The admission fee at a fair is $3.25 for children and $6.75 for adults. On a certain day, 870 people enter the fair and $3,772.50 is collected. Write a system of linear equations that you can use to determine how many children and adults attended. Be sure to define your variables. Solve the system. SHOW YOUR WORK PLEASE!

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].

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

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

Solution is given in attachment.

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

Answer: 225

Step-by-step explanation:

n₁ = 2(1) - 1

    = 2 - 1

    = 1

n₁₅ = 2(15) - 1

     = 30 - 1

      = 29

[tex]S_{15} =\frac{n_{1}+ n_{15}}{2}*15[/tex]

   [tex]=\frac{1+29}{2}*15[/tex]

    [tex]=\frac{30}{2}*15[/tex]  

    = 15 * 15

     = 225  

➷ The sum would be 225

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:

The plane is at an altitude of 3597 feet

Step-by-step explanation:

Airplane is flying at an altitude of 3000 feet.

Now it dives 630 feet, then the altitude is 2370 (3000-630).

Then it rapidly climbs 1048 feet, then the altitude will be 3418 (2370+1048).

Then it again drops 888 feet, meaning now its at at altitude 2530 (3418-88).

Then it again climbs 1067 feet, now the altitude will be 3597 (2530+1067)

Therefore, the plane is at an altitude of 3597 feet. (Assuming that Again 888 feet before making another climb of 1067 feet has been typed twice by mistake. I considered only 1 drop of 888 and climb of 1067)

9/16 divided by 39/8

KCF

9/16 x 8/39

Simplify

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

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]

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.

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.

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

[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

$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!!!!!!                                      : )

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 which is equal to 7(3m-7n)

[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

the answer is 12,000

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

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)

a. is unreasonable because 96/48 = 2

b. is unreasonable because 713/99=7.2020.... which would be rounded to 7.2 not 72

hope this helps :)p

Final answer:

By rounding the numbers, we find that 96 ÷ 48 is roughly 2, not 20, and 713 ÷ 99 is roughly 7, not 72, indicating both provided answers are not reasonable.

Explanation:

When rounding to check if answers are reasonable, we look at the numbers given and round them to numbers that are easier to work with. Let's apply this to the provided problems:

2x + 7 <= 3x - 5

Treat <= as an = sign unless you divide or multiply by a negative number.

2x + 12 <= 3x

x <= 12

The answer is all real numbers less than or equal to 12.

2x + 7 ≤ 3x - 5

Isolate the x. Subtract 3x and 7 from both sides

2x (-3x) + 7 (-7) ≤ 3x (-3x) - 5 (-7)

2x - 3x ≤ -5 - 7

Combine like terms

(2x - 3x) ≤ (-5 - 7)

-x ≤ -12

Isolate the x. Divide -1 from both sides. Remember that when dividing by a negative number, you must flip the sign.

(-x)/-1 ≤ (-12)/-1

x ≥ -12/-1

x ≥ 12

x ≥ 12 is your answer

~Rise Above the Ordinary

Answer:

{x,y} = {12,5}

Step-by-step explanation:

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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}