Given the plane 3x + 5y - z = 9, give an equation of a plane parallel to the given plane, and a plane orthogonal to the given plane.

Answer:

Your numbers are +7, -9, and 25

Step-by-step explanation:

Reverse the values of -7 and +9

Then you get +7 and -9

And also take radius squared which is 25

So, [tex](x--7)^{2} +(y-9)^{2}  = 25[/tex]

Answer:

[tex]\frac{\sqrt{51} }{10}[/tex]

Step-by-step explanation:

Using the Pythagorean identity

sin²x + cos²x = 1 ⇒ cosx = ± [tex]\sqrt{1-sin^2x}[/tex], hence

cosΘ = [tex]\sqrt{1-(7/10)^2}[/tex]

        = [tex]\sqrt{1-\frac{49}{100} }[/tex]

        = [tex]\sqrt{\frac{51}{100} }[/tex]

        = [tex]\frac{\sqrt{51} }{\sqrt{100} }[/tex] = [tex]\frac{\sqrt{51} }{10}[/tex]

Answer:

He should have divided 4 by  [tex]\frac{1}{2}[/tex]:

[tex]shifts=\frac{4}{\frac{1}{2}}\\\\shifts=8[/tex]

Step-by-step explanation:

You know that the students work [tex]\frac{1}{2}[/tex]-hour shifts at the charity event and Zack worked in the event for four hours.

Then, to calculate the number of shifts he worked, he should not have divided [tex]\frac{1}{2}[/tex] by 4. He should have divided 4 by  [tex]\frac{1}{2}[/tex].

Let's make the correct procedure to calculate the number of shifts Zack worked  at the charity event. This is:

[tex]shifts=\frac{4}{\frac{1}{2}}\\\\shifts=8[/tex]

Therefore, he worked 8 shifts.

To calculate the number of shifts Zack worked, we need to follow these steps:
1. Determine the length of one shift. According to the information provided, one shift lasts 1/2 hour.
2. Determine the total amount of time Zack volunteered. Zack volunteered for 4 hours.
3. To find out the total number of shifts Zack worked, we need to divide the total number of hours he volunteered by the length of one shift.
So, we take the total volunteer time (4 hours) and divide it by the shift length (1/2 hour):
\[ \text{Number of shifts} = \frac{\text{Total volunteer time}}{\text{Shift length}} \]
\[ \text{Number of shifts} = \frac{4}{1/2} \]
Now, when dividing by a fraction, you can multiply by its reciprocal. The reciprocal of 1/2 is 2/1, or just 2.
\[ \text{Number of shifts} = 4 \times 2 \]
\[ \text{Number of shifts} = 8 \]
So Zack should have determined that he worked 8 shifts in total during his volunteer time.

[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=1.5\\ h=5 \end{cases}\implies V=\cfrac{\pi (1.5)^2(5)}{3}\implies V=\cfrac{11.25\pi }{3} \\\\\\ V= 3.75\pi \implies V\approx 11.78~cm^3\qquad \leftarrow \textit{for one candle} \\\\\\ \stackrel{\textit{how many times does 11.78 go into 301.59?}}{301.59\div 11.78\implies 26}\qquad \leftarrow \textit{rounded up}[/tex]

The volume of the cone is one-third of the product of its base area and its height. The maximum number of candles that can be made from the liquid wax is 25.

The volume of the cone is one-third of the product of its base area and its height. It is given by the formula,

The Volume of Cone = (1/3) × π × (d/2)² × h

The volume of wax that is needed to make a single candle with a diameter of 3 cm and height of 5 cm is,

The Volume of Cone = (1/3) × π × (d/2)² × h

The Volume of Candle = (1/3) × π × (3/2)² × 5 = 11.78 cm³

The total wax available is 301.59 cm³, while the amount of wax needed to make a candle is 11.78 cm³, therefore, the number of candles that can be made with the total wax is,

The Number of candles = (301.59 cm³/ 11.78 cm³) = 25.5999

Since a half candle can not be produced, therefore, the maximum number of candles that can be made from the liquid wax is 25.

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Answer:

1.   Absolute value :  d.  | - 7| = 7

2.  All real numbers :  b.  3x = 3x

3.  x = -5  : c.  5x = -25

4.  No solution : a.  |2x| = -10

5.  Adding the opposite to both sides of the equation. : e.  Canceling

Step-by-step explanation:

1.   Absolute value :  d.  | - 7| = 7

The absolute value is considered the distance to 0... so if there's a negative sign in the value, the negative sign disappears.

2.  All real numbers :  b.  3x = 3x

If we divide both sides by 3, we have x = x, which will always be true.

3.  x = -5  : c.  5x = -25

If we multiply each side by 5, we have 5(x) = 5(-5) thus 5x = -25

4.  No solution : a.  |2x| = -10

The result of an absolute value cannot be a negative number.  So, that has no solution since there's no value of x that would make this true.

5.  Adding the opposite to both sides of the equation. : e.  Canceling

If you have for example (x = -5) and you add 5 on both sides, you cancel the value on the right side... (becomes x + 5 = 0).

Answer:

x = 5/16

Step-by-step explanation:

"Solving this equation" means determining the x value that makes the equation true.  Since it's a linear equation, there can be only one solution.

Starting with 32x – 1 = 16x + 4, subtract 16x from both sides, obtaining:

16x - 1 = 4

and then add 1 to both sides, obtaining 16x = 5.  Then x = 5/16.

ANSWER

A.

EXPLANATION

The parent function is

[tex]f(x) = \sqrt[3]{x} [/tex]

This function is transformed to obtain

[tex]g(x) = \sqrt[3]{x + 2} - 4[/tex]

The +2 is a horizontal translation, that shifts the graph of the parent function to the left by 2 units.

The -4 is a vertical translation, that shifts the graph of the parent function down by 4 units.

The correct option is A.

Answer:

A)

Step-by-step explanation:

First we will graph th parent function which is a cube root and we can see it in the attachment #1.

In this excercise there are two types of transformations of the parent function:

[tex]f(x)=\sqrt[3]{x}[/tex]

First:

[tex]f(x+b)[/tex] shifts the function b units to the left.(Attachment #2 )

[tex]f(x)=\sqrt[3]{x+2}[/tex]

[tex]b=2[/tex]

Second:

[tex]f(x)-c[/tex] shifts the function c units downward. (Attachment #3)

[tex]f(x)=\sqrt[3]{x+2}+4[/tex]

[tex]c=4[/tex]

Slope intercept formula: y = mx + b where m equals slope and b equals the y-intercept.

Answer: y = -6x + 3

Final answer:

The equation in slope-intercept form for a line with y-intercept 3 and slope -6 is y = -6x + 3, showing a line decreasing by 6 units in y for each unit increase in x.

Explanation:

To write an equation in slope-intercept form, which is y = mx + b, we need to know the slope (m) and the y-intercept (b). In this case, we have a y-intercept of 3 and a slope of -6. Plugging these values into the slope-intercept form, we get the equation of the line:

y = -6x + 3

This equation tells us that the line crosses the y-axis at (0, 3) and for each unit increase in x, the value of y decreases by 6 units, since the slope is negative. This is a direct application of the algebra of straight lines and the concepts of slope and y-intercept.

Answer:

B. The lines have the same slope, but different intercepts.

Step-by-step explanation:

The solution of a system of linear equations doesn't exist if the lines do not intersect each other at any point. So if there is no solution that means the lines of both equations will not intersect.

Lets look at the options one by one.

For option A:

If the lines are perpendicular, they might intersect at any point so this is not the correct option.

For Option B:

If the lines have same slop and different intercepts that means the lines are parallel. We know that parallel lines never cross each other so option B is the correct answer.

For Option C:

The lines with same intercept and different might also intersect so option C is not correct.

For Option D:

The lines being on top of each other means that the lines intersect on all points. So option D is also not correct.

[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{4}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{-4}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{8+4}{2}~~,~~\cfrac{-4-6}{2} \right)\implies (6,-5) \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{-6}~,~\stackrel{y_1}{7})\qquad \stackrel{\textit{the midpoint}}{(\stackrel{x_2}{6}~,~\stackrel{y_2}{-5})}[/tex]

[tex]\bf slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-5-7}{6-(-6)}\implies \cfrac{-12}{6+6}\implies \cfrac{-12}{12}\implies -1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-7=-1[x-(-6)]\implies y-7=-1(x+6) \\\\\\ y-7=-x-6\implies y=-x+1[/tex]

Answer:

Price of sweatshirt = $24

Price of t-shirt=$8

Price of shorts= $12

Step-by-step explanation:

Let

w be the price of one sweat shirt

t be the price of t-shirt

h be the price of shorts

The first statement is:  

The price of a sweatshirt at a local shop is twice the price of a pair of shorts.

w=2h     Eqn 1

Then,

The price of a T-shirt at the shop is $4 less than the price of a pair of shorts.  

t=h-4    Eqn 2

And

Brad purchased 3 sweatshirts, 2 pairs of shorts, and 5 T-shirts for a total cost of $136.

3w+2h+5t=136   Eqn 3

Putting the value of w and t in equation 3

3w+2h+5t=136

3(2h)+2h+5(h-4)=136

6h+2h+5h-20=136

13h=136+20

h=156/13

h=12

So the price of pair of shorts is $12.

Putting the value of h in equation 1

w=2(12)

w=24

Price of sweatshirt is: $24

Putting the value of h in eqn 2:

t=12-4

t=8

Price of T-shirt is $8 ..  

Answer:

angle x will be 17

Step-by-step explanation:

ATP,

3x+4=72–x

3x+x=72–4

4x=68

x=68/4

x=17

Answer:

x = 17

Step-by-step explanation:

Since triangles are similar then corresponding angles are congruent.

∠I and ∠ P are corresponding and congruent, hence

3x + 4 = 72 - x ( add x to both sides )

4x + 4 = 72 ( subtract 4 from both sides )

4x = 68 ( divide both sides by 4 )

x = 17

Answer:

Step-by-step explanation:

D=RT

10=1T

T=10 HOURS FOR THE TURTLE.

10=5(T-8)

10=5T-40

5T=10+40

5T=50

T=50/5

T=10 HOURS FOR THE RABBIT.

LOOKS LIKE A TIE .

Answer:

Yes.

Step-by-step explanation:

If you graph it you can see that they all the points match up to the perfect right triangle. You may have to rotate it to see it though. Point Z is the angle of the triangle that is the corner of the 90 degree triangle.

Answer:

True

Step-by-step explanation:

The formula for the circumference of a circle is:

C=2πr

So we can substitute in the numbers we have:

Radius=4, so:

C=8π (we multiplied the radius by 2)

So the statement is true.

Hope I... yeah you get it y now I've been answering your questions a lot.

I'm still gonna copyright it.

Copyright Potato 2019.

Answer:

True

Step-by-step explanation:

The circumference (C) of a circle is

C = 2πr ← r is the radius

For C = 8π, then

2πr = 8π ( divide both sides by 2π )

r = 8π ÷ 2π = 4

Hence the radius must be 4

ANSWER

y varies inversely as x exponent 4.

EXPLANATION

The inverse variation equation is given as:

[tex]y = \frac{1}{ {x}^{4} } [/tex]

We can see that there is an inverse relation between the quantity y and x.

If the it were [tex]y = \frac{1}{ {x}^2 } [/tex], we say y varies inversely as the square of x.

Hence for the given relation,the precise definition is that, y varies inversely as x exponent 4.

Answer:

d. x^4

Step-by-step explanation:

Just got it right

Answer:

c. (3.75, 3.5)

Step-by-step explanation:

Let's call the given segment AB, and the dividing point P. Then you want AP:PB = 1:3.

There are a couple of ways you can get there.

1. Recognize that when you subtract the coordinates of A from P, the difference will be 1/4 of the result of subtracting A from B. That is, ...

P-A = (1/(1+3))·(B-A)

We can see that B-A = (6,8) -(3,2) = (3, 6), so 1/4 of that is (3/4, 3/2) = (0.75, 1.5). Adding these values to the coordinates of A gives ...

P = A + (.75, 1.5) = (3.75, 3.5)

__

2. Finish working out the equation above to solve for P:

4(P -A) = B -A

4P = B + 3A

P = (3A + B)/4 . . . . . note the multiplier for A is the relative length of PB and vice versa

P = (3(3, 2) +(6, 8))/4 = (15/4, 14/4) = (3.75, 3.5)

_____

Comment on choosing an answer

You only need to determine one of the coordinates in order to pick the correct answer. Finding both coordinates can help give you assurance that you have worked it out correctly.

subtract 17, not 22, from both sides. 17 – 17 = 0 and 22 – 17 = 5. The answer should be x = 5.

Step-by-step explanation:

An equation between two variables that gives a straight line when plotted on a graph.

Lester made mistake in first steps he subtract 22 from the equation.

The correct solution of the equation is x =5.

Lester was solving an equation but he made a mistake.

The given equation is;

[tex]\rm x + 17 = 22[/tex]

An equation between two variables that gives a straight line when plotted on a graph.

The equation represents the linear equation and to solve the equation following all the steps given below.

Then,

The correct way to solve the equation is,

[tex]\rm x + 17 = 22\\\\x+17-17 = 22-17\\\\x +0=5\\\\x=5[/tex]

Hence, the correct solution of the equation is x =5.

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Answer:

7

Step-by-step explanation:

3x - 6 = 15

+6 +6

____________

3x = 21

3x = 21/3

x = 7

The value of x that satisfies the equation 3x - 6 = 15 is x = 7. This was calculated by isolating x and solving the equation.

The equation provided is 3x - 6 = 15, and the value for x that satisfies this equation is what we are looking for. To solve for x, we can start by adding 6 to both sides of the equation to isolate 3x on one side which results in 3x = 21. Finally, we divide each side by 3 to find the solution which gives us x = 7. Therefore, the solution to the equation 3x - 6 = 15 is x = 7

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Answer:

A 65.5%

Step-by-step explanation:

Percent decrease = (original - new)/ original * 100 percent

                              = (290-100)/290 * 100 %

                              = 190/290* 100%

                              =.655172414 * 100%

                               =65.5172414%

To the nearest tenth percent %

                                65.5%

The answer to your question is B. 65

Answer:

b

Step-by-step explanation:

you add them all together and divide 11 because there are 11 numbers.

i used to have problem on mean, median, and mode too.

15 hours is the answer to this

1.69×5+9.95

Answer:

15 hours.

Step-by-step explanation:

In order to solve this, we just have to create an inequality, for ti to be more convenient for us to work with the first company we shouldn´t be spending more than 19.95 a month, otherwise we would be better off with the second one, so the total would be 19.95, and the base fee is $9.95 for the first ten hours, so X would be the number of extra hours we will use:

[tex]Base+Extra,hours=Budget[/tex]

Now we just insert the values in to the formula:

[tex]10+1.68x=19.95\\[/tex]

We clear X:

[tex]10+1.68x=19.95\\[/tex]

[tex]1.68x=19.95-10\\[/tex]

[tex]1.68x=9.95\\[/tex]

[tex]x=\frac{9.95}{1.69}[/tex]

[tex]x=5.91\\[/tex]

So the as the number of extra hours that we could use without going over the budget is 5.91, and the company wouldn´t charge us the .91, the number of extra hours is 5, plus the base hours, the total number of hours would be 15.

Answer:

The correct answer is: d=9m

Step-by-step explanation:

Ok, the ladders leaned against a building make two right triangles with same the same height, which we will call h. For the 20m ladder, its leg is (7+d) and for the 15m ladder, its leg is d, and the two hypotenuses are 20 and 15 respectively.

Then, using the Pythagorean Theorem we have:  

20m ladder:

20^2 = h^2 + (d+7)^2    (Eq. 1)

400 = h^2 + d^2 + 2*7*d + 7^2  (expanding the theorem)

400 = (h^2 + d^2) + 14*d + 49   (Eq. 2)

15m ladder:

 15^2 = h^2 + (d)^2         (Eq. 3)

Since h^2 + (d)^2 is equal to 15^2, we can substitute (2) into (3):

400 = (15^2) + 14*d + 49

400 = 225 + 14*d + 49

14*d = 400 - 225 - 49  (clearing the variable d)

14*d = 126

d = 9 m

And since we now know that d is equal to 9m. For the longer ladder is (d+7)=(9+7)=16m.

And, then the shorter ladder is 9m from the building and the longer ladder is 16m from the building

Answer:

B

Step-by-step explanation:

30 are unusable in 200. So how many are unusable in 17,000??

We can set up a ratio and figure out the answer right away! Let x be the number of unusable bolts in 17,000, so we can write:

[tex]\frac{30}{200}=\frac{x}{17,000}\\200x=30*17000\\200x=510,000\\x=\frac{510,000}{200}\\x=2550[/tex]

THus, number of unusable bolts is 2550. B is right.

Answer:

(x, y) → (−x, y)(x, y)

Step-by-step explanation:

To do a transformation over the Y-axis, you just have to change the sign on the x in order to create a matching point on the other side of the Y axis, for example if you wish to make a reflection of the point (8,9), the reflection over the Y axis would be (-8,9), the same with X and Y, if you wish to make a reflection of (x,y) you just change the sign of the x like this: (-x,y)

The correct answer is option 1. [tex](x,y) \rightarrow (-x,y)[/tex]

To determine which transformation represents a reflection over the y-axis, we examine the options provided:

A reflection over the y-axis transforms the x-coordinate of a point to its opposite while keeping the y-coordinate unchanged. Therefore, the correct transformation is [tex](x,y) \rightarrow (-x,y)[/tex].

Reflection over the y-axis results in the point (x, y) being mapped to (−x, y). This is because the x-coordinate is negated while the y-coordinate remains the same.

The complete question is:

Which transformation represents a reflection over the y-axis?

1. [tex](x,y) \rightarrow (-x,y)[/tex]

2. [tex](x,y) \rightarrow (x,-y)[/tex]

3. [tex](x,y) \rightarrow (y,x)[/tex]

4. [tex](x,y) \rightarrow (-y,x)[/tex]

Answer:

Perpendicular

Step-by-step explanation:

Think of a ladder.  It has 2 long sides that are parallel to each other.  If a step is perpendicular to one long side then it is perpendicular to the other long side BECAUSE the 2 long sides are parallel to each other.

In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other.

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Answer:

the multiplicative inverse or reciprocal.

Step-by-step explanation:

Answer:

The answer is 31.5

Step-by-step explanation:

Similar triangles have their corresponding sides to be in equivalent ratios

The length of PR is 31.5 inches

△WKT∼△NRP  means that, the following sides are similar

So, we have the following equivalent ratio

[tex]WK : TK = NR : PR[/tex]

From the complete question, we have the following parameters:

So, the ratio becomes

[tex]14 : 18 = 24.5 : PR[/tex]

Express the ratio as fraction

[tex]\frac{18}{14}= \frac{PR}{24.5 }[/tex]

Multiply both sides by 24.5

[tex]\frac{18}{14} \times 24.5= PR[/tex]

This gives

[tex]\frac{441}{14} = PR[/tex]

Divide 441 by 14

[tex]31.5 = PR[/tex]

Rewrite the above equation as

[tex]PR = 31.5[/tex]

Hence, the length of PR is 31.5 inches

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Here is the set up:

We know the given dimensions are increased by the same number.

Let x be that number.

The garden is a rectangle.

Area = length times width.

5m = 5 meters

12m = 12 meters

Area is 120 meters^2.

Here is your equation:

120 = (5 + x)(12 + x)

Take it from here.

The answer is:

The first option:

[tex]Volumen_{max}=(8-2x)(6-2x)*x[/tex]

From the statement, we know the dimensions of the box, and the length of the sides to be cut (x).

So,

Working with the length of the box, we have:

Let be 8 the length of the cardboard for the length of the box, so, if we cut out the side of length "x", we have:

[tex]Length=(8-(x+x))=(8-2x)[/tex]

Now,

Working with the width of the box, we have:

Let be 6 the length of the cardboard for the width of the box, so, if we cut out the side of length "x", we have:

[tex]Length=(6-(x+x))=(6-2x)[/tex]

Now that we already know the length and the width of the box, we know that the bottom of the box will have the same length "x", so, the greatest possible volume of the cardboard box will be:

[tex]Volumen_{max}=Length*Width*Bottom=(8-2x)(6-2x)*x[/tex]

Have a nice day!