From the calculation carried out below, the number of children admitted was 1,400 and the number of adults admitted was 700.
How do we calculate the different numbers of people admitted?
This question can be solved using the substitution method as follows:
x = Number of children admitted
y = Number of adults admitted
x + y = 2,100 ............................................. (1)
1.50x + 4y = 4,900 ................................ (2)
From equation (1), we have:
x = 2,100 - y ................................................. (3)
Substituting x = 2,100 - y into equation (2) and solving for y, we have:
1.50(2,100 - y) + 4y = 4,900
3,150 - 1.50y + 4y = 4,900
2.50y = 4,900 - 3,150
2.50y = 1,750
y = 1,750 / 2.50
y = 700
Substituting y = 700 into equation (3), we have:
x = 2,100 - 700
x = 1,400
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Use the Exterior Angle Inequality Theorem to list all of the angles that satisfy the stated condition.
Measures less than m∠ 5
The exterior angle (∠ 5) is larger than either remote interior angle (∠ 7 and ∠ 8).
What is meant by Exterior Angle Inequality Theorem?According to the exterior angle inequality theorem, the measure of any exterior angle of a triangle is greater than the measure of either of the opposite interior angles. The adjacent interior angle and the exterior angle are supplementary. A triangle's exterior angles add up to 360º.
A triangle's exterior angle is always greater than its two remote interior angles.
By the Exterior Angle Inequality Theorem, the exterior angle (∠ 5) is larger than either remote interior angle (∠ 7 and ∠ 8).
m ∠ 7 < m ∠ 5 and m ∠ 8 < m ∠ 5 .
Therefore, the correct answer is ∠ 7 and ∠ 8.
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Write an equation of a circle with the given center and radius. Check your answers.
center (-6,10) , radius 1
The equation of the circle with radius 1 and center at (-6 , 10) is (x + 6)^2 + (y - 10)^2 = 1.
The general form of the equation of circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.
Given the radius and center of the circle, substitute these values to the general form of the equation of the circle.
(x - h)^2 + (y - k)^2 = r^2
where (h , k) = (-6 , 10)
r = 1
(x - -6)^2 + (y - 10)^2 = 1^2
(x + 6)^2 + (y - 10)^2 = 1
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Determine whether the given function is linear. f(x) = 3 + 1/3x
you can either graph this or plug in values.
[tex]f(x)=3+\frac{1}{3}x[/tex]
[tex]f(-1)=3+\frac{1}{3}(-1)\\\\f(-1)=3-\frac{1}{3}\\\\f(-1)=2\ \frac{2}{3}\\\\f(0)=3\\\\f(1)=3\ \frac{1}{3}[/tex]
[tex]\therefore[/tex] we can conclude that this function is linear.
Also here is a graph
Simplify each expression.
8. (-3)+4
8. (-3)+4
= -24 +4
= -20
What is algebric equation?In algebraic equation or polynomial equation is an equation of the frame P=0 where P could be a polynomial with coefficients in a few field, regularly the field of the rational numbers.
algebraic equation, statement of the equality of two expressions defined by applying to a set of factors the algebraic operations, namely, expansion, subtraction, increase, division, raising to a control, and extraction of a root.
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Below is the relationship for miles per hour for 3 different people and their car speeds. Which "Will" has a greater slope? Identify EACH slope for all THREE graphs to come to a conclusion.
Answer:
Step-by-step explanation:
A sloping line on a speed-time graph represents an acceleration . The sloping line shows that the speed of the object is changing. The object is either speeding up or slowing down. The steeper the slope of the line the greater the acceleration.
A rental car company charges $48 per day to rent a car and $0.08 for every mile
driven. Bilquis wants to rent a car, knowing that:
. She plans to drive 175 miles.
. She has at most $110 to spend.
Write and solve an inequality which can be used to determine x, the number of days Bilquis can afford to rent while staying within her budget.
The number of days Bilquis can afford to rent while staying within her budget is 2 days.
How to solve the inequalityThe question has the following data
amount charged = $48
Rent per mile = $0.08
The mile to drive = 175 miles.
Amount to spend = 110 dollars
The inequality would be written as
48x + 0.08(175) ≤ 110
we are to solve for the value of x
this would be
48x + 14 ≤ 110
48x ≤ 110 - 14
48x ≤ 96
We have to divide through by 48
x ≤ 96 / 48
x ≤ 2
Hence we can say that the number of days Bilquis can afford to rent while staying within her budget is 2 days.
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A 3-gallon bucket of paint costs $ 81.60. What is the price per pint?
Answer: $3.40 per pint
Step-by-step explanation:
1 gallon=8 pints
3 gallons * 8 pints/1 gallon=
3*8/1=
3*8=24 pints in 3 gallons
$81.6 for 24 pints of paint
81.6/24=$3.40 per pint
I've been trying to figure this out for a while now, can I get some help? -53<9x+1<-26
Answer:
- 9 < x < - 3
Step-by-step explanation:
- 53 < 9x + 1 < - 26 ( subtract 1 from each interval )
- 54 < 9x < - 27 ( divide each interval by 9 )
- 6 < x < - 3
what is y if 3y+20=5y-16
Answer:
y is equal to 18
Step-by-step explanation:
[tex]3y+20-20=5y-16-20\\3y=5y-36\\3y-5y=5y-36-5y\\-2y=-36\\\frac{-2(y)}{-2}=\frac{-36}{-2}\\(\frac{-a}{-b} = \frac{a}{yb}) =\frac{2y}{2}\\\frac{2(y)}{2}=y\\=\frac{36}{2}\\=18\\y = 18[/tex]
3(4x −2)=2(5x +3) yo i need this fast
Answer:
x=2
Step-by-step explanation:
Answer:
x=6
Step-by-step explanation:
3(4x-2)=2(5x+3)
12x-6=10x+6
+6 +6
12x=10x+12
-10x -10x
2x=12
Divide by 2.
x=6
Hope this helps.
[tex]\frac{1}{4} + \frac{-3}{4}[/tex]
Answer:
-1/2
[tex] - \frac{1 }{2} [/tex]
First the two fours cancel out so it's becomes
[tex] \frac{1 - 3}{4} [/tex]
then subtract
[tex] \frac{ - 2}{4} [/tex]
simplify
[tex] \frac{ - 1}{2} [/tex]
The diagrams below show two cereal boxes of different sizes and prices. (a) big box 500 g $8.00 small box 300 g $5.40 Which of the boxes is better value for money? Show your workings.
Answer: Small box has the lowest amount when divided, that box has the best value.
Step-by-step explanation:
Given data,
Big box = 500 g
It cost is $8.00
Small box = 300 g
It cost is $ 5.40
First switch the box that's in kilograms into grams.
One kilogram=1000 grams.
Then, Big box = 500 g = $ 8.00
Small box = 300 g = $ 5.40
Next divide the amount in each box by the cost of each box.
Big box = 500/8
Big box = 62.5
Small box = 300/540
Small box = 0.5555
Therefore,
So, since small box has the lowest amount when divided, that box has the best value.
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Divide the quantity 3.185 times ten raised to the seventeenth power end quantity divided by the quantity 9.1 times ten raised to the eighth power end quantity.. write the final answer in scientific notation. 3.5 x 108 0.35 x 109 3.5 x 109 0.35 x 1025
On dividing 3.185 × [tex]10^{17}[/tex] by 9.1 × [tex]10^{8}[/tex] the final answer in scientific notation is 3.5 ×[tex]10^{8}[/tex] .
The quantity 3.185 times ten raised to the seventeenth power can written as 3.185 × [tex]10^{17}[/tex] .
The quantity 9.1 times ten raised to the eighth power can written as 9.1 × [tex]10^{8}[/tex] .
On dividing 3.185 × [tex]10^{17}[/tex] by 9.1 × [tex]10^{8}[/tex] ,
( 3.185 × [tex]10^{17}[/tex] )/( 9.1 × [tex]10^{8}[/tex] ) = 0.35 × [tex]10^{17-8}[/tex] = 0.35 ×[tex]10^{9}[/tex] = 3.5 ×[tex]10^{8}[/tex] (in scientific notation)
Scientific notation is a floating-point system in which the numbers are expressed as the products consisting of a number between one to ten multiplied by an appropriate power of ten.
On dividing 3.185 × [tex]10^{17}[/tex] by 9.1 × [tex]10^{8}[/tex] the final answer in scientific notation is 3.5 ×[tex]10^{8}[/tex] .
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Write the equation of the line in slope-intercept form.
(x/6) - (5/12)y = 5/8
The equation of the line in slope-intercept form is y = (2/5)x + (-3/2) .
The equation of a line in slope-intercept form can be written as follows,
y = mx + c equation 1
m in the above equation represents slope of the line and c represents the intercept.
The given equation is (x/6) - (5/12)y = 5/8 .
To get the equation of the line in slope-intercept form we need to convert the given equation in the format of equation of a straight line i.e., equation1. So, now we will rearrange the given equation as
(x/6) - (5/12)y = 5/8
On multiplying both sides of above equation by (12/5), we will get
(2/5)x - y = 3/2
⇒ y = (2/5)x + (-3/2) equation 2
On equating equation 1 and equation 2, we will get
Slope of the line = m = 2/5
Intercept = c = -3/2
The equation of the line in slope-intercept form is y = (2/5)x + (-3/2) .
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The measure of an angle is 51.1°. What is the measure of its complementary angle?
Answer:
let the complementary angle be x
51.1°+x=90°
x=90°-51.1°
x=38.9°
In the expression 38+27 y , which number is a coefficient?
27 is the number that is a coefficient.
An expression in math is a sentence with a minimum of two numbers/variables and at least one math operation in it.
A coefficient is a number or an alphabet that is multiplied by a variable of a single term or the terms of a polynomial. For example, in the term 7x, 7 is the coefficient. The coefficient of x in the term 3xy is 3y.
The variable is a symbol for a value we don't know yet. It is usually a letter like x or y.
In Algebra, a constant is a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number.
In the expression 38 + 27y the coefficient of y is 27, 38 is the constant and y is the variable.
we can identify a coefficient since it is always associated with a variable.
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Find the value of each variable (3x+31)° (2x-6)°
Answer:
x = 31°Step-by-step explanation:
Angle (3x+31)° and angle (2x-6)° are supplementary angles
(3x + 31)° + (2x - 6)° = 180°
5x + 25° = 180°
5x = 155°
x = 31°
-----------------
check
3 * 31 + 31 + 2 * 31 - 6 = 180
180 = 180 (remember PEMDAS)
the answer is good
Please resolve it and list the steps the simplest way possible, thanks. ASAP if possible
Step-by-step explanation:
Looks like it's a piecewise defined function. Where you see a circle, means it's not inclusive so at f(1) it should be define at y=3
If x = −4 and y = −5, what is the value of 5x + 3y + 14? A. −49
B. −21 C.41 D. 49
Answer:
the value it's -21
Step-by-step explanation:
5×(-4)+3×(-5)+14=
-20 + (-15) + 14=
-20 -15 + 14=
-35 + 14=
-21.
9.233050612 es el número racional o irracional
9.233050612 is a rational number.
What are rational and irrational numbers?Real numbers that can be expressed as a ratio of two integers, such as P/Q, where Q is not equal to zero, are referred to as rational numbers. Finite or repeating numbers are included in the category of rational numbers.
Real numbers are referred to as irrational numbers if they cannot be represented as the ratio of two integers. These are composed entirely of non-terminating, non-repeating numbers.
The given number 9.233050612 can be written in the form P/Q as :
9.233050612 = [tex]\frac{9.233050612}{1000000000}[/tex]
Hence, the given number is a rational number.
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The correct question is:
"9.233050612 is a rational or irrational number"
Isabel is on a ride at an amusement park that slides the rider to the right, and then rotates counterclockwise about its own center 60° every 2 seconds. How many seconds pass before Isabel completes one full rotation?
Isabel to complete one full rotation is 12 seconds.
In statistics, what does a probability mean?
The probability serves as a gauge for how likely an event is to occur. It gauges how likely an event is. P(E) = Number of Favorable Outcomes/Number of Total Outcomes is the formula for probability.P ( E ) = Number of favourable outcome Total number of outcomes. Hence, the probability is the possibility of the occurrence of a random event.In every 2 seconds the ride rotates 60º.
So, it takes 6 turns to rotate 6 × 60º or 360º.
Therefore, the time it takes
Isabel to complete one full rotation is 12 seconds.
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Solve the word problem below using the steps given in the lesson.
Skylar needs $56 to buy a new video game. If he doubles the amount of money he has now, he will have enough to buy the game with $8 left over.
How much money does Skylar have right now?
Answer:
32
Step-by-step explanation:
Step-by-step explanation:
If he doubles the amount of money he has now, he will have enough to buy the game with $8 left over. 2x=56+8 ; 2x=64 ; x=64/2 ; x=32. Skylar has $32 right now.Nov 12, 2020©
Determine whether each function is linear or quadratic. Identify the quadratic, linear, and constant terms. y=6 x-x²+1
The function y = 6x - x² + 1 already defined is a quadratic function.
-x² is its quadratic term6x is its linear term1 is its constant valueWhat is a function?A function is the definition of a mathematical expression or equation that helps us to give a visual representation, through graphs to analyze the behavior of the same, a function is not real when it cuts the vertical axis at a same point of x.
The given function is given by means of the expression
y=6x -x²+1
y = -x² + 6x + 1 , it is a quadratic function because of its exponent "2".
Where we can separate each of the terms or parts:
y =f(x) is the image of the function-x² is the quadratic term6x is the linear term1 is the constantLearn more about functions at:
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Question below, only answer if you know
Answer:
1. translate
2.rotate
explanation:
first, translate a to the next quadrant.
second, rotate it 180 degrees.
Answer:
Figure A translated 2 figures down and mirrored to the right.
Figure A then rotated 180 degrees.
i need help asap!!!!!!!
Draw a right triangle with side lengths that form a Pythagorean triple. If you double the length of each side, is the resulting triangle acute, right, or obtuse? if you halve the length of each side? Explain.
If you double or halve the length of each of Pythagorean triplet the resulting triangle will always be Right Triangle.
Pythagoras Theorem states that the sum square of two sides of triangle is equal to the square of longest side.
Let us take Pythagorean triplet as (6,8,10).
where base=6
perpendicular = 8
hypotenuse = 10
Part(a)
Let us double the length of each value
base = 12
perpendicular = 16
hypotenuse = 20
By Pythagoras Theorem
[tex]base^{2} +perpendicular^{2} =hypotenuse^{2}[/tex]
[tex]12^{2} +16^{2} =20^{2} \\ \\ 144+256=400\\ \\ 400=400[/tex]
Therefore the Triangle will be a Right Triangle as Pythagoras Theorem is satisfied.
Part (b)
Let us halve the length of each value
base=3
perpendicular = 4
hypotenuse = 5
By Pythagoras Theorem
[tex]base^{2} +perpendicular^{2} =hypotenuse^{2}\\\\3^{2} +4^{2} =5^{2}[/tex]
[tex]9+16=25\\ \\ 25=25[/tex]
Therefore the Triangle will be a Right Triangle as Pythagoras Theorem is satisfied.
Therefore , If you double or halve the length of each of Pythagorean triplet the resulting triangle will always be Right Triangle.
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7
2-2
3-3
Question 6(Multiple Choice Worth 1 points)
(02.05 MC)
If the parent function f(x) = |x| is transformed to g(x) = |x - 3|, what transformation occurs from f(x) to g(x)?
The graph of f(x) is shifted upward to create g(x).
The graph of f(x) is shifted downward to create g(x).
The graph of f(x) is shifted to the right to create g(x).
The graph of f(x) is shifted to the left to create g(x).
Question 7(Multiple Choice Worth 1 points)
(02.05 MC)
Set
Answer: The graph of f(x) is shifted to the right to create g(x).
Step-by-step explanation:
g(x) is the graph of f(x) shifted right 3 units.
the andersons can set up 6 tables in 1 hour how many tables can they set up in 5 hours
They can set up total 30 tables in 5 hours.
How is a multiplication explained?Multiply in mathematics refers to the continual addition of sets of same size.
2 × 3 = 6
It can be interpreted this way:
Three times two equals six.
Three times two equals six.
Six is two threes.
Given,
Andersons can set up 6 tables in 1 hour
Tables they can set up in 5 hours = 5 × 6
= 30
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A 3-gallon bottle of fabric softener costs $40.32. What is the price per pint?
round 13.891 to the nearest tenth, i need help with math homework
Answer:
13.9
Step-by-step explanation:
13.891
the 9 is greater than 4 so it can round up the 8 to a 9
