solve each system by graphing.​

Answer: (A) [tex]A=300l-l^{2}[/tex]

               (B) Length varies between 1 and 150

               (C) Largest area is 22500ft²

Step-by-step explanation: Suppose length is l and width is w.

The rectangular garden has perimeter of 600ft, which is mathematically represented as

[tex]2l+2w=600[/tex]

Area of a rectangle is calculated as

[tex]A=lw[/tex]

Now, we have a system of equations:

[tex]2l+2w=600[/tex]

[tex]A=lw[/tex]

Isolate w, so we have l:

[tex]2w=600-2l[/tex]

w = 300 - l

Substitute in the area equation:

A = l(300 - l)

A = 300l - l²

(A) Function of area in terms of length is given by A = 300l - l²

(B) The practical domain for this function is values between 1 and 150.

(C) For the largest area, we need to determine the largest garden possible. For that, we take first derivative of the function:

A' = 300 - 2l

Find the values of l when A'=0:

300 - 2l = 0

2l = 300

l = 150

Replace l in the equation:

w = 300 - 150

w = 150

Now, calculate the largest area:

A = 150*150

A = 22500

The largest area the fence can enclose is 22500ft².

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

[tex]\frac{7}{5} m - \frac{6}{15} m - \frac{3}{5} [/tex]

[tex] \frac{21}{15} m - \frac{6}{15} m - \frac{3}{5} [/tex]

[tex]( \frac{(21 - 6)m}{15} ) - \frac{3}{5} [/tex]

[tex] \frac{15}{15} m - \frac{3}{5} [/tex]

[tex]1m - \frac{3}{5} [/tex]

[tex]m - \frac{3}{5} [/tex]

Answer:

If the discrimination of a quadratic function is 13, then the function will have two distinct real roots.

Step-by-step explanation:

Given the quadratic function

[tex]y=ax^2+bx+c[/tex]

where D = b²-4ac is called the discrimination of a quadratic function.

The discriminant D=b²-4ac indicates the type of roots the equation may have.

If D > 0, then the equation has two distinct real roots.

Given that the discrimination of a quadratic function is 13.

i.e. D = 13

Thus, we conclude that if the discrimination of a quadratic function is 13, then the function will have two distinct real roots.

Answer:

yes

Step-by-step explanation:

Answer: x=16

Step-by-step explanation:

shown in screenshot below

Answer:

if want to know is true or flas. this is true

Step-by-step explanation:

Answer:

Step-by-step explanation:

Out of the whole class, if 35% of students voted for Leandro voted for Leonardo , this means that 64% of the class voted for Gerardo.

Let the total number of people in the class be x;

If 70 students voted for Leandro, then;

35% of x = 70

0.35x = 70

x = 70/0.35

x = 200

The total number of people that voted for Gerardo will be 200 - 70 = 130

Hence 130 voted for Gerardo

Answer:

Option A) angle B = 67°

Step-by-step explanation:

I'll use " [ " symbol for saying angle.

Alright so ...

since triangle ABC and triangle DEF are congruent

it means [ A = [ D

[ B = [ E

[ C = [ F

here [ A = 78° (which means [ D is also 78°)

and ..[ F = 35° (which means [ C is also 35°)

-->So now all you need to know to find [ B is to know the other two angles in the triangle. and thats where ..

you write.. [ A + [ B + [ C = 180° (angle sum property)

78° + [ B + 35° = 180°

113° + [ B = 180°

[ B = 180 - 113

= 67°

I hope that clears the concept , if you have any questions regarding it I'd love to help .

Answer:

$48

Step-by-step explanation:

24/3 = 8

8 x 6 = $48

Answer:

48

Step-by-step explanation:

because butterfly method 6 time 24 =144 and didved 144 by 3 which gives you 48

Answer:

2nd option on the top right

Step-by-step explanation:

Answer:each fraction is greater than the one before it is not true

Source:trust me bro

The one that is highlighted

Answer:

2/10 (4/5)-(5/2)+ (10)=7.66

Answer:

[tex]\frac{383}{50} = 7.66[/tex]

Step-by-step explanation:

[tex]\frac{2}{10}(\frac{4}{5})-(\frac{5}{2})+10[/tex]

[tex]= \frac{4}{25} -\frac{5}{2}+10[/tex]

[tex]=\frac{383}{50} = 7.66[/tex]

Answer:

A

Step-by-step explanation:

Answer:

Interest = $1.75

Step-by-step explanation:

Maria invest $600, and receives interest of $30 per year

We know that PRT/100= INTEREST

R=( 100*INTEREST)/(PT)

R = (100*30)/(600*1)

R= 3000/600

R= 5%

Jane invest $350 at Sam rate with Maria , that is 5% , for a year, her interest

Interest= 350*5*1/100

Interest = $1.75

Answer:

the crate weighs 26.31

Step-by-step explanation:

add 32.8 and 39.34 together and then subtract 98.45 from the sum. ^^

Answer:

the crate weighs 26.31

Step-by-step explanation:

add 32.8 and 39.34 together and then subtract 98.45 from the sum. ^^

Step-by-step explanation:

Complete question :

A student forgets to study for an exam consisting of ten multiple choice questions, each with three possible answers. Instead, the student will have to randomly guess, so that there is a 1 3 probability of getting any arbitrary question right. If 6 or more correct answers is a passing score, what is the probability of passing

Answer:

0.07656

Step-by-step explanation:

Given that:

P(correct guess) = 1/3 ; p= 0.33333

Number of questions /trials = 10

P(x ≥ 6) = p(6) + p(7) + p(8) +... + p(10)

This is the sum of the probabilities of getting exactly 6, 7, 8, 9 or 10 questions.

Using the binomial probability calculator to save computation time :

P(x ≥ 6) = 0.07656

Answer:

So wouldn't  it be like $6 as the actual price now.

Step-by-step explanation:

Hope this helps if not let me know.

Sorry if it is wrong,

9514 1404 393

Explanation:

1. Consider the attachment. Angle CDF is a circumscribed angle. It is formed at the intersection of two tangents to the circle. Angles BCE, CBE, and BEC are inscribed angles. Their vertices are on the circle, and they are formed by two chords.

If a chord degenerates to zero length, the ray it represents with respect to an inscribed angle becomes a tangent. That is, angles BCD and ECD can also be considered to be inscribed angles. Similarly, straight angle DFG at tangent point F can be considered to be a degenerate case of both an inscribed angle and a circumscribed angle. (Some authors may not include degenerate cases in their definitions. YMMV)

__

2. The general form of the equation of a circle is ...

  Ax² +Ay² +Dx +Ey +F = 0

Any equation of a circle can be put in this form. If we divide by A, this can be written as ...

  x² +y² -2hx -2ky +c = 0 . . . . where h = -D/(2A), k = -E/(2A), c = F/A

and the equation can be further transformed to the standard form ...

  (x -h)² +(y -k)² = r² . . . . . where r² = h² +k² -c

The last equation is the result of "completing the square" by adding h² and k² to both sides of the second equation shown. The values of h and k are as shown above, given the coefficients of the general form equation.

__

3. Again refer to the attached diagram.

a) a radius is a line segment with the circle center at one end and a point on the circle at the other end. AB and AC are radii.

b) A diameter is a line segment whose ends are on the circle and whose midpoint is the center of the circle. BC is a diameter.

c) A chord is a line segment whose end points lie on the circle. BC, BE, and CE are chords.

d) A secant is a line containing two points of the circle. Lines CG and CE are secants.

e) A tangent is a degenerate case of a secant in which the two points of intersection merge to one point of intersection. It is a line that touches the circle at exactly one point, the point of tangency. DG and DC are tangents.

f) The point of tangency is the single point where a tangent intersects a circle. A radius to the point of tangency (such as AC) is always perpendicular to the tangent line (DC).

Answer:25

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

6/7 divided by 2/7

=

6/7 divide 7/2 (cancel out 7)

=

6 multiply 1/2 (reduce)

=

3

Answer:

40

Step-by-step explanation:

Answer:

$4,236

Step-by-step explanation:

34-27=7

360-7=353

353(12)=4,236

Answer:

$38.25

Step-by-step explanation:

Answer:

Sale Price: $85 * 0.55 = $46.75

Step-by-step explanation:

Answer:

Step-by-step explanation:

They are equal, and thus, the triangle is a right triangle. ... These sides are 6: 8: 10, then the triangle is a right one.

Answer:

b

Step-by-step explanation:

the answer to 7/8 is 0.875 it is not recurring as it has no dot at the top