Please help me solve this, and show your work

6r + 5 = 11r

&

2x-4
---------- = 6x+3
2

[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]

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

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

Answer: 3x - 5

Step-by-step explanation:

1. Expand:

7x - 14 - 4x + 9

2. Collect like terms:

(7x - 4x) + (-14 + 9)

3. Simplify:

3x - 5

Hope this helps! :)

The answer is 3x-5.

Hope this helps!

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

Answer:

P(made 2nd attempt|made 1st attempt)=P(made 2nd attempt)

Step-by-step explanation:

Here given that a basketball player that shoots 80% from the free throw line attempts two free throws.

If x is the no of shoots he makes (say) then we find that each throw is independent of the other.

In other words, because he made successful first attempt, his chances for second attempt will not change

Prob for success in each attempt remains the same as 0.80

Hence I throw is independent of II throw.

When A and B are independent,then we have

P(A/B) = P(A)

Hence answer is

P(made 2nd attempt|made 1st attempt)=P(made 2nd attempt)

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

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]

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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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: 10

Step-by-step explanation:

Find the GCF of 20 (balloons) and 30 (party horns)

20: 2 x 5 x 2

30: 2 x 5 x 3

GCF = 10

Note: There will 2 balloons and 3 party horns in each basket.

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]

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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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]

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

Answer:

IV Figure  represent the given function f(x)=[tex]\mid x+2\mid[/tex]+1.

Step-by-step explanation:

Given function

f(x)=[tex]\mid x+2 \mid[/tex]+1

The given function can be write as

f(x)=(x+2)+1=x+3 when [tex]x\geq -2[/tex]

f(x)=-(x+2)+1  when [tex]x<-2[/tex]

f(x)=-x-1     when [tex]x<-2[/tex]

Put x= 0 in the function

f(x)=x+3=0+3=3

Hence, the function intersect the y-axis at point (0,3).

Therefore, we can say I figure is false.Because in I figure the function intersect  y-axis at point (0,-3).

The function break at x=-2 .

Hence, we can say II figure and III figure  are false. Because in II figure the function break at x=2 and in III figure the function break at x=-1.

Put x=-2 in the given function

f(x)= x+3  when [tex]x\geq -2[/tex]

Therefore, f(x)= -2+3=1

Hence, IV figure is correct option.

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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Here we want to analyze some properties of the probability of getting a prize in a cereal box.

a) p(x) = (0.8)^x

b)  0.0768

c)  0.1808

d) 30 boxes in total, 28 of them without the prize.

We know that the probability for a box of having a prize is 0.2.

a) The probability of not having the prize is p = 1 - 0.2 = 0.8

And this is the probability for each one of the x boxes, remember that the joint probability will be the product of the individual probabilities, then the probability that in x boxes you don't have a prize is:

p(x) = (0.8)^x

b) The probability of only purchasing two boxes is:

p = (0.2)^2*(0.8)^2

So two have the prize and two dont, one of the boxes with a prize must be the last one, and the other box can by any of the first 3. Then we have 3 permutations, and the actual probability is:

P = 3*(0.2)^2*(0.8)^2 = 0.0768

c) This is the probability of purchasing two plus the probability of purchasing 3 plus the probability of purchasing four.

For two boxes the probability is:

p₂ = (0.2)^2 = 0.04

For 3 boxes is:

p₂ = 2*(0.2)^2*(0.8) = 0.064

Where the factor "2" represents the permutations of the first box with the prize.

For 4 boxes we know:

p₄ = 0.0768

The total probability is:

P(4)= = p₂ + p₃ + p₄ = 0.04 + 0.064 + 0.0768 = 0.1808

d) before we got the probability for getting the two prizes in a maximum of four boxes, and we got something around 18%.

We just need to keep adding boxes to that sum, until it reaches the 99.9%.

for x boxes the total probability of getting the prize witin the X boxes is:

P(x) = (0.2)^2*(1  + 2*(0.8) + 3*(0.8)^2  + 4*(0.8)^3 + ... + (x-1)*(0.8)^(x-2))

We must find X such that:

P(x) = 1.

Or, we can just find x such that the last term does not contribute anymore, this means that we can solve:

(x-1)*(0.8)^(x - 2) ≈ 0

Notice that this never does become actually equal to zero, but there is a tendency that we can see graphically below:

In the graph we can see that for x = 30, the tendency to zero starts.

This means that for x = 30 the expression (x-1)*(0.8)^(x- 2) becomes almost zero, we can evaluate that:

(30-1)*(0.8)^(30 - 2) = 0.06

This may be large compared with the numbers we saw before, but remember that this is multiplied by (0.2)^2.

This means that for around 30 boxes you are almost sure to get the two prizes you want (there will always be a really small probability that this does not happen, smaller than 5%.).

So you will get 30 boxes in total, and in 28 without prize.

If you want to learn more, you can read:

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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.

he will be 55 in 1999

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.

[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]

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:

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.