Determine the point of intersection of the lines x + y = 4 and 2x + 3y = 12

Answer:

The shortest side of the triangle is 18

Step-by-step explanation:

Let the sides the triangle be x, y and z.

From the question, the perimeter of the rectangle is 64, that is

x + y + z = 64 ...... (1)

Also, the ratio of two of its sides is 4:3, that is x:y = 4:3, then we can write that x/y = 4/3 ⇒ 3x = 4y ...... (2)

The third side, z, is 20 less than the sum of the other two, that is

z + 20 = x + y ...... (3)

Substitute equation (3) into (1)

Then,

z + 20 + z = 64

2z +20 = 64

2z = 64 - 20

2z = 44

z = 44/2 k

z = 22

From equation (3)

z + 20 = x + y

Then, k

22 + 20 = x +y

42 = x + y

x = 42 - y ...... (4)

Substitute this into equation 2

3x = 4y

3(42-y) = 4y

126 - 3y = 4y

4y + 3y = 126

7y = 126

y = 126/7

y = 18

Substitute this into equation (4)

x = 42 - y

x = 42 - 18

x = 24

∴ x = 24, y = 18 and z = 22

Hence, the shortest side of the triangle is 18.

Answer:

E. 248

Step-by-step explanation:

1 to 500 in set A, 250 to 750 in set B

500 - 250 = 250

100 and 200 are divisible by 100.

250 - 2 = 248

Answer:

-9

Step-by-step explanation:

11+15u=-7+13u

or, 15u-13u = -7-11

or, 2u = -18

or, u = -9

Answered by GAUTHMATH

you can go for option g cause ans is 14:5

Answer:

the red marble was kept out so you can not draw it again

Answer:

Yes; you may not get a red marble again.

Step-by-step explanation:

there is a chance to get a red marble but it is not high

Step-by-step explanation:

(f*g) (x)=f(x) * g(x)

=(x+3)(2x^2-4)

=2x^3-4x+6x^2-12

Answer:

780

Step-by-step explanation:

Let x be the original price

x - x*72% is the new price

x - .72x = 218.40

.28x = 218.40

Divide each side by .28

.28x/.28 = 218.40/.28

x =780

Answer:

Hence the degrees of freedom are associated with the critical value is 25.

Step-by-step explanation:

Using two independent samples, two population means are  

compared to determine if a difference exists, the population standard deviation is equal.  

sample size 1 = [tex]n_{1}[/tex]= 15 and sample size 2 = [tex]n_{2}[/tex] = 12  

since, population standard deviations are equal, required degrees of freedom              

[tex]= n_{1} + n_{2} - 2 \\= 15 + 12 - 2\\ = 25[/tex]  

Answer:

x = 23.5

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp / hyp

sin 54 = x / 29

29 sin 54 = x

x=23.46149

To the nearest tenth

x = 23.5

Break it into two shapes, a rectangle that is 7 x 10 x 6

And a triangle with a base of 12-10 = 2 and a height of 7

Volume of rectangle : 7 x 10 x 6 = 420

Volume of triangle: 1/2 x 2 x 7 = 7 x 6 = 42

Total volume = 420 + 42 = 462 cubic centimeters.

Answer: 462

Step-by-step explanation: 7 x 12 x 6 = 504                                                                                        7 x 10 x 6 = 420

504 - 420 =84   84/2=42

420 + 42=462

Answer:

Scale factor = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

From the picture given in the question,

If the larger figure is dilated to form the smaller figure,

Scale factor by which a figure is dilated with is determined by the expression,

Scale factor = [tex]\frac{\text{Measure of one side of the smaller figure}}{\text{Measure of the corresponding side of the larger figure}}[/tex]

                    = [tex]\frac{3}{6}[/tex]

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

Answer:

there was a decrease of 2.25%

Step-by-step explanation:

Let me illustrate with an example

Assume the population is 100

percentage increase = 100 + 15 = 115% = 1.15%

Population after 15% increase = 100 x 1.15 = 115

Percentage decrease = 100 - 15 = 85% = 0.85

Population after 15% decreases 115 x 0.85 = 97.75

rate of increase = (97.75 / 100) - 1 = -2.25%

[tex]\\ \sf\longmapsto 1+tan^2A[/tex]

[tex]\boxed{\sf tanA=\dfrac{sinA}{cosA}}[/tex]

[tex]\\ \sf\longmapsto 1+\dfrac{sin^2A}{cos^2A}[/tex]

[tex]\\ \sf\longmapsto \dfrac{cos^2A+sin^2A}{cos^2A}[/tex]

[tex]\boxed{\sf cos^2A+sin^2A=1}[/tex]

[tex]\\ \sf\longmapsto \dfrac{1}{cos^2A}[/tex]

[tex]\\ \sf\longmapsto \dfrac{1}{1-sin^2A}[/tex]

[tex]\\ \sf\longmapsto \dfrac{1}{1}-\dfrac{1}{sin^2A}[/tex]

[tex]\\ \sf\longmapsto \dfrac{1}{sin^2A}[/tex]

Hence verified

Answer:

y=113*(1+0.82)^x

x=7

y=113*(1.82)^7=7474.43

Answer:

C

Step-by-step explanation:

as we can see on the graph, the lowest y value is the vertex/corner at x=3, y=-6.

all other y values are above (=are larger) that level.

and it goes up without appearant limit, so up to infinity.

Answer:

13.2%

or 115.2%

Step-by-step explanation:

hope it's correct. lemme know which one is correct

Answer:

50

Step-by-step explanation:

Given,

96 + 2² / 2

96 + 4 / 2

100 / 2

50

Answer:

14

Step-by-step explanation:

2a -b

Let a = 9 and b = 4

2(9) - 4

Multiply first

18-4

14

Answer:

arc GH = 74°

Step-by-step explanation:

The inscribed angle GFH is half the measure of the intercepted arc aGH, then

arc GH = 2 × 37° = 74°

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

m=7

c=5

balance=26.802

Answer: 20.58

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

A perpendicular bisector, intersects a line at its mid point and is perpendicular to it.

Calculate slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 7, 1) and (x₂, y₂ ) = (9, 13)

m = [tex]\frac{13-1}{9-(-7)}[/tex] = [tex]\frac{12}{9+7}[/tex] = [tex]\frac{12}{16}[/tex] = [tex]\frac{3}{4}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{3}{4} }[/tex] = - [tex]\frac{4}{3}[/tex] ←  slope of perpendicular bisector

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

([tex]\frac{x_{1}+x_{2} }{2}[/tex], [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

using (x₁, y₁ ) = (- 7, 1) and (x₂, y₂ ) = (9, 13) , then

midpoint = ( [tex]\frac{-7+9}{2}[/tex], [tex]\frac{1+13}{2}[/tex] ) = ( [tex]\frac{2}{2}[/tex], [tex]\frac{14}{2}[/tex] ) = (1, 7 )

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - [tex]\frac{4}{3}[/tex] , then

y = - [tex]\frac{4}{3}[/tex] x + c ← is the partial equation

To find c substitute the midpoint (1, 7) into the partial equation

7 = - [tex]\frac{4}{3}[/tex] + c ⇒ c = [tex]\frac{21}{3}[/tex] + [tex]\frac{4}{3}[/tex] = [tex]\frac{25}{3}[/tex]

y = - [tex]\frac{4}{3}[/tex] x + [tex]\frac{25}{3}[/tex] ← equation of perpendicular bisector

Answer:

1. -4

2. 8/ 5 - 1. 6

Step-by-step explanation:

1 . 3 × -4  

    = (-12)

2. 2/5 × 4

  = 8 / 5

  = 1.6

Hope this answer helps you :)

Have a great day

Mark brainliest

DC=CF

We know

[tex]\boxed{\sf L=\dfrac{\theta}{180}\times πr}[/tex]

[tex]\\ \large\sf\longmapsto L=\dfrac{90}{180}\times \dfrac{22}{7}\times 10[/tex]

[tex]\\ \large\sf\longmapsto L=\dfrac{1}{2}\times \dfrac{220}{7}[/tex]

[tex]\\ \large\sf\longmapsto L=\dfrac{110}{7}[/tex]

[tex]\\ \large\sf\longmapsto L=15.5[/tex]

Now

[tex]\\ \large\sf\longmapsto CF=L+r-DE[/tex]

[tex]\\ \large\sf\longmapsto CF=15.7+10-16[/tex]

[tex]\\ \large\sf\longmapsto CF=25.7-16[/tex]

[tex]\\ \large\sf\longmapsto CF=9.7cm[/tex]

[tex]\large\sf\red{⟼L=18090×722×10}[/tex]

[tex]\begin{gathered}\\ \large\sf\red{ ⟼ L=\dfrac{1}{2}\times \dfrac{220}{7}}\end{gathered}[/tex]

[tex]\begin{gathered}{ \large\sf\red{⟼ L=\dfrac{110}{7}}\end{gathered}[/tex]

⟼ L=15.5

Now

⟼ CF=L+r−DE

⟼ CF=15.7+10−16

⟼ CF=25.7−16

Answer:

1.137 m

Step-by-step explanation:

The volume of a cube is given as the cube of the side. A cube is a 3 dimensional shape with equal sides and 6 faces. If the volume is V and the side is s then

V = s * s * s

Given that the volume is 1.468mcube​ then

s^3 = 1.468

s = cube root of 1.468

= 1.137 m

Answer:

-5x - 7y

Step-by-step explanation:

Answer:

Rate of plane 735 km/hr

Rate of wind 65 km/hr

Step-by-step explanation:

Calculation to determine the rate of the plane in still air

Let Va represent the velocity of the airplane

Let Vw represent the velocity of the wind

When flying with the wind:

(Va+Vw)*(6 hours) = 4800

6Va + 6Vw = 4800

6Vw = 4800 - 6Va

Vw=4800/6-Va

Vw = 800 - Va

When flying against the wind:

(Va-Vw)*(6 hours) = 4020 km

6Va - 6Vw = 4020

Substitute 800-Va for Vw and solve for Va:

6Va - 6(800-Va) = 4020

6Va -4800 + 6Va = 4020

12Va = 8820

Va=8820/12

Va = 735 km/hr

Therefore the rate of the plane in still air is 735 km/hr

Calculation to determine the rate of the wind

Rate of wind:

Vw = 800 - Va

Vw= 800 -735

Vw= 65 km/hr

Therefore the rate of the wind is 65 km/hr

Answer:

441

Step-by-step explanation:

sqrt81=9

9 x 49=441

Answer:

441

Step-by-step explanation:

√ 9 ^2  ⋅  49

9  ⋅  49 = 441