help please its URGENT!!!!!!!!

Help Please Its URGENT!!!!!!!!

Answers

Answer 1

This is a relation but not a function.

Functions must have that there is a unique y for a given x, which clearly doesn't work here because all lines of a given x have 2 y-values. However, it is a relation because there is a given set of points which are defined to be within the set of the ellipse (if it's defined which members of two sets, the range and domain, go together, then you have a relation)

Answer 2

iam thinking its D but iam not 100% sure.


Related Questions

Jamin wants to paint a wall in his bedroom. Not only does he need to buy paint, but he also needs to buy tape to tape off all sides of the wall and the window. How many feet of painter's tape will Jamin need to buy (assume no overlap)? [Note: The wall and window are both rectangular.]



17.5 ft
35 ft
28 ft
21 ft

Answers

The perimeter of the walls is  6 + 6 + 8 + 8 = 28 feet.

The perimeter of the window is 2 + 2 + 1.5 + 1.5 = 7 feet.

Total = 28 + 7 = 35 feet of tape.

I would say B.35 is the answer.

Find the coordinates of P so that P partitions the segment AB in the ratio 1:3 if A(5,8) and B(−1,4).


A. (-6.5, -9)

B. (-1.5, -1)

C. (3.5, 7)

D. (-4, -6)

Answers

Answer:

The coordinates of point P are (3.5 , 7) ⇒ answer C

Step-by-step explanation:

* Lets explain how to solve the problem

- If the point (x , y) divide a line whose endpoints are (x1 , y1) , (x2 , y2)

 at ratio m1 : m2 from the point (x1 , y1), then the coordinates of the

 point (x , y) are [tex]x=\frac{x_{1}m_{2}+x_{2}m_{1}}{m_{1}+m_{2}},y=\frac{y_{1}m_{2}+y_{2}m_{1}}{m_{1}+m_{2}}[/tex]

* Lets solve the problem

∵ A is (5 , 8) and B is (-1 , 4)

∵ P divides AB in the ratio 1 : 3

∴ m1 = 1 and m2 = 3

- Let A = (x1 , y1) and B = (x2 , y2)

∴ x1 = 5 , x2 = -1 and y1 = 8 , y2 = 4

- Let P = (x , y)

∴ [tex]x=\frac{(5)(3)+(-1)(1)}{1+3}=\frac{15+(-1)}{4}=\frac{14}{4}=3.5[/tex]

∴ [tex]y=\frac{(8)(3)+(4)(1)}{1+3}=\frac{24+4}{4}=\frac{28}{4}=7[/tex]

∴ The coordinates of point P are (3.5 , 7)

Use row reduction to solve the system of equations. x-2y+z=4, 3x-5y-17z=3, 2x-6y+43z=-5

Answers

Answer:

x = -1223, y = -629, and z = -31.

Step-by-step explanation:

This question can be solved using multiple ways. I will use the Gauss Jordan Method.

Step 1: Convert the system into the augmented matrix form:

•  1    -2    1       |  4

•  3   -5   -17     |  3

•  2   -6   43     |  -5

Step 2: Multiply row 1 with -3 and add it in row 2:

•  1    -2    1       |  4

•  0    1   -20     |  -9

•  2   -6   43     |  -5

Step 3: Multiply row 1 with -2 and add it in row 3:

•  1    -2    1       |  4

•  0    1   -20     |  -9

•  0   -2   41      |  -13

Step 4: Multiply row 2 with 2 and add it in row 3:

0 2 -40 -18

•  1    -2    1       |  4

•  0    1   -20     |  -9

•  0    0     1      |  -31

Step 5: It can be seen that when this updated augmented matrix is converted into a system, it comes out to be:

• x - 2y + z = 4

• y - 20z = -9

• z = -31

Step 6: Since we have calculated z = -31, put this value in equation 2:

• y - 20(-31) = -9

• y = -9 - 620

• y = -629.

Step 8: Put z = -31 and y = -629 in equation 1:

• x - 2(-629) - 31 = 4

• x + 1258 - 31 = 4

• x = 35 - 1258.

• x = -1223

So final answer is x = -1223, y = -629, and z = -31!!!

For the function y=x^5+1x^3-30x, find all real zeros.

Answers

Answer:

The real zeroes are -√5 , 0 , √5

Step-by-step explanation:

* Lets explain how to solve the problem

- The function is y = x^5 + x³ - 30x

- Zeros of any equation is the values of x when y = 0

- To find the zeroes of the function equate y by zero

∴ x^5 + x³ - 30x = 0

- To solve this equation factorize it

∵ x^5 + x³ - 30x = 0

- There is a common factor x in all the terms of the equation

- Take x as a common factor from each term and divide the terms by x

∴ x(x^5/x + x³/x - 30x/x) = 0

∴ x(x^4 + x² - 30) = 0

- Equate x by 0 and (x^4 + x² - 30) by 0

x = 0

∴ (x^4 + x² - 30) = 0

* Now lets factorize (x^4 + x² - 30)

- Let x² = h and x^4 = h² and replace x by h in the equation

∴ (x^4 + x² - 30) = (h² + h - 30)

∵ (x^4 + x² - 30) = 0

∴ (h² + h - 30) = 0

- Factorize the trinomial into two brackets

- In trinomial h² + h - 30, the last term is negative then the brackets

 have different signs (     +     )(     -     )

∵ h² = h × h ⇒ the 1st terms in the two brackets

∵ 30 = 5 × 6 ⇒ the second terms of the brackets

∵ h × 6 = 6h

∵ h × 5 = 5h

∵ 6h - 5h = h ⇒ the middle term in the trinomial, then 6 will be with

  (+ ve) and 5 will be with (- ve)

∴ h² + h - 30 = (h + 6)(h - 5)

- Lets find the values of h

∵ h² + h - 30 = 0

∴ (h + 6)(h - 5) = 0

∵ h + 6 = 0 ⇒ subtract 6 from both sides

h = -6

∵ h - 5 = 0 ⇒ add 5 to both sides

h = 5

* Lets replace h by x

h = x²

∴ x² = -6 and x² = 5

∵ x² = -6 has no value (no square root for negative values)

∵ x² = 5 ⇒ take √ for both sides

x = ± √5

- There are three values of x ⇒ x = 0 , x = √5 , x = -√5

The real zeroes are -√5 , 0 , √5

PLEASE HELP ASAP
Of the three functions in the tables, which represent linear relationships?
A. f and h
B. all three functions
c. f and g
D. g and h

Answers

Answer:

A. f and h

Step-by-step explanation:

For a linear function the First Differences of the y-values must be a constant. i.e. if we take the difference between any two consecutive y values or values of f(x) it should be the constant. For this rule to work, x values must change by the same number every time, which is true for all three given functions.

For function f:

The values of f(x) are: 5,8,11,14

We can see the difference in consecutive two values is a constant i.e. 3, so the First Difference is the same. Hence, function f is a linear function.

For function g:

The values of g(x) are: 8,4,16,32

We can see the difference among two consecutive values is not a constant. Since the first differences are not the same, this function is not a linear.

For function h:

The values of h(x) are: 28, 64, 100, 136

We can see the difference among two consecutive values is a constant i.e. 36. Therefore, function h is a linear function.

Final answer:

To identify the linear relationships in the tables, we need to look for constant rates of change. Functions f and g have this property, while h does not.

Explanation:

In order to identify which functions represent linear relationships, we need to look for patterns in the tables. A linear relationship is characterized by a constant rate of change.

Looking at the tables, we can see that functions f and g have a constant difference between the values in the input column (x) and the output column (y). However, function h does not have a constant rate of change, so it does not represent a linear relationship.

Therefore, the correct answer is A. f and h, as these two functions represent linear relationships.

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What is the solution to the system?

X+y+z=2
2x+y-z=-1
X=5-2z

Answers

Answer:

x = 1, y = -1, z = 2 → (1, -1, 2)

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}x+y+z=2&(1)\\2x+y-z=-1&(2)\\x=5-2z&(3)\end{array}\right\\\\\text{Substitute (3) to (1) and (2):}\\\\\left\{\begin{array}{ccc}(5-2z)+y+z=2\\2(5-2z)+y-z=-1&\text{use the distributive property}\end{array}\right\\\left\{\begin{array}{ccc}5-2z+y+z=2\\10-4z+y-z=-1\end{array}\right\qquad\text{combine like terms}\\\left\{\begin{array}{ccc}5+y-z=2&\text{subtract 5 from both sides}\\10+y-5z=-1&\text{subtract 10 from both sides}\end{array}\right[/tex]

[tex]\left\{\begin{array}{ccc}y-z=-3\\y-5z=-11&\text{change the signs}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}y-z=-3\\-y+5z=11\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad4z=8\qquad\text{divide both sides by 4}\\.\qquad\qquad \boxed{z=2}\\\\\text{Put it to the first equation:}\\\\y-2=-3\qquad\text{add 2 to both sides}\\\boxed{y=-1}\\\\\text{Put the values of}\ z\\text{to (3):}\\\\x=5-2(2)\\x=5-4\\\boxed{x=1}[/tex]

Find the greatest common factor of 4c and 18c

Answers

Answer:

2c

Step-by-step explanation:

c is a common factor of both terms

Consider the factors of the coefficients 4 and 18

factors of 4 : 1, 2, 4

factors of 18 : 1, 2, 3, 6, 9, 18

The common factors are 1, 2

The greatest common factor is 2

Combining with c gives

Greatest common factor of 2c

To find the greatest common factor of 4c and 18c, the common factor is 2c.

To find the greatest common factor of 4c and 18c, you need to identify the largest factor that both numbers share. In this case, the common factor is 2c. Here's how you can determine it:

Write the numbers as a product of their prime factors: 4c = 2 * 2 * c and 18c = 2 * 3 * 3 * c.

Identify the common factors: The common factors are 2 and c.

Multiply the common factors together: 2 * c = 2c.

I want to start a lemonade stand and determine how much lemonade I need to sell to break even each day.
If I know I spend $5 on supplies and sell lemonade at $0.50 per glass determine the number of glasses I must sell to break even. After you find the number of glasses tell me what the x-intercept, y-intercept and slope. Represent in the function you determined

Answers

.50x -5=0
Add 5 to both sides
.50x=5
Divide both sides by.5

X =10. You must sell 10 to break even

The slope is .50
The y intercept is -5

Answer:

Total cost spent on supplies = 5 dollars

Lemonade will be sold at 0.5 dollars.

Let the total glasses of lemonade sold be x

So, revenue generated will be = 0.5x

To get the break even we will equal both.

[tex]0.5x=5[/tex]

[tex]x=5/0.5[/tex]

x = 10

Hence, number of glasses to be sold are 10.

The profit or y can be found as;

[tex]y=0.5x-5[/tex]

So, putting x = 11

[tex]y=0.5(11)-5[/tex]

y = 0.5

Putting x = 12

[tex]y=0.5(12)-5[/tex]

y = 1

Putting x = 13

[tex]y=0.5(13)-5[/tex]

y = 1.5

The slope is 0.5.

The y-intercept is -5. This means if 0 glasses of lemonade are sold then there is a loss of $5.

The y intercept is obtained when x=0.

[tex]y=0.5(0)-5[/tex]

y = -5

The x-intercept is 10 or the number of glasses I must sell to break even.

Find the length of RJ

Answers

Answer:

Option C 89

Step-by-step explanation:

In this problem we  know that

KJ=KR+RJ

we have

KJ=95 units

KR=6 units

substitute and solve for RJ

95=6+RJ

subtract 6 both sides

RJ=95-6=89 units

Answer:

The correct option is C.

Step-by-step explanation:

We need to find the length of line segment  RJ.

From the given figure it is clear that line segment KJ is the sum of line segments KR and RJ.

[tex]KJ=KR+RJ[/tex]

The length of line segment KJ is 95 units and the length of KR is 6 units.

Substitute KJ=95 and KR=6 in the above equation.

[tex]95=6+RJ[/tex]

Subtract 6 from both the sides.

[tex]95-6=6+RJ-6[/tex]

[tex]89=RJ[/tex]

The length of segment RJ is 89 units. Therefore the correct option is C.

You have $60. The jacket you want costs $25.50 and 7% tax. what is the top tag price (excludes sales tax) left to also buy a pair of shorts?​

Answers

the assumption being, that there's a 7% sales tax on any item in the store.

so if you buy the jacket, you pay 25.5 plust 7% of 25.5.

and if you buy the shoes for price say "s", then you pay "s" plus 7% of "s".

whatever those two amounts are, they must be $60, because that's all you have in your pocket anyway.

[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{7\% of 25.5}}{\left( \cfrac{7}{100} \right)25.5}\implies 0.07(25.5)~\hfill \stackrel{\textit{7\% of "s"}}{\left( \cfrac{7}{100} \right)s}\implies 0.07s \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \stackrel{\textit{jacket}}{25.5}+\stackrel{\textit{jacket's tax}}{0.07(25.5)}+\stackrel{\textit{shoes}}{s}+\stackrel{\textit{shoe's tax}}{0.07s}~~=~~\stackrel{\textit{in your pocket}}{60} \\\\\\ 25.5+1.785+s+0.07s=60\implies 27.285+1.07s=60 \\\\\\ 1.07s=60-27.285\implies 1.07s=32.715\implies s=\cfrac{32.715}{1.07}\implies s\approx 30.57[/tex]

Which of the following is an integer?
0
4
© -12.5
0 0.454545...

Answers

Answer: 4

Step-by-step explanation: 4 is the answer because an integer is any whole number, but not 0.

I need help to solve this problem Simplify (6^7)^3​

Answers

Answer:

C.

Step-by-step explanation:

(6^7)^3 means (6^7)(6^7)(6^7).

When multiply numbers with same base, add the exponents.

6^(7+7+7)=6^(3*7)=6^(21).

In the beginning you could have just multiply 7 and 3 so the answer is 6^(21).

Answer: The Answer to this question is C bc of the brackets it multiplies the exponents if that makes sense, hope this helps

Step-by-step explanation:

Suppose BC is congruent to CA. Can you use the SSS Postulate or the SAS Postulate to prove ABD is congruent to DCA

Answers

Answer:

probably sas

Step-by-step explanation:

sas because the 2 sides are congruent, but i don't have enough information to know for sure

- The whole batch cost $28,000 and contained 140 items. Write the two rates (ratios) implied
by this statement. What would be the price for 200 items?
Please show work

Answers

Answer:

The answer would be 14

Step-by-step explanation:

you just divide 28,00 by 200 and that gives you 14

What is the coefficient of xy^4 in the expansion of (2x+y)^5

Answers

Answer:

The coefficient of xy^4 is 10

Step-by-step explanation:

to solve the questions we proceed as follows:

(2x+y)^5

=(2x+y)²(2x+y)²(2x+y)

We will solve the brackets by whole square formula:

=(4x²+4xy+y²)(4x²+4xy+y²)(2x+y)

By multiplying the brackets we get:

=32x^5+32x^4y+8x³y²+32x^4y+32x³y²+8x²y³+8x³y²+4x²y³+2xy^4+16x^4y+

16x³y²+4x²y³+16x³y²+16x²y³+4xy^4+4x²y³+4xy^4+y^5

=32x^5+80x^4y+80x³y²+40x²y³+10xy^4+y^5

Therefore the coefficient of xy^4 is 10

The answer is 10....

Answer: 10

Step-by-step explanation: a p e x

Polygon ABCD is translated to create polygon A’B’C’D’. Point A is located at (1,5), and point A’ is located at (-2,3). Which expression defines the transformation of any point (x,y) to (x’,y’) on the polygons?

Answers

Answer:

The expression is (x,y) -----> (x-3,y-2)

Step-by-step explanation:

we have that

A(1,5) ----> A'(-2,3)

so

The rule of the translation is equal to

(x,y) -----> (x',y')

(x,y) -----> (x-3,y-2)

That means-----> the translation is 3 units at left and 2 units down

Using the given points and line, determine the slope of the line.
(1, 2) and (2, 1)

Answers

Answer:

-1

Step-by-step explanation:

To find the slope of a line given two points, you can use [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are points on the line.

Or you could just line up the points vertically and subtract them vertically, then put 2nd difference over first.

Like so:

 (  2   ,     1   )

-(    1  ,     2   )

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

    1          -1

So the slope is -1/1 or just -1.

Please help, I'm stuck​

Answers

Answer: Option B

[tex]k> 0[/tex]

Step-by-step explanation:

The graph shows a radical function of the form [tex]f(x)=a(x+k)^{\frac{1}{n}}+c[/tex]

Where n is a even number.

This type of function has its vertex at the origin when [tex]k = 0[/tex] and [tex]c = 0[/tex]

If [tex]k> 0[/tex] the graph moves horizontally k units to the left

If [tex]k <0[/tex] the graph moves horizontally k units to the right.

Note that in this case the vertex of the function is horizontally shifted 5 units to the left. Therefore we know that [tex]k = 5> 0[/tex]

The correct answer is option B

Given the triangle below, what is m

Answers

Answer:

82.8 degrees

Step-by-step explanation:

The information given here SSS.  That means side-side-side.

So we get to use law of cosines.

[tex](\text{ the side opposite the angle you want to find })^2=a^2+b^2-2ab \cos(\text{ the angle you want to find})[/tex]

Let's enter are values in.

[tex]12^2=10^2+8^2-2(10)(8) \cos(B)[/tex]

I'm going to a little simplification like multiplication and exponents.

[tex]144=100+64-160 \cos(B)[/tex]

I'm going to some more simplification like addition.

[tex]144=164-160\cos(B)[/tex]

Now time for the solving part.

I'm going to subtract 164 on both sides:

[tex]-20=-160\cos(B)[/tex]

I'm going to divide both sides by -160:

[tex]\frac{-20}{-160}=\cos(B)[/tex]

Simplifying left hand side fraction a little:

[tex]\frac{1}{8}=\cos(B)[/tex]

Now to find B since it is inside the cosine, we just have to do the inverse of cosine.

That looks like one of these:

[tex]\cos^{-1}( )[/tex] or [tex]\arccos( )[/tex]

Pick your favorite notation there.  They are the same.

[tex]\cos^{-1}(\frac{1}{8})=B[/tex]

To the calculator now:

[tex]82.81924422=B[/tex]

Round answer to nearest tenths:

[tex]82.8[/tex]

An Information Services Manager is purchasing a large number of word processing software licenses at a cost of $125 each. the software company gives a volume discount of 3.5% for large purchases. If the department manager has a budget of $17,300 to purchase the licenses, approximately how many licenses can she purchase.

Answers

Answer:

143

Step-by-step explanation:

17300=.965(125X)

17927.46=125X

143.41=X

Final answer:

To calculate the number of software licenses the department manager can purchase, we first find the discounted price of a single license, then divide the total budget by this single license price. In this case, the manager can purchase approximately 143 licenses with a budget of $17,300.

Explanation:

The subject of this question is a typical real-life application of Mathematics, specifically in percentages and budgeting. Given the scenario, the Information Services Manager plans to buy word-processing software licenses for each cost of $125. However, a volume discount of 3.5% is offered for large purchases.

Firstly, we need to figure out the discounted price of one license, which can be calculated as 96.5% (100% - the 3.5% discount) of $125, leading to $120.63 approximately (rounding the number to two decimal places).

With a total budget of $17,300, the number of licenses she can purchase can be found by dividing the total budget by the price of a single license after the discount: $ 17,300 divided by $120.63, which gives us approximately 143.

Therefore, the department manager can buy approximately 143 licenses when considering the volume discount.

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True or false? An angle whose vertex is at the center of the circle is a central angle of that circle.

Answers

This statement would be true: if the vertex of an angle is at the center of the circle, then it would be the central angle.

If f(a) =11, then use the table above to find f(a-2)​

Answers

Answer:

7

Step-by-step explanation:

From the table

f(a) = 11 → a = 7

a - 2 = 5

f(a - 2) = f(5) = 7

Find a linear equation satisfying the conditions:
x-intercept at (-2,0) and y-intercept at (0, -3).

Answers

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 2, 0 ) and (x₂, y₂ ) = (0, - 3)

m = [tex]\frac{-3-0}{0+2}[/tex] = - [tex]\frac{3}{2}[/tex]

Note the line crosses the y- axis at (0, - 3) ⇒ c = - 3

y = - [tex]\frac{3}{2}[/tex] x - 3 ← equation in slope- intercept form

janis jogs around a rectangular park that is 3/4 mi long and 1/4 mi wide. how far is it around the park?

Answers

Answer:

[tex]2\ miles[/tex]

Step-by-step explanation:

we know that

The distance around the park is equal to the perimeter of the rectangular park

The perimeter is equal to

[tex]P=2(L+W)[/tex]

we have

[tex]L=\frac{3}{4}\ mi[/tex]

[tex]W=\frac{1}{4}\ mi[/tex]

substitute the values

[tex]P=2(\frac{3}{4}+\frac{1}{4})[/tex]

[tex]P=2(\frac{4}{4})[/tex]

[tex]P=2\ mi[/tex]

Answer:

3 219⁄1000 km. [2 mi.]

Step-by-step explanation:

P = 2l + 2w

P = 2[¾] + 2[¼]

P = 1½ + ½

P = 2

I am joyous to assist you anytime.

celest
Guided Practice
4. Find the next three terms in the sequence.
etric Sequences
-3, 6, -12, 24, ...
A - 48,96, -1923
hential Growth and
B 48, -96, 192
stest
C -36, 72, -144
mials
mials and Factoring
nic Equations and

Answers

Answer:

A - 48,96, -192

Step-by-step explanation:

Given:

geometric sequence:

-3, 6, -12, 24,

geometric sequence has a constant ratio r and is given by

an=a1(r)^(n-1)

where

an=nth term

r=common ratio

n=number of term

a1=first term

In given series:

a1=-3

r= a(n+1)/an

r=6/-3

r=-2

Now computing next term a5

a5=a1(r)^(n-1)

    = -3(-2)^(4)

   = -48

a6=a1(r)^(n-1)

    = -3(-2)^(5)

   = 96

a7=a1(r)^(n-1)

    = -3(-2)^(9)

   = -192

So the sequence now is -3, 6, -12, 24,-48,96,-192

correct option is A!

the terminal side of an angle in standard position passes through P(-3,-4). what’s the value of tan(Theta)

Answers

Answer:

4/3

Step-by-step explanation:

I drew a picture in the attachment to show what we are looking at.

I found the point (-3,-4).  I drew my angle my triangle from the x-axis and the origin to the point.

The angle that is theta is the one formed by the x-axis and the hypotenuse of the triangle where this hypotenuse was formed from the line segment from the origin to the given point.

[tex]\tan(\theta)=\frac{\text{opposite to }\theta}{\text{adjacent to }\theta}=\frac{-4}{-3}=\frac{4}{3}[/tex]

So we could have said [tex]\tan(\theta)=\frac{y}{x}[/tex].

A triangular field has sides of 120.32 m and 204.61 m, and the angle between them measures 60.881°. Find the area of the field

Answers

Answer:

A=10753.5715 m^2.

Step-by-step explanation:

The area of a triangle with the information SAS given is:

A=1/2 * (side) * (other side) * sin(angle between)

A=1/2 * (204.61)*(120.32) * sin(60.881)

A=10753.5715 m^2.

SAS means two sides with angle between.

Answer: [tex]10,753.57\ m^2[/tex]

Step-by-step explanation:

You need to use the SAS area formula. This is:

[tex]A=\frac{a*b*sin(\alpha)}{2}[/tex]

You know that the  triangular field has sides of 120.32 meters and 204.61 meters and the angle between them measures 60.881°. Then:

[tex]a=120.32\ m\\b=204.61\ m\\\alpha =60.881\°[/tex]

Substituting these values into the formula, you get that the area of this triangle is:

[tex]A=\frac{(120.32\ m)(204.61\ m)*sin(60.881\°)}{2}\\\\A=10,753.57\ m^2[/tex]

The length of a new rectangular playing field is 5 yards longer than triple the width. If the perimeter of the rectangular playing field is 346 ​yards, what are its​dimensions?​

Answers

Final answer:

The length and width of the rectangular field are determined using algebra by setting up and solving two equations which represent the relationships between the length, width, and perimeter of the field. The dimensions are found to be 46 yards for the width and 137 yards for the length.

Explanation:

The dimensions of the rectangular playing field can be found using algebra, specifically the formulas for the dimensions and perimeter of a rectangle. The problem can be translated into two equations reflecting the relationships of the field's width and length to the perimeter.

The first equation is: L = 3W + 5, which represents the relationship that the length is 5 yards longer than triple the width.

The second equation is derived from the formula for the perimeter of a rectangle (P = 2L + 2W), which given the problem's perimeter of 346 yards gets us: 2L + 2W = 346.

Substitute the first equation into the second to solve for the width, then use that result to find the length. The solution indicates that the width of the rectangular playing field is 46 yards, and the length is 137 yards.

Learn more about Rectangle Dimensions here:

https://brainly.com/question/35474401

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If f(x) = -x + 8 and g(x) = x^4, what is (gºf)(2)?

Answers

Answer:

[tex]\large\boxed{(g\circ f)(2)=1296}[/tex]

Step-by-step explanation:

[tex](g\circ f)(x)=g\bigg(f(x)\bigg)\\\\f(x)=-x+8,\ g(x)=x^4\\\\(g\circ f)(x)=\g\bigg(f(x)\bigg)=(-x+8)^4\\\\(g\circ f)(2)\to\text{put x = 2 to the equation}\ (g\circ f)(x):\\\\(g\circ f)(2)=(-2+8)^4=(6)^4=1296[/tex]

[tex]\bf \begin{cases} f(x)=&-x+8\\ g(x)=&x^4\\ (g\circ f)(x) =& g(~~f(x)~~) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ f(2)=-(2)+8\implies f(2)=\boxed{6} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{(g\circ f)(2)}{g(~~f(2)~~)}\implies g\left( \boxed{6} \right) = (6)^4\implies \stackrel{(g\circ f)(2)}{g(6)} = 1296[/tex]

Apply the distributive property to create an equivalent expression.
\dfrac12(10x + 20y +10z) =
2
1
​ (10x+20y+10z

Answers

Step-by-step explanation:

[tex]\text{The distributive property:}\ a(b+c)=ab+ac\\\\\dfrac{1}{2}(10x+20y+10z)=\dfrac{1}{2\!\!\!\!\diagup_1}\cdot10\!\!\!\!\!\diagup^5x+\dfrac{1}{2\!\!\!\!\diagup_1}\cdot20\!\!\!\!\!\diagup^{10}y+\dfrac{1}{2\!\!\!\!\diagup_1}\cdot10\!\!\!\!\!\diagup^5z\\\\=5x+10y+5z[/tex]

Answer:

5x+10y+5z

Step-by-step explanation:

I did it on Khan Academy :)

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