Answers
Remember the formula for calculating volume is: Volume = Area by height. V = A X h.
For a triangle the area is calculated using the formula: Area = half of base by altitude. A = 0.5 X b X a.
So to calculate the volume of a triangular prism, the formula is: V = 0.5 X b X a X h. i hoped this helped sorry if it didnt
Related Questions
A jar contains 100 marbles. There are 21 blue marbles, 19 green marbles, 37 red marbles, and 23 yellow marbles. What is the probability of randomly selecting a yellow marble? Enter the correct answer
Answers
Answer:
23% or 23/100
Step-by-step explanation:
Since there are 23 in 100 is is 23/100 or 23%
Answer:
4.348%
Step-by-step explanation:
blue marbles = 19
yellow marbles = 23
probably of getting yellow = 23/100
= 4.34782608696
then you round then number to three decimal places and there you go
Prove that:
( 1 - tan^4 A)cos^4 A = 1 - 2 sin^2 A
Answers
Here we go ~
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
[tex]\qquad \sf \dashrightarrow \: (1 - \tan {}^{4} (a) ) \cos {}^{4} (a) [/tex]
[tex]\qquad \sf \dashrightarrow \: (1 + \tan {}^{2} (a) )(1 - { \tan}^{2} (a)) \cos {}^{4}(a ) [/tex]
[ a² - b² = (a + b)(a - b) ]
[tex]\qquad \sf \dashrightarrow \: ( \sec {}^{2} (a) )(1 - ( \sec{}^{2} (a) - 1) )\cos {}^{4} (a) [/tex]
[ sec² a = 1 + tan² a, so : tan² a = sec²a - 1 ]
[tex]\qquad \sf \dashrightarrow \: \bigg( \dfrac{1}{{}cos^{2} (a)} \bigg)(2 - \sec{}^{2} (a) ) \cos {}^{4} (a) [/tex]
[tex]\qquad \sf \dashrightarrow \: \bigg(2 - \dfrac{1}{ \cos {}^{2} (a) } \bigg) \cos {}^{2} (a) [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{2 \cos {}^{2} (a) - 1}{ \cos {}^{2} (a) } \times \cos {}^{2} (a) [/tex]
[tex]\qquad \sf \dashrightarrow \: 2 \cos {}^{2} (a) - 1[/tex]
[tex]\qquad \sf \dashrightarrow \: 2(1 - \sin {}^{2} (a) ) - 1[/tex]
[ sin²a + cos² a = 1, hence sin²a = 1 - cos²a ]
[tex]\qquad \sf \dashrightarrow \: 2 - 2 \sin {}^{2} (a) - 1[/tex]
[tex]\qquad \sf \dashrightarrow \: 1 - 2 \sin {}^{2} (a) [/tex]
Answer:
See proof below
Step-by-step explanation:
Prove [tex]\left(\:1\:-\:tan^4A\right)cos^4A\:=\:1\:-\:2\:sin^2A[/tex]
[tex]\left(1-\tan ^4\left(A\right)\right)\cos ^4\left(A\right)[/tex] can be expressed in sin, cos terms
Use the trigonometric identity [tex]\tan \left(x\right)=\frac{\sin \left(x\right)}{\cos \left(x\right)}[/tex]
[tex]\left(1-\tan ^4\left(A\right)\right)\cos ^4\left(A\right) = \left(1-\left(\frac{\sin \left(A\right)}{\cos \left(A\right)}\right)^4\right)\cos ^4\left(A\right)[/tex]
[tex]\mathrm{Simplify}\:\left(1-\left(\frac{\sin \left(A\right)}{\cos \left(A\right)}\right)^4\right)\cos ^4\left(A\right)[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}[/tex]
= [tex]\left(1-\frac{\sin ^4\left(A\right)}{\cos ^4\left(A\right)}\right)\cos ^4\left(A\right)[/tex]
Multiplying the expression in parentheses by [tex]\cos ^4\left(A\right)[/tex] we get
[tex]\frac{\cos ^4\left(A\right)-\sin ^4\left(A\right)}{\cos ^4\left(A\right)}\cos ^4\left(A\right)[/tex]
Cancel the common factor [tex]\cos ^4\left(A\right)[/tex]
This gives us
[tex]\cos ^4\left(A\right)-\sin ^4\left(A\right)[/tex]
Now,
[tex]\sin ^4\left(A\right)=\left(\sin ^2\left(A\right)\right)^2[/tex]
[tex]\cos ^4\left(A\right)=\left(\cos ^2\left(A\right)\right)^2[/tex]
[tex]\:\cos ^4\left(A\right)-\sin ^4\left(A\right)[/tex] = [tex]\left(\cos ^2\left(A\right)\right)^2-\left(\sin ^2\left(A\right)\right)^2[/tex]
[tex]\mathrm{Apply\:Difference\:of\:Two\:Squares\:Formula:\:}x^2-y^2=\left(x+y\right)\left(x-y\right)[/tex]
[tex]\left(\cos ^2\left(A\right)\right)^2-\left(\sin ^2\left(A\right)\right)^2=\left(\cos ^2\left(A\right)+\sin ^2\left(A\right)\right)\left(\cos ^2\left(A\right)-\sin ^2\left(A\right)\right)[/tex]
= [tex]\cos ^2\left(A\right)-\sin ^2\left(A\right)[/tex] [tex]\textrm{ since }\cos ^2\left(A\right)+\sin ^2\left(A\right)[/tex] = 1
Using the fact that [tex]\cos ^2\left(A\right)=1-\sin ^2\left(A\right)[/tex]
we get
[tex]\cos ^2\left(A\right)-\sin ^2\left(A\right) = 1-\sin ^2\left(A\right)-\sin ^2\left(A\right)\\\\= 1-2\sin ^2\left(A\right)[/tex]
Proved
Consider the relationship chart for the a fast-food restaurant,
Assume that the areas required for each department are:
Department Area Required (Square feet)
(CB) 300
(CF) 200
(PS) 200
(DD) 200
(CS) 300
Assume facility dimension of 6 (horizontal) by 8 (vertical) squares, where each square is 5 feet on a side. As a result, for example the CB department requires 12 squares. Develop a layout for the fast-food restaurant.
Answers
The layout of the fast-food restaurant of dimensions 6 by 8 5 feet squares is presented in the attached table created with Sheets.
How can the required layout be found?The dimensions of the facility are;
Horizontal = 6 squares
Vertical = 8 squares
The side length of each square = 5 feet
Therefore;
Area of each square = 5² ft.² = 25 ft.²
Number of squares, n, required by each dependent are therefore;
CB department, n = 300 ÷ 25 = 12 squares
CF department, n = 200 ÷ 25 = 8 squares
PS department, n = 8 squares
DD department, n = 8 squares
CS department, n = 12 squares
A layout for the fast-food restaurant is therefore;
The first three vertical columns of 8 squares each are occupied by the CF, PS, and DD departments. The remaining 3 by 8 squares are occupied by the CB department, (3 by 4 squares), and the CS department, (3 by 4 squares)Please see the attached table layout created using Sheets.
Learn more about finding the area of regular figures here:
https://brainly.com/question/316492
#SPJ1
Write the following in terms of sin x and cos x ; then simplify if possible. sec x csc x cot x =
Answers
The expression sec x csc x cot x in terms of sin x and cos x is
1/ (sin x)^2.
According to the given question.
We have an expression sec x csc x cot x.
Here, we have to write the above expression in terms of sinx and cosx.
As we know that,
sec x = 1/cos x
csc x = 1/sin x
cot x = cos x/ sin x
Thereofore, the expression sec x csc x cot x in terms of sin x and cos x is given by
sec x csc x cot x
= (1/cos x) (1/sinx) (cosx/ sinx)
= 1/ (sin x)^2
Hence, the expression sec x csc x cot x in terms of sin x and cos x is
1/ (sin x)^2.
Find out more information about sinx and cos x here:
https://brainly.com/question/14096659
#SPJ1
The upper arm length of males over 20
years old in the United States is approximately Normal with mean 39.1
centimeters (cm) and standard deviation 5.1
cm. Use the 68−95−99.7
rule to answer the following questions. (Start by making a sketch of the Normal distribution for upper arm lengths for this population.)
A normal plot shows the range of Iowa test scores for 68% of the data, 95% of the data and 99.7% of the data. About 68% of the distribution of scores ranges from 5.29 to 8.39. About 95% of the distribution of scores ranges from 3.74 to 9.94. About 99.7% of the distribution of scores ranges from 2.19 to 11.49. There is an annotation that One standard deviation is 1.55 and another annotation that 2.5% of sores are below 3.74.
What percentage of men over 20
have upper arm lengths greater than 44.2 cm?
Provide your answer to one decimal place.
Answers
Using the Empirical Rule, it is found that 16% of men over 20 have upper arm lengths greater than 44.2 cm.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.For the distribution in this problem, we have that:
The mean is of 39.1 cm.The standard deviation is of 5.1 cm.Hence, 44.2 is one standard deviation above the mean, as 44.2 = 39.1 + 1 x 5.1.
The normal distribution is symmetric, meaning that 50% of the measures are above the mean and 50% are below. Of those measures above the mean, 68% are less than 44.2 and 32% are more than 44.2 cm, hence:
0.5 x 32 = 16%.
16% of men over 20 have upper arm lengths greater than 44.2 cm.
More can be learned about the Empirical Rule at https://brainly.com/question/24537145
#SPJ1
please help simplify !
Answers
Answer:
B
Step-by-step explanation:
using the rule of exponents
[tex]a^{m}[/tex] ÷ [tex]a^{n}[/tex] = [tex]a^{(m-n)}[/tex] , then
[tex]6^{9}[/tex] ÷ 6³ = [tex]6^{(9-3)}[/tex] = [tex]6^{6}[/tex]
Let D={12,15,17), E = {12,14,15,16) and F = {11,13,14,15,17).
List the elements in the set D UE.
DUE= (Use commas to separate answers.)
Answers
The elements that will be coming in the set D∪E will be {12, 14, 15, 16, 17}.
A set may be defined as a collection of letters or numbers that are written in order to depict a certain value or entity. A set is always represented by a capital letter symbol and is always written in curly brackets { }. Union of two sets may be defined as a new set which has the collection of all the elements of the two individual sets. Union of two sets is represented by the symbol '∪'. Union of two Indvidual sets, set A and set b is written as A∪B.
Now, according to the question set D is = {12, 15, 17} and set E is = {12, 14, 15, 16}.
The union of the two sets contains all the elements of the sets D and E.
Thus, D∪E will be given by {12, 14, 15, 16, 17}.
Learn more about Union of sets at:
brainly.com/question/5402405
#SPJ9
Question
The following data set represents the dollar amounts of donations collected at the entrance to a free museum during one hour.
Donation Amount ($) Frequency
1 1
5 5
10 3
15 1
600 1
Is the median a reasonably good measure of central tendency for this data set? What if the outlier were removed from consideration?
Select the correct answer below:
The median is a good measure regardless of whether the outlier is included.
The median is a very poor measure regardless of whether the outlier is included.
The median is a good measure when the outlier is included, but it would be a very poor measure if the outlier were removed from consideration.
The median is a very poor measure when the outlier is included, but it would be a good measure if the outlier were removed from consideration.
Answers
In the given situation (A) the median is a good measure regardless of whether the outlier is included.
What do we mean by media?The median is the value that separates the upper and lower halves of a data sample, population, or probability distribution in statistics and probability theory. It is sometimes referred to as "the middle" value in a data set. The basic difference between the median and the mean in describing data is that the median is not skewed by a small proportion of extremely large or small values, and thus provides a better representation of a "typical" value.To find the median:
1, 5, 5, 5, 5, 5, 10, 10, 10, 15, 600The number of terms is 11, so the middle number will be the 5th term from both ends.The 5th term is 5.So, regardless of whether the outlier is included, the median is a good measure in the given situation.Therefore, in the given situation (A) the median is a good measure regardless of whether the outlier is included.
Know more about median here:
https://brainly.com/question/26151333
#SPJ9
The correct question is given below:
The following dataset represents the dollar amounts of donations collected at the entrance to a free museum for one hour.
(Refer to the table given below)
Is the median a reasonably good measure of central tendency for this dataset? What if the outlier were removed from consideration?
Select the correct answer below:
(A) The median is a good measure regardless of whether the outlier is included.
(B) The median is a very poor measure regardless of whether the outlier is included.
(C) The median is a good measure when the outlier is included, but it would be a very poor measure if the outlier were removed from consideration.
(D) The median is a very poor measure when the outlier is included, but it would be a good measure if the outlier were removed from consideration.
two classes each with 21 students were given a physical fitness test. the result of the number of pull ups performed in 30 seconds were recorded in the table below
Answers
Based on the results of the physical fitness test, the reason why we are unable to calculate the mean number of pull-us done by the students in each class is that we don't have the exact number of pull-ups done by each student.
What is needed to calculate mean?To calculate the simple mean of a distribution of numbers, we would need the value of all the numbers to be known. These numbers will then be summed up and divided by the number of the distribution.
In this case of the physical fitness test, the number of pull-ups is not known for all the students as there are some that either did below 5 or above 10 and we don't know the exact number of pull-ups done.
As a result, we are unable to calculate the mean.
Question is:
Explain why we are unable to calculate the mean number of pull-ups done by the students in each class.
Find out more on calculating mean at https://brainly.com/question/20118982
#SPJ1
A small class has 9 students, 4 of whom are girls and 5 of whom are boys. The teacher is going to choose two of the students at random. What is the probability that the first student chosen will be a boy and the second will be a girl? Write your answer as a fraction in simplest form.
Answers
The probability that the first student chosen will be a boy and the second will be a girl is 0.28.
What is probability?Probability is also called the chance because if you flip a coin then the probability of coming head and tail is nothing but chances that either head will appear or not.
Total students = 9
Number of girls = 4
Number of boys = 5
Probability of choosing first boy = Number of boys / total students
⇒ 5/9
Now since 1 boy extract so remaining students = 9 - 1 = 8
Probability of choosing second girl = Number of girls / Total students
⇒ 4//8
Probability of A and B = P(A) × P(B)
Therefore,
The probability that the first student chosen will be a boy and the second will be a girl = (5/9) × (4/8) = 0.28
Hence "The probability that the first student chosen will be a boy and the second will be a girl is 0.28".
For more information about the probability,
brainly.com/question/11234923
#SPJ1
Helpppp meeeee!!!! Ayudaaamee
Answers
It’s q 7 becaues if you add x and 6 it’s be 7 and q is the main one
Using company C’s phone plan, the cost of an overseas phone call is a $0.80 connection fee plus 23 cents per minute. If the total cost of the call is 7.93, how long is the phone call?
Answers
Answer: 31 Minutes
Step-by-step explanation:
Minus 0.80 from 7.93, and then divide 7.13 by 0.23 and you get 31
Simplify, if possible.
8ab² +3ab+2a-3b+5
A. The expression is in its simplest form.
B. -10ab² +5
2
C. 8ab² + 2ab +5
D.
8ab²-3ab+5
Please select the best answer from the choices provided
Answers
Answer:
A. The expression is in its simplest form.
Step-by-step explanation:
Answer:
i tried this i think the answer is 11a plus 2a subract3b ppus 5
i need the scientific notation of 0.0000018(430,000,000) over 0.00008(0.0075)
Answers
Answer:
1.29 x [tex]10^{9}[/tex]
Step-by-step explanation:
{(1.8 x 10^-6) x (4.3 x 10^8)} / [(8 x 10^-5) x (7.5 x 10^-3)]
[(1.8 x 4.3)x(10^-6 x 8)] / [(8 x 7.5) x(10^-5 x 10^ -3)]
(.129 x 10^[2-(-8)]
.129 x 10^10
1.29 x 10^-1 x 10^10
1.29 10^9
Kaleb determined how much money he would spend if he stopped at McDonalds each day after school. His cost can be modeled using c(m)=2.3m+2.50, where m is the number of McGriddle he orders each time. What is the cost that Kaleb would spend at McDonalds if he ordered 3 McGriddles?
Answers
Answer:
The cost that Kaleb would spend at McDonalds if he ordered 3 McGriddles would be 11.50.
Step-by-step explanation:
We know this is the answer because, when solving for c(3), we would get c(3)=2.3(3)+2.50=11.50.
Which equations have the same value of x as Two-thirds (6 x + 12) = negative 24? Select two options.
Answers
4 x + 8 = negative 24 , 9 x + 18 = negative 24 are equations have the same value of x .
What in mathematics is a linear equation?
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.A - 4 x + 8 = negative 24
E - 4 x = negative 32
ARE CORRECT ON EDGE.
Learn more about linear equation
brainly.com/question/11897796
#SPJ9
The complete question is-
Which equations have the same value of x as Two-thirds (6 x + 12) = negative 24? Select two options.
4 x + 8 = negative 24
9 x + 18 = negative 24
4 x = negative 16
StartFraction 18 x + 36 over 2 EndFraction = negative 24
4 x = negative 32
What is the area of the polygon if the side length of the square is 4
Answers
Answer:
16
Step-by-step explanation: This is because when we look at the square we realize by definition it is a 4-sided shape with 4 equal side lengths this means that if one side is 4 all the 4 sides of a square are also 4 and in this case, we would do length times width and get an answer of an area of 16 units.
The tax on a $30 item is $1.50.
Find the tax on a $50 item.
Answers
Answer: $2.50
Step-by-step explanation: To find the tax rate, you need to divide 1.50 by 30
1.5/30 = .05, which is the percent taxed. To find the tax amount for a $50 item, you just need to multiply $50 by the tax rate, which is .05, to get $2.50
find the value of ...B
Answers
Answer:
b=–2
Step-by-step explanation:
we've got:
(3+bx)⁵===> b⁵x⁵+15b⁴x⁴+90b³x³+720b²x²+405bx+243
and we've also got the coefficient of x³ as –720
90b³=–720===> b³=–8===> b=–2
Wilson hires a financial analyst to analyse costs and profits for his cereal production business. The analyst determines that Wilson’s eventual profit function is given as: , where x is the number of bags of cereal produced. At what point or number of bags of cereal will Wilson’s profit start decreasing
Answers
If Wilson produces only one 1 bag, then his profit starts decreasing
How to determine the pointGiven the function;
Let f ( x ) = [tex]2x^4 - 4x^3 + 7[/tex]
Where;
x is the number of bags of cereal produced
[tex]f'x = 2x^4 - 4x^3 + 7[/tex]
[tex]f'(x) = 8x^3 - 12x^2[/tex]
Factorize the expression
[tex]f'(x) = 4x^2(2x - 3)[/tex]
If the value of x is decreasing, we have;
f ′ ( x ) ≤ 0
4x² (2x - 3) ≤ 0
If x² ≥ 0, then;
2x - 3 ≤ 0
x ≤ 3/ 2
With x as the number of bags
x ∈ N
x = 1 is the only possibility
Thus, if Wilson produces only one 1 bag, then his profit starts decreasing
Learn more about functions here:
https://brainly.com/question/2456547
#SPJ1
The complete question:
Wilson hires a financial analyst to analyse costs and profits for his cereal production business. The analyst determines that Wilson’s eventual profit function is given as: pi = 2x ^ 4 - 4x ^ 3 + 7, where x is the number of bags of cereal produced. At what point or number of bags of cereal will Wilson’s profit start decreasing
Can y’all help me please??
Answers
Answer: 29/21
Quotient: 1
Reminder: 8
Step-by-step explanation:
Add up the amount of 7th graders playing instruments (not including drums) total and put that number under the amount of 8th graders playing a instrument.
Use the 1st digit 2 from dividend 29
21 & 29 squared root
Since 2 is less than 21, use the next digit 9 from dividend 29 and add 0 to the quotient. Find the closest multiple of 21 to 29.
1×21=21 is the nearest. Now subtract 21 from 29 to get reminder 8. Add 1 to quotient.
Since 8 is less than 21, stop the division. The reminder is 8. The topmost line 01 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
1. Let f be the function given by f(x)= X/ √x²-4 Find the domain of f.
Answers
Interval Notation:
(−∞,∞)
Which of the following equations represents a linear function?
Question 8 options:
y =[tex]\sqrt4{x}[/tex]
y =6/x
2x – 4y = 6
x3 – y = –2
Answers
Answer:
2x – 4y = 6
x3 – y = –2
Step-by-step explanation:
When graphing these two are linear.
Answer:
2x - 4y = –2
x3 – y = –2
Step-by-step explanation:
'cause they both have two unknown digits and this can be worked out with 3 methods;
1. substitution method
2. elimination method
3. grahical method
please rate brainliest if found helpful
I have 6 quarts of paint. How many shelves can be painted if each one takes one third of a quart.
Answers
6 multiplied by 3 =
28 shelves
A quadratic function has its vertex at the point
(
2
,
−
10
)
(
2
,
-
10
)
. The function passes through the point
(
−
6
,
−
5
)
(
-
6
,
-
5
)
. Find the quadratic and linear coefficients and the constant term of the function.
Answers
the standard form equation is y=ax²+bx+c where a is the quadratic coefficient, b is the linear coefficient, and c is the constant coefficient.
therefore, for y = 5/16x² - 5x/4 -35/4
Quadratic coefficient = 5/16, linear coefficient = 5/4, constant term = -35/4
What are zeros ?
zeros denotes the factors of the given equation in other words the zeros of the function are the values that make the factors zero. The factors need to multiply out to give the original standard-form equation.
Polynomial roots are the same as polynomial zeros, so they can be found by factoring the quadratic equation into two linear factors, after which they can be equating to zero.
Its easiest to first start out with a vertex form equation because it can then be converted to a standard quadratic equation.
given a vertex at (2,-10) , and point of intersection at (6,-5), the equation can be set up like this in the form of :
y = a(x-h)²+ k
y = a(x-2)^2-10, as we know h and k from the vertex.
We also know y and x from the given point of intersection so a can be solved by substituting the values of x and y to get value of a.
y = a(x-2)²-10
-5 = a(6-2)² - 10
16a = 10-5
a = 5/16
a = 5/16 which is also known as the quadratic coefficient because it is part of a second degree quantity and a Trinomial as a whole(quadratic).
since all the variables are known, you can expand the equation and set it to standard form :
y = 5/16(x-2)²-10
y = 5/16(x-2)² - 10
y = 5/16(x²+4-4x) -10
y = 5/16x² + 5/4 - 5x/4 - 10
y = 5/16x² - 5x/4 -35/4
For reference, the standard form equation is y=ax²+bx+c where a is the quadratic coefficient, b is the linear coefficient, and c is the constant coefficient.
In this instance, 5/16x² - 5x/4 -35/4 = ax²+bx+c
Learn more on quadratic function here:
https://brainly.com/question/21442266
#SPJ1
Determine whether the quadratic function shown below has a minimum or
maximum, then determine the minimum or maximum value of the functio
ƒ(x) = x² + 6x + 7
Answers
Answer:
Minimum = (-3, -2)
Step-by-step explanation:
Standard form of a quadratic function:
[tex]f(x)=ax^2+bx+c[/tex]
If a > 0 the parabola opens upwards and the curve has a minimum point.
If a < 0 the parabola opens downwards and curve has a maximum point.
Given function:
[tex]f(x)=x^2+6x+7[/tex]
As a > 0, the parabola opens upwards and so the curve has a minimum point.
The minimum/maximum point of a quadratic function is its vertex.
Vertex form of a quadratic function:
[tex]f(x)=(x-h)^2+k[/tex]
Where (h, k) is the vertex.
To rewrite the given function in vertex form, complete the square.
Add and subtract the square of half the coefficient of the term in x:
[tex]\implies f(x)=x^2+6x+7 +\left(\dfrac{6}{2}\right)^2-\left(\dfrac{6}{2}\right)^2[/tex]
[tex]\implies f(x)=x^2+6x+7 +9-9[/tex]
[tex]\implies f(x)=x^2+6x+9+(7 -9)[/tex]
[tex]\implies f(x)=x^2+6x+9-2[/tex]
Factor the perfect square trinomial formed by x²+6x+9:
[tex]\implies f(x)=(x+3)^2-2[/tex]
Compare with the vertex form:
h = -3k = -2Therefore, the vertex is (-3, -2) and so the minimum value of the given function is (-3, -2).
12. If √1225 = 35 then √12.25
Answers
[tex] \sqrt{12.25 } = 3.5[/tex]
a movie theater has a seating capacity of 329. the theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. there are half as many adults as there are children. if the total ticket sales was $ 2392, how many children, students, and adults attended?
Answers
Taking into account the definition of a system of linear equations, 178 children, 62 students and 89 adults attended to the movie theater.
System of linear equationsA system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values of the unknowns must be found, with which when are replaced in the equations, they must give the solution proposed.
This caseIn this case, a system of linear equations must be proposed taking into account that:
C is the number of children who attended the movie theater.S is the number of students who attended the movie theater.A is the number of adults who attended the movie theater.On the other hand, you know:
A movie theater has a seating capacity of 329. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. The total ticket sales was $ 2392.There are half as many adults as there are children.So, the system of equations to be solved consists of the following equations:
Equation 1: C + S + A= 329
Equation 2: 5C + 7S + 12A= 2392
Equation 3: A= C÷2= 1/2C
There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
Replacing equation 3 in equation 1 and isolating the variable S you get:
C + S + 1/2C= 329
3/2C + S= 329
S= 329 - 3/2C
Replacing this expression and equation 3 in equation 2 you get:
5C + 7(329 - 3/2C) + 12×1/2C= 2392
Solving:
5C + 7×329 - 7×3/2C + 12×1/2C= 2392
5C + 2303 - 21/2C + 6C= 2392
5C - 21/2C + 6C= 2392 -2303
1/2C= 89
C= 89÷ 1/2
C= 178
Remembering that S= 329 - 3/2C, you get S= 329 - 3/2×178 → S= 62
Finally, substituting the value of C in Equation 3: A= 1/2C= 1/2×178 → A=89
In summary, 178 children, 62 students and 89 adults attended to the movie theater.
Learn more about system of equations:
brainly.com/question/14323743
brainly.com/question/1365672
brainly.com/question/20533585
brainly.com/question/20379472
#SPJ1
What is the image of the point (-7,-6) after a rotation of 270° counterclockwise
about the origin?
Submit Answer
Drivsar Police Tormer Sondico
hp
attempt 2 out of 2
Answers
Answer:
(-6, 7)
Step-by-step explanation:
90 degrees counterclockwise / 270 degrees clockwise:
(x,y) -> (-y,x)
180 degrees counterclockwise / 180 degrees clockwise:
(x,y) -> (-x,-y)
270 degrees counterclockwise / 90 degrees clockwise:
(x,y) -> (y,-x)
question is in the photos
Answers
Answer:
n(AuB)=15
n(AnB)=8 is the answer!