Factor Completely. Show ALL steps (as best as possible)

16b2 + 60b − 100

Answer:

x=9^6

Step-by-step explanation:

convert the logarithm into exponential form using the fact that loga (x)=b is equal to x=a^b

x=9^6

Answer: 803.84cm3

Step-by-step explanation:
The formula for finding the volume of a cylinder is πr2h.
In other words, the area of the top face's circle times the height.

To find the circle's area, we first find the radius of the circle. Since the diameter is 8cm, we divide by 2 to get the radius, which is 4cm.

4cm squared is 4cm x 4cm, which is 16cm. 16cm times 3.14 is 50.24cm squared.

Now, we have the area of the circle. 50.24cm squared!

The height is 16cm, so to find the cylinder, we times the area of the circle by the height of the cylinder! So,

16cm x 50.24cm squared = 803.84cm cubed.

The volume of the can of soup is 803.84cm cubed.

The number of suspects had less than two prior arrests are 3.

Given that, While reviewing the previous day’s arrest report.

Let x be the number of suspects have been arrested once before and y be the number of suspects arrested twice before.

Here, x+y=5 -----(i)

2x+3y=12 -----(ii)

From equation (i), x=5-y in equation (ii), we get

2(5-y)+3y=12

10-2y+3y=12

10+y=12

y=2

Substitute y=2 in equation (i), we get

x+2=5

x=3

Therefore, the number of suspects had less than two prior arrests are 3.

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Be,

x = number of large boxes

y = number of small boxes

According to the statement there are 125 boxes (large and small) in a truck, so

x + y = 125 (Equation 1)

We are also told that the large boxes weigh 45 pounds, so

45x --> Weight of an "x" number of large boxes

And the small boxes 30 pounds

30y --> Weight of a "y" number of small boxes

According to the statement, the weight of the 125 boxes (large and small) is 4800 pounds, so

45x + 30y = 4800 (Equation 2)

x + y = 125

45x + 30y = 4800

To solve this system we will apply the equalization method, which consists of solving for the same variable (x or y) in each equation.

In this case we will isolate x.

From the first equation

x = 125 - y

And from the second equation

45x = 4800 - 30y

\(\mathsf{x = \frac{4800-30y}{45} }\)

We equate both expressions

\(\mathsf{125 - y = \frac{4800-30y}{45} }\\\\\mathsf{45(125-y)=4800 - 30y}\\\\\mathsf{5625 - 45y = 4800 - 30y}\\\\\mathsf{5625 - 4800 = 45y - 30y}\\\\\mathsf{825 = 15y}\\\\\mathsf{\frac{825}{15}=y }\\\\\mathsf{55 = y}\)

There are 55 small boxes in the truck, we need to find the number of large boxes, for this we will use equation 1.

x + y = 125 (Equation 1)

x = 125 - y = 125 - 55

x = 70

Substituting both x, y into Equation 2, we have that

45x + 30y = 4800

45(70) + 30(55) = 4800

4800 = 4800

Correct!

The answer to your math homework on 2x2 equations is: The truck has 70 large boxes and 55 small boxes.

Answer:

a=29×36

Step-by-step explanation:

just do 29×36 to get your answer

Answer:

four, two

Step-by-step explanation:

1/2 of 4/3 is half of four thirds. Half of four is two, so it would be two thirds

I hope this helps! :)

We can see that the dot plot is seen below.

We can see here that An example of a graphical representation of data is a dot plot. It is a number line with dots above each value to indicate the frequency or count of that value.

Depending on the type of data being shown, the dots are often arranged either horizontally or vertically.

Dot plots are known to be useful for showing the distribution of data, particularly for small data sets.

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the last one Step-by-step explanation:

Hey sorry for the late response but:

Answer:

I think its -C  : e and f r paraller cause of alternative exterior angles ...

Step-by-step explanation:

I feel C is right as :

Option a - The lines a and b's alternative exterior angles r not congruent(as not given)

Option b- there is no such rule like tht

Option c- Yes as the alternative exterior angles r  congruent

Option d- No as there is no such rule and its not even true.

iI hope im right ..!!

(Pls tell me if im right or wrong)

The expression that is equivalent to the given quantity is \(\frac{1}{8^6}\). Therefore, option B is the correct answer.

Given that, \((8^{-2}(8^4))^{-3}\).

Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.

Using laws of exponents, solve the given expression

Now, \((8^{-2}(8^4))^{-3}\)

= \((8^{-2+4})^{-3}\) (∵ \(a^m\times a^n=a^{m+n}\))

= \((8^2)^{-3}\)

= \(8^{2\times(-3)}\) (∵ \((a^m)^n=a^{m\times n}\))

= \(8^{-6}\)

= \(\frac{1}{8^6}\) (∵ \(a^{-m}=\frac{1}{a^m}\))

The expression that is equivalent to the given quantity is \(\frac{1}{8^6}\). Therefore, option B is the correct answer.

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There are 156 almonds in the box.

We have a box for cereal consisting of raisins and almonds.

We have to find the number of almonds in the box.

In mathematics, a ratio is a comparison of two or more numbers that indicates their sizes in relation to each other.

According to the question, we have -

Ratio of raisins to almonds is - 3 : 4.

Number of raisins = 117.

Number of almonds = x.

Therefore -

3/4 = 117/x

x = (117 x 4)/3

x = 39 x 4

x = 156

Hence, there are 156 almonds in the box.

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Answer:

period = 12π

Step-by-step explanation:

the period illustrates how shifting the graph by one period to the left or right results in the same function.

starting from (0, 3 )

one complete cycle to the right from here is (12π, 3 )

then period = 12π - 0 = 12π

Step-by-step explanation:

the period of a function or graph is simply the x-distance from one "top of the hill" to the next "top of the hill", or from one "bottom of the valley" to the next "bottom of the valley".

if the function has that same distance across the whole x-axis (or whatever part is valid), we are calling this a periodic function.

in our case here :

from -9pi to 3pi = 12pi

from 3pi to 15pi = 12pi

from 15pi to 27pi = 12pi

...

so, yes, it is periodic, and the period is 12pi.

Thus, the boat travels x = 139.18 miles in North direction  and y = 143.62 miles east from the harbor.

It is possible to break down a "two-dimensional vector" into its horizontal as well as vertical parts. By using the Pythagorean theorem and the vector's magnitude as the hypotenuse of a right triangle, we may determine these components of vector.

As indicated below, we must determine how far east and north the boat has moved relative to the harbour.

X miles north:

cos 51 = x/200

x = 200*cos51

x = 139.18 miles

y miles east:

sin 53 = y/200

y = 200*sin 51

y = 143.62 miles

Thus, the boat travels x = 139.18 miles north and y = 143.62 miles east from the harbor.

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15,30 is the answer to thois promblem

Answer:

\(\displaystyle \displaystyle \int {sin(3x)} \, dx = \frac{-cos(3x)}{3} + C\)

General Formulas and Concepts:

Calculus

Antiderivatives - Integrals

Integration Constant C

Integration Property [Multiplied Constant]: \(\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx\)

Trig Integration: \(\displaystyle \int{sin(x)} \, dx = -cos(x) + C\)

U-Substitution

Step-by-step explanation:

Step 1: Define

\(\displaystyle \int {sin(3x)} \, dx\)

Step 2: Identify Substitution Variables

u = 3x

du = 3dx

Step 3: Integrate

Answer:

d. x = 7

Step-by-step explanation:

\(\frac{32}{8} = \frac{28}{x}\)

Cross multiply, the denominator "8" is multiplied by numerator "28", while the numerator "32" is multiplied by denominator "x":

8 * 28 = 224

32 * x = 32x

\(32x = 224\)

Divide both sides by 32:

\(\frac{32}{32} = \frac{224}{32}\)

[x = 7]

To find the value of N, we need the future value of the retirement fund. If you provide the desired future value, I can calculate the exact value of N.

To find the value of N, we need to calculate the number of monthly deposits Sam made for his retirement fund over 20 years.

Sam deposited $1000 every month for 20 years, which is a total of 20 x 12 = 240 deposits. Each deposit has a compounded interest rate of 5% per year, compounded monthly.

The formula to calculate the future value of a series of monthly deposits is given by:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value of the investment,

P is the monthly deposit amount,

r is the monthly interest rate, and

n is the number of deposits.

In this case, P = $1000, r = 5% / 12 = 0.05 / 12 = 0.00417 (monthly interest rate), and FV is the value of the retirement fund after 20 years.

By rearranging the formula, we can solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Plugging in the values, we get:

n = log((FV * 0.00417) / (1000 * 0.00417 + FV)) / log(1 + 0.00417)

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The correct option is,

⇒ −3 > −11; the bass is at a higher elevation than the flounder.

Option B is true.

What is Elevation?

Elevation is distance above the sea.

Given that;

A stripes bass is swimming at an elevation of −3 feet.

And, A flounder is swimming at an elevation of −11 feet.

Clearly, The bass is at higher elevation than the flounder.

So, -3 > -11

Hence, The correct option is,

⇒ −3 > −11; the bass is at a higher elevation than the flounder.

Option B is true.

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Answer:

u just asked 2 questions so..... you typed them? i really dont understand ur question but 2 + 2 =

Step-by-step explanation:

loll

Answer: you just did

Step-by-step explanation:

you just sked a question

2+2=fish

2+2=4

The sum of integers from 33 to 47 is 600.

So, the sum of integers:

Simply perform addition as follows:

Therefore, the sum of integers from 33 to 47 is 600.

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Answer:

8

Step-by-step explanation:

(4/5) / (1/10)

(4/5) * 10 = 40/5 = 8

The statement can be proved by the property of similarity and adjacent angles of a line property.

An orthocenter can be defined as the point of intersection of altitudes that are drawn perpendicular from the vertex to the opposite sides of a triangle. In a triangle, it is that point where all the three altitudes of a triangle intersect.

Given here: A triangle ABC with an orthocenter O.

Now let BD and A-F be the altitudes that intersect on the sides of AC and BC

then we have in the triangles AOD and ACF we have

∠ADO=∠AFC=90 and ∠A is common and therefore ΔAOD≈ΔACF

thus ∠AOD=∠ACF=∠ACB

now ∠ACB and ∠AOB lie on a line BD thus we must have

∠ACB +∠AOB=180

Hence, The statement  ∠ACB +∠AOB=180 is proved.

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Using common factor method, sum of the given expressions is 17.14m + 9.37

what is common factor ?

In mathematics, a common factor is a factor that two or more numbers have in common. For example, the numbers 12 and 18 have common factors of 1, 2, 3, and 6. The greatest common factor (GCF) is the largest number that divides evenly into two or more numbers.

In algebra, we often use the term "common factor" when referring to expressions. When two or more algebraic expressions have a factor in common, we can use the distributive property to factor out the common factor.

According to the question:
To add the expressions (5.19+4m)+(4.18+3.95m), we can first group the like terms:

(5.19 + 4.18) + (4m + 3.95m)

9.37 + 7.95m

So, the sum of the expressions is:

(5.19+4m)+(4.18+3.95m) = 9.37 + 7.95m

Now, we can use the distributive property to factor out a common factor of m from 7.95m:

9.37 + 7.95m = 4m + (5.19 + 7.95)m

We can factor out a common factor of 1 from (5.19 + 7.95)m:

4m + (5.19 + 7.95)m = (4 + 5.19 + 7.95)m

Adding the coefficients, we get:

4 + 5.19 + 7.95 = 17.14

Therefore, the sum of the expressions is:

(5.19+4m)+(4.18+3.95m) = (4m+5.19)+(3.95m+4.18)= 17.14m + 9.37.

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Answer:

A) 27/4 pi in^3

Explanation:

Given

Length of edge of the cube = 3in

If a cylinder is inscribed in thos cube, then;

Height of the cylinder = length of edge of the cuve = 3in

Radius of the cylinder = 3in/2 = 1.5in

Get the volume of the cylinder:

V = \pi r^2h

Substitute the given value

V = \pi (1.5)^2(3)

V = \pi * 2.25 * 3

V = 6.75\pi in^3

V = 6 75/100 \pi in^3

V = 6 3/4 \pi in^3

V = 27/4 pi in^3

Hence the volume of the cylinder is 27/4 pi in^3

Answer:

36x^2+gy^2-324=0

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

23%

Step-by-step explanation:

Answer:

N=18

Step-by-step explanation:

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Answer:

18

Step-by-step explanation:

use the concept of similarity and enlargement.

\( \frac{15}{n} = \frac{5}{6 } \)

\(n = \frac{15 \times 6}{5} \)

\(n = 18\)