analyzing distance and time

To multiply 64 • 8.32, use the logarithmic equation (2)  log 64 + log 8.32

The product is given as:

64  * 8.32

As a general rule, the product of a and b can be calculated using:

a * b = antilog(log(a) +log(b))

This means that:

64  * 8.32 = antilog(log(64) +log(8.32))

Hence, we make use of the logarithmic equation (2)  log 64 + log 8.32

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Answer:

\(\displaystyle \frac{cd^6}{a^4b^2}\)

Step-by-step explanation:

\(\displaystyle \frac{a^{-4}b^{-2}cd^6}{e^{-7}}\\\\=a^{-4}b^{-2}cd^6e^7\\\\=\frac{cd^6}{a^4b^2}\)

Notice that the variables with negative exponent that were originally in the denominator went to the numerator (like with \(e^{-7}\)) and became positive, and vice versa with those originally in the numerator went in the denominator (like with \(a^{-4}b^{-2}\)) and also became positive.

Step-by-step explanation:

a‐⁴b‐²cd⁶

_______

e‐⁷

cd⁶e⁷

_____

a⁴b²

Answer:

37

Step-by-step explanation:

well, since we're using Sine, we'll need the opposite side to ∡A, and that'd be side BC, so let's first find BC

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{61}\\ a=\stackrel{adjacent}{47}\\ o=\stackrel{opposite}{BC} \end{cases} \\\\\\ BC=\sqrt{ 61^2 - 47^2}\implies BC=\sqrt{ 3721 - 2209 } \implies BC=\sqrt{ 1512 }\)

now let's get ∡A

\(\sin( A )=\cfrac{\stackrel{opposite}{\sqrt{1512}}}{\underset{hypotenuse}{61}} \implies \sin^{-1}(~~\sin( A )~~) =\sin^{-1}\left( \cfrac{\sqrt{1512}}{61} \right) \\\\\\ A =\sin^{-1}\left( \cfrac{\sqrt{1512}}{61} \right)\implies A \approx 39.60^o\)

Make sure your calculator is in Degree mode.

Answer:

(4,0) & (9,5)

Step-by-step explanation:

Where the equations cross are the solutions!

Hope this Helps! :)
Happy Studies

Answer:

Rate of Change is 2

Step-by-step explanation:

The y values are changing by 4

The x values are changing by 2

Rate of change = Change of y/Change of x

4/2=2

The value of "k" that is missing will be 1  -2

From the given table, we can see that the coefficients and the constant of the polynomial function are written inside the division

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Answer:

the answer is 2

Step-by-step explanation:

just got it wrong

Assuming you mean isolate for x

Answer:

\(x=-1\)

Step-by-step explanation:

We can subtract \(4x\) from both sides to get \(3x-4x=4x-4x+1\).

That simplifies to \(-x=1\).

We can multiply by \(-1\) to get \(-x*-1=1*-1\).

That simplifies to \(x=-1\).

So, \(x=-1\) and we're done!

The given equation is

We just have to subtract 4(x+2) from each side

Then, we use the distributive property

Answer:

\({ \boxed{ \mathfrak{ \: answer : \: { \rm{ - \infin}} }}}\)

Step-by-step explanation:

\({ \rm{ \frac{( \cos \theta - \sin \theta) }{ \theta - \frac{\pi}{4} } }} \\ { \tt{ \{lim _{ \theta = \frac{\pi}{4} } \} }} \\ \\ \dashrightarrow \: { \rm{ \frac{( \cos \frac{\pi}{4} - \sin \frac{\pi}{4} ) }{ \frac{\pi}{4} - \frac{\pi}{4} } }} \\ \\ = { \rm{ \frac{0 - 1}{0} }} \\ \\ = { \rm{ \frac{ - 1}{0} }}\)

If n is an integer and m + 5 is odd, then n must be even.

To prove this statement using contraposition, we need to show that if n is odd, then m + 5 must be even. Assume that n is odd, which means we can write n = 2k + 1 for some integer k.

Then, we can rewrite m + 5 as (2k + 1) + 5 = 2k + 6 = 2(k + 3), which is even.

Therefore, we have shown that if n is odd, then m + 5 is even.

By contraposition, we can conclude that if m + 5 is odd, then n must be even. Overall, the proof uses the fact that odd + odd = even and even + odd = odd, along with the definition of even and odd integers.

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Answer:

11. x=18, y=5

12. x=17, y=9

Step-by-step explanation:

Use the angle property https://www.proprofs.com/quiz-school/story.php?title=angle-properties-parallel-lines (REFER TO THIS LINK)

The cost of one hosta is approximately $7 and the cost of one geranium is approximately $4.

To find the cost of one hosta and one geranium, we can set up a system of equations based on the given information.

Let's assume the cost of one hosta is represented by 'h' and the cost of one geranium is represented by 'g'.

From the information given, we can set up the following equations:

Eugene's spending:

18h + 6g = $150

Jessica's spending:

7h + 16g = $113

We can now solve this system of equations to find the values of 'h' and 'g'.

Multiplying the first equation by 2 and the second equation by 3 to eliminate 'g', we get:

36h + 12g = $300

21h + 48g = $339

Now, we can subtract the second equation from the first to eliminate 'h':

(36h + 12g) - (21h + 48g) = $300 - $339

36h - 21h + 12g - 48g = -$39

15h - 36g = -$39

Simplifying further, we have:

15h - 36g = -$39

Now we can solve this equation for 'h' and substitute the value back into any of the original equations to find 'g'.

Let's solve for 'h':

15h = 36g - $39

h = (36g - $39) / 15

Substituting this value of 'h' into Eugene's equation:

18[(36g - $39) / 15] + 6g = $150

(648g - $702) / 15 + 6g = $150

648g - $702 + 90g = $150 * 15

738g - $702 = $2250

738g = $2250 + $702

738g = $2952

g = $2952 / 738

g ≈ $4

Now, substituting the value of 'g' back into Eugene's equation:

18h + 6($4) = $150

18h + $24 = $150

18h = $150 - $24

18h = $126

h = $126 / 18

h ≈ $7

Therefore, the cost of one hosta is approximately $7 and the cost of one geranium is approximately $4.

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Using the Factor Theorem and limits, the end behavior of g(x) is that the function decreases to the left and increases to the right.

The Factor Theorem states that a polynomial function with roots \(x_1, x_2, \codts, x_n\) is given by:

\(f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)\)

In which a is the leading coefficient.

Considering the table, the roots are given as follows:

\(x_1 = -4, x_2 = 5, x_3 = 12\)

Hence the function is:

f(x) = a(x + 4)(x - 5)(x - 12).

f(x) = a(x² - x - 20)(x - 12)

f(x) = a(x³ - 13x² - 32x + 240).

When x = 0, y = 1, hence the leading coefficient is found as follows:

240a = 1

a = 0.004167

Then:

f(x) = 0.004167(x³ - 13x² - 32x + 240).

The end behavior is given by the limits of f(x) as x goes to infinity, hence:

Hence the end behavior is that the function decreases to the left and increases to the right.

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Answer:

Step-by-step explanation:

The standard algorithm is a way of doing multiplication by using partial products or multiplying in parts. What you do with this algorithm is multiply the top number by the bottom number one digit at a time, working your way from right to left.

Answer:

35

Step-by-step explanation:

if not correct I'm very very sorry I tried my best for this</3

The expressions that are equivalent to 3^8 are:

We have to solve these out

3^8. = 6561

From the options

A. 3^2x3^4

= 9 x 81

= 729

B  3²x3^6

= 9 x 729

= 6561

C.  3^16/3^2

= 43046721/9

= 4782969

d. 3^12/3^4

= 531441 / 81

= 6561

E.  (3^4)²

= 3⁴ x 3⁴

= 3⁴⁺⁴

= 3⁸

= 6561

F. (3¹)^7

= 3⁷

= 2187

The expressions that are equivalent to 3^8 are:

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Answer:

20 days

Step-by-step explanation:

Answer:

4+4+4+4=16+8х2=32 hope it help,have a nuce day!

Answer:

∠X in the pre-image will be equal to ∠L in the main image

Step-by-step explanation:

△LMN is the result of a reflection of ​ △XYZ which means △LMN is the mirror image​ △XYZ

hence, the left of △XYZ will be equivalent to the right of △LMN and the right of △XYZ will be equivalent to the left of △LMN

Hence, ∠X in the pre-image will be equal to ∠L in the main image

The weighted average length of a nail from the carpenter's box whose distribution is give in image is: 3.5cm.

What is weighted average ?

Weighted average is a type of average that takes into account the relative importance or weight of each data point. In a weighted average, each data point is multiplied by a corresponding weight, which reflects its relative importance, and the products are then summed and divided by the sum of the weights.

To find the weighted average length of a nail, we need to multiply each nail length by its percent abundance, then add up all the products and divide by the total percent abundance.

Let's start by calculating the product of each nail length and its percent abundance:

Short nail: (2.5 cm) x (70.5%) = 1.7625 cm

Medium nail: (5.0 cm) x (19%) = 0.95 cm

Long nail: (7.5 cm) x (10.5%) = 0.7875 cm

Now, we add up all the products:

1.7625 cm + 0.95 cm + 0.7875 cm = 3.5 cm

Finally, we divide by the total percent abundance:

70.5% + 19.0% + 10.5% = 100%

Therefore, the weighted average length of a nail from the carpenter's box is: 3.5 cm ÷ 100% = 3.5cm

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The amount of time he spent on bicycle is 4.5 hours.

Given Jim began a 145 mile bicycle trip.

The whole trip took 7 hours.

Jim walks at a rate of 4 miles per hour  and rides at 30 miles per hour.

speed = distance / time

time = distance / speed

ride:

d = distance ridden

t = d/30 (given from the problem)

walk:

t = (145 - d)/4 (given from problem)

total trip time:

7 = d/30 + (145 - d)/4.

7 = 4d/120 + 30(145 - d)/120

7×120 = 4d + 30(145 - d)

840= 4d +4350-30d

840 ₋ 4350 = ₋30d ₊ 4d

₋3510 = ₋26d

d = 3510/26

d = 135

d=135 then from here using the formula t = d / s we can solve

t=135/30 = 4.5 hours

hence the amount of time Jim spent on the bicycle is 4.5 hours.

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Answer:16x16

Step-by-step explanation:

Using trigonometric function the length to the nearest foot of the shortest ladder that will safely reach a roof that is 23 feet high is calculated as 25 feet.

What are trigonometric functions?

Simply put, trigonometric functions—also called circular functions—are the functions of a triangle's angle. This means that these trigonometric functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.

Given the angle a ladder makes with the ground should be no greater than 67°.

So the angle θ ≤ 67°.

Let us assume the angle to be equal to 67°

The height of the roof from the ground is 23 feet.

The ladder and wall form the right triangle where the ladder works as hypotenuse and the wall as perpendicular.

With the sine function, find the length of the ladder -

sin θ = perpendicular/hypotenuse

Let the length of ladder be x.

sin 67° = 23/x

x = 23/sin 67°

x = 23/0.920

x = 25 feet

Therefore, the length of the ladder is 25 feet.

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Answer:

n=0

Step-by-step explanation:

both numbers have the same bases which is 5 so we can say that their exponents are equal to each other:

-2n = -2n-3

now we isolate the n variables to one side:

-2n + 2n = -3

0n = -3

n = 0

Answer:

85 x 64 = 5440

Step-by-step explanation: