A 60-foot monument casts a 25-foot shadow. How long is the shadow of a 4.5-foot-tall person​

Answer:

1.256637061 x 10 (to the power of 20)

Step-by-step explanation:

Just apply these digits into your calculator.

Answer: 12x3−21x2+67x−15

Step-by-step explanation:

(3x−5)(4−9x)+(2x+1)(6x2+5)

=12x+−27x2+−20+45x+12x3+10x+6x2+5

=12x+−27x2+−20+45x+12x3+10x+6x2+5

=(12x3)+(−27x2+6x2)+(12x+45x+10x)+(−20+5)

=12x3+−21x2+67x+−15

Answer:

12x^3 - 21x^2 + 67x - 15!

Step-by-step explanation:

Answer:

C. The value of the comic book decreased by an average of $0.04 each month between m = 36 and m = 60.

Step-by-step explanation:

The average rate of change for the function f(x) from [tex]x_1=a[/tex] and [tex]x_2=b[/tex] is

[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]

It is a measure of how much the function changed per unit, on average, over that interval.

Actually, this is the slope of the line passing through two points on the graph of the function.

If the average rate of change of the function f(x) between m = 36 and m = 60 is -0,04, it means that the value of the comic book decreased (because of negative number -0.04) by an average of $0.04 each month (a unit in this case is a month) between m = 36 and m = 60.

Answer:

C. The value of the comic book decreased by an average of $0.04 each month between m = 36 and m = 60.

Step-by-step explanation:

Answer:

2 * ( [2w-8]   + w)

Step-by-step explanation:

width = w

Length = 2w -8

Perimeter of Rectangle  = 2 (l+b)

                                        = 2 * ( [2w-8]   + w)

Answer:

[4, -1]

Step-by-step explanation:

Using the Elimination Method:

3x + y = 11

5x - y = 21

__________

8x = 32

__ ___

8 8

x = 4 [Plug this back into both equations to get the y-coordinate of -1]; -1 = y

The y's are already additive inverses [result in 0], canceling each other out.

I am joyous to assist you anytime.

Answer: C. 3.2 × 10^4

Step-by-step explanation:

for this case the multiplication of the values with exponent are summed, as the exponent are the 6 and -3

6 - 3 = 3

this will be the exponent of the common value which is the 10.

after you only need to multiply 8 and 4 by separate the

8 * 4 = 32.

then we only need to place the values one by one

32 × 10^3

3 is the result of the sum of the exponent.

10 is the common value.

32 is the result of the product.

if we add another zero to the multiplication we get 3.2 and exponent finish with one more zero, then we get this result

3.2 × 10^4

because of that the C is the correct answer, keep in mind that the other answers do not apply correctly the rule of the exponent, because the rest of answer give us wrong answer with final result of the exponent.

To simplify the expression (8 × 10^6) × (4 × 10^-^3) in scientific notation, we multiply the numbers (8 x 4) and add the exponents (6 + -3) resulting in 32 x 10^3. To represent the coefficient within the range of 1 and 10, we revise 32 as 3.2 x 10 yielding the answer 3.2 x 10^4.

To answer the question, 'Which shows the expression below in simplified form? (8 × 10^6) × (4 × 10^-^3)', we need to understand the rules for multiplying numbers in scientific notation. To multiply two numbers in scientific notation, we multiply the coefficients (the numbers) first and separately add the powers of ten.

Here, the coefficients are 8 and 4 which multiply to give 32. The powers of ten are 10^6 and 10^-3. When multiplying powers of 10, we add the exponents, so 6 + -3 = 3. Therefore, the simplified form of the expression is 32 × 10^3. However, in scientific notation, we usually want the coefficient to be a number between 1 and 10. Therefore, we rewrite 32 as 3.2 x 10 to get the final answer: 3.2 x 10^4. So, the correct answer is option D. 3.2 x 10^4

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Answer: X intercept= (-3,0) Y intercept= (0,4)

Step-by-step explanation:

Answer: B is the answer

Step-by-step explanation:

Why? It is equal to 0

Answer:

d. -24/-6 - 4​

Step-by-step explanation:

Use order of operation (PEMDAS) to solve.

There are no parentheses.

There are no exponents.

There is multiplication and/or division. Do this first, from left to right.

There is addition and/or subtraction. Do this second, from left to right.

Solve. Remember that a negative times (or divided by) a negative makes a positive.

-24 / -6 = 4

4 - 4 = 0

Check your work. None of the other expressions are equal to 0.

a. -24 / 6 - 4 = -4 - 4 = -8

b. -24 / -6 + 4 = 4 + 4 = 8

c. 24/6 + 4 = 4 + 4 = 8

Answer:

3n + 2

Step-by-step explanation:

-n+(-4)-(-4n)+6

= -n -4 +4n +6        [positive plus negative =  negative; ∴  +(-4) = -4

=4n - n +6 - 4                      negative plus negative = positive; ∴ -(-4n) = 4]

now subtract n from 4n and subtract 4 from 6

=3n + 2

Answer: 0.93

Explanation: write out the problem and sub in 4, for "x". So it would look like this; 6 (4) + 5=27

6 (4)= 24, then add 5, which equals 29. so your next step would look like this; 29=27. Once you get this you want to divide each side by 29. The 29 cancels and 27/29 is equal to 0.93

[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount \underline{for 1 year}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$6500\\ r=rate\to 12\%\to \frac{12}{100}\dotfill &0.12\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &1 \end{cases}[/tex]

[tex]\bf A=6500\left(1+\frac{0.12}{1}\right)^{1\cdot 1}\implies A=6500(1.12)\implies A=7280 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount \underline{for 2 years}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$6500\\ r=rate\to 12\%\to \frac{12}{100}\dotfill &0.12\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &2 \end{cases}[/tex]

[tex]\bf A=6500\left(1+\frac{0.12}{1}\right)^{1\cdot 2}\implies A=6500(1.12)^2\implies A=8153.6[/tex]

Answer:

Step-by-step explanation:

To find the equation of a parallel line, we first need to find the slope of 3y + 7 = 2x.

We need to find it because, if two lines are parallel, then that means they have the same slope.

The best way to do this is solve for y:

[tex]3y+7=2x\\3y=2x-7\\y=\frac{2}{3}-\frac{7}{3}[/tex]

Due to the rule that in y = mx + b, m = the slope, we find that the slope is 2/3.

Now we use that slope in the same formula to find b of the line we're trying to find the equation for, and then we'll have our answer. We find b by plugging in (2, 6) for x and y:

[tex]y = mx+b\\y=\frac{2}{3}x+b\\6=\frac{2}{3}(2)+b\\18=4+3b\\ 14=3b\\\frac{14}{3} = b[/tex]

So our line is:

[tex]y=\frac{2}{3}x+\frac{14}{3}[/tex]

To find the equation of a line parallel to a given line and passing through a given point, first find the slope of the original line. Then, using the slope-intercept form of a line, substitute the given point's coordinates and the slope to find the equation of the parallel line.

To find an equation of the line parallel to 3y+7=2x and passing through point (2,6), we need to find the slope of the original line and then use it to create the equation of the parallel line. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.

The given equation 3y+7=2x can be rearranged to y = (2/3)x + 7/3.

The slope of this line is 2/3. Since a line parallel to another line has the same slope, the slope of the parallel line is also 2/3.

Using the point (2,6) and the slope 2/3, we can use the slope-intercept form to find the equation of the parallel line: y = (2/3)x + b. Plugging in the coordinates of the given point, we get 6 = (2/3)(2) + b.

Solving for b, we find that b = 5/3. Therefore, the equation of the line parallel to 3y+7=2x and passing through (2,6) is y = (2/3)x + 5/3.

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Answer:

If adding, 43.2.

If subtracting, -34.2.

If multiplying, 174.15.

If dividing, 8.6.

Step-by-step explanation:

Addition: Line up and add.

Subtraction: Add the first number and opposite of the second. 4.5+(-38.7)=-34.2.

Multiplication: Multiply as normal, count up how many decimal places are in the factors (2), and add that to your answer, 174.15.

Division: Turn both number into whole numbers by multiplying by 10. Then divide 387/45= 8.6.

CAN EXPLAIN FURTHER

Answer:

1. ABE and CBD

Notice that the vertex is B, so these two angles share the same vertex. Accordingly, these two angles are vertical angles.

2. ABC and EBD

The same reasoning is applied here. The vertex is also B. Notice that the angles CBD and ABD add up to 180 degrees.

Step-by-step explanation:

Vertical angles are a pair of opposite angles formed by intersecting lines. The pair of angles which are vertical angles are ∠ABE and ∠CBD.

Vertical angles are a pair of opposite angles formed by intersecting lines.

As we know about the vertical angles, it is formed by two intersecting lines as in the given figure below, therefore, the angles which are a pair of vertical angles are ∠ABE and ∠CBD.

Hence, the pair of angles which are vertical angles are ∠ABE and ∠CBD.

Learn more about Vertical Angles:

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Answer:

he number 7 is a prime number because it can't be divided by any other other number

Step-by-step explanation:

Answer: Prime

Step-by-step explanation: To find out if 7 is a prime or composite number, we can begin by finding the factors of 7.

7 ÷ 1 = 7

This means that 1 and 7 are factors. Notice however that 7 does not divide evenly between 2, 3, 4, 5, or 6. The only other number that 7 divides by evenly is 7. When we divided 7 by 7, we get 1. Notice however that 7 and 1 are repeat factors so we can stop. This means that the factors of 7 are 1 and 7. When a number only has 2 factors, it's called a prime number. Therefore, 7 is considered a prime number.

Answer:

384

Step-by-step explanation:

If 48 is 50% of something, that means

48 + 48 = 96. Now, what number is 96 25% of? well 96 • 4 = 384. Now let's do the math backwards!

25 % of 384 is 96. 50 % of 96 is 48! so your answer is 384! Hope this helps!!!

Answer:

384

Step-by-step explanation:

If 48 is 50% of something, that means

48 + 48 = 96. Now, what number is 96 25% of? well 96 • 4 = 384. Now let's do the math backwards!

25 % of 384 is 96. 50 % of 96 is 48! so your answer is 384! Hope this helps!!!

Step-by-step explanation:

Answer:

11/15 bought food and 4/15 bought a drink

Step-by-step explanation:

2/5 x 3 = 6/15 bought a hamburger

1/3 x 5 = 5/15 bought chips

6/15 + 5/15 = 11/15 bought food

11/15 - 15/15 = 4/15 bought a drink

Final answer:

The slope of the line represented by the equation 2x + 5y = 10, passing through points (5, 0) and (0, 2), is calculated as -2/5, meaning the slope is negative two-fifths.

Explanation:

The slope of the line represented by the equation 2x + 5y = 10 can be calculated by using the coordinates of two points through which the line passes. In this case, the points are (5, 0) and (0, 2). According to the slope formula, slope (m) is defined as the change in y (the rise) over the change in x (the run). Therefore, the slope is:

The slope of the line is negative two-fifths (-2/5). Since the slope is negative, this indicates that as the x-value increases, the line moves down the y-axis.

Answer:

Step-by-step explanation:

10^0=1

10^-3 = 1/10^3

4.0=4

so : 1.72×10^0/4.0×10^-3 = (1.72× 10^3)/4 =430  

scientific notation is : 4.30× 10^2

Answer:

Jamie has 14 dimes and 26 nickels

Step-by-step explanation:

nickels : x

dimes : y

[tex]x + y = 40 \\ x = y + 12 \\ \\ replace \: x \:in \: the \: first \: equation \\ y + 12 + y = 40 \\ 2y = 28 \\ y = 14[/tex]

Jamie has a total of 40 coins out of which there are 14 dimes and 26 nickels.

Let x represent the number of dimes. Since Jamie has 12 more nickels, the number of nickels is x + 12.

The total number of coins is 40, so x + x + 12 = 40.

Solve for x:

2x + 12 = 40, 2x = 28

x = 14.

Answer:

The location of the sum is 2 units before P (left to P)

Step-by-step explanation:

* Lets describe the number line

- A number line is a horizontal straight line with numbers placed at

 an equal units

- A number line can be extended infinitely to the left and to the right

- A number line represents both positive and negative integers

- The numbers come on it from left to right

- The negative numbers come on the left of zero and the positive

  numbers come on the right of zero

- Ex: -5 , -4 , -3 , -2 , -1 , 0 , 1 , 2 , 3 , 4 , 5 part of the numbers on the

 number line

- To add numbers on the number line we start from first number of

  the addition and if this number is added by a positive number we

  go to right , if the number is added by a negative number

  we go to left

- Ex: 5 + 3 ⇒ go from 5 to the right 3 units, then your position is at 8

 2 + (-3) ⇒ go from 2 to the left 3 units then your position is at -1

* Now lets solve the problem

- The sum of P + (-2)

∵ Your location is P

∵ You will add P by (-2)

- Negative number means you go to the left

∴ Your position will be before P by two units

∴ The location of the sum is 2 units before P (left to P)

The sum of p + (-2) will always be located to the left of p on a number line.

To describe the location of the sum P+(−2) on a number line, you would start at the point represented by

P and then move 2 units to the left.

This is because adding a negative number is equivalent to moving to the left on the number line.

For example, if P is located at the number 5 on the number line, then

P+(−2) would be located at 5−2=3.

So, the sum is 3 units to the left of the point P on the number line.

Answer:

11:16

Step-by-step explanation:

The ratio cannot be simplified any further.

Answer:

Part a) [tex]f(2)=1.57\ sec[/tex]

It takes 1.57 seconds for an object to fall a distance of 2 feet

Part b) see the explanation

Part c) [tex]2,165.43\ sec[/tex]

Step-by-step explanation:

Let

f(d) -----> the time in seconds it takes for an object to fall

d -----> distance in feet

we have

[tex]f(d)=1.11\sqrt{d}[/tex]

Part a): Determine f(2) and explain what it represents

we know that

f(2) represent the time in seconds it takes for an object to fall a distance of 2 feet

For [tex]d=2\ ft[/tex]

substitute in the function above and solve for f(2)

[tex]f(2)=1.11\sqrt{2}[/tex]

[tex]f(2)=1.57\ sec[/tex]

therefore

It takes 1.57 seconds for an object to fall a distance of 2 feet

Part b) The imbrium basin is the largest basin on the moon. A reasonable domain for the height above the lowest point in the basin is given by {d|0 ≤ d ≤ 3805774}

What does this tell you about the basin?

The height of the basin is greater than or equal to 0 ft and less than or equal to 3,805,774 ft  

so

The maximum height of the basin is 3,805,774 ft

Part c) How long would it take a rock to drop from the rim to the bottom of the basin?

we know that

The distance from the rim to the bottom of the basin is equal to the maximum height of the basin

so

[tex]d=3,805,774\ ft[/tex]

substitute the value of d in the function f(d)

[tex]f(d)=1.11\sqrt{3,805,774}[/tex]

[tex]f(d)=2,165.43\ sec[/tex]

The function f(d) = 1.11√d helps us find the time to fall a specific distance on the moon. It would take approximately 2 hours for a rock to fall from the highest point to the lowest point in the Imbrium Basin on the moon.

The given function for time it takes for an object to fall on the moon is f(d) = 1.11√d. Here, d represents the distance the object falls.

Part A: To find f(2), we substitute d with 2 in the provided function, which gives us f(2) = 1.11√2 = 1.57 seconds (rounded to two decimal places). This represents the time it would take for an object to fall a distance of 2 feet on the moon.

Part B: The given domain {d|0 ≤ d ≤ 3805774} indicates the height variation in the Imbrium Basin on the moon, where 'd' represents the height in feet. The height could be any value between 0 feet (the lowest point) and 3805774 feet (the highest point), which is approximately 720 miles.

Part C: To find the time it would take for a rock to drop from the rim to the bottom of the basin in the given domain, we substitute the highest point, d = 3805774, into the function. So, f(3805774) = 1.11 √3805774 = 7317 seconds, which is approximately 2 hours.

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Answer:

67.5 seconds

Step-by-step explanation:

I can run faster :D

Find the mean of the runner's speeds as (72 + 63)/2 = 67.5

The runners take 67.5 seconds to cover 1/4 mi if Joel can run around a 1/4 mi track in 72 sec and Jason can run around the track in 63 seconds.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

It is given that:

Joel can run around a 1/4 mi track in 72 sec and Jason can run around the track in 63 seconds.

The runners start at the same spot and run in opposite directions.

The runner's speeds = (72 + 63)

The time they take = 135/2        

The time they take = 67.5 seconds

Thus, the runners take 67.5 seconds to cover 1/4 mi if Joel can run around a 1/4 mi track in 72 sec and Jason can run around the track in 63 seconds.

Learn more about the arithmetic operation here:

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Answer:  9(5 + 1)

Step-by-step explanation:

Factor out the GCF (greatest common factor) of 45 and 9, which is 9.

[tex]9\bigg(\dfrac{45}{9}+\dfrac{9}{9}\bigg)\\\\\\=\large\boxed{9(5+1)}[/tex]

Answer:

(3,1),(-2,3),(4.5,-3),(-6,2.3)

Answer:

$56.34

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

1 Donut, 4 Bagels/2 donuts, 3 bagels/3 donuts, 2 bagels, 3 combinations that are possible

The answer is choice A.

Answer:

the answer is A that stuff is real easy

Answer:

H

Step-by-step explanation:

The total cost of the call is $2.50

Since the first three minutes cost $0.60

x minutes = $2.50 - $0.60

x minutes = $1.9

Each additional minutes cost $0.17

So: $1.9 / $0.17 = 11

To find the total minutes

$0.60 + $1.9 = $2.50

3 + 11 = total minutes

14 = total minutes