5^3 = 5 x 5 x 5 = 125
4^4 = 4 x 4 x 4 x 4 = 256
256 > 125
4^4 is larger than 5^3
Write the equation of a circle with a radius of 8 and a center at (4, -9).
The equation of a circle with radius r and center at (h,k) is given by:
(x + h)² + (y + k)² = r²
If r = 8 and (h,k) = (4,-9), we have:
(x-4)² + (y + 9)² = 8²
Janet, Li Na, and Katie have 68 beads altogether.Janet has 3 times as many beads as Li Na.Katie has 5 more beads than Janet.How many beads does Katie have?
EXPLANATION:
Given;
We are told that Janet, Li Na and Katie all have a total of 68 beads.
We are also told that;
(i) Janet has 3 times as many beads as Li Na
(ii) Katie has 5 more beads than Janet.
Required;
We are required to find out how many beads Katie has.
Step-by-step solution;
From the conditions given, Janet has 3 times as many beads as Li Na. That means if Li has an y number of beads, Janet's would be times 3.
Therefore, if Li Na is L and Janet is J, then it means;
[tex]\begin{gathered} Li\text{ }Na=l \\ Janet=3l \end{gathered}[/tex]Also we are told that Katie has 5 more beads than Janet. That means, if Katie is K, then;
[tex]\begin{gathered} Janet=3l \\ Katie=3l+5 \end{gathered}[/tex]Bear in mind that they all have a total of 68 beads. Hence, we add up their beads as follows;
[tex]\begin{gathered} LiNa+Janet+Katie=68 \\ l+3l+3l+5=68 \end{gathered}[/tex][tex]7l+5=68[/tex]Subtract 5 from both sides;
[tex]7l+5-5=68-5[/tex][tex]7l=63[/tex]Divide both sides by 7;
[tex]\frac{7l}{7}=\frac{63}{7}[/tex][tex]l=9[/tex]This means Li Na has 9 beads. If Katie's bead is given by the expression 3l + 5, then she will have;
[tex]\begin{gathered} Katie=3l+5 \\ Katie=3(9)+5 \\ Katie=18+5 \\ Katie=23 \end{gathered}[/tex]ANSWER:
Katie has 23 beads.
what doesnt belong and why? please someome help me will make brainlist
The one that doesn't belong is 4² = 4² + 4²
Explanation:
2² = 2 × 2
4² = 4 × 4
4² is not equal to 4² + 4²
this is because 4² + 4² = 16 + 16 = 32
while 4² = 4 × 4 = 16
The one that doesn't belong is 4² = 4² + 4²
Problem 12a) solve for x, 3(-2x +5) = 9(x-5), x=b) x = –27, x =
The given equation is
[tex]3(-2x+5)=9(x-5)[/tex]Dividing by 3 both sides, we get
[tex]\frac{3\mleft(-2x+5\mright)}{3}=\frac{9\mleft(x-5\mright)}{3}[/tex][tex]-2x+5=3(x-5)[/tex]Multiplying 3 and (x-5) as follows.
[tex]-2x+5=3\times x-3\times5[/tex][tex]-2x+5=3x-15[/tex]Adding 15 on both sides, we get
[tex]-2x+5+15=3x-15+15[/tex][tex]-2x+20=3x[/tex]Adding 2x on both sides, we get
[tex]-2x+20+2x=3x+2x[/tex][tex]20=5x[/tex]Dividing by 5, we get
[tex]\frac{20}{5}=\frac{5x}{5}[/tex][tex]4=x[/tex]Hence the value of x is 4.
What would be the transformation of point A when reflected across the x-axis?(1, -2)(-1, 2)(-1, -2)(1, 2)
Given:
The coordinates of point A is (-1, 2).
To find:
The reflection of point A across the x-axis.
Solution:
It is known that the reflection of a point (x, y) about the x-axis is (x, -y).
So, the reflection of point A is (-1, -2).
Thus, option C is correct.
How to find slope & y interceptAnd solve for Y-6x+2y=10
Slope intercept form
y= mx + b
Where:
m= slope
b= y-intercept
So, first, we have to solve for y:
-6x +2y = 10
2y = 6x + 10
y = (6x + 10) /2
y = 3x + 5
Slope = 3
y-intercept = 5
[tex]\displaystyle\sum_{ k = 1}^{ n } ( - 21 + 5k) = 996[/tex]Solve for "n" value.
Given an equation to solve for n:
[tex]\sum ^n_{k\mathop=1}(-21+5k)=996[/tex]The expansion of the given sum is as follows:
[tex]\begin{gathered} -21+5(1)+(-21+5(2))+(-21+5(3))+\cdots+(-21+5n)=996 \\ -21n+(5+10+15+\cdots+5n)=996 \\ -21n+5(1+2+3+\cdots+n)=996 \\ -21n+5(\frac{n(n+1)}{2})=996 \\ -21n+\frac{5}{2}(n^2+n)=996 \\ -42n+5(n^2+n)=1992 \\ -42n+5n^2+5n=1992 \\ 5n^2-37n-1992=0 \end{gathered}[/tex]Now, factorise the above quadratic equation:
[tex]\begin{gathered} 5n^2+83n-120n-1992=0 \\ n(5n+83)-24(5n+83)=0 \\ (5n+83)(n-24)=0 \end{gathered}[/tex]Use zero product rule in the equation to get:
5n + 83 = 0 or n - 24 = 0 which implies n = -83/5 and n = 24.
Neglect the negative solution of the equation to get n = 24.
Thus, the answer is 24.
The point (-2, 1) is translated 3 units down and 2 units to the left. What are the coordinates of the newpoint?Use the grid below if it helps.-65-43-214-4-3-2-1130-1--2-3-4-5-6(2,-4)o(-4,-2)(0, -4)(0,4)
Given that the point (-2, 1) is translated 3 units down and 2 units to left. The coordinate of the new point would follow the translation rule
[tex]T(x,y)\to(x-2,y-3)[/tex]Therefore, the coordinates of the new point following the translation rule are:
[tex]\begin{gathered} T(-2,1)\to_{}(-2-2,1-3) \\ =(-4,-2) \end{gathered}[/tex]The correct answer is (-4,-2)
if D equals 6x - 7 + 8 equals 4x + 9 find the DB
If DE = 6x - 7 and AE = 4x + 9, find DB.
DE and AE are line segments. We need to equal DE = AE
[tex]DE=AE[/tex][tex]6x-7=4x+9[/tex][tex]6x-4x=9+7[/tex][tex]2x=16[/tex][tex]x=8[/tex]Now, DB = DE + EB
[tex]DB=6x-7+4x+9[/tex][tex]DB=10x+2[/tex]x = 8
[tex]DB=10(8)+2\rightarrow DB=82[/tex]DB is 82
Reduce to lowest terms 24/36
To reduce to the lowest terms we notice that:
[tex]\frac{24}{36}=\frac{6\cdot4}{6\cdot6}=\frac{6\cdot2\cdot2}{6\cdot2\cdot3}[/tex]now, we can eliminate the 6 and 2 that repeat in the numerator and denominator, thereforew the fraction in lowest terms is:
[tex]\frac{2}{3}[/tex]There are as many even counting numbers as there are counting numbers. Is this true or false?
The sets of even and odd counting numbers are both infinite in size (number of elements). However, we can map each even counting number to each odd counting number as follows:
[tex]\begin{gathered} 2\rightarrow1 \\ 4\rightarrow3 \\ 6\rightarrow5 \\ 8\rightarrow7 \\ \text{And so on}\ldots \end{gathered}[/tex]So we have the mapping rule:
[tex]\begin{gathered} 2n\rightarrow2n-1 \\ \text{Where }n=1,2,3,\ldots \end{gathered}[/tex]Then, we can say that there are as many even counting numbers as there are counting numbers, or equivalently, that both sets have the same cardinality.
Answer: True
Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting.f(x) = -2(x + 1)2 + 2
Okay, here we have this:
Considering the provided function, we are going to graph it, so we obtain the following:
First, we are going to start with the graph of the basic function, so the graph so far is:
Now, we are going to add 1 inside the square, which is reflected in a shift of the graph one unit to the left, so we have:
We continue, multiplying the entire function by -2, which results in a compression of the graph, and in a reflection on the x-axis due to the change of sign, now we have:
And finally we add two units to the whole function, therefore it means that the graph will move up two units, leaving the following graph:
Finally we obtain that the correct answer is the first answer choice.
At a local restaurant, the amount of time that customers have to wait for their food is normally distributed with a mean of 32 minutes and a standard deviation of 5 minutes. What is the probability that a randomly selected customer will have to wait less than 21 minutes, to the nearest thousandth?
Given:
[tex]\begin{gathered} mean(\mu)=32 \\ Standard-deviation(\sigma)=5 \end{gathered}[/tex]To Determine: The probability that a randomly selected customer will have to wait less than 21 minutes, to the nearest thousandth
Solution
Using normal distribution formula below
[tex]P(Z<\frac{x-\mu}{\sigma})[/tex]Substitute the given into the formula
[tex]\begin{gathered} P(Z<\frac{21-32}{5}) \\ =P(Z<-\frac{11}{5}) \\ =P(Z<-2.2) \end{gathered}[/tex][tex]\begin{gathered} P(X<-2.2)=1-P(X>-2.2) \\ =1-0.986097 \\ =0.01390345 \\ \approx0.014(Nearest\text{ thousandth\rparen} \end{gathered}[/tex]Hence, the probability that a randomly selected customer will have to wait less than 21 minutes, to the nearest thousandth is 0.014
A baseball player has a batting average of 0.33. What is the probability that he has exactly 4 hits in his next 7 atbats? Round to 3 decimal places.The probability is
Given that the player can or cannot hit the ball, then this situation can be modeled with the binomial distribution.
Binomial distribution formula
[tex]P=_nC_xp^x(1-p)^{n-x}^{}[/tex]where
• P: binomial probability
,• nCx: number of combinations
,• p: probability of success in a single trial
,• x: number of times for a specific outcome within n trials
,• n: number of trials
Substituting with n = 7, x = 4, and p = 0.33, we get:
[tex]\begin{gathered} P=_7C_4(0.33)^4(1-0.33)^{7-4} \\ P=35(0.33)^4(0.67)^3 \\ P\approx0.125 \end{gathered}[/tex]The probability is 0.125
Demetrius is single but would like to take care of his mother in the event of his death. He would like to replace her income of $25,000 a year with a multiple of 30. How much life insurance should he buy?
Answer:
750000
Step-by-step explanation:
I need a deep explanation we are doing this in school pulled out my notes and still don't understand.
For an isosceles triangle, two sides are equal and for right triangle o angle should be of 90 degree.
Let the third point coordinate be (x,y).
The distane between given point (-2,-4) and (4,-4) is 6.
The on angle is 90 degree which means one side is perependicular to the given side.
The coordinate of third point must be equal to (4,y) or (-2,y).
As triangle is isosceles so distance between point (4,y) and (4,-4) is equal to 6.
[tex]\begin{gathered} 6=\sqrt[]{(4-4)^2+(y+4)^2} \\ 6=(y+4) \\ y=6-4 \\ =2 \end{gathered}[/tex]Thus coordinate of third point can be (4,2).
Second case if third point is (-2,y).
Distance between point (-2,y) and (-2,-4) is 6, as triangle is isosceles triangle.
[tex]\begin{gathered} 6=\sqrt[]{(-2+2)^2+(y+4)^2} \\ 6=(y+4) \\ y=2 \end{gathered}[/tex]Thus third coordinate can be (-2,2).
As from the options only (4,2) is correct.
Approximate the median in each of the three graphs. Explain how you determined the answer.
The median is the centermost data in a set of values.
Since these graphs are for the year 2013, meaning, these graphs contained 365 days of recorded temperature.
For 365 days, the centermost data would be the 183rd day.
Let's take a look at each graph what is the temperature on the 183rd day when data is arranged from lowest to the highest temperature.
As we can see above, the first two bins of the histogram only cover 180 days. Since we are looking for the 183rd day, we moved to the third bin. Hence, the median temperature for City A is between 65 to 75 ℉.
For City B,
The 183rd day in City B is found on the interval 55-75. Hence, the median temperature for City B is between 55-75℉.
Lastly, for City C:
As we can see in the graph above, the 183rd day is approximately closed to the third bin. Hence, for the 183rd day, we can say that the temperature is between 65 to 75℉. The median temperature for City C is between 65 to 75℉.
a line intercepts the point (-2, 1) and it has a slope of 2 input the correct values into the point slope formula. y- ? = ? ( x- ?)
We know that the point-slope forumal is given by:
[tex]y-y_1=m(x-x_1)[/tex]where the terms: m, y₁ and x₁ are numbers.
Given that the line passes through a given points we have that:
m is the slope of the line
y₁ is the y value of that given point
x₁ is the x value of that given point
In this case we have that
1. It has a slope of 2, then m = 2
2. The line intercepts the point (-2, 1). Since (-2, 1) = (x₁, y₁) then
x₁ = -2 and y₁ = 1
We have that
m = 2
x₁ = -2
y₁ = 1
Let's replace those values in the first formula:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \downarrow \\ y-1=2(x-(-2)) \\ y-1=2(x+2) \end{gathered}[/tex]Answer- the point-slope formula of this line is: y - 1 = 2(x + 2)7. Given an arithmetic sequence, find a26if a4 = 71 and a32 = 1. 8. Given a geometric sequence, find az ifa1 = 729 and a2 = – 243.
Arithmetic sequence
a= 26
a4 = 71
a32 = 1.
an = a1 + (n-1)d
a4 = a1 + (3)*d
71 = a1 + (3)*d (I)
a32 = a1 + (31)*d
1 = a1 + 31 d (II)
to find a1 and d we subtract (II)- (I)
1 = a1 + 31 d (II)
-( 71 = a1 + (3)*d) (I)
________________
-70 = 0 28 d
-70 = 28 d
d= -70/ 28
d= -5/2
Replacing d in (I)
71 = a1 - (3)(5/2)
a1= 71 + (3)(5/2)
a1= 78.5
The arithmetic sequence is
an = a1 + (n-1)d
an = 78.5 + 2.5 (n-1)
Verifying
a4 = 78.5 - 2.5 (3) = 78.5 -7.5= 71
a32 = 78.5 +2.5 (31) =78.5 -77.5 = 1
a26 = 78.5 + 2.5 (25) = 78.5 - 62.5 = 16
Give me some minutes
______________________
Answer
a26 = 16
Line a is parallel to line b line a passes through the points (1,7) and (2,-4)Line b passes through the point (6,14)The equation of line b is y=__
Given:
Line a is parallel to line b.
Line a passes through the points (1,7) and (2,-4).
Line b passes through the point (6,14).
The objective is to find the equation of the line b in slope intercept form.
For parallel lines the slope of the two lines will be equal.
Consider the coordinates of the line a as,
[tex]\begin{gathered} (x_1,y_1)=(1,7) \\ (x_2,y_2)=(2,-4) \end{gathered}[/tex]The slope of line a can be calculated as,
[tex]\begin{gathered} m_a=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{-4-7}{2-1} \\ =-11 \end{gathered}[/tex]Since both are given as parallel lines, the slop of line b will be,
[tex]m_b=-11[/tex]If the line b passes throught the point (6,14), the equation can be represented as,
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-14=-11(x-6) \\ y-14=-11x+66 \\ y=-11x+66+14 \\ y=-11x+80 \end{gathered}[/tex]Hence, the equation of line b is y = -11x+80.
Write the equation in slope-intercept form through the point (3, 1) and is perpendicular to the y-axis and graph
Write the equation in slope-intercept form through the point (3, 1) and is perpendicular to the y-axis and graph
step 1
we know that
If the line is perpendicular to the y-axis, that means that the line is parallel to the x-axis
so
Its a forizontal line
the slope is equal to zero
therefore
the equation is
y=1
using a graphing tool
see the attached figure
please wait a minute
what digit is in the
7 more than t
The algebraic expression is:
[tex]t+7[/tex]Answer: t + 7
9) write in standard formthrough: (4,4), parallel to y=-6x + 5
Data
Point (4, 4)
Equation
y = -6x + 5
Procedure
As the straight line is parallel we use the same slope of the original straight line.
m = -6
Now we will calculate y-intercept
[tex]\begin{gathered} b=y-mx \\ b=4-(-6)\cdot4 \\ b=4+24 \\ b=28 \end{gathered}[/tex]The equation would be:
[tex]y=-6x+28[/tex][tex]6x+y=28[/tex]Now in the standard form: 6x+y=28
(x²y³z)^1/5Rewrite the rational exponent expression as a radical expression.
Given the following rational exponent:
(x²y³z)^1/5
Putting it into a radical expression will be:
[tex]\text{ \lparen x}^2y^3z)^{\frac{1}{5}}\text{ = }\sqrt[5]{x^2y^3z^}[/tex]Karl borrowed $5,700 from the bank for a year at 9% simple interest. What was the amount he paid back to the bank?
Simple interest = PRT /100
where P is the principal
R is the rate
T is the time in year
From the question
P=$5700 R=9 T=1
substitute the values into the formula;
S.I = 5700 x 9 x 1 /100
=$513
Amount pay back = $5700 + $513 = $6,213
What is the difference of the complex numbers below? (6+81)-(1-21 ) O A. 7+10) O O O B. 5+10) O C. 5+67 O 0 7 D. 7 +62
we have the expression
[tex](6+8i)-(1-2i)[/tex]Remove parenthesis
[tex]6+8i-1+2i[/tex]Group similar terms
[tex](6-1)+(8i+2i)[/tex]Combine like terms
[tex]5+10i[/tex]The answer is option BI need help with the transition from red to blue
5 units left and 2 units down
According to the graph, what is the solution to this system of equations? O (-4,-3) 0 (-3,-4) O (-5, 5) O (5,-5)
The intersection of the 2 lines is the point of the solution of the graph . Using the graph above , the meeting point of the 2 lines are
[tex](-4,-3)[/tex]Given: F(x) = 3x^2+ 1, G(x) = 2x - 3, H(x) = xF(x) + G(x) =
Explanation
to add two functions just add like terms,Like terms" are terms whose variables and their exponents, are the same
so
Step 1
let
[tex]\begin{gathered} f(x)=3x^2+1 \\ g(x)=2x-3 \end{gathered}[/tex]hence
[tex]f(x)+g(x)=3x^2+1+2x-3[/tex]we can see the only pair of like terms ar +1 and (-3), so
[tex]\begin{gathered} f(x)+g(x)=3x^2+1+2x-3 \\ \text{add like terms} \\ f(x)+g(x)=3x^2+2x-2 \end{gathered}[/tex]I hope this helps you
Comelius conducts an experiment where he selects a letter tile from the tiles shown, records the letter, then replaces it in the bag The table shows the results after 50 trialsA 1 0E 18T 18U 4What is the relative frequency that a letter was T? Express your answer as a fraction in simplest form
Relative frequency of T = 9/25
Explanation:Total number of T's = 18
Total number of A's = 10
Total number of E's = 18
Total number of U's = 4
Total = 18 + 10 + 18 + 4 = 50
Relative frequancy = number of time the letter occurred/total letters
Relative frequency = 18/50
To the simplest form:
Relative frequency of T = 9/25