Which geometric figures are drawn on the diagram? Check all that apply. Line segment C A Ray A C ∠ABC Circle C Ray B E ∠BCE Line segment A E

Statement 1: [tex]\angle 2[/tex] and [tex]\angle 4[/tex] are vertical angles

Reason 1: Given

We basically just restate the given information word for word. This is true of any two column proof.

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Statement 2:  [tex]m \angle 2 + m \angle 3 = 180[/tex]

Reason 2: [tex]\angle 2[/tex] and [tex]\angle 3[/tex] are a linear pair

The term "linear pair" means the angles are adjacent and supplementary (they form a straight line), so this is why the two angles add to 180.

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Statement 3: [tex]m \angle 3 + m \angle 4 = 180[/tex]

Reason 3: [tex]\angle 3[/tex] and [tex]\angle 4[/tex] are a linear pair

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Statement 4: [tex]m \angle 2 + m \angle 3 = m \angle 3 + m \angle 4[/tex]

Reason 4: Substitution

Each of the equations formed in statements 2 and 3 above have 180 on the right side, so the left hand sides must be the same

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Statement 5: [tex]m \angle 2 = m \angle 4[/tex]

Reason 5: Subtraction property of equality

We subtracted the quantity [tex]m \angle 3[/tex] from both sides (they go away)

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Statement 6: [tex]\angle 2 \cong \angle 4[/tex]

Reason 6: Definition of congruence

If two items are congruent, then they have the same measure. In other words, they are the same.

The proof of  [tex]\angle 2 \ and \ \angle4[/tex] are vertical angles is explained below.

Given, [tex]\angle 2 \ and \ \angle4[/tex] are vertical angles as shown in fig.

We know that, Vertical angles are formed when two straight lines intersect at a point.Vertical angles are two angles which are vertically opposite and have the same measure. So, the two angles are to be congruent.

We have to prove that angle 2 and angle 4 congruent.

Given [tex]\angle 2 \ and\ \angle 3[/tex] makes linear pair so,  

[tex]\angle 2+\angle 3= 180[/tex]

[tex]\angle 3 =180-\angle 2[/tex]..........(1)

Again [tex]\angle 3 \ and \ \angle 4[/tex] makes linear pair so,

[tex]\angle 3+\angle 4= 180[/tex]

[tex]\angle 3 =180-\angle 4[/tex].......(2)

From (1) and (2) we get,

[tex]180-\angle 2=180-\angle 4[/tex]

Subtracting 180 from both the sides we get,

[tex]-\angle 2=-\angle 4[/tex]

Or, [tex]\angle 2=\angle 4[/tex]

Hence angle 2 and angle 4 are congruent.

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Answer:

z = 27

Step-by-step explanation:

Given that z² is proportional to x³ then the equation relating them is

z² = kx³ ← k is the constant of proportion

To find k use the condition z = 8 when x = 4, thus

8² = k × 4³

64 = 64k ( divide both sides by 64 )

k = 1

z² = x³ ← equation of proportion

When x = 9, then

z² = 9³ = 729 ( take the square root of both sides )

z = [tex]\sqrt{729}[/tex] = 27

Answer:

14

Step-by-step explanation:

You have the values for the hypotenuse (50) and one of the sides (48).  You now have to find the second side using the Pythagorean Theorem.

a² + b² = c²

(48)² + b² = (50)²

2304 + b² = 2500

b² = 196

b = √196

b = 14

Answer:

The vertex is ( -4,1)

Step-by-step explanation:

The equation for a parabola can be written as

y = a( x-h)^2 +k  where ( h,k) is the vertex

y = 2 (x + 4)² + 1

Rewriting

y = 2 (x -  -4)² + 1

The vertex is ( -4,1)

Answer:

the vertex is located at (-4, 1)

Step-by-step explanation:

The vertex equation of a vertical parabola is

y = a(x - h)^2 + k

where (h, k) is the vertex.  

Comparing this to the given

y = 2(x + 4)² + 1, we see that the vertex is located at (-4, 1) and that the graph is stretched vertically by a factor of 2.

Answer:

B

Step-by-step explanation:

The clock at six o clock form a line:

         12

           |

9         |           3

           |

          6

Answer:

- 7 - i

Step-by-step explanation:

Given

(- 10 - 2i) + (3 + i) ← remove parenthesis

= - 10 - 2i + 3 + i ← collect like terms

= - 7 - i

Hi there! :)

Answer:

[tex]\huge\boxed{L = 9 \text { units}}[/tex]

Given:

Perimeter = 28

Let the breadth = x. The length is 4 units greater, so we can represent this as (x + 4).

Set up an expression. Remember that the formula for the perimeter of a rectangle is:

P = 2(l) + 2(w)

Substitute:

28 = 2(x) + 2(x+ 4)

Distribute:

28 = 2x + 2x + 8

Combine like terms and simplify:

28 = 4x + 8

20 = 4x

x = 5.

The length of the breadth is 5 units. Substitute in 5 to solve for the length:

(5) + 4 = 9 units.

The length of the rectangle is 9 units.

Answer:

ummm

Step-by-step explanation:

look it up

I'm helping you look it up right now

il comment when I find ... ok?

Answer:

(-1, 3, 1)

x=-1, y=3, z=1.

Step-by-step explanation:

So we have the three equations:

[tex]3x+2y-z=2\\2y+z=7\\-2x-4z=-2[/tex]

And we want to find the value of each variable.

To do so, look at the equations and try to think about what we can do to isolate one of the variables by itself.

We can see that both the second and equation has a variable and then the variable z.

In other words, we can solve for y in the second equation and x in the third equation and then substitute them in the first equation to isolate the variable z and then solve for z. With that, we can then easily arrive at our solution.

Therefore, solve for y in the second equation:

[tex]2y+z=7[/tex]

Subtract z from both sides. The zs on the left side cancels:

[tex](2y+z)-z=(7)-z\\2y=7-z[/tex]

Now, divide both sides by 2. The 2s on the left cancel and we've isolated the y variable:

[tex]\frac{(2y)}{2} = \frac{(7-z)}{2}\\y=\frac{(7-z)}{2}[/tex]

Now, do the same for the third equation. Isolate the x variable:

[tex]-2x-4z=-2[/tex]

First, divide everything by -2 to make things simpler:

[tex]\frac{(-2x-4z)}{-2}=\frac{(-2)}{-2}\\ x+2z=1[/tex]

Now, subtract 2z from both sides to isolate the x variable:

[tex](x+2z)-2z=1-2z\\x=1-2z[/tex]

We have isolated the x and y variables. They are:

[tex]y=\frac{(7-z)}{2}\\x=1-2z[/tex]

Now, we can substitute them back into the first equation. Therefore:

[tex]3x+2y-z=2\\3(1-2z)+2(\frac{7-z}{2})-z=2[/tex]

Distribute the first and second terms. The second term cancels out:

[tex]3(1)-3(2z)+(7-z)-z=2\\3-6z+7-z-z=2[/tex]

Combine like terms:

[tex]-6z-z-z+3+7=2\\-8z+10=2\\[/tex]

Subtract 10 from both sides:

[tex](-8z+10)-10=2-10\\-8z=-8[/tex]

Divide both sides by -8:

[tex]z=1[/tex]

Now that we've determined that z=1, plug it back into the isolated second and third equations:

Second equation:

[tex]y=\frac{(7-z)}{2}\\y=(7-1)/2\\y=(6)/2=3[/tex]

Third equation:

[tex]x=1-2z\\x=1-2(1)\\x=1-2=-1[/tex]

Therefore, our answer is (-1, 3, 1)

Answer:

  (x, y, z) = (-1, 3, 1)

Step-by-step explanation:

Any of a number of web sites will solve systems of equations for you. Your graphing calculator will, too.

The solution is the right-most column in reduced row echelon form. Top to bottom, the variables are in order x, y, z.

  (x, y, z) = (-1, 3, 1)

_____

If you like, you can use substitution to do this by hand.

  z = 3x +2y -2 . . . . from the first equation

  2y +(3x +2y -2) = 7 . . . . substituting into the second equation

  3x +4y = 9 . . . . . in standard form

  -2x -4(3x +2y -2) = -2 . . . . substituting for z into the third equation

  14x +8y = 10 . . . . . in standard form

Subtract half the second equation from the first:

  (3x +4y) -(7x +4y) = (9) -(5)

  -4x = 4 . . . simplify

  x = -1 . . . . . divide by 4

  y = (9 -3x)/4 = (9 -3(-1))/4 = 12/4 = 3

  z = 3(-1) +2(3) -2 = 1

The solution is (x, y, z) = (-1, 3, 1).

Answer: Hi!

To solve this equation, we first distribute to the terms inside of the parentheses.

10*4 = 40

10*-3i = -30i

Our equation now looks like this:

40 - 30i

There is nothing left to simplify, so you're done!

Hope this helps!

Answer:

Step-by-step explanation:

Amount of Jeff tuition per year = $9,000

If Jeff has a scholarship that pays 70% of his tuition, the amount the scholarship will pat Jeff = 70% of his yearly tuition fee.

Scholarship amount = 70/100 * $9,000

Scholarship amount  = 70*90

Scholarship amount  = $6,300

Hence the scholarship will pay Jeff $6,300

If the amount saved by Jeff is $3,000

Total amount that Jeff has = Scholarship amount + Amount saved

Total amount that Jeff has = $6,300 + $3000 = $9300

Since the total amount that Jeff has is more than the yearly tuition fee, this shows that he has enough to pay for the first year's tuition

Answer:

x = - 7

Step-by-step explanation:

8x - 2 = -9 + 7x   (add 2 to both sides)

8x - 2 + 2 = -9 + 7x + 2

8x = 7x - 7           (subtract 7x from  both sides)

8x - 7x = 7x - 7 - 7x

x = - 7

Answer:x=-7

Step-by-step explanation:

Regroup terms.

8x-2=7x-98x−2=7x−9

2 Subtract 7x7x from both sides.

8x-2-7x=-98x−2−7x=−9

3 Simplify  8x-2-7x8x−2−7x  to  x-2x−2.

x-2=-9x−2=−9

4 Add 22 to both sides.

x=-9+2x=−9+2

5 Simplify  -9+2−9+2  to  -7−7.

x=-7x=−7

Answer:

we

Step-by-step explanation:

ee

Answer:

-577

Step-by-step explanation:

−4 − 6 + 2 + 5 + 8 − 3 (8 − 6 − 3) − (−6 − 2 − 5) (9 − 4)(−6 − 3)

Answer:

1/-30

Step-by-step explanation:

5/6/-5/6

= 5/6 x 6/-5

= 5/30 x 6/-30

= 30/-900

= 1/-30

Answer:

125

×

250

_____

000

6250

25000

answer 31250

125

⋅

250

is

31250

Answer:$31250

Step-by-step explanation: 125x250=000+6250+25000=$31250

The solution is 2 roots

The number of roots the equation will have if the value of the discriminant is 73 will be 2 roots

What is Quadratic Equation?

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

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 data ,

Let the quadratic equation be A

where A = ax² + bx + c=0

Let the discriminant of the equation be D

Now , the value of D = 73

To calculate the number of roots a quadratic equation A

We need to compute the discriminant (b² - 4ac).

If the discriminant is less than 0, then the quadratic has no real roots.

If the discriminant is equal to zero then the quadratic has equal roots.

If the discriminant is more than zero then it has 2 distinct roots.

So , the value of D > 0

Therefore , the equation has 2 roots

Hence , the number of roots of the quadratic equation is 2 roots

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Answer:

x          y

10   →   6

4    →    0

8    →    4

Step-by-step explanation:

Using the given rule, plug in any known values:

[tex]y=x-4\\\\6=x-4[/tex]

Solve for x. Add 4 to both sides of the equation to isolate the variable:

[tex]6+4=x-4+4\\\\x=10[/tex]

Repeat:

[tex]y=x-4\\\\0=x-4\\\\0+4=x-4+4\\\\x=4[/tex]

[tex]y=x-4\\\\4=x-4\\\\4+4=x-4+4\\\\x=8[/tex]

:Done

Answer:

The y-intercept is –2.

The slope is Negative three-fifths

Step-by-step explanation:

A linear function is a function whose graph is a straight line. A linear function can be represented as:

f(x) = y = a + bx

where y is the dependent variable and x is the independent variable. The equation of a linear function in slope intercept form is given as:

y = mx + c

Where m is the slope and c is the y intercept.

Given that:

[tex]y=-\frac{3}{5}x-2[/tex], and comparing with y = mx + c:

The slope (m) = [tex]-\frac{3}{5}[/tex]

The y intercept (c) = -2

Answer:

The y-intercept is –2.

The slope is Negative three-fifths

Step-by-step explanation:

Answer:

His average rate of speed for the entire trip is 10 miles/hour.

Step-by-step explanation:

We are given that John went on a bike ride to the store 4 miles away. If it took John 3/10 of an hour to get there and 1/2 of an hour to get back.

And we have to find his average rate of speed (miles per hour) for the entire trip.

As we know that the Distance-Speed-Time formula is given by;

                    [tex]\text{Speed}=\dfrac{\text{Distance}}{\text{Time}}[/tex]  

Here, the distance for the entire trip = 8 miles (4 miles for reaching store and 4 miles for returning back)

The time taken for the entire trip = [tex](\frac{3}{10} )[/tex] of an hour to reach the store and [tex](\frac{1}{2})[/tex] an hour to get back.    

So, the average rate of speed for the entire trip = [tex]\frac{\text{Total Distance}}{\text{Total Time}}[/tex]

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

                             =  [tex]\frac{8}{\frac{8}{10} }[/tex]  =  10 miles per hour

Hence, his average rate of speed for the entire trip is 10 miles/hour.

Answer:

9b+1

Step-by-step explanation:

combine like terms

7b-1b+3b=9b

Answer:

9b+1

Step-by-step explanation:

7b-b+1+3b

(7b-b+3b) +1

(7-1+3)b +1

9b+1

Answer:

The simplest form of the given expression is 7x³ + 5x² + x + 2

Step-by-step explanation:

(4x³ + 6x - 7) + (3x³ - 5x² - 5x + 9)

Group like terms together.

(4x³ + 3x³) + 5x² + (6x - 5x) + (-7 + 9)

Combine like terms.

7x³ + 5x² + x + 2

So, this will be your simplest form of the given equation.

Answer:

7x³ + 5x² + x + 2

Step-by-step explanation:

For the smaller triangle, the rise is 2 since this is the length of the vertical component. The horizontal component is 3, meaning the run is 3

Slope = rise/run

Slope = 2/3

---------------

The larger triangle leads to the same slope because

slope = rise/run

slope = 4/6

slope = (2*2)/(2*3)

slope = 2/3

Because we get the same slope value, this confirms that both triangles have their hypotenuse on the same straight line.

The two triangles are similar. The larger triangle's sides are twice as long as its smaller counterpart.

Answer:

[tex]\huge \boxed{25>23} \\ \\ \huge \boxed{25 \geq 23}[/tex]

Step-by-step explanation:

25 is greater than 23.

greater than ⇒ [tex]>[/tex]

25 is greater than or equal to 23.

greater than or equal to ⇒ [tex]\geq[/tex]

Answer:

1) [tex]25 > 23[/tex]

2) [tex]25 \geq 23[/tex]

Step-by-step explanation:

25 is greater than 23

=> [tex]25 > 23[/tex]

25 is also almost equal to 23

=> [tex]25 \geq 23[/tex]

Given that :-

To Find :-

Solution :-

→ x = 4y + 3 equation 1st

→ y = -2x -3 equation 2nd .

Now putting the value of x from first equation to second equation.

→ y = -2(4y +3 ) -3

→ y = -8y - 6 - 3

→ y + 8y = -9

→ 9y = -9

→ y = -1

Now putting the value of y in equation first .

→ x = 4(-1) + 3

→ x = -4 + 3

→ x = -1

Now multiply and X and y.

→ x.y = -1(-1)

→ x.y = 1 .

[tex]\huge {\bold {\star {\fcolorbox {black} {yellow} {Answer}}}} [/tex]

Putting the value of x in ii, we get ;

➝ y = - 2(4y+3) - 3

➝ y = - 8y - 6 - 3

➝ y = - 8y - 9

➝ y + 8y = - 9

➝ 9y = - 9

∴ y = - 1

Putting the value of y in i, we get ;

➝ x = 4y + 3

➝ x = 4(-1) + 3

➝ x = - 4 + 3

∴ x = - 1

➛ xy = (- 1)(-1)

⛬ xy = 1

Answer:

Distributive property (Reversed)

Step-by-step explanation:

With the distributive property, it is possible to simplify expressions that consist of an expression term such as (a + b) being multiplied by one singular term such as c given as follows

c ×(a + b) = c·a + c·b

Factoring, which is the reverse  use of the distributive property enables the difference or the sum of two products, each having a common factor to be the presented as the difference  or the sum of two numbers multiplied by the common factor as follows;

2·x - 2·y = 2·(x - y).

Answer:

2x (x - 4)

Step-by-step explanation:

Answer:

Perimeter = 2 x length + 2 x width

Width = x

Length = x + 71

234 = 2*(x + 71) + 2*(x)

234 = 2x + 142 + 2x

234 = 4x + 142

4x = 234 - 142

4x = 92

x = 23

Width = 23 inches

Length = 94 inches

Step-by-step explanation:

The dimensions of the rectangular carpet are 100 and 17 inches.

Given the following data:

Translating the word problem into an algebraic equation, we have;

[tex]L = W + 83[/tex]

To find the dimensions of the rectangular carpet;

Mathematically, the perimeter of a rectangle is given by the formula;

[tex]Perimeter = 2(L+W)[/tex]

Substituting the values into the formula, we have;

[tex]234 = 2(W + 83 + W)[/tex]

[tex]234 = 2(2W + 83)\\\\234 = 4W + 166\\\\4W = 234 - 166\\\\4W = 68\\\\W = \frac{68}{4}[/tex]

Width, W = 17 inches

Next, we would find the value of L;

[tex]L = W + 83[/tex]

Substituting the value of W, we have;

[tex]L = 17 + 83[/tex]

L = 100 inches.

Therefore, the dimensions of the rectangular carpet are 100 and 17 inches.

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