Multiply (4x - 5)(4x + 5).
A) 8x2 - 10
B) 16x2 - 25
C) 8x2 - 40x - 10
D) 16x2 - 40x - 25

The answer is: 22 inches.

We are given a cylinder shape, with the information about it's diameter, meaning that we also can know the radius.

The height of a cylinder goes from the bottom to the top of the shape, so, from the given shape, the height is 22 inches.

With the information, we can also calculate the volume of the cylinder using the following formula:

[tex]V=\pi *r^{2}*h\\\\V=\pi *(\frac{Diameter}{2})^{2} *h\\\\\V=\pi *(\frac{16}{2})^{2}*22=\pi *8^{2} *22=4423.4inches[/tex]

Have a nice day!

Answer:

22 inches

Step-by-step explanation:

We are given a figure of a cylinder with two known lengths. We are to determine whether which of them is the height of the cylinder.

We know that the base of the cylinder is round so the length mentioned on the round base is its diameter.

While the other length running from the top to bottom (or from left to right as shown in the picture) is the height of the cylinder which is 22 inches.

Answer:

∠A = ∠B = 80°

Step-by-step explanation:

The angles are corresponding angles where a transversal crosses parallel lines, so are congruent. That means ...

∠A = ∠B

8x -8° = 5x +25° . . . . . substitute the given expressions

3x = 33° . . . . . . . . . . . . add 8°-5x

x = 11° . . . . . . . . . . . . . . divide by 3

Then the angles are ...

8·11° -8° = 80°

Answer: $78

Step-by-step explanation:

Find the number of blocks as following:

[tex]blocks=\frac{9pounds}{\frac{3}{4}pounds}\\\\blocks=12[/tex]

You know that they sell each block for $6.50.

Therefore, if they sell all the fudge then you can calculate the amount of money they will make (which you can call x)  by multiplying the number of blocks by the price of each one of them. Therefore, you obtain:

[tex]x=\$6.50*12\\x=\$78[/tex]

Answer:

The Daniels family will make $78.

Step-by-step explanation:

We know that 9 pound cake made by the Daniels family was separated into 3/4 pound block.

So we will divide the total amount of cake by 3/4 to find the number of blocks:

[tex] \frac { 9 } { \frac { 3 } { 4 } } = \frac { 9 \times 4 } { 3 } = 12 [/tex]

We are given that each block is sold at $6.50 so we need to find the total amount of money they will make if all blocks are sold.

Total money = [tex]12 \times 6.5[/tex] = $78

The solution is : the area, in square feet, of the mat is 169π/4 ft^2.

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object. The space enclosed by the boundary of a plane figure is called its area. The area of a figure is the number of unit squares that cover the surface of a closed figure. Area is measured in square units like cm² and m². Area of a shape is a two dimensional quantity.

here, we have,

we know that,

Circumference = π * d

Diameter = 2r

Area of a circle = πr²

From our first equation, we can find our value for our diameter:

We do this by dividing 13π by π to get 13.

so, we get,

C = πd

or, 13π = πd

or, d = 13π/π

or, d = 13

Using our second equation, we can find out the value for our radius:

d = 2r

so, r = 13/2

Now we have a value for our radius, we can use our third equation to find out our area:

A = πr²

so, A = π(13/2)²

or, A = 169π/4

Hence, The solution is : the area, in square feet, of the mat is 169π/4 ft^2.

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The area of the circular mat with a circumference of 13π feet is 42.25π square feet, calculated by first determining the radius from the circumference and then using the area formula.

To find the area of the circular mat when given the circumference, we can start by recalling the relationship between the circumference (C) and the radius (r) of a circle. The formula for circumference is C = 2πr. From this, we can solve for the radius:

C = 2πr
13π = 2πr
r = 13π / 2π
r = 6.5 feet

Now we have the radius, so we can find the area (A) of the circle using the formula A = πr²:

A = π(6.5)²
A = π×42.25
A = 42.25π square feet

Thus, the area of the circular mat is 42.25π square feet.

Answer:

40,320

Step-by-step explanation:

The first object in the arrangement can be chosen 8 ways. The second, 7 ways (after the first one is chosen). And so on down to the last object, which will be the only remaining one. Altogether, the number of ways you can arrange the objects is ...

8·7·6·5·4·3·2·1 = 8! = 40,320

Answer:

8! = 40320

Step-by-step explanation:

there are 8 for first, then 7 for second and so on for 1 for the 8th  , so it's 8!

Answer:

Step-by-step explanation:

Brackets in mathematics are a little like periods in grammar.

They tell you exactly what you need to do.

In the question you have listed

3z^3 means that only the z is raised to the third power.

(3z)^3 means both the 3 and the z are raised to the third power. 3^3 * z^3 =

27 z^3     This is a valuable question to know the answer to.

Answer:

[tex]\frac{5}{12}[/tex]  feet

Step-by-step explanation:

Let height of mandy be m, sophia be s, and alexis be a

"sophia is 3/4 as tall as mandy":

[tex]s=\frac{3}{4}m[/tex]

"alexis is 5/6 as tall as mandy":

[tex]a=\frac{5}{6}m[/tex]

Since mandy is 5 feet, we plug in 5 into m in both of the equations to find height of alexis and sophia.

Sophia  =  [tex]\frac{3}{4}(5)=\frac{15}{4}[/tex]

Alexis  =  [tex]\frac{5}{6}(5)=\frac{25}{6}[/tex]

Difference in height of Alexis and Sophia is  [tex]\frac{25}{6}-\frac{15}{4}=\frac{5}{12}[/tex] feet

Answer:

224 in^3

Step-by-step explanation:

The foruma appropriate to the calculation of the cone's volume is ...

V = (1/3)Bh

where B represents the area of the base and h represents the height.

For your numbers, this is ...

V = (1/3)·(48 in^2)(14 in) = (16 in^2)(14 in) = 224 in^3

Answer:

x = 1/14

Step-by-step explanation:

You can work it as is by subtacting ln(14), then taking antilogs:

ln(x) = -ln(14)

x = 14^-1

x = 1/14

___

Or you can rewrite to a single log and then take antilogs:

ln(14x) = 0

14x = 1

x = 1/14 . . . . . divide by the coeffient of x

Answer:

Interest Earned = $1958

Value of total investment - $6490

Step-by-step explanation:

We can solve for both the questions by using the formula:

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Where,

A is the future amount (original PLUS interest)

P is the initial amount

r is the rate of interest

n is the number of times interest is compounded per year

t is the time in years

For out problem, P = 4532, r is 0.06 (6%), n is 12 (since monthly compounding in 1 year), t = 6. Plugging these into the equation, we get A (the future amount).

[tex]A=P(1+\frac{r}{n})^{nt}\\A=4532(1+\frac{0.06}{12})^{(12)(6)}\\A=4532(1.005)^{72}\\A=6490[/tex]

This is the amount including interest. Hence,

Interest earned = 6490 - 4532 = $1958

Your total investment would be A, which is $6490

Answer:

Step-by-step explanation:

The negative coefficient of x^2 tells you the parabola opens downward. (Any even-degree polynomial with a negative leading coefficient will open downward.)

Going through the steps for completing the square, we ...

1. Factor out the leading coefficient from the x-terms

  -1(x^2 +14x) +1

2. Add the square of half the x-coefficient inside parentheses, subtract the same amount outside parentheses.

  -1(x^2 +14x +49) -(-1·49) +1

3. Simplify, expressing the content of parentheses as a square.

  -(x +7)^2 +50

4. Compare to the vertex form to find the vertex. For vertex (h, k), the form is

  a(x -h)^2 +k

so your vertex is ...

  (h, k) = (-7, 50) . . . . . . . . . a = -1 < 0, so the curve opens downward. The vertex is a maximum.

The maximum value of the expression is 50.

Answer:

4g = 64

Step-by-step explanation:

Let n = the number of nectarines

and g = the number of grapefruit

We have two conditions that must be satisfied to represent the situation:

(1)         n = 3g

(2) n + g = 64

If you need one equation, we can substitute (1) into (2) and get

4g = 64

Answer:

4 hours

Step-by-step explanation:

Let h represent the number of hours the high-power pump requires to fill the pool. Then the number of pools it can fill per hour is 1/h. The low-power pump can fill 1/(h+2) pools in an hour. Together, they can fill 1 pool in 1.2 hours:

1/h + 1/(h+2) = 1/2.4

h+2 +h = h(h+2)/2.4 . . . . . . . multiply by h(h+2)

4.8h +4.8 = h^2 +2h . . . . . . multiply by 2.4

h^2 -2.8h = 4.8 . . . . . . . . . . put in form suitable for completing the square

h^2 -2.8h +1.96 = 6.76 . . . add (2.8/2)^2 = 1.96 to complete the square

h - 1.4 = √6.76 . . . . . . . . . . take the square root of both sides

h = 1.4 +2.6 = 4 . . . . . . . . . hours

Answer:

  Table B

Step-by-step explanation:

The table represents a linear function if the ratio of change in y (∆y) to change in x (∆x) is a constant.

A — first two points: ∆y/∆x = (1-2)/(3-0) = -1/3

  second two points: ∆y/∆x = (6-1)/(4-3) = 5 ≠ -1/3

__

B — first two points: ∆y/∆x = (2-(-3))/(4-(-1)) = 5/5 = 1

  second two points: ∆y/∆x = (4-2)/(6-4) = 2/2 = 1, the same as for the first points. This is the table that answers the question.

__

C — first two points: ∆y/∆x = (0-(-2))/(0-(-3)) = 2/3

  second two points: ∆y/∆x = (4-0)/(2-0) = 4/2 = 2 ≠ 2/3

__

D — first two points: ∆y/∆x = (-2-(-7))/(0-5) = 5/-5 = -1

  second two points: ∆y/∆x = (2-(-2))/(2-0) = 4/2 = 2 ≠ -1

Table 3, with the ordered pairs (-3, -2), (0, 0), and (2, 4), appears to represent a linear function due to the consistent changes in 'y' as 'x' increases.

Let's analyze each table to determine which one appears to represent a linear function:

Table 1:

In this table, as 'x' increases by 3 units (from 0 to 3) and then by 1 unit (from 3 to 4), 'y' changes from 2 to 1 and then to 6. The changes in 'y' are not consistent, so this table does not appear to represent a linear function.

Table 2:

In this table, as 'x' increases by 5 units (from -1 to 4) and then by 2 units (from 4 to 6), 'y' changes from -3 to 2 and then to 4. The changes in 'y' are not consistent, so this table does not appear to represent a linear function.

Table 3:

In this table, as 'x' increases by 3 units (from -3 to 0) and then by 2 units (from 0 to 2), 'y' changes from -2 to 0 and then to 4. The changes in 'y' are consistent, indicating a linear relationship between 'x' and 'y.'

Table 4:

In this table, as 'x' increases by 5 units (from 0 to 5) and then by 2 units (from 2 to 0), 'y' changes from -2 to 2 and then to -7. The changes in 'y' are not consistent, so this table does not appear to represent a linear function.

Based on the consistent changes in 'y' as 'x' increases in Table 3, it appears to represent a linear function. So, Table 3 is the one that shows a set of ordered pairs that appears to lie on the graph of a linear function.

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Assuming scores are normally distributed, a score of 82% on Ms. Smith's test corresponds to the [tex]p[/tex]-th percentile, i.e.

[tex]P(X_S\le82)=p[/tex]

where [tex]X_S[/tex] is a random variable denoting scores on Ms. Smith's test.

Transform [tex]X_S[/tex] to [tex]Z[/tex], which follows the standard normal distribution:

[tex]P(X_S\le82)=P\left(\dfrac{X_S-75}2\le\dfrac{82-75}2\right)=P(Z\le3.5)\approx0.9998[/tex]

which means Amy scored at the 99.98th percentile.

This makes it so that Karina needs to score [tex]X_A=x[/tex] on Mr. Adams' test so that

[tex]P(X_A\le x)=0.9998[/tex]

Their test scores have the same [tex]z[/tex] score computed above, so

[tex]\dfrac{x-73}3=3.5\implies x=83.5[/tex]

so Karina needs to get a test score of at least 83.5%.

Answer:

the answer is 84%

Step-by-step explanation:

Answer:

23/15

Step-by-step explanation:

find g(-3)

    g(-3) = 2(-3)² + 5 = 2(9) + 5 = 18 + 5 = 23

Now find p(-3)

    p(-3) = (-3)² - 2(-3) = 9 - (-6) = 9 + 6 = 15

Now find g(-3)/p(-3)

  23/15

Answer:

(C) -11

Step-by-step explanation:

The given functions are;

[tex]f(x)=x+4[/tex]

Plug in x=3.

This implies that; [tex]f(3)=3+4=7[/tex]

and

[tex]g(x)=12x-6[/tex]

Plug in x=-1

This implies that; [tex]g(-1)=12(-1)-6=-18[/tex]

[tex]f(3)+g(-1)=7+-18=-11[/tex]

Answer:

Luke drew the greater garden plan

The area of the greatest garden  = 225 feet²

Step-by-step explanation:

* The gardens are in the shape of rectangle and square

- The Nancy's garden is in a shape of a rectangle because it has

  two different dimensions, 18 feet and 12 feet

- The Luke's garden is in a shape of a square because it has

  two same dimensions, 15 feet and 15 feet

- The area of the rectangle = L × W

- The area of the square = L × L = L²

∵ In Nancy garden, L = 18 feet and W = 12 feet

∴ The area = 18 × 12 = 216 feet²

∵ In Luke garden, L = 15 feet

∴ The area = 15² = 225 feet²

∵ 225 > 216

* The area of Luke garden is greater than the area of Nancy garden

* Luke drew the greater garden plan

* The area of the greatest garden = 225 feet²

Luke drew the garden plan with the greater area. His plan measures 15 feet by 15 feet, resulting in an area of 225 square feet compared to Nancy's 18 feet by 12 feet garden plan, which has an area of 216 square feet.

To determine who drew the garden plans with the greater area, we must calculate the area of each rectangle. The area of a rectangle is found by multiplying its length by its width. For Nancy's garden plan, which is 18 feet by 12 feet, the area is calculated as follows:

Area = Length × Width = 18 feet × 12 feet = 216 square feet.

For Luke's garden plan, which is a square of 15 feet by 15 feet, the area is calculated as:

Area = Length × Width = 15 feet × 15 feet = 225 square feet.

Comparing the two areas, Luke's garden plan is 225 square feet and Nancy's is 216 square feet. Therefore, Luke drew the garden plans with the greater area.

Answer:

Step-by-step explanation:

The volume of a cuboid is given by the product of its dimensions. Here, that is ...

  (12 cm)·(6 cm)·(3.5 cm) = 252 cm³

We are told the mass of each cm³ is 8.6, so 252 of them will have a mass of ...

  8.6·252 cm³ = 2167.2 . . . . . no units specified

Try this suggested option (see the attached picture).

For this case we must indicate the value of the following expression, expressed in scientific notation:

[tex](1.2 * 10^{-3}) * (1.1 * 10^{8}) =[/tex]

We have that for multiplication properties of powers of the same base, the same base is placed and the exponents are added:

[tex]a ^ n * a ^ m = a ^ {n + m}[/tex]

Then, rewriting the expression we have:

[tex](1.2 * 1.1) * 10 ^{- 3 + 8} =\\1.32 * 10 ^ 5[/tex]

Answer:

[tex]1.32 * 10 ^ 5[/tex]

Answer:

  see the attachment

Step-by-step explanation:

f(x) = x defines a line with a slope of 1 (upward to the right). Only the bottom two graphs have such a line.

The inequality symbol ≥ means the function has this definition for the case when x = 1. That is, f(x) ≥ x for x≥1 means f(1) = 1. The solid dot means that point on the graph is a point that satisfies the function definition.

The graph at lower right is a graph that includes the point f(1) = 3, which is not the same function as the one in the problem statement.

Answer:

[tex]\large\boxed{x=-8\ and\ y=9\to(-8,\ 9)}[/tex]

Step-by-step explanation:

[tex]a)\ \text{Elimination method:}\\\\\left\{\begin{array}{ccc}3x+4y=12\\x+2y=10&\text{multiply both sides by (-2)}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}3x+4y=12\\-2x-4y=-20\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad \boxed{x=-8}\\\\\text{Put the value of x to the second equation:}\\-8+2y=10\qquad\text{add 8 to both sides}\\2y=18\qquad\text{divide both sides by 2}\\\boxed{y=9}[/tex]

[tex]b)\ \text{Substitution method:}\\\\\left\{\begin{array}{ccc}3x+4y=12\\x+2y=10&\text{subtract 2y from both sides}\end{array}\right\\\\\left\{\begin{array}{ccc}3x+4y=12&(1)\\x=10-2y&(2)\end{array}\right\qquad\text{subtract (2) to (1)}\\\\3(10-2y)+4y=12\qquad\text{use distributive property}\\(3)(10)+(3)(-2y)+4y=12\\30-6y+4y=12\qquad\text{subtract 30 from both sides}\\-2y=-18\qquad\text{divide both sides by (-2)}\\\boxed{y=9}\\\\\text{Put the value of y to (2):}\\x=10-2(9)\\x=10-18\\\boxed{x=-8}[/tex]

Answer:

Step-by-step explanation:

The altitude to the hypotenuse of a right triangle create two smaller triangles, all of which are similar to the original. This means corresponding sides are proportional.

3. Using the above relationship, ...

short-side/hypotenuse = 8/y = y/(8+23)

y^2 = 8·31

y = 2√62

__

long-side/hypotenuse = z/(8+23) = 23/z

z^2 = 23·31

z = √713

__

short-side/long-side = 8/x = x/23

x^2 = 8·23

x = 2√46

_____

4. The picture is fuzzy, but we think the lengths are 25 and 5. If they're something else, use the appropriate numbers. Using the same relations we used for problem 3,

y = √(5·25) = 5√5 . . . . . . . = √(short segment × hypotenuse)

z = √(20·25) = 10√5 . . . . . = √(long segment × hypotenuse)

x = √(5·20) = 10 . . . . . . . . . = √(short segment × long segment)

Answer:

Hope this helps you on your Assignment :D

Answer:

[tex]-4.8[/tex] degrees Fahrenheit

Step-by-step explanation:

Let [tex]t[/tex] be temperature.

[tex]t[/tex] at 3:00PM: [tex]5.2[/tex] degrees.

Every hour, the temperature falls by [tex]2.5[/tex] degrees per hour for the next four hours. Let's multiply 2.5 by 4 to find out the total temperature drop in four hours.

[tex](2.5)(4)=10[/tex]

In four hours, the temperature dropped 10 degrees. Since it is getting colder, let's subtract this from the original 5.5 degrees to get the temperature at 7:00PM.

[tex]5.2-10=-4.8[/tex]

The temperature at 7:00PM was -4.8 degrees Fahrenheit.

We can employ a simple repeated decimal trick:

[tex]x=1.111\ldots[/tex]

[tex]0.1x=0.111\ldots[/tex]

[tex]\implies x-0.1x=1\implies0.9x=1\implies x=\dfrac1{0.9}=\dfrac{10}9[/tex]

###

Alternatively, we can compute the partial sum of the series.

[tex]\displaystyle S_n=\sum_{k=0}^n\dfrac1{10^k}[/tex]

[tex]S_n=1+0.1+0.01+\cdots+\dfrac1{10^n}[/tex]

[tex]0.1S_n=0.1+0.01+0.001+\cdots+\dfrac1{10^{n+1}}[/tex]

[tex]\implies S_n-0.1S_n=0.9S_n=1-\dfrac1{10^{n+1}}[/tex]

[tex]\implies S_n=\dfrac{10}9-\dfrac9{10^n}[/tex]

As [tex]n\to\infty[/tex], the second term vanishes and we're left with [tex]\dfrac{10}9[/tex]. Notice that this is really just a more formal version of the earlier trick.

Answer:

1.11

Step-by-step explanation:

Answer:

[tex]m\angle MEJ=25^{\circ}.[/tex]

Step-by-step explanation:

The arcs LY, KM, KL and MJ together form the full revolution angle, thus

[tex]4x+50^{\circ}+6x+x+10^{\circ}+4x=360^{\circ},\\ \\15x=300^{\circ},\\ \\x=20^{\circ}.[/tex]

Note that

[tex]m\angle MOJ=4x=80^{\circ},[/tex]

then

[tex]m\angle MLJ=\dfrac{1}{2}\cdot 80^{\circ}=40^{\circ}.[/tex]

So,

[tex]m\angle ELM=180^{\circ}-40^{\circ}=140^{\circ}.[/tex]

Also

[tex]m\angle LOK=30^{\circ},[/tex]

so

[tex]m\angle KML=\dfrac{1}{2}\cdot 30^{\circ}=15^{\circ}.[/tex]

In triangle EML,

[tex]m\angle MEL+m\angle EML+m\angle ELM=180^{\circ},\\ \\m\angle MEL=180^{\circ}-15^{\circ}-140^{\circ}=25^{\circ}.[/tex]

Thus, [tex]m\angle MEJ=25^{\circ}.[/tex]

A "100 chart" is a listing of all the numbers 1 to 100, in rows of 10. This results in columns of numbers that all end in the same digit. For your purpose of instructing your little brother, I recommend you web-search for "100 chart" and print one of the ones available.

Locating the given numbers on a "100 chart", you find they are in the last 4 columns of the rows ending in 20, 30, 40, 50. Overlaying the boxes onto the chart, you see they correspond to number positions ...

  17 _ _ 20

  27 _ 29 _

  _ 38 _ 40

  47 _ _ 50

Answer:

The equation of the line is y = 3/2x + 5/2

Step-by-step explanation:

To find the equation of this line, start by using the two points with the slope formula to find the slope.

m(slope) = (y2 - y1)/(x2 - x1)

m = (4 - 1)/(1 - -1)

m = 3/(1 + 1)

m = 3/2

Now that we have the slope, we can use that and either point in point-slope form to find the equation.

y - y1 = m(x - x1)

y - 4 = 3/2(x - 1)

y - 4 = 3/2x - 3/2

y = 3/2x + 5/2