Bernard is one and half times old as Henry six years ago he was twice as old as Henry how old are the boys now

Answer:

13) 13.7     14) 78.3 cm

Step-by-step explanation:

13)   6²+x²=15²

       x = 13.7

14)   2πr/2 = 2(3.14)(5.5)/2 = 17.3

      25 + 11 + 25 + 17.3 = 78.3 cm

Answer:

the root is 2 . thus, the correct graph is graph 2

Answer:

The last one on the bottom right

Step-by-step explanation:

When we are trying to fit a line for a number of points, we can fix this line at several points on the graph. However, out of the several lines that we can fit, only one of these lines would work perfectly and it is called the line of best fit.

The reason why it is called the line of best fit is that it is drawn in a manner in which it leaves equal number of points above it as below it.

Supposed we have 15 points for our graph with the line of the slope passing thorough 5, the line of best fit in this case would leave 5 points above and another 5 below the line.

Leaving 6 and 4 is also manageable, but in case where 3 and 7 are left above and below the line, then it becomes a problem

Thus, out of all the representations we have, the one on the bottom right best works

Answer:

The answer is 210°.

Step-by-step explanation:

Given that ∠BOE = 130° and ∠COB is 80°. So in order to find ∠CBE, you have to add up together :

∠CBE = ∠BOE + ∠COB

∠CBE = 130° + 80°

∠CBE = 210°

(Correct me if I am wrong)

please see the attached picture...

Hope it helps...

Good luck on your assignment...

Answer:

21x+4

Step-by-step explanation:

To find the perimeter you have to add up all the sides

Answer:

(3)13.2

Step-by-step explanation:

c²=a²+b²

20²=15²+b²

20²-15²=b²

400-225=b²

175=b²

b=√175

b=13.2inches

Answer:

Step-by-step explanation:

:D

Answer: ill try to do #3 for you

A. money= dependent (depends on days)

days= independent

B. im guessing its this: m=250d

C. $250x 10 days= $2,500 he will need to save

also #4 is y-2x-2

if this is all correct could u mark my answer brainliest if you want to thanks!

Answer:

5th term of sequence = -18

nth term of the sequence = -5n + 7

Step-by-step explanation:

Difference between successive and previous term of the output,

[tex]T_{2}-T_{1}[/tex] = -3 - 2

           = -5

Similarly, [tex]T_{3}-T_{2}=-8-(-3)[/tex]

                            = -5

There is a common difference 'd' = (-5)

Therefore, the sequence formed will be an arithmetic sequence.

First term of the sequence 'a' = 2

Explicit formula of an arithmetic sequence, [tex]T_{n}[/tex] = a + (n - 1)d  [n = input value]

[tex]T_{n}[/tex] = 2 + (n - 1)(-5)

    = 2 - 5n + 5

    = -5n + 7

5th term of this sequence,

[tex]T_{5}=2+(5-1)(-5)[/tex]

    = 2 - 20

    = -18

Therefore, 5th term of sequence = -18

                  nth term of the sequence = -5n + 7

Answer:

7

Step-by-step explanation:

y=mx+b

b= y-intercept

So 7 is your answer

[tex]answer \\ \sqrt{208} \\ solution \\ hypotenuse = c \\ perpendicular = 8 \\ base = 12 \\ using \: pythagoras \: theorem \\ {h}^{2} = {p}^{2} + {b}^{2} \\ or \: {c}^{2} = {8}^{2} + {12}^{2} \\ or \: {c }^{2} = 64 + 144 \\ or \: {c}^{2} = 208 \\ c = \sqrt{208} \\ hope \: it \: helps[/tex]

Answer:

P=32m

A=48 m^2

Step-by-step explanation:

if two shorter sides are 4m each and the two longer sides are 12 m

4+4+12+12 to find the total P

Area, time the LENGTH by WIDTH to find the squared meters in the rectangle .

4x12 = AREA

Answer:

common ratio(r) = 10

place of the term = n

a = 3

now

sequence of 1 term = ar^(n-1)

= 3×10^(1-1)

= 3× 10^0

= 3×1

= 3

sequence of 2 term = ar^(n-1)

= 3×10¹

= 30

and so on

Answer:

The probability that it will  rain in all 3 cities on that day

P(V∪ C∪S) = 0.93 = 93%

Step-by-step explanation:

Let 'V' be the event of  rain in Vancouver

Given that the probability of rain in Vancouver

             P( V) = 20% = 0.20

             P( V⁻) = 1- P( V) = 1 - 0.20 =0.80

Let 'C' be the event of  rain in Calgary

Given that the probability of rain in Calgary

             P( C) = 65% = 0.65

            P( C⁻) = 1- P( C) = 1 - 0.65 =0.35

Let 'S' be the event of  rain in Saskatoon

Given that the probability of rain in Saskatoon

             P( S) = 75% = 0.75

             P( S⁻) = 1- P( S) = 1 - 0.75 =0.25

First we will prove that the probability that it will not rain in all 3 cities on that day

P( V⁻ ∩  C⁻ ∩  S⁻  ) =  P( V⁻) P( C⁻) P(S⁻)

                              =  0.80 × 0.35 × 0.25

                             = 0.07

The probability that it will  rain in all 3 cities on that day

P(V∪ C∪S) = 1-(P( V⁻ ∩  C⁻ ∩  S⁻  )

                   = 1 - 0.07

                  = 0.93

Answer:

AC ≅ BD

Step-by-step explanation:

A parallelogram is a shape that have two pairs of parallel sides with opposite sides having the same length and opposite angles having the same size.

A rectangle is a shape that have two pairs of parallel sides with opposite sides having the same length and each of the four angles is 90°.

A parallelogram is said to be a rectangle if the diagonals of the parallelogram are of the same size (congruent). Therefore in parallelogram ABCD, ABCD is a rectangle if AC is equal to BD. where AC and BD are the diagonals

AC ≅ BD or say Measure of AC = Measure of BD diagonal.

Given that:

ABCD is a parallelogram

AC and BD intersect at E.

A parallelogram is defined as a closed geometric figure that has got 4 straight sides and  opposite sides are parallel to each other.

Set of all parallelogram is superset of set of all rectangles.

There is a property about diagonals of a parallelogram that states as;

" A parallelogram is a rectangle if and only if both of its diagonals are equal in size".

Now given parallelogram is ABCD thus its diagonals are AC and BD.

Thus for ABCD to be rectangle we need:

magnitude of AC = magnitude of BC

or

AC ≅ BD

Learn more here:

https://brainly.com/question/1563728

Answer:

Because they are in the ratio 2:3 we'll call red and blue paint 2x and 3x respectively. We know that there are 15 liters of blue paint which means that 3x = 15. Solving for x we get x = 5. Since red paint is denoted by 2x it would be 2 * x = 2 * 5 = 10.

Answer:

10 liters

Step-by-step explanation:

Red : Blue

2          3

We want 15 blue liters

15/3 = 5

Multiply each term by 5

Red : Blue

2*5      3*5

10 :    15

Answer :

is approximately 100 cm ²

Step -by-step explanation

[tex]r \: = 10 \\ l \: = 21.81 \\ T.S.A \: of a \: cone\: = \pi \times r(r + l)[/tex]

[tex] \frac{22}{7} \times 10(10 + 21.81) \\ \frac{22}{7} \times 10(31.81) \\ \frac{22}{7} \times 318.1[/tex]

[tex] \frac{22}{7} \times 318.1 \\ = 999.7 \\ = 100 {cm}^{2} [/tex]

Answer:

– 21x^3 y – 9x^2 y^2 e) is your answer

Step-by-step explanation:

Solve the following system for A and B:

{A = 7 x^2 + 3 x y

B = -3 x y

Express the system in matrix form:

(1 | 0

0 | 1)(A

B) = (7 x^2 + 3 x y

-3 x y)

Write the system in augmented matrix form and use Gaussian elimination:

(1 | 0 | 7 x^2 + 3 x y

0 | 1 | -3 x y)

Collect results:

Answer: {A = 7 x^2 + 3 x y  , B = -3 x y

then we multiply the results (7 x^2 + 3 x y) ( -3 x y) =  – 21x^3 y – 9x^2 y^2

68 is the area of the given polygon

Answer:

the answer to this is 3

Step-by-step explanation:

hope this helps

Answer:

your answer to this question is 3

Step-by-step explanation:

Answer:

10 minutes

Step-by-step explanation:

5/6 of an hours is 50 min. Assume x is the time she spends on each skill.

5x=50

x=10

She spent 1/6 of an hour i.e. 10 minutes on each skill.

In area model for multiplication a rectangle is used to represent multiplication between two quantities. Width and Length of the rectangle are assigned the numerical value of the two quantities being multiplied.

Let the number of skills be represented by the length of the rectangle in the figure.

Let the time spent(in hours), which is same for all skills, on each skill be represented by the width of the rectangle in the figure.

The area of the rectangle = length × width = 5 × t = 5t hours.

This area represents total time spent on five skills, which is 5/6 hours.

The smaller rectangles into which the whole rectangle is divided have area 1 × t = t hours. This represents time spent on one skill.

From the figure, such five smaller and equal rectangles constitutes the whole rectangle.

So, area of one smaller rectangle = Area of big rectangle / number of small rectangles = (5/6)/5 = 1/6 hours.

Since, this represents time spent on one skill. So, the required time is 1/6 hours.

She practice each skill for 1/6 of an hour.

Learn more about the area model here

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Answer:

6

Step-by-step explanation:

Since they have the same x - value, just find the distance between the y - values.

6

_______________________________

Hey!!

Solution,

Radius(r)= 6 mm

Circumference of circle=?

Now,

Circumference of circle=2 pie r

=2*pi*6

=12 pie

So the answer is 12 pie.

Hope it helps...

Good luck on your assignment

______________________________

The circumference of the circle is 12[tex]\pi[/tex] mm.

The boundary of a circle, i.e. the length of the full arc of a circle is called circumference of circle.

Let, radius of the circle be r

Then, Circumference of circle = [tex]2\pi r[/tex] unit

Given, The radius is 6 mm

∴ Circumference of the circle = [tex]2\pi r[/tex]

                                                  = ([tex]2\pi[/tex]× 6) mm

                                                  = 12[tex]\pi[/tex] mm

Hence, Circumference of the circle = 12[tex]\pi[/tex] mm

Learn more about circumference of circle here :

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Answer: U = 600 m/s

Step-by-step explanation:

Given that an aeroplane covers a distance of 1500km in a certain time t at a certain speed U.

After increasing the speed by 100km/hr, that is, V = U + 100 it covers the same distance in a time which is half an hour less than the previous time. That is t2 = t - 0.5.

From the first statement

Speed = distance/ time

Distance = speed × time

1500 = Ut

Make t the subject of the formula

t = 1500/U ..... (1)

From the second statement

Distance = speed × time

1500 = (U + 100) × ( t - 0.5 )

Open the bracket

1500 = Ut - 0.5U + 100t - 50

Collect the like terms

1550 = Ut - 0.5U + 100t .... (2)

Substitutes equation 1 into 2

1550 = 1500U/U - 0.5U + 100(1500/U)

1550 = 1500 - 0.5U + 150000/U

1550 - 1500 = (150000 - 0.5U^2)/U

Cross multiply

50U = 150000 - 0.5U^2

0.5U^2 + 50U - 150000 = 0

Divide all by 0.5

U^2 + 100U - 300000 = 0

Using completing the square method

U^2 + 100U = 300000

U^2 + 100U + 50^2 = 300000 + 50^2

(U + 50)^2 = 302500

U + 50 = sqrt(302500)

U + 50 = +/-(550)

U = 50 + 550 or 50 - 550

U = 600 or - 500

Since U is of the same direction, it is

positive. Therefore, the previous speed of the aeroplane is 600 m/s

Answer:

500km/hr

Step-by-step explanation:

The formula for Speed (km/hr) = Distance / Time

Where S = Speed

D = Distance

T = Time

S = D/T

From the question, the aeroplane covered a distance of 1500 km

S = 1500/ T

ST = 1500

Time taken( T ) = 1500/S ......... Equation 1

We are told from the question that speed was increases by 100km/hr, it covers the same distance in a time which is half an hour less than the previous time

This is expressed mathematically as:

The new speed =S + 100km/hr

The new Time taken = 1500/ S - 1/2....... Equation 2

Also since Time = Distance / Speed

The new Time taken also = 1500/ S + 100 ......... Equation 3

Step 1

We would simplify Equation 2:

Time = 1500/S - 1/2

Find the Lowest common multiple = 2

Time = (2 × 1500 - S )/ 2S

Time = 3000 - S / 2S ......... Equation 4

Step 2

Equate Equation 4 and 3 together since they are both equal to time taken

1500/ S + 100 = 3000 - S / 2S

We cross multiply

2S × 1500 = (S + 100) ( 3000 - S)

3000S = 3000S - S² + 300000 - 100S

3000S - 3000S + S² - 300000 + 100S = 0

S² + 100S - 300000 = 0

Step 3

We solve for S = Speed by using factorisation method.

S² + 100x - 300000 = 0

S² - 500S + 600S - 300000 = 0

(S² - 500S) + (600S - 300000) = 0

S(S - 500) + 600(S - 500) = 0

(S - 500) (S + 600) = 0

S - 500 = 0, S = 500

S + 600 = 0 , S = -600

Our answer cannot be in negative form, hence, the previous speed of the aeroplane = 500km/hr

Answer:

f(3) = 14

Step-by-step explanation:

Using the recursive formula and f(1) = 3 , then

f(2) = f(1) + 5.5 = 3 + 5.5 = 8.5

f(3) = f(2) + 5.5 = 8.5 + 5.5 = 14

Answer:

14

Step-by-step explanation:

Answer:

  (-2, 2)

Step-by-step explanation:

Plotting the points on the graph can show you which is in the shaded area. That point is (-2, 2).

Answer:

(-2,2)

Step-by-step explanation:

Answer:

x = 9/4

Step-by-step explanation:

Since the x coordinates are the same, it is a veritcal line with x = 9/4

Answer: $36.97

Step-by-step explanation:

The cost of the meal was $32.57 and he used a 10% off coupon. You can make 10% equal to 0.1 because [tex]\frac{10}{100}=0.1[/tex]. Now do [tex]0.1 *32.57=$3.26[/tex]. This is the discount, so you want to subtract this from the original to get the actual price of the meal, [tex]32.57-3.26=29.31dollars[/tex].

The tax was 8% so this means he is adding it to his total cost instead of subtracting it. Do 0.08 of $29.31 to get $2.34. Add $2.34 to the now $29.31 to get $31.69.

The tip is also adding to the total cost, so do 0.18 of $29.31 to get $5.28. Add $5.28 to $31.69 to get $36.97

Answer:

$37.51

Step-by-step explanation:

Original cost of meal is $32.57.

Since he has a coupon for 10% off, he pays for 90% of the cost of the meal.

90% of $32.57 = 0.9 * $32.57 = $29.31

Now he pays tax on the new discounted total. Let the new total be called 100%. Since he pays 8% tax, he needs to pay 108% of the new total.

108% of $29.31 = 1.08 * $29.31 = $31.65

He adds a tip of 18% of $32.57.

The tip amount is

18% of $32.57 = 0.18 * $32.57 = $5.86

The total is: $31.65 + $5.86 = $37.51

Answer:

-9

Step-by-step explanation:

[tex](-7)^{2}[/tex] = 49

when you have a negative number to any power make sure you plug it in correctly into the calculator.

[tex]\frac{49+5}{-7+1}[/tex]  = [tex]\frac{54}{-6}[/tex]

54÷-6= -9

I hope this helps

Answer:

[tex]-9[/tex]

Step-by-step explanation:

[tex]\frac{x^2+5}{x+1}[/tex]

If [tex]x=-7[/tex] then:

[tex]\frac{-7^2+5}{-7+1} =\\\\\frac{49+5}{-6} =\\\\\frac{54}{-6} =\\\\-9[/tex]

The expression equals [tex]-9[/tex] if [tex]x=-7[/tex]