25) (1,-5) parallel to y = - 10x - 3

In cylindrical coordinates, we take

x = r cos(t)

y = r sin(t)

z = z

(a) Then

6x + 5y + z = 6

transforms to

6r cos(t) + 5r sin(t) + z = 6

(b) We have

x² + y² = r² (cos²(t) + sin²(t)) = r²

so

-4x² - 4y² + z² = 5

converts to

-4r² + z² = 5

The equation of circle is x² + y² = 36.

We have,

Center= (0, 0)

Passing point = (0, 6)

We know the equation of circle is

(x-h)² + (y-k)² = r²

where (h, k) be the center and r be the radius.

Now, the radius of circle is

= √(6-0)² + (0-0)²

= √36

= 6 unit

So, the equation of circle

(x-0)² + (y-0)² = 6²

x² + y² = 36

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Answer:

3/8

Step-by-step explanation:

3/8 of 16 is 6

1/4 of 16 is 4

6+4 = 10

16-10 = 6

3/8 of 16 = 6

From the provided graph, Due to the greater impact of the internet on education and news, PPF on the x-axis (education and news axis) moves more than the shift on the y-axis.

Mathematicians use graphs to lοgically convey facts or values using visual representations or charts. A graph pοint will typically reflect a relationship between two or more things. Nοdes, or vertices, and edges make form a graph, a nοn-linear data structure. Glue together the nodes, often referred tο as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representatiοns of expοnential growth. a lοgarithmic graph in the shape of a triangle.

Assume that in the "οld PPF," which existed befοre the internet, equal amounts of news, educatiοn, and other commodities and services are generated.

Due to the greater impact οf the internet on education and news, PPF on the x-axis (education and news axis) moves mοre than the shift on the y-axis.

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Question:

Look at the following pairs of numbers (a, b) which are related by a proportion b= k·a. (5, 20), (6, 24), (7, 28), (8, 32) What is the value of k?

Solution:

Take any of the given points. For example. take the point (a,b) = (5,20) and replace it into the proportion equation

this gives us:

now, solve for k:

then, the correct answer

4

A

x=75°

B

We know that ∠EFG=∠ABF because they are corresponding angles.

We also know that ∠x+∠ABF=180, because angles along a straight line always equal 180:

x+105=180

x=75°

Answer:

Number of TAILS outcomes = 100 - 58 = 42

Experimental probability of TAILS = Number of TAILS outcomes / Total number of outcomes = 42/100 = 0.42

The theoretical probability of getting HEADS or TAILS is 0.5 each, assuming the penny is fair.

The experimental probability of HEADS is 58/100 = 0.58, which is close to the theoretical probability of 0.5. This suggests that Aaron's experiment is consistent with the theoretical probability. Similarly, the experimental probability of TAILS is 0.42, which is also close to the theoretical probability of 0.5. This further supports the idea that the penny is fair.

The missing values are:

angle DGE = 45 degrees

angle EDG = 85 degrees

FD = 10

GD = 10√2

EG = (20 + 13√3) / 2

The missing sides in the figure is solved as follows

angle DGE = angle BAG = 45 degrees (alternate angles are equal)

angle EDG = angle ADC (vertical angles are equal)

angle ADC + 45 + 50 = 180 (sum of angles in a triangle)

angle ADC = 180 - 50 - 45

angle ADC = 85 degrees

Since DGE = 45 degrees and FG = 10

tan 45 = FD / FG

tan 45 = FD / 10

FD = 10

solving for GD

GD² = FD² + FG² = 10² + 10² = 200

GD = 10√2

solving for EG

EG = EF + FG

cos 50 = EF / 13

EF = 13 cos 50 = 13√3 / 2

EG = EF + FG = 13√3 / 2  + 10 = (20 + 13√3) / 2

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Answer:

D. Kelsey graphed the slope as the y-intercept and the y-intercept as the slope.

Step-by-step explanation:

The equation to graph was : y= 3x + 1 where the slope is 3 and the y-intercept is 1

However, Kelsey graph line passes through points (-3, 0)and (0, 3).From these points the equation of the line is;

m=Δy/Δx  where

m=the slope of the graph

Δy= 3-0 =3

Δx= 0--3 =3

m=3/3 = 1

The equation of the line should be;

m=Δy/Δx

1=y-3/x-0

1x= y-3

3+1x= y

y= 1x + 3 ----------where the slope is 1 and y-intercept is 3

So you can see here that in the original equation, the slope m is 3 and y-intercept is 1 as shown in the first attached graph.

While in the Kelsey's graph, the slope is 1 and the y-intercept is 3 as in the second attached graph.

Thus, the correct answer is D : Kelsey graphed the slope,3 as the y-intercept and the y-intercept,1, as the slope.

Answer choice A is incorrect because Kelsey didnot graph the y-intercept, 1 on the x-axis but graphed point (-3,0) on the x-axis.

Answer choice B is incorrect because on Kelsey's equation the y-intercept is 3 and not -3. i.e. y=1x + 3

Answer choice C is incorrect because Kelsey graphed the slope as up 1 right 1 which is okay per the equation , y=1x+3.However, this incorrect because the correct graph has a slope of 3.

Answer:

the answer is the last option  

Step-by-step explanation:

hope this helps

have a good day

did the test on edge

the sequence g is a decreasing sequence.

Here is the step-by-step solution to the problem based on the information given in the question:

Wanahton purified a portion of water with 900 grams of contaminants. Each hour, a third of the contaminants was filtered out.Let g(n) be the amount of contaminants (in grams) that remained by the beginning of the nth hour. g is a sequence. We need to determine the kind of sequence.The amount of contaminants in the beginning

= 900 grams

Amount of contaminants filtered out

= (1/3) * 900 = 300

grams Amount of contaminants left after first

hour = 900 - 300 = 600

gramsAmount of contaminants filtered out in the second

hour = (1/3) * 600 = 200

grams Amount of contaminants left after the second

hour = 600 - 200 = 400 grams

Amount of contaminants filtered out in the third

hour = (1/3) * 400 = 133.33 grams

(rounded to two decimal places)Amount of contaminants left after the third

hour = 400 - 133.33 = 266.67 grams

(rounded to two decimal places)In this way, the sequence will continue. We can observe that the amount of contaminants in the beginning is decreasing and the sequence is decreasing as well

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Answer:

2x^3 - 9x^2 + 7x + 6

Step-by-step explanation:

(2x + 1)(x - 3)(x - 2)=2x^3 - 9x^2 + 7x + 6

Answer:

i think it would be B.The slope is approximately 1.33 and the y-intercept is 2.

it would be more clear if you put a graph :)

Answer:

Step-by-step explanation:

A=1/2 a p                 a is apothem;  p is perimeter of base

p=22*5 =110

a you need to find by making a triangle with the radius and finding the angle of the right triangle

All external angles of any polygon =360

divide by 5 and then 2 to find triangle

=54

Use tan 54 = a/11

a=15.14

A= 1/2 *15.14 *54

408.8

Answer:

14 students have to retake the test

Step-by-step explanation:

to calculate the mean mark as

sum of ( product of mark and frequency ) ÷ total

mean = \(\frac{14(2)+15(10)+16(2)+17(3)+18(13)}{30}\)

        = \(\frac{28+150+32+51+234}{30}\)

       = \(\frac{495}{30}\)

      = 16.5

students who score less than 16.5 will retake the test , that is

2 scored 16 , 10 scored 15 , 2 scored 14

number who have to retake test = 2 + 10 + 2 = 14

The quantity of the hardener added to 18 containers of resin will be 990 ml.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that the formula for glue says to add 55ml of hardener to each container of resin.

The quantity of hardener for 18 containers will be calculated as,

Q = 18 x 55

Q = 990 ml

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Answer:

B and c and e

Step-by-step explanation:

Sorry if late I need points

The sums 5 + (–2), –3 + 4, and –2 + 4 are positive option (B), (C), and (E) are correct.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

It is given that:

A.–5 + (–2)

= -5 + (-2)

= -5 - 2

= -7 (negative)

B. 5 + (–2)

= 5 - 2

= 3 (positive)

C. –3 + 4

= -3 + 4

= 1 (positive)

D. 0 + (–3)

= -3 (negative)

E. –2 + 4

= -2 + 4

= 2 (positive)

Thus, the sums 5 + (–2), –3 + 4, and –2 + 4 are positive option (B), (C), and (E) are correct.

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Answer:

68°

Step-by-step explanation:

Total angle in a quadrant = 90°

x + 22° = 90°

x = 90 - 22

x = 68°

Answer:

A=pi x r^2

A= 3.14 x 9^2 feet

A= 3.14 x 81 feet^2

A= 254.34 ft^2

The augmented matrix corresponding to the system of equations in this problem is given as follows:

[-6 -5 -4 7].

[7 -9 -1 -7].

[-9 -3 -6 7].

The first row is constructed according to the coefficients of the first equation, hence it is given as follows:

[-6 -5 -4 7].

The second row is constructed according to the coefficients of the second equation, hence it is given as follows:

[7 -9 -1 -7].

The third row is constructed according to the coefficients of the third equation, hence it is given as follows:

[-9 -3 -6 7].

Hence the matrix is given as follows:

[-6 -5 -4 7].

[7 -9 -1 -7].

[-9 -3 -6 7].

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Answer:

B:17

Step-by-step explanation:

Because it logically is the only answer that makes sense.

49

Step-by-step explanation:

i dont even know tbh i just guessee

Replace x with 2 and solve each equation:

1/2(2) + 4 = 1 + 4 = 5

2+ 6 -1/2(2) -2 = 8-3 = 5

The answer is:

both expressions equal 5 when substituting 2 for x because the expressions are equivalent.

Answer:

y = 6

Step-by-step explanation:

Given system of equations:

\(\begin{cases}-x+3y=9\\y = \dfrac{2}{3}x\end{cases}\)

Step 1: Substitute the second equation into the first and solve for x.

\(\\\implies -x+3\left(\dfrac{2}{3}x\right)=9\ \textsf{[ Multiply. ]}\\\\\implies -x+2x=9\ \textsf{[ Combine like terms. ]}\\\\\implies \boxed{x=9}\)

Step 2: Substitute 9 as the value of x in any equation and solve for y.

\(\\\implies-9+3y=9\ \textsf{[ Add 9 to both sides. ]}\\\\\implies -9+9+3y=9+9\\\\\implies 3y=18\ \textsf{[ Divide both sides by 3. ]}\\\\\implies \dfrac{3y}{3}=\dfrac{18}{3}\\\\\implies \boxed{y=6}\)

The solution to the given system of equations is (9, 6).

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Step-by-step explanation:

answer is in the above photo

there are 29 boys total

Answer:

y = 5/2x + 11

Step-by-step explanation:

If a line is perpendicular to another it's slope is a negative reciprocal

First let's solve for y in the equation that l is perpendicular to

2x + 5y = 10

5y = -2x + 10

y = -2/5x + 2

Now the slope of L is 5/2

Next let's find the y-intercept on L

y = 5/2x + b

To do plug (-2,6) into the equation

6 = -5 + b

b = 11

y = 5/2x + 11

I'm assuming your equation was:

        \(y-2=\dfrac{1}{5}(x-3)\)

Both Jules' line and Lauren's line have a slope of -5 or \(-\dfrac{5}{1}\) and those two lines are parallel since they have the same slope.

Perpendicular lines have slopes that are opposite reciprocal values.  

The opposite reciprocal of \(-\dfrac{5}{1}\) is a positive \(\dfrac{1}{5}\), which is why these two lines are perpendicular to the line at the top of my answer.

Answer:

Step-by-step explanation:

X³

Answer:

$10.12

Step-by-step explanation:

Step one:

given data

we are told that the cost of binoculars is $155.75

and also the sales tax is 7%

Step two:

We want to first solve for the sales tax which is 7% of  $155.75

=7/100* 155.75

=0.070*155.75

=10.12

Cassie will pay a tax of $10.12

Also Cassie will pay a total amount of

= 155.75+10.12

=$165.87