subtracting linear expressions (6x+2)-(9x+3)

addition (+) expression the students used to find the answer.

Solution:

Given data: A student is asked to find the sum of 197 and 413.

Sum means adding two numbers or variables.

For addition, we use + symbol to add two numbers.

First add last digit of the numbers (7+3) = 10.

Put 0 in last and carry 1 to the next left digit top.

Add middle digits with carry over 1 (1 + 9 + 1) = 11

Put 1 and carry another 1 to the next left digit top.

Add first digit of the numbers with carry over 1 (1 + 1 + 4) = 6

Sum of 197 + 413 = 197 + 413

                            = 610

The addition image attached below.

Hence, addition (+) expression the students used to find the answer.

Answer:

Step-by-step explanation:

Percent change= (1/4-1/8)/1/4 × 100%

= {(2 -1)/8} ÷ 1/4 × 100%

= (1/8 ÷ 1/4) × 100%

= 1/8 × 4/1 × 100%

=1/2 × 100%

= 50%

It is 50% change

Answer:

I believe the answer is 50%.

1/4 x 1/2 = 0.125

125/1000

125/1000 <-- divide numerator and denominator by 125

the above fraction simplifies to 1/8

So, one 1/4 is double the value of one 1/8

Answer:

The actual weight is 1.1% less (100 - 98.9) than the labeled weight.

Step-by-step explanation:

1. Let's review the information given to us to answer the question properly:

Labeled weight of the bag of chocolates = 0.384 pounds

Actual weight of the bag of chocolates = 0.3798 pounds

2.  How much have you or lighter are the chocolates and the stated on the label. Show your reasoning.

Let's find how much we have comparing the labeled weight and the actual weight, using a Direct Rule of Three, this way:

Weight               Percentage

0.384                    100 %

0.3798                      x %

0.384x = 0.3798 * 100

0.384x = 37.98

x = 37.98/0.384

x = 98.9 (Rounding to one decimal place)

The actual weight is 1.1% less (100 - 98.9) than the labeled weight.

The chocolates are 0.0042 pounds lighter than what is stated on the label.

The difference in weight between the labeled weight and the actual weight of the chocolates is 0.0042 pounds. This means that the chocolates are 0.0042 pounds lighter than the label indicates.

To calculate this, subtract the actual weight from the labeled weight: 0.384 - 0.3798 = 0.0042 pounds.

So, the chocolates are 0.0042 pounds lighter than what is stated on the label.

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Answer:

scale factor is 4 so it will be 8mm

Answer:

143/9 = 15.89

Step-by-step explanation:

Answer:

J= 45

Step-by-step explanation:

j ÷ 9 = 5

×9. ×9

J= 45

you multiply by to cancel out the nine. you do it on both sides of the equal sign so it's proportionate

Answer:

j=45

j/9=5

Step-by-step explanation:

j equals fourty five

j over or divided (by) nine equals five

The point (1, 9) with a slope of 4 on a graph corresponds to the answer of 13.

The answer is 13.

To calculate this, we use the formula for the equation of a straight line: y = mx + b, where m is the slope and b is the y-intercept. In this case, the equation would be y = 4x + 9. Substituting x = 1 into the equation gives y = 4(1) + 9 = 13.

Therefore, the point (1, 9) has a slope of 4 on the graph.

You can't really convert that becasue cups is a volume and pounds is a weight. If I have a cup of feathers and a cup of iron filings, then the iron filings will weigh much less than the feathers. A cup different items would not have the same weight - if you know what I mean.

Answer:

6

Step-by-step explanation:

Using the sine ratio in the right triangle and the exact value

sin45° = [tex]\frac{1}{\sqrt{2} }[/tex], then

sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{3\sqrt{2} }{hyp}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )

hyp = 3[tex]\sqrt{2}[/tex] × [tex]\sqrt{2}[/tex] = 3 × 2 = 6

The domain is all possible values for x.

Here we can see a parabola the goes sideways.

The vertex of the parabola is at (3,-1).

That means the domain is [tex]x\geq 3[/tex]

Think about it this way, is there any point on the parabola that can have a x coordinate of 4?

The range of a function is all possible y values. Is seems that the parabola stretches infinitely up and down, meaning that all values of y are possible.

Answer:

what does it look like we need that

Step-by-step explanation:

Answer:

Rise

Step-by-step explanation:

The vertical change between two points is called the rise, and the horizontal change is called the run. Just think of the rise as your going up from the bottom to the top. And run as if you were just going from one side to the other.

Answer: +81

Explanation: To find the next term in the pattern, begin by studying the pattern. Here, notice that 3 x 3 is equal to 9 and 9 x 3 is equal to 27.

Continuing the same pattern, 27 x 3 is equal to 81.

So the next term in the pattern is +81.

In similar triangles ΔFGH and ΔLMN, only the corresponding angles are congruent (thus ∠H ≅ ∠N). The sides are proportionate, not necessarily congruent. Other listed options are either incorrect or unclear due to potential misinterpretations or typographical errors.

Given that triangles ΔFGH and ΔLMN are similar (ΔFGH ~ ΔLMN), the following must be true based on the concept of similar triangles:

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Answer:

60$

Step-by-step explanation:

Shipping is 7.50 and the 7 items are 52.5 total

Answer:

50%

Step-by-step explanation:

He has a 4/8 that he picks a rocky and a 4/8 that he doesn't. That gives us 1/2 and 1/2. 1/2=0.5 0.5×100%=50%

Answer:

The radius of the cylinder is 4 cm.

Step-by-step explanation:

Given:

radius of cone = 6 cm

height of the cone = 8 cm

height of cylinder = 6 cm

We need to find the radius of cylinder.

Solution:

First we will find the volume of cone.

Volume of cone is one third time square of radius times height times π.

framing in equation form we get;

Volume of cone = [tex]\frac{1}{3}\pi r^2h = \frac{1}{3}\pi\times 6^2\times 8 \approx 301.44 \ cm^3[/tex]

Now Volume of cylinder is given by square of radius times height times π.

framing in equation form we get;

Volume of cylinder = [tex]\pi r^2h=18.84r^2[/tex]

Now it has been given that;

Volume of cone is equal to Volume of cylinder.

so we can say that

[tex]18.84r^2=301.44[/tex]

Dividing both side by 18.84 we get;

[tex]\frac{18.84r^2}{18.84}=\frac{301.84}{18.84}\\\\r^2\approx16[/tex]

Taking square root on both side we get;

[tex]\sqrt{r^2}=\sqrt{16} \\\\r=4\ cm[/tex]

Hence the radius of the cylinder is 4 cm.

The population of the town in 5 years is 12763

The given parameters are:

Initial value (a) = 10000

Rate (r) = 5%

A population growth model is represented as:

[tex]y = a(1 + r)^x[/tex]

So, we have:

[tex]y = 10000 * (1 + 5\%)^x[/tex]

In 5 years, we have:

[tex]x = 5[/tex]

So, we have:

[tex]y = 10000 * (1 + 5\%)^5[/tex]

Evaluate

[tex]y = 12763[/tex]

Hence, the population in 5 years is 12763

Read more about exponential functions at:

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Answer:

x = 29

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Sum the 3 given angles and equate to 180

x + 2x + 2 + 3x + 4 = 180, that is

6x + 6 = 180 ( subtract 6 from both sides )

6x = 174 ( divide both sides by 6 )

x = 29

Answer:

According to my calculations, the answer is (x, y)= ( -1, -3 ). In other words, x= -1 and y= -3

Step-by-step explanation:

Answer:

10 is the greatest common factor

Step-by-step explanation:

Find the prime factors of each term in order to find the greatest common factor (GCF).

10

Answer:

The slope of the least squares regression line is:

0.32

The units of the slope of the line are:

centimeters per day.

The slope of the line tells you that for each new day you can predict that a plant's height will increase by about 0.32 centimeters.

The y-intercept of the least square regression line is:

-1.72

The units of the y-intercept of the line are:

centimeters.

The y intercept:

Typical height compared to the soil line.

Step-by-step explanation:

The area of the figure is 40 units. (rounded off from 39.998 units)

Step-by-step explanation:

1. Area of the figure = Area of Rectangle + Area of Parallelogram.

2. Naming points:

Let the rectangle consist of points A(-6,-1), B(-5,-5), C(3,-3) and D(2,1).

Let the parallelogram consist of points C(3,-3), D(2,1), E(2,7) and F(3,3).

3. Each coordinate has a point on the x-axis and a point on the y-axis. We shall refer to these points as x', x'' ,x''' and so on corresponding to the x-axis values of A, B, C and so on in that order till F. For the y-axis points, we will name them in the series of y', y'', y''' and so on.

In simple words, in A(-6,1), x' = -6; y' = -1

4. Formula for finding area:

Area of a rectangle = length (l) × width (w)

Area of a parallelogram = base (b) x height (h)

5. Finding area of the rectangle:

l = AD = [tex]\sqrt{[x'''' - x']^{2} - [y'''' - y']^{2}}[/tex]

, i.e. AD = [tex]\sqrt{[2 - (-6)]^{2} - [1 - (-1)]^{2}}[/tex]

, i.e. AD = √68 = 8.246 (rounded to 3 decimals) = l

Now, w = AB = [tex]\sqrt{[x'' - x']^{2} - [y'' - y']^{2}}[/tex]

, i.e. AB = [tex]\sqrt{[(-5) - (-6)]^{2} - [(-5) - (-1)]^{2}}[/tex]

, i.e. AB = √17 = 4.123 (rounded to 3 decimals) = w

Area of rectangle = l x w = 8.246 x 4.123 = 33.998 units.

6. Finding area of the parallelogram:

b = DE = 6 units (we can observe this from the graph, i.e. points from 1 to 7 on the y axis)

h = Height is the line drawn perpendicular to the base from point F, which as we can see is 1 unit long.

Hence, Area of parallelogram = b x h = 6 x 1 = 6 units.

7. Now, adding both, we can arrive at the final answer.

Area of the figure = Area of rectangle + Area of parallelogram,

i.e. 33.998 units + 6 units = 39.998 units. (can be rounded off to 40 units)

Answer:

D

Step-by-step explanation:

6b>-18

b>-3

This is shown by the line going from -3 into infinity.

Answer:

6b > -18

Step-by-step explanation:

[tex]6b > -18 \\then \\b >\frac{-18}{6} \\then\\b > -3[/tex]

Answer:

The correct option is third one m∠2 =106° , m∠3 =37°.

Therefore,

[tex]m\angle 2 = 106\°\\m\angle 3 = 37\°[/tex]

Step-by-step explanation:

Given:

Consider ABCD as a Rhombus such that,

∠A = ∠1 = 106°

∠C = ∠2

∠BDC = ∠3

AB=BC=CD=DA

To Find:

∠2 = ?

∠3 = ?

Solution:

ABCD is a Rhombus

∠A ≅ ∠C  ............opposite angles of Rhombus are equal. ( property )

Substituting the values we get

∠1 = ∠2

But ∠1 = 106°

∴ ∠2 = 106°    ....... Transitive property,

As BC = CD   ...Given

ΔBCD is an Isosceles triangle

∴ ∠CBD ≅ ∠BDC = ∠3  ........base angle of Isosceles triangle are congruent.

we know that in a triangle,

Sum of measures of all angles is 180°

in Triangle BCD

[tex]\angle 3 +\angle 2 +\angle 3 =180[/tex]

Substituting the values we get

[tex]2m\angle 3 =180-106=74\\\\\angle 3=\dfrac{74}{2}=37\\\\m\angle 3 = 37\°[/tex]

Therefore,

[tex]m\angle 2 = 106\°\\m\angle 3 = 37\°[/tex]

Answer:

-8

Step-by-step explanation:

I believe it is -8

first you 2(-2) - 4

then you  -4 -4= -8

Hope that was helpful.

[tex] \huge\boxed{\mathfrak{Answer}}[/tex]

[tex]f(x) = 2x - 4 \\ f( - 2) = {?} \\ \\ x = - 2 \\ \\ f( - 2) = 2( - 2) - 4 \\ f( - 2) = - 4 - 4 \\ f( - 2) = - 8[/tex]

=> The answer is -8.

Answer:

$60,000

Step-by-step explanation:

100,000 / 10 = 10,000, 10- 4=6, 10,000 * 6 = 60,000

To determine the monthly income of a family after 40% is withheld from a $100,000 annual income, subtract the amount withheld ($40,000) from the annual income and divide by 12, yielding a monthly income of $5,000.

To calculate the monthly income after taxes for the family, we first need to determine the amount withheld from the annual income for taxes and retirement plans. With an annual income of $100,000 and 40% being withheld, we do the following calculation:

Therefore, the family's monthly income after the 40% is taken off would be $5,000.

Answer:

B

Step-by-step explanation:

Linc c moving upward will intersect line b

Option (B) shows that lines a, b, and c are coplanar. Lines a and b intersect. Line c intersects only with line b.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

It is given that:

Lines a, b, and c are coplanar. Lines a and b intersect.

Line c intersects only with line b

As we can see in the picture, the lines are given:

As we know, the coplanar plane is the plane in which all lines or points lie (ie. in the same plane) known as coplanar.

In option (B) the lines a, b, and c are coplanar. Lines a and b intersect. Line c intersects only with line b.

Thus, option (B) shows that lines a, b, and c are coplanar. Lines a and b intersect. Line c intersects only with line b.

Learn more about the straight line here:

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Answer:

f(x) = (x - 3)² - 1

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

To obtain this form use the method of completing the square

Add/subtract ( half the coefficient of the x- term )² to x² - 6x

f(x) = x² + 2(- 3)x + 9 - 9 + 8

     = (x - 3)² - 1

Answer:

1. m∠MKN = 41°

Step-by-step explanation:

1.

KM bisects so NKM and MKL are equal

2 (3x + 5) + 8x + 2 = 180 (straight angle)

6x + 10 + 8x + 2 = 180

6x + 8x = 180 - 10 - 2

14x = 168

x = 168/14

x = 12

3*12+5 = 41

m MKN = 41