I'm a little confused about a math lesson about equations with variables on both sides. Could someone explain this to me.
Heres a random question: Solve for m 4m + 2(m + 1) = 9m + 5?

Answer:

1/10

Step-by-step explanation:

Answer:

1/10

Step-by-step explanation:

In its simplest form, expressing the decimal as a fraction to its simplest form will give one over ten.

Therefore if you divide 1/10, the answer will be 0.1. it is also called one-tenth.

Although there are other expressions or fractions that give 0.1, but 1/10 is the simplest of them all, and the question specified to use it in its simplest form.

The length of the edge of the cube is 3.23 cm .

Step-by-step explanation:

We have , The relationship between the weight y gram and the edge x cm for a cube of gold is y = 19.3x3 or [tex]y = 19.3x^3[/tex] .  A cube of gold weighs 652 grams i.e. y = 652 . Let's calculate value of x from above data:

[tex]y = 19.3x^3[/tex]

⇒ [tex]y = 19.3x^3[/tex]

⇒ [tex]652= 19.3x^3[/tex]

⇒ [tex]19.3x^3=652[/tex]

⇒ [tex]\frac{19.3}{19.3}x^3=\frac{652}{19.3}[/tex]

⇒ [tex]x^3=\frac{652}{19.3}[/tex]

⇒ [tex]\sqrt[\frac{1}{3} ]{x^3} = \sqrt[\frac{1}{3} ]{\frac{652}{19.3}}[/tex]

⇒ [tex]({x^3})^\frac{1}{3} =({\frac{652}{19.3}})^\frac{1}{3}[/tex]

⇒ [tex]x =(33.78)^\frac{1}{3}[/tex]

⇒ [tex]x =3.23[/tex]

Therefore, the length of the edge of the cube  is 3.23cm.

Answer:

3 3/8

Step-by-step explanation:

Answer:

Option A, -4

Step-by-step explanation:

Step 1:  Make an equation to represent the problem

(-9)(x) = 36

Step 2:  Solve for x by dividing both sides by -9

-9x / -9 = 36 / -9

x = -4

Answer:  Option A, -4

Answer:

D: Pay less than the minimum amount due.

Step-by-step explanation:

Answer:

Θ = 52°

Step-by-step explanation:

Once you've set up the triangle, you can see that the adjacent side is 170 cm and the opposite side is 220 cm.

tanΘ = [tex]\frac{220}{170}[/tex]

Θ = tan-1 (220/170)

Θ = 52°

The angle of elevation of the sun when a person 170 cm tall casts of shadow 220 cm long is 37.694°.

Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.

A person 170 cm tall casts of shadow 220 cm long.

Then the angle will be

[tex]\rm tan \theta = \dfrac{Perpendicular }{Base}[/tex]

We have

Perpendicular = 170 cm

Base = 220 cm

Then

[tex]\rm tan \theta = \dfrac{170}{220}\\\\\\ \theta \ \ \ \ = tan^{-1} \dfrac{170}{220}\\\\\\\theta \ \ \ \ = 37.694^o[/tex]

More about the trigonometry link is given below.

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Answer:

34°

Step-by-step explanation:

The boy is 5 feet 6 inches tall.

The boy casts a shadow that is 8 feet and 3 inches long.

We know 12 inches equal 1 foot.

Therefore the boy's height is 5.5ft and the shadow is 8.25ft.

The angle of elevation of the sun is given by the tangent of the angle A.

[tex] \tan(A) = \frac{5.5}{8.25} [/tex]

[tex]\tan(A) = 0.6667[/tex]

[tex]A= {\tan}^{ - 1} (0.6667)[/tex]

[tex]A=33.69 \degree[/tex]

To nearest degree is 34°

Answer: 34 degrees

Step-by-step explanation:

the boy is 5’6

5x12=60+6=66

The shadow is 8’3

8x12=96+3=99

You would use tan(X)= 5.5/8.25

calculate to get 33.69 round to 34.

Answer:

C = 6pi units

or

C is approximately 18.84 units

Step-by-step explanation:

The circumference of a circle is given by

C = pi *d

The diameter is 6 units

C = 6*pi units

If we approximate pi by 3.14

C = 6*3.14

C = 18.84 units

The fish is 2.25 ft above the water surface.

Step-by-step explanation:

⇒ y = -16(0.375)² + 12 × 0.375

      = -2.25 + 4.5

      = 2.25 ft

Answer:

C. (-5,0) and (3,0)

Step-by-step explanation:

y= x² + 2x-15

y = 0

x² + 2x-15 = 0

(x - 3) (x + 5) = 0

x = 3 or x = -5

The x-intercepts of the graph of the function are (-5,0) and (3,0).

Option C is the correct answer.

A function has an input and an output.

A function can be one-to-one or onto-one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

To find the x-intercepts of the graph of the function,

We need to set y = 0 and solve for x.

So we have:

x² + 2x - 15 = 0

Factoring this quadratic equation.

(x + 5) (x - 3) = 0

Setting each factor equal to zero.

x + 5 = 0 or x - 3 = 0

Solving for x.

x = -5 or x = 3

Therefore,

The x-intercepts of the graph of the function are (-5,0) and (3,0).

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Answer:

The 10th term will be:

                                                         [tex]a_{10}=\frac{1}{512}[/tex]

Step-by-step explanation:

Considering the sequence

[tex]1,\:\frac{1}{2},\:\frac{1}{4}...[/tex]

A geometric sequence has a constant ratio r and is defined by

[tex]a_n=a_0\cdot r^{n-1}[/tex]

[tex]\mathrm{Compute\:the\:ratios\:of\:all\:the\:adjacent\:terms}:\quad \:r=\frac{a_{n+1}}{a_n}[/tex]

[tex]\frac{\frac{1}{2}}{1}=\frac{1}{2},\:\quad \frac{\frac{1}{4}}{\frac{1}{2}}=\frac{1}{2}[/tex]

[tex]\mathrm{The\:ratio\:of\:all\:the\:adjacent\:terms\:is\:the\:same\:and\:equal\:to}[/tex]

[tex]r=\frac{1}{2}[/tex]

[tex]\mathrm{The\:first\:element\:of\:the\:sequence\:is}[/tex]

[tex]a_1=1[/tex]

[tex]\mathrm{Therefore,\:the\:}n\mathrm{th\:term\:is\:computed\:by}\:[/tex]

[tex]a_n=\left(\frac{1}{2}\right)^{n-1}[/tex]

Putting n = 10 to determine in the nth term to determine the 10th term

[tex]a_{10}=\left(\frac{1}{2}\right)^{10-1}[/tex]

[tex]a_{10}=\left(\frac{1}{2}\right)^9[/tex]

[tex]\mathrm{Apply\:exponent\:rule}:\quad \left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}[/tex]

[tex]a_{10}=\frac{1^9}{2^9}[/tex]

[tex]a_{10}=\frac{1}{2^9}[/tex]     ∵ [tex]1^9=1[/tex]

[tex]a_{10}=\frac{1}{512}[/tex]     ∵  [tex]2^9=512[/tex]

Therefore, the 10th term will be:

                                                         [tex]a_{10}=\frac{1}{512}[/tex]

Step-by-step explanation:

Hope it helps you in your learning process.

To simplify the expression 4 + (14 - 2), subtract 2 from 14, then add 4 to get the equivalent expression. The three equivalent expressions are: 20, -12, and 16.

To simplify the expression 4 + (14 - 2), we need to perform the operations inside the parentheses first. This means subtracting 2 from 14, which gives us 12. Then, we add 4 to 12, resulting in 16. Therefore, the expression 4 + (14 - 2) is equivalent to 16.

The three expressions that are equivalent to 4 + (14 - 2) are:

A. 4 - (-14 - 2) = 4 - (-16) = 4 + 16 = 20

B. (4 - 14) - 2 = -10 - 2 = -12

C. 4 - (-14) - (2) = 4 + 14 - 2 = 16

Answer:

39

Step-by-step explanation:

Let the three consecutive odd numbers be:

x+2, x+4, x+6.

The sum of the consecutive numbers is 123 i.e

x+2 + (x+4) + (x+6) = 123

x + 2 + x + 4 + x + 6 = 123

3x + 12 = 123

Collect like terms

3x = 123 — 12

3x = 111

Divide both side by the coefficient of x i.e 3

x = 111/3

x = 37

Now let us find the value of the three odd numbers. This is illustrated:

1st : x + 2 = 37 + 2 = 39

2nd : x + 4 = 37 + 4 = 41

3rd : x + 6 = 37 + 6 = 43

The smallest of the three consecutive odd numbers is 39

The required formula with b subject is [tex]b = a^{2} - 6[/tex].

Given that ,

a is the subject of the formula,

[tex]a = \sqrt{ b + 6}[/tex]

We have to make b is the subject for the formula,

[tex]a = \sqrt{ b + 6}[/tex]

Squaring both the sides,

[tex]a^{2} = b + 6[/tex]

[tex]b = a^{2} - 6[/tex]

Hence , The required formula with b subject is [tex]b = a^{2} - 6[/tex]

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To make b the subject of the formula a = √(b+6), you need to isolate b on one side of the equation. The solution is b = a² - 6.

To make b the subject of the formula a = √(b+6), we need to isolate b on one side of the equation. Here are the steps:

Therefore, b = a² - 6.

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Answer:

  84.14 square units, total

Step-by-step explanation:

Use the formulas for area of the figures you're interested in.

Rectangle Area

  A = LW

Circle Area

  A = πr^2

__

Your rectangle area will be ...

  A = 5 × 14 = 70 . . . . square units

The area of a full circle with diameter 6 (radius = 6/2 = 3) will be ...

  A = π × 3^2 = 9π

The area of a semicircle of that size is half that:

  semicircle area = 9π/2 = 4.5π

Then the total area of the two figures is ...

  70 + 4.5π ≈ 70 +14.14 = 84.14 . . . square units

Answer:

110

Step-by-step explanation:

Answer:

105 miles

Step-by-step explanation:

first we have to find her speed before it is reduced

so

60/1.5

thats equal to 40

she can travel 40 mph

reduce that by 5 so her speed is now 35mph

35*3=105

Answer:

y= -2

Step-by-step explanation:

Please see attached picture for full solution.

(From the 4th to 5th line, I multiplied both sides by 8)

Answer:

y=2x+3

Step-by-step explanation:

Answer:

y = -3x - 1

Step-by-step explanation:

Point Slope Form:  (y - y1) = m(x - x1)

Step 1:  Find the slope using [tex]\frac{y2 - y1}{x2 - x1}[/tex]

(x1, y1) = (-1, 2)

(x2, y2) = (1, -4)

m = [tex]\frac{-4 - 2}{1 -(-1)}[/tex]

m = [tex]\frac{-6}{1+1}[/tex]

m = [tex]\frac{-6}{2}[/tex]

m = -3

Step 2:  Plug into point slope form and solve for y

(y - y1) = m(x - x1)

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

y - 2 = -3(x + 1)

y - 2 + 2 = -3x - 3 + 2

y = -3x - 1

Answer:  y = -3x - 1

Answer:

Step-by-step explanation:

Given that

AB=4x+9

BC=5x+2

Then, AC=56

From vector

AC=AB+BC

Then,

56=4x+9+5x+2

56=9x+11

Subtract 11 from both sides

56-11=9x+11-11

45=9x

Divide both sides by 9

45/9=9x/9

5=x

Then, x=5

Now,

1. AB=4x+9, x=5

AB=4(5)+9

AB=20+9

AB=29

2. Also

BC=5x+2

BC=5(5)+2

BC=25+2

BC=27

Answer:

one solutions

Step-by-step explanation:

graph both points on a graph if they cross you have one solution, if they never meet you have no solution and if it's one line you have infinite solutions

Final answer:

The two given linear equations y = -3x + 6 and y = 2x - 4 have different slopes, which means they will intersect at exactly one point, indicating that there is one solution to the system.

Explanation:

To find out how many solutions can be found for the system of linear equations represented on the graph, we can observe the slopes and y-intercepts of the given equations. The two equations are:

y = -3x + 6

y = 2x - 4

These are both linear equations in the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. The first equation has a slope of -3 and the second has a slope of 2. Because the slopes are not equal, these lines are not parallel and will, therefore, intersect at one point. When two lines intersect at exactly one point, the system of equations has one solution.

Moreover, since they intersect, they do not have the same line, so they do not have infinitely many solutions. Therefore, the correct answer is one solution (B).

Answer:

=3

=2

Step-by-step explanation:

12−5+6=0

using the Quadratic Formula where

a = 1, b = -5, and c = 6

=−±2−4‾‾‾‾‾‾‾‾√2

=−(−5)±(−5)2−4(1)(6)‾‾‾‾‾‾‾‾‾‾‾‾‾‾√2(1)

=5±25−24‾‾‾‾‾‾‾√2

=5±1‾√2

The discriminant 2−4>0

so, there are two real roots.

Simplify the Radical:

=5±12

=62=42

which becomes

=3

=2

hope this helps :)

Answer:

1 + 2

Step-by-step explanation:

When we look at the number line, we can see that the inequality is:

x ≤ 19

This means that all values of "x", must be equal to or less than 19.

To find the correct answer choices, we must keep that equation in mind.

1. at most 19 cups   -   this answer choice does work, because it shows that 19 is the limit (which is what our inequality represents)

2. 19 cups or less    -     this answer choice works as well because it shows that 19 is the maximum and all other values of "x" must be below that.

3. more than 19 cups   -  this goes against our inequality, since "x" can't exceed 19. This means that this answer choice must be incorrect.

4. a minimum of 19 cups   -   this answer choice also cannot be correct since it shows that "x" can go over 19 (which we know is false).

5. no fewer than 19 cups   -    this is also wrong because it wants "x" to go over the value of 19, which it can't do.

Answer:

Step-by-step explanation:

A and b

Answer:

The negation to the given statement "At least one gift in the bag is wrapped - true" is " At least one gift in the bag is not wrapped" - False

Step-by-step explanation:

Given statement is At least one gift in the bag is wrapped is true

The negation to the given statement is " At least one gift in the bag is not wrapped" - False

To determine whether the statement is a negation of the given statement is True or False :

Answer:

your answer would be 2

Step-by-step explanation:

Convert 1 3/12 into an improper fraction which is 5/4

Then add it with 9/12

5

/4  + 9

/12

(5 × 12) + (9 × 4)

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

        4 × 12

= 96/48

=    96 ÷ 48

 -------------------

     48 ÷ 48

= 2

2 is your answer hope this helps :)

Answer:

2 feet

Step-by-step explanation:

To find the total amount of snow that fell, we add

1 3/12 + 9/12

add the fractions

3/12+9/12 = 12/12 =1

Add the whole numbers

1  plus the whole number from the fraction

1+1 =2

Answer:

12

Step-by-step explanation:

Just take 35 and subtract 23.

Answer:

The associative property states that you can add or multiply regardless of how the numbers are grouped. By 'grouped' we mean 'how you use parenthesis'. In other words, if you are adding or multiplying it does not matter where you put the parenthesis. Add some parenthesis any where you like!.

The Commutative property states that order does not matter. Multiplication and addition are commutative.

hope this helps please mark brainliest!

The another way to state the transformation would be [tex](x,y)>(-x,-y)[/tex]

Solution:

Rotation about the origin at [tex]180^\circ[/tex]: [tex]R_{180^\circ}A \rightarrow O = R_{180^\circ} (x, y) \rightarrow (-x,-y)[/tex]

The term R0 means that the rotation is about the origin point. Therefore, (R0,180) means that we are rotating the figure to [tex]180^\circ[/tex] about the origin.

So, the transformation of the general point (x,y) would be (-x,-y) when it is rotated about the origin by an angle of [tex]180^\circ[/tex].

Hence according to the representation, the expression would be [tex](x, y) \rightarrow (-x, -y)[/tex].

The transformation R0, 180° is equivalent to reflecting each point (x, y) in a Pentagon across the origin, resulting in the new coordinates (-x, -y).

The transformation rule R0, 180° involves rotating a point (x, y) within a Pentagon by 180 degrees around the origin. In this transformation, each point is mirrored or reflected across the origin. To express this transformation differently, we can say that (x, y) is mapped to its mirror image in both the x-axis and y-axis. In other words, the x-coordinate is reversed (negated), and the y-coordinate is also reversed (negated).

So, the alternative way to state this transformation is: (x, y) > (-x, -y). This means that any point (x, y) in the original Pentagon will become (-x, -y) after the transformation.

For example, if we have a point (2, 3) within the Pentagon, applying the transformation yields (-2, -3). This means the point's x-coordinate is changed from 2 to -2, and the y-coordinate is changed from 3 to -3. This transformation is essentially a 180° rotation or a reflection through the origin.

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