In an activity, students are pulling marbles from a large jar containing blue and red marbles. In their sample,

One positive integer is 5 less than twice another. The sum of their squares is 725. Find the integers.

finlep [7]

Let the numbers are a and b; a - 5 = 2b, and -------------- (1)a2 + b2 = 250 ----------------(2) rewriting and squaring of (1) is given as; a2 = 4b2 + 20b + 25 -------- (3) substituting (3) into (2) (4b2 + 20b + 25) + b2 = 250, thus 5b2 + 20b - 225 = 0 by dividing both sides by 5 b2 + 4b - 45 = 0 solving the quadratic for b, we will get b = -9 or 5, substituting these for b in (1), we will get a asa = -13 or 15 However, if a and b must be positive integer, then a = 15 and b = 5 is the answer

4 0

4 years ago

Can someone help me with all this? Lol idk any of this and E-learning sucks I need to show my work as well

Margarita [4]

Answer:

1a) 230 feet

1b) 3.75s

1c) t=7.54s

2) t=2s

3) t=2.32s

Step-by-step explanation:

The equation that models Brett's last home run is $h(t)=-16t^2+120t+5$

We need to complete the square to obtain the function in the vertex form:

$h(t)=-16(t^2-7.5t)+5$

$h(t)=-16(t^2-7.5t+3.75^2)+5+-16(-3.75)^2$

$h(t)=-16(t-3.75)^2+230$

1a) The vertex is (3.75,230).The maximum value is the y-coordinate of the vertex, which is 230 feet.

1b) The time it takes to reach the maximum value is the x-coordinate of the vertex. It reach the maximum heigth after t=3.75 seconds

1c) To find the time the ball hit the ground, we equate the h(t)=0 and solve for t.

$-16(t-3.75)^2+230=0$

$-16(t-3.75)^2=-230$

$(t-3.75)^2=14.375$

$t-3.75=\pm \sqrt{14.375}$

$t=3.75\pm \sqrt{14.375}$

$t=3.75\pm 3.79$

$t=3.75-3.79\:\:or\:t=3.75+3.79$

$t=3.75-3.79\:\:or\:t=3.75+3.79\\t=-0.04\:\:or\:t=7.54$

The time is positive, so the ball hit the ground after 7.54 seconds.

Question 2)

The function that models the amusement ride is $h(t)=-16t^2+64t+60$

We want to find the time it takes for the riders to reach the maximum height.

This time is given by: $t=-\frac{b}{2a}$

Comparing $h(t)=-16t^2+64t+60$ to $h(t)=at^2+bt+c$ we have a=-16, b=64, c=60.

We substitute to obtain:

$t=-\frac{64}{2*-16} \\t=-\frac{64}{-32} \\t=2$

Hence it took 2 seconds to rech the maximum height.

Question 3)

The equation that models the height f the catridge is $h(t)=-16t^2+35t+5$

To find the time that the catridge will land, we equate the function to zero and solve for t.

$-16t^2+35t+5=0$

This is a quadratic equation with =-16, b=35, an c=5

The solution is given by:

$t=\frac{-b\pm \sqrt{b^2-4ac} }{2a}$

We substitute the values to get:

$t=\frac{-35\pm \sqrt{35^2-4*-16*5} }{2*-16}$

This gives:

$t=\frac{35-\sqrt{1545} }{32} \:or\: t=\frac{35+\sqrt{1545} }{32}$

This simplifies to:

$t=-0.13\:or\: t=2.32$

The time it takes to land must be positive thefore t=2.32 seconds

7 0

3 years ago

Use the quadratic polynomial 12x2+5x−2 to answer the questions.

Advocard [28]

Answer:

A: This polynomial has a degree of 2 , so the equation 12x2+5x−2=0 has two or fewer roots.

B: The quadratic equation 12x2+5x−2=0 has two real solutions, x=−2/3 or x=1/4 , and therefore has two real roots.

Step-by-step explanation:

f(x) = 12x^2 + 5x - 2.

Since this is a quadratic equation, or a polynomial of second degree, one can easily conclude that this equation will have at most 2 roots. At most 2 roots mean that the function can have either 2 roots at maximum or less than 2 roots. Therefore, in the A category, 2nd option is the correct answer (This polynomial has a degree of 2 , so the equation 12x^2 + 5x − 2 = 0 has two or fewer roots).

To find the roots of f(x), set f(x) = 0. Therefore:

12x^2 + 5x - 2 = 0. Solving the question using the mid term breaking method shows that 12*2=24. The factors of 24 whose difference is 5 are 8 and 3. Therefore:

12x^2 + 8x - 3x - 2 = 0.

4x(3x + 2) -1(3x+2) = 0.

(4x-1)(3x+2) = 0.

4x-1 = 0 or 3x+2 = 0.

x = 1/4 or x = -2/3.

It can be seen that f(x) has two distinct real roots. Therefore, in the B category, 1st Option is the correct answer (The quadratic equation 12x2+5x−2=0 has two real solutions, x=−2/3 or x=1/4 , and therefore has two real roots)!!!

4 0

3 years ago

A recipe calls for 2/3 cup of white flour and 3 1/5 cups of wheat flour how much flour will be used in all

ss7ja [257]

Answer:

58/15 or 3 13/15 of flour will be used in all.

8 0

2 years ago

H*es on me left and..

son4ous [18]

Answer:

gl*ck 9 put em out like a light

Step-by-step explanation:

Coupe tinted like a thief in the night

4 0

3 years ago