Bill walks 1/2 mile south, then 3/4 mile east, and finally 1/2 mile south. How many miles is he, in a direct line, from his starting point? Express your answer as a decimal to the nearest hundredth.

Answer:

7x² + 5x

Step-by-step explanation:

Given

(9x² + 8x) - (2x² + 3x) ← distribute parenthesis, second by - 1

= 9x² + 8x - 2x² - 3x ← collect like terms

= (9x² - 2x² ) + (8x - 3x)

= 7x² + 5x

Distribute the negative sign:

[tex](9x^2+8x)-(2x^2+3x)=9x^2+8x-2x^2-3x[/tex]

Gather like terms:

[tex]9x^2+8x-2x^2-3x = (9x^2-2x^2) + (8x-3x) = 7x^2+5x[/tex]

Answer

130,000

Hope it helps!

The gross profit margin calculates as 15.38% for the given business scenario, calculated with the values provided in the sales, purchases, inventory, and transfers.

The subject of this question is gross profit margin in a business, which can be calculated using certain financial figures and simple arithmetic. We start by determining the cost of goods sold (COGS), which includes the beginning inventory, any additional purchases, and transfers from other locations, subtracted by the ending inventory. Using your figures, we get the following calculation: $26,000 (beginning inventory) + $24,000 (purchases) + $12,000 (transfers) - $29,000 (ending inventory) = $33,000 (COGS).

Next, we subtract the cost of goods sold from the total sales to determine the gross profit: $39,000 (total sales) - $33,000 (COGS) = $6,000 (gross profit).

Finally, to find the gross profit margin percentage, we divide the gross profit by total sales, and then multiply by 100, which gives us: $6,000/$39,000 * 100 = 15.38%.So, your gross profit margin percentage is 15.38%.

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Answer:

3 days

Step-by-step explanation:

First multiply 10 by 400 to find how many meters she runs each day.

10*400 = 4,000

1 kilometer = 1,000 meters

Now convert the meters to kilometers

To convert it to kilometers you divide 4,000 by 1,000, which equals 4 kilometers.

So she runs 4 kilometers each day.

Now divide 12 by 4 to find out how many days it will take to run 12 kilometers.

12/4 = 3 days

Answer:

Since she is selling 1.49 per iced tea bottle, and 1.25 per water bottle, and she only consitered how many water bottles she would sell, and not iced tea bottle, the awnser would be: "Barbara's equation did not consider the number of iced tea drinks."

or

the equation did not account for the number of iced tea drinks.

it should be:

let x = number of water drinks.

let y = number of ice tea drinks.

1.25x + 1.49y = 100

Answer:

b. 2

Step-by-step explanation:

[tex]\bf ~~~~~~\textit{parabola vertex form} \\\\ \begin{array}{llll} \stackrel{\textit{we'll use this one}}{y=a(x- h)^2+ k}\\\\ x=a(y- k)^2+ h \end{array} \qquad\qquad vertex~~(\stackrel{}{ h},\stackrel{}{ k}) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \textit{we know that } \begin{cases} h=2\\ k=-4 \end{cases}\implies y=a(x-2)^2-4 \\\\\\ \textit{we also know that } \begin{cases} y = -3\\ x = -3 \end{cases}\implies -3=a(-3-2)^2-4\implies 1=a(-5)^2 \\\\\\ 1=25a\implies \boxed{\cfrac{1}{25}=a}[/tex]

Answer:

it is not 5

so there are only three options left

Answer:

The number of men = 108

Step-by-step explanation:

Total person = 396

ratio of women to men = 2:3

ratio of men to children = 1:2=2:4=3:6

Women = 2

Men = 3

Children = 6

Hence,

women+men+children = 2+3+6 = 11

Now finding out the percentage of each

Women = 2/11 * 396

= 792/11

=72

Men = 3/11 * 396

=1188/11

=108

Children = 6/11 *396

=2376/11

=216

Thus the number of men = 108 ....

Answer

Congruent by dilation

Step-by-step explanation:

They are not the same size, nor have the same area and are not currently congruent because they are different sizes.

Answer:

Step-by-step explanation:

From the figures, you can observe that the triangles don't have the same size or area, that means they cannot be congruent.

However, if we dilate the first triangle by a scale factor of 2, then both triangles will be congruent, because 5 x 2 = 10, 4 x 2 = 8 and 3 x 2 = 6.

Therefore, the right answer is D. Because if you dilate the first triangle, both would be congruent. Also, because they don't have the same area, size, and they aren't congruent.

Answer:

x = 1/2

Step-by-step explanation:

The equation in correct format is:

[tex]log_{5}(25)=x[/tex]

We have to solve this logarithmic equation to find the value of x. This can be done by using the rules of logarithm i.e the power rule and same base rule shown below:

[tex]log(a)^{b}=b \times log(a)\\\\log_{a}(a)=1[/tex]

Using these rules on our equation, we get:

[tex]log_{5}(25)=x\\\\log_{5}(5^{\frac{1}{2} })=x\\\\ \frac{1}{2} log_{5}(5)=x\\\\ \frac{1}{2} (1)=x\\\\ x=\frac{1}{2}[/tex]

Thus the value of x would be 1/2

Answer:

Step-by-step:

Write in exponential form

Simplify the expression

Swap sides

Answer:

the answer is 10^2

thanks. hope full it help you

Answer:

10^2

your welcome :>

Answer:

it 15cm im sure of it tell me if you get it right

Answer:

Step-by-step explanation:

The central angle for this problem is:

[tex]\frac{7 \pi}{10}rad \approx 2.2 rad[/tex]

To solve this problem, we have to use an expression that relates, central angle, arc length and radius, which is:

[tex]s=\theta r[/tex]

So, we isolate the radius and solve:

[tex]r=\frac{s}{\theta}=\frac{33cm}{2.2rad}=15cm[/tex]

Therefore, the right answer is the second option.

Answer:

C=3

Step-by-step explanation:

C-(-8) = 5 + 2C

C+8 = 5+2C

Subtract C from each side

C-C+8 = 5+2C-C

8 = 5+C

Subtract 5 from each side

8-5 = 5-5+C

3 =C

Answer:

The correct answer is C=3.

Step-by-step explanation:

To solve this problem, we should first eliminate the parentheses on the left side of the equation.  To do this, we must recognize that there is subtraction of a negative number, which is the same as adding a positive number.  This gives us:

C + 8 = 5 + 2C

Next, we should move all of the variable C's to one side of the equation and move all of the constants (the number terms) to the other side.  To do this, we should subtract C from both sides of the equation (to cancel out the C on the left side, moving them to the right) and subtract 5 from both sides (to cancel out the 5 on the right side and move all of the constant terms to the left).

C - C + 8 - 5 = 5 - 5 + 2C - C

If we recognize which terms cancel, we get:

8 - 5 = 2C - C

When we combine like terms through subtraction on both sides, we get:

3 = C

Therefore, the answer is that C = 3.

Hope this helps!

Answer:

f(a+2)= 3((a+2)+5) +4/(a+2)

Step-by-step explanation:

Since X was exchanged for a+2, you have to set a+2 as x in the problem.

Answer:

[tex]\large\boxed{f(a+2)=3(a+7)+\dfrac{4}{a+2}}[/tex]

Step-by-step explanation:

[tex]f(x)=3(x+5)+\dfrac{4}{x}\\\\f(a+2)-\text{put x = a + 2 to the equation of f(x):}\\\\f(a+2)=3\bigg((a+2)+5\bigg)+\dfrac{4}{a+2}=3(a+2+5)+\dfrac{4}{a+2}\\\\f(a+2)=3(a+7)+\dfrac{4}{a+2}[/tex]

Answer:

3/4=x/9

Step-by-step explanation:

I think we use the side slitter theorem for this case so x/9 pair together and 3/4 also.

This mathematics question from a high school student is about geometric relationships in a three-dimensional coordinate system, with details specifically on parallel lines, vector addition, and a Weissenberg diagram relevant to crystallography.

The question on which assistance is sought pertains to geometric concepts, specifically those related to parallel lines and coordinates in a plane or space. In this context, VW being parallel to YZ implies that these lines are in the same geometric plane and maintain a constant distance from each other. Given that the z-axis is horizontal, the x-axis points backward, and the y-axis points upward, we are discussing a three-dimensional Cartesian coordinate system.

Understanding the Weissenberg diagram involves knowledge of crystallography and rotation-oscillation methods. The passage also explains that the vector w lies in the y'z' plane indicating that the vector has no x-component, as mentioned by Wx' = 0. When solving problems like these, it's important to follow vector addition rules and define your axis system correctly, as in the statement that defines +x to be eastward and +y to be northward, which is related to navigation and mapping conventions.

Figures from MIT OCW suggest that the concept of 'contour lines' and their relationship to topographical features such as valleys and ridges is also being examined.

Answer:

A. 10

Step-by-step explanation:

RT = XZ

With this being stated, XZ also has to be 10.

I am joyous to assist you anytime.

Answer:

[tex]28w^2-476w[/tex]

Step-by-step explanation:

The general rule we are going to use to multiply this out is the distributive property. Which is:

a(b+c) = ab + ac

Note: x * x = x^2

Now multiplying, we get:

[tex]28w(w-17)\\=28w*w-28w*17\\=28w^2-476w[/tex]

This is the multiplied out form, answer.

For this case, we must find two points that belong to the line and thus find the slope.

We have:

[tex](x1, y1) :( 1,1)\\(x2, y2) :(0,4)[/tex]

We found the slope:

[tex]m = \frac {y2-y1} {x2-x1} = \frac {4-1} {0-1} = \frac {3} {- 1} = - 3[/tex]

It is also observed that the cut-off point with the y-axis is 4.

In this way, we discard options A and B.

We evaluate option C:

[tex]y> -3x + 4[/tex]

We substitute the point (0,0) that belongs to the shaded region and verify the inequality:

[tex]0> -3 (0) +4\\0> 4[/tex]

It is not fulfilled!

Thus, the correct option is option D.

ANswer:

Option D

Answer:

For this case, we must find two points that belong to the line and thus find the slope.

We have:

We found the slope:

It is also observed that the cut-off point with the y-axis is 4.

In this way, we discard options A and B.

We evaluate option C:

We substitute the point (0,0) that belongs to the shaded region and verify the inequality:

It is not fulfilled!

Thus, the correct option is option D.

ANswer:

Option D

[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \textit{we also know that }~~ \begin{cases} y=-4\\ x=8 \end{cases}\implies -4=k(8)\implies \cfrac{-4}{8}=k\implies -\cfrac{1}{2}=k \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=-\cfrac{1}{2}x~\hfill[/tex]

Answer:

k = -1/2

y= -1/2x

Step-by-step explanation:

y = kx

We know y = -4 and x=8

-4 = k*8

Divide each side by 9

-4/8 = 8k/8

-1/2 =k

y= -1/2x

Answer:

B(-7,-3)

Step-by-step explanation:

When you reflect across the x axis, your y coordinate is multiplied by -1.

(-7,-1(3))

(-7,-3)

The only answer choice that is the same as my result is B.(-7,-3).

Answer:

"6 units left and 9 units down"

Step-by-step explanation:

Suppose a function is given in this form:

[tex]y=(x-a)^2+b[/tex]

This is the parent function y = x^2

Now, to go from  [tex]y=(x-5)^2+7[/tex]  to  [tex]y= (x+1)^2-2[/tex] , we can see that:

Thus, "6 units left and 9 units down" is the transformation(translation).

Step-by-step explanation:

[tex]\dfrac{5}{10}=\dfrac{5:5}{10:5}=\dfrac{1}{2}\\\\\dfrac{5}{10}=0.5[/tex]

Let m = slope

m = (0-2)/(0-7)

m = -2/-7

m = 2/7

y - 0 = (2/7)(x - 0)

y = (2/7)x

Did you follow?

The equation of the line for the given coordinates [tex](7,2) , \ (0,0)[/tex] is equal to [tex]y= \frac{2}{7}x[/tex].

"Equation is defined as the relation between the variables using the sign of equality."

Formula used

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

Equation of line passing through a point

[tex]y- y_{1} = m (x- x_{1})[/tex]

According to the question,

Given coordinates,

[tex](x_{1} ,y_{1}) = (7,2)\\\\(x_{2} ,y_{2}) = (0,0)[/tex]

Substitute the value in the formula to get slope,

[tex]m = \frac{0-2}{0-7}[/tex]

   [tex]= \frac{2}{7}[/tex]

Substitute the value in the formula to get equation of the line,

[tex]y-2= \frac{2}{7} (x-7)\\\\\implies y-2 = \frac{2}{7}x -2\\ \\\implies y = \frac{2}{7}x[/tex]

Hence, the equation of the line for the given coordinates [tex](7,2) , \ (0,0)[/tex] is equal to [tex]y= \frac{2}{7}x[/tex].

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The new line with the equation y = 2x + 6 will be less steep than the original line y = 4x + 1 due to its lower slope, and will start higher on the y-axis with a y-intercept of 6 compared to the original line's y-intercept of 1.

When comparing the graph of the equation y = 4x + 1 with the new graph of the equation y = 2x + 6, there are two main features to consider: slope and y-intercept. For the original line, the slope is 4, meaning that for every one unit increase in x, y increases by 4 units.

The y-intercept, where the line crosses the y-axis, is at (0,1). On the other hand, the new line has a slope of 2, which indicates a less steep incline; for every one unit increase in x, y increases by only 2 units. Additionally, the y-intercept of this new line is at (0,6), which is higher on the y-axis as compared to the original line.

Check the picture below.

Answer:

A)

Step-by-step explanation:

The 30-60-90° triangle has the side lengths of 1, √3, 2, so you should find the triangle that fits this measurement.

A) is your answer for:

Side with measurement 1 (30°): 5

5 is your measurement for the side measurement of 1. The next measurement (60°) must be x √3: 5 x √3 = 5√3 (Side on the bottom).

The last measurement (90°) 2 is twice the measurement of 1: 5 x 2 = 10 (Hypotenuse, side on top).

A) is your answer.

~

Answer:

x=2 or x=5

Step-by-step explanation:

0−(x^2−7x+10)

=x^2−7x+10−(x^2−7x+10)

−x^2+7x−10=0

(−x+2)(x−5)=0

−x+2=0 or x−5=0

x=2 or x=5

Answer:

x = 2 or x = 5

Step-by-step explanation:

Several ways to do this.. but i'll use completing the square:

x²-7x +10 = 0

x²-7x  = -10   (take the x coefficient , divide that by two and then square the result and add it back to both sides)

x² - 7x   + ( -7/2 )²  = -10 + ( -7/2 )²  (simply the left side using the property (a + b)² = a² + 2ab + b² )

[x  + (-7/2)]² = -10 +  ( -7/2 )²

[x - (7/2)]² = -10 +  ( 49/4 )

[x - (7/2)]² = 9/4

x - (7/2) = ±√(9/4)

x - (7/2) = ±(3/2)

x = (7/2) ± (3/2)

x = 2 or x = 5

Answer:

Bryce purchased 3 games.

Step-by-step explanation:

To find the number of songs and games that Bryce downloaded, we need to solve the following system of equations:

s + g = 8

2s + 5g = 25

We know that:

s + g = 8 → 2s + 2g = 16 → 2s = 16 -2g

2s + 5g = 25 → 16 - 2g + 5g = 25

→3g = 25 - 16

→3g = 9

→ g = 3

Therefore, bryce downloaded 3 games and 5 songs!

Answer:      3

dont forget to thank and rate plz!!!

also plz may u mark me as brainliest!! : )  ):

Answer:

[tex] x = 2 + \sqrt{42} [/tex]   or   [tex] x = 2 - \sqrt{42} [/tex]

Step-by-step explanation:

[tex] x^2 - 4x - 9 = 29 [/tex]

Subtract 29 from both sides.

[tex] x^2 - 4x - 9 - 29 = 29 - 29 [/tex]

[tex] x^2 - 4x - 38 = 0 [/tex]

There are no two integers whose sum is -4 and whose product is -38, so the trinomial is not factorable. We can use the quadratic formula.

a = 1; b = -4; c = -38

[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]

[tex] x = \dfrac{-(-4) \pm \sqrt{(-4)^2 - 4(1)(-38)}}{2(1)} [/tex]

[tex] x = \dfrac{4 \pm \sqrt{16 + 152}}{2} [/tex]

[tex] x = \dfrac{4 \pm \sqrt{168}}{2} [/tex]

[tex] x = 2 \pm \dfrac{\sqrt{4 \times 42}}{2} [/tex]

[tex] x = 2 \pm \dfrac{2\sqrt{42}}{2} [/tex]

[tex] x = 2 \pm \sqrt{42} [/tex]

[tex] x = 2 + \sqrt{42} [/tex]   or   [tex] x = 2 - \sqrt{42} [/tex]

Answer:

v-5u = <13,-35>

||v − 5u|| = 37.33

Step-by-step explanation:

If u = <-4, 8> and v = <-7, 5>

a) v-5u

Multiply u with 5 and then subtract from v

v-5u = <-7,5>-5<-4,8)>

v-5u = <-7,5> - <-20,40>

v-5u = <-7+20,5-40>

v-5u = <13,-35>

b) ||v − 5u||

We already have found v-5u=<13,-35>

Now, we will find ||v − 5u|| = [tex]\sqrt{(v)^2+(u)^2}[/tex]

||v − 5u|| = [tex]\sqrt{(13)^2+(-35)^2}[/tex]

||v − 5u|| = [tex]\sqrt{169+1225}[/tex]

||v − 5u|| = [tex]\sqrt{1394}[/tex]

||v − 5u|| = 37.33

By multiplying vector 'u' by the scalar 5 and subtracting it from 'v', we derive the resultant vector <13,-35>. The magnitude of this vector is approximately 37.36 units.

The question involves vector operations, specifically the subtraction of a scalar multiple of a vector from another vector. Let's break down the process. First, multiply vector 'u' by the scalar 5, resulting in: 5u = <5*(-4),5*8> = <-20,40>. Next, subtract this new vector from 'v': v - 5u = <-7,5> - <-20,40> = <(-7)-(-20), 5-40> = <13,-35>. That's the result for v-5u.

To find the magnitude of a vector, we use the formula ||v||= sqrt(x^2 + y^2). So ||v - 5u|| = sqrt((13)^2 + (-35)^2) = sqrt(169 + 1225) = sqrt(1394) ≈ 37.36.

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[tex]\dfrac{12!}{6!4!2!}=\dfrac{7\cdot8\cdot9\cdot10\cdot11\cdot12}{2\cdot3\cdot4\cdot2}=13860[/tex]