In an arithmetic sequence with a1=-5 and d=-3, which term is -24?The term -24 is the ___th term of the sequence
Answers
Given:
[tex]\begin{gathered} a_1=-15 \\ d=-3 \\ a_n=-24 \end{gathered}[/tex]To find:
The value of n.
Explanation:
The nth term formula for the arithmetic sequence is,
[tex]a_n=a_1+(n-1)d[/tex]Substituting the given values we get,
[tex]\begin{gathered} -24=-15+(n-1)(-3) \\ -24=-15-3n+3 \\ -24=-3n-12 \\ -3n=-24+12 \\ -3n=-12 \\ n=4 \end{gathered}[/tex]Thus, -24 is the 4th term of the sequence.
Final answer:
The term -24 is the 4th term of the sequence.
Related Questions
In a survey, 12 people were asked how much they spent on their child's last birthday gift. The results wereroughly bell-shaped with a mean of $39.1 and standard deviation of $17.4. Estimate how much a typical parentwould spend on their child's birthday gift (use a 99% confidence level). Give your answers to 3 decimal places.Express your answer in the format of ī + Error.$£ $
Answers
Given:
number of people (n) = 12
mean = 39.1
standard deviation = 17.4
99% confidence level
Using the confidence level formula, we can find the estimate of how much a typical parent would spend on their child's birthday:
[tex]\begin{gathered} CI\text{ = x }\pm\text{ }\frac{z\varphi}{\sqrt[]{n}} \\ \text{where x is the mean} \\ z\text{ is the z-score at 99\% confidence interval} \\ \varphi\text{ is the standard deviation} \\ n\text{ is the number of people asked} \end{gathered}[/tex]The z-score at 99% confidence level is 2.576
Substituting, we have:
[tex]\begin{gathered} CI\text{ = 39.1 }\pm\text{ }\frac{2.576\text{ }\times\text{ 17.4}}{\sqrt[]{12}} \\ =26.161\text{ and 52}.039 \end{gathered}[/tex]Hence, a typical parent would spend between $26.161 and $52.039 or :
[tex]39.1\text{ }\pm\text{ 12.939}[/tex]Mario constructs a scale model of a building with a rectangular base. His model is 4.2 inches in length and 2 inches in width. The scale of the model is 1 inch = 15 feet What is the actual area, in square feet, of the base of the building?
Answers
First let's use two rules of three to determine the actual dimensions of the building.
For the length, we have:
[tex]\begin{gathered} 1\text{ inch}\to15\text{ feet} \\ 4.2\text{ inches}\to x\text{ feet} \\ \\ \frac{1}{4.2}=\frac{15}{x} \\ x=15\cdot4.2=63 \end{gathered}[/tex]For the width:
[tex]\begin{gathered} 1\text{ inch}\to15\text{ feet} \\ 2\text{ inches}\to x\text{ feet} \\ \\ \frac{1}{2}=\frac{15}{x} \\ x=15\cdot2=30 \end{gathered}[/tex]Now, calculating the area of the building base, we have:
[tex]\text{Area}=63\cdot30=1890\text{ ft2}[/tex]So the area of the building base is 1890 ft².
URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100 POINTS!!!!!
Order the numbers from least to greatest
Answers
Answer:
-1, √4/5, -6/5, √3, 2, -3√9, 2√125
Step-by-step explanation:
STRUCTURE Quadrilateral DEFG has vertices D(-1, 2), E(-2, 0), F(-1,-1) and G(1, 3). A translation maps quadrilateral DEFG to
quadrilateral D'EFG. The image of D is D'(-2,-2). What are the coordinates of E, F, and G'?
E (
FD
G' (
Answers
The coordinates are;
E' = (-3, -4)F' = (-2, -5)G' = (0, -1)Given,
Quadrilateral DEFG with vertices;
D = (-1, 2)E = (-2, 0)F = (-1,-1) G = (1, 3)We have to find the coordinates of E', F', G'.
A figure is translated when it is moved to the left, right, up, or down.
The original figure's points are all translated (moved) by the same amount and in the same direction.
Here,
Compare the coordinates of D with the coordinates of D' to determine the mapping rule that converts DEFG to D'E'F'G'.
D = (-1, 2)
D' = (-2, -2)
The x-coordinate has be translated 1 unit to the left.
The y-coordinate has been translated 4 units down.
Then,
The mapping rule is:
(x, y) → (x-1, y-4)
To find the coordinates of E', F' and G', apply the mapping rule to the given vertices of the pre-image:
⇒ E' = (-2-1, 0-4) = (-3, -4)
⇒ F' = (-1-1, -1-4) = (-2, -5)
⇒ G' = (1-1, 3-4) = (0, -1)
That is,
The coordinates are;
E' = (-3, -4)F' = (-2, -5)G' = (0, -1)Learn more about translation maps here;
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24. The base of a 13-foot ladder stands 5 feet from a house. Sketch a drawing to model this situation. How many feet up the side of the house does the ladder reach? Explain how drawing the picture helped you solve the problem.
Answers
The draw that describes this situation looks like this:
Drawing this helped us to know that the ladder forms a right triangle with one of the walls of the house.
When we have right triangles we can apply the Pythagoras theorem, from the Pythagoras theorem we can express:
[tex]13^2=5^2+h^2[/tex]Solving for h, we get:
[tex]\begin{gathered} 13^2-5^2=5^2-5^2+h^2 \\ 13^2-5^2=h^2 \\ h=\sqrt[]{13^2-5^2}=\sqrt[]{169-25}=\sqrt[]{144}=12 \end{gathered}[/tex]Then, the ladder reach 12 feet up the side of the house
Lola needs 2/3 cup of lemon-lime soda for every 2 cups of punch. Find ____ cups of soda/cup of punch
Answers
We know that
• There are needed 2/3 cups of lemon soda for every 2 cups of punch.
To find the answer, we have to divide.
[tex]\frac{\frac{2}{3}}{2}=\frac{2}{6}=\frac{1}{3}[/tex]Therefore, the answer is 1/3 of soda/cup of punch.First try was incorrect Fill in the blank. Constant: a number that is next to a variable.
Answers
A number that is right next to a variable. For instance,
[tex]5x+6[/tex]the number 6 is a constant.
solve for missing variable: 11y-36=63
Answers
The equation can be solved as,
[tex]\begin{gathered} 11y-36=63 \\ 11y=63+36 \\ 11y=99 \\ y=\frac{99}{11} \\ y=9 \end{gathered}[/tex]Therefore, the value of y is 9.
Factor by grouping:y^3-5y^2+3y-15
Answers
we have the expression
y^3-5y^2+3y-15
Grouping terms
(y^3-5y^2)+(3y-15)
factor y^2
y^2(y-5)+(3y-15)
factor 3
y^2(y-5)+3(y-5)
factor (y-5)
(y-5)[y^2+3]Answer parts a through E for the function shown below
Answers
Solution
We are given the function
[tex]f(x)=x^3+4x^2-x-4[/tex]First, Let us do the simplification or factorization
[tex]\begin{gathered} f(x)=x^2(x+4)-1(x+4) \\ f(x)=(x^2-1)(x+4) \\ f(x)=(x-1)(x+1)(x+4) \end{gathered}[/tex](a).
The coefficient of x^3 is positive
(b).
So basically, we set f(x) = 0 to get the x - intercepts
[tex]\begin{gathered} f(x)=(x-1)(x+1)(x+4) \\ (x-1)(x+1)(x+4)=0 \\ x=1,-1,-4 \end{gathered}[/tex]The x - intercepts are
[tex]x=1, -1, -4[/tex]The graph of f(x) is also given below
Write 6.5123 x 10^8 in standard
Answers
The standard form is a standard method of writing numbers such that we have it in the form:
[tex]a\times10^b[/tex]where
[tex]0Therefore, 6.5123 x 10^8 in standard form is:[tex]6.5123\times10^8[/tex]Solve the method.simultaneous equation by graphicaly + 3x = 6y - 2x = 1
Answers
The equations given are
[tex]\begin{gathered} y+3x=6............1 \\ y-2x=1............2 \end{gathered}[/tex]The graph of the equations will be shown below
Hence, the solution to the equations is the point where the two equations intersect.
Therefore, the solution is
[tex](1,3)[/tex]A triangular pyramid has a base shaped like an equilateral triangle. The legs of the equilateral triangle are all 5 millimeters long, and the height of the equilateral triangle is 4.3 millimeters. The pyramid's slant height is 3 millimeters. What is its surface area?
Answers
The surface area of the triangular base pyramid is 19.75 mm².
How to find the surface area of a pyramid?The surface area of a triangular pyramid is the sum of the area of the whole sides of the triangular pyramid.
Therefore,
Surface area of a triangular pyramid = base area + 1 / 2 (perimeter × slant height)
The base of the triangular pyramid is an equilateral triangle. An equilateral triangle has congruent sides.
Therefore,
base area = 1 / 2 × 5 × 4.3
base area = 10.75 mm²
Hence,
perimeter of the base = 5 + 5 + 5 = 15 mm
Surface area of a triangular pyramid = 10.75 + 1 / 2 (15 × 3)
Surface area of a triangular pyramid = 10.75 + 1 / 2(18)
Surface area of a triangular pyramid = 10.75 + 9
Surface area of a triangular pyramid = 19.75 mm²
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Two ships are sailing across the Atlantic ocean at the equator. The dofference in solar time between them is two hours. How many degrees of longitude are they apart?
Answers
Answer:
30 degrees
Step-by-step explanation:
There are 360 degrees of longitude ( 360 degrees is a complete circle)
It takes 24 hours to complete a complete rotation of the earth
360 degrees / 24 hours = 15 degrees / hr
15 degrees/ hr * 2 hr = 30 degrees
Maya started to run on a treadmill after setting its timer for 96 minutes. The display says that she has finished 47% of her run. How many minutes have gone by? Round your answer to the nearest tenth.
Answers
Answer:
45.1
Step-by-step explanation:
96 x .47 = 45.12
Rounded to the nearest tenth is 45.1
Percent means per hundred [tex]\frac{47}{100}[/tex] to divide by 100 you move the decimal place to places to the left.
the sum of the angle measures of a polygon with n sides is given find n1440
Answers
Given in the question:
a.) The sum of all angles of a polygon is 1,440 degrees.
To be able to determine what polygon has a total sum of angles of 1,440 degrees, we will be using the following formula:
[tex]\text{ }\Theta=(n-2)x180^{\circ}[/tex]We get,
[tex]\text{ 1},440^{\circ}=(n-2)x180^{\circ}[/tex][tex]\text{ 1},440^{\circ}=180n-360^{\circ}[/tex][tex]180n=1,440^{\circ}\text{ + 360}^{\circ}[/tex][tex]180n=1,800^{\circ}[/tex][tex]\frac{180n}{180}=\frac{1,800^{\circ}}{180}[/tex][tex]n\text{ = 10}[/tex]Therefore, that polygon is a decagon or a polygon with 10 sides.
-353-0-- * GR-35-21-2700-3s 6 - 2y-6- - +28+82-80 -592-35-07-2+27-35-30 9815+ Seesters << RB- --3-1-1-12) 6-5-3= LG - 5+13-2225 SVE -3-5y+6=-24 -*- 4y +50=-21 5r - 55 - 5 = 3r-S-=
Answers
Explanation:
5x - 4y + 2z = 21 ...equation 1
-x - 5y + 6z = -24 ....equation 2
-x - 4y + 5z = -21 ...equation 3
Using elimination method:
multiply equation 2 by 5:
-5x - 25y + 30z = -120 ....equation 2a
add equation 2a from 1:
5x - 5x -4y -25y + 2z + 30z = 21 - 120
0 - 29y + 32z = -99
-29y + 32z = - 99 ....equation 4
multiply equation 3 by 5:
-5x - 20y + 25z = -105 ...equation 3a
add equation 1 and 3a
5x - 5x - 4y - 20y + 2z +25z = 21 - 105
0 - 24y + 27z = -84
-24y + 27z = -84 ...equation 5
-29y + 32z = - 99 ....equation 4 (×-24)
-24y + 27z = -84 ...equation 5 (×-29)
696y - 768x = 2376 ...(4a)
696y -783x = 2436 ...(5a)
subtract 5a from 4a
696y - 696y -768x -(-783x) = 2376 - 2436
0 - 768x + 783x = -60
15x = -60
x = -60/15
x = -4
substitute for x in equation 4a:
696y - 768(-4) = 2376
696y + 3072 = 2376
696y = 2376 -3072
696y = -696
y = -696/696
y = -1
substitute for y in equation 4:
-29(-1) + 32z = -99
29 + 32z = -99
32z = -99 - 29
32z = -128
z = -128/32
z = -4
To graph the inequality y>-3x-4, you would draw a dashed line.O A. TrueO B. False
Answers
True.
Since it is strictly greater
Jordan owns a house painting service. For each house, they charge $95 plus $60 per hour of work. A linear equation that expresses the total amount of money Jordan earns per house is y=60x+95. What are the independent and dependent variables? What is the y-intercept and the slope?
Answers
Answer:
The slope is 60
The y intercept is 95
The independent variable is x (the number of hours)
The dependent variable is y (The amount earned.)
Step-by-step explanation:
I will send u a picture of my equation
Answers
Answer:
where is the picture????
Lily likes to collect records. Last year she had 12 records in her collection. Now she has 15 records. What is the percent increase of
her collection?
The percent increase of her collection is
Answers
Find The distance DB from Cassini yo Tethys when AD is tangent to the circular orbit. Round to the nearest kilometer
Answers
we have that
triangle ABD is a right triangle , because AD is a tangent
so
Apply the Pythagorean Theorem
DB^2=AB^2+AD^2
we have
AB is a diameter (two times rhe radius)
AB=2*295,000=590,000 km
AD=203,000 km
substitute
DB^2=590,000^2+203,000^2
DB=623,946 kmPls someone help me! Giving brainless
Answers
Answer:
ANSWER=5
Step-by-step explanation:
GIVEN=8+(-3)
(+)×(-)=(-)
SO 8-3=5
PLEASE MARK ME AS BRILLINT
Square ABCD is inscribed in a circle with radius 20 m . What is the area of the part of the circle outside of the square
Answers
ANSWER:
456 square meters
STEP-BY-STEP EXPLANATION:
The first thing is to represent the problem in the following figure:
To calculate the area of the part of the circle outside of the square, we must calculate the area of the circle and subtract the area of the inscribed square.
To calculate the area of the square, we plant the following, taking into account that the diagonal of the square is equal to twice the radius and the sides equal to the radius times the root of two, like this:
Knowing the value of the side of the square, we can directly calculate the area of the part of the circle outside of the square, subtracting the corresponding areas like this:
[tex]\begin{gathered} A=A_C-A_S_{} \\ A=\pi\cdot r^2-\mleft(r\cdot\sqrt{2}\mright)^2 \\ \text{replacing} \\ A=3.14\cdot20^2-\mleft(20\cdot\sqrt{2}\mright)^2 \\ A=1256-800 \\ A=456 \end{gathered}[/tex]The area of the part of the circle outside of the square is equal to 456 square meters
prism x imprison wire similar. the volume of prison why is 92 cm3 find the volume of prism x.
Answers
If they are similar, then their side measures are proportional
Prism X, volume = 92 cm^3
can anyone help me? solve using system of linear equations using elimination x – y - 3z = 4 2x + 3y – 3z = -2 x + 3y – 2z = -4
Answers
The solution is x = 2, y = -2 and z =0
How to solve the system of equations?The system of equations is given as
x – y - 3z = 4
2x + 3y – 3z = -2
x + 3y – 2z = -4
Start by eliminating y
To do that, we subtract (2) from (3)
x + 3y – 2z = -4 - (2x + 3y – 3z = -2)
This gives
-x + z = -2
Make x the subject in the above equation
x = z + 2
Substitute x = z + 2 in (1) and (2)
z + 2 – y - 3z = 4
z + 2 + 3y – 2z = -4
Solve the equations
-2z - y = 2
-z + 3y = -6
Multiply -z + 3y = -6 by 2
-2z + 6y = -12
Start by eliminating z
Subtract -2z + 6y = -12 from -2z - y = 2
7y = -14
Evaluate
y = -2
Substitute y = -2 in -z + 3y = -6
-z + 3(-2) = -6
Evaluate
-z - 6 = -6
Evaluate
z = 0
Recall that x – y - 3z = 4
So, we have
x + 2 - 3(0) = 4
Evaluate
x = 2
Hence, the values of the variables are x = 2, y = -2 and z =0
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| 5-6x | -12 = 0Solve the absolute. equation for 2 values of x
Answers
Given
[tex]|5-6x|-12=0[/tex]To solve this equation for both possible values of x, you have to separate it into two calculations.
1) One will be for the case that the values inside the absolute term are multiplied by "+1":
[tex]\begin{gathered} 1\cdot(5-6x)-12=0 \\ 5-6x-12=0 \\ -6x+5-12=0 \\ -6x-7=0 \\ -6x=7 \\ -\frac{6x}{-6}=\frac{7}{-6} \\ x=-\frac{7}{6} \end{gathered}[/tex]The first value of x is -7/6
2) The second will be the case that the absolute values are negative, that is as if they are multiplied by -1
[tex]\begin{gathered} (-1)(5-6x)-12=0 \\ -5+6x-12=0 \\ 6x-5-12=0 \\ 6x-17=0 \\ 6x=17 \\ \frac{6x}{6}=\frac{17}{6} \\ x=\frac{17}{6} \end{gathered}[/tex]The second value of x is 17/6
So for this absolute equation, the possible values of x are -7/6 and 17/6
You must show your work as you... determine whether QR and ST are parallel, perpendicular, or neither. Q(9, 10), R(-5, 2), S(-8, -2), T(-1, 2) Parallel Perpendicular Neither
WILL MARK BRAINLIEST
PLS HELP ASAP
Answers
Slope of QR = 4/7; Slope of ST = 4/7, therefore, the lines are parallel to each other.
How to Determine if Two Lines are Parallel or Perpendicular?To determine if two given lines are perpendicular to each other or parallel to each other, find their slopes.
Slope, m = change in y / change in x.
If they have the same slope, m, then they are parallel lines. If they have slopes that are negative reciprocal to each other, then they are perpendicular lines.
Given:
Q(9, 10)
R(-5, 2)
S(-8, -2)
T(-1, 2)
Find the slope of QR and ST:
Slope of QR = (10 - 2)/(9 -(-5)) = 8/14 = 4/7
Slope of ST = (-2 - 2)/(-8 -(-1)) = -4/-7 = 4/7
The slope are the same, therefore they are parallel to each other.
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Which of the equations below could be the equation of this parabola? A. y = 1/2 x² B. x-1/2 y2 c. y = -1/2 x² D. x = 1/2 y2SUBMIT
Answers
The equation of the parabola is given as;
[tex]y=\frac{1}{2}x^2[/tex]The correct answer is option A.
What is the inverse function of y = (x-4)^2+2
Answers
One way to find the inverse of a function is by first swapping x and y, then solving for y, like this:
[tex]\begin{gathered} y=(x-4)^2+2\text{ }\Rightarrow x=(y-4)^2+2 \\ \end{gathered}[/tex]Now, let's solve for y, like this:
[tex]\begin{gathered} x=(y-4)^2+2 \\ x-2=(y-4)^2+2-2 \\ (y-4)^2=x-2 \\ \sqrt[]{\mleft(y-4\mright)^2}=\sqrt[]{x-2} \\ y-4=\sqrt[]{x-2} \\ y-4+4=\sqrt[]{x-2}+4 \\ y=\sqrt[]{x-2}+4 \end{gathered}[/tex]Then, the inverse function of y = (x-4)^2+2 is:
[tex]y=\sqrt[]{x-2}+4[/tex]