Multiply the polynomials. Simplify the answer. Show your work.
(5x^2+8x-6)(8x^2+3x+1)

To solve the given problem, we set up an equation based on the information that one number is 4 more than the other and the difference between their squares is 56. After simplifying the equation, we find that the numbers in question are 5 and 9.

Let's denote the two numbers as n and n+4.

According to the problem, one number is 4 more than the other, and the difference between their squares is 56.

We can create an equation based on this information:

(n+4)^2 - n^2 = 56

Expanding the equation:

n^2 + 8n + 16 - n^2 = 56

The n^2 terms cancel out:

8n + 16 = 56

Subtracting 16 from both sides gives us:

8n = 40

Dividing by 8:

n = 5

The other number would be:

n+4 = 5+4

n+4 = 9

So, the two numbers are 5 and 9.

Final answer:

To find the numbers, set up an equation using variables. Solve for the variables to find the values of the numbers.

Explanation:

To solve this problem, let's assign variables to the numbers. Let the first number be x. Since the other number is 4 more than the first number, we can represent it as x + 4. The difference between their squares is 56, so we can set up the equation (x + 4)² - x² = 56.

Expanding the equation, we get x² + 8x + 16 - x² = 56. Simplifying further, we have 8x + 16 = 56. Subtracting 16 from both sides, we get 8x = 40. Dividing both sides by 8, we find x = 5.

So, the numbers are 5 and (5 + 4) = 9.

y-intercept: First, find the y-intercept: it crosses the y-axis at 5 so b = 5

slope: Next, find the slope by counting the rise over run from the y-intercept to another point: the point they provided is (3, 0), which which is down 5 and to the right 3 so m = [tex]-\frac{5}{3}[/tex]

slope-intercept form: Then, insert m = [tex]-\frac{5}{3}[/tex] and b = 5 into the slope-intercept equation: y = mx + b, so y = [tex]-\frac{5}{3}x[/tex] + 5

standard form: The standard equation Ax + By = C can be found by multiplying everything by the denominator and moving Ax and By to one side and the number to the other side.  Remember that Ax must be positive.

       y = [tex]-\frac{5}{3}x[/tex] + 5

    3(y) = [tex](3)-\frac{5}{3}x[/tex] + (3)5

       3y = -5x + 15

+5x         +5x      

5x + 3y = 15

Answers: m = [tex]-\frac{5}{3}[/tex], b = 5, y = [tex]-\frac{5}{3}x[/tex] + 5, 5x + 3y = 15

Initial amount deposited (a) = $1,700.

Rate of interest (c) = 0.1% compounded quarterly =0.001 quarterly = 0.001/4 = 0.00025.

Number of years = t.

Let us assume amount after t years would be = $b.

We know, compund interest formula.

Total balance = Deposited amount (1- rate of interrest)^time.

Plugging values in formula,

[tex]b = a (1+c)^t[/tex]

We have a=$1700, c =0.00025.

Plugging those values, we get

[tex]b=1700(1+0.00025)^t[/tex]

Or

[tex]b=1700(1.00025)^t[/tex]

18.85 = 3.14d

Divide both sides by 3.14

x=6

The answer is C. 6m

For this case we have to:

The circumference or perimeter of a circle is given by:

[tex]c = \pi d\\[/tex]

where d is the diameter of the circle.

Substituting the given value of c, [tex]c = 18.85m[/tex], we have:

[tex]18.85 = \pi d\\[/tex]

[tex]d = \frac{18.85}{\pi } \\\\d = 6\\[/tex]

Therefore, the diameter of the circle is 6m.

Answer:

Option C

The values of a and b in the population function n = f(t) = a(1 + be-0.5t) are a = -40 and b = -1.5.

The population of yeast cells in a laboratory culture can be modeled by the function n = f(t) = a(1 + be-0.5t). Given that at time t = 0 the population is 20 cells and is increasing at a rate of 8 cells/hour, we can find the values of a and b.

First, substitute the given values into the equation:

20 = a(1 + be0)

Next, find the derivative of the function with respect to t to find the rate of change:

f'(t) = -0.5abe-0.5t

Since the population is increasing at a rate of 8 cells/hour, we can set the derivative equal to 8:

8 = -0.5abe-0.5(0)

Now, we have two equations:

20 = a(1 + b)

8 = -0.5ab

Solving these equations simultaneously will give us the values of a and b.

Using the first equation, we can solve for b:

b = (20/a) - 1

Substituting this value of b into the second equation:

8 = -0.5a((20/a) - 1)

Simplifying and solving for a:

a = -40

Substituting the value of a back into the first equation to solve for b:

b = (20/(-40)) - 1 = -1.5

Therefore, the values of a and b are a = -40 and b = -1.5.

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At time t = 0, the population is 20 cells and is increasing at a rate of 8 cells/hour. After solving the equation, we find that a = 20 and b = 16.

To find the values of a and b in the function n = f(t) = a(1 + be-0.5t), we can use the given information.

At time t = 0, the population is 20 cells and is increasing at a rate of 8 cells/hour.

This means that the derivative of the function with respect to time is equal to 8 at t = 0.

Using the chain rule, we can differentiate the function f(t) with respect to t and set it equal to 8 to solve for a and b.

After solving the equation, we find that the growth will be a = 20 and b = 16.

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Since you already know the solution, you need to substitute every occurrence of x and y with those values: the first equation checks out, because it becomes

[tex] 3\cdot 4 - 2 \cdot 2 = 12-4 = 8 [/tex]

The second becomes

[tex] 2 \cdot 4 + 3 \cdot 2 = Q \iff 8+6 = Q \iff Q = 14 [/tex]

Keep in mind both of these angles are equal to each other meaning the equation will have a = So...

4x+7=5(x-4)

Now multiply 5 to x and 4

4x+7=5x-20

Now subtract 4x from 5x

7=1x-20

Now add  20 to both sides

27=x

So x=27

Sugar is actually sweet and lemons are sour, both those statements are false so the answer is: F F → F

A triangle has 3 sides, a rectangle has 4, both those statements are also false, so the answer would be: F F → F

Answer:

Step-by-step explanation:

1)

We are given first statement as:

           Sugar is sour, and lemons are sweet.

This is a false statement since both the statements are opposite.

Sugar is sweet while lemons are sour.

Hence, the truth value of the given statements is:

              F  F → F

2)

The statement is given as:

A triangle has four sides, and a rectangle has three sides.

It is again a false statement since a triangle is a polygon with three sides and a rectangle is a polygon with four sides.

Hence, both the statements given in it are false.

Hence, the answer is:

                 F  F → F

Answer:

3.88

Step-by-step explanation:

The horizontal velocity in miles per minute will be 14.49 miles per minute.

The quantity which has magnitude, and direction, and follows the law of vector addition is called a vector.

A missile is fired at an angle of 75 from the horizontal. At one point, its speed was 900 mph.

Then the horizontal velocity in miles per minute will be

V = 900 x sin 75°

V = 869.33 mph

Then we have

V = 869.33 / 60 miles per minutes

V = 14.488

V ≅ 14.49 miles per minutes

More about the vector link is given below.

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Answer:  D. If an angle does not measure ninety degrees then it is not a right angle.

Step-by-step explanation:

Hi, to obtain the inverse of a conditional statement we have to negate the hypothesis and the conclusion of the conditional statement.

In this case, the hypothesis is "If an angle measures ninety degrees"

The negative form is  "If an angle does not measure ninety degrees" .

The conclusion of the statement is, "then it is a right angle."

The negative form is  "then it is not a right angle."

In conclusion, the correct option is option  D. If an angle does not measure ninety degrees then it is not a right angle.

Feel free to ask for more if it´s necessary or if you did not understand something.

In our (positional) numerical system, the first digit form the right represents the units, and going leftwards, every digit is worth 10 times more than its previous one.

So, in your number, the 9 to the right means "9 units", because it's the rightmost digit.

On the other hand, the leftmost 9 is worth 9 millions, because you shift 6 positions from the right, and the digits are worth:

In 9,000,009, the first '9' stands for nine million, and the second '9' represents nine, given its position in one's place. This is because the value of a numeral in any number varies depending on its position, which is determined by the place value concept.

In the number 9,000,009, the digit '9' appears twice - once at the beginning (in the millions place) and once at the end (in the ones place). Each position of these two '9's has a different place value based on its position.

A clear understanding of the place value concept reveals that the first '9' (from left to right) is positioned in the millions place, which means it represents nine million, or 9,000,000 in numeric representation. The second '9' is in the one's place, representing simply '9.' Therefore, the place value of 9 in the number 9,000,009 can be either nine million or nine, depending on which '9' we are referring to.

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Answer: Point-Slope

Step-by-step explanation:

Point-Slope: y - y₁ = m(x - x₁)  ; where m is the slope and (x₁ , y₁) is the point

Slope-Intercept: y = mx + b  ; where m is the slope and b is the y-intercept

************************************************************************************************

y - 2 = -3(x - 1) is in Point-Slope form where -3 is the slope and (1, 2) is the point

[tex]f(a+h)=(a+h)^2+3(a+h)+5\\\\f(a+h)=a^2+2ah+h^2+3a+3h+5\\\\[/tex]

[tex]\bf f(x)=x^2+3x+5~~ \begin{cases}f(a+h)\\x=a+h\end{cases}\implies f(a+h)=(a+h)^2+3(a+h)+5\\\\\\f(a+h)=(a^2+2ah+h^2)+(3a+3h)+5\\\\\\f(a+h)=a^2+2ah+h^2+3a+3h+5[/tex]

Solution

The general form of the equation is y = mx + b, where m is the slope and b is the y-intercept.

Given: m = 2/3 and b = 9

y = 2/3x + 9

The answer is y =2/3x + 9.

Answer:

square meters.

Step-by-step explanation:

Area = lengthxwidth for any rectangle.

If length and width are in meters area will be in square meters.

Here length = 105 m and width = 67 m

Area = 105x67 =7035sqm

Answer:

square meters

Step-by-step explanation:

its false or open because 17-8 = 9 and you cannot divide 8 by 9 so you will not find x

we are given

6 × 8 = 48

we know that

commutative property of multiplication:

[tex]a \times b =b \times a[/tex]

now, we will verify each options

option-A:

we have

6 × 8 = 48

now, we can find it's commutative

so, we get

8 × 6 = 48

so, this is TRUE

option-B:

we have

6 × 8 = 48

now, we can find it's commutative

so, we get

8 × 6 = 48

so, this is FALSE

option-C:

we have

6 × 8 = 48

now, we can find it's commutative

so, we get

8 × 6 = 48

so, this is FALSE

–31.7 + 4.5x, when x = 2.1.

-31.7 + 4.5(2.1)

-31.7 + 9.45

Myra should have multiplied 4.5 and 2.1 first.

Answer:

B.Myra should have multiplied 4.5 and 2.1 first.

Step-by-step explanation:

We are given that Myra is evaluating the expression

-31.7+4.5 x when x=21.

We have to find the error in Myra's calculation

When x=2.1

-31.7+4.5(2.1)

-31.7+9.45

=-22.25

By using DMAS rule

D=Divide

M=Multiply

A=Addition

S=Subtraction

But Myra first add  -3.7 to 4.5 then multiply

Hence, Myra should have multiplied 4.5 and 2.1 first instead of add.

Answer:B.Myra should have multiplied 4.5 and 2.1 first.

the subset of -3 and 8 is: { }, {-3}, {8}, {-3,8}, {8,-3}

Answer: First portion is greater than second portion.

Step-by-step explanation:

Time taken to hiked down a trail = 10 minutes

Change in elevation = (-) 170 feet

Speed is given by

[tex]Speed=\frac{Distance}{Time}\\\\Speed=\frac{170}{10}\\\\Speed=17\text{ feet per minute}[/tex]

Similarly,

Time taken to hiked down a trail = 20 minutes

Change in elevation = (-)220 feet

Speed is given by

[tex]Speed=\frac{Distance}{Time}[/tex]

[tex]Speed=\frac{220}{20}\\\\Speed=11\text{ feet per minutes}[/tex]

So, we can see that first portion of the hike where he hiked down a trail at a steady rate for 10 minutes and her change in elevation was (-) 170 feet, was her rate of change in elevation greater.

As 17 feet per minutes is greater than 11 feet per minutes.

[tex]f(x)=-4x^2-6x-1\\\\g(x)=-x^2-5x+3\\\\(f-g)(x)=f(x)-g(x)=(-4x^2-6x-1)-(-x^2-5x+3)\\\\=-4x^2-6x-1+x^2+5x-3=(-4x^2+x^2)+(-6x+5x)+(-1-3)\\\\=-3x^2-x-4\to\boxed{B.}[/tex]

Substitute the value of b = -2 to the expression

[tex]-4b-8+(-1)-b^2+2b^3=2b^3-b^2-4b-8-1=2b^3-b^2-4b-9\\\\2(-2)^3-(-2)^2-4(-2)-9=2(-8)-4+8-9=-16-4+8-9=-21[/tex]

900. You round up, because it is above 850. :-)

Answer:

x = 10 / (y + 4)

Step-by-step explanation: