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Answer:

The y-value of Function A when x = 2 is GREATER than the y-value of Function B when x = 2

Step-by-step explanation:

✔️Find the equation of Function A:

To do this, find the y-intercept (b) and slope (m):

Slope (m) = change in y/change in x

Using (4, 13) and (5, 17),

Slope (m) = (17 - 13)/(5 - 4) = 4/1

m = 4

To find b, substitute (x, y) = (4, 13) and m = 4 into y = mx + b

13 = 4(4) + b

13 = 16 + b

13 - 16 = b

b = -3

To write the equation for Function A, substitute m = 4 and b = -3 into y = mx + b

Thus:

y = 4x - 3

Next, find the y-value of Function A when x = 2 by substituting x = 2 into y = 4x - 3

Thus:

y = 4(2) - 3

y = 8 - 3

y = 5

✅The y-value of Function A when x = 2 is 5

✔️Equation for Function B is given as,

y = ½x + 1

Find the y-value of Function B when x = 2 by substituting x = 2 into y = ½x + 1

Thus:

y = ½(2) + 1

y = 1 + 1

y = 2

✅The y-value of Function B when x = 2 is 2

Therefore, the correct statement is:

The y-value of Function A when x = 2 is greater than the y-value of Function B when x = 2

Answer:

740

Step-by-step explanation:

42% of 1761 = 0.42 * 1761 = 739.62

Answer: 740

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Explanation:

Use the pythagorean theorem

a^2+b^2 = c^2

to find that c = 13 when a = 12 and b = 5.

So that makes the hypotenuse MO = 13 units long.

The opposite side is MN = 12 units long as this side is furthest we can get from angle O.

The sine ratio involves opposite over hypotenuse

sin(angle) = opposite/hypotenuse

sin(O) = MN/MO

sin(O) = 12/13

Answer:

C.    12/13

Step-by-step explanation:

a² + b² = c²

5² + 12² = c²

25 + 144 = c²

169 =  c²

c = 13

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

sin = opp/hyp

sinO = 12/13

Answer:

[tex]\displaystyle y=-\frac{1}{10}x^2-\frac{4}{5}x-\frac{11}{10}[/tex]

Step-by-step explanation:

By definition, any point (x, y) on the parabola is equidistant from the focus and the directrix.

The distance between a point (x, y) on the parabola and the focus can be described using the distance formula:

[tex]d=\sqrt{(x-(-4))^2+(y-(-2))^2[/tex]

Simplify:

[tex]d=\sqrt{(x+4)^2+(y+2)^2}[/tex]

Since the directrix is an equation of y, we will use the y-coordinate. The vertical distance between a point (x, y) on the parabola and the directrix can be described using absolute value:

[tex]d=|y-3|\text{ or } |3-y|[/tex]

The two equations are equivalent. Therefore:

[tex]\sqrt{(x+4)^2+(y+2)^2}=|y-3|[/tex]

Solve for y. We can square both sides. Since anything squared is positive, we can remove the absolute value:

[tex](x+4)^2+(y+2)^2 = (y-3)^2[/tex]

Expand:

[tex](x^2+8x+16)+(y^2+4y+4)=(y^2-6y+9)[/tex]

Isolate:

[tex]x^2+8x+11=-10y[/tex]

Divide both sides by -10. Hence, our equation is:

[tex]\displaystyle y=-\frac{1}{10}x^2-\frac{4}{5}x-\frac{11}{10}[/tex]

Answer:

30'000 gallons approx

Step-by-step explanation:

day 2 - 500,000 gallons

day 4 - 250,000 gallons

day 6 - 125,000 gallons

day 8 - 62,500 gallons

day 10 - 31,250 gallons

Given:

[tex]\cos \theta =\dfrac{3}{5}[/tex]

[tex]\sin \theta <0[/tex]

To find:

The quadrant of the terminal side of [tex]\theta[/tex] and find the value of [tex]\sin\theta[/tex].

Solution:

We know that,

In Quadrant I, all trigonometric ratios are positive.

In Quadrant II: Only sin and cosec are positive.

In Quadrant III: Only tan and cot are positive.

In Quadrant IV: Only cos and sec are positive.

It is given that,

[tex]\cos \theta =\dfrac{3}{5}[/tex]

[tex]\sin \theta <0[/tex]

Here cos is positive and sine is negative. So, [tex]\theta [/tex] must be lies in Quadrant IV.

We know that,

[tex]\sin^2\theta +\cos^2\theta =1[/tex]

[tex]\sin^2\theta=1-\cos^2\theta[/tex]

[tex]\sin \theta=\pm \sqrt{1-\cos^2\theta}[/tex]

It is only negative because [tex]\theta [/tex] lies in Quadrant IV. So,

[tex]\sin \theta=-\sqrt{1-\cos^2\theta}[/tex]

After substituting [tex]\cos \theta =\dfrac{3}{5}[/tex], we get

[tex]\sin \theta=-\sqrt{1-(\dfrac{3}{5})^2}[/tex]

[tex]\sin \theta=-\sqrt{1-\dfrac{9}{25}}[/tex]

[tex]\sin \theta=-\sqrt{\dfrac{25-9}{25}}[/tex]

[tex]\sin \theta=-\sqrt{\dfrac{16}{25}}[/tex]

[tex]\sin \theta=-\dfrac{4}{5}[/tex]

Therefore, the correct option is B.

Answer: 5 Seconds

Step-by-step explanation: Given the equation of the height expressed ad;

h(t) = - 16t^2 + initial height

Given that initial height = 400feet

h(t) = - 16t^2 + 400

The waste will hit the ground at when h(t) = 0

substitute

0 =  - 16t^2 + 400

16t^2 = 400

t² = 400/16

t² = 25

t = √25

t = 5secs

Answer:

pi

Step-by-step explanation:

First find the area of a full circle with radius 2

A = pi r^2

A = pi 2^2

A = 4 pi

We know that this is 1/4 of a circle so take 1/4 of the area

1/4 A = 1/4 (4 pi) = pi

Answer:

I would answer but I have no numbers to give the answer

Answer:

42.4

Hope that this helps!

Answer: 66.25%

Step-by-step explanation:

53/80 x 100= 66.25%

Answer:

1.39 m

Step-by-step explanation:

sin 63 = x/13.5 (x = CD)

sin 52 = x/13.5 (x=AC)

take the difference between the two

Answer:

D

Step-by-step explanation:

g(x) will be -x^2-3. The minus in front of the x makes the graph flip upside down, and the "-3" indicates its position on the y-axis. Hope this helps!!

Answer: Choice D.  g(x) = -x^2-3

==============================================

Explanation:

Start with the curve y = x^2.

Reflect it over the horizontal x axis to get y = -x^2

Then shift everything down 3 units to arrive at g(x) = -x^2-3

You can use a tool like Desmos or GeoGebra or anything similar to help verify this.

Answer:

The center of the circle is (3, -4)

The diameter of the circle is 2

Step-by-step explanation:

The given equation of the circle is x² - 6·x + y² + 8·y = 24

The general form of the equation of a circle is x² + y² + 2·g·x + 2·f·y + c = 0

The center of the circle = (-g, -f)

The radius of the circle = √(g² + f² - c)

By comparing the given equation of the circle with the general form of the equation of a circle, we have;

2·g = -6, 2·f = 8, and c = 24

From 2·g = -6, we get;

∴ g = -6/2 = -3

g = -3

from 2·f = 8, we get;

∴ f = 8/2 = 4

f = 4

Therefore;

The center of the circle, (-g, -f) = (-(-3), -4) = (3, -4)

The center of the circle = (3, -4)

The radius of the circle, r = √(g² + f² - c) = √((-3)² + 4² - 24) = 1

The diameter of the circle, d = 2×r = 2 × 1 = 2

The diameter of the circle = 2.

Answer:

[tex]a = 3\sqrt{7}[/tex]

Step-by-step explanation:

Given

See attachment

Required

Determine (a)

To do this, we make use of Pythagoras theorem.

[tex]12^2 = a^2 + 9^2[/tex]

[tex]144 = a^2 + 81[/tex]

Collect like terms

[tex]a^2 = 144 -81[/tex]

[tex]a^2 = 63[/tex]

Take square roots

[tex]a = \sqrt{63}[/tex]

Expand

[tex]a = \sqrt{9*7}[/tex]

Split

[tex]a = \sqrt{9}*\sqrt{7}[/tex]

[tex]a = 3\sqrt{7}[/tex]

Step-by-step explanation:

when numbers are negative, the bigger the number looks the smaller it is therefore

-6 is smaller than -5

but 6 is bigger than 5

however, the numbers are;

-5.99, -3, -6, -5.9, -1, -5.999, -5 ,2

Answer:

22 feet

Step-by-step explanation:

When graphing the equation, the peak or the maximum of the equation is reached the 1st second of the throw and it reaches 22 feet.

Answer:

6x+30<102

0 ≤ x ≤ 12 gives all possible solutions for this problem.

Answer:

Your total would be 180 so with the extra you could donate or something like that

Step-by-step explanation:

I hope this helped:)

Answer:

Yes

Step-by-step explanation:

As long as no x values repeat it is considered a function

In the given set no x values repeat therefore it is a function

Answer:

Yes.

Step-by-step explanation:

Each input has exactly one output. Therefore, this is indeed a function.

Answer:

x = 8

Step-by-step explanation:

According to trigonometry identity

sin x = Cos (90-x)

Hence if we have;

Sin (4x + 10) º = Cos (6x)

Sin (4x + 10) º = Sin(90- 6x)

4x + 10 = 90 - 6x

4x+6x = 90 - 10

10x = 80

x = 80/10

x = 8

Hence the value of x is 8

Answer:

3x - 4

Step-by-step explanation:

(6x^2 − 8x) ÷ (2x) =

(6x^2)/2x - 8x/2x =                 

3x - 4

Answer:

(C). 3x - 4

Step-by-step explanation:

It will be easily to break this down so,

6/2=3

x^2/x=x

therefore, 6x^2/2x = 3x

Minus stay minus

8/2 = 4

x/x=1

therefore, 8x/2x=4

If we put it all together,

3x - 4

if this helps you, please give brainliest!

Answer:

:D

Step-by-step explanation:

Step-by-step explanation:

2 to the power x =1/32

2 to the power x =1/2 to the power 5

2 to the power x = 2 to the power -5

then,

x = -5

Answer:

Option 4

Step-by-step explanation:

3x(x+2)-4(x+2)

(3x-4)(x+2)

3x²+6x-4x-8

3x²+2x-8

Brainliest please

Answer:

(x + 2)(3x - 4)

3x^2 + 2x - 8

Step-by-step explanation:

Factor out x + 2.

You get: (x + 2)(3x - 4)

Now multiply it out:

(x + 2)(3x - 4) = 3x^2 - 4x + 6x - 8 = 3x^2 + 2x - 8

Slope is 0.75 or 3/4 I believe!

Answer:

[tex]n + 5 = 12[/tex]

Step-by-step explanation:

"A number increased by a 5 is 12".

The value of n.

[tex]n + 5 = 12[/tex]

[tex]n = 12-5[/tex]

[tex]n = 7[/tex]

Answer:

7

Step-by-step explanation:

subtract the sum, in this case 12. by 5 to get the answer. 12-5=7

Answer:

translate 2 units to the left and compress by 1/2 in the y direction

Step-by-step explanation:

f(x)=x²

y = f(x + C)  C > 0 moves it left

We add 2 to move it 2 units to the left

h(x) = (x+2)^2

y = Cf(x) 0 < C < 1 compresses it in the y direction

g(x) = 1/2 (x+2)^2