The diagram shows a right-angled triangle and a parallelogram.

The area of the parallelogram is 5 times the area of the triangle.
The perpendicular height of the parallelogram is
h
cm.
Find the value of
h
(3 marks)

h=
cm

Answer:

The legnth of AC is about 6.364

Explanation:

Answer:

13

Step-by-step explanation:

Calculate the distance d using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (- 4, - 6) and (x₂, y₂ ) = (- 9, 6)

d = [tex]\sqrt{(-9+4)^2+(6+6)^2}[/tex]

   = [tex]\sqrt{(-5)^2+12^2}[/tex]

   = [tex]\sqrt{25+144}[/tex]

   = [tex]\sqrt{169}[/tex]

   = 13

Answer:

because this is a parallelogram

=> 3t - 15 = 2t + 10

⇔ t = 10 + 15

⇔ t = 25

with t = 25 => 3t - 15 = 3.25 - 15 = 60

we also have:

4r + (3t - 15) = 180°

⇔ 4r + 60° = 180°

⇒ 4r = 120°

⇔ r = 30

we also have;

4r = 3s

=> 4.30 = 3s

⇔ s = 4.10

⇔ s = 40

Step-by-step explanation:

You can use the fact that sum of all angles of a parallelogram is 360 degrees and the sum of two adjacent angles in a parallelogram is 180 degrees.

The value of the variables used in the figure are:

r = 30

s = 40

t = 25

[tex]4r + (3t - 15) + (2t + 10) + 3s = 360^\circ\\4r + 3s + 5t = 365[/tex]

And

[tex]3t - 15 + 4r = 180 \cdots (1)\\3t - 15 + 3s = 180\cdots (2)\\3s + 2t + 10 = 180\cdots (3)\\4r + 2t + 10 = 180\cdots (4)[/tex]

We get 2 systems of linear equations.

First system consists of equation 1 and equation 4

Second system consists of equation 2 and equation 3

From equation 1 and 4, as both's left side is equal to 180, thus they are equal too, or

[tex]3t - 15 + 4r = 4r + 2t + 10\\3t - 2t = 4r - 4r + 10 + 15\\t = 25[/tex]

Putting it in equation 1, we get:

[tex]3t - 15 + 4r = 180\\3 \times 25 + 4r = 180 + 15\\75 + 4r = 195\\\\r = \dfrac{195 - 75}{4} = 30[/tex]

Putting the value t = 25 in second equation, we get:

[tex]3t - 15 + 3s + 180\\3 \times 25 - 15 + 3s = 180\\60 + 3s = 180\\\\s = \dfrac{180 - 60}{3} = 40[/tex]

Thus, the values of the specified variables in the given graph are:

r = 30

s = 40

t = 25

Learn more about system of linear equations here:

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Answer:

10x times 1000 y minus 4x

Answer:

I love algebra anyways

The ans is in the picture with the  steps how i got it

(hope this helps can i plz have brainlist :D hehe)

Step-by-step explanation:

Answer: -1/25 / -1/5 / 1/25

Step-by-step explanation:

Answer: 67.5 mph

Step-by-step explanation:

The formula for speed is:

= Distance / Time

Distance = 658.125 miles

Time will need to be converted to a decimal. You may convert only the minutes into hours as the hours are already hours.

= 45/60 minutes

= 0.75 hrs

= 9 + 0.75

= 9.75 hours

Speed = 658.125 / 9.75

= 67.5 mph

The value of x is approximately (7√3) / 3.

Given that a right triangle with base = x and the perpendicular side = 7 and the reference angle is 60°, we need to find the value of x.

To find the value of x in a right triangle with a base of x and a perpendicular side of 7, and with a reference angle of 60 degrees, we can use the tangent function.

The tangent of an angle is defined as the ratio of the length of the side opposite the angle (in this case, 7) to the length of the side adjacent to the angle (in this case, x). So we have:

tan(60°) = 7 / x

Now, we can solve for x by multiplying both sides of the equation by x:

xtan(60°) = 7

To find the value of x, we need to know the value of tan(60°). The tangent of 60 degrees is √3. So we have:

x√3 = 7

To isolate x, we divide both sides of the equation by √3:

x = 7 / √3

To simplify the expression, we multiply both the numerator and the denominator by √3:

x = (7 / √3)(√3 / √3)

= (7√3) / 3

Therefore, the value of x is approximately (7√3) / 3.

Learn more about tangent functions click;

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Answer:

40%

Step-by-step explanation:

20-12 = 8 difference

8/ 20  x100 = the percentage change  = 40%

Hypotenuse-Leg (HL) Theorem. If the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the two right triangles are congruent.

Mark as brainlist

Answer:

[tex]18r+\frac{1}{2}(14)(r)=182[/tex]

Step-by-step explanation:

Area of the composite figure ABCDE = Area of triangle ABE + Area of the rectangle BCDE

Area of triangle ABE = [tex]\frac{1}{2}(32-18)(r)[/tex]

                                  = [tex]\frac{1}{2}(14)(r)[/tex]

Area of rectangle BCDE = 18 × r

                                        = 18r

Total Area = [tex]\frac{1}{2}(14)r+18r[/tex]

Therefore, equation to get the value of 'r' will be,

[tex]18r+\frac{1}{2}(14)(r)=182[/tex]

Answer:

(4x - 3)(x + 1)

Step-by-step explanation:

=4x² + x - 3

=4x² + 4x - 3x - 3

=4x(x + 1 ) - 3( x + 1)

=(4x - 3)(x + 1)

Answer:

20

Step-by-step explanation:

(2x)° + (2x)° + (6x - 20)° = 180°

10x = 200

x = 20

Answer:

22.5m

Step-by-step explanation:

IF 2 inches = 5 meters

9 inches =( 9 x 5) / 2 = 22.5 meters

Answer:

hi so i have the answer for the 1st one but not the second one.

the first one

16, 11, 6, 1, -4 is arithmetic

5/9, 5/3, 5, 15, 45 is geometric

and 1/2, 1,2,3,4 is neither

Step-by-step explanation:

Answer:

4(12x + 32) = 48x + 128

Step-by-step explanation:

Answer:

Step-by-step explanation:

one point is (-2,5)

5y-25=-11x-22

11x+5y=25-22

11x+5y=3

5y=3-11x

[tex]y=\frac{3-11x}{5} \\x=-2,y=5\\x=3,y=-6\\[/tex]

so points are (-2,5) and (3,-6)

draw a line through these points.

Answer:

(5,15)

Step-by-step explanation:

Check x = 0,the P(x)=-225 : not an inequality solution

Check x = 10 to get -3*-5*5> 0 solutions in 5< x < 10

Check x = 20 to get -3*+5*+15<0 so no solutions in (15,+inf)

Ans: Profit for (5,15)

Answer:

hi

Step-by-step explanation:

Answer:

(10,6) in point form

and in equation form its x=10,y=6

Step-by-step explanation:

[tex] • \:  {( \sqrt{3} )}^{x + y}  = 9\:  \:  \: \: (i)[/tex]

[tex]• \:  {( \sqrt{2} )}^{x - y}  = 32 \:  \:  \: \: (ii)[/tex]

[tex] \\ [/tex]

[tex]  •   {\sf{The  \: value  \: of}} \:   \: 2x+ y.[/tex]

[tex] \\ [/tex]

[tex] \huge\bf \purple{ \underline{Solution :- }}[/tex]

[tex]  \sf{From \:  equation \:  (i), }[/tex]

[tex] {( \sqrt{3} )}^{x + y}  = 9 [/tex]

[tex]⇒ {( \sqrt{3} )}^{x + y}  =  ({ \sqrt{3} })^{4} [/tex]

[tex] ⇒ x + y = 4 \:  \:  \: \: (iii)[/tex]

[tex] \\ [/tex]

[tex] \sf{From \:  the  \: equation \:  (ii)}[/tex]

[tex]{( \sqrt{2} )}^{x - y}  = 32[/tex]

[tex] ⇒( { \sqrt{2} })^{x - y}  =(  { \sqrt{2} })^{10} [/tex]

[tex]⇒x - y = 10 \:  \:  \: \: (iv)[/tex]

[tex] \\ [/tex]

[tex]\sf{We \:  have \:  to  \: add \:  equation \:  (iii)  \: and \:  equation  \: (iv)}[/tex]

[tex] x + y + x - y = 4 + 10[/tex]

[tex] ⇒2x = 14[/tex]

[tex] ⇒x = 7[/tex]

[tex] \\ [/tex]

[tex] \sf{Subtracting \:  equation \:  (iii)  \: from  \: equation  \: (ii),  }[/tex]

[tex]x  - y - x - y = 10 - 4[/tex]

[tex]⇒ - 2y = 6[/tex]

[tex]⇒y =  - 3[/tex]

[tex] \\ [/tex]

[tex] \bf\therefore x = 7 \: \:  and  \: \: y =  - 3[/tex]

[tex] \\ [/tex]

[tex] { \sf{Th e \:  value \:  of }}= 2x +y [/tex]

[tex]\:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: \: \: \: \: \: =2 \times 7  + ( - 3)[/tex]

[tex]\:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: \: \: \: \: \: =14 - 3[/tex]

[tex] \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: \: \: \: \: =11[/tex]

[tex] \bf \red{Hence,  \: the  \: value \:  of  \: 2x + y  \: is  \: 11. }[/tex]

Answer:

HIIIII GVJJHGNKJMJNNJ SEXIIIJBH

Step-by-step explanation:

Answer: Hi there are sex11  sigZaghahahahah

Step-by-step explanation:  What????????

Answer: look at the picture of you want me to solve s or a here

Step-by-step explanation: hope this help:)

Answer:

151

Step-by-step explanation:

132.88 is 88% of the original price

132.88= p x .88=151

Answer:

p(blue) =

[tex] \frac{3}{10} [/tex]

Step-by-step explanation:

p (b)=

[tex] \frac{no \: of \: favourable \: outcomes}{no \: of \: total \: outcomes} [/tex]

so therefore ur answer will be 3/10

thank u hope it helped

Answer:

[tex]a\geq 16[/tex]

Step-by-step explanation:

Let [tex]a[/tex] represents the age at which a person gets a student learner's permit to drive in New Jersey.

Also, an individual must be at least [tex]16[/tex] years old to get a student learner's permit to drive in New Jersey.

So, inequality is [tex]a\geq 16[/tex]

(Inequality explains a relationship of greater than or greater than or equal to or less than, or less than or equal to between two mathematical expressions)

Answer:

All real numbers are solutions to this problem.

Step-by-step explanation:

I) Simplify:

2(x + 4) - 1 = 2x + 7

x + 4 - 0.5 = x + 3.5 (Divide by 2)

x + 3.5 = x + 3.5 (Simplify x + 4 - 0.5)

x = x

II) Conclusion:

Any real number will work as a solution.

Answer:

This is what it should look like:

Answer:

ill just do the first page

Step-by-step explanation:

3(x-8)=5x+6

3x-24=5x+6

3x-5x-24=6

3x-5x=6+24

-2x=6+24

-2x=30

x=-15

4x+20+2(x-7)=0

4x+20+2x-14=0

6x+20-14=0

6x+6=0

6x=-6

x=-1

Answer:

Step-by-step explanation:

90(5/6)

450/6

75

9514 1404 393

Answer:

  75

Step-by-step explanation:

90 = 6 × 15

There are 15 6-day periods in 90 days. The gardener will have mowed ...

  15 × 5 = 75

times in those 15 periods.

He will mow 75 times in a 90-day period.

__

If you like, you can set up a proportion for the unknown number of mowings (m).

  mows/days = m/90 = 5/6

Multiply by 90 to solve for m.

  m = 90(5/6) = (90/6)(5) = 15(5) = 75 . . . . . . this should look like the above