Given:-
[tex]6,8,10,\ldots[/tex]To find:-
The sequence in it.
Since the sequence is 6 for 1st term and 8 for 2nd term and 10 for 3rd term.
So the sequence is,
[tex]2n+4[/tex]The required sequence is 2n+4.
Now when n=1. we have,
[tex]\begin{gathered} 2(1)+4=2+4 \\ \text{ =6} \end{gathered}[/tex]When n=2. we have,
[tex]\begin{gathered} 2(2)+4=4+4 \\ \text{ =8} \end{gathered}[/tex]When n=3. we have,
[tex]\begin{gathered} 2(3)+4=6+4 \\ \text{ =10} \end{gathered}[/tex]So from this we can conform that the sequence is 2n+4.
How do you find the domain I don't know we're to start??
hello
to find the domain of a graph, simply check the length of the x-axis
assmuing each box as 1 unit
first graph
the domain of the first grap is (0, 10)
second graph
A large bucket of 200 golf balls is divided into 4 smaller buckets. hiw many golf balls are in each small bucke?
Given:
Number of golf balls in larger bucket, N=200
The larger bucket is divided into 4 smaller buckets
The objective is to find the number of golf balls (x) in the smaller buckets.
The formula to find the smaller bucket is,
What is the range of the function y=x+5 ?O y2-5O y20O y 15Oy25
Since the value inside a square root needs to be positive or zero, the minimum value y can assume is 0, wheorn x = -5.
Then, for values of x greater than -5, the values of y increases, towards positive infinity.
The range of a function is all y-values the function can assume.
If the minimum value of the function is y = 0, the range is:
[tex]y\ge0[/tex]Therefore the correct option is the second one.
Use the graph of f(x) below, and the fact that x2 + 3x + 3 is a factor of f(x), to find the equation of the third degreepolynomial f(x), with leading coefficient one.
Answer:
Explanation:
From the given graph, we see that its x-intercept is 3
This means x - 3 is a factor.
The third degree polynomial is now:
[tex](x^2+3x+3)(x-3)[/tex]This is also written as:
[tex]undefined[/tex]blake thinks that the mass of a baby mouse will increase similar to what is shown on the graph belowwhat is the value of the independent variable at point A on the graph?
We are given a graph that shows the growth of a baby mouse over time.
On the x-axis, we have independent variable time (in days)
On the y-axis, we have dependent variable mass (in grams)
On the graph, the value of the independent variable at point A is the value of the time (in days)
The graph shows that the mass (in grams) of the baby mouse is increasing as the time (in days) increases.
Let us point out the value on the given graph,
As you can see, the value of the independent variable at point A is 6 days
Therefore, the answer is 6 days
d the slope of the altitude on each side of triangle ABC. ises 11.3 Complete the following: (c) A (2,5), B(-2, 1), C(8,-1)
The coordinates of triangle ABC are given as A(2, 5), B(- 4, 5), C(8, - 1). The diagram of the triangle with altitude on each side is shown below
The formula for determining slope is expressed as
Slope = (y2 - y1)/(x2 - x1)
The altitudes are AX, CY and BZ
For line BC,
Slope = (- 1 - - 2)/(8 - 1) = (- 1 + 2)/7
Slope = 1/7
The altitude on BC is AX
Slope of AX = - 1// Slope of BC
Slope of AX = - 1/(1/7) = - 1 * 7/1
Slope of AX = - 7
For line AC,
Slope = (- 1 - 5)/(8 - 2) = - 6/6
Slope = 1
The altitude on AC is BZ
Slope of BZ = - 1/Slope of AC
Slope of BZ = - 1/1
Slope of BZ = - 1
For line AB,
Slope = (1 - 5)/(- 2 - 2) = - 4/- 4 = 1
The altitude on AB is CY
Slope of CY = - 1/Slope of AB
Slope of CY = - 1/1
Slope of CY = - 1
Move numbers to the blanks to rewrite each square root. 2i -2 4i V51 -15 ivs
To rewrite each square root, factor each number and use one of the properties of roots, this way:
[tex]\sqrt[]{-4}=\sqrt[]{4\cdot-1}=\sqrt[]{4}\cdot\sqrt[]{-1}=2i[/tex][tex]\sqrt[]{-5}=\sqrt[]{5\cdot-1}=\sqrt[]{5}\cdot\sqrt[]{-1}=i\sqrt[]{5}[/tex]The blanks must be filled in with 2i and i sqrt(5) respectively.
There are 5 blue marbles, 2 red marbles, and 3 green marbles in a bag. What is theprobability of selecting NOT a green marble? Your answer can be a fraction, decimalor percent.
Given
Total marbles 5+2+3 =10
[tex]\begin{gathered} \text{probability of selecting blue=}\frac{5}{10}=\frac{1}{2} \\ \\ \text{porbability of selceting red =}\frac{2}{10}=\frac{1}{5} \\ \text{Probalility of selecting gr}een\text{=}\frac{3}{10} \\ \end{gathered}[/tex]Now probability of NOT selecting green Marble
[tex]\begin{gathered} \text{Probability of selecting NOT gr}een\text{ marbles=1-}\frac{3}{10} \\ \\ \text{Probability of selecting NOT gr}een\text{ marbles=}\frac{1}{1}\text{-}\frac{3}{10} \\ \text{Probability of selecting NOT gr}een\text{ marbles=}\frac{10-3}{10}=\frac{7}{10} \end{gathered}[/tex]Alternatively (second method )
Probability of selecting NOT a green marble means you will be selecting either blue marbles or red marbles
[tex]\text{Probability of selecting NOT a green =}\frac{5}{10}+\frac{2}{10}=\frac{7}{10}[/tex]The final answer
[tex]\begin{gathered} \text{Fraction }\frac{7}{10} \\ \text{Decimal 0.7} \\ \text{Percetages 70\%} \end{gathered}[/tex]
Question 11 or 12 whichever u can answer see photo
Explanation
(11)
[tex]f(t)=\frac{t^2}{t^3+4}[/tex]
the average value of a function is given by:
[tex]average=\frac{F(b)-f(a)}{b-a}[/tex]Step 1
evaluate the function in the given limits
a)t=3
[tex]\begin{gathered} f(t)=\frac{t^2}{t^3+4} \\ f(3)=\frac{3^2}{3^3+4} \\ f(3)=\frac{9}{27+4}=\frac{9}{31} \\ f(3)=\frac{9}{31} \\ so \\ a=3,\text{ f\lparen a\rparen=}\frac{9}{31} \end{gathered}[/tex]b) t= 6
[tex]\begin{gathered} f(t)=\frac{t^2}{t^3+4} \\ f(6)=\frac{6^2}{6^3+4} \\ f(6)=\frac{36}{216+4}=\frac{36}{220}=\frac{18}{110}=\frac{9}{55} \\ f(6)=\frac{9}{55} \\ b=6\text{ and F\lparen b\rparen=}\frac{9}{55} \end{gathered}[/tex]Step 2
now, replace in the formula
[tex]\begin{gathered} average=\frac{F(b)-f(a)}{b-a} \\ average=\frac{\frac{9}{55}-\frac{9}{31}}{6-3} \\ average=\frac{\frac{9}{55}-\frac{9}{31}}{3}=\frac{-\frac{216}{1705}}{\frac{3}{1}}=-\frac{216}{5115} \end{gathered}[/tex].so the answer is
[tex]-\frac{216}{5115}[/tex]I hope this helps you
what is the value of r?
I need help with this practice It is trig from my ACT prep guideI will send an additional picture later of my attempted answer of this
ANSWER
EXPLANATION
Angle α lies in quadrant II, which means that its sine is positive and its cosine is negative.
Angle β lies in quadrant IV, which means that its cosine is positive and its sine is negative,
The cosine of a difference of two angles is,
[tex]undefined[/tex]Troy is training for a wrestling tournament, and he eats eggs every day. The graph shows thetotal number of eggs Troy eats over a period of days. What is the constant of proportionality,and what does it mean?a) 3; Troy eats 3 eggs per day.b) 12; Troy eats 12 eggs per day.c) 6; Troy eats 6 eggs per day.d) 2: Troy eats 2 eggs per day.
Answer:
C) 6; Troy eats 6 eggs per day.
Explanation:
From the graph:
When days = 2, Number of eggs = 12
When days = 4, Number of eggs = 24
[tex]\frac{\text{Number of eggs}}{Day}=\frac{12}{2}=\frac{24}{4}=6[/tex]Therefore, Troy eats 6 eggs per day.
The correct choice is C.
ines 2. AC is parallel to FG. BD is the bisector of ZCBE and DE is the bisector of ZBEG. Write a two-column proof that shows m/BDE = 90°.
m/BDE = 90°. An slope is formed when two straight lines or rays intermingle at a common endpoint. The vertex of an angle is the familiar point of contact. The term angle comes from the Latin word angulus, which means "corner."
What is meant by parallel?Parallel lines are two lines in the same plane that are equal distance apart and never intersect. They can be both horizontal and vertical in orientation. Parallel lines can be found in everyday life, such as zebra crossings, notebook lines, and railway tracks. Parallel lines are lines that are always the same distance apart in a plane. Parallel lines never cross. Perpendicular lines are those that intersect at a right angle (90 degrees).Parallel lines are lines in a plane that never meet, no matter how far they are extended. The distance between the parallel lines is constant because they never meet.The vertex of an angle is the common point of contact. The term angle comes from the Latin word angulus, which means "corner."Given,
BE is perpendicular to CA and GF
Therefore,
∠CBD = ∠EBD because BD is the bisector of ∠CBE
∠GED = ∠BED because DE is the bisector of ∠BEG
∠CBE = ∠GEB = 90° because BE is perpendicular to CA and GF
∠EBD = 45° because ∠CBD + ∠EBD = 90°
∠BED = 45° because ∠GED + ∠BED = 90°
∠D + ∠EBD + ∠BED = because the sum of angles of a triangle is 180°
∠D = 180° - 90° = 90°
∠D = 180 - ( ∠EBD + ∠BED )
Hence, ∠BDE = 90°
To learn more about angles, refer to
brainly.com/question/25770607
#SPJ1
quadrilateral ABCD is inscribed in circle O as shown below. which of the following would be used to find the measure of angle 3
Answer:
180° -m∠1
Explanation:
• Quadrilateral ABCD is a cyclic quadrilateral.
,• The opposite angles of a cyclic quadrilateral add up to 180 degrees.
Therefore:
[tex]\begin{gathered} m\angle3+m\angle1=180\degree \\ \implies m\angle3=180\degree-m\angle1 \end{gathered}[/tex]Therefore, the second option would be used to find the measure of angle 3.
question will be in picture
The simple interest formula is given by
[tex]A=P\times r\times t[/tex]where A is the future value, P is the initial value (Principal), r is the rate and t is the time. In our case P=1200, r=0.08 and t= 2 years. By substituting these values into our formula, we get
[tex]\begin{gathered} A=1200\times0.08\times2 \\ A=192 \end{gathered}[/tex]then, the answer is option a: $192
Find the solution set of this inequality. Select the correct graph
Given
The inequality,
[tex]|5x-15|<-5[/tex]To find the solution set for this inequality.
Explanation:
It is given that,
The inequality is,
[tex]|5x-15|<-5[/tex]Also, it is known that,
Absolute value cannot be less than 0.
Then, the inequality
[tex]|5x-15|<-5[/tex]has no solution.
Hence, the answer is option A).
What are the values of a and b in the exponential function given two points on thegraph?(2, 6400) and (4, 4096)
Ok, so:
I suppose that the exponential function you mean is this one: y = ae^(bx).
To find a and b, we replace:
6400 = ae^(2b) (1 equation)
4096 = ae^(4b). (2 equation)
We can solve this system as this:
If we find a in the first equation:
a = (6400) / (e^(2b).
Now we replace this fact in equation 2:
4096 = (6400)/e^(2b)) * (e^(4b)).
Simplifying:
4096 = 6400 * e^(2b)
0.64 = e^(2b)
Now, we apply the natural logarithm to both sides:
ln (0.64) = ln(e^(2b)).
This is
ln (0.64) = 2b.
Then, b= ln(0.64)/2. which is approximately -0.22.
Now, we find a if we replace b in any equation:
6400 = ae^(2b)
6400 = ae^(2(-0.22))
6400 = ae^(-0.44))
a = 6400 / e^(-0.44) which is approximately 9937.3
what is the slope intercept for the following line y=2x + __
EXPLANATION
The slope-intercept form is:
y= 2x + b
where b is the y-intercept
Simplify the expression. Answer should be written with positive exponent
The given expression is
(x^5)^3 * x^5/x^4
We would apply the following rules of exponents
(a^b)^c = a^bc
a^b * a^c = a^(b + c)
a^b / a^c = a^(b - c)
By applying the first rule,
(x^5)^3 becomes x^(5 * 3) = x^15
By applying the third rule,
x^5/x^4 becomes x^(5 - 4) = x^1 = x
The expression becomes
x^15 * x
Finally, we would apply the second rule. The final expression would be
x^(15 + 1)
= x^16
12. 10 6 5 4 3 2 1 x N -12-11-10-9-8-7 -6 -5 -4 -3 -2 -11 1 2 3 4 5 6 7 8 9 10 11 12 -2 IT 2 3 456 8 9 -8 -10 -11 -12
First, we find the slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Let's replace the points (0,6) and (1,1), where
[tex]\begin{gathered} x_1=0 \\ x_2=1 \\ y_1=6 \\ y_2=1 \end{gathered}[/tex][tex]m=\frac{1-6}{1-0}=\frac{-5}{1}=-5_{}[/tex]Then, we use the slope-intercept form
[tex]y=mx+b[/tex]Where m = -5 and b = 6.
[tex]y=-5x+6[/tex]One morning Nick walks 1/4 mile from home zoo.He walks around the zoo and covers 9/10 mile before walking back home . How many miles does Nick walk that morning?
Given the following parameters from the question:
Distance walked by Nick from home zoo = 1/4 mile
Distance covered around the zoo = 9/10 miles
In order to get the total distance covered by Nick that morning, we will take the sum of the distances including the distance he walked back home as shown:
[tex]\text{Total distance walked=}\frac{1}{4}+\frac{9}{10}+\frac{1}{4}[/tex]Fins the Least common denominator
[tex]\begin{gathered} \text{Total distance walked=}\frac{5(1)+2(9)+5(1)}{20} \\ \text{Total distance walked}=\frac{5+18+5}{20} \\ \text{Total distance walked}=\frac{28}{20}\text{miles} \end{gathered}[/tex]Note that I have to add another 1/4 miles since he will also walk back home at the same distance he walked to the zoo
Expressing the total distance as a mixed fraction
[tex]\begin{gathered} \text{Total distance walked=1}\frac{\cancel{8}2}{\cancel{20}5} \\ \text{Total distance walked}=1\frac{2}{5}miles \end{gathered}[/tex]This shows that Nick walked 1 2/5 miles that morning
Find the area of the triangle with a = 19, b = 14, c = 19. Round to the nearest tenth.
In order to find the area of a triangle with 3 sides, we use the Heron's formula which says if a, b, and c are the three sides of a triangle, then its area is,
[tex]\begin{gathered} Area=A=\sqrt[]{S(S-a)(S-b)(S-c)} \\ S=\text{Semiperimeter}=\frac{a+b+c}{2} \end{gathered}[/tex]Given a triangle with a = 19, b = 14, c = 19, the area is as shown below:
[tex]\begin{gathered} S=\frac{19+14+19}{2} \\ S=\frac{52}{2} \\ S=26 \end{gathered}[/tex][tex]\begin{gathered} A=\sqrt[]{S(S-a)(S-b)(S-c)} \\ A=\sqrt[]{26(26-19)(26-14)(26-19)} \\ A=\sqrt[]{26(7)(12)(7)} \\ A=\sqrt[]{15288} \\ A=123.6447 \\ A=123.6(\text{nearest tenth)} \end{gathered}[/tex]Hence, the area of the triangle is 123.6 square unit correct to the nearest tenth
coefficient of nm2 in expansion of (n-5m)^3
Not homework review for test not worth any points number 2
Solution
We can conclude the following:
y> -2x+1 All points would be above the dashed line
y<= x-2 All points will be in and below the solid line
all you need is on the photo this is a homework
We have the quadratic function:
[tex]f(x)=x^2-4x-12[/tex]1) We have to factorize it in this way:
[tex]f(x)=(x-x_1)(x-x_2)[/tex]To do that we have to find the roots x1 and x2.
We can apply the quadratic formula as:
[tex]\begin{gathered} f(x)=ax^2+bx+c\longrightarrow x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-(-4)\pm\sqrt[]{(-4)^2-4\cdot1\cdot(-12)}}{2\cdot1} \\ x=\frac{4}{2}\pm\frac{\sqrt[]{16+48}}{2} \\ x=2\pm\frac{\sqrt[]{64}}{2} \\ x=2\pm\frac{8}{2} \\ x=2\pm4 \\ x_1=2-4=-2 \\ x_2=2+4=6 \end{gathered}[/tex]We have the values of both of the roots, so we can factorize f(x) as:
[tex]f(x)=(x+2)(x-6)[/tex]2) We have to express f(x) in vertex form.
To do that we can rearrange the expression as:
[tex]\begin{gathered} x^2-4x-12 \\ x^2-4x+4-4-12 \\ (x^2-4x+4)-16 \\ (x-2)^2-16 \end{gathered}[/tex]The vertex form for f(x) is:
[tex]f(x)=(x-2)^2-16[/tex]3)
a) The x-intercepts are the roots of the function: x1=-2 and x2=6. For this values of x, the function has a value of 0. X-intercepts can be expressed as (-2,0) and (6,0).
b) The y-intercept is given by the independent value in the equation, c=-12. The is the value of the function when x=0, that is, f(0)=-12. It can be expressed as (0,-12).
c) The vertex is (2,-16) and can be deduced from the vertex expression f(x)=(x-2)^2-16.
d) The axis of symmetry, as it is a parabola, is a vertical axis that pass through the vertex. Then, its definition is x=2, as the vertex is at (2,-16).
e) The quadratic funtion in this case, as the quadratic coefficient is positive, has a minimum.
f) The minimum is located at the vertex and has a value of y=-16.
Question 3(Multiple Choice Worth 1 points)(08.02 LC)Complete the square to transform the expression x2 – 2x – 2 into the form a(x – h)2 + k.(x - 1)2 + 3(x - 1)2 - 3(x - 2)2 - 3(x - 2)2 + 3
We need to add and subtract the same number in the expression so we can write it as a square and a constant, as in the following expression:
[tex]a\left(x-h\right)^2+k[/tex]The given expression is:
[tex]x^2-2x-2[/tex]In order to find the number that must be added and subtracted, let's expand the general expression:
[tex]\begin{gathered} a(x-h)^{2}+k \\ \\ a(x^2-2hx+h^2)+k \\ \\ ax^2-2ahx+ah^2+k \end{gathered}[/tex]Comparing the coefficients of the general and the given expression, we have:
[tex]\begin{gathered} x^{2}-2x-2 \\ \\ ax^{2}-2ahx+ah^{2}+k \\ \\ x^2=ax^2\Rightarrow a=1 \\ \\ -2x=-2ahx=2hx\Rightarrow h=1 \\ \\ -2=ah^2+k=1+k\Rightarrow k=-3 \end{gathered}[/tex]So, using a = 1, h = 1, and k = -3, we can write:
[tex]x^2-2x-2=1(x-1)^2-3=(x-1)^2-3[/tex]Notice that we obtain the same result by adding 3-3 to the original expression:
[tex]x^2-2x-2=x^2-2x-2+3-3=(x^2-2x+1)-3=(x-1)^2-3[/tex]Therefore, the answer is:
[tex]\begin{equation*} (x-1)^2-3 \end{equation*}[/tex]Given the formula of sample interest where I is the interest in dollars P is the principal in dollars are is the interest rate as a decimal and te is the time period in years
Interest: Subtract the principal from the maturity value:
[tex]I=9,270-9,000=270[/tex]I= $270Principal: Value of the loan
P=$9,000time: Turn the 3-months into years:
[tex]3\text{months}\cdot\frac{1\text{year}}{12\text{months}}=0.25\text{years}[/tex]t=0.25 yearsHaving the data for P, I and t, use the formula (I=Prt) to solve r:
[tex]\begin{gathered} I=P\cdot r\cdot t \\ r=\frac{I}{P\cdot t} \\ \\ r=\frac{270}{9,000\cdot0.25}=\frac{270}{2,250}=0.12 \end{gathered}[/tex]Interest rate: r=0.12Multiply the interest rate by 100 to write it as a percent:
[tex]0.12\cdot100=12[/tex]Annual simple interest rate: 12%can you help me please? im doing practice questions for when school opens next month and this is the answer i got. is this correct?
Given:
Amount = $3000
Interest rate = 18% per year
A = 3000(1.18)^t
To find:
[tex]\frac{A(12)-A(6)}{12-6}[/tex]Step-by-step solution:
We will now the value in the given expression:
[tex]\begin{gathered} =\frac{A(12)-A(6)}{12-6} \\ \\ =\frac{3000[(1.18)^{12}-(1.18)^6]}{6} \\ \\ =500[7.28-2.69] \\ \\ =500\times4.59 \\ \\ =2294.02 \end{gathered}[/tex]From the above calculation, we can say that the average total amount between t = 6 years to t = 12 years is 2294.02
Thus we can say that Option A is the correct answer.
What is the probability, in simplest form, that a digit picked at random from thefirst 100 digits of pi would be a 2?
The first 100 digits of pi are:
3.14159265358979323846264338327950288419716939937510 5820974944592307816406286208998628034825342117067
WE can see that the number of 2 in the first 100 digits if pi above occurs 12 times.
Therefore, the probability that a digit picked at random from the
first 100 digits of pi would be a 2 is:
[tex]\frac{12}{100}\text{ = 0.12}[/tex]ANSWER:
0.12
2. If CD + DE = CE, then CD = CE - DE
The statement is true