A medical clinic is reducing the number of incoming patients by giving vaccines before flu season. During week 5 of flu season, the clinic saw 85 patients. In week 10 of flu season, the clinic saw 65 patients. Assume the reduction in the number of patients each week is linear. Write an equation in function form to show the number of patients seen each week at the clinic.

A.f(x) = 20x + 85
B.f(x) = −20x + 85
C.f(x) = 4x + 105
D.f(x) = −4x + 105

Answer:

Interquartile Range = 90.5

Step-by-step explanation:

We are given the following data set for which we have to find its interquartile range:

[tex]120,140,150,195,203,226,245,280[/tex]

Since we have an even number data set here so dividing the data set into two halves and taking the average of two middle values for each date set to find [tex]Q_1[/tex] and [tex]Q_3[/tex].

[tex]Q_1=\frac{140+150}{2} =145[/tex]

[tex]Q_3= \frac{226+245}{2}=235.5[/tex]

Interquartile Range [tex](Q_3-Q_1) = 235.5-145[/tex] = 90.5

Answer:

There are 925 in half of a year

There are 1321 in 2 years

There are 8838 in 10 years

Step-by-step explanation:

* Lets revise the exponential function

- The original exponential formula was y = ab^x, where a is the initial

 amount and b is the growth factor

- The new growth and decay functions is y = a(1 ± r)^x. , the b value

 (growth factor) has been replaced either by (1 + r) or by (1 - r).

- The growth rate r is determined as b = 1 + r

* Lets solve the problem

∵ The number of fish is growth every month

∴ We will use the growth equation y = a(1 + r)^x, where a is the initial

  amount of the fish, r is the rate of growth every month and x is the

  number of months

- There are 821 of a type of fish

∴ The initial amount is 821 fish

∴ a = 821

- Their growth rate is 2% each month

∴ The rate of growth is 2% per month

∴ r = 2/100 = 0.02

- We want to find how many of them be in half year

∵ There are 6 months in half year

∴ y = 821(1 + 0.02)^6

∴ y = 821(1.02)^6 = 924.58 ≅ 925

* There are 925 in half of a year

∵ There are 24 months in 2 years

∴ y = 821(1 + 0.02)^24

∴ y = 821(1.02)^24 = 1320.53 ≅ 1321

* There are 1321 in 2 years

∵ There are 120 months in 10 years

∴ y = 821(1 + 0.02)^120

∴ y = 821(1.02)^120 = 8838.20 ≅ 8838

* There are 8838 in 10 years

Answer:

20%

Step-by-step explanation:

step 1

Find 50% of x

we know that

50%=50/100=0.50

so

Multiply the number x by 0.50 to determine 50% of x

(x)(0.50)=0.50x

step 2

Find 40% of 50% of x

we know that

50% of x is equal to 0.50x (see the step 1)

40%=40/100=0.40

so

Multiply the number 0.50x by 0.40 to determine 40% of 0.50x

(0.50x)(0.40)=0.20x

therefore

The percent of x is equal to 0.20*100=20%

Answer:

20%

Step-by-step explanation:

there's really no point of explaining since the other person just explained and I don't wanna copy pasta their explanation

Answer:

12 km

Step-by-step explanation:

So the situation is:

8 km/h for X hours

6 km/h for y hours

X * 8 + y * 6 = 26.4

and X + Y = 3.9 hours

Since 234/60 = 3.9 hours

You could write that X = 3.9 - Y

(3.9-Y) * 8 + y * 6 = 26.4

31.2 -8Y +6Y = 26.4

-2Y = -4.8

Y = 2.4 hours

X = 3.9-2.4 = 1.5 hours

So 1.5 * 8 = 12 km

Answer:

AB = 12km

Step-by-step explanation:

From the question we can get the following information,

The whole trip is 26.4 km and 3.9 hours ([tex]\frac{234}{60}[/tex]), and we can form the following two equations.

[tex]x + y = 3.9[/tex]   and [tex](x*8km/h) + (y*6km/h) = 26.4km[/tex]

Where X is distance between A and B, and Y is distance between B and C. We can solve the first equation for X and plug X into the second equation.

[tex]x = 3.9 - y[/tex]  ........   and we can plug it into the the second equation and solve for y

[tex]((3.9-y)*8)+(6y) = 26.4[/tex]

[tex](31.2-8y)+6y = 26.4[/tex]

[tex]31.2-2y = 26.4[/tex]

[tex]-2y = -4.8[/tex]

[tex]y = 2.4[/tex]

Now we can plug in y to the first equation to solve for x

[tex]x = 3.9-2.4[/tex]

[tex]x = 1.5[/tex]

Finally, we can multiplay 8km/h by 1.5 hours to find the distance from A to B

[tex]AB = 8km/h * 1.5h[/tex]

[tex]AB = 12km[/tex]

Answer:

C

Step-by-step explanation:

if u try and find the median you get 50.5 because it is the middle of 50 (fourth term) and 51 (fifth term) and only c has the correct median

Final answer:

To calculate vector AB from points A=(-2,5) and B=(3,1), subtract the coordinates of A from B to get AB = (5, -4). Then, use the Pythagorean theorem to find the magnitude |AB|, which is the square root of 41 units.

Explanation:

The question asks for the calculation of the magnitude of the vector AB, given two points A and B with coordinates A=(-2,5) and B=(3,1), respectively. To find vector AB, we subtract the coordinates of point A from point B. This results in AB = (Bx - Ax, By - Ay) = (3 - (-2), 1 - 5) which simplifies to AB = (5, -4). The magnitude of vector AB, often denoted as |AB|, can then be found using the Pythagorean theorem: |AB| = √((5)2 + (-4)2) = √(25 + 16) = √41 units.

Answer:

Option C (2556.1 meters).

Step-by-step explanation:

This question can be solved using one of the three trigonometric ratios. The height of the airplane from the ground is 1200 meters and the angle of depression is 28°. It can be seen that the required distance is given by x meters. This forms a right angled triangle, as it can be seen in the diagram. The perpendicular is given by 1200 meters, the hypotenuse is unknown, and the angle of 28° is given, as shown in the attached diagram. Therefore, the formula to be used is:

sin θ = Perpendicular/Hypotenuse.

Plugging in the values give:

sin 28 = 1200/x.

x = 1200/sin 28.

x = 2556.06536183 meters.

Therefore, the airplane is 2556.1 meters (to the nearest tenths) far away from the building!!!

The distance from the airplane to the building is approximately 2256.6 meters, rounded to the nearest tenth.

To find the distance d from the airplane to the building on the ground, we can use trigonometry, specifically the tangent function.

Given:

- Altitude of the airplane h = 1200 m

- Angle of depression [tex]\( \theta = 28^\circ \)[/tex]

The tangent of the angle of depression [tex]\( \theta \)[/tex] is defined as the ratio of the opposite side altitude h to the adjacent side (distance d from the airplane to the building):

[tex]\[ \tan(\theta) = \frac{h}{d} \][/tex]

Substitute the given values:

[tex]\[ \tan(28^\circ) = \frac{1200}{d} \][/tex]

Now, solve for d:

[tex]\[ d = \frac{1200}{\tan(28^\circ)} \][/tex]

Calculate [tex]\( \tan(28^\circ) \)[/tex]:

[tex]\[ \tan(28^\circ) \approx 0.5317 \][/tex]

Now, plug in this value:

[tex]\[ d = \frac{1200}{0.5317} \][/tex]

[tex]\[ d \approx 2256.6 \][/tex]

Answer:

A BT = CT

Step-by-step explanation:

BAT ≅ CAT

That means

The angles are the same and the sides are the same by CPCTC

AB = AC

CT = BT

AT=AT

and

< BAT = <CAT

< ATB = <ATC

< TBA = <TCA

Given the choices on the left

A BT = CT is one of them

Answer:

Step-by-step explanation:

Each one of those options is a coordinate point; the first number represents x and the second represents y.  In order for a coordinate point to be a solution to an equation, one side of the equation has to equal the other side when you plug in the number that represents x where x is, and the number that represents y wher y is and then solve.

The first coordinate point filled in looks like this:

If y = 4x + 5, then where x = 0 and y = 10

10 = 4(0) + 5. Solv that to get

10 = 5

Does 10 equal 5?  No.  10 equals 10, not anything else.  So that point doesn't work.

The next point (0, -2) filled in looks like this:

-2 = 4(0) + 5

Does -2 = 5?  No.  Not a solution.

The next point (-4, 0) filled in looks like this:

0 = 4(-4) + 5 and

0 = -16 + 5 and

0 = -11

True?  No.

The next point (-6, 4)

4 = 4(-6) + 5

4 = -24 + 5 and

4 = -19

None of them work. At least according to what you have as your equation and as your points.

Answer:

The sides are equal to

x=6.9 ft and y=39.4 ft

Step-by-step explanation:

step 1

Find the adjacent side to the angle of 80 degrees

Let

x ----> the adjacent side to the angle of 80 degrees

we know that

The function cosine of angle of 80 degrees is equal to divide the adjacent side to the angle of 80 degrees by the hypotenuse (40 ft)

cos(80°)=x/40

x=(40)cos(80°)

x=6.9 ft

step 2

Find the opposite side to the angle of 80 degrees

Let

y ----> the opposite side to the angle of 80 degrees

we know that

The function sine of angle of 80 degrees is equal to divide the opposite side to the angle of 80 degrees by the hypotenuse (40 ft)

sin(80°)=y/40

y=(40)sin(80°)

y=39.4 ft

Answer:

Step-by-step explanation:

[tex]\text{The vertex form of an an equation of a quadratic function:}\\\\y=a(x-h)^2+k\\\\(h,\ k)-vertex\\\\\text{We have}\ g(x)=(x-h)^2+k,\ \text{and the vertex in}\ (9,\ 8).\\\\\text{Therefore}\ h=9\ \text{and}\ k=8.\ \text{substitute:}\\\\g(x)=(x-9)^2+8[/tex]

Answer:

The answer is g(x) = (x - 9)^2 + -8

So 9 and -8 are the correct answers

Step-by-step explanation:

The guy above got the first one right but not the second one, it's supposed to be negative.

Answer:

s is neding some more in fo

Step-by-step explanation:

Answer:

x³ - 3x² - 13x + 15

Step-by-step explanation:

Each term in the second factor is multiplied by each term in the first factor, that is

x(x² - 6x + 5) + 3(x² - 6x + 5) ← distribute both parenthesis

= x³ - 6x² + 5x + 3x² - 18x + 15 ← collect like terms

= x³ - 3x² - 13x + 15

[tex]\bf (\stackrel{x_1}{x}~,~\stackrel{y_1}{-9})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-(-9)}{0-x}=\stackrel{\stackrel{slope}{\downarrow }}{-4}\implies \cfrac{1+9}{-x}=-4 \\\\\\ \cfrac{10}{-x}=-4\implies 10=4x\implies \cfrac{10}{4}=x\implies \cfrac{5}{2}=x[/tex]

Answer:

7 inches

Step-by-step explanation:

The dimension of the rectangular gift is 10 by 12 inches so let us find the perimeter of this rectangle.

Perimeter of rectangular gift = 2 (L+ W) = 2 (10 +12) = 44 inches

Since we are to use the same length of ribbon to wrap a circular clock so the perimeter or circumference should be 44 inches.

[tex]2\pi r=44[/tex]

[tex]r=\frac{44}{2\pi }[/tex]

[tex]r=7.003[/tex]

Therefore, the maximum radius of the circular clock would be 7 inches.

Answer:

The maximum radius of the circular clock is 7 in

Step-by-step explanation:

We must calculate the perimeter of the rectangle

We know that the rectangle is 10 in x 12 in

If we call L the rectangle length and we call W the width of the rectangle then the perimeter P is:

[tex]P = 2L + 2W[/tex]

Where

[tex]L = 10[/tex]

[tex]W = 12[/tex]

[tex]P = 2 * 10 + 2 * 12\\\\P = 20 + 24[/tex]

[tex]P = 44\ in[/tex]

Now we know that the perimeter of a circle is:

[tex]P = 2\pi r[/tex]

In order for the perimeter of the circumference to be equal to that of the rectangle, it must be fulfilled that:

[tex]2\pi r = 44\\\\r=\frac{44}{2\pi}\\\\r=7\ in[/tex]

We solve the equation for r

The image of Q after QRST has been reflected across the y-axis and then rotated 90 degrees about the origin is (-2,9 ), (2,-9) is correct .

The point Q(-9,2) undergoes a reflection across the y-axis, resulting in Q'(9,2).

Subsequently, two possible 90-degree rotations about the origin are considered.

For a counterclockwise rotation, the coordinates become Q'(-2,9), while for a clockwise rotation, the coordinates become Q'(2,-9).

The process of reflection across the y-axis involves negating the x-coordinate, and the rule for this transformation is (x, y) → (-x, y).

Applied to Q(-9,2), it yields Q'(9,2).

For a counterclockwise rotation of 90 degrees, the rule is (x, y) → (-y, x). Applying this to the reflected point Q'(9,2) results in Q'(-2,9).

Alternatively, for a clockwise rotation of 90 degrees, the rule is (x, y) → (y, -x). Applying this rule to the reflected point Q'(9,2) yields Q'(2,-9).

Therefore, after a reflection across the y-axis followed by a 90-degree rotation (either counterclockwise or clockwise) about the origin, the coordinates of the final image point Q' can be either (-2,9) or (2,-9), depending on the direction of rotation.

Answer:

The Answer is D

Step-by-step explanation:

If the Exponent is 1 or just x then it is linear.

* If the Exponent has and x, then this graph is exponential because anything to the power of X is exponential.

1/2(1/2)=0.25^x

Answer:

The Answer is C

Step-by-step explanation:

Just took ed2020 test

Answer:

-2

Step-by-step explanation:

Let's plug your functions f(x)=x^2-2x and g(x)=6x+4 into (f+g)(x)=0 and then solve your equation for x.

So (f+g)(x) means f(x)+g(x).

So (f+g)(x)=x^2+4x+4

Now we are solving (f+g)(x)=0 which means we are solve x^2+4x+4=0.

x^2+4x+4 is actually a perfect square and is equal to (x+2)^2.

So our equation is equivalent to solving (x+2)^2=0.

(x+2)^2=0 when x+2=0.

Subtracting 2 on both sides gives us x=-2.

Answer:

x=-2

Step-by-step explanation:

f(x) = x^2 - 2x

g(x) = 6x + 4

Add them together

f(x) = x^2 - 2x

g(x) =       6x + 4

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

f(x) + g(x) =x^2 +4x+4

We want to find when this equals 0

0 =x^2 +4x+4

Factor

What two numbers multiply together to give us 4 and add together to give us 4

2*2 =4

2+2=4

0=(x+2) (x+2)

Using the zero product property

x+2 =0    x+2=0

x+2-2=0-2

x=-2

Answer: [tex]36z^2+12z-21[/tex]

Step-by-step explanation:

 You need to remember the multiplication of signs:

[tex](+)(+)=+\\(+)(-)=-\\(-)(-)=+[/tex]

In order to simplify the given the expression:

 [tex](11z^2+4z-6)+(4z-7+12z^2)+(-8+13z^2+4z)[/tex]

You must distribute signs:

[tex]=11z^2+4z-6+4z-7+12z^2-8+13z^2+4z[/tex]

And finally, you must add the like terms:

[tex]=36z^2+12z-21[/tex]

Answer:

huifytyjctrxrtfygvjhk

Step-by-step explanation:

yeah he is right

Answer:

=1050 wildebeests

Step-by-step explanation:

We can form an arithmetic series for the wildebeest migration.

Sₙ=n/2(2a+(n-1)d) where  n is the number of terms, d is the common difference and a is the first term.

a=24

n=20

d=3

Sₙ=(20/2)(2(24)+(20-1)3)

Sₙ=10(48+57)

=1050 wildebeests

[tex]V=\dfrac{1}{3}\pi r^2h\\\\h=2r\\V=\dfrac{1}{3}\pi r^2\cdot(2r)=\dfrac{2}{3}\pi r^3[/tex]

Answer:

[tex]V=\frac{2}{3}\pi R^{3}[/tex]

Step-by-step explanation:

The Volume of a cone is by definition 1/3 of the volume of a Cylinder. In this question, the height equals to diameter (2R).

So, We have:

[tex]h_{cone}=2R\\V=\frac{1}{3}\pi R^{2}h \Rightarrow V=\frac{1}{3}\pi R^{2}2R \Rightarrow V=\frac{2}{3}\pi R^{3}[/tex]

We conclude that under this circumstance, a cone with a height equal to its diameter will turn its volume to be equal to 2/3 of pi times the radius raised to the third power.

In other words, when the height is equal to the diameter. The relation between radius, height and Volume changes completely.

Answer:

10

Step-by-step explanation:

9 1/6 × 1 1/11

Change each number to an improper fraction

9 1/6 = (6*9 +1)/6 = 55/6

1 1/11 = (11*1 +1) /11 = 12/11

55/6 * 12/11

Rearranging

12/6 *55/11

2/1 *5/1

10

Answer:

10

Step-by-step explanation:

[tex]\tt 9\cfrac{1}{6}\cdot 1\cfrac{1}{11}= \cfrac{55}{6}\cdot\cfrac{12}{11}=\cfrac{5}{1}\cdot\cfrac{2}{1}=10[/tex]

Answer:

x=48

Step-by-step explanation:

Answer:

17x

Step-by-step explanation:

combine like terms,you would end up with 20x because if you combine 3x and 2x=5 then 5x+15x is 20x.then 20x-3 is 17x.

Answer:

d (last choice)

Step-by-step explanation:

The explicit form of a geometric sequence is [tex]a_n=a_1 \cdot r^{n-1}[/tex] where [tex]a_1[/tex] is the first term while [tex]r[/tex] is the common ratio.

We are given the first term [tex]a_1=47[/tex].

We are given the sixth term [tex]a_6=-789929[/tex].

If we divide 6th term by 1st term this is the result:

[tex]\frac{a_1 \cdot r^5}{a_1 }=\frac{-789929}{47}[/tex]

Simplify both sides:

[tex]r^5=-16807[/tex]

Take the fifth root of both sides:

[tex]r=-7[/tex]

The common ratio is -7.

So all we have to do is start with the first term and keep multiplying by -7 to get the other terms.

[tex]a_1=47[/tex]

[tex]a_2=47(-7)=-329[/tex]

[tex]a_3=47(-7)^2=2303[/tex]

[tex]a_4=47(-7)^3=-16121[/tex]

[tex]a_5=47(-7)^4=112847[/tex]

[tex]a_6=47(-7)^5=-789929[/tex]

The terms -329,2303,-16121,112847 are what we are looking for in our choices.

That's the last choice.

The two chords on top of each other are the same length as the single vertical chord.

The vertical chord is  2 + 4 +2  = 8 units long.

Z = 8-2 = 6

The answer is A.

Length of chord z is 6.

It is defined as the line segment joining any two points on the circumference of the circle, not passing through its center. Therefore, the diameter is the longest chord of a given circle, as it passes through the center of the circle.

From the figure we can write,

[tex]z+2=2+4+2[/tex]

[tex]z+2=8[/tex]

[tex]z=8-2=6[/tex]

Length of chord z is 6.

Find out more information about chord length here

https://brainly.com/question/9857445

#SPJ2

Answer:

z=312 if you meant x=26

Step-by-step explanation:

Direct proportional means there is a constant k such that z=kr. k is called the constant of proportionality. The constant k will never change no matter your (x,z).

So using our equation z=kr with point (18,216) we will find k.

216=k(18)

Divide both sides by 18

216/18=k

k=216/18

Simplify

k=12

So we now know the equation fully that satisfies the given conditions of directly proportion and goes through (x,z)=(18,216).

It is z=12x.

Now we want to know the value of z if x=26.

Plug it in. z=12(26)=312

z=312

[tex]\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{-10}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-10-6}{-2-2}\implies \cfrac{-16}{-4}\implies 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-6=4(x-2) \\\\\\ y-6=4x-8\implies y=4x-2[/tex]

Answer:

y = 4x - 2.

Step-by-step explanation:

The slope is  difference in y values  / difference in x values

= (6 - -10) /  (2 - -2)

= 16 / 4

= 4.

Using the point-slope form of a line

y - y1 = m(x - x1)  where m = slope and (x1, y1) is a point on the line, we have:

y - 6 = 4(x - 2)

y = 4x - 8 + 6

y = 4x - 2.

Answer:

[tex]4x^2+20x+25[/tex] square units

Step-by-step explanation:

We are given that side of a square has the dimension [tex]s = 2x + 5[/tex] and using this, we are to write an expression for the area of this square.

We know that the formula of area of a square is given by:

Area of square = [tex]s^2[/tex]

So substituting the given value in the above formula to get:

Area of square = [tex](2x+5)^2 = (2x+5)(2x+5) = 2x(2x)+2x\times5+5(2x)+5\times5 = 4x^2+20x+25[/tex] square units

Answer:

[tex]A = 4x ^ 2 + 20x +25[/tex]

Step-by-step explanation:

Remember that all sides of a square have the same length. Therefore, the Area of a square is defined as:

[tex]A = s ^ 2[/tex]

Where s is the length of the sides of the squares.

In this case we know that the length of the sides is:

[tex]s = 2x + 5[/tex]

So the area is:

[tex]A = (2x +5) ^ 2[/tex]

We develop the expression and we have left that the area is:

[tex]A = 4x ^ 2 + 20x +25[/tex]

Answer:

4/15.

Step-by-step explanation:

In probability, there are two types of events: the ones that are not related to each other and the ones that are related to each other. The former types of events are called independent events. In such cases, since the occurrence of one event is not related to and does not affect the other event, therefore, the probabilities of both events can be multiplied if they occur together. It is given that:

P(Q) = 7/15.

P(R) = 4/7.

P(Q and R) = P(Q)*P(R) = 7/15 * 4/7 = 4/15.

Therefore, the probability is 4/15!!!

Answer:

Graph 1 has two solutions

Graph 2 has one solution

Graph 3 has no solution

Graph 4 has two solutions

Step-by-step explanation:

* Lets explain the solution of the quadratic equation

- The quadratic equation represented graphically by a parabola

- The solution of the quadratic equation is the intersection point

  between the parabola and the x-axis

- At the x-axis y coordinate of any point is zero, then the solution is

 the value of x-coordinate of this point

- If the parabola cuts the x-axis at 2 points then there are 2 solutions

- If the parabola cuts the x-axis at 1 point then there is 1 solutions

- If the parabola doesn't cut the x-axis then there is no solution

* Lets solve the problem

# Graph 1:

∵ The parabola cuts the x-axis at two points

∴ There are two solutions

# Graph 2:

∵ The parabola cuts the x-axis at one point

∴ There is one solution

# Graph 3:

∵ The parabola doesn't cut the x-axis

∴ There is no solution

# Graph 4:

∵ The parabola cuts the x-axis at two points

∴ There are two solutions

A quadratic function is given in the general form ax^2 + bx + c = 0, where a, b, and c are constants, and a ≠ 0.
The solutions of a quadratic function are found using the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
The number of solutions is determined by the discriminant, which is the expression inside the square root: b² - 4ac.
Here's how the discriminant determines the number of solutions:
1. If the discriminant is positive (b² - 4ac > 0), there are two distinct real solutions.
2. If the discriminant is zero (b² - 4ac = 0), there is exactly one real solution.
3. If the discriminant is negative (b² - 4ac < 0), there are no real solutions (but there are two complex solutions).
Now, let's apply this to the quadratic functions that you've been given. Unfortunately, you haven't provided the specific functions, so I'll give you a generic example for each case. You will be able to use this method to determine the number of solutions for any given quadratic function.
Example 1: One Solution
Consider the equation x^2 - 4x + 4 = 0.
Here, a = 1, b = -4, c = 4.
Discriminant = (-4)² - 4(1)(4) = 16 - 16 = 0.
Since the discriminant is zero, there is exactly one solution.
Example 2: Two Solutions
Consider the equation x^2 - 4x + 3 = 0.
Here, a = 1, b = -4, c = 3.
Discriminant = (-4)² - 4(1)(3) = 16 - 12 = 4.
Since the discriminant is positive, there are two distinct real solutions.
Example 3: No Real Solutions
Consider the equation x^2 + 2x + 5 = 0.
Here, a = 1, b = 2, c = 5.
Discriminant = (2)² - 4(1)(5) = 4 - 20 = -16.
Since the discriminant is negative, there are no real solutions.
Drag and label each quadratic function with the number of solutions based on your calculation of the discriminant:
- If the discriminant is zero, label it "one solution."
- If the discriminant is positive, label it "two solutions."
- If the discriminant is negative, label it "no real solutions."
Remember to apply this method to each of the quadratic functions that you have by calculating their discriminants.