Answer:
- 98Step-by-step explanation:
Given
[tex]a_{21}=-32[/tex][tex]a_{50}=-119[/tex]Find [tex]a_{43}[/tex]
We know that
[tex]a_n=a_1+(n-1)d[/tex]Appy this to the two known terms and find the first term and the common difference
[tex]a_1+20d=-32[/tex] ⇒ [tex]a_1=-20d-32[/tex] [tex]a_1+49d=-119[/tex] ⇒ [tex]a_1=-49d-119[/tex]Find the coomon difference
-20d - 32 = - 49d - 11949d - 20d = 32 - 11929d = - 87d = - 87/29d = - 3Find the first term
a₁ = - 20(- 3) - 32 = 60 - 32 = 28Now find the 43th term
a₄₃ = 28 + 42(- 3) = 28 - 126 = - 98Answer:
-98
Step-by-step explanation:
General form of an arithmetic sequence:
[tex]a_n=a+(n-1)d[/tex]
where:
[tex]a_n[/tex] is the nth terma is the first termd is the common difference between termsGiven:
[tex]a_{21}=-32[/tex][tex]a_{50}=-119[/tex]To find the 43rd term we need to construct an equation for the nth term. To do this, find the first term and the common difference by substituting the given information into the general formula to create a system of equations that can be solved.
[tex]\begin{aligned} \underline{\textsf{Equation 1}}} \\ a_{21} & =-32 \\ \implies a+(20-1)d & = -32 \\a+20d & =-32 \end{aligned}[/tex]
[tex]\begin{aligned} \underline{\textsf{Equation 2}}} \\ a_{50} & =-119 \\ \implies a+(50-1)d & = -119 \\a+49d & =-119 \end{aligned}[/tex]
Subtract Equation 1 from Equation 2 to eliminate a:
[tex]\begin{array}{r l}a+49d & = -119\\- \quad a+20d & = -32\\\cline{1-2}29d & = -87\end{aligned}[/tex]
Solve for d:
[tex]\implies d=\dfrac{-87}{29}=-3[/tex]
Substitute the found value of d into one of the equations and solve for a:
[tex]\implies a + 20(-3)=-32[/tex]
[tex]\implies a=28[/tex]
Substitute the found values of a and d into the general formula to create an equation for the nth term:
[tex]\implies a_n=28+(n-1)(-3)[/tex]
[tex]\implies a_n=31-3n[/tex]
Finally, substitute n = 43 into the found formula to find the 43rd term of the sequence:
[tex]\implies a_{43}=31-3(43)=-98[/tex]
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The wood on the back deck of a house needs waterproofing. The shape of the deck is a rectangle with the length * 35 feet and a width of 5 yards. A gallon can of waterproof stain covers 80 square feet and costs $19.99 per can plus 7% sales tax. You go to the hardware store to purchase the waterproof stain needed to complete the job. You give the cashier $150.
How much change do you receive, or how much additional cash must you find in order to be able to pay for all of the
stain you need? You must show all calculations.
Area of Rectangle = length X width
You cannot split up a can of stain.
You must show all calculations.
A copy machine makes 44 copies per minute. How many copies does it make in 4 minutes and 15 seconds?
Answer: 102 copies
Step-by-step explanation:
4 minutes and 15 seconds are 4.25 minutes, so it will make 102 copies in that time
PLS HELP!!! No links pls and Ty <3333
Answer:
The area is 176.6
Step-by-step explanation:
The formula for the area of a circle is "πr²"
This means you square the radius, and multiply it by pi.
Our diameter is 15, and the radius is half of the diameter.
15 ÷ 2 = 7.5
Next, we square the radius. (7.5)
Let's fill it into the formula.
π7.5²
After squaring, it's this:
π56.25
In your question, pi is 3.14, so let's replace that.
(3.14)56.25
After multiplying we get 176.625, after we round, we get 176.6
176.6 is the area.
Brainliest please?
Answer:
The area is 176.6
Step-by-step explanation:The formula for the area of a circle is "πr²"This means you square the radius, and multiply it by pi.Our diameter is 15, and the radius is half of the diameter.15 ÷ 2 = 7.5Next, we square the radius. (7.5)Let's fill it into the formula.π7.5²After squaring, it's this:π56.25In your question, pi is 3.14, so let's replace that.(3.14)56.25After multiplying we get 176.625, after we round, we get 176.6176.6 is the area.
Step-by-step explanation:
Help me with this question, please
Answer:
Step-by-step explanation:
x+y=10
1.50x+2.50y=22
Then use the the elimination method. The final answer is x=3, y=7.
Choose the square with a perimeter of 24 inches.
A) A
B) B
C) C
Answer:
A. 6+6+6+6=24
Hope this helps!
Answer:
its a
Step-by-step explanation:
⇒ because if you add 6 four types it equals = 24 inches hope this helped
Lars read that there are about
210,000 grains of salt in one
teaspoon.
How is 210,000 written as a power
of ten?
A. 210 X 104
B. 21 X 104
C. 21 X 108
D. 2.1 X 10^
Answer
the answer is a
Step-by-step explanation:
13/6 renamed as a mixed number
Answer:
2 1/6
Step-by-step explanation:
13/6 is 6/6 + 6/6 + 1/6... each 6/6 = 1 sooo. 2 and 1/6 :)
orrr
6*2 is 12 (closest multiple of 6 to 13, so 2 is whole number w/ 1(/6) as a remainder
Need help with this problem
Answer: B) 86°
Step-by-step explanation:
The angles of a triangle always add to equal 180.
So let's call the third angle x and add the other two angles with it.
32+62+x=180
94+x=180
Now we solve for x
Subtract 94 from both sides
94-94+x=180=94
x=86
Which of the following equations does not have an x-intercept? Select all that apply.
A) y=x+0
ОВ) y=x
C) y=0x + 3
OD) y=0
E)y=5
F) y 3x+0
We can conclude from the slope intercept result, the equation with no x-intercept is C) y=0x + 3, D) y=0, E) y=5
What is slope intercept?In mathematics, the slope-intercept form of a linear equation is an equation of the form y = mx + b, where m is the slope of the line and b is the y-intercept, which is the point on the line where it intersects the y-axis.
Because it allows you to easily view the line and identify its slope and y-intercept, the slope-intercept form is a useful way to describe a line's equation. The slope of the line denotes its steepness, while the y-intercept indicates where the line intersects the y-axis.
The x-intercept of an equation is the point at which the equation's graph intersects the x-axis. When the value of y is zero, something happens. As a result, an equation lacks an x-intercept horizontal line that does not intersect the x-axis.
C) y=0x + 3 (A horizontal line with a y-intercept of 3 that does not cross the x-axis.)
D) y=0 (This is a horizontal line that passes through the origin but does not intersect the x-axis.)
E) y=5 (This is a horizontal line that passes through (0,5) but does not cross the x-axis.)
F) y=3x+0 (This is a straight line travelling through the origin and does cross the x-axis) (This is a straight line passing through the origin and does cross the x-axis)
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Answer:
C and E
Step-by-step explanation:
because i did the assignment and got it right
If an orthocenter lies inside of a triangle, then the triangle must be
isosceles.
obtuse.
right.
acute.
Answer:
acuteStep-by-step explanation:
Remember :the orthocenter of a triangle is the point of concurrency of the 3 altitudes.
[tex]\large \text{If an orthocenter lies inside of a triangle, then the triangle must be}\ :\\\\\large isosceles. \\\\\large obtuse. \\\\\large right. \\\\\large acute \checkmark[/tex]
If an orthocenter lies inside of a triangle, then the triangle must be acute.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Orthocenter of a triangle is the intersection of any two of three altitudes of a triangle.
The third altitude usually pass through the point of the first two altitudes.
When the orthocenter lies inside a triangle, the angles formed by the intersection of the three altitudes is less than 90 degrees.
An acute triangle is a type of triangle whose angles are less than 90 degrees.
Hence, If an orthocenter lies inside of a triangle, then the triangle must be acute.
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Write −0.258
as a fraction in simplest form. ITS NOT 129/500
A point has zero dimension.
Q.A. True
• B. False
SUBMIT
Parallelogram ABCD has the following vertices: A(3,6), B(6,8), C(9,6), and D(6,4). In two ut more complete sentences, explain how you can use the coordinates of the vertices to prove that parallelogram ABCD is a rhombus.
Explanation:
A rhombus is a parallelogram in which the diagonals are mutual perpendicular bisectors. The coordinates of the vertices can be used to show ...
the diagonals bisect each otherthe diagonals are perpendicularWhen both these conditions are met, the quadrilateral is a rhombus.
__
Mutual BisectorsThe diagonals will have the same midpoint (bisect each other) if the sum of the coordinates at the ends of one diagonal is the same as the sum of the end point coordinates of the other diagonal:
A +C = B +D
(3, 6) +(9, 6) = (6, 8) +(6, 4)
(3+9, 6 +6) = (6 +6, 8 +4)
(12, 12) = (12, 12) . . . . . . midpoints are the same; ABCD is a parallelogram
__
PerpendicularThe diagonals will be perpendicular if the sum of the products of the coordinate differences of their end points is zero.
AC⋅BD = (C -A)⋅(D -B) = (9 -3, 6 -6)⋅(6 -6, 4 -8)
= (6, 0)⋅(0, -4) . . . . . end point differences; we want their dot-product
= (6)(0) +(0)(-4) = 0 +0 = 0 . . . . diagonals are perpendicular
_____
Additional comment
The midpoints are computed as (A+C)/2 and (B+D)/2. We have multiplied each of them by 2 to simplify the arithmetic. Our resulting sums of (12, 12) must be divided by 2 to get the actual midpoint of the rhombus: (6, 6).
The notion of "dot product" is a vector notion. Two vectors are perpendicular when their dot product is zero. The dot product is the scalar sum of the products of corresponding coordinates.
Find f(3) if f(x) = 4x + 12.
I NEED HELP! I don’t get it at all
Answer:
5.83 cubic feet
Step-by-step explanation:
Volume of block1 :
l = 4 ft
[tex]\sf w = \dfrac{5}{6} \ ft\\\\ h = 1\dfrac{1}{6}=\dfrac{7}{6} \ ft[/tex]
[tex]\sf Volume \ of \ block1 = l*w*h\\[/tex]
[tex]\sf =4 *\dfrac{5}{6}*\dfrac{7}{6}\\\\ =\dfrac{5}{3}*\dfrac{7}{3}\\\\= \dfrac{35}{9} \ cubicfeet[/tex]
Volume of block2:
l = 4 ft
[tex]w = 1\dfrac{2}{3}-\dfrac{5}{6}\\\\ =\dfrac{5}{3}-\dfrac{5}{6}\\\\ =\dfrac{5*2}{3*2}-\dfrac{5}{6}\\\\=\dfrac{10}{6}-\dfrac{5}{6}\\\\w =\dfrac{5}{6} \ ft\\\\h =\dfrac{7}{12} \ ft[/tex]
[tex]\sf Volume \ of \ block2 = 4 *\dfrac{5}{6}*\dfrac{7}{12}[/tex]
[tex]\sf = \dfrac{5}{6}*\dfrac{7}{3}\\\\= \dfrac{35}{18} \ cubicft[/tex]
Amount of concrete to build stairs = Volume of block1 + volume of block2
[tex]\sf = \dfrac{35}{9}+\dfrac{35}{18}\\\\=\dfrac{35*2}{9*2}+\dfrac{35}{18}\\\\=\dfrac{70}{18}+\dfrac{35}{18}\\\\=\dfrac{105}{18}\\\\= 5.83 \ cubic feet[/tex]
What is the product? (2 x minus 1)(x 4) 2 x squared minus 4 2 x squared 4 2 x squared 7 x minus 4 2 x squared minus 7 x minus 4
The product of the given equation (2x - 1)(x +4) is 2x^{2} +7x -4.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
The given expression is
[tex](2x - 1)(x +4)[/tex]
Multiply term by term,
[tex]2x \times x + 2x \times 4+ (-1)\times x + (-1)\times 4\\2x^{2} +8x -x -4\\2x^{2} +7x -4[/tex]
Thus, The product of the given equation is [tex]2x^{2} +7x -4[/tex].
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Sam has 3 candy bars and he wants to divide them into 8 equal portions to give to friends. What fraction will each person receive?
Answer: [tex]\frac{3}{8}[/tex] of the 3 candy bars
Step-by-step explanation:
We will divide the total number of candy bars by the portions.
3 candy bars / 8 portions = [tex]\frac{3}{8}[/tex]
Each friend will receive [tex]\frac{3}{8}[/tex] of the 3 candy parts
Complete the equation below to make an equation that is equal to 1.
Answer: 5/10 +5/10 =10/10 =1
Step-by-step explanation: I don't think this requires much explanation. Any number with same numerator and denominator equals 1.
When you get 10/10, the first and second box can be figures that sum up to be 10.
It can be 7 and 3, it can be 6 and 4
7 pounds of turkey cost $21
Answer:
1 pound of turkey is 3 dollars
Step-by-step explanation:
Answer:
1 lb of turkey costs 3$
Step-by-step explanation:
You divide the cost by the pound to find the answer
21/7 =3
Help me please thanks
5(w. 9)
hope it really helps...!!!
which graph represents the solution set of this inequality?
please help!!!
Answer:
C is the correct answer due to two-step inequality process
Step-by-step explanation:
Your inequality is: 5a + 18 < -27
First, you must remember that the < or > shall not be shaded in.
You could automatically eliminate answer A.
Now you need to do two-step inequalities which is the same thing as two-step equations but with an inequality sign.
5a + 18 < -27
5a < -27-18
5a < -45
**Now, here's something important: If you are multiplying with negatives while dealing with inequalities you must switch the sign to its opposite.
-9 > a
You need to find a number line that has numbers less than -9. It could be -10, -11, -12, -122, etc.
C is the correct answer.
If you donate $150 in total a year , How much money did you donate on the first month of the year.
Answer:
$12.50
Step-by-step explanation:
You donate $150 in total in a year.
To find out how much you donated on the first month, remember the relation between a year and number of months.
⇒ 1 year = 12 months
⇒ 1 month = 1/12 year
Finding the amount donated
Divide the money donated in a year by 12$150/12$12.50To estimate the product of 44 x 52, what is the best way to round the factors?
45 x 55
40 x 50
50 x 50
40 x 55
WILL MARK BRAINLIEST
Given C = 119º, B= 44°, and c = 15, use the
Law of Sines to solve the triangle for the
value of a. Round answer to two decimal
places.
Step-by-step explanation:
A+B+C=180° (Sum of angles in a triangle)
A+44°+119°=180
A+163°=180°
A=17°
Using Sine Rule
a/Sin A=c/Sin C
Subtitute the value of A, c and C into the formula
a/Sin 17°=15/Sin 119°
Cross Multiply
a=15Sin17°/Sin119°
a=5.01 (2 d.p)
hello brainly team I need help
Answer:
5)
x=13.856
y=8
6)
u=4
v=3.464
Step-by-step explanation:
5)
y=hypothesis * sin(opposing angle)/sin(angle opposite of hypothesis)
y = 16*sin(30)/sin(90)
y=8
x=hypothesis * sin(opposing angle)/sin(angle opposite of hypothesis)
x=16*sin(60)/sin(90)
x=13.856
6)
sinA/(opposite of angle A) = sinB/(opposite side of angle B) = sinC/(opposite of side of angle C)
sin(90)/u= sin(30)/2
u *sin(30) = 2* sin(90)
u *sin(30) = 2
u=2/sin(30)
u=2/0.5
u=4
sin(60)/v= sin(30)/2
v *sin(30) = 2* sin(60)
v *sin(30) = 2 * 0.866
v * sin(30) = 1.73
v = 1.73/sin(30)
v = 3.464
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
[5] x = 8 and y = 13.856
[6] v = 4 and u = 3.464
≤ Step-by-step explanation ≥-------------------------------------------------------------------------------------------------------------
[5]
sin60° = x/16 = 1/2
x = 16/2 = 8
cos60° = y/16 = √3/2
y = 16√3/2 = 8√3
Can also be : 8√3 = 13.856
-------------------------------------------------------------------------------------------------------------
[6]
sin30° = 2/u = 1/2
u = 2 x 2 = 4
tan30° = 2/v = √3
v = 2√3
can also be: 2√3= 3.464
-------------------------------------------------------------------------------------------------------------
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~lenvy~
Is 6x^-3x a polynomial
Write these as ordinary numbers:
A. 4×10³
B. 7×10⁹
C. 4×10⁰
= 4000
B. 7×10⁹= 7000000000
C. 4×10⁰= 4
( to convert back to ordinary form just move the decimal point according to the power. )
Answer:
A. 4000
B. 7000000000
C. 4
Step-by-step explanation:
A. 4×10³
= 4 × 1000
= 4000
B. 7×10⁹
= 7×1000000000
= 7000000000
C. 4×10⁰
(a⁰=1)
= 4×1
= 4
!!PLEASE PLEASE PLEASE PLEASE MARK ME THE BRAINLIEST!!
Beth and Leslie are trying to decide which one of them gets to portray the lead character in a student play. They will use a random number generator to produce an integer. If the integer that comes up is odd, Beth gets to play the lead, and if the integer is even, Leslie gets to play the lead. Having the random integer generated be in which interval will make this a fair decision?
A) from 2 to 10 B) from 3 to 15 C) from 5 to 20 D) from 5 to 25
The fair interval illustrates a sample space
The interval that will make a fair decision is from 5 to 20
How to determine the fair interval?From the question, we understand that:
Beth plays the lead, and if the integer is even, Leslie plays the lead, if otherwiseSince they choose odd and even integers, then the sample space must be divisible by the number of people (i.e 2 people)
The sample space (S) is calculated as:
S = Highest - Least + 1
A) from 2 to 10S = 10 - 2 + 1 = 9
B) from 3 to 15S = 15 - 3 + 1 = 13
C) from 5 to 20S = 20 - 5 + 1 = 16
D) from 5 to 25S = 25 - 5 + 1 = 21
Only 16 can be divisible by 2
Hence, the interval that will make a fair decision is from 5 to 20
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Describe the difference between rotation and revolution. Your answer should include a definition of each as well as what each one causes.
Answer:
Rotation" refers to an object's spinning motion about its own axis.
"Revolution" refers the object's orbital motion around another object.
For example, Earth rotates on its own axis, producing the 24-hour ( a day.)
Earth revolves about the Sun, producing the 365-day (a year).
A football is thrown into the air from an initial height of 4 feet with an upward velocity of 46 ft/sec. The function h = -16t² + 46t + 4 gives the height after t sec.
whats the vertex?
axis of symmetry?
solutions?
2 other points?
and i know the balls max height is 37.06
Answer:
Vertex = (1.4375, 37.0625)
Axis of symmetry: t = 1.4375
x-intercept: (2.9595, 0)
y-intercept: (0, 4)
another point: (2, 32)
Step-by-step explanation:
Given function: [tex]h(t)=-16t^2+46t+4[/tex]
(where h is the height in feet and t is the time in seconds)
The vertex is the turning point of the parabola.
To find the x-value of the turning point, differentiate the function:
[tex]\implies h'(t)=-32t+46[/tex]
Set it to zero:
[tex]\implies h'(t)=0[/tex]
[tex]\implies -32t+46=0[/tex]
Solve for t:
[tex]\implies 32t=46[/tex]
[tex]\implies t=\dfrac{23}{16}[/tex]
Input found value of t into the function to find the y-value of the vertex:
[tex]\implies h(\frac{23}{16})=-16(\frac{23}{16})^2+46(\frac{23}{16})+4=\dfrac{593}{16}[/tex]
Therefore, the vertex is [tex]\left(\dfrac{23}{16},\dfrac{593}{16}\right)[/tex] or (1.4375, 37.0625) in decimal form.
The axis of symmetry is the x-value of the vertex.
[tex]\implies \textsf{Axis\:of\:Symmetry}:t=\dfrac{23}{16}=1.4375[/tex]
To find the x-intercepts, use the quadratic formula.
Quadratic Formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when}\:ax^2+bx+c=0[/tex]
[tex]\implies t=\dfrac{-46 \pm \sqrt{46^2-4(-16)(4)} }{2(-16)}[/tex]
[tex]\implies t=\dfrac{-46 \pm \sqrt{2372}}{-32}[/tex]
[tex]\implies t=\dfrac{23 \pm \sqrt{593}}{16}[/tex]
As time is positive,
[tex]\implies t=\dfrac{23 + \sqrt{593}}{16}=2.959474458...\:\sf s\quad only[/tex]
The y-intercept is when t = 0:
[tex]h(0)=-16(0)^2+46(0)+4=4[/tex]
So the curve intercepts the y-axis at (0, 4)
Because of the modelling of the function, there will be a restricted domain: 0 ≤ t ≤ 2.9595
Therefore, to find another point, input a value in the domain into the function and solve:
[tex]t=2 \implies h(2)=-16(2)^2+46(2)+4=32[/tex]
⇒ (2, 32)