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Answer: [tex]7.81\ km[/tex]

Step-by-step explanation:

Given

Runner A runs towards North at speed of 10 km/h

Runner B runs towards East at speed of 12 km/h

After half hour, they covered a distance of

[tex]\Rightarrow d_a=10\times 0.5\\\Rightarrow d_a=5\ km[/tex]

[tex]\Rightarrow d_b=12\times 0.5\\\Rightarrow d_b=6\ km[/tex]

They are running in perpendicular direction to each other

So, the distance between them is  given by

[tex]\Rightarrow d=\sqrt{d_a^2+d_b^2}\\\Rightarrow d=\sqrt{5^2+6^2}\\\Rightarrow d=\sqrt{61}\\\Rightarrow d=7.81\ km[/tex]

Answer:

[tex]1\text{ inch}=\frac{1}{9}\text{ foot}[/tex]

Step-by-step explanation:

To get a scale of inches to feet, divide both 54 and 6 by 54:

[tex]54\:\text{inches}=6\:\text{feet},\\\implies 1\:\text{inch}=\frac{6}{54}\:\text{ft}\implies \boxed{1\:\text{inch}=\frac{1}{9}\:\text{foot}}[/tex]

Answer:

€270

Step-by-step explanation:

If a fruit vendor has bought 165kg of apples at € 2 per kilo, the total amount spent is expressed as;

Cost price = 165 * 2 = €330

If 15kg spoilt, the amount of fruit remaining will be 165 - 15 = 150kg

If he rests he sells for € 4 per kilo, then;

Selling price = 150 * 4 = €600

Amount earned = €600 - €330

Amount earned = €270

Answer:

sqrt(106) =c

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2+b^2 = c^2  where a and b are the legs and c is the hypotenuse

5^2 +9^2 = c^2

25+81 = c^2

106 = c^2

Taking the square root of each side

sqrt(106)= sqrt(c^2)

sqrt(106) =c

Answer:

Length of missing side is 10.44/ √106.

Step-by-step explanation:

Here we have

A right triangle with

1st side = a = 5

2nd sidd = b = 9

and , we need to find 3rd side of triangle

let the 3rd side be x.

Using Pythagoras theorem

a ² + b ² = c ²

( 5 ) ² + ( 9 ) ² = ( c)²

25 + 81 = ( c) ²

106 = ( c) ²

Taking square root of each side

√106 = √ c ²

√106 = c

10.44 = c

So, missing side if triangle is 10.44 /√106.

Given:

The data points are:

(1, 0), (2, 3), (3,1), (4,4), (5,5)

To find:

The equation of best fit line in the form of [tex]y=mx+b[/tex] and then find the value of b.

Solution:

The general form of best fit line is:

[tex]y=mx+b[/tex]              ...(i)

Where, m is the slope of best fit line and b is the y-intercept of the line.

Using the graphing calculator, we get the equation for the best fit line and the equation is

[tex]y=1.1x-0.7[/tex]          ...(ii)

On comparing (i) and (ii), we get

[tex]b=-0.7[/tex]

Therefore, the value of b is equal to -0.7.

Answer:

M1=44 M2=136 M3=44 M4=136

Step-by-step explanation:

M3= 44 so M1=44 due to opposite angles being equal

then if two of the angles add to 88

360-88= 272

divide 272 by 2 as M2 and M4 are equal

272/2=136

Answer:

m∠1 = 44°

m∠2 = 136°

m∠4 = 136°

Step-by-step explanation:

m∠1 explanation:

I got it from m∠3 since they're both congruent

m∠2 explanation:

Since we already have the measure of 3 and 1, we can easily add both of the measures (44 + 44 = 88°) then subtract it from 360° (total) = 272°

Then since both measures (2 and 4) are congruent (measuring the exact same length and angle) we can divide 272° ÷ 2 = 136°

m∠4 explanation:

I got it from m∠2 since they're both congruent

Answer:16500

Step-by-step explanation:

That is, for every 100 people, there are 26 people aged between 11 and 20. So 63500 will have 16500 people aged 20.

Answer:

The values of [tex]a[/tex] and [tex]b[/tex] are [tex]33[/tex] and [tex]\frac{20\sqrt{3}}{3}[/tex], respectively.

Step-by-step explanation:

The statement is equivalent to the following mathematic expression:

[tex]\left(5 + 2\sqrt{2})^{2} = a + b\cdot \sqrt{6}[/tex] (1)

By definition of the perfect square trinomial:

[tex]25 + 20\cdot \sqrt{2} + 8 = a + b\cdot \sqrt{6}[/tex]

[tex]33 + 20\sqrt{2} = a + b\cdot \sqrt{6}[/tex]

And by direct comparison we have the following system:

[tex]a = 33[/tex] (2)

[tex]b\cdot \sqrt{6} = 20\sqrt{2}[/tex] (3)

By (3), we solve for [tex]b[/tex]:

[tex]b = \frac{20}{\sqrt{3}}[/tex]

[tex]b = \frac{20\sqrt{3}}{3}[/tex]

The values of [tex]a[/tex] and [tex]b[/tex] are [tex]33[/tex] and [tex]\frac{20\sqrt{3}}{3}[/tex], respectively.

Answer:

5/9

Step-by-step explanation:

If a variable y is directly proportional to x, then;

y = kx where;

k is the constant of proportionality

Given the expression y = 5/9 x

On comparing with the general formula;

kx = 5/9 x

k = 5/9

Hence the constant of proportionality of the expression is 5/9

Answer:

5/9

Step-by-step explanation:

i tried it on khan and its right trust me

Answer: hello your question has some missing data attached below is the missing data

answer:

The second scatter plot

Step-by-step explanation:

The scatter plot that matched the data is the second scatter plot while the first scatter plot wrongly represents the data because values of the Iron not present in the data is also represented in the scatter plot and also some values present in the data table is also missing in the First scatter plot

Answer:

Hello, I am currently doing the same assignment and the brothers scatter plot would be wrong.

Step-by-step explanation:

If you do not believe me then check and see how the table says the iron used were 2, 3, 4, 5, 6, 7, 8, and 9 but in the brothers scatter plot it is shown to have the irons down as 1, 2, 3, 4, 5, 6, 7, and 8.

(in other words the other person who answered is correct)

(3) 8

Step-by-step explanation:

Note that ∆ADE is similar to ∆ABC. As such, the ratios of their legs are equal. Also note that AD = AB + BD.

BC/AB = DE/AD

BC/10 = 12/(10 + 5) = 12/15 = 4/5

or

BC = 10(4/5) = 8

Answer:

Alternate Interior Angles

Step-by-step explanation:

Angles can be corresponding; alternate or same side; or interior or exterior. The angles 2 and 8 are on opposite sides of the transversal; this means that they must be alternate angles. Additionally, they are both within the parallel lines, so they are interior. Alternate interior angles are always congruent. Therefore, their measurements must be equal.

Answer:

They are alternate interior angles

Step-by-step explanation:

<2 and <8 are inside the parallel lines and on opposite sides of the transversal

They are alternate interior angles

Answer:

3 = 20

5 = 20

8= 160

Step-by-step explanation:

angle 2 and 3 are on the same line, so 180 - 160 is 20 degrees

rule of alternate interior angles: angle 5 is equal to 3

rule of alternate exterior angles: angle 8 is equal to 2

Answer:

Step-by-step explanation:

9)  (25-x^2 )(a+2) = (5-x)(5+x)(a+2)

11) 9(v-3)+u^2(3-v)

   9(v-3)+u^2( -v+3)

   9(v-3)-u^2( v-3)

   (9-u^2)(v-3)

 (3-u)(3+u)(v-3)

Answer:

19.20

Step-by-step explanation: used

a calc

Answer: Choice B

Explanation: The rule you use is [tex]\sqrt{m*n} = \sqrt{m}*\sqrt{n}[/tex]

Answer:

Step-by-step explanation:

A: is not the answer. The answer is √144 which is 12

B: is correct. You can do it this way, by breaking the 9 and 16 apart.

C: I don't know exactly what the logic of 36 is, but it is not the right answer.

D: I can't explain why the choice would be division. It is multiplication of some sort. D is incorrect.

Answer: 50.24

Step-by-step explanation:

=3.14x4 squared

=3.14x16

=50.24

the first, (f+g)(x) is f(x) + g(x)

calculating it like:

x² + 7x + (8 -x²)

= x² + 7x + 8 -x²

= 7x + 8

you just writ it down as a calculation and calculate it. i hope that helps understanding the concept/basic idea. please let me know wich ones you need more help with.

edit1: the domain is the range of possibilities wich x we can plug into the new equation

Answer:

1st onne I believe I couldd be wrong but thats what I got

Step-by-step explanation:

Answer:

Hi, there your answer is 25

Step-by-step explanation:

Here's the Pythagorean Theorem formula [tex]a^{2} +b^{2}=c^{2}[/tex]

[tex]7^{2}+24^{2}[/tex]=[tex]c^{2}[/tex]

49+576=[tex]c^{2}[/tex]

625=[tex]c^{2}[/tex]

[tex]\sqrt{625}=c^{2}[/tex]

[tex]25=c[/tex]

Hope this helps :)

Answer:

x =  [tex]\sqrt{14}[/tex]

Step-by-step explanation:

[tex]\sqrt{7}[/tex] / sin(45) = x / sin(90)  (Cause its a square, the edges are 90 degrees)

[tex]\sqrt{14}[/tex] = x / 1

x = [tex]\sqrt{14}[/tex]

Answer:

x = 71.5 in

Step-by-step explanation:

Remember the SOHCAHTOA rule

Soh...

Sine = Opposite / Hypotenuse

...cah...

Cosine = Adjacent / Hypotenuse

...toa

Tangent = Opposite / Adjacent

In this case, we use: CAH.

cos(52) = 44/x

x = 44/cos(52)

x = 71.5 inches

Answer:

Step-by-step explanation:

[tex](2x -3)(x-1) = 2x(x-1) -3(x-1)[/tex]

                     [tex]=2x^2 -2x -3x +3\\= 2x^2 - 5x + 3[/tex]

Answer:

Step-by-step explanation:

Angles on a straight line add up to 180 so 180-135 equals 45. Vertically opposite angles are equal so the second angle inside the triangle equals 100. Henceforth, we can solve this equation:

x +45+100 = 180 (angles in triangle add up to 180)

x+145=180

x=35

Vertically opposite angles are equal so x will become 35.

Hope this helps!

Answer:

29,800

Step-by-step explanation:

that will be 149 x 2 which equals 298

149

 ×2         Multiply 9 × 2 = 18

------        Keep the 8 carry the 1 multiply 4 by 2 then add 1 finally multiply 2 by 1

298

Then add two zeros at the end since we're multiplying a number with two zeros. (This method only works for numbers that end with zeros)

Final answer: 29800

Answer: 70 degrees 35 times 2

Answer:

Gradient = -5

Step-by-step explanation:

The gradient of a line is the slope of the line.

The standard form of the line equation is y = mx  + b

where m is the slope ( or gradient) b is the y - intercept.

Given :

2y = -10x + 1

[tex]y = -\frac{10}{2} x + \frac{1}{2}\\\\y = -5x + \frac{1}{2}\\\\Therefore , \ gradient \ is \ -5[/tex]

The gradient of the line whose equation is 2y=-10x+1 is -5.

Gradient could be a measure of how steep a slope or a line is.

The equation of the road is 2y=-10x+1

y=-5x+1/2

Therefore the gradient of the line is that the coefficient of x which is -5.

Hence the gradient of the line is -5.

Learn more about gradient at https://brainly.com/question/23016580

#SPJ2

Given:

In a right angle triangle,

Hypotenuse = 25 cm

Base = x

Angle between base and hypotenuse = 18 degrees.

To find:

The value of x.

Solution:

In a right angle triangle,

[tex]\cos \theta =\dfrac{Base}{Hypotenuse}[/tex]

In the given right triangle,

[tex]\cos (18^\circ) =\dfrac{x}{25}[/tex]

[tex]\cos (18^\circ) \times 25=x[/tex]

[tex]0.9510565 \times 25=x[/tex]

[tex]23.7764125=x[/tex]

Round the answer to the nearest hundredth (two decimal).

[tex]x=23.78[/tex]

Therefore, the value of x is about 23.78 cm.

Answer:

[tex] {8x}^{3} + 27 \\ = {8x}^{3} + {3}^{3} \\ let : 8x \: be \: a \\ : 3 \: be \: b \\ = > {a}^{3} + {b}^{3} : \\ {(a + b)}^{3} = (a + b)( {a}^{2} + 2ab + {b}^{2} ) \\ {(a + b)}^{3} = ( {a}^{3} + 3{a}^{2} b + 3a {b}^{2} + {b}^{3} ) \\ ( {a}^{3} + {b}^{3} ) = {(a + b)}^{3} - 3ab(a + b) \\ \therefore( {8x}^{3} + 27) = {(8x + 3)}^{3} - 72(8x + 3)[/tex]