Taking into account the definition of a system of linear equations, the number of adults attended the Saturday matinee showing is 29 and the number of children attended the Saturday matinee showing is 16.
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 sought, with which when replacing, they must give the solution proposed in both equations.
Amount of adults that attended the showingIn this case, a system of linear equations must be proposed taking into account that:
"x": number of adults attended the Saturday matinee showing."y": number of children attended the Saturday matinee showing.The tickets to gone with the wind, at the classic movie house, cost $4.50 for adults and $2 for children.
45 people attended the Saturday matinee showing and the Classic movie House sold $162.50 worth of tickets.
So, the system of equations to be solved is
[tex]\left \{ {{x+y=45} \atop {4.50x+2y=162.5}} \right.[/tex]
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.
In this case, isolating the variable "x" from the first equation you get:
x=45 - y
Then, substituting the expression in the second equation you get:
4.50×(45 - y) +2y=162.5
Solving:
4.50×45 - 4.50y +2y=162.5
4.50×45 - 4.50y +2y=162.5
202.5 -2.5y= 162.5
-2.5y= 162.5 -202.5
-2.5y= -40
y= (-40)÷ (-2.5)
y=16
Now, replacing in the expression x=45 - y you get:
x=45 -y
x= 45-16
x= 29
Finally, the number of adults attended the Saturday matinee showing is 29 and the number of children attended the Saturday matinee showing is 16.
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A line contains the following points left to right: r, t, u, s. the space between r and t is 12 units. the space between r and s is 24 units. if tu = 6 units, what must be true? su ut = rt rt tu = rs rs su = ru tu us = rs
Given thet SU = UT = 6 units, hence 6 + 6 = 12 showing that the expression SU + UT = RT is TRUE. Option A is correct
Measure of line segmentsA line is defined as the distance between two points
From the given line, RT = TU = 12 unitsSince the point T bisects RT and TU = 6 units, hence the point U bisects TS.
The sum of the segment SU and UT will be RT
SU + UT = RTGiven that SU = UT = 6 units, hence 6 + 6 = 12 showing that the expression SU + UT = RT is TRUE
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Write an equation of the circle with center (-3, 2) and diameter 12.
Answer:
i d k the answer soory about that
Step-by-step explanation:
just for points
What type of sampling is described in this study?
A company that sells hair-care products wants to
determine if a product that combines shampoo and
conditioner works better than a shampoo and
conditioner used separately. A researcher recruits 60
volunteers and pairs them according to age, hair color,
and hair type. For each pair, the researcher flips a coin
to determine which volunteers will use the
shampoo/conditioner combination and which ones will
use the separate shampoo and conditioner. After using
the products for one month, the subjects are asked to
rate their satisfaction with the hair products on a scale
of 1-10 (1 = highly dissatisfied and 10 = highly
satisfied). What type of sampling is described in this study?
one sample
paired data
two samples
more than two samples
The sampling type in this study, where a researcher recruits 60 paired volunteers and asks them to rate their satisfaction after product use, is B. paired data.
What is a paired data test?A paired data test or sampling is used when the researcher is interested in the difference between two variables for the same subject.
For instance, in this experiment, the researcher wants to find the satisfaction level of the volunteers who used the shampoo and conditioner separately or combined.
Thus, the sampling type in this study, where a researcher recruits 60 paired volunteers and asks them to rate their satisfaction after product use, is B. paired data.
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Calculate the volume of the figure below.
Answer:
600 cm³
Step-by-step explanation:
Figure is of cuboid
length (l) = 10cm
breadth (b) = 4 cm
height (h) = 15cm
volume of cuboid = l.b.h
= 10 × 4 × 15
= 40 × 15
= 600
Therefore,volume of given figure is 600 cm³.
you need to reflection it over the y - axis , please help
Answer:
y axis please set in star then I will tell
Answer:
a'= (10,-9) b'= (9,0) c'= (1,0) d'= (10,-1)
Step-by-step explanation:
whenever you reflect over the y you change the x
which is bigger -32 or 13.8?
After stepping into a room with unusual lighting, Reagan's pupil has a radius of 1 millimeter. What is the pupil's area?
Use 3.14 for .
[tex]f(n)=3^n[/tex]
find expressions for [tex]f(n+3)[/tex] and [tex]f(n+1)[/tex]
hence find the value of [tex]k[/tex] such that [tex]f(n+3)-f(n+1)= kf(n)[/tex] where k ∈ N
Answer:
[tex]24(f(n))[/tex]
Step-by-step explanation:
[tex]f(n+3) = 3^{n+3}\\f(n+1) = 3^{n+1}[/tex]
so
[tex]f(n+3) - f(n+1) = 3^{n+3} - 3^{n+1}[/tex]
[tex]= 27(3^n) - 3(3^n)[/tex]
[tex]= 24(3^n)[/tex]
[tex]= 24(f(n))[/tex]
hope this helped! :)
A cube has a surface area of 486 inches square. Can the length of each side of the cube be 11 inches? Explain
Answer:
The volume of cube whose total surface area is 486 cm² is 729 cm³
Step-by-step explanation:
714 divided by 7
this will really help me!
(im bad at division)
Answer:
102
Step-by-step explanation:
So 714 divided by 7 = 102
Simplify sqrt{5-n}^2 if n<5
The expression √(5 - n)² is a rational expression, and the simplified expression of √(5 - n)² is 5 - n
How to simplify the expression?The expression is given as:
√(5 - n)²
Where n < 5
The inequality n < 5 has no effect on the expression.
So, we have:
√(5 - n)² = 5 - n
Hence, the simplified expression of √(5 - n)² is 5 - n
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Last week, Emma painted her fence. She used 6 cans of paint. There were 4 liters of paint in each can.
Answer:
I'm guessing you want how many liters of paint she used?
she used 24 liters of paint to paint her fence.
Step-by-step explanation:
theres 6 cans
4 liters in each can
6×4=24
A right prism has a rectangular base. The length is 5ft, width is 2ft, and its height is 10ft.
What is the volume of the prism?
ft³
If the dimensions of the prism are doubled the surface area of the enlarged prism is 640 cm²
Surface area of a rectangular prism:Area = 2lw + 2lh + 2whwhere
h = height
l = length
w = width
Therefore, if the dimension of the prism are doubled the new dimension will be as follows:
l = 5(2) = 10 cm
w = 2(2) = 4 cm
h = 10(2) = 20 cm
Therefore,
surface area = 2(10 × 4) + 2(10 × 20) + 2(20 × 4)
surface area = 2(40) + 2(200) + 2(80)
surface area = 80 + 400 + 160
surface area = 640 cm²
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Volume
LBH5(2)(10)10²100ft³I'LL GIVE BRANLY!!!!!
How many 3-coin combinations exist if we can choose from nickels, dimes, quarters, and half-dollars?
20
4!
4
12
Answer:
12
Step-by-step explanation:
Answer:
20
Step-by-step explanation:
If the order matters, we can use the product rule to show each of the [tex]20[/tex] coins can be chosen in [tex]5[/tex] ways, for a total of [tex]5^{20[/tex] ways, assuming you have enough of each type of coins.
If the order does not matter (which in the case it probably does not) you have to use an r-combination. The formula is[tex]C(n+r-1,r)[/tex]. Here [tex]n=5[/tex] and [tex]r=20[/tex]. So we get [tex]C(24,20)[/tex].
Define bisect and midpoint. Using constructions, draw and label an angle bisector and a perpendicular bisector. Show segment addition postulate and angle addition postulate with examples of solving for a variables
Bisect is a word that means to divide a thing, line or a circle into two parts. While midpoint is known as the middle point that exist in a line segment.
What is Angle addition postulate?This theory states that if two angles are said to be put beside each other, the resulting angle is said to be equal in terms of the sum of the two real angle measures.
Note therefore, that that Bisect is a word that means to divide a thing, line or a circle into two parts. While midpoint is known as the middle point that exist in a line segment.
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In a group of 30 high school students, 15 play football, 19 play basketball and 6
do not play either sport. DRAW a Venn Diagram in the space below to DETERMINE
how many students play basketball but not football.
Answer:
Hope the picture will help you........
Express the area A of a circle as a function of its circumference C. (A = πr² and C = 2πr)
AnswerI dont know
Step-by-step explanation:
how do you expect me to k
solve (-24) ÷ -6 + 10 and explain
so the answer is 4
how to get the answer
[tex](-24)[/tex] ÷ [tex]-6+10[/tex]
take the last part
[tex]-6+10[/tex]
and you would solve that
it would be 4
Find the gradients of lines A and B
What is f(−3) for the function f(a)=−2a2−5a 4? −29 −23 1 37
The value of f(-3) for the function f(a) = -2a² - 5a + 4 is 1.
What are functions?Function relates input and outputs. The outputs are called the ranges of dependent variables while the input are called domain or independent variables.
Therefore,
f(a) = -2a² - 5a + 4
Hence,
f(-3) = -2(-3)² - 5(-3) + 4
Therefore,
f(-3) = -18 + 15 + 4
f(-3) = -3 + 4
f(-3) = 1
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WHAT IS THE LENGTH!!!
the area is 107.95
the base is 12
the height is 12.7
the length is x
The figure is a trapezoid (or trapezium), and the exact length of the trapezoid is 5 units
How to determine the length?The figure is a trapezoid with the following parameters:
Area = 107.95
Base= 12
Height = 12.7
Length = x
The area of a trapezoid is:
Area = 0.5 * (Base + Length) * Height
So, we have:
0.5 * (12 + Length) * 12.7 = 107.95
Evaluate the product
(12 + Length) * 6.35 = 107.95
Divide both sides by 6.35
12 + Length = 17
Subtract 12 from both sides
Length = 5
Hence, the length of the trapezoid is 5 units
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Actually 100 points check for yourself (Easiest 100 points) Match each ordered pair on the left with the functions on the right.
Answer:
(-4, 40) y = -9x + 4
(8, 50) y = 6x + 2
(9, -36) y = -3x - 9
(5, 38) y = 8x - 2
Do you want an explanation?
#1
y=-9x+4Put (-4,40)
40=-9(-4)+440=40Verified
#2
y=-3x-9put (9,-36)
-36=-3(9)-9-36=-36Verified
#3
y=8x-2Put (5,38)
38=8(5)-238=38Verified
#4
y=6x+2Put (8,50)
50=6(8)+250=50Hence verifiedl
what interest rate do you need for an $5000 investment compounded annually to double in 10 years?
What interest rate do you need to double your money in 10 years?
R = 72/t = 72/10 = 7.2% Example Calculation in Months If you invest a sum of money at 0.5% interest per month, how long will it take you to double your investment? t=72/R = 72/0.5 = 144 months (since R is a monthly rate the answer is in months rather than years)
Therefore, since R is a monthly rate the answer is in months rather than years, the interest rate that you need for an $5000 investment compounded annually to double in 10 years is 7.2%
A____________ is sometimes a rhombus
A. Triangle
B. Square
C. Rectangle
D. Trapezoid
Answer:
C (Square)
Step-by-step explanation:
Squares are quadrilaterals with 4 congruent sides. Since rhombuses are quadrilaterals with 4 congruent sides, squares are by definition also rhombuses.
The function f(x)= x3 - 10x² + 29x-20 is graphed below. Over which interval
is the rate of change negative?
Answer:
2.2 ≤ x ≤ 4.5
Step-by-step explanation:
The rate of change simply is asking when the gradient is negative and since a graph is provided you can tell where the line is declining which is in between 2.2 and 4.5. Without a graph, you can use the derivative to find out the negative rate of change of a cubic instead.
line pass through the line (-3, -7.5)tahila determined that the equation of line n is y=0.5x explain the error tahila made while dterming her equation and include the correct equation in your answer
The equation of the line will be (assuming the y-intercept equal to zero):
y = 2.5*x
What is Tahila's mistake?
We know that we have a linear equation of the form:
y = a*x + b
Such that we know that the line passes through (-3, -7.5), notice that the proposed equation is:
y = 0.5*x
If you evaluate that in -3, you get:
y = 0.5*-3 = -1.5
So this line does not pass through (-3, -7.5).
If we assume that b = 0 in the linear equation, then we can find the value of a as:
-7.5 = a*-3
a = 7.5/3 = 2.5
Then the linear equation is:
y = 2.5*x
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if g (x) = 3x²-4, then find g (-3)
Answer:
g(-3) = 23
Step-by-step explanation:
This question is telling us that x = -3. Knowing this, we can plug x into the equation and solve to find g(-3).
[tex]g(-3) = 3(-3)^{2} -4[/tex]
[tex]g(-3) =3(9)-4[/tex] Square -3 to get 9
[tex]g(-3) = 27-4[/tex] Multiply 9 by 3 to get 27
[tex]g(-3) = 23[/tex] Subtract 4 from 27 to get 23
Thus, g(-3) is equal to 23.
I hope this helps! Good luck!
Need some help! Please be specific.
Write a system of equations to represent the following word problem:
ASB sold 340 raffle tickets. Advanced tickets cost $2 each and same-day tickets cost $3 each. If a total of $810 was collected, how many of each type of ticket was sold?
Answer: 210 advanced tickets were sold. 130 same day tickets were sold.
Step-by-step explanation:
x= advanced tickets y=same day tickets
2x+3y=810 this equation represents the money
x+y=340 this equation represents the total number of tickets
x+y=340
-x -x
y=-340-x 2x+3(340-x)=810 210+y=340
2x+1020-3x=810 -210 -210
-x+1020=810 y=130
-1020 -1020
-x=-210
-1 -1
x=210
** BRAINLIEST!! **
A triangle has one side that is 4 centimeters long and
one that is 9 centimeters long.
The third side is a whole number of centimeters.
What is the LONGEST possible third side?
( these are the incorrect answers
35 and 9 )
we have three sides, let's look at the two smaller sides first.
check the picture below atop
if we move the sides closer and ever closer to each other, to the extent that one is right on top of the other, what is the length of the red side? Well, assuming the two smaller sides are one pancaked on top of the other, the red side will be as long as 9 - 4 = 5. However, the sides can't be on top of each other, because if that's so, we have a flat-line, and thus we wouldn't have a triangle. So whatever the third side may be, it must be greater than 5.
check the picture below at the bottom
Now, if we move the sides away from each other, farther and farther to the extent that one is parallel to the other, then the third side will just be as long as 4 + 9 = 13. However, we can't do that, because if that were to happen, we again will have a flat-line and not a triangle. So whatever the third side may be, it must be less than 13.
Complete the sequence.
1/2,3/5,5/8,7/11, ___ , ____
(will mark brainliest)
Answer:
1/2,3/5,5/8,7/11,9/14,11/17
Explanation:
Each time, the numerator of the fraction goes up by 2 and the denominator goes up by 3.
Answer:
9/14, 11/17
Step-by-step explanation:
The pattern observed is :
Numerator increases by 2Denominator increases by 3Hence, the next 2 terms are :
9/14, 11/17