how do you know a mixed number in a decimal

Answer:

length of rectangle=6cm

width of rectangle=11cm

Step-by-step explanation:

let, width of rectangle=x

length of rectangle=x-5

area of rectangle=[tex]length\times(width)[/tex]

given area of rectangle=66

so 66=[tex]x\times(x-5)[/tex]

66=x^2-5x

x^2-11x+6x-66=0

x(x-11)+6(x-11)=0

(x+6)(x-11)=0

x=-6,11

here x=11 is acceptable

length of rectangle=x-5=11-5=6cm

length of rectangle=6cm

width of rectangle=11cm            answer

Answer:

True

Step-by-step explanation:

Because angles on a straight line are supplementary and these anglea <1 and <2 are supplementary angles

Answer: True

Step-by-step explanation:

Nevermind someone already answered it.

Answer:

Step-by-step explanation:

20 km to 95 minutes = x km to 285 minutes

20 / 95 = x / 285.....cross multiply

(95)(x) = (20)(285)

95x = 5700

x = 5700/95

x = 60 km <======

Answer:

k=-1

Step-by-step explanation:

1-2k-2k=5

1-4k=5

4k=1-5

4k=-4

k=-4/4

k=-1

Answer:

7 without going over

Step-by-step explanation:

The number 7 can go into 50 a total of 7 times with 1 remainder.

A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9.

The number 7 can go into 50 a total of 7 times because 50 / 7 = 7 with 1 remainder.

To understand this, consider that when you divide 50 by 7, you are trying to find out how many groups of 7 can be created from 50. Since 50 is a multiple of 7 (50 is divisible by 7 with 1 remainder), there will be an integer number of groups. In this case, that integer is 7, so 7 groups of 7 can be created from 50.

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Answer:

The Proof is below.

Step-by-step explanation:

Given:

[]MNOP is a Parallelogram

U is any point on side OP

To Show:

ar(Δ MUN)= ar ( Δ PUM)+ar (Δ UNO)

Proof:

Theorem:

If a triangle and parallelogram are on the same base and have the same altitude, the area of the triangle will be half that of the parallelogram.

If they have same altitude, they will lie between the same parallels.

Hence the area of the triangle will be equal to half that of the parallelogram.

Area of Parallelogram will be twice of Area of Triangle

∴ [tex]\textrm{Area of Parallelogram MNOP}=2\times (area\ of\ Triangle\ MUN)[/tex].............( 1 )

Also,

[tex]\textrm{Area of Parallelogram MNOP}=Ar(MUN) + Ar(PUM)+ Ar(UNO)[/tex]

Substituting equation 1 we get

[tex]2\times Ar(MUN)=Ar(MUN) + Ar(PUM)+ Ar(UNO)[/tex]

[tex]2\times Ar(MUN)-Ar(MUN) = Ar(PUM)+ Ar(UNO)[/tex]

[tex]Ar(MUN) = Ar(PUM)+ Ar(UNO)[/tex]...........Proved

Answer:

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

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

The corresponding vertical sides are y and 2

The corresponding horizontal lines are x and 1

so

The proportion is equal to

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

Answer:

Problem 4:

Radius = 11 cm.

Circumference = 69.08 cm.

Problem 5:

Radius = 14 mm.

Circumference = 87.92 mm.

Problem 6:

Radius = 9 inches.

Circumference = 56.52 inches.

Problem 7:

Diameter = 32 ft.

Circumference = 100.48 ft.

Problem 8:

Diameter = 26 yards.

Circumference = 81.64 yards.

Problem 9:

Diameter = 12 cm.

Circumference = 37.68 cm.

Step-by-step explanation:

Problem 4:

Given:

Diameter GH = 22 cm

We need to find the radius EF and Circumference of the circle.

Now radius is given by half of the diameter

Also Circumference is given by π times diameter.

Radius EF = [tex]\frac{1}{2}\times Diameter = \frac{1}{2}\times 22 = 11 \ cm[/tex]

Circumference = [tex]\pi \times Diameter = 3.14 \times 22 = 69.08\ cm[/tex]

Hence Radius = 11 cm

Circumference = 69.08 cm.

Problem 5:

Given:

Diameter OP = 28 mm

We need to find the radius MN and Circumference of the circle.

Now radius is given by half of the diameter

Also Circumference is given by π times diameter.

Radius MN = [tex]\frac{1}{2}\times Diameter = \frac{1}{2}\times 28 = 14 \ mm[/tex]

Circumference = [tex]\pi \times Diameter = 3.14 \times 28 = 87.92\ mm[/tex]

Hence Radius = 14 mm

Circumference = 87.92 mm.

Problem 6:

Given:

Diameter EF = 18 inches

We need to find the radius CD and Circumference of the circle.

Now radius is given by half of the diameter

Also Circumference is given by π times diameter.

Radius CD = [tex]\frac{1}{2}\times Diameter = \frac{1}{2}\times 18 = 9 \ in[/tex]

Circumference = [tex]\pi \times Diameter = 3.14 \times 18 = 56.52\ in[/tex]

Hence Radius = 9 inches.

Circumference = 56.52 inches.

Problem 7:

Given:

Radius GH = 16 ft

We need to find the Diameter CD and Circumference of the circle.

Now Diameter is given by twice the radius.

Also Circumference is given by π times diameter.

Diameter KJ = [tex]2 \times radius = 2 \times 16 = 32 \ ft[/tex]

Circumference = [tex]\pi \times Diameter = 3.14 \times 32 = 100.48\ ft[/tex]

Hence Diameter = 32 ft.

Circumference = 100.48 ft.

Problem 8:

Given:

Radius LM = 13 yards

We need to find the Diameter CD and Circumference of the circle.

Now Diameter is given by twice the radius.

Also Circumference is given by π times diameter.

Diameter NO = [tex]2 \times radius = 2 \times 13 = 26 \ yards[/tex]

Circumference = [tex]\pi \times Diameter = 3.14 \times 26 = 81.64\ yards[/tex]

Hence Diameter = 26 yards.

Circumference = 81.64 yards.

Problem 9:

Given:

Radius NO = 6 cm

We need to find the Diameter CD and Circumference of the circle.

Now Diameter is given by twice the radius.

Also Circumference is given by π times diameter.

Diameter PQ = [tex]2 \times radius = 2 \times 6 = 12 \ cm[/tex]

Circumference = [tex]\pi \times Diameter = 3.14 \times 12 = 37.68\ cm[/tex]

Hence Diameter = 12 cm.

Circumference = 37.68 cm.

Answer:

r=39.75

Step-by-step explanation:

7(5*9.5-R)+3r=173.5

7(47.5-R)+3r=173.5

332.5-7R+3r=173.5

332.5-4r=173.5

4r=332.5-173.5

4r=159

r=159/4

r=39.75

Step-by-step explanation:

7 (5x - R) + 3r = 173.5

let x = 9.5 as given

solve for R

substitute the value of x=9.5 into the equation:

7 (5 * 9.5 - R) + 3R = 173.5

7 (47.5 - R) + 3R = 173.5   expand

332.5 - 7R + 3R = 173.5    combine similar terms

332.5 - 173.5 = 7R - 3R     simplify

159 = 4R                            divide 4 on each side

R = 159/4                           simplify

R = 39.75

Answer:

14.3

Step-by-step explanation:

percent: 14.3%

decimal: 14.3

fraction: 14 3/10

Answer:

I got 143/10 ;-;

But as a decimal it's 143.0 and percent is 14.3%

Answer:

Option D. [tex]y=2x+2[/tex]

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Verify each case

case A) we have

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

Is a equation of the form [tex]y=kx[/tex]

The value of k=-2

This equation represent a proportional relationship

case B) we have

[tex]y=2x[/tex]

Is a equation of the form [tex]y=kx[/tex]

The value of k=2

This equation represent a proportional relationship

case C) we have

[tex]y=-2x+0[/tex]

The line passes through the origin, because the y-intercept is b=0

This equation represent a proportional relationship

case D) we have

[tex]y=2x+2[/tex]

The line not passes through the origin, because the y-intercept is not equal to zero (b=2)

This equation not represent a proportional relationship

Answer:

20%

Step-by-step explanation:

A pair of jeans cost $45  before the sale.

The sale is taking $9 off of the original price.

Then

$45 - 100%

$9 - x%

Write a proportion:

[tex]\dfrac{45}{9}=\dfrac{100}{x}[/tex]

Cross multiply:

[tex]45\cdot x=9\cdot 100\\ \\45x=900\\ \\x=\dfrac{900}{45}\\ \\x=20\%[/tex]

Answer:

The sale price is $46.75

Step-by-step explanation:

Answer:

x = 9, y = 2

Step-by-step explanation:

Given the 2 equations

x + 10y = 29 → (1)

x - y = 7 → (2)

Subtracting (2) from (1) term by term will eliminate the term in x

(x - x) + (10y - (- y)) = (29 - 7), that is

11y = 22 ( divide both sides by 11 )

y = 2

Substitute y = 2 in either of the 2 equations

Substituting in (2)

x - 2 = 7 ( add 2 to both sides )

x = 9

Answer:

x=7, -2.

Step-by-step explanation:

x^2-5x=14

x^2-5x-14=0

factor out the trinomial,

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

zero property,

x-7=0, x+2=0,

x=0+7=7,

x=0-2=-2

Answer:

x = - 2, x = 7

Step-by-step explanation:

Given

x² - 5x = 14 ( subtract 14 from both sides )

x² - 5x - 14 = 0 ← in standard form

Consider the factors of the constant term (- 14) which sum to give the coefficient of the x- term (- 5)

The factors are - 7 and + 2, since

- 7 × 2 = - 14 and - 7 + 2 = - 5, thus

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

Equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

x - 7 = 0 ⇒ x = 7

Answer:

-1/2

Step-by-step explanation:

The format your equation in is called slope-intercept form:

y=mx+b

m stands for slope, the slope basically determines how much the line is tilted. b stands for the y intercept, the y intercept is when the line intercepts with the y axis.

Your equation is:

y= -1/2x+1/4

y=   m x+ b

Answer:

The interest earned was $50.95

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=1\ year\\ P=\$1,000\\ r=5\%=5/100=0.05\\n=4[/tex]  

substitute in the formula above

[tex]A=1,000(1+\frac{0.05}{4})^{4*1}[/tex]  

[tex]A=1,000(1.0125)^{4}[/tex]  

[tex]A=\$1,050.95[/tex]  

Find the interest earned I

we know that

[tex]I=A-P[/tex]

substitute the values

[tex]I=\$1,050.95-\$1,000=\$50.95[/tex]

Answer:

Therefore the expression is option A)

[tex]2x-8[/tex]

Step-by-step explanation:

Given:

Statement as ' 8 less than two times X'

To Find :

Expression for the statement

'8 less than two times X'

Solution:

[tex]Two\ times\ 'x'\ means=2\times x[/tex]

Now 8 less than two times X  means Subtract 8 from '2x'

[tex]2x-8[/tex]

Therefore the expression is option A)

[tex]2x-8[/tex]

Answer:

The equation of the circular wheel is [tex]x^2+(y-74)^2=(70)^2[/tex].

Step-by-step explanation:

Given :

Radius of Ferris wheel r = 70 feet.

The distance between the wheel and the ground = 4 feet.

Also, the rectangular coordinate system shown has its origin on the ground directly below the center of the wheel.

So the x coordinate of center of wheel must  be 0 , and y coordinate = 70 + 4 = 74

Thus, Coordinates of center = (0,74)

The equation of circle is given by :-

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Now center (h,k) = (0,74) and r = 70 , we get

[tex]x^2+(y-74)^2=(70)^2[/tex]

Hence, the equation of the circular wheel is [tex]x^2+(y-74)^2=(70)^2[/tex].

Answer:

63

Step-by-step explanation:

85 * .75 = 63 hats

Answer:

Total length of running track is 371.24 m .

Step-by-step explanation:

Total running track = Running track around straight region + running track around curved region.

Running track around straight region = 2 × length of straight region

= 2×82 m

= 164 m

Running track around curved region = 2 × length of curved region

= 2 × π × radius of curved region

= 2 × 3.14 × 33 m

= 207.24 m

Therefore , total length  of running track = 164 + 207.24 m

= 371.24 m

Answer:

$7.6825

Step-by-step explanation:

65%=0.65

0.65*21.95=14.2675

21.95-14.2675=7.6825

Answer:

7.6825

Step-by-step explanation:

Answer:45x-5 is the answer

Step-by-step explanation:

(4,1) and 5,5 add them both

Answer:

B.) The graph is a line that goes through the points (1,4) and (2,8).

Step-by-step explanation:

1.) (4) + 4 = 4((1) +1)

2.) 8 = 4 + 4

3.) 8 = 8 --> Correct

4.) (8) + 4 = 4((2) + 1)

5.) 12 = 8 + 4

6.) 12 = 12 --> Correct

The acceleration of the object is 5 m/s^2

Step-by-step explanation:

Given

Mass of object = m = 40 kg

Force = F = 200 N

Newton's 2nd law states that:

[tex]F = ma[/tex]

As we have to find the acceleration

[tex]a = \frac{F}{m}[/tex]

Putting the values

[tex]a = \frac{200}{40}\\a = 5\ ms^{-2}[/tex]

The acceleration of the object is 5 m/s^2

Keywords: Force, acceleration

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To calculate the acceleration of the object, we can use Newton's second law of motion which states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass. Using the given force of 200 N and mass of 40 kg, we can determine that the acceleration of the object is 5 m/s^2.

To calculate the acceleration of the object, we can use Newton's second law of motion which states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass.

Therefore, the acceleration of the object is 5 m/s^2.

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Answer:

Therefore,

[tex]BC=a=10\ units\\\\AC=b=13.66\ units[/tex]

Step-by-step explanation:

Consider a Δ ABC with

m∠ A = 45°

m∠ C = 30°

AB = c = 5√2

To Find:

BC = a = ?

AC = c = ?

Solution:

Triangle sum property:

In a Triangle sum of the measures of all the angles of a triangle is 180°.

[tex]\angle A+\angle B+\angle C=180\\\\45+30+\angle B=180\\\ttherefore m\angle B =180-75=105\°[/tex]

We know in a Triangle Sine Rule Says that,

In Δ ABC,

[tex]\frac{a}{\sin A}= \frac{b}{\sin B}= \frac{c}{\sin C}[/tex]

substituting the given values we get

[tex]\frac{a}{\sin 45}= \frac{b}{\sin 105}= \frac{5\sqrt{2} }{\sin 30}[/tex]

∴ [tex]\frac{a}{\sin 45}= \frac{5\sqrt{2} }{\sin 30}\\\\a=\sin 45\times \frac{5\sqrt{2} }{\sin 30}\\\\a=\frac{1}{\sqrt{2} }\times \frac{5\sqrt{2} }{0.5} \\\\\\a=\frac{5}{0.5} =10\\\therefore BC = a = 10\ units[/tex]

Similarly for 'b',

[tex]\frac{b}{\sin 105}= \frac{5\sqrt{2} }{\sin 30}\\\frac{b}{0.9659}= \frac{5\sqrt{2} }{0.5}\\\\b=0.9659\times \frac{5\sqrt{2} }{0.5}\\\\b=\frac{6.8301}{0.5} \\\\b=13.66\\\therefore AC = b =13.66\ units\\[/tex]

Therefore,

[tex]BC=a=10\ units\\\\AC=b=13.66\ units[/tex]

By using the Law of Sines, side BC of the triangle is found to be approximately 10 m, and AC is approximately 8.66 m. These calculations take into account the given lengths and angles of triangle ABC.

To find the lengths of sides BC and AC in triangle ABC with given angles and side AB, we will employ trigonometry and the properties of triangles. Since the sum of the angles in any triangle is 180 degrees, we know that m∠B = 180° - 45° - 30° = 105°. With this information, we can use the Law of Sines, which states:
[tex]\(\frac{AB}{\sin(C)} = \frac{BC}{\sin(A)} = \frac{AC}{\sin(B)}\)[/tex]

From the given, AB = 5√2 m, m∠A = 45°, and m∠C = 30°, we know that:

[tex]\(\frac{5\sqrt{2}}{\sin(30°)} = \frac{BC}{\sin(45°)}\)[/tex]

[tex]Knowing \ that\ \(\sin(30 ) = 0.5\) and \(\sin(45) = \frac{\sqrt{2}}{2}\), we can find BC:[/tex]

[tex]BC = \(\frac{5\sqrt{2}}{0.5} \times \frac{\sqrt{2}}{2}\) = 5√2 \times \sqrt{2} = 10 m[/tex]

Now, to find AC, we set up the ratio:

[tex]\(\frac{5\sqrt{2}}{\sin(30°)} = \frac{AC}{\sin(105°)}\)[/tex]

Solving for AC, we get:

[tex]AC = 5\sqrt{2} \times \frac{\sin(105°)}{0.5}[/tex]
 Since \(\sin(105°)\) is not a standard angle, we can use the sine sum identity where [tex]\(\sin(105) = \sin(60 + 45\),[/tex]which gives us:

[tex]AC = 10 \times (\(\frac{\sqrt{3}}{2}\times\frac{\sqrt{2}}{2} + \frac{1}{2}\times\frac{\sqrt{2}}{2}\)) = 10 \times (\(\frac{\sqrt{6} + \sqrt{2}}{4}\))[/tex]

AC ≈ 8.66 m

Answer:

x=2, y=1. (2, 1).

Step-by-step explanation:

x=2y

2x+5y=9

-------------

2(2y)+5y=9

4y+5y=9

9y=9

y=9/9

y=1

x=2(1)=2

Answer:

Step-by-step explanation:

-3(c-1) = 33

c - 1 = 33/ -3

c -1 = -11

c = -11 +1

c = -10

Answer:

-10

Step-by-step explanation:

-3 (c-1 ) = 33

Divide both sides by -3

c-1 = -11

Add 1 to both sides

c = -10

Answer:

730

Step-by-step explanation:

Answer:

350+160+220 = 730

Step-by-step explanation:

There were 730 boxes. After moving 350 boxes out of 730 boxes, there were left 380 boxes. Again after moving 160 boxes out of 380 boxes, there were remained 220 boxes.