A plant costs p dollars and a bush costs b dollars. Ana buys 2 plants and 4 bushes for $42. Paola buys 7 plants and 9 bushes for $107. Write down a pair of simultaneous equations and solve them to find out the value of p and the value of b.

Answer:

(1 + 2h)(1 - 2h)

Step-by-step explanation:

[tex]1 - 4h^2 = 1 ^2 - (2h)^2[/tex]

          [tex]=(1 - 2h)(1 + 2h)[/tex]                       [tex][ \ a^2 - b^2 = (a - b)(a+b) \ ][/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

Answer:

The 24,003 is the fastest

Answer:

0.89 m is the answer

Step-by-step explanation:

the wall, the ground and portion of pipe form a right angle triangle with pipe portion being the hypotenuse.

for a right triangle

[tex]{hypotenuse}^{2} = {base}^{2} + {height}^{2} [/tex]

here we have base = 3m and height = 2m.

thus

[tex] {h}^{2} = {3}^{2} + {2 }^{2} \\ = 9 + 4 \\ = 13 \\ h = \sqrt{13} [/tex]

portion of pipe overhanging = 4.5 - sqrt (13)

= 4.5 - 3.61

= 0.89 m

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:

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:

D

Step-by-step explanation:

I believe this is correct

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:

39.6 degrees

Step-by-step explanation:

There are 176 baseball answers out of 1600

There are 360 degrees in a circle

Multiply the fraction of baseball responses by the degrees in a circle

176/1600 * 360

198/5

39.6 degrees

Answer:

x = 11

Step-by-step explanation:

<4 and <5 are alternate interior angles and alternate interior angles are equal when the lines are parallel

<4 = <5

7x+5 = 5x+27

Subtract 5x from each side

7x+5-5x = 5x+27-5x

2x+5 = 27

Subtract 5 from each side

2x+5-5=27-5

2x =22

Divide by 2

2x/2 =22/2

x =11

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

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:

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:

[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:

42.4

Hope that this helps!

Answer: 66.25%

Step-by-step explanation:

53/80 x 100= 66.25%

Answer:

:D

Step-by-step explanation:

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:

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

Slope is 0.75 or 3/4 I believe!

Answer:

5 five-dollar coins and 3 ten-dollar coins

Step-by-step explanation:

10x3=30

5x5=25

30+25=55

Answer:

y-y1=m(x-x1)

y-1/3=3/4(x-4)

y=3/4x-8/3

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