y+3= 2/3(x - 2)
Solve the system by graphing

Answer:

Horizontal distance = 0 m and 6 m

Step-by-step explanation:

Height of a rider in a roller coaster has been defined by the equation,

y = [tex]\frac{1}{3}x^{2}-2x+8[/tex]

Here x = rider's horizontal distance from the start of the ride

i). [tex]y=\frac{1}{3}x^{2}-2x+8[/tex]

      [tex]=\frac{1}{3}(x^{2}-6x+24)[/tex]

      [tex]=\frac{1}{3}[x^{2}-2(3x)+9-9+24][/tex]

      [tex]=\frac{1}{3}[(x^{2}-2(3x)+9)+15][/tex]

      [tex]=\frac{1}{3}[(x-3)^2+15][/tex]

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

ii). Since, the parabolic graph for the given equation opens upwards,

    Vertex of the parabola will be the lowest point of the rider on the roller coaster.

    From the equation,

    Vertex → (3, 5)

    Therefore, minimum height of the rider will be the y-coordinate of the vertex.

    Minimum height of the rider = 5 m

iii). If h = 8 m,

    [tex]8=\frac{1}{3}(x-3)^2+5[/tex]

    [tex]3=\frac{1}{3}(x-3)^2[/tex]

    (x - 3)² = 9

    x = 3 ± 3

    x = 0, 6 m

    Therefore, at 8 m height of the roller coaster, horizontal distance of the rider will be x = 0 and 6 m

Answer:

UV corresponds to RS.

[tex]\angle R[/tex] corresponds to [tex]\angle U[/tex]

Step-by-step explanation:

Given

[tex]\triangle SRQ[/tex] and [tex]\triangle VUT[/tex]

Transformation: Rigid

Required

Determine the true options

When a rigid transformation occurs from SRQ to VUT, the following are the corresponding sides:

SR to VU, SQ to VT, RQ to UT

And the corresponding angles are:

<S to <V, <R to <U and <Q to <T

From the corresponding sides above, we have:

SR to VU

Rewrite:

RS to UV

Hence: (c) is correct

From the corresponding angles above, we have:

[tex]\angle R[/tex] to [tex]\angle U[/tex]

Hence:

(b) is correct

Answer:

Step-by-step explanation:

Yes they are similar.

The triangles are similar by AA~ postulate.

Answer:

Step-by-step explanation:

As per given we have:

If two angles of one triangle are congruent with another, they triangles are similar

Correct choice is C

Answer:

m∠GFT = 142°

Step-by-step explanation:

∠GFT and ∠DFT are supplementary.

m∠GFT + m∠DFT = 180

7f + 163 + 6f + 56 = 180

13f + 219 = 180

13f = -39

f = -3

m∠GFT = 7f + 163 = 7(-3) + 163 = -21 + 163 = 142

Answer:

2,000

Step-by-step explanation:

take 10×200 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer: $24

Step-by-step explanation:

12% = 0.12

200 × 0.12 = $24

I am not a professional, simply using prior knowledge!

Note- It would mean the world to me if you could mark me brainliest!

5. b1= 8, b2= 11+9=20, h= 15, A= 210

8. b1= 4, b2= 10, h= 5.2, A= 36.4

9. b1= 7, b2= 13, h= 4.2, A= 42

Answer:

44° , acute angle

Step-by-step explanation:

Given

y = 8x + 12 ← substitute x = 4

y = 8(4) + 12 = 32 + 12 = 44°

Since 44° < 90° then angle y is acute

Step-by-step explanation:

4.5÷4= 1.125

so each time she goes around the rectangle she's covering 1.125 km and we seed the length is twice the breadth x+2x=1.125

so 1.125 / 3 to give x which is the breadth=0.375 x 2 is equal to 0.75 km or 750 m this is the length of the field

Step-by-step explanation:

The length of a rectangular field is twice it's breadth. A girl jogged around it 4 times and covered a distance of 4.5 km. What is the length of the field?

The distance cover in 4 laps is 4.5 km, So one lap is 4.5/4 = 1.125 km.

Let the breadth of the field be B so the length will be L or 2B.

The perimeter of the field is 2L+2B or 4B+2B = 6B = 1.125, so B = 1.125/6 = 0.1875 km and the length is 2*0.1875 = 0.375 km.

Check: perimeter = 2*0.375 + 2*0.1875 = 1.125 km and 4 laps covers 4*1.125 = 4.5 km. correct.

The field is 375 m long.

Answer:

the answer is WU is congruent to UV

Given:

The endpoints of line segment CD are C(-4,7) and D(0,-3).

To find:

The midpoint of CD.

Solution:

Midpoint formula:

[tex]Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]

Using the midpoint formula, the midpoint of CD is

[tex]Midpoint=\left(\dfrac{-4+0}{2},\dfrac{7-3}{2}\right)[/tex]

[tex]Midpoint=\left(\dfrac{-4}{2},\dfrac{4}{2}\right)[/tex]

[tex]Midpoint=\left(-2,2\right)[/tex]

Therefore, the midpoint of the line segment CD is (-2,2).

Answer:

y = 5x - 24

Step-by-step explanation:

please let me know if you want me to add an explanation :)

Answer:

Step-by-step explanation:

y-1 = 5(x-5)

Answer:

b. x=2

Step-by-step explanation:

The axis of symmetry of a parabola gives us a line of symmetry where the parabola appears the same but flipped on either side. It passes through the parabola's vertex, or the minimum/maximum point of the parabola. Here, we can see that the parabola's minimum point occurs when x=2. Therefore, its axis of symmetry is x=2.

I hope this helps!

Answer:

When a file has an extension, the computer is allowed to store additional metadata about it.

Hope that helped :)

Answer:

1.2 * 10^-5 or 0.000012

Step-by-step explanation:

Use commutative property to reorder the terms

Multiply the terms

Multiply the terms with the same base by adding their exponents

Calculate the sum

Write the number in scientific notation

1.2 * 10^-5 or 0.000012

Answer:

3/2

Step-by-step explanation:

Answer:

3/2

Step-by-step explanation:

Answer:

y=-x-6

Step-by-step explanation:

y-y1=m(x-x1)

y-(-5)=-1(x-(-1))

y+5=-(x+1)

y=-x-1-5

y=-x-6

Answer:

51.89085

Step-by-step explanation:

area = 49pi

150/360 * 49pi = 64.14085

triangle area = 7 * sin(75 degrees) * 7 * cos(75 degrees) = 12.25

==> white region = 64.14085 - 12.25 = 51.89085

Answer:

3 hours

Step-by-step explanation:

$30 + $10 = $40

* Just for a hour and the fee*

$128 ÷ $40 = 3

Answer:

he paid 8 hours

Step-by-step explanation:

kasi ibawas mo ang 30£ sa booking tapos i add mo yung 80£ sa

hours sa hall kasa naging 8 hours

answer is 170

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

50% of 850 = 425

30% of 850 = 255

425 + 255 = 680

850 - 680 = 170

There are 170 kg mass of parsnips left after distributing to the local market and local supermarket.

To calculate the mass of parsnips left after distributing them to the local market and the local supermarket, we need to subtract the quantities allocated to these places from the total harvest.

The farmer harvested 850 kg of parsnips.

30% of the harvest goes to the local market, which is (30/100) * 850 kg = 0.3 * 850 kg = 255 kg.

50% of the harvest goes to the local supermarket, which is (50/100) * 850 kg = 0.5 * 850 kg = 425 kg.

To find the mass of parsnips left, we subtract the quantities allocated to the market and supermarket from the total harvest:

Total harvest - (Quantity for market + Quantity for supermarket)

= 850 kg - (255 kg + 425 kg)

= 850 kg - 680 kg

= 170 kg.

Therefore, there are 170 kg of parsnips left after distributing to the local market and local supermarket.

To know more about mass click here :

https://brainly.com/question/30117675

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Answer:

divide 1.5008 and 0.56

which will be 2.68

Answer:

The value of the car will be

4450.15

Step-by-step explanation:

we know that

11.75%=11.75/100=0.1175

so Let

x-----> the value of the car after 11 years

X=17600(1-0.1175)11=4450.15

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given equation is,

x² + (p + 1)x = 5 - 2p

x² + (p + 1)x - (5 - 2p) = 0

x² + (p + 1)x + (2p - 5) = 0

Properties for the roots of a quadratic equation,

1). Quadratic equation will have two real roots, discriminant will be greater than zero. [(b² - 4ac) > 0]

2). If the equation has exactly one root, discriminant will be zero [(b² - 4ac) = 0]

3). If equation has imaginary roots, discriminant will be less than zero [(b² - 4ac) < 0].

Discriminant of the given equation = [tex](p+1)^2-4(1)(2p-5)[/tex]

For real roots,

[tex](p+1)^2-4(1)(2p-5)>0[/tex]

p² + 2p + 1 - 8p + 20 > 0

p² - 6p + 21 > 0

For all real values of 'p', given equation will be greater than zero.

Answer:

this would be the area

Step-by-step explanation:

0.049 you take the square root of pie and you divide it by 1/4 and see what you get will help you towards this answer

Answer:

1/1 or 1

Step-by-step explanation:

the rise is 1 and the run is 1

Answer:

1

Step-by-step explanation:

slope is found by rise/run.

in this case, the rise is 1, and the run is 1. so, the slope is 1/1=1