Which formula gives the area of a parallelogram? (3)

Answer:

385/pi

Step-by-step explanation:

Circumference is given by

C= pi * d  where d is the diameter

385 = pi *d

Divide each side by pi

385/pi = pi * d/pi

385/pi = d

Rectangular prism: 6 faces (4 lateral, 2 bases), 8 vertices, 12 edges, meeting all criteria specified.

let's break down the characteristics of each of the options provided:

1. **Square Pyramid**:

  - Faces: A square pyramid has five faces. It has a square base and four triangular faces.

  - Vertices: A square pyramid has five vertices.

  - Edges: A square pyramid has eight edges (the base square has four edges, and each triangular face has one edge).

2. **Triangular Prism**:

  - Faces: A triangular prism has five faces. It has two triangular bases and three rectangular lateral faces.

  - Vertices: A triangular prism has six vertices.

  - Edges: A triangular prism has nine edges (three on each base triangle and three connecting the lateral faces).

3. **Rectangular Prism**:

  - Faces: A rectangular prism has six faces. It has two rectangular bases and four rectangular lateral faces.

  - Vertices: A rectangular prism has eight vertices.

  - Edges: A rectangular prism has 12 edges (four on each base rectangle and four connecting the lateral faces).

4. **Triangular Pyramid**:

  - Faces: A triangular pyramid has four faces. It has a triangular base and three triangular lateral faces.

  - Vertices: A triangular pyramid has four vertices.

  - Edges: A triangular pyramid has six edges (three on the base triangle and three connecting the lateral faces).

Given the characteristics you provided: six faces, four lateral faces, two bases, eight vertices, and 12 edges, we can eliminate the options of square pyramid and triangular pyramid because they don't fit all the criteria.

Now let's look at the remaining options:

- **Triangular Prism** has five faces, six vertices, and nine edges. It doesn't match the given criteria.

- **Rectangular Prism** has six faces (two bases and four lateral faces), eight vertices, and 12 edges, which perfectly matches all the provided characteristics.

Therefore, the correct answer is the **Rectangular Prism**.

Answer:

see explanation

Step-by-step explanation:

1

6 = 3x - 9 ( add 9 to both sides )

15 = 3x ( divide both sides by 3 )

5 = x

2

x + 4 < 1 ( subtract 4 from both sides )

x < - 3

3

[tex]\frac{x}{2}[/tex] + 3 = - 5

Multiply terms on both sides by 2

x + 6 = - 10 ( subtract 6 from both sides )

x = - 16

Answer:

[tex]x\:<\:50[/tex].

Step-by-step explanation:

The z-score for a normal distribution is calculated using the formula:

[tex]Z=\frac{x-\mu}{\sigma}[/tex].

From the question, the distribution has a mean of 50.

[tex]\implies \mu=50[/tex] and the standard deviation is [tex]\sigma=5[/tex].

For a z-score to be negative, then, [tex]\frac{x-\mu}{\sigma}\:<\:0[/tex].

[tex]\frac{x-50}{5}\:<\:0[/tex].

[tex]x-50\:<\:0\times 5[/tex].

[tex]x-50\:<\:0[/tex].

[tex]x\:<\:0+50[/tex].

[tex]\therefore x\:<\:50[/tex].

Any value less than 50 will produce a negative z-score

Answer:

[tex]\large\boxed{b.\ 0,\ \pi,\ \dfrac{\pi}{3},\ \dfrac{5\pi}{3}}[/tex]

Step-by-step explanation:

[tex]\text{Use}\ \sin2x=2\sin x\cos x\\\\\sin2\O=\sin\O\\\\2\sin\O\cos\O=\sin\O\qquad\text{subtract}\ \sin\O\ \text{from both sides}\\\\2\sin\O\cos\O-\sin\O=0\qquad\text{distribute}\\\\\sin\O(2\cos\O-1)=0\iff\sin\O=0\ \vee\ 2\cos\O-1=0[/tex]

[tex]\sin\O=0\iff\O=0\ \vee\ \O=\pi\\\\2\cos\O-1=0\qquad\text{add 1 to both sides}\\\\2\cos\O=1\qquad\text{divide both sides by 2}\\\\\cos\O=\dfrac{1}{2}\iff\O=\dfrac{\pi}{3}\ \vee\ \O=\dfrac{5\pi}{3}[/tex]

This is the final function f(x) = (-2(x-2))^5 after a horizontal shrink, reflection, and shift.

To determine which function results after applying a given sequence of transformations to the original function f(x) = x^5, we need to apply each transformation in the correct order. Transformations affect the graph and the function's formula. Here is how you would apply the transformations in the correct order:

f(2x): Multiply the independent variable by 2, which shrinks the graph horizontally by half. The function becomes f(x) = (2x)^5.

f(-2x): Negate the independent variable x, which flips the graph across the y-axis. The function becomes f(x) = (-2x)^5.

f(-2x-2): Subtract 2 from the result of -2x. This is incorrect as the sequence of operations should reflect transformations applied directly to the independent variable x. Instead, it should be f(x-2) after step (ii), which translates the graph to the right by 2 units.

If we were to correct the third operation and apply the transformations properly, the resulting function after applying a horizontal shrink, reflection across the y-axis, and horizontal shift would be f(x) = (-2(x-2))^5.

Answer:

16 hours

Step-by-step explanation:

Speed=distance/time

Let S be speed, D be distance, and t be time.

Let's solve the speed equation for t since we are looking for time, t.

[tex]S=\frac{D}{t}[/tex]

Multiply both sides by t:

[tex]St=D[/tex]

Divide both sides by S:

[tex]t=\frac{D}{S}[/tex]

So our distance is 239000 and our speed is 250 so plug them in:

[tex]t=\frac{239000}{250}[/tex]

Putting into the calculator now:

t=956 minutes (I knew this was in minutes because the speed was 250 miles per minute)

We need to convert this to hours.  60 minutes=1 hour.

60 minutes=1 hour

956 minutes=x hours

You can setup a proportion if you don't know you just need to take 956 and divide it by 60.  Like so:

[tex]\frac{60}{956}=\frac{1}{x}[/tex]

Cross multiply:

[tex]60x=956(1)[/tex]

[tex]60x=956[/tex]

Divide both sides by 60:

[tex]x=\frac{956}{60}[/tex]

Putting into calculator now:

x=15.9333333333333 which mean we have almost 16 hours

The fourth term of the arithmetic series is 38.

Given that, the first number in arithmetic series (a)=8 and common difference (d) =10.

The nth term of the arithmetic series is [tex]a_{n} =a+(n-1) \times d[/tex].

Now, the fourth term= [tex]a_{4} =8+(4-1) \times 10[/tex]

=8+30=38

Therefore, the fourth term of the arithmetic series is 38.

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Answer:

(1, 0)

Step-by-step explanation:

Given the 2 equations

2x - 4y = 2 → (1)

- 4x + 6y = - 4 → (2)

Multiplying (1) by 2 and adding to (2) will eliminate the x- term

4x - 8y = 4 → (3)

Add (2) and (3) term by term

(- 4x + 4x) + (6y - 8y) = (- 4 + 4), simplifying gives

- 2y = 0 ⇒ y = 0

Substitute y = 0 in (1) or (2)

Substituting in (1) gives

2x - 0 = 2, that is

2x = 2 ( divide both sides by 2 )

x = 1

Solution is (1, 0 )

Answer:

You should invest $820 in account A and $940 in account B

Step-by-step explanation:

* Lets use the system of linear equations to solve the problem

- Simple Interest Equation I = Prt , Where:

# P = Invested Amount

# I = Interest Amount

# r = Rate of Interest per year in decimal; r = R/100

# t = Time Period involved in months or years

* Lets solve the problem

- The total money invested is $1760

- Account A pays 7​% annual interest

- Account B pays 4​% annual interest

- Let A represent the amount of money invested in the account A

- Let B represent the amount of money invested in the account B

- You would like to earn $ 95 at the end of one year

∴ The interest from both accounts at the end of one year is $95

- Lets write the equations

# Account A :

∵ Account A has $A invested

∴ P = $A

∵ Account A pays 7​% annual interest

∴ r = 7/100 = 0.07

∵ t = 1 year

∵ I = Prt

∴ I = A(0.07)(1) = 0.07A

# Account B :

∵ Account B has $B invested

∴ P = $B

∵ Account A pays 4​% annual interest

∴ r = 4/100 = 0.04

∵ t = 1 year

∵ I = Prt

∴ I = B(0.04)(1) = 0.04B

- The total amount of interest from both accounts at the end of one

  year is $95

∴ I from A + I from B = 95

∴ 0.07A + 0.04B = 95 ⇒ multiply both sides by 100

∴ 7A + 4B = 9500 ⇒ (1)

- The total money to invest in both accounts is $1760

∵ Account A has $A invested

∵ Account B has $B invested

∴ A + B = 1760 ⇒ (2)

* Lets solve the system of equations to find the amount of money

  invested in each account

- Multiply equation (2) by -4 to eliminate B

∵ A + B = 1760 ⇒ × -4

∴ -4A - 4B = -7040 ⇒ (3)

- Add equation (1) and (3)

∵ 7A + 4B = 9500 ⇒ (1)

∵ -4A - 4B = -7040 ⇒ (3)

∴ 7A - 4A = 9500 - 7040

∴ 3A = 2460 ⇒ divide both side by 3

∴ A = 820

- Substitute the value of A in equation (1) or (2)

∵ A + B = 1760 ⇒ (2)

∴ 820 + B = 1760 ⇒ subtract 820 from both sides

∴ B = 940

- From all above

* You should invest $820 in account A and $940 in account B

Answer:

The correct options are 1, 4 and 7.

Step-by-step explanation:

From the given figure it is clear that the vertices of preimage are A(-4,2), B(-4,-2) and C(-1,-2).

The vertices of image are A'(1,5), B'(1,1) and C'(4,1).

The relation between vertices of preimage and image is defined by the rule

[tex](x,y)\rightarrow (x+5,y+3)[/tex]

It means the figure ABC translated 5 units right and 3 units up.

Translations a rigid transformation. It means the size and shape of image and preimage are same.

We can say that,

(a) The sides of the image and preimage are congruent.

(b) The angles in the image and angles in the pre-image are same.

(c) The image is a slide of the preimage.

(d) The image and pre-image have same shape.

(e) Each point has moved in same direction.

(f) Each point has moved the same number of units.

Therefore the correct options are 1, 4 and 7.

Answer:

x=1, x=7

Step-by-step explanation:

Firstly, you can simplify by dividing both sides by 3, which will make the equation easier to simplify:

(x-4)^2=9

Next, you can take the square root of each side, which will cancel the square, and make the 9 even easier to work with:

(x-4)=(± )3

*Note the (± ) sign, this is because there is a positive and negative answer*

After this, you will basically have two equations:

(x-4)=3

and

(x-4)=-3

You are going to solve both to get both answers, but lets start with the positive first:

x-4=3     Add 4 to both sides to get an x= equation

x=7

And it's the same thing for the negative:

x-4=-3     Add 4 to both sides to get an x= equation

x=1

Hope this helps

Final answer:

To solve the equation 3(x-4)²=27, divide by 3 to get (x-4)²=9, then take the square root to find the solutions x=7 and x=1.

Explanation:

When we're tasked with solving a quadratic equation, such as 3(x-4)²=27, we first need to get it into the standard form of a quadratic equation, which is ax² + bx + c = 0. To do so in this case, we can divide both sides of the equation by 3 to isolate the squared term, yielding (x-4)²= 9. We then take the square root of both sides, giving us x - 4 =3. Solving for x results in two solutions: x = 4 + 3 and x = 4 - 3, which simplifies to x = 7 and x = 1 respectively. These are the solutions to the given equation.

To verify these solutions, you can substitute them back into the original equation to ensure that they satisfy the equation, which in this case, they will. This critical step confirms the accuracy of our solutions.

Answer:

Step-by-step explanation:

sin θ= - cos θ

if :    cos θ  ≠  0  

you have :   tan θ = -1

 tan θ = - tan π/4

    tan θ = tan(- π/4 )

θ = - π/4 +kπ       k ∈ Z  

calculate: k   when θ is in quadrant IV :  3π /2 ≤ θ ≤2π

3π /2 ≤  - π/4 +kπ ≤2π

add π/4:         3π /2 + π/4 ≤  - π/4 +kπ+π/4  ≤2π +π/4

                     7π/4 ≤ kπ  ≤9π/4

                   7/4 ≤ k ≤9/4

                  1.75 ≤ k ≤ 2.25

 k ∈ Z  : k =2

so :  θ = - π/4 +2π

     θ = 7π/4

θ = 7(180°)/4 = 315°

Answer:

+/- 1, [tex]\frac{+-1}{+-3},\frac{+-1}{+-9},+-2,\frac{+-2}{+-3},\frac{+-2}{+-9},+-4,\frac{+-4}{+-3}, \frac{+-4}{+-9}[/tex] ....

Step-by-step explanation:

The Rational root theorem states that If f(x) is a Polynomial with integer coefficients and if there exist a rational root of the form p/q then p is the factor of the constant term of the function and q is the factor of the  leading coefficient of the function

Given: f(x)= 9x^4-2x^2-3x+4

Factors of q (leading coefficient) are: +/-9, +/-3, +/-1

Factors of p (constant term) are: +/-4 , +/-2, +/- 1

According to the theorem we write the roots in p/q form:

Therefore,

p/q =+/- 1, [tex]\frac{+-1}{+-3},\frac{+-1}{+-9},+-2,\frac{+-2}{+-3},\frac{+-2}{+-9},+-4,\frac{+-4}{+-3}, \frac{+-4}{+-9}[/tex] ....

The expression 7 + 3^2(-5 + 1) divided by 2 equals -14.5, after calculating the exponent, solving the parenthesis, multiplying, adding to 7, and then dividing by 2.

To find the value of the expression 7 + 32(-5 + 1) divided by 2, follow these steps:

The value of the expression is -14.5.

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Answer:

Problem 1: [tex]\frac{2x-3}{5}=x+6[/tex] gives x=-11

Problem 2: [tex]2x-\frac{3}{5}=x+6[/tex] gives x=33/5

Step-by-step explanation:

I will do it both ways:

Problem 1:

[tex]\frac{2x-3}{5}=x+6[/tex]

I don't like the fraction so I'm going to clear by multiplying both sides by 5:

[tex]2x-3=5(x+6)[/tex]

Distribute:

[tex]2x-3=5x+30[/tex]

Subtract 2x on both sides:

[tex]-3=3x+30[/tex]

Subtract 30 on both sides:

[tex]-33=3x[/tex]

Divide both sides by 3:

[tex]-11=x[/tex]

Problem 2:

[tex]2x-\frac{3}{5}=x+6[/tex]

Clear the fraction by multiplying both sides by 5:

[tex]5(2x-\frac{3}{5})=5(x+6)[/tex]

Distribute:

[tex]10x-3=5x+30[/tex]

Subtract 5x on both sides:

[tex]5x-3=30[/tex]

Add 3 on both sides:

[tex]5x=33[/tex]

Divide both sides by 5:

[tex]x=\frac{33}{5}[/tex]

For this case we must solve the following equation:

[tex]\frac {2x-3} {5} = x + 6[/tex]

Multiplying by 5 on both sides we have:

[tex]2x-3 = 5 (x + 6)\\2x-3 = 5x + 30[/tex]

We add 3 to both sides of the equation:

[tex]2x = 5x + 30 + 3\\2x = 5x + 33[/tex]

Subtracting 5x on both sides:

[tex]2x-5x = 33\\-3x = 33[/tex]

Dividing between -3 on both sides:

[tex]x = \frac {33} {- 3}\\x = -11[/tex]

Answer:

-11

The graph of the inequality x > 34 is graphed

An inequality is an expression that shows the non equal comparison of two or more numbers and variables.

Given the inequality:

3x > 102

Divide the inequality by 3:

x > 34

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Answer:

A

Step-by-step explanation:

they're proportional

Answer: the answer is A

Step-by-step explanation:

have a good day

Answer:

Two Angles are Supplementary when they add up to 180 degrees.

Step-by-step explanation:

Notice that together they make a straight angle.

Answer:

- 230°

Step-by-step explanation:

A coterminal angle is the given angle ± 360n ( where n is an integer )

Given 130°

Then a coterminal angle = 130° - 360° = - 230°

OR 130° + 360° = 490°

Answer:

2) (5,4) and (-1,4)

These have the same y so this line will be horizontal making it parallel to the x-axis.

Step-by-step explanation:

All horizontal lines are parallel to each other.  The x-axis is horizontal. So we are looking for a horizontal line.  On a horizontal line, all the y-coordinates are the same; their equation is in the form y=a number after all.

Anyways we looking for a pair of points with the same y-coordinate.

1) (2,3) and (2,-5)

These have the same x-coordinate so this line is vertical. This would actually be perpendicular to the line given.

2) (5,4) and (-1,4)

These have the same y so this line will be horizontal making it parallel to the x-axis.

3) (2,2) and (-1,-1)

y's aren't the same so not horizontal

x's aren't the same so not vertical

4)  (3,4) and (6,2)

y's aren't the same so not horizontal

x's aren't the same so not vertical

For a pair of points to be parallel to the x-axis, the points have to consist the same x-coordinates.

In this case, only (1) (2,3), (2,-5) have the same x-coordinates.

Therefore, the answer is (1) (2,3), (2,-5).

Hope it helps!

Answer:

see explanation

Step-by-step explanation:

If A +B = 45° then tan(A+B) = tan45° = 1

Expanding (1 + tanA)(1 + tanB)

= 1 + tanA + tanB + tanAtanB → (1)

Using the Addition formula for tan(A + B)

tan(A+B) = [tex]\frac{tanA+tanB}{1-tanAtanB}[/tex] = 1 ← from above

Hence

tanA + tanB = 1 - tanAtanB ( add tanAtanB to both sides )

tanA + tanB + tanAtanB = 1 ( add 1 to both sides )

1 + tanA + tanB + tanAtanB = 2

Then from (1)

(1 + tanA)(1 + tanB) = 2 ⇒ proven

Answer:

The perimeter of the square in the projection is [tex]224\ cm[/tex]

Step-by-step explanation:

we know that

1 cm of the image on the monitor represents 8 cm on the screen

so

using proportion

Find out how much represent on the screen  7 cm on a computer monitor

Let

x ----> the length side of the square image on the screen

[tex]\frac{1}{8}\frac{monitor}{screen} =\frac{7}{x}\frac{monitor}{screen} \\ \\x=8*7\\ \\x=56\ cm[/tex]

Find the perimeter of the image on the screen

the perimeter of a square is equal to

[tex]P=4b[/tex]

[tex]b=56\ cm[/tex]

substitute

[tex]P=4(56)=224\ cm[/tex]

Answer:

224cm

Step-by-step explanation:

The scale factor of the dilation is 8, so a 1 cm by 1 cm square on the monitor represents a 8 cm by 8 cm

square on the screen.

The figure shows two squares. The larger square has a side of 56 centimeters. The smaller square has a side of 7 centimeters. The sides of the larger square are parallel to the sides of the smaller one.

The side length of the square in the projection is the product of the side length of the preimage and the scale factor.

h=7(8)

cm

Simplify.

h=56

cm

The perimeter of the square is

P=4(56)

cm

Simplify.

P=224

cm

Therefore, the perimeter of the square in the projection is 224

cm.

To find the surface area of a right triangular prism, we have to calculate the area of all its faces, which include the two triangular bases and the three rectangular faces.
1. **Triangular Bases:** If the right triangle base has sides of lengths `a`, `b`, where `b` is the base and `a` is the height of the triangle, then the area of one triangular base will be given by the formula:
  \[\text{Area of one triangular base} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times a \times b.\]
  Since there are two identical triangular bases, we multiply this area by 2:
  \[\text{Total area of triangular bases} = 2 \times \left( \frac{1}{2} \times a \times b \right) = a \times b.\]
2. **Rectangular Faces:** The three rectangular sides include two rectangles that are formed by the sides of the triangle (`a` and `b`) with the height (`h`) of the prism and one rectangle that is the width of the base `b` and the height of the prism. The areas of these rectangles will be:
  - Rectangle with side `a` and height `h`: \[a \times h.\]
  - Rectangle with base `b` and height `h`: \[b \times h.\]
  - Rectangle with the side corresponding to the hypotenuse `c` of the base triangle and height `h`: \[c \times h.\]
  Therefore, the total area of the three rectangles is the sum of the areas:
  \[\text{Total area of rectangular faces} = a \times h + b \times h + c \times h = h \times (a + b + c).\]
Putting it all together, the formula for the total surface area (SA) of the right triangular prism is:
\[ SA = a \times b + h \times (a + b + c).\]
So, the expression that will help you find the surface area of a right triangular prism is the sum of the areas of the two triangles and the three rectangles as given by this formula.

Answer:

b=4

Step-by-step explanation:

subtract the exponents

6-2=4

The value of b is 4.

Exponent is a mathematical method to express large numbers in power form. It will describe how many times a number multiplied by itself.

Example : 7⁵ , where the number 7 multiplied 5 times by itself.

Given, 5⁶/5² = 5ᵇ

We know that, in exponent, if [tex]a^{m}=a^{n}[/tex], then m=n

Here, 5⁶/5² = 5ᵇ

         ⇒ [tex]5^{6-2} =5^{b}[/tex]

         ⇒ [tex]5^{4} =5^{b}[/tex]

∴ By the above rule, b = 4

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Answer:

a.  A.  49m  B 30.5 m

Step-by-step explanation:

If I have understood the question correctly:

Ball A:

After each second the total distance travelled increases by 5 meters.

Ball A: after 10 seconds it has rolled 4 + (10-1) * 5 = 49m

Ball B:  after 10 seconds it has rolled 3.5 + (10-1)* 3 =  30.5 m.

Answer:

Option A. A: 49 m: B: 30.5 m

Step-by-step explanation:

Ball A rolls 4 meters in the 1st second, 9 meters in the 2nd second, 14 meters in the 3rd second, and so on.

We can see that after each second the total distance traveled by ball increases by 5 meters.

So, we can solve this as an arithmetic sequence that is [tex]a+(n-1)d[/tex]

For ball A, a = 4 n = 10 d = 5

Ball B rolls 3.5 meters in the 1st second, 6.5 meters in the 2nd second, 9.5 meters in the 3rd  second, and so on.

For ball B, a = 3.5 n = 10 d = 3

For ball A:

After 10 seconds, the distance will be [tex]4+(10-1)5[/tex]

= [tex]4+45[/tex] = 49 meters

For ball B:

After 10 seconds, distance covered will be [tex]3.5+(10-1)3[/tex]

= [tex]3.5+27[/tex] = 30.5 meters.

Hence, the answer is option A.