evaluate the expression.

Step-by-step explanation:

the solutions for a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = -4

c = k

x = (4 ± sqrt(16 - 4k))/2 = 2 ± sqrt(4 - k)

x1 = 2 + sqrt(4 - k)

x2 = 2 - sqrt (4 - k)

x1 = 2 + x2

2 + sqrt(4 - k) = 2 + 2 - sqrt(4 - k)

2×sqrt(4 - k) = 2

sqrt(4 - k) = 1

4 - k = 1

k = 4 - 1 = 3

x1 = 3

x2 = 1

Answer:

The roots are 1 and 3.

k = 3.

Step- by-step explanation:

We use the facts that if α and β are the roots of ax^2 + bx + c = o then α+ β = -b/a and  α β = c/a.

The roots are written as  α and α+2, then:

α + α + 2 = -(-4)

2α + 2 = 4

α + 1 = 2

α = 1

also

α (α + 2) = k

Substituting for α:

1(1 + 2) = k

k = 3.

The roots are 1 and 1 + 2 = 3.

Answer: I Got No solution for this problem

Step-by-step explanation:

Graph each side of the equation. The solution is the x-value of the point of intersection.

No solution

Answer:

x =  - 11

Step-by-step explanation:

Solving

(x + 5)² = 36 ( take square root of both sides )

x + 5 = ± [tex]\sqrt{36}[/tex] = ± 6 ( subtract 5 from both sides )

x = - 5 ± 6

Then

x = - 5 + 6 = 1

x = - 5 - 6 = - 11

The other solution is x = - 11

Answer:

D. 1.25. 30 31 - 35. Convert the answer into a mixed number by dividing ... 8.7 6 5. 4.235. Subtract the two numbers. B. 4.235. 14) V81. 8) 0.2 * 0.3 * 0.4.

Step-by-step explanation:

Answer:

There is something wrong in the answer options.  Please check the equations and formatting.  

Step-by-step explanation:

Assuming the referenced equation is y = 3x + 1 (and not y - 3x + 1), we can say the following.

This is written in the form of y=mx+b, where m is the slope and b the y-intercept (the value of y when x=0).

The slope, as I've written it, is 3.  Parallel lines will have the same slope (but a different b).  Perpendicular lines will have a slope that is the negative inverse of the slope of the reference line.  In this case, it would have a slope of -(1/3).

None of the answer options come close to this.  So something is wrong in the question, unless "NONE" is an option.

Answer:

y = 2/3x

Step-by-step explanation:

Answer:

p=2/5

p=0.4

Step-by-step explanation:

Answer:

p=2/5

Step-by-step explanation:

6p+13.5=159/10

Answer:

The tax is 8%

Step-by-step explanation:

Take the final price and subtract the original price

513-475 = 38

Divide by the original price

38/475 =.08

Change to percent form

8%

The tax is 8%

Answer:

after 25 minutes the temperature was at 78 degrees

Step-by-step explanation:

Answer:

Approximately [tex]68.5\; \rm mm[/tex].

Step-by-step explanation:

Convert the angle of this sector to radians:

[tex]\begin{aligned}\theta &= 127^{\circ} \\ &= 127^{\circ} \times \frac{2\pi}{360^{\circ}} \\ &\approx 2.22\end{aligned}[/tex].

The formula [tex]s = r\, \theta[/tex] relates the arc length [tex]s[/tex] of a sector of angle [tex]\theta[/tex] (in radians) to the radius [tex]r[/tex] of this sector.

In this question, it is given that the arc length of this sector is [tex]s = 36\; \rm mm[/tex]. It was found that [tex]\theta = 2.22[/tex] radians. Rearrange the equation [tex]s = r\, \theta[/tex] to find the radius [tex]r[/tex] of this sector:

[tex]\begin{aligned} r&= \frac{s}{\theta} \\ &\approx \frac{36\; \rm mm}{2.22} \\ &\approx 16.2\; \rm mm\end{aligned}[/tex].

The perimeter of this sector would be:

[tex]\begin{aligned}& 2\, r + s \\ =\; & 2 \times 16.2\; {\rm mm} + 36\; {\rm mm} \\ =\; & 68.5\; \rm mm\end{aligned}[/tex].

Answer:

430 > 33.73x + 27      ---->         x < 11

Step-by-step explanation:

The inequality describes the total amount that can be spent for a whole number of days. To solve for the number of days, solve for x (x<11.95). Because she can't rent for only a part of a day, and because she can't spend more than $430, the inequality becomes x<11.

Answer:

Step-by-step explanation:

33.73x + 27 <= 430

0.06 is for every mile. She plans to drive 450 miles. So 0.06 times 450. Which is 27.

Then your have the 33.73 for each day for the rent of the car. We don't know how many days so we'll just put x.

Answer:

Twelve and a half weeks

Step-by-step explanation:

Answer:

12 and a half weeks

Step-by-step explanation:

150/12=12 and a half since she takes 7 days to earn 12 dollars, 12x12 and 1/2=150

Usando proporciones, se encuentra que 400 africanos han participado.

En total, hay x participantes.

[tex]\frac{5}{6}[/tex] de los corredores son europeos, o sea:

[tex]E = \frac{5x}{6}[/tex]

Los americanos son la dècime parte de los europeos, o sea:

[tex]Am = \frac{1}{10}E = \frac{5x}{60} = \frac{x}{12}[/tex]

Los africanos son la quinta parte de los americanos, o sea:

[tex]Afr = \frac{1}{5}Am = \frac{x}{60}[/tex]

En la carrera han inscritos 24 000 participantes, o sea, [tex]x = 24000[/tex]. Por eso, la cantidad de africanos es:

[tex]Afr = \frac{x}{60} = \frac{24000}{60} = 400[/tex]

Para obtener más información sobre las proporciones, puedes visitar a https://brainly.com/question/24615636

Answer: Quiere preguntar alguna perosnas que sabe los importante preguntas.

Step-by-step explanation:

Answer:

34.2 m

Step-by-step explanation:

We know that

Area of parallelogram = Base × Height

690.84 = B × 20.2

690.84/20.2 = B

34.2 = B

Hence,

Base of parallelogram is 34.2 m

[tex]\huge{\purple{\underline{\underline{\bf{\pink{ANSWER:-}}}}}}[/tex]

Here we've been given:

[tex]:\longrightarrow\tt{Area \: of \: parallelogram = Base \times Height} \\ \\ :\longrightarrow\tt{690.84 = B \times 20.2} \\ \\ :\longrightarrow\tt{ \frac{690.84}{20.2} = B} \\ \\ :\longrightarrow\tt{34.2 = B} \\ \\ :\longrightarrow\tt{B = 34.2 \: m}[/tex]

Answer:

B

Step-by-step explanation:

(Meeting character limit)

Answer:

N=3

Step-by-step explanation:

use cross multiplication to find 28N=84 and then divide both sides by 28 to get N=3

Answer:

N = 3

Step-by-step explanation:

Given Δ ABC is similar to Δ DEF , then the ratios of corresponding sides are in proportion, that is

[tex]\frac{AB}{DE}[/tex] = [tex]\frac{BC}{EF}[/tex] , substitute values

[tex]\frac{21}{N}[/tex] = [tex]\frac{28}{4}[/tex] = 7 ( multiply both sides by N to clear the fraction )

21 = 7N ( divide both sides by 7 )

3 = N

The total amount Mr Page paid for the oil he bought in February was $21,580.

Since Mr Page uses oil to heat his home, and at the beginning of November there were 1000 liters of oil in his oil tank, and Mr Page bought enough oil to fill the tank completely, and he has paid $50 per liter for this oil, and he has paid a total amount of $750, while at the end of February Mr Page had 600 liters of oil in the tank, and he has bought enough oil to fill the tank completely, and the cost of oil had increased by 4%, to determine the total amount Mr Page paid for the oil he bought in February, the following calculation must be performed:

Therefore, the total amount Mr Page paid for the oil he bought in February was $21,580.

Learn more about maths in https://brainly.com/question/16933803

Answer:

a = 22

AB = 50

Step-by-step explanation:

[tex]a-5=17[/tex]

[tex]a=17+5[/tex]

[tex]a=22[/tex]

Line AB=2a+6

[tex]2(22)+6=44+6=50[/tex]

[tex]AB=50[/tex]

Hope this helps

Answer:

5 tickets

Step-by-step explanation:

45 - 6.75 = 37.35

37.35 ÷ 4 = 9.3375

So, she still has enougg for one more ticket. 4 + 1 is 5. 5 tickets

Answer:

3.7 and east.

Step-by-step explanation:

Answer:

3.7 and east

Hope this helps! Good luck!! :)

Answer:

y = [tex]\frac{2}{5}[/tex] x + [tex]\frac{4}{5}[/tex]

Step-by-step explanation:

Calculate the slope of line m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 2, 2) and (x₂, y₂ ) = (0, - 3) ← 2 points on the line

m = [tex]\frac{-3-2}{0-(-2)}[/tex] = [tex]\frac{-5}{0+2}[/tex] = - [tex]\frac{5}{2}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{5}{2} }[/tex] = [tex]\frac{2}{5}[/tex] , then

y = [tex]\frac{2}{5}[/tex] x + c ← is the partial equation in slope- intercept form

To find c substitute (3, 2 ) into the partial equation

2 = [tex]\frac{6}{5}[/tex] + c ⇒ c = 2 - [tex]\frac{6}{5}[/tex] = [tex]\frac{4}{5}[/tex]

y = [tex]\frac{2}{5}[/tex] x + [tex]\frac{4}{5}[/tex] ← equation of perpendicular line

Answer:

Value of [tex]x=-12[/tex]

Step-by-step explanation:

The given triangle is isosceles

Here

[tex]m\angle2+m\angle2+36^0=180^0\\\\2m\angle2=144^0\\\\m\angle2=72^0\\\\x+84=72\\\\x=72-84\\\\=-12[/tex]

[tex]m∠2+m∠2+36⁰= 180°[/tex]

[tex]2m∠2 = 144°[/tex]

[tex]m∠2 = 72⁰[/tex]

[tex]x +84 = 72[/tex]

[tex]x = 72 - 84[/tex]

[tex]x= -12[/tex]

Answer:

Step-by-step explanation:

There are 81 calories in a 0.75 cup serving of chicken noodle soup. How many calories are in a 2 cup serving?

0.75*2=2 cups

81*2=162

Answer:

x = 216

Step-by-step explanation:

[tex]\frac{81}{0.75}[/tex] = [tex]\frac{?}{2}[/tex]

I hope this helps!!

Answer:

The answer is 0.6

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

If you take 19 6-cylinder sedans and add 12 4-door sedans you get 31, therefore making 2 red and neither 6-cylinder nor 4-door sedans. Hope this helps!

Answer:

-2.1

Step-by-step explanation:

Answer:

Hi, I hope i'll help you.

Step-by-step explanation:

The answer is 2.1, hope it helps!

Answer:

-71

Step-by-step explanation:

Answer:

-71

Step-by-step explanation:

[-18+(-22)]-43+12

=(-18+22)-43+12

=-40-43+12

=-83+12

=-71

Answer:

y=1/2-8

Step-by-step explanation:

slope is 1/2

-4-y=1/2(8-x)

-4-y=4-1/2

-y=-1/2+8

y=1/2-8

Answer:

-21z-35t+21g

Step-by-step explanation:

Use the distributive property of multiplication to distribute -7 to 3, 5, and -3. -7*3 is -21, so we are left with -21z. -7*5 is -35, so we are left with -35t. Finally, -7*-3 is 21, so we are left with +21g