Write the quadratic equation whose roots are 1 and -6, and whose leading coefficient is 5.
(Use the letter x to represent the variable.)

Answer:

After solving the equation [tex]\frac{x+4}{4}=\frac{x}{x-2}[/tex] we get x=-2 and x= 4 i.e {-2,4}.

Option B is correct.

Step-by-step explanation:

We need to solve [tex]\frac{x+4}{4}=\frac{x}{x-2}[/tex]

Solving:

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

Cross multiply

[tex](x-2)(x+4)=x*4[/tex]

Multiplying:

[tex]x(x+4)-2(x+4)=4x\\x^2+4x-2x-8=4x\\x^2+2x-8-4x=0\\x^2-2x-8=0[/tex]

Now, we have got quadratic equation [tex]x^2-2x-8=0[/tex]

Solving this quadratic equation using quadratic formula

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

We have a=1, b=-2 and c=-8 Putting values

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\x=\frac{-(-2)\pm\sqrt{(-2)^2-4(1)(-8)}}{2(1)}\\x=\frac{2\pm\sqrt{4+32}}{2}\\x=\frac{2\pm\sqrt{36}}{2}\\x=\frac{2\pm6}{2}\\x=\frac{2+6}{2} \ or \ x=\frac{2-6}{2}\\x=\frac{8}{2} \ or \ x=\frac{-4}{2}\\x=4 \ or \ x=-2[/tex]

So,after solving the equation [tex]\frac{x+4}{4}=\frac{x}{x-2}[/tex] we get x=-2 and x= 4 i.e {-2,4}.

Option B is correct.

Answer:

Step-by-step explanation:

Let x and y be the number of plants bought. Then we have equations:

Substituting y in the first equation:

Correct option is the second one

Step-by-step explanation:

-2(3x+2)>-8x+6

when eq. is divided by 2,

-3x-2>-4x+3

x >5

The solution set of -2(3x+3)>-8x+6 is {x/x>5}.

Answer:

The width of the garden is 12 feet.

The length of the garden is 20 feet.

Step-by-step explanation:

Let l be the length and w be the width

Then according to given statements

[tex]l = 2w-4\ \ \ Eqn\ 1[/tex]

Second equation is:

[tex]2l+2w = 64\ \ \ \ Eqn\ 2[/tex]

Putting l = 2w -4 in equation 2

[tex]2(2w-4)+2w = 64\\4w-8+2w = 64\\6w -8 = 64\\6w = 64+8\\6w = 72\\\frac{6w}{6} = \frac{72}{6}\\w = 12[/tex]

Putting w = 12 in equation 1

[tex]l = 2(12)-4 = 24-4 = 20[/tex]

Hence,

The width of the garden is 12 feet.

The length of the garden is 20 feet.

Answer:

3

Step-by-step explanation:

Answer:

f-96=124

Step-by-step explanation:

This is the equation of the sentence that has been mentioned.

Answer:

C

Step-by-step explanation:

Adding 30and 70 first gives 100.

Answer:

i think so

Step-by-step explanation:

everyting looks good to me cuz that would be what my answer was?

Answer:

Step-by-step explanation:

Hi. You need to answer the questions that people have. Just like I'm answering yours, I get some points. This way you get help on your homework and you can help others.

The graph is attached in the figure where the area between the curves has been shaded. As can be seen, the triangle formed is a right triangle whose lengths of its legs is 7. Therefore, its area will be:

[tex]A =\dfrac{7\cdot 7}{2} = \dfrac{49}{2} = 24.5\;u^2[/tex]

Answer:

x = 50

Step-by-step explanation:

these are vertical angles meaning they are congruent so

[2(x+10)] = (3x-30) then use distributive property

(2x+20) = (3x-30) subtract 2x from both sides

20 = x - 30 add 30 to both sides

x = 50

Answer:

x = 50

Step-by-step explanation:

We know that 2(x+10) = (3x-30) because it is on opposite sides of an "x".

We just set them equal to each other and solve for x!

2(x+10) = 3x - 30

2x + 20 = 3x - 30

20 = x - 30

50 = x

Answer:

The time the ball will hit the ground is 1.4s

Step-by-step explanation:

Given;

function of the ball's motion; h(t)= -5t²+ 14t + 3h

The final velocity of the ball, v , is given as;

v = dh/dt

v = -10t + 14

When the ball hits the​ ground, the final velocity, v = 0

v = -10t + 14

0 = -10t + 14

10t = 14

t = 14 / 10

t = 1.4s

Therefore, the time the ball will hit the ground is 1.4s

Answer:

c = 6

a = 14

l = 28

t = 18

Step-by-step explanation:

Free throws are usually worth one point each. We can assign variables and use equations to link information between Adam, Cheryl, Laura, and Tom. Then, we can just substitute in our information and solve.

"Adam scored 8 more points than Cheryl"

a = c + 8

"Laura scored twice as many points as Adam"

l = 2a

"Tom scored 10 points less than Laura"

t = l - 10

"Together the four friends scored a total of 66 points"

a + c + l + t = 66

Now we substitute in our variables and solve from there (see attached image)

c = 6

a = 14

l = 28

t = 18

Answer:

This is the given information for which system of equations would be used to find out how many dimes and quarters Amir has?

x = dimes          x = 0.10 or 0.1

y = quarters      y = 0.25

31 coins

worth $5.20       = 5.2

x + y = 31

0.1x + 0.25y = 5.2

Step-by-step explanation:

Answer:

the last one.

(x^3)^3--3^2

x^6-3^2

x^6-9

(x^3)^3--3^2

Step-by-step explanation:

Answer:

[tex]X=12[/tex]

[tex]Y=8[/tex]

[tex]Z=4[/tex]

Step-by-step explanation:

Comencemos definiendo las variables ⇒

[tex]X:[/tex] '' Número de impresoras Epson ''

[tex]Y:[/tex] '' Número de impresoras Hp ''

[tex]Z:[/tex] '' Número de impresoras Cannon ''

Ahora , dado que tenemos las variables definidas podemos escribir el sistema de ecuaciones lineales

''El número de impresoras Epson y Hp es cinco veces el número de las Cannon''

Para esa oración escribimos la siguiente ecuación :

[tex]X+Y=5Z[/tex] (I) que se puede reescribir como

[tex]X+Y-5Z=0[/tex] (II)

''El número de impresoras Epson es el triple que el de las Cannon''

Para esa oración escribimos la siguiente ecuación :

[tex]X=3Z[/tex] (III) que se puede reescribir como

[tex]X-3Z=0[/tex] (IV)

''El total de impresoras Cannon y Hp asciende a 12''

Para ésta última frase escribimos la última ecuación :

[tex]Y+Z=12[/tex] (V)

Con (II), (IV) y (V) armamos el sistema de ecuaciones lineales :

[tex]X+Y-5Z=0\\X-3Z=0\\Y+Z=12[/tex]

Lo resolvemos a través del método de Gauss insertando el sistema en una matriz y realizando operaciones de fila entre las respectivas filas de la matriz :

[tex]\left[\begin{array}{ccxc}1&1&-5&0\\1&0&-3&0\\0&1&1&12\end{array}\right][/tex]

Realizando operaciones entre filas se lleva a la siguiente matriz equivalente :

[tex]\left[\begin{array}{cccc}1&1&-5&0\\0&-1&2&0\\0&0&3&12\end{array}\right][/tex]    En esta matriz el sistema de ecuaciones asociado es

[tex]X+Y-5Z=0\\-Y+2Z=0\\3Z=12[/tex]

De aquí encontramos que [tex]Z=4[/tex] , [tex]Y=8[/tex] y [tex]X=12[/tex]  (encontramos primero el valor de [tex]Z[/tex] en la última ecuación, de allí reemplazamos en la segunda ecuación para hallar el valor de [tex]Y[/tex]. Finalmente el valor de [tex]X[/tex] se calcula con la primera ecuación)

La solución a éste sistema de ecuaciones es

[tex]X=12[/tex]

[tex]Y=8[/tex]

[tex]Z=4[/tex]

Es recomendable reemplazar éstos valores en el sistema original para verificarlos.

Given:

Total debt ratio (total debt to total assets) = 0.365

Total debt = $500,000

To find:

The total assets.

Solution:

We know that,

[tex]\text{Total debt ratio}=\dfrac{\text{Total debt}}{\text{Total assets}}[/tex]

On substituting the given values, we get

[tex]0.365=\dfrac{500,000}{\text{Total assets}}[/tex]

[tex]\text{Total assets}=\dfrac{500,000}{0.365}[/tex]

[tex]\text{Total assets}=1369863.0137[/tex]

Therefore, the value of total assets is $1369863.0137.

The whole assignment?

Answer:

y=1x+1

Slope is 1

Step-by-step explanation:

Slope = rise/run.

We go up 1 and run 1. The slope is 1.

Let me double check.

The line passes through the points (-1,0) and (0,1).

m = delta y ÷ delta x

m = (0 - 1)/(-1 - 0)

m = -1/-1

m = 1

Yep. The slope is 1.

Answer:

Step-by-step explanation:

What's the answer?

Answer:

Step-by-step explanation:

Tgjh +=%##

Answer:

It will cost $4.25 for 5 liters.

Step-by-step explanation:

$2.55 ÷ 3 = $0.85

$0.85 x 5 = $4.25

Step-by-step explanation:

answer is done over here step by step

Answer:

Manny: 37 years old

Jeremey: 35 years old

David: 30 years old

Step-by-step explanation:

First, we must divide 102 by 3, since there are 3 people in this scenario.

102 ÷ 3 = 34

We know that 34 is an estimate of each person's age, but there's still more work to do.

Manny is seven years older than David:

30 + 7 = 37

Jeremey is 2 years younger than Manny:

37 - 2 = 35

37 + 35 + 30 = 102

Hope this helps! :)

Answer:

y=3/2

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

5y+ −1/2=7

Step 2: Add 1/2 to both sides.

5y+/−1/2+1/2=7+1/2

5y=15/2

Step 3: Divide both sides by 5.

5y/5

=

15/25

y=3/2

The solution of the given equation is y = 3/2.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.

The operator that performs the arithmetic operations is called the arithmetic operator.

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

/ Division operation: Divides left-hand operand by right-hand operand

For example 4/2 = 2

We have given the equation as

⇒ 5y - 1/2 = 7

Add 1/2 to both sides in the above equation.

⇒ 5y - 1/2 + 1/2 = 7 + 1/2

⇒ 5y = 15/2

Divide both sides by 5

⇒ y = 15/10

⇒ y = 3/2

Hence, the solution of the given equation is y = 3/2.

Learn more about the equation here:

brainly.com/question/10413253

#SPJ2

Answer:

[tex]-2^{\circ}\text{F}[/tex]

Step-by-step explanation:

Let [tex]x[/tex] be the temperature on the first day

Second day temperature

[tex]x+7[/tex]

Third day temperature

[tex]x+7-10[/tex]

Fourth day temperature was [tex]1^{\circ}\text{F}[/tex]

[tex]x+7-10+6=1\\\Rightarrow x+3=1\\\Rightarrow x=1-3\\\Rightarrow x=-2^{\circ}\text{F}[/tex]

On the first day the temperature was [tex]-2^{\circ}\text{F}[/tex]

Answer: D) All real numbers greater than or equal to -4.

Explanation:

The lowest point occurs when y = -4, which is where the vertex is located.

The range consists of y values such that y = -4 or y > -4. We can shorten that last sentence to say [tex]y \ge -4[/tex]. So y is greater than or equal to -4.

As you can probably tell, the range is the set of all possible outputs of a function.

Answer:

4

Step-by-step explanation:

4/5 x 5  

y = mx + b

m = slope or rate of change

b = y-intercept

x = input

y = output

Answer:

x= input

y= output

Step-by-step explanation: