Ms.Metz had her students estimate the length and width of a math book. Dana's estimate was 40cm by 20cm. The book measured 24cm by 16cm. How far off was her estimate?

The midpoint and distance between (-3,10) and (15,-2) are ( 6,4 ) and 6√13 respectively.

The midpoint formula is expressed as;

[ (x₁ + x₂)/2, (y₁ + y₂)/2 ]

The distance formula used in finding the distance between two points is expressed as;

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

Given the data in the question;

Point 1(-3,10)

Point 2( 15,-2 )

Plug the given values into the midpoint formula and simplify.

[ (x₁ + x₂)/2, (y₁ + y₂)/2 ]

[ ( -3 + 15)/2, ( 10 + (-2) )/2 ]

[ ( 12)/2, ( 10 - 2 )/2 ]

[ ( 12)/2, ( 8 )/2 ]

( 12/2, 8/2 )

( 6,4 )

Therefore, the midpoint is (6,4).

Plug the given values into the distance formula and simplify.

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

D = √( ( 15 - (-3)  )² + ( -2 - 10 )² )

D = √( ( 15 + 3  )² + ( -2 - 10 )² )

D = √( ( 18  )² + ( -12 )² )

D = √( 324 + 144 )

D = √( 468 )

D = 6√13

Therefore, the distance between the points is 6√13.

Learn more about the distance formula here: brainly.com/question/24509115

#SPJ1

Answer:

1 [tex]\frac{1}{4}[/tex] miles

Step-by-step explanation:

the routes from Lexington to Somerville are

Lexington → Brookfield → Somerville with distance

[tex]\frac{3}{8}[/tex] + [tex]\frac{7}{8}[/tex] = [tex]\frac{3+7}{8}[/tex] = [tex]\frac{10}{8}[/tex] = 1 [tex]\frac{2}{8}[/tex] = 1 [tex]\frac{1}{4}[/tex] miles

the other route is

Lexington → Brookfield → Yardley → Somerville with distance

[tex]\frac{3}{8}[/tex] + [tex]\frac{1}{2}[/tex] + [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{8}[/tex] + [tex]\frac{4}{8}[/tex] + [tex]\frac{4}{8}[/tex] = [tex]\frac{3+4+4}{8}[/tex] = [tex]\frac{11}{8}[/tex] = 1 [tex]\frac{3}{8}[/tex] miles

the shortest distance is

Lexington → Brookfield → Somerville , a distance of 1 [tex]\frac{1}{4}[/tex] miles

Answer:

if the scale used 1/4 inch = 3 feet, then what is the perimeter of the actual garden? AI Recommended Answer: The perimeter of the actual garden is 144 feet.

Step-by-step explanation:

First, let's find Maura's running speed by using the information that Carlos runs at a rate that is 25% slower than Maura's rate. If Carlos runs at a rate of 6 miles per hour, then Maura runs at a rate of 6 * 1.25 = 7.5 miles per hour.

Next, let's calculate how long it takes for Carlos to finish the marathon. We know that Carlos runs at a rate of 6 miles per hour and the marathon is 26 miles long. So we can use the formula:

time = distance/rate

time = 26/6

time = 4.33 hours

Now let's find how long it takes for Maura to finish the marathon. We know that Maura runs at a rate of 7.5 miles per hour and the marathon is 26 miles long. So we can use the formula again:

time = 26/7.5

time = 3.47 hours

Finally, let's convert Jacob's time of 2 hours and 36 minutes to hours. We can use the formula:

time = 2 + (36/60)

time = 2 + 0.6

time = 2.6 hours

In conclusion, Carlos takes 4.33 hours, Maura takes 3.47 hours and Jacob takes 2.6 hours to finish the marathon.

To learn more about Average Speed visit:

https://brainly.com/question/12322912

#SPJ1

The equation of p(x) in vertex form is p(x) = 3(x - 1)² - 2.

Option C is the correct answer.

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

We have,

From the table,

From p(x) = 10 to p(x) = -2 the value of p(x) is decreasing and from p(x) = -2 to p(x) = 46 it is increasing.

So,

The vertex is (1, -2).

The vertex form of p(x).

p(x) = a ( x - h)² + k

Where (h, k) is the vertex.

Now,

(1, -2) = (h, k)

Make (0, 1) = (x, p(x))

1 = a (0 - 1)² + (-2)

1 = a - 2

a = 1 + 2

a = 3

Thus,

The vertex equation of p(x).

p(x) = 3(x - 1)² - 2

Learn more about polynomials here:

https://brainly.com/question/2284746

#SPJ1

The half life of the iodine is obtained as 6.2 s.

Let us recall that the half  life would be the time that is taken for about half of the original radioactive isotope that remains in the sample, to become depleted in the thyroid treatment.

Given that we have the fact that the decay constant that we have in the process is given as 0.1113 in the question and we know that;

Half life = 0.693/K

Half life = 0.693/0.1113

Half life = 6.2 s

It would have the half life about 6.2 s.

Learn more about half life:https://brainly.com/question/24710827

#SPJ1

Answer:

  DNE

Step-by-step explanation:

You want the value of 'b' so that the system of equations has no solution.

In order for the system of two linear equations to have no solution, the equations must describe parallel lines. That is, the lines must have the same slope.

The slope of the line written in the form px -qy = c is the coefficient of x when the equation is rearranged to "y=" form. Here, that is p/q.

The slope of the first line is 5/2; the slope of the second line is 5/6. These values are different and do not depend on 'b'.

There is no value of 'b' that will make this system have no solution. It does not exist (DNE).

Answer:

-sqrt(2)/2 , the last option of your document.

Step-by-step explanation:

sin(7pi/4) = -sin(7pi/4 - pi)

                = -sin(7pi/4 - 4pi/4)

                 = - sin(3pi/4)

sin(3pi/4) is a special angle , which is sqrt(2)/2

Hence, sin(7pi/4) = -sin(3pi/4)

                             = -sqrt(2)/2

Answer:

-sqrt(2)/2

Step-by-step explanation:

did the test

Answer: y = 17x - 19

Step-by-step explanation:

17x + y = -19

Subtract 17 on both sides

Y= -19 - 17x

Then put it in y= mx + b

Y= -17x - 19

Answer:

y = -17x -19

Step-by-step explanation:

Slope intercept form is

y = mx+b  where m is the slope and b is the y intercept

17x+y = -19

Solve for y

y = -17x -19

On solving the provided question, we can say that - by doing the equation, we have -12 +18 = p + 7 => 6 = p + 7 => p = -1

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

here,

-12 +18 = p + 7

6 = p + 7

p = -1

To know more about equation visit:

https://brainly.com/question/649785

#SPJ1

Answer:

y=-3.5

Step-by-step explanation:

substitute -4 for x

add 4 on both sides to get rid of the -4

divide -2 on both sides to isolate y

and you get 3.5 for y

The value of y that will satisfy the equation given is -3.5.

Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”.

Given that, the missing coordinate in the ordered pair (−4, ?), we need to find the missing value that will satisfy the equation x-2y = 3,

To find the same, just replace the value of x by -4,

-4-2y = 3

-2y = 7

y = -3.5

Hence, the value of y that will satisfy the equation given is -3.5.

Learn more about equations, click;

https://brainly.com/question/29657988

#SPJ2

Total cost of gazebo's floor is $3556.8 when the gazebo has 12 feet on each side. 10.4 feet tall is the apothem.

Given that,

In Clark's backyard, a sizable gazebo is being constructed. It has a typical hexagonal form. The gazebo has 12 feet on each side. 10.4 feet tall is the apothem. He must get stones for the flooring. The price of a particular kind of interlocking stone is $9.50 per square foot.

We have to identify the gazebo's floor's cost.

We know that,

The distance from the center of the regular polygon to the mid point of the side. Here, AB is the chord and AM =BM. O is the center of the circumcircle.

Segments joining the center of a circle to the midpoint of the chord is perpendicular to the chord.

So, OM ⊥AB

In ΔOAB,

AB is the base and OM is the height.

AB = 12 feet

OM = 10.4 feet.

The area of the triangle OAB =1/2×base×height

= 1/2×12×10.4

=62.4 square feet.

A regular hexagon is divided into 6 equilateral triangle having each side  12 feet.

Area of the regular hexagon = 6× area of the one triangle

=6×62.4=374.4 square feet

Cost of inter locking stones = $9.50 per square feet.

Total cost of gazebo's floor = 374.4× 9.50 =$3556.8

Therefore, Total cost of gazebo's floor is $3556.8 when the gazebo has 12 feet on each side. 10.4 feet tall is the apothem.

To learn more about feet visit: https://brainly.com/question/15658113

#SPJ1

Answer:

The magnification is the ratio of the size of the image to the size of the object. In this case, the length of the insect is the size of the object, and the length of the drawing is the size of the image.

To find the magnification, we can divide the size of the image by the size of the object:

Magnification = size of image / size of object

Plugging in the values, we have:

Magnification = 85mm / 23mm

Calculating, we find that the magnification is approximately 3.7. This means that the length of the drawing is 3.7 times the length of the insect.

Step-by-step explanation:

The equation that corresponds to fraction   [tex]\frac{7^{-10} }{(7^{4} )(7^{0} )}[/tex] is [tex]\frac{1}{7^{14} }[/tex] . A phrase by itself could contain an action .

It is possible to multiply, divide, add, or subtract in math. An expression has the following structure: Expression: (Math Operator, Number/Variable, Math Operator). A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) It is possible to compare expressions and phrases. In English, a phrase by itself could contain an action, but it doesn't constitute a full sentence.

given

[tex]\frac{7^{-10} }{(7^{4} )(7^{0} )} \\= \frac{1}{7^{4} } *\frac{1}{7^{10} } * 1\\= \frac{1}{7^{14} }[/tex]

The equation that corresponds to fraction   [tex]\frac{7^{-10} }{(7^{4} )(7^{0} )}[/tex] is  [tex]\frac{1}{7^{14} }[/tex] .

To know more about expression visit :-

https://brainly.com/question/14083225

#SPJ1

The number in the replacement set that will make the equation true is (c) 112

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

x ÷ 2 = 56

Rewrite the expression properly

so, we have the following representation

x/2 = 56

Also, we have the replacement set to be

{28, 56, 112}

In the given equation, we have the variable to be

The variable is x

Multiply 2 to both sides of the expression

So, we have the following representation

2  * x/2 = 56 * 2

Evaluate the products on both sides of the equation

x = 112

Hence, the solution is x = 112

Read more about equation at

brainly.com/question/2972832

#SPJ1

Answer:

Yes, it is possible

Step-by-step explanation:

Answer:

90 degree

Step-by-step explanation:

since the original angle BAC is 90 degree, no matter the triangle is rotated or translated, the angle remain unchanged

Answer:

Perpendicular line ⇒ 2x + 9y + 42 = 0

midpoint: (-1,1)

Step-by-step explanation:

Let's find the coordinates of midpoint of AB

Here, from figure, A = (-3,-2), B = (1,4)

So midpoint:

[tex]P = (\frac{-3+1}{2},\frac{-2+4}{2})[/tex]

∴ P = (-1, 1)

Now, given straight line is x - 2y = -8(x-8)

⇒x - 2y = -8x+64

⇒9x - 2y - 64 = 0

Perpendicular line to 9x - 2y - 64 = 0 is 2x + 9y + k = 0

Perpendicular line passes though (6,-6)

Putting the values, we get

2(6) + 9(-6) + k = 0

⇒12 - 54 + k = 0

⇒k = 42

∴ Perpendicular line ⇒ 2x + 9y + 42 = 0

Answer: 16.10

Step-by-step explanation:

$14 + 15% increase rate = 16.10

15% = 2.10

Answer:

-3

Step-by-step explanation:

i hope this helps

The values that are solutions to the inequality -3 < 2x -3 are all real numbers greater than 0.

Given the inequality in the question;

-3 < 2x -3

Solve for x, by making it the subject of the formula.

Subtract 2x from both sides

-3 < 2x -3

-3 - 2x < -3

Add 3 to both sides

-3 + 3 - 2x < -3 + 3

-2x < -3 + 3

-2x < -3 + 3

-2x < 0

Next, divide both sides by -2

-2x/-2 >  0/2

x > 0/2

x > 0

Therefore, the solution to the inequality is x > 0.

Learn more about inequalities here: https://brainly.com/question/20383699

#SPJ1

The complete table is given below.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

1)

Time after         change in water     expression      water in tank  

sensor starts

0                              0                        770 + (0)(-14)        770

1                             -14                        770 + (1)(-14)         756

5                            -70                       770 + (5)(-14)        700

10                          -140                      770 + (10)(-14)       630

2)

Time after         change in water     expression      water in tank  

sensor starts

1                           -14                          770 + (1)(-14)         756

0                          0                           770 + (0)(-14)        770

-1                           14                          770 + (-1)(-14)        784

-2                          28                         770 + (-2)(14)        798
-3                          42                         770 + (-3)(14)         812

-4                          56                         770 + (-4)(14)         826

-5                          70                          770 + (-5)(-14)       840

Thus,

The complete table is given above.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ1

The complete question is given below.

The second step of calculating the present value of an ordinary annuity by the table lookup is to look up the periods and rates in the PV annuity table.

The present value of an ordinary annuity is the current value based on future cash inflows of the annuity, given a specified discount rate.

The present value is higher when the discount rate is lower, and vice versa.

The present value of an ordinary annuity, which discounts the annuity to the current time, is computed as Annuity Payment x Present value of the ordinary annuity table.

In conclusion, an annuity simply means a series of periodic payments and may involve payment at the beginning (annuity due) or at the end of the period (ordinary annuity).

Learn more about annuities at https://brainly.com/question/25792915

#SPJ1

When we divide 26 by 3 we get 8 as a quotient and 2 as a remainder, the Mixed Fraction is [tex]8\frac{2}{3}[/tex]

A full number plus a legal fraction are combined to form a mixed number. Mixed numbers, commonly referred to as mixed fractions, make it easier for humans to comprehend numbers.

A full number and a legal fraction make up a mixed number. A mixed number like [tex]2\frac{x}{y}[/tex] is one where 1/4 is the correct fraction and 2 is the whole number portion. It should be emphasized that once mixed numbers are transformed into an incorrect fraction, they are simple to add, subtract, multiply, and divide.

Steps to convert Improper fraction to Mixed Fraction :

So when we divide 26 by 3 we get 8 as a quotient and 2 as a remainder so the Mixed Fraction is : [tex]8\frac{2}{3}[/tex]

To learn more about Mixed Fraction refer to :

brainly.com/question/20329706

#SPJ1

Answer:

The answer is D (2 1/2)

Hope u helped

Answer:

The table with (-3, 2), (0, 2), etc.

Every input has exactly one output.

Hope this helps :)