Anwen walks at an average
speed of 3 km/h for 2 hours
20 minutes. How far has Anwen
walked?​

9514 1404 393

Answer:

  y -3 = -2(x +4)

Step-by-step explanation:

The slope of the given line is ...

  m = (y2 -y1)/(x2 -x1)

  m = (1 -(-3))/(4 -(-4)) = 4/8 = 1/2

The perpendicular line will have slope -1/(1/2) = -2.

__

The point-slope equation of the line with slope m through point (h, k) is ...

  y -k = m(x -h)

For point (-4, 3) and slope -2, the equation is ...

  y -3 = -2(x +4)

Answer:

2 and 30

Step-by-step explanation:

2/3=20/30

2 and 30 means the extremes and 3 and 20 are the means

Answer:

The resultant velocity is 12.21 m/s.

Step-by-step explanation:

We are given that the water from a fire hose follows a path described by y equals 2.0 plus 0.9 x minus 0.10 x squared ​(units are in​ meters).

Also, v Subscript x is constant at 10.0 ​m/s.

The water from a fire hose follows a path described by the following equation below;

[tex]y=2.0 + 0.9x-0.10x^{2}[/tex]

The velocity of the [tex]x[/tex] component is constant at =  [tex]v_x=10.0 \text{ m/s}[/tex]

and the point at which resultant velocity has to be calculated is (9.0,2.0).

Let the velocity of x and y component be represented as;

[tex]v_x=\frac{dx}{dt} \text{ and } v_y=\frac{dy}{dt}[/tex]

Now, differentiating the above equation with respect to t, we get;

[tex]y=2.0 + 0.9x-0.10x^{2}[/tex]

[tex]\frac{dy}{dt} =0 + 0.9\frac{dx}{dt} -(0.10\times 2)\frac{dx}{dt}[/tex]

[tex]\frac{dy}{dt} = 0.9\frac{dx}{dt} -0.2\frac{dx}{dt}[/tex]

[tex]v_y = 0.9v_x -0.2v_x[/tex]

[tex]v_y = 0.7v_x[/tex]

Now, putting [tex]v_x=10.0 \text{ m/s}[/tex] in the above equation;

[tex]v_y = 0.7 \times 10.0[/tex] = 7 m/s

Now, the resultant velocity is given by = [tex]v=\sqrt{v_x^{2}+v_y^{2} }[/tex]

                            [tex]v=\sqrt{10^{2}+7^{2} }[/tex]

                               = [tex]\sqrt{149}[/tex] = 12.21 m/s

Answer:

[tex]Total = 7\frac{1}{2} cups[/tex]

Step-by-step explanation:

Given

Initially, he drank 3 pints of water

Then, [tex]1\frac{1}{2}[/tex] more cups

Required

How many cups did Ian drink altogether

This question can be solved by adding the size of water he drank during the hike and when he got home

i.e.

[tex]Total = 3\ pints + 1\frac{1}{2} cups[/tex]

But the answer should be in cups;

So, number of pints has to be converted to number cups

Given that 1 pint = 2 cups;

3 pints will be 3 * 2 cups

3 pints = 6 cups;

So,

[tex]Total = 3\ pints + 1\frac{1}{2} cups[/tex]

[tex]Total = 6\ cups + 1\frac{1}{2} cups[/tex]

[tex]Total = 7\frac{1}{2} cups[/tex]

Altogether, he drank [tex]7\frac{1}{2} cups[/tex] of water

Answer:

Ray KM is an angle bisector of [tex]\angle NKL[/tex].

Step-by-step explanation:

Given that there are 4 lines that are extended from a point K.

Angle between KJ and KN is [tex]58^\circ[/tex] i.e. [tex]\angle JKN =[/tex] [tex]58^\circ[/tex]

Angle between KN and KM is [tex]61^\circ[/tex] i.e.  [tex]\angle NKM =[/tex] [tex]61^\circ[/tex].

Angle between KM and KL is [tex]61^\circ[/tex] i.e.  [tex]\angle MKL =[/tex] [tex]61^\circ[/tex]

Please refer to the attached image for the conditions and dimensions of angles given in the question statement.

Now, let us have a look at the options given:

1. Point K is a midpoint of Line segment JL

JL is not a straight line first of all, and secondly there is no condition given about the line segments.

So, it is incorrect.

2. [tex]m \angle JKN = \dfrac{1}{2}m \angle JKM[/tex]

[tex]\angle JKN =[/tex] [tex]58^\circ[/tex] and

[tex]m \angle JKM =58+61=139^\circ\\\Rightarrow \dfrac{1}{2} m \angle JKM = 64.5^\circ[/tex]

So, it is also incorrect.

3. Ray KM is an angle bisector of [tex]\angle NKL[/tex].

Ray KM divides the [tex]\angle NKL[/tex] into two equal angles [tex]\angle NKM =[/tex] [tex]61^\circ[/tex] and [tex]\angle MKL =[/tex] [tex]61^\circ[/tex] so it is correct.

Answer:

D

Step-by-step explanation:

subsitute each of the x and y values for each of the equations and if they both equal each other It is correct.

Answer:

x = 2, y= -1

Step-by-step explanation:

12x - y = 25

9x + y = 17

add both equations to eliminate y

21x = 42

divide by 21

x = 42/21

x = 2

sub x in equation i to find y

12(2) - y = 25

24 - y = 25

-y = 1

therefore y = -1, x = 2

Answer:

The correct option is SSS (Side-Side-Side) Theorem

Step-by-step explanation:

The question is incomplete because the diagrams of ΔLON and ΔLMN are not given. I have attached the diagram of both triangles below for better understanding of the question.

Consider the diagram attached below. We have to find the congruence theorem which can be used to prove that ΔLON ≅ ΔLMN

We can see in the diagram that both triangle have a common side that is LN. It means 1 side of both triangles is congruent because LN≅LN

Consider the sides ON and MN. Both side have a single bar on them, which means that it is given that both of these side are congruent. Hence ON≅MN

Consider the sides LO and LM. Both side have a double bars on them, which means that it is given that both of these side are also congruent. Hence LO≅LM

SSS theorem states that if all sides of the triangles are congruent, then the triangles themselves are also congruent, which is the same case in this question

Answer:

D. SSS

Step-by-step explanation:

I hope this helps.

Answer:

this question is roung

Answer:

$6.89

Step-by-step explanation:

To find unit price divide the dollar by the amount. The dollar is 20.67. The amount of socks are 3. The equation would then be 20.67/3. Then solve and the answer would be $6.89.

Answer:

A.

Step-by-step explanation:

BC ≅ EF

BC needs to be congruent to EF to show that ΔABC ≅ ΔDEF by SAS(Side -Angle-Side) Postulate.

Answer:

$0.40 per oz

Step-by-step explanation:

given that the cereal is $3.60 for a 9 oz box

i.e

9 oz ----> costs $3.60

1 oz ----> costs $3.60 ÷ 9 = $0.40

hence the unit rate is $0.40 per oz

Answer:

0.40 per ounce

Step-by-step explanation:

The question asks is to find the unit rate, or price per ounce.

To find this, we need to divide the price by the number of ounces.

price/ ounces

It costs $3.60 for 9 ounces of cereal.

$3.60/9 ounces

Divide $3.60 by 9 (3.60/9=0.4)

$0.4/ounce

It costs $0.40 per ounce of cereal.

Answer:

3600.

Step-by-step explanation:

8 =   2*2*2

12=   2*3

18=   2*3*3

30 =  2*3*5

The lowest common multiple of the these is

2 * 2 * 2 * 3*3* 5 = 360.

So the smallest square number = 2*2*2*2*3*3*5*5

(We make all the sets of factors a square).

So it's 16 * 9 * 25 = 3600.

Answer:

3600

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

The product of 6 and 7 is 42.

Let x be the number of times needed to add 5 to 17 to reach 42.

17 + 5x = 42

5x = 42 - 17

5x = 25

x = 5

Answer: I’m pretty sure it’s 5

Step-by-step explanation:

Answer:

B. points C, F and G

Step-by-step explanation:

B. Points G C F

Answer:

11/8 or, 1 and 3/8

Step-by-step explanation:

First, we have to make both the denominators the same. In this case, we can multiply 3/4 by 2, to make 4, the denominator, into 8. What we do to the denominator, we must do to the numerator! So, we multiply 3 by 2, and get 6!

Now we have, 5/8 + 6/8, which equals 11/8! Which can also be simplified to 1 and 3/8 (because the numerator is larger than the denominator)

Hope this helps! :)

Answer:

[tex]x = 6[/tex]

Step-by-step explanation:

Given

[tex]2y-x=-6[/tex]

Required

Determine the x intercept

To get the value of x intercept; we simply substitute 0 for y;

i.e. y = 0

[tex]2y-x=-6[/tex] becomes

[tex]2(0)-x=-6[/tex]

[tex]0-x=-6[/tex]

[tex]-x=-6[/tex]

Multiply both sides by -1

[tex]-1 * -x=-6 * -1[/tex]

[tex]x=-6 * -1[/tex]

[tex]x = 6[/tex]

Hence, the x intercept is 6

Answer:

x = 59/7, y = -15/7

Step-by-step explanation:

4x= 2y + 38;

2 - 3y=x

We can substitute for x  in the first equation since the second equation is solved for x

4(2-3y) = 2y+38

Distribute

8 - 12y = 2y+38

Add 12y to each side

8-12y+12y = 2y+12y+38

8 = 14y+38

Subtract 38 from each side

-30 = 14y

Divide by 14

-30/14 = y

-15/7 = y

Now solve for x

2 - 3y = x

2 - 3*-15/7 = x

2 +45/7 = x

14/7 + 45/7 = x

59/7 =x

Answer:

A. 52% and B. 104/200

Step-by-step explanation:

To find the answer, we first have to find how many pet owners own cats. As percentages are x/100, when we have x/200 we divide the numerator and denominator by 2 to bring the fraction to 48/100. (96/200 divided by 2 equals 48/100). Now that we have the percentage of pet owners that own cats (48%), we need to find how many do not own cats. To do so, we just subtract 100-48 to get 52. Then, we do the same to the fraction of 96/200. (200-96 = 104). This brings our answers to A. 52% and B. 104/200

The percentage of owners that do not own cat is 52%

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

Given here, 96 out of 200 pet owners own cats then the owners who do not own cat are 104

Therefore the number of non cat owners in percentage terms is

= (104/200) ×100

= 52.5%

Hence, the answer is 52.5%

Learn more about percentages here:

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Answer:given below

Step-by-step explanation:

sqrt x^2 +81= x + 10

x^2 + 81 = (x+10)^2

x^2 + 81 = x^2 + 20x + 100

so answer is:  

x^2 + 81 = x^2 +20x + 100

..HOPE IT HELPS YOU...ALL THE BEST

Answer:

The answer is D on egdge2020

Answer:

1. A letter, A, added to a letter, B, equals ten.

2. A letter, x, which is multiplied by 4, then has a number, y, subtracted from it to equal a letter, a.

If you try write these out, I'm sure you'd get the algebraic expression given.

Answer:

6 1/6 ft

Step-by-step explanation:

12 inches = 1 ft

So 2 inches is 2/12 of a foot

2/12 = 1/6

6 ft 2 inches = 6  1/6 ft

Answer:

B.

Step-by-step explanation:

A =  C = 40°

40+40+ 4x = 180

4x = 100

x = 25°

Answer: The vertex form is h(x)=(x-3)^2-6

Step-by-step explanation:

Using the complete the square method, first complete any squares

X^2-6x+(-3)^2-(-3)^2+3

Use the binomial formula

(x-3)^2 - (-3)^2 +3

Simplify

(x-3)^2-6

Answer:

Converges

Sum = 20.8333

Step-by-step explanation:

A geometric series has a general formula of:

[tex]\sum ar^n[/tex]

Where 'a' is the initial term, 'n' is the number of terms, and 'r' is the constant ratio. If |r| < 1 than the series converges.

In this particular case, the initial term is a=25, and each term is being divided by -5, or multiplied by -0.2, so the general form would be:

[tex]\sum 25*(-0.2)^n[/tex]

Since 0.2 < 1.0, the series converges.

The sum of the series is given by:

[tex]S=\frac{a}{1-r}\\S=\frac{25}{1-(-0.2)}\\S=20.8333[/tex]

The sum is 20.8333.

The geometric series converges and the sum is equal to 20.83.

A geometric series is the sum of an infinite number of terms that have a constant ratio between successive terms .

A geometric series has a general formula of:

∑arⁿ

Where 'a' is the initial term, 'n' is the number of terms, and 'r' is the constant ratio. If |r| < 1 than the series converges.

In this particular case, the initial term is a=25 and each term is divided by -5 or multiplied by (-0.2)

Therefore r = -0.2 and as it is <1 therefore the series converges

The sum of a convergent series is

S = a/(1-r)

S = 25/(1-(-0.2))

S= 25/1.2

S = 20.83

Therefore the sum of the series is 20.83

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Answer:

(22/7)/6=0.523809

Step-by-step explanation:

V=4/3πr^3

V=4/3π(1/2)^3=π/6

or (22/7)/6=0.523809

Answer: she is 215m from her starting point

Step-by-step explanation:

The diagram representing the situation is shown in the attached photo. Triangle ABC is formed with AC representing her distance from her starting point.

Angle B = 28 + 90 = 118°

To determine AC, we would apply the law of Cosines which is expressed as

a² = b² + c² - 2abCosA

Where a,b and c are the length of each side of the triangle and B is the angle corresponding to b(AC). Likening the expression to the given triangle, it becomes

AC² = AB² + BC² - 2(AB × BC)CosAC

AC² = 60² + 180² - 2(60 × 180)Cos118

AC² = 3600 + 32400 - 21600Cos118

AC² = 36000 - 21600(-0.46947156)

AC² = 36000 + 10140.59

AC² = 46140.59

AC = √46140.59

AC = 215 m

Answer:

Hi there!

The correct answer is: True

Step-by-step explanation:

If there is a line, there are infinite planes that pass through that line, therefore since the 4 points are in a line, they are coplanar .