When you have an arithmetic sequence you can use the next general formula to get the explicit formula:
[tex]a(n)=a(1)+d(n-1)[/tex]Where a(1) is the first term in the sequence, d is the difference between each term in the sequence, and n is the nth term
You have the sequence: 28,38,48,58
The difference in this sequence is d=10
The first term is: a(1)=28
Then:
[tex]a(n)=28+10(n-1)[/tex][tex]a(n)=28+10n-10[/tex][tex]a(n)=18+10n[/tex]Then, the explicit rule for the given arithmetic sequence is: a(n)=18+10nThe function h(x) is a transformed function of f(x) = |x|. The transformation is as follows: 1 units vertical shift up, 4 units horizontal shift left.a). Write the transformed equation, h(x).b). Graph f(x) and h(x) on the same coordinate plane. Be sure to label the functions f(x) and h(x). This must be graphed by hand or by using the tools in Word.
To transform a function 1 unit up, we add 1 outside of the function
h(x) = |x| +1
shifting it 4 units to the left, we will add 4 units from x inside
h(x) = |x+4| +1
The transformed function is
h(x) = |x+4| +1
can you help with this question please
We need to give the steps for proving the corresponding angles theorem for parallel lines crossed by a transverse line.
Westart with the
p || q as Given info
Next we use that
< 1 = <7 due to internal alternate angles among parallel lines
< 7 = <5 due to angles opposed by vertex
<1 = <5 due to transitive property <1 = <7 = <5
ifvx varies directly as y and x =36 when y=6 find x when y=9
Answer:
54
Step-by-step explanation:
Hello!
A direct variation can be expressed as [tex]y = ax[/tex], where a is multiplied.
As you can see, x is 6 times greater than y, proving that when y is 6, x is 36 (6*6 = 36).
Therefore, we can say that if y is 9, we can multiply the value by 6 to find the x-value:
x = 6 * 9x = 54So the value of x is 54.
Solve the inequality: 3x + 4 ≤ 5
Answer in interval notation.
Answer: [tex]x\leq 1/3\\[/tex]
Step-by-step explanation:
complete the following: 1. Find the locus of points whose: (a) ordinate saquare decressed by the square of the abscissa is the sum of the coordinates
P(x,y) is the coordinate point of the locus
ordinate is y
abscissa is x
Following the sentence we have
ordinate square y^2
decreased means subtract
square of the abscissa x^2
is means equal
the sum of the coordinates x+y
[tex]y^2-x^2=x+y[/tex]A glass aquarium is in the form of a rectangular parallelepiped with dimensions 50cm by 100cm, and its depth is 30cm.How many liters of water will it hold?
Hello! To find the number of liters of water, we have to calculate the volume of the parallelepiped:
The formula of the volume is:
[tex]\begin{gathered} \text{Volume = a}\times\text{ b }\times\text{c} \\ \text{Volume = 50}\times\text{100}\times\text{30} \\ \text{Volume = }150,000\operatorname{cm}^3 \end{gathered}[/tex]Now that we know the volume, we have to convert cm³ to liters.
For this, we must remember:
1cm³ = 0.001 liter
Multiplying by rule of three, we will obtain:
[tex]\begin{gathered} 1\cdot x\text{ = 150,000 }\cdot\text{ 0.001} \\ x\text{ = 150 liters} \end{gathered}[/tex]Find a unit vector u with the same direction as v = : (-3, 8)
Given:
The vector
[tex]v=<-3,8>[/tex]Required:
To find the unit vector u with the same direction.
Explanation:
Unit formula is the vector is divided by its magnitude.
Now the magnitude of v is,
[tex]\begin{gathered} mag.v=\sqrt{(-3)^2+8^2} \\ =\sqrt{9+64} \\ =\sqrt{73} \end{gathered}[/tex]Now the unit vector is,
[tex]u=<-\frac{3}{\sqrt{73}},\frac{8}{\sqrt{73}}>[/tex]Final Answer:
[tex]u=<-\frac{3}{\sqrt{73}},\frac{8}{\sqrt{73}}>[/tex]A boat travels 82 km on a 160 degree course. Find the distances it travel south and east, respectively
A boat travels 82 km on a 160-degree course. Find the distances it travels south and east, respectively
see the attached figure to better understand the problem
step 1
Find out the East's distance (dx)
we have that
cos(20)=dx/82
dx=82*cos(20)
dx=77.05 Kmstep 2
Find out the South's distance (dy)
sin(20)=dy/82
dy=82*sin(20)
dy=28.05 Kmplot the graph f on the graphf(x)=|1/2x-2|
• We will determine the domain, range and x ;y intercept then plot the graph
1. The domain is given by :
[tex]\begin{gathered} \text{Domain = }x<0\text{ = (-}\infty\text{ },\text{ 0) } \\ \text{ x >0 = ( 0 },\infty)\text{ } \\ \text{ =(-}\infty;0)\text{ U ( 0 ;}\infty) \end{gathered}[/tex]2. Range is given by :
[tex]\begin{gathered} \text{Range = f(x) }\ge0\text{ } \\ \text{ =}\lbrack0;\infty) \end{gathered}[/tex]3. x - and y -intercept :
[tex]x\text{ - intercept = ( }\frac{1}{4};\text{ 0) }[/tex]4. asymptote :
[tex]\begin{gathered} \text{vertical : }x\text{ = 0 } \\ \text{horizontal : y = 2 } \end{gathered}[/tex]Now that we have the necessary points to plot the f(x) = | 1/2x -2 | , the graph will look as follows :f(n) = -11 + 22(n - 1)Complete the recursive formula of f(n).f(1) = f(n) = f(n - 1) +
F(n) = -11 + 22(n-1)
[tex]\begin{gathered} f(1)\text{ implies that n=1} \\ F(1)\text{ = -11+22(1-1)} \\ f(1)=-11 \end{gathered}[/tex]Hence F(1) = -11
[tex]\begin{gathered} f(n-1)\text{ implies n=n-1} \\ f(n-1)=-11\text{ +22(n-1-1)} \\ f(n-1)=-11+22(n-2)_{} \\ =\text{ -11+22n-44} \\ f(n-1)=22n-55 \end{gathered}[/tex][tex]\begin{gathered} f(n)=\text{ -11+22(n-1)} \\ =-11+22n-22 \\ 22n-33 \\ \end{gathered}[/tex]
let An = F(n) -F(n-1)
[tex]\begin{gathered} 22n-33\text{ - (22n-55)} \\ 22n\text{ - 33-22n+55} \\ =-33+55 \\ =22 \end{gathered}[/tex]Hence F(n)= f(n-1) +22
Describe the translation:A) 4 units right and 6 units downB) 4 units left and 6 units upC) 6 units left and 4 units upD) 6 units right and 4 units down
To describe the transfer we will review what the points of the blue and red triangle are.
Blue triangle
I = (-2, 8)
I' = (4, 4)
First, we will determine the x-axis translation
[tex]\begin{gathered} \Delta x=x2-x1 \\ \Delta x=4-(-2) \\ \Delta x=6 \end{gathered}[/tex]6 units right
Now let's calculate the y-axis transfer
[tex]\begin{gathered} \Delta y=y2-y1 \\ \Delta y=4-8 \\ \Delta y=-4 \end{gathered}[/tex]4 units down
The answer would be 6 units right and 4 units down
Select the similarity transformation(s) that make ABC similar to EDC.
Given the triangles ABC and EDC
We will find the transformation that makes the triangles are similar
As shown: the triangles are reflected over the y-axis
the rule of the reflection over the y-axis will be as follows:
[tex](x,y)\rightarrow(-x,y)[/tex]And as shown, the length of the side AB = 3 units
And the length of the side ED = 1 units
So,
[tex]ED=\frac{1}{3}AB[/tex]So, the answer will be:
D) (x,y) ⇒ (-x, y)
E) (x,y) ⇒ (1/3 x, 1/3 y)
kmarks Solve the following system of equations graphically on the set of axes below 1 y 22 - 4 y = -X – 7 Plot two lines by clicking the graph. Click a line to delete il. y 10 9 8 7 6 5 4 3 2. 1 5 6 7 8 9 10
Explanation:
For the first line :
1. Draw a line which has a slope of 1 /2
2. Adjust the line so that it has a y-intercept of -4.
For the second line:
1. Draw a line which has a slope of -1
2. Adjust this line so that it has a y-intercept of -7.
Finally, find the point where the two lines intersect.
The coordinates of the point of intersection are the solution to our system.
To get a line which has a slope 1/2, you start from (0, -4 ) and then move 2 units to the right and then 1 unit up.
....................
Answer:
oop
Step-by-step explanation:
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Which one of the following angle measurements is the largest?
We have
[tex]\pi\approx3.14\text{ radians}[/tex]and
[tex]\pi=180^0[/tex]From these,
[tex]2\text{ radians<3 radians<}\pi<200^o[/tex]The largest measurement is 200 degrees. Thus, option B is correct.
Find the probability of at least 2 girls in 6 births. Assume that male and female births are equally likely and that the births are independent events.0.6560.1090.2340.891
We need to use Binomial Probability.
Of 6 births, we want to find the probability of at least 2 of them being girls.
To solve this, we need to find:
Probability of exactly 2 girls
Probability of exactly 3 girls
Probability of exactly 4 girls
Probability of exactly 5 girls
Probability of exactly 6 girls
If we add all these probabilities, we get the probability of at least 2 girls.
To find the probabilities, we can use the formula:
[tex]_nC_r\cdot p^r(1-p)^{n-r}[/tex]Where:
n is the number of trials (in this case, the number of total births)
r is the number of girls we want to find the probability
p is the probability of the event occurring
[tex]_nC_r\text{ }is\text{ }the\text{ }combinatoric\text{ }"n\text{ }choose\text{ }r"[/tex]The formula for "n choose r" is:
[tex]_nC_r=\frac{n!}{r!(n-r)!}[/tex]Then, let's find the probability of exactly 2 girls:
The probability of the event occurring is:
[tex]P(girl)=\frac{1}{2}[/tex]Because there is a 50% probability of being a girl or a boy.
let's find "6 choose 2":
[tex]_6C_2=\frac{6!}{2!(6-2)!}=\frac{720}{2\cdot24}=15[/tex]Now we can find the probability of exactly 2 girls:
[tex]Exactly\text{ }2\text{ }girls=15\cdot(\frac{1}{2})^2(1-\frac{1}{2})^{6-2}=15\cdot\frac{1}{4}\cdot(\frac{1}{2})^4=\frac{15}{4}\cdot\frac{1}{16}=\frac{15}{64}[/tex]We need to repeat these calculations for exactly 3, 4, 5, and 6 girls:
Exactly 3 girls:
let's find "6 choose 3":
[tex]_6C_3=\frac{6!}{3!(6-3)!}=\frac{720}{6\cdot6}=20[/tex]Thus:
[tex]Exactly\text{ }3\text{ }girls=20\cdot(\frac{1}{2})^3(1-\frac{1}{2})^{6-3}=20\cdot\frac{1}{8}\cdot\frac{1}{8}=\frac{5}{16}[/tex]Exactly 4 girls:
"6 choose 4":
[tex]_6C_4=\frac{6!}{4!(6-4)!}=\frac{720}{24\cdot2}=15[/tex]Thus:
[tex]Exactly\text{ }4\text{ }girls=15\cdot(\frac{1}{2})^4(1-\frac{1}{2})^{6-4}=15\cdot\frac{1}{16}\cdot\frac{1}{4}=\frac{15}{64}[/tex]Exactly 5 girls:
"6 choose 5"
[tex]_6C_5=\frac{6!}{5!(6-5)!}=\frac{720}{120}=6[/tex]Thus:
[tex]Exactly\text{ }5\text{ }girls=6\cdot(\frac{1}{2})^5(1-\frac{1}{2})^{6-5}=6\cdot\frac{1}{32}\cdot\frac{1}{2}=\frac{3}{32}[/tex]Exactly 6 girls:
"6 choose 6"
[tex]_6C_6=\frac{6!}{6!(6-6)!}=\frac{720}{720\cdot0!}=\frac{720}{720}=1[/tex]Thus:
[tex]Exactly\text{ }6\text{ }girls=1\cdot(\frac{1}{2})^6(1-\frac{1}{2})^{6-6}=\frac{1}{64}\cdot(\frac{1}{2})^0=\frac{1}{64}[/tex]now, to find the answer we need to add these 5 values:
[tex]\frac{15}{64}+\frac{5}{16}+\frac{15}{64}+\frac{3}{32}+\frac{1}{64}=\frac{57}{64}=0.890625[/tex]To the nearest tenth, the probability of at least 3 girls is 0.891, thus, the last option is the correct one.
Find the value of x so that f(x) = 7.YA6f4200246XX =
The blue line in the graph indicates the function f(x).
The values in the y-axis are the value of the function, that is, the value of f(x) for a given value of x. The x-axis indicates what value of x generates the value in the y-axis.
So, if we want to find the value of x that gives us f(x) = 7, we need to find where is the value '7' in the y-axis, then we draw an horizontal line from this value toward the line of the function (blue line).
This horizontal line will intersect the function in a certain point. This point is where the function has the value 7.
Now, to find the value of x of this point, we draw a vertical line from this point downwards, until it intersects the x-axis.
This way, looking at the image, we can see that the value of x that gives us f(x) = 7 is the value x = 5.
can someone please help me find the mesauser of the following?
Answer:
The measure of the given arcs are;
[tex]undefined[/tex]Given the figure in the attached image.
we want to find the measure of the given arcs.
For arc ED.
The measure of arc ED is equal to the measure of arc AB;
[tex]\begin{gathered} ED=AB=\measuredangle AOB=50^{\circ} \\ ED=50^{\circ} \end{gathered}[/tex]To get the measure of BC, we can see that AB, BC, and CD will sum up to 180 degrees.
[tex]\begin{gathered} AB+BC+CD=180^{\circ} \\ 50^{\circ}+BC+40^{\circ}=180^{\circ} \\ BC=180^0-(50^{\circ}+40^{\circ}) \\ BC=90^{\circ} \end{gathered}[/tex]To get arc BED;
[tex]\begin{gathered} \text{BED}=BE+ED \\ \text{BED}=180+50 \\ \text{BED}=230^{\circ} \end{gathered}[/tex]can u help me w this i got it incorrect and can’t figure out why
1) We can see here a case in which there are two secant lines coming from a single point over that circle.
2) So, we can write out the following relation
[tex]\begin{gathered} PA\cdot PB=PC\cdot PD \\ 4(4+x)=5(5+7) \\ 16+4x=25+35 \\ 16+4x=60 \\ 16-16+4x=60-16 \\ 4x=44 \\ \frac{4x}{4}=\frac{44}{4} \\ x=11 \end{gathered}[/tex]
A shop, had a sale.
(a) In the sale, normal prices were reduced by 15%.
The normal price of a chair was reduced in the sale by $24.
Work out the normal price of the chair.
Answer:
$160
Step-by-step explanation:
A shop, had a sale. In the sale, normal prices were reduced by 15%. The normal price of a chair was reduced in the sale by $24. Work out the normal price of the chair.
if 15% of normal price equals $24 then:
24/15% or 24/0.15 = $160 normal price
CHECK:
$160 * 0.15 = $24
Answer:
$160
Step-by-step explanation:
We want to know the price of the chair
So:
24 / 0.15 = 160$
or
24 / 15% = 160
Jamal is comparingprices of several different brandsof peanuts. Which brand is thebest buy? Explain.
So we need to figure out which is the best buy. In order to do this we must look at a particular variable: the price per ounce of peanuts. This price is given by dividing the total price of a certain amount of peanuts divided by its weight in ounces. So for the Barrel brand we get:
[tex]\frac{3.39}{10}=0.339[/tex]So the Barrel peanuts cost $0.339 per ounce. For the Mr. Nut peanuts we get:
[tex]\frac{4.54}{14}=0.324[/tex]Then the Mr. Nut peanuts cost $0.324 per ounce. Finally, the price per ounce of the Chip's peanuts is:
[tex]\frac{6.26}{18}=0.348[/tex]Then, the cheapest peanuts are those of the brand Mr. Nut and that is the best buy.
8. Kayla finds the multiplication
facts for 12
by doubling the multiplication facts for 6.
Does Kayla's strategy work?
Use words, numbers, or pictures to explain.
A strategy is a way to manipulate numbers, use connections and interactions between numbers to solve an issue. For each procedure, there are a few key tactics. The first thing you do with the statistics is frequently used to categorize, characterize, or label a technique.
What is a doubling strategy?By doubling the multiplication facts for 6, Kayla discovers the 12 multiplication facts.The participant does as instructed, multiplying the number twice or three times. Lily, for instance, rolls "4" and "DDD." She believes that double 4 is equal to 8, double 8 to 16, and double 16 to 32. Four times eight equals 32.A number is simply doubled when multiplied by two, according to the two times table. Any number plus itself is the same as any number multiplied by two.The card below depicts the mental image of two groups of six, or double six, that we want pupils to have. (Students who have been using ten-frames may interpret the amount as ten plus two extra.)To Learn more about strategy refer to:
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A sphere has a radius that is 2.94 centimeters long. Find the volume of the sphere. Round to the nearest tenth.
The volume of a sphere is given as
[tex]V=\frac{4}{3}\pi r^3^{}[/tex]Where r = 2.94 cm
π = 3.14
Substituting values,
[tex]\begin{gathered} V=\frac{4}{3}\times3.14\times2.94^3=1.33\times3.14\times25.41 \\ V=106.12 \end{gathered}[/tex]The volume to the nearest tenth is 106.1 cubic centimeters.
Find the length and width of a rectangle with the following information belowArea = 2x^2 + 3x Perimeter = 6x + 6
Length: L
Width: W
The area of a rectangle is:
[tex]A=L\cdot W[/tex]The perimeter of a rectangle is:
[tex]P=2W+2L[/tex]Given information:
[tex]\begin{gathered} A=2x^2+3x \\ \\ P=6x+6 \end{gathered}[/tex][tex]\begin{gathered} L\cdot W=2x^2+3x \\ 2W+2L=6x+6 \end{gathered}[/tex]Solve L in the second equation (Perimeter):
[tex]undefined[/tex]how do I know which picture goes with the correct equation
If B is between A and C, but B is not midpoint, then the graph would be
The equation would be
[tex]AC=AB+BC[/tex]On the other hand, if B is between A and C, and B is a midpoint, the graph would be
The equation would be
[tex]AB=BC[/tex]convert this number into scientific notation 0.00098
We have to convert the number into scientific notation.
The number is 0.00098.
We start by expressing it as a fraction.
If we divide it by 10, we can express it as:
[tex]\frac{0.00098\cdot10}{10}=\frac{0.0098}{10}[/tex]Dividing by 10 is not enough. In the same way, we have to look a numerator that is multiple of 10 that gives us a numerator that is 9.8.
We would get:
[tex]\frac{0.00098\cdot10000}{10000}=\frac{9.8}{10000}[/tex]Now we have the numerator we need.
We now express the denominator 10,000 as a power of 10 and we get the number in scientific notation as:
[tex]\frac{9.8}{10000}=\frac{9.8}{10^5}=9.8\cdot10^{-5}[/tex]Answer: 0.00098 = 9.8 * 10^(-5)
Farrah borrows $18,000 to purchase a new car. The annual interest rate for the 60-month loan is 4.3%.If she makes all the monthly payments, what is the total amount of interest she will pay on the loan?
SOLUTION:
Step 1:
In this question, we are given the following:
Principal = $ 18,000
Time = 60 month = 60/ 12 = 5 years
Interest = 4. 3%
Step 2:
The total amount she will pay at the end of the 5 -year period is given as follows:
[tex]\begin{gathered} A\text{ = P ( 1 + }\frac{R}{100})^t \\ A\text{ = 18000 ( 1 + }\frac{4.3}{100})^5 \\ \end{gathered}[/tex][tex]\begin{gathered} A\text{ = 22,217. 4416} \\ A\text{ }\approx\text{ }22,217.44\text{ dollars} \end{gathered}[/tex]Step 3:
Now, we have that the amount = 22, 217. 44 dollars.
And the Principal = 18,000 dollars
If she makes all the monthly payments,
Then, the total amount of interest she will pay on the loan is:
[tex]22,\text{ 217. 44 - 18,000 = 4,217. 44 dollars}[/tex]CONCLUSION:
The total amount of interest she will pay on the loan = 4, 217. 44 dollars.
Madeline is a salesperson who sells computers at an electronics store. She makes a base pay of $80 each day and then is paid a $20 commission for every computer sale she makes. Make a table of values and then write an equation for P, in terms of x, representing Madeline's total pay on a day on which she sells x computers.
I need the Equation.
The linear equation that gives the values of P in terms of x which is Madeline's total pay on a given day is; P + 20·x + 80
What is an equation in mathematics?An equation consists of two expressions that are joined by an equal to sign to complete a mathematical statement.
The given parameters are:
Madeline's daily base pay = $80
Madeline's commission for each computer sold = $20
The given table of values is presented as follows:
Daily pay, in Dollars, P; [tex]{}[/tex] 80, 100, 120, 140
Number of computers sold, x; [tex]{}[/tex] 0, 1, 2, 3
From the above table of values, given that the independent variable, x, is increasing at a constant rate, and that the first difference is constant, we have that the relationship is a linear relationship, that has an equation of the form; P = m·x + c
Where:
m = The slope
c = The y-intercept
The slope which gives the ratio of the rise to the run of the graph is given by the equation; [tex]m = \dfrac{100-80}{1-0} =20[/tex]
The equation in point and slope form is therefore: P - 80 = 20·(x - 0) = 20·x
P - 80 = 20·x
P = 20·x + 80
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Find the length of AC
The rule of the length of an arc is
[tex]L=\frac{x}{360}\times2\pi\text{ r}[/tex]Where L is the length of the arc
x is the central angle subtended by the arc
r is the radius of the circle
∵ BC = r
∵ BC = 16 ft
∴ r = 16
∵ < ABC is a central angle subtended by the arc AC
∴ ∵ < ABC = 51 degrees
∴ x = 51
→ Substitute the values of x and r in the rule above to find The length of arc AC
[tex]\begin{gathered} AC=\frac{51}{360}\times2\times3.14\times16 \\ AC=14.23466667 \end{gathered}[/tex]→ Round it to 2 decimal places
∴ AC arc = 14.23 ft
5. (20 x 5 + 10) - (8 × 8 - 4)=
a. 58
b. 50
c. 40
Answer:
b. 50
Step-by-step explanation:
20 x 5 + 10 = 110
8 × 8 - 4 = 60
110 - 60 = 50
Answer:
b. 50
Step-by-step explanation:
(20x5+10)- (8x8-4)
(100+10) - (64-4)
110 - 60
equals 50