Solve the equation and enter the value of x below.
x+ 272 = 298​

The adult's ticket will cost $20 while the children's ticket will cost $15.

From the question, we have that;

Three adults and four children must pay $120

Representing this in an equation

Let adults = a

Let children = c

3a + 4c = 120 -----1

Also;

Two adults and three children must pay $85.

Representing this in an equation

2a + 3c = 85 -----2

From equation 1

a = [tex]\frac{120 - 4c}{3}[/tex] ----- 3

Substituting a in equation 2

[tex]2 (\frac{120 - 4c}{3} ) + 3c = 85[/tex]

[tex]\frac{240 - 8c}{3} + 3c = 85[/tex]

Multiplying through by 3

240 - 8c + 9c = 255

c = 15

To find a when c = 15

Substitute c = 15 in equation 3

[tex]a = \frac{120 - 4(15)}{3}[/tex]

[tex]a = \frac{120 - 60}{3}[/tex]

a = 20

Therefore, the Adult's ticket is $20 and the children's ticket is $15.

To find more about cost: https://brainly.com/question/28147009

#SPJ1

The quotient of 3 and 1/5 is 15.

A quotient is a quantity produced by the division of two numbers in arithmetic. The quotient is widely used in mathematics and is also known as the integer part of a division, a fraction, or a ratio.

The quotient is the result of performing division operations on two numbers. It is essentially the result of the division method. In arithmetic division, four main terms are used: divisor, dividend, quotient, and remainder

In this case, we want to divide 3 and 1/5. This will be:

= 3 ÷ 1/5

= 3 × 5

= 15.

The quotient is 15.

Learn more about quotient on:

https://brainly.com/question/11418015

#SPJ1

Answer:

130 ft

Step-by-step explanation:

The distance across the canyon is 130 feet.

When Christian moved 100 feet from the tree on his side, the angle formed by the tree on his side and the tree on the other side was 70°. This means that the distance across the canyon is the length of the opposite side of the right triangle formed by Christian's position, the tree on his side, and the tree on the other side.

To find the length of the opposite side of the triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, the hypotenuse is the distance across the canyon, and the other two sides are 100 feet and the length of the opposite side of the triangle.

We can write this as an equation: (distance across the canyon)^2 = (100 feet)^2 + (opposite side of the triangle)^2.

To solve for the distance across the canyon, we can take the square root of both sides of the equation: distance across the canyon = √((100 feet)^2 + (opposite side of the triangle)^2).

Since the length of the opposite side of the triangle is equal to the length of the adjacent side (100 feet) divided by the tangent of the angle formed by the tree on his side and the tree on the other side, we can substitute this value into the equation above: distance across the canyon = √((100 feet)^2 + (100 feet / tan 70°)^2).

To calculate the value of tan 70°, we can use a calculator or look up the value in a table of trigonometric functions. The value of tan 70° is approximately 1.73. We can substitute this value into the equation above to get: distance across the canyon = √((100 feet)^2 + (100 feet / 1.73)^2).

We can now use a calculator to evaluate this expression and find the distance across the canyon. When we do this, we get: distance across the canyon = √((100 feet)^2 + (100 feet / 1.73)^2) ≈ 130 feet.

Therefore, the distance across the canyon is approximately 130 feet.

To obtain a smaller margin of error, choose a smaller confidence level.

Margin of error is defined as the degree of the sampling errors in statistics. It can be calculated using the formula below.

MOE = z x (SD / √n)

where MOE = margin of error

z = found by using a z-score table

SD = sample standard deviation

n = sample size

Based on the formula, to reduce the margin of error, the z-score, z, must be small. In order to have a smaller value of z, the probability, p, should also be small. And to obtain a small probability, choose a smaller confidence level.

Hence, to reduce the margin of error, use a lower confidence level.

Learn more about margin of error here: brainly.com/question/10218601

#SPJ4

The solution to the system of equation is x = -12 and y = 3.

System of equation can be solved using different method such as elimination method, graphical method and substitution method,

Therefore, let's solve the system of equation by using substitution method.

1 / 2 x + 6y = 12

y = x + 15

substitute the value of y in equation(i)

1 / 2 x + 6(x + 15) = 12

1 / 2 x + 6x + 90 = 12

6 1 / 2 x = 12 - 90

13 / 2 x  = - 78

cross multiply

13x = -78 × 2

13x = -156

divide both sides by 13

x = -156 / 13

x = - 12

Let's find the value of y.

y = -12 + 15

y = 3

Therefore,

x = -12

y = 3

learn more on system of equations here:https://brainly.com/question/25535303

#SPJ1

Answer:

B.  X = 8 degree

Step-by-step explanation:

8x - 4 = 60 degree

8x = 64 degree

x = 8 degree

So, the answer is B

Answer:

x = 8°

Step-by-step explanation:

The angle that say 60° and the angle that says 8x -4 ARE BOTH EQUAL.

They are called Alternate Interior Angles

Let's write an equation to represent this relationship, then we solve it to find x

8x - 4 = 60

SOLVE

8x = 60 + 4

8x = 64

x = 64 / 8

x = 8 °

The side length of the square is (b) 8n¹⁸ units

See below for the complete question

From the question, we have the following parameters that can be used in our computation:

Area = 64n36 square units

Express the exponents as superscripts

So, we have the following representation

Area = 64n³⁶ square units

Take the square roots of both sides

So, we have the following representation

√Area = √64n³⁶ square units

Evaluate the exponents

Length = √64n³⁶ units

So, we have

Length = 8n¹⁸ units

Hence, the side length is (b) 8n¹⁸ units

Read more about area at

https://brainly.com/question/15990258

#SPJ1

Complete question

The area of a square is 64n36 square units. What is the side length of one side of the square?

8n6 units

8n18 units

64n6 units

64,18 units

When the variables r = 3 and y = -6, the value of the expression is -27.

In Mathematics, an expression is sometimes referred to as an equation and it can be defined as a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables, parameters, and numerical quantities (number).

Based on the information provided, the mathematical expression is given by;

Mathematical expression = √x⁴ - y²

Substituting the given parameters into the mathematical expression, we have;

Mathematical expression = √(3)⁴ - (-6)²

Mathematical expression = √81 - 36

Mathematical expression = 9 - 36

Mathematical expression = -27.

Read more on expression here: https://brainly.com/question/25767785

#SPJ1

Complete Question:

Type the correct answer in the box. use numerals instead of words. Enter the number of the topic sentence.

Consider this expression. √x⁴ - y². When r = 3 and y = -6, the value of the expression is____.

The value of the given expression, 3^4 + 18 ÷ 3 +2, is 89

From the question, we are to determine the value of the given expression

The given expression is

3^4 + 18 ÷ 3 +2

First, we will write the expression properly

The given expression written properly is

3⁴ + 18 ÷ 3 +2

Using PEMDAS

P - Parentheses

E - Exponent

M - Multiplication

D - Division

A - Addition

S - Subtraction

Then,

3⁴ + 18 ÷ 3 +2

81 + 18 ÷ 3 + 2

81 + 6 + 2

= 89

Hence, the value is 89

Learn more on Evaluating an expression here: https://brainly.com/question/21778942

#SPJ1

Answer:

Erik's chips are a better buy by 10 cents per ounce

Step-by-step explanation:

Erik's chips cost by ounce: $0.32

Al's chips cost by ounce: $0.42

This means the Eriks chips are better to buy

Second one:

Answer: 1.26

Step-by-step explanation:

Since he bought a 18 gallon tank of gas with regular fuel for 55.08.

The station across the street sold regular fuel for 2.99 per gallon. A 18 gallon tank will cost:

= 18 × 2.99

= 53.82

The amount that could have been saved would be:

= 55.08 - 53.82

= 1.26

Answer:

£9.40

Step-by-step explanation:

Given variables:

Defined variables:

1 pound = 100 pence  ⇒  1 pence = 0.01 pounds

Therefore, the equation that models the given scenario is:

[tex]y = 0.01px +f[/tex]

Given:

Substitute the given information into the equation to create two equations:

[tex]\implies f+0.01(4)p=5.40[/tex]

[tex]\implies f+0.01(7)p=7.80[/tex]

Therefore:

[tex]\implies f+0.04p=5.40[/tex]

[tex]\implies f+0.07p=7.80[/tex]

Subtract the first equation from the second to eliminate f:

[tex]\implies 0.03p=2.40[/tex]

Solve for p:

[tex]\implies \dfrac{0.03p}{0.03}=\dfrac{2.40}{0.03}[/tex]

[tex]\implies p=80[/tex]

Substitute the found value of p into one of the equations and solve for f:

[tex]\implies f+0.04(80)=5.40[/tex]

[tex]\implies f+3.20=5.40[/tex]

[tex]\implies f=2.20[/tex]

Substitute the found values of p and f into the equation to create an equation for the cost of x miles:

[tex]\implies y=0.8x+2.2[/tex]

To find the cost of a 9-mile journey, substitute x = 9 into the found equation:

[tex]\implies 0.8(9)+2.2=9.40[/tex]

Therefore, the cost of a 9-mile journey is £9.40.

Answer:

Step-by-step explanation:

To write a linear function for a given set of points, we can use the slope-intercept form of the equation, which has the form f(x) = mx + b. The coefficient m is the slope of the line and the constant b is the y-intercept, where the line crosses the y-axis.

To find the slope m of the line, we can use the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are any two points on the line. For example, we can use the points (-2, -6) and (-1, -2.5) to find the slope:

m = (y2 - y1) / (x2 - x1) = (-2.5 - (-6)) / (-1 - (-2)) = 3.5 / 1 = 3.5

Now that we know the slope, we can use any of the given points to find the y-intercept b. For example, we can use the point (0, 1):

f(x) = mx + b

1 = 3.5 * 0 + b

b = 1

Therefore, the linear function that passes through the given points is:
f(x) = 3.5x + 1

Note that we could also have used any of the other points to find the y-intercept, and we would have arrived at the same result.

If MX, MY, sX, and sY are known, the additional number that would be the most helpful to know for calculating the regression line for X and Y is r.

In the context of simple linear regression, r means the correlation between the predictor variable, x, and the response variable, y. And r² means the proportion of the variance in the response variable which can be explained by the predictor variable in the regression model.

It is also considered as denotation of the Pearson correlation coefficient, that is a measure of any linear trend between two variables. The value of r ranges between −1 and 1. When r = zero, it means that there is no linear association between the variables.

Learn more about regression line at: https://brainly.com/question/7656407

#SPJ4

The values of the variables and the measures of the angles, found using the congruency of ΔAOI and ΔIEA are;

w = 2        [tex]{}[/tex]   ∠EAI = 45°

x = 4   [tex]{}[/tex]         ∠AOI = 128°

y = 7 [tex]{}[/tex]           ∠OIA = 45°

z = 20 [tex]{}[/tex]        ∠IEA = 128°

Two triangles are congruent if two angles and a non included side of one triangle are congruent to two angles and a non included side of another triangle.

The relationship between the triangles ΔAOI and ΔIEA is ΔAOI ≅ ΔIEA

Therefore; ∠IEA is congruent to ∠AOI, by Corresponding Parts of Congruent Triangles are Congruent, CPCTC

∠IEA ≅ ∠AOI

Therefore; ∠IEA = ∠AOI by the definition of congruency

(6·z + 8)° = (7·z - 12)°

7·z - 6·z = (8 + 12)° = 20°

z = 20°

∠AOI = (7·z - 12)°

Therefore;

∠AOI = (7 × 20 - 12)° = 128°

∠IEA = 128°

Similarly; AO ≅ EI by CPCTC

AO = EI definition of congruency

5·w - 6 = 2·w

5·w - 2·w = 6

3·w = 6

w = 6 ÷ 3 = 2

w = 2

∠OIA ≅ ∠EAI by CPCTC

Therefore; ∠OIA = ∠EAI definition of congruency

(7·x + 17)° = 3·(4·x - 1)° substitution property

(7·x + 17)° = 3·(4·x - 1)° = (12·x - 3)°

12·x - 7·x = 17° + 3° = 20°

5·x = 20°

x = 20° ÷ 5 = 4°

x = 4°

∠EAI = 3·(4·x - 1)°

∠OIA = (7·x + 17)°

Therefore;

∠EAI = 3·(4×4 - 1)° = 45°

∠OIA = (7×4 + 17)° = 45°

y° + (7·z - 12)° + 3·(4·x - 1)° = 180° (angle sum property of a triangle)

∠AOI = (7·z - 12)° = 128°

∠EAI = 3·(4·x - 1)° = 45°

Therefore;

y° + 128° + 45° = 180°

y° = 180° - (128° + 45°) = 7°

y° = 7°

Learn more about congruent triangles here:

https://brainly.com/question/2273907

#SPJ1

The rate of change of the plot is 2

The initial value the line joining points is 3

The rate of change between 2 points is defined as the change of y cordinate with respect to change of x cordinate

rate of change = slope of line =  Δy/ Δx =[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

point a(0,3) is the initial point and point b(2,7) is the 2nd point

so [tex](x_1,y_1)[/tex] = (0,3) and [tex](x_2, y_2)[/tex] = (2,7)

rate of change  = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

=> (7-3)/(2-0)

=>4/2

so rate of change = 2

Initial value is the y intercept of the line i.e is we write an equation of the line the value of y when x=0 is the inital value

so at point a (0,3)  value of x=0 and at that time value of y=3

and hence initial value = 3

To know more about slope click on below link:

https://brainly.com/question/16180119#

#SPJ4

to see the overall long-term tendency of the series, we should set large weight w in exponential smoothing is True statement.

Exponential smoothing is a technique used to smooth out data to uncover trends and make predictions. When setting the weight (w) for exponential smoothing, a large w will result in a longer-term trend being captured by the smoothing. This is because a larger w will give more weight to the older data points, and thus the overall long-term tendency of the series will be more visible. Therefore, it is true that setting a large weight w in exponential smoothing will help to see the overall long-term tendency of the series.

Learn more about exponential here

https://brainly.com/question/28596571

#SPJ4

Answer: P(WY)=1/10*2/9=1/45

P(YW)=2/10*1/9=1/45

P(WY or YW)=2/45

Also 2C1*1C1/10C2=2×1/45=2/45

2/5

Step-by-step explanation:

The angle of elevation of the sun to the nearest hundredth of a degree is 66.83°.

Since we are giving with the height of the building which is 34.98 feet and the length of the shadow which is 38.85 feet long. , so we can use the trigonometric ratios, where we  know that about tan, that is:

angle = arctan (length of the shadow/height of the building )

=>angle = arctan (38.85/34.98)

=> angle = arctan (1.1056)  

=> angle = 66.83°

so,it is the angle of elevation of the sun.

To know more about the angle of elevation refer to the link  brainly.com/question/21137209

#SPJ4

The parameters for the exponential function are given as follows:

Hence the exponential function that gives the value of the book in t years after 2010 is of:

V(t) = 500(1.18)^t.

2017 is 7 years after 2010, hence the value is calculated as follows:

V(7) = 500 x (1.18)^7 = $1,592.74.

First we obtain the rate of change, dividing consecutive entries of the table, as follows:

b = 62.99/34.99 = 1.8.

Thus the function is defined as follows:

f(x) = a(1.8)^x.

When x = 3, f(x) = 34.99, hence the intercept a is calculated as follows:

34.99 = a(1.8)³

a = 34.99/(1.8)³

a = 6.

Then the function is:

f(x) = 6(1.8)^x.

Taking 2016 as the reference year, the initial value is of:

a = 80.

Then the growth rate is of:

b = 132/80.

b = 1.65.

Then the function for the amount in x years after 2016 is of:

f(x) = 80(1.65)^x.

2023 is 7 years after 2016, hence the estimate is given as follows:

f(7) = 80 x (1.65)^7 = 2664 people.

More can be learned about exponential functions at https://brainly.com/question/25537936

#SPJ1

By using multiplication and division, it can be calculated that-

The multiple according to the number 3 = 162

The submultiple according to the number 7 = 7

What is multiplication and division?

Repeated addition is called multiplication. Multiplication is used to find the product of two or more numbers.

Division is the process in which a value of single unit can be calculated from the value of multiple unit.

The number to be divided is called dividend. The  number by which dividend is divided is the divisor. The result obtained is called quotient and the remaining part is the remainder.

This is a problem of multiplication and division.

One segment measures 161 cm

So, to find the multiple according to the number 3, we have to divide 161 by 3

161 [tex]\div[/tex] 3 = 53.67

Nearest integer of 53.67 is 54

The multiple according to the number 3 = 54 [tex]\times[/tex] 3 = 162

To find the submultiple according to the number 7, we have to divide 161 by 7

161 [tex]\div[/tex] 7 = 23

Nearest integer of 23 is 23

The submultiple according to the number 7 = 161 [tex]\div[/tex] 23 = 7

To learn more about multiplication and division, refer to the link-

https://brainly.com/question/28337146

#SPJ1

Which function is growing on the (-, ) interval? O A. g(x) = "-4(2^x)" O B. f(x)= "-3x"+7 O C. h(x)= 2x—1 O D. j(x)= x2 + 8x+1

Try searching for Which function is rising on the range (-, ) instead. O A. g(x) = -4(2^x) O B. f(x) = -3x + 7, O c. h(x) = 2x - 1, and O D. j(x) = x2 + 8x + 1.

Which function is increasing on the interval (- ∞ ∞?

Image result for Which function is increasing on the interval (-∞, ∞)? O A. g(x) = -4(2^x) O B. f(x) = -3x + 7 O c. h(x) = 2^x - 1 O D. j(x) = x² + 8x + 1

Since, x and y are arbitrary values, therefore, f (x) < f (y) whenever x < y. Therefore, the interval (-∞, ∞) is a strictly increasing interval for f(x) = 3x + 5

The interval is increasing if the value of the function f(x) increases with an increase in the value of x and it is decreasing if f(x) decreases with a decrease in x.

To learn more about increasing on the interval visit:

https://brainly.com/question/11051767

#SPJ1

The  implicit differentiation of [tex]\dfrac {dz}{dx}[/tex] is [tex]\dfrac {yz}{7e^{7z}-xy}[/tex] and for [tex]\dfrac {dz}{dy}[/tex]  it is [tex]\dfrac {xz}{7e^{7z}-xy}[/tex].

In implicit differentiation, we differentiate every aspect of an equation with variables (commonly x and y) through treating one of the variables as a feature of the other.

It is given that,

[tex]e^{7z}=xyz[/tex]

Differentiate both sides with respect to x,

Only treat y as constant and z and x as variables.

[tex]\frac{{e^{7z}}{dx} }{\frac{dz}{dx}} =\frac{yd(xz)}{dx}[/tex]

use chain rule in left hand side

[tex]\frac {e^{7z}}{dx} \times \frac{dz}{dx} =\frac{yd(xz)}{dx}[/tex]

use product rule in RHS

[tex]7e^{7z} \times\frac{dz}{dx}=yx \times\frac{dz}{dx+z} \\\\7e^{7z} \times\frac{dz}{dx}=xy \times\frac{dz}{dx} +yz\\\\\frac{dz}{dx}=\frac{yz}{7e^{7z-xy}}[/tex]

It is given that,

[tex]e^{7z}=xyz[/tex]

Differentiate both sides with respect to y,

Only treat x as constant and z and y as variables.

[tex]\dfrac {d (e^7z)}{dy}= \dfrac {d(xyz)}{dy}[/tex]

use chain rule in left hand side

[tex]\dfrac {d (e^7z)}{dy} \times \dfrac{dy}{dx}=\dfrac {yd(xz)}{dy}[/tex]

use product rule in RHS

[tex]7 (e^{7z}) \times \dfrac{dz}{dy}=xy \dfrac{dz}{dy+z}\\\\(7e^{7z})\times \dfrac{dz}{dy}=xz\\\\\dfrac{dz}{dy}=\dfrac {xz}{7e^{7z}-xy}[/tex]

To learn more about differentiation check the link below:

https://brainly.com/question/954654

#SPJ4

Answer: 0

Solution Steps:

m=25     n=5

25/5-5

Answer:

Step-by-step explanation:

11 = 5 * 2 * 22 + 2 * 5

11 = 110 + 10

11 = 120

11 = 5 * 4 * 22 + 2 * 3

11 = 440 + 6

11 = 446

Please let me know if you have any questions.

Answer:

3m

Step-by-step explanation:

hope this helps :D

Gina uses 11 shipping boxes to pack 32 items. For this, she requires about 5 large boxes and 6 small boxes.

A box is a type of container used to store contents. The majority of boxes have rectangular sides that are flat, parallel, and straight. Boxes can be very small or very large, and they can be used for everything from functional to decorative purposes.

Given that Gina has 32 items and 11 shipping boxes to pack. The large box can hold 4 items and the small can hold 2 items. Then, the total number of large and small boxes required is calculated logically as follows.

The first five boxes are large and the next five boxes are small. Then we can pack about 20 (4×5) items in large boxes and about 10 (2×5) items in small boxes. The remaining 2 items are left and these will be packed in small boxes. So she requires about 5 large boxes and 6 small boxes.

The complete question is -

Gina has 32 items to ship and 11 shipping boxes. The large shipping box can hold 4 items each. The small shipping boxes can hold 2 items each. Gina has exactly enough boxes for her item. How many of each type of box does she have?

To know more about logical reasoning:

https://brainly.com/question/16052800

#SPJ4

Corey would be needing six L-brackets to have one for every angle that is congruent to angle 6 in order to meet the requirement .

As we know that in order to support the  shelves, Corey needs to buy six L-brackets. This is to be done in such a way that the two shelves, combined with the connecting piece, will form a shape with six congruent angles.

This is so because the connecting piece, the two shelves, and the form they make have six congruent angles. Corey will therefore require six brackets to hold up all the angles.

Corey will require one bracket for each angle in order to support it. To make sure he orders the proper size bracket for each angle,  the length of the angle should be measured correctly.

To learn more about angle

brainly.com/question/28451077

#SPJ4

Answer:

14

Step-by-step explanation:

To find the value of K, we need to use the remainder theorem. The remainder theorem states that if a polynomial is divided by (x - a), where a is a number, the remainder of the division will be equal to the value of the polynomial when x is equal to a. In this case, the remainder of the division is 10, so we need to find the value of the polynomial when x is equal to 1.

To find this value, we need to plug 1 into the original polynomial and evaluate it. This gives us (- 5 * 1^3 + 4 * 1^2 – 3 * 1 + K) = (- 5 + 4 – 3 + K) = (- 4 + K). Since the remainder of the division is 10, we know that (- 4 + K) = 10. This means that K = 14.

Therefore, the value of K in the original polynomial is 14.

The value of K is 14.

If a polynomial function f(x) is divided by (x - c), the remainder R is given by: R = f(c)

According to the remainder theorem, if a polynomial f(x) is divided by (x - c), where c is a constant, the remainder is equal to f(c).

In this case, we know that the remainder is 10 when the expression is divided by (x - 1). So, we can substitute x = 1 into the expression and set it equal to 10 to find the value of K.

Substituting x = 1 into the expression, we get:

(-5 (1)³ + 4(1)² - 3(1) + k)= 0

-5 + 4 -3 + k = 0

k -4 = 0

k = 4

Therefore, the value of K is 14.

Learn more about remainder theorem here:

https://brainly.com/question/30062238

#SPJ2

This article would be best suited to a text structure of Problem and Solution.

Research on the development of literacy during the previous two decades has revealed:

A literary device that introduces a problem in the first paragraph and section before moving on to how to solve it in the following paragraph or section.

Example:

To know more about the text structure, here

https://brainly.com/question/12053427

#SPJ4

The length of side AC of the triangle ABC using cosine rule is; 10.252 cm

The cosine formula to find the side lengths of the triangle is given by:

b = √[a² + c² – 2ac cos B]

Where a, b and c are the sides of the triangle.

The Cosine Rule is useful in any triangle that we are trying to relate all three sides to one angle. Thus, when we want to find the length of a side, we need to know the other two sides and the opposite angle.

Considering triangle ABC, we have;

a = 8cm

c = 11 cm

B = 63°

Thus;

b = √[8² + 11² – 2(8 * 11) cos 63]

b = √(185 - 79.9)

b = 10.252 cm

Read more about Cosine Rule at; https://brainly.com/question/23720007

#SPJ1