Z varies directly as x/y² and y varies inversely as x,if z=⅓ when x =2 and y=¼. Express (a). Y interms of x and (b). Z interms of x

[tex] \\ \tt \longmapsto 2 \frac{1}{3} \div 4\frac{1}{3} = \frac{7}{x} \\ \\ \tt \longmapsto \frac{7}{3} \div \frac{13}{3} = \frac{7}{x} \\ \\ \tt \longmapsto \frac{7}{3} \times \frac{3}{13} = \frac{7}{x} \\ \\ \tt \longmapsto \frac{7}{13} = \frac{7}{x} \\ \\ \tt \longmapsto 7x = 7 \times 13 \\ \\ \tt \longmapsto 7x = 91 \\ \\ \tt \longmapsto x = \frac{91}{7} \\ \\ \tt \longmapsto x = 13[/tex]

Answer:

[tex]x = 13[/tex]

Step-by-step explanation:

[tex] \frac{2 \frac{1}{3} }{4 \frac{1}{3} } = \frac{7}{x} \\ \frac{7}{3} \div \frac{13}{3} = \frac{7}{x} \\ \frac{7}{ 3} \times \frac{3}{13} = \frac{7}{x} \\ \frac{7}{13} = \frac{7}{x} \\ 7x = 13 \times 7 \\ x = \frac{13 \times 7}{7} \\ x = 13[/tex]

Answer:

1       a

2      b

3      c

4      d

Step-by-step explanation:

1b

2d

3c

4a

Answer:

10(4) > 10,000

10-(4) > 0.0001

10(4)/10(2) > 0.000001

10-(4) * 10(2) > 1/10(4) 0.01

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

√(x2 - x1)² + (y2 - y1)²

√[6 - (-5)]² + (6 - 6)²

√(11)² + (0)²

√121

= 11

Answer:

5

Step-by-step explanation:

(4/7)/(?/-6)=(-24/35)

(4/7)×(-6/?)=(-24/35)

(4×-6)/(?×7)=(-24/35)

-24/(?×7)=(-24/35)

-->7×?=35

-->?=35÷7

-->?=5

Answer:

g(x) = 5x + 1

Step-by-step explanation:

Given data

We have the following expressions to work with

f(x) = 2x − 6 and

g(x) = 5x + 1

say the value of x = 3

let us put x into the two expressions above and compare the output

f(x) = 2*3 − 6= 6-6= 0

g(x) = 5*3 + 1= 15+1= 16

Hence the second function has the greatest output

Answer:

We can define the algebraic transformations used here as:

Horizontal translation.

For a general point (x, y), a horizontal translation of N units is written as:

(x + N, y)

if N < 0, the translation is to the left

if N > 0, the translation is to the right.

Vertical translation:

For a general point (x, y), a vertical translation of N units is written as:

(x , y + N)

If N < 0, the translation is downwards

if N > 0, the translation is upwards.

Vertical dilation:

For a point (x, y), a vertical dilation of scale factor k is given by:

(y, k*y)

Horizontal dilation:

A dilation of scale factor k is written as:

(x/k, y)

Here we go from:

(x, y) to (3x - 4, (1/5)*y - 2)

So we have:

An horizontal dilation of scale factor 1/3 followed of a horizontal translation of 4 units.

And a vertical dilation of scale factor (1/5) followed by a translation downwards of 2 units.

Step-by-step explanation:

Hey there!

From the given figure;

Measure of angle V + measure of angle W = measure of angle VUF {exterior angle is equal to the sum of opposite interior angles}

Therefore, angle VUF= 94°.

Hope it helps!

Answer:

<V + <W = < VUF

94 = < VUF

Step-by-step explanation:

The exterior angle is equal to the sum of the opposite interior angles

<V + <W = < VUF

71+ 23 = < VUF

94 = < VUF

Answer:

Equation: y=45x+1000

A. $45

B. 1,000

C. y=45x+1000-->Independent=1,000-->Dependent=45

D. y=45(20)+1,000=1,900

E. 30 weeks

Step-by-step explanation:

To solve step "E", you must set up an equation.

Specifically--> 45x+1,000=2350, then solve

45x=1350

x=30

Answer:

q = 80 degrees

r = 70 degrees

s = 10 degrees

t = 70 degrees

u = 40 degrees

v = 60 degrees

Step-by-step explanation:

starting with the fact that all angles in any triangle always sum up to 180 degrees :

q = 180 - 60 - 40 = 80 degrees

r = 180 - (60+10) - 40 = 180 - 70 - 40 = 70 degrees

the triangle 40-60-q and v-u-blank are similar triangles. your can say the smaller triangle is just a projection of the large triangle through the focal point at angle q.

that means the angles must be equal.

v = 60 degrees

u = 40 degrees

similar for 10-r-blank and t-s-blank.

s = 10 degrees

t = 70 degrees

u=60°

v=40°

q=80°

r=70°

s=70°

t=10°

Answer:

Solution given:

t=10°[inscribed angle on a same chord or arc is equal]

V=40°[inscribed angle on a same chord or arc is equal]

u=60°[inscribed angle on a same chord or arc is equal]

AGAIN;

40+60+10+r=180°[sum of interior angle of triangle]

r+110°=180°

r=180°-110°

r=70°

again

r=s=70°[inscribed angle on a same chord or arc is equal]

again

q=r+10°[exterior angle is equal to the sum of two opposite interior angle]

q=70+10=80°

Answer:

The first one

Step-by-step explanation:

Answer:

x = 14

Step-by-step explanation:

x - 42 = 98 - 9x

+42      +42

x = 140 - 9x

+9x       +9x

10x = 140

/10     /10

x = 14

Answer:

there is only one way to to roll a 3

1/36 = .044 = 4.4%

Step-by-step explanation:

Answer:

Step-by-step explanation:

From the picture attached,

If ΔPRQ ~ ΔPTS,

By the property of similar triangles,

Corresponding sides of the similar triangles are proportional.

[tex]\frac{PR}{PT}= \frac{PQ}{PS}[/tex]

[tex]\frac{7.5+4.5}{4.5}= \frac{20}{7.5}[/tex]

[tex]\frac{12}{4.5}=\frac{20}{7.5}[/tex]

[tex]\frac{120}{45}= \frac{200}{75}[/tex]

[tex]\frac{8}{3}=\frac{8}{3}[/tex]

By the converse of similar triangles,

If two triangles ΔPRQ and ΔPTS are similar, sides ST and QR will be parallel.

Answer:

To graph this line, move one of the points to positive three on the horizontal (side to side) line and negative six on the vertical (up and down) line. To get a slope of negative 1/2 you move down one point and right two points, and you continue until you reach the edge of the graph. Then you do the opposite on the way up (up one and left two).

Hope this helps!

Answer:  Plot the two points (3,-6) and (1, -5). Draw a straight line through those points.

See the graph below.

=============================================

Explanation:

Plot the point (3, -6)

The slope -1/2 means the rise is -1 and the run is 2

If we moved to the right, then we'd drop down 1 and move to the right 2. That would move us from (3,-6) to (5,-7)

We can go in reverse of this. So instead of "move down 1", we move up 1. We're going left instead of right.

-----------

So we start at (3,-6) and move up 1 and to the left 2 to arrive at (1,-5)

Two points on this line are (1, -5) and (3, -6)

Once we have two points, we have enough to graph the line.

See the graph below.

Answer: If he walked 20 blocks west straight from his exited appartment, then added an additional 5 blocks to the west, he would have walked a total of 25 blocks and to return to his appartment must walk 25 blocks straight back from where he cam from to return back to his appartment.

Step-by-step explanation:

Answer:

Q3. Last option Q4. 3rd option

Step-by-step explanation:

s^2 = 9.8^2+5.1^2-2(9.8)(5.1)cos39

s^2=44.366489...

s=6.7

Step-by-step explanation:

a. 78 b.128 c. 165 d. 156 e. 180 f.208

Answer:

first year

$2180

Step-by-step explanation:

9% of $2000 =$180

Step-by-step explanation:

1year $2180. so the ans is send me I'd and password of zoom Answer of ur Question bro

Answer:

x < 7

Step-by-step explanation:

4x-4<24

Add 4 to each side

4x-4+4<24+4

4x<28

Divide by 4

4x/4 <28/4

x < 7

Answer:

15

Step-by-step explanation:

Answer:

Step-by-step explanation:

For question a: odd + even will always equal odd. so we can use 15 + 40.

For question b: 15 itself is a multiple of b.

For question c: 15 is a factor of 60. There are other answers in there.

For question d: 4^3 = 64, so 64 is one of them.

Answer:

system of equations: set of one or more equations involving a number of variables

substitution method:

1. Solve one equation for one of the variables.

2. Substitute (plug-in) this expression into the other equation and solve.

3. Resubstitute the value into the original equation to find the corresponding variable.

ex:

-4x+3y=-2           y=x-1

plug in: -4x+3(x-1)=-2

simplify:  -x-3=-2

              -x=-2+3

              -x=1

answer:  x=1

Answer:

let g(x)=y

y=6(x-1)

interchange the values of x and y

x=6(y-1)

Make y the subject

x=6y-6

x+6=6y

(x+6)/6=y

Equation: (x - 3)^2 + (y + 4)^2 = 36

General Equation of a Circle: (x - h)^2 + (y - k)^2 = r^2

Susan did not account for the fact that the minus sign in front of the x actually indicates a positive x-coordinate. The plus sign in front of the y actually indicates a negative y-coordinate, as well. Therefore, the actual center is (3,-4).

Susan did not take the square root of 36, instead dividing it by 2. The square root of 36 is 6, which means the radius of the circle is 6.

Hope this helps!

Answer:

x = 60

Step-by-step explanation:

Since m is parallel to n, that means they are equal to each other.

In other words:

135 = 2x + 15

Solve for the variable:

120 = 2x

60 = x

Check your work:

135 = 2(60) + 15

135 = 120 + 15

135 = 135

Correct!

Answer:

x = 60

Step-by-step explanation:

For these two lines to be parallel, the angles m and n must be equal. Thus, 135 = 2x + 15.

Excellent. Let’s solve this equation. Subtract 15 from each side. 120 = 2x. Divide by 2, and we get 60 = x, so x = 60.

Hope this helps!

Answer:

I think it's 12

Step-by-step explanation:

Hope it helps!

Answer:

ratio 2 : 3 : 5

size of smallest angle

[tex]180 \times \frac{2}{10} \\ = 36[/tex]

Answer:

The smallest angle of a triangle is 36°.

Step-by-step explanation:

Given, the ratio of angles of a triangle is 2 : 3 : 5

Let the angles of a triangle be ∠A, ∠B and ∠C.

∠A = 2x, ∠B = 3x, ∠C = 5x

∠A+∠B + ∠C= 180°

[sum of all the angles of a triangle is 180°]

2x + 3x + 5x = 180°

10x = 180°

x=180°/10 =18°

∠A=2x=2 x 18° = 36°

∠B = 3x = 3 x 18° = 54°

∠C = 5x = 5 x 18° = 90°

Hence, the smallest angle of a triangle is 36°.

HOPE IT HELPS!!!

Answer:

[tex]118 cm^2[/tex]

Step-by-step explanation:

[tex]===========================================[/tex]

Formulas:

Area of a rectangle/square:

[tex]A=lw[/tex]

Area of a triangle:

[tex]A=bh\frac{1}{2}[/tex]

[tex]===========================================[/tex]

Side rectangles(2):

7*5=35

Multiply by 2

35*2= 70 cm

Middle rectangle:

4*7= 28 cm

Triangles(2):

[tex]4*5*\frac{1}{2} =10 cm[/tex]

Multiply by 2

10*2= 20 cm

Total:

Add.

70+28+20= 118 cm2

let:

3x+2=0

then solve it

then put the velue of x in p(x)

Answer:

The answer is -13.

Step-by-step explanation:

The formula of the nth term of an AP(arthimetic progression) is a+(n-1)d.

So the 7th term will be a+6d= -1  ---(1)

The 16th term will a+15d=17  ---(2)

Subtract (2) and (1)

a+15d-(a+6d)=17-(-1)

=a+15d-a-6d=17+1

9d=18

d=18/9

d=2.

Substitute d in eq (1)

a+6(2)= -1

a+12=-1

a= -1-12= -13

Thus the general term of the ap is -13

If polygons are similar ratio if sides will be same

[tex]\\ \sf\longmapsto \frac{x}{50} = \frac{48}{40} \\ \\ \sf\longmapsto 40x = 48 \times 50 \\ \\ \sf\longmapsto x = \frac{48 \times 50}{40} \\ \\ \sf\longmapsto x = \frac{2400}{40} \\ \\ \sf\longmapsto x = 60[/tex]