(Full question above)
The three-dimensional figure below is a solid rectangular prism with a hole in the shape of another rectangular prism going through the center of it. Find the volume of the solid in cubic millimeters.
A.60
B.300
C.540
D.780

Answer:

The equation of the line normal to the curve of y=cos1/3x, where x=pi is y= 2√3 x - 10.38

Step-by-step explanation:

The equation of the normal to the curve is

Y- y1 = - 1/m (x- x1)

Where m is the gradient.

See attached picture for the complete solution.

The equation of the line normal to the curve of y=cos(1/3)x, where x=pi, can be found by taking the negative reciprocal of the derivative of the curve at that point and using the point-slope form of a line.

The equation of the line normal to the curve of y=cos(1/3)x at x=pi can be found by taking the negative reciprocal of the derivative of the curve at that point.

The derivative of cos(1/3)x is -sin(1/3)x*(1/3).

At x=pi, the derivative is -sin(pi/3). Taking the negative reciprocal of this gives the slope of the line normal to the curve

So the slope is 1/ tan(pi/3).

Now, we can use the point-slope form of a line to find the equation of the line.

The point-slope form is given by y - y1 = m(x - x1), where (x1, y1) is the point on the line and m is the slope.

Plugging in the values, we get y - cos(pi/3) = (1/tan(pi/3))(x - pi).

Simplifying further will give us the equation of the line normal to the curve at x=pi.

Answer:

Step-by-step explanation:

What's the question?

Answer:

Step-by-step explanation:

in y = mx + b form, the slope is in the m position and the y int is in the b position

y = -2x + 3.....slope is -2 and y int is 3

y = -2x - 1...slope is -2 and y int is - 1

same slope, different y int's....means parallel lines...NO SOLUTION

learn this...it helps

same slope, different y int's = no solution

different slopes, different y int's = 1 solution

same slope, same y int's = infinite solutions

Final answer:

The given system of equations represents two parallel lines with the same slope and different y-intercepts, implying there are no solutions where the lines intersect.

Explanation:

The system of equations provided is:

y = –2x + 3

y = –2x – 1

These two equations represent two separate lines. To determine the number of solutions to the system, we observe the slopes of the two lines. Both equations have the same slope of –2. Because they have the same slope but different y-intercepts, these two lines are parallel and will never intersect. Therefore, the system has no solutions.

Answer:

$0.45

Step-by-step explanation:

Unit price is basically the same as unit rate. Unit rate is the cost of one item.

So $3.15 divided by seven is point fourty-five.

Answer: 45 cents

Step-by-step explanation: Unit price means the cost per unit. In this case, the cost per notepad.

Since we know that it costs $3.15 for 7 notepads, to find the cost for 1 notepad, we need to divide 7 into $3.15 or 7 into 3.15.

I used long division wish I have shown in the image attached and ended up with .45 which means that each notepad costs 45 cents.

So the unit price for 7 notepads is 45 cents.

Answer:

h = -3

The value h = -3 translates the graph of the parent function [tex]y=x^2[/tex] 3 units to the left.

Step-by-step explanation:

The graph of [tex]f(x)=(x-h)^2+k[/tex] contains the points (-6, -2) and (0, -2).

This is the equation of parabola in vertex form, where [tex](h,k)[/tex] are the coordinates of the vertex.

If the graph has a vertex at [tex](h,-5),[/tex] then [tex]k=-5.[/tex]

So, the equation of the parabola is

[tex]f(x)=(x-h)^2-5[/tex]

If the graph passes through the points (0,-2) and (-6,-2) (these two points lie on the same horizontal line y = -2), then the parabola vertical line of symmetry divides the segment between these points into two congruent segments. Hence, the equation of the line of symmetry is

[tex]x=\dfrac{0+(-6)}{2}=-3[/tex]

The vertex lies on the line of symmetry, so its x-coordinate is -3. Thus, (-3,-5) is the vertex.

The value h = -3 translates the graph of the parent function [tex]y=x^2[/tex] 3 units to the left.

Answer:

Sample Response: The absolute value function is symmetric. Since the points (–6, –2) and (0, –2) have the same output, the points are the same distance from the line of symmetry. Between –6 and 0 is the value of –3. So, the vertex must have an x-coordinate of –3, which is the value of h. This would translate the graph of the parent function 3 units to the left.

Answer:

10

Step-by-step explanation:

Answer:

  $1551.57

Step-by-step explanation:

Each month, the account balance is multiplied by 1+.04/12, so after 132 months, it will be ...

  $1000×(1 +.04/12)^132 ≈ $1551.57

Answer:

A) 2x+50

Step-by-step explanation:

First, let's make a variable for each person

Sam = x

Hector = h

Ted = t

Gina = g

We know that Hector has twice the amount hat Sam has so his equation is

h = 2x

We know that Ted has 100 more than Hector so his equation is

t = h + 100

Gina has 50 less than Ted to she has

g = t - 50

Since we need to find out how much Gina has using units of Sam the equation will be

g = 2x + 100 - 50 or simplified g = 2x + 50

Answer:

10

Step-by-step explanation:

The square length of hypotenuse is equal to two sides' length square added together

C = 10^2 + 7.5^2 = √156 approximately 12.5

The answer is 10 if needed to round to nearest tenth.

Answer:

Answer D

Step-by-step explanation:

Answer:Option D

Step-by-step explanation:

Answer:

Step-by-step explanation:

1.3 < Length/3.5 < 2.5

4.55 < Length < 8.75

Graph:

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| 4.55  --------  8.75  |

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Answer:

1/3

Step-by-step explanation:

We can solve using algebra: let x be the unknown number.

so 11/3 ÷ x = 11.

Solving:

11/3 = 11x.

x = 11/3 ÷11  = 1/3

You can also check the answer by going:

11/3 ÷ 1/3 = 11/3 x 3/1  = 33/3 = 11 (using fraction rules for multiplying and dividing ie. to divide by a fraction we multiple by it's reciprocal, and to multiply by a fraction, we multiple the numerators and the denominators).

11/3 divided by 1/3 so that it will be equals to 11.

When facing a division problem like 11/3 divided by what equals 11, we need to find a number which, when 11/3 is divided by it, gives us the result of 11. To solve this, let's set up an equation where the unknown number is represented by a variable, such as 'x':

11/3 ÷ x = 11

To find 'x', we need to isolate it. This can be done by multiplying both sides of the equation by 'x', and then dividing both sides by 11 to solve for 'x'.

(11/3) ÷ x = 11

(11/3) ÷ x × x = 11 × x

11/3 = 11x

Now we divide both sides by 11 to get:

x = (11/3) ÷ 11

x = 1/3

So, the fraction that you must divide 11/3 by to get 11 is 1/3.

Answer:

200 additional gallons of water are used when 40 people take a bath instead of a shower

Step-by-step explanation:

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

Amount of water used when we take a bath = 20 gallons

Amount of water used when we take a shower = 15 gallons

Number of people who wants to take a bath = 40

2.  How much extra water is used?

Extra water is used = Number of people * (Amount of water used when we take a bath - Amount of water used when we take a shower)

Replacing with the real values, we have:

Extra water is used = 40 * (20 - 15)

Extra water is used = 40 * 5 = 200 gallons

To represent the situation algebraically, we use the equation 54 = 0.60G, and solving it gives us Noah's fundraising goal of $90.

Let's represent Noah's fundraising goal as G. According to the problem, Noah has raised $54, which is 60% of his goal. This situation can be translated into the algebraic equation:

To find Noah's fundraising goal (G), we can divide both sides of the equation by 0.60:

Therefore, Noah's fundraising goal is $90.

Events A and B are not independent because [tex]P(A / B) \neq P(A)[/tex]

Step-by-step explanation:

Given that [tex]P(A)=0.25[/tex], [tex]P(B)=0.3[/tex] and [tex]P(A \text { and } B)=0.05[/tex]

Two events are said to be independent events, if it satisfies any one of the following conditions,

[tex]P(A / B) = P(A)[/tex] or [tex]P(B / A) = P(B)[/tex] or [tex]P(AB)=P(A)P(B)[/tex]

First, let us substitute the values in the equation [tex]P(A / B) = P(A)[/tex]

The formula to find [tex]P(A / B)[/tex] is [tex]P(A / B)=\frac{P(A \cap B)}{P(B)}[/tex]

Substituting the values, we get,

[tex]P(A / B)=\frac{0.05}{0.3} =0.1667[/tex]

But [tex]P(A)=0.25[/tex]

Hence, [tex]P(A / B) \neq P(A)[/tex]

Thus, A and B are not independent events.

Answer:

72y

Step-by-step explanation:

Multiplication can be done in any order

8x9=72

72 times y is 72y

Answer:10

Step-by-step explanation:

4 x 5 = 20

20/2 or 20 x 1/2

= 10

Answer: 10 meters squared

Step-by-step explanation:

You find the area of a triangle by doing base x height ÷2 therefore 4x5=20÷2=10

Amanda learns 2.5 recipes per week, so over 6 weeks of training, she would be expected to learn 15 appetizer recipes.

To establish the rate of Amanda learning new appetizer recipes, we need to determine the relationship between time (in weeks) and the number of recipes she learned. After 2 weeks of training, she learned 5 recipes, so we can assume that she learns at a rate of 5 recipes per 2 weeks, or 2.5 recipes per week.

Consequently, to estimate how many recipes she will learn after 6 weeks, we multiply the rate by the amount of weeks, which is: 2.5 recipes per week * 6 weeks = 15 recipes. Therefore, Amanda would be expected to learn 15 appetizer recipes after 6 weeks of training.

https://brainly.com/question/16549128

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The length of diagonal of park is √200 feet.

Step-by-step explanation:

Given,

Perimeter of square playground = 40 feet

Let,

a be the length of one side.

Perimeter = 4a

[tex]4a=40\\\\a=\frac{40}{4}\\\\a=10[/tex]

Length of one side of square is 10 feet.

A diagonal will form a right triangle, where,

Diagonal = c

a = 10

b = 10

Using pythagoras theorem

[tex]a^2+b^2=c^2\\(10)^2+(10)^2=c^2\\100+100=c^2\\200=c^2\\c^2=200[/tex]

Taking square root on both sides

[tex]\sqrt{c^2}=\sqrt{200}\\c=\sqrt{200}[/tex] feet

The length of diagonal of park is √200 feet.

Keywords: perimeter, square

Learn more about perimeter at:

#LearnwithBrainly

Answer:

10√2 (Simplest Radical Form)

Step-by-step explanation:

While Absor201 got √200, it is still not in simplest radical form. If you got this question from MathNation, then 10√2

Final answer:

The equation 40w + 12.50 = 492.50 best represents Nicole paying $40 per week for self-defense classes, plus a one-time registration fee of $12.50, totaling $492.50.

Explanation:

The situation best represented by the equation 40w + 12.50 = 492.50 is option A) Nicole paid $40 for self-defense classes. She paid a $12.50 registration fee and $492.50 for each week she was enrolled in the classes. Here, w represents the number of weeks Nicole was enrolled in self-defense classes. The equation can be understood as follows: $40 is multiplied by the number of weeks (w), and $12.50 is added for the registration fee, summing to a total of $492.50.

Answer:

x=-2

Step-by-step explanation:

[tex]2(3x - 1) = 6x - 2 = 4x - 6 \\ 2x = - 4 \\ x = - 2[/tex]

Answer:

Hope this helps!

Step-by-step explanation:

1. Do all of the homework. ...

2. Fight not to miss class. ...

3. Find a friend to be your study partner. ...

4. Establish a good relationship with the teacher. ...

5. Analyze and understand every mistake. ...

6. Get help fast. ...

7. Don't swallow your questions. ...

8. Basic skills are essential.

Answer:

5, 6, 7

Step-by-step explanation:

5+6+7=18

Answer:

5+6+7

Step-by-step explanation:

Intergers: Three consecutive integers)

18 = (X-1) + (X) + (X+1)

18 = 3X

X = 6

SUbstitute =

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

5+6+7

= 18

Equation for solving: (13+x)2= -10-x

Step one: 26+2x=-10-x

step two: 26+3x=-10

step three: 3x=-36

answer: -12

Answer:

x=-2 OR x=-10 i.e.

Solution Set = {-2,-10}

Step-by-step explanation:

The equation described in words is typed and solved below:

[tex]3+4|\frac{x}{2}+3|=11 \\4|\frac{x}{2}+3|=11-3\\4|\frac{x}{2}+3|=8\\|\frac{x}{2}+3|=\frac{8}{4} \\|\frac{x}{2}+3|=2\\\frac{x}{2}+3=2 OR \frac{x}{2}+3=-2\\\frac{x}{2}=2-3 OR \frac{x}{2}=-2-3\\\frac{x}{2}=-1 OR \frac{x}{2}=-5\\x=-2ORx=-10\\[/tex]

Answer:

it is -10

Step-by-step explanation:

Answer:

Step-by-step explanation:

10

Answer:

Step-by-step explanation:

Since 2 and 5 are co-prime then

LCM(2 , 5) = 2×5 = 10

:)

Answer:

x-intercept: -4

y-intercept: 2

Step-by-step explanation:

ax+by=c

divide c by a and then c by b

-3x+6y=12

X-intercept: 12/-3= -4

Y-intercept: 12/6=2

Answer:

Step-by-step explanation:

if ur gonna graph it, u should put it in y = mx + b form

-3x + 6y = 12

6y = 3x + 12

y = 3/6x + 12/6

y = 1/2x + 2

in y = mx + b form, the slope is in the m position, and the y int is in the b position.

y = mx + b

y = 1/2x + 2.....so ur slope (which will help u in graphing) is 1/2, and ur y intercept is 2 or (0,2) <===

u could also find ur y intercept by subbing in 0 for x and solving for y...in ur original equation.

to find ur x intercept, sub in 0 for y and solving for x

-3x + 6y = 12

-3x + 6(0) = 12

-3x = 12

x = -12/3

x = -4...so ur x int is -4 or (-4,0) <=====

Answer: m = -2

Step-by-step explanation: Using our slope formula, we take the second y minus the first y which in this case is 12 - 8 over our second x minus our first x which in this case is 2 - 4.

So 12 - 8 is 4 and 2 - 4 is -2. So we have 4/-2 which can be simplified to -2.

The variable that's used to represent slope is m.

So we would say m = -2.

Work is provided in the image attached.

Answer:

I believe the answer to this question is: B.

Answer: The first part is the 2nd & 4th.

The second part is the 1st & 3rd.

Step-by-step explanation:

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