Given:
The sequence is:
8, 4, 2, 1,...
Required:
Find a recursive formula for the given sequence.
Explanation:
The given sequence is:
8, 4, 2, 1,...
The common ratio of the sequence is:
[tex]\begin{gathered} \frac{4}{8}=\frac{1}{2} \\ \frac{2}{4}=\frac{1}{2} \\ \frac{1}{2} \end{gathered}[/tex]Since the common ratio for the given series is 1/2.
[tex]\begin{gathered} \frac{T_{n+1}}{T_n}=\frac{1}{2} \\ T_{n+1}=\frac{1}{2}T_n \end{gathered}[/tex]Final Answer:
The recursive formula for the given sequence is
[tex]T_{n+1}=\frac{1}{2}T_{n}[/tex]Use f(x)=-x-8 and g(x) = x² + 8x − 15 to answer the following: a) f(1) + g(–3) b) g(−9) − f(–7)
ANSWER:
a) -37
b) 9
Given:
f(x)=-x-8 and g(x) = x² + 8x − 15
a) f(1) + g(–3)
f(1) = 1 - 8 = -7
g(-3) = -3² + 8(-3) - 15 = 9 - 24 - 15 = -30
f(1) + g(–3) = -7 + (-30)
= -7 - 30
-37
b) g(−9) − f(–7):
g(-9) = -9² + 8(-9) - 15 = 81 - 72 - 15 = -6
f(-7) = -7 - 8 = -15
Thus,
g(−9) − f(–7) = -6 - (-15)
= -6 + 15
= 9
A sector with a central angle measure of \purpleD{\dfrac{\pi}{6}} 6π start color #7854ab, start fraction, pi, divided by, 6, end fraction, end color #7854ab (in radians) has a radius of \maroonD{12\,\text{cm}}12cmstart color #ca337c, 12, start text, c, m, end text, end color #ca337c.
EXPLANATION:
Given;
We are given a sector of a circle with the following dimensions;
[tex]\begin{gathered} radius=12 \\ central\text{ }angle=\frac{\pi}{6} \end{gathered}[/tex]Required;
We are required to calculate the area of the sector with the details given.
Step-by-step solution;
To calculate the area of a sector with the central angle given in radians, we will use the following formula;
[tex]Area\text{ }of\text{ }a\text{ }sector=\frac{\theta}{2\pi}\times\pi r^2[/tex]We can now substitute and solve;
[tex]Area=\frac{\frac{\pi}{6}}{2\pi}\times\pi r^2[/tex][tex]Area=(\frac{\pi}{6}\div\frac{2\pi}{1})\times\pi r^2[/tex][tex]Area=(\frac{\pi}{6}\times\frac{1}{2\pi})\times\pi\times12^2[/tex][tex]Area=\frac{1}{12}\times144\times\pi[/tex][tex]Area=12\pi[/tex]ANSWER:
In terms of pi the area of the sector is
[tex]undefined[/tex]Which number is located between 8710and95?
-8 7/10 and -9 2/10
-8-7/10 = -87/10
-9 - 2/10= -92/10
Answer is -9 1/10 = -91/10
because -91 is between -87 and -92
Answer is OPTION B))
Aaron received credit of$48 on a purchase of $960. What percent of$960 is 48%?
we have
[tex]\begin{gathered} \frac{48}{960}=\frac{x}{100} \\ 100\times\frac{48}{960}=100\times\frac{x}{100} \\ x=5 \end{gathered}[/tex]answer: 5%
Show how Aaliyah can finish her work using complexnumbers. As a reminder, her last step before requiringassistance is:(x- 3)2=1Be sure to show ALL steps that lead to your finalsolution set!
aAs given by the question
There are given that the equation
[tex]x^2-6x+10=0[/tex]Now,
The solution of the Aaliyah is:
[tex](x-3)^2=-1[/tex]Then,
The next step of the given solution is:
[tex]\begin{gathered} (x-3)^2=-1 \\ x-3=\sqrt[]{-1} \end{gathered}[/tex]According to the concept of complex number
[tex]i=\sqrt[]{-1}[/tex]So,
[tex]\begin{gathered} x-3=\sqrt[]{-1} \\ x-3=i \\ x=i+3 \end{gathered}[/tex]Provide reasons for the proofGiven line m is parallel to line nprove angle 1 is supplementary to angle 3
The first reason is Given.
The second is corresponding angles theorem.
The third one is definition of congruent angles.
The fourth is definition of linear pair.
The fifth is linear pair theorem.
The sixth is definition of supplementary angles.
The seventh is addition property of equality.
The eighth is definition of supplementary angles.
A gold bar is similar in shape to a rectangular prism. A gold bar is approximately 7 1 6 in. x2 in. x 1 in. If the value of gold is $1,417 per ounce, about how much 8 2 is one gold bar worth? Use the formula w ~ 11.15n, where w is the weight in ounces and n= volume in cubic inches, to find the weight in ounces. Explain how you found your answer.
ANSWER and EXPLANATION
We want to find how much the gold bar is worth.
First, we have to find the volume of the gold bar.
The volume of a rectangular prism is:
[tex]\begin{gathered} V=L\cdot W\cdot H \\ L=\text{length;} \\ W=\text{width;} \\ H=\text{height} \end{gathered}[/tex]Therefore, the volume of the gold bar is:
[tex]\begin{gathered} V=6\cdot2\frac{7}{8}\cdot1\frac{1}{2} \\ V=6\cdot\frac{23}{8}\cdot\frac{3}{2} \\ V=25.88\text{ cubic inches} \end{gathered}[/tex]Now, convert the volume to weight y using:
[tex]\begin{gathered} w\approx11.15n \\ \text{where w = weight in ounces; n = volume in cubic inches} \end{gathered}[/tex]Therefore, its weight is:
[tex]\begin{gathered} w\approx11.15\cdot25.88 \\ w\approx288.56\text{ ounces} \end{gathered}[/tex]Finally, multiple the weght by the value of gold:
[tex]\begin{gathered} \text{Worth}=288.56\cdot1417 \\ \text{Worth}=\text{ \$}408,889.52 \end{gathered}[/tex]Therefore, the volume of the gold bar is about 25.88 in³, so the weight is approximately 288.56 ounces. So one gold bar is worth about $408,889.52
Peter, a cyclist, rides 5.673 kilometers, takes a break, and then rides an additional 4321 meters.a. How many hectometers total did he ride?How many decimeters did he ride?
Explanation:
a) First Distance = 5.673 kilometers
2nd distance = 4321 meters
Total distance = 1st distance + 2nd distance
Total distance = 5.673 kilometers + 4321 meters
Conversion from kilometers to meters:
1 kilometer = 1000meters
5.673 kilometers = 5673 meters
Total distance in meters = 5673 meters + 4321 meters
Total distance in meters = 9994 meters
Conversion of meters to hectometers:
100 meters = 1 hectometers
9994 meters = x
cross multiply:
100(x) = 9994(1)
100x = 1994
x = 1994/100
x = 19.94 hectometers
Hence, he rode 19.94 in hectometers
b) converting to decimeters:
It is easier to convert from meters to decimeters
0.1 meters = 1 decimeter
9994 meters = y
y(0.1) = 1(9994)
0.1y = 9994
y = 9994/
y=3sin(1/2 x+pi/6)please find amplitude period and phase shift
The given function is
[tex]y=3\sin (\frac{1}{2}x+\frac{\pi}{6})[/tex]We have to use the following form
[tex]a\sin (bx-c)+d[/tex]Where the amplitude is a, the period is 2pi/b, and the phase shift is c/b. In the given function a = 3, b = 1/2, and c = pi/6.
[tex]\begin{gathered} a=3 \\ T=\frac{2\pi}{b}=\frac{2\pi}{\frac{1}{2}}=4\pi \\ \theta=\frac{c}{b}=\frac{\frac{\pi}{6}}{\frac{1}{2}}=\frac{2\pi}{6}=\frac{\pi}{3} \end{gathered}[/tex]Therefore, the amplitude is 3, the period is 4pi, and the phase shift is pi/3.Emmanuel added two integers Which condition will always give Emmanuel a negative solution when he adds two integers? Both integers have negative values Both integers have positive values O. One integer has a positive value, and one integer has a negative value O The values of the two integers are opposites
Both integers have negative values
Explanation
Let
x and y represents the number
so, the options are
[tex]\begin{gathered} +\text{ + +} \\ +\text{ + -} \\ -\text{ + +} \\ -\text{ +-} \end{gathered}[/tex]a) Both integers have negative values Both integers
[tex]-x-y=-(x+y)\rightarrow you\text{ will always get a negative number}[/tex]b) Both integers have positive values
[tex]x+y=+\text{ + += you will always get a positive number}[/tex]c)One integer has a positive value, and one integer has a negative value
[tex]\begin{gathered} -x+y\text{ or x-y} \\ the\text{ sign of the result depends on the greates absolute value, it means the answer will have the same of the bigger number( absolute value)} \end{gathered}[/tex]d)The values of the two integers are opposites
as the point C , the sign depends on the bigger number
for example
[tex]\begin{gathered} 8-5=3\text{ positive because 8 is the bigger} \\ 5-8=-3\text{ negative because (-8) is has the bigger absolute value} \end{gathered}[/tex]so, the answer is Both integers have negative values
I hope this helps you
levon scored 38 points in the first half of the basketball game, and he scored p points in the second half of the game. write an expression to determine the number of points he scored in all. then, find the number of points he scored in all if he scored 20 points in the second half of the game.
By the given information you can raise the following equation, and since levon scored 38 points in the first half of the basketball game, then
[tex]\begin{gathered} TP=38+n \\ \text{Where} \\ TP\colon\text{ the number of points that he scored in total.} \\ n\colon\text{ the number of points that he scored in the second half of the game} \end{gathered}[/tex]So, if n=20
[tex]\begin{gathered} TP=38+n \\ TP=38+20 \\ TP=58 \end{gathered}[/tex]Therefore, if Levon scored 20 points in the second half of the game, in all he scored 58 points.
Given that every tenth person in line will get a coupon for a free box of popcorn at the movies what is the probability that you don't get a coupon when your in line
SOLUTION:
Step 1:
In this question, we are given the following:
Given that every tenth person in line will get a coupon for a free box of popcorn at the movies.
We are meant to find the probability that you don't get a coupon when you are in the line.
Step 2:
We can see that the probability that the person was in the line and got a coupon is:
[tex]\frac{1}{10}[/tex]Then, the probability that the person did not get a coupon when he was in the line is:
[tex](\text{ 1 -}\frac{1}{10})\text{ = }\frac{9}{10}[/tex]The answer and how to do it
Answer:
v ≈ 4 cm
Step-by-step explanation:
using the Sine rule in Δ VWX
[tex]\frac{v}{sinV}[/tex] = [tex]\frac{w}{sinW}[/tex]
where v = WX and w = VX
∠ W = 180° - (126 + 21)° = 180° - 147° = 33° , then
[tex]\frac{v}{sin21}[/tex] = [tex]\frac{6}{sin33}[/tex] ( cross- multiply )
v × sin33° = 6 × sin21° ( divide both sides by sin33° )
v = [tex]\frac{6sin21}{sin33}[/tex] ≈ 4 cm ( to the nearest cm )
what is the perimeter of 6.05m and 3.5m
Recall that the perimeter P of a rectangle is given as
P = 2(L + B)
where L is the length and B is the width of the rectangle
Given that the length is 6.05m and the width is 3.5m
Then the perimeter
= 2(6.05 + 3.5)
= 2 (9.55)
= 19.10m
Find the area of a circle with a diameter of 15 units round your answer to the nearest whole
The area of the circle is 177 units^2
Explanation:Given:
diameter of the circle = 15 units
To find:
the area of the circle
The formula for the area of a circle = πr²
let π = 3.14
diameter = 2(radius)
radius = diameter/2
radius = 15/2 = 7.5 units
[tex]\begin{gathered} Area\text{ of the circle = 3.14}\times7.5^2 \\ \\ Area\text{ of the circle = 176.625} \\ \\ To\text{ the nearest whole number, the area of the circle is 177 units}^2 \end{gathered}[/tex]Write the sequence of transformations that changes figure ABCD to figure A’B’C’D. Explain your answer and write the coordinates of the figure obtained after each transformation. Are the two figures congruent? Explain your answer.
SOLUTION:
We can compare a point to get the translation.
We can use the point;
[tex]A(-4,4)[/tex]which transforms to;
[tex]A^{\prime}^^{\prime}(3,-4)[/tex]The first transformation is a reflection over the x-axis to map point A to;
[tex]A^{\prime}(-4,-4)[/tex]The next transformation is a translation 7 units to the right.
Therefore, the sequence of transformations are;
Part B: The two figures are congruent because the transformations used are non-rigid.
Brad thinks that 2.2.2.2 is represented by 4^2.What is wrong with this answer?
There is nothing wrong in the answer because
[tex]2\cdot2\cdot2\cdot2=4\cdot4=4^2[/tex]but it should be represented by
[tex]2\cdot2\cdot2\cdot2=2^4[/tex]Hannah bought a total of 5.12 pounds of fruit at the market. she bought 2.5 pounds of pears and she also bought some bananas. how many pounds of bananas did she buy please show work and answer
Hannah bought pears and bananas only, so let's write the following equation:
[tex]\text{total}=\text{pears}+\text{bananas}[/tex]If the total weight bought is 5.12 and 2.5 pounds are pears, we can calculate the weight of bananas bought:
[tex]\begin{gathered} 5.12=2.5+\text{bananas} \\ \text{bananas}=5.12-2.5 \\ \text{bananas}=2.62 \end{gathered}[/tex]So Hannah bought 2.62 pounds of banana.
Graph the line x=3 .
According to the given equation, x=3, the line that represents it is a vertical line that passes throught the x axis at x=3.
This is a constant line, which means that for all the values of y, x will always be 3.
The graph of this line is the following:
A line cuts the y-axis at (0, -6) and passes through the point (9, -3). Find the equation of the line.
point 1 (0,-6) and point 2 (9,-3)
the equation is
[tex]y-y1=m(x-x1)[/tex]where m =
[tex]m=\frac{y2-y1}{x2-x1}=\frac{-3-(-6)}{9-0}=\frac{-3+6}{9}=\frac{3}{9}=\frac{1}{3}[/tex]answer: the equation of the line is
[tex]\begin{gathered} y-(-6)=\frac{1}{3}(x-0) \\ y+6=\frac{1}{3}x \\ y+6-6=\frac{1}{3}x-6 \\ y=\frac{1}{3}x-6 \end{gathered}[/tex]I need help with these two problems.Use the given functions solve:f(x)=6x+7. g(x)= -2x-4. h(x)= -3x/41. g(-6)2. h(-12)I also need help with this.I attached the graph that goes along with the questions.1. If Unit Produced is a function of Labor Hours,f(5)=?A. 3B. 4C. 8D. 102. What can be determined, when f(x)=8?A. Units produced are 5B. Labor hours are 5C. Units produced are 10D. Cannot be determined
We are given the following functions
[tex]f\mleft(x\mright)=6x+7\qquad g(x)=-2x-4\qquad h(x)=-\frac{3x}{4}[/tex]We are asked to find out g(-6) and h(-12)
1. g(-6)
it simply means that we have to plug x = -6 into the function of g(x)
[tex]\begin{gathered} g(x)=-2x-4 \\ g(-6)=-2(-6)-4 \\ g(-6)=12-4 \\ g(-6)=8 \end{gathered}[/tex]Therefore, g(-6) = 8
2. h(-12)
Once again we have to plug x = -12 into the function of h(x)
[tex]\begin{gathered} h(x)=-\frac{3x}{4} \\ h(-12)=-\frac{3(-12)}{4} \\ h(-12)=\frac{36}{4} \\ h(-12)=9 \end{gathered}[/tex]Therefore, h(-12) = 9
Solve the equation for t:8t - r = 12t
ANSWER
[tex]t=-\frac{r}{4}[/tex]EXPLANATION
We want to solve the given equation for t:
[tex]8t-r=12t[/tex]To do this, separate the variables of the equation and simplify it:
[tex]\begin{gathered} 8t-12t=r \\ -4t=r \\ t=\frac{r}{-4} \\ t=-\frac{r}{4} \end{gathered}[/tex]That is the solution to the equation for t.
how to find the length of side x. really having a hard time on this
Since the figure is a square the diagonal divide it in two congruent right triangles. One of them is shown below:
Since we have right trisang
Select the correct answer.What is the range of Piecewise and Absolute Value Functions
Given the function :
g(x) = -1/2 |x-6| + 1
• Th,e, 1 ,, highlighted in yellowabove, indicates the maximum y- intercept that the graph will ever reach .
,• The equation follows y = Mx + b structure , meaning range is from -infinity.
,• So the range of this equation will be (-∞ ; 1]
,• Option A is the correct choice .
Absolute value:
asymptote : none
extreme point (6;1)
critical point : x = 6
7 in. 6in. 9 in. it's the formula of a triangle
Area of a Triangle
Given a triangle of base length B and height length H, the area can be calculated by the formula:
[tex]A=\frac{B\cdot H}{2}[/tex]The base and the height must be perpendicular.
The height of the given triangle is H=7 in. We need to calculate the length of the base.
We are providing a new image where a variable x is introduced to help us calculate the base length:
The triangle formed by the sides 9-7-x is right, so we can calculate the value of x by applying the Pythagora's Theorem:
[tex]7^2+x^2=9^2[/tex][tex]49+x^2=81[/tex]Solving for x:
[tex]\begin{gathered} x^2=81-49=32 \\ x=\sqrt[]{32} \end{gathered}[/tex]The length of the base is:
[tex]B=9+\sqrt[]{32}[/tex]Thus, the area of the triangle is:
[tex]A=\frac{7\cdot(9+\sqrt[]{32})}{2}[/tex]Calculating:
A = 51.3 square inches
For each scenario, use the tape diagram to help answer the question. Think of different labels to use for the diagram depending on the situation. Mai has picked 1 cup of strawberries for a cake, which is enough for 3/4 of the cake. How many cups does she need for the whole cake?Priya has picked 1 1/2 cups of raspberries. which is enough for 3/4 of a cake. How many cups does she need for the whole cake?
Answer:
The number of cups of strawberries needed to make a whole cake is;
[tex]\begin{gathered} \frac{4}{3}\text{ cups} \\ or \\ 1\frac{1}{3}\text{ cups} \end{gathered}[/tex]Explanation:
Given that;
[tex]1\text{ cup of strawberries can make }\frac{3}{4}of\text{ a cake}[/tex]To get the number of cups of strawberries needed for a whole cake.
Let us multiply both sides by 4/3;
[tex]\begin{gathered} 1\times\frac{4}{3}\text{ cup of strawberries can make }\frac{3}{4}\times\frac{4}{3}of\text{ a cake} \\ \frac{4}{3}\text{ cup of strawberries can make 1-whole }of\text{ a cake} \end{gathered}[/tex]Therefore, the number of cups of strawberries needed to make a whole cake is;
[tex]\begin{gathered} \frac{4}{3}\text{ cups} \\ or \\ 1\frac{1}{3}\text{ cups} \end{gathered}[/tex]Fill in the blanks using these answer choices: always, never, sometimes, once.
The complete text would be as following:
Parallel lines cross never
Perpendicular lines cross once
Lines that are neither parallel or perpendicular cross once
Lines that are the same cross always
Perpendicular lines cross at a 90 degree angle
84 is 75% of what number
Answer:
112
Explanation:
We need to find a number that represents 100% when 84 represents 75%, so we will use the following
[tex]100\text{ \% }\times\frac{84}{75\text{ \%}}=\frac{100\times84}{75}=\frac{8400}{75}=112[/tex]Therefore, 84 is 75% of 112.
Answer:112
Step-by-step explanation: - 84 is 75% of 112. 100% of 112 is 112, hope this helps
question 1 estimated number of dogs = 6.99 × 107=6.99 • 10,000,000=69,900,000estimated number of cats = 3.61 × 107=3.61 • 10,000,000= 36,100,000estimated number of birds = 8.3 × 106= 8.3 • 1,000,000= 8,300,000-------------------------------------------Question 2The estimated number of dogs is 6.99 x 10⁷The estimated number of cats is 3.61 x 10⁷The estimated number of birds is 8.3 x 10⁶The power of 10 in 8.3 x 10⁶ is 6 which is less than the power of 10 in the other two numbers. To make the calculation simpler, convert this number so the exponents are all the sameMultiply and divide 8.3 x 10⁶ by 10 to increase its exponent by 18.3x 10⁶= 10/10 • 8.3x 10⁶=8.3/10 •10⁶ •10= 0.83 x 10⁷
SOLUTION
For question 1, we have
[tex]\begin{gathered} 6.99\times10^7=69,900,000 \\ 3.61\times10^7=36,100,000 \\ 8.3\times10^6=8,300,000 \end{gathered}[/tex]Take the sum of the number above, we have
[tex]\begin{gathered} 69,900,000+36,100,000+8,300,000 \\ =114,300,000 \end{gathered}[/tex]For Question 2, we have
We need to add the number without converting to the ordinary form i.e will add the number in thier exponential form.
[tex]6.99\times10^7+3.61\times10^7+0.83\times10^7[/tex]The exponent is the common factor, hence we add the other numbers
[tex]\begin{gathered} (6.99+3.61+0.83)\times10^7 \\ =11.43\times10^7 \end{gathered}[/tex]Changin the result in question 2 to ordinary form, we have
[tex]11.43\times10^7=11.43\times10,000,000=114,300,000[/tex]Hence
Yes the answer in question 1 and question 2 are the same.
We can tell this because the nunbers have the same values(they are the same) but are in different forms(ordinary form and the exponential form). Hence the numbers can be use interchangeably.
the diagram show a side (a) find the height of the top of the side(b) find the length of the side
Part a
Find out the height of the triangle of the figure
we have that
sin(70)=h/2 -----> by opposite side divided by the hypotenuse
solve for h
h=2*sin(70)
h=1.88 mPart b
Find the base of complete triangle
so
Let
x-----> the base of complete triangle
we have that
x=2*cos(70)+h/tan(40)
substitute the value of h
x=2*cos(70)+1.88/tan(40)
x=2.92 m