Calculate:
[tex]81^{\frac{3}{2}}[/tex]The fractional exponent can be written as:
[tex]\sqrt[2]{81^3}=(\sqrt[]{81})^3[/tex]The square root of 81 is 9, thus:
[tex](\sqrt[]{81})^3=9^3=729[/tex]The graph used Is below ill attach a picture of the question and options after
Using the triangle sum theorem:
[tex]\begin{gathered} m\angle L+m\angle K+20=180 \\ 2m\angle L=180-20 \\ 2m\angle L=160 \\ m\angle L=\frac{160}{2} \\ m\angle L=80 \end{gathered}[/tex]Using the exterior angle theorem:
[tex]\begin{gathered} m\angle E=m\angle L+m\angle J \\ m\angle E=80+20 \\ m\angle E=100 \end{gathered}[/tex]Answer:
100
Which is the factored form of 3a2 - 24a + 48?а. (За — 8)(а — 6)b. 3a - 4)(a 4)c. (3a - 16)(a − 3)d. 3( -8)(a -8)
Ok, so:
We're going to factor this expression:
3a² - 24a + 48
First of all, we multiply and divide by 3 all the expression, like this:
3(3a² - 24a + 48) / 3
Now, we can rewrite this to a new form:
( (3a)² - 24(3a) + 144) / 3
Then, we have to find two numbers, whose sum is equal to -24 and its multiplication is 144.
And also we distribute:
((3a - 12 ) ( 3a - 12 )) / 3
Notice that the numbers we're going to find should be inside the brackets.
So, these numbers are -12 and -12.
Now, we factor the number 3 in the expression:
(3(a-4)*3(a-4))/3
And we can cancel one "3".
Therefore, the factored form will be: 3 (a - 4) (a - 4)
So, the answer is B.
(I don't know if there are tutors here right now at this time but it's worth a try.) Please help me I really really don't understand this, it's going to take me a while to understand this. X(
by the distributive law x(y+z)=zy+xz, we have
[tex]\begin{gathered} 3b+3(5)=4(2b)-4(5) \\ 3b+15=8b-20 \end{gathered}[/tex]Then we use the properties of inequalities, we can switch both sides, and if we add or multiply something on both sides the equality remains
[tex]\begin{gathered} 3b+15=8b-20 \\ \end{gathered}[/tex]we want the variables and the numbers without variables to be in different side, so, first we add 20 to both sides, note that the -20 will be cancelled
[tex]\begin{gathered} 3b+15+20\text{ = 8b-20+20} \\ 3b+15+20=8b \end{gathered}[/tex]we want to left all the numbers with variable on the right side so we substract 3b (add -3b) to both sides. Same as before, the 3b will be cancellated (we can change the order in the sum)
[tex]\begin{gathered} -3b+3b+15+20=-3b+8b \\ 15+20=8b-3b \end{gathered}[/tex]of course, you're welcome
I was asking if you have understood my explanation so far
tell me
it doesn't matter the order, in fact, when you get used to the method you can work with both at the same time
any other question?
yes, you could substrac 3b first
For example
[tex]\begin{gathered} 2+3x=6-x \\ 2+3x+x=6-x+x \\ 2+3x+x=6 \\ -2+2+3x+x=-2+6 \\ 3x+x=6-2 \\ 4x=4 \\ \end{gathered}[/tex]sadly I will need to leave since my shift is over, but if you ask another question one of my partners will help you
Have a nice evening!!!!
then we add like terms and switch both sides
[tex]5b=35[/tex]And then we multiply by 1/5 both sides
[tex]\begin{gathered} 5\frac{1}{5}b=\frac{35}{5} \\ b=\frac{35}{5} \\ b=7 \end{gathered}[/tex]In circle G with m_FGH = 150 and FG = 12 units find area of sector FGH.Round to the nearest hundredth.Fa.
The formula for the area of sector is,
[tex]A=\frac{\theta}{360}\pi(r)^2[/tex]Substitute the values in the formula to obtain the area of sector FGH.
[tex]\begin{gathered} A=\frac{150}{360}\cdot\pi(12)^2 \\ =188.4955 \\ \approx188.50 \end{gathered}[/tex]So area of sector FGH is 188.50.
Using the conjugate zeros theorem to find all zeros of a polynomial
We know that 1+i is a root of the polynimial. This also implies that 1-i is also a root of the polynomial. In other words, the term
[tex](x-1+i)(x-1-i)[/tex]is a factor of our polynomial. This last expression can be written as
[tex](x-1+i)(x-1-i)=x^2-2x+2[/tex]so, in order to find the remaining zero, we can compute the following division of polynomials,
which gives
Therefore, the remaining root is x=1.
In summary, the answer is:
[tex]1+i,1-i,1[/tex]Mr. Santos cycled a total of 16 kilometers by making 4 trips to work. After 5 trips to work, how many kilometers will Mr. Santos have cycled in total? 5 Kilometers
According to the information given in the exercise, you know that he cycled a total of of 16 kilometers by making 4 trips to work.
Let be "d" the total amount of kilometers Mr. Santos will have cycled after 5 trips to work.
Based on the above, you can set up the following proportion:
[tex]\frac{16}{4}=\frac{d}{5}[/tex]Finally, you must solve for the variable "d" in order to find its value. This is:
[tex]\begin{gathered} 4=\frac{d}{5} \\ \\ (4)(5)=d \\ d=20 \end{gathered}[/tex]Therefore, the answer is:
[tex]20\operatorname{km}[/tex]What is the least common denominator of 1/20 and 7/50
Considering the given fractions
[tex]\frac{1}{20};\frac{7}{50}[/tex]You have to find the least common denominator between the denominators "20" and "50"
For these values, the least common denominator is the least common multiple between both values:
[tex]20\cdot50=100[/tex]So, the least common denominator is 100.
Janelle is conducting an experiment to determine whether a new medication is effective in reducing sneezing. She finds 1,000 volunteers with sneezing issues and divides them into two groups. The control group does not receive any medication; the treatment group receives the medication. The patients in the treatment group show reduced signs of sneezing. What can Janelle conclude from this experiment?
Answer:
Step-by-step explanation:
Which expression represents the area of the rectangle below in square units
Area of rectangle is given by:-
[tex]\begin{gathered} l\times b \\ =(3x+2)\times2x \\ =6x^2+4x \end{gathered}[/tex]So the correct answer is
[tex]6x^2+4x[/tex]Simplify by combining like terms,8t3 + 8y + 7t3 + 6y + 9t2
The simplification of the expression will be; 15t³ + 9t² + 14y
What are equivalent expressions?Those expressions that might look different but their simplified forms are the same expressions are called equivalent expressions. To derive equivalent expressions of some expressions, we can either make them look more complex or simple.
Given that the expression as 8t³ + 8y + 7t³ + 6y + 9t²
Now combining like terms;
8t³ + 7t³ + 9t² + 8y + 6y
Simplify;
15t³ + 9t² + 14y
It cannot be solved further because of unlike terms in the expression.
Therefore, the simplification of the expression will be; 15t³ + 9t² + 14y
Learn more about expression here;
https://brainly.com/question/14083225
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Bobby says the dilation can be represented by (1\3X, 1,\3Y)Betty says the dilation can be represented by (3X, 3Y)who is correct and why?
Bobby is right because the measurements were made smaller so the dilation factor must be a number less than 1, and 1/3 is less than 1
Calculate Sample Variance for the following data collection: 10, 11, 12, 13, 14,18.
The Variance of a set of data is defined as the average of the square of the deviation from the mean.
The first step is to calculate the mean of the data.
[tex]\frac{10+11+12+13+14+18}{6}=13[/tex]Now we take the difference from the mean, square it, and then average the result.
[tex]\frac{(10-13)^2+(11-13^2)+(12-13)^2+(13-13)^2+(14-13)^2+(18-13)^2}{6}[/tex][tex]\Rightarrow\frac{9+4+1+0+1+25}{6}[/tex][tex]\Rightarrow6.67[/tex]Hence, the variance of the data is 6.7 (rounded to the nearest tenth)
Let f(x) = 8x^3 - 3x^2Then f(x) has a relative minimum atx=
1) To find the relative maxima of a function, we need to perform the first derivative test. It tells us whether the function has a local maximum, minimum r neither.
[tex]\begin{gathered} f^{\prime}(x)=\frac{d}{dx}\mleft(8x^3-3x^2\mright) \\ f^{\prime}(x)=\frac{d}{dx}\mleft(8x^3\mright)-\frac{d}{dx}\mleft(3x^2\mright) \\ f^{\prime}(x)=24x^2-6x \end{gathered}[/tex]2) Let's find the points equating the first derivative to zero and solving it for x:
[tex]\begin{gathered} 24x^2-6x=0 \\ x_{}=\frac{-\left(-6\right)\pm\:6}{2\cdot\:24},\Rightarrow x_1=\frac{1}{4},x_2=0 \\ f^{\prime}(x)>0 \\ 24x^2-6x>0 \\ \frac{24x^2}{6}-\frac{6x}{6}>\frac{0}{6} \\ 4x^2-x>0 \\ x\mleft(4x-1\mright)>0 \\ x<0\quad \mathrm{or}\quad \: x>\frac{1}{4} \\ f^{\prime}(x)<0 \\ 24x^2-6x<0 \\ 4x^2-x<0 \\ x\mleft(4x-1\mright)<0 \\ 0Now, we can write out the intervals, and combine them with the domain of this function since it is a polynomial one that has no discontinuities:[tex]\mathrm{Increasing}\colon-\infty\: 3) Finally, we need to plug the x-values we've just found into the original function to get their corresponding y-values:[tex]\begin{gathered} f(x)=8x^3-3x^2 \\ f(0)=8(0)^3-3(0)^2 \\ f(0)=0 \\ \mathrm{Maximum}\mleft(0,0\mright) \\ x=\frac{1}{4} \\ f(\frac{1}{4})=8\mleft(\frac{1}{4}\mright)^3-3\mleft(\frac{1}{4}\mright)^2 \\ \mathrm{Minimum}\mleft(\frac{1}{4},-\frac{1}{16}\mright) \end{gathered}[/tex]4) Finally, for the inflection points. We need to perform the 2nd derivative test:
[tex]\begin{gathered} f^{\doubleprime}(x)=\frac{d^2}{dx^2}\mleft(8x^3-3x^2\mright) \\ f\: ^{\prime\prime}\mleft(x\mright)=\frac{d}{dx}\mleft(24x^2-6x\mright) \\ f\: ^{\prime\prime}(x)=48x-6 \\ 48x-6=0 \\ 48x=6 \\ x=\frac{6}{48}=\frac{1}{8} \end{gathered}[/tex]Now, let's plug this x value into the original function to get the y-corresponding value:
[tex]\begin{gathered} f(x)=8x^3-3x^2 \\ f(\frac{1}{8})=8(\frac{1}{8})^3-3(\frac{1}{8})^2 \\ f(\frac{1}{8})=-\frac{1}{32} \\ Inflection\: Point\colon(\frac{1}{8},-\frac{1}{32}) \end{gathered}[/tex]Write the equation of the circle given the following graph.
Given:
Equation of a circle on a graph with center(3, -2).
To find:
Equation of a circle.
Explanation:
General eqution of a circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex]Solution:
From the graph, we can see that center is (3, -2) and radius equal 3.
So, equation of a circle is
[tex](x-3)^2+(y+2)^2=3^2[/tex]Hence, this is the equation of a circle.
use geometric relationship to develop the sequence represented in the table
The first figure has 3 tiles
The second figure has 8 tiles
The third figure has 15 tiles
The 4th figure has 24 tiles
The 5th figure has 35 tiles
The 6th figure has 48 tiles
Each time we increased row and column
So the rule is
a(n) = n(n + 2)
Let us use the rule to find figure 46
n = 46
[tex]a_{46}=46(46+2)=2208[/tex]The number of tiles in figure 46 is 2208
Ms. Morgan is the cafeteria manager. She keeps track of how many students select each type of drink. Today during breakfast, 32 children picked milk while 44 children picked juice. What is the ratio of the numbe of children who picked juice to those who picked milk?
Answer:
ratio of those who picked juice to milk
it refers to division
Prove that every differentiable function is continuous
To prove :
every differentiable function is continuous.
thus, every differentiable function is continuous.
Determine the reasonableness of a solution to a logarithmic equation
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given equation
[tex]\log_3x=7[/tex]STEP 2: State the law of logarithm
[tex]\begin{gathered} If\text{ }\log_ab=c \\ \Rightarrow b=a^c \\ By\text{ substitution,} \\ \therefore\log_aa^c=c \end{gathered}[/tex]STEP 3: Substitute the given values in the question to get the correct answer
[tex]\begin{gathered} \log_3x=7 \\ x=3^7 \\ By\text{ substitution,} \\ \log_3(3^7)=7 \end{gathered}[/tex]Hence, Answer is:
[tex]\log_3(3^7)=7[/tex]OPTION A
In how many ways can 3 students from a class of 23 be chosen for a field trip?aYour answer is:
SOLUTION:
This is a combination problem.
The number of ways 3 students from a class of 23 be chosen for a field trip is;
[tex]23C_3=\frac{23!}{(23-3)!3!}=1771\text{ }ways[/tex]How do the coordinates of the blue point relate to the solution of the equation 3x = x + 4
we have the following:
They are related in the way taht if we replace, in both equations it gives the same result:
[tex]\begin{gathered} 3x=2\cdot3=6 \\ x+4=2+4=6 \end{gathered}[/tex]A cash register contains only five dollar and ten dollar bills. It contains twice as many fives as tens and the total amount of money in the cash register is 740 dollars. How many tens are in the cash register?
ANSWER
There are 37 tens in the cash register
EXPLANATION
Given that;
The total amount in the cash register is $740
The cash register contain five dollar and ten dollar
Follow the steps below to find the number of ten dollar in the cash register.
Let x represents the number of $5 and $10 in the cash register.
Recall, that the register contain twice as many $5 as ten dollars and this can be expressed mathematically as
[tex]\text{ 5\lparen2x\rparen+ 10\lparen x\rparen= 740}[/tex]Evaluate x in the above expression
[tex]\begin{gathered} \text{ 10x + 10x = 740} \\ \text{ 20x = 740} \\ \text{ Divide both sides by 20} \\ \text{ }\frac{\text{ 20x}}{\text{ 20 }}\text{ = }\frac{\text{ 740}}{\text{ 20}} \\ \text{ x = 37} \end{gathered}[/tex]Therefore, we have 37 tens in the cash register
polynomials: classifying, simplifying adding and subtracting polynomials write in standard formplease do minimum steps
Solve the System of Equations8x + 15y = -1174x + 9y=-75Write your answer as an ordered pair: (x,y)
We have to solve the system of linear equations:
[tex]\begin{gathered} 8x+15y=-117 \\ 4x+9y=-75 \end{gathered}[/tex]We can substract 2 times the second equation for the first equation and solve for y:
[tex]\begin{gathered} (8x+15y)-2(4x+9y)=-117-2(-75) \\ 8x+15y-8x-18y=-117+150 \\ 0x-3y=33 \\ y=\frac{33}{-3} \\ y=-11 \end{gathered}[/tex]Now, we can solve for x:
[tex]\begin{gathered} 4x+9y=-75 \\ 4x+9(-11)=-75 \\ 4x-99=-75 \\ 4x=-75+99 \\ 4x=24 \\ x=\frac{24}{4} \\ x=6 \end{gathered}[/tex]Answer: (x,y)=(6,-11)
can you please help me on e. f. and g.
His temperature was 100.1 degree farad initially which is around 6 pm. At 7 pm it became 101 degree farad.
[tex]\begin{gathered} \text{slope = }\frac{y_2-y_1}{x_2-x_1}=\frac{101-100.1}{7-6}=\frac{0.9}{1}=0.9 \\ m=0.9 \end{gathered}[/tex]y = mx + b
where
m = slope
b = y - intercept
let find the y intercept
[tex]\begin{gathered} 101=0.9(7)+b \\ 101-6.3=b \\ b=94.7 \end{gathered}[/tex]Therefore, the equation is
[tex]y=0.9x+94.7[/tex]e. let us draw a graph
His temperature will be critical above 22 minutes past 9 pm.
f . He should go to emergency room.
g.
[tex]\begin{gathered} y=0.9x+94.7 \\ 98.6=0.9x+94.7 \\ 98.6-94.7=0.9x \\ 3.9=0.9x \\ x=\frac{3.9}{0.9} \\ x=4.33333333333 \end{gathered}[/tex]His temperature will be normal around past 4 pm which is 98.6 degree farad.
Estimate the difference between 7,472 and 3,827 by rounding each number to the nearest hundred.
Answer:
The difference is aproximately 3700.
Step-by-step explanation:
First, we'll round each number to the nearest hundred:
[tex]\begin{gathered} 7472\rightarrow7500 \\ 3827\rightarrow3800 \end{gathered}[/tex]Now, we can estimate the difference:
[tex]7500-3800=3700[/tex]This way, we can conlcude that the difference is aproximately 3700.
-Зе - 10 - 4Solve and graph the inequality
The given inequality is expressed as
[tex]\begin{gathered} -\text{ 3e - 10 }\leq-4 \\ \end{gathered}[/tex]We would add 10 to both sides of the inequality. It becomes
[tex]\begin{gathered} -\text{ 3e - 10 + 10 }\leq-\text{ 4 + 10} \\ -\text{ 3e }\leq6 \end{gathered}[/tex]We would divide both sides by - 3. This would cause the inequality symbol to reverse. It becomes
[tex]\begin{gathered} \frac{-3e}{-3}\text{ }\ge\frac{6}{-3} \\ e\text{ }\ge-2 \end{gathered}[/tex]The graph would be
The shaded circle at the position of - 2 indicates that- 2 is inclusive
Jackie planted a tomato plant that was 4 inches tall. The plant grew by 150% of its height after 3 weeks. How tall was the plant after the 3 weeks?
1) Problems like these, we can solve by writing an equation.
2)Since that tomato plant grew 150% after three weeks we can write the following
[tex]\begin{gathered} 4\cdot(1+1.5)= \\ 4(2.5)=10 \\ \end{gathered}[/tex]Note that in the parentheses we have the factor of growth. Since it's 150% we can add to 1 and write 1 +1.5=2.5
3) Thus, the answer is:
[tex]10\:inches[/tex]=Given f(x) = -0.4x – 10, what is f(-12)? If it does not exist,enter DNE.
We have the function:
[tex]f\mleft(x\mright)=-0.4x-10[/tex]And we need to find its value when x = -12. So, replacing x with -12, we obtain:
[tex]f(-12)=-0.4(-12)-10=4.8-10=-5.2[/tex]Notice that the product of two negative numbers is a positive number.
Therefore, the answer is -5.2.
solve the quadratic equation below.3x^2-9=0
Explain why the product of 20 x 30 is equal to 600.
BIU
Answer:
600
Step-by-step explanation:
2 X 3 = 6
20 has one 0
30 has one 0
one 0 and one 0 is two 0s
6 plus two 0s = 600
