A building in a city has a rectangle base. The length of the base measures 70 feet less than three times the width. The perimeter of this base is 900 feet. What are the dimensions of the base?

Answer:

Yes it is a function given by f(x) = 2x

Step-by-step explanation:

Any function can approximated as series or a polynomial. For example,

[tex]e^{x} = 1 + \frac{x}{1!} + \frac{x^{2}}{2!} + \frac{x^{3}}{3!} ...[/tex]    (exponential function)

(n! or n factorial is equal to n(n-1)(n-2)...3.2.1 ;  3! = 3.2.1 = 6)

and for the series to converge(the sum does not go to infinity), higher order terms must tend to zero.

General form of a polynomial/series: [tex]f(x) = a + bx +cx^{2} + ...[/tex]

For the given set of points, we can start with the straight line equation:

[tex]f(x) = y = a + bx[/tex]    ........(1)

Let us take two points from the given relation: (-5, -10), (-1, -2)

and put the respective x and y values in equation (1), we get two equations, which we can then solve simultaneously to get values of [tex]a[/tex] and [tex]b[/tex]:

[tex]-10=a-5b[/tex]    ........(2)

[tex]-2=a-b[/tex]    ..........(3)

Now (3) - (2) gives us: [tex]b=2[/tex] and putting the value of [tex]b[/tex] in any of the above equation gives us [tex]a=0[/tex]

Hence, we get the equation, [tex]f(x)=y=2x[/tex]

It can be seen that all the given points satisfies this relation and since we get a unique [tex]y[/tex] for every [tex]x[/tex], we can call this a function.

Final answer:

The provided relation is a function because each x-value is unique and maps to exactly one y-value, fulfilling the criterion that every element of the domain is associated with exactly one element of the range.

Explanation:

The question asks if a relation containing the points (-5,-10), (-2,-4), (-1,-2), (4,8), and (5,10) is a function. To determine if this relation is a function, we need to examine if any x-value (the first number in each pair) repeats with a different y-value (the second number in each pair). Upon inspection, we see that each x-value is unique to a single y-value, which means that each element of the domain maps to a unique value in the range. Therefore, we can conclude that this relation is indeed a function.

In general, a function is defined as a relation in which every element of the domain (set of all first elements) is associated with exactly one element of the range (set of all second elements). This criterion is met in the relation provided as each x-value is unique and paired with only one y-value.

Answer:

30×3=90 10×9=90 45×2=90 . .

Answer: 5, 10, 18

Step-by-step explanation:

Answer:

my answer is 707

Step-by-step explanation:

i used a calculator lol

Answer:

707

Step-by-step explanation:

Answer:

27 can go into 224 8 times by dividing 224 by 27 .

Answer:

x/8

Step-by-step explanation:

7x/56=x/8

Answer:

180 points.

Step-by-step explanation:

Given:

A class will have 1 test and 5 homework assignments to complete.

The test is worth 80 points.

Each homework assignment is work 25% of the test.

Question asked:

How many points may be earned during this unit ?

Solution:

By unitary method:

Points may be earned from 1 assignments = [tex]25\% of 80[/tex] (given)

                                                                       = [tex]\frac{25}{100} \times 80 = \frac{2000}{100} = 20[/tex]

Points may be earned from 5  assignments = [tex]5\times 20 = 100[/tex]

Points may be earned from 1 test = [tex]80[/tex]

Total points may be earned = 100 + 80 = 180

Therefore, 180 points may be earned during this unit.

She made 15 cookies

Solution:

Let "x" be the number of cookies she made

She gave 1/3 of cookies for her husband

Therefore,

[tex]Husband = \frac{1}{3}x[/tex]

Find the remaining

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

1/4 of the cookies to her son

Therefore,

[tex]son = \frac{1}{4} \times \frac{2x}{3} = \frac{x}{6}[/tex]

Now again find the remaining

[tex]Remaining = \frac{2x}{3} - \frac{x}{6} = \frac{x}{2}[/tex]

1/6 of a cookies to her neighbor

[tex]Neighbor = \frac{1}{6} \times \frac{x}{2} = \frac{x}{12}[/tex]

Now again find the remaining

[tex]Remaining = \frac{x}{2} - \frac{x}{12} = \frac{5x}{12}[/tex]

She ate the remaining six cookies

Therefore,

[tex]\frac{5x}{12} = 6\\\\5x = 72\\\\x = 14.4[/tex]

Thus she made approximately 15 cookies

Answer:

2 dollars cuz ur poor

Step-by-step explanation:

From this problem, we know that during the weekend Fiona bought some frozen seafood at the market. She bought the following things:

Let:

x: The large tray of sardines

y: The 3 kg bag of squid

z: The 2kg box of mussels

Then, we have the following information:

The sardines and the squid cost €50:

[tex]x+y=50 \ ... \ eq1[/tex]

The sardines and the mussels cost €43:

[tex]x+z=43 \ ... \ eq2[/tex]

The squid and the mussels cost €26:

[tex]y+z=26 \ ... \ eq3[/tex]

Isolating x from eq 1 and substituting into eq 2:

[tex]From \ eq1: \\ \\ x=50-y \\ \\ \\ Substituting \ into \ eq2: \\ \\ (50-y)+z=43 \\ \\ -y+z=43-50 \\ \\ -y+z=-7 \ ... \ eq4[/tex]

Adding eq3 and eq4:

[tex]\ \ y+z=26 \\ \\ -y+z=-7 \\ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \\ \\ 2z=19 \\ \\ z=9.5[/tex]

From eq 3:

[tex]y+z=26 \\ \\ y+9.5=26 \\ \\ y=26-9.5 \\ \\ y=16.5[/tex]

From eq 1:

[tex]x=50-y \\ \\ x=50-16.5 \\ \\ x=33.5[/tex]

Finally:

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Answer:

x-y=-2

Step-by-step explanation:

Divide both sides if the equations by 3.

(3y-3x)÷3=6÷3

y-3x÷3=2

calculate the quotient

y-x=2

multiply both sides of the equation bub -1

-1x(-x)-1y=-1x2

any expression multiplied by -1

x-1y=-1x2

any expression multiplied by 1 remains the same.

x--y=-1x2

x-y=-2

Answer:

π units²

Step-by-step explanation:

The area (A) of a circle is calculated as

A = πr² ← r is the radius

Here diameter d = 2, thus r = 2 ÷ 2 = 1, thus

A = π × 1² = π × 1 = π units² ← exact solution

or A = 3.14 units² ← as a decimal

Answer:

y = 2x + 5

Step-by-step explanation:

The 2 would be the coefficient with x as a variable, and the 5 would be the constant.

At the beginning of the day Jessica had 5 dollars (constant), and for every hour she worked (variable), she made 2 dollars (coefficient).

An example of an expression with two terms is 3x + 5, where 3 is the coefficient, x is the variable, and 5 is the constant. A word phrase for this expression is "Three times a number plus five."

An example of an expression with two terms where one term has a coefficient with a variable and the other term is constant is:

3x + 5

In this expression:

The coefficient is 3.

The variable is x.

The constant is 5.

A word phrase for this expression could be: "Three times a number plus five."

Answer:

Step-by-step explanation:

First,you take 3 and 3/7 and line it up with 4 and 5/7 and first you add your whole numbers which come before the fractions and get 7.Next,you add the fractions and get 8/7. Now you know it needs symplified because its an improper fraction. To symplify you have to × or ÷ and whatever one you do you have to do it to both the numerator and denominator. If you divide 8÷7=1 R1  7÷7=1.  Last add 7+1+1/7=8 1/7.

Answer:

radius=diameter÷2=36÷2=13

Yo sup??

diameter=2*radius

36=2 r

r=18

therefore the radius is 18 units

Hope this helps

The maximum height of the ball is found at 64 feet

Hello! remember to write complete and clear questions in order to get good and exact answers. I've found a similar question so I have written it in a comment above. We know that h(t) models the height, in feet, of a ball that is kicked into the air where t is given as time in seconds. This equation follows a quadratic function so from math we know that the maximum or minimum of this type of functions is found at the vertex of its graph. So:

[tex]f(x)=ax^2+bx+c \\ \\ \\ Vertex \ (h,k): \\ \\ h=-\frac{b}{2a} \\ \\ k=f(-\frac{b}{2a}) \\ \\ \\ Our \ function \ is: \\ \\ h(t)=-16t^2+64t \\ \\ \\ Comparing: \\ \\ a=-16 \\ \\ b=64 \\ \\ c=0 \\ \\ \\ h=-(\frac{64}{2(-16)})=2 \\ \\ k=-16(2)^2+64(2) \\ \\ k=64[/tex]

Finally, the maximum height of the ball is found at 64 feet

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Answer:

F=29

Step-by-step explanation:

27+2

Answer:

f=29

Step-by-step explanation:

Answer:

[tex]4 \sqrt{6} \times \sqrt{3} = 12 \sqrt{2} [/tex]

Step-by-step explanation:

We want to simplify the radical expression:

[tex]4 \sqrt{6} \times \sqrt{3} [/tex]

We write √6 as √(2*3).

This implies that:

[tex]4 \sqrt{6} \times \sqrt{3} = 4 \sqrt{2 \times 3} \times \sqrt{3} [/tex]

We now split the radical for √(2*3) to get:

[tex]4 \sqrt{6} \times \sqrt{3} = 4 \sqrt{2} \times \sqrt{3} \times \sqrt{3} [/tex]

We obtain a perfect square at the far right.

[tex]4 \sqrt{6} \times \sqrt{3} = 4 \sqrt{2} \times (\sqrt{3} )^{2} [/tex]

This simplifies to

[tex]4 \sqrt{6} \times \sqrt{3} = 4 \sqrt{2} \times 3[/tex]

This gives us:

[tex]4 \sqrt{6} \times \sqrt{3} = 4 \times 3 \sqrt{2} [/tex]

and finally, we have:

[tex]4 \sqrt{6} \times \sqrt{3} = 12 \sqrt{2} [/tex]

See picture for solution to your problem.

Answer:

36

Step-by-step explanation:

The first thing to simplify is the Exponents

3^2 means 3 multiplied by it self 2 times

3×3=9

4×3^2

4×9

36

Answer:

y = - 4

Step-by-step explanation:

Given

y = 2 - 9x ← substitute x = [tex]\frac{2}{3}[/tex]

y = 2 - ( 9 × [tex]\frac{2}{3}[/tex] ) ← cancel the 9 and 3 by 3

  = 2 - (3 × 2 )

  = 2 - 6

  = - 4

Answer:

The total area of the two rooms is 188.25 square feet

Step-by-step explanation:

Given:

Area of the kitchen = 132 square feet.

Dimension of the Laundry room =  8 1/3 feet by 6 3/4 feet.

To Find:

The total area of the two rooms = ?

Solution:

Area of the two rooms   =  Area of the kitchen + Area of the laundry room

Area of the two rooms   =    132 +  Area of the laundry room

Area of the laundry room  =[tex](8 \frac{1}{3}) \times (6 \frac{3}{4})[/tex]

Area of the laundry room  =[tex]\frac{25}{3} \times \frac{27}{4}[/tex]

Area of the laundry = [tex]\frac{675}{12}[/tex]

Area of the two rooms   =    [tex]132 + \frac{675}{12}[/tex]

Area of the two rooms   = 132 + 56.25

Area of the two rooms   = 188.25 square feet

Final answer:

The total area of Elle's kitchen and laundry room combined is 188.25 square feet. This is found by first calculating the area of the laundry room with given dimensions and then adding it to the area of the kitchen.

Explanation:

The question involves finding the total area of two rooms, given the area of one and the dimensions of the other. The kitchen has an area of 132 square feet. For the laundry room, we need to calculate the area by multiplying its length and width. The dimensions are 8 1/3 feet by 6 3/4 feet. To find the area, convert mixed numbers to improper fractions: 8 1/3 becomes 25/3 feet, and 6 3/4 becomes 27/4 feet. The area is then calculated as (25/3) * (27/4) square feet.

To compute this, multiply the numerators and denominators separately: (25*27) / (3*4) = 675 / 12, which simplifies to 56.25 square feet. Now, add the area of the laundry room to the area of the kitchen to get the total area of both rooms: 132 + 56.25 = 188.25 square feet. Therefore, the total area of the two rooms is 188.25 square feet.

Answer:Her Aunt paid her 4.50 and hour and her neighbor 6 an hour. The difference is 1.5

Step-by-step explanation:

Answer: 2,204

Step-by-step explanation:

Final answer:

To solve 2453 minus 249, align the numbers by place value and subtract each column starting from the rightmost digit, borrowing where necessary. The result of 2453 minus 249 is 2204.

Explanation:

The question is a basic arithmetic problem involving subtraction. The task is to subtract 249 from 2453. We write the numbers in column form, aligning the units, tens, hundreds, and thousands places properly:

2453
-  249
------

We start subtracting from the rightmost digit (units place) and proceed to the left:

Finally, subtract in the thousands place: 2 minus 0 is 2.

After completing the subtraction, we have the result:

2204

Therefore, 2453 minus 249 equals 2204.

The total time that Anton's family spent driving to and from the lake is 8.5 hours

Solution:

Time taken is given by formula:

[tex]Time = \frac{distance}{speed}[/tex]

Anton's family drove 216 mi to the lake averaging 48 ​ mi/h

⇒ Anton's family drove total distance = 216 mi les

⇒ Speed of Antony's family driving to lake = 48 miles per hour

[tex]Time = \frac{216}{48} = 4.5[/tex]

Therefore, time taken to drive to lake is 4.5 hour

On the return trip home they averaged 54 mi/h

[tex]Time = \frac{216}{54} = 4[/tex]

Therefore, time taken to return home is 4 hours

Total time = 4.5 + 4 = 8.5 hours

Thus the total time that Anton's family spent driving to and from the lake is 8.5 hours

Answer:

Explanation:

[tex]391\:\mathrm{divides\:by}\:17\quad \:391=23\cdot \:17[/tex]

[tex]=17\cdot \:23[/tex]

17, 23 are all prime number. So no further factorization possible

[tex]=17\cdot \:23[/tex]

So,

Answer:

Explanation:

[tex]291\:\mathrm{divides\:by}\:3\quad \:291=97\cdot \:3[/tex]

[tex]=3\cdot \:97[/tex]

3, 97 are all prime number. So no further factorization possible

[tex]=3\cdot \:97[/tex]

So,

Answer:

Explanation:

37 is a prime number. So no further factorization possible

[tex]=37[/tex]

So,

Answer:

Explanation:

[tex]411\:\mathrm{divides\:by}\:3\quad \:411=137\cdot \:3[/tex]

[tex]=3\cdot \:137[/tex]

3, 137 are all prime number. So no further factorization possible

[tex]=3\cdot \:137[/tex]

So,

Answer:

Explanation:

[tex]387\:\mathrm{divides\:by}\:3\quad \:387=129\cdot \:3[/tex]

[tex]=3\cdot \:129[/tex]

[tex]129\:\mathrm{divides\:by}\:3\quad \:129=43\cdot \:3\\=3\cdot \:3\cdot \:43[/tex]

3, 43 are all prime number. So no further factorization possible

[tex]=3\cdot \:3\cdot \:43[/tex]

So,

Answer:

Explanation:

113 is a prime number. So no further factorization possible

[tex]=113[/tex]

So,

Answer:

Explanation:

293

[tex]\mathrm{Prime\:factors\:of\:}293:\quad 293[/tex]

[tex]=293[/tex]

[tex]293\mathrm{\:is\:a\:prime\:number,\:therefore\:no\:factorization\:is\:possible}[/tex]

[tex]=293[/tex]

So,

Answer:

Explanation:

[tex]451\:\mathrm{divides\:by}\:11\quad \:451=41\cdot \:11[/tex]

[tex]=11\cdot \:41[/tex]

11, 41 are all prime number. So no further factorization possible

[tex]=11\cdot \:41[/tex]

So,

Answer:

Explanation:

[tex]459\:\mathrm{divides\:by}\:3\quad \:459=153\cdot \:3[/tex]

[tex]=3\cdot \:153[/tex]

[tex]153\:\mathrm{divides\:by}\:3\quad \:153=51\cdot \:3[/tex]

[tex]=3\cdot \:3\cdot \:51[/tex]

[tex]51\:\mathrm{divides\:by}\:3\quad \:51=17\cdot \:3[/tex]

[tex]=3\cdot \:3\cdot \:3\cdot \:17[/tex]

3, 17 are all prime number. So no further factorization possible

[tex]=3\cdot \:3\cdot \:3\cdot \:17[/tex]

So,

Answer:

Explanation:

[tex]385\:\mathrm{divides\:by}\:5\quad \:385=77\cdot \:5[/tex]

[tex]=5\cdot \:77[/tex]

[tex]77\:\mathrm{divides\:by}\:7\quad \:77=11\cdot \:7[/tex]

[tex]=5\cdot \:7\cdot \:11[/tex]

5, 7, 11 are all prime number. So no further factorization possible

[tex]=5\cdot \:7\cdot \:11[/tex]

So,

Answer:

Explanation:

So,

Keywords: prime factor

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Find total of non blue socks:

7 + 8 + 4 = 19

There are 9 blue socks.

Ratio is blue / non blue = 9/19

Answer:

74°

Step-by-step explanation:

all angles of a triangle will always end up equal to 180°

68 + 38 = 106

180 - 106 = 74