Let's look at an example.
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Problem:
At a high school play, tickets are sold at two different prices: student prices and parent prices. The student price is $2 while the parent prices is $3. On one night, 145 tickets were purchased and the total revenue was $335.
How many student tickets were purchased? How many parent tickets were purchased?
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Solution:
Let x be the number of student tickets sold and y be the number of parent tickets sold.
We know that 145 people attended so x+y = 145 is the first equation we can set up. This equation is in standard form since standard form is Ax+By = C. Here we have A = 1, B = 1, C = 145.
The second equation we can form is 2x+3y = 335. This is also in standard form. This time we have A = 2, B = 3, C = 335.
The 2x is the amount of money made from just the students only. The 3y is from the parents only. The expression 2x+3y is the total from both groups. This total is set equal to 335 as this is the amount of money pulled in.
After forming both equations, we can write this system of equations
[tex]\begin{cases}x+y = 145\\2x+3y = 335\end{cases}[/tex]
To solve this system, we could isolate y in the first equation to get y = -x+145. Then plug this into the second equation to solve for x
2x+3y = 335
2x+3(-x+145) = 335
2x-3x+435 = 335
-x = 335-435
-x = -100
x = 100 .... number of student tickets bought
Use this to find y
y = -x+145
y = -100+145
y = 45 .... number of parent tickets bought
We can see that x+y = 100+45 = 145
And also 2x+3y = 2*100+3*45 = 200+135 = 335
These two facts help confirm we have the correct x,y values.
what is there in between the two rational numbers .
An infinity of IRrational numbers, and an infinity of other rational ones.
what is the percent of 65 minutes out of 24 hours
Answer:
2.7
Step-by-step explanation:
65/24
Answer:
4.5%
Step-by-step explanation:
24*60 to make the hrs into minutes
24*60=1440
65/1440= 4.51388888889
round the number
4.5%
HURRY PLSS
Which values are in the solution set of the compound inequality -8 <3x +7s 10? Select three options.
O-15
O-5
O-3
O1
Step-by-step explanation:
-8 < 3x + 7 <= 10
-15 < 3x <= 3 (subtract 7)
-5 < x <= 1 (divide by 3)
Hence the correct options are -3, 0 and 1.
Triangle ABC has side lengths 8 cm, 17 cm, and x cm. The side length of x is shorter than the longest side. What does the value of x need to be in order for the triangle to be considered a right triangle?
Answer:
8 cm and 15 cm
The measure of the side is 15 cm
The measure of the right angle triangle is 8 cm, 15 cm and 17 cm
What is a Triangle?
A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
Given data ,
Let the triangle be represented as ΔABC
Now , the base of the triangle BC = 8 cm
The height of the triangle be AB = x cm
The hypotenuse of the triangle AC = 17 cm
So , for the triangle to be a right angle triangle ,
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
Substituting the values in the equation , we get
AC² = AB² + BC²
So , AB² = AC² - BC²
On simplifying the equation , we get
AB² = 17² - 8²
AB² = 289 - 64
AB² = 225
Taking square roots on both sides of the equation , we get
AB = 15 cm
Therefore , the value of x is 15 cm
Hence , The measure of the side is 15 cm
The measure of the right angle triangle is 8 cm, 15 cm and 17 cm
To learn more about triangle click :
https://brainly.com/question/16739377
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enter the value of 5/6+-(4/9)- (-2)
For each equation, find a value x that makes the equation true.
(PLLLLLZZZ help me)
1 x( divided) by 3=12
2 2x+3=20
3 4/3x=10/3
4 -4x=-24
5 2(x-4)=10
6 -0.5x+1.1+2.9
Determine the number of lines of symmetry for the figure.
Answer:
theres 26 lines of symmetry i think....hope this helps:)
Describe how the graph of y= x2 can be transformed to the graph of the given equation. (2 points)
y = x2 - 20
Shift the graph of y = x2 left 20 units.
Shift the graph of y = x2 up 20 units.
Shift the graph of y = x2 down 20 units.
Shift the graph of y = x2 right 20 units.
Answer:
Equation : y = x2 - 20
Intercepts
when y is zero (0), x is 10
when x is zero (0), y is -20
Therefore, shift the graph, y=2x down to the negative y-axis 20 units
ALTERNATIVELY: Shift the graph to the right of positive x-axis 10 units.
find the measures of the numbered angles in the rhombus, will give brainliest ! pls show how you solved it :)))
Answer:
1= 38
2= 90
3 =2 = 90
4= 1 = 38
for explanation check your own previous question
its the same thing
Answer:
see explanation
Step-by-step explanation:
• The diagonals bisect each other at right angles, then
∠ 2 = ∠ 3 = 90°
∠ 1 = 180° - (90 + 52)° ← angle sum of a triangle
∠ 1 = 180° - 142° = 38°
• Diagonals bisect the endpoints, then
angle at vertex with ∠ 1 = 76° and
angle at vertex with ∠ 4 = 76°, thus
∠ 1 = ∠ 4 = 38°
In conclusion
∠ 1 = 38°, ∠ 2 = 90°, ∠ 3 = 90°, ∠ 4 = 38°
What value completes the square for the expression x²+8x+_
Which expression is equal to 9(6 - t)? How do you know?
Answer:
54-9t
Step-by-step explanation:
multiply the 9 with 6 and multiply 9 with the t which has an invisible 1
Find the equation of the line that is parallel to the given line and passes through the given point. y = −2x + 1; (8, 7)
Answer: y= -2x + 1
y= -2x + 23
Step-by-step explanation:
13. Describe the number of solutions for the equation. (1 point)
3(x – 3) = 3x
O one solution
O no solution
O infinite solutions
What one
Answer:
no solution
Step-by-step explanation:
Given
3(x - 3) = 3x , that is
3x - 9 = 3x ( add 9 to both sides )
3x = 3x + 9 ( subtract 3x from both sides )
0 = 9 ← not possible
This indicates the equation has no solution
a wholesaler received 5,000.00 for 50 raincoats . how much did the wholesaler get for each raincoat
Answer:
100
Step-by-step explanation:
..................
write a story for this equation y = 0.5x + 5
help x
Answer:
John has a phone plan that has a $5 initial fee and costs $0.5 per call. How much money would John spend if he has made 17 calls?
what's the square root of 15 divided by 5 square root of 20?
Answer:
√3/10 = 0.1732
Step-by-step explanation:
√15 / 5√20 = (√5 x √3) / 5(√5 x √4) = √3 / (5 x√4) = √3 / 10
Identify the like terms:
4x - 7+ 6y + 2x + x + 16 - 3x
Answer:
4x−7+6y+2x+x+16−3x
=4x+−7+6y+2x+x+16+−3x
Combine Like Terms:
=4x+−7+6y+2x+x+16+−3x
=(4x+2x+x+−3x)+(6y)+(−7+16)
=4x+6y+9
Answer:
=4x+6y+9
Which expression has a positive quotient?
Negative three-fourths divided by Negative two-thirds
Negative StartFraction 1 over 8 EndFraction divided by 3 and one-fifth
2 and StartFraction 2 over 7 EndFraction divided by negative one-fifth
Negative 6 divided by Five-thirds
Answer:
Only 1st option Negative three-fourths divided by Negative two-thirds has positive quotient.
Option A is correct.
Step-by-step explanation:
We will solve to find out Which expression has a positive quotient.
We know the division rule: [tex]\frac{-a}{-b}=\frac{a}{b}[/tex] and [tex]\frac{-a}{b}=\frac{-a}{b}[/tex]
We will use these rules
1) Negative three-fourths divided by Negative two-thirds
[tex]=\frac{-\frac{3}{4} }{-\frac{2}{3} }\\=-\frac{3}{4}\times -\frac{3}{2}\\=\frac{9}{8}[/tex]
The quotient is positive.
2) Negative StartFraction 1 over 8 EndFraction divided by 3 and one-fifth
[tex]\frac{-\frac{1}{8} }{3\frac{1}{5} }\\=\frac{-\frac{1}{8} }{\frac{16}{5} }\\=-\frac{1}{18} \times \frac{5}{16}\\=-\frac{5}{288}[/tex]
The quotient is negative.
3) 2 and StartFraction 2 over 7 EndFraction divided by negative one-fifth
[tex]\frac{2\frac{2}{7} }{-\frac{1}{5} }\\= \frac{\frac{16}{7} }{-\frac{1}{5} }\\=\frac{16}{7} \times -5\\=-\frac{80}{7}[/tex]
The quotient is negative.
4) Negative 6 divided by Five-thirds
[tex]\frac{-6}{\frac{5}{3} }\\=-6 \times \frac{3}{5}\\=-\frac{18}{5}[/tex]
The quotient is negative.
So, only 1st option Negative three-fourths divided by Negative two-thirds has positive quotient.
Option A is correct.
Answer:
its A
Step-by-step explanation:
i did the test
Please help with this thanks lol
Answer:
-70
Step-by-step explanation:
multiply each sides with (7/4)
(7/4)* 40 = (x/(-4/7)) * (7/4)
(7/4) *40 = -x
70= -x
x= -70
in exercise 4 and 5 find the unkown or marked angles
Answer:
Ф = 110°, β = 110°
Step-by-step explanation:
∠Ф and the 110° angle are corresponding angles since the vertical lines are parallel and a horizontal line cut across both lines. Thus Ф = 110°.
∠β and ∠Ф are alternate angles since the horizontal lines are parallel and a vertical line cut across both lines. Thus Ф = 110° and ∠β = 110°.
(3z + 1) + (5 + 72)=
Please help quick
Answer:
3z + 78
Step-by-step explanation:
Simplify
(3z + 1) + (5 + 72)
(3z+1) + 77
3z + 78
Hope this helped you!! If you want to ask any questions about it, I will answer them!! Or if you want it explained more or in a different way, just let me know :))
When you multiply a function by –1, what is the effect on its graph?
A.
The graph flips over the y-axis.
B.
The graph flips over the line y = x.
C.
The graph flips over the x-axis.
Answer: C) The graph flips over the x axis.
This is because we're multiplying the y outputs by -1, to make them flip in sign from positive to negative (or vice versa).
Let's say the point (1,2) is on the f(x) curve. Multiplying y = f(x) by -1 will make the point turn into (1,-2). Apply this logic to every point on the f(x) curve and we end up with f(x) reflected over the horizontal x axis.
The notation we could write is either g(x) = -1*f(x) or g(x) = -f(x).
16d=10
What’s the answer??
I need it quick plz
Answer: d = 5/8
Step-by-step explanation:
first, you divide both sides.
16d / 16 = 10 / 16
then, you divide and rewrite.
d = 16/10
then, reduce the fraction.
d = 5/8
Answer:
d=1
Step-by-step explanation:
kfkfkdlsldkfnskkd THAT'S THE ANSWER
When I multiply two variables, what operation do I use for the exponents to combine them?
Answer:
Multiplying exponents with the same base
When you multiply two variables or numbers that have the same base, you simply add the exponents.
Step-by-step explanation:
Help asap please!! I will mark you as brainliest :)
Answer:
12Step-by-step explanation:
The answer is 12 because is you subtract 2 by 12 then you get 10.
Here's why that's correct.
[tex]\frac{5}{2}[/tex] [tex]or[/tex] [tex]2.5[/tex] is equal to [tex]\frac{10}{4}[/tex] which is also [tex]2.5[/tex]
This is correct because if you multiply both the numerator and the denominator by 2, you get [tex]\frac{10}{4}[/tex] because if you multiply 5 times 2, that equals 10. Then if you multiply 2 times 2, you get 4, which eventually makes 10 over 4, or [tex]\frac{10}{4}[/tex].
Hope this helps! <3
Given that cosA = -8/17 and sinA is negative, determine the value of tanA.
Answer:
tan A = -15/8.
Step-by-step explanation:
sin^2a = 1 - cos^2A
= 1 - (-8/17)^2
= 225/289
So sin A= 15/17
tan A = sin A / cos A
= 15/17 / -8/17
= 15/-8
= -15/8.
What are the output values for this data set:
{ (0,8), (1,9), (2,13), (3,23) }?
Answer:
its 8,9,13,23 or b
Step-by-step explanation:
toke the test
Answer:
8,9,13,23
Step-by-step explanation:
i took the test as well\
the slope of the graph 4 y 4 x
Answer:
_5-_2-_4 is the answer I hope it helps
A company purchased equipment for $150,000 by paying $50,000 and signing a $100,000 note payable. The entire $150,000 is reported as a cash outflow in the financing section of the statement of cash flows.
Answer: False
Step-by-step explanation:
The financing section deals with only the transactions that have to do with equity and debt. The Investing section deals with capital expenditure such as fixed assets and investments in other company securities.
The $50,000 should therefore be recorded in the Investing section as a Cash outflow.
The $100,000 is not a cash transaction but will be recorded in the Notes to the Statement of Cashflows as a Non-Cash transaction for disclosure purposes.
what is another name for proportional relationships?
Answer:
equivalent i think
Step-by-step explanation: