A restaurant has 4 pizza toppings to choose from. How many different 3 topping pizzas are possible

Answer:

1.

a. 2.75 seconds

b. 169 feet

2. x - 3 is a factor

Other factors: x + 2, 2x + 1, 3x - 4

3. Real zeros: [tex]x = -2[/tex]

Complex zeros: [tex]x_{2,3}=-3\pm 2i[/tex]

Step-by-step explanation:

1. Given equation of parabola

[tex]s(t)=-16t^2+88t+48[/tex]

a) The rocket reaches its maximum height at the vertex of parabola. Find t-coordinate of the vertex:

[tex]t_v=\dfrac{-b}{2a}\\ \\=\dfrac{-88}{2\cdot (-16)}\\ \\=\dfrac{11}{4}\\ \\=2.75\ seconds[/tex]

b) The maximum height is s-coordinate of the vertex. Find it:

[tex]s\left(\dfrac{11}{4}\right)\\ \\=-16\cdot \left(\dfrac{11}{4}\right)^2+88\cdot\left(\dfrac{11}{4}\right)+48\\ \\=-121+22\cdot 11+48\\ \\=169\ feet[/tex]

2. For x – 3 to be a factor of  [tex]f(x)=6x^4-11x^3-35x^2+34x+24,[/tex] the Factor Theorem says that x = 3 must be a zero of  f(x). Check it (whether f(3)=0):

[tex]f(3)\\ \\=6\cdot 3^4-11\cdot 3^3-35\cdot 3^2+34\cdot 3+24\\ \\=6\cdot 81-11\cdot 27-35\cdot 9+102+24\\ \\=486-297-315+126\\ \\=0[/tex]

So, x = 3 is zero of the function f(x) and x - 3 is the factor of the function f(x). Rewrite the function as follows:

[tex]f(x)\\ \\=6x^4-11x^3-35x^2+34x+24\\ \\=6x^4-18x^3+7x^3-21x^2-14x^2+42x-8x+24\\ \\=6x^3(x-3)+7x^2(x-3)-14x(x-3)-8(x-3)\\ \\=(x-3)(6x^3+7x^2-14x-8)\\ \\=(x-3)(6x^3+12x^2-5x^2-10x-4x-8)\\ \\=(x-3)(6x^2(x+2)-5x(x+2)-4(x+2))=\\ \\=(x-3)(x+2)(6x^2-5x-4)\\ \\=(x-3)(x+2)(6x^2+3x-8x-4)\\ \\=(x-3)(x+2)(3x(2x+1)-4(2x+1))\\ \\=(x-3)(x+2)(2x+1)(3x-4)[/tex]

3. [tex]x=-2[/tex] is a zero of the function [tex]f(x)=x^3+8x^2+25x+26,[/tex] then

[tex]f(x)\\ \\=x^3+8x^2+25x+26\\ \\=x^3+2x^2+6x^2+12x+13x+26\\ \\=x^2(x+2)+6x(x+2)+13(x+2)\\ \\=(x+2)(x^2+6x+13)[/tex]

Find the discriminant of the quadratic polynomial [tex]x^2+6x+13;[/tex]

[tex]D=6^2-4\cdot 1\cdot 13=36-52=-16[/tex]

This expression has no more real zeros (the discriminant is less than 0), it has two complex zeros:

[tex]x_{1,2}=\dfrac{-6\pm \sqrt{-16}}{2\cdot 1}=\dfrac{-6\pm 4i}{2}=-3\pm 2i[/tex]

To reciprocal the term for dividing, then multiply both fractions and get the solution to model  2/3 ÷ 3/4 = 8/9.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.

The numeral model is given in the question following:

⇒ 2/3 ÷ 3/4 = 8/9

According to the given question, the required solution would be as:

Find the reciprocal in this situation to divide by a fraction:

3/4 divided by 2/3

This would be: 2/3 x 4/3

When you multiply the components, you get 8/9.

Thus, to reciprocal the term for dividing, then multiply both fractions and get the solution.

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Final answer:

To show that 2/3 divided by 3/4 equals 8/9, we multiply 2/3 by the reciprocal of 3/4, which is 4/3, yielding the answer 8/9. This illustrates that division by a fraction involves multiplying by its reciprocal.

Explanation:

To explain how the model shows that 2/3 ÷ 3/4 = 8/9, we need to understand division of fractions and the concept of reciprocals. Division of fractions is the same as multiplying by the reciprocal of the divisor. The reciprocal of 3/4 is 4/3. Therefore, to divide 2/3 by 3/4, we multiply 2/3 by 4/3:

(2/3) × (4/3) = 8/9

This demonstrates that dividing by a fraction is equivalent to multiplying by its reciprocal. We can also use familiar scenarios to rationalize the answer. For instance, we know that half of one half (1/2 × 1/2) equals one quarter (1/4) and this helps us understand the process - we are scaling a number by another when we multiply fractions.

When discussing multiplication and division of fractions, it is useful to remember that these operations are fundamentally linked; division is essentially multiplication by a reciprocal. Hence, dividing 2/3 by 3/4 is the same as multiplying 2/3 by the reciprocal of 3/4, which is 4/3, resulting in 8/9.

Answer:

No solution.

Step-by-step explanation:

2x+1/3=2x

1/3=2x-2x

1/3=0

no solution

Answer:

12.1583333333 miles/hr.

Step-by-step explanation:

24 * 5 = 120  hrs

1459/120 = 12.1583333333

Answer:

12.158 miles/hour

Step-by-step explanation:

[tex]\frac{1459 miles}{5 days} = 291.8 miles/day\\\frac{291.8 miles}{1 day} x \frac{1 day}{24 hours} = 12.158 miles/hour[/tex]

Answer:

on the top is 124 - 115 whille in the bottom is 115

Step-by-step explanation:

To calculate the percent change in the number of employees, use the formula (Change in Quantity / Original Quantity) × 100. The original number of employees is 115, and it increased to 124, resulting in a change of 9. The percent change is approximately 7.83%.

To find the percent change in the number of employees, you can use the following formula:

Percent Change (p) = (Change in Quantity / Original Quantity) × 100

In this case, the Original Quantity is the number of employees at the start of the year (115) and the Change in Quantity is the difference between the number at the end of the year (124) and the number at the start of the year (115).

So, we calculate Change in Quantity as 124 - 115 = 9.

Now, using the formula:

p = (9 / 115) × 100

Calculating this gives us the percentage change:

p = (9 / 115) × 100 ≈ 7.83%

The percent change in the number of employees is approximately 7.83%.

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Answer:

110889

Step-by-step explanation:

Answer:

110,889 is the answer dude..

Answer:

x > 68 and x < 84

Step-by-step explanation:

The length of KD in triangle △AKM, with AK = 6 and KM = 10, and m∠AKM = 93° is 10, since KD is the height of a right triangle and KM is the hypotenuse.

The question asks to find the length of KD in triangle △AKM where KD is perpendicular to AM. Given AK = 6, KM = 10, and m∠AKM = 93º, we can solve for KD using trigonometric ratios.

Since KD ⊥ AM, we have a right triangle △KDM.

We know the hypotenuse KM and angle AKM, so we can use the sine function, where sin(AKM) = opposite/hypotenuse, to find the length of KD. The sine of angle AKM (which is slightly adjusted from 93º to 90º since we are looking for the height in a right triangle) gives us:

sin(90º) = KD/ KM

We know sin(90º) = 1 and KM = 10, so:

1 = KD / 10

Therefore, KD = 10.

Answer:

[tex]\large \boxed{\text{5.00 lb}}[/tex]

Step-by-step explanation:

[tex]\begin{array}{rcl}1.20x + 3.60 & \leq & 9.60\\1.20x & \leq & 6.00\\x &\leq & \mathbf{5.00}\\\end{array}\\\text{Rammy can buy $\large \boxed{\textbf{5.00 lb}}$ of peaches.}[/tex]

Check:

[tex]\begin{array}{rcl}1.20(5.00) + 3.60 & \leq & 9.60\\6.00 + 3.60 & \leq & 9.60\\9.60 & \leq & 9.60\\\end{array}[/tex]

OK.

The number of pounds of peaches that Rammy can buy is 5 pounds.

Based on the information given in the question, the equation to solve the question will be:

1.20x + 3.60 ≤ 9.60

Collect like terms

1.20x ≤ 9.60 - 3.60

1.20x ≤ 6.00

Divide both side by 1.20

1.20x/1.20 ≤ 6.00/1.20

x ≤ 5.00

Therefore, the number of pounds of peaches that Rammy can buy is 5 pounds

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Answer:

The value of g'(10)=[tex]\frac{(-1)}{16}[/tex]

Step-by-step explanation:

Given function is f(x)=[tex]\frac{4}{x} + 2[/tex]

Take f(x)=y

y=[tex]\frac{4}{x} + 2[/tex]

Subtract 2 from both side.

y-2=[tex]\frac{4}{x}[/tex]

x=[tex]\frac{4}{y-2}[/tex]

The inverse of f(x) is written as [tex] \frac{4}{y-2}[/tex]

It is said as g is inverse of f

g(y)=\frac{4}{y-2}[/tex]

g(y)=[tex]\frac{4}{y-2}[/tex]

g(10)=[tex]\frac{4}{10-2}[/tex]

g(10)=[tex]\frac{1}{2}[/tex]

Differentiating both sides we get,

g'(y)=[tex]\frac{4(-1)}{(y-2)^{2}}+0[/tex]

g'(y)=[tex]\frac{(-4)}{(y-2)^{2}}[/tex]

To find g'(10)=[tex]\frac{(-4)}{(10-2)^{2}}[/tex]

g'(10)=[tex]\frac{(-1)}{16}[/tex]

Answer:

Ultraviolet (UV) radiation.

Step-by-step explanation:

Mutagen is part of genetics, it is chemical or physical agent which are present in atmosphere and causes changes or mutation in the genetic materials i.e. in DNA (these changes can be permanent as well). Example of mutagen are radioactive substances, ultraviolet radiation, etc.

UV radiation is an electromagnetic radiation which is present in sunlight. It is a strong mutagen which is when absorbed by DNA can cause extreme damage, for example, uncontrolled division of skin cell can cause skin cancer, that's the reason why UV radiation is the most common mutagen to which we are exposed to when we are outside in the sunlight.

Answer:

x=-5, y=6. (-5, 6).

Step-by-step explanation:

x=y-11

2x+3y=8

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

2(y-11)+3y=8

2y-22+3y=8

5y-22=8

5y=8+22

5y=30

y=30/5=6

x=6-11=-5

The unit rate is $2 per can.

Step-by-step explanation:

You divide 6 by 3 which then equals 2.

Answer:

$2.00 per can

Step-by-step explanation:

Answer:

48

Step-by-step explanation:

Answer:

The answer is 48 games out of 84.

Step-by-step explanation:

So first we go through a step by step process.

We have a problem set up that looks something like this.

8/14 = ?/84

Step 1:

So we will first divide 84 by 14, giving us 6.

Step 2:

So 14x6 is equal to 84. Now we have to multiply the top half of the equation by 6. This is 8x6 giving us 48.

Step 3:

Now we substitute the ? with the 48. In the end if playing 84 games the hockey team would win 48 at the rate it was going.

Hope this helped!

Answer:

7x - 8y = 37

Explanation:

y+2 = ⅞(x-3) (distribute ⅞ -- x times 7/8, -3 times 7/8)

y+2 = ⅞x - 21/8 (subtract ⅞x from both sides)

y+2-⅞x = -21/8 (subtract 2 from both sides)

y-⅞x = -37/8 <--- result of -21/8 - 2

Multiply both sides by 8 to get ride of fractions

8y - 7x = -37 (rearrange)

-7x + 8y = -37

It's better to have a positive coefficient for x if you can.  So multiply both sides by -1.  That just means changing the sign of every term on both sides, you get

7x - 8y = 37

The area of the circle is approximately [tex]\(69.46 \, \text{mm}^2\)[/tex] and the circumference is approximately [tex]\(53.49 \, \text{mm}\).[/tex]

To find the area A and circumference C of a circle given its diameter d, we can use the following formulas:

1. Area A of a circle:

[tex]\[ A = \pi \times \left(\frac{d}{2}\right)^2 \][/tex]

2. Circumference C of a circle:

[tex]\[ C = \pi \times d \][/tex]

Given that the diameter d is 17 mm, we can plug this value into the formulas to find the area and circumference.

1. Area A of the circle:

[tex]\[ A = \pi \times \left(\frac{17}{2}\right)^2 \]\[ A = \pi \times \left(\frac{17}{2}\right) \times \left(\frac{17}{2}\right) \]\[ A = \pi \times \frac{17 \times 17}{4} \]\[ A = \pi \times \frac{289}{4} \]\[ A = \frac{289}{4} \pi \][/tex]

[tex]\[ A \approx 69.46 \, \text{mm}^2 \][/tex]

2. Circumference (\(C\)) of the circle:

[tex]\[ C = \pi \times 17 \]\[ C = 17\pi \][/tex]

[tex]\[ C \approx 53.49 \, \text{mm} \][/tex]

Answer:

The distance Shawn went is 40.

Step-by-step explanation:

Given:

N= 5 and M =6

Mountain hike = N = 5

Back down the other side = 2N+1 = 2×5 + 1 = 10 + 1 =11

From Mountain back to truck = 4M = 4×6 = 24

We need to find the total distance he went and can be calculate by adding Mountain hike with back down the other side and then from Mountain back to truck.

Total distance Shawn went = Mountain hike+ Back down the other side + From Mountain back to truck = 5 + 11 + 24 = 40

Hence Shawn went the distance of 40.

Answer:

my 12 inch pito that pito good

Answer:

X= -0.4545

Step-by-step explanation:

YOU HAVE TO SUBTRACT .2Z FROM .4Z WHICH GETS YOU .2 ON THE RIGHT SIDE

THAT WOULD MEAN YOU HAVE TO CLEAR OUT THE SEVEN BY ADDING IT ON BOTH SIDES GETTING -1

THEN YOU WOULD HAVE -1=.2Z

THEN DIVIDE BY .2 GETTING YOU A TOTAL OF -0.4545 WHEN YOU FINISH DIVIDING

Answer:

y = sqrt(29)/2 - 1/2 or y = -1/2 - sqrt(29)/2

Step-by-step explanation:

Solve for y:

y^2 + y - 7 = 0

Add 7 to both sides:

y^2 + y = 7

Add 1/4 to both sides:

y^2 + y + 1/4 = 29/4

Write the left hand side as a square:

(y + 1/2)^2 = 29/4

Take the square root of both sides:

y + 1/2 = sqrt(29)/2 or y + 1/2 = -sqrt(29)/2

Subtract 1/2 from both sides:

y = sqrt(29)/2 - 1/2 or y + 1/2 = -sqrt(29)/2

Subtract 1/2 from both sides:

Answer: y = sqrt(29)/2 - 1/2 or y = -1/2 - sqrt(29)/2

Answer:

y=sqrt(29)/2-1/2, -sqrt(29)/2-1/2

Step-by-step explanation:

y^2+y-7=0

completing the square,

(b/2)^2=(1/2)^2=1/4

(y+1/2)^2=7+1/4

(y+1/2)^2=28/4+1/4

(y+1/2)^2=29/4

y+1/2=sqrt(29/4)

y=sqrt(29/4)-1/2

y=sqrt(29)/2-1/2

y=-sqrt(29)/2-1/2

Number of fruit baskets purchased by Mrs. William is 5

Given that  

Annual membership fee of store where Mrs. William shops = $30

Cost of one fruit basket which Mrs. William as gifts for her co-workers = $15

Total amount spent by Mrs. William = $150

Given that "b" represents number of basket purchased

Equation which models the above scenario is as follows

15b+ 30=105   ------ (1)

Where b represents number of fruit basket purchased by Mrs. William

Need to calculate number of fruit basket purchased by Mrs. William

For which we need to solve equation (1) for b  

On solving we get

15b+ 30 = 105    

On Subtracting 30 from both sides we get

15b + 30 – 30 = 105 – 30

=> 15b = 75

On dividing both sides by 15 we get  

[tex]\begin{array}{l}{\frac{15 b}{15}=\frac{75}{15}} \\\\ {=>b=5}\end{array}[/tex]

As variable "b" represents number of basket purchased, hence we can conclude that number of fruit baskets purchased by Mrs. William is 5

Answer:

A) 3x-5=25

I'll try my best on the others

B) x+y^2=18

C)x•6/5=x+4 ????

D).5+x=2-4???

That's all I know :/

Step-by-step explanation:

yeah I'm not sure lol

Answer:

[tex]k = - \frac{3}{2}[/tex]

Step-by-step explanation:

If y varies directly with x, then from the relation of direct variation we can write y ∝ x

Now, converting the variation relation to equation relation,

⇒ y = kx  ........... (1) {Where k is the constant of variation}

Now, given that at y = - 3, x = 2 and this solution will satisfy the equation (1).

Hence, - 3 = 2k

⇒ [tex]k = - \frac{3}{2}[/tex] (Answer)

Answer:

The answer is 2000 g

Step-by-step explanation:

We use the following equivalence:

1 kg-------1000g

2kg----- X = (2kgx1000g)/1kg= 2000g

Step-by-step explanation:

Arthur got because a pizza is shared by 4 people. however only

2/3 of the pizza is there so it is divided by the four people.

The correct option is b.

The correct problem that can be solved by calculating 4 divided by 2/3 is determining the number of 2/3 cup servings of soup in 4 cups. By understanding how division of fractions work, we can see that there are 6 such servings in 4 cups.

The subject matter of the question is related to basic division and fractions. Specifically, it's asking about when we would need to find the result of 4 divided by 2/3. Given the answer choices, option B is the correct one. The question here is not about sharing a pizza or calculating the quantity of apples for pies, or the amount of sandwich eaten. It's rather about how many 2/3 cup servings fit within 4 cups of soup. When we do the division 4 ÷ 2/3, we're essentially figuring out how many 2/3s there are in 4. This concept can be a bit tricky because dividing by a fraction is equivalent to multiplying by its reciprocal. The reciprocal of 2/3 is 3/2, so 4 × 3/2 = 6. Hence, there are 6 servings of 2/3 cup soup in 4 cups.

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The solution of the equation is  [tex]x=\frac{11}{7}[/tex]

Step-by-step explanation:

To simplify an equation of x

∵ The equation is [tex]2x + \frac{1-x}{4}=3[/tex]

- Multiply all terms of the equation by 4 to cancel the denominator

 of the 2nd term in the left hand side

∵ The equation is [tex]4(2x) +4 (\frac{1-x}{4})=4(3)[/tex]

∴ 8x + (1 - x) = 12

∴ 8x + 1 - x = 12

- Add like terms

∴ (8x - x) + 1 = 12

∴ 7x + 1 = 12

- Subtract 1 from both sides

∴ 7x = 11

- Divide both sides by 7

∴ [tex]x=\frac{11}{7}[/tex]

The solution of the equation is  [tex]x=\frac{11}{7}[/tex]

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Answer:D

Step-by-step explanation:

Your first solution is to look at the 10x^2y in order to get 8 from ten you would need to subtract 2x^something y and there is only one answer with that

Answer:

yes its D.

Step-by-step explanation:

Answer:

y=-20

Step-by-step explanation:

-6(y+5)-24=66

-6y-30-24=66

-6y-54=66

-6y=66+54

-6y=120

y=120/-6=-20

Final answer:

To factor −1/2 out of −1/2x+6, we identify the common factor, divide each term by −1/2, and write the expression as −1/2 times the simplified expression. The result is −1/2(x − 12).

Explanation:

To factor −1/2 out of −1/2x+6, we can think of pulling out the −1/2 as a common factor from both terms in the expression. Here's a step-by-step breakdown:

Applying these steps, we get:

So, −1/2x+6 factored with −1/2 taken out is −1/2(x − 12).