According to the problem, the recursive rule is
[tex]\begin{gathered} f(1)=15 \\ f(n)=f(n-1)-6 \end{gathered}[/tex]This means the first term of the sequence is 15.
So, for n = 2, we have
[tex]f(2)=f(2-1)-6=f(1)-6[/tex]But, we know that f(1) = 15, so
[tex]f(2)=15-6=9[/tex]The second term is 9.
For n = 3.
[tex]f(3)=f(3-1)-6=f(2)-6[/tex]But, we know that f(2)=9, so
[tex]f(3)=9-6=3[/tex]Therefore, the third term is 3.hi can you help please, I have to turn this in soon
The sum of the interior angles of a triangle is 180. Besides, the angle that is missing is suplementary (sums 180) to 153. So we have the next equation
[tex]\begin{gathered} (x-4)+(2x+10)+(180-153)=180 \\ x+2x=180+4-10-180+153 \\ 3x=147 \\ x=49 \end{gathered}[/tex]what is the value of x in the equation below √x+2=5
Can u please help me. I'll send the other options to u as well
Explanation
We are told to fi
In how many ways can 6 photos be arrangedon a wall?
Solution
We can use the multiplication principle and we have:
6!= 6*5*4*3*2*!= 720 ways
Luigi uses 39 cups of flour for every 6 pizzas he makes. Complete the table using equivalent ratios. Flour (cups) Pizzas 39 6 I Mla 13
Given:
39 cups of floor = 6 pizzas
Let's find the number of cups of floor for 1 pizza:
[tex]\frac{39}{6}=6.5\text{ cups}[/tex]Therefore, to make 1 pizza, 6.5 cups of floor is needed.
From the table, we have:
4 pizzas = 6.5 x 4 = 26 cups of floor
13 cups of floor =
[tex]\frac{13}{6.5}=2[/tex]ANSWER:
Floor(cups) Pizzas
39 6
26 4
13 2
find the surface area of the tunnel created inside the block.
The surface area of the tunnel passing through the block is simply the curved surface area of the cylindrical shape.
The Surface Area is given by
[tex]A=2\pi rh[/tex]where the following are given from the question:
[tex]\begin{gathered} r=\frac{4}{2}=2ft \\ h=4ft \end{gathered}[/tex]Substituting these values:
[tex]\begin{gathered} A=2\times\pi\times2\times4 \\ A=50.27 \end{gathered}[/tex]Therefore, the surface area of the tunnel created inside the block is 50.27 ft² (50.27 square feet)
Describe all numbers x that are at a distance of 14 from the number −5. Express this using absolute value notation.
The distance (d) between two numbers a and b equals the absolute value of their difference:
[tex]d=|a-b|[/tex]If a number x is at a distance of 1/4 from the number -5, then:
[tex]|x-(-5)|=\frac{1}{4}[/tex]Solve for x. Remember that when an equation involves a variable inside an absolute value, two cases must be considered: If the expression inside the absolute value is positive or if it is negative.
Case 1: x-(-5) is positive.
Then:
[tex]|x-(-5)|=x-(-5)[/tex]Solve for x:
[tex]\begin{gathered} |x-(-5)|=\frac{1}{4} \\ \Rightarrow x-(-5)=\frac{1}{4} \\ \Rightarrow x+5=\frac{1}{4} \\ \Rightarrow x=\frac{1}{4}-5 \\ \therefore x=-\frac{19}{4} \end{gathered}[/tex]Case 2: x-(-5) is negative.
Then:
[tex]|x-(-5)|=-(x-(-5))[/tex]Solve for x:
[tex]\begin{gathered} |x-(-5)|=\frac{1}{4} \\ \Rightarrow-(x-(-5))=\frac{1}{4} \\ \Rightarrow-(x+5)=\frac{1}{4} \\ \Rightarrow x+5=-\frac{1}{4} \\ \Rightarrow x=-\frac{1}{4}-5 \\ \therefore x=-\frac{21}{4} \end{gathered}[/tex]Therefore, all the numbers that are at a distance of 1/4 from the number -5 are -21/4 and 19/4. They can be described by the equation:
[tex]|x-(-5)|=\frac{1}{4}[/tex]
Simplify each of the fractions. If there is no answer, enter "undefined."A. 4/12
Answer:
undefined
Step-by-step explanation:
What is 0 if 0degrees is less than or equal to 0 less than 360 degrees
Solution
On a unit circle,
Since it's a unit circle, the radius is 1.
[tex]\begin{gathered} \sin\theta=\frac{\sqrt{2}}{2} \\ \\ \Rightarrow\theta=\arcsin(\frac{\sqrt{2}}{2})=45^0 \end{gathered}[/tex]Hence, the correct option is C. 45
Can someone help me with these geometry questions it’s a three parter?The options for A are cone,cylinder,rectangular prism, and sphere
Part A.
In the picture, we can see that it has a circular base and from it it goes right with the same shape for each section, so this is a prism. Since its base is a circle, this is close to a cylinder.
Part B.
The diameter of the base and the length is shown, so we just need to draw a cylinder and put these measures:
The net of a cylinder has the two circles of the base and the middle part is unfolded to form a rectangle:
Part C.
The amount of plastic they will need corresponds to the surface area of the cylinder, and the net draw unfold the shape into a 2 dimensional draw, so we can use it to determine the surface area of the cylinder, which will lead us to the amount of plastic needed.
what is the volume in cubic inches of a cylinder with a height of 20 inches and a base radius of 2in to the nearest tenths place
1) We've been told that this is a cylinder. So we can find out its volume by making use of this formula below:
[tex]V_{\text{cylinder}}=\pi\cdot r^2\cdot h[/tex]2) So let's plug into that the given information:
[tex]\begin{gathered} V_{\text{cylinder}}=\pi\cdot r^2\cdot h \\ V_{\text{cylinder}}=\pi\cdot(2)^2\cdot20 \\ V_{\text{cylinder}}=80\pi in^3 \\ V_{\text{cylinder}}\approx251.3in^3 \end{gathered}[/tex]3) Hence, the volume of that cylinder rounded off to the nearest tenth is 251.3 in³
Tools - Question 1 In the right triangle shown, what is the value of PQ? 17 cm 15 cm A 2 cm B 4 cm с 8 cm OLULI Illuminate Education TM Inc.the answer choices is a. 2cm, b, 4cm. c,8cm.d, 16cm
Answer:
c. 8
Explanation:
The Pythagorean theorem says that if we have a right triangle with sides a, b, and c, where c is the longest side, then, the following equation applies:
[tex]c^2=a^2+b^2[/tex]In this case, we know the value of c and the value of one of the sides, so we can replace the values and solve the equation for the missing side. Therefore, the value of PQ can be calculated as:
[tex]17^2=15^2+\bar{PQ}^2[/tex]So, solving for PQ, we get:
[tex]\begin{gathered} 289=225+\bar{PQ}^2 \\ 289-225=225+\bar{PQ}-225 \\ 64=\bar{PQ} \\ \sqrt[]{64}=\bar{PQ} \\ 8=\bar{PQ} \end{gathered}[/tex]Therefore, the value of PQ is 8 cm.
1) The depth of a lake in Lowell changes over time due to rainfall and evaporation. A few months ago, the depth was 70 feet. Currently, the depth is 63 feet. By what percent has the depth of the lake decreased?
To find the percentage decrease, we will simply use the the formula;
new depth - original depth /original depth x100%
new depth =63 feet
original depth = 70 feet
63 - 70 / 70 x100%
-7/70 x100%
= -10% or 10% decrease.
Find the value of the variable,3m + 5 4m - 10A )-5B) - 3/4C)0D)15
A to B is same distance as B to C
We can thus say:
AB = BC
AB is 3m + 5
BC is 4m - 10
So,
AB = BC
3m + 5 = 4m - 10
Now, we simply do algebra and solve this equation for m. Shown below:
[tex]undefined[/tex]Matilda builds model. The model is a right rectangular prism and a small cube. How much area does she have to paint if she paints all of the exterior? cube: l:4 w:4 h:4rectangular prism: l:17 w: 14 h: 15
The exterior area for the paint consist of 5 faces of cube and six faces of rectangular prism minus one face of cube, as one face of cube is placed on upper surface of rectangular prism and covers the certain area of rectangular prism.
Determine the exterior area available for the paint.
[tex]\begin{gathered} A=2(15\cdot14+17\cdot14+17\cdot15)-4\cdot4+5\cdot4\cdot4 \\ =2(210+238+255)-16+80 \\ =1406-16+80 \\ =1470 \end{gathered}[/tex]So area for the paint to the exterior is 1470 square inch.
Compare: 0.008 O 0.08A.>B.
We have the next two numbers
[tex]0.008\text{ and }0.08[/tex]To compare two decimal numbers we need to know that the smaller number will be
1. The one with the smallest integer
2. If the numbers have the same integer part, the one with the smallest decimal part.
In this case, the numbers have the same integer part, so we must compare their decimal parts.
To compare the decimal parts we need to take the numbers after the decimal point
[tex]008\text{ and }08[/tex]Then, We must add 0 to the right of the number with the least amount of digits until the 2 numbers have the same amount
So, we would have
[tex]008\text{ and }080[/tex]Now, we can see that 8 < 80. Then,
[tex]0.008<0.08[/tex]ANSWER:
B) <
show the opposite of 10
To find the opposite of a number we can draw a number line.
If we go to the right of zero, we have positive numbers.
TO the left, we have negative numbers.
The opposite of a number is the number that is the same distance from zero but on the other side.
So, the opposite of 10 is -10.
Consinder this set of expressions.3 -4. -2 + -3. -5 - 4part a: Simplfy each expression.A: 3 =B: -4 =C: -2 + -3 =D: -5 - -4=part b: graph each value on the number line. label the points.
The absolute value of a negative number is the positive of that same number. Therefore,
Part A
[tex]\lvert3\rvert=3[/tex][tex]-\lvert4\rvert=-4[/tex][tex]\lvert-2\rvert+\lvert-3\rvert=2+3=5[/tex][tex]\lvert-5\rvert-\lvert4\rvert=5-4=1[/tex]part B
Which of the following statements says that a number is between -3 and 3?Olx = 3Olx <3Olx > 3
If |x|=3, then x can either be 3 or -3.
If |x| < 3, then x < 3 or -x < 3. Multiplying -1 on both sides of the second inequality, we have the following.
[tex]\begin{gathered} x<3 \\ \\ x>-3 \end{gathered}[/tex]This mea
which equation represents a circle with a center located at ( -2, 2) and a circumference of 16 pi?
Explanation:
The equation of a circle with center located at (x1, y1) and radius r is:
[tex](x-x_1)^2+(y-y_1)^2=r^2[/tex]We have the point but we need to find r. For that we can use the equation of the circumference:
[tex]C=2\pi r[/tex]We have C = 16pi:
[tex]\begin{gathered} 16\pi=2\pi r \\ \frac{16\pi}{2\pi}=r \\ r=8 \end{gathered}[/tex]Now we have r = 8, therefore r²=64. The answers could be either option 1 or option 3. To find out which one is it we have to check the point.
If the point is (-2, -2) then the part with x is (x - (-2))² = (x+2)² and the part with y is (y - 2)²
Answer:
The correct equation is option 3:
[tex](x+2)^2+(y-2)^2=64[/tex]during one day in a hardware store, 37 people came in and made a purchase, and 13 people looked around but didnt purchase anything. Express the following ratios
In the day the number of purchasers was 37 and the number of nonpurcharses is 13
To determine the purchasers/nonpurchasers you have to divide the number of people that purchased something by the number of people that only browsed the store
[tex]\frac{37}{13}[/tex]The nonpurchasers to purcharsers ratio follows the same logic, divide the number of people that didn't buy something by the number of people that made purchases
[tex]\frac{13}{37}[/tex]The total customers of the store is
[tex]37+13=50[/tex]The ratio purchasers to total customers ratio is
[tex]\frac{37}{50}[/tex]Find the 5th term ofSn = 4h + 5n
Given the equation of the sequence:
[tex]S_n=4n+5n[/tex]To find the 5th term, substitute with n = 5
So,
[tex]S_5=4\cdot5+5\cdot5=20+25=45[/tex]So, the answer will be the 5th term = 45
the cost C in dollars sign of producing X items in the equation C equals x over 7 plus 1 which of the following choices will find the cost C if x is 35
Writing the equation described, we have:
[tex]C=\frac{x}{7}+1[/tex]Now, calculating the value of the cost C for x equal to 35, we have:
[tex]\begin{gathered} C=\frac{35}{7}+1 \\ C=5+1 \\ C=6 \end{gathered}[/tex]So the cost C for 35 products is $6.
Which table shows a constant rate of change of $3.25? *Which table shows a constant rate of change of $3.25?Cost of Ham Sandwiches13 5 73.25 10.50 16 22.25Cost of Ham Sandwiches1 3 5 73.25 9.75 16.25 22.75HhСhСF3GCost of Ham Sandwiches1 3 S 73.25 9.50 16.25 22.50Cost of Ham Sandwiches1 3 5 73.25 9.75 15.25 21.75hсhc С
The costant rate of change can be expressed as,
[tex]R=\frac{\Delta C}{\Delta h}[/tex]Consider table H.
The constant rate of change can be calculated as,
[tex]\begin{gathered} R=\frac{\Delta C}{\Delta h}=\frac{9.75-3.25}{3-1}=3.25 \\ R=\frac{\Delta C}{\Delta h}=\frac{16.25-9.75}{5-3}=3.25 \\ R=\frac{\Delta C}{\Delta h}=\frac{22.75-16.25}{7-5}=3.25 \end{gathered}[/tex]Therefore, table H shows a constant rate of change of $3.25.
Find the equation of the line with the given slope and containing the given point: Slope -6/5 through (- 9,0)
From the given: Slope (m) = -6/5 and point (-9, 0), we will use the Slope-Intercept Form in making the equation.
[tex]\text{ y = mx + b}[/tex]The slope-intercept form is given a y=mx+b where m is the slope and b is the y-intercept at point (0,b).
Let's solve for the y-intercept (b) substituting the slope (m) = -6/5 and (x,y) = (-9,0).
Thus, we get,
[tex]\text{ y =mx + b}[/tex][tex]\text{ 0 = (}\frac{-6}{5})(-9)\text{ + b }\rightarrow\text{ b = -(}\frac{-6\text{ x -9}}{5})\text{ = }\frac{-54}{5}[/tex]Let's now make the equation substituting the slope (m) = (-6/5) and y-intercept (b) = (-54/5). We get,
[tex]\text{ y = (}\frac{-6}{5})x\text{ + (}\frac{-54}{5})[/tex][tex]\text{ y = -}\frac{6}{5}x\text{ - }\frac{54}{5}[/tex]just so you know you can use half numbers for example 46.5 or 24.5 etc.
Given:
[tex]61,63,63,64,67,67,69,72,73,74,75,79,81,85,86,87,89,92[/tex]To draw:
The box and whisker plot.
Explanation:
According to the given data,
The minimum of the data is 61.
The maximum of the data is 92.
Since the total number of data is n = 18 which is even.
So, the median formula is given by,
[tex]\begin{gathered} Q_2=\frac{(\frac{n}{2})^{th}term+(\frac{n}{2}+1)^{th}term}{2} \\ =\frac{(\frac{18}{2}){^{th}term+(\frac{18}{2}+1)^{th}term}}{2} \\ =\frac{9^{th}term+10^{th}term}{2} \\ =\frac{73+74}{2} \\ =\frac{147}{2} \\ Q_2=73.5 \end{gathered}[/tex]Therefore, the median is 73.5.
Then, the lower quartile is the median of the lower half of the data.
The lower half data are,
[tex]\begin{equation*} 61,63,63,64,67,67,69,72,73 \end{equation*}[/tex]The middle term is 67.
Therefore, the lower quartile is 67.
The upper quartile is the median of the upper half of the data.
The upper half data are,
[tex]\begin{equation*} 74,75,79,81,85,86,87,89,92 \end{equation*}[/tex]The middle term is 85.
Therefore, the upper quartile is 85.
So, the box and whisker plot is,
Andy rode his bike 2 4/5 miles on monday. tuesday 1 3/10 miles. how many total miles did andy ride on the 2 days?
The problem is asking us to add two mixed numbers in order to calculate the number of miles ridden.
So in order to be able to add them, we need to convert them in fraction form and afterwards find a common denominator to add them.
The mixed number: 2 4/5 is the same as 10/5 + 4/5 = 14/5
The mixed number 1 3/10 = 10/10 + 3/10 = 13/10
Noe, we need to add them:
14/5 + 13/10, and we notice that the Least Common Denominator for these two fractions is: "10". So we write the first one with denominator 10 by multiplying numerator and denominator by "2":
14/5 + 13/10 = 28/10 + 13/10 = 41/10
Now, we write this improper fraction in mixed number form:
41/10 = 40/10 + 1/10 = 4 1/10
So the person rode a total of 4 1/10 miles
Use the tables to name the zeros,their multiplicity,and the effect of the multiplicity on the graph. (In the effect boxes it should be either bounces or intersects) SPELL PROPERLY
We have
[tex]x^2(x-1)^4(x+5)[/tex]First we will find the zeros,
for the term x^2
[tex]x^2=0[/tex][tex]x=0[/tex]for the term (x-1)^4
[tex](x-1)^4=0[/tex][tex]x-1=0[/tex][tex]x=1[/tex]for the terms (x+5)
[tex]x+5=0[/tex][tex]x=-5[/tex]zeros
x=-5
x=0
x=1
Then with the multiplicity
Because we have a power of 1 in (x+5), x=-5 has a multiplicity of 1
Because we have a power of two in x^2, x=0 has multiplicity 2
Because we have a power of 4 in (x-1)^4, x=1 has a multiplicity of 4
For the effect
x+5 has an odd power the effect will be crosses
x^2 has an even power the effect will be bounces
(x-1)^4 has an even power the effect will be bounces
, x
What are the sides of the triangle in order ?
Solution:
To solve this problem, we need to know a principle:
The higher the angle is, the longer the side opposite the angle.
Since the largest angle is angle C which is 81 degrees, the side opposite it is the longest which is AB.
The second-largest angle is angle A which is 60.4 degrees and its opposite side is side BC.
The smallest angle is angle B which is 38.6 degrees with an opposite side of side AC.
ANSWER: AB, BC, AC (Last Option)
15x + 21 ≥ 120 what's the inequality
Given the inequality:
[tex]\text{ 15x + 21 }\ge\text{ 120}[/tex]Let's determine the solution to the inequality.