Given:
The total admission price for a group of 4 adults and 10 children is $57.
The total admission price for a group of 3 adults and 7 children is $41.
To find:
The admission prices for an adult and for a children.
Solution:
Let the price of an adult be x and price of children be y.
According to the question,
[tex]4x+10y=57[/tex] ...(i)
[tex]3x+7y=41[/tex] ...(ii)
Multiply equation (i) by 3.
[tex]12x+30y=171[/tex] ...(iii)
Multiply equation (i) by 4.
[tex]12x+28y=164[/tex] ...(iv)
Subtract (iv) from (iii).
[tex]12x+30y-12x-28y=171-164[/tex]
[tex]2y=7[/tex]
Divide both sides by 2.
[tex]y=3.5[/tex]
Put y=3.5 in (i).
[tex]4x+10(3.5)=57[/tex]
[tex]4x+35=57[/tex]
[tex]4x=57-35[/tex]
[tex]4x=22[/tex]
Divide both sides by 4.
[tex]x=5.5[/tex]
Therefore, the price for an adult is $5.5 and price for a child is $3.5.
2 2/9 +1 4/9 please help
Answer:
3 2/3
Step-by-step explanation:
In addition, the denominator has to be the same and it doesn't change when 2 fractions are added together, unless ur trying to simplify the equation, anyways:
2 2/9 +1 4/9
3 6/9
simplify
3 2/3
PLEASE ANSWER FAST
what is the length of rt?
a - 3 cm
b - 1 cm
c- 9 cm
d - 4 cm
Answer:
I would say 3cm
Step-by-step explanation:
sorry if it's wrong but I sure it's right
On a coordinate plane, a straight red line with a positive slope, labeled g of x, crosses the x-axis at (negative 3, 0) and the y-axis at (0, 3). A straight blue line with a positive slope, labeled f of x, crosses the y-axis at (0, negative 3) and the x-axis at (1, 0). Both lines intersect at (3, 6).
Answer:
f(6) = g(3)
Step-by-step explanation:
Which statement is true regarding the functions on the graph?
f(6) = g(3)
f(3) = g(3)
f(3) = g(6)
f(6) = g(6)
Solution:
g(x) passes through the points (-3, 0) and the y-axis at (0, 3). The equation of g(x) is given as:
g(x) = y
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]
[tex]y-0=\frac{3-0}{0-(-3)}(x-(-3))\\\\y=x+3\\\\g(x)=y= x+3\\\\g(x)=x+3[/tex]
f(x) passes through the points (0, -3) and the y-axis at (1, 0). The equation of f(x) is given as:
f(x) = y
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]
[tex]y-(-3)=\frac{0-(-3)}{1-0}(x-0))\\\\y+3=x\\\\f(x)=y= x-3\\\\f(x)=x-3[/tex]
f(6) = x-3 = 6 - 3 = 3
g(3) = x + 3 = 3 + 3 = 3
f(6) = g(3)
An isosceles triangle has two sides of equal length, a, and a base, b. The perimeter of the triangle is 15.7 inches, so the equation to solve is 2a + b = 15.7.
Which lengths make sense for possible values of b? Check all that apply.
–2 in.
0 in.
0.5 in.
2 in.
7.9 in.
Answer:
0.5 in, 2 in
Step-by-step explanation:
It cannot be a negative number, so -2 is out.If we use Pythagorean's theorem ([tex]a^2+b^2=c^2[/tex]), we know that only 0.5 and 2 are correct values of b.Consider the enlarged triangle.
A smaller triangle has side lengths 4, 5, 3. A larger triangle has side lengths 8, 10, 6.
Which steps should be used to find the perimeter? Check all that apply.
Find the scale factor: enlarged over original = 6 over 3 = 2
Find the scale factor: enlarged over original = 3 over 6 = one-half
Calculate the perimeter of the original figure.
Divide the perimeter of the original figure by the scale factor.
Multiply the perimeter of the original figure by the scale factor.
Find the scale factor: StartFraction enlarged over original EndFraction = StartFraction 6 over 3 EndFraction = 2
Calculate the perimeter of the original figure.
Multiply the perimeter of the original figure by the scale factor.
Step-by-step explanation:
A, C, D
The steps which could be used to find the perimeter are Find the scale factor: enlarged over original = 6 over 3 = 2, Calculate the perimeter of the original figure and Multiply the perimeter of the original figure by the scale factor.
What is Scale Factor?Scale factor is the ratio of the dimension of the given original object and the dimension of the new object from the original.
Given that,
A smaller triangle has side lengths 4, 5, 3. A larger triangle has side lengths 8, 10, 6.
First find the scale factor.
Scale factor of enlarged over original = 8/4 = 10/5 = 6/3 = 2
Now, find the perimeter of the original figure.
Perimeter of the original figure = 4 + 5 + 3 = 12
Now.
Perimeter of enlarged figure = Scale factor × Perimeter of original figure
= 2 × 12
= 24
Hence the correct steps are first, third and last step.
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Please HELP!!!!!!!! THANK YOU!!!!!!!!
Answer:
200 animals is the correct answer to the first question.
A rectangular poster is to contain 578 square inches of print. The margins at the top and bottom of the poster are to be 2 inches, and the margins on the left and right are to be 1 inch. What should the dimensions of the poster be so that the least amount of poster is used?
Answer:
19 by 38
Step-by-step explanation:
The area of the poster, A=xy
Margin at both up and bottom is 2inches, at the right and left is 1 inch
Then we can say
(x-4)(y-2)= 578
Let us make y subject of the formula
(y-2)= 578/(x-4)
y=[ 578/(x-4)] + 2
If we substitute into the area A equation we have
A= x { [ 578/(x-4)] + 2}
A= 2x + (578x)/(x - 4)
If we differentiate we have
A'(x)= [2+578(x-4)+578x ]/ (x-4)^2
=[ 2(x-4)^2 + 578(x -4) + 578x ] / (x-4)^2
=[ 2(x^2 - 8x +16) + 578(x-4) + 578x ] /(x-4)^2
If we simplify this we have
=[ 2x^2 -16x +32+578x -578x - 2312]/ (x-4)^2
=( 2x^2 -16x - 2312) / (x-4)^2
At A'(x)= 0
= ( x^2 - 8x - 2312) / (x-4)^ =0
If we divide through by 2 we have
x^2 - 8x - 1156= 0
Solving the quadratic eqn( CHECK THE ATTACHMENT)
X= 38 or -30 then we choose the positive one, then x= 38
Then from area of the poster
A= (x-4)(y-2)= 578
Substitute 38 as value of x
(38-4)(y-2)= 578
34(y-2)=578
34y-68=578
34y=646
y=19
Hence dimensions of the poster is 19 by 38
CHECK THE ATTACHMENT FOR QUADRATIC SOLUTION
In this system of equations below solve for x
2x+2y=12
x-4y=6
Answer:
X = 6
y = 0
Step-by-step explanation:
use elimination method. Multiply (x -4y = 6) by -2.
2x + 2y = 12
-2x + 8y = -12
add them together
10y = 0
y = 0
plug in for y
x - 4(0) = 6
x = 6
Put the following numbers in order from least to greatest.
1/4 1/8 1/2
Answer:
1/8 1/4 1/2
Step-by-step explanation:
i hope it will help you
Step-by-step explanation:
1\8 1\4 1 \2
(01.02 MC)Which of the following expressions shows how to rewrite 4 − 5 using the additive inverse and displays the expression correctly on a number line?
1.The expression 4 plus negative 5 is written on top. A number line from negative 10 to positive 10 is shown, with numbers labeled at intervals of 1. An arrow is shown from point 0 to 4. Another arrow points from 4 to negative 1.
2.The expression 4 plus negative 5 is written on top. A number line from negative 10 to positive 10 is shown, with numbers labeled at intervals of 1. An arrow is shown from point 0 to 4. Another arrow points from 4 to 5.
3.The expression 4 minus negative 5 is written on top. A number line from negative 10 to positive 10 is shown, with numbers labeled at intervals of 1. An arrow is shown from point 0 to 4. Another arrow points from 4 to negative 5.
4.The expression 4 minus negative 5 is written on top. A number line from negative 10 to positive 10 is shown, with numbers labeled at intervals of 1. An arrow is shown from point 0 to 4. Another arrow points from 4 to 1.
Answer:
I think the answer is 1. The expression 4 plus negative 5 is written on top. A number line from negative 10 to positive 10 is shown, with numbers labeled at intervals of 1. An arrow is shown from point 0 to 4. Another arrow points from 4 to negative. So the answer is A
hope this helps sorry if it wrong
pls let me now if right or wrong
The expression 4 plus negative 5 is written on top. A number line from negative 10 to positive 10 is shown, with numbers labeled at intervals of 1. An arrow is shown from points 0 to 4. Another arrow points from 4 to negative 1. Option A is correct.
A number line is defined as the number marked on the line calibrated into an equal number of units. For example -1, 0, 1, and so on.
Here,
4 + (- 5)
The expression 4 plus negative 5 is written on top. A number line from negative 10 to positive 10 is shown, with numbers labeled at intervals of 1. An arrow is shown from points 0 to 4. Another arrow points from 4 to negative 1.
Thus, option A is correct.
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A standard painkiller is known to bring relief in 3.5 minutes on average LaTeX: \muμ. A new painkiller is hypothesized to bring faster relief to patients. A sample of 40 patients are given the new painkillers. The sample yields a mean of 3.0 minutes and a standard deviation of 1.1 minutes. Using a level of significance LaTeX: \alpha = 0.05α = 0.05, the rejection region for the test is:
Answer:
Reject H0 if Z ≤ critical value
- 2.8747978 ≤ 1.645
Step-by-step explanation:
Setting the null and alternative hypothesis :
H0 : μ = 3.5
H1 : μ < 3.5
Sample size (n) = 40
Mean (m) = 3 minutes
Standard deviation (s) = 1.1 minutes
Test statistic : Z = (m - μ) / (s/√n)
Z = (3 - 3.5) / (1.1/√40)
Z = - 0.5 / 0.1739252
Z = - 2.8747978
Zcritical at α 0.05 = 1.645
This is a left tailed test :
Hence rejection region:
Reject H0 if Z ≤ critical value
- 2.8747978 ≤ 1.645
I really need help with this
Solve the following inequality:
55 – 5q > 4(7–9).
Step-by-step explanation:
55 – 5q > 4(7–9)
4(-2)
55- 5q > -8
-5q > -63
q=12.6
What is the equation of the line through the origin and (-4,-9)?
OA. y= 9x
O B. y=
OC. y= 4x
OD.y
Answer:D
Step-by-step explanation:
plzzzzzzzzzzzzzzzzzzzzzzzzz
Answer:
Exact rule : 77
Approximate rule : 80
Step-by-step explanation:
find the value of the expression n+2×m
for m=6 and n =4
Answer:n=4
m=6
Step-by-step explanation:
(solve for bracket first the add)
4+2×6
4+12
16
Which fraction is equivalent to 0.4?
StartFraction 4 over 100 EndFraction
One-fourth
Four-tenths
StartFraction 4 over 1 EndFraction
Answer:
Four-tenths
Step-by-step explanation:
Four-tenths
Hope it helps you in your learning process.
Help ASAP anyone :)!!!??!
Answer:j
Step-by-step explanation:
In the diagram, line A is parallel to line B. Which angles are congruent to angle 1?
(20 Points)
Select All that apply
angle 2
angle 3
angle 4
angle
angle 6
angle 7
angle 8
Answer:
angle 8
Step-by-step explanation:
Follow Me Please
Find the slope of the line passing through the points
(-3. 7) and (2. -6).
Answer:
( 3 , 7 )
Step-by-step explanation:
maybe this will help you
Solve for the missing amount.
Of the 300 Sequoyah Cougars that play a sport, 20 % will go on to play high school sports.
How many Cougars will play a sport in high school?
Answer:
60
Step-by-step explanation:
Answer:
60 Cougars will play a sport in high school
Step-by-step explanation:
20% of 300 is 60.
could someone help please? this is hard
Step-by-step explanation:
1/8+1/4+1/8=1/8+2/8+1/8=4/8=1/2
Answer:
1,2,1, 4, 1
These numbers correspond with the boxes in order from left to right.
what isvequivalent to y=23x−6?
Answer:
Slope = 46.000/2.000 = 23.000
x-intercept = 6/23 = 0.26087
y-intercept = -6/1 = -6.00000
Which equation describes a line perpendicular to line R that passes through the point
(3, –6)?
A.x – 3y = 21
B.3x + y = 3
C.3x – y = 15
D.3x – y = 3
Answer:a
Step-by-step explanation:
In the following table, y is a function of x. True or false: The table below represents a function.
Which point is located at (4, 1)?
A
B
C
D
Answer:
A is located at (4,1)
Step-by-step explanation:
The first number will always be on the x-axis and the second will always be on the y-axis. For example: (x,y) so A is (4,1) , B is (-4,1), C is (1,4) and D is (-1,4).
Hope this helps! ;)
Final Answer: Point A
Steps/Reasons/Explanation:
Question: Which point is located at [tex](4, 1)[/tex]?
The x-axis would be 4 and the y-axis would be 1. The x-axis is horizontal and the y-axis is vertical.
For the x-axis, it tells you the markings of the numbers, so moving to the right would be positive and left would be negative.
For [tex](4, 1)[/tex] we would go four to the right and one up. Point A is located there.
~I hope I helped you :)~
Two hikers hike two different trails for 3 days: Hiker 1: Climbs up in elevation 500 m per day Hiker 2: Goes down in elevation 500 m per day Write an equation using multiplication that represents each hiker's elevation after 3 days. Explain what each number means. What is the final elevation of each hiker?
Answer:
i. y = 3(x)
ii. This implies that: hiker 1 has an altitude of 1500 m, while hiker 2 has a depth of 1500 m with respect to the surface of the earth after the 3 days.
Step-by-step explanation:
Let assume that the horizontal surface of the earth is taken to be zero. Thus any distance moved upward is positive, and any distance moved downward is negative. As compared to a number line.
Thus, after 3 days, the equation for each hiker is;
y = 3(x)
Where y is the total distance covered after 3 days, and x is the elevation of the hiker per day.
For Hiker 1, the elevation was upwards;
y = 3(500)
= 1500 m
For Hiker 2, the elevation was downwards;
y = 3(-500)
= -1500 m
This implies that: hiker 1 has an altitude of 1500 m, while hiker 2 has a depth of 1500 m with respect to the surface of the earth after the 3 days.
Pls someone help me!
Answer:
When present,outliers will have an effect of the range since one of the outliers will either be highest or lowest number in a given data set and the range is found by finding the difference of the highest and lowest numbers.
Find what x equals please
Answer:
180-(35+28)->180-63=117 and 180-117=63 then 63+36=99 and 180-99=81 so x=99°
Eight children sit together at story time. Seven children sit in a circle and one child sits in the middle to tell the story. In how many different ways can the children sit
Answer: 40320
Step-by-step explanation: I think thats correct because the kids on the outside is 1234567 so then there is a kid in the middle.
The number of ways for the children sit will be 40,320.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Eight children sit together at story time.
And, Seven children sit in a circle and one child sits in the middle to tell the story.
Now,
Since, There are 8 students.
Hence, The number of ways for the children sit = 8!
= 40,320
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