EXERCISE 22.3
1.Divide 250 in the ratio 3:2
2.Divide 144 in the ratio 1:2
3.Divide 10 kg in the ratio 2:3
4.Divide 1 hour in the ratio 5:7
5.Divide 8m in the ratio 3:13
6.Divide 45 km in the ratio 7:8.
7.Divide 4 hours in the ratio 5:3
8 .Divide 2 kg in the ratio 3:7
9 .Divide 3 litres in the ratio 7:5
10.Divide 1 cm in the ratio 2:3
11.Divide 70 in the ratio 60% to 40%
12.Divide 1 hour in the ratio 20% to 80%
13 .Express the ratio 3:17 as percentages.
14 .Express the ratio 9:31 as percentages.

Answer:

4th answer

Step-by-step explanation:

g(h(x)) means to put the formula for h(x) into the formula for g(  ).

[tex]g(h(x))=g(2x-2)=-3(2x-2)^3-2(2x-2)^2\\=-3(8x^3-24x^2+24x-8)-2(4x^2-8x+4)\\=-24x^3+72x^2-72x+24-8x^2+16x-8\\=-24x^3+64x^2-56x+16[/tex]

Cubing the binomial 2x - 2 can take some time!

Answer:

30°

Step-by-step explanation:

it is the alternating angle.

Answer:

-$12

Step-by-step explanation:

Working backwards from the $63, you need to add back what was withdrawn and subtract what was deposited.

63+75+9+41+85-285= -$12

Answer:

B.

Step-by-step explanation:

1) the area of the given circle is: A=π*r²=256π (in²).

2) the part of the shaded sector is 110/360=11/36, it means that the required area of the shaded sector is: 11/36 * A = 256* π * 11 / 36≈246 (in²).

Answer:

$1.44

Step-by-step explanation:

Tax is a compulsory sum levied by the government. it increases the price of the good

tax paid = tax rate x price of the book

18 x 8%

18 x 0.08 = $1.44

Answer:

1/4

Step-by-step explanation:

Let's call the aces for hearts, diamonds, clubs, and spades. So,  are red and [tex] c, s[/tex] is black.

Since the first card is replaced, the two picks are identical. This means that the sample space is given by all the possible couple

There are 16 such couples (we have four choices for the first card, and the same four choices for the second card). Now let's compute the odds in our favor to deduce the probability of winning:

If we want a player to draw two cards of the same color, the following couples are good:

so 8 possible couples over 16. This means that a player's probability of drawing two cards of the same color is 8/16 = 1/2.

Similarly, the probability of drawing a red ace first and then a black ace is represented by the following couples:

which are 4 over the same 16 as above, thus leading to a probability of 4/16 = 1/4.

Answer:

-5

Step-by-step explanation:

12-7=5

7-12=-5

If this helps please mark as brainliest

Arithmetic

7-12

Meaning, 12 less than 7.

7-12=-5

Answer:

Top row, third one from left to right

Step-by-step explanation:

Use test points:

when x = 0 , y = 2(0) - 4 = 0 - 4 = -4

(0, -4)

when y = 0, 0 = 2x - 4, 4 = 2x, 2 = x

(2, 0)

Top row, third one from left to right

Answer:

∅ ≈ 34º

Step-by-step explanation:

sin = opp/hyp

∅ = arcsin opp/hyp

∅ = arcsin 14/25

Use calculator

∅ = 34.055797742567906

∅ ≈ 34º

Answer:

is 55

Step-by-step explanation:

×[tex]\frac{x}{1}*\frac{14}{25}[/tex]⇒0.56

cos0.56

55

Answer:

x = 145

Step-by-step explanation:

The angles are same side exterior angle and same side exterior angles are supplementary

x +35 =180

Subtract 35 from each side

x = 180-35

x =145

Answer:

x=145

Step-by-step explanation:

180 -35 = 145

angle in a straight line add up to 180

x=145

F angle /corresponding angle are the same

Given:

Darcy harvests [tex]8\dfrac{3}{4}[/tex] acres of corn every [tex]\dfrac{5}{6}[/tex] of an hour.

Darcy harvests corn at a constant rate.

To find:

How many acres does she harvest per hour?

Solution:

We have,

Acres harvest in [tex]\dfrac{5}{6}[/tex] of an hours = [tex]8\dfrac{3}{4}[/tex]

Acres harvest in 1 hour = [tex]8\dfrac{3}{4}\times \dfrac{6}{5}[/tex]

                                      = [tex]\dfrac{32+3}{4}\times \dfrac{6}{5}[/tex]

                                      = [tex]\dfrac{35}{4}\times \dfrac{6}{5}[/tex]

Cancel out the common factors, we get

Acres harvest in 1 hour = [tex]\dfrac{7}{2}\times \dfrac{3}{1}[/tex]

                                      = [tex]\dfrac{21}{2}[/tex]

                                      = [tex]10\dfrac{1}{2}[/tex]

Therefore, she can harvest [tex]10\dfrac{1}{2}[/tex] acres of corn per hour.

Answer:

x = 121°

Step-by-step explanation:

∠ 1 + 115° = 180°

∠ 1 = 180 - 115

∠ 1 = 65°

∠ 2 + 304° = 360°

∠2 = 360 - 304

∠ 2 = 56°

∠ 1 + ∠ 2 + ∠ 3 = 180°

65° + 56 ° + ∠ 3 = 180°

∠3 = 180 - 65 - 56

∠ 3 = 59°

∠3 + x = 180°

59° + x = 180°

x = 180 - 59

x =  121 °

Refer to the attachment for complete calculation.

3²× 11^-9

Answer:

4*4=16+7=23

Step-by-step explanation:

4 inches x 4 weeks is 16 inches

7 + 16 = 23

Answer:

Num. 2: A = 25, Num. 3 = 63, Num. 4 = 80

Step-by-step explanation:

I'll help with as many as I can, so a few of them I won't be able too answer. You should re-post those later. Good luck, hope this helps.

For number 2:

First, turn the triangle into a rectangle by cutting it in half and attaching it to the other half so it forms a rectangle.

Since you cut the triangle in half, you also have to split 5 in half, so the bottom length is now 2.5.

Now, simply multiply 2.5 by 10, and you have the area for number 2.

The area for number 2 is 25.

For number 3:

This one is much easier. Just think of the shape as a normal square that has been tipped to the side. That means that you would solve for area the same way: 9 x 7, which means that the area for number 3 is 63.

For number 4:

This one is also easy. Simply cut, and paste. Now the right side is 10, and the top side is 8. Multiply, and the area will be 80 m.

Please re-post 1 and 5, as I am not able to solve them. Sorry this answer took so long!

Answer:

D.

Step-by-step explanation:

Standard Form (Quadratic): [tex]y=ax^2+bx+c[/tex]

Vertex Form (Quadratic): [tex]y=a(x-h)^2+k[/tex]

Intercept Form (Quadratic): [tex]y=a(x-p)(x-q)[/tex]

      p,q are x-intercepts

x-intercepts given in graph: -2,4

[tex]y=a[x-(-2)](x-4)[/tex]

eqn 1: [tex]y=a(x+2)(x-4)[/tex]

Plug in the given point to find 'a' : (3,-5)

[tex]-5=a(3+2)(3-4)[/tex]

[tex]-5=a(5)(-1)[/tex]

[tex]1=a[/tex]

Substitute 'a' in to eqn 1.

[tex]y=1(x+2)(x-4)[/tex]

eqn 2: [tex]y=(x+2)(x-4)[/tex]

Expand eqn 2. (can use FOIL)

[tex]y=x^2-2x-8[/tex]

Answer:

huh???

Step-by-step explanation:

Answer:

top answer, domain and range have no restrictions

Step-by-step explanation:

Answer:

Option d) 2.1 + 2x = 7.5

Step-by-step explanation:

An isosceles triangle is a triangle with two equal sides.

Perimeter of a triangle is some of all the 3 sides.

Let the equal sides be x

Let the third side be y

Therefore,

              Perimeter = x + x + y

                         7.5 = 2x + y    

                          7.5 = 2x + 2.1                    [ given shortest side, y = 2.1m ]

Answer and Step-by-step explanation:

The last answer choice is correct.

Set the product of 7 and 24 equal to the product of 8 and x, and then solve for x

The process being used in the last answer choice is called Cross multiplication, and is used to find the unknown value in fractions.

[tex]\frac{7}{8}[/tex] × [tex]\frac{x}{24}[/tex]

7 × 24 = 8x

168 = 8x

21 = x

#teamtrees #PAW (Plant And Water)

Answer:

Aseem’s : 8.3, Stana’s : 11.6

Step-by-step explanation:

Aseem: x

Stana: 2x-5

X+2x-5=20

3x=25

X = 8.3

Answer:

Step-by-step explanation:

it should be

9x+1y+8

      ^it could be just y instead of 1y

Answer:

the answer is = 9x+y+8

Step-by-step explanation:

...

Answer:

-1 and 3

Step-by-step explanation:

The real roots of a function are located where the function passes through the x-axis. In this case, the function passes through x=-1 and x=3, making them the real roots of the function.

Answer:

The percentage change is 140%

Step-by-step explanation:

Given

[tex]L= 3W_1[/tex] ---- initial dimension

[tex]W_2 = 6m[/tex] --- new width

[tex]A_2 = 45m^2[/tex] --- new dimension

Required

The percentage increment

The length remains constant because only the width is extended.

The new area is:

[tex]Area =Length * Width[/tex]

[tex]A_2=L * W_2[/tex]

Make L the subject

[tex]L = \frac{A_2}{ W_2}[/tex]

Substitute values for A and W

[tex]L = \frac{45m^2}{6m}[/tex]

[tex]L = \frac{45m}{6}[/tex]

[tex]L = 7.5m[/tex] --- this is the length of the garden

Calculate the initial width:

[tex]L= 3W_1[/tex]

Make W1 the subject

[tex]W_1 = \frac{1}{3} * L[/tex]

[tex]W_1 = \frac{1}{3} * 7.5[/tex]

[tex]W_1 = 2.5[/tex]

So, the initial area is:

[tex]A_1 = L_1 * W_1[/tex]

[tex]A_1 = 2.5 * 7.5[/tex]

[tex]A_1 = 18.75[/tex]

The percentage change in area is:

[tex]\%A = \frac{A_2 - A_1}{A_1}[/tex]

[tex]\%A = \frac{45 - 18.75}{18.75}[/tex]

[tex]\%A = \frac{26.25}{18.75}[/tex]

[tex]\%A = 1.4[/tex]

Express as percentage

[tex]\%A = 1.4*100\%[/tex]

[tex]\%A = 140\%[/tex]

Complete Question

David bought a chain of fast food restaurants that operated 200 stores in 2009. The number of restaurants has grown at a rate of 12% annually.how many stores does the restaurant operate in 2020?

Answer:

[tex]N_{11} \approx 749[/tex]

Step-by-step explanation:

From the question we are told that:

Number of Fast Food Restaurants [tex]P=200[/tex]

Number of years [tex]t=11yrs[/tex]

Rate [tex]r=12%[/tex]

Generally the equation for the Number of restaurant in operation in 2020 is mathematically given by

 [tex]N(t)=Pe^{rt}[/tex]

Therefore

For t=11

 [tex]N_{11}=200*e^{0.12*11}[/tex]

 [tex]N_{11}=748.7[/tex]

 [tex]N_{11} \approx 749[/tex]