hiring sports hall costs £30 booking fee and then £10 per hour. Chris hires and pays £120. How many hours did chris hire the hall for?​

Answer:

that would be 40 and 20 !

Step-by-step explanation:

40 + 20 = 60

and 40 = 20 + 20.

Answer:

the answer is 40+20

20+20

Answer:

the measure of angle P is 61.93°

The value of angle P of the triangle ΔPQR is ∠P = 61.93°

What are trigonometric relations?

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the triangle be ΔPQR

Let the angle ∠P = θ

Triangle ΔPQR  is a right angle triangle

where ∠Q = 90°

Now , the value of the sides are

PQ = 8 cm

QR = 15 cm

PR = 17 cm

Now , from the trigonometric relations

∠QPR = θ

tan θ = opposite side / adjacent side

Opposite side of Triangle PQR is QR

Adjacent side of Triangle PQR is PQ

So , substituting the values in the equation , we get

tan θ = opposite side / adjacent side

tan θ = QR / PQ

tan θ = 15 / 8

tan θ = 1.875

Now , the value of θ is

The value of θ = tan⁻¹ ( 1.875 )

The value of θ = 61.93°

Therefore , the value of θ is 61.93°

Hence , The value of angle P of the triangle ΔPQR is ∠P = 61.93°

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Answer: A!!

Step-by-step explanation:

i just got it right lol

Answer:

45

Step-by-step explanation:

((100-25)/100)× 60 is the correct answer

Answer:

y = 10 and x =18

Step-by-step explanation:

From the parallelogram,

DH + HF = DF

x+2 + 2y = DF

Also DH = HF

x+2 = 2y

x - 2y = -2 .... 1

Also GH = HE

3x-3 = 5y+1

3x - 5y = 1 + 3

3x-5y = 4 .... 2

Solve  1 and 2 simultaneously

x - 2y = -2 .... 1 * 3

3x-5y = 4 .... 2 * 1

_____________

3x-6y = -6

3x-5y = 4

Subtract

-6y + 5y = -6-4

-y = -10

y = 10

Substitute y = 10 into 1

x- 2y = -2

x - 2(10) = -2

x - 20 = -2

x = -2+20

x = 18

Hence y = 10 and x =18

Answer: Choice A.

Knowing that 5^2 + 12^2 = 13^2, draw the 5 cm side and the 12 cm side with a right angle between them. The 13 cm side will fit to form a right triangle.

The diagram is shown below.

The converse of the pythagorean theorem states that if a^2+b^2 = c^2, then we have a right triangle with hypotenuse c. The hypotenuse is always the longest side and always opposite the 90 degree angle.

Note how 5^2+12^2 = 25+144 = 169 while 13^2 = 169, so that shows how 5^2+12^2 = 13^2 is true.

Answer:

yes for the final exam its A

Step-by-step explanation:

Find miles per hour by dividing total miles by total time:

240 miles / 3 hours = 80 miles per hour.

Now multiply miles per hour by time:

80 miles per hour x 2 hours = 160 miles.

The answer is 160 miles.

Answer:

d≈49.02cm

Step-by-step explanation:

C=2πr

d=2r

Solving ford

d=C

π=154

π≈49.01972cm

Answer:

All you have to do

Step-by-step explanation:

All you have to do is divide the number pie by 154 or if does not work try doing 154 by number pie

Answer:

9.000009000009

Step-by-step explanation:

h

Answer:

A reflection over the line x=3

Step-by-step explanation:

Answer:

x+3 > 21

the is a line under the greater than symbol

Step-by-step explanation:

Answer:

yes it is

Step-by-step explanation:

a squared + b squared= c squared

8^2+15^2=17^2

64+225=289

Answer:

9 square inches is your answer. √9=3

Answer:

It would end up becuase it is positive

Step-by-step explanation:

9514 1404 393

Answer:

  a) NT = 8

  b) RS = 8

  c) RT = 16

  d) ZR = 24

Step-by-step explanation:

All of the marked sides are congruent. (That's what the marks mean.) It might help you to put 8 next to each hash mark like it is on NS. So, you have ...

  NT = RS = ST = TZ = NS = 8

Segments on the same line sum, so ...

  RT = RS +ST = 2RS = 16

  ZR = RS +ST +TZ = 3RS = 24

a) NT = 8

b) RS = 8

c) RT = 16

d) ZR = 24

Answer:

y=4-3x/2

Step-by-step explanation:

Move all terms that don't contain  y  to the right side and solve.

Answer:

Step-by-step explanation:

Answer:

the equation of yours is wrong. the equation would be y=1/3x.

Step-by-step explanation:

here's the graph. hope it helps.

9514 1404 393

Answer:

  g(x) = 3x^2 -2

Step-by-step explanation:

Reflection in the y-axis replaces x with -x.

  g(x) = f(-x) = 3(-x)^2 -2

  g(x) = 3x^2 -2

_____

The given function is symmetrical about the y-axis, so its reflection is itself.

Answer:

about 2.253 centimeters

Step-by-step explanation:

Answer:

Center = (5,-3) and radius = 7

Step-by-step explanation:

(5) If Oskar bisects the diameter of a circle, what is he trying to construct the radius of the circle.

(6) The given equation is :

[tex](x-5)^2+(y+3)^2=49[/tex]

The general equation of circle is given by :

[tex](x-a)^2+(y-b)^2=r^2[/tex] ...(1)

Where

(a,b) are the coordinates of the centre and r is the radius.

The given equation can be written as :

[tex](x-5)^2+(y+3)^2=7^2[/tex] ..(2)

Comparing equation (1) and (2) we get :

a = 5, b = -3 and r = 7

So,

Center = (5,-3) and radius = 7

Hence, this is the required solution.

Answer:

Step-by-step explanation:

These represent the points on the graph with w as the x-axis and l as the y -axis. You only need two pairs to make a line, but it is always best to use a 3rd point as a check.

Answer: p= 2 and q= 1

Answer:

neither

Step-by-step explanation:

parallel lines have the same slope and different y-intercept

perpendicular lines have the reciprocal as slopes( 2/5 and 5/2)

as these slopes have neither the answer in NEITHER

Answer:

your best bet is 67.38

Step-by-step explanation:

Step-by-step explanation:

Please refer to the attachment

Answer:

x = 18

Step-by-step explanation:

5x/9 = x/6 + 7

multiply both sides by 9

5x = 9x/6 + 63

multiply both sides by 6

30x = 9x + 378

subtract 9x from each side

21x = 378

divide both sides by 21

x = 18

check by substituting 18 for x:

5(18)/9 = 18/6 + 7

5(2) = 3 + 7

10 = 10

Answer:

-17x2 - 14x + 10

 ————————————————

        2        

Step-by-step explanation:

STEP

1

:

           25

Simplify   ——

           2

Equation at the end of step

1

:

             25

 (((4•(x2))-(——•x2))-7x)+5

             2

STEP

2

:

Equation at the end of step 2

                 25x2            

 (((4 • (x2)) -  ————) -  7x) +  5

                  2              

STEP

3

:

Equation at the end of step

3

:

           25x2            

 ((22x2 -  ————) -  7x) +  5

            2              

STEP

4

:

Rewriting the whole as an Equivalent Fraction

4.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  2  as the denominator :

            22x2     22x2 • 2

    22x2 =  ————  =  ————————

             1          2    

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

4.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

22x2 • 2 - (25x2)      -17x2

—————————————————  =  —————

        2               2  

Equation at the end of step

4

:

  -17x2          

 (————— -  7x) +  5

    2            

STEP

5

:

Rewriting the whole as an Equivalent Fraction :

5.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  2  as the denominator :

         7x     7x • 2

   7x =  ——  =  ——————

         1        2  

Adding fractions that have a common denominator :

5.2       Adding up the two equivalent fractions

-17x2 - (7x • 2)     -17x2 - 14x

————————————————  =  ———————————

       2                  2    

Equation at the end of step

5

:

 (-17x2 - 14x)    

 ————————————— +  5

       2          

STEP

6

:

Rewriting the whole as an Equivalent Fraction :

6.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  2  as the denominator :

        5     5 • 2

   5 =  —  =  —————

        1       2  

STEP

7

:

Pulling out like terms :

7.1     Pull out like factors :

  -17x2 - 14x  =   -x • (17x + 14)

Adding fractions that have a common denominator :

7.2       Adding up the two equivalent fractions

-x • (17x+14) + 5 • 2     -17x2 - 14x + 10

—————————————————————  =  ————————————————

          2                      2        

STEP

8

:

Pulling out like terms :

8.1     Pull out like factors :

  -17x2 - 14x + 10  =   -1 • (17x2 + 14x - 10)

Trying to factor by splitting the middle term

8.2     Factoring  17x2 + 14x - 10

The first term is,  17x2  its coefficient is  17 .

The middle term is,  +14x  its coefficient is  14 .

The last term, "the constant", is  -10

Step-1 : Multiply the coefficient of the first term by the constant   17 • -10 = -170

Step-2 : Find two factors of  -170  whose sum equals the coefficient of the middle term, which is   14 .

     -170    +    1    =    -169

     -85    +    2    =    -83

     -34    +    5    =    -29

     -17    +    10    =    -7

     -10    +    17    =    7

     -5    +    34    =    29

     -2    +    85    =    83

     -1    +    170    =    169

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Final result :

 -17x2 - 14x + 10

 ————————————————

        2        

Answer: n = 152 m

Step-by-step explanation:

write a proportion to find n.

46/n = 92/204

n = 102 m

The length of the lake shown in the provided image using similar triangles and a proportion is 102 meters.

In the two similar triangle, the ratio of two sides of one triangle is equal to the ratio of corresponding sides of the other triangle.

In the figure shown,

The total length of the base of the larger triangle is,

[tex]112+92=204\rm\; m[/tex]

The height of this triangle is n meters, which is equal to the length of lack. Thus, by the similar triangle proportion property,

[tex]\dfrac{n}{204}=\dfrac{46}{92}\\n=\dfrac{46\times204}{92}\\n=120\rm\; meters[/tex]

Thus, the length of the lake shown in the provided image using similar triangles and a proportion is 102 meters.

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Answer:

Step-by-step explanation:

volume = LWH/3 = 40·30·60/3 = 24,000 ft³