A rectangular pyramid has a base that measures 8 inches by 10 inches, a height of 12 inches, and a slant height of 15 inches. elena calculated the volume of the pyramid as shown. v = 1 3 bh v = 1 3 (80)(15) v = 400 in.3 what was her mistake? elena used the wrong units. elena incorrectly used the slant height instead of the height. elena multiplied incorrectly. elena should not have multiplied by one third.

Answer:

$ 30, 021.39

Step-by-step explanation:

3759( 1 + .11875/12 )^(211)  = 30, 021.39

---Divide the numerator and denominator by 4. We do this because we want to know how many orders are in 1 day and 4 / 4 = 1.

392 orders / 4 days

98 orders / 1 day

Hope this helps!

Answer:

J(-9,-5)

K(-9,3)

L(0,-2)

M(0,-5)

The visitor data is best modeled by a quadratic function, and the state park management should plan for more than 400 visitors next year.

To do this, we simply plot the points on a graph.

See attachment for the graph that represents the table.

From the attached graph, we can see that the points on the graph follows an approximately quadratic path

Hence, the visitor data is best modeled by a quadratic function

Also, the state park management should plan for more than 400 visitors next year.

This is so because the range of a quadratic function is the set of all real numbers.

This means that the table can accept a value of 400 (or greater) as one of its data points

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Expression represents the radius of the cylinder, 2x units.

A cylinder is simply a 3-dimensional shape having two parallel circular bases joined by a curved surface.

Given that:

Volume of cylinder =[tex]4\pi x^{3}[/tex]

we know that, Volume of cylinder = [tex]\pi r^{2} h[/tex]

[tex]4\pi x^{3}[/tex]= π * [tex]r^{2}[/tex] *h

[tex]4x^{3} = r^{2}*h[/tex]

[tex]4x^{3} = r^{2}*x[/tex]      [since, height=x]

[tex]4x^{2} = r^{2}[/tex]

r= 2x

Hence the radius of the cylinder is 2x units

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Answer:

∠ EDF = 23°

Step-by-step explanation:

angles on the circumference of a circle ( inscribed angles) subtended by the same arc are congruent.

∠ FGE and ∠ EDF are inscribed angles subtended by arc EF

then ∠ EDF = ∠ FGE = 23°

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant. The size of ∠EDF is 23°.

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.

As it is known that the angles made from the same chord in a circle are of equal measurement.

Since EF is the chord of the circle and the measure of ∠EGF is 23°, the measure of ∠EDF will be 23° as well.

Hence,  the size of ∠EDF is 23°.

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One morning the temperature in Bangor, Maine was 18 degrees. By afternoon, it had dropped 20 degrees. The afternoon temperature in Bangor, Maine, was -2 degrees.

To find the afternoon temperature, we need to subtract 20 degrees from the morning temperature of 18 degrees.

Afternoon temperature = Morning temperature - Temperature drop

Afternoon temperature = 18 degrees - 20 degrees

To perform the subtraction, we have to handle negative numbers:

Afternoon temperature = 18 degrees - 20 degrees

Afternoon temperature = -2 degrees

So, the afternoon temperature in Bangor, Maine, was -2 degrees.

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Step-by-step explanation:

2x + 18

x = 18÷2

x=9

hence the answer is 9

Answer:

[tex]x=13[/tex]

Step-by-step explanation:

Step 1: Isolate the square root on the left hand side

 Radical already isolated

  √x-4 = x-10

Step 2: Eliminate the radical on the left hand side

Raise both sides to the second power

    (√x-4)2 = (x-10)2

    After squaring

    x-4 = x2-20x+100

Step 3: Solve the quadratic equation

    Rearranged equation

    x2  - 21x  + 104 = 0

    This equation has two rational roots:

      {x1, x2}={13, 8}

Step 4: Check that the first solution is correct

    Original equation

    √x-4 = x-10

    Plug in 13 for  x

     √(13)-4 = (13)-10

     Simplify

     √9 = 3

     Solution checks !!

    Solution is:

     x = 13

Step 5: Check that the second solution is correct

    Original equation

    √x-4 = x-10

    Plug in 8 for  x

     √(8)-4 = (8)-10

     Simplify

     √4 = -2

     Solution does not check

     2 ≠ -2

One solution was found :

     x = 13

Answer:

2

Step-by-step explanation:

2x -4= 0

2x-4+4=0

2x=0+4

2x=4

2x/2=4/2

x=2

Answer:

Step-by-step explanation:

Since the x-axis is the line of symmetry, the missing vertex is the reflection of the given vertex over the line of symmetry.

Connect these points with the vertex on the x-axis to complete the triangle.

See the attachment

Answer:

3/25

Step-by-step explanation:

1/5 x 3/5 = 3/25

Answer:

The integers are 2.

Step-by-step explanation:

Answer: 3 and 6

Step-by-step explanation:

3+6=9

3x6=18

Using geometric sequence concepts, it is found that:

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

As a function of the mth term, the nth term is given by:

[tex]a_n = a_mq^{n - m}[/tex]

Hence, considering the 8th and the 11th term, the common ratio is found as follows:

[tex]a_{11} = a_8q^3[/tex]

[tex]32q^3 = 256[/tex]

[tex]q^3 = 8[/tex]

q = 2.

Then, considering the 11th term and the common ratio, the 13th term is given as follows:

[tex]a_{13} = a_{11}q^2 = 256 \times 2^2 = 1024[/tex]

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Associative property

Multiplication properties are different statements that are always true. These statements help prove that different operations can be performed on equations and still remain equal.

Associative Property

The associative property states that (a x b) x c = a x (b x c). This means that in any equation where only multiplication is present, the parentheses can be moved and the equation remains equal.

Other Examples

The associative property is always true; this means that we can create other examples.

Let's take the expression 4 x (2 x 9). As the property states, we can move the parentheses and create the new expression (4 x 2) x 9. Now we can set these expressions equal to each other.

Due to the property we know that this equation must be true.

We can prove this property by working out each side of the equation. If we multiple both sides out we are left with 72 = 72. Since this is true the equation above must also be true.

Answer:

Step-by-step explanation:

It's called The Associative Property of Multiplication

(a * b) * c = a * (b * c)

Answer: 31.0

Step-by-step explanation:

Answer:

i got 17.4km/H pretty sure im right

Answer:

( x-7)^2+(y-6)^2 = 25

Step-by-step explanation:

The equation of a circle is given by

(x-h)^2 + (y-k)^2 = r^2

where ( h,k) is the center and r is the radius

( x-7)^2+(y-6)^2 = 5^2

( x-7)^2+(y-6)^2 = 25

Answer:

(x-7)^2+(y-6)^2=25

Explanation:

If I were you, I would mark 7 as x and 6 as y. Whatever is in your parenthesis for center of the circle, do the opposite in your equation. Since you have positive 7 & positive 6, turn those into negative numbers for your equation. And for the radius, just times it two times. So 5•5=25

Answer:

Amanda's percent of error: = .03 or 3% Dwyane's percent of error: = .02 = 2%

Looks like Amanda had the larger error.

Step-by-step explanation:

A. AT1,2).B1.0).C'(4.0).D*(4,2)

your answer

Answer:

159.25cm²

Step-by-step explanation:

A=lw

A=12×10cm

The rectangle’s area is 120cm² 

First, substitute the given information into the equation for the area of a circle.

A=πr²

A=(3.14)(5²)

A=3.14×25

A=78.5

Next, because the figure is only half of a circle, divide this in two.

78.5/2= 39.25cm²

Asc=39.25cm²

Add the two areas together.

A=Ar+Asc

120cm²+39.25cm²

The area of the combined figure is 159.25cm²

The interest rate which is required in order for Leah to end up with $40,000 in his account which is compounded daily, is 4.11%.

Compound interest is the amount charged on the principal amount and the accumulated interest with a fixed rate of interest for a time period.

The formula for the final amount with the compound interest formula can be given as,

[tex]A=P\times\left(1+\dfrac{r}{n\times100}\right)^{nt}\\[/tex]

Here, A is the final amount (principal plus interest amount) on the principal amount P of with the rate r of in the time period of t.

Leah is going to invest P=$30,000 and leave it in an account for t=7 years.

Put the values in the above formula to find rate of interest.

[tex]A=P\times\left(1+\dfrac{r}{n\times100}\right)^{nt}\\40000=30000\times\left(1+\dfrac{r}{12\times30\times100}\right)^{12\times30\times(7)}\\r=4.11 \5[/tex]

Thus, the interest rate which is required in order for Leah to end up with $40,000 in his account which is compounded daily, is 4.11%.

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Answer:

    27. (4) 4 in

    28. (2) 13

Step-by-step explanation:

Question 27

Question 28

Answer:

[tex]3^{n}+3^{n-1}[/tex]

Step-by-step explanation:

Since the sequence is geometric (it multiplies the previous number each time). The nth term sequence would be [tex]x^n + yn[/tex]

Because the sequence multiplies by 3 each time, The base number in that equation would be [tex]3^n +yn[/tex].

So [tex]3^n[/tex] of the equation would be:
[tex]3, 9, 27[/tex].

Compare the 2 equations:
4, 12, 36

3, 9 ,27

The difference between the 2 equations is: 1, 3, 9 which itself is a geometric sequence so the nth term of this new equation is: [tex]3^{n-1}[/tex].

Combine these 2 equations together and you get:

[tex]3^{n}+3^{n-1}[/tex].

Answer:

4

Step-by-step explanation:

The figure can be split into 2 triangles, the larger one is the whole figure with base 18 and height 9. while the other small triangle has base 8 and height h. Since they are both right angled triangles with a shared angle, they are similar.

With similar triangles, we get the ratio of base : height = 8 : 8+10 = h : 9

Hence, 8 : 18 can be simplified to 4 : 9, which is also equal to h : 9. From here, we get h = 4.

Answer:

4

Step-by-step explanation:

The figure can be split into 2 triangles, the larger one is the whole figure with base 18 and height 9. while the other small triangle has base 8 and height h. Since they are both right angled triangles with a shared angle, they are similar.

Answer:

B.3x+8=66

Step-by-step explanation:

i think ito po Ang answer hehehe

Part A

x = some unknown number

x+8 = add on 8 to the number

3(x+8) = triple the previous result

Therefore, one equation to set up is 3(x+8) = 66

This is the same as 3x+24 = 66 because 3(x+8) = 3x+3*8 = 3x+24. Use the distributive property to multiply that outer 3 to each term inside.

C)  3x+24 = 66

D)   3(x+8) = 66

============================================================

Part B

Let's solve for x. I'll show the steps for each equation mentioned. When you write out the steps, you probably only need to pick one equation to solve.

3(x+8) = 66

x+8 = 66/3

x+8 = 22

x = 22-8

x = 14

Or

3x+24 = 66

3x = 66-24

3x = 42

x = 42/3

x = 14

Either way, we get the same x value. To confirm this answer, replace x with 14 in either equation and simplify fully. You should get 66 on both sides.