Solve & Justify: 7(x + 3) + 9 = 5(x - 2) - 3x

Step-by-step explanation:

[tex]m = - \frac{2}{3} \\ ( - 10 ,\: 8) = (x_1,y_1)[/tex]

[tex]y-y_1=m(x-x_1)[/tex]

Plug in the values into the equation

[tex]y - 8 = - \frac{2}{3} (x - ( - 10)) \\ y - 8 = - \frac{2}{3}( x + 10) \\ [/tex]

[tex]y - 8 = - \frac{2}{3} x - \frac{20}{ 3 } \\ y = - \frac{2}{3} x - \frac{20}{3} + 8 \\ [/tex]

[tex]y = - \frac{2}{3} x + \frac{4}{3} [/tex]

To solve for x-intercept , Arrange the values in

[tex]ax + by + c = 0[/tex]

=

[tex] - \frac{2}{3} x - y + \frac{4}{3} = 0[/tex]

To find x-intercept .let y = 0 in the above equation

[tex] - \frac{2}{3} x - y + \frac{4}{3} = 0 \\ - \frac{2}{3} x - 0 + \frac{4}{3} = 0 \\ [/tex]

[tex] - \frac{2}{3} x + \frac{4}{3} = 0 \\ - \frac{2}{3} x = - \frac{4}{3} [/tex]

Solve for x ;

[tex]x = 2[/tex]

To find y intercept , let x = 0

and solve for y .

I hope it helps <3

y = mx + b    

m = -²/₃ and line pases  through (-10, 8) so:

8 = -²/₃(-10) + b

8 = ²⁰/₃ + b

b = 8 - ²⁰/₃

b = 8 - 6²/₃

b = 1¹/₃

b = ⁴/₃

Slope Intercept Form:

x-intercept:

-²/₃x + ⁴/₃ = 0

-²/₃x =- ⁴/₃

x = - ⁴/₃ ÷(-²/₃)

x = 2                  

y-intercept:

y =  -²/₃•0+ ⁴/₃ =  ⁴/₃

Answer:

169.2 cm

Step-by-step explanation:

Because the boxes are identical, the height of the combined boxes = 56.4 cm x 3 = 169.2 cm

Answer:

.2 miles per minute or .2x

Step-by-step explanation:

it move one tenth in half a minute so it moves 2 tenths in a minute.

Answer:

66666.67 miles/hr

Step-by-step explanation:

Given that:

Earth complete its orbit of the Sun which is 584 million miles

Time taken to complete the orbit = 365 days

To find:

Speed of earth in miles per hour = ?

Solution:

First of all, we need to convert the distance in miles and time in hours to get our answer.

Let us have a look at the conversion units:

1 day = 24 hours

So, 365 days = 24 [tex]\times[/tex] 365 hours = 8760 hours

Distance traveled = 584 million miles

1 million miles = 1000000 miles

584 million miles = 584000000 miles

Formula for speed is given as:

[tex]Speed = \dfrac{Distance}{Time}[/tex]

Let us put the values of Distance and time given in miles and hours to get the speed in miles/hr.

[tex]Speed = \dfrac{584000000}{8760}\\\Rightarrow \bold{Speed = 66666.67\ miles/hr}[/tex]

So, the answer is: 66666.67 miles/hr

Answer:

x = 5

Step-by-step explanation:

Given

9x - 3 - 8x = 7 - x , that is

x - 3 = 7 - x ( add x to both sides )

2x - 3 = 7 ( add 3 to both sides )

2x = 10 ( divide both sides by 2 )

x = 5

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]y = 11x + 11b\\Move \: 11x\:to\:the \:left\:and\:change\:its\:sign\\\\y -11x =11b\\\\Divide\:both\:sides\:of\:the\:equation\:by\: 11\\\frac{y}{11} -\frac{11x}{11} = \frac{11b}{11} \\y/11 -x =b\\\\b = \frac{y}{11} - x[/tex]

Answer: b = y/11 - x

Step-by-step explanation: You have to isolate your variable by dividing each side of the equation by your factors that DO NOT contain any variable.

I hope this helps you out.

Answer:

r = P / vt

Step-by-step explanation:

P = vrt

P / vt = r

r = P / vt

Answer:

2 + 4(n-1).

Step-by-step explanation:

As x increases from 1,  f(x) increases  by 4.

Arithmetic sequence.

So the formula is  a1 + d(n - 1)

= 2 + 4(n-1).

The function which defines the series will be 2 + 4(n-1).

A series of numbers is called a number series. We must identify the laws that lead to the production of a number series in order to answer the questions about number series. The questions that might arise from these topics are as varied as these series themselves.

Given functions are f(1) = 2, f(2) = 6, f(3) = 10,f(4) = 14 f(5) = 18. The sequence will be represented by the function:-

As x increases from 1,  f(x) increases by 4. Arithmetic sequence.

F = a₁+ d(n - 1)

F = 2 + 4(n-1).

Therefore, the function which defines the series will be 2 + 4(n-1).

To know more about the number series follow

https://brainly.com/question/6561461

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Answer:

6

Step-by-step explanation:

(-2)(3-4-(-1)+6

(-2)(-1-(-1)+6

(Since a negative and a negative make a positive that becomes -1+1.)

(-2)(0)+6

0+6

6

Answer:

Hello! :) I hope I am correct!

Step-by-step explanation:

The answer would be -12

(Look below for steps!!)

-2(-1-(-1)+6)

⇒-2(0+6)

⇒(-2)(6)

(Do the calculations above to find the answer)

=-12

Hope this helps!

By; BrainlyAnime

(Also I attached a picture of other ways to solve this problem!)

Answer:

  see below

Step-by-step explanation:

If your equations are the ones shown in the second attachment, then their solution is the one shown in the first attachment.

_____

Apparently, your "interactive graph" needs two points to draw a line through. For these equations, the x- and y-intercepts are found easily enough.

  -3x +3y = 9

To find the x-intercept, set y=0 and divide by the coefficient of x: 9/-3 = -3

To find the y-intercept, set x=0 and divide by the coefficient of y: 9/3 = 3.

  2x -7y = -14

Same procedure: x-intercept = -14/2 = -7; y-intercept = -14/-7 = 2.

All of these intercepts are shown in the third attachment. Using them, you can use your tool to plot the lines and estimate their point of intersection.

Answer:

15x + 13

Step-by-step explanation:

Product of a number 'x' & 15 : x *15 = 15x

Sum of 15x & 13:

15x + 13

Answer:

[tex]4^{10}[/tex]

Step-by-step explanation:

Using the rule of exponents

[tex]a^{m}[/tex] × [tex]a^{n}[/tex] ⇔ [tex]a^{(m+n)}[/tex] , thus

4² × [tex]4^{8}[/tex] = [tex]4^{(2+8)}[/tex] = [tex]4^{10}[/tex]

Answer:

x=2 y = 0

Step-by-step explanation:

good luck

Answer:

Step-by-step explanation:

first convert feet to inches because the measure of cubes is in inches

( 12 inches=1 foot)

9 ft = 12*9=108 inches

8 ft=12*8=96 inches

7 ft= 12*7=84

the volume of the one cube= 5*5*5=125

volume of the classroom: 108*96*84=870912

divide : 870912/125=6967 cubes

Answer:

17

Step-by-step explanation:

$4.25 - 17 quarters

$3.10 - 31 dimes

Answer:

17 quarters and 31 dimes are in the jar

Step-by-step explanation:

First, you need to set up two equations based on the information given.

First is an equation for the total number of coins:

48 = d + q

d = dimes

q = quarters

Second is an equation for the total amount in the jar and the respective amount per variable (d = .1 , q = .25).

7.35 = .1d + .25q

Using the first equation, you need to solve for one variable. In this case well solve for d, so we can later plug it in to solve for q.

48 = d + q

d =  48 - q

Next, we can plug our formula for d into our second equation, so we only have one variable to solve for, q.

.1(48-q) +.25q = 7.35

4.8 - .1q + .25q = 7.36

4.8 + .15q = 7.35

.15q = 2.55

q = 17

Finally, to solve for d with a number, we can plug q = 17 back into our first formula : 48 = d + q

48 = 17 + d

d = 31

I hope this helps!

-TheBusinessMan

Answer:

.837537537 =  

837537537

1000000000

Step-by-step explanation:

Answer:

0

-

1000000000

i think it will help you

Answer:

1. The two numbers are 56 and 15

2. The two angles are 56 and 34 degrees

3. The two angles are 110 and 70 degrees

4.The largest number is -10

Step-by-step explanation:

Solving (1):

Represent both numbers with x and y

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

[tex]x + y = 71[/tex]

Solving for x and y

Substitute [tex]11 + 3y[/tex] for x in the second equation

[tex]11 + 3y + y = 71[/tex]

Collect Like Terms

[tex]3y + y =71 - 11[/tex]

[tex]4y = 60[/tex]

Divide both sides by 4

[tex]y = 15[/tex]

Recall that

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

[tex]x = 11 + 3 * 15[/tex]

[tex]x = 56[/tex]

Hence, the two numbers are 56 and 15

Solving (2)

Represent the two angles with x and y

[tex]x = 22 + y[/tex]

Since they are complementary;

[tex]x + y = 90[/tex]

Substitute 22 + y for x in [tex]x + y = 90[/tex]

[tex]22 + y +y= 90[/tex]

[tex]22 + 2y =9 0[/tex]

Collect Like Terms

[tex]2y = 90 - 22[/tex]

[tex]2y = 68[/tex]

Divide both sides by 2

[tex]y = 34[/tex]

Recall that [tex]x = 22 + y[/tex]

[tex]x = 22 + 34[/tex]

[tex]x = 56[/tex]

Solving (3):

Represent the two angles with x and y

[tex]x = 40 + y[/tex]

Since they are supplementary;

[tex]x + y = 180[/tex]

Substitute 40 + y for x in [tex]x + y = 180[/tex]

[tex]40 + y + y = 180[/tex]

[tex]40 + 2y = 180[/tex]

Collect Like Terms

[tex]2y = 180 - 40[/tex]

[tex]2y = 140[/tex]

Divide both sides by 2

[tex]y = 70[/tex]

Recall that [tex]x = 40 + y[/tex]

[tex]x = 40 + 70[/tex]

[tex]x = 110[/tex]

Solving (4):

Let the smallest number be x

[tex]x + x + 2 + x + 4 = -36[/tex]

Collect Like Terms

[tex]x + x + x = -36 - 2 - 4[/tex]

[tex]3x =-42[/tex]

Divide through by 3

[tex]x = -14[/tex]

The largest number; x + 4 is

[tex]x + 4 = -14 + 4[/tex]

[tex]x + 4 = -10[/tex]

Hence, the largest number is -10

Answer:

The correct option is D.

Hoped I helped

Answer:D

Step-by-step explanation:

Answer:

15.71 ft

Step-by-step explanation:

Given that:

width of the circular track = 2.5ft

Suppose the radius of the inner circle is 57 ft since it is not given

Then the radius of the outer circle = (2.5 + 57) ft = 59.5 ft

The circumference of a circle = 2πr

For inner circle now, the circumference = 2 × π × 57 ft

For inner circle now, the circumference = 358.14 ft

For the outer circle, the circumference = 2 × π × 59.5 ft

For the outer circle, the circumference = 373.85 ft

The difference between the circumference of the outer wheel from the inner wheel shows how farther does a wheel on the outer rail travel than a wheel on the inner rail of the track in one​ turn

∴

= ( 373.85 - 358.14 ) ft

= 15.71 ft

Answer:

3.5% because 1.035 * 100 = 3.5

Answer:

3.5

if you take 100 times 1.035 you get 103.5

Answer:

The number is 39

Step-by-step explanation:

Let the number at the tens place be x and the number at ones place be y.

Hence, The number is 10x + y.

From the question, the digit at ones place (y) is three times the digit at tens place (x). That is, y is three times x. This means

y = 3x ...... (1)

Also, When 54 is added to the number, its digits are reversed (That is, the resulting number would be 10y + x). This means

10x + y + 54 = 10y + x ...... (2)

Put the value of y = 3x from equation (1) into equation (2) to solve for x

Then,

10x + y + 54 = 10y + x

10x + 3x + 54 = 10(3x) + x

13x + 54 = 30x + x

13x + 54 = 31x

31x - 13x = 54

18x = 54

x = 54/18

x = 3.

Now, Put the value of x = 3 into equation (1) to solve for y

y = 3x

y = 3(3)

y = 9.

Hence, x = 3 and y = 9.

Since the number is 10x + y

Substitute the values of x and y.

Then,

10x + y = 10(3) + 9

=30 + 9

= 39

Hence, the number is 39.

Answer:

3/5

Step-by-step explanation:

The teacher has six novels more than the doctor.

A fraction is defined as a numerical representation of a part of a whole that represents a rational number.

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

We have been given that 4/5 of the teacher's books and 2/3 of the doctor's books are novels.

Since a teacher and a doctor each have 45 books.

As per the fractions of the book,

The number of teacher's books = 4/5(45) = 36

The number of doctor's  books = 2/3(45) = 30

Therefore the required difference would be 36- 30 = 6 books

Hence, the teacher has six novels more than the doctor.

Learn more about the fraction here:

brainly.com/question/10354322

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Answer:

Step-by-step explanation:

Average speed is the change in distance of a body with respect to time. This is expressed as:

[tex]v = \delta y/\delta t\\v = \dfrac{y(t_2)-y(t_1)}{t_2-t_1}[/tex]

Given the function of the height in metres expressed as y = 56t − 1.86t² and time interval [1,2]

t₁ = 1sec and t₂ = 2 secs

y(t₂) = 56t₂ − 1.86t₂²

y(2) = 56(2) − 1.86(2)²

y(2) = 112-7.44

y(2) = 104.56

y(t₁ ) = 56t₁  − 1.86t₁ ²

y(1) = 56(1) − 1.86(1)²

y(1) = 56-1.86

y(1) = 54.14

Substituting the derived value into the formula for finding the average speed:

[tex]v = \dfrac{y(t_2)-y(t_1)}{t_2-t_1}\\\\v = \dfrac{104.56-54.14}{2-1}\\\\v = \dfrac{50.42}{1}\\\\v = 50.42m/s[/tex]

Hence, the average speed over the given time intervals. [1, 2] is 50.42m/s

Answer:

1,8.9

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

hope this helps

Answer:

She had 22 friends at her graduation party.

Step-by-step explanation:

70 chocolates total minus 3 chocolates times the number of friends she had at the party = 4

70-3x=4

Subtract 70 from both sides of the equation

-3x=4-70

Simplify

-3x=-66

Divide both sides of the equation by -3

-3x/-3=-66/-3

Simplify

x=22

Answer:

-2380

Step-by-step explanation:

you first multiply 17 by 4

next multiply 68 by 35

you get 2380

finally add a negative sign in front of it

Answer:

59

Step-by-step explanation:

Step-by-step explanation:

Hey, there!!

While simplifying the algebraic expression, you must be very careful about the signs.

Here,

(6x-4) (9x-2)

Multiply 2nd expression by 1st expression,

= 6x ( 9x - 2) -4 ( 9x - 2)

[tex] = (54 {x}^{2} - 12x) - (36x - 8)[/tex]

Opening brackets,

[tex] = 54 {x}^{2} - 12x - 36x + 8[/tex]

Simplifying them we get,

[tex] = 54 {x}^{2} - 48x + 8[/tex]

Therefore, the answer is 54x^2 - 48x +8.

Hope it helps..

Answer:

x<4

Step-by-step explanation:

[tex]x + 1 > -5( 7-2x) \\\\\mathrm{Expand\:}-5\left(7-2x\right):\quad -35+10x\\x+1>-35+10x\\\\\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}\\x+1-1>-35+10x-1\\\\Simplify\\x>10x-36\\\\\mathrm{Subtract\:}10x\mathrm{\:from\:both\:sides}\\x-10x>10x-36-10x\\Simplify\\-9x>-36\\\\\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}\\\left(-9x\right)\left(-1\right)<\left(-36\right)\left(-1\right)\\\\Simplify\\9x<36[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}9\\\frac{9x}{9}<\frac{36}{9}\\\\x<4[/tex]