Solve for x. Round to the nearest tenth of a degree, if necessary.

[tex]\sf \bf {\boxed {\mathbb {GIVEN:}}}[/tex]

Sum of three consecutive odd integers = [tex]27[/tex]

[tex]\sf \bf {\boxed {\mathbb {TO\:FIND:}}}[/tex]

The values of the three integers.

[tex]\sf \bf {\boxed {\mathbb {SOLUTION:}}}[/tex]

[tex]\sf\purple{The\:three\:consecutive \:odd\:integers\:are\:7,\:9\:and\:11.}[/tex]

[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:\:EXPLANATION:}}}[/tex]

Let us assume the three consecutive odd integers to be [tex]x[/tex], [tex](x+2)[/tex] and [tex](x+4)[/tex].

As per the condition, we have

[tex]Sum \: \: of \: \: the \: \: three \: \: consecutive \: \: odd \: \: integers = 27[/tex]

[tex]➺ \: x + (x + 2) + (x + 4) = 27[/tex]

[tex]➺ \: x + x + 2 + x + 4 = 27[/tex]

Now, collect the like terms.

[tex]➺ \: (x + x + x) + (2 + 4) = 27[/tex]

[tex]➺ \: 3x + 6 = 27[/tex]

[tex]➺ \: 3x = 27 - 6[/tex]

[tex]➺ \: 3x = 21[/tex]

[tex]➺ \: x = \frac{21}{3} \\[/tex]

[tex]➺ \: x = 7[/tex]

Therefore, the three consecutive odd integers whose sum is [tex]27[/tex] are [tex]\boxed{ 7 }[/tex], [tex]\boxed{ 9 }[/tex] and [tex]\boxed{ 11 }[/tex] respectively.

[tex]\sf \bf {\boxed {\mathbb {TO\:VERIFY :}}}[/tex]

[tex]⇢ 7 + 9 + 11 = 27[/tex]

[tex]⇢ 27 = 27[/tex]

⇢ L. H. S. = R. H. S.

[tex]\sf\blue{Hence\:verified.}[/tex]

[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35ヅ}}}}}[/tex]

Answer:

Option D is correct

Step-by-step explanation:

In the above polynomial, 2 is degree of polynomial because the highest degree of polynomial is 2.

Answer:

Sin (67°)

Step-by-step explanation:

Cos (23°) = sin(90-23) = sin (67°)

Answered by GAUTHMATH

Step-by-step explanation:

hope it helps

Answer:

Step-by-step explanation:

Multiply the numbers. For multiplying variables, if they have same variables, add the exponents.

(3a²b⁷)*(5a³b⁸) = 3*5* a²⁺³ *b⁷⁺⁸

                         = 15a⁵b¹⁵

Therefore, f(c) = 3c+5

OPTION B is the correct answer

Answer:

(B) f(c) = 3c + 5

Step-by-step explanation:

Since variable "c" is the independent variable, that means in terms of y = mx + b, c would be the variable "x".

So that means to rewrite 6c = 2p - 10, you would solve for p, because p would equal y in the formula.

Use basic algebra to solve for p:

6c = 2p - 10

6c + 10 = 2p

3c + 5 = p

p = 3c + 5 or f(c) = 3c + 5

Hope it helps (●'◡'●)

Answer:its Graph C

(According to the law of Nicoloas Sadi Carnot)

Answer:

2/5

Step-by-step explanation:

18x+12x=-4+16

30x=12

x=2/5

Answer:

18x-16=-12x-4

18x+12x=-4+16

30x=12

x=12/30

x=2/5

Answer:

5/6

Step-by-step explanation:

When dividing fractions, multiply by the reciprocal:

2/3 ÷ 4/5

2/3 x 5/4

Multiply the numerators and denominators by each other:

= 10/12

Simplify by dividing the numerator and denominator by 2:

= 5/6

The answer is 5/6

Answer:

- voluntary response sample

- convenience sample

Step-by-step explanation:

Any method of sampling can be biased depending on how they are cared out; however, both voluntary response and convenience are almost always biased. This is because in both the sample is not controlled. In voluntary response, there is no way to ensure that the sample will be representative of everyone since it is based on volunteers. Convenience is also biased because the sample is skewed towards whatever is convenient not what is fair and representative.

Answer:

y=-1

Step-by-step explanation:

Answer:

Augusto vivió durante 75 años cumplidos, muriendo casi un mes antes de cumplir 76 años.

Step-by-step explanation:

Dado que Augusto nació en Roma el 23 de septiembre del año 63 a. C y fue el primer emperador romano que gobernó entre el año 27 a. C y 14 d. C considerándose como el emperador con el reinado más prolongado de la historia, y después de su muerte el 19 de agosto del año 14 d. C el senado romano lo inmortalizó glorificando su legado, por esta razón, varios de los emperadores que lo siguieron adoptaron sus nombres, para determinar cuántos años cumplidos vivió Augusto se debe realizar el siguiente cálculo:

Nacimiento: 23/09/63 AC

Primer año: 23/09/62 AC

Tercer año: 23/09/60 AC

Sesenta y dos años: 23/09/01 AC

Sesenta y tres años: 23/09/01 DC

Setenta y tres años: 23/09/11 DC

Setenta y cinco años: 23/09/13 DC

Así, Augusto vivió durante 75 años cumplidos, muriendo casi un mes antes de cumplir 76 años.

Answer:

[tex]C(n)=30-20n[/tex]

Step-by-step explanation:

Arithmetic sequence given in the question is,

10, -10, -30, -50........

Explicit formula of an Arithmetic sequence is given by,

[tex]C(n)=C(1)+(n-1)d[/tex]

Here, [tex]C_1=[/tex] First term

[tex]n=[/tex] number of terms

[tex]d=[/tex] common difference

From the given sequence,

[tex]C(1)=10[/tex]

[tex]d=-10-10[/tex]

  [tex]=-20[/tex]

Substitute the values in the formula,

[tex]C(n)=10+(n-1)(-20)[/tex]

[tex]C(n)=10-20n+20[/tex]

[tex]C(n)=30-20n[/tex]

Answer:

Values of y in order: 0, 2, 4, 6

Step-by-step explanation:

Hi there!

In the table, the first value of x is -2. To find the value of y for this row of the table, we can use the given equation [tex]y=2x+4[/tex].

[tex]y=2x+4[/tex]

Plug in -2 as the value of x

[tex]y=2(-2)+4\\y=-4+4\\y=0[/tex]

Therefore, y is 0 when x is -2. (In the table, in the row where x is -2, y would be 0.)

We repeat this process for the rest of the values in the table.

When x=-1:

[tex]y=2(-1)+4\\y=-2+4\\y=2[/tex]

When x=0:

[tex]y=2(0)+4\\y=0+4\\y=4[/tex]

When x=1:

[tex]y=2(1)+4\\y=2+4\\y=6[/tex]

I hope this helps!

Answer:

23

Step-by-step explanation:

-18+(18+5) = 5,

so adding any integer that is greater than (18+5)=23 will give a sum that is greater than 5.

Answered by GAUTHMATH

Answer:

0.0238

Step-by-step explanation:

Total number of persons to be chosen from = 7

If each person has an equal probability of being selected ;

Number of persons to be selected = 2

Probability = required outcome / Total possible outcomes

P(Anna first) = 1 / 7

Recall; this is a selection without replacement ;

P(Darlene second) = 1 / 6

1/7 * 1/ 6 = 1 / 42 = 0.0238

Answer:

0.75

Step-by-step explanation:

Given the table :

Number of sodas 24

28

32

36

Total Cost ($)

18

21

24

27

The rate of change :

Rate of change = Rise / Run

Rise = y2 - y1 ; Run = x2 - x1

From the table :

Take number of sodas as X - axis

Total cost as Y - axis

Taking the points :

(24, 18) ;(36, 27)

x1 = 24 ; x2 = 36

y1 = 18 ; y2 = 27

Rise = (y2 - y1) = (27 - 18) = 9

Run = (x2 - x1) = (36 - 24) = 12

Rate of change = 9 / 12 = 0.75

Answer:

x = 2.5

Step-by-step explanation:

Because the triangles are similar, you can divide the sides and equal the results:

24/6 = 10/x

24•x/6 = 10

24•x = 10•6

24•x = 60

x = 60/24

x = 2.5

Answer:

x = 2.5 km

Step-by-step explanation:

In similarity triangles, corresponding sides are in same ratio.

[tex]\frac{DF}{BC}=\frac{EF}{AC}\\\\\frac{10}{24}=\frac{x}{6}\\\\\frac{10}{24}*6=x\\\\x=\frac{10}{4}\\\\x=\frac{5}{2}\\\\x= 2.5[/tex]

Answer:

D

Step-by-step explanation:

First find h(3)

2(3)-2= 4

then find g(4)

4³-5= 59

Answer:

3x - y +5=0

Step-by-step explanation:

Slope:-

=> m = 2-8/-1-1 = -6/-2

=> m = 3

Using point slope form :-

=> y - 2 = 3 ( x - (-1))

=> y - 2 = 3x + 3

=> 3x - y +5 = 0

Answer:

y=3x+5

Step-by-step explanation:

first find the gradient

m=y2-y1/x2-x1

from the coordinates you are given x one is -1,x two is1,y one is 2,y two is 8

8-2/1-(-1)

=3

therefore the gradient is 3

after finding the gradient use the equation

y-y1=m(x-x1)

substitute x1,y1 and the gradient..y and x are constant

y-2=3(x-(-1))

y-2=3x+3

y=3x+3+2

y=3x+5

Hello,

[tex]f^{-1}(-3)=-1\\[/tex]

You have just to read the arrows un reversed order:

in f we find (-1,-3)  so in f^{-1} we find (-1,-3)^{-1}=(-3,-1)

Answer:

13.9188 dollars

Step-by-step explanation:

1.1599 * 12 = 13.9188

Answer:

1 gallon fill = $1.1599

Step-by-step explanation:

we have to fill 12-gallons

Simple-Answer:

12 gallon  = 12 * $1.1599

12 gallon = $13.9188

Answer:

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Step-by-step explanation:

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Answer:

14.8f + 1.8g + 12.1d

Step-by-step explanation:

combine like terms.

3.6+8.5= 12.1

6.2+8.6= 14.8

-2.7+4.5= 1.8

Hello,

the line passing through (5,2) and (1,0) has for equation:

y-0=(x-1)*(-2)/(-4) or y=x/2-0.5

if y= 5 then 5=x/2-0.5 ==> 5.5=x/2 ==> x=11

Answer C

Answer:

C

Step-by-step explanation:

Since the points lie on the same line then the slope between consecutive points will be the same.

Calculate the slope m using the slope formula

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

with (x₁, y₁ ) = (5, 2) and (x₂, y₂ ) = (1, 0)

m = [tex]\frac{0-2}{1-5}[/tex] = [tex]\frac{-2}{-4}[/tex] = [tex]\frac{1}{2}[/tex]

Calculate the slope again and equate to [tex]\frac{1}{2}[/tex]

with (x₁, y₁ ) = (1, 0) and (x₂, y₂ ) = (a, 5)

m = [tex]\frac{5-0}{a-1}[/tex] = [tex]\frac{1}{2}[/tex] , so

[tex]\frac{5}{a-1}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

a - 1 = 10 ( add 1 to both sides )

a = 11

Given:

Slope of line F = [tex]-\dfrac{6}{3}[/tex]

Slope of line G = [tex]-\dfrac{8}{4}[/tex]

To find:

The conclusion about distinct lines F and G.

Solution:

We have,

Slope of line F = [tex]-\dfrac{6}{3}[/tex]

                        = [tex]-2[/tex]

Slope of line G = [tex]-\dfrac{8}{4}[/tex]

                        = [tex]-2[/tex]

The slopes of lines F and G are equal and we know that the slopes of two parallel lines are always equal.

Therefore, the line F and line G are parallel to each other.

Answer:

Tom earns $7.00 per hour

Answer:

AG = 18

Step-by-step explanation:

The relationship of the segments created is one is 1/3 (shorter) and the other (longer) is 2/3 of the total length.

Lets make x represent AG.

So, 2/3 of x is 12

or

[tex]\frac{2}{3}[/tex]x = 12

Multiply both sides by the reciprocal of [tex]\frac{2}{3}[/tex] , which is [tex]\frac{3}{2}[/tex].

( [tex]\frac{3}{2}[/tex]) [tex]\frac{2}{3}[/tex]x = 12 ([tex]\frac{3}{2}[/tex])  (x is left alone, the fractions = 1 when multiplied)

x = 12 ([tex]\frac{3}{2}[/tex])         ( 12 times 3 = 36, divided by 2 = 18)    

x = 18

Answer:

x = –1

Step-by-step explanation:

From the question given above, the following data were obtained:

y = √(–2x + 7)

y = 3

x =?

The value of x can be obtained as follow:

y = √(–2x + 7)

3 = √(–2x + 7)

Take the square of both side

3² = –2x + 7

9 = –2x + 7

Collect like terms

9 – 7 = –2x

2 = –2x

Divide both side by –2

x = 2 / –2

x = –1

Answer:

Line that connects points (0,4) to (4,0)

Step-by-step explanation:

Just imagine where you should fold the paper to overlap one figure on another

Step-by-step explanation:

What equation are you talking about