Solve the equation 3(2x + 2) = 3x − 15.

Answers

Answer 1

Hi there! :)

Answer:

x = -7.

Step-by-step explanation:

Starting with:

3(2x + 2) = 3x - 15

Begin by distributing '3' with the terms inside of the parenthesis:

3(2x) + 3(2) = 3x - 15

Simplify:

6x + 6 = 3x - 15

Isolate the variable by subtracting '3x' from both sides:

6x - 3x + 6 = 3x - 3x - 15

3x + 6 = -15

Subtract 6 from both sides:

3x + 6 - 6 = -15 - 6

3x = -21

Divide both sides by 3:

3x/3 = -21/3

x = -7.

Answer 2

Answer:

x = -7

Step-by-step explanation:

3(2x+2) = 3x - 15

First, we should simplify on the left side.

6x + 6 = 3x - 15 ; Now we subtract six from both sides.

      -6          -6

6x = 3x - 21 ; next we just subtract 3x from both sides.

-3x   -3x

3x = -21

Finally, we divide 3 from both sides to separate the three from the x.

x = -7

Hope this helps!! <3 :)


Related Questions

A regular polygon inscribed in a circle can be used to derive the formula for the area of a circle. The polygon area can be expressed in terms of the area of a triangle. Let s be the side length of the polygon, let r be the hypotenuse of the right triangle, let h be the height of the triangle, and let n be the number of sides of the regular polygon. polygon area = n(12sh) Which statement is true? As h increases, s approaches r so that rh approaches r². As r increases, h approaches r so that rh approaches r². As s increases, h approaches r so that rh approaches r². As n increases, h approaches r so that rh approaches r².

Answers

Answer:

Option (D)

Step-by-step explanation:

Formula to get the area of a regular polygon in a circle will be,

Area = [tex]n[\frac{1}{2}\times (\text{Base})\times (\text{Height})][/tex]

        = [tex]n[\frac{1}{2}\times (\text{s})\times (\text{h})][/tex]

Here 'n' is the number of sides.

If n increases, h approaches r so that 'rh' approaches r².

In other words, if the number of sides of the polygon gets increased, area of the polygon approaches the area of the circle.

Therefore, Option (4) will be the answer.

In this exercise it is necessary to have knowledge about polygons, so we have to:

Letter D

Then using the formula for the area of ​​a regular polygon we find that:

[tex]A=n(1/2*B*H)\\=n(1/2*S*H)[/tex]

So from this way we were not able to identify the option that best corresponds to this alternative.

See more about polygons at  brainly.com/question/17756657

The screening process for detecting a rare disease is not perfect. Researchers have developed a blood test that is considered fairly reliable. It gives a positive reaction in 94.8% of the people who have that disease. However, it erroneously gives a positive reaction in 3.3% of the people who do not have the disease. Consider the null hypothesis "the individual does not have the disease" to answer the following questions.

a. What is the probability of Type I error?
b. What is the probability of Type II error?

Answers

Answer:

Probability of Type 1 error = 0.033

Probability of type II error = 0.952

Step-by-step explanation:

H0: Individual does not have disease

H1: individual has disease

Type 1 error occurs when we fail to accept a correct null hypothesis and accept an alternate Instead

Type ii error occurs when we accept a false null hypothesis instead of the alternate hypothesis

Probability of people with disease = 98.4%

Probability of people without disease = 3.3%

1.probability of type 1 error = 3.3/100

= 0.033

2. Probability of type ii error = (1-98.4%) = 1-0.948

= 0.052

please help me to answer this question​

Answers

Where’s the question

Answer:

I can not see any questions

find the straight time pay $7.60 per hour x 40 hours

Answers

Answer:

The straight time pay for $ 7.60 per hour and 40 work hours per week is $ 304.

Step-by-step explanation:

Let suppose that worker is suppose to work 8 hours per day, so that he must work 5 days weekly. The straight time is the suppose work time in a week, the pay is obtained after multiplying the hourly rate by the amount of hours per week. That is:

[tex]C = \left(\$\,7,60/hour\right)\cdot (40\,hours)[/tex]

[tex]C = \$\,304[/tex]

The straight time pay for $ 7.60 per hour and 40 work hours per week is $ 304.

Use the given data to find the minimum sample size required to estimate the population proportion. Margin of error: 0.028; confidence level: 99%; p and q unknown

Answers

Answer:

The minimum sample size is [tex]n = 2123[/tex]

Step-by-step explanation:

From the question we are told that

    The margin of error is  [tex]E = 0.028[/tex]

   

Given that the confidence level is  99% then the level of significance is evaluated as

        [tex]\alpha = 100 - 99[/tex]

        [tex]\alpha = 1 \%[/tex]

        [tex]\alpha =0.01[/tex]

Next we obtain the critical value of  [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table

   The  value is  [tex]Z_{\frac{ \alpha }{2} } = 2.58[/tex]

Now let  assume that the sample proportion is  [tex]\r p = 0.5[/tex]

  hence  [tex]\r q = 1 - \r p[/tex]

=>            [tex]\r q = 0.50[/tex]

   Generally the sample size is mathematically represented as

                [tex]n =[ \frac{Z_{\frac{ \alpha }{2} }}{ E} ]^2 * \r p * \r q[/tex]

                [tex]n =[ \frac{2.58}{ 0.028} ]^2 * 0.5 * 0.5[/tex]

              [tex]n = 2123[/tex]

Which expression would produce the largest answer? Select one: a. 3(9 + 3) + 4(6 ÷ 2) b. 2(32) + 3(2 • 2) c. 12(8 ÷ 1) + 5(4 - 5) d. 15(2 + 3) - 3(1 + 3)

Answers

Answer:

C

Step-by-step explanation:

In order to solve these you have to use pemdas, which is the order for which you solve these equations from left to right.

Its, parenthesis, exponents, multiplication, division, addition, subtraction.

when using this strategy it will show that

a=48

b=76

c=91

d=63

4.9x10^_8 In decimal notation

Answers

Answer:

490000000

Step-by-step explanation:

For every exponent of 10, move the decimal point one place to the right.

A washer and dryer cost a total of $980. The cost of the washer is three times the cost of the dryer. Find the cost of each item.

Answers

Answer:

Washer $735

Dryer $245

Step-by-step explanation:

If x is the cost of the washer, and y is the cost of the dryer, then:

x + y = 980

x = 3y

Solve with substitution.

3y + y = 980

4y = 980

y = 245

x = 735

which of the following not between -10 and -8

-17/2
-7
-9
-8.5​

Answers

The answer is -7 because -17/2=-8.5 and 9 and 8.5 are both in between -10 and -8

Answer:

-7

Step-by-step explanation:

This is best read on the number line.

Look at the picture.

[tex]-\dfrac{17}{2}=-8\dfrac{1}{2}=-8.5[/tex]

will rate7 you brainliest

Answers

Answer:

[tex]\Large \boxed{\sf \bf \ \ \dfrac{x^2-x-6}{x^2-3x+2} \ \ }[/tex]

Step-by-step explanation:

Hello, first of all, we will check if we can factorise the polynomials.

[tex]\boxed{x^2+6x+8}\\\\\text{The sum of the zeroes is -6=(-4)+(-2) and the product 8=(-4)*(-2), so}\\\\x^2+6x+8=x^2+2x+4x+8=x(x+2)+4(x+2)=(x+2)(x+4)[/tex]

[tex]\boxed{x^2+3x-10}\\\\\text{The sum of the zeroes is -3=(-5)+(+2) and the product -10=(-5)*(+2), so}\\\\x^2+3x-10=x^2+5x-2x-10=x(x+5)-2(x+5)=(x+5)(x-2)[/tex]

[tex]\boxed{x^2+2x-15}\\\\\text{The sum of the zeroes is -2=(-5)+(+3) and the product -15=(-5)*(+3), so}\\\\x^2+2x-15=x^2-3x+5x-15=x(x-3)+5(x-3)=(x+5)(x-3)[/tex]

[tex]\boxed{x^2+3x-4}\\\\\text{The sum of the zeroes is -3=(-4)+(+1) and the product -4=(-4)*(+1), so}\\\\x^2+3x-4=x^2-x+4x-4=x(x-1)+4(x-1)=(x+4)(x-1)[/tex]

Now, let's compute the product.

[tex]\dfrac{x^2+6x+8}{x^2+3x-10}\cdot \dfrac{x^2+2x-15}{x^2+3x-4}\\\\\\=\dfrac{(x+2)(x+4)}{(x+5)(x-2)}\cdot \dfrac{(x+5)(x-3)}{(x+4)(x-1)}\\\\\\\text{We can simplify}\\\\=\dfrac{(x+2)}{(x-2)}\cdot \dfrac{(x-3)}{(x-1)}\\\\\\=\large \boxed{\dfrac{x^2-x-6}{x^2-3x+2}}[/tex]

So the correct answer is the first one.

Thank you.

Hayley bought a bike that was on sale with a 15% discount from the original price of $142. If there is a 6% sales tax to include after the discount, how much did Hayley pay for the bike?

Answers

Answer:

$12,78

Step-by-step explanation:

$142 × 0,15 = $21,3

$21,3 × 0,6 = $12,78

(1 point) Consider the function f(x)=2x3−9x2−60x+1 on the interval [−4,9]. Find the average or mean slope of the function on this interval. Average slope: By the Mean Value Theorem, we know there exists at least one value c in the open interval (−4,9) such that f′(c) is equal to this mean slope. List all values c that work. If there are none, enter none . Values of c:

Answers

Answer: c = 4.97 and c = -1.97

Step-by-step explanation: Mean Value Theorem states if a function f(x) is continuous on interval [a,b] and differentiable on (a,b), there is at least one value c in the interval (a<c<b) such that:

[tex]f'(c) = \frac{f(b)-f(a)}{b-a}[/tex]

So, for the function f(x) = [tex]2x^{3}-9x^{2}-60x+1[/tex] on interval [-4,9]

[tex]f'(x) = 6x^{2}-18x-60[/tex]

f(-4) = [tex]2.(-4)^{3}-9.(-4)^{2}-60.(-4)+1[/tex]

f(-4) = 113

f(9) = [tex]2.(9)^{3}-9.(9)^{2}-60.(9)+1[/tex]

f(9) = 100

Calculating average:

[tex]6c^{2}-18c-60 = \frac{100-113}{9-(-4)}[/tex]

[tex]6c^{2}-18c-60 = -1[/tex]

[tex]6c^{2}-18c-59 = 0[/tex]

Resolving through Bhaskara:

c = [tex]\frac{18+\sqrt{1740} }{12}[/tex]

c = [tex]\frac{18+41.71 }{12}[/tex] = 4.97

c = [tex]\frac{18-41.71 }{12}[/tex] = -1.97

Both values of c exist inside the interval [-4,9], so both values are mean slope: c = 4.97 and c = -1.97

An inequality is shown: −np − 4 ≤ 2(c − 3) Which of the following solves for n?

Answers

Answer:

[tex]\huge\boxed{n\leq\dfrac{2-2c}{p}\ \text{for}\ p<0}\\\boxed{n\geq\dfrac{2-2c}{p}\ \text{for}\ p>0}[/tex]

Step-by-step explanation:

[tex]-np-4\leq2(c-3)\qquad\text{use the distributive property}\\\\-np-4\leq2c-6\qquad\text{add 4 to both sides}\\\\-np\leq2c-2\qquad\text{change the signs}\\\\np\geq2-2c\qquad\text{divide both sides by}\ p\neq0\\\\\text{If}\ p<0,\ \text{then flip the sign of inequality}\\\boxed{n\leq\dfrac{2-2c}{p}}\\\text{If}\ p>0 ,\ \text{then}\\\boxed{n\geq\dfrac{2-2c}{p}}[/tex]

Pimeter or area of a rectangle given one of these...
The length of a rectangle is three times its width.
If the perimeter of the rectangle is 48 cm, find its area.

Answers

Answer:

A=108 cm²

Step-by-step explanation:

length (l)=3w

perimeter=2l+2w

P=2(3w)+2w

48=6w+2w

width=48/8

w=6

l=3w=3(6)=18

l=18 cm  ,  w=6 cm

Area=l*w

A=18*6

A=108 cm²

PLEASE HELP ! (4/5) - 50 POINTS -

Answers

Answer:

[tex]\large \boxed{\sf A) \ 12}[/tex]

Step-by-step explanation:

Frequency of a specific data value at an interval is the number of times the data value repeats in that interval.

Cumulative frequency is found by adding each frequency to the frequency that came before it.

cStep-by-step explanation:

PLEASE HELP!!! (1/5) - 50 POINTS-

Answers

Answer:

consistent independent

Step-by-step explanation:

This is a graph of consistent independent equations

The lines cross and there is one solution

Inconsistent equations never cross and there is no solutions

Consistent dependent equations are equations of the same line

Answer:

Linear

Step-by-step explanation:

This is a graph of linear system of equation.

The two lines represent different equations connected with each other.

They intersect at a common point showing the solution to the system of equation.

Determina el valor absoluto de 13 – 11|

Answers

Responder:

2

Explicación paso a paso:

El valor absoluto de una expresión es el también conocido como valor positivo devuelto por la expresión. Una expresión en un signo de módulo se conoce como valor absoluto de la expresión y dicha expresión siempre toma dos valores (tanto el valor positivo como el negativo).

Por ejemplo, el valor absoluto de x se escribe como | x | y esto puede devolver tanto + x como -x debido al signo del módulo.

Pasando a la pregunta, debemos determinar el valor absoluto de | 13-11 |. Esto significa que debemos determinar el valor positivo de la expresión como se muestra;

= | 13-11 |

= | 2 |

Este módulo de 2 puede devolver tanto +2 como -2, pero el valor absoluto solo devolverá el valor positivo, es decir, 2.

Por tanto, el valor absoluto de la expresión es 2

Graph the following set of parametric equations on your calculator and select the matching graph.

Answers

Answer:

Graph 2

Step-by-step explanation:

As you can see the first equation is present with a negative slope, and none of the graphs have a line plotted with a negative slope, besides the second graph. That is your solution.

Which of the following represents "next integer after the integer n"? n + 1 n 2n

Answers

Answer:

n + 1

Step-by-step explanation:

Starting with the integer 'n,' we represent the "next integer" by n + 1.

What expression is equal to6 e + 3 (e-1)

Answers

Answer:

9e -3

Step-by-step explanation:

Perform the indicated multiplication:

6 e + 3 (e-1) = 6e + 3e - 3

This, in turn, simplifies to

9e -3, or 3(3e - 1).

Answer:

ANSWER: 9e-3

Step-by-step explanation:

6e+3(e−1)

As we need to simplify the above expression:

First we open the brackets :

3(e-1)=3e-33(e−1)=3e−3

Now, add it to 6e.

So, it becomes,

$$\begin{lgathered}6e+3e-3\\\\=9e-3\end{lgathered}$$

Hence, equivalent expression would be 9e-3.

sorry to keep asking questions

Answers

Answer:

y = [tex]\sqrt[3]{x-5}[/tex]

Step-by-step explanation:

To find the inverse of any function you basically switch x and y.

function = y = x^3 + 5

Now we switch x and y

x = y^3 +5

Solve for y,

x - 5 = y^3

switch sides,

y^3 = x-5

y = [tex]\sqrt[3]{x-5}[/tex]

Answer:

[tex]\Large \boxed{{f^{-1}(x)=\sqrt[3]{x-5}}}[/tex]

Step-by-step explanation:

The function is given,

[tex]f(x)=x^3 +5[/tex]

The inverse of a function reverses the original function.

Replace f(x) with y.

[tex]y=x^3 +5[/tex]

Switch variables.

[tex]x=y^3 +5[/tex]

Solve for y to find the inverse.

Subtract 5 from both sides.

[tex]x-5=y^3[/tex]

Take the cube root of both sides.

[tex]\sqrt[3]{x-5} =y[/tex]

Need help!!!! Show work plz

Answers

Answer:

24 units²

Step-by-step explanation:

A rhombus is divided into 4 right triangles when it's two diagonals intersect at right angles. All the sides are of equal lengths.

Therefore, a simple method to use to find the area of the given rhombus is to calculate the area of one of the right triangles, and multiply by 4.

Area of right triangle = ½*base*height

Height = 3

Base = [tex]\sqrt{5^2 - 3^2} = \sqrt{16} = 4[/tex] (Pythagorean theorem)

Area of right triangle = ½*4*3 = 2*3 = 6 units²

Area of rhombus = 4(6 units²) = 24 units²

Suppose that Y1, Y2,..., Yn denote a random sample of size n from a Poisson distribution with mean λ. Consider λˆ 1 = (Y1 + Y2)/2 and λˆ 2 = Y . Derive the efficiency of λˆ 1 relative to λˆ 2.

Answers

Answer:

The answer is "[tex]\bold{\frac{2}{n}}[/tex]".

Step-by-step explanation:

considering [tex]Y_1, Y_2,........, Y_n[/tex] signify a random Poisson distribution of the sample size of n which means is λ.

[tex]E(Y_i)= \lambda \ \ \ \ \ and \ \ \ \ \ Var(Y_i)= \lambda[/tex]

Let assume that,  

[tex]\hat \lambda_i = \frac{Y_1+Y_2}{2}[/tex]

multiply the above value by Var on both sides:

[tex]Var (\hat \lambda_1 )= Var(\frac{Y_1+Y_2}{2} )[/tex]

            [tex]=\frac{1}{4}(Var (Y_1)+Var (Y_2))\\\\=\frac{1}{4}(\lambda+\lambda)\\\\=\frac{1}{4}( 2\lambda)\\\\=\frac{\lambda}{2}\\[/tex]

now consider [tex]\hat \lambda_2[/tex] = [tex]\bar Y[/tex]

[tex]Var (\hat \lambda_2 )= Var(\bar Y )[/tex]

             [tex]=Var \{ \frac{\sum Y_i}{n}\}[/tex]

             [tex]=\frac{1}{n^2}\{\sum_{i}^{}Var(Y_i)\}\\\\=\frac{1}{n^2}\{ n \lambda \}\\\\=\frac{\lambda }{n}\\[/tex]

For calculating the efficiency divides the [tex]\hat \lambda_1 \ \ \ and \ \ \ \hat \lambda_2[/tex] value:

Formula:

[tex]\bold{Efficiency = \frac{Var(\lambda_2)}{Var(\lambda_1)}}[/tex]

                  [tex]=\frac{\frac{\lambda}{n}}{\frac{\lambda}{2}}\\\\= \frac{\lambda}{n} \times \frac {2} {\lambda}\\\\ \boxed{= \frac{2}{n}}[/tex]

The mean area of 7 halls is 55m².If the mean of 6 of them be 58m², find the area of the seventh all.​

Answers

Answer:

Area of 7th hall = 37 m^2

Step-by-step explanation:

Total area of 7 halls = 7*55 = 385

Total area of 6 halls = 6*58 = 348

Area of 7th hall = 385-348 = 37 m^2

Answer:

The area of the seventh hall = 37m²

Step-by-step explanation:

for 6 halls

Mean area of 6 halls = 58m²

[tex]Mean\ area = \frac{sum\ of\ areas}{Number\ of\ halls} \\58\ =\ \frac{sum\ of\ areas}{6} \\sum\ of\ areas\ of\ 6\ halls\ = 58\ \times\ 6 = 348\\sum\ of\ areas\ of\ 6\ halls\ = 348[/tex]

Let the area of the 7th hall be x

The sum of the areas of 7 halls = 348 + x   - - - - - - (1)

[tex]Mean = \frac{sum\ of\ the\ areas\ of\ 7\ halls}{7} \\55 = \frac{sum\ of\ the\ areas\ of\ 7\ halls}{7} \\sum\ of\ the\ areas\ of\ 7\ halls\ = 55\ \times\ 7\ = 385\\sum\ of\ the\ areas\ of\ 7\ halls\ =\ 385 - - - - (2)[/tex]

notice that equation (1) = equation (2)

348 + x = 385

x = 385 - 348 = 37m²

Therefore, the area of the seventh hall = 37m²

The greater than symbols looks like this ____________, and the less than symbol looks like?

Answers

Answer:

The greater than symbols looks like this    >    , and the less than symbol looks like? <

Answer:

Greater than symbol: >

Less than symbol: <

Greater than or equal to symbol: ≥

Less than or equal to symbol: ≤

Equal symbol: =

In this case, you are answering with the greater than symbol as well as the less than symbol.

The greater than symbols looks like this > , and the less than symbol looks like < .

What would the 60 is x% of 12. Find the value of x.

Answers

Answer:

The value of x= 20

Step-by-step explanation:

I believe the question is ,"60% of x is us, find x"

So , if the percentage of x to 60 is 12.

60/100 * x = 12

0.6 *x = 12

Dividing both sides by 0.6

X= 12/0.6

X= (12/6) *(10)

X= 2*10

.x= 20

The value of x= 20

Suppose we randomly selected 250 people, and on the basis of their responses to a survey we assigned them to one of two groups: high-risk group and low-risk group. We then recorded the blood pressure for the members of each group. Such data are called

Answers

Answer:

Matched or paired data

Step-by-step explanation:

In statistics the different types of study included experimental and observational with the matched or paired data.

The observational study is one in which there is no alteration in the obseravtions or any change. It is purely based on observations.

The experimental study is one in which some experiment or change is brought about to see the effects of the experiment and the results are recorded as before and after treatment etc.

The matched or paired study is one in which two or more groups are simultaneously observed , recorded to find the difference between them or other parameters which maybe useful for the differences or similarities.

i will rate you brainliest

Answers

Answer:

Option (3)

Step-by-step explanation:

For a geometric progression,

[tex]a,ar,ar^{2},ar^3.........a(r)^{n-1},a(r)^n[/tex]

First term of the progression = a

Common ratio of each successive term to the previous term = r

Recursive formula for geometric progression will be,

[tex]a_1=a[/tex]

And [tex]a_{n}=a_{n-1}(r)[/tex]

Following this rule for the G.P. given in the question,

[tex]a_1=4[/tex]

[tex]a_n=-1.5a_{n-1}[/tex]

Therefore, from the recursive formula,

Common ration 'r' = -(1.5)

Option (3) will be the correct option.

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the
correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag
the item to the trashcan. Click the trashcan to clear all your answers.
Perform the following computation with radicals. Simplify the answer.
V6 18
311
123 45
6
7
8
+
x

Answers

Question: Perform the following computation with radicals. Simplify the answer.  √6 • √8

Answer:

[tex] 4\sqrt{3} [/tex]

Step-by-step explanation:

Given, √6 • √8, to perform the computation, we would simply evaluate the radicals and try as much as possible to leave the answer in the simplest form in radicals.

Thus,

[tex] \sqrt{6}*\sqrt{8} = \sqrt{6*8} [/tex]

[tex] = \sqrt{48} [/tex]

[tex] = \sqrt{16*3} = \sqrt{16}*\sqrt{3}[/tex]

[tex] = 4\sqrt{3} [/tex]

The expression $16x^2-106x-105$ can be written as $(8x + a)(2x + b),$ where $a$ and $b$ are integers. What is $a + 2b$?

Answers

Answer:

-23

Step-by-step explanation:

16x² - 106x - 105

factoring X

14 x -120 = -1680

14 - 120 = -106

16x² + 14x - 120x - 105

(16x² + 14x) -(120x - 105)

factor out 2 and -15 to get the same expression (8x + 7)

2x(8x + 7) - 15(8x + 7)

(8x + 7)(2x - 15)

a = 7

b = -15

a + 2b

7 + (-15 x 2)

7 + (-30)

= -23

Other Questions
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