It is 3 miles from Belle's house to Rosa's house and a straight-line distance of 5 miles from Cora's house to Rosa's house. How far is Belle's house from Cora's house?

Luke save $10 after buying 5 boxes.

What is a function?

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

Here, we have

Given: Luke buys a certain brand of cereal that costs $11 per box. Luke changes to a super-saving brand of the same size.

The function of the first cereal is

y = 11x

Now, another cereal that Luke decides to buy is $9 per box, which is expressed

y = 9x

Now, the difference between the costs is $2, because 11-9=2.

So, the original brand costs $2 more than the super-saving brand.

Now, if Luke buys 5 cereal boxes per month, the cost in each case would be

y = 11(5) = 55

y = 9(5) = 45

Luke is saving per month 55 - 45 = $10

Hence, Luke save $10 after buying 5 boxes.

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Answer: $34.25

Step-by-step explanation:

number of tickets for adult = 170 and number of tickets for children = 151

What is equation with two variables?

The equation that has two unknown variables and express the equality between two or more expression is called equation with two variables.

let, x denotes the number of adults went to theater.

y denotes the number of children went to theater

price of ticket for each adult = $3.50

price of tickets for each child = $2.50

if the number of total tickets = 321

x + y = 321

total cost of tickets = $3.50x + $2.50y = 972.21 dollar

we will solve the above two equations, y = 321 - x

by putting the y value in the second equation,

3.50x + 2.50 (321- x) = 972.21

3.50x + 802.5 - 2.50x = 972.21

x = 169.71

number of adults went to theater = 170

from, y = 321 -169.71

    y = 321 - 169.71

y = 151.3, y= 151

number of children went to theater = 151

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Answer:

A G.P is a sequence of numbers such that the ratio of any two consecutive terms is a constant, called the common ratio. Given the first term (3) and the common ratio (0.25) of the G.P, we can find the sum of the first 5 terms using the formula:

S_n = a(1 - r^n) / (1 - r)

Where:

S_n is the sum of the first n terms of the G.P.

a is the first term of the G.P.

r is the common ratio of the G.P.

n is the number of terms in the sum.

So, to find the sum of the first 5 terms of the G.P, we can substitute the given values into the formula:

S_5 = 3(1 - (0.25)^5) / (1 - 0.25)

S_5 = 3(1 - (0.25)^5) / (1 - 0.25) = 3(1 - 0.25^5) / (1 - 0.25) = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75

S_5 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75

S_5 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.75 = 3(1 - 0.25^5) / 0.

Answer:

3.996

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7 cm}\underline{Sum of the first $n$ terms of a geometric series}\\\\$S_n=\dfrac{a(1-r^n)}{1-r}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $r$ is the common ratio.\\\end{minipage}}[/tex]

Given:

Substitute the given values into the formula to find the sum of the first 5 terms of a geometric progression whose first term is 3 and common ratio is 0.25:

[tex]\implies S_5=\dfrac{3(1-0.25^5)}{1-0.25}[/tex]

[tex]\implies S_5=\dfrac{3(1-0.00097656...)}{0.75}[/tex]

[tex]\implies S_5=\dfrac{3(0.999023437...)}{0.75}[/tex]

[tex]\implies S_5=\dfrac{2.99707031...}{0.75}[/tex]

[tex]\implies S_5=3.99609375[/tex]

[tex]\implies S_5=3.996\; \sf (4\;s.f.)[/tex]

Using the decay constant on the exponential function, the mass of the sample that will be left in 2013 is 35g

An exponential function is a function that can be expressed in the form     f(x) = b^x, where b is a positive real number and x is a real number. The graph of an exponential function is a curve that increases or decreases rapidly as x increases or decreases.

In the exponential decay, the decay function can be given as;

y = ae⁻ⁿˣ

The disintegration constant is also know as the rate of decay and we can calculate it as;

260 = 470e⁻ⁿ⁽³⁾

n = 0.197

n = 0.2

The disintegration constant is 0.2

The amount left in 2013 will be;

y = 470e⁻⁽⁰.²⁾⁽¹³⁾

y = 34.90

The mass in 2013 is 35g

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Answer:

Answer and Explanation: As a fraction 3.83 (3 repeating) is 38399 3 83 99 . To convert 3.83 (3 repeating) to a fraction, we ignore the units as they will remain units. We then set up one equation of our unknown x being equal to 0.83333... and another that is 100 times greater, 100x=83.3333...

well, the interest is going to be the increase factor on both cases, so we can simply check how much each will accumulate to in those 4 years

[tex]~~~~~~ \stackrel{\textit{\LARGE University Bank}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4000\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &4 \end{cases}[/tex]

[tex]A = 4000\left(1+\frac{0.05}{4}\right)^{4\cdot 4} \implies A=4000(1.0125)^{16}\implies \boxed{A \approx 4879.56} \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~ \stackrel{\textit{\LARGE Rosemont Savings Bank}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4000\\ r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus two} \end{array}\dotfill &2\\ t=years\dotfill &4 \end{cases}[/tex]

[tex]A = 4000\left(1+\frac{0.055}{2}\right)^{2\cdot 4} \implies A=4000(1.0275)^8\implies \boxed{A \approx 4969.52} ~~ \textit{\LARGE \checkmark}[/tex]

The solution is Option A.

The coordinate of the triangle after the translation is given by A' ( 0 , -3 ) with 4 units right and 4 units down

A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.

Given data ,

Let the coordinate of the triangle be represented as A

Now , the coordinate A = A ( -4 , 1 )

Now , the coordinate of the triangle after translation is A' ( 0 , -3 )

when there is a translation of the coordinate A by 4 units to the right , we get

A to 4 units right = A ( -4 + 4 , 1 )

The new coordinate of A = A ( 0 ,  1 )

Now , A to 4 units down , we get

The coordinate of A' = A' ( 0 , 1 - 4 )

The coordinate of A' = A' ( 0 , -3 )

Hence , the translated coordinate is A' ( 0 , -3 )

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The student is not correct. Y = 16x^2 is a function of X.

A function is a mathematical relationship between two variables, where each value of the independent variable (in this case, X) corresponds to exactly one value of the dependent variable (in this case, Y). The equation Y = 16x^2 satisfies this definition.

The fact that X is squared in the equation does not mean that it is not a function of X. In this case, Y is a function of X because for each value of X, there is a unique value of Y determined by the equation Y = 16x^2.

This equation represent the distance an object falls (Y) in a certain amount of time (X) assuming that the only force acting on the object is gravity, and the acceleration due to gravity is constant (approximately 9.8 m/s^2 or 32 ft/s^2). The equation Y = 16x^2 is known as the equation of motion under gravity.

Answer:

145

Step-by-step explanation:

We have the equation 5x+20 for the line of best fit

Let x = 25

y = 5*25+20

  = 125 + 20

  = 145

The score should be 145 when he plays for 25 minutes

Using pythagoras theorem formula, c² = a² +b²  We can see that the two shorter sides have the same length which is 5cm

Since all the sides of the triangle are the same, hence the two triangles are congruent.

What is Pythagoras' theorem ?

Pythagoras' theorem is the square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.

The two shorter sides have the same length which is 5cm

Since all the sides of the triangle are the same, hence the two triangles are congruent.

Let the sides of the triangles be a, b and c. According to Pythagoras theorem;

c² = a² +b²

where:

a is the hypotenuse (longest side)

For triangle A:

c = 13

b = 12

Get "a"

13² = 12² +b²

b² = 25

=> b = 5 cm

Similarly for triangle B:

c² = 5² +12²  = 169

=> c=13 cm

We can see that the two shorter sides have the same length which is 5cm

Since all the sides of the triangle are the same, hence the two triangles are congruent.

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Answer:

(14x+13)(x-1)

Step-by-step explanation:

14x²-x-13

14 × 13 = 182

Search for factors of 182 that contain a difference of 1 when subtracted because -x is the same as -1x.

Since 14 × 13 = 182

and

13 - 14 = -1

They are our 2 chosen numbers which will be displayed as :

14x² - 14× + 13x - 13

where -x is replaced by -14x + 13x

Proceed to factorise normally

14x(x-1) + 13(x-1)

Grouping

(14x+13)(x-1)

The relationship between a young person's height and the recommended wheel diameter is a function, as each input is associated to a single output.

To verify whether a relation represents a function, we need to observe if each input is mapped to only one output.

The input and output variables for this problem are given as follows:

As for each height, there is only one recommended wheel diameter, we have that each input is mapped to a single output, and thus the relationship between a young person's height and the recommended wheel diameter is a function.

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Answer:

B)  4√2

Step-by-step explanation:

Given expression:

[tex]7 \sqrt{2}-3\sqrt{8}+\sqrt{18}[/tex]

Rewrite 8 as 4 · 2 and 18 as 9 · 2:

[tex]\implies 7 \sqrt{2}-3\sqrt{4 \cdot 2}+\sqrt{9 \cdot 2}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]

[tex]\implies 7 \sqrt{2}-3\sqrt{4} \sqrt{2}+\sqrt{9} \sqrt{2}[/tex]

Carry out √4 and √9:

[tex]\implies 7 \sqrt{2}-3\cdot 2 \sqrt{2}+3 \sqrt{2}[/tex]

Multiply -3 and 2:

[tex]\implies 7 \sqrt{2}-6 \sqrt{2}+3 \sqrt{2}[/tex]

Factor out √2:

[tex]\implies (7 -6+3) \sqrt{2}[/tex]

Carry out the operations inside the parentheses:

[tex]\implies 4\sqrt{2}[/tex]

Answer:

The correct answer is: parallel

The two equations are in the form of y = mx + b and y = mx + b, which are the standard forms of linear equations.

and the slope of the two equations are different, so they are not coincident and not intersecting. They are parallel lines that never meet, so the system of equations is parallel.

Answer:

y = 4/5x + 3

Step-by-step explanation:

The equation y + 1 = 4/5(x + 5) can be solved by first isolating the y variable on one side of the equation. To do this, we'll first distribute the 4/5 across the parenthesis:

y + 1 = 4/5x + 4

Next, we'll subtract 1 from both sides of the equation:

y = 4/5x + 3

This is the equation in standard form, with the y variable on the left side and the x variable on the right side, and the constants added and subtracted.

The following are the values for the length of each rectangles:

(a) L = 37.5 m

(b) L = 26.2 cm

(c) L = 25.5 km

(d) L = 20 m

In calculating for the area of rectangle, the breadth is multiplied by the length of the rectangle.

We shall evaluate for the Lengths of the rectangles as follows:

Length = 375 m²/ 10 m

Length = 37.5 m

Length = 393 cm²/ 15 cm

Length = 26.2 cm

Length = 280.5 km²/ 11 km

Length = 25.5 km

Length = 340 m²/ 17 m

Length = 20 m

Hence, 37.5 m, 26.2 cm, 25.5 km, and 20 m are the respective values for the length of rectangles with area 375 m², 393 cm², 280.5 km², and 340 m².

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(a) -3,-11,-19, -27, -35,-43, -51, -59, -67, -75.

(b) -9,-18,-36,-72,-144,-288,-576,-1152,-2304,-4608.

(c) 2, 6, 12, 20, 30, 42, 56, 72, 90, 110.

In the provided sequence, we will find the difference between two consecutive integers.

The difference between the second and first numbers is 622=4.

The difference between the third and second numbers is 126=6.

The difference between the fourth and third numbers is =2012=8.

We can see that the difference between two consecutive integers starts at 4 and grows by 2 each time.

As a result, the supplied sequence is created by adding the difference between a number and the preceding number, as well as 2 to the number.

Using the rule, we can determine the following three words.

The difference between the fifth and fourth numbers is =8+2=10.

As a result, the fifth number of the series equals the fourth number of the sequence plus ten.

As a result, we get the fifth number from the series =20+10=30

The difference between the sixth and fifth numbers is 10+2=12.

As a result, the sixth number of the series equals the fifth number of the sequence plus twelve.

As a result, we receive the sixth number as the sequence's sixth number =30+12=42.

The difference between the seventh and sixth numbers is 12+2=14.

As a result, we get the sequence's seventh number = the sequence's sixth number + 14

As a result, we receive the seventh number as the sequence's seventh number =42+14=56.

As a result, the following three terms in the specified sequence are 30, 42, and 56.

The sequence is changed to 2, 6, 12, 20, 30, 42, 56.

The word 'prime numbers' was used in the answer. The numbers are known as prime numbers. It has just two variables, 1 and the number itself. For instance, 2 is the sum of 2 and 1. As a result, the components of 2 are 2 and 1. As a result, 2 is a prime number.

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Answer:

1,2,3,4,6,12,18

Step-by-step explanation:

uh

Answer:

x = 9

Step-by-step explanation:

[tex] - 1 + 14x = 12x + 17 \\ 2x = 18 \\ x = 9[/tex]

Answer:

10 cupcakes

Step-by-step explanation:

6 cupcakes have mint icing. This means there are 24 cupcakes left. 7/12 of these, or 14 cupcakes, have chocolate frosting. This means that there are 10 vanilla frosted cupcakes.

The domain and range of the function y = 1/2 - 1 lies on  (-∞, ∞)

The collection of all input values (sometimes referred to as independent variables) for which a function is defined and yields a valid output is known as the domain of the function. It is the collection of all possible values that can be entered into a function.

All real numbers, for instance, fall inside the domain of the function        f(x) = x², since any real number may be squared to yield an accurate result.

On the other hand, a function's range is the collection of all feasible output values (also known as the function's dependent variable) that it can generate. It is the collection of all outcomes that the function is capable of producing.

For instance, since squaring real numbers makes the range of the function f(x) = x² all non-negative values.

It's vital to remember that not all functions have the same range or are defined for all conceivable input values. For instance, because the square root function x is not defined for negative numbers, all real numbers that are not negative fall within its domain.

In conclusion, the collection of all input values for which a function is defined and yields a valid output is known as the domain of the function. The collection of all potential output values that a function may produce is known as its range.

In the given function;

y = 1/2x - 1

The domain of this function is (-∞, ∞)

The range of the function f(x) = 1/2x - 1 is (-∞, ∞)

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6. The measure of angle BEC is 48°

7. The measure of angle 1 is 41°

8. The value of x is 12

   The measure of angle UST is 36°

6. The angles AEB and BEC form a straight line whose angle measure is 180°.

So that,

∠AEB + ∠BEC = 180°

132° + ∠BEC = 180°

∠BEC = 180° - 132°

∠BEC = 48°

7. The angles 1 and 5 form a right angle whose measure is 90°.

So that,

∠5 + ∠1 = 90°

49° + ∠1 = 90°

∠1 = 90° - 49°

∠1 = 41°

8. The angles RSU and UST form a right angle whose measure is 90°.

∠RSU + ∠UST = 90°

(5x - 6)° + (2x + 12)° = 90°

(7x + 6)° = 90°

7x° = (90 - 6)°

7x° = 84°

x = 12

∠UST =  (2x + 12)°

∠UST =  (2(12) + 12)°

∠UST =  (24 + 12)°

∠UST = 36°

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Answer:

[tex]\boxed{y = 4x + 7}[/tex]

Step-by-step explanation:

The equation of a line in slope-intercept form is

y = mx + b

where m is the slope and b the y-intercept

To find the slope, take the two points, find the difference in y values and divide by the corresponding difference in x values

Two points are [tex](- 1, 3)[/tex] and [tex](- 2, -1)[/tex]

Difference in y values [tex]= -1 -3 = -4[/tex]

Difference in corresponding x values [tex]= -2 - (-1) = -2 + 1 = -1[/tex]

Slope

 [tex]m = \dfrac{-4}{-1} = 4[/tex]

So the equation of the line is of the form
[tex]y = 4x + b[/tex]

To find b, take the coordinates of any of the two points and plug the x and y values into the above equation and solve for b

Let's take point (-1, 3)

Plug in values:

[tex]3 = -4 + b\\\\3+4 = b\\ \\b = 7[/tex]

Therefore the equation of the line is
[tex]\boxed{y = 4x + 7}[/tex]

The plotted graph is shown below.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

s (h) = √64h

now, when h=0

s(0) = √64h = 0

and, when h= 5

s(5) = √64h

        = √64 x 5

       = 8 x 2.25

       = 17.88

and, when h= 10

s(25) = √64h

        = √64 x 10

       = 8 x 3.162

       = 25.29

and, when h= 15

s(25) = √64h

        = √64 x 15

       = 30.98

and, when h= 20

s(25) = √64h

        = √64 x 20

       = 35.77

and, when h= 25

s(25) = √64h

        = √64 x 25

       = 8 x 5

       = 40

The plotted graph is shown below.

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The quantity of additive which Belle put in each can as required is; 1/8 pint.

It follows from the task content that the quantity of additive which Belle put in each can be determined if 1/2 of a pint of special paint additive is shared among 4 cans of paint.

The resulting expression which given the required quantity is;

1/2 ÷ 4

= 1/2 × 1/4

= 1/8.

On this note, the quantity of additive in each can of paint is 1/8 pint of special paint additive.

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Answer:

x = arccos(3/4) + 2πn where n = 0,1,2,3,4, ....

Step-by-step explanation:

We can solve the equation 4cos(x) + 3 = 6 by isolating the cos(x) term on one side of the equation.

4cos(x) + 3 - 3 = 6 - 3

4cos(x) = 3

cos(x) = 3/4

Now we can find the solutions of the equation by finding the values of x that make cos(x) equal to 3/4. Since -π < x < π, we can find the solutions in the range of -π < x < π.

x = cos^-1(3/4) + 2πn, where n is an integer

x = cos^-1(3/4) + 2πn, where n = 0, 1, 2, ...

The solutions are x= cos^-1(3/4) and x = cos^-1(3/4) + 2π, x = cos^-1(3/4) + 4π

Keep in mind that cos^-1(3/4) is the inverse cosine function or arccos(3/4) so the final solution is x = arccos(3/4) + 2πn where n = 0,1,2,3,4, ....