Triangle PQR is similar to triangle STU. Find the measure of side TU. Figures are not drawn to scale.

9514 1404 393

Answer:

  a) a=1, b=4, c=-5

  b) opens up; a > 0

  c) minimum = -9, the y-value of the vertex

  d) x = -5, 1

  e) y = -5, the value of c

  f) (-2, -9)

Step-by-step explanation:

A graph drawn by a graphing calculator can answer all of these questions quickly and easily.

__

a) The values of 'a', 'b', and 'c' are the values of the coefficients of the terms in the function definition. They refer to the coefficients in the standard form:

  f(x) = ax^2 +bx +c

  f(x) = x^2 +4x -5 . . . . . . . your equation with a=1, b=4, c=-5

__

b) The parabola opens up. This is because the value of 'a' is greater than zero.

__

c) The minimum is the y-value of the vertex. When the function is written in vertex form it is ...

  f(x) = (x -h)^2 +k . . . . . . . . . . . vertex (h, k)

Your function can be put into this form:

  f(x) = x^2 + 4x +4 -5 -4 . . . . . . add and subtract 4 to complete the square

  f(x) = (x +2)^2 -9 . . . . . . . . vertex form. The vertex is (-2, -9).

The y-value of the vertex is -9, the minimum value of the function.

__

d) Solving f(x) = 0, you get ...

  (x +2)^2 -9 = 0

  (x +2)^2 = 9 . . . . . . . . add 9

  x +2 = ±√9 = ±3 . . . . . take the square root; next, subtract 2

  x = -2 ±3 = {-5, 1} . . . . . the x-intercepts

__

e) The y-intercept is f(0) = c = -5.

__

f) The vertex was found in part (c) to be (-2, -9).

    This is because of the law of indices which says:

[tex]\sqrt[x]{n}[/tex]= [tex]x^{\frac{1}{m} }[/tex]

    So, if we have:

[tex]\sqrt{n}[/tex]

    Then the following will be true because of this math law:

[tex]n^{\frac{1}{2} }[/tex]

Side note: The m value can be greater than n and or less than n, but if it is equal the m and n values cancel out.

Have a nice day!

    I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer:

4 7/20

Step-by-step explanation:

8 1/4 - 3 9/10

get a common denominator of 20

8 1/4 *5/5 - 3 9/10 *2/2

8 5/20 - 3 18/20

borrow 1 from the 8 in the form of 20/20

7 +20/20 + 5/20 - 3 18/20

7 25/20 - 3 18/20

4 7/20

Answer: 4.35

Step-by-step explanation: 8 1/4 as a decimal is 8.25. 3 9/10 as a decimal is 3.9. 8.25 - 3.9 = 4.35.

Answer:

1 -9 09u and than add

Step-by-step explanation:

Step-by-step explanation:

hope it helps thanks this is the answer

Answer:

A r = kt

Step-by-step explanation:

Answer:

is no solution an answer choice cause thats what i got

Step-by-step explanation:

Answer:

40%

Step-by-step explanation:

Answer:

a = 3x

b = -6x^2

c = 4

Step-by-step explanation:

to find b we have to multiply (x - 3) with 2x^2

= 2x^3 - 6x^2

b = - 6x^2

to find a

in the second step of division to get -9x

we have to multiply x - 3 with 3x

a = 3x

to find c we have to add next term after x in the first equation that is 4

in equation 8x + 4

so c = 4

Answer:

3

Step-by-step explanation:

Answer:

70%

Step-by-step explanation:

Answer:

-5 ≤x≤6

[-5,6]

Step-by-step explanation:

The domain is the values that the input takes

x goes from -5 (inclusive) to 6 (inclusive)

-5 ≤x≤6

[-5,6]

Answer:

[-5, 6]

Step-by-step explanation:

    The domain of a function is the list of x values. Since the endpoints are shaded, that means those x values are included as well. Therefore, the domain of f is [-5, 6].

Answer:

1638 cm, also please mark brainliest

Answer:

-79.8

Step-by-step explanation:

The change can be found by subracting the ending distance from the beginning distance.

In this case, its 200.6-120.8= 79.8

It is negative because the distance in the end became lower than the beginning distance.

Hope this helps!

The velocity of the particle at the first instance it is at the origin (approximately t ≈ 2.944) is approximately 16.885 units per time unit.

To find the velocity of the particle at the first instance it is at the origin, we need to find the value of t when x(t) = 0.

Since the particle is at the origin when x(t) = 0, we have:

[tex]0.5t^4 - 1.5t^3 - 2t^2 + 6t - 1 = 0[/tex]

Using numerical methods or graphing the equation, we find that the roots are approximately t ≈ -0.618, t ≈ 1.532, t ≈ 3.143, and t ≈ 2.944.

Since t > 0, the first instance the particle is at the origin corresponds to t ≈ 2.944 (the smallest positive real root).

Now, to find the velocity of the particle at this instance, we need to find the derivative of the position function x(t) with respect to time t, which gives us the velocity function v(t):

v(t) = dx/dt

[tex]v(t) = d/dt (0.5t^4 - 1.5t^3 - 2t^2 + 6t - 1)\\v(t) = 2t^3 - 4.5t^2 - 4t + 6[/tex]

Now, we can find the velocity at t ≈ 2.944:

[tex]v(t = 2.944) = 2(2.944)^3 - 4.5(2.944)^2 - 4(2.944) + 6[/tex]

v(t ≈ 2.944) ≈ 16.885

So, the velocity of the particle at the first instance it is at the origin (approximately t ≈ 2.944) is approximately 16.885 units per time unit.

learn more on velocity :

https://brainly.com/question/29290259

#SPJ4

Answer:..

Step-by-step explanation:..

Answer:

The trigonometric ratio that I would use to find the distance from the base of the tower to the keys is the tangent; tan (86°) = height / distance.

Step-by-step explanation:

You can draw a right triangle with angle 86°, opposite leg equal to the height (50 meter) and adjacent leg equal to the distance from the base of the tower to the keys: tan (86°) = 50 m / x

=> x = 50 m / tan(86°)

x = 50 m / 14.30 = 0.98 m

Answer:

.05x+50=55

100 minutes

Step-by-step explanation:

simplify

.05x=5 (subtract 50 on both sides)

5/.05=x

100=x

she can call for 100 minutes

Answer:

r = 27 cm

Step-by-step explanation:

[tex]Volume \ of \ ball = \dfrac{4}{3}\pi r^{3}\\\\\\\dfrac{4}{3}\pi r^{3}= 26244\pi \\\\\\r^{3}=\dfrac{26244*\pi *3}{4*\pi }\\\\\\r^{3}= 6561*3\\\\r^{3} = 3*3*3*3*3*3*3*3*3\\\\\\r=\sqrt[3]{3*3*3*3*3*3*3*3*3}=3*3*3\\\\r = 27[/tex]

Answer:

b = 4

Step-by-step explanation:

The y- intercept is the point on the y- axis where the line crosses it

Here the line crosses the y- axis at b = 4

Answer:138

Step-by-step explanation:

2x+49=5x+19

x=10

mqp = 7x+68

mqp = 138

Answer:

$1,497

Step-by-step explanation:

I hope this helps!

Answer:

Question 1 answer: B

Question 2: 30,300 tax is 757.5 so they earn 29542 dollars 5 ceents

question 3: tax is 2234 they make 53615

Answer:

yes

Step-by-step explanation:

because i used my brain#

Answer:

triangle 1. 10•6=60m²

triangle 2. 25•14= 350cm²

* in case u need help, to find the area of a triangle use this formula;

b • h = a

base • height = area

hope this helps

#1

Area:-

[tex]\\ \sf\longmapsto \dfrac{1}{2}BH[/tex]

[tex]\\ \sf\longmapsto \dfrac{1}{2}(6)(10)[/tex]

[tex]\\ \sf\longmapsto 3(10)=30m^2[/tex]

#2

Area:-

[tex]\\ \sf\longmapsto \dfrac{1}{2}(25)(14)[/tex]

[tex]\\ \sf\longmapsto 25(7)[/tex]

[tex]\\ \sf\longmapsto 175cm^2[/tex]

Answer:

I got -1/2

Step-by-step explanation:

Answer:

30√85 or 276.5863 meters

Step-by-step explanation:

Use pythag theorom. a^2+b^2=c^2

180^2+210^2=c^2

c=276.5863

9514 1404 393

Answer:

  4 : 1

Step-by-step explanation:

Each segment joining midpoints is called a "midline." It is parallel to the segment not being joined, and is half its length. All the dimensions of the smaller triangle are half those of the larger triangle. (They are similar triangles.) The ratio of areas is the square of the ratio of side lengths:

  2² : 1² = 4 : 1 . . . . . . ratio of triangle areas

Answer: y = -5/2 -17

Step-by-step explanation: First put the equation in point slope form

Y-y1 = m(x-x1)

y + 2 = -5/2(x+6) then simplify to slope int. form

Y= mx + b

Y = -5/2x-17

Answer:

y = (-5/2)x - 17

Step-by-step explanation:

y = mx + b

m = slope

b = y-intercept

y = mx + b

Slope = -5/2

y = (-5/2)x + b        [tex]\longmapsto\\[/tex]         Input x and y values from given point

-2 = (-5/2)-6 + b

-2 = (-5 * -6)/(2) + b

-2 = 30/2 + b

-2 = 15 + b

b = -2 - 15

b = -17

y = mx + b

m = -5/2

b = -17

y = (-5/2)x - 17

-Chetan K

-Chetan K