When rolling two dice , there are blank different ways to roll at least one 4.

Answer:

[tex]f(x)=-\frac{1}{16} x^2[/tex]

Step-by-step explanation:

We are to derive the equation of the parabola with a focus at [tex](0, -4)[/tex] and a directrix of y = 4.

We know that a parabola is the locus of all the points as long as the distance from the fixed point on the parabola to the fixed line directrix is kept same.

This parabola is facing downwards. So assuming any point on the parabola to be [tex](x,y)[/tex].

Distance from focus [tex](0,-4)[/tex] to [tex](x,y)[/tex] = [tex]\sqrt{(x-0)^{2} +(y+4) ^{2}}=\sqrt{x^{2}+ (y+4)^{2}}[/tex]

Distance from [tex](x,y)[/tex] to directrix [tex](y=4)[/tex] = [tex]\left | y-4 \right |[/tex]

Equating these distances as they are equal:

[tex]\sqrt{x^{2}+ (y+4)^{2}}=\left | y-4 \right |[/tex]

[tex]{x^{2}+ (y+4)^{2}=(y-4)^{2}[/tex]

[tex]x^2+y^2+8 y +16 = y^2 - 8 y+16[/tex]

[tex]x^2 = -8 y - 8 y= -16 y[/tex]

[tex]x^2= - 16 y[/tex]

So the equation of the parabola is [tex]f(x)=-\frac{1}{16} x^2[/tex].

Answer:

The equation of the parabola is y = -1/16 x²

Step-by-step explanation:

* Lets revise some facts about the parabola

- Standard form equation for a parabola of vertex at (0 , 0)  

- If the equation is in the form  x² =  4py, then  

- The axis of symmetry is the y-axis,  x = 0  

- 4p equal to the coefficient of y in the given equation to  

  solve for  p  

- If  p  >  0, the parabola opens up.  

- If  p <  0, the parabola opens down.

- Use p to find the coordinates of the focus,  (0 , p)

- Use p to find equation of the directrix ,  y = - p

* Lets solve the problem

∵ The focus at (0 , -4)

∵ The coordinates of the focus are (0 , p)

∴ p = -4

∵ The directrix is y = 4

∵ The equation of the directrix ,  y = - p

∴ -p = 4 ⇒ p = -4

∵ the equation is in the form  x² =  4py

∵ p = -4

∴ x² = 4(-4)y

∴ x² = -16y ⇒ divide both sides by -16

∴ y = -1/16 x²

* The equation of the parabola is y = -1/16 x²

Answer:

24 ways

Step-by-step explanation:

4P3 = 4*3*2

=24

Final answer:

The total number of three-digit numbers that can be made using the digits 1, 2, 3, and 4 with repetition allowed is 64. This is computed by multiplying the number of digit options available for each place value in a three-digit number (4 options each for hundreds, tens, and ones).

Explanation:

To determine the number of possible three-digit numbers that can be created using the digits 1, 2, 3, and 4, with the possibility of repeating digits, we need to consider that each place value (hundreds, tens, and ones) can be filled by any of the four digits available.

Therefore, for the hundreds place, there are 4 options (1, 2, 3, or 4). The same is true for the tens and ones place, since repetition is allowed, giving 4 options for each. We calculate the total number of combinations by multiplying the number of options for each place value:

Hundreds place: 4 options

Tens place: 4 options

Ones place: 4 options

The total number of possible numbers is 4 (for the hundreds) × 4 (for the tens) × 4 (for the ones) = 64 numbers.

Answer:

Step-by-step explanation:

It depends on how many green and orange marbles their are...If their is 30 marbles in a bag and 10 of them are orange and green it would be 10/30 divide both of them by 10 and you would get 1/3 But that is just an example.

Hope my answer has helped you in any way!

Answer:0.04444

Step-by-step explanation:

Number of red balls = 5  

Number of orange balls = 2

Number of yellow balls = 1

Number of green balls = 2

Therefore total number of balls = 10.

Probability of getting a ball =

 P(choosing orange ball) =  

After picking an orange ball, we are left with 9 balls

P ( choosing a green ball) =

P(choosing an orange marble and a green marble) =

0.04444 is the approximate probability of choosing an orange marble and a green marble.

Answer:

$ 70.4

Step-by-step explanation:

Data:

The opening balance = $ 153.82

Withdrawal made        = - $ 40

Check for payment     =  - $ 54.12

Deposited a check for payment = + $ 215. 70

Transferred amount to the savings = - $ 75.00

Debit for the sports equipment      = -$ 130

The total amount left will be = $ (153.82- 40-54.12+ 215.70-75-130)

                                               = $ 70.4

Answer:

The account balance is $70.40.

Explanation:

Please make the brainliest :)

Answer:

Step-by-step explanation:

46-21=25

Answer:  25 miles

Step-by-step explanation:

Given : The distance is remaining to travel to reach the beach from the sign = 21 miles

The distance between the beach and his house = 46 miles

Now, the distance Cameron traveled already is given by :-

[tex]\text{Total distance-Remaining distance}\\\\=46-21=25\text{ miles}[/tex]

Hence, Cameron already traveled 25 miles.

Answer:

r = 7/16 inch

Step-by-step explanation:

The radius is 1/2 of the diameter

r = 1/2 d

r =1/2 (7/8)

r = 7/16 inch

Answer:

61728394.5

Step-by-step explanation:

Using order of operations, you can either perform the multiplication first or the division first.

123,456,789 × 2 / 4 =

123,456,789 / 2 =

61728394.5

Answer:

61,728,394.5

Step-by-step explanation:

Remember to follow PEMDAS & left->right rule.

In this case, they are multiply & divide, so you can solve through left - > right rule:

123,456,789 x 2 = 246,913,578

246,913,578/4 = 61,728,394.5

61,728,394.5 is your answer.

~

Answer:

-6b

Step-by-step explanation:

In this question, its simple math,how?

All the terms are alike, so just apply subtraction method;

[tex]=12b-17b-b\\\\\\\\=12b-18b\\\\=-6b[/tex]

For this case we have the following expression:

[tex]12b-17b-b=[/tex]

We have that by definition of Law of the Signs of the Sum that: Equal signs are added and the same sign is placed, while different signs are subtracted and the sign of the greater is placed. So:

[tex]-5b-b =\\-6b[/tex]

Answer:

-6b

Answer:

12 feet

Step-by-step explanation:

By Pythagoras theorem, a²+b²=c², where c represents the diagonal and a and b represents the other sides of a right angled triangle

As a flag is a rectangle, the two triangles cut would be  right angled triangles

Therefore, a²+9²=15²

a²+81=225

a²=144

a=√144

a=12 feet

Final answer:

To calculate the length of the Scottish flag, the Pythagorean theorem is applied. With a diagonal (hypotenuse) of 15 feet and a height of 9 feet, the length is found to be 12 feet.

Explanation:

The question involves calculating the length of the Scottish flag given the length of one diagonal and the flag's height. To find the length of the Scottish flag, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Here, we know the length of the diagonal (hypotenuse) is 15 feet and the height (one side) is 9 feet.

Let x be the length of the Scottish flag (the other side of the right-angled triangle). According to the Pythagorean theorem, [tex]x^2 + 9^2 = 15^2.[/tex]

Solving for x, we get:

Therefore, the length of the Scottish flag will be 12 feet to the nearest foot.

Answer:

x/4

Step-by-step explanation:

(y+3)/3=y/3+3/3=y/3+1

So to find y/3 in your equation all we would need to do is subtract 1 on both sides giving:

(x+4)/4-1

This can be simplified

x/4+4/4-1

x/4+1-1

x/4+0

x/4

Answer: x/4

3(x - 4) > 5x + 2

First you must distribute the 3 to the numbers inside the parentheses

(3 * x) + (3 * (-4)) > 5x + 2

3x + (-12) > 5x + 2

3x - 12 > 5x + 2

Now you must combine like terms

3x goes with 5x

^^^To do this subtract 3x to both sides of the equation

(3x - 3x) - 12 > (5x - 3x) + 2

0 - 12 > 2x + 2

-12 > 2x + 2

-12 goes with 2

^^^To do this subtract 2 to both sides

-12 - 2 > 2x + (2 - 2)

-14 > 2x + 0

-14 > 2x

Isolate x by dividing 2 to both sides

-14/2 > 2x/2

-7 > x

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

105

Step-by-step explanation:

425 - 320 = 105 miles

Final answer:

The drive from Santa Barbara to Los Angeles is 105 miles, which is the difference between San Jose to Los Angeles (425 miles) and San Jose to Santa Barbara (320 miles).

Explanation:

The question asks how far it is to drive from Santa Barbara to Los Angeles. To determine this distance, we utilize the total distance from San Jose to Los Angeles and subtract the distance from San Jose to Santa Barbara. Starting with the overall distance of San Jose to Los Angeles, which is 425 miles, we deduct the San Jose to Santa Barbara distance of 320 miles. This calculation will provide us with the distance from Santa Barbara to Los Angeles.

By subtracting 320 miles from 425 miles, we find that the distance from Santa Barbara to Los Angeles is 105 miles.

Answer:

The correct option is 3.

Step-by-step explanation:

We need to find a table of ordered pairs that represents a proportional relationship.

Proportional relationship: It means y-values are proportional to x-values.

[tex]y\propto x[/tex]

[tex]y=kx[/tex]

where, k is constant of proportionality.

For table 1,

[tex]\frac{y_1}{x_1}=\frac{8}{4}=\frac{2}{1}[/tex]

[tex]\frac{y_2}{x_2}=\frac{11}{7}[/tex]

[tex]\frac{2}{1}\neq \frac{11}{7}[/tex]

Table 1 does not represents a proportional relationship.

Similarly,

For table 2,

[tex]\frac{25}{5}\neq \frac{49}{7}[/tex]

Table 2 does not represents a proportional relationship.

For table 3,

[tex]\frac{3}{6}=\frac{5}{10}=\frac{7}{14}=\frac{1}{2}[/tex]

Table 3 represents a proportional relationship.

For table 4,

[tex]\frac{6}{3}\neq \frac{11}{8}[/tex]

Table 4 does not represents a proportional relationship.

Only table 3 represents a proportional relationship. Therefore the correct option is 3.

Answer:

53 1/3 mph

Step-by-step explanation:

Speed equals distance over time.

She covered 300 miles in 60mph, which took 5 hours.

(300/60=5 )

She also covered 100 miles in 40mph, which means she took 2.5 hours.

(100/40=2.5)

So the total distance is 400miles and the total time is 7.5 hours.

s=d/t substitute values which gives you 400/7.5 which equals 53 1/3 mph

Answer:

Step-by-step explanation:

(f + g)x translates into a more readable f(x) + g(x) so all you do is

f(x) + g(x) = 4x^2 + 1 + x^2 - 5

f(x) + g(x) = 5x^2 - 4

Answer:3x^2+6

Step-by-step explanation: I'm not really good at math but the correct answer is 3x^2+6

56 large boxes and 40 small boxes.

To solve this problem, we need to use the concept of multiples. By definition, a multiple of a number is that number multiplied by an integer. For instance, 3, 6, 9, 12 are multiples of 3. So let's do a chart and list the multiples of large and small boxes:

[tex]\begin{array}{cccccccccc}Number\,of\,boxes & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9\\Large & 8 & 16 & 24 & 32 & 40 & 48 & 56 & 64 & 72\\Small & 10 & 20 & 30 & 40 & 50 & 60 & 70 & 80 & 90\end{array}[/tex]

From this, our goal is to select the number of small and large boxes such that the sum is 96 boxes of hamburger burns and the number of large boxes is greater than the number of small boxes. From the table, the correct solution is:

56 large boxes and 40 small boxes, and this meets our requirement, because 56 + 40 = 96 and 56 > 40

For this case we add the quantities of calories consumed per day, that is:

[tex]1,405 + 1,219 + 1,119 + 1,353 = 5,096[/tex]

So Serena consumed 5,096 calories in 4 days. If we want to know the average calorie content per day, we divide the amount obtained by 4:

[tex]\frac {5,096} {4} = 1,274[/tex]

ANswer:

5,096 total calories

Consumes on average 1,274 calories per day.

Answer:520

Step-by-step explanation:

Suppose the original prize is=x

If the discount is of 80%,the selling prize is of 20%

20% of x=112

20x/100=112

X=520

Its the original prize...

Answer:

£560

Step-by-step explanation:

80% off means that the sale price is 20% of the original price.

The original price is represented by 100%

Divide the sale price by 20 to find 1% then multiply by 100 to obtain the original price

original price = [tex]\frac{112}{20}[/tex] × 100 = £560

Answer:

B

Step-by-step explanation:

for a linear equation y = mx + b,

the steepness of the graph is denoted by the slope, m

The larger the absolute number of the slope, the steeper it is

in this case it is quite clear that B has the largest absolute number for m.

i.e abs (-10) = 10

Answer:

G. -10

Step-by-step explanation:

Let one number = x

Let the second one = y

Equations

y = 5x

x + y = -60

Solution.

Put 5x in for y in the second equation.

x + 5x = -60             Combine like terms on the left

6x = -60                   Divide by 6

6x/6 = -60/6             Do the division

x = -10

So one of the numbers is minus 10

Answer:

2 is your answer

Step-by-step explanation:

If h(x)= 5 then 5= 2x +1

so 5 = 2x + 1

   -1            -1 on both sides

then 2x = 4

        2      2 divide by 2

which x = 2

Hope my answer has helped you!

Answer:

Any number less than 1

Step-by-step explanation:

Let x be the number Lin multiplies by 7/8. So, we have:

(7/8)*x < 7/8

We need to find the possible values for x. Lets start by dividing both sides of our inequality by (7/8) in order to get x alone on the left side.

(7/8)*x / (7/8) < (7/8)/(7/8)

Reordering:

(7/8) / (7/8) * x < (7/8)/(7/8)

As any number divided by itself (except from 0) is equal to 1:

x < 1

So, the number that Lin multiplied by 7/8 MUST be less than 1. This is evident, as any positive number multiplied by a number less than 1 will decrease, doesn't matter if its a negative or positive number.

So, such number is less than 1. Any number less than 1 could be Lin's number.

Answer:

[tex]\frac{37}{400}[/tex]

Step-by-step explanation:

9.25% as a fraction would be [tex]\frac{9.25}{100}[/tex], since a percentage is always out of 100.

Multiply the fraction by 100 to convert the decimal into fraction form

[tex]\frac{9.25}{100} \rightarrow\frac{925}{10000}[/tex]

Reduce to the simplest terms

[tex]925\div25=37\\\\ 10000\div25=400\\\\ \frac{37}{400}[/tex]

Answer:

30

Step-by-step explanation:

The length from one point on the edge of a circle to the middle will always be the same otherwise it isn't a circle. If QC is the same as CR than 15 and 15 would get you 30.

Answer:

70.686

Step-by-step explanation:

In order to know the length of QPR, we have to notice that QR=1/4 of the perimeter of the circle (circumference), then QPR= 3/4 of the perimeter of the circle.

Remember:

Circumference of a circle= 2[tex]\pi[/tex]*radius

Where:

[tex]\pi[/tex]= 3.1416 (its a constant value)

radius=15

Circumference of a circle=2*3.1416*15=94.248

Then:

QPR= 3/4 of the circumference of the circle

QPR= 3/4*94.248

QPR= 70.686

Answer:

[tex]-3x^2-15x-30[/tex]

Step-by-step explanation:

The given expression is [tex]-3(x+3)^2-3+3x[/tex].

We expand to obtain:

[tex]-3(x^2+6x+9)-3+3x[/tex].

We apply the distributive property to get:

[tex]-3x^2-18x-27-3+3x[/tex].

Group and combine the like terms;

[tex]-3x^2-18x+3x-27-3[/tex].

[tex]-3x^2-15x-30[/tex].

This polynomial expression is in standard form because it is descending powers of x.

The simplification of the algebraic expression in standard form is  -3x² - 15x - 30

An algebraic expression is the expression of mathematical variables with their coefficients(numbers), integers, and arithmetic operations. The simplification of algebraic expression usually follows a pattern such as;

From the given algebraic expression, we have:

= -3(x + 3)²  - 3 + 3x

Let's expand the above terms in the bracket, we have:

= -3(x² +6x + 9) - 3 + 3x

= -3x² - 1x - 27 - 3 + 3x

By rearrangement, we have:

= -3x² - 18x + 3x - 27 - 3

= -3x² - 15x - 30

Learn more about algebraic expression here:

https://brainly.com/question/4344214

Answer:

31/10 or 3 1/10 more miles.

Step-by-step explanation:

=  

(17 × 5) - (27 × 2)

2 × 5

Answer:

[tex]3\frac{1}{10}[/tex] miles

Step-by-step explanation:

The total distance of Charles bike ride is  = [tex]8\frac{1}{2}[/tex] miles

He has covered the distance = [tex]5\frac{2}{5}[/tex] miles

We will subtract his covered distance from total distance.

He still have to go = [tex]8\frac{1}{2}[/tex] - [tex]5\frac{2}{5}[/tex]

                              = [tex]\frac{17}{2}[/tex] - [tex]\frac{27}{5}[/tex]

                              = [tex]\frac{85-54}{10}[/tex]

                              = [tex]\frac{31}{10}[/tex]

                              = [tex]3\frac{1}{10}[/tex] miles

He still have to go [tex]3\frac{1}{10}[/tex] miles

Answer:

Step-by-step explanation:

1 surface area of the cube is s*s.

There are 6 faces on such a cube.

Area = 6*s^2                  Divide by 6

Area/6 = 6s^2 / 6           Do the divsion

Area/6 = s^2

s = sqrt(area/6)

Answer:

x=1  y = -1/2

(1,-1/2)

Step-by-step explanation:

7x-2y=8  

5x+2y=4

I would use elimination since we have 2y in one equation and -2y in the other

7x-2y=8  

5x+2y=4

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

12x = 12

Divide each side by 12

12x/12 = 12/12

x =1

The substitute back into equation 2

5(1) +2y = 4

5 +2y = 4

Subtract 5

5-5+2y = 4-5

2y = -1

Divide by 2

2y/2 = -1/2

y = -1/2

Answer:

The best method is the elimination method. The solution is (1, -1/2).

Step-by-step explanation:

7x - 2y = 8

5x + 2y = 4

12x = 12

x = 1

7(1) - 2y = 8

7 - 2y = 8

-2y = 1

y = -1/2

Make sure to write the answer in the form of an ordered pair.

Note: Alternative methods are graphing and the substitution method.

Answer:

Step-by-step explanation:

the area is :A= L×W

                   A= (2x²-x+3)(4x²+2x-1).....calculate

the perimeter is : P= 2(L+W)

                             P= 2(2x²-x+3)+(4x²+2x-1))....calculate

Answer:  see table below

Step-by-step explanation:

[tex]\left\begin{array}{c|l}T&\qquad w(t)\\1&\dfrac{1}{1^2}=1\implies 1.00\\\\2&\dfrac{1}{2^2}=\dfrac{1}{4}\implies 0.25\\\\10&\dfrac{1}{10^2}=\dfrac{1}{100}\implies 0.01\\\\50&\dfrac{1}{50^2}=\dfrac{1}{2500}\implies 0.0004\\\\100&\dfrac{1}{100^2}=\dfrac{1}{10000}\implies 0.0001\\\\200&\dfrac{1}{200^2}=\dfrac{1}{40000}\implies 0.000025\\\\500&\dfrac{1}{500^2}=\dfrac{1}{250000}\implies 0.000004\\\\1000&\dfrac{1}{1000^2}=\dfrac{1}{100000}\implies 0.000001\\\end{array}\right[/tex]