Jim lives three miles east of State College. At noon, he leaves his house and begins to walk due east at a constant speed of 2 miles per hour. Annie lives four miles north of State College. At noon, she leaves her house and begins to bicycle due north at a constant speed of 8 miles per hour. Calculate the rate at which the distance between the two people is changing when it is 1 p.m.

Answer:

2.3km in meters is 2300 Meters

Step-by-step explanation:

Multiply the length value by 1000

Answer:

your answer would be 6

Step-by-step explanation:

hope this helps

Answer:

b^2-4ac, the value of the discriminant is 4

Step-by-step explanation:

The part b^2-4ac called the discriminant will tell you how many solutions a particular equation has, after plugging in the values you can tell how many solutions and what type of solutions that equation has by looking at whether the result is positive and a perfect square, positive, zero, or negative.  If the result is a positive perfect square, there will be two rational solutions; if the result is positive there will be two real zeros; if the result is zero, there is one real zero; if the result is negative, there will be two complex conjugates or imaginary terms.

To find the value of the discriminant plug in the values of the equation.

6^2-4(4)(2)=4

The value of the discriminant in this particular equation is a perfect square, that means that there are two rational solutions.  Put simply, this equation is factorable.

4x^2 + 6x + 2 = 0

(x+1)(4x+2)=0

x=-1 or -1/2

Answer:

The above explanation was correct.

To make it clear, just type 4 as the answer

Answer:

(x+2) + x + (x+4) = 2(1/2) + 2(x+3)

Step-by-step explanation:

They are equal to each other and the rectangle has 2x more perimeter

The triangle would be divided in half from that rectangle.

Sorry If this is confusing I am not very good at explaining things.

Answer:

If you can draw one straight line through a polygon and cross more than two sides, the polygon is concave - A.

Answer:

0.089: eighty-nine thousandths, 3.71: three and 71 hundredths, 0.3: three tenths, 13.701: thirteen and 701 thousandths, 5.005: five and five thousandths

Step-by-step explanation:

The first place back is the tenths place (0.0), the second is the hundredths place (0.00), the third place is the thousandths (0.000).

Answer:

4

Step-by-step explanation:

An exterior angle of a triangle is equal to the sum of the opposite interior angles. For more on this see Triangle external angle theorem. If the equivalent angle is taken at each vertex, the exterior angles always add to 360° In fact, this is true for any convex polygon, not just triangles.

The exterior angle of the triangle [tex]\Delta LMN[/tex] is [tex]\angle 4[/tex] that is [tex]\angle N[/tex] which is the adjacent to [tex]\angle LNM[/tex].

Given that in the triangle [tex]\Delta LMN[/tex] marked with angles:
[tex]\angle MLN = \angle1\\\angle LMN = \angle2\\\angle LNM = \angle3[/tex]

And in the triangle, MN  is extended to some point marked with angle [tex]\angle 4[/tex].

To find angle is an exterior angle of the triangle by using the definition of exterior angle:

Definition of exterior angle:

The exterior angle of the triangle is formed by extending one of its sides.

In the triangle, MN  is extended to some point marked with angle [tex]\angle 4[/tex].

By using the definition implies:

exterior angle  = [tex]\angle 4[/tex]

Therefore, the exterior angle of the triangle [tex]\Delta LMN[/tex] is [tex]\angle 4[/tex] that is [tex]\angle N[/tex] which is the adjacent to [tex]\angle LNM[/tex].

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Answer: 1. 3 can be made  2. i believe it is only one way to put three books on a shelf 3. 3 i believe, its been awhile since i studied this

Step-by-step explanation:

[tex]\bf \begin{cases} 3x+6y=21\\ \cline{1-1} -8x+y=63\\ \boxed{y}=63+8x \end{cases}~\hspace{7em}\stackrel{\textit{substituting on the 1st equation}}{3x+6\left( \boxed{63+8x} \right)}=21[/tex]

[tex]\bf 3x+378+48x=21\implies 51x+378=21\implies 51x=-357 \\\\\\ x=\cfrac{-357}{51}\implies \blacktriangleright x=-7 \blacktriangleleft \\\\\\ \stackrel{\textit{since we know that}}{y=63+8x\implies }y=63+8(-7)\implies y=63-56\implies \blacktriangleright y=7 \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (-7,7)~\hfill[/tex]

Answer:

Answer choice 4

Step-by-step explanation:

Since alternate interior angles create congruent angles, angle 5 and 3 are congruent as well as 4 and 2, and since the only option that has these statements is answer choice 4, it is the correct answer.

Answer:

it is d

Step-by-step explanation:

For this case we must find the quotient of the following expression:

[tex]\frac {2196} {12}[/tex]

According to the attached figure, we must build a quotient that, when multiplied by the divisor, cancels the terms of the dividend, until we reach the remainder. In this case the division is exact and the quotient is 183.

Answer:

See attached image

The equation of a circle is written as (x-h)^2 + (y-k)^2 = r^2

where h and k is the center point and r is the radius.

Using the center point and radius given the equation becomes:

(x-4)^2 + (y+3)^2 = 3^2 or (x-4)^2 + (y+3)^2 = 9

Answer:

46°

Step-by-step explanation:

BE is the bisector so abe is the same as ebc

2x+20=4x-6

26=2x

13=x

so now plug x back into abe to find its measure

2(13)+20

26+20

46

The answer is 46°.

BE is the bisector so abe is the same as ebc

2x+20=4x-6

26=2x

13=x

So now plug x back into abe to find its measure

2(13)+20

26+20

46

Bisecting a line is cutting a line exactly in half. It may also be referred to as constructing a perpendicular bisector as the line you are drawing will be at a right angle to the original line. You will need a compass, pencil, and ruler.

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Answer:

it should be 3.3

Step-by-step explanation:

I did it with friend

Answer:

C) 3.3

Step-by-step explanation:

this is the correct answer on ed-genuity, hope this helps! :)

Answer:

y = - 6x - 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 6x + 2 ← is in this form with slope m = - 6

• Parallel lines have equal slopes, hence

y = - 6x + c ← is the partial equation of the parallel line.

To find c substitute (- 1, 2) into the partial equation

2 = 6 + c ⇒ c = 2 - 6 = - 4

y = - 6x - 4 ← equation of parallel line

Answer:

[tex]\large\boxed{m=\dfrac{y-b}{x}}[/tex]

Step-by-step explanation:

[tex]y=mx+b\to mx+b=y\qquad\text{subtract}\ b\ \text{from both sides}\\\\mx+b-b=y-b\\\\mx=y-b\qquad\text{divide both sides by}\ x\neq0\\\\\dfrac{mx}{x}=\dfrac{y-b}{x}\\\\m=\dfrac{y-b}{x}[/tex]

Answer: [tex]m=\frac{y-b}{x}[/tex]

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope of the line and "b" is the y-intercept.

Then, to solve for the slope "m", you can follow these steps:

- You need to subtract "b" from both sides of the equation:

[tex]y-b=mx+b-b\\\\y-b=mx[/tex]

- Finally, you can divide both sides of the equation by "x". Then:

[tex]\frac{y-b}{x}=\frac{mx}{x}\\\\m=\frac{y-b}{x}[/tex]

Answer:

B. y + 2 = ½(x + 3)

Step-by-step explanation:

Insert the coordinates into the formula with their CORRECT signs. Remember, in the Point-Slope Formula [y - y₁ = m(x - x₁)], all the negative symbols give the OPPOSITE terms of what they really are, which is the reason why you see two "+" in the equation. The ordered pair of [-3, -2] has two negative numbers, therefore you need to make them both positive in the equation [see above answer].

I am joyous to assist you anytime.

Answer:

(x+5)(x-1)(x+1)

Step-by-step explanation:

Let's attempt factoring by grouping:

So what this means we first want to group the first two terms together and second two terms together, like so:

(x^3+5x^2)+(-x-5)

Now we factor what we can from each pair:

x^2(x+5)+1(-x-5)

Notice x+5 doesn't appear to be the same as -x-5 so we should factor out -1 instead of 1 in the second pair of terms:

x^2(x+5)-1(x+5)

You have two terms: x^2(x+5) and -1(x+5); they have a common factor of (x+5) so we can factor it out:

(x+5)(x^2-1)

You can actually factor this more because x^2-1 is a difference of squares.

The formula for factoring a difference of squares is u^2-v^2=(u-v)(u+v).

So the factored form of x^2-1 is (x-1)(x+1).

So the complete factored form of our expression we had initially is

(x+5)(x-1)(x+1).

Answer:

[tex]\large\boxed{x^3+5x^2-x-5=(x+5)(x-1)(x+1)}[/tex]

Step-by-step explanation:

[tex]x^3+5x^2-x-5\qquad\text{distributive}\\\\=x^2(x+5)-1(x+5)\\\\=(x+5)(x^2-1)\\\\=(x+5)(x^2-1^2)\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=(x+5)(x-1)(x+1)[/tex]

Answer:

D:  (9, 23)

Step-by-step explanation:

Substitute the given value, 9, for x in y = 3x - 4.  We get:

y = 3(9) - 4, or y = 23.  Thus, the solution is (9, 23) (Answer D)

D. (9, 23) is the required ordered pair.

Substitution method is a mathematical method in which we have to pick one variable from one equation and substitute it to another equation.

Given equations are,

y = 3x - 4  .....(1)  &  x = 9   .....(2)

By using substitution method,

We have to put the value of x of (2) in (1),

i.e. we have to put x = 9 in (1),

∴ y = (3×9) - 4

     = 27 - 4

     = 23

So, the required ordered pair is (9, 23)

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Answer: $3.75

Step-by-step explanation

(This may not be the way teachers see it)

So take the $1.50 and multiply it by two and you get $3 for four hours

Then you would take the $0.75 and add it to the $3 to get $3.75

(would it be 0.75 for 15 min?)

Answer:

n = 2 + 2√3 and n = 2 - 2√3

Step-by-step explanation:

Let the number be n.

Then n² + 1 = 4n.

Rearranging this in proper quadratic format:

n² - 4n + 1

Here the coefficients are a = 1, b = -4 and c = 1.

Then the discriminant is b²-4ac, or (-4)²-4(1)(1) ), or 16 - 4, or 12.

By applying the quadratic formula, we find that the roots are:

      - (-4) ± √12

n = ------------------

              2

or n = 2 + 2√3 and n = 2 - 2√3

Answer:

3.732 or 0.268 to the nearest thousandth.

Exact values are 2 + √12/2  or 2 - √12/2.

Step-by-step explanation:

Let the original number be x, then:

x^2 + 1 = 4x

x^2 - 4x + 1 = 0

x = [-(-4) +/- sqrt(16 - 4*1*1]) / 2

x =  (4 + sqrt12)/ 2  , (4 - sqrt12) / 2

= 3.732, 0.268.

Answer:

The triangle with vertices A (2 , 0) , B (3 , 2) , C (5 , 1) is isosceles right Δ

The triangle with vertices A (-3 , 1) , B (-3 , 4) , C (-1 , 1) is right Δ

The triangle with vertices A (-5 , 2) , B (-4 , 4) , C (-2 , 2) is acute scalene Δ

The triangle with vertices A (-4 , 2) , B (-2 , 4) , C (-1 , 4) is obtuse scalene Δ

Step-by-step explanation:

* Lets explain the relation between the sides and the angles in

 a triangle

- The types of the triangles according the length of its sides:

# Equilateral triangle; all its sides are equal in length and all the angles

  have measures 60°

# Isosceles triangle; tow sides equal in lengths and the 2 angles not

  included between them are equal in measures

# Scalene triangles; all sides are different in lengths and all angles

  are different in measures

- The types of the triangles according the measure of its angles:

# Acute triangle; its three angles are acute and the relation between

  its sides is the sum of the squares of the two shortest sides is

  greater than the square of the longest side

# Obtuse triangle; one angle is obtuse and the other 2 angles are

  acute and the relation between its sides is the sum of the squares

  of the two shortest sides is smaller than the square of the longest

  side

# Right triangle; one angle is right and he other 2 angles are

  acute and the relation between its sides is the sum of the squares

  of the two shortest sides is equal to the square of the longest side

- The distance between the points 9x1 , y1) and (x2 , y2) is

  [tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]

* Lets solve the problem

# The triangle with vertices A (2 , 0) , B (3 , 2) , C (5 , 1)

∵ [tex]AB=\sqrt{(3-2)^{2}+(2-0)^{2}}=\sqrt{1+4}=\sqrt{5}[/tex]

∵ [tex]BC=\sqrt{(5-3)^{2}+(1-2)^{2}}=\sqrt{4+1}=\sqrt{5}[/tex]

∵ [tex]AC=\sqrt{(5-2)^{2}+(1-0)^{2}}=\sqrt{9+1}=\sqrt{10}[/tex]

- Lets check the relation between the sides

∵ AB = BC = √5 ⇒ shortest sides

∵ AC = √10

∵ (AB)² + (BC)² = (√5)² + (√5)² = 5 + 5 = 10

∵ (AC)² = (√10)² = 10

∴ The sum of the squares of the shortest sides is equal to the square

  of the longest side

∴ Δ ABC is right triangle

∵ Δ ABC has two equal sides

∴ Δ ABC is isosceles right triangle

# The triangle with vertices A (-3 , 1) , B (-3 , 4) , C (-1 , 1)

∵ [tex]AB=\sqrt{(-3--3)^{2}+(4-1)^{2}}=\sqrt{0+9}=3[/tex]

∵ [tex]BC=\sqrt{(-1--3)^{2}+(1-4)^{2}}=\sqrt{4+9}=\sqrt{13}[/tex]

∵ [tex]AC=\sqrt{(-1--3)^{2}+(1-1)^{2}}=\sqrt{4+0}=2[/tex]

- Lets check the relation between the sides

∵ AB = 3

∵ BC = √13 ⇒ longest sides

∵ AC = 2

∵ (AB)² + (AC)² = (3)² + (2)² = 9 + 4 = 13

∵ (BC)² = (√13)² = 13

∴ The sum of the squares of the shortest sides is equal to the square

  of the longest side

∴ Δ ABC is right triangle

∴ Δ ABC is right triangle

# The triangle with vertices A (-5 , 2) , B (-4 , 4) , C (-2 , 2)

∵ [tex]AB=\sqrt{(-4--5)^{2}+(4-2)^{2}}=\sqrt{1+4}=\sqrt{5}[/tex]

∵ [tex]BC=\sqrt{(-2--4)^{2}+(2-4)^{2} }=\sqrt{4+4}=\sqrt{8}[/tex]

∵ [tex]AC=\sqrt{(-2--5)^{2}+(2-2)^{2}}=\sqrt{9+0}=3[/tex]

- Lets check the relation between the sides

∵ AB = √5

∵ BC = √8

∵ AC = 3 ⇒ longest sides

∵ (AB)² + (BC)² = (√5)² + (√8)² = 5 + 8 = 13

∵ (AC)² = (3)² = 9

∴ The sum of the squares of the shortest sides is greater than the

   square of the longest side

∴ Δ ABC is acute triangle

∵ Δ ABC has three different sides in lengths

∴ Δ ABC is acute scalene triangle

# The triangle with vertices A (-4 , 2) , B (-2 , 4) , C (-1 , 4)

∵ [tex]AB=\sqrt{(-2--4)^{2}+(4-2)^{2}}=\sqrt{4+4}=\sqrt{8}[/tex]

∵ [tex]BC=\sqrt{(-1--2)^{2}+(4-4)^{2} }=\sqrt{1+0}=1[/tex]

∵ [tex]AC=\sqrt{(-1--4)^{2}+(4-2)^{2}}=\sqrt{9+4}=\sqrt{13}[/tex]

- Lets check the relation between the sides

∵ AB = √8

∵ BC = 1

∵ AC = √13 ⇒ longest sides

∵ (AB)² + (BC)² = (√8)² + (1)² = 8 + 1 = 9

∵ (AC)² = (√13)² = 13

∴ The sum of the squares of the shortest sides is smaller than the

   square of the longest side

∴ Δ ABC is obtuse triangle

∵ Δ ABC has three different sides in lengths

∴ Δ ABC is obtuse scalene triangle

Where the above is given,
The triangle with vertices A (2 , 0) , B (3 , 2) , C (5 , 1) is isosceles right Δ

The triangle with vertices A (-3 , 1) , B (-3 , 4) , C (-1 , 1) is right Δ

The triangle with vertices A (-5 , 2) , B (-4 , 4) , C (-2 , 2) is acute scalene Δ

The triangle with vertices A (-4 , 2) , B (-2 , 4) , C (-1 , 4) is obtuse scalene Δ

Here is the definition of all the Triangles according to their respective sides:

Triangle classification based on angle measurement:

To determined the kind of triangles we are given from the above information, we use the distance formula:

The distance from (x₁, y₁) and (x₂, y₂)

[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]

The triangle with vertices A (2 , 0) , B (3 , 2) , C (5 , 1)

AB  [tex]= \sqrt{(-3- -3)^2 + (4 - 1)^2[/tex]

= √(0+9)

= 3

BC [tex]= \sqrt{(-1- -3)^2 + (1 - 4)^2[/tex]

= √(4+9)

= √13

AC  [tex]= \sqrt{(-1- -3)^2 + (1 - 1)^2[/tex]

AC = √(4+0)

= 2

- Lets evaluate the relation between the respective sides

AB = 3

BC = √13 ⇒ longest sides

AC = 2

(AB)² + (AC)² = (3)² + (2)² = 9 + 4 = 13

(BC)² = (√13)² = 13

The sum of the squares of the shortest sides is equal to the square of the longest side

Δ ABC is right triangle

Δ ABC is right triangle

The triangle with vertices A (-5 , 2) , B (-4 , 4) , C (-2 , 2)
AB = √[(-4- -5)² + (4-2)²]

= √(1+4)

= √5

BC = √[(-2- -1)² +(2-4)²

= √(4+4)

= √8

AC = √[(-2- -5)² +(2-2)²
=  √(9+0)

= 3

Checking the relation between the sides we know that

AB = √5

BC = √8

AC = 3 ⇒ longest sides

(AB)² + (BC)² = (√5)² + (√8)² = 5 + 8 = 13

(AC)² = (3)² = 9

Hence, the sum of the squares of the shortest sides is greater than the square of the longest side

Δ ABC is acute triangle

Δ ABC has three different sides in lengths

Δ ABC is acute scalene triangle



The triangle with vertices A (-4 , 2) , B (-2 , 4) , C (-1 , 4)

AB = √[(-2- -4)² + (4-2)²]
= √(4+4)
= √8

BC = √[(-1- -2)² + (4-4)²]
= √(1+0)
= 1

AC = √[(-1- -4)² + (4-2)²]

= √(9+4)
= √13


Thus, - checking the relation between the sides

AB = √8

BC = 1

AC = √13 ⇒ longest sides

(AB)² + (BC)² = (√8)² + (1)² = 8 + 1 = 9

(AC)² = (√13)² = 13

The sum of the squares of the shortest sides is smaller than the square of the longest side

Δ ABC is obtuse triangle

Δ ABC has three different sides in lengths

Δ ABC is obtuse scalene triangle


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Answer:

Area = 16

Step-by-step explanation:

The plan is to find the area of the large triangle (blue and white together) and subtract the white triangle's area.

Area of blue + white.

h = 8

b = 5 + 4

b = 9

Area = 1/2 * 8 * 9

Area = 1/2 * 72

Area = 36

===============

Area of white.

h = 8

b = 5

Area = 1/2 * 8 * 5

Area = 20

==============

Area of the shaded region (blue) = Area of both triangles - Area of the white

Shaded = 36 - 20

Shaded = 16

Answer:

The required expression is f = 3+6t

Step-by-step explanation:

Let t represent number of tens

Let f represent number of fives

So, the expression for number of fives can be formed by using:

The number of fives is 3 more than six times the number of tens.

f = 3+6t

So, the required expression is f = 3+6t

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

(x₁, y₁) - point on a line

We have the slope m = -5, and the point (2, 6).

Substitute:

[tex]y-6=-5(x-2)[/tex]

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

Convert:

[tex]y-6=-5(x-2)[/tex]           use the distributive property a(b + c) = ab + ac

[tex]y-6=-5x+(-5)(-2)[/tex]

[tex]y-6=-5x+10[/tex]            add 6 to both sides

[tex]y=-5x+16[/tex]

The standard form of an equation of a line:

[tex]Ax+By=C[/tex]

Convert:

[tex]y=-5x+16[/tex]            add 5x to both sides

[tex]5x+y=16[/tex]

Answer:

[tex]f(x)=a(x-h)^2+k[/tex]

Vertex form.

Step-by-step explanation:

You are talking about the vertex form for a parabola.

[tex]f(x)=a(x-h)^2+k[/tex] tells us:

A) The vertex is (h,k).

B) Open up (if a is positive) or open down (if a is negative)

C) a also tells us how much it is vertically stretched or compressed.

Answer:

See below.

Step-by-step explanation:

That is a one-to-one function.

Answer: One-to-One function.

Step-by-step explanation:

A One-to-One function (also written as 1-1) is that function for which every element of the Range corresponds to one and only one element of the Domain.

 Given a Set A (Domain of a function) and a Set B (Range of the function), if [tex]If\ f(a) = f (b),\ then\ a = b[/tex] and it is a One-to-One function.

Given the graph of a function, you can determine if it is a One-to-One function if it passes the Horizontal Line Test.

The conclusion is:  A function in which each y-value has only one corresponding x-value is called a One-to-One function.

Answer:

i

Step-by-step explanation:

The square root of -1 is i which is an imaginary number

According to Side Angle Side theorem the correct option is d)

[tex]\rm \dfrac{AC}{GI}=\dfrac{BC}{HI}[/tex]

According to SAS theorem:

From the given triangles we can see that,

[tex]\rm \dfrac{AC}{BC}=\dfrac{GI}{HI}[/tex]      ----       (according to SAS theorem)

Therefore, the correct option is D).

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Answer:

D !!!!!

Step-by-step explanation:

According to Side Angle Side theorem the correct option is d

AC / GI = BC / HI

-edge did the test

An expression for the given statement is (x²/3)+4.

The given statement is 4 more than the quotient of x squared and 3.

We need to find an expression for the given statement.

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be addition, subtraction, multiplication, or division.

The terms involved in an expression in math are:

Constant: A constant is a fixed numerical value.

Variable: A variable is a symbol that doesn't have a fixed value.

According to the question, we get (x²/3)+4.

Therefore, an expression for the given statement is (x²/3)+4.

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