Angles R and S are vertical angles. Angle R has a measure of (4x + 20). Angle S has a measure of 84. What is the value of x?

Answer:

2x– 3y = –18

3x + y = -5

Converting the equation in slope-intercept form

2x-3y= -18

-3y= -2x-18

-3y= -(2x+18)

3y=2x+18

y=(2x+18)/3

And for equation 2

y= -5-3x

For plotting the graph, the online graphing calculator desmos.com can be used.

The points can be calculated by putting negative and positive values of x in both equations.

The graph is attached as a picture.

As we can see from the graph that two lines intersect at (-3,4) so it is the solution of the given system of linear equations.

Answer:

[tex](-3,4)[/tex],

Step-by-step explanation:

The given system of equations is

[tex]\left \{ {{2x-3y=-18} \atop {3x+y=-5}} \right.[/tex]

To solve this system, we could multiply the second equation by 3, and solve for x:

[tex]\left \{ {{2x-3y=-18} \atop {9x+3y=-15}} \right.\\11x=-33\\x=\frac{-33}{11}=-3[/tex]

Now, we replace this value in a equation to find y-value:

[tex]3x + y = -5\\3(-3)+y=-5\\-9+y=-5\\y=-5+9\\y=4[/tex]

Therefore, the solution for the system is [tex](-3,4)[/tex], you can observe this in the graph attached.

650000(0.025) = $16,250

Answer:

$16250 commission

($650,000 times .025 (2.5%) = $16250)

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}3x+4y=-23&(1)\\x=3y+1&(2)\end{array}\right\\\\\text{Substitute (2) to (1):}\\\\3(3y+1)+4y=-23\qquad\text{use the distributive property}\\\\(3)(3y)+(3)(1)+4y=-23\\\\9y+3+4y=-23\qquad\text{subtract 3 from both sides}\\\\13y=-26\qquad\text{divide both sides by 13}\\\\\boxed{y=-2}\\\\\text{Put the value of }\ y\ \text{to (2)}:\\\\x=3(-2)+1\\\\x=-6+1\\\\\boxed{x=-5}[/tex]

Answer:

x = -5

y = -2

Step-by-step explanation:

Answer:

[tex]13.96\%[/tex]  

Step-by-step explanation:

we know that

The  formula to calculate the depreciated value  is equal to  

[tex]V=P(1-r)^{x}[/tex]  

where  

V is the depreciated value  

P is the original value  

r is the rate of depreciation  in decimal  

x  is Number of Time Periods  

in this problem we have  

[tex]P=\$18,000\\r=?\\x=10\ years\\V=\$4,000[/tex]

substitute in the formula

[tex]\$4,000=\$18,000(1-r)^{10}[/tex]  

Simplify

[tex](2/9)=(1-r)^{10}[/tex]  

[tex](2/9)^{1/10}=(1-r)[/tex]  

[tex]r=1-(2/9)^{1/10}[/tex]  

[tex]r=0.1396[/tex]  

convert to percent

[tex]r=0.1396*100=13.96\%[/tex]  

Answer:

Required inequality is [tex]4800+183x>8000[/tex].

Step-by-step explanation:

Given that Mrs. Robinson, an insurance agent, earns a salary of $4,800 per year plus a 3% commission on her sales. The average price of a policy she sells is $6,100. Write an inequality to find how many policies Mrs. Robinson must sell to make an annual income of at least $8,000.

Calculation is given by:

Salary per year = $4,800

Average price of a policy = $6,100.

commission on her sales = 3%

Then commission on $6,100 = 3% of $6,100 = 0.03 ($6,100) = $183

Let number of policies Mrs. Robinson must sell to make an annual income of at least $8,000 = x

then total commission on x policies = 183x

Total income using x policies = 4800+183x

Since she wants to make an annual income of at least $8,000. so we can write inequality as:

[tex]4800+183x>8000[/tex]

Hence required inequality is [tex]4800+183x>8000[/tex].

Answer:

C.

Step-by-step explanation:

C is true because we already know g(0) is -2, and functions cannot repeat themselves with different numbers like that. A is not true because the range does not go that far down. B is not true because the domain does not go that far up.

Answer:

C is the answer

Step-by-step explanation:

C is the answer because

3.5 cookies

Friend one: 3 Friend two: 3

One leftover cookie

Split in half give one to each and that makes 3.5

Each of the 2 friends gets 3.5 cookies when sharing 7 cookies equally.

When 2 friends share 7 cookies equally, you divide the total number of cookies by the number of friends. Here, you need to divide 7 cookies by 2 to find out how many cookies each person gets. The calculation would be:

Divide 7 by 2: 7 \/ 2 = 3.5

So, each friend gets 3.5 cookies. However, since you cannot share a cookie perfectly in half without changing its state, we assume this division is hypothetical. In a real-world scenario, they might have to decide how to divide the last cookie or simply share it equally, giving each friend half of the last cookie.

Answer: Mika walks 16 days and 26.5 total miles.

Step-by-step explanation: You count each x to figure out the days and and them all together like so: 1 1/2 x 5 = 7 1/2. 7 1/2 + 1 5/8 = 12.1875, and so forth and so on.

hence the answer is 16units

hope helps you!!!!!!

The equation of diagonals of kite are x = 0 and y = 0 and their point of intersection is (0,0)

A straight line is a one-dimensional figure that never ends and has no breadth.

Equation of line : y = mx + c

m - slope of the line

c - y intercept

Let the vertices of the Kite ABCD be A(-4 , 0), B(0 , 4), C(4 , 0), D(0 , -4)

The equation of Diagonal AC is y = 0

The equation of Diagonal BD is x = 0

The point of intersection of diagonals will be ( 0 , 0)

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it is the same as subtraction 34

50+(-34)=50-34

When substituting x=2 and t=4 into the expression 1/8 (x^3 - 4)(t^2 + 8), it simplifies to 12.

If x=2 and t=4, to find the value of 1/8 (x3 - 4)(t2 + 8), we must substitute the values of x and t into the expression and simplify.

Firstly, calculate x3:

x^3 = 23 = 8

Then, calculate t2:

t^2 = 42 = 16

Now we substitute x^3 and t^2 into the expression:

1/8 (8 - 4)(16 + 8) = 1/8 (4)(24) = 1/8 * 96 = 12

Hence, the value of the expression is 12 when x = 2 and t = 4.

Polygon D'E'F'G' is larger than polygon DEFG, because the scale factor is greater than 1.

An equation is an expression that shows the relationship between two or more numbers and variables.

Polygon DEFG is dilated with the origin as the center of dilation using the rule (x, y) → (2x, 2y) to create polygon D'E'F'G'. Therefore:

Polygon D'E'F'G' is larger than polygon DEFG, because the scale factor is greater than 1.

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The dilation doubles the distances between corresponding vertices, indicating an enlargement.

Therefore, choice A is correct: Polygon D'E'F'G' is larger due to the scale factor exceeding 1.

To determine whether polygon D'E'F'G' is larger or smaller than polygon DEFG after dilation with the origin as the center and using the rule (x, y) → (2x, 2y), we need to understand the effect of the dilation on the coordinates of the vertices.

Let's assume the coordinates of the vertices of polygon DEFG are as follows:

D(x₁, y₁)

E(x₂, y₂)

F(x₃, y₃)

G(x₄, y₄)

Now, applying the dilation rule (x, y) → (2x, 2y) to each vertex, we get the coordinates of the corresponding vertices of polygon D'E'F'G':

D'(2x₁, 2y₁)

E'(2x₂, 2y₂)

F'(2x₃, 2y₃)

G'(2x₄, 2y₄)

Now, let's compare the distances between the vertices of the original and dilated polygons to determine if the dilation resulted in enlargement or reduction.

1. Distance between D and E:

  Original: √((x₂ - x₁)² + (y₂ - y₁)²)

  Dilated: √((2x₂ - 2x₁)² + (2y₂ - 2y₁)²) = √(4(x₂ - x₁)² + 4(y₂ - y₁)²)

  The distance between D' and E' is twice the distance between D and E. So, the scale factor is indeed 2, indicating an enlargement.

2. Similarly, for the other sides (DE, EF, FG), we'll find the same result.

Since the scale factor is greater than 1, we can conclude that polygon D'E'F'G' is larger than polygon DEFG.

So, the correct answer is:

A) Polygon D'E'F'G' is larger than polygon DEFG, because the scale factor is greater than 1.

The geometric sequence is B: 32

Final answer:

To find the 6th term in the given geometric sequence, the common ratio is calculated and the nth term formula is applied. However, the calculated value doesn't match any of the provided options, indicating a possible error in calculation or the sequence itself.

Explanation:

To find the 6th term of the geometric sequence 1024, 528, 256, we first need to determine the common ratio. We get this by dividing the second term by the first term:

Common ratio (r) = 528 / 1024 = 0.515625

Now, using the formula for the nth term of a geometric sequence, which is an = a1 × r(n-1), where a1 is the first term and n is the term number:

a6 = 1024 × 0.515625(6-1) = 1024 × (0.515625)5

Calculating this, we get:

a6 = 1024 × 0.1184844970703125 = 121.234375

This value does not match any of the options provided (64, 32, 16, or 8), suggesting that there may have been a miscalculation or misunderstanding of the sequence. Please double-check the sequence or provide additional information.

Answer:

y= |x|-2.5

Step-by-step explanation:

The attached picture is the graph for the function y=|x|

The picture you asked differs in the origin of the graph, which resides in the point (0, -2.5).

So our equation should look like the following

y=a|x|+b

From the first point you have (0, -2.5), This means 0=a*|0|+b, we have obtained that b=-2.5

Now 'a' is the slope, we need to find another point in the graph. that would be (2.5, 0) (obtained from the given graph)

the slope is obtained using the equation

[tex]a=\frac{x_{2}-x_{1} }{y_{2}-y_{1}  }[/tex]

Where (x1, y1)= (0, -2.5), (x2,y2)=(2.5,0)

thus we have that a=1

So our equation is y=|x|-2.5

$160 marked down 25% would be 40

Answer:

2x=30 degrees

Step-by-step explanation:

Add up all of the angles and set them equal to 180 degrees, because triangles are always made up of angles with a sum of 180 degrees.

2x+4x+6x=180

12x=180

x=15

smallest angle is 2x

2(15)=30

Answer: b 11.9

Step-by-step explanation:

the chord and the line to the center can be used to create a triangle

the radius is the hypotenuse of this triangle

4.5squared + 11 squared= 11.9

Answer:

f(x) = x3 − 3x2 − 13x + 15    Factor:   x+3

f(x) = x4 + 3x3 − 8x2 + 5x − 25   Factor:  x+5

f(x) = x3 − 2x2 − x + 2     Factor:  x-2

f(x) = -x3 + 13x − 12  Factor:  x+4

Step-by-step explanation:

f(x) = x^3 − 3x^2 − 13x + 15

Solving:

We will use rational root theorem: -1 is the root of x^3 − 3x^2 − 13x + 15 so, factor out x+1

x^3 − 3x^2 − 13x + 15 / x+1 = x^2-2x-15

Factor: x^2-2x-15 =(x+3)(x-5)

So, factors are: (x+1)(x+3)(x-5)

Factor: (x+5)

f(x) = x^4 + 3x^3 − 8x^2 + 5x − 25

Solving:

We will use rational root theorem: -5 is the root of x^4 + 3x^3 − 8x^2 + 5x − 25, so factour out (x+5)

x^4 + 3x^3 − 8x^2 + 5x − 25 / x+5 = x^3-2x^2 +2x -5

So, factors are (x+5) (x^3-2x^2 +2x -5)

  Factor:  x+5

f(x) = x^3 − 2x^2 − x + 2    

Solving:

x^2(x-2)-1(x-2)

(x-2)(x^2-1)

(x-2) (x-1) (x+1)

Factor:  x-2

f(x) = -x^3 + 13x − 12

Solving:

-(x^3 + 13x -12)

We will use rational root theorem:

The 1 is a root of (x^3 + 13x -12) so, factor out x-1

Now solving (x^3 + 13x -12)/x-1 we get (x-3)(x+4)

So, roots are: - (x-1)(x-3)(x+4)

Factor (x+4)

Answer:

Polynomial 1 = x + 3

Polynomial 2 = x + 5

Polynomial 3 = x - 2

Polynomial 4 = x + 4

Step-by-step explanation:

We are given with Polynomials and and some factors.

We have to match the correct Pair.

We Map the polynomials on the graph then check which factors matches.

Polynomial 1).

x³ - 3x² - 13x + 15

factors are ( x + 3 ) , ( x - 1 ) , ( x - 5 )

Polynomial 2).

[tex]x^4+3x^3-8x^2+5x-25[/tex]

factors are ( x + 5 )

Polynomial 3).

[tex]x^3-2x^2-x+2[/tex]

factors are ( x + 1 ) ,( x - 1 ) , ( x - 2 )

Polynomial 4).

[tex]-x^3+13x-12[/tex]

factors are ( x + 4 ) ,( x - 1 ) , ( x - 3 )

Therefore,

Polynomial 1 = x + 3

Polynomial 2 = x + 5

Polynomial 3 = x - 2

Polynomial 4 = x + 4

Answer:

No, the bolt won't fit into the hole

Step-by-step explanation:

We need to convert the diameter of the bolt into decimal by dividing:

2/9 = 0.222...

The hole has diameter of 0.2

Hence, 0.222 is larger than 0.2, so the bolt won't fit.

For an equation to be linear, the slope has to be the same/constant.

To find the slope (m), you use the slope formula:

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]  and substitute in 2 points

(1 , 60) [x₁ , y₁] and (5 , 70) [x₂ , y₂]

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]  

[tex]m=\frac{70-60}{5-1}[/tex]

[tex]m=\frac{10}{4} =\frac{5}{2}[/tex] or 2.5

Try a different point to see if the slope is the same:

(5, 70) and (20, 80)

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m=\frac{80-70}{20-5}[/tex]

[tex]m=\frac{10}{15} =\frac{2}{3}[/tex] or 0.6666666

Since the slopes are different, a linear equation can not be used

Final answer:

To solve the given system of linear equations, the elimination method is used, resulting in the solution x = 63/26 and y = -97/26.

Explanation:

The system of equations presented by the student:

-4x + 5y = 8

6x - y = 11

belongs to the topic of algebra, specifically to solving systems of linear equations. To find the values of x and y that satisfy both equations, we can use methods like substitution or elimination. Let's use elimination in this case:

Multiply the second equation by 5 so that the y terms will cancel out when we add the two equations together. The second equation becomes 30x - 5y = 55.

Add the modified second equation to the first equation:

-4x + 5y = 8
+ 30x - 5y = 55

____________________

26x         = 63

Solving for x, we find that x = 63/26.

Substitute x into one of the original equations to find y.

Using 6x - y = 11:

6(63/26) - y = 11

378/26 - y = 11

y = 378/26 - 286/26

y = 92/26

Therefore, the solution to the system of equations is x = 63/26 and y = 92/26.

8-2x = 10x+3 Subtract 3 from both sides

5-2x = 10x Add 2x to both sides

5 = 12x Divide 12 to both sides

Final answer X=5/12

The solution to the algebraic expression 8-2x=10x+3 is: x = 12/5

An algebraic expression in mathematics is defined as an expression which is made up of variables and constants, along with algebraic operations

We are given the algebraic expression as:

8 - 2x = 10x + 3

Using addition property of equality, add 2x - 3 to both sides to get:

8 - 2x + 2x - 3 = 10x + 3 + 2x - 3

5 = 12x

x = 12/5

x = 2.4

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51 is the interquartile range for the set of data hope this helps;)

Answer:

Thank youuu

Step-by-step explanation:

Answer:

£7,878

Step-by-step explanation:

she gets:

40p× 260 miles = 10,400p

she pays:

52 : 5.36= £9.70 per mile

260 x 9.70 = £2,522

to find out what she claimes more than she pays: 10,400 - 2,522 = 7,878

Amal claims £77.2 more than what she spends on petrol for a 260 miles journey for work.

To solve this problem, we need to calculate how much Amal earns for the journey and how much she pays for petrol.

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You pess the thing that looks like a paperclip. Then you take a picture and crop it

Answer:

52$

Step-by-step explanation:

ok so 2 pins cost 4$ so if you buy one pin its 2$ correct? take 12 and multiply it by 2 and take 14 and multiply by 2,

12×2=24$

14×2=28$

add those two together and you get 52$

The given expression simplifies to 0.

To simplify the expression (2√6÷√2+√3)+(6√2÷√6+√3)-(8√3÷√6+√3), we need to simplify each term and then combine like terms. Let's break it down step by step:

Simplify 2√6÷√2 by realizing that √6÷√2 is equivalent to √3. So, 2√3 remains.

In the second term, 6√2÷√6, √6÷√6 simplifies to 1, so we just have 6√2.

For the last term, 8√3÷√6, √3÷√6 simplifies to √(3÷6), which simplifies further to √(1÷2), or 8÷√2.

Combine like terms with the common denominator of √3, resulting in:
(2√3 + 6÷√3 - 8÷√3).

The terms with the square root denominators can be combined into (-2√3).

After combining, we have (2√3 - 2√3), which simplifies to 0. Therefore, the simplified expression is 0.

Answer:96

Step-by-step explanation:

A; 480/16 = 30 students per classroom

B: 192/12 =16 students per classroom

we need x such that [tex]\frac{480-x}{16} = \frac{192+x}{12}[/tex]

which means

(480-x )* 12 should be equal to (192+x) * 16

5,760 - 12x = 3,072+16x

5,760 - 3,072 = 12x + 16x

2,688 = 28x

x = 96

Answer:

1.  52

2. 2.9

Step-by-step explanation:

To find the mean, we take all the numbers, add them up then divide by the number of numbers.

1.  mean height

mean = (50+54+52+56+48)/5

            =260/5

            =52

52 inches

2.  mean score

There are 5+3+12+2+6+6+4 students = 38 students

Multiply the number of students times the score and add together

total points =  (0*5+1*3+2*12+3*2+4*6+5*6+6*4)

        = 111

The mean is the total points  divided by the number of students

mean = 111/38

        =2.92

Answer:

[tex]\bar x = 52inch\\\bar x_w = 2.92[/tex]

Step-by-step explanation:

According to the data recorded in the table, the average of the students' heights is calculated with the expression for the arithmetic mean:

[tex]\bar x =\frac{1}{n} \sum x_i[/tex]

[tex]\bar x = \frac{1}{5}(48 + 50 + 52 + 54 + 56) = \frac{260}{5} = 52[/tex]inch.

In the same way, the weighted average must be used to find the average football score:

[tex]\bar x_w = \frac{\sum x_i * w_i}{\sum w_i}[/tex], where wi are the frequencies of each response.

[tex]\bar x_w = (0 * 5 + 1 * 3 + 2 * 12 + 3 * 2 + 4 * 6 + 5 * 6 + 6 * 4) / (5 + 3 + 12 + 2 + 6 + 6 + 4) = \frac{111}{38} = 2.92[/tex]

Answer:

C- 42

Step-by-step explanation:

there are 8 ounces in a cup so 12 x 8 = 96 oz

96/2.25 = 42.6666666667

Rounded back to 42

By using all the chocolate cream, at most the number of eclairs that can be made is:

                 C) 42

It is given that:

You have 12 cups of chocolate cream to fill eclairs.

Each eclair requires 2.25 ounces of filling.

We know that:

The universal conversion that is used is:

  1 cups=8 ounces

and hence,

12 cups= 12×8=96 ounces.

Hence, the number of ounces of chocolate cream to fill eclairs= 96 ounces

Also,

amount of filling required by 1 eclair= 2.25 ounces.

Hence, Number of eclairs that can be made is:

[tex]Number\ of\ eclairs=\dfrac{96}{2.25}\\\\i.e.\\\\Number\ of\ eclairs=42.67[/tex]

This means that:

Atmost the number of eclairs than can be made= 42