The number of seats are 1953 seats in the theater.
How to deal with arithmetic sequence?To find the total number of seats in the theater, we need to find the number of seats in each row and then add them up. We can notice that the number of seats in each row increases by 3 from the previous row. This means we can use an arithmetic sequence to represent the number of seats in each row:
a = 18 (the first term)
d = 3 (the common difference)
n = 31 (the number of terms)
We can use the formula for the sum of an arithmetic sequence to find the total number of seats:
\($S = \dfrac{n}{2}(2a + (n-1)d)$\)
\($S = \dfrac{31}{2}(2(18) + (31-1)(3))$\)
\($S = \dfrac{31}{2}(36 + 30(3))$\)
\($S = \dfrac{31}{2}(36 + 90)$\)
\($S = \dfrac{31}{2}(126)$\)
\($S = 1953$\)
Therefore, there are 1953 seats in the theater.
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Which sum does the model below represent?
04+ (-7)= -3
0 4+ 7 = 11
8 + (-3) = 4
11+ (-4) = -3
Answer:
It represents that it is false
Step-by-step explanation:
Instructions: Use the graph to identify the vertex and then fill in the vertex form of the
quadratic function.
taking a peek at the picture, we can see that the U-turn or vertex occurs at the point (2 , -9), and we can also see that the graph passes through the point say (5 , 0).
\(~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\)
\(\stackrel{vertex}{(2~~,~-9)}\qquad y=a(x-2)^2-9\qquad \qquad \textit{we know that} \begin{cases} x=5\\ y=0 \end{cases} \\\\\\ 0=a(5-2)^2-9\implies 9=9a\implies \cfrac{9}{9}=a\implies 1=a~\hfill \\\\\\ y=1(x-2)^2-9\implies \boxed{y=(x-2)^2-9}\)
What is the answer of the question
Answer:
part a) will be pie r +2r
i m not sure about others
Answer:
a
Step-by-step explanation:
i hope this help
Write the inequality this number line represents.
Answer:
x > 10
Step-by-step explanation:
the dot isn't filled, meaning x can't equal 10. it goes up, meaning x is greater than 10 :) hope this helps
If triangles ABC and DEF are similar, what is y? Show your work.
The value of y is 18
What are similar triangles?Similar triangles have the same corresponding angle measures and proportional side lengths. The angles of the two triangle must be equal and it not necessary they have equal sides.
Therefore the corresponding angles of similar triangles are congruent and the ratio of corresponding sides of similar triangles are equal.
Therefore;
14/21 = 12/y
14y = 21 × 12
14y = 252
divide both sides by 14
y = 252/14
y = 18
Therefore the value of y is 18.
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What number equals 2 4/5?
O 0.28
O 0.357
O 2.45
O 2.8
I think its 2.8.
Reason why:
4/5 = 0.8
Then the 2 would a whole number...
so 2.8.
Translate to an equation please.
four less than thirteen times a number is equal to that number added to eight
Hi
let call "a number" X.
then we have: 4-13X = X + 8 ..
The new floor in the school cafeteria is
going to be constructed of square tiles that
are either gray or white and in the pattern
that appears below. What is the ratio of
Answer:
Step-by-step explanation:
18 tiles and 10 shaded in
ILL GIVE BRAINLIEST!! Pls answer A
Find the mÁB
104°
126°
B
D
Answer:ILL GIVE BRAINLIEST!! Pls answer A
Find the mÁB
104°
126°
B
D
Step-by-step explanation:ILL GIVE BRAINLIEST!! Pls answer A
Find the mÁB
104°
126°
B
D
Number graph |x-2|>3
The solution set for the inequality |x-2|>3 is x < -1 or x > 5, represented by the union of the open intervals (-∞, -1) and (5, ∞) on the number line.
To graph the inequality |x-2| > 3 on a number line, we can start by finding the values of x that satisfy the inequality:
|x-2| > 3
x-2 > 3 or x-2 < -3
x > 5 or x < -1
This means that any value of x that is greater than 5 or less than -1 will satisfy the inequality.
On a number line, we can mark -1 and 5 with open circles to indicate that they are not included in the solution set, and shade the regions to the left of -1 and to the right of 5 to show that any value in those regions satisfies the inequality.
The graph should look like this:
<=========(================>)=========
-1 2 5
The open circles at -1 and 5 indicate that those values are not included in the solution set, while the shaded regions to the left of -1 and to the right of 5 indicate that any value in those regions satisfies the inequality.
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Find the magnitude and direction of the vector using the given information. V=<6,7>
Answer:
The magnitude of the vector is 9.165 and it's direction is 40.6°
Step-by-step explanation:
Vector Quantities:A vector quantity is a quantity that has both size (magnitude) and direction. Examples of vector quantities are force, velocity and impulse.
Magnitude of vector v is given by
|v| = √6²+7²
= √36+49
= √84
= 9.165
Direction of vector v is obtained by:
\( \tan( \theta) = \frac{x}{y} \)
\(\theta = {tan}^{ - 1} ( \frac{6}{7}) \)
\(\theta = {40.6°}\)
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Which of these is a dependent variable and which of these is an independent variable.
I did Jumping Jacks
I spent 1 minute on the jumping jacks
I did 68 Jumping jacks in 1 minute.
BRAINLIEST, A LIKE, 5 STARS, 100 POINTS
Answer:
I did jumping jacks
Step-by-step explanation:
conditioning exercise performed from a standing position by jumping to a position with our legs spread and arms raised and then to the normal position.
Answer:
I hope nothing
hope. it helps
If the value of x is 14, what is the value of y?
I would need a bit more to answer that one my friend
The sequel to a popular movie will be available in
theaters soon. The theater holds 175 seats. If the movie
is shown 45 times, how many tickets can be sold for the
movie?
Using multiplication as an arithmetic operator, the number of tickets sold is 7875
What is MultiplicationMultiplication is an arithmetic operation that involves multiplying two or more numbers together. It can be written in a variety of ways, such as using a multiplication symbol, an "x" sign, or by writing out the equation. The result of multiplication is called the product.
In this problem, we can use a simple arithmetic operation to find the number of tickets sold, but we can also work it out in a step by step process.
1 times = 175 seats (tickets)
45 times = x tickets
Cross multiply both sides;
x = 45 * 175
x = 7875
The number tickets sold is 7875 tickets.
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IIf two ounces of cheese has 200 calories, how many calories are in 5 ounces of cheese?
Answer:
500 calories
Step-by-step explanation:
200 / 2 = 100
1 ounce = 100 calories
5 * 100 = calories.
OR
200 * 5 = 1000
1000 / 2 = 500
Therefore, 5 ounces of cheese = 500 calories.
hi! Can someone please help me out? Thank you so much :) I’ll give brainly. Question is in image
Answer:
d) 189.3 in²
Step-by-step explanation:
Area of rectangle is,
→ w × l
→ 10 × 15
→ 150 in²
Area of semi circle is,
→ (1/2)πr²
→ (1/2) × 3.14 × (5)²
→ 1.57 × 25
→ 39.3 in²
Now the total area will be,
→ 150 + 39
→ 189.3 in²
Thus, total area is 189.3 in².
(X-2)^2 - (x-4)^2 simplify
7. Sydney cleans her room for 45 minutes. 'She starts at 11:13 a.m. What time does Sydney finish cleaning her room?
Answer:11:58 duh
Step-by-step explanation I can count
Answer:
SYDNEY FINISH CLEANING HER ROOM AT 11:58 a.m.
what is an eqivalent ratio to 10:8
Answer:
5:4
Step-by-step explanation:
divide by 2 on both sides
Answer:
© iCalculator: Read more at: https://math.icalculator.info/ratio-calculators.html a website
Step-by-step explanation:
find the equation of the line best fit for the following data. pls explain im kind of lost lol
The equation of the line of best fit for the set of data is given as follows:
y = 4.24773x - 0.32726
How to find the equation of linear regression?To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator.
From the table in this problem, the points are given as follows:
(0.9, 3.51), (1.7, 6.61), (3, 12.27), (0.1, 0.15), (2.3, 9.59), (1.3, 5.35), (0.5, 1.65), (2.1, 8.8).
Inserting these points into a calculator, the line of best fit is given as follows:
y = 4.24773x - 0.32726
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CAN YA’LL PLEASE HELP ASAP! IF SO THANK YOU SO MUCHHHHHHHHHHHH
EASY 10 POINTS
The quadratic functions shown are written in factored form. The roots of a quadratic function will make the factors equal to 0
0
.
Drag each function to show whether it has roots at
The functions that have roots at x = -1 and x = 4 are
j(x) = (-1-x)(2x-8) and g(x) = (x+1)(x-4)
The functions that have roots at x = -4 and x = -1 are
h(x) = (-3-3x)(3x+12) and k(x) = (x+1)(x+4)
The functions that have roots at neither are
f(x) = (x-1)(x-4) and (3-3x)(3x-12)
Quadratic equationFrom the question, we are to determine the quadratic functions that have the given roots
First, we will determine the roots of the given functions
For k(x) = (x+1)(x+4)Since the roots of a quadratic function will make the factors equal to 0,
Then,
(x+1)(x+4) = 0
x + 1 = 0 OR x + 4 = 0
x = -1 OR x = -4
For m(x) = (3-3x)(3x-12)(3-3x)(3x-12) = 0
Then,
3 - 3x = 0 OR 3x -12 = 0
3x = 3 OR 3x = 12
x = 3/3 OR x = 3/12
x = 1 OR x = 4
For g(x) = (x+1)(x-4)(x+1)(x-4) = 0
Then,
x+1 = 0 OR x-4 = 0
x = -1 OR x = 4
For f(x) = (x-1)(x-4)(x-1)(x-4) = 0
Then,
x -1 = 0 OR x -4 = 0
x = 1 OR x = 4
For h(x) = (-3-3x)(3x+12)(-3-3x)(3x+12) = 0
Then,
-3 -3x = 0 OR 3x + 12 = 0
3x = -3 OR 3x = -12
x = -3/3 OR x = -12/3
x = -1 OR x = -4
For j(x) = (-1-x)(2x-8)(-1-x)(2x-8) = 0
Then,
-1 -x = 0 OR 2x - 8 = 0
x = -1 OR 2x = 8
x = -1 OR x = 8/2
x = -1 OR x =4
Hence,
The functions that have roots at x = -1 and x = 4 are
j(x) = (-1-x)(2x-8) and g(x) = (x+1)(x-4)
The functions that have roots at x = -4 and x = -1 are
h(x) = (-3-3x)(3x+12) and k(x) = (x+1)(x+4)
The functions that have roots at neither are
f(x) = (x-1)(x-4) and (3-3x)(3x-12)
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Find the missing angle I think...
Answer:
Step-by-step explanation:
Since this is a test/homework, I'll give you a hint.
A triangle always is 180 degrees. If you add up all the sides, it should be 180.
A horizontal line is 180, if you add up the two sides (or the "line" that is crossing through the horizontal one) it'll be 180.
Just think of it like this: 180 is king. No matter what you add together, if its not 180, its wrong.
Hope this helps!
Let T: R2→R2 be the linear transformation that first rotates points clockwise through 30∘ and then reflects points through the line y=x. Find the standard matrix A for T.
A = ?
The standard matrix A is [ (1/2, √3/2) (√3/2, -1/2) ]
To find the standard matrix of a linear transformation, we need to find the images of the standard basis vectors under the transformation.
The standard basis vectors in R2 are (1,0) and (0,1). Let's find their images under T.
The image of (1,0) under a 30∘ clockwise rotation is (√3/2, 1/2). The image of this under reflection through the line y=x is (1/2, √3/2).
The image of (0,1) under a 30∘ clockwise rotation is (-1/2, √3/2). The image of this under reflection through the line y=x is (√3/2, -1/2).
The standard matrix of T is then the matrix whose columns are the images of the standard basis vectors:
A = [ (1/2, √3/2) (√3/2, -1/2) ]
= \(\left[\begin{array}{cc}1/2&\sqrt{3} /2\\\sqrt{3} /2&-1/2\end{array}\right]\)
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H(p)=p/5 + 15
What is the independent variable in this function
In the given function H(p) = p/5 + 15, the independent variable is "p" ,
The independent variable in this function is denoted by "p." The independent variable can also be referred to as the input variable, which means that it is the value that is inputted into the function to produce an output. In this specific function, "p" represents the price of a good or service.
It is important to distinguish between the independent and dependent variables in a function. The dependent variable is denoted by "H(p)" in this case, and it is the output of the function. The value of the dependent variable is determined by the independent variable. In this function, "H(p)" represents the total cost of the good or service, which is dependent on the price "p." p is the input variable representing the price of the good or service.
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If you drive 72 miles and use 6 gallons of gas, what is your rate
Answer:
Well, it depends if you are asking the rate per gallon it would be 12 miles per gallon.
help asap ty
will possibly mark brainliest.
Answer:
Step-by-step explanation:
Letter B is the correct answer
Initial population is 200, tripled every hour
200 x 3 = 600
First hour 200
Second hour = 600 + 200 = 800
Third hour 800x3 = 2400 + 800 = 3200
and so on.
What is the surface area of the rectangular prism below?
Answe: there is no pic
Step-by-step explanation:
Greg took an Uber home from the airport.
The fare was $2.30 a mile and he gave a $7.50 tip to the driver.
His total with tip was $54.65
How many miles was the trip from the airport to Greg's house?
What is the position of B on the number line below?
Write your answer as a fraction or mixed number
The requried position of point B on the number line is 1/4 or 0.25.
Since point B represents the number 0.25 on the number line, its position can be described as 0.25 units to the right of 0 or as 0.25 units to the left of 0.5.
Alternatively, we can describe its position as a fraction or mixed number using the length of the number line as the denominator. If the number line extends from 0 to 1, then the position of point B can be expressed as:
B = 0 + 0.25 = 1/4
Therefore, the position of point B on the number line is 1/4 or 0.25.
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write an equation for the given ellipse that satisfied the following conditions.
Given:
Center ==> (4, 1)
Length = 8
c = 3
Let's find the equation for the given ellipse that statisfies the conditions above.
Take the equation:
\(\frac{(x-x1)^2}{a^2}+\frac{(y-y1)^2}{b^2}=1\)Here, we have a vertical minor axis with points: (x, y) ==> (4, 1) which has the equation below:
Substitute 4 for x1 and substitute 1 for y1
\(\frac{(x-4)^2}{a^2}+\frac{(y-1)^2}{b^2}=1\)Where:
\(c^2=a^2+b^2\)Since the minor axis is vertical and has a length of 8, we have:
\(\begin{gathered} 2b=8 \\ \\ \text{Divide both sides by 2:} \\ \frac{2b}{2}=\frac{8}{2} \\ \\ b=4 \end{gathered}\)Given: c = 3
To find the value of a, substitute 3 for c and 4 for b:
\(\begin{gathered} c^2=a^2+b^2^{} \\ \\ 3^2=a^2-4^2 \\ \\ \text{Add 4}^2\text{ to both sides:} \\ 3^2+4^2=a^2-4^2+4^2 \\ \\ 3^2+4^2=a^2 \\ \\ \text{Take the square root of both sides:} \\ \sqrt[]{3^2+4^2}=\sqrt[]{a^2} \\ \\ \sqrt[]{3^2+4^2}=a \\ \\ \sqrt[]{9+16}=a \\ \\ \sqrt[]{25}=a \\ \\ 5=a \\ \\ a=5 \end{gathered}\)Therefore, from the general equation, substitute 5 for a, and 4 for b
\(\begin{gathered} \frac{(x-4)^2}{a^2}+\frac{(y-1)^2}{b^2}=1 \\ \\ \\ \frac{(x-4)^2}{5^2}+\frac{(y-1)^2}{4^2}=1 \\ \\ \frac{(x-4)^2}{25^{}}+\frac{(y-1)^2}{16^{}}=1 \end{gathered}\)Therefore, the equation for thr given ellipse that satisfies the given conditions is:
\(\frac{(x-4)^2}{25^{}}+\frac{(y-1)^2}{16^{}}=1\)ANSWER:
\(\frac{(x-4)^2}{25^{}}+\frac{(y-1)^2}{16^{}}=1\)