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:

y is 8/5 when x = -4.

Step-by-step explanation:

If the value of "Y" varies directly with "X", we can write y = kx, where k is the constant of proportionality.

If "y=-8,when x=20," then we can find k:    -8 = 20k, or k = -2/5.

Then y = (-2/5)x.

If x = -4, then y = (-2/5)(-4) = 8/5

y is 8/5 when x = -4.

Answer:

Horizontal

Step-by-step explanation:

Answer:

35          50

1             2

5            5

7            10

35         25

             50

Factor Trees are in the images!

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Answer;

B3 = 72°

C3 = 84°

Solution

B3: x = 180° - 55° - [ 180° - 127° ] = 127°- 55° = 72°

C3: x = 180° - 133°+ [ 180°-143° ] = 47°+37°= 84°

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Answer:

(a). The bus decelerated to rest through 75 miles for 1.25 hours and accelerated through same distance for 1.25 hours.

b.

[tex]s _{1} = \frac{d _{1} }{t _{1} } \\ = \frac{15}{1.5} \\ s _{1} = 10 \: miles \: per \: hour \\ \\ s _{2} = \frac{d _{2} }{t _{2}} = \frac{45}{2} \\ = 22.5 \: miles \: per \: hour \\ average = \frac{22.5 + 10}{2} \\ = 16.25 \: miles \: per \: hour[/tex]

a) The bus decelerated to rest through 75 miles for 1.25 hours and accelerated through same distance for 1.25 hours.

b)The average rate of change represent is 16.25 miles per hour.

a) The bus decelerated to rest through 75 miles for 1.25 hours and accelerated through same distance for 1.25 hours.

b)

s1 = d1/t1

15/1.5

s1 = 10 miles per hour

s2 = d2/t2

22.5 miles per hour

Average = 16.25 miles per hour.

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Answer:

a) there are 6 possible outcomes. b) the probability of getting 3 heads would be 3/6. c) the probability of getting 1 head is 1/6.

Answer:

[tex]h^-^1(x)=0.5x+1.5[/tex]

Step-by-step explanation:

Finding the inverse of a function is similar to solving for the complete opposite of a function. An easy trick to do so is the think of the resulting value (h(x)) as another variable. Solve the equation for (x) in terms of (h(x)). Finally, switch the variable and evalutator so that one has the funciton in inverse function notation.

[tex]h(x) = 2x - \frac{4}{3}[/tex]

Inverse operations,

[tex]h(x)=2x-\frac{4}{3}\\\\h(x)+\frac{4}{3}=2x\\\\\frac{h(x)+\frac{3}{4}}{2}=x[/tex]

Simplify,

[tex]0.5(h(x))+1.5=x[/tex]

Write in inverse function notation,

[tex]h^-^1(x)=0.5x+1.5[/tex]

Answer:

Step-by-step explanation:

x+y=94 degree(sum of two interior opposite angles is equal to the exterior angle formed)

 let third angle be y because the base of an isosceles triangle are always equal.

y+x+y=180 degree (sum of interior angles of a triangle)

y+94=180

y=180-94

y=86 degree

for angle x

substitute the value of x

x+y=94

x+86=94

x=8 degree

Answer:

Step-by-step explanation:

-10 g

Answer:

Step-by-step explanation:

the given equation is in the form of quadratic formula i.e.ax^2+bx+c=0.

So ,here a=-1 ,b=-6 and c=-9

b^2=(-6)^2

=36

4ac=4*(-1)*(-9)

=4*9

=36

b^2-4ac=36-36

=0

number of solutions =1

Hope this helps u !!

Answer:

Option C is correct

Step-by-step explanation:

[tex]8 + 8 + 8 + 8 + 8 + 8 = 48[/tex]

[tex]6 \times 8 = 48[/tex]

Answer:

6y^3 + 17y^2 +22y + 15

Step-by-step explanation:

Multiply each term in the first expression by each term in the second expression and combine like terms.

Answer:

Step-by-step explanation:

Angle b and the one that measures 76 are vertical angles. That means that they also have the same exact angle values. Therefore, b = 76 degrees

Answer:

Step-by-step explanation:

center at the origin means

x^2 + y^2 = r^2

9^2 + (-2)^2 = 81+4 = 85, so the circle is

x^2 + y^2 = 85

center at (0,-2) means

x^2 + (y+2)^2 = r^2

(-6)^2 + (0+2)^2 = 36+4 = 40

x^2 + (y+2)^2 = 40

The equation of circle which is centered at the origin that passes through (9,-2) is,

⇒ x² + y² = 85

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

We have to given that;

Circle o centered at the origin that passes through (9,-2).

Now, We can find the radius of circle as;

Radius of circle is distance between (0, 0) and point (9, - 2).

⇒ r = √ (- 2 - 0)² + (9 - 0)²

⇒ r = √4 + 81

⇒ r = √85

Thus, The equation of circle which is centered at the origin that passes through (9,-2) is,

⇒ x² + y² = (√85)²

⇒ x² + y² = 85

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Answer:

a

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

in fact if we look at the graph we can see that sausages are 7.5 % and mushrooms 5%, while in the table this datas are inverted.

Answer:

[tex]A=P (1 + \frac{r}n)} ^{nt}[/tex]

A = 500(1 + .028/1)^ (3*1)

$543.19

Step-by-step explanation:

Answer:

Step-by-step explanation:

Arc BAD is intercepted by inscribed angle BCD which measures 110. The rule is that an intercepted arc is twice the measure of the angle that intercepts it. Therefore, arc BAD is 110(2) which is 220.

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Explanation:

Imagine that we're able to move the xy grid freely but keep the f(x) curve fixed in place. Now imagine that we move the xy grid 3 units to the left. This would give the illusion the f(x) curve moves 3 units to the right.

If we replace each input x with x-3, then that will effectively move the xy grid 3 units to the left. So that's why f(x-3) is a translation of 3 units to the right.

The negative out front will reflect the curve over the x axis. Points of the form (x,y) become (x,-y). For example, if (1,2) is on the curve then (1,-2) is on the reflected curve.

Putting this all together and it leads us to -f(x-3) which is choice D.

Answer

8,98

Step-by-step explanation:

the minimum amount of weight you can use is the barbell alone which is 8lbs by itself and the maximum is 98 because there are 6 15lb plates which equal to 90lb total and when you add the 6 plates to the barbell you get 98lbs

Mikes pet shop: add the ratio: 7+ 3 = 10

Divide total animals by the sum:

300/10 = 30

The ratio of cats is 7

Total cats = 30 x 7 =210

Do the same for Pets R Us:

Ratio: 6 + 4 = 10

150/10 = 15

Cats = 15 x 6 = 90

Total cats = 210 + 90 =300

Total animals = 300 + 150 = 450

Fraction that are cats = 300/450 = 2/3

2/3 of the animals are cats

Answer:

200

Step-by-step explanation:

6.6/3.3 = 2

10^-2 / 10^-4 = 10^2

10^2 = 100

2 x 100 = 200

Answer:

Surface area of four outer sides = 1,320 inch²

Step-by-step explanation:

Given:

Height of trap = 30 inches

Length of trap = 12 inches

Width of trap = 10 inches

Find:

Surface area of four outer sides

Computation:

Lateral Surface area of cuboid = 2h[l + b]

Surface area of four outer sides = Lateral Surface area of cuboid

Surface area of four outer sides = 2h[l + b]

Surface area of four outer sides = 2(30)[12 + 10]

Surface area of four outer sides = 2(30)[22]

Surface area of four outer sides = 1,320 inch²

Here is all of my work from answering the question. I’ll put pictures too, my handwriting is pretty good so it should be easy to see. ;)

Part A-

1) 4x-3 = -2x+9

2) 4x+2x -3 = -2x+2x + 9

3) 6x -3 = 9

4) 6x -3+3 = 9+3

5) 6x = 12

6) 6x/6 = 12/6

7) x = 2

Part B-

1) y=4x-3

2) y=4(2)-3

3) y=8-3

4) y= 5

Therefore, x = 2 and y = 5.

I used substitution in Part B. 4x and x = 2.

I really hope this is right and helps, good luck! ;)

Answer:

Step-by-step explanation:

Ahh

Answer:

x=9

Step-by-step explanation:

so the angles of a triangle add up to 180 and since it shows two angles of 60 which makes 120, you have 60 more degrees which means A has to be 60 degrees. so if all of the angles are the same then the side lengths are the same so since it already shows one side =9 then x=9

Answer:

x=9

Step-by-step explanation:

missing angle + 60 + 60=180 degree (sum of interior angles of a triangle

missing angle + 120 =180

missing angle =180 -120

missing angle =60 degree

since all angles are 60 degree it is an equilateral triangle and all sides of a equailateral triangle are equal .So, x is also 9

Answer:

use substitution

(5 x 7) - (3 x 8) + 11= 35 - 24 + 11= 22

Answer:

22

Step-by-step explanation:

Answer:

the pattern is 4, 13, 4, 13. I dont know what the answer choices are, but the first 4 legths put together are 34 inches.

Step-by-step explanation:

look above, hope this helps...

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Answer:

The order of the first four strings is 1: 4in 2: 13in 3: 40in 4: 121in