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Explanation:
We have the arithmetic sequence {15, 18, 21, ...} and we want to add up the first n = 15 terms.
The first term is a = 15 and the common difference is d = 3
Plug these values into the arithmetic sum formula below
S = 0.5*n*(2*a + d(n-1))
S = 0.5*15*(2*15 + 3*(15-1))
S = 7.5*(30 + 42)
S = 7.5*(72)
S = 540
There are 540 seats total in the theater.
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The slower less efficient way to do this problem would be to list out the first 15 terms by hand like so
{15,18,21,24,27,30,33,36,39,42,45,48,51,54,57}
Then adding those fifteen terms up gives us
15+18+21+24+27+30+33+36+39+42+45+48+51+54+57 = 540
This helps confirm we have the correct answer.
Which expression is equivalent to the given expression? 3(x-7)+4(x^2-2x+9)
Answer is c on Plato
4x - 5x + 15
Convert the number to scientific notation.
62,004,100=
x10
+
VI
B.
ILL GIVE 50 POINTS
Which set of statements explains how to plot a point at the location (Negative 3 and one-half, negative 2)?
Start at the origin. Move 3 and one-half units right because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between 3 and 4. Move 2 units down because the y-coordinate is -2.
Start at the origin. Move 3 and one-half units down because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units left because the y-coordinate is -2.
Start at the origin. Move 3 and one-half units down because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units right because the y-coordinate is -2.
Start at the origin. Move 3 and one-half units left because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units down because the y-coordinate is -2.
Answer:
Option 3 is right
Start at the origin. Move 3 and one-half units down because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units right because the y-coordinate is -2.
Hope this helps:)
It is B from my point of view
express x^2 +-8x + 22 in the form (x-a)^2 + b
Answer:
(x-4)^2 + 6
Step-by-step explanation:
(x-a)^2 + b = x^2 - 2xa + a^2 + b
x^2 -2xa +a^2 + 6 = x^2 -8x +22
Hence:
-2xa = -8xa
a^2 + b = 22
b = 22 - a^2
b = 22 - 16
b = 6
Write an equation of the line that passes through point P and is parallel to the line with the given equation:
P(3,5); y=2x-6
Answer:
y = 2x -1
Step-by-step explanation:
The line y = 2x - 6 is in slope-intercept form, so the slope = 2. The line you are looking for is parallel, hence also has a slope of 2.
Now, use the point-slope form of a line [tex]y - y_{1} = m(x - x_{1} )[/tex]
y - 5 = 2(x - 3)
y - 5 = 2x - 6
y = 2x -1
Kisha ran 8 7/15 miles then walked 1 7/10. Find the total distance she traveled.
Answer:
the total distance she traveled is 10 1/5
Answer:
What you need to do, in this situation, is simplify the equation-- so it is able to be added" and solve
Step-by-step explanation:
First, find the lcm of 15 and 10. This value is 30 because 15*2 is 30 and 10*3 is 30.
Next, convert the two fractions so that each of them has a denominator of 30.
8 7/15 = 8 14/30
1 7/10 = 1 21/30
Clean up your values:
8 14/30 + 1 21/30
Finally, solve for d, distance (Hint: distance can never be negative; that is why absolute value exists)
You will result with 9 35/30
Simplify this and you will receive 10 5/30
Is this relatively prime? No: we need to simplify again
Final Answer: 10 1/6 miles
loook below find the area
Step-by-step explanation:
step 1. this is a trapezoid. the area A = (b1 + b2)h/2 where b1 is the bottom base and b2 is the top base (per se), and h is the height. this formula is the definition of the area of a trapezoid.
step 2. A = (b1 + b2)h/2 = (22 + 9)(5)/2
step 3. A = 31(5)/2 = 155/2 = 77.5in^2.
The price of a flight was increased by 3% to £720. What was the price before the increase?
Give your answer to the nearest penny.
Which triangle is conguent to ABC
Answer:
Step-by-step explanation:
Triangle MLK
Is the function y = -x5 - 5 linear or nonlinear?
a recipe uses 2 1/4 cup of flower for a batch of cookies and henry makes 10 batch how much flower did he use
Answer:
22.5 flower
Step-by-step explanation:
Ms. Turkovich sees that pizzas are on sale (yes!!). A small pizza costs $8.95. She will receive a 20% discount.
Amy picks 3 of 7 colors of the rainbow, but she doesn't pick red with green, she doesn't use blue at all. How many different combinations of 3 colors can Amy pick?
Answer:
red orange yellow, green purple orange,yellow green purple, red orange purple, green orange yellow, 4
Step-by-step explanation:
Escriba el simbolo correcto (<,> o =) en el espacio. 27. A) 3__ 2/2 b) -3__-2/2 c) 3.5__ 2/2 28. A) 2/3__0.67 b)2/3__-0.67 c)
Answer:hey
Step-by-step explanation:
At the Mercer County Fair, 6 of the last 18 people to spin the
prize wheel won a prize. What is the experimental probability
that the next person to spin the wheel will win a prize?
Write your answer as a decimal rounded to the nearest tenth.
Answer:
0.3
Step-by-step explanation:
Experimental Probability formula: p(event) = number of times the event occurs/total number of trials
6/18 (division) = 0.33333
As a decimal rounded to the nearest tenth = 0.3
I'm not exactly sure on this one, but it should be the answer. I hope this helps
si 33 es multiplo 11 setiene que 11 es divisor de 33
Answer:
ABOOMABALACACA VETE ALA VERGA
Step-by-step explanation:
CITA TIEMPOS
what is the sum of 5x2+3x-7 and 12x + 12
Answer: 5x^2 +15x + 5
Step-by-step explanation:
(5x^2 + 3x - 7) + (12x + 12)
=> 5x^2 +15x + 5
Urgent!
1 1/6 - 3/6 =?
Answer:
1 4/6
Step-by-step explanation:
Answer:
I got 0.66
Step-by-step explanation:
Alexa bought 4.7 pounds of apples. The apples cost $1.60 per pound. How much did she pay for the apples?
Answer:
Alexis spent $7.52 on her apples
What is the slope of the graph of y = -3x?
3
-
-3
Answer:
I love algebra anyways
The ans is in the picture with the steps how i got it
(hope this helps can i plz have brainlist :D hehe)
Step-by-step explanation:
Cal's go cart has a gas tank with the dimensions shown below. He uses a gas can that holds 111 liter of gas, to fill the go cart tank. 111 liter = 1000\text{ cm}^31000 cm 3 1000, start text, space, c, m, end text, cubed
Answer:
8
Step-by-step explanation:i got it wrong to see what the answer was :)
Answer:
8
Step-by-step explanation:
answer=== -5
process???
Answer:
x=-5
Step-by-step explanation:
First, you have to cross multiply.
2*2x+3 1*3x+1
4x+6=3x+1
Then, you subtract 3x from both sides.
4x+6=3x+1
-3x -3x
x+6=1
Next, you subtract 6 from both sides.
x+6=1
-6 -6
x=-5
Answer:
x = -5 (process below)
Step-by-step explanation:
1) To solve this easily, you can cross multiply. Multiply the numerator of the first fraction with the denominator of the second fraction, and multiply the denominator of the first fraction with the numerator of the second fraction:
[tex]\frac{2}{3x+1} = \frac{1}{2x+3} \\2(2x +3) = 1(3x + 1)\\4x + 6 = 3x + 1[/tex]
2) Next, isolate x to find its values. Subtract both sides by 3x.
[tex]4x + 6 = 3x +1\\x + 6 = 1[/tex]
3) Finally, subtract both sides by 6.
[tex]x + 6 = 1 \\x = -5[/tex]
Find the area of the figure. 4 in. 6 in. 6 in. 10 in. A 64 square inches B 68 square inches C 72 square inches D 66 square inches
Answer:
72 I am pretty sure
Step-by-step explanation:
6 x 10 = 60 and 4 x 6 = 24 ÷ 2 = 12 = 72
a^8/a^3
hey can someone help me
Rewrite 5 ⋅ x + 5 ⋅ 8 using parentheses.
Answer:
(5 ⋅ X) + (5 ⋅ 8) =
Step-by-step explanation:
please please please helpppp, (please show work if you can)
Answer:
∴ m∠KIJ = 18° and m∠HIJ = 50°
Thus, option a is correct.
Step-by-step explanation:
From the figure, it is clear that:
m∠KIH = m∠HIJ + m∠KIJ
Given
m∠KIH = 68°m∠KIJ = (2x + 6)°m∠HIJ = (9x - 4)°now substituting m∠KIH = 68°, m∠KIJ = (2x + 6)° and m∠HIJ = (9x - 4)° in the equation
m∠KIH = m∠HIJ + m∠KIJ
68° = (2x + 6)° + (9x - 4)°
switch sides
[tex]\left(2x+6\right)+\left(9x-4\right)=68[/tex]
Group like terms
[tex]2x+9x+6-4=68[/tex]
[tex]11x+2=68[/tex]
Subtract 2 from both sides
[tex]11x+2-2=68-2[/tex]
Simplify
[tex]11x=66[/tex]
Divide both sides by 11
[tex]\frac{11x}{11}=\frac{66}{11}[/tex]
Simplify
[tex]x=6[/tex]
Hence, the value of x = 6
Therefore,
m∠KIJ = (2x + 6)° = 2(6) + 6 = 12 + 6 = 18°
m∠HIJ = (9x - 4)° = 9(6) - 4 = 54 - 4 = 50°
∴ m∠KIJ = 18° and m∠HIJ = 50°
Thus, option a is correct.
Expand and simplify (x - 1)(x+4)
Answer:
x^2+4x-1x-4. simplified: x^2+3x-4
Answer:
x^2+3x-4
Step-by-step explanation:
I count on in equal steps my first number is -5 my fifth number is three write in the correct number for the third card
Answer:
-1
Step-by-step explanation:
The difference between -5 and 3 is 8. We get to 3 in 4 steps. 8÷4=2, so we count two numbers every step. So the second card is -3 and then the third card is -1
Jake spent 5 hours and 17 minutes at the Air and Space Museum. He left the museum at 4:10 p.m. What time did Jake
arrive at the museum?
Answer:
10:53 A.M
Step-by-step explanation:
Answer:
What you need to do is count back the time by 5 hours and 17 minutes.
Step-by-step explanation:
17 minutes from 4:10 PM is 3:53 PM
5 hours from 3:53 PM is 10:53 AM
Your answer is 10:53 AM
Which is the quotient if 3/5 and 1/10?
Answer:
6
Step-by-step explanation:
We have two fractions and are asked to find the answer if they both are divided.
3/5 and 1/10.
When we divide fractions, we need to follow KCF
KEEP - Keep the fractions
CHANGE - Change the division sign to a multiplication sign
FLIP - Flip the second fraction
Follow :
KEEP :
3/5 / 1/10
CHANGE :
3/5 * 1/10
FLIP :
3/5 * 10/1
Now we need to multiply, which is simple because it's multiplying across :
[tex]\frac{3*10}{5*1}[/tex]
30/5
Simplify by dividing the numerator and denominator by 5 :
[tex]\frac{30/5}{5/5} = \frac{6}{1}[/tex]
Divide the numerator by denominator :
[tex]\frac{6}{1} = 6[/tex]