The coordinate plane below represents a city.


Points A through F are schools in the city. graph of coordinate plane. Point A is at negative 3, negative 4. Point B is at negative 4, 3. Point C is at 2, 2. Point D is at

The coordinate plane is below

Part A: Using the graph above, create a system of inequalities that only contain points C and F in the overlapping shaded regions. Explain how the lines will be graphed and shaded on the coordinate grid above.


Part B: Explain how to verify that the points C and F are solutions to the system of inequalities created in Part A.


Part C: Natalie can only attend a school in her designated zone. Natalie's zone is defined by y < −2x + 2. Explain how you can identify the schools that Natalie is allowed to attend.

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

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]

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.

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]

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.

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)

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]

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.

Answer: 4

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

Answer:

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]

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]

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.

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.

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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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

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].

Answer:

Step-by-step explanation:

From the table

f(a) = 11 → a = 7

a - 2 = 5

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

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 :)

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:

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.

Answer:

143

Step-by-step explanation:

17300=.965(125X)

17927.46=125X

143.41=X

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.

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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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!!!

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

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!

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.

Answer:

The answer would be 14

Step-by-step explanation:

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

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

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.

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

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.

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.

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.

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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