Find the discriminant and the number of real roots for this equation.
x^2+3x+8=0
Apex

Answer:

-3

Step-by-step explanation:

-2x+8=14

Subtract 8 from each side

-2x+8-8=14-8

-2x = 6

Divide by -2

-2x/-2 = 6/-2

x = -3

-2x + 8 = 14

Step 1: Bring 8 to the right side of the equation. To do this subtract 8 to both sides (this is the opposite of addition and will cancel 8 from the left side)

-2x + (8 - 8) = 14 - 8

-2x + 0 = 6

-2x = 6

Step 2: Isolate x by dividing -2 to both sides (division is the opposite of multiplication and will cancel -2 from the left side)

-2x/-2 = 6/-2

x = -3

Check:

Plug -3 where you see x and solve

-2(-3) + 8 = 14

6 + 8 = 14

14 = 14...............................Correct!

Hope this helped!

Answer:  56 mph

Step-by-step explanation:

48 miles x 2 hours = 96 miles

60 miles x 4 hours =  240 miles

240 + 96 = 360 total miles

360 / 6 (hours) = 56 mph

Answer: 100 cm = 1 m

Step-by-step explanation:

Like most metric measurements, 100 centimeters are equal to 1 meter.

Answer:

Area: 135 ft^2

Perimeter: 50 ft

Step-by-step explanation:

area:

take the rectanle so length 12 x 9 = 108 so that is the length of the rectangle and now we need to find that of the triangle left over

subract 18 - 12 = 6 so that is the base of the trianle and we know the side length is 9 so plus it in A = (9)(6)/2

A = 54/2

A = 27

add 27 + 108 to get the total area

135

perimeter:

18 + 9 + 11 + 12 = 50

For this case we have that by definition, the perimeter of the trapezoid is given by the sum of its sides:

[tex]p = 9 + 18 + 11 + 12\\p = 50[/tex]

So, the perimeter is 50ft

On the other hand, the area is given by:

[tex]A = \frac {1} {2} (b_ {1} + b_ {2}) * h[/tex]

Where:

[tex]b_ {1}:[/tex] It is the largest base

[tex]b_ {2}:[/tex] It is the minor base

h: It's the height

Substituting the values:

[tex]A = \frac {1} {2} (18 + 12) * 9\\A = \frac {1} {2} (30) * 9\\A = \frac {1} {2} (270)\\A = 135[/tex]

So, the area of the trapezoid is [tex]135 \ ft ^ 2[/tex]

Answer:

the perimeter is 50ft

the area of the trapezoid is [tex]135 \ ft ^ 2[/tex]

Answer:

[tex]\large\boxed{Q1:\ x=2\ or\ x=5}\\\boxed{Q2:\ x=1-\sqrt{21}\ or\ x=1+\sqrt{21}}[/tex]

Step-by-step explanation:

[tex]\text{Use the quadratic formula:}\\\\ax^2+bx+c=0\\\\\text{If}\ b^2-4ac<0,\ \text{then the equation has}\ \bold{no\ solution}\\\\\text{If}\ b^2-4ac=0,\ \text{then the equation has one solution}\ x=\dfrac{-b}{2a}\\\\\text{If}\ b^2-4ac>0,\ \text{then the equation has two solutions}\ x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\==========================================[/tex]

[tex]\bold{Q1}\\\\x^2-7x+10=0\\\\a=1,\ b=-7,\ c=10\\\\b^2-4ac=(-7)^2-4(1)(10)=49-40=9>0\\\\\sqrt{b^2-4ac}=\sqrt9=3\\\\x_1=\dfrac{-(-7)-3}{2(1)}=\dfrac{7-3}{2}=\dfrac{4}{2}=2\\\\x_2=\dfrac{-(-7)+3}{2(1)}=\dfrac{7+3}{2}=\dfrac{10}{2}=5\\\\========================================[/tex]

[tex]\bold{Q2}\\x^2-2x=20\qquad\text{subtract 20 from both sides}\\\\x^2-2x-20=0\\\\a=1,\ b=-2,\ c=-20\\\\b^2-4ac=(-2)^2-4(1)(-20)=4+80=84>0\\\\\sqrt{b^2-4ac}=\sqrt{84}=\sqrt{4\cdot21}=\sqrt4\cdot\sqrt{21}=2\sqrt{21}\\\\x_1=\dfrac{-(-2)-2\sqrt{21}}{2(1)}=\dfrac{2-2\sqrt{21}}{2}=1-\sqrt{21}\\\\x_2=\dfrac{-(-2)+2\sqrt{21}}{2(1)}=\dfrac{2+2\sqrt{21}}{2}=1+\sqrt{21}[/tex]

Answer:

Step-by-step explanation:

x^2 - 7x + 10 = 0 can be factored as follows:  (x - 5)(x - 2).  Note that -5x -2x combine to -7x, the middle term of this quadratic, and that (-5)(-2) = +10, the constant term.  Setting each of these factors = to 0 separately, we get:

x = 5 and x = 2.

x^2 - 2x = 20 should be rewritten in standard form for a quadratic equation before you attempt to solve it:  x^2 - 2x - 20 = 0.  This quadratic is not so easily factored as was the previous one.  Let's use the quadratic formula:

      -b ± √(b²-4ac)

x = --------------------

             2a

Here, a = 1, b = -2 and c = -20, so the discriminant b²-4ac = (-2)^2 - 4(1)(-20), or 4 + 80, or 84.  84 has only one perfect square factor:  4·21.  Because the discriminant is +, we know that this equation has two real, unequal roots.

They are:

       -(-2) ± √(4·21)         2 ± 2√21

x = ----------------------  =  ----------------- =   1 ± √21

             2(1)                            2

ANSWER

The graph in option D.

EXPLANATION

The given function is:

[tex]y = 3 {x}^{2} - 12x + 10[/tex]

We complete the square to obtain:

[tex]y = 3( {x}^{2} - 4x) + 10[/tex]

[tex]y = 3( {x}^{2} - 4x + {( - 2)}^{2} ) + 10 - 3 {( - 2)}^{2}[/tex]

[tex]y = 3{( x- 2)}^{2}+ 10 - 12[/tex]

[tex]y = 3{( x- 2)}^{2} - 2[/tex]

The graph of this function opens upwards and has its vertex at (2,-2).

The y-intercept is 10.

From the options the graph that satisfies all these properties is D.

Answer:

b

Step-by-step explanation:

using pythagoras theorem:

d=(5^2+4^2)^1/2

=6.4 units

Answer:

The approximate length of the diagonal of the rectangle = 6.4 units ⇒ B

Step-by-step explanation:

* Lets revise the properties of the rectangle

- The rectangle has 4 sides

- Each two opposite sides are parallel and equal in length

- It has for right angles

- Its two diagonals are equal in length

- The diagonal divide the rectangle into two congruent right triangles

* Now lets solve the problem

∵ The length of the rectangle = 5 units

∵ The width of the rectangle = 4 units

∵ The diagonal of the rectangle with the length and the width formed

  right triangle, the length and the width are its two legs and the

  diagonal is its hypotenuse

- To find the length of the hypotenuse use Pythagoras theorem

∵ Hypotenuse = √[(leg1)² + (leg2)²]

∴ The length of the diagonal = √[5² + 4²] = √[25 + 16] = √41

∴ The approximate length of the diagonal of the rectangle = 6.4 units

Answer:

Step-by-step explanation:

Y=20. X=10. Y=5. X=2.5

X is half of Y so 20 is y

Answer:

20

Step-by-step explanation:

Answer:

Transactional service

Step-by-step explanation:

If Allison pays all her bills using her bank's online bill pay, it will be considered as transactional service which is a type of electronic banking service.

A transaction involves paying a supplier for its services provided or any goods delivered.

Here the services used will include electricity, water, internet, gas, etc for which the bills are paid. Therefore, the correct answer is transactional service.

Answer:

Transaction service

Step-by-step explanation:

f(x) = x³ + 2x² + x

f(x) = x.(x² + 2x + 1)

f(x) = x.(x + 1)²

So, f(x) = 0 when x = 0 or when x = -1

But

f(x) = x.(x + 1)² = x.(x + 1).(x + 1)

So we have three roots, x = 0, x = -1 and x = -1, although two of them are equal.

So we have a multiple zero x = -1 with a multiplicity 2.

Alterativa A.

Answer:

A

Step-by-step explanation:

The answer is:

The correct option is:

A) $74.55

To calculate how much does Sonya pay for the four pairs altogether, we need to calculate the original price after the 50% discount and the taxes.

Calculating we have:

[tex]PriceAfterDiscount=35*50(percent)=35*\frac{50}{100}\\\\35*\frac{50}{100}=35*0.5=17.5[/tex]

We have that before the tax, the price of the shoes was $17.5, then, calculating the price after the taxes, we have:

[tex]AfterTaxes=17.5(1+6.5(percent))=17.5(1+\frac{6.5(percent)}{100})\\\\AfterTaxes=17.5(1+\frac{6.5(percent)}{100})=17.5*(1+0.065)\\\\AfterTaxes=17.5*(1+0.065)=17.5*1.065=18.637[/tex]

So, we have that the price after discount and the taxes is $18.637 per each pair of shoes.

Hence, the price for the four pairs of shoes will be:

[tex]TotalPrice=4*18.637=74.548=74.55[/tex]

Have a nice day!

Step-by-step explanation:

Shift to the right 5 units and down 2 units.

Answer:

Step-by-step explanation:

Answer:

I think it’s 28 but I’m not sure

(sorry if it’s wrong)

Step-by-step explanation:

Answer:

A. [tex]y-5=1.5(x-4)[/tex].

B. [tex]y=1.5x-1[/tex].

Step-by-step explanation:

The given line passes through (2,2) and (4,5).

The slope the given line can be found using the formula;

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{5-2}{4-2}[/tex]

This gives [tex]m=\frac{3}{2}=1.5[/tex].

The slope-intercept form is [tex]y-y_1=m(x-x_1)[/tex].

We substitute the second point to get:

[tex]y-5=1.5(x-4)[/tex].

We expand to get:

[tex]y-5=1.5x-6[/tex].

[tex]y=1.5x-6+5[/tex].

[tex]y=1.5x-1[/tex].

C is the correct answer. Good luck!

Answer:

Average = 1

Step-by-step explanation:

Let us define the average first:

Average is calculated by adding up all the values and then dividing the sum by total number of values.

The formula for average may be written as:

[tex]Average = \frac{Sum}{count}[/tex]

In the following case,

Sum of numbers = -3-2+2+2+6 = 5

Count = 5

So,

Average = 5/5

=> Average = 1

Answer:

the answer is 1

Step-by-step explanation:

Sum of numbers = -3-2+2+2+6 = 5

Count = 5

So,  

Average = 5/5

=> Average = 1

Answer:

a.)The total 4-letters passwords when repetition of letters is allowed are 456976

b.)The total 4-letters passwords when repetition of letters is not allowed are 358800

Step-by-step explanation:

Some situations of probability involve multiple events. When one of the events affects others, they are called dependent events. For example, when objects are chosen from a list or group and are not returned, the first choice reduces the options for future choices.

There are two ways to sort or combine results from dependent events. Permutations are groupings in which the order of objects matters. Combinations are groupings in which content matters but order does not.

How many 4-letter passwords can be made using the letters A throught Z if...

a)Repetition of letters is allowed?

There are only 26 possible values for each letter of the password (The English Alphabet consists of 26 letters). The total 4-letters passwords when repetition of letters is allowed are [tex]26^{4} =456976[/tex]

b) Repetition of letters is not allowed?

If repetition of  letters is not allowed, we can only choose 4 letters out of 26. Using the permutation equation [tex]nP_{k} =\frac{n!}{(n-k)!}[/tex]

The total 4-letters passwords when repetition of letters is not allowed are [tex]26P_{4} =\frac{26!}{(26-4)!}=26.25.24.23=358800[/tex]

.

When repetition of letters is allowed, there are 456,976 possible 4-letter passwords that can be made using the letters A through Z. When repetition of letters is not allowed, there are 358,800 possible passwords that can be made.

a) When repetition of letters is allowed, we have 26 choices for each of the 4 positions in the password. Therefore, the number of 4-letter passwords that can be made is 26 * 26 * 26 * 26 = 456,976.

b) When repetition of letters is not allowed, the number of choices for the first position is 26. For the second position, there are 25 choices left, since we can't repeat the letter used in the first position. Similarly, for the third position, there are 24 choices, and for the fourth position, there are 23 choices. Therefore, the number of 4-letter passwords that can be made without repetition is 26 * 25 * 24 * 23 = 358,800.

https://brainly.com/question/19866551

#SPJ3

Answer:

see explanation

Step-by-step explanation:

Given

f(x) = x² - p(x + 1) - c

     = x² - px - p - c ← in standard form

with a = 1, b = - p and c = - p - c

Given that α and β are the zeros of f(x), then

α + β = - [tex]\frac{b}{a}[/tex] and αβ = [tex]\frac{c}{a}[/tex], thus

α + β = - [tex]\frac{-p}{1}[/tex] = p , and

αβ = [tex]\frac{-p-c}1}[/tex] = - p - c

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

(α + 1)(β + 1) ← expand factors

= αβ +α + β + 1 ← substitute values from above

= - p - c + p + 1

= - c + 1 = 1 - c ← as required

Final answer:

By applying Vieta's formulas to the given polynomial, we can determine that the product (α + 1)(β + 1) equals 1 - c.

Explanation:

Given the polynomial f(x) = x2 - p(x + 1) - c, whose zeroes are alpha (α) and beta (β), we can use the relationship between the coefficients of a polynomial and its zeroes to find the value of (α + 1)(β + 1). According to Vieta's formulas for a second-degree polynomial ax2 + bx + c = 0, the sum of its roots (-b/a) is equal to α + β, and the product of its roots (c/a) equals αβ.

For this specific polynomial, a = 1, b = -p, and c = -c. Thus, we have:

α + β = p

αβ = -c

Now, let's calculate (α + 1)(β + 1):

(α + 1)(β + 1) = αβ + α + β + 1 = (-c) + (p - 1) + 1 = 1 - c

first off, let's recall that supplementary angles are just two sibling angles that add up to 180°.

so we have ∡T and ∡S, but we also know that ∡T = 3∡S, namely T = 3S.

[tex]\bf T+S=180\implies \stackrel{T}{3S}+S=180\implies 4S=180\implies S=\cfrac{180}{4}\implies S=45 \\\\\\ T=3S\implies T=3(45)\implies T=135[/tex]

Answer:

10q

Step-by-step explanation:

Answer:

tan e = -1

cot e = -1

sin e = √2/2

cosec e = √2

cos e = -√2/2

sec e = -√2.

Step-by-step explanation:

6/6-  is the tangent of e  so tan e = -1.

cot e = 1/tan e = -1.

The hypotenuse  of the triangle containing angle e = √(-6)^2 + (6)^2 ( By the pythagoras theorem) and = √72 =  6√2.

Therefore sin e =   6/6√2

= 1/√2

= √2/2

cosec e  = 1 ./ sin e = √2.

cos e = -6 / 6√2

= -√2/2.

sec e = 1/cos e = -√2.

Final answer:

The domain of the function g(x) = -[x] + 3 is all real numbers because the floor function is defined for all real numbers.

Explanation:

The given function is g(x) = -[x] + 3. To determine the domain of g(x), we look for the set of all input values (x) that the function can accept.

The square brackets around x indicate that we are dealing with the floor function, which takes a real number and rounds it down to the nearest integer.

Since the greatest integer function is defined for all real numbers, the only restriction we have is when the function involves division by zero.

Since the process of rounding down to the nearest integer is defined for all real numbers, the domain of g(x) is all real numbers, which is expressed as ∞ < x < ∞ or –∞ < x < ∞.

Answer:

60cm^2

Step-by-step explanation:

5 * 12 = 60cm^2

Answer:

[tex]6050(1+\frac{0.031}{12})^{3}(1+\frac{0.206}{12})^{9}[/tex]

Step-by-step explanation:

p = $6050

The card offered an introductory APR of 3.1% for the first 3 months

r = 3.1% or 0.031

t = 3

n = 12

So, compound interest formula for this period is :

[tex]6050(1+\frac{0.031}{12})^{3}[/tex]

And a standard APR of 20.6% thereafter,

r = 20.6% or 0.206

t = 9

n = 12

So, compound interest formula for this period is :

[tex]6050(1+\frac{0.206}{12})^{9}[/tex]

Now as the p is common, we can re write the expressions as :

[tex]6050(1+\frac{0.031}{12})^{3}(1+\frac{0.206}{12})^{9}[/tex]

Answer:

242 mm²

Step-by-step explanation:

Given 2 similar figures with

ratio of sides = a : b, then

ratio of areas = a² : b² and

ratio of volumes = a³ : b³

Here the ratio of volumes = 27 : 1331, hence

ratio of sides = [tex]\sqrt[3]{27}[/tex] : [tex]\sqrt[3]{1331}[/tex] = 3 : 11, thus

ratio of areas = 3² : 11² = 9 : 121

let x be the surface area of the larger figure then by proportion

[tex]\frac{18}{9}[/tex] = [tex]\frac{x}{121}[/tex] ( cross- multiply )

9x = 18 × 121 ( divide both sides by 9 )

x = [tex]\frac{18(121)}{9}[/tex] = 2 × 121 = 242

The surface area of the larger figure is 242 mm²

the last one on the right

Answer:

A. different probabilities