisecting a line
2. Bisecting a line segment
A paralallel line is not correct. The draw is for bisecting AB, not for a parallel line to AB.
Therefore, the correct answers are:
A, C and D.
suppose that the amount of time it takes to build a highway varies directly with the length of the highway and inversely with the number of workers. suppose that it takes 100 workers 6 weeks to build 4 miles of Highway. how long will it take a 160 workers to build 16 miles of Highway?___weeks
Answer:
The amount of time it would take 160 workers to build 16 miles of Highway is;
[tex]15\text{ weeks}[/tex]Explanation:
Given that the amount of time it takes to build a highway varies directly with the length of the highway and inversely with the number of workers.
Let t represent the time in weeks, l represents the length of the highway in miles, and n represent the number of workers;
So, we have;
[tex]\begin{gathered} t\propto\frac{l}{n} \\ t=k\frac{l}{n} \\ k=\frac{nt}{l} \end{gathered}[/tex]Given;
it takes 100 workers 6 weeks to build 4 miles of Highway
[tex]\begin{gathered} n=100 \\ t=6 \\ l=4 \\ k=\frac{nt}{l} \\ k=\frac{100\times6}{4} \\ k=150 \end{gathered}[/tex]so, for 160 workers to build 16 miles of Highway the time it will take is;
[tex]\begin{gathered} n=160 \\ l=16 \\ k=150 \\ t=k\frac{l}{n} \\ t=150\times\frac{16}{160} \\ t=\frac{150}{10} \\ t=15 \end{gathered}[/tex]Therefore, the amount of time it would take 160 workers to build 16 miles of Highway is;
[tex]15\text{ weeks}[/tex]How much money to feed to 20 people if two pizzas are $12 and 3 people will eat 1 pizza?
When completing a composition translation (more then one translation) we move from right to left?
In right triangle ABC, C is the right angle. Which of the following is cos B if sin A = 0.4
Answer:
Given that,
In right triangle ABC, C is the right angle.
sin A=0.4
To find cos B,
we get the triangle as,
we know that,
Hypotenuse of the triangle is AB
For the angle A, opposite side is CB
For the angle B, adjacent side is CB
From the definition of sine and cosine we get,
[tex]\sin A=\frac{CB}{AB}[/tex]Also,
[tex]\cos B=\frac{CB}{AB}[/tex]Comparing both we get,
[tex]\sin A=\cos B[/tex]It is given that sinA=0.4
Hence we get, cosB=0.4
Answer is: 0.4
Erica wants to build the birdhouse shown. She bought a 29-inch by 45-inch sheet of plywood. Does Erica have enough wood to make the birdhouse? Explain. Find the area of the base and the sides. A(base) = 7x7 = 49 A(sides) = 7x11 = 77 Find the total area. th Total Area = 2x +4x)= 98+=in?
We can divide our birdhouse in 4 rectangles and 2 squares. Each rectangle has measure
and eac square has measure
Then, the total area of our birdhouse is
[tex]\text{Total area=2}\times49+4\times77[/tex]which gives
[tex]\begin{gathered} \text{Total area=98+}308 \\ \end{gathered}[/tex]the birdhouse has an area:
[tex]\text{Total area=}406in^2[/tex]Now, sinde Erica buy a plywood with dimensions 29x45 in^2, she has
[tex]29\times45=1305in^2[/tex]By comparing both numbers, we can see that she have enough wood to make the birdhouse because 1305 in^2 is greater than 406 in^2.
9. Connect Mr. Douglas works at thecomputer store four days a week from10:15 A.M. until 4:45 P.M. How many hoursdoes Mr. Douglas work in four weeks?First find the differencebetween 10:15 AM. andnoon and then between noonand 4:45 P.M.
From 10:15 a.m. to 12:00 p.m. there are 1:45 hours. From 12:00 p.m. to 4:45 p.m. there are 4:45 hours therefore, each day Mr. Douglas works
[tex]1\colon45+4\colon45=6\colon30[/tex]hours.
Now, each week, Mr. Douglas works 4 days therefore, in one week, he works:
[tex]4\times6\colon30[/tex]hours. Simplifying the above resut we get:
[tex]26\text{ hours.}[/tex]Finally, in four weeks Mr.Douglas works:
[tex]26\times4\text{ hours=104 hours.}[/tex]Answer:
[tex]104\text{ hours.}[/tex]The question is in the image. Need help with #8
SOLUTION
The graph is a function
The domain is all real numbers apart from 0 given by the interval
(-∞,0) ∪ (0,∞)
The Range of the function is all positive numbers given by the interval
(0,∞)
The function is increasing on the interval
(-∞,0)
The function is decreasing on the interval
(0,∞)
The difference of two numbers is 16. But large number is five less than four times the smaller number. Find the two numbers.
Let x be the larger number and y be the smaller number.
Given the difference between two numbers is 16.
[tex]x-y=16\ldots\text{..}(1)[/tex]Given larger number is five less than four times the smaller number.
[tex]x=4y-5\ldots\text{.}\mathrm{}(2)[/tex]Now, solve the equation (1)
[tex]x=16+y[/tex]Put x in the 2nd equation.
[tex]\begin{gathered} 16+y=4y-5 \\ 4y-y=16+5 \\ 3y=21 \end{gathered}[/tex]Further solved as,
[tex]y=7[/tex]Now, put the value of y in equation (1)
[tex]\begin{gathered} x-y=16 \\ x-7=16 \\ x=16+7 \\ x=23 \end{gathered}[/tex]Thus,
[tex]x=23[/tex]Therefore, the two numbers are 23 and 7.
