a pyramid is made of metal balls. the lowest layer consists of 4 by 4 balls ,the next layers of 3 by 3 and 2 by 2 and one ball at the top. every two balls that touch each other are connected with screw. how many screws are used to build this pyramid?

Therefore the first five terms are 5, 9, 13, 17, and 21.

Given the first term is 5

a₁ = 5

Given the recursive formula  of an arithmetic sequence is

aₙ = aₙ ₋ ₁ + 4

We have to find the first five terms of the arithmetic sequence below

a₂ = a₂ ₋ ₁ + 4

   = a₁ + 4

   = 5 + 4

   = 9

a₃ = a₃ ₋ ₁ + 4

   = a₂ + 4

   = 9 + 4

   = 13

a₄ = a₄ ₋ ₁ + 4

   = a₃ + 4

   = 13 + 4

   =17

a₅ = a₅ ₋ ₁ + 4

   = a₄ + 4

   = 17 + 4

   = 21

Therefore the first five terms are 5, 9, 13, 17, and 21.

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Hey there!

(78 - x) + (84 - 3x)

= 78 - x + 84 - 3x

= 78 - 1x + 84 - 3x

= (78 + 84) - (1x - 3x)

= (78 + 84) - (x - 3x)

= (1x - 3x) + (78 + 84)

= (x - 3x) + (78 + 84)

= x - 3x + 78 + 84

= -4x + 162

Therefore, your answer should be:

-4x + 162

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Few friends want to visit the amusement park. They can only spend a total of $325 on parking and entrance. Tickets are $39 per person, tax included, and parking is $13. Create and resolve an inequality that may be used to calculate p, the maximum number of visitors to the theme park.

the maximum number of visitors to the theme park p=14.

Given that few friends want to visit the amusement park .

They are limited to spending $325 for parking and admission.

Tickets are $39 per person, tax included, and parking is $13.

We have to find the the maximum number of visitors to the amusement park p.

We can write as $13+$39p[tex]\leq[/tex]$325

$39p[tex]\leq[/tex]$325-$13

p[tex]\leq[/tex]14

Therefore, the maximum number of visitors to the amusement park p=14.

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Answer:

Step-by-step explanation:

Write equation in point slope form:

y - y1 = m(x - x1), where m is slope and (x1,y1) is a point on the line

Here m = 1/4 and (x1,y1) = (0,-6)

y--6 = 1/4(x - 0)

y+6 = 1/4x

in slope-intercept form

y = 1/4x - 6

to find x-intercept, substitute 0 for y and solve for x

to find y-intercept, substitute 0 for x and solve for y

Answer:

x≤1

Step-by-step explanation:

Answer:

Step-by-step explanation:

The most appropriate form of like terms is given below-

[tex]\frac{2}{5} c[/tex], [tex]\frac{1}{4} c[/tex] are like terms of this expression.

What are like terms?

The terms having same variable raised to same power are called like terms.

Here,

In  [tex]\frac{2}{5}c+\frac{1}{4} c -1\\[/tex], [tex]\frac{2}{5} c[/tex] and [tex]\frac{1}{4} c[/tex] have same variable, [tex]c[/tex].

So they are like terms

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Option C) is correct which is Adam started the construction at the wrong place. He should have started at point R and drawn an arc across both rays.

According to the question we can see that Adam first draws an arc on a line and draws the bisector, which gives him the error.

We know that when we construct an angle bisector, first we put the compass on the point of the angle and make an arc and from that arc we make two arcs that intersect at a point. Then we draw a ray from the point of angle to that intersecting point which gives us the angle bisector.

Here Adam didn't draw the arc from point R.

Thus, Adam started the construction at the wrong place. He should have started at point R and drawn an arc across both rays.

Hence option C) is the correct option.

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Answer:

One geranium is $3

Step-by-step explanation:

Let r = roses and g = geraniums

14r + 8g = 122

12r + 12g = 120

Multiply first equation by -3 and the second by 2 (we are trying to get terms that cancel when we add the two equations)

-42r - 24g = -366

+24r + 24g = 240

Add

18r = 126

r = 7, so one rose is $7

Put this into either of the original equations

14(7) + 8g = 122

98 +8g = 122

8g = 24

g = 3, so one geranium is $3

Answer:

this is not the answering phone num I was just saying I don't know how many people are going to get it

Answer:

The better deal is 1 cookie for 42 cents

Step-by-step explanation:

We need to find the price of 1 cookie when the cookies are 8 for 3.44

Divide the total price by the number of cookies

3.44/8

.43

We can get 1 cookie for 42 cents  or 1 cookie for 43 cents

The better deal is 1 cookie for 42 cents because it is less money.

Answer:

169,578$

Step-by-step explanation:

If you divide 2 million 5 hundred and 43 thousand 6 hundred and 66 by 15, the answer you would get would be 169,577.733333 (digit 3 goes on and on), but the question says we would need to round it to the nearest dollar. Therefore, the answer is 169,578$!!!

The inequality to represent the given situation is W≤1500.

Given that, the maximum load in a freight elevator is 1500 lb let W equal the weight in the elevator.

We need to write an inequality to describe the allowable weight in the elevator.

Inequalities are mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Now, W≤1500

Therefore, the inequality to represent the given situation is W≤1500.

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Answer:

There are 12 tigers and 36 elephants.

Step-by-step explanation:

If the ratio of tigers to elephants is 1 to 3, that means that the total would be 4,

so 1/4 of the total would be tigers and 3/4 of the total would be elephands.

1/4 x 48 is 12

and

3/4 of 48 = 36

The gestation period of humans ​ is​ 309.23% percent longer than the gestation period of dogs.

Percentage is the fraction out of an amount that is expressed as a number out of hundred. Percentage is a measure of frequency. The sign used to represent percentages is %. In order to convert a number to percentage, express the number as a fraction and multiply by 100.

Percent of gestation period = (difference in the gestation period of dogs and humans / gestation period of humans) x 100

[(266 - 65) / 56] x 100

(210 / 65) x 100 = 309.23%

A second method :[ (gestation period of humans / gestation period of dogs) - 1] x 100

[(266 / 65) - 1] x 100 = 309.23%

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for the two given fractions 3/4 and 1/6 we have:

Here we have two fractions, 3/4 and 1/6, and we want to find the sum, product, and quotient between them.

First let's do the sum:

3/4 + 1/6

We just need to find a common denominator, which can be 12, so we can rewrite it as:

9/12 + 2/12 = 11/12

The sum of the two fractions is 11/12

Now the product, it is, we multiply denominator with denominator and numerator with numerator, we will get:

(3/4)*(1/6) = (3*1)/(4*6) = 3/24 = 1/8

The product between the two fractions is equal to 1/8.

Finally, the quotient, this is:

The product between the first numerator and second denominator, and between the first denominator and second numerator, so the quotient becomes:

(3/4)/(1/6) = (3/4)*(6/1) = (3*6)/(4*1) = 18/4 = 9/2

Then we conclude that for the two given fractions 3/4 and 1/6 we have:

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Answer:(0,4)

Step-by-step explanation:

Answer:

  (c)  inconsistent equation

Step-by-step explanation:

You want to know if the equation -6x+6x-6=2-5 is an identity, conditional, or inconsistent.

The simplified equation, after combining like terms, is ...

  -6 = -3

This is an "inconsistent" equation, always false.

The points that are located 3 units from (-4,-2) are (-1, 2), (-7, 2), (-4, -1) and (-4, 5)

The point is given as

Point = (-4, 2)

The distance is given as

Distance = 5

The points that are located 3 units from (-4,-2) are calculated using

Points = (x ± 3, y) and (x, y ± 3)

So, we have

Points = (-4 ± 3, 2) and (-4, 2 ± 3)

Expand

Points = (-4 + 3, 2), (-4 - 3, 2), (-4, 2 - 3) and (-4, 2 + 3)

Evaluate the sum and the difference

Points = (-1, 2), (-7, 2), (-4, -1) and (-4, 5)

Hence, the points that are located 3 units from (-4,-2) are (-1, 2), (-7, 2), (-4, -1) and (-4, 5)

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The numerical length of BC is 36

The given parameters are:

AC= 64, AB = 7x + 8, and BC = 3x + 6.

The above means that the point B is between points A and C

So, we  have

AC = AB + BC

Substitute the known values in the above equation

64 = 7x + 8 + 3x + 6

Evaluate the like terms

10x = 50

Divide both sides by 10

x = 5

Substitute x = 5 in BC = 3x + 6

So, we have

BC = 3 x  10 + 6

Evaluate

BC = 36

Hence, the numerical length of BC is 36

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Complete question

AC= 64, AB = 7x + 8, and BC = 3x + 6. Find BC

The items that you can add with not breaking the weight limit are:

The hair dryer, the souvenir, the boots, the boots and the souvenir, and the hair dryer and the souvenir.

The maximum weight allowed is 50 pounds, and you already have 44.9 pounds, then the weight you can add is:

50lb - 44.9lb = 5.1lb

Now, the items that you have are:

2.5 lb hair dryer.

1.3 lb souvenir.

3.6 lb pair of boots.

The only things that you can't add together are the hair dryer and the boots, because the weight adds up to:

2.5lb + 3.6lb = 6.1lb

Which is more than the 5.1lb left that you have.

Obviuously, you can't take the 3 items.

Then you can add:

The hair dryer, the souvenir, the boots, the boots and the souvenir, and the hair dryer and the souvenir.

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Han llenaría 8 tazas con jugo de naranja porque si tomas la mitad de 1 taza de jugo de naranja puedes hacer 2 tazas ahora haz eso 4 veces y obtendrás 8 tazas de jugo de naranja

Answer:

12

Step-by-step explanation:

Suppose i want a 2 digit number and i specifically want it to be even okay, and it can only contain the numbers, 245 and 8 point well in order for it to be even the end would have to be 248 right. An even number. The last digit is divisible by 2 or it even so, there's 3 possibilities here. My question is: can my numbers repeat there's nothing that says my numbers can't repeat so: im gonna some they can so i could use 2 twice, 4 twice and so on and so for, but i can only use 5 once and there's 5 other possibilities here. So 4 possibilities for the first digit 3 possibilities for the second. I'M gonna multiply these together: 4 times 3 there's a total of 122 digit numbers.

The area of the given circle is 36.298 cm square.

Here, we are given that f is the function that determines the area of a circle (in square cm) that has a radius of r cm.

The area of a circle is given the the formula as follows-

area of a circle = πr^2

⇒ f(r) = πr^2

The value of π is approximately 3.14

⇒ f(r) = 3.14r^2

Now, we are given that the radius of a circle is 3.4 cm.

Thus, its area will be-

f(3.4) = 3.14 × 3.4 × 3.4

= 3.14 × 11.56

= 36.298

Thus, the area of the given circle comes out to be 36.298 cm square.

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Using the relation between velocity, distance and time, it is found that a rate of 102 km/h is needed for the rest of the trip to achieve the desired rate for the entire trip.

Velocity is distance divided by time, that is:

v = d/t.

For the first 120 km, the rate is of 90 km/h, hence the parameters are given as follows:

d = 120, v = 90.

Hence the time is given by:

90 = 120/t1

t1 = 120/90

t1 = 1.33 hours.

For the second part of the trip, the parameters are given as follows:

t = 1.25, v = 64.

The time is 1.25 hours because 15 minutes is one fourth(15/60) = 0.25 of an hour.

Hence the distance found as follows is:

64 = d/1.25

d = 1.25 x 64

d = 80

The distance for the first two parts is given by:

120 + 80 = 200 km.

This is equivalent to 7/8 of the trip, hence the total distance is:

7/8d = 200

d = 200 x 8/7

d = 228.57 km.

For a rate of 80 km, we have that the time has to be of:

80 = 228.57/t

t = 228.57/80

t = 2.86 hours.

The time of the first two parts is:

1.33 + 1.25 = 2.58 hours.

2.86 - 2.58 = 0.28 hours.

Hence the last 228.57 - 200 = 28.57 km have to be traveled in 0.28 hours, for a rate of:

v = 28.57/0.28 = 102 km/h.

A rate of 102 km/h is needed for the rest of the trip to achieve the desired rate for the entire trip.

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The two values of y after factorizing the given quadratic equation are 0, -0.5

The given equation is quadratic as the order of the equation is 2. In a quadratic equation with a single variable, the variable will have two different values which satisfy the equation. These values of the variable can be real and different, real and equal, or imaginary.

So, there will be two values of y.

Consider the given equation,

10y^2 + 12y = 7y

10y^2 +12y - 7y = 0

10y^2 + 5y = 0

Since the coefficients of y and y^2 are both multiples of 5,

5*(2y^2 + y) = 0

2y^2 + y = 0

Taking y as a common factor,

y*(2y+1) = 0

Now, we get two cases,

y = 0 or 2y + 1 = 0 => y = -(1/2) = -0.5

Therefore, y = 0 or y = -0.5

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Answer:

It has been 8 months since I joined the gym.

Step-by-step explanation:

1. Subtract the registration fee from the total (which would be $281 - $25 = $256)

2. divide that total by $32 and you will get the total number of months you've gone to the gym. ( which would be $256 ÷ $32 = 8)

3. check your work

Answer:

An equivalent numerical expression with whole-

number exponent using these laws can be written as:

1) 2² × 2³ = 2^5     => using product of Powers

2) 2² × 3² = (2×3)² = 6²      => using power of a Product

3) (2²)³ = 2^6      => using power of a power

Step-by-step explanation:

First of all, let us understand some terms like;

1) Exponentiation: It is the mathematical process of raising one integer to the power of another. The base is the first integer, while the exponent is the second.

2) Power: A power is a phrase that depicts the same component being multiplied repeatedly.

3) Exponent: The number of times the base is used as a factor is represented by the exponent.

Now, let us understand the 7 Laws of Exponents;

1) a^m × a^n = a^(m+n)   => Product With the Same Bases

2) a^m / a^n = a^(m-n)    => Quotient with Same Bases

3) (a^m)^n = a^(m×n)    => Power Raised to a Power

4) a^n × b^n = (ab)^n    => Product to a Power

5) a^n / b^n = (a/b)^n    => Quotient to a Power

6) a^0 = 1     => Zero Power

7) a^(-m) = 1/a^m    => Negative Exponent Rule

Furthermore, an equivalent numerical expression with whole-

number exponent using these laws can be written as:

1) 2² × 2³ = 2^5     => using product of Powers

2) 2² × 3² = (2×3)² = 6²      => using power of a Product

3) (2²)³ = 2^6      => using power of a power

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