You travel at an average speed of 20 km/h in a straight line to get to your grandmother's house. It takes you 3 hours to get to her house. How far away is her house from where you started ?

Parabola A: directrix is at x = -1 and focus is at (2,2) so the vertex is the midpoint between those.  Vertex = (0.5, 2)

Parabola B: directrix is at x = 5 and focus is at (2,2) so the vertex is the midpoint between those.  Vertex = (3.5, 2)

Distance between Vertex A and Vertex B is the distance between (0.5, 2) and (3.5, 2) = 3

Answer: B

55a and 22b both are terms in that equation

Answer:

x intercepts   (0,0) and (3,0)

y intercept (0,0)

Step-by-step explanation:

To find out x intercepts we look at the points on the graph where it crosses or touches x axis. x axis is the horizontal line. y axis is the vertical line

The graph touches the x axis at x=0  and x=3

Always write the x intercepts as (x,0)

So our x intercepts are (0,0) and (3,0)

To find out y intercepts we look at the points on the graph where it crosses or touches y axis

the graph touches y axis at y=0

So y intercept of the graph is (0,0)

Answer:

Given : A parallelogram ABC D in which BD is the Diagonal.

 ∠ABD =1, ∠ CDB =2, ∠CBD =3, ∠ ADB =4

To prove: Opposite sides of parallelogram are congruent.

Proof : AB is parallel to DC and AD is parallel to BC Definition of parallelogram

2 angle 1 = angle 2, angle 3 = angle 4 If two parallel lines are cut by a transversal then the alternate interior angles are congruent

3 BD = BD Reflexive Property

4 triangles ADB and CBD are congruent [If two angles and the included side of a triangle are congruent to the corresponding angles and side of another triangle, then the triangles are congruent by[ ASA]

5 AB = DC,  

AD = BC Corresponding parts of congruent triangles are congruent

Out of four options given

2. ASA postulate is the correct answer

A- angle, S-side,A-angle

Answer:

ASA postulate is the answer

Answer:

1)

Given the triangle RST with Coordinates  R(2,1), S(2, -2) and T(-1 , -2).

A dilation is a transformation which produces an image that is the same shape as original one, but is different size.  

Since, the scale factor [tex]\frac{5}{3}[/tex] is greater than 1, the image is enlargement or a stretch.  

Now, draw the dilation image of the triangle RST with center (2,-2) and scale factor [tex]\frac{5}{3}[/tex]

Since, the center of dilation at S(2,-2) is not at the origin, so the point S and its image [tex]S{}'[/tex] are same.

Now, the distances from the center of the dilation at point S to the other points R and T.  

The dilation image will be[tex]\frac{5}{3}[/tex] of each of these distances,

[tex]SR=3[/tex], so [tex]S{}'R{}'[/tex]=5 ;

[tex]ST=3[/tex], so [tex]S{}'T{}'=5[/tex]  

Now, draw the image of RST i.e R'S'T'

Since, [tex]RT=3\sqrt{2}[/tex] [By using hypotenuse of right angle triangle] and [tex]R{}'T{}'=5\sqrt{2}[/tex].

2)

(a)

Disagree with the given statement.

Side Angle Side postulate (SAS) states that:

If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle then these two triangles are congruent.

Given: B is the midpoint of [tex]\overline{AC}[/tex] i.e [tex]\overline{AB}\cong \overline{BC}[/tex]

In the triangle ABD and triangle CBD, we have

[tex]\overline{AB}\cong \overline{BC}[/tex]   (SIDE)            [Given]

[tex]\overline{BD}\cong \overline{BD}[/tex]   (SIDE)            [Reflexive post]

Since, there is no included angle in these triangles.

∴ [tex]\Delta ABD[/tex] is not congruent to [tex]\Delta CBD[/tex] .

Therefore, these triangles does not follow the SAS congruence postulates.

(b)

SSS(SIDE-SIDE-SIDE) states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

Since it is also given that  [tex]\overline{AD}\cong \overline{CD}[/tex].

therefore, in the triangle ABD and triangle CBD, we have

[tex]\overline{AB}\cong \overline{BC}[/tex]   (SIDE)            [Given]

[tex]\overline{AD}\cong \overline{CD}[/tex]   (SIDE)           [Given]

[tex]\overline{BD}\cong \overline{BD}[/tex]   (SIDE)            [Reflexive post]

therefore by, SSS postulates [tex]\Delta ABD\cong \Delta CBD[/tex].

3)

Given that:  [tex]\angle1=\angle 3[/tex] are vertical angles, as they are formed by intersecting lines.

Therefore

, by the definition of linear pairs

[tex]\angle 1[/tex] and [tex]\angle 2[/tex] and [tex]\angle 3[/tex]  and [tex]\angle 2[/tex] are linear pair.

By linear pair theorem, [tex]\angle 1[/tex] and [tex]\angle 2[/tex]   are supplementary, [tex]\angle 2[/tex] and [tex]\angle 3[/tex]  are supplementary.

[tex]m\angle1+m\angle 2=180^{\circ}[/tex]

[tex]m\angle2+m\angle 3=180^{\circ}[/tex]

Equate the above expressions:

[tex]m\angle 1+m\angle 2=m\angle 2+m\angle 3[/tex]

Subtract the angle 2 from both sides in the above expressions

∴[tex]m\angle 1=m\angle 3[/tex]

By Congruent Supplement theorem: If two angles are supplements of the same angle, then the two angles are congruent.

therefore, [tex]\angle 1\cong \angle 3[/tex].

[tex]4y-8-2y+5=0\\\\(4y-2y)+(-8+5)+0\\\\2y-3=0\qquad|\text{add 3 to both sides}\\\\2y=3\qquad|\text{divide both sides by 2}\\\\y=\dfrac{3}{2}\\\\\boxed{y=1\dfrac{1}{2}}\to\boxed{c.}[/tex]

4y - 8 - 2y + 5 = 0

2y - 3 = 0

2y = 3

y = 3/2

9/16 divided by 39/8

KCF

9/16 x 8/39

Simplify

9/2 x 1/39 = 9/78 or 3/26

p^q , p-> q and ~p ^ q . all these three statements will give false when p is true and q is false

Multiply the two together.

(13/2)(11/4)

143/8

= 17 and 7/8

There are 17 and 7/8 feet in 2 and 3/4 lengths of rope.

Answer: The answer is A. s

The center of the circle shown below will be S.Option A is corect.

It is a point locus drawn equidistant from the center. The radius of the circle is the distance from the center to the circumference.

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

The equation of a circle with center (h,k) with radius r is;

[tex]\rm (x-h)^2 + (y-k)^2 = r^2[/tex]

The center of the circle is equidistant from all the points on its locus forming circumferrence.

The center of the circle shown below will be S.

Hence, option A is corect.

To learn more about the circle, refer to the link: https://brainly.com/question/11833983

#SPJ2

Answer:

90.5

Step-by-step explanation:

 0 9 0. 5 0 0

1 1 9 9 5. 5 0 0

 − 0          

   9 9        

 − 9 9        

     0 5      

   −   0      

       5 5    

     − 5 5    

         0 0  

       −   0  

           0 0

         −   0

             0

$129 x .80 = $103.20 (80% discount)

$129 (original price) - $103.20 ( 80% discounted amount) = $25.80 (sale price)

Answer: The sale price is $25.80

You want to buy something that costs $129, and it's on sale for 80% off. What is the item's sale price?

First, convert the 80% to a real mathematical number. For percent's, this is always done by dividing the 80% by 100%, or 80% / 100%    =    0.800.

Second, find out what 80% of $129 is. This is the amount of the sale discount. This is always found by multiplying 0.800 by the item's cost $129, like this:  

0.800  x    $129     =     $103.20.

So for this sale, you'll save $103.20 on this item.

This means, the cost of the item to you is

$129   -    $103.20     =   $25.80.

Before Price:    $129.00

Discount %:      80%

Answer  =====>   Sale Price:    $25.80 would be the sale price of the bicycle.

Amount Saved:    $103.20

Alternatively, you can think about it this way.

The item is 80% off. This means you'll pay 20.000% of the total cost (100%     -     80%     =     20.000%).

Now what's 20.000% of the total cost?  

0.200 x $129   =   $25.80.

Just like the result above, the sale price on the item is $25.80.

Hope that helps!!!!!!                                      : )

<7 = 62° ----alternate exterior angle

Answer is C) < 7

The correct choice is D!

Hope this helped you out! :)

Answer:

x= 1  and y = -1

Step-by-step explanation:

3x + y = 2

y+ 4 = 3x

For the following system, use the second equation to make a substitution for y in the first equation.

LEts start with second equaiton y+4 = 3x

Solve for y, subtract 4 from both sides

y = 3x- 4

Now substitute y = 3x -4 in first equation

3x + y = 2

3x + 3x -4 = 2

combine like terms

6x -4 = 2

Add 4 from both sides

6x = 6 (divide by 6)

x= 1

To solve for y we plug in x=1 in y= 3x-4 equation

y=3(1)-4= -1

so x= 1  and y = -1

[tex]|\Omega|=1+2+3+3=9\\|A|=3\\\\P(A)=\dfrac{3}{9}=\dfrac{1}{3}\approx33\%[/tex]

The probability of drawing a red marble out of the bag without looking is 1/3

Probability is the likelihood or chance that an event will occur

Probability = expected outcome/total outcome

If a bag contains 1 blue, 2 green, 3 yellow, and 3 red marbles, the total outcome will be;

Total outcome = 1 + 2 + 3 + 3 = 9 marbles

If  a red marble out of the bag without looking, the expected outcome is 3

Pr(drawing a red marble) = 3/9 = 1/3

Hence the probability of drawing a red marble out of the bag without looking is 1/3

Learn more here: https://brainly.com/question/23417919

Answer:

{x,y} = {12,5}

Step-by-step explanation:

Tiger Algebra Solver logo

The Tiger Algebra Tiger

Algebra Calculator | Latest | Discuss | About | Help | Translation

23,965,445 solved | 1,065 online

3x-7y=1;-x+y=-7

Solution :

{x,y} = {12,5}

System of Linear Equations entered :

  [1]    3x - 7y = 1

  [2]    -x + y = -7

Graphic Representation of the Equations :

   -7y + 3x = 1        y - x = -7  

Solve by Substitution :

// Solve equation [2] for the variable  y

 [2]    y = x - 7

// Plug this in for variable  y  in equation [1]

  [1]    3x - 7•(x -7) = 1

  [1]    -4x = -48

// Solve equation [1] for the variable  x

  [1]    4x = 48

  [1]    x = 12

// By now we know this much :

   x = 12

   y = x-7

// Use the  x  value to solve for  y

   y = (12)-7 = 5

Solution :

{x,y} = {12,5}

Final answer:

Joseph's new balance, after borrowing more money which equals 5 times his initial debt of $15, is -$75.

Explanation:

Joseph initially owes his older brother $15, which can be represented as a balance of -$15. If Joseph's new balance is 5 times the previous amount, we would perform the following calculation:

Previous balance x 5 = New balance

So we would multiply -$15 by 5:

-$15 x 5 = -$75

Therefore, Joseph's new balance with his brother is -$75.

Answer:

To solve this problem, we need to use the following formula

[tex]d=\sqrt{\frac{3h}{2} }[/tex]

Where [tex]h[/tex] is the eye-level height and [tex]d[/tex] is the horizontal distance to the horizon.

For Pam, we know that [tex]h=256ft[/tex],

[tex]d=\sqrt{\frac{3(256)}{2} }=\sqrt{384} \approx 19.6[/tex]

She can see around 19.6 feet to the horizon.

For Adam, we know that [tex]h=400 ft[/tex]

[tex]d=\sqrt{\frac{3(400)}{2} }=\sqrt{600} \approx 24.5[/tex]

He cansee around 24.5 feet to the horizon.

Now, the difference is

[tex]\Delta d= d_{Adam} -d_{Pam} \\\Delta d= 24.5 - 19.6 = 4.9[/tex]

Therefore, Adam can see 4.9 feet much farther than Pam.

Additionally, the expression that models this situation is [tex]\Delta d= d_{Adam} -d_{Pam}[/tex]

the answer is 12,000

how i get this is because you do 2000 multiplied by 6

The values of the slope and y-intercept are m=8 and b=−25

m=8

b=−25

To find the slope you would use the slope formula since you have two point coordinates. The slope formula is:

[tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where y2 and y1 are the y coordinates of the two points and x2 and x1 are the x coordinates of the two points.

Substitute in 7 and -1 for y2 and y1; substitute in 4 and 3 for x2 and x1. Now your expression should look like:

[tex]\frac{7-(-1)}{4-3}[/tex]

Subtract -1 from 7, which is basically the same as 7 + 1. Then subtract 3 from 4. Once you complete these steps you can rewrite your fraction.

[tex]\frac{7+1}{4-3} =\frac{8}{1} =8[/tex]

The final answer is 8 after substituting the appropriate coordinates into the slope formula. This means that the slope of the line passing through the points (3, -1) and (4, 7) is 8.

The answer is: the slope of the line is 8.

Hello there!

[tex]1-f=\frac{9}{10}[/tex]

Explanation:

↓↓↓↓↓↓↓↓↓↓↓↓↓

First you had to subtract by 1 from both sides of the equation.

[tex]1-f-1=\frac{9}{10}-1[/tex]

Simplify

[tex]-f=-\frac{1}{10}[/tex]

Then you divide by -1 from both sides of the equation.

[tex]\frac{-f}{-1}=-\frac{1}{10}/-1[/tex]

Simplify it should the correct answer.

[tex]f=\frac{1}{10}[/tex]

Answer⇒⇒⇒f=1/10

Hope this helps!

Thank you for posting your question at here on Brainly.

Have a great day!

-Charlie

Given my current rate = $129.00 per month.

Savings of 15% over your prices.

Therefore, saving = 15% of $129.00 = 0.15 × 129.00 =$19.35.

Adjusted rate = current rate - saving = 129 - 19.35 = $109.65

Therefore, We can rewrite above expression as :

My current rate is $129.00 per month." Representative: "We will match any competitive offer. Your adjusted rate will be 109.65 dollars per month."

If my current rate is $129.00 per month. Your adjusted rate will be $109.65 dollars per month.

Using this formula

Adjusted rate = Current rate - Adjustment

Where:

Current rate=$129

Adjustment=(15%×$129)

Let plug in the formula

Adjusted rate=$129-(15%×$129)

Adjusted rate = $129 - $19.35

Adjusted rate =$109.65 per month

Inconclusion your adjusted rate will be $109.65 dollars per month.

Learn more about adjusted rate here:https://brainly.com/question/545887

Solution is given in attachment.

So 8^2 is need to add both sides for completing square.