Let price of adult ticket is $x
And price of child ticket is $y
So we can make two equations using the given data
[tex] 3x+4y = 122 [/tex]
[tex] 2x+3y = 87 [/tex]
Now we can use eliminator method to solve the two equations
Multiply first equation by 2 and second equation by -3
[tex] 2(3x+4y = 122) [/tex]
[tex] -3(2x+3y = 87) [/tex]
[tex] 6x+8y = 244 [/tex]
[tex] -6x-9y =-261 [/tex]
now add both the equations so we get
[tex] 6x-6x+8y-9y=244-261 [/tex]
combine the like terms
[tex] -y=-17 [/tex]
Divide both sides by -1
[tex] y=17 [/tex]
Plug y=17 in any one of the equations to solve for x
[tex] 3x+4(17) = 122 [/tex]
[tex] 3x+68 = 122 [/tex]
Subtract 68 from both sides
[tex] 3x = 54 [/tex]
Divide both sides by 3
[tex] x=18 [/tex]
So x=18 and y=17
So
Price of adult ticket= $18
Price of child ticket = $17
In Mr.Martinez's sixth period class, there are 8 boys and 12 girls. what is the probability of randomly selecting a girl?
need help with question 20
The length of a rectangle is 6 cm longer than the width. If the length is increased by 9 cm and the width by 5 cm, the perimeter will be 160 cm. Find the dimensions of the ORIGINAL rectangle.
Simon's water cooler can hold up to 4.2 gallons of water in it. Simons fills the cooler so that there is water in all but 25% of the cooler. How much more water would Simon need to add to fill the entire 100% of the cooler?
A 1.05 gallons
B 3.95 gallons
C 3.15 gallons
D 1.7 gallons
Which is one way to check 102 ÷ 6 = 17?
A. 105 ÷ 5 = 21
B. 105 ÷ 10 = 10.5
C. 100 ÷ 5 = 20
D. 102 ÷ 10 = 10.2
I have no idea why the answer choices have different numbers from the question. Please explain your answer to me to understand. I don't want just an answer
Solution:
102 ÷ 6 = 17
As you can see , 102 has unit digit of 2 ,it means it is divisible by 2
Sum of digits of (102) = 1 + 2 =3, it means it is divisible by 3 also.
So , if a number is divisible by 2 and 3 it means it is divisible by 6 also.
Option (A) and Option (C) are true options which are
105 ÷ 5 = 21, and 100÷5 =20
The reason being if you will look at the unit digit of 105 and 100 , it is 5 and 0. So if a number have unit digit either 5 or 0 it is divisible by 5.
Is the domain {1.8,3.4,9,9.8}
{3.2,3.9,5.8,8.4,9.1}
{2.4,4.8,6.3,8.8,10.1}
{3,4.6,6.7,8.9,10.8}
name the quadrilateral with exactly one pair of parallel sides?
A. Kite
B. Parallelogram
C. Rhombus
D. Trapezoid
For the end-of-year party, Mt.Rise Middle School ordered 112 pizzas. There were eight fewer veggie pizzas than there were pepperoni pizzas. There were three times as many combo pizzas as pepperoni pizzas. Use the 5-D process to define a variable and write an equation for this situation. Then determine how many of each kind of pizza were ordered.
Shauna bought a flat cardboard box
WILL GIVE 99 POINTS IF ANSWERED ASAP PLEASE
Answer:
Part A
1. Perimeter of the outside edges = 24 inches
2. One possibility is: length = 8 in. and width = 8 in.
second possibility is: length = 16 in. and width = 4 in.
3. Area of the wood portion = 11 [tex]inches^{2}[/tex]
4. New dimensions are:
Length = 17.5 ft.
Width = 12.5 ft.
Part B
Area of the picture = 24 [tex]inches^{2}[/tex]
Area of the frame = 35 [tex]inches^{2}[/tex]
Step-by-step explanation:
Part A
1. Perimeter of the outside edges = 2(length + width)
= 2(7 + 5)
= 2(12)
= 24 inches
2. If the area of the frame was 64 [tex]inches^{2}[/tex], then the two possible dimensions are:
8 × 8 and 16 × 4
i.e., one possibility is: length = 8 in. and width = 8 in.
second possibility is: length = 16 in. and width = 4 in.
3. Area of the wood portion = Area of the frame - Area of the picture
= (5 × 7) - (4 × 6)
= 35 - 24
= 11 [tex]inches^{2}[/tex]
4. The scale factor is:
1 in. = 2.5 ft.
So, its length = 7 in. = 7(2.5) = 17.5 ft.
width = 5in. = 5(2.5) = 12.5 ft.
Part B:
Length of the picture = 6in.
Width of the picture = 4 in.
Area of the picture = Length × Width
= 6 × 4
= 24 [tex]inches^{2}[/tex]
Length of the frame = 7in.
Width of the frame = 5 in.
Area of the frame = 7 × 5 = 35 [tex]inches^{2}[/tex]
Part A
1) Perimeter of the outside edges
24 inches
2) One possibility is:
length- 8 inches
and width - 8 inches
3) Area of the wood portion
= 11
4) New dimensions are:
Length - 17.5 feet
Width - 12.5 feet
Part B
Area of the picture
- 24
Area of the frame
- 35
Step-by-step explanation:
first part-
1) Perimeter of the outside edges = 2(length + width)
= 2(7 + 5)
= 2(12)
= 24 in
2) if the area of the frame was 64 then there are two possible dimensions
8 × 8 and 16 × 4
the first possibility
length = 8 inches
width = 8 inches
the second possibility
length = 16 inches
width = 4 inches
3) Area of the wood portion= Area of frame - Area of picture
= (5 × 7) - (4 × 6)
= 35 - 24
= 11
4)The scale factor
1 inches = 2.5 feet
length = 7 inches
= 7(2.5)
= 17.5 feet
width = 5 inches
= 5(2.5)
= 12.5 feet
Second part-
Length of picture
= 6 inches
Width of picture
= 4 inches
Area of the picture
(Length × Width)
= 6 × 4
= 24
Length of frame = 7 inches
Width of frame = 5 inches
Area of frame = 7 × 5 = 35
If this helped you please say thanks and mark brainliest
Rewrite the following expression in standard form by finding common denominator and collecting like terms
Fred pays 2/5 of his annual salary in federal, state, and local taxes. His annual salary is 102,000. How much of his salary does he get to keep after taxes are paid? 1) $61,000 2) $72,300 3) $61,200 4) $94,900
Javier bought 47 sports cards. 3/8 of them were baseball cards. How many baseball were baseball cards?
What is the surface area in square feet of a rectangular prism with dimensions of 2 feet by 3 feet by 4 feet as shown in the net?
Answer: 52 square feet
Step-by-step explanation:
The surface area of a rectangular prism is given by :-
[tex]S.A.=2(lw+wh+hl)[/tex], where l is length , w is width and h is height of then prism.
Given: Dimensions of the rectangular prism : [tex]l\times w\times h=[/tex] 2 feet by 3 feet by 4 feet
Then , the surface area of a rectangular prism will be:-
[tex]S.A.=2(2(3)+(3)(4)+(2)(4))\\\\\Rightarrow\ S.A.=52\text{ inches}^2[/tex]
Hence, the surface area of a rectangular prism= 52 square feet
A computer was on sale for 2/3 of the original price. If the original price was $900 what was the sale price? show work please.
a) A square has an area of 121 cm^2. What is the length of each side?
b) A square has a perimeter of 28m . What is the length of each side?
which expression does not give the area of the shaded figure?
Which number is written in scientific notation? 7.8 x 10−5 0.84 x 106 3.4 x 1002 −5 x 10−12
A picture is 5 inches wide and 8 inches tall:
A rectangle is shown. The length of the rectangle is labeled 5 inches. The width of the rectangle is labeled 8 inches.
A photographer wants to use a scale factor of 2.5 to enlarge a picture. What will the area of the picture be after it is enlarged? (5 points)
40 in2
250 in2
100 in2
81.9 in2
Final answer:
The area of the enlarged picture will be 250 square inches, calculated by multiplying the new width and height which are scaled up by the factor of 2.5 from the original dimensions.
Explanation:
To find the area of the enlarged picture, we begin by scaling up the dimensions of the original picture using the given scale factor. The original width is 5 inches, and the original height is 8 inches. Applying a scale factor of 2.5 to both dimensions, we calculate the new dimensions as follows:
New width = 5 inches × 2.5 = 12.5 inchesNew height = 8 inches × 2.5 = 20 inchesNow, to find the area of the enlarged picture, we multiply the width by the height:
New area = New width × New height = 12.5 inches × 20 inches = 250 square inches
Therefore, the area of the picture after it is enlarged will be 250 square inches.
what is the probability of spinning a 2 and flipping tails
X is 85% of 13, 60% of 4.5 is Y
Rose bought some spinach. She used 3/5 of the spinach on a pan of spinach pie for a party and 3/4 of the remaining spinach for a pan for her family. She used the rest of the spinach to make a salad.
What fraction of the spinach did she use ti make the salad?
b. If Rose used 3 pounds of spinach to make the pan of spinach pie for the party , how many pounds of spinach did Rose use to make salad?
what is the value 1/2 ×3+5.2y when x=2 and y=3
a tyrannosaurus rex weighed about 1.4 tons more than one tenth the weight of a Patagotitan mayorum. About how much did the tyrannosaurus rex weigh?
A Patagonian mayorum was a tyrannosaur that weighed about 76 tons
The Tyrannosaurus rex weighed approximately 9 tons.
Explanation:To determine the weight of the Tyrannosaurus rex, we need to find one tenth the weight of Patagotitan mayorum, which is 76 tons. One tenth of 76 tons is 7.6 tons. We then add 1.4 tons to this, as the Tyrannosaurus rex weighs about 1.4 tons more than one tenth the weight of Patagotitan mayorum. Therefore, the weight of the Tyrannosaurus rex is approximately 9 tons.
The drama club members buy 864 bags of popcorn to serve during the intermission of their play. Popcorn comes in cases of 24 bags, and they pay $18 for each case. How much did they pay for all of the popcorn
Final answer:
The drama club purchased 36 cases of popcorn at $18 per case, resulting in a total cost of $648 for all the popcorn.
Explanation:
The question involves calculating the total amount spent on popcorn by the drama club, which requires some basic arithmetic and understanding of multiplication and division. To find the total cost, we first need to determine how many cases of popcorn the club bought and then multiply that number by the cost per case.
Step-by-Step Calculation
Determine the number of cases: Divide the total number of bags of popcorn (864) by the number of bags per case (24).
Calculate the total cost: Multiply the number of cases by the cost per case ($18).
Now, let's perform these steps:
Number of cases = 864 bags ÷ 24 bags/case = 36 cases
Total cost = 36 cases × $18/case = $648
Therefore, the drama club paid $648 for all the popcorn.
What is the volume of this pyramid?
7560 cm³
5040 cm³
2520 cm³
1728 cm³
Answer:
C) 2520 cm^3
Step-by-step explanation:
The given pyramid is a triangle base pyramid.
Volume of a pyramid = 1/3(base area* height)
Here the base is a right triangle with base 24 cm and height 18.
The height of the pyramid is 35 cm.
Plug in the given values in the formula, we get
V = 1/3 (1/2*24*18)*35
= 1/3(216)(35)
= 72*35
V= 2520 cm^3
The volume of the given pyramid is C) 2520 cm^3
Hope this will helpful.
Thank you.
1/2m-4=5
What is the variable 'M' equal to.
rob works part time at the fallbrook riding stable. He makes $5 an hour exercising horses and $10 hour cleaning stalls. Because Rob is a full time student he can work no more than 12 hours per week. however he must make $60 per week. write a system of inequalitites
Answer: 5x + 10y ≥ 60 ⇒ x+2y ≥ 12 .................. (i)
x + y ≤ 12 ................. (ii)
Step-by-step explanation:
Let the hours spent on exercising horse be x
Let the hours spent on cleaning stalls be y
According to question:
Rob can't work more than 12 hours. So eq. (i) will be x + y ≤ 12
Rob earns $5 an hour by exercising horses and $10 an hour cleaning stalls and he must make $60 . So eq. (ii) will be 5x + 10y ≥ 60.
Dividing eq. (ii) by 5, it will become x + 2y ≥ 12.
∴ system of inequalities are x + y ≤ 12 and x + 2y ≥ 12.
A grasshopper coved a distance of 5 yards in 9 equal hops. How many yards did the grasshopper travel on each hop.
Don wrote the expression 8 less than the product of m and 10. What algebraic expression did he write? What is the value of the expression for m = 7?