Find the pre-image of 10 under the function f:x ->3x+1​

The solution of the given quadratic equation is x = -2.

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.

Given is a quadratic equation x²+4x+4 = 0, we need to solve it using the Quadratic Formula:

The formula for the same is given by -

x = -b ± √b²-4ac / 2a

Here,

a = 1, b = 4 and c = 4

Put in the formula,

x = -4 ± √4²-4(1)(4) / 2

x = -4 ± √16-16 / 2

x = -4 ± √0 / 2

x = -4/2

x = -2

Hence, the solution of the given quadratic equation is x = -2.

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Answer:

Mean

Step-by-step explanation:

Finding the mean, or the average, of the different weights that were measured, would best estimate the true mass of the solid.

This would find the average mass, which would be the most accurate estimate of the solid's actual mass.

Using the minimum, maximum, and mode will not take into account the other weights that were measured. This makes it much more inaccurate.

So, the correct answer is Mean.

Answer:

110.8 feet

Step-by-step explanation:

Find the difference in sea level by subtracting 236 from 346.8:

346.8 - 236

= 110.8

So, the difference in sea level is 110.8 feet

Answer:

1/7

Step-by-step explanation:

negative reciprocal

Answer:

y=58°

x=122°

Step-by-step explanation:

y=58°[°•°being corresponding angles]

Now,

x+y=180[°•°co-interior angles]

or, x=180-58

•°•x=122

C. Because C right now

Option C is correct, the equivalent expression of √8x⁷y⁸ is 2x³y⁴√2x

An expression is combination of variables, numbers and operators.

The given expression is √8x⁷y⁸

Square root of eight times x power seven y power eight.

Now we have to find the equivalent expression.

Equivalent expressions are expressions that work the same even though they look different.

We have to simplify the given expression

√4×2x⁶.xy⁸

We get 2x³y⁴√2x

Hence, Option C is correct, the equivalent expression of √8x⁷y⁸ is 2x³y⁴√2x

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Answer:

3[tex]\sqrt{11}[/tex] + 2[tex]\sqrt{11}[/tex] = 5[tex]\sqrt{11}[/tex]

Step-by-step explanation:

[tex]\sqrt{99}[/tex] = [tex]\sqrt{(9)(11) }[/tex] = 3 [tex]\sqrt{11}[/tex]    (separate perfect squares using factoring)

[tex]\sqrt{44}[/tex] = [tex]\sqrt{(4)(11)}[/tex] = 2 [tex]\sqrt{11}[/tex]

3 [tex]\sqrt{11}[/tex] + 2 [tex]\sqrt{11}[/tex] = 5 [tex]\sqrt{11}[/tex]   (add like terms. Think of the [tex]\sqrt{11}[/tex] like x's.)

                                        (Just add the coefficients)  

Answer:

5[tex]\sqrt{11}[/tex]

Step-by-step explanation:

Using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b[/tex] = [tex]\sqrt{ab}[/tex]

Simplifying the radicals

[tex]\sqrt{99}[/tex]

= [tex]\sqrt{9(11)}[/tex]

= [tex]\sqrt{9}[/tex] × [tex]\sqrt{11}[/tex]

= 3[tex]\sqrt{11}[/tex]

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

[tex]\sqrt{44}[/tex]

= [tex]\sqrt{4(11)}[/tex]

= [tex]\sqrt{4}[/tex] × [tex]\sqrt{11}[/tex]

= 2[tex]\sqrt{11}[/tex]

Then

[tex]\sqrt{99}[/tex] + [tex]\sqrt{44}[/tex]

= 3[tex]\sqrt{11}[/tex] + 2[tex]\sqrt{11}[/tex]

= 5[tex]\sqrt{11}[/tex]

with a = 5 and b = 11

Answer:

5.5%

Step-by-step explanation:

Firstly, we find the difference between the fixed cost and the price above the fixed cost

We have this as;

1, 671,120 - 1,584,000 = 87,120

now, we have to divide this value by the fixed cost and express as a percentage

we have this as;

87,120/1,584,000 * 100% = 5.5%

Answer:

Step-by-step explanation:

The slope of line u is 9/2; the line perpendicular to that is the opposite reciprocal...opposite sign and the flip of the fraction. The perpendicular slope is -2/9

Answer:

Y= -1/2X- 2

Step-by-step explanation:

-3 - 11 = -14

2-(-5) = 7

7/-14 = -1/2

-3 = 2(-1/2) + b

-3 = -1 + b

-2 = b

Y= -1/2X-2

Answer:

functions are expressions that involve 2 variables, a dependent and an independant variable

example: x=3 isn't a function, but 2y=6-x is

Answer:

4.5

Step-by-step explanation:

The triangles are similar

QT       QS

------ = ______

QR       QP

3                 5

-----------  = ---------

(4x-3)+3     25 +5

3                 5

-----------  = ---------

4x             30

Using cross products

3*30 = 5*4x

90 = 20x

90 /20 = 20x/20

4.5 =x

Answer:

(0,1,3,5)

Step-by-step explanation:

Set g(x) equal to each respective range and solve for x

[tex]3x + 2 = 2[/tex]

[tex]3x + 2 = 5[/tex]

[tex]3x + 2 = 11[/tex]

[tex]3x + 2 = 17[/tex]

If we solve for each, we get

[tex]x = 0[/tex]

[tex]x = 1[/tex]

[tex]x = 3[/tex]

[tex]x = 5[/tex]

So our domain is

(0,1,3,5)

Answer:

The sum  of the present age of Juan and Maria is 32 years.

Step-by-step explanation:

Maria's age is three times Juan's age. In 7 years the sum of their ages will be 46 years. The sum of the current ages of Juan and Maria is

Let the Juan's present age is p.

Maria's present age is 3 p.

After 7 years,

Juan's age = p + 7

Maria's age = 3 p + 7

According to the question

p + 7 + 3 p + 7 = 46

4 p + 14 = 46

4 p = 32

p = 8

So, the present age of Juan is 8 years and Maria is 24 years, the sum is 8 + 24 = 32.  

Answer:

The correct answer, pertaining to the proposed interrogate, is acknowledged as x = 3.

Step-by-step explanation:

To evaluate for such, a comprehension of linear data must be obtained:

Slope = rise/run, defined as the agglomerate distance between two differentiated points.

X-intercept: The peculiar point in which linear data is observed to intersect the x-axis.

Y-intercept: The peculiar point in which linear data is observed to intersect the y-axis.

If there is a vertical line intersecting the x-axis, the particular point (x, y) is identified as what x is equated to.

Likewise, if there is a horizontal line intersecting the y-axis, the particular point (x, y) is identified as what y is equated to.

Thus, the following must be applied to the interrogate:

- Vertical line, thus determine the point in which the data intersects the x-axis.

- Such is identified as (3,0).

Thus, since that is the only linear figure intersecting at such peculiar axis, 3 is the equated value of x.

Hence, x = 3.

*I hope this helps.

Answer:

Entran 9 cuadrados en la hoja

Se puden hacer 10 tarejtas por que hay un cuadradro de 10*10 extra.

Step-by-step explanation:

El area de la hoja sera:

[tex]A_{Hoja}=30*30=900 \:cm^{2}[/tex]

Ahora el area de cada tarjeta es:

[tex]A_{tarjeta}=10*10=100\: cm^{2}[/tex]

Para determinar cuantos tarjetas entran en la hoja debemos vidivir las aras encontradas arriba:

[tex]\frac{A_{Hoja}}{A_{tarjeta}}=\frac{900}{100}=9[/tex]

Entonces entran 9 cuadrados en la hoja

Se puden hacer 10 tarejtas por que hay un cuadradro de 10*10 extra.

Espero te haya sido de ayuda!

Answer:

There are no solutions.

Step-by-step explanation:

im assuming that the equation is x^2+20=2x, but if not, x=10.

quadratic formula is

(-b+-√(b^2-4ac))/2a, and a=1, b=-2, and c=20. plug these values in and you will find that you are asked to square root a negative number. There are no solutions.

Answer: 6, 7

Step-by-step explanation:

x · y = 42

x · (13 - x) = 42

13x - x² = 42

-x² + 13x - 42 = 0

(-1)(-x² + 13x - 42) = 0(-1)

x² - 13x + 42 = 0

(x - 6)(x - 7) = 0

y = 13 - x

Answer:

These figures are not similar

Step-by-step explanation:

The two sides are proportional, but the angle between them are not congruent.

One angle is marked with one arc.

The other is marked with two arcs.

They must have the same number or arcs to be considered congruent.

Tricky

Answer:

[tex]6(\frac{1}{3} \times\frac{7}{5} )=(6\times\frac{1}{3} )\frac{7}{5}[/tex]

[tex]Answer: B[/tex]

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

Hope it helps...

Have a great day!!

Answer: [tex]26,400\ ft[/tex]

Step-by-step explanation:

Given

Each side of the pentagon measures [tex]1760\ ft[/tex]

A complete trip is equivalent to the perimeter of the perimeter

[tex]\Rightarrow \text{Perimeter of the Pentagon P=}5\times 1760\\\Rightarrow P=8800\ ft[/tex]

For Three rounds, he completed a distance of  

[tex]\Rightarrow P=3\times 8800\\\Rightarrow P=26,400\ ft[/tex]

x=-13

x=2

Answer:

Solution given:

5-2x=[tex]\sqrt{2x²+x-1}-x[/tex]

keep square root alone

5-2x+x=[tex]\sqrt{2x²+x-1}[/tex]

5-x=[tex]\sqrt{2x²+x-1}[/tex]

squaring both side

(5-x)²=2x²+x-1

25-10x+x²=2x²+x-1

2x²+x-1-25+10x-x²=0

x²+11x-26=0

doing middle term factorisation

for this

coefficient of first and last terms should be multiplied

here

1*26=26

factor product

26=2*13*1

remember that check the sigh of last term

in here it is - so

we need to get 11 by subtracting factor of 26

we get

13-2=11

keep 13-2 value in place of 11

x²+(13-2)x-26

now

distribute

x²+13x-2x-26=0

take common from each two term

x(x+13)-2(x+13)=0

(x+13)(x-2)=0

either

x=-13

or.x=2

Answer:

A and B

Step-by-step explanation:

we would like to solve the following equation:

[tex] \rm\displaystyle 5 - 2x = \sqrt{ {2x}^{2} + x - 1 } - x[/tex]

to do so isolate -x to the left hand side and change its sign:

[tex] \rm\displaystyle 5 - 2x + x = \sqrt{ {2x}^{2} + x - 1 } [/tex]

simplify addition:

[tex] \rm\displaystyle 5 - x = \sqrt{ {2x}^{2} + x - 1 } [/tex]

square both sides:

[tex] \rm\displaystyle (5 - x {)}^{2} = (\sqrt{ {2x}^{2} + x - 1 } {)}^{2} [/tex]

simplify square of the right hand side:

[tex] \rm\displaystyle (5 - x {)}^{2} = {2x}^{2} + x - 1 [/tex]

use (a-b)²=a²-2ab+b² to expand the left hand side:

[tex] \rm\displaystyle {x}^{2} - 10x + 25= {2x}^{2} + x - 1 [/tex]

swap the equation:

[tex] \rm\displaystyle {2x}^{2} + x - 1 = {x}^{2} - 10x + 25[/tex]

isolate the right hand side expression to the left hand side and change every sign:

[tex] \rm\displaystyle {2x}^{2} + x - 1 - {x}^{2} + 10x - 25 = 0[/tex]

simplify:

[tex] \rm\displaystyle {x}^{2} + 11x - 26= 0[/tex]

rewrite the middle term as 13x-2x:

[tex] \rm\displaystyle {x}^{2} + 13x - 2x - 26= 0[/tex]

factor out x:

[tex] \rm\displaystyle x({x}^{} + 13)- 2x - 26= 0[/tex]

factor out -2:

[tex] \rm\displaystyle x({x}^{} + 13)- 2(x + 13)= 0[/tex]

group:

[tex] \rm\displaystyle (x- 2)(x + 13)= 0[/tex]

by Zero product property we obtain:

[tex] \displaystyle \begin{cases}x- 2 = 0\\ x + 13= 0 \end{cases}[/tex]

solve for x:

[tex] \displaystyle \begin{cases}x = 2\\ x = - 13 \end{cases}[/tex]

to check for extraneous solutions we can define the domain of equation recall that a square root of a function is always greater than or equal to 0 therefore

[tex] \rm\displaystyle 5 - x \geq0[/tex]

solve the inequality for x:

[tex] \rm\displaystyle x \leqslant 5[/tex]

since 2 and -13 is less than 5 both solutions are valid for x hence,

[tex] \displaystyle \begin{cases}x _{1} = 2\\ x_{2} = - 13 \end{cases}[/tex]

and we're done!

Answer:

D

Step-by-step explanation:

Answer:

4628

Step-by-step explanation:

We are given that

In 2000

The population of a small industrial town  in 2000=12910

Depreciation rate, r=5% per year

We have to find the  population in the year 2020.

Time from 2000 to 2020=20 years

[tex]FV=PV(1-\frac{r}{100})^n[/tex]

Where FV=Future value

PV=Present value

Using the formula

[tex]FV=12910(1-\frac{5}{100})^{20}[/tex]

[tex]FV=12910(\frac{95}{100})^{20}[/tex]

FV=4628

Hence, the population in 2020 =4628

Answer:

4

Step-by-step explanation:

Answer:

(a) 25

(b) $4816

Step-by-step explanation:

Let's say the starting amount of ducks is d, and the starting amount of chickens is c. Since there are only ducks and chickens, we can say that d + c= 455.

Next, the farmer sells 2/5 of the ducks, so we subtract 2/5 of the ducks so that the ending duck amount is d - (2/5)d = (3/5) d

After that, the farmer buys another 104 chickens, so we add 104 chickens to the current amount of chickens to get the ending chicken number as 104+c

Given the ending duck and chicken count, we can say that the ending farm animal count (we can represent this as a) is (3/5)d + 104 + c = a

The number of ducks is 2/3 the total number of animals at the end, so (3/5)d = (2/3)a

Let's list our equations out so it is easier to solve:

d+c = 455

(3/5)d + 104 + c = a

(3/5)d = (2/3)a

We have three equations and need to solve for three variables. One common variable in all three equations is d, so it might help if we put everything in terms of d.

Starting with d+c=455, if we subtract d from both sides, we get c=455-d. We can substitute this in the second equation to get

(3/5)d + 104 + 455 - d = a

-(2/5)d + 559 = a

(3/5)d = (2/3)a

Next, we can substitute for a. If we multiply both sides by 3 and then divide by 2 in (3/5)d = (2/3)a , we get

(9/10)d = a

Substitute that in to the second equation to get

-(2/5)d + 559 = (9/10) d

-(4/10)d + 559 = (9/10) d

add (4/10)d to both sides to isolate the variable and its coefficient

(13/10)d = 559

multiply both sides by (10/13) to isolate the coefficient

d = 430

Therefore, the starting number of ducks is 430 and the starting amount of chickens is 455-430 = 25

For (b), 2/5ths of the ducks are sold, so this is (430) * (2/5) = 172. Each duck is sold for 28 dollars, so this is 172*28=$4816 as the total price

Answer:4

Step-by-step explanation:

but they said it would have toend