Number of ticket sold for adult = 70
Number of ticket sold for child = 30
Given that,
The number of tickets sold = 100
Cost of ticket for adult = £5.50
Cost of ticket for child = £1.50
Total sold amount = £430.
Let number of ticket for adult = x
And number of tickets for child = y
We know that,
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
Therefore,
Forming the equation according to the given information,
We get two equation as,
5.50x + 1.50y = 430 ...(i)
x + y = 100 ...(ii)
Now, Subtract equation (ii) with multiplication 1.50 from (i)
4x = 280
x = 70
Now put the values of x in equation (ii)
y = 30
Hence number of ticket for child is 30 and for adult is 70.
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write in slope-intercept form the equation of a line which passes through (4,1) with a slope of 1/2
The equation of the line which passes through (4, 1) in slope - intercept form is y = 1/2x - 1
How to find the equation of the line?The equation of a line takes the form:
y = Slope (x) + y - intercept
The slope is already given as 1 / 2 and we have a point on the line. This point can be substituted into the equation of a line to find the value of the y - intercept.
y = Slope (x) + y - intercept
1 = 1/2 (4) + y - intercept
y - intercept = 1 - 2
y - intercept = - 1
The equation of the line will then be:
y = 1/2x - 1
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you are making purple paint in the ratio of 2 cups blue paint to 1/4 cups of red paint use the information in the table to complete the rest of the table
The table to show the number of cups for the colors will be:
Red cups Blue cups
1. 8
2. 16
3. 24
How to illustrate the information?Given that the person is making purple paint in the ratio of 2 cups blue paint to 1/4 cups of red paint.
Therefore, for every 1 cup of red paint, the number of blue paint will be:
= 2 ÷ 1/4
= 2 × 4
= 8 cups
Therefore, to get other values, you simply have to multiply by 8.
2 red paint will be:
= 2 × 8
= 16 blue cups.
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Solve the following equation. 8x-6=10
Answer:
x = 2
Step-by-step explanation:
8x - 6 = 10 ( add 6 to both sides )
8x = 16 ( divide both sides by 8 )
x = 2
Answer:
x = 2
Step-by-step explanation:
8x-6 = 10
8x-6+6 = 10+6
8x = 16
8x/8 = 16/8
x = 2
To solve the system of equation below zach isolated X^2 in the first equation and then substituted into the second equation. What was the resulting equation
{x^2 + y^2 = 25
{x^2/16 - y^2/9 = 1
The resulting equation of isolation and substitution is 9y⁴-466 y² + 5481 = 0
How to get the resulting equation?
Given:
{x² + y² = 25
{x²/16 - y²/9 = 1
Zach isolated x² in the first equation, we have:
x² + y² = 25
x² = 25- y²
Zach then substituted the x² into the second equation:
x²/16 - y²/9 = 1 (put x² = 25- y²)
(25- y²)²/16 - y²/9 = 1 (Expand the bracket)
(625- 50y²+y⁴)/16 - y²/9 = 1 The LCM of 9 and 16 is 144
( 9(625- 50y²+y⁴) - 16 y² ) /144 = 1 Cross multiply
9(625- 50y²+y⁴) - 16 y² = 144
5625 - 450y² + 9y⁴-16 y² = 144
9y⁴-466 y² + 5625 = 144
9y⁴-466 y² + 5625-144 = 0
9y⁴-466 y² + 5481 = 0
Therefore, the resulting equation is 9y⁴-466 y² + 5481 = 0
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Find a degree 3 polynomial with real coefficients having zeros 3 and 4 i and a lead coefficient of 1. Write P in expanded form. Be sure to write the full equation, including P ( x ) = .
Answer:
[tex]P(x)=x^3-3x^2+16x-48[/tex]
Step-by-step explanation:
Given information:
Polynomial function with real coefficients.Zeros: 3 and 4iLead coefficient of 1.For any complex number [tex]z=a+bi[/tex], the complex conjugate of the number is defined as [tex]z^*=a-bi[/tex].
If f(z) is a polynomial with real coefficients, and z₁ is a root of f(z)=0, then its complex conjugate z₁* is also a root of f(z)=0.
Therefore, if P(x) is a polynomial with real coefficients, and 4i is a root of f(x)=0, then its complex conjugate -4i is also a root of P(x)=0.
Therefore, the polynomial in factored form is:
[tex]P(x)=1(x-3)(x-4i)(x-(-4i))[/tex]
[tex]P(x)=(x-3)(x-4i)(x+4i)[/tex]
Expand the polynomial:
[tex]P(x)=(x-3)(x^2+4ix-4ix-16i^2)[/tex]
[tex]P(x)=(x-3)(x^2-16(-1))[/tex]
[tex]P(x)=(x-3)(x^2+16)[/tex]
[tex]P(x)=x^3+16x-3x^2-48[/tex]
[tex]P(x)=x^3-3x^2+16x-48[/tex]
Find the coordinates of the y-intercept for the given equation y+3/7x
Answer:
The y-intercept would be zero, if the original equaion equaled zero.
Step-by-step explanation:
y + [tex]\frac{3}{7}[/tex]x = 0 ? Subtract [tex]\frac{3}{7}[/tex]x from both sides
y = [tex]\frac{-3}{7}[/tex] x + 0
One of the legs of a right triangle measures 9 cm and the other leg measures 1 cm. Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
Answer: 9.1
Step-by-step explanation:
1. Pythagorean Theorem
a^2+b^2=c^2
(9)^2+(1)^2=c^2
2. Solve
81+1=c^2
82=c^2
3. Solve for c
[tex]\sqrt{82}[/tex]=[tex]\sqrt{c}[/tex]
c=9.05
4. Round
c=9.1
Suppose that you borrow $17,000 for five years at 6% toward the purchase of a car. Find the monthly payments and the
total interest for the loan.
The monthly payment is $
The amount of the monthly payments is $368.34, and the total interest on the loan is $5,100.
The initial amount of money that we borrow is $17,000. We borrow this amount for a total of five years. The interest charged is 6%. We borrowed the money for the purchase of a car. We need to find the monthly payments and the total interest for the loan.
Let the total amount to be paid and the interest be denoted by the variables "A" and "I", respectively.
I = P*R*T
I = $17,000*0.06*5
I = $5,100
The total amount of money to be paid is the sum of the initial amount and the interest charged.
A = P + I
A = $17,000 + $5,100
A = $22,100
The total number of months in five years is 12*5 = 60.
The amount of the monthly payment is the ratio of the total amount to be paid to the total number of months.
M = $22,100/60
M = $368.34
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Solve for x and y . Special right triangle lesson
Answer:
hope this helps!!!
1.
Find the values of the sine, cosine, and tangent for
It depends on how accurate you want to be, but two straight lines between 0° and 30° and 30° and 90° will not be too bad for Sine.
Thus for angles less than 30°
sinx≈x/60
and for angles greater than 30°
sinx≈(30+x)/120
For Cosine you use the identity
cosx=sin(90−x)
And for Tangent you use the identity
tanx=sinxcosx
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-7) El promedio de 3, 8, 9 y 12 es 8.
a) O Cierto
b)
Falso
Previous
El promedio de los números enteros 3, 8, 9 y 12 es igual a 8. (Opción correcta: Cierto)
¿Cómo determinar el promedio de un conjunto de datos?
En este problema tenemos un conjunto de cuatro números enteros positivos, del cual debemos comprobar si el promedio uniforme es igual a 8. El promedio uniforme es definido por la siguiente operación:
[tex]\bar {x} = \frac {1}{n} \cdot \sum \limits_{i = 1}^{n} x_{i}[/tex]
Donde:
[tex]\bar x[/tex] - Promedio uniforme del conjunto de datos.n - Cantidad de elementos del conjunto de datos. [tex]x_{i}[/tex] - Elemento i-ésimo del conjunto de datos.Si sabemos que n = 4, x₁ = 3, x₂ = 8, x₃ = 9 y x₄ = 12, entonces el promedio uniforme del conjunto de datos es:
[tex]\bar {x}[/tex] = (3 + 8 + 9 + 12) / 4
[tex]\bar x[/tex] = 8
El promedio del conjunto de datos, correspondiente a los números enteros positivos 3, 8, 9 y 12, es igual a 8.
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x -1 , 3, 7 , 11 and y 3, 6, 10, 15 is the relationship linear, exponential, or neither
Answer:
Yes i the relationship linear,exponential,or neither
what is the kinetic energy of a 158 kg Green Sea Turtle swimming at 0.42 m/s? With work shown
Kinetic energy is defined as the work required to accelerate a body of a given mass from rest to its stated speed. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes.
Mass - (Measured in Kilogram) - Mass is the amount of matter in a body, regardless of its volume or the forces acting on it.
Velocity - (Measured in Meters per Second) - Velocity is a vector quantity (has both magnitude and direction) and is the rate of change of an object's position with respect to time.
What is the kinetic energy of a 158 kg Green Sea Turtle swimming at 0.42 m/s? With work shownWe have that the data is:
m = 150 kgv = 0.42 m/sThe formula to calculate kinetic energy is:
Ec = m * v²/2
Since it only asks us to calculate the kinetic energy, it is not necessary to clear the formula.
[tex]\boldsymbol{\sf{Ec=\dfrac{158 \ kg*\left(0.42 \ \frac{m}{s}\right)^2 }{2} }}[/tex]
[tex]\boldsymbol{\sf{Ec=\dfrac{158 \ kg*0.1764 \ \frac{m^2}{s^2} }{2} }}[/tex]
[tex]\boldsymbol{\sf{Ec=13.9356 \ kg*\dfrac{m^2}{s^2} }}[/tex]
We work with the units, in this case with m^2 = m*m.
[tex]\boldsymbol{\sf{Ec=13.9356 \boxed{\boldsymbol{\sf{Kg*\frac{m}{s^2} }}}*m }}[/tex]
Newton's units are: Kg*m/s^2.
[tex]\boldsymbol{\sf{Ec=13.9356 \ N*m \longmapsto Joule \ units=N*m}}[/tex]
[tex]\boldsymbol{\sf{Ec=13.9356 \ J}}[/tex]
The kinetic energy (E) of a body with mass m = 158 kilograms and speed v = 0.42 m/s is equal to 13.9356 JBut if you need the rounded answer, then 13.94 Joules.
IXL Please Help Fast!
Answer:
Step-by-step explanation:
given:
line f: y+3 = [tex]\frac{1}{6}[/tex](x-2)
line g: P1=(x1,y1) = ( -6,1) and parallel to f ( same slope)
use point-slope, again
y-y2 = m(x-x1)
y-1=[tex]\frac{1}{6}[/tex](x-(-6))
y-1 =[tex]\frac{1}{6}[/tex](x+6)
y-1 = [tex]\frac{1}{6}[/tex]x +1
y = [tex]\frac{1}{6}[/tex]x + 1 +1
y = [tex]\frac{1}{6}[/tex]x + 2 ( in slope intercept form y= mx+b)
Help I know the answer just need to know that it is correct
what the question............
A triangle has vertices at A(-2,3,) B(2,1) and C(1,0) after a transformation the image of the triangle has vertices at A(-2,-3) B(2,-5) and C(1,-6) identify the transformation
The transformation is applied to ΔABC to get the ΔA'B'C' is vertical translation of 6 units downwards.
The triangle has the vertices A(-2, 3), B(2, 1), and C(1, 0)
They are transformed such that:
A(-2, 3)→A'(-2,-3)
B(2, 1)→B'(2,-5)
A(-1, 0)→A'(-2,-6)
Now, if we pay close attention, we can notice that A's y-coordinate is 6 less than A's.
Similar to A, B and C have coordinates that are 6 units lower than the object's coordinates but with the same x-coordinate.
This demonstrates that the graph undergoes a vertical translation; the graph is translated 6 units lower since the new ordinates are 6 units smaller.
A transformation, or f: X→X', is a function that maps to itself. The transformation will result in the pre-image X becoming the image X'. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, may be used in this transformation.
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The equation of line L1, is y=5x+1
The equation of line L2, is 2y-10x+3=0
Answer:
y = 5x + 1
y = 5x + [tex]\frac{-3}{2}[/tex]
When the slopes are the same (5) the equations are parallel.
Step-by-step explanation:
You can look at the graph of the two equaions attached to see that there paralle.
2y - 10x +3 = 0 Add 10 to both sides of the equation
2y -3 = 10x Add three to both sides of the equation
2y = 10x -3 Divide all the way through by 2
y = 5x + [tex]\frac{-3}{2}[/tex]
Eleanor and Luke started on a trip to the mountains with their six-year old car. Their
odometer read 87,236.2 miles at the start of the trip and 87,626.2 miles at the end of the trip.
They used 14.5 gallons of gas on the trip. How many miles per gallon did they achieve with
their car?
They achieved 26.9 miles per gallon approximately with that car in this trip.
Given that the initial odometer reading is = 87236.2 miles
Final odometer reading after trip is = 87626.2 miles
So the distance of the total trip is = 87626.2-87236.2 = 390 miles
They used 14.5 gallons of gas on the tri[p.
So the mileage is = 390/14.5 = 26.9 miles per gallon approximately.
Their car achieved 26.9 miles per gallon approximately.
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complete the missing numbers, please .
The cost of the sweater is $ 30 and
1 dollar = 17 pesos, $ 25 = 425 pesos and $ 3 dollar = 51 pesos.
Mathematical Operations:Mathematical Operations are activities or mathematical processes used to solve given problems. The most used mathematical activities are adding, subtracting, multiplying, and dividing.
The basic operations and their symbols are given below
Addition (+); Subtraction (-); Division (÷); and Multiplication (x).
Here we have
Priya exchanged 250 dollars for 4250 pesos
[Here we used division and multiplication to solve the problem ]
Then the value of 1 dollar in pesos = [tex]\frac{4250}{250}[/tex] = 17 pesos
⇒ 1 dollar = 17 pesos
⇒ 25 dollars = 25 × 17 = 425 pesos
⇒ 3 dollar = 3 × 17 = 51 pesos
Given the cost of the sweater = 510 pesos
The cost of the sweater in pesos = [tex]\frac{250}{4250} \times510[/tex] = 30
Therefore,
The cost of the sweater is $ 30 and
1 dollar = 17 pesos, $ 25 = 425 pesos and $ 3 dollar = 51 pesos
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Consider the equation and the following ordered pairs: (1,y) and (x,3).
6x+1.2y=−2.4
The value of the variable in the given ordered pairs: (1,y) and (x,3) are x = -1 and y = -7.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
We have to find the values of the variable in the given ordered pairs: (1,y) and (x,3).
Equation is 6x + 1.2y = −2.4
For ordered pairs: (1,y)
6(1)+1.2y =-2.4
1.2y=-8.4
y=-7
For Pair (x,3)
6(x)+1.2(3) =-2.4
6x = -6
x=-1
Hence, the value of the variable in the given ordered pairs: (1,y) and (x,3) are x = -1 and y = -7.
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A car dealership increased the price of a certain car by 6%. The original price was $33,600.
(a) Fill in the blank to write the new price in terms of the original price.
Write your answer as a decimal.
New Price = blank * Original Price
(b) Use your answer in part (a) to determine the new price.
The new price for the car when there's an increase of 6% is $35616.
How to calculate the new price?Given that the dealership increased the price of a certain car by 6% and the original price was $33,600.
The new price will be:
= Original price + Increase in price
= $33600 + (6% × $33600)
= $33600 + $2016
= $35616
The new price is $35616.
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What sentence represents this equation?
8 3/4=17−x
The sentence that represents this equation 8 3/4 = 17 - x is B) 8 3/4 is the same as 17 decreased by a number.
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.
In this case, 8 3/4 is the same as 17 decreased by a number will be 8 3/4=17−x.
Therefore, the correct option is B.
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Complete question
What sentence represents this equation?
8 3/4 = 17 - x
A) A number is the same as the difference of 17 and 8 3/4.
B) 8 3/4 is the same as 17 decreased by a number.
C) 17 decreased by 8 3/4 is the same as a number.
D) 8 3/4 is the same as a number decreased by 17.
Find the total surface area of this triangular prism.
13 cm
15 cm
12 cm
20 cm
5 cm
9 cm
Answer:
1008cm^2
Step-by-step explanation:
Please see photo
The Singapore Navy acquired 4 Swedish- build Sjoormen class submarine to beef up its defence capabilities in the late 1990s. The submarine is capable of attaining a top speed of 16 knots (nautical miles per hour) when submerged. Convert 16 knots to (a) km/h (b) m/s. (Take 1 nautical mile to be 1 853 m.)
The speeds when converted are 29.648 km/h and 8.24 m/s
How to convert the units of speed?From the question, we have the following parameters that can be used in our computation:
Speed = 16 knots
Also, from the question, we have
1 nautical mile to be 1853 m
This means that
Speed = 16 * 1853 m per hour
Convert meters to kilometers
So, we have
Speed = 16 * 1.853 km per hour
Evaluate the products
Speed = 29.648 km/h
Also, we have
Speed = 16 * 1853 m per hour
Convert hour to seconds
So, we have
Speed = 16 * 1853/3600 m/s
Evaluate
Speed = 8.24 m/s
Hence, the speed in m/s is 8.24 m/s
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add put your answer in lowest terms 1/7 + 1/2
6/14
2/9
9/14
7/9
Answer:
c) 9/14
Step-by-step explanation:
Given problem,
→ (1/7) + (1/2)
Let's solve the problem,
→ (1/7) + (1/2)
→ (2/14) + (7/14)
→ (2 + 7)/14
→ 9/14
Hence, answer is 9/14.
The table shows telephone charges for different companies. Which table shows a linear relationship between length of call and the cost
Answer: they both go up in cents by 5s. they may not be only five but five's. Therefore, they are adding by 5s and that is the linear relationship
Step-by-step explanation:
Determine whether the series converges or diverges
Please, check the image
The series as represented in the task content is divergent and hence; diverges.
What convergence and divergence in series?It follows from the task content that the series defined by the summation expression as represented above is to be identified as divergent or convergent.
It is noteworthy to know that;
If a sequence converges, it means that the limit of the sequence exists as n → ∞. Also, if the limit of the sequence as n → ∞ does not exist, Then, such series is said to diverges.
Therefore, by evaluation as the limit of the expression k sin²k / 1 + k³ as k → ∞ is; Undefined and hence does not exist.
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mary invests 12500 in savings rate of 1.5 percent for 2 years
Answer:The question is very brief, im not sure if i understand what your asking
Step-by-step explanation:
The top face of the latest music player measures 4.33 inches by 1.54 inches. Find the perimeter of the rectangular face.
Answer: 11.74
Step-by-step explanation:
4.33+4.33+1.54*1.54+11.74
A rectangle has two pairs of equal sides.
Given a quadratic function in vertex form:
a) A vertical stretch happens for values of a such that |a| > 1.
b) A vertical compression happens for values of a such that |a| > 0.
c) For a vertical stretch, the graph increases vertically, and for a vertical compression, the graph increases horizontally.
d) A reflection across the x-axis takes place when a < 0.
How to obtain the transformations?The definition of the quadratic function is given as follows:
f(x) = a(x - h)² + k.
The transformations to the function are given as follows:
Vertical stretch: multiplication of the function by a value with absolute value greater than 1, hence |a| > 1, increasing the graph vertically.Vertical compression: multiplication of the function by a value with absolute value less than 1, hence |a| < 1, increasing the graph horizontally.Additionally, for a reflection over the x-axis, the function is multiplied by a negative number, hence:
a < 0.
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