For each given sequence: write down term to term rule and position to term rules 2,5,8,11,14
Answer:
Tn = 3n + 1
Step-by-step explanation:
The given sequence 2,5,8,11,14 is an arithmetic sequence
The nth term of an arithmetic sequence is expressed as;
Tn = a + (n-1)d
a is the first term
d is the common difference
n is the number of terms
Given
a = 2
d = 5-2 = 8-5 = 3
Substitute into the formula
Tn = 2 + (n-1) * 3
Tn = 2 + 3n - 3
Tn = 3n + 1
This gives the term rule for the sequence
click on the image of you can’t see the answers !
Answer:
C
Step-by-step explanation:
plz mark brainliest would really help
Find the sum. Enter your answer in the box below as a fraction, using the slash mark (/) for the fraction bar. 7/17 + 9 /17
Evaluate the radical.
3√27
Enter the answer in the box.
The answer is 3
Hope this Helped :T
At the art store, Aisha bought a few blocks of clay to make a teapot and matching mugs for her aunt. She used 2 1 2 pounds of clay to make the mugs and 1 1 2 times as much clay for the teapot. If each block of clay weighed 2 pounds, how many blocks did Aisha use in all?
Answer:
Step-by-step explanation:
I jus sacrificed for you, the answer is 3 1/8
Aisha must have used 4 blocks of clay in all, as 3 blocks of clay would not have been enough and 4 blocks would be more than enough.
What is an expression?In mathematics, an expression is a combination of numbers, variables, and mathematical operations that represents a value or a quantity. Expressions can contain arithmetic operators such as addition, subtraction, multiplication, and division, as well as functions and constants.
Aisha used 2.5 pounds of clay to make the mugs (2 1/2 = 5/2) and 1.5 times as much clay for the teapot, which means she used 1.5 x 2.5 = 3.75 pounds of clay for the teapot.
Therefore, Aisha used a total of 2.5 + 3.75 = 6.25 pounds of clay.
Since each block of clay weighed 2 pounds, Aisha used 6.25 / 2 = 3.125 blocks of clay.
However, since she cannot use a fraction of a block of clay, Aisha must have used 4 blocks of clay in all, as 3 blocks of clay would not have been enough and 4 blocks would be more than enough.
To know more about an expression follow
https://brainly.com/question/28415327
#SPJ2
Line m is represented by the equation y + 2 = 3/2(x + 4). Select all equations that
represent lines perpendicular to line m.
A. y = -3/2x +4
B. y = -2/3x +4
C. y = 2/3x +4
D. y = 3/2x +4
E.y+1=-4/6(x+5)
F.y+ 1 = 3/2(x + 5)
The equations representing the lines that are perpendicular to line m are:
B. y = -2/3x +4
E. y+1=-4/6(x+5)
What is the Slope of Perpendicular Lines?Lines that are perpendicular to each other have slopes that are negative reciprocal of each other.
For example, if a line has a slope of 2, the slope of a line that is perpendicular to it would be, -1/2 (negative reciprocal of 2).
Determine the slope of the given line whose equation is, y + 2 = 3/2(x + 4). Rewrite the equation in slope-intercept form [y = mx + b]:
y + 2 = 3/2x + 6
y = 3/2x + 6 - 2
y = 3/2x + 4
The slope is therefore 3/2.
Negative reciprocal of 3/2 is -2/3.
Examine each of the equations given and see which equation has a slope of -2/3.
A. y = -3/2x +4, the slope is -3/2.
B. y = -2/3x + 4, the slope is -2/3. (perpendicular)
C. y = 2/3x +4, the slope is 2/3.
D. y = 3/2x +4, the slope is 3/2.
E. y+1=-4/6(x+5), rewrite in slope-intercept form
y+1=-4/6x + 20/6
y + 1 = -2/3x + 10/3
The slope is -2/3. (perpendicular)
F. y+ 1 = 3/2(x + 5), the slope is 3/2.
Therefore, the equations representing the lines that are perpendicular to line m are:
B. y = -2/3x +4
E. y+1=-4/6(x+5)
Learn more about equations of perpendicular lines on:
https://brainly.com/question/7098341
Find the value for x
Answer:
Value of x --> 15°
Step-by-step explanation:
(2x + 60°) and 6x lie on a straight line. So, they form a linear pair. Their sum gives 180°.
---> (2x + 60°) + 6x = 180°
2x + 60° + 6x = 180°
8x + 60° = 180°
8x = 180°- 60°
8x = 120
x = [tex]\frac{120}{8}[/tex]
x equals 15°What is the slim of the fractions? Use the number line to help find the answer.
3/5 + (-7/5)?
Zina goes shopping. She buys in the same store two scarves and three T-shirts for
49 euros. A week later, it was the sales: reduction of 1.5 euros on scarves and 2 euros
on t-shirts. Zina took the opportunity and for 40 euros, she was able to buy four scarves and five T-shirts.
What was the price of a scarf and a T-shirt before the sales?
THX FOR HELPING!
Answer:
The price of T-shirts before the sale = 42 euros
The price of scarves before the sale = -77/2 euros
Step-by-step explanation:
The cost of the items Zina buys from the store initially are;
Two scarves and three T-shirts for 49 euros
The reduction in the price of scarves a week later during sales = 1.5 euros
The reduction in the price of T-shirts a week later during sales = 2 euros
The items Zina bought for 40 euros at the reduced price of the sales opportunity are;
Four scarves and five T-shirts for 40 euros
Let 'x' represent the initial price of a scarf and let 'y' represent the initial price of a T-shirt, we have;
2·x + 3·y = 49...(1)
4·(x - 1.5) + 5·(y - 2) = 40...(2)
Expanding equation (2) gives;
4·x - 6 + 5·y - 10 = 40
4·x + 5·y = 40 + 6 + 10 = 56
∴ 4·x + 5·y = 56...(3)
By multiplying equation (1) by 2 and subtracting the result from equation (3), we get;
4·x + 5·y - 2 × (2·x + 3·y) = 56 - 2 × 49 = -63
-y = -42
y = 42
The price of T-shirts before the sale = 42 euros
x = (49 - 3 × 42)/2 = -77/2
x = -77/2
The price of scarves before the sale = -77/2 euros
(However, if the had bought the 4 scarves and 5 T-shirts during sales at 70 euros, we get;
The price of T-shirts before the sale = 12 euros
The price of scarves before the sale = 6.5 euros.
The allowable total price for the reduced 4 scarves and 5 T-shirts is between 66 and about 82 for both initial prices to be +ve)
PLEASE HELP FAST 100 POINTS!
Construct the graph of the following function and identify its zeros on the same document. f(x) = (-x + 2)(x + 1)(x +2). Upload your document in the box below.
Answer:
Given function:
f(x) = (-x + 2)(x + 1)(x +2)We can rewrite it as:
f(x) = - (x - 2)(x + 1)(x +2)Zeros are:
- (x - 2)(x + 1)(x +2) = 0x - 2 = 0 ⇒ x = 2x + 1 = 0 ⇒ x = -1x + 2 = 0 ⇒ x = -2As leading coefficient is negative the function is decreasing.
As the function is of degree 3, it is odd.
Considering the above two factors we can define the shape of the graph:
It is decreasing function with one local minimum and one local maximum.See the graph and zero's reflected.
Analyze the function:
[tex]f(x) = \\ ( - x + 2)(x + 1)(x + 2)[/tex]
Write properties of function:
Solution:
x-intercept/zero
[tex] {x}^{1} = - 2 \\ {x}^{2} = - 1 \\ {x}^{3} = 2[/tex]
y-intercept:
[tex]y = 4[/tex]
domain:
[tex]( - \infty \: . \: + \infty )[/tex]
type of function:
[tex]cubic \: function[/tex]
standard form:
[tex]f(x) = - {x}^{3} - {x}^{2} + 4x + 4[/tex]
factorized form:
[tex]f(x) = - ( - (x + 1)( x + 2) ( - 2x + 2))[/tex]
even/odd:
[tex]neither[/tex]
bounce/cross x-axis:
[tex]x = - 2 \: . \: cross \: . \: x = - 1 \: . \: cross \: . \: x = 2 \: . \: cross[/tex]
increasing interval:
[tex]{ - \frac{1}{3} - \frac{ \sqrt{13} }{3} - \frac{1}{3} + \frac{ \sqrt{13} }{3} }[/tex]
decreasing interval:
[tex]( - \infty - \frac{1}{3} - \frac{ \sqrt{13} }{3} )( - \frac{1}{3} + \frac{ \sqrt{13} }{3} \infty )[/tex]
number of possibles real zero:
[tex]3[/tex]
number of possible turning points:
[tex]2[/tex]
order/degree:
[tex]3[/tex]
leading term:
[tex] - {x}^{3} [/tex]
leading coefficient:
[tex] - 1[/tex]
constant terms:
[tex] - 1[/tex]
end behavior:
[tex]as \: x + \infty \: f(x) - \infty \\ as \: x - \infty f(x) \infty [/tex]
The cost of a barrel of beans, b, fluctuates by 17% in both directions during a three-month period.
Match each verbal description of the high and low cost of a barrel of beans with all equivalent expressions.
Answer:
A, H, I, J, E, and F I think. In order from b + 0.17b to 1.17b
Step-by-step explanation:
This kind of doesn't make sense but I just went with my best shot.
Answer:
b increased by 17% =b + 17% of b =b + 0.17b = 1.17bCorrect ones A and F
------------------------------------------
b decreased by 17% =b - 17% of b =b - 0.17b = 0.83bCorrect ones H and K
Latifah drew this obtuse, scalene triangle.
A triangle has side lengths 8 and 10. The angle between the 2 sides has a measure of 116 degrees.
She will draw a congruent triangle and use it to form a 4-sided polygon. What type of quadrilateral could it be?
a quadrilateral that is a parallelogram
a rectangle that is not a rhombus
a rhombus
a square
Answer:
i'd say its a rhombus (C)
Step-by-step explanation:
i have this question on my exam on edg. and that is the answer i came up with after reviewing the image that was provided on the exam.
other people say that its a quadrillateral that is a parallelogram but i drew out the shape and the lines were intersecting. so its probably not A. :)
Jesus is King!!
Which of the following is the equation of a circle with center Left-parenthesis 5 comma negative 2 right-parenthesis and a radius of 3?
Answer:
A.
Step-by-step explanation:
(x-5)^2 +(y+ 2)^2= 9 radius
Rest of the questions...
1. A. (x-5)^2 +(y+ 2)^2= 9 radius
2. C. (x-3)^2+(y+5)^2= 64
3. A. Center =(-8,-9) radius 3
4. The equation of a circle is (x-7)^2 + y^2=225
5. A circle with center (-2,6) passes through the point (-2,10).
6. A circle with center (1,2) passes through the point (0,6).
7. Write the equation of the circle shown here.
8. C. (x-4)^2 + (y-3)^2
9. C. x^2+Y^2 = 15,81,600
10. Part B which of the following is the length of a 1 degree arc on the equator, to the nearest mile.
classifying triangles
Answer:
What you are looking at is a scalene triangle!
Step-by-step explanation:
By definition scalene triangles are triangles where each side is a different length... hope this one helps you!
Answer:
C
Step-by-step explanation:
Because all its corners are below 90 degrees
Yuki just bought a big-
screen TV set. The
screen has a diagonal
measure of 40 in. If the
screen is 32 in. wide,
how high is it?
Answer:
24 I think..
Step-by-step explanation:
a^2 + b^2 = c^2
32^2 + b^2 = 40^2
b^2 = 1600 - 1024
b^2 = 576
b = 24
I will mark you brainlest!
On Saturday Leon biked an average speed of 14.5 miles per hour for 1.5 hours. Then on Sunday he biked in average speed of 15 per hour for 2.75 hour. What was the total distance Leon bike in miles in weekend?
Answer: 63
Step-by-step explanation:
14.5x1.5=21.75
15x2.75=41.25
21.75+41.25=63
What is 70×100000? will give 30 points.
Answer:
70000000
Step-by-step explanation:
Fill in the missing number. 7 + __ = 88
Answer:
[81 is the missing number.]
Step-by-step explanation:
7+x=88
Let us substitute the mixing number as x.
To find a variable we must ISOLATE it.
To isolate in this situation, we must remove the 7.
We must subtract 7 from both sides, to isolate x. like this-
7-7+x=88-7
This results in,
x=81
So this missing number or (x) is equal to 81
Calculate AC
Round to the nearest tenth.
Answer:
3,266.53
Step-by-step explanation:
i looked it up :)
Answer:
AC = 11.4
Step-by-step explanation:
6/sin 23 = AC/sin 132
6 sin 132/sin 23 = AC
AC = 11.4
Evaluate the following:
F(x) = 4x - 9 for f(5)
Answer:
f(5)=11
Step-by-step explanation:
f(x)=4x-9
f(5)=4(5)-9
f(5)=20-9
f(5)=11
Answer:
f(5) = 11
Step-by-step explanation:
F(x) = 4x - 9 for f(5)
x gets replaced with 5
f(5) = 4(5) - 9
f(5) = 20 - 9
f(5) = 11
Answer in the 10-1 quiz intro to circles, central angles, arcs, and chord
Answer:
1.5
Step-by-step explanation:
The answers are given in the solution below.
What is a circle?A circle is a round-shaped figure that has no corners or edges. In geometry, a circle can be defined as a closed, two-dimensional curved shape.
Given is topics related to circle and its part we need to answer the question asked,
1) to 7) Given is a circle T,
a) Radius = TS, QT and RT all are the radius
b) Diameter = QS
c) Chord = PS
d) Central angle = ∠ RTQ
e) Minor arc = arc QR
f) Major arc = arc QSR
g) Semicircle = QPS
8) to 9) :-
a) Circle with radius 18 in :-
Circumference = 2π×radius = 2×3.14×18 = 113.04 in
Area = π·radius² = 3.14×18² = 1017.36 in²
b) Circle with diameter 25 m :-
Circumference = 2π×radius = 2×3.14×12.5 = 78.5 m
Area = π·radius² = 3.14×12.5² = 490.625 m²
10) The circle is having an area of 201.06 cm², we need to find the circumference and diameter,
Area = π·radius² = 201.06 cm²
radius² = 201.06 / 3.14
= 64
radius = 8 cm
Diameter = 16 cm
Circumference = 2π×radius = 2×3.14×8 = 50.24 cm
11) :-
Circle with radius P :-
The rule we will use here is :- arcs equal to central angle opposite to it, and full circle measures 360°
a) ∠ KPL = 90°
So, by linear pair sum, ∠ NPL = 90°
Now, by angle substitution law, ∠ NPM + ∠ MPL = 90°
∠ NPM = 27°
By using vertical angles rule, ∠ JPK = ∠ NPM = 27°
Therefore, arc JK = 27°
b) arc NJ = 180° - 27° = 153°
c) arc JL = 90°+27° = 117°
d) arc KNM = 360°-(90°+63°) = 207°
e) arc MJL = 360°-63° = 297°
f) arc JLK = 360°-27° = 333°
12) :-
arc CD + arc AD = 180°
Therefore,
19x-49°+5x+37° = 180°
24x-12 = 180°
24x = 192°
x = 8
Therefore,
arc CD = 5x+37 = 74°
13) :-
Length of an arc = central angle / 360° × 2π×radius
= 232° / 360° × 2 × 3.14 × 5 = 20.23 mm
14) :-
= 73° / 360° × 2 × 3.14 × 14.5 = 18.46 ft
Learn more about circles, click;
https://brainly.com/question/29142813
#SPJ2
If angle a has the terminal ray that falls in the fourth quadrant and cosine a equals 5/9 then determine the value of sin a in simplest radical form
Answer: [tex]-\dfrac{2\sqrt{14}}{9}[/tex]
Step-by-step explanation:
Given
[tex]\cos a=\dfrac{5}{9}[/tex]
[tex]a[/tex] lies in the fourth quadrant
So, sine must be negative in the fourth quadrant
Using identity [tex]\sin ^2 x+\cos^2 x=1[/tex] to find sine value
[tex]\Rightarrow \sin^2 a=1-\dfrac{5^2}{9^2}[/tex]
[tex]\\\\\Rightarrow \sin^2 a=1-\dfrac{25}{81}\\\\\\\Rightarrow \sin^2 a=\dfrac{56}{81}\\\\\\\Rightarrow \sin a=-\sqrt{\dfrac{56}{81}}\\\\\\\Rightarrow \sin a=-\dfrac{2\sqrt{14}}{9}[/tex]
If a box has 5 red, 3 green, and 4 blue jelly beans, then what is the probability of choosing
at random a red jelly bean?
7/12, 5/12, 1/12, 2/7
Answer:
2/7
Step-by-step explanation:
Answer:
5/12
Step-by-step explanation:
All the beans are equally likely to be chosen, so the bottom (denominator) of the fraction is 12 (there are 12 beans in the box).
The numerator is 5 because that's the number of red beans in the box.
A rectangle has an area of 96 in2. The rectangle's base is 4 in. What is the height of the rectangle?
A. 384in
b. 24in
c. 92in
d. 100in
Answer:
B. 24
Step-by-step explanation:
Formula for area of a rectangle: base × height/ length × width
To find the height, divide the area by the base.
[tex]96/4=24in[/tex]
[tex]formula=base *height/length*width[/tex]
[tex]4*24=96in^2[/tex]
PLEASE HELP!!!!!!!!!
Answer:
if I had to guess I whould say i
I need help, and a step by step explanation! :)
Answer:
90°
Step-by-step explanation:
There is no work. We know the right angle in the triangle and the x are supplementary. Meaning, they add up to 180 degrees. Therefore, 180-90 = 90. Think of it as a full triangle. If the 40 at the top was not half, but a full triangle, the 40 at the top would become 80. The 50 in the bottom left would mean there would be a 50 in the bottom right when you mirror the triangle. Therefore, you also need x to be 90 to make it a right triangle.
A part of an exponential function is graphed on the grid
Which inequality best represents the domain of the part shown?
Option A is correct, x≥-2 inequality best represents the domain of the part shown,
What is a function?A relation is a function if it has only One y-value for each x-value.
The domain of a function is the set of all possible inputs for the function
Domain is the set of x values in a function such as f(x).
The range of a function is the set of values that the function assumes.
This set is the values that the function shoots out after we plug an x value in.
In a graph, it is the values that the x-axis assumes.
As we observe the graph, x assumes values of -2 and greater, hence, the inequality is x≥-2.
Hence, x≥-2 inequality best represents the domain of the part shown, Option A is correct.
To learn more on Functions click:
https://brainly.com/question/21145944
#SPJ5
square root of 225/16 AS A FRACTION!!!
The solution is, square root of 225/16 is 15/4.
What is Square root?A square root of a number is a value that, when multiplied by itself, gives the number. In mathematics, a square root of a number x is a number y such that y² = x; in other words, a number y whose square is x.
For example, 4 and −4 are square roots of 16, because 4² = ² = 16.
here, we have,
225/16
=15^2/4^2
so, square root of 225/16
=√15^2/4^2
=15/4
Hence, The solution is, square root of 225/16 is 15/4.
To learn more on square root click:
brainly.com/question/29286039
#SPJ5
Please Help!!!! Write an exponential function. In your own words, describe the rate of change of this function and what the graph looks like.
Answer:
A rate of change is a rate that describes how one quantity changes in relation to another quantity. If x is the independent variable and y is the dependent variable, then. rate of change=change in y change in x. Rates of change can be positive or negative.
Step-by-step explanation:
Answer:
A rate of change is a rate that describes how one quantity changes in relation to another quantity. If x is the independent variable and y is the dependent variable, then. rate of change=change in y change in x. Rates of change can be positive or negative.
Step-by-step explanation:
Please help me asap
Answer:
2) 25%
Step-by-step explanation:
Answer:
The answer is (2)
Step-by-step explanation: