Answer:
59 Adults And 147 Children
Step-by-step explanation:
Since there were a total of 206 people, this means that x%2By=206
Also, because "The Jurassic Zoo charges $11 for adult admission and $9 for each child. the total bill for the 206 people from a school trip was $1972", this means that 11x%2B9y=1972
So we have the system:
system%28x%2By=206%2C11x%2B9y=1972%29
Let's solve it by substitution
Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.
So let's isolate y in the first equation
x%2By=206 Start with the first equation
y=206-x Subtract x from both sides
y=-x%2B206 Rearrange the equation
---------------------
Since y=-x%2B206, we can now replace each y in the second equation with -x%2B206 to solve for x
11x%2B9highlight%28%28-x%2B206%29%29=1972 Plug in y=-x%2B206 into the second equation. In other words, replace each y with -x%2B206. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.
11x%2B%289%29%28-1%29x%2B%289%29%28206%29=1972 Distribute 9 to -x%2B206
11x-9x%2B1854=1972 Multiply
2x%2B1854=1972 Combine like terms on the left side
2x=1972-1854Subtract 1854 from both sides
2x=118 Combine like terms on the right side
x=%28118%29%2F%282%29 Divide both sides by 2 to isolate x
x=59 Divide
-----------------First Answer------------------------------
So the first part of our answer is: x=59
Since we know that x=59 we can plug it into the equation y=-x%2B206 (remember we previously solved for y in the first equation).
y=-x%2B206 Start with the equation where y was previously isolated.
y=-%2859%29%2B206 Plug in x=59
y=-59%2B206 Multiply
y=147 Combine like terms
-----------------Second Answer------------------------------
So the second part of our answer is: y=147
-----------------Summary------------------------------
So our answers are:
x=59 and y=147
This means that 59 adults and 147 children went to the zoo.
if sin A=1/2 find the cos A
Answer:
Sin A = 1/2 means taking the inverse of Sin which is arcsin and then solving for A.
Do the same thing for Cos A = 1/2. The inverse of Cos is arccos and then solve for A.
The answer is pi/3. Knowing the unit circle helps too.
Good luck!
If sin A is 1/2. Then the value of cos A will be √3 / 2.
What is trigonometry?The connection between the lengths and angles of a triangular shape is the subject of trigonometry.
If sin A is 1/2. Then the value of cos A will be
We know that
sin² A + cos² A = 1
Then we have
(1/2)² + cos²A = 1
cos² A = 1 - 1/4
cos² A = 3/4
cos A = √(3/4)
cos A = √3 / 2
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Select all of the expressions which correctly show how to convert 18 inches into yards.
18 in. ⨉ 1yd36in.
18 in. ⨉ 36 yd
18 in. ⨉ 36in.1yd
18 in. ⨉ 1yd12in.
18 in. ⨉ 1ft12in. ⨉ 1yd3ft
Answer:
All correct ones:
18in. x 36in. 1yrd.
18in. x 1ft 12in. x 1yrd 3ft
Step-by-step explanation:
The correct expressions to convert 18 inches into yards are:
18 in ⨉ 1yd/36 in. Thus, option a is correct.
What is the Measurement Conversion?Measurement conversion refers to the process of changing a quantity from one unit of measurement to another unit of measurement.
The first expression uses the conversion factor of 1 inch = 1/36 yards
Then, 18 inches = 18 × 1/36 yards
or,
18 in ⨉ 1yd/36 in
The correct expressions to convert 18 inches into yards are:
18 in ⨉ 1yd/36 in. Thus, option a is correct.
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Complete question:
If 30 feet of a fencing material weighs 21 pounds, what does 75 feet of the same material weigh?
Answer:
52.5 lbs
Step-by-step explanation:
We can use a ratio to solve
30 ft 75 ft
-------------- = ------------
21 lbs x lbs
Using cross products
30x = 75*21
30x = 1575
Divide each side by 30
30x/30 =1575/30
x =52.5 lbs
An 18-foot long ramp is placed at a loading
dock that is 5 feet above ground. How far is
the bottom of the ramp from the dock?
What is the measure of ∠A, to the nearest degree?
17°
33°
57°
73°
Answer:
73
Step-by-step explanation:
this is the answer bc it is near a 90 degree angle but not there yet but close
3 divided by9 draw a picture that show the division expression
Answer:
1/3
Step-by-step explanation:
3/9 = 1/3
Mrs. Rodriguez has 63 packages of pens in stock at her store on Monday. On Tuesday, she has 7/9 the number of pens she had on Monday. On Wednesday, she has 1/7 of the number of pens she had on Tuesday. How many packages of pens does she have on Wednesday
Answer:
7 packages
Step-by-step explanation:
Tuesday:
To work this out you would first need to work out how many she has on Monday. First you would divide 63 by 9 to work out 1 ninth, which gives you 7. Then you would multiply 7 by 7 to work out 7 ninths, which gives you 49.
1) Divide 63 by 9.
[tex]63/9=7[/tex]
2) Multiply 7 by 7.
[tex]7*7=49[/tex]
3) She has 49 packages on Tuesday
Wednesday:
To work this out for Wednesday you would first divide 49 by 7 to work out what one seventh is, Which gives you 7. Then you would multiply 7 by 1, which gives you 7.
1) Divide 49 by 7.
[tex]49/7=7[/tex]
2) Multiply 7 by 1.
[tex]7*1=7[/tex]
3) She has 7 packages on Wednesday
whal is P()
im so confused
what is P(12)
and how does it = to 1/30
Answer:
2/60
Step-by-step explanation:
Solve the equation:
|x+1|+|x−2|=3
The only solution to the equation |x+1|+|x-2|=3 is x=2. To find this, we broke the problem into cases based on the nature of absolute values and verified the solution by substitution.
To solve the equation |x+1|+|x-2|=3, we need to consider the different cases due to the absolute value functions.
If x = 2, both x+1 and x-2 are non-negative, and our equation simplifies to x+1+x-2=3, which results in x=2.
If -1 \\leq x < 2, x+1 is non-negative, and x-2 is negative, so the equation becomes x+1-(x-2)=3, which is an identity and does not yield a solution.
If x < -1, both x+1 and x-2 are negative, so the equation becomes -(x+1)-(-x+2)=3, simplifying down to -1=3, which is false and cannot be a solution.
Therefore, the only solution is x=2. We can verify this by substituting back into the original equation. This is consistent with the properties of absolute value equations. Always verify your solutions to ensure they hold in the original equation.
6.77 times 7 times 7.4 by the nearest whole number
Answer:
351
Step-by-step explanation:
Calculate the numbers on a calculator (6.77*7*7.4) and you'll get the answer 350.686. With that number, round the 600 up (makes the 0 in 350 to 1) which will give you the new number of 351. Hope this helps.
Simplify 5(x-4) HELPPP PLS HURRY ILL GIVE U BRAINLIEST
Answer:
5x-20
Step-by-step explanation:
multiply and distribute the 5
Solve: 12^x2+5x-4 = 12^2x+6
x=2
x = -5
x=2x=-5
no solution
Answer:
x=2
Step-by-step explanation:
12x^2+5x-4 = 12x^2+6
Subtract 12x^2 from each side
12^x2-12x^2+5x-4 = 12^2x-12x^2+6
5x-4 = 6
Add 4 to each side
5x-4+4 = 6+4
5x = 10
Divide each side by 5
5x/5 = 10/5
x = 2
Answer:
IT EQUALS 2
Step-by-step explanation:
solve for x. log10x=4
Final answer:
To solve the equation log10x = 4, we convert it to its exponential form, which is 10^4 = x. By doing the calculation, we find that x equals 10,000. This value is the inverse log of the number 4.
Explanation:
To solve the equation log10x=4, we need to understand that this is a common logarithmic equation where the base of the logarithm is 10. The equation essentially asks what power we must raise 10 to in order to get x. In this case, the power is 4.
According to the properties of logarithms, we can rewrite the equation in its exponential form which is 10^4 = x. So, x = 10,000.
This value of x is obtained by taking the inverse log of 4 or calculating 10^4 using a calculator, which yields the result 10,000. Therefore, x = 10,000 is the solution to the equation log10x = 4.
The Petersons hotel has a lazy river that is shaped like a circle with a diameter of 120 ft. If mr. Peterson has made one full rotation how many feet has he traveled?
Mr. Peterson has traveled approximately 376.8 feet after making one full rotation in a lazy river with a diameter of 120 feet, by calculating the circumference of the circle using the formula C = πd.
Explanation:The question asks how many feet Mr. Peterson has traveled after making one full rotation in a lazy river shaped like a circle with a diameter of 120 ft. To find the distance traveled, we need to calculate the circumference of the circle, which is the total distance around the circle.
The formula for the circumference of a circle is C = πd, where C is the circumference and d is the diameter of the circle. Using π approximately equal to 3.14 and the given diameter of 120 feet, we calculate the circumference as follows:
C = πd = 3.14 × 120 ft = 376.8 ft
Therefore, Mr. Peterson has traveled approximately 376.8 feet after making one full rotation around the lazy river.
Factor the following polynomial:
2x^2+8x
Look at the attached picture⤴
Hope it will help u..
if anyone doesn't get trigonometry here are some ways to help remember through picture memory.
If anyone has a picture that's different please describe it as your answer with the calculation that helps you remember away from usual way.
Picture 1. Right angle
Sunrise Ah looks for side measure.
The number above is the hypotenuse
A/H = cos ( ) x hyp =base
A/H = cos ( ) x hyp = side
Picture 2.
Sunrise Soh looks for side measure.
The number above it is the hypotenuse
O/H = sin ( ) =p (for product) take the p x hyp.
Picture 3 Sunrise Toast (oa) looks for side measure = O/A
Tan ( lower angle ) x base = side
Picture 4
Side of car with window as hypotenuse.
Two wheels are the 2 angles given and the back seat is perpendicular to both wheels = so the triangle structure looks like this /00|7
so you type in 7/sin ( 1st wheel) x (2nd wheel) = hypotenuse.
Both angles given or worked out this is when this is used.
Picture 5
Electric mast looking for slope
SIN =S/P = O/A
Angle at top
We have the side at 70 and looking for the slope
Sin( top angle) = p then side/p = hyp
Picture 6
Top angle and base given creates a T this means half both of them before dividing.
Half = 1/2 base / sin (1/2) = hypotenuse
Picture 7
Top angle and base given creates a T this means half both of them before dividing.
To find height =
Half = 1/2 base /Tan 1/2) = Triangle height.
Key checker after pictures are drawn is;
sunrise = low angle x side or low angle x base = hypotenuse.
car = backseat x wheels = hypotenuse
Half = 1/2 base / sin (1/2) = hypotenuse
Half = 1/2 base / tan (1/2) = height
Just take care with top angle and lower angle key words in the drawing descriptions and then the pictures will help.
Which describes the graph of the function shown?
A) linear and discrete
B) nonlinear and discrete
C) linear and continuous
D) nonlinear and continuous
Use the graph to write a linear function that relates y to x
Answer:
y = 3
Step-by-step explanation:
This is a constant function
y = 3
The equation of a line can be predicted easily if two points are given. Thus, the equation of the required line is [tex]\bold{y=4}[/tex].
We need to determine the equation of the line with the help of the given graph.
Now, take two points from the graph. The points are ( 1, 4 ) and ( 2, 4 ).
The if a line passed through the two points say [tex](x_1,y_1)\;\rm{and}\;(x_2,y_2)[/tex], then the equation of the line can be formulated as:
[tex](y-y_1)=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
Therefore, apply the formula and solve it further.
[tex]\begin{aligned} (y-4)&=\dfrac{4-4}{3-2}(x-1)\\y-4&=0\\y&=4 \end{aligned}[/tex]
Thus, the equation of the line is [tex]\bold{y=4}[/tex]
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A playground is 224 square feet. How many square inches is that?
Answer:
32256 square inches
Step-by-step explanation:
Formula
multiply the area value by 144
What fraction of 150 gallons is 189 l? Give your answer in simplest form. 1 gallon = 4.5 l.
Answer:
[tex]\frac{25}{7}[/tex]
Step-by-step explanation:
Given:
1 gallon = 4.5 liters
Question asked:
What fraction of 150 gallons is 189 liters ?
Solution:
First of all we will convert gallons to liters:-
1 gallon = 4.5 liters
150 gallons = 4.5 [tex]\times[/tex] 150 = 675 liters
Now, to know the fraction :-
675 gallons [tex]\div[/tex] 189 liters
[tex]=\frac{675}{189} \\ \\ Dividng\ both\ numerator\ and\ denominator\ by\ 9\\ \\ =\frac{75}{21} \\ \\ Dividng\ both\ numerator\ and\ denominator\ by\ 3\\ \\ =\frac{25}{7}[/tex]
Therefore, 150 gallons (675 liters) is [tex]\frac{25}{7}[/tex] of 189 liters.
micchel and jennefer each worked 25 hours last week. micchel eared $10 per hour jennifer earned $12 per hour how much more did jennifer earn for the week
Answer:Jennifer earn 50$ more than micchel
Step-by-step explanation:
All 12 members of the glee club went to eat at the Hibachi Grill restaurant. The chicken costs $10 per person, while the beef costs $14 per person. At the end of the evening, the club members received a bill for $136, not including tax.
Assuming that each person ordered only one type of meal (chicken or beef), how many club members ordered chicken?
URGENT
Answer:
8 chicken, 4 beef
Step-by-step explanation:
No. of chicken: x
No. of beef: y
x + y = 12
x = 12 - y
10x + 14y = 136
10(12 - y) + 14y = 136
120 - 10y + 14y = 136
4y = 16
y = 4
x = 12 - 4
x = 8
Grayson charges $35 per hour plus a $35 administration fee for tax preparation, lan charges $45 per hour plus a $15
administration fee. If h represents the number of hours of tax preparation, for what number of hours does Grayson charge
more than lan?
Oh> 2
on<5
h>5
Answer:
h < 2
Step-by-step explanation:
The charges by Grayson are ...
35h +35
The charges by Ian are ...
45h +15
We want to find h for ...
Grayson > Ian
35x +35 > 45h +15 . . . . use expressions we found
20 > 10h . . . . . . . . . . . . add -15-35h
2 > h . . . . . . . . . . . . . . . divide by 10
Grayson will charge more for less than 2 hours.
Answer:
A: h < 2
Step-by-step explanation:
18 is 25% of what number?
Answer:
72
Step-by-step explanation:
Kathi and Robert Hawn had a pottery stand at the annual Skippack Craft Fair. They sold some of their pottery at the original price of $9.50 each, but later decreased the price of each by
$3.00. If they sold all 95 pieces and took in $707.50, find how many they sold at the original price and how many they sold at the reduced price
The number sold at $9.50 is
The number sold at $6.50 is
Answer:
Amount of potteries sold at $9.50 is 30
And that of $6.50 is 65 potteries
Step-by-step explanation:
Kindly refer to the attached image for explanations
solve 5+x/2=16. show your work please
Answer:
Download photomath it's really helpful
Evaluate each expression.
Answer:
-1
Step-by-step explanation
Answer:
-1
Step-by-step explanation:
-9-3 = -12
18-6 = 12
-12/12 = -1
Classwork/Homework:
Which of the following equations represent exponential functions
A. f(x) = 2x3 + 1
B. f(x) = -4*
C. f(x) = 1+
D. f(x) = 3(2)*
Option D, f(x) = 3(2)^x, represents an exponential function.
Explanation:The equation that represents an exponential function is f(x) = 3(2)x. The exponential function has the form y = ab^x, where a and b are constants, and b is greater than 0 and not equal to 1. In this equation, b is equal to 2, which satisfies the condition. Therefore, option D, f(x) = 3(2)x, represents an exponential function.
What is the answer to this question?
Answer:
Perpendicular
Step-by-step explanation:
Parallel lines have equal slopes.
The product of perpendicular slopes = - 1
Calculate the slopes of u and v using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 51, 65) and (x₂, y₂ ) = (- 46, 96)
m = [tex]\frac{96-65}{-46+51}[/tex] = [tex]\frac{31}{5}[/tex]
Repeat with (x₁, y₁ ) = (- 37, 85) and (x₂, y₂ ) = (- 6, 80)
m = [tex]\frac{80-85}{-6+37}[/tex] = - [tex]\frac{5}{31}[/tex]
Since [tex]\frac{31}{5}[/tex] × - [tex]\frac{5}{31}[/tex] = - 1
Then the lines are Perpendicular
Solve the equation. SHOW your work. SHOW which properties of equality you used to solve each equation.
3( y + 4) = 24
Answer:
y = 4
Step-by-step explanation:
We have to use the distributive property. Remember that the distributive property states that when expanding out a parentheses, you must find the sum of the product of the "outside term" with each of the "inside terms".
In this case, the "outside term" is 3 and the "inside terms" are y and 4. So, we need to multiply 3 by each of y and 4 and then add those together:
3(y + 4) = 24
3 * y + 3 * 4 = 24
3y + 12 = 24
Now, we subtract 12 from both sides to isolate the variable:
3y + 12 - 12 = 24 - 12
3y = 12
Finally, divide by 3 from both sides to get y alone:
3y/3 = 12/3
y = 4
Thus, y = 4.
Hope this helps!
Answer:
y = 4
Step-by-step explanation:
3(y+4) = 24 <- This is a linear equation so its solved as such
3y+12 = 24 <- Distribute the (PEMDAS)
-12 -12 <- Get y alone
3y = 12 <- Rewrite with y alone
[tex]\frac{3y}{3}[/tex] = [tex]\frac{12}{3}[/tex] <- Divide both sides
y = 4