In Hillsdale, the library is due south of the courthouse and due west of the community
swimming pool. If the distance between the library and the courthouse is 15 miles and the
distance between the courthouse and the city pool is 25 miles, how far is the library from the
community pool?

Answer:

The rule for reflection along the x axis (x;y) to (x; -y)

A' (x ; -(y) )

A' (4 ; -(5) )

A' (4 ; -5 )

Answer:The volume would be 8,341,984

Step-by-step explanation:

This is consistent with the solutions for the equation [tex]x^{2}[/tex] - 6x + 5 = 0 being x = 1 and x = 5.

An equation is a mathematical statement that expresses the equality of two expressions. It consists of one or more terms, each of which contains one or more variables. The terms are separated by an equal sign (=) and are usually written in a standard form known as an algebraic equation. Equations can be used to model and solve problems in a wide variety of fields, from physics and chemistry to economics and finance.

The graph of the quadratic equation is a parabola that opens upward and intersects the x-axis at two points. The x-intercepts occur when the equation is equal to zero, so the x-intercepts for the equation [tex]x^{2}[/tex] - 6x + 5 = 0 are the solutions for x. These solutions are x = 1 and x = 5.

The graph of the quadratic equation also shows that the two solutions of the equation, x = 1 and x = 5, are the x-intercepts of the parabola. This means that when x equals 1 or 5, the equation is equal to zero, so the x-intercepts are the solutions of the equation. This is consistent with the solutions for the equation [tex]x^{2}[/tex] - 6x + 5 = 0 being x = 1 and x = 5.

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The event with the highest probability is "reaching into a bag full of 50 strawberry chews and 10 cherry chews without looking and pulling out a strawberry chew", with a probability of 5/6 or approximately 0.83. Option D

To determine which event is most likely to occur, we need to compare the probabilities of each event happening.

Rolling a multiple of 4 on an eight-sided die:

There are 8 possible outcomes when rolling an eight-sided die, and 2 of them are multiples of 4 (4 and 8). So, the probability of rolling a multiple of 4 is 2/8, or 1/4.

Spinning a spinner and landing on pink:

There are 4 possible outcomes when spinning the spinner, and only one of them is pink. So, the probability of landing on pink is 1/4.

Winning a raffle that sold a total of 100 tickets, if you buy 53 tickets:

The total number of possible outcomes is the total number of tickets sold, which is 100. The number of favorable outcomes is the number of tickets the person bought, which is 53. So, the probability of winning the raffle is 53/100.

Reaching into a bag full of 50 strawberry chews and 10 cherry chews without looking and pulling out a strawberry chew:

The total number of possible outcomes is the total number of candies in the bag, which is 50 + 10 = 60.

The number of favorable outcomes is the number of strawberry chews in the bag, which is 50. So, the probability of pulling out a strawberry chew is 50/60, which simplifies to 5/6.

Comparing the probabilities, we can see that the event with the highest probability is "reaching into a bag full of 50 strawberry chews and 10 cherry chews without looking and pulling out a strawberry chew", with a probability of 5/6 or approximately 0.83. Therefore, this event is the most likely to occur.

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Answer:

x = 10182634

y = - 462847/46

Step-by-step explanation:

Divide both sides of the equation by the coefficient of variable

x =   -1012y

y = - 10182634/ 1012

x =   -1012y(  - 10182634/ 1012)

Answer:

translation point a cross the coordinator

The variable which is always positive will be a, b, c, d, p, and q. The constant that lies between 0 to 1 will be 'b'. And the two constants that are definitely equal will be 'a' and 'c'.

Let 'a' is the leading coefficient and 'b' is the factor.

The exponent is given as,

y = a(b)ˣ

Some points regarding the exponent function:

The variable which is always positive will be a, b, c, d, p, and q. The constant that lies between 0 to 1 will be 'b'. And the two constants that are definitely equal will be 'a' and 'c'.

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Answer:

The answer is A my friend! Good luck on your test Mr Rush.

Using Pythagoras' Theorem, we found the length of Road C and the respective time taken to travel along each road.

What is meant by Pythagoras' theorem?

The Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse. In essence, Pythagoras' theorem is used to determine a triangle's angle and length of an unknown side. This theorem allows us to obtain the hypotenuse, perpendicular, and base formulas.

The given figure is a right triangle.

The length of road A = 16.01 km

The length of road B = 10 km

a) The length of road C can be found using Pythagoras' theorem.

From figure,

A² = B² + C²

16.01 ² = 10² + C²

C² = 156.32

C = 12.5 km

b) Speed of bike = 19.5 km/h

   Length of road C = 12.5 km

Time = Length/speed = 12.5/19.5 = 0.64 hours

 Length of road B =10 km

Time = Length/speed = 10/19.5 = 0.51 hours

c) Length of road A = 16.01

Time taken = Length/speed = 16.01/19.5 = 0.82 hours.

Therefore using Pythagoras' Theorem, we found the length of Road C and the respective time taken to travel along each road.

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The number of each denomination is: 13 of the $10-dollars bills.

Let x be number of the $20 dollars bills. Then, the number of the $10 dollars bills is (x+2), according to the condition.

The money equation will then be:

20x + 10*(x+2) = 350

Now, solve for x.  

20x + 10x + 20 = 350

30x = 350 -20

30x = 330

x = 330/30

x = 11

So, 11 of the $20 dollars bills and 11 +2 = 13 of the $10-dollars bills.

Full question "Part of the proceeds from a garage sale was ​$350 worth of ​$10 and ​$20 bills. If there were 2 more $10 bills than $20 bills, find the number of each denomination.

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Step-by-step explanation:

1/2 cup per 1/4 bag goes to the less than

all the other ones should be in the greater than category

Answer:

66.67

Step-by-step explanation:

8 people stayed home, 8/12=2/3=66.67(approx)

a. Thor works more hours each week, the quantity of donations the organization raises each week declines, but the link is not very strong.

When two variables are correlated negatively, the other variable's value falls as the value of the first variable rises.

The correlation coefficent, which expresses correlation on a scale from +1 to -1, is used. Numbers less than 0 indicate a negative connection. An increase in one variable confidently foretells a drop in the other when there is a perfect negative correlation, with a coefficient of -1. Non-zero coefficients between +1 and -1 are used to show lower degrees of connection. 0 means there is no propensity for the variables to change simultaneously, either positively or negatively.

a. A weak negative linear relationship between hours worked and donations collected in this context means that as Thor works more hours each week, the quantity of donations the organization raises each week declines, but the link is not very strong.

b. When we say there is a weak correlation between two variables, we are referring to their level of relationship. The negative correlation in this instance indicates that there is a propensity for the amount of donations collected to decline as the time spent working increases, but the relationship is not very strong, indicating that there is a lot of variability in the data and making firm predictions or conclusions based on this correlation alone is challenging.

c. Tom's boss's claim is wrong as the negative correlation or the decline in donation is a mere coincidence and does not have a relation to Thor's work.

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Answer: The value of a=29/23 and b=124/23

Step-by-step explanation:

Given equations are,

2b-3a=7       _(1)

3b+7a=25     _(2)

Multiplying (1) by 7

14b-21a=49

Multiplying (2) by 3

9b+21a=75

solving the above equations,

14b-21a=49

9b+21a=75

23b      =124

b=124/23

Substituting the value of b in eq. (1)

a=29/23

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Answer: f=756

Step-by-step explanation:

f/28=7

multiply both sides of the equation by 28

28 x f/28=28 x 27

cancel out the greatest common factor 28

f=28 x 27

multiply 28 x 27

f=756

Using the graph of the line, we can see that the inequality, including the line which is the boundary of inequality, is:

 y + 2x ≥ -3

What is meant by inequality?

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using inequality symbols.

Given that the boundary line of equality has points (4,5) and (1,-1) on it.

So we can write the equation of the line.

Slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] = -1-5 / 1-4 = 2

Equation of the line:

y - y1 = m (x-x1)

y - 5 = 2(x - 4)

y - 5 = 2x - 8

y = 2x - 3

y + 2x = -3

Point (−3, −5) makes the inequality false.

Substituting,

-5 + 2 * -3 = -5 - 6 = -11

y + 2x should not be -11

When graphing the line it should not include the point (−3, −5).

This point is present on the lower portion of the line.

So the upper portion of the line should be the inequality including the line itself.

Therefore using the graph of line, we can see that the inequality, including the line which is the boundary of inequality, is:

 y + 2x ≥ -3

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The point slope equation with the point (x1, y1) is given as (y - y1) = m (x - x1).

As a line has length but no width, it is a one-dimensional figure in geometry. A line is constructed from a collection of points that can be stretched indefinitely in opposite directions. In a two-dimensional plane, it is determined by two points. In a two-dimensional coordinate plane, there are various ways to express line equations. The general or standard form of the equation of a line, the slope-intercept form, and the point-slope form are the three most often used ways. The point-slope form, as its name implies, combines a line's point with the straight-line slope. The equations of infinite lines with a specified slope can be written, however when we specify that the line passes through a certain point, we obtain a singular straight line.

The point slope equation with the point (x1, y1) is given by the formula:

(y - y1) = m (x - x1)

Here, (x1, y1) are the coordinates of the point on the graph.

m is the slope of the line.

Hence, the point slope equation with the point (x1, y1) is given as (y - y1) = m (x - x1).

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Quadrilateral R'S'T'V' is smaller than Quadrilateral RSTV because a scale factor is less then 1.

A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

Given that;

Quadrilateral RSTV is dilated with the origin as the center of dilation using the rule (x, y) = (3/2x, 3/2y) to create quadrilateral R'S'T'V'.

Here, All the coordinates of vertex of Quadrilateral RSTV are,

R = (- 3, - 2)

S = (- 2, 3)

T = (2, 2)

V = (3, - 1)

Hence, By applying rule we get;

All the coordinates of vertex of Quadrilateral R'S'T'V' are,

R' = (- 3 × 3/2, - 2× 3/2) = (- 9/2. - 3)

S' = (- 2 × 3/2, 3 × 3/2) = (- 3, 9/2)

T' = (2 × 3/2, 2× 3/2) = (3, 3)

V' = (3 × 3/2, - 1 × 3/2) = ( 9/2. - 3/2)

Now, Distance between R and S;

RS = √ (- 3- (- 2))² + (- 2 - 3)²

     = √1 + 25

     = √26

And, Distance between R' and S';

R'S' = √ (- 3- (- 9/2))² + (- 3 - 9/2)²

     = √(3/2)² + (15/2)²

     = √9/4 + 225/4

    = √234/4

Hence, The scale factor is,

⇒ RS / R'S' = √26 / (√234/4)

                  = 2√26/ √234

                  = 2/3

                  = 0.67 < 1

Thus, Quadrilateral R'S'T'V' is smaller than Quadrilateral RSTV because a scale factor is less then 1.

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Answer:

Error refresh.

Step-by-step explanatithanksforfreepointlolon:

Answer:

a. The y-intercept of the estimated line of best fit is at (0, b). Enter the approximate value of b.

b. Approximately 8.

b. Enter the approximate slope of the estimated line of best fit in the second box. slope=24 (Enter your estimate to the nearest tenth.)

Approximately 2.4.

Answer:

fraction:26/100

decimal:0.26

The correct matching of the fractions

0.1 - 1/10

0.01 - 1/100

100% - 1

A fraction is a way of representing a part of a whole or a quantity that is less than one. Fractions consist of two numbers separated by a horizontal or diagonal line, with the number above the line being called the numerator and the number below the line being called the denominator.

The numerator represents how many parts of the whole are being considered, while the denominator represents the total number of equal parts that the whole is divided into.

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Answer:

[tex]S_n= n^2+4n[/tex]

[tex]n=11[/tex]

Step-by-step explanation:

The given arithmetic series is 5 + 7 + 9 + ...

From inspection of the given series, we can see that the first term is 5.

The common difference is the difference between consecutive terms. Therefore, the common difference of the given series is 2.

[tex]\boxed{\begin{minipage}{7.3 cm}\underline{Sum of the first $n$ terms of an arithmetic series}\\\\$S_n=\dfrac{1}{2}n[2a+(n-1)d]$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $d$ is the common difference.\\ \phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]

To determine an equation for the sum of the first n terms of the given series, substitute a = 5 and d = 2 into the formula.

[tex]\implies S_n=\dfrac{1}{2}n\left[2(5)+(n-1)(2)\right][/tex]

[tex]\implies S_n=\dfrac{1}{2}n\left[10+2n-2\right][/tex]

[tex]\implies S_n=\dfrac{1}{2}n\left[2n+8\right][/tex]

[tex]\implies S_n= n^2+4n[/tex]

To find the value of n, substitute Sₙ = 165 into the formula and solve for n:

[tex]\implies n^2+4n=165[/tex]

[tex]\implies n^2+4n-165=0[/tex]

[tex]\implies n^2+15n-11n-165=0[/tex]

[tex]\implies n(n+15)-11(n+15)=0[/tex]

[tex]\implies (n-11)(n+15)=0[/tex]

Apply the zero product property:

[tex](n-11)=0 \implies n=11[/tex]

[tex](n+15)=0 \implies n=-15[/tex]

Therefore, as the value of n is positive, the value of n for which the series has a sum of 165 is 11.

The x and y values are x=5 and y= -2

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

y=4x-22 ----(1)

2x+3y=4------(2)

Substitute (1) into (2)

=> 2x+3(4x-22)=4

=> 2x+12x-66 = 4

=> 14x = 4+66

=> 14x = 70

=> x=70/14 = 5

(1) => y=4*5-22 = 20 - 22 = -2

So, the x and y values are x=5 and y= -2

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The statement 3/4> 13/16 is false and the statement 6/7> 5/8is true.

Least Common Multiple is the meaning of the acronym LCM. The smallest number that both numbers can divide by is known as the least common multiple (LCM) of two numbers. It can also be computed for two or more different numbers. There are numerous ways to calculate the LCM of a given collection of numbers. Using the prime factorization of each number and then calculating the product of the highest powers of the common prime factors yields the LCM of two integers in a short amount of time.

The first statement is:

3/4 > 13/16

Take the LCM:

12/16 > 13> 16

Comparing the numerator we see that, 12 > 13 is false. Hence, the statement is false.

The second statement is:

6/7 > 5/8

Take the LCM:

48/56 > 35/56

Comparing the numerator we see that, 48 > 35 is True.

Hence, the statement is True.

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Answer:

f(x)-g(x)

= [tex](x^{2} - 13x + 36) - ( x -4)[/tex]

= [tex]x^{2} -13x+36-x+4[/tex]

= [tex]x^{2} -14x-40[/tex]

The value of expression 50% of 36 is,

⇒ 50% of 36 = 18

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

The expression is,

⇒ 50% of 36

Now, We can simplified as;

The expression is,

⇒ 50% of 36

By definition of percent we get;

⇒ 50/100 × 36

⇒ 1/2 × 36

⇒ 36/2

⇒ 18

Thus, The value of 50% of 36 is,

⇒  50% of 36 = 18

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The triangle whose sides are √13, 6, and 7, is a right triangle.

What is the right triangle?

A right triangle is defined as a triangle with one right angle or two perpendicular sides. The longest side of a right triangle is called the hypotenuse.

Pythagorean Theorem :

The square on the hypotenuse is equal to the total of the squares on the legs of a right triangle.

Mathematically, let r be the length of the hypotenuse of a right triangle. Again let p, q be the lengths of other sides of this triangle. By the Pythagorean Theorem,

r² = p² + q².

How to solve this problem?

We just check which triangle's sides follow the above theorem.

Option A (Triangle with sides √13, 6, and 7 ):

13 + 36 = 49

i.e. (√13)² + 6² = 7²

This triangle's sides follow the Pythagorean Theorem.

So, the triangle with sides √13, 6, and 7 is a right triangle.

Option B (Triangle with sides 7, 8, and 13 ):

49 + 64 ≠ 169

i.e. 7² + 8² ≠ 13²

This triangle's sides do not follow the Pythagorean Theorem.

So, the triangle with sides 7, 8, and 13 is not a right triangle.

Option C (Triangle with sides 10, 11, and 12 ):

100 + 121 ≠ 144

i.e. 10² + 11² ≠ 12²

This triangle's sides do not follow the Pythagorean Theorem.

So, the triangle with sides 10, 11, and 12 is not a right triangle.

Option D (Triangle with sides √10, 9, and 8 ):

10 + 64 ≠ 81

i.e. (√10)² + 8² ≠ 9²

This triangle's sides do not follow the Pythagorean Theorem.

So, the triangle with sides √10, 9, and 8 is not a right triangle.

Therefore the triangle whose sides are √13, 6, and 7, is a right triangle. So, option A is correct.

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Answer:

7.25

Step-by-step explanation:

Divide 8.99 by 1.24

Substituting this expression for BD into the area formula, we get:b

1/2 * 10 * (4z/5) = 1/2 * z * 8

Simplifying and solving for z, we get:

20z/25 = 4z

16z = 100

z = 6.25

Therefore, the value of z is 6.25.

A triangle is a closed geometric figure that is formed by connecting three straight line segments called sides. These sides meet at three points called vertices. Triangles are one of the simplest and most fundamental shapes in geometry and can be found in many natural and man-made objects.

Triangles can be classified into different types based on their sides and angles.

By sides:

Equilateral triangle: all three sides are equal in length.

Isosceles triangle: two sides are equal in length.

Scalene triangle: all three sides are different in length.

By angles:

Acute triangle: all three angles are acute (less than 90 degrees).

Right triangle: one angle is a right angle (exactly 90 degrees).

Obtuse triangle: one angle is an obtuse angle (greater than 90 degrees).

Triangles have many properties and are used in various fields such as architecture, engineering, physics, and mathematics. They are also commonly used in trigonometry to solve problems involving angles and distances.

We can use the Pythagorean theorem to find the value of z:

[tex]AC^2 = AD^2 + DC^2[/tex]

Since BD is perpendicular to AC, we know that DC = BC. We can also use the fact that AB and BD are altitudes of triangle ABC to find the area of the triangle in two different ways:

Area of triangle ABC = 1/2 * AB * BD = 1/2 * AC * AD

Substituting the given values, we get:

1/2 * 10 * BD = 1/2 * z * 8

Simplifying this equation, we get:

BD = 4z/5

Substituting this expression for BD into the area formula, we get:b

1/2 * 10 * (4z/5) = 1/2 * z * 8

Simplifying and solving for z, we get:

20z/25 = 4z

16z = 100

z = 6.25

Therefore, the value of z is 6.25.

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The system of inequalities that can be used to find the possible original prices of a laptop, x, and of a printer, y is: x + y ≥ 1050 and 0.8x + 0.9y > 860

Let x be the original price of the laptop and y be the original price of the printer.

So, the discounted price of the laptop is 0.8x and the discounted price of the printer is 0.9y

If the two are purchased together, the total discounted price is:

0.8x + 0.9y

This exceeds $860

0.8x + 0.9y > 860

The original prices of the two together is at least $1,050.

This can be written as:

x + y ≥ 1050

So, we have

x + y ≥ 1050 and 0.8x + 0.9y > 860

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