Brandy is trying to factor the quadratic $3x^2 - x - 10.$ She starts by assuming that the quadratic factors as \[3x^2 - x - 10 = (x + B)(3x + D),\]for some integers $B$ and $D.$ After some work, Brandy successfully factors the quadratic. Find the ordered pair $(B,D).$

Answer: [tex]\bold{(A)\ \dfrac{\text{51 miles}}{\text{1 hour}}}[/tex]

Step-by-step explanation:

Consider the formula "distance (d) = rate (r) x time(t)" and solve for r.

d = r · t

÷ t  ÷ t  

[tex]\dfrac{d}{t}=r[/tex]

Now plug in the given d and t values from the table to solve for r:

[tex]r=\dfrac{\text{204 miles}}{\text{4 hours}}[/tex]

    [tex]=\dfrac{\text{51 miles}}{\text{1 hour}}[/tex]   simplified the fraction

You can check this by plugging in the other 3 values from the table:

[tex]r=\dfrac{\text{306 miles}}{\text{6 hours}}[/tex]

    [tex]=\dfrac{\text{51 miles}}{\text{1 hour}}[/tex]  

[tex]r=\dfrac{\text{408 miles}}{\text{8 hours}}[/tex]

    [tex]=\dfrac{\text{51 miles}}{\text{1 hour}}[/tex]  

[tex]r=\dfrac{\text{510 miles}}{\text{10 hours}}[/tex]

    [tex]=\dfrac{\text{51 miles}}{\text{1 hour}}[/tex]  

Answer:

2. It can be solved by using the multiplication property of equality.

3. The equation should be: [tex]\frac{x}{18}=109.8[/tex]

6. The answer is 1,976.4.

Step-by-step explanation:

Let x be the number.  

We have been given that the quotient of a number and 18 is 109.8.

Since we know that in a division problem the number which is being divided called dividend and by which number we divide is called divisor.

[tex]\text{Dividend}\div \text{Divisor }=\text{ Quotient}[/tex]

We can represent our given information as:

[tex]\frac{x}{18}=109.8[/tex]

By using multiplication property of equality we will get,

[tex]18*\frac{x}{18}=18*109.8[/tex]

[tex]x=18*109.8[/tex]

[tex]x=1976.4[/tex]

Upon looking at our given choices we can see that 2nd, 3rd and 6th statements are correct choices.

Answer:

4/15

Step-by-step explanation:

Experimental probability is the actual times the event occurs divided by the number of trials

Actual times : 8

Number of trials: 30

Experimental probability of a 2: 8/30 = 4/15

Answer: ITS B

Step-by-step explanation:

Answer:

D) y = -1/3 x+6

Step-by-step explanation:

If we want to find a line parallel to 3x+9y=7, the slopes will have to be the same because parallel lines have the same slope.  Knowing y= mx+b we need to find the slope of the old line.

3x+9y=7

Subtract 3x from each side

3x-3x +9y = -3x+7

9y = -3x+7

Divide each side by 9

9y/9 = -3x/9 + 7/9

y = -1/3 x + 7/9

We know the slope of the  old line is -1/3, so the slope of the parallel line is -1/3.

If we know the slope of the line and a point, we can use the point slope form of a line

y-y1 = m(x-x1)

y-4 = -1/3(x-6)

Distribute the -1/3

y-4 = -1/3 x -1/3*-6

y-4 = -1/3x +2

Add 4 to each side

y-4+4 = -1/3x +2+4

y = -1/3x+6

Answer:

x ---> 1

y ---> 5

Step-by-step explanation:

We are given paired values for two variables x and y and we are to determine the constant number by which each term is increased such that they are in a proportional relationship.

For x, we have the following paired values:

[tex]x: 1, 2, 3, 4[/tex]

So here the difference between each consecutive term is 1 so the constant is 1.

And for y, we have:

[tex]y: 5, 10, 15, 20[/tex]

In this case, the difference between each consecutive term is 5 so the constant is 5.

Answer:

20%

Step-by-step explanation:

Percentage means out of 100

We need to get 2/10 to be out of 100

Multiply by 10/10

2/10*10/10

= 20/100

This is 20%

Answer:

3

Step-by-step explanation:

The zero at the point x=3 is a result of a factor of even degree, because the function does not change sign as the value of (x -3) changes sign. Since a cubic only has 3 factors, the even degree must be 2. That is, (x -3)² is a factor of f(x) and the root at x=3 has multiplicity 2.

Answer:

[tex]\frac{5}{8}[/tex]

Step-by-step explanation:

We have been given that our Einstein has baked a cake and cut it into 8 slices. So each slice will be equal [tex]\frac{1}{8}[/tex].

He hands out 3 slices to his guests. Let us find out part of the cake given to guests.

[tex]\text{The part of the cake given to guests}=\frac{1}{8}+\frac{1}{8}+\frac{1}{8}[/tex]

[tex]\text{The part of the cake given to guests}=\frac{1+1+1}{8}[/tex]

[tex]\text{The part of the cake given to guests}=\frac{3}{8}[/tex]

To find the fraction of left cake we will subtract [tex]\frac{3}{8}[/tex] from 1 as Einstein has 1 whole cake.

[tex]\text{fraction of cake is left}=1-\frac{3}{8}[/tex]

[tex]\text{fraction of cake is left}=\frac{8}{8}-\frac{3}{8}[/tex]

[tex]\text{fraction of cake is left}=\frac{8-3}{8}[/tex]

[tex]\text{fraction of cake is left}=\frac{5}{8}[/tex]

Therefore, [tex]\frac{5}{8}[/tex] of the cake is left.

Answer:

As per the given statement: Our Einstein has baked a cake and cut it into 8 slices.

⇒ Total slice of cake Einstein has baked = 8

Also, it is given that if he hands out 3 slices to his guests.

⇒ Number of slice he hands out to his guests = 3

Remaining slice of a cake Einstein left with = 8 -3 = 5.

We have to find the fraction of the cake is left.

Fraction states that a fraction is a number that represents a part of a whole. Also, It consists of a numerator and a denominator, where numerator represents the number of equal parts of a whole, while the denominator is the total number of parts.

Fraction of the cake is left = [tex]\frac{\text{Slices of cake left}}{\text{Total number of slices of a cake}}[/tex]

Substitute the given values we get;

[tex]\text{Fraction of the cake is left} =\frac{5}{8}[/tex]

therefore, the fraction of the cake is left is,  [tex]\frac{5}{8}[/tex]

Answer:

f(x) = 2x

Step-by-step explanation:

Remark

What I'm about to do is probably not the best way to do this question, but it is right. The plan is to take out a common factor on the right of f(x - 2) and then derive f(x) from that.

Solution

Check

Final answer:

To find f(x), replace x - 2 with y to get f(y) = 2(y + 2) - 4, simplify to f(y) = 2y, then revert y back to x to find f(x) = 2x.

Explanation:

To find the function f(x) when you know that f(x - 2) = 2x - 4, you need to replace x - 2 with y so that x = y + 2. Therefore, f(y) = f(x - 2) = 2x - 4 becomes f(y) = 2(y + 2) - 4.

Simplifying this, we get:
f(y) = 2y + 4 - 4
f(y) = 2y.

Now, to revert back to the original function, replace y with x to get f(x) = 2x. This is the function we were looking to find.

Final answer:

Starting with Saul in the 3rd position and counting the 3 children between him and Enid, Enid is determined to be in the 7th position in the line.

Explanation:

To find the position of Enid in line, we start with Saul who is third in line. If there are 3 children between Saul and Enid, and Enid is last, we need to count the positions:

Saul is 3rd in line.

1st child after Saul is in the 4th position.

2nd child after Saul is in the 5th position.

3rd child after Saul is in the 6th position.

Enid is after the 3rd child, placing her in the 7th position.

Therefore, Enid is in the 7th position in line.

Final answer:

To subtract the polynomials, we subtract the coefficients of like terms: the a⁴ terms give -4a⁴, there are no changes to the ab² term since it's not present in both polynomials, and for the a terms, we get 46a. So, the result is -4a⁴ + 2ab² + 46a.

Explanation:

The question asks us to perform polynomial subtraction. Specifically, the question requires subtracting 7a⁴ - 4a²b² + 67a from 3a⁴ + 2ab² + 113a. To do this, we subtract the coefficients of like terms, which are terms with the same variable raised to the same power.

Let's subtract step-by-step:

Putting it all together, the result of our subtraction is -4a⁴ + 2ab² + 46a.

Answer:

There were 275 computers

Step-by-step explanation:

Computers replaced = total computers * percent replaced

What do we know?

The percent replaced is 20  = .2

55 computers were replaced.

Substitute this in

55 = total computers * .2

Divide each side by .2

55/.2 = total computers *.2 /.2

275 = total computers

There were 275 computers

Answer:

Step-by-step explanation:

Answer:

there would be 420 cards in total

Step-by-step explanation:

Answer:

The numbers are 8 and 13

Step-by-step explanation:

In order to find this, we set the smaller number as x. Then we can set the larger one as x + 5, since it is 5 more than the smaller.

Given these two, we can then set them equal to 3x - 3, since the answer is three less than three times the larger.

x + x + 5 = 3x - 3

2x + 5 = 3x - 3

5 = x - 3

8 = x

Now to find the larger number, put into the larger number equation.

x + 5

(8) + 5

13

The numbers are 8 and 13.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The algebraic expression is,

''One number is five more than another and their sum Is there less than three times the smaller''.

Now,

Let the smaller number = x

Then, The another number = x + 5

Write the expression as;

x + x + 5 = 3x - 3

2x + 5 = 3x - 3

2x - 3x = - 3 - 5

- x = - 8

x = 8

And, The another number = x + 5

                                        = 8 + 5

                                        = 13

Thus, The numbers are 8 and 13.

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180-(x+50)+180-4x+180-(2x+40)+180-3x=360

720-x-50-4x-2x-40-3x=360

630 - 10x=360

-10x=360-630

-10x=-270  /:(-10)

x=27

This problem deals with dependent events in probability. The probability of picking two good apples in a row from a bag containing 7 good and 3 bad apples, without replacement, is calculated as (7/10)*(6/9), which equals 0.467.

The subject of this question is Mathematics, specifically probability. When Nick picks two apples without replacement, we are dealing with dependent events, since the outcome of the second event depends on the outcome of the first event. Dependent events require a different calculation for the probability.

The total apples in the bag initially are 7 good + 3 bad = 10 apples. The probability of picking a good apple on the first draw is 7/10 or 0.7. When one apple is taken out, there are now 9 apples left in the bag. If the first apple was good, the probability of picking the second good apple is now 6/9 or 2/3.

Since these are dependent events, the total probability of picking two good apples in a row would be (7/10) * (6/9) which reduces to 14/30 or approximately 0.467.

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Answer: -2

=====================================================

Draw a vertical line through 4 on the x axis. This vertical line crosses the parabola at some point (which we'll call point A). Draw a horizontal line from point A to the y axis and note how it lands on y = 12. Therefore the point (4,12) is on this parabola.

Repeat the same steps as before to find that (8,4) is also on the parabola

We need to find the slope of the line through (4,12) and (8,4)

m = (y2 - y1)/(x2 - x1)

m = (4-12)/(8 - 4)

m = -8/4

m = -2

The slope of this line is -2 meaning that the average rate of change from x = 4 to x = 8 is -2.

The line goes down 2 units each time you move to the right 1 unit.

Answer:$38.75

Step-by-step explanation:

35(number of feet) * $1.75(cost per foot) = $61.25(total cost)

$100(bill used) - $61.25(total cost) = $38.75(amount given in change)

Answer:

$38.75

Step-by-step explanation:

We have given that : The trim cost per foot  =$1.75

for 35 feet of window trim cost = 35×1.75 = $61.25

Now, Fatima paid $100.00 bill

Amount she received = Amount she pay - cost of trim she buy

                                     = $100 - $61.25

                                      =$38.75            

Answer:

the answer is 3

Step-by-step explanation:

3 pizzas equal $9.00 so in order to know how much each pizza was, we will have to do division:

9 divided by 3

9/3

3

A recursive rule for a geometric sequence:

[tex]a_1\\\\a_n=r\cdot a_{n-1}[/tex]

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

[tex]a_1=3\\\\a_n=\dfrac{1}{2}a_{n-1}\to \boxed{r=\dfrac{1}{2}}[/tex]

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

Exciplit rule:

[tex]a_n=a_1r^{n-1}[/tex]

Substitute:

[tex]a_n=3\left(\dfrac{1}{2}\right)^{n-1}=3\cdot\left(\dfrac{1}{2}\right)^n\cdot\left(\dfrac{1}{2}\right)^{-1}=3\cdot\left(\dfrac{1}{2}\right)^n\cdot2\\\\\boxed{a_n=6\cdot\left(\dfrac{1}{2}\right)^n}[/tex]

Answer:

The answer is: a_n = 6*(1/2)^n

Answer:

143 miles

Step-by-step explanation:

Let the distance Karly biked be x

Then Dory biked 11x

So x+11x=156

x=156/12=13

So Dory biked 11 ⋅ 13= 143 miles

Is this correct?

Answer:

the footballer's average pay would be $4 million/annum.

Answer:

Option d is correct.

Both the x and y coordinates of the point on δa'b'c' have opposite signs from the corresponding points on δabc.

Step-by-step explanation:

The rule of 180 degree rotation about the origin is:

[tex](x, y) \rightarrow (-x , -y)[/tex]

Since a Rotation of a point through 180°, about the origin when a point a(h, k)  is rotated about the origin through 180° in anticlockwise or clockwise direction.

then, By the rule of 180 degree rotation;

[tex]a(h, k) \rightarrow a'(-h , -k)[/tex]

so, it takes the new position i.e, [tex]a'(-h , -k)[/tex]

Therefore, both the x and y coordinates of the point on δa'b'c' have opposite signs from the corresponding points on δabc.

The membership went up by 10%.

There are now 55 total students in the club.

The formula for calculating the percentage change is

[tex]p=\frac{N-O}{O}.100[/tex]

where p is the percent change, N is the New Value and O is the Old Value.

In this problem we are given the Old Value (50) and the percent change (10). We can substitute this into the formula and solve for N:

[tex]10=\frac{N-50}{50} .100\\10=2(N-50)\\5=N-50\\N=55[/tex]

There are now 55 total students in the club.

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Answer: x = 3

Step-by-step explanation:

If 3x is the midsegment of the triangle, then it is half the length of the base, which implies that the length of the base equals twice the length of the midsegment:

base = 2 * midsegment

 18   =  2 (3x)

  18  =   6x

  ÷6     ÷6  

   3   =  x