2xsquared-9x+1=0 value of discriminant and number of real solutions

Answer:

A)13.3

Step-by-step explanation:

20² + y² = 24²

400 + y² = 576

y²  = 176

y=13.3

By Pythagoras theorem, in the given right triangle, the missing length to the nearest tenth is Option(A) 13.3 ft.

According to Pythagoras theorem, the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides.

Mathematically,

(Hypotenuse)² = (Base)² + (Height)² .

For the given triangle, length of hypotenuse is 24ft., height is 20ft and base is y ft.

Using Pythagoras theorem,

⇒ (24)² = y² + (20)²

⇒ y² = 24² - 20²

⇒ y² = 176

∴ y = √176 = 13.2665 ≈ 13.3 ft.

Thus, by Pythagoras theorem, in the given right triangle, the missing length to the nearest tenth is Option(A) 13.3 ft.

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Answer:

This is frankly impossible.

Step-by-step explanation:

What you have given me are three x-intercepts. And it is impossible for a quadratic function to have more than two roots. However, if this was an cubic function, we could multiply (x+5)(x-1)(x-4) which results in the equation which simplifies into x^3 -21x + 20. However, this is a cubic function, not a quadratic function, so something must be wrong with this problem all together.

Answer:

k = 25

Step-by-step explanation:

Step 1: Isolate k by adding 2 on both sides.

1/5k = 5

Step 2: Simplify by multiplying 5 on both sides.

k = 25

[tex]x+2[/tex] is a factor of [tex]x^5+32[/tex] because (by the remainder theorem) the remainder upon dividing [tex]x^5+32[/tex] by [tex]x+2[/tex] is [tex](-2)^5+32=0[/tex].

There's also the sum of fifth powers formula,

[tex]a^5+b^5=(a+b)(a^4-a^3b+a^2b^2-ab^3+b^4)[/tex]

ANSWER

The correct answer is A

EXPLANATION

The given polynomial is

[tex]p(x) = {x}^{5} + 32[/tex]

According to the remainder theorem, if p(x) is divided by x+2 the remainder is p(-2).

If the remainder is zero then x+2 is a factor of f(x).

We plug in x=-2 into the function to obtain;

[tex]p( - 2) = { (- 2)}^{5} + 32[/tex]

[tex]p( - 2) = - 32 + 32[/tex]

[tex]p( - 2) = 0[/tex]

Since the remainder is zero, x+2 is a factor.

The correct answer is A

Answer:

The coefficients would be 4 and/or 3.

Step-by-step explanation:

The coefficient is always the number before the variable.

Answer:

a = 4, b = 3, and c = -3

Step-by-step explanation:

A quadratic equation of a variable is an equation that has the general form of:

[tex]ax^{2}+bx+c=0[/tex], [tex]a\neq 0[/tex]

Where x is the variable, and a, b and c constants; a is the quadratic coefficient (other than 0), b the linear coefficient and c is the independent term. This polynomial can be interpreted by means of the graph of a quadratic function, that is, by a parabola. This graphical representation is useful, because the abscissas of the intersections or point of tangency of this graph, in the case of existing, with the X axis are the real roots of the equation. If the parabola does not cut the X axis the roots are complex numbers, they correspond to a negative discriminant.

So, the coefficients are  a = 4, b = 3, and c = -3

Check the picture below.

Answer:

y= (.37)x + 3

Step-by-step explanation:

1. Best thing to use would be y=mx + b.

2. Flat fee is $3 so that is your b.

3. Every additional message is $0.37, that is your slope(m)

4. That is your answer, x represents the number of text messages

Answer:

The monthly cost for x messages is (3 + 0.37x)$.

Step-by-step explanation:

We are given the following information in the question:

Monthly cost for text message = $3 per month

Cost of each text message = $0.37

Let x be the number of total text messages.

Monthly cost for x messages =

Formula:

[tex]\text{Monthly charges} + (\text{Text messages}\times \text{Cost of each message})\\\text{Putting the values, we get}\\= 3 + (0.37\times x)\\=3 + 0.37x[/tex]

Hence, the monthly cost for x messages is (3 + 0.37x)$.

The volume of Zara's sandwich formed as a rectangular prism, is 421.2 cm³, calculated by multiplying the sandwich's length, width, and height. The surface area is 561.6 cm² which is calculated by adding the areas of each face of the prism. When the sandwich is cut and stacked, the volume remains the same, but the surface area increases.

A. To find the volume of a prism (such as Zara's sandwich), we multiply the length by the width by the height. So, for Zara's sandwich, we would calculate the volume as follows (in cubic centimeters): 13cm × 10.8cm × 3cm = 421.2 cm³.

B. The surface area of a rectangular prism is calculated by 2lw + 2lh + 2wh (where l is the length, w is the width, and h is the height. Plugging in the dimensions Zara measured, we find the surface area to be: 2(13cm × 10.8cm) + 2(13cm × 3cm) + 2(10.8cm × 3cm) = 561.6 cm².

C. When Zara cuts her sandwich in half and stacks one half on top of the other, she is effectively doubling the height while keeping the length and width the same. However, since neither the volume nor surface area formulas have a square or cube factor in the height, the volume will be the same. As for the surface area, because the height is now equivalent to two sandwich halves, and the 'length' is not shared between the two halves, the surface area increases. So, Zara's conclusions are incorrect. The volume stays the same, while the surface area increases.

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a. The volume of Zara's sandwich is 421.2 cm³.

b. The surface area of Zara's sandwich is 561.6 cm².

c. Zara's conclusions are incorrect. The volume stays the same, while the surface area increases.

A. To calculate the volume of a prism (such as Zara's sandwich), multiply its length by breadth by height. So, for Zara's sandwich, the volume would be calculated as follows (in cubic centimeters): 13cm 10.8cm 3cm = 421.2 cm³.

B. A rectangular prism's surface area is computed as 2lw + 2lh + 2wh (where l is the length, w is the width, and h is the height). Using Zara's measurements, we calculate the surface area to be: 2(13cm 10.8cm) + 2(13cm 3cm) + 2(10.8cm 3cm) = 561.6 cm².

C. By cutting her sandwich in half and stacking one half on top of the other, Zara essentially doubles the height while maintaining the length and width. The volume, however, will be the same because neither the volume nor surface area formulae include a square or cube element in the height. The surface area grows since the height is now equivalent to two sandwich half and the 'length' is not split between the two halves. Zara's conclusions are thus wrong. The volume remains constant while the surface area grows.

That is very true.

In mathematics, an inverse operation is an operation that undoes what was done by the previous operation. The four main mathematical operations are addition, subtraction, multiplication, division. The inverse of addition is subtraction and vice versa. The inverse of multiplication is division and vice versa.

Addition and subtraction are indeed inverse operations. They are algebraic operations that do the opposite of one another and can thus 'undo' each other's effects.

The statement that Addition and subtraction are inverse operations is indeed true. In mathematics, an inverse operation is an operation that undoes what was done by the previous operation. In the case of addition and subtraction, they do exactly that. For instance, if you were to add 3 and 4 to get 7, you can undo this operation by subtracting 3 or 4 from 7 which will give back the other original number. Hence, addition and subtraction are deemed as inverse operations.

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The answer is:

[tex]FirstCarSpeed=41mph\\SecondCarSpeed=55mph[/tex]

To calculate the speed of the cars, we need to write two equations in order to create a relation between the two speeds and be able to isolate one in function of the other.

So, let be the first car speed "x" and the second car speed "y", writing the equations we have:

For the first car:

[tex]x_{FirstCar}=x_o+v*t[/tex]

For the second car:

We know that the speed of the second car is the speed of the first car plus 14 mph, so:

[tex]x_{SecondCar}=x_o+(v+14mph)*t[/tex]

Now, we already know that both cars met after 2 hours and 45 minutes, meaning that positions will be the same at that moment, and the distance between A and B is 264 miles,  so, we can calculate the relative speed between them:

If the cars are moving towards each other the relative speed will be:

[tex]RelativeSpeed=FirstCarSpeed-(-SecondCarspeed)\\\\RelativeSpeed=x-(-x-14mph)=2x+14mph[/tex]

Then, since we know that they covered a combined distance which is equal to 264 miles of distance in 2 hours + 45 minutes, we  have:

[tex]2hours+45minutes=120minutes+45minutes=165minutes\\\\\frac{165minutes*1hour}{60minutes}=2.75hours[/tex]

Writing the equation, we have:

[tex]264miles=(2x+14mph)*t\\\\264miles=(2x+14mph)*2.75hours\\\\2x+14mph=\frac{264miles}{2.75hours}\\\\2x=96mph-14mph\\\\x=\frac{82mph}{2}=41mph[/tex]

We have that the speed of the first car is equal to 41 mph.

Now, for the second car we have that:

[tex]SecondCarSpeed=FirstCarSpeed+14mph\\\\SecondCarSpeed=41mph+14mph=55mph[/tex]

Hence, we have that:

[tex]FirstCarSpeed=41mph\\SecondCarSpeed=55mph[/tex]

Have a nice day!

Answer:

55 miles per hour and 41 miles per hour.

Step-by-step explanation:

Enjoy...It is correct because RSM told me so.

I believe we would need some more information to help you answer

Answer:

ATP is an unstable molecule

Explanation:

Recall that ATP and ADP are too unstable to serve as long-term energy storage units. In contrast, glucose has a stable molecular structure, so it stores energy more efficiently than ATP.

#pennfosternotes

See page Biology (v2): Lesson 2: Page 65 in Biology_Lesson 2.pdf

Thanks so much! I hope this helps! =)

Answer:

[tex]\large\boxed{x^2+10x+5=\left(x+5+2\sqrt5\right)\left(x+5-2\sqrt5\right)}[/tex]

Step-by-step explanation:

[tex]\text{Use the quadratic formula:}\\\\ax^2+bx+c=a\left(x-\dfrac{-b-\sqrt{b^2-4a}}{2a}\right)\left(x-\dfrac{-b+\sqrt{b^2-4ac}}{2a}\right)\\======================================[/tex]

[tex]\text{We have:}\ x^2+10x+5\to a=1,\ b=10\ \text{and}\ c=5\\\\\text{Substitute}\\\\b^2-4ac=10^2-4(1)(5)=100-20=80\\\sqrt{b^2-4ac}=\sqrt{80}=\sqrt{16\cdot5}=\sqrt{16}\cdot\sqrt5=4\sqrt5\\\\x_1=\dfrac{-10-4\sqrt5}{2(1)}=-5-2\sqrt5\\\\x_2=\dfrac{-10+4\sqrt5}{2(1)}=-5+2\sqrt5\\\\\bigg(x-\left(-5-2\sqrt5\right)\bigg)=\left(x+5+2\sqrt5\right)\\\\\bigg(x-\left(-5+2\sqrt5\right)\bigg)=\left(x+5-2\sqrt5\right)[/tex]

For the equation to work, you have to have the same number on both sides of the equal sign

so to find ?, you can do:

13 - 2 = 12 - ?       Simplify

11 = 12 - ?       Subtract 12 on both sides

-1 = - ?     Multiply -1 on both sides

1 = ?

To find the missing number in the equation 13-2=12-?, we subtract the known numbers on both sides of the equation.

To find the missing number in the equation 13-2=12-?, we subtract the known numbers on both sides of the equation.

In the equation 13-2=12-x, we need to find the missing number x.

We can solve this equation by subtracting the known numbers on both sides.

Using the concept of simple mathematics, we found the subtraction of the given number.

So the missing number in the equation 13-2=12-x is 11.

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class b median is 80

class a median is 77

the comparison tells me in terms of the situation the data represents is that class b did better than class a

Answer:

There are 50 multiples of 8 between 100 and 500

Step-by-step explanation:

1. We need to find out the multiple of 8 closest and higher than 100.

......80, 88, 96, 104, 112, 120..... It's 104

2. We need to find out the multiple of 8 closest and lower than 500.

....480, 488, 496, 504, 512, 520......It's 496

3. Now, we use 104 and 496, this way:

(496 - 104)/8 + 1 =

392/8 + 1 =

49 + 1 = 50

There are 50 multiples of 8 between 100 and 500

Answer:

50

Step-by-step explanation:

The smallest multiple of 8 in this range is 13 ∙ 8 = 104, and the largest is 62 ∙ 8 = 496. The number of multiples of 8 in this range is the same as the number of numbers in the list

13, 14, 15, ...,60, 61, 62.

To count these, we subtract 12 from each, obtaining the new list

1, 2, 3, ..., 48, 49, 50,

which clearly contains 50 integers. There is one number in the original list for each number in the revised list, so the original list has 50 numbers in it, and there are 50 multiples of 8 between 100 and 500.

Answer:

$432.00

Step-by-step explanation:

$12.00x36= $432.00

The sum of first 10 terms is 620.

Arithmetic Progression (AP) is a numerical series in which the difference between any two subsequent numbers is always the same.

Here a1= 8,a2 = 20,a3  = 32 and a4= 44

Find the difference between two terms

a2 - a1 = 20 - 8 = 12

a3 - a2 = 32 - 20 = 12

a4 - a3 = 44 - 32 = 12 sum of n terms is = n/2[2a1 + (n-1)d]

For the given sequence we have n = 10, a1= 8 and d = 12

substituting values of a1 and n in S = 10/2[2x8 + (10-1)x12]

S = 5[16+9x12]

S = 5[16+108]

S = 5[124]

S = 5x124

S = 620

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I believe the answer is B

Final answer:

The slope of the line containing the points (4,8) and (9,8) is 0, indicating that it is a horizontal line. The correct answer is B. Slope = 0; horizontal line.

Explanation:

The slope of a line is calculated by taking the difference in the y-values of two points on the line (rise) and dividing by the difference in the x-values (run). Using the points (4,8) and (9,8), we can calculate the slope as follows:

Slope (m) = rise / run = 0 / 5 = 0.

Since there is no change in the y-value as we move from one point to the other, the line is horizontal. Thus, the line has a slope of 0. The correct answer to the student's question is B. Slope = 0; horizontal line.

Answer:

All positive integers and zero

A is correct

Step-by-step explanation:

A box of pencils costs $10

The total cost (c) as a function of the number of boxes (b) is expressed as

c = f(b) = 10b

The function, f(b) = 10b

b is independent variable and c is dependent variable.

For any function find domain using independent variable.

b represents number of boxes.

Number of boxes neither be negative nor decimal.

Possible value of b: {0,1,2,3,4,5,.......}

All positive integers and zero.

Domain: All positive integers and zero

Answer: Option A and Option B.

Step-by-step explanation:

You need to remember the logarithms properties:

[tex]log(a)+log(b)=log(ab)\\\\log(a)-log(b)=log(\frac{a}{b})\\\\log(a)^b=b*log(a)[/tex]

You can observe in Option A:

[tex]logM^p=p*logM[/tex] (This is true)

You can observe in Option B:

[tex]logM+logN=log(MN)[/tex] (This is true)

You can observe in Option C:

[tex]logM-logN=log(M-N)[/tex] (This is not true)

You can observe in Option D:

[tex](logM)^p=p*logM[/tex] (This is not true)

Answer:

17%

Step-by-step explanation:

4/24=1.6666666667 rounded up is 17%

The probability that the next tee shot ends up on green is 1 / 6.

It's a field of mathematics that studies the probability of a random event occurring. From 0 to 1, the value is expressed.

P(Event) = Favourable outcomes / Total no. of outcomes

Total no. of shots taken = 4 + 5 + 7 + 3 + 5 = 24

Shots that landed on Green = 4

P( Shot will land on green) = 4 / 24 = 1 / 6

Hence, the probability that the next show will land on green is 1/6.

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Answer:

[tex]\boxed{\text{160 ft}}[/tex]

Step-by-step explanation:

The angle of depression from the ranger at point A and the angle of elevation from the fire on the ground at Point C are congruent (interior opposite angles).

The distance from the ranger up in the tower to the fire on the ground is the hypotenuse AC  of the right triangle ABC.

sin 30 = 80/AC

AC  = 80/sin30 = 80/0.5 = 160 ft

The distance is [tex]\boxed{\textbf{160 ft}}[/tex]

For this case we must solve the following quadratic equation:

[tex]-3x ^ 2 + 1467x-86940 = 0[/tex]

If we divide both sides of the equation by 3 we have:

[tex]-x ^ 2 + 489-28980 = 0[/tex]

The solutions will come from:

[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}[/tex]

Where:

[tex]a = -1\\b = 489\\c = -28980[/tex]

Substituting:

[tex]x = \frac {-489 \pm \sqrt {(489) ^ 2-4 (-1) (- 28980)}} {2 (-1)}\\x = \frac {-489 \pm \sqrt {239121-115920}} {- 2}\\x = \frac {-489 \pm \sqrt {123201}} {- 2}\\x = \frac {-489 \pm351} {- 2}[/tex]

The roots are:

[tex]x_ {1} = \frac {-489 + 351} {- 2} = \frac {-138} {- 2} = 69\\x_ {2} = \frac {-489-351} {- 2} = \frac {-840} {- 2} = 420[/tex]

ANswer:

[tex]x_ {1} = 69\\x_ {2} = 420[/tex]

Answer:

46

Step-by-step explanation:

There is an open + in the middle. It does not have any brackets around it. Therefore you do it at the very last.

Left side of the plus sign.

[16 ÷ (2 + 3*2)] Do the multiplication inside the parenthesis ( 2*3) first.

= [16 ÷ (2 + 6)] Add inside the parenthesis.

= [16 ÷ 8 ]         Do the division

= 2

Right side of the open plus sign

[4 * (36 - 25)]   Do the subtraction first.

[4 * 11 ]             Do the multiplication

44

Now combine both right and left side.

2 + 44

46

The answer is 46.

46

I don’t think I helped

The answer is:

The function is greater or equal to 0 at the points (-3,6), (-2,0), (0,6) and (4,0).

To find where the function is greater or equal to 0, we need to look (using the graph) where the function is above the x-axis

So, we can see that the function is above the x-axis from the point (-3,6)  to the point (4,0), for these points, the function is greater or equal to 0.

Hence, the function is greater or equal to 0 at the points (-3,6), (-2,0), (0,6) and (4,0), or the function is greater or equal to 0,  from -3 to 4 (x-axis values or input).

We have that:

[tex]f(-3)=6\\6\geq 0\\\\f(-2)=0\\0=0\\\\f(0)=6\\6\geq 0\\\\f(4)=0\\0=0[/tex]

Have a nice day!

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}\dfrac{1}{3}x+y=\dfrac{0}{3}&\text{multiply both sides by 3}\\\\\dfrac{1}{6}x+\dfrac{1}{5}y=\dfrac{9}{10}&\text{multiply both sides by 30}\end{array}\right\\[tex]\left\{\begin{array}{ccc}x+3y=0&\text{multiply both sides by (-2)}\\5x+6y=27\end{array}\right\\\underline{+\left\{\begin{array}{ccc}-2x-6y=0\\5x+6y=27\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad3x=27\qquad\text{divide both sides by 3}\\.\qquad\boxed{x=9}\\\\\text{Put the value of x to the first equation:}\\\\9+3y=0\qquad\text{subtract 9 from both sides}\\3y=-9\qquad\text{divide both sides by 3}\\\boxed{y=-3}[/tex][/tex]

Answer: 432 units²

Step-by-step explanation:

The figure is composed by two trapezoids.

The formula for calculate the area of a trapezoid is:

[tex]A=\frac{h}{2}(B+b)[/tex]

Where "B" is the larger base, "b" is the smaller base and "h" is the height.

Let be [tex]A_f[/tex] the area of the figure, [tex]A_1[/tex] the area of the trapezoid on the left and [tex]A_2[/tex] the area of the trapezoid of the right. Then the area of the figure will be:

 [tex]A_f=A_1+A_2[/tex]

[tex]A_f=\frac{h_1}{2}(B_1+b_1)+\frac{h_2}{2}(B_2+b_2)[/tex]

Substituting values, you get:

[tex]A_f=\frac{16units}{2}(25units+4units)+\frac{10units}{2}(25units+15units)=432units^2[/tex]

Answer:

Area of given figure = 432 unit ²

Step-by-step explanation:

Points to remember

Area of trapezoid = h(a + b)/2

Where h - height  and a and b  are two parallel sides

To find the area of given figure

It is given two trapezoid

Area of 1st trapezoid

h = 16, a = 25 and b = 4

Area = h(a+ b)/2

 = 16(25 + 4)/2

 = 232 units ²

Area of 2nd trapezoid

h = 10, a = 25 and b = 15

Area = h(a+ b)/2

 = 10(25 + 15)/2

 = 200 units ²

Total area = 232 + 200 = 432 units²

The volume of the cylinder is:

3.14 x 0.3^2 x 0.75 = 0.21 cubic meters.

Multiply the density of the kerosene by the volume of the cylinder:

0.21 x 815 = 17.85 kg.

Answer:

173

Step-by-step explanation:

Answer:

C) 6.6 gallons

Step-by-step explanation:

10oz * 85 = 850oz

There are 128 ounces in a gallon.

850/128 = 6.64

Answer:  Option 'c' is correct.

Step-by-step explanation:

Since we have given that

Number of servings = 85

Number of ounces per serving = 10 ounce

Total number of ounces would be

[tex]85\times 10\\\\=850[/tex]

As we know that

1 gallon = 128 ounces

So, Number of gallons of the soup were sold on Monday would be \

[tex]\dfrac{850}{128}\\\\=6.64\\\\\approx 6.6 \ gallons[/tex]

Hence, Option 'c' is correct.