Factor the expression. 9b2 – 25 a. (5b + 3)(5b – 3) b. (3b – 5)(3b – 5) c. (3b + 5)(3b + 5) d. (3b + 5)(3b – 5)

Answer:

okay so it would be 2 or 1.5 i dont know if you want it whole number but i will explain

if the number is 5 or more like 5.1 or even 5 you round up

if the number is under 5 like 4,3,2,1 your round down

Step-by-step explanation:

Answer:

To The Nearest Tenth : 1.5

To The Nearest Whole Number : 2

Tip:

If the number is 4 or below like 1.42 it would be rounded to 1.4

If the number if 5 or above like 2.58 it would be rounded to 2.6 or 3

I didnt know which one you wanted so I put both

Answer: 13/25

Step-by-step explanation:

The canoe's actual speed is approximately 9.66 mph at a bearing of 12° south of east.

To determine the canoe's actual speed and direction, we need to consider the vector addition of the canoe's velocity and the current.

Let's start by drawing a diagram to visualize the problem.

We'll use a scale where 1 cm represents 10 mph.

Draw a line segment representing the canoe's velocity of 10 mph at a bearing of 25° south of east.

From the endpoint of the canoe's velocity vector, draw another line segment representing the current's velocity of 2 mph at a bearing of 80° west of south.

Connect the starting point of the canoe's velocity vector with the endpoint of the current's velocity vector to form a triangle.

Next, we can find the resultant velocity (actual speed and direction) of the canoe by calculating the vector sum of the canoe's velocity and the current's velocity.

Using the law of cosines, we can find the magnitude of the resultant velocity:

c² = a² + b² - 2ab \(\times\) cos(C)

Where:

a = 10 mph (canoe's velocity)

b = 2 mph (current's velocity)

C = 80° (angle between the velocities)

Substituting the values:

c² = 10² + 2² - 2 \(\times\) 10 \(\times\) 2 \(\times\) cos(80°)

c² = 100 + 4 - 40 \(\times\) cos(80°)

Solving for c, the magnitude of the resultant velocity:

c ≈ √(100 + 4 - 40 \(\times\) cos(80°))

c ≈ √(104 - 40 \(\times\) cos(80°))

To find the direction, we can use the law of sines:

sin(A) / a = sin(C) / c

Where:

A = 25° (angle of the canoe's velocity)

a = 10 mph (magnitude of the canoe's velocity)

C = 80° (angle between the velocities)

c ≈ √(104 - 40 \(\times\) cos(80°)) (magnitude of the resultant velocity)

Substituting the values:

sin(25°) / 10 = sin(80°) / √(104 - 40 \(\times\) cos(80°))

Solving for sin(80°):

sin(80°) ≈ (sin(25°) \(\times\) √(104 - 40 \(\times\) cos(80°))) / 10

Finally, we can use the inverse sine function to find the direction:

Direction ≈ arcsin((sin(25°) \(\times\)√(104 - 40 \(\times\) cos(80°))) / 10)

Calculating the numerical values using a calculator will give us the actual speed and direction of the canoe.

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Answer:

it would be x =11*49

Step-by-step explanation:

Answer:

504

Step-by-step explanation:

The simplification of the expressions in the question using the rules of indices are as follows;

1.) 6·e⁰ + (11·f)⁰ - 5/g⁰ = 2

2. (3⁻⁴ + 5⁻³)⁻¹ = \(49\frac{31}{206}\)

3. (3⁻⁴ + 5⁻³)⁻² = \(2415\frac{32685}{42436}\)

4.) \(\dfrac{-5\cdot \left(m^{-4}\cdot n^{-5} \right)^{-3}}{10\cdot c^{-5} \cdot d^6 \cdot e^{-8}}\) = \(\dfrac{c^5\cdot e^8}{2\cdot d^5}\)

5.)  \(\dfrac{-5\cdot \left(m^{-4}\cdot n^{-5}\right)^{-3 }}{7\cdot \left(p^{-6} \cdot q^8\right)^{-4}} =\dfrac{-5\cdot m^{12}\cdot n^{15}\cdot q^{32}}{7\cdot p^{24}}\)

An index or indices is the power by which a number or variable or expression raised.

1.) 6·e⁰ + (11·f)⁰ - 5/g⁰

6·e⁰ + (11·f)⁰ - 5/g⁰ = 6 × 1 + 1 - 5/1

6 × 1 + 1 - 5/1 = 6 + 1 - 5 = 2

Therefore;

6·e⁰ + (11·f)⁰ - 5/g⁰ = 2

2.) (3⁻⁴ + 5⁻³)⁻¹

(3⁻⁴ + 5⁻³)⁻¹ = (1/(3⁴) + 1/(5³))⁻¹ = 1/(1/(3⁴) + 1/(5³))

1/(1/(3⁴) + 1/(5³)) = 1/(1/81 + 1/125) = 1/((125 + 81)/(81×125))

1/((125 + 81)/(81×125)) = (81 × 125)/(125+81) = 10125/209

10125/206 = 49 + 31/206

(3⁻⁴ + 5⁻³)⁻¹ = \(49 \frac{31}{206}\)

3.) (3⁻⁴ + 5⁻³)⁻²

(3⁻⁴ + 5⁻³)⁻² = 1/((1/3⁴ + 1/5³)²)

1/((1/3⁴ + 1/5³)²) = 1/((1/81 + 1/125)²)

1/((1/81 + 1/125)²) = 1/(((125 + 81)/(81 × 125))²)

1/(((125 + 81)/(81 × 125))²) = 1/((206/10125)²)

1/((206/10125)²) = (10125)²/(206)² = 102515625/42436

102515625/42436 = 2415 32685/42436

(3⁻⁴ + 5⁻³)⁻² = \(2415\frac{32685}{42436}\)

4.)  \(\dfrac{5\cdot (2\cdot a^{-1}\cdot b^3)^0}{10\cdot c^{-5}\cdot d^6\cdot e^{-8}}\)

\(\dfrac{5\cdot (2\cdot a^{-1}\cdot b^3)^0}{10\cdot c^{-5}\cdot d^6\cdot e^{-8}} = \dfrac{5\times 1}{10\times \left(\frac{1}{c^5}\times d^6 \times \frac{1}{e^8} \right) }\)

\(\dfrac{5\times 1}{10\times \left(\frac{1}{c^5}\times d^6 \times \frac{1}{e^8} \right) } = \dfrac{5}{10\times \left(\frac{d^6}{c^5\times e^8} \right) }\)

\(\dfrac{5}{10\times \left(\frac{d^6}{c^5\times e^8} \right) } = \dfrac{1}{2\times \left(\frac{d^6}{c^5\times e^8} \right) }\)

\(\dfrac{1}{2\times \left(\frac{d^6}{c^5\times e^8} \right) } = \dfrac{c^5\times e^8}{2\cdot d^6}\)

\(\dfrac{5\cdot (2\cdot a^{-1}\cdot b^3)^0}{10\cdot c^{-5}\cdot d^6\cdot e^{-8}}= \dfrac{c^5\times e^8}{2\cdot d^6}\)

5.) \(\dfrac{-5\cdot \left(m^{-4}\cdot n^{-5} \right)^{-3}}{7\cdot \left(p^{-6}\cdot q^8\rright)^{-4}}\)

\(\dfrac{-5\cdot \left(m^{-4}\cdot n^{-5} \right)^{-3}}{7\cdot \left(p^{-6}\cdot q^8\right)^{-4}} =\dfrac{-5\cdot \dfrac{1}{\left(\frac{1}{m^{4}}\times \frac{1}{n^{5}} \right)^{3}} }{7\cdot \dfrac{1}{\left(\frac{1}{p^{6}}\times q^8\right)^{4}} }\)

\(\dfrac{-5\cdot \dfrac{1}{\left(\frac{1}{m^{4}}\times \frac{1}{n^{5}} \right)^{3}} }{7\cdot \dfrac{1}{\left(\frac{1}{p^{6}}\times q^8\right)^{4}} } = \dfrac{-5\cdot {\left(m^4\times n^5\right)^3} }{7\cdot \left( \dfrac{p^6}{q^8\right)^{4}} }\)

\(\dfrac{-5\cdot {\left(m^4\times n^5\right)^3} }{7\cdot \left( \dfrac{p^6}{q^8\right)^{4}} } = \dfrac{-5\cdot {\left(m^{12}\times n^{15}\right)} }{7} \times \left(\dfrac{q^8}{p^6}\right)^4 }\)

\(\dfrac{-5\cdot {\left(m^{12}\times n^{15}\right)} }{7} \times \left(\dfrac{q^8}{p^6}\right)^4 } = \dfrac{-5\cdot {\left(m^{12}\times n^{15}\right)} }{7} \times \left(\dfrac{q^{32}}{p^{24}}\right) }\)

\(\dfrac{-5\cdot {\left(m^{12}\times n^{15}\right)} }{7} \times \left(\dfrac{q^{32}}{p^{24}}\right) } = \dfrac{-5\times {m^{12}\times n^{15}\times q^{32}} }{7\times p^{24}}\)

\(\dfrac{-5\cdot \left(m^{-4}\cdot n^{-5} \right)^{-3}}{7\cdot \left(p^{-6}\cdot q^8\right)^{-4}} = \dfrac{-5\times {m^{12}\times n^{15}\times q^{32}} }{7\times p^{24}}\)

6.) (3·x⁻⁴·y⁻⁵·z⁻²)⁻²

(3·x⁻⁴·y⁻⁵·z⁻²)⁻² = \(3\cdot \left(\dfrac{1}{\left(\dfrac{1}{x^4} \cdot \dfrac{1}{y^5} \cdot \dfrac{1}{z^2} } \right)^2\right)\)

\(3\cdot \left(\dfrac{1}{\left(\dfrac{1}{x^4} \cdot \dfrac{1}{y^5} \cdot \dfrac{1}{z^2} } \right)^2\right) = 3\cdot \left(x^4\cdot y^5\cdot x^2\right)^2\)

3·(x⁴·y⁵·x²)² = 3·x⁸·y¹⁰·x⁴

Therefore;

(3·x⁻⁴·y⁻⁵·z⁻²)⁻² = 3·x⁸·y¹⁰·x⁴

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Answer:

the answers are three sides, closed figure and at least two sides the same length

Step-by-step explanation:

The attributes that represent the isosceles triangle should include three sides, a closed figure, and at least two sides of the same length.

In terms of geometry, the isosceles triangle refer to the triangle where it does have two sides of the equal length. Also, it have exactly two sides of equivalent length.

Therefore, we can conclude that The attributes that represent the isosceles triangle should include three sides, a closed figure, and at least two sides of the same length.

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Answer:

\(\sqrt[3]{125^2} \\\)= 125^2/3

125^2/3=25

So Jen is correct

Given the image in the question, it can be seen that the roof forms a right angled triangle. Therefore, we can get the length of the roof rafters (x) by using the Pythagoras theorem.

Step 1: We define the Pythagoras theorem and state our parameters

Step 2: We substitute the values into the theorem to solve for x

Hence, the length of the roof rafters (x) is 33.94ft to the nearest hundredth.

Answer: 1.

PEMDAS

Parenthesis- (8÷4) +12

2.You should multiply first because of the math pharse

PEMDAS

parenthesis, exponents, multiplication, division, addition, subtraction

You do whichever is first in this order.

Step-by-step explanation:Sorry if number one might be wrong

Using an algebraic equation to represent the word problem, the smallest integer is 1

This is a way of representing mathematical problems with words. To solve this, we have to use algebraic equations or expressions.

Let the integers be represented as

We can write an equation from the word problem given as

7 × (x + 2) = 15 + [x + (x + 4)]

7x + 14 = 15 + x + x + 4

7x + 14 = 15 + 2x + 4

collect like terms

7x - 2x = 15 - 14 + 4

5x = 5

Divide both sides by coefficient of x

5x / 5  = 5 / 5

x = 1

The smallest integer is 1

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Translation:

Find the smallest of three consecutive odd integers such that 7 times the middle integer is 15 more than the sum of the first and third integers

Step-by-step explanation:

4a - 7a + 9a

6a

I think this should be the answer

Answer:

The answer is

Step-by-step explanation:

√16a - √49a + √81a

Simplify the surds

That's

(√16)(√a) - (√49)(√a) + (√81)(√a)

Which is

4√a - 7√a + 9√a

= 4√a + 2√a

Hope this helps you

Answer:

  30%: 35 liters

  50%: 35 liters

Step-by-step explanation:

The desired concentration is halfway between the concentrations of available solutions, so the mixture will be equal amounts of each.

  35 liters of 30% acid and 35 liters of 50% acid must be used

_____

If you want to write an equation, it usually works well to let the variable represent the amount of the most concentrated constituent: 50% acid. Then the amount of acid in the final mix is ...

  0.50x +0.30(70 -x) = 0.40(70)

  0.20x +21 = 28 . . . . simplify

  0.20x = 7 . . . . . . . . . subtract 21; next, divide by 0.20

  x = 35 . . . . . . amount of 50% solution (liters)

  70-x = 35 . . . amount of 30% solution (liters)

Solving a third-degree equation implies testing some possible solutions until we find them all.

The equation to solve is:

Dividing the factors of the independent coefficient by the factors of the leading coefficient will give us some candidates solutions:

+/- 6, +/-3, +/- 2, +/- 1

Testing x = -1

The equation is verified, so x = -1 is a solution.

Testing x = 1

The equation does not verify, so x = 1 is not a solution.

Testing x = 2

x = 2 is a solution.

Finally, testing x = -3

The real zeros are x = -1, x = 2, x = -3.

Factoring:

Answer:

x = 15

y = 15√3

Step-by-step explanation:

This is a special right triangle with angle measures 30° 60° 90°

The side lengths should be x 2x x√3

If the measure of hypotenuse 30 then the side length that sees 30° should be half of it so x = 15 and y = 15√3

Answer:

12, 14, 16

Step-by-step explanation:

Let's say x is the lowest number:

x+x+2+x+4=42

Simplify the equation:

3x+6=42

Subtract 6 on each side to isolate 3x:

3x=36

x=12

So the lowest number is 12, which means the next number(x+2) would be 14, and the following number(12+4) would be 16.

Happy learning!

--Applepi101

Answer:

let x be = three consecutive even numbers

x, (x+2),(x+4) = 42

x+x+2+x+4 = 42

3x+6 = 42

3x = 42-6

3x = 36

x = 12

so the first consecutive number is x = 12

second consecutive number is x+2 = 14

third consecutive number is x+4 = 16

Answer:

28.52

Step-by-step explanation:

105.87 - 77.35 = 28.52

Missing side in the triangle is equal to \(\boldsymbol{5}\) units.

A triangle is a polygon that consists of three sides.

A right angled triangle in which one angle is equal to \(\boldsymbol{90^{\circ}}\)

Area of a triangle \(=\boldsymbol{\frac{1}{2}bh}\) where \(b,h\) denote base and height of a triangle respectively.

So,

\(25=\frac{1}{2}(10)h\)

  \(h=\frac{50}{10}\)

     \(=\boldsymbol{5}\) units

So, missing side is equal to \(\boldsymbol{5}\) units.

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The y-intercept of any function is the value of the function when x = 0.

Therefore, g(x) has the greatest y-intercept.

Answer:

nice

Step-by-step explanation:

whats the rest of the problem or is it just that she rolled a dice

Answer: The minuend is 20000

Step-by-step explanation:

To calculate the minuend, we use the equation:

\(\text{Subtrahend}=\text{Minuend-Difference}\)

We are given:

Difference between the two numbers = 7194

Subtraend = 12806

Putting values in above equation, we get:

\(\text{Minuend}=12806+7194\\\\\text{Minuend}=20000\)

Hence, the minuend is 20000

(a) The maximum number of snack bags he could make,

= 18 snack bags.

(b) 18 juice boxes.

(c) 18 cookies in each bag.

The greatest number that can divide the numbers in equal parts.

It is called as greatest common factor.

Given:

Brady is making snack bags with 18 juice boxes and 27 cookies.

He wants each bag to have the same number of juice boxes and the same number of cookies.

(a) The maximum number of snack bags he could make,

= GCF(18, 27)

= 18 snack bags.

(b) 18 juice boxes.

(c) 18 cookies in each bag.

Therefore, all the required values are given above.

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Answer:

-25+? = -5

cross -5 over and it the negative sign would turn to postive sign

-25+(5)=?

Therefore answer = 20

To confirm this answer

-25+20= -5

Using Pythagorean theorem, the length of the ladder is 10ft

In mathematical terms, if y and z are the lengths of the two shorter sides (also known as the legs) of a right triangle, and x is the length of the hypotenuse, the Pythagorean theorem can be expressed as:

x² = y² + z²

In the questions given, the only one we can use Pythagorean theorem to solve is the one with ladder since it's forms a right-angle triangle.

To calculate the length of the ladder, we can write the formula as;

x² = 8² + 6²

x² = 64 + 36

x² = 100

x = √100

x = 10

The length of the ladder is 10 feet

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Answer: \(m\angle 2=75^{\circ}, m\angle 1=105^{\circ}\)

Step-by-step explanation:

By the alternate interior angles theorem, \(m\angle 2=75^{\circ}\).

Using linear pairs, \(m\angle 1=105^{\circ}\).

Answer:

3,952 ft

Step-by-step explanation:

Use the sine function since you need to find the hypotenuse but know the opposite side of the angle, since sine is equal to opposite/hypotenuse.

sin8°=\(\frac{550}{c}\)

csin8°=550

c=550/sin8°

c= 3,952

Answer:

A. 0.78 and 1.255.

B.  0.095

C. -0.475

Step-by-step explanation:

The given regression line is

y=-0.17+0.095x

A.

The true average flow rate for a pressure drop of 10 inch can be computed by putting x=10 in above equation.

y=-0.17+0.095*10

y=-0.17+0.95

y=0.78

The true average flow rate for a pressure drop of 10 inch is 0.78.

The true average flow rate for a pressure drop of 15 inch can be computed by putting x=15 in above equation.

y=-0.17+0.095*15

y=-0.17+1.425

y=1.255

The true average flow rate for a pressure drop of 15 inch is 1.255.

B.

The slope represents average change in y due to unit change in x.

So, the true average change in flow rate associated with a 1 inch increase in pressure drop is 0.095(1)= 0.095.

C.

When pressure drops decreases by 5 in. then the average change in flow rate is 0.095(-5)=-0.475.

The flow rate in the device is an illustration of average rates.

The function is given as:

\(\mathbf{y = -0.17 + 0.095x}\)

(a) The true average flow rate when pressure drops 10 and 15 in

When x = 10, we have:

\(\mathbf{y = -0.17 + 0.095 \times 10}\)

\(\mathbf{y = 0.78}\)

When x = 15, we have:

\(\mathbf{y = -0.17 + 0.095 \times 15}\)

\(\mathbf{y = 1.255}\)

Hence, the true average flow rates when pressure drops 10 and 15 in are 0.78 and 1.255 respectively

(b) The true average flow rate when pressure increases by 1 in

This simply represents the slope of the function.

The function is given as:

\(\mathbf{y = -0.17 + 0.095x}\)

A linear regression equation is represented as:

\(\mathbf{y = b + mx}\)

Where m represents the slope

By comparison:

\(\mathbf{m = 0.095}\)

Hence, the true average flow rates associated to a 1 in pressure increment is 0.095

(c) The average change in flow rate when pressure drops decreases by 5 in

The domain of the function is given as:

\(\mathbf{x = 5\ to\ 20}\)

A decrement of -5 in means: x = -5

This is out of the domain of the function

Hence, the average change at a decrement of 5 in cannot be calculated

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Answer: 28 pairs

Step-by-step explanation:

12 times 5 is 60, so she has 60 pairs in total. She gives 32 pairs to one son, so 60-32 is 28. The other son receives 28 pairs of socks.

Answer:

Step-by-step explanation: