The chairs in the auditorium illustrates an arithmetic sequence
The recursive rule is: an = an-1 + 8; a1 = 26The explicit rule is: an = 18 + 8nThere are 74 seats in the 7th row840 chairs can fit the auditoriumThe recursive ruleFrom the question, we have the following sequence:
Seats: 18, 26, 34
Rewrite as:
26 = 18 + 8
34 = 26 + 8
The above means that:
The number of seats on a row is 8 added to the the number of seats on the previous row.
Hence, the recursive rule is:
an = an-1 + 8; a1 = 26
The explicit ruleIn (a), we have:
a1 = 26 and d = 8
The explicit rule is calculated using:
an = a1 + (n -1) * d
This gives
an = 26 + (n - 1) * 8
Expand
an = 26 - 8 + 8n
Evaluate the difference
an = 18 + 8n
Hence, the explicit rule is:
an = 18 + 8n
The number of seats in the row 7This means that n = 7.
So, we have:
a7 = 18 + 8 * 7 = 74
Hence, there are 74 seats in the 7th row
The sigma notationWe have the maximum number of rows to be 12.
So, the sigma notation would be:
[tex]\sum\limits^{12}_{n=1} {18 + 8n}[/tex]
The total number of seats is:
Sn = n/2(2a + (n -1) * d)
This gives
S12 = 12/2(2 * 26 + (12 -1) * 8)
S12 = 840
Hence, 840 chairs can fit the auditorium
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Winston drove 70 mph. If he drives for 3.5 hours how many miles will Winston drive?
I need the answer ASAP
find the equation of a line passing through (3,2) and (5,6)
Answer:
y=1/-2x+2.5
Step-by-step explanation:
Y=Mx+c
Mx(slope)=y2-y1/x2-x1= 6-2/-5-3 =4/-8= 1/-2
C(y-intercept)= replace one of of the points here to find C
2=1/-2(3)+c, c= 2.5
Final answer > y=1/-2x+2.5
 Find the length of the third side. If necessary, write in simplest radical form.
IMAGE DOWN BELOW!
SOMEONE PLEASE HELP ME!! ILL GIVE YOU BRAINLIST ANSWER
math please help !!!
Answer:
a = -2
Step-by-step explanation:
Ok, so for parallel lines you need to make slopes for both the lines equal. So for line y = x + 4 the slope is 1. (slope is the coefficent infront of the x value while in y=mx+b form. To make the other line have a slope of 1 a needs to be a number as so that 2a+5 = 1
2a+5 = 1
2a = 1 - 5
a = -4/2
a = -2
Find the length of b to the nearest tenth.
(BRAINLIEST :D)
Answer:
1.7
Step-by-step explanation:
You can use the 30/60/90 triangle rule, but it was quicker for me to do. SIN(60)=b/2. If you want a more in depth explanation just reply to this but I have to go right now so I will do it later.
A
Complete the transformation on the rectangle
ABCD shown and choose the resulting vector
Use [ABCD]
Answer:
(3 -1 -1 3
4 4 1 1)
reflection across the y-axis
Step-by-step explanation:
Please help me with question 1.
Answer:
C =66
Step-by-step explanation:
WILL GIVE BRAINLIEST The points Q(0,1), R(-9,-5), s(-7, -8), and T(2,-2) form rectangle QRST. Plot the points then click the "Graph Quadrilateral" button. Then find the area of the rectangle.
well, we know its a rectangle, so hmmm opposite sides are not just parallel but equal, hmmm so the area of this rectangle we can get by Length * Width, in this case that'll be QT * TS
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ Q(\stackrel{x_1}{0}~,~\stackrel{y_1}{1})\qquad T(\stackrel{x_2}{2}~,~\stackrel{y_2}{-2})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ QT=\sqrt{[2 - 0]^2 + [-2 - 1]^2}\implies QT=\sqrt{2^2 + (-3)^2}\implies QT=\sqrt{13} \\\\[-0.35em] ~\dotfill[/tex]
[tex]T(\stackrel{x_1}{2}~,~\stackrel{y_1}{-2})\qquad S(\stackrel{x_2}{-7}~,~\stackrel{y_2}{-8})~\hfill TS=\sqrt{[-7 - 2]^2 + [-8 - (-2)]^2} \\\\\\ TS=\sqrt{(-9)^2 + (-8+2)^2}\implies TS=\sqrt{117} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{area of the rectangle}}{\sqrt{13}\cdot \sqrt{117}\implies \sqrt{1521}\implies 39}[/tex]
Please help!! 40 Points!!!!!
Answer:
see explanation
Step-by-step explanation:
A
when 2 equal bases are being multiplied together their exponents are added together, that is
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]
B
[tex]12^{5x}[/tex] × [tex]12^{-7}[/tex] = [tex]12^{5x-7}[/tex]
C
[tex]x^{4}[/tex][tex]y^{6k+2}[/tex] × x²[tex]y^{-1}[/tex]
= [tex]x^{4}[/tex] × x² × [tex]y^{6k+2}[/tex] × [tex]y^{-1}[/tex]
= [tex]x^{(4+2)}[/tex] × [tex]y^{(6k+2-1)}[/tex]
= [tex]x^{6}[/tex][tex]y^{6k+1}[/tex]
#A
a^b+a^c=a^b+c#B
12^5x×12^-712^5x-7#C
x⁴y^6k+2×x²y^-1x⁶y^6k+2-1x⁶y^6k+1Two mechanics worked on a car. The first mechanic worked for 15 hours, and the second mechanic worked for 5 hours. Together they charged a total of $2100. What was the rate charged per hour by each mechanic if the sum of 2 rates was $190 per hour?
Answer: 115/hr & $75/hr
Step-by-step explanation: please see attached PDF document for detailed instructions including step by step.
What is the value of x in the equation 2.5(6x - 4) = 10 + 4(1.5 + 0.5 x)?
Answer:
x=2
Step-by-step explanation:
You can simplify the equation with all the x's on one side and the numerical values on the other. After solving, the answer would be x=2
Answer:
x=2
Step-by-step explanation:
Distribute the 2.5 and 4 out
15x - 10 = 10 + 6 +2x
Add the constant variables together
15x - 10 = 16 +2x
Move the x on one side and the constant on the other
13x = 26
Divide both sides to find x
x=2
NEED HELP ASAP GEOMETRY
Answer:
BBCADD that is the awnser
Step-by-step explanation:
or a triangle XD
If 15% of sum is Rs 45, find the sum.
answer : the sum so obtained is rupees 300
You are curious about the amount of coffee that the giant fountain cup could
actually hold.
The dimensions of the fountain cup are as follows:
• Height is 8 feet.
• Diameter of the top is 6 feet.
• Diameter of the base is 4 feet.
Use this formula with height, h, radius of the base, base, and radius of the
top, "top, to determine the volume of the cup:
V =
(an) ((base)? + (Pbase) (Ftop) + (rtop) 3).
There are 7. 5 gallons of liquid per cubic foot.
Enter the volume, in gallons, of the fountain cup.
Assuming there are 7. 5 gallons of liquid per cubic foot. The volume of the cup is: 1,193.8 gallons.
Volume of the cupUsing this formula
V =πh/3 [(r base)²+ ( r base) (r top) + (r top) ²]
Where:
height of cup (h)= 8 feet
radius of base of cup (r base)= 4 feet/2=2 feet
radius of top of cup (r top)= 6 feet/2=3 feet
Let plug in the formula
V =πh/3 [(8)²+ (2) (3) + (3) ²]
V =πh/3×8×19
V=152 π/3
Hence:
Volume of the cup in gallons=152 π/3 ×7.5
Volume of the cup in gallons=477.52208334564/3×7.5
Volume of the cup in gallons=1,193.8gallons
Therefore the volume of the cup is: 1,193.8 gallons.
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a porsche, can travel 576 m in 32 s. what is its average speed?
Step-by-step explanation:
Displacement = 576 m
Time taken = 32s
Now
[tex]average \: speed = \frac{distance \: travelled}{time \: taken} \\ = \frac{576}{32} \\ = 18 m/s[/tex]
32° x x
Please help
180°-32°=2x (angles in a triangle always sum up to 180)
2x= 148°
x= 74° (they are (at least) 2 angles that are even in an isosceles triangle)
What is the resulting product of 4 × 8 and description of the product?
Answer:
32
Step-by-step explanation:
The answer is 32 because 8 x 3 is 24 so then just add 8
URGENT HELP PLEASE!
find the surface area and volume of the following possible cereal boxes determine the cost of making the box assuming the cardboard costs 5 cents per square inch
box 1 rectangle: 12 inch in height 7.5 inches wide 2 inches thick
Box 2 picture attached please give accurate answer thanks!
Answer:
One square inch is equal to . So, your box have square inches and it costs or $36 to manufacture it.
Step-by-step explanation:
The illustration below shows the graph of
y
yy as a function of
x
xx.
Complete the following sentences based on the graph of the function.
(Enter the
x
xx-intercepts from least to greatest.)
This is the graph of a
function.
The
y
yy-intercept of the graph is the function value
y
=
y=y, equals
.
The
x
xx-intercepts of the graph (in order from least to greatest) are located at
x
=
x=x, equals
and
x
=
x=x, equals
.
The greatest value of
y
yy is
y
=
y=y, equals
, and it occurs when
x
=
x=x, equals
.
For
x
xx between
x
=
2
x=2x, equals, 2 and
x
=
6
x=6x, equals, 6, the function value
y
yy
0
00.
This is the graph of a NON-LINEAR FUNCTION
The y intercept of the graph is the function value y=-6
The x intercepts of the graph are located at x=2 and x=6
The greatest value of y is y= 2 and it occurs when x=4
For x between x=2 and x=6, the function value y≥0
Hope this helped :>
Does anyone know the answer to this?
Answer:
Excuse me, Where is the question??
The equation d = 11 cosine (startfraction 8 pi over 5 endfraction t) models the horizontal distance, d, in inches of the pendulum of a grandfather clock from the center as it swings from right to left and left to right as a function of time, t, in seconds. according to the model, how long does it take for the pendulum to swing from its rightmost position to its leftmost position and back again? assume that right of center is a positive distance and left of center is a negative distance. 0.625 seconds 0.8 seconds 1.25 seconds 1.6 seconds
The time it take for the pendulum to swing from its rightmost position to its leftmost position and back again is 1.25 seconds.
What is time period of pendulum?Pendulum is the body which is pivoted a point and perform back and forth motion around that point by swinging due to the influence of gravity.
The time period of pendulum is time taken by it to complete one cycle of swing left to right and right to left.
The equation models the horizontal distance of the pendulum of a grandfather clock from the center as it swings from right to left and left to right as a function of time, t, is given as,
[tex]d = 11 \cos\left( \dfrac{8\pi}{5}t\right)[/tex]
At the maximum position, the time period is zero. Thus,
[tex]\dfrac{8\pi}{5}t=0\\t=0[/tex]
At the minimum position, the period equal to the π. Thus,
[tex]\dfrac{8\pi}{5}t=\pi\\t=\dfrac{5}{8}\\t=0.625[/tex]
This time is for one side of motion. The time for swing from its rightmost position to its leftmost position and back again is,
[tex]t=0.625+0.625\\t=1.25\rm\; s[/tex]
Thus, the time it take for the pendulum to swing from its rightmost position to its leftmost position and back again is 1.25 seconds.
Learn more about the time period of pendulum here;
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Answer:
C:1.25
Step-by-step explanation:
PLEASE SOLVE THIS I DONT HAVE MUCH TIME I WILL GIVE BRAINLYZ
A rectangle has a length of 10 cm and a width of 6 cm
How long is the diagonal of the rectangle?
Answer:
d = 2√34
Explanation:
d² = 10² + 6²d² = 100 + 36d² = 136d = √136d = 2√34A map has a scale of 1 cm to 4km.
The road from Carton to Ambridge measures 5.8cm on the map.
How far is it from Carton to Ambridge in Kilometers?
A rectangle has a width of 8 inches. The perimeter of the rectangle is 40inches. What is the length of the rectangle, in inches?
Show the formula please and work plus answer thank you
Answer:
12
Step-by-step explanation:
You want to add 8+8 and you get 16. Subtract 16 from 40 and you get 24 (This is both lengths). Divide 24 by two to get 12 (One length Vaule).
Convert 3 kilometres into metres
Answer:
3000m
Step-by-step explanation:
First, note that km is the same as kilometers and m is the same as meters. Thus, when you are asking to convert 3 km to m, you are asking to convert 3 kilometers to meters.
A kilometer is larger than a meter. Simply put, km is larger than m. In fact, a kilometer is "10 to the power of 3" larger than a meter.
Since a kilometer is 10^3 larger than a meter, it means that the conversion factor for km to m is 10^3. Therefore, you can multiply 3 km by 10^3 to get 3 km converted to m.
Here is the answer with the math showing you how to convert 3 km to m by multiplying 3 by the conversion factor of 10^3.
3 x 10^3
= 3000
3 km
= 3000 m
Answer:
3000 m
Step-by-step explanation:
Unit conversion :
1000 m = 1 kmSolving :
Let the missing value be 'x' mThen, according to this ratio :x/3 = 1000/1x = 1000 * 3x = 3000 mi need help 9th grade math
Answer:
(f + g)(x) = x + 5
Explanation:
f(x) = 2x + 3
g(x) = 3x + 2
===========
(f + g)(x)f(x) + g(x)2x + 3 + 3x + 25x + 5Answer:
[tex](f+g)(x)=5x+5[/tex]
Step-by-step explanation:
Given:
[tex]f(x)=2x+3[/tex]
[tex]g(x)=3x+2[/tex]
[tex]\begin{aligned}(f+g)(x) & =f(x)+g(x)\\ & = (2x+3)+(3x+2)\\ & = 2x+3+3x+2\\ & =2x+3x+3+2\\ & = 5x + 5\end{aligned}[/tex]
In pensacola in june, high tide was at noon. the water level at high tide was 12 feet and 2 feet at low tide. assuming the next high tide is exactly 12 hours later and that the height of the water can be modeled by a cosine curve, find an equation for water level in june for pensacola as a function of time (t). f(t) = 12 cospi over 2t 5 f(t) = 5 cospi over 2t 12 f(t) = 5 cospi over 6t 7 f(t) = 7 cospi over 6t 12
An equation for water level in june for pensacola as a function of time (t) is f(t) = 5 cos pi/6 t + 7.
Which equation of cos show period amplitude ?
The equation given below show aplitude and period
[tex]y = A cos bx + c[/tex]
where A = amplitude,
b = 2 pi/Period,
Period = 12 hrs,
c = midline,
x = t and y = f(t)
We have to find the amplitude
What is the formula for the amplitude?
[tex]A = 1/2 (Xmax - Xmin)[/tex]
[tex]12 - 2 / 2 = 10/2 = 5[/tex]
[tex]b = 2 pi / 12 = pi/6[/tex]
[tex]c = 1/2 (Xmax + Xmin)[/tex]
[tex]12+2/2 = 7[/tex]
Therefore, the an equation for water level in june for pensacola as a function of time (t)
[tex]f(t) = 5 cos pi/6 t + 7[/tex]
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what is the equation of the straight line that passes through the point (2,-4) with the slope -2?
Answer:
y = - 2x
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = - 2 . then
y = - 2x + c ← is the partial equation
to find c substitute (2, - 4 ) into the partial equation
- 4 = - 4 + c (add 4 to both sides )
0 = c
y = - 2x + 0 , that is
y = - 2x ← equation of line
I need help with this question.
Step-by-step explanation:
the volume of a cylinder is as for any regular shaped object
ground area × height
here the ground area is a circle, so we get
pi×r²×h
with r being the radius (half the diameter), and h the height.
therefore,
pi×(2.7/2)²×10 = 3.14×1.8225×10 = 57.25552611... cm³
so, the first option is correct.
PQRS is a rectangle and OS = 16. Find the blanks below:
mments
ssions
S
R
es
le
О
s
bus
P
O
zes
dules
OQ =
16
BlueButton
aborations
PR =
ogle Drive
uce 365
mZQRS =
ogle Drive
Answer: 48
Step-by-step explanation:
