The first 4 terms of the sequence defined by the rule f(n) = -4 x f(n - 1) - 50 are 7,
Sequence:
A sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
Given,
The rule of the sequence is f(n) = -4 x f(n - 1) - 50
Value of the first term = f(1) = 7
Now we need to find the other 4 others in the sequence.
To find the value of the sequence we have to apply the value of n.
Here we have to take the value of n as 1, 2, 3, and 4.
We already know that the value of f(1) is 7.
So, now we need to find the value of f(2), that is calculated by apply the value on the given rule,
f(2) = -4 x f(2 - 1) - 50
f(2) = -4 x f(1) - 50
f(2) = -4 x 7 - 50
f(2) = -28 - 50
f(2) = -78
Similarly, the value of n as 3, then the value of f(3) is,
f(3) = -4 x f(3 - 1) - 50
f(3) = -4 x f(2) - 50
f(3) = -4 x - 78 - 50
f(3) = 312 - 50
f(3) = 262
Finally, when we take the value of n as 4 then the value of f(4) is,
f(4) = -4 x f(4 - 1) - 50
f(4) = -4 x f(3) - 50
f(4) = -4 x 262 - 50
f(4) = -1048 - 50
f(4) = -1099
Therefore, the first 4 sequence are 7, - 78, 262 and -1099.
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A school debate team has 4 girls and 6 boys. A total of 4 of the team members will be chosen top participate in the district debate. What is the probaility that 2 girland 2 boys will be selected?
The probability that 2 girls and 2 boys are selected is given by:
[tex]P(\text{ 2 boys, 2 girls })=\frac{4C2\times6C2}{10C4}=\frac{6\times15}{210}=\frac{3}{7}[/tex]Therefore, the correct choice is option D) 3/7.
are these places correctly.and yes it is math. pls answer fast
we have that
Costs that stay the same from week to week or month to month
-savings for college
-Rent
Costs that cannot be adjusted within a budget
-Car insurance
-Health care
Costs that can be adjusted within a budget
-cell phone
-gasoline
-hair cut
-Groceries
Use the following function rule to find f(48).
f(x) = 12 + x/4
Answer:
See image
depending on what is in the numerator of your question:
24 OR 15 SEE IMAGE!
Step-by-step explanation:
f(48) just means to use 48 in place of x in your work.
f(x) = 12 + x/4
f(48) = 12 + 48/4
Hopefully, your text/worksheet/screen is clear on which problem you are doing.
At the airport, the new runway will be parallel to a nearby highway. The equation that represents the highway is 6y = 8x - 11. Which equation could represent the new runway? A. 9y = 12x + 5B. 9x = 12y + 8C. 12y = -9x + 2 D. 12x = -9y + 4
At the airport, the new runway will be parallel to a nearby highway. The equation that represents the highway is 6y = 8x - 11. Which equation could represent the new runway?
A. 9y = 12x + 5
B. 9x = 12y + 8
C. 12y = -9x + 2
D. 12x = -9y + 4
______________________________________________________
Parallel equations have the same slope
6y = 8x - 11
y= 8/6 x - 11/6
y= 4/3 x-11/6
y = m x +b (m is the slope )
_____________________________________________
You need to find the other equation with the same slope
____________________________
A. 9y = 12x + 5
y = 12/ 9 x + 5/9
y = 4/3 x + 5/9
_________________________
B. 9x = 12y + 8
12 y= 9x-8
y= 9/ 12 x- 8/12
y= 3/4 x - 4/6
discarded
________________________
C. 12y = -9x + 2
y = -9/12 x + 2/12
y = -3/4 x + 1/6
discarded
_________________________
D. 12x = -9y + 4
12x -4 = -9y
y = -12/9 x +4/9
y = -4/3 x+4/9
discarded
_______________
So then, A 9y = 12x + 5 is the equation that could represent the new runway because is parallel to the highway 6y = 8x - 11.
there are twelve inches in one foot,creating the equation y=12x. if a door frame is 6.5 feet tall,how many inches tall is it
Let's begin by listing out the information given to us:
[tex]\begin{gathered} 12in=1ft \\ y=12x \end{gathered}[/tex]The height of the door frame is 6.5 feet. To convert to inches, we have:
[tex]\begin{gathered} y=12(6.5)=78inches \\ y=78inches \end{gathered}[/tex]Solve the equation-3 + a = 13a = ???
ANSWER
a = 16
EXPLANATION
To solve for a we have to add 3 on both sides of the equation:
[tex]\begin{gathered} -3+3+a=13+3 \\ a=16 \end{gathered}[/tex]What are the slope and the y-intercept of the linear function that is represented by the table? -- Nicol у 3 2 1 0 -2 / 0 Nlw 3 1 2 -1 The slope is -3, and the y-intercept is 3 The slope is -3, and the y-intercept is z. 1 The slope is 3, and the v-intercept is -
We will assume the next table to answer this question (a linear function) (since the data in the question is not clear):
Having this information, we can find the slope using the formula for it:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]If we pick up from the table the next points:
x1 = 1, y1 =6
x2 = 2, y2 = 8
Then
[tex]m=\frac{8-6}{2-1}=\frac{2}{1}\Rightarrow m=2[/tex]We can use the slope-point formula to find the y-intercept. We can use the point (3, 10). Then, we have:
[tex]y-y_1=m\cdot(x-x_1)\Rightarrow y-10=2\cdot(x-3)\Rightarrow y-10=2x-6[/tex][tex]y=2x-6+10\Rightarrow y=2x+4[/tex]We end up with the slope-intercept formula for the line. Then the y-intercept is 4. In other words, if we have x = 0, then y = 4.
Then the slope for the values represented in the proposed table is m = 2, and the y-intercept is y = 4.
Solve for the Limit of Function by applying appropriate Limit Theorems
Answer:
Given to solve,
[tex]\lim _{x\to-1}(2x+2)(x+2)[/tex]From the rules for limits, we can see that for any polynomial, the limit of the polynomial when x approaches a point k is equal to the value of the polynomial at k.
The given function of the limit is a quadratic function, the limit of the quadratic equation when x approaches a point -1 is equal to the value of the quadratic equation at -1.
we get,
[tex]\lim _{x\to-1}(2x+2)(x+2)=(2(-1)+2)((-1)+2)[/tex][tex]=(-2+2)(1)=0[/tex][tex]\lim _{x\to-1}(2x+2)(x+2)=0[/tex]
Answer is : 0
The graph below and to the left shows the time of sunsets occurring every other day during September in a certain town. The graph at the lower right shows the time of sunsets on either the 21st or 22nd day of each month for an entire year in the same town. The vertical axis is scaled to reflect hours after midnight. Round to 4 decimal places. a) Find a linear model for the data in the graph at the left. Include units to your variables. b) Find a cosine model for the data in the graph to the right. Include units to your variables,
A) Given the points (1,18.35) and (29,17.5), we can find the linear model with the following formulas:
[tex]\begin{gathered} \text{slope:} \\ m=\frac{y_2-y_1}{x_2-x_1}=\frac{71.5-18.35}{29-1}=\frac{-0.85}{28}=-0.03 \\ \text{equation of the line:} \\ y-y_1=m(x-x_1) \\ \Rightarrow y-18.35=-0.03(x-1)=-0.03x+0.03 \\ \Rightarrow y=-0.03x+0.03+18.35=-0.03x+18.38 \\ y=-0.03x+18.38 \end{gathered}[/tex]therefore, the linear model is y = -0.03x+18.38
B)We have the general cosine model:
[tex]y(t)=A+B\cos (\omega(t-\phi))[/tex]Where A is the vertical shift, B is the amplitude, w is the frequency and phi is the phase shift.
First, we can find the vertical shift with the following formula:
[tex]A=\frac{y_{\max }+y_{\min }}{2}[/tex]in this case, we have that the maximum value for y is 19.47 and the minimum value for y is16.18, then:
[tex]A=\frac{19.47+16.18}{2}=17.825[/tex]next, we can find the amplitud with the following formula:
[tex]B=y_{\max }-A[/tex]We have then:
[tex]B=19.47-17.825=1.645[/tex]Now, notice that the graph will repeat every 356 values for t, then, for the frequency we have the following expression:
[tex]\omega=\frac{2\pi}{356}=\frac{\pi}{178}[/tex]To find the phase shift, notice that for the point (172,19.47), we have the following:
[tex]\begin{gathered} y(172)=19.47 \\ \Rightarrow17.825+1.645\cos (\frac{\pi}{178}(172-\phi))=19.47 \\ \Rightarrow1.645\cos (\frac{\pi}{178}(172-\phi))=1.645 \\ \Rightarrow\cos (\frac{\pi}{178}(172-\phi))=1 \end{gathered}[/tex]notice that if the cosine equals 1, then its argument must equal to 0, then, we have:
[tex]\begin{gathered} \frac{\pi}{178}(172-\phi)=0 \\ \Rightarrow172-\phi=0 \\ \Rightarrow\phi=172 \end{gathered}[/tex]we have that the phase shift is phi = 172, then, the final cosine model is:
[tex]y(x)=17.825+1.465\cos (\frac{\pi}{178}(x-172))[/tex]Point S is on line segment \overline{RT} RT . Given RT=3x,RT=3x, RS=3x-5,RS=3x−5, and ST=3x-1,ST=3x−1, determine the numerical length of \overline{RT}. RT .
The numerical length of the line segment RT is 6.
Length:
Length is the measuring unit used to identifying the size of an object or distance from one point to the other.
Given,
There is a point on the line segment RT.
And the values of the pots are,
RT = 3x, RS = 3x - 5 and ST = 3x - 1.
Now we need to find the length of the line segment RT.
To find the line of the line segment RT,
We have to add the length of the segments,
That can be written as,
=> RT = RS + ST
Now, we have to apply the values of the point to the equation, then we get,
=> 3x = 3x - 5 + 3x - 1
=> 3x = 6x - 6
=> 6x - 3x - 6
=> 3x - 6
=> 3x = 6
=> x = 2
If the value of x is 2, then the length of the line segment RT is,
RT = 3x => 3 x 2 = 6
Therefore, the length of the line segment RT is 6.
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Soue se compound inequality and give your answer in intentel notation- 10 AND-80-72-1
S= (-4, 1 ]
1) Solving that compounded inequality
4x +6 > -10 and -8x+7 ≥ -1
2) Let's start by 4x +6 > -10
4x +6 > -10 Subtracting 6 from both sides
4x > -10-6
4x > -16 Dividing both sides by 4
x > -4
And with -8x+7 ≥ -1
-8x+7 ≥ -1 Subtract 7 from both sides
-8x ≥ -1 -7
-8x ≥ -8 Multiply by -1
8x ≤ 8
x ≤ 1
3) Graphing the solution interval:
So the solution is the interval S= (-4, 1 ] not including x= -4 and including the value x = 1
Suppose a charity received a donation of $19.4 million. If this represents 43% of the charity's donated funds, what is the total amount of its donated funds? Round your answer to the nearest million dollars.
Given :
a charity received a donation of $19.4 million
Which represents 43% of the charity funds
Let the total funds = x
So,
43% of x = 19.4 million
So,
[tex]\begin{gathered} 43\%\cdot x=19.4 \\ \\ 0.43\cdot x=19.4 \\ \\ x=\frac{19.4}{0.43}\approx45.12 \end{gathered}[/tex]Rounding to the nearest million ,
The answer is : total donated funds = 45 million
O GRAPHS AND FUNCTIONSDomain and range from the graph of a piecewise function
ANSWER:
[tex]Domain:(-5,-4]\cup[-1,2][/tex][tex]Range:[-3,0)\cup[1,4][/tex]EXPLANATION:
Given:
To find:
The domain and the range
Recall that the domain of a function is the set of possible input values for which the function is defined.
To determine the domain of a function from a graph, we consider the possible x-values from left to right.
So the domain of the given function can be written as;
[tex]Domain:(-5,-4]\cup[-1,2][/tex]The range of a function is the set of possible output values.
To determine the range of a function from a graph, we consider the possible y-values from the bottom to the top.
So the range of the given function can be written as;
[tex]Range:[-3,0)\cup[1,4][/tex]5. There are 9.75 ounces of Cinnamon Toast Crunch in a bowl. Additional cereal ispoured into the bowl at a rate of 1.5 ounces per second. How many ounces are inthe bowl after 3 seconds?
Question:
There are 9.75 ounces of Cinnamon Toast Crunch in a bowl. Additional cereal is poured into the bowl at a rate of 1.5 ounces per second. How many ounces are in the bowl after 3 seconds?
Solution:
If additional cereal is poured into the bowl at a rate of 1.5 ounces per second, then in 3 seconds the additional cereal into the bowl is 1.5x 3 = 4.5 ounces. Thus after 3 seconds, the bowl has the original amount that it already had and the new aggregate:
9.75 ounces + 4.5 ounces = 14.25
then, the correct answer is:
14.25
In New York, the tax on a property assessed at $520,000 is $10,400. If tax rates are proportional in this city, how much would the tax be on a property assessed at $370,000? Answer: $
Given that the tax on a property assessed at $520,000 is $10,400 and the tax
quick!! will give brainliest!! Given g(x) = -x + 3, solve for a when g(2) = -1
We have the following:
[tex]g(x)=-x+3[/tex]replacing when x is 2:
[tex]g(2)=-2+3=1[/tex]Answer this, please
Zachariah and Khai collect stamps. Zachariah has 7 American stamps out of 12 stamps. Khai has 15 American stamps out of 24 stamps. Which statement is correct?
Zachariah has a higher ratio of American stamps than Khai because 7 over 12 is greater than 15 over 24.
Khai has a higher ratio of American stamps than Zachariah because 7 over 12 is less than 15 over 24.
Zachariah has a higher ratio of American stamps than Khai because 7 over 12 is less than 15 over 24.
Zachariah and Khai have the same ratio of American stamps.
The last statement would be true, because you would convert 7/12 into a fraction and 15/24 into a fraction. From their fraction eyes to State you would turn them into decimals and then percentiles.
Answer:
D: They are both the same
Step-by-step explanation:
I took the test
Describe the transformation from the graph of f to the graph of h. Write an equation that represents h in terms of x. Look at image for example. Let’s do problem number 11
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given functions.
[tex]\begin{gathered} f(x)=-(x+5)^2-6 \\ h(x)=\frac{1}{3}f(x) \end{gathered}[/tex]STEP 2: Explain the transformation that occurs
What are Vertical Stretches and Shrinks?
While translations move the x and y intercepts of a base graph, stretches and shrinks effectively pull the base graph outward or compress the base graph inward, changing the overall dimensions of the base graph without altering its shape. When a graph is stretched or shrunk vertically, the x -intercepts act as anchors and do not change under the transformation.
This can be explained further as:
For the base function f (x) and a constant k > 0, the function given by:
[tex]\begin{gathered} h(x)=k\cdot f(x) \\ A\text{ vertical shrinking of f\lparen x\rparen by k factor where }0Calculate the equation that represents h in terms of x[tex]\begin{gathered} f(x)=-(x+5)^2-6 \\ h(x)=\frac{1}{3}\cdot f(x)=\frac{1}{3}\cdot-(x+5)^2-6 \end{gathered}[/tex]Hence, the transformation from the graph is a vertical shrinking by 1/3 factor and the equation that represents h in terms of x is given as:
[tex]\frac{1}{3}\times(-(x+5)^2-6)[/tex]Give the slope and y - intercept for each of the following equations, then sketch the graph. Give the slope ofany line perpendicular to the given line.y =22 +5Slope =y - intercept = (0,_ ) Slope of a Line Perpendicular =
The slope is 2.
The y-intercept is 5 or (0, 5)
See graph below
Explanation:Given:
y = 2x + 5
To find:
the slope, y-intercept, and plot a graph
To determine the slope and y-intercept, we will use the equation of line formula:
y = mx + b
m = slope
b = y-intercept
Comparing both equations:
y = y
2x = mx
m = 2
The slope = 2
5 = b
The y-intercept = 5
To plot the graph, we will assign values to x in order to get values to y that will be plotted:
let x = -4, 0, 4
when x = -4
y = 2(-4) + 5 = -3
when x = 0
y = 2(0) + 5 = 5
when x = 4
y = 2(4) + 5 = 13
Plotting the points:
Each line on the graph represents 1 unit
Is the slope the same or different?Is the Y-intercept same or different?Is there infinitely many solutions or not?
Answer:
Explanation:
Here, we want to answer the questions given
a) To answer this, we have to write the equations in the slope-intercept form:
The slope-intercept form is:
[tex]y\text{ = mx + b}[/tex]m is the slope while b is the y-intercept
The equations would be:
[tex]\begin{gathered} y\text{ = 7x-2} \\ y\text{ = 7x-2} \end{gathered}[/tex]We can see that the equations are same
Since the equations are same, the slope is same which is 7
b) The y-intercept value is same too
c) Since the equations are same, there are infinitely many solutions for the system of equations
I need help finding the exact perimeter. Special right triangles.
Answer:
The exact perimeter of the square is;
[tex]56\sqrt[]{2}[/tex]Explanation:
Given the square in the attached image.
The length of the diagonal is;
[tex]d=28[/tex]Let l represent the length of the sides;
[tex]\begin{gathered} l^2+l^2=28^2 \\ 2l^2=784 \\ l^2=\frac{784}{2} \\ l^2=392 \\ l=\sqrt[]{392} \\ l=14\sqrt[]{2} \end{gathered}[/tex]The perimeter of a square can be calculated as;
[tex]\begin{gathered} P=4l \\ P=4(14\sqrt[]{2}) \\ P=56\sqrt[]{2} \end{gathered}[/tex]Therefore, the exact perimeter of the square is;
[tex]56\sqrt[]{2}[/tex]In the rhombus m<1 = 160 what are m<2 and m<3. This diagram is not drawn to scale. Show all work
We are given a rhombus shape.
The measure of angle ∠1 = 160°
Recall that in a rhombus, the oppsite angles are equal, this means ∠1 = ∠2
So, ∠2 = 160°
Recall that the sum of all four interior angles in a rhombus must be equal to 360°
The diagonal line divides the angles in half.
This means that angle 3 and angle x are equal.
[tex]\begin{gathered} 160\degree+160\degree+2(\angle3+x)=360\degree_{} \\ 320\degree+2(\angle3+x)=360\degree \\ 2(\angle3+x)=360\degree-320\degree \\ 2(\angle3+x)=40\degree \\ \angle3+x=\frac{40\degree}{2} \\ \angle3+x=20\degree \end{gathered}[/tex]Since we know that ∠3 and ∠x are equal then
∠3 = 10° and ∠x = 10°
Therefore,
∠2 = 160°
∠3 = 10°
What is the domain for the following function? 2x . - 3 O A. (x+3) O B. {**-3) O c. {*#0 O D. all real number ers
Given,
y = 2x/x - 3
to solve this,
let's equate the denominator to 0
so,
y = 2x/0
this means undefined
recall,
Domain is the set of all possible values of x. Since the function is undeined when the denominator is zero, the domain is the set of all real numbers except the value which will make the denominator zero
so the domain for the function y = 2x/x - 3
is x is not equal to 3
therefore, the correct option is
[tex]A.\mleft\lbrace x\ne3\mright\rbrace[/tex]Solve the inequality X - (5 - 3x) = 2x - 1
hi,
x - (5 - 3x) = 2x - 1
x - 5 + 3x = 2x - 1
x - 2x + 3x = -1 + 5
2x = 4
x = 4/2
x =< 2
[tex]\text{ x }\leq\text{ 2}[/tex]
The result is letter A, the first choice
What is the missing coefficient of the x-term of the product (−x−5)^2 after it has been simplified?−25−101025
Given:
The terms is
[tex](-x-5)^2[/tex]Required:
What is the missing coefficient of the x-term of the product after it has been simplified?
Explanation:
We have to find the missing coefficient of the x term of the given product
We know
[tex](a-b)^2=a^2-2ab+b^2[/tex]So,
[tex](-x-5)^2=x^2+10x+25[/tex]Therefore, the missing coefficient of the x-term is 10.
Answer:
Therefore, the missing coefficient of the x-term is 10.
how do you find the exponential equation for growth? or what is the exponential equation for growth?
Answer:
The equation f(x) = a(1 + r)x can also be used to compute exponential growth, where:
The function is represented by the word f(x).
The initial value of your data is represented by the a variable.
The growth rate is represented by the r variable.
Time is represented by the variable x.
26.219 Miles in 128 minutes. what is speed in km per minute?
26.219 Miles in 128 minutes.
First we have to convert miles to km:
Since 1 mile = 1,609 km
26.219 x 1,609 = 42,041.561 km
Then divide the distance by the time:
42,041.561/ 128 = 192.85 km per minute
What 3D shape will be formed when the following are rotated around the axis
a)
A washer will be formed
b)
A cone will be formed
C)
A sphere will be formed
Which system of inequalities is shown?-5O A. y>xy<4OB. y> xy> 4C. y< xy<4OD. y< xy> 45
Given:
a graph of the inequalities is given.
Find:
we have to find the correct inequalities.
Explanation:
From the graph , it is observed that the value of y > x and y < 4,
Therefore, the correct inequalities are y > x,
y < 4.
Hence, correct option is A.
the bears have won 7 and tied 2 of their last 13 games. the not forfeited any games . which ratio correctly campares their to losses
Explanation:
Number of games won = 7
Number of games drawn = 2
Total number of games = 13
Number of games lost = Total number of games - (Number of games won + Number of games drawn)
Number of games lost = 13 - (7 + 2) = 13 - 9
Number of games lost = 7
The ratio of