find the distance between the two points in simplest radical form. (8,-1) and (2,-9)

Answer:

10

Step-by-step explanation:

Use the distance formula to determine the distance between two points.
√[(x₂ - x₁)² + (y₂ - y₁)²]

Answer:

yes

Step-by-step explanation:

you have to divide by the top and bottom to get the answer to the lowest number

Answer:

yes

Step-by-step explanation:

Check by changing to a common denominator

Answer:

101

Step-by-step explanation:

Linda had walked 2 5/8 miles or 2.625 miles on the Tremont trail

We are told in the question that

Linda walked 3/4 of the length of the Tremont Trail before stopping for a rest.

From the question, the length of the Tremont Trail = 3 1/2 miles

Hence, the distance (how far )Linda has walked =

3/4 of 3 1/2 miles

= 3/4 × 3 1/2 miles

= 3/4 × 7/2 miles

= 21/8 miles

= 2 5/8 miles or 2.625 miles

Therefore, Linda had walked 2 5/8 miles or 2.625 miles on the Tremont trail.

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Answer:

37.9 units (nearest tenth)

Step-by-step explanation:

As ABCD is a rectangle, AD = BC and AB = DC.

Find the length of AD and AB using the distance formula.

[tex]\boxed{\begin{minipage}{7.5 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}}[/tex]

From inspection of the given diagram:

Therefore:

[tex]\begin{aligned}AD & =\sqrt{(x_D-x_A)^2+(y_D-y_A)^2}\\& =\sqrt{(-7-(-5))^2+(-3-(-9))^2}\\& =\sqrt{(-2)^2+(6)^2}\\& =\sqrt{4+36}\\& =\sqrt{40}\end{aligned}[/tex]

[tex]\begin{aligned}AB & =\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\& =\sqrt{(7-(-5))^2+(-5-(-9))^2}\\& =\sqrt{(12)^2+(4)^2}\\& =\sqrt{144+16}\\& =\sqrt{160}\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Perimeter of a rectangle} & = \sf 2(length + width)\\& = 2(AB+AD)\\& = 2(\sqrt{160}+\sqrt{40})\\& = 2(18.97366596...)\\& = 37.94733192...\\& = 37.9\: \sf units\:(nearest\:tenth)\end{aligned}[/tex]

Therefore, the perimeter of the rectangle ABCD is 37.9 units (nearest tenth).

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The amount that the married couple filing jointly would pay in federal income taxes is C. $9,000.

Income tax is the compulsory obligation a taxpayer must remit to the IRS for each fiscal year based on the taxpayer's taxable income.

The tax rate based on the filer's tax bracket is applied to the taxable income to determine the tax payable.

Using the graduated system, of the $75,000, the first $20,550 is taxed at 10%, which gives $2,055. That leaves $54,450 in income. The next portion of the taxable income from $20,550 to $83,550 is taxed at 12%. This means $54,450 is getting taxed at 12%, which gives $6,534. The total tax due is $8,589, which averages $9,000.

Taxable income = $75,000

Tax bracket = 12%

Tax liability = $9,000 ($75,000 x 12%)

Tax Rates for married couples filing jointly are as follows:

10% tax rate for income between $0 and $20,550

12% tax rate for income between $20,551 and $83,550

22% tax rate for income between $83,551 and $178,150

24% tax rate for income between $178,151 and $340,100

32% tax rate for income between $340,101 and $431,900

35% tax rate for income between $431,901 and $647,850

37% tax rate for income of $647,851 or more

Thus, the amount that the married couple filing jointly would pay in federal income taxes is C. $9,000.

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Answer:

I believe R is congruent to U

Step-by-step explanation:

I don't exactly remember much about these types of problems but I hope it helps! =D

Answer:

∠VS is congruent to ∠UR

Step-by-step explanation:

congruent means same size or shape and the markings are the little lines

the little curves over the angles are congruent as well

Answer:

The Answer is y=5.

Step-by-step explanation:

Firstly, multiply what is outside of the parentheses into the parentheses.

2(40-5y)=10y+5(1-y) --> 80-10y=10y+5-5y

Combine like terms

80-10y=5y+5

Add 10y

80=15y+5

Subtract 5

75=15y

Divide by 15

y=5

The solution to the equation is 5.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

2(40-5y)=10y+5(1-y)

Now, solving

80 - 10y = 10y + 5 - 5y

80 - 5 = 10y - 5y + 10y

75 = 20y- 5y

75 = 15y

y= 75/15

y= 5

Hence, the solution is 5.

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Answer: DE = CE

Step-by-step explanation: AB is a continuous line so the distance from A to E could be different than the distance from D to E.

DE = CE is true.

A perpendicular bisector is a line that divides another line into two equal parts and is also perpendicular to it.

Here, we are given that AB is the perpendicular bisector of DC and DC is a perpendicular bisector of AB.

This means that AB and DC are the perpendicular bisectors of each other at the point of intersection, that is, E.

Now, since AB bisects DC at point E

⇒ DE = CE

and similarly, DC bisects AB

⇒ AE = BE

Apart from these two equalities, we cannot infer anything else from the given information.

Thus, out of the given options, we can see that only option 3, that is, DE = CE is true.

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Answer:

1 : 5

Step-by-step explanation:

Circles + Triangles = Total shapes

8 + 2 = 10

Number of triangles : Total shapes

2 : 10

Both can be divided(simplified) by 2

= 1 : 5

Hope this helped! ^^

Step-by-step explanation:

Technically what you have to do is find what changed in the table charts

find the difference between the output values

find the difference between the input values

then calculate the ratio between the change in the Y and X values

To solve this problem we need to be aware of the concepts of angles in a circle. Also we need to know what is a major angle and what is a minor angle.

That major part of an angle is equal to (360-minor part of the angle).

We know the total angle in a circle is 360°.

Here, ∠SKL=120+2x; ∠JKS=28° and ∠JKL=x+148.

Sum of all the angles will give us 360°.

According to question,

  ∠SKL+∠JKS+∠JKL=360°

⇒(120+2x)°+28°+(x+148)°=360°

⇒3x+296°=360°

⇒3x=360°-296°

⇒x=[tex]\frac{64}{3}[/tex]

∴ x=21.3

Hence, the value of x is 21.3 in the given problem.

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Answer:

15. x<-2 or x>1

16. -5<=x<=-1

17. -0.5<=x<0.25

18. x<=-1.2 or x>=-0.4

Step-by-step explanation:

The smaller number is 1389. We get this by using the technique of subtracting the bigger from the smaller number and equate it to the difference product.

Given the difference between two numbers is 2811.

The bigger number is 4200.

The smaller number is = ?

let the smaller number be 'x'

as the statement says difference between two numbers = 2811

Subtract the largest number from the smallest number to determine the difference between two integers. This sum is a product, and the difference between the two values is the product.

⇒ bigger number ₋ smaller number = 2811

⇒ 4200 ₋ x = 2811

⇒ ₋ x = 2811 ₋ 4200

⇒ ₋ x = ₋ 1389

cancel the negative sign from both sides.

x = 1389

hence we get the smaller number as 1389.

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The ordered pairs are;

A (2, 4)

B ( -1, 2 ) ,

C (-3, -2) ,

D (2, 0) ,

E ( 0, -4 )

F ( 5, -4 )

What is Coordinate?

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

Now, To find ordered pairs we can count the number of intervals on horizontal and vertical lines.

Horizontal line gives the coordinate of x - axis and vertical line gives the coordinate of y - axis.

So, To find ordered pairs as;

We start at the origin ( where the axis cross).

The point A move 2 units to the right and 4 units up.

So, The ordered pair of A is;

⇒ A (2, 4)

The point B move 1 units to the left and 2 units up.

So, The ordered pair of B is;

B ( -1, 2 ) ,

The point C move 3 units to the left and 2 units down.

So, The ordered pair of C is;

C (-3, -2) ,

The point D move 2 units to the right and on x - axis.

So, The ordered pair of D is;

D (2, 0) ,

The point E on y- axis and move 4 down.

So, The ordered pair of E is;

E ( 0, -4 )

The point F move 5 units to the right and 4 units down.

So, The ordered pair of F is;

F ( 5, -4 )

Therefore, The ordered pairs are;

A = (2, 4)

B = ( -1, 2 ) ,

C = (-3, -2) ,

D = (2, 0) ,

E = ( 0, -4 )

F = ( 5, -4 )

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Answer:

(7.5, -2)

Step-by-step explanation:

Label the coordinates(x₁,y₁) and (x₂,y₂)

Input the values into the formula  (x₁ + x₂)/2, (y₁ + y₂)/2

Add the values in the parentheses and divide each result by 2

The equation of a line is y = [tex]\frac{-x}{5}[/tex] ± √2.

Given Line : 5x - y = 1

slope of line = [tex]\frac{-5}{-1}[/tex] = 5

product of slopes of two perpendicular lines is - 1.

m₁ × 5 = -1

slope of required line m₁ = [tex]\frac{-1}{5}[/tex]

Let the equation of the required line be

y = mx + c where m is slope

y = [tex]\frac{-x}{5}[/tex] + c

Area of the triangle formed by a line with intercepts a,b = [tex]\frac{1}{2} ab[/tex]

Here, x-intercept = 5c

y-intercept = c

Area of triangle = [tex]\frac{1}{2} (5c)(c)[/tex]

                          =[tex]\frac{5c^{2} }{2}[/tex]

Given area = 5

⇒ [tex]\frac{5c^{2} }{2}[/tex] = 5

⇒ c² = 2

⇒ c = ±√2

Hence, The equation of a line is y = [tex]\frac{-x}{5}[/tex] ± √2.

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Answer:

27.5 years old

Step-by-step explanation:

We are given the formula: [tex]P=0.006A^{2} -0.02A+120[/tex] relating a patient's pressure to age.

We are also given the value for pressure (P) as 124 mmHg and need to find age (A). In order to do this, we can substitute the value 124 for P in the equation and solve the quadratic equation to obtain A:

[tex]124=0.006A^{2} -0.02A+120[/tex]

1. Set equation to 0 by subtracting 124 from both sides:

[tex]124-124=0.006A^{2} -0.02A+120-124\\= > 0.006A^{2} -0.02A-4=0[/tex]

2. Solve equation using a calculator:

It should give the solutions: [tex]A= 27.54, -24.2[/tex]

It doesn't really make sense for someone's age to be negative, therefore we can accept the positive solution as our answer.

The man whose normal blood pressure measures 124 mmHg is 27.5 years old.

Hope this helped!

Answer:

5.83

Step-by-step explanation:

You just divide the total amount by 3

Answer:

Each will pay $5.83

Step-by-step explanation:

450c > 900 + 250c;

For business to be profitable;

Selling price of daycare services > Cost price;

Payment for daycare of 1 child =  $450

Payment for daycare of 'c' children = $450 × c;

                                                       = $450c;

Operating cost for 1 child = $250;

Operating cost for 'c' children = $250c;

Total daily operating cost = $900 + $250c;

Therefore;

450c > 900 + 250c;

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hi  

2* 5/8  =   10/8  =  5*2 /4*2 = 5/4

and  2*1/4 =  1/2

so :   2*5/8   /  2/4   =    5/4   / 1/2  =  5/4 * 2/1  =   5*2 / 2*2*1 =  5/2

Answer:

[tex]=1\frac{1}{6}[/tex] or 7/6

Step-by-step explanation:

[tex]=\frac{21}{8}\div \frac{9}{4}[/tex] <- Convert to improper fraction
[tex]=\frac{21}{8}\times \frac{4}{9}[/tex] <- Fraction Rule
[tex]=\frac{84}{72}[/tex]
[tex]=\frac{7}{6}[/tex]
[tex]=1\frac{1}{6}[/tex]

Answer:

-6.23 is the answer

Answer:

-6.23

Step-by-step explanation:

The solution will be,

→ 2.67 + (−8.9)

→ 2.67 - 8.9

→ -6.23

So, the answer is -6.23.

Answer:

12 ×13.5 y 13.5

Step-by-step explanation:

es igual a 400

Answer:

y=4x

Step-by-step explanation:

Answer:

x · 0.28 = 13.44

Equation: X multiplied by 0.28 = 13.44.

How to solve: Divide 13.44 ÷ 0.28 = 48.

Multiply to check. 48 x 0.28 = 13.44.

Give me a crown.

The number predicted is 98765 and using calculator gives 888888 which confirms it is correct.

Given data

9*9+7=88

98*9+6=888

987*9+5=8888

9876*9+4=88888

Using inductive reasoning and the given data as the premise we can see that the number multiplying 9 is gotten by adding a new digit which is a lesser digit of the preceding number while counting backwards.

Using the last  operation as instance we have that

9876*9+4=88888

the last digit that joined is 6, and this number is the next digit after 7 while counting backwards. Also the number 4 added is the next after 5 while counting backwards.

so we can predict the next row by counting backwards in the two occasions as follows:

counting backwards after 6 is 5 therefore we have 98765

counting backwards after 4 is 3 therefore we have 3

arranging the numbers into row gives

98765 * 9 + 3

adding with a calculator gives

98765 * 9 + 3 = 888888

The number predicted is 98765

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Answer:

the nearest thousand is 63000