PLEASE HELP. Prove that the value of the expression: b (36^5−6^9)(38^9−38^8) is divisible by 30 and 37.

Answer: There are 180 dogs in the shelter.

Step-by-step explanation:

Let be "c" the number of cats in the shelter and "d" the number of dogs in the shelter.

You know that the total number of dogs and cats in the animal shelter is 275. Then you can express this with:

[tex]d+c=275[/tex]

If the number of cats is 5 more than one half of the number of dogs, you can express it with:

[tex]c=\frac{d}{2}+5[/tex]

Then, substitute [tex]c=\frac{d}{2}+5[/tex] into [tex]d+c=275[/tex] and solve for "d" to calculate the number of dogs that are in the shelter. Then:

[tex]d+c=275\\\\d+\frac{d}{2}+5=275\\\\d+\frac{d}{2}=275-5\\\\\frac{2d+d}{2}=270\\\\\frac{3d}{2}=270\\\\3d=270*2\\\\d=\frac{540}{3}\\\\d=180[/tex]

X is 3

Refer to picture

The answer is:

[tex]A(13)=107.37Km^{2}[/tex]

We can calculate the area of the lake after 13 years using the following equation:

[tex]A(t)=A(initial)(1-ShrinkingRate)^{t}[/tex]

Where,

A(t), is the area after t time (years)

A(Initial), is the initial area

Shrinking Rate, is the rafe of shrinking and it's 6% or 0.06.

t, is the time

So, substituting we have:

[tex]A(13)=240(1-0.06)^{13}=240*0.447=107.37Km^{2}[/tex]

So, the are after 13 years will be:

[tex]A(13)=107.37Km^{2}[/tex]

Have a nice day!

Answer: GCF = x

Step-by-step explanation:

x(x^3/x + x^2/x + -6x/x)

x(x^2 + -6)

x(x - 2)(x + 3)

Answer:

x(x + 3)(x - 2)

Step-by-step explanation:

Factor out x from each term

= x(x² + x - 6)

To factor the quadratic

Consider the factors of the constant term (- 6) which sum to give the coefficient of the x - term (+ 1)

The factors are + 3 and - 2, since

+ 3 × - 2 = - 6 and + 3 - 2 = + 1, hence

x² + x - 6 = (x + 3)(x - 2)

---------------------------------------

x³ + x² - 6x = x(x + 3)(x - 2) ← in factored form

To find the slope of a line passing through the origin and a point, use the formula slope = (y2 - y1)/(x2 - x1). For a line passing through origin and the point (-8,-5), the slope is 5/8.

The topic at hand revolves around the concept of slope and the algebra of straight lines. The slope is calculated by finding the change in y (vertical axis) over the change in x (horizontal axis). To find the slope of a line passing through the origin and the point (-8,-5), use the formula slope = (y2 - y1)/(x2 - x1).

In this case, the origin is point (0,0) and the given point is (-8,-5). So to find the slope, we substitute these values into the slope formula: slope = (-5 - 0)/(-8 - 0) = 5/8. Therefore, the slope of the line passing through the origin and the point (-8,-5) is 5/8.

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The slope of the line is 5/8.

The slope of a line, denoted by m, represents the rate of change between the vertical and horizontal components of two points on the line.

To find the slope of a line passing through the origin and intersecting the point (-8, -5), we can use the slope formula. The slope formula is given by: m = (y2 - y1) / (x2 - x1).

Plugging in the values from the given point gives: m = (-5 - 0) / (-8 - 0)

= -5 / -8

= 5/8.

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Answer:

145°

Step-by-step explanation:

The angle is 90°+55°=145°

Answer: 145°

Step-by-step explanation:

The angle of straight lines is always 180°, so I took 180 and subtracted 55 from it, and then 90 to get 35. I got 90 because the x and y axis are perpendicular to each other, and the angle between perpendicular lines is always 90. 35° is the angle of the small un marked section to the left of the circles, so to get the angle of the circle-like line, I did 180-35 to get 145°.

p(x) * r(x) = ab^x * cd^x

p(x) * r(x) = (a*c)*(b^x*d^x)

p(x)*r(x) = ac(bd)^x

For the last step, I used the rule that (ab)^x = a^x*b^x

The product of two exponential functions p(x) = ab^x and r(x) = cd^x is calculated by following the rules of exponents in mathematics, resulting in p(x) * r(x) = a * c * (bd)^x

The student is asking for the product of two exponential functions. If p(x) = ab^x and r(x) = cd^x, their product can be calculated as follows:

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Answer:

x=1

Step-by-step explanation:

8x+4y=12y

-4y         -4y

8x=8y

x=1

Answer:

x=5, y=22.36, z=11.18

Step-by-step explanation:

Use mean extremes

10^2=sqrt(20x)

Solving x = 5

for y:

y=sqrt(20(20+5))=22.36

for z:

z=sqrt(5(20+5))=11.18

5/15 or 1/3 would be the correct answer

Answer:

Equation: $21.50•n=c

Answer:

[tex](2,200\pi +8,000)\ ft^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the figure is equal to the volume of cube plus the volume of the cylinder

step 1

Find the volume of the cube

The volume of the cube is equal to

[tex]V=b^{3}[/tex]

we have

[tex]b=2(10)=20\ ft[/tex] ----> the length side of the cube is equal to the diameter of the cylinder

so

[tex]V=20^{3}=8,000\ ft^{3}[/tex]

step 2

Find the volume of the cylinder

The volume of the cylinder is equal to

[tex]V=\pi r^{2} h[/tex]

we have

[tex]r=10\ ft[/tex]

[tex]h=42-20=22\ ft[/tex]

substitute

[tex]V=\pi (10)^{2} (22)[/tex]

[tex]V=2,200\pi\ ft^{3}[/tex]

step 3

The volume of the figure is equal to

[tex](2,200\pi +8,000)\ ft^{3}[/tex]

The volume of the figure = volume of oblique cylinder + volume of cube = 2,200π + 8,000 cubic feet.

Volume of oblique cylinder = πr²h [radius of cylinder = r].

The volume of the figure = volume of oblique cylinder + volume of cube = πr²h + s³

Given the following:

Plug in the values into πr²h + s³:

The volume of the figure = π(10²)(22) + 20³

The volume of the figure = 2,200π + 8,000 cubic feet.

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Answer:

Step-by-step explanation:

Tracey Earns in week= $102.45

Tracy=2x-12.45

102.45=2x-12.45

2x= 102.45+12.45

2x=114.90

x= 114.90/2

x=$57.45

Kayla earns 57.45 dollars

The equation is n = (102.45 + 12.45) x 2.

And Kayla earns $229.8.

Two algebraic expressions having same value and symbol '=' in between are called as an equation.

Given:

In a week, Tracey earns $12.45 less than twice the amount Kayla earns. Tracy earns $102.45.

Let n be the amount Kayla earns.

Then,

Kayla earns,

n = (102.45 + 12.45) x 2

n = $229.8

Therefore, Kayla earns $229.8.

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Answer:false

Step-by-step explanation: divide each side by 7 you get b ≤ -7. The red line needs to go the other way since it is less than

Answer:

False, it is incorrect

Step-by-step explanation:

7b≤ -49

Divide by 7

7b/7 ≤-49/7

b ≤-7

We have a closed circle at -7  (closed because of the equals)

b is less than so the lines goes to the left

Answer:

The product of the slopes of line a and line is -1.

Perpendicular lines a and b intersect at a right angle, or 90 degrees. This is independent of whether they are increasing or decreasing, or their steepness on a graph.

The statement about lines a and b that is true when they are perpendicular is that they form a 90-degree angle with each other. The concept of perpendicularity in geometry refers to lines, planes, or surfaces that intersect at a right angle.

Terms like increasing or decreasing line or the steepness of a line do not apply here as they pertain to the slope of the line in the context of a graph, which is distinct from the concept of perpendicularity.

For example, saying line A is a decreasing line while line B is an increasing line, does not describe their perpendicular relationship. Instead, they intersect or meet at a right angle (90 degrees), proving their perpendicular nature.

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Well, this is just a big guess, but probably the most sense-able, B) 400 ft²

To simplify the expression, combine the exponents and evaluate the values to get the simplified expression 1/12.

To simplify the expression, we can combine the exponents of the same base. Let's break it down step-by-step:

So, the simplified expression is 4-1 * 3-1 * 40. Any number raised to the power of 0 is equivalent to 1, so the expression can be further simplified to 4-1 * 3-1 * 1. Finally, we can evaluate the values: 4-1 = 1/4, and 3-1 = 1/3.

Therefore, the simplified expression is (1/4) * (1/3) = 1/12.

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The expression [tex]\(\frac{4^{-3} \times 3^4 \times 4^2}{3^5 \times 4^{-2}}\)[/tex] simplifies to [tex]\(\frac{4}{3}\).[/tex]

To simplify the expression [tex]\(\frac{4^{-3} \times 3^4 \times 4^2}{3^5 \times 4^{-2}}\)[/tex], follow these steps:

So the simplified expression is [tex]\(\frac{4}{3}\)[/tex] .

Corrected question:

What is the simplified expression for [tex]\(\frac{4^{-3} \times 3^4 \times 4^2}{3^5 \times 4^{-2}}\)[/tex]

Answer:

0.8 cup(s)

Step-by-step explanation:

2 x 0.4 = 0.8

Answer:

0.8

Step-by-step explanation:

So to get this answer you had to mulyiply the 2 cups of flour by the size you want which is 0.4 . 2(0.4)=0.8

Answer:

$2280

Step-by-step explanation:

I see you've already found part a, which is to find the amount of interest earned. The next part is easy, to find the balance of the account after four years, just add the interest you've found back to the principal (the original size of the account or loan). $2000 + $280 equals $2280.

The interest earned on the account is $280. The balance of the account after 4 years is $2280.

To find the interest earned on the account, we use the formula for simple interest:

I = PRT

where:

Substituting the given values:

I = $2000 * 3.5/100 * 4 = $280

To find the balance of the account, we add the interest earned to the principal:

Balance = P + I = $2000 + $280 = $2280

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The awnser is 20 x 3

Hope this helps!

The area of a rectangle with length 4x^3 and width 5 is expressed as the monomial 20x^3 by multiplying the length and width.

To express the area of a rectangle as a monomial when given the length and width, we simply need to multiply these two dimensions together. In this case, the rectangle has a length of 4x^3 and a width of 5. The area (A) of a rectangle is given by the formula A = length * width.

So, the area of this rectangle can be calculated as:

A = 4x^3  * 5

Now, we multiply the numerical coefficients (4 and 5) and then combine them with the variable part:

A = (4 * 5) x^3

A = 20x^3

This expression, 20x^3, represents the area of the rectangle as a monomial

Answer:

The answer to 4-3 is 1.

Step-by-step explanation:

The quadratic code '4 - 3' corresponds to the mathematical expression "4 minus 3," which equals 1.

The quadratic equation '4 - 3' is a simple algebraic equation that can be decoded as follows:

Start with the number 4.

Subtract 3 from it.

So, the decoded mathematical expression is:

4 - 3 = 1

The result is 1.

Therefore, the quadratic code '4 - 3' corresponds to the mathematical expression "4 minus 3," which equals 1.

This demonstrates how to decode and interpret a simple algebraic expression, showing that when you subtract 3 from 4, the result is 1.

It's a basic example of performing arithmetic operations on numbers.

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The probable question may be:

Decode the quadratic expression '4 - 3​' to reveal the mathematical expression it represents. Provide the complete mathematical expression that corresponds to the given quadratic code.

Answer:

Step-by-step explanation:

4b-1=b

3b-1=0

3b=1

b=1/3

24b=

24(1/3)=

8

Equations are expression separated by an equal sign. The value of 24b if 4b-1 = b is 8

Equations are expression separated by an equal sign

Given the expresion

4b - 1 = b

Find the value of "b"

4b - b = 1

3b = 1

b = 1/3

Determine the value of 24b

24b = 24(1/3)

24b = 8

Hence the value of 24b if 4b-1 = b is 8

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Answer:

2

Step-by-step explanation:

3(2)+30=36

ANSWER

A. (x+4)

EXPLANATION

The given binomial is

[tex] {x}^{2} + 12x + 32[/tex]

Split the middle term:

[tex] {x}^{2} + 8x + 4x + 32[/tex]

Factor;

[tex]x(x + 8) + 4( x + 8)[/tex]

Factor further;

[tex](x + 8)(x + 4)[/tex]

Therefore

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

is a factor.

Answer:   c) 286.5 in²

Step-by-step explanation:

S.A.= 2π r · h

      = 2π (7.3/2) · 12.5

      = 2π (3.65) (12.5)

      = 286.5

Answer:

C

Step-by-step explanation:

In translating graphs of functions, we can follow 2 rules:

1. The graph of  [tex]f(x)+a[/tex] is the graph of  [tex]f(x)[/tex] shifted a units UP VERTICALLY and the graph of   [tex]f(x)-a[/tex] is the graph of  [tex]f(x)[/tex] shifted a units DOWN VERTICALLY.

2. The graph of  [tex]f(x+a)[/tex]  is the graph of   [tex]f(x)[/tex]  shifted a units to the LEFT HORIZONTALLY and the graph of  [tex]f(x-a)[/tex]  is the graph of  [tex]f(x)[/tex]  shifted a units RIGHT HORIZONTALLY.

If we understand the 2 rules above, we clearly know that f(x+2) will be a horizontal shift to the LEFT, of course, with respect to the function  [tex]f(x)=x^3[/tex]. Looking at the answer choices, C is right.

Answer:15

Step-by-step explanation:h=2 A/b meaning h=2 67.5/9

Answer:

h = 15 meters

Step-by-step explanation:

The area of a triangle is determined by its height multiplied by its base.

The equation is A = 1/2*bh.

Plugging in the numbers gives us 67.5 = 1/2*9h.

Dividing by 4.5 in both sides gives us that h = 67.5/4.5 = 15 meters.

Answer:

option C is the correct answer

Step-by-step explanation:

The trigonometric equation you are using has a general form

y = A* tan w*(x - r)

Where

A is the amplitude of the function

w is the frequency rad/s

r  is the phase shift

In your case

A = -2

The frequency is

w = (2*pi)/period

period = pi/4

w = 8

r = -pi/2

y = -2* cos 8*(x + pi/2)

Answer:

Step-by-step explanation:

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