Here, we want to calculate the fourth term of the sequence, given the formula for the nth term of the sequance and the first term of the sequence
From the formula given for the nth term, we will need to add 11 to the previous term
In this case, the first t
The triangle below is an equilateral triangle. Find yy = 10y = 180y = 7y = 13
Solution
For this case we have the following
y+3 = x = 10
Then x= 10
So we can set up this equation:
y+3 = 10
y= 7
Then the answer is:
y=7
To become a member at a local nature preserve, applicants must pay an initiation fee of $100 plus their yearly membership dues , as shown in the graph . What is the slope of the line joining these points, and what does the slope represent?
The points are (2,150), (4,200).
The slope of the line joining the points is,
[tex]\begin{gathered} m=\frac{200-150}{4-2} \\ =25 \end{gathered}[/tex]Thus, the slope represents the increse in cost per year of membership.
I need help with this practiceI am brand new to this type of math, please explain and tutor me step-by-step (with words as well)*I’m also trying to find the most efficient way to solve this Thank you in advance. I’ll be taking notes with a pencil and paper as you work, so please take your time no need in rushing
If 5x=55, x+y=23 and y-z=2 we need to find the value of (2x+y)/z
To get the last value, we need to know the value for each variable, it means we need to know the value for x, the value for y and the value for z.
You have three equations and from these equations, you need to get the values for the variables.
We have the following
[tex]5x=55[/tex][tex]x+y=23[/tex]and
[tex]y-z=2[/tex]We can notice that almost all the equations have two variables, with exception of the first one. For example, the second one has the variables x and y, and the last equation has the variables y and z. So, the first thing that we are going to do, is to choose the equation which has less variables than the other equations. So we'll work with 5x=55.
To get x apart from the numbers we can divide in both sides by 5, as follows
[tex]5x=55\leftrightarrow\frac{5x}{5}=\frac{55}{5}[/tex]Then
[tex]\frac{5x}{5}=x[/tex]and on the other hand
[tex]\frac{55}{5}=11[/tex]Then
[tex]x=\frac{5x}{5}=\frac{55}{5}=11,\text{ }\leftrightarrow x=11[/tex]Now, we've got that x=11.As we have one value, we need to look for the other equations and try to change the x by its numerical value. We notice that now we only have two equations, the second one and the third one.
[tex]x+y=23[/tex]and
[tex]y-z=2[/tex]Since the third equation doesn't have an x, we need to use the second one, i.e. x+y=23 and put the numerical value for x. Then
[tex]x+y=23\leftrightarrow11+y=23[/tex]Now, once again we get an equation with only one variable, it means that we can solve it.
[tex]11+y=23[/tex]To apart the y from the numbers, we can substract 11 from both sides to get
[tex]11+y-11=23-11[/tex]On the left hand side we get
[tex]11+y-11=y[/tex]and from the right hand side we have
[tex]23-11=12[/tex]Then,
[tex]y=11+y-11=23-11=12\leftrightarrow y=12[/tex]Now, we got that y=12.Now, we only have to solve the last equation,
[tex]y-z=2[/tex]As we found the value for y=12, we can use it to get a new equation and get the value for z.
[tex]y-z=2\leftrightarrow12-z=2[/tex]So, after changing the value of y, we get
[tex]12-z=2[/tex]Once more time, we have gotten an equation with one variable. In this case we are going to apart the z, from the numbers.
The first thing to do is substract 12 from both sides. Then
[tex]12-z-12=2-12[/tex]For the Left hand side we will get
[tex]12-z-12=-z[/tex]and for the right hand side we get
[tex]2-12=-10[/tex]Then
[tex]-z=12-z-12=2-12=-10\leftrightarrow-z=-10[/tex]We've gotten that -z=-10, but we need to get the value for z, so we need to do one step more. In this case, you need to multiply in both sides by -1
[tex](-1)(-z)=(-1)(-10)[/tex]Then
it means that the value for z is 10. z=10To get the answer for the expression
[tex]\frac{2x+y}{z}[/tex]we need to replace the values x=11, y=12, z=10
[tex]\frac{2x+y}{z}=\frac{2(11)+12}{10}=\frac{22+12}{10}=\frac{34}{10}[/tex]and by simplifying we get that
[tex]\frac{2x+y}{z}=\frac{34}{10}=\frac{17}{5}[/tex]So your answer is 17/5A coat that usually sells for $100 is marked $20 off. The amount off is what fraction of the usual price? (Express As Fraction)
Given data:
The given usual price is P=$100.
The given off amount is a=$20.
The expression for the fraction is,
[tex]\begin{gathered} \frac{a}{P}=\frac{20}{100} \\ =\frac{1}{5} \end{gathered}[/tex]Thus, the fraction is 1/5.
What is the system of equations, and a example of them?
x = 2
y = 2
see explanation below
Explanation:Using an example of system of equations:
x + y = 4
2x + y = 6
The equations are above are two systems of equations having two unknown x and y. There are different methods to solve the two equations. We can use elimination method or substitution method.
In elimination method, we eliminate one of the variables in order to get the other variable.
In substitution variable, we substitute for one of the variables in any of the equations.
Using elimination method to solve the two equations, the variable we want to eliminate must have the same coefficient.
Let's eliminate y. This is because the coefficient of y is the same in both equation.
The coefficient of y is 1.
Note: if we want to eliminate x, we will need the coefficent of both to be the same. One coefficent is 1, the order is 2.
This means we would multiply equation 1 by 2 and multiply equation 2 by 1. This will ensure they have same coefficient of 2.
x + y = 4 ...equation 1
2x + y = 6 ...equation 2
subtract equation 1 from 2:
2x - x + y - (+y) = 6 - 4
2x - x + y - y = 6 -4
x + 0 = 2
x = 2
We replace 2 with x in any of the equations in order to get y.
using equation 1: x + y = 4
2 + y = 4
y = 4 - 2
y = 2
Without graphing, describe the transformations of each parabola or absolute value function. 2) y = (x +4)2 + 4 3) y = -2(x + 4)² + 4 (-4,4 For The 194 4) y = x-3+3 5) y = 2(x - 1)2 +4 7) y = -3/x-21 6) y = -x +4)+3 8) y = 22-31 +4 9) y = 2x + 1
2) The given expression is
y = (x + 4)^2 + 4
If a function, f(x) undergoes horizontal translation, c units left, it becomes
f(x + c)
Also, If a function, f(x + c) + d undergoes vertical translation, c units upwards, it becomes
f(x + c) + d
Looking at the given function, it underwent a horizontal translation, 4 units left and a vertical translation, 4 units upwards
Solve: - ( 2/3 a - 1/3) + 5/3a = -4.Solve the equation.
3
4
(2a − 6) + 1
2
= 2
5
(3a + 20)
a =
To solve the equation for a, we first apply the distributive property to the left side:
[tex]\begin{gathered} -\mleft(\frac{2}{3}a-\frac{1}{3}\mright)+\frac{5}{3}a=-4 \\ -\frac{2}{3}a+\frac{1}{3}+\frac{5}{3}a=-4 \end{gathered}[/tex]Now, we add similar terms on the left side of the equation:
[tex]\begin{gathered} \text{ Reorder} \\ -\frac{2}{3}a+\frac{5}{3}a+\frac{1}{3}=-4 \\ \mleft(-\frac{2}{3}+\frac{5}{3}\mright)a+\frac{1}{3}=-4 \\ \mleft(\frac{-2+5}{3}\mright)a+\frac{1}{3}=-4 \\ \frac{3}{3}a+\frac{1}{3}=-4 \\ 1\cdot a+\frac{1}{3}=-4 \\ a+\frac{1}{3}=-4 \end{gathered}[/tex]Now, we subtract 1/3 from both sides of the equation:
[tex]\begin{gathered} a+\frac{1}{3}-\frac{1}{3}=-4-\frac{1}{3} \\ a=-\frac{4}{1}-\frac{1}{3} \\ a=-\frac{4\cdot3}{1\cdot3}-\frac{1}{3} \\ a=-\frac{12}{3}-\frac{1}{3} \\ a=\frac{-12-1}{3} \\ \boldsymbol{a=-\frac{13}{3}} \end{gathered}[/tex]Therefore, the value of a that satisfies the equation is -13/3.
Answer:
a = 40
Step-by-step explanation:
Solve the equation. Check your solution. x/6+x/3=3/4-2/3-3/2-5/6-6/5-2/23-23/2
Solution:
This is a fractional algebraic equation.
To solve it, we simplify the left-hand side of the equation as a single fraction and then equate to the right-hand side to get the solution.
[tex]\begin{gathered} \frac{x}{6}+\frac{x}{3}=\frac{3}{4} \\ \\ U\sin g\text{ the Lowest Common Multiple (LCM) of the left-hand side,} \\ \text{The }LCM\text{ is 6} \\ \frac{x+2x}{6}=\frac{3}{4} \\ \frac{3x}{6}=\frac{3}{4} \\ \text{Cross multiplying the equation;} \\ 4\times3x=3\times6 \\ 12x=18 \\ \text{Dividing both sides by 12;} \\ x=\frac{18}{12} \\ x=\frac{3}{2} \end{gathered}[/tex]Therefore, the solution to the equation is;
[tex]x=\frac{3}{2}[/tex]You need to treat a lawn to control grubs with WabashWarriorBUG 20 G at the rate of1 pound of active ingredient per 1000 square feet. The lawn is 10,000 square feet insize. how much product do you need to treat the entire lawn?
We were told that
1 pound of active ingredient is required per 1000 square feet.
Given that lawn is 10,000 square feet in size, let x represent the amount of product needed for the lawn. We would set up the equation as shown below
1 = 1000
x = 10000
By cross multiplying, it becomes
x * 1000 = 1 * 10000
1000x = 10000
x = 10000/1000
x = 10
10 pounds of active ingredient would be needed to treat the entire lawn
Picture Perfect a photo company sells prints in venous sizes. The cost of 4Y6 prinis can be represented by y= 25X-2 where is the number of prints oroered. Max is going to order between 15 and 20 4x6 prints The domain for this stuaron is
y = 25x - 2
the above equation represent the cost of 4Y6 prints
he wants to order between 15 and 20 of 4Y6 prints
the minimum is 15 and maximum is 20
x could be 15 or 20
Y = 25(15) - 2
y = 375 - 2
y = 373
for x = 20
y = 25(20) -2
y = 500 - 2
y = 498
The dimensions of a rectangle are 5x+3 and 4x - 6. Write an expression that represents the perimeter the rectangle.
The perimeter of a Rectangle.
[tex]\begin{gathered} Perimeter\text{ of a rectangle = 2(L+}B) \\ \text{ P = 2\lbrack(5x+3)}+(4x-6)\rbrack \\ P=2(5x+3+4x-6) \\ P=\text{ 2(5x+4x+3-6)} \\ P=2(9x-3) \\ P=18x-6 \end{gathered}[/tex]The correct expression for the required perimeter is 18x - 6
Solve the formula Ax + By = C for x.A. X= C+ByAB. X= C-C. x = CFR+C-ByD. X=+ By
Step 1:
Write the equation
[tex]Ax\text{ + By = C}[/tex]Step 2:
To make x subject of the relation, you will need to solve for x.
[tex]\begin{gathered} Ax\text{ + By = C} \\ Ax\text{ = C - By} \\ \text{Divide through by A} \\ \frac{Ax}{A}\text{ = }\frac{\text{C - By}}{A} \\ \text{x = }\frac{\text{C - By}}{A} \end{gathered}[/tex]Final answer
[tex]\begin{gathered} \text{x = }\frac{\text{C - By}}{A} \\ \text{Option C} \end{gathered}[/tex]let the graph GPA horizontal shrink by a factor of four, followed by a translation two units up of the graph of f(x)=x^3-6x-1
By the rules of transformation of functions, you know that
*f(bx), where b>1, the function shrinks the curve horizontally by a factor of b.
*f(x)+k moves the function k units up
So, in this case, you have
*b=4 and
*k=2
[tex]\begin{gathered} g(x)=f(bx)+k \\ g(x)=f(4x)+2 \\ f(x)=x^3-6x-1 \\ g(x)=(4x)^3-6(4x)-1+2 \\ g(x)=64x^3-24x+1 \end{gathered}[/tex]To verify you can graph the functions f(x) and g(x), like this
Therefore, the function g(x) is
[tex]g(x)=64x^3-24x+1[/tex]Help, I just need examples for these two questionsplease try to keep the answers short. thank you!
Question 1)
We can detonate a line segment and its measure as:
[tex]\begin{gathered} \bar{AB},\text{ line segment} \\ \text{and} \\ \lvert\bar{AB}\rvert,\text{ measure of a line segment} \end{gathered}[/tex]In the case of congruence and equality of figures, remember that two equal figures are congruent, they have the same measures in terms of sides and angles and they even occupy the same space on the plane or space. Then, the notation is:
[tex]\begin{gathered} C\cong D,\text{ congruence} \\ C=D,\text{ equality} \end{gathered}[/tex]Where C and D are two figures.
Question 2)
When we cross a pair of parallel lines with a transversal, we obtain 8 angles. Given any of them, we can determine the rest with the corresponding, alternate interior, alternate exterior, and consecutive angles relations that can be applied to the specific arrangement of 2 parallel lines being cut by another line. The answer is yes, you can do so.
The table represents a linear function. What is the slope of the function? x -2, -1, 0, 1, 2 ... y -2, 1, 4, 7, 10
The function passes through points (-2,-2) and (0,4).
The general formula for the slope of the linear function is,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Determine the slope of linear function.
[tex]\begin{gathered} m=\frac{4-(-2)}{0-(-2)} \\ =\frac{6}{2} \\ =3 \end{gathered}[/tex]Thus slope of linear function is 3.
Given y = -3 + 9 sin 7x , the amplitude is ___
Solution
Step 1:
Amplitudedefinition}.
[tex]\mathrm{For\:f\left(x\right)=A\cdot \sin \left(Bx-C\right)+D\:the\:amplitude\:is\:|A|}[/tex]Step 2:
[tex]\begin{gathered} f\left(x\right)=-3+9\sin \left(7x\right),\:A=9 \\ \mathrm{Therefore,\:\:the\:amplitude\:|A|\:is\:}9 \\ 9 \end{gathered}[/tex]Final answer
Amplitude is 9
What value of x makes this equation true? 10x - 6 = 3 = 3/x+ 1 /
Answer:
15/14
Explanation:
Given the below equation;
[tex]\begin{gathered} 10x-6=3(x+\frac{1}{2}) \\ \end{gathered}[/tex]The 1st step to solving the above is to open the parenthesis;
[tex]10x-6=3x+\frac{3}{2}[/tex]The 2nd step is to add subtract 3x and add 6 to both sides of the equation and solve for x;
[tex]\begin{gathered} 10x-3x=6+\frac{3}{2} \\ 7x=\frac{15}{2} \\ 14x=15 \\ x=\frac{15}{14} \end{gathered}[/tex]I need help with this. There are 3 other options. 2 only. 1 only. Or none of the above.
Given: An expression-
[tex]\sqrt{36}+\sqrt{49}-\sqrt{16}[/tex]Required: To simplify the expression and determine the correct solution.
Explanation: The square root of a number can be simplified by factorizing the term inside the square root into the product of its factors as follows-
[tex]\sqrt{6\times6}+\sqrt{7\times7}-\sqrt{4\times4}[/tex]Now, we take out a number outside the square root from the pairs of numbers to give the following-
[tex]6+7-4=9[/tex]Also, we know that the square of 9 is 81. Hence,
[tex]\sqrt{81}=9[/tex]Hence, the given expression is equal to 9 and the square root of 81.
Final Answer: Option A (1 and 4) is correct.
Trapezoid RSTU is shown on the coordinate grid below.Trapezoid RSTU will be reflected over the x-axis to create trapezoid R’S’T’U’. What will be the coordinate of point R’, the image of point R after the reflection
The given trapezoid RSTU is reflected over x axis;
When a point is reflected across the x-axis, the x-coordinate remains the same, but the y-coordinate is transformed into its opposite sign.
i.e. ( x, y ) → (x, -y )
In the given image, the coordinates of R is R(-4, 5)
Here, x = -4 and y = 5
Since, x will be same
and y will change its sign, thus y = - (5)
i.e. y = -5
So, coordinates of R after reflected across x axis is (-4, -5)
Answer : (-4, -5)
2. THERE ARE A NUMBER of students SITTING IN Acircle. They ARE EVENly spaced and the 7thSTUDENT IS SEATEd directly Across from the18th STUDENTHow many STUDENTS ARE THERE Altogether?2)
There are 10 guys betwwen 7th and 18th.
Since circle, between 18th and 7th (other side), there are another more 10 guys.
Now, counting 7th and 18th member, we can say total number of studens are:
10 + 10 + 2 = 22 students
can I get some help?
From the given figure
The two triangles ABC and DEF are congruent
[tex]\Delta ABC\cong\Delta DEF[/tex]So all sides are equal and all angles are equal too because the two triangles are congruent
Find the measure of each angle. angle UVW and angle XYZ are complementary angles, m angle UVW = (x - 10)° and m angle XYZ = (4x - 10)°. What is the value of x?
When 2 angles are complementary, it means they add up to 90 degrees.
Note: There is also another term, supplementary. It means two angles add up to 180 degrees.
Now, we can write:
[tex](x-10)+(4x-10)=90[/tex]We do algebra and figure out the value of x:
[tex]\begin{gathered} (x-10)+(4x-10)=90 \\ x-10+4x-10=90 \\ 5x-20=90 \\ 5x=90+20 \\ 5x=110 \\ x=\frac{110}{5} \\ x=22 \end{gathered}[/tex]What is the nature of the result of the expression ?
Answer:
The nature of the result of the given expression is irrational. (Option 2)
Explanation:
Let's simplify the given expression by rationalizing the denominator. To rationalize the denominator, multiply both numerator and denominator by √2.
[tex]\frac{4+\sqrt{3}}{\sqrt{2}}\times\frac{\sqrt{2}}{\sqrt{2}}[/tex][tex]=\frac{4(\sqrt{2)}+\sqrt{3}(\sqrt{2})}{\sqrt{2}(\sqrt{2})}[/tex][tex]=\frac{4\sqrt{2}+\sqrt{6}}{2}[/tex]The result is shown above. When converted to a decimal number, it is equivalent to 4.053171996.
As we can see, the result is neither an integer nor a whole number because these two don't have decimal points.
In addition, the result is not a rational number because the equivalent decimal number is both non-terminating and non-repeating decimal.
Hence, the result is an irrational number. (Option 2)
a. Think of polynomials as a system. For each of the following operations, determinewhether the system is closed under the operation. In each case, explain why it is closedor provide an example showing that it isn't1. AdditionType your response here:2. SubtractionType your response here:3. MultiplicationType your response here:4. DivisionType your response here:
1. Polynomials are closed under addition because the addition of two polynomials gives always as result a new polynomial
2. Polynomials are closed under subtraction because the subtraction between two polynomials gives always as result a new polynomial
3. Polynomials are closed under multiplication because the multiplication between two polynomials gives always as result a new polynomial
4. Polynomials are not closed under division. For example:
[tex]\frac{x+1}{x^2}=\frac{x}{x^2}+\frac{1}{x^2}=\frac{1}{x}+\frac{1}{x^2}[/tex]The result is not a polynomial.
4. ( -1 , 3 ) and ( 4, -7 ) 5. ( 3, 2) and (6, 5)
Find the slope passong between the points
(-1, 3) and (4, -7)
We will use the following formula
[tex]m=\frac{y2-y1}{x2-x1}[/tex][tex]\begin{gathered} m=\frac{-7-3}{4-(-1)} \\ m=\frac{-10}{5} \\ m=2 \end{gathered}[/tex](-1, 3) and (4, -7) the slope would be 2
Now, for ( 3, 2) and (6, 5)
[tex]\begin{gathered} m=\frac{5-2}{6-3} \\ m=\frac{3}{3} \\ m=1 \end{gathered}[/tex]for ( 3, 2) and (6, 5) the slope would be 1
What is the approximate probability that a person will be a female and prefer suspense movies? MaleFemale Horror Movies 8294Suspense Movies1846Comedy Movies4891
Probability that a person will be a female and prefer suspense movies = 0.12
Explanation:Total number of males = 82 + 18 + 48 = 148
Total number of females = 94 + 46 + 91 = 231
Total population = 148 + 231 = 379
Number of females that prefer suspense movies = 46
Probability that a person will be a female and prefer suspense movies = 46/379
Probability that a person will be a female and prefer suspense movies = 0.12
After a transformationthe coordinates of J'are (0, - 1) . Write the translation using translation notation.
Looking at the diagram, the original coordinates of J are (- 1, 1) After the translation, the coordinates of J' are (0, -1)
By comparing both coordinates, we can see that from -1 to 0 is 0 - - 1 = 1
Thus, there was a shift, 1 unit to the right along the x axis
Also, from 1 to - 1 is 1 - - 1 = 2
Thus, there was a shift, 2 units downwards along the y axis
In translation notation, it is
(x, y) --- (x + 1, y - 2)
i need help solving this equation for x(5^x/6) (5^x/2) = 5^16
Given equation:
[tex]\begin{gathered} (5^{\frac{x}{6}})(5^{\frac{x}{2}})\text{ = 5}^{16} \\ 5^{\frac{2x}{3}}\text{ = 5}^{16} \\ \frac{2x}{3}=16 \\ x\text{ = 24} \end{gathered}[/tex]The formula, F = 9/5C ×+ 32, converts temperatures between Celsius and fahrenheit degrees. What is the temperature in degrees Celsius that is equivalent to 50 degrees Fahrenheit?A) 9B) 10C) 11D) 12
we have the formula
[tex]F=\frac{9}{5}C+32[/tex]in this problem we have
F=50
substitute
[tex]50=\frac{9}{5}C+32[/tex]Solve for C
[tex]\begin{gathered} \frac{9}{5}C=50-32 \\ \\ \frac{9}{5}C=18 \end{gathered}[/tex]C=(18*5)/9
C=10 degrees
the answer is option BQuestion 131 f(x) = x2 and g(x) = 2x + 3, what is f(g(x))?x2 + 2.0 + 3AB20c2 +3С4.2 +9D4.2 + 12x + 9
We need to know what is the composition function
[tex]\begin{gathered} f(g(x))=(g(x))^2=(2x+3)^2 \\ =4x^2+12x+9 \end{gathered}[/tex]