When asked his age, the algebra teacher said, “if you square my age, then subtract 23 times my age, the result is 50.” how old is he?

Answer: 0.2

Step-by-step explanation:

To calculate the distance that Joanie run during her lunch break is necessary to multiply the total distance around the outside of Cedar Park (0,8) by the 1/4 of the total distance that she ran (0,25).

So, the expression is:

0,25 . 0.8 = 0,2

Joanie run 0,2 miles during  her  lunch break.

Answer:

[tex]y=m^2-4m-45[/tex]

Step-by-step explanation:

An equation has solutions of m = –5 and m = 9

WE are given with the solution. Lets write the solution as factors

When x=a is a solution then factor is (x-a)

[tex]m=-5[/tex] is a solution. change the sign of the solution while writing factor. factor is (m+5)

[tex]m=9[/tex] is a solution, factor is (m-9)

we use the factors to find the equation

[tex]y=(m+5)(m-9)[/tex]

Multiply the factors using FOIL method

[tex]y=m^2-9m+5m-45[/tex]

[tex]y=m^2-4m-45[/tex]

False, because the difference between two negative numbers is not always negative.

Here,

Given that, The difference between two negative numbers is always negative.

We have to prove this statement is true or false.

What is Negative number?

In the real number system, a negative number is a number that is less than zero.

Now,

We can prove it false with a counter example.

Let two negative number -6 and -8.

Hence, difference between -6 and -8 is,

⇒-6 - ( -8 )

⇒-6 + 8

⇒2

it is not negative number.

Hence, the difference between two negative numbers is not always negative.

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Answer:

[tex]\dfrac{2x^2}{x} + x(100-15x)[/tex] at x=5

135

Step-by-step explanation:

Given: The expression [tex]\dfrac{2x^2}{x} + x(100-15x)[/tex]

This is rational expression of variable x.

Put x=5 into the expression and then simplify

[tex]\Rightarrow \dfrac{2\cdot 5^2}{5} + 5(100-15\cdot 5)[/tex]

[tex]\Rightarrow 2\cdot 5 + 5(100-75)[/tex]

[tex]\Rightarrow 2\cdot 5 + 5\cdot 25)[/tex]

[tex]\Rightarrow 10+125[/tex]         (Addition of two integer)

[tex]\Rightarrow 135[/tex]

Hence, The value of given expression is 135

The sin(a + b), cos(a + b) and tan(a + b) for angles a and b where sin a = 12/13 and sin b = -15/17 respectively, can be calculated using the formulas for the sine, cosine, and tangent of the sum of two angles. The results are -252/221 for sin(a+b), 56/221 for cos(a+b) and -4.5 for tan(a+b).

The given sin values represent the sides of the right triangles in terms of opposite/hypotenuse. Given we are in the second and third quadrants, where cos values are negative, we can use Pythagoras' Theorem, for example, to find cos a = -√(1 - sin²a) = -√(1 - (12/13)²) = -5/13 and analogously, we obtain cos b = -√(1 - sin²b) = 8/17.

Using the formulas for the sine, cosine, and tangent of the sum of two angles:

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Answer:

Emanuel made huis mistake in first step and step 1 is incorrect.

Step-by-step explanation:

The given expression is

[tex](\frac{3}{5})(\frac{4}{9})(-\frac{1}{2})[/tex]

It can be written as

[tex]\frac{3}{5})(\frac{4}{9})(\frac{-1}{2}[/tex]

Step 1: [tex](\frac{(3)(4)(-1)}{(5)(9)(2)})[/tex]

Emanuel used negative sign with both numbers 1 and 2. Therefore the first step of Emanuel is incorrect.

Step 2: [tex]\frac{-12}{90}[/tex]

Step 3: [tex]\frac{-2}{15}[/tex]

Therefore Emanuel made huis mistake in first step and step 1 is incorrect.

20 books / 5 months = 4 books per month

4 books  * 7 months = 28 books total

Final answer:

Two events A and B are considered independent if the probability of A given B (P(A|B)) is equal to the probability of A, and the probability of B given A (P(B|A)) is equal to the probability of B. In this case, events a and b are not independent.

Explanation:

Two events A and B are considered independent if the probability of A given B (P(A|B)) is equal to the probability of A, and the probability of B given A (P(B|A)) is equal to the probability of B.

In this case, if p(a|b) = 0.35, p(b) = 0.75, and p(a) = 0.44, we can determine if events a and b are independent by comparing the given probabilities.

To check if events a and b are independent, we need to find p(a|b) and compare it to p(a), and find p(b|a) and compare it to p(b).

p(a|b) = 0.35 means that the probability of event a occurring given that event b has occurred is 0.35. Since p(a|b) is not equal to p(a), events a and b are not independent.

Final answer:

To round 5,503,569 to the nearest hundred, observe the hundreds and the following digit. Since the following digit is a 9, round the hundreds digit up to 7 and zeros follow. The rounded number is 5,503,600.

Explanation:

To round the number 5,503,569 to the nearest hundred, we need to look at the digit in the hundreds place and the digit following it. In 5,503,569, the hundreds digit is 6, and the digit to its right is 9. According to rounding rules, if the digit right after the one we are rounding is 5 or greater, we round up. Since 9 is greater than 5, we round the hundreds place up from 6 to 7 and change all the digits to the right of the hundreds place to zero.

The final answer, therefore, is 5,503,600 when 5,503,569 is rounded to the nearest hundred.

You need to represent the number of males in terms of females.

Since you know the number of males relative to females, it makes sense to represent the number of females as a variable, let's say f.

So then the number of males is f+240 and we know that the number of males plus the number of females is 2500. Knowing this, we can write an equation: f+(f+240)=2500. I put the number of males in brackets there just to make it easy to recognize.

This equation can be condensed into 2f+240=2500 and then solved:

2f=2500−240
f=2500−2402
f=1130

Then, we know the number of females, and we can solve for the number of males from here using our male formula: males=f+240. You should then get 1370 as the number of males.

Checking this answer, we see that 1130 + 1370 does equal 2500.

The rate of change of the height of the water in the pool when the depth is 5 feet is approximately 0.089 feet per minute.

To find the rate of change of the height of the water in the pool, we can use the formula for the volume of a cylinder.

The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.

So, when the depth of the water is 5 feet, we can find the rate of change of the height by differentiating the volume equation with respect to time.

Let's calculate it:

V = π(5^2)(h)

dV/dt = π(25)(dh/dt)

Since the volume is increasing at a constant rate of 7 cubic feet per minute, we have dV/dt = 7.

Substituting the given values, we have:

7 = π(25)(dh/dt)

dh/dt = 7/π(25)

So, the rate of change of the height of the water in the pool when the depth is 5 feet is approximately 0.089 feet per minute.

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To find the rate of change of the height of the water in the pool, we can use the concept of related rates. The rate of change is approximately 0.089 cubic feet per minute.

To find the rate of change of the height of the water in the pool, we can use the concept of related rates. Let's call the height of the water in the pool 'h' and the rate of change of the height 'dh/dt'. We know that the volume of water in the pool is flowing at a constant rate of 7 cubic feet per minute, therefore the rate of change of the volume of water in the pool is also constant at 7 cubic feet per minute. The volume of a cylinder is given by V = πr^2h, where r is the radius of the pool and h is the height of the water. We can differentiate this equation with respect to time to find the rate of change of the volume.

dV/dt = πr^2(dh/dt)

Since the radius of the pool is constant at 5 feet and the rate of change of the volume is 7 cubic feet per minute, we can substitute these values into the equation and solve for dh/dt.

7 = π(5^2)(dh/dt)

dh/dt = 7/(π(5^2))

Therefore, the rate of change of the height of the water in the pool when the depth of the water is 5 feet is approximately 0.089 cubic feet per minute.

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Answer:

The explicit equation for the given geometric sequence is [tex]a_n=4(-2)^{n-1}[/tex]. The domain for the geometric sequence is all positive integers except 0.

Step-by-step explanation:

It is given that the first term of the geometric sequence is 4 and the second term is -8.

[tex]a_1=4,a_2=-8[/tex]

The common ratio for the sequence is

[tex]r=\frac{a_2}{a_1}=\frac{-8}{4}=-2[/tex]

The explicit equation for a given geometric sequence is

[tex]a_n=ar^{n-1}[/tex]

where, a is first term, n is number of term and r is common ratio.

The explicit equation for the given geometric sequence is

[tex]a_n=4(-2)^{n-1}[/tex]

Here n is the number of term. So, the value of n is must be a positive integer except 0.

Therefore the domain for the geometric sequence is all positive integers except 0.

Answer:

(10−2x)(30−2x)x

Step-by-step explanation:

I know how to explain it, but the other person's answer already has a good explanation. I'm just confirming this to be correct! :D

The number is 30+ 3x².

When an integer is multiplied by itself, the resultant number is known as its square number. Basically, a square number is a number that is obtained by the product of two same numbers. In geometry, the area of a square with 'n' as the side length (where n is an integer) is the finest example of a square number.

When an integer is multiplied by the same integer, the resultant number is known as a square number. For example, when we multiply 5 × 5 = 52, we get 25. Here, 25 is a square number. Square numbers are always positive, they cannot be negative because when a negative number is multiplied by the same negative number, it results in a positive number.

let the number be x

Now, 3 times square of a number

3x²

and, 30 increased

=30+ 3x²

Hence, the number is 30+ 3x².

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The amount of an investment of $5,000 at an interest rate of 4.5% compounded monthly for 10 years will be $7,847, rounded to the nearest whole dollar.

To determine the amount of an investment that starts at $5,000, with an interest rate of 4.5% compounded monthly for 10 years, we use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

Plugging the values into the formula:

A = 5000(1 + 0.045/12)^(12*10)

A = 5000(1 + 0.00375)^(120)

A = 5000(1.00375)^(120)

A = 5000 * 1.569463137

A = $7,847 (rounded to the nearest whole dollar)

The amount of the investment after 10 years, compounded monthly at 4.5% interest, will be $7,847.

Answer:

The graph in the attached figure

Step-by-step explanation:

Let

x------> the number of hammers

y------> the number of of wrenches

we know that

[tex]10x+6y\leq 120[/tex] -----> inequality A

[tex]x+y\geq 14[/tex] -----> inequality B    

using a graphing tool

The solution of the system of inequalities is the shaded area  

see the attached figure

Answer:

The required vertex of ∠YVT is V

Step-by-step explanation:

To find : Vertex of ∠YVT

Vertex of an angle is defined as the point about which the corresponding angle is formed or measured.

Also, the angle is formed when two rays meet or intersect is each other. so the point of intersection at which the angle is formed is called the vertex of the angle thus formed.

Now, we need to find the vertex of ∠YVT

First check by which two lines the given ∠YVT is formed.

Now, from the diagram ∠YVT is formed by meeting of the lines YV and TV

And the point of meet is V therefore, the angle is formed at V

Hence, The required vertex of ∠YVT is V