Rachel used 2/3 of a string to tie some books together. She used 1/3 of the remaining string for his art project. She had 30cm of the string left. What was the orignal length of string. Express your ans in meter.

Answer:

3, 8, 12, 12, 14, 20, 21, 23, 26, 34

stem         leaf

0               3     8

1                 2     2       4               (you have 12,12,14)

2                0      1       3        6    ( numbers 20,21,23,26)

3                 4                               ( number 34)

Answer:

Slope = -6/7

Step-by-step explanation:

You need to use the formula m = y2 - y1 ÷ x2 - x1

The formula means: slope = the y coordinate of point 2 subtract the y coordinate of point 1, divided by the x coordinate of point 2 subtract the x coordinate of point 1

So,

m = 2 - 5 ÷ 3/2 - (-2)

m = -3 ÷ 7/2

m = -6/7

Hope this helps :)

Answer: 16 units

Step-by-step explanation:

Given that in triangle ABC, m∠C=90,

it means m∠A +∠B= m∠BAC + m∠ABC = 90

m∠ABC = 90 - m∠BAC

Also given that;m∠BAC = 2m∠ABC

So,

m∠BAC = 2(90 - m∠BAC) = 180 - 2m∠BAC

m∠BAC +2m∠BAC = 180

3m∠BAC = 180

m∠BAC=180/3 = 60

m∠ABC = 60/3 = 30

thus,ΔBAC is a 30-60-90 right triangle, in which the ratio of the side lengths is 1:√3:2AC:BC=1:√3, AC=BC/√3BC=24, So,

AC=24/√3=8√3AL bisects angle A =>m∠LAC=30

ΔALC is a 30-60-90 right triangle, in which the ratio of the side lengths is 1:√3:2AC:AL=√3:2AL=2AC/√3=2x8√3/√3=16

Let d equal the final amount it depreciates.

Let m equal the number of months.

Since d is the final amount, we put this at the very end of the equation.

Since it depreciates $25 every month, this number is going to be subtracted from the total price of the tablet ($650).

The final equation comes out too: d = 650 - 25m

Best of Luck!

Answer:

1. a=9     2. f=1    3. b=6

Step-by-step explanation:

1.) 4a-1=3a+8

subtract 3a from both sides

a-1+8

add 1 to both sides

a=9

2.) 1+f+3+f=f+5

combine like terms that are on the same side

2f+4=f+5

subtract f from both sides

f+4=5

subtract 4 from both sides

f=1

3.) construct a equation

b+5=11

subtract 5 from both sides

b=6

(i) Note that it is given to you that 3a + 2b = 9

You are trying to find the value of 9a + 6b. Find what is multiplied to both the variable a & b. Divide:

(9a + 6b)/(3a + 2b) = 3

Next, multiply 3 to the 9 on the other side of the equation:

3 x 9 = 27

27 is the value of 9a + 6b.

(ii) Note that it is given to you that 8x + 6y = 60

You are trying to find the value of 4x + 3y. Find what is multiplied to both the variable x & y. Divide:

(8x + 6y)/(4x + 3y) = 2

Next, divide 2 from the 60 on the other side of the equation:

60/2 = 30

30 is the value of 4x + 3y.

~

Answer:

(i) 27, (ii) 30

Step-by-step explanation:

i. since 9a + 6b is 3 times 3a + 2b then the and is 3 times 9 = 27

ii. since 4x + 3y is half of 8x + 6y then 60 /2 = 30

Answer:

[tex]\huge\boxed{\cot\theta=\dfrac{1}{xy}}[/tex]

Step-by-step explanation:

[tex]\bold{METHOD\ 1}[/tex]

[tex]\sin\theta=x\\\\\sec\theta=y\\\\\cot\theta=?\\\\\text{We know:}\\\\\sec x=\dfrac{1}{\cos x};\ \cot x=\dfrac{\cos x}{\sin x}\\\\\sec\theta=y\to\dfrac{1}{\cos \theta}=y\to\dfrac{\cos\theta}{1}=\dfrac{1}{y}\to\cos\theta=\dfrac{1}{y}\\\\\cot \theta=\dfrac{\frac{1}{y}}{x}=\dfrac{1}{xy}[/tex]

[tex]\bold{METHOD\ 2}[/tex]

[tex]\text{We know}\\\\\tan x=\dfrac{\sin x}{\cos x}\\\\\cot x=\dfrac{\cos x}{\sin x}=\dfrac{1}{\tan x}\\\\\sec x=\dfrac{1}{\cos x}\\\\\text{therefore}\\\\(sin x)(\sec x)=(\sin x)\left(\dfrac{1}{\cos x}\right)=\dfrac{\sin x}{\cos x}=\tan x\\\\\dfrac{1}{(\sin x)(\sec x)}=\dfrac{1}{\tan x}=\cot x[/tex]

[tex]\\\sin \theta=x;\ \sec\theta=y\\\\\text{substitute}\\\\\cot\theta=\dfrac{1}{xy}[/tex]

Answer:

16 and 40

Step-by-step explanation:

Hello,

We need to find the factors of 80

1, 2, 4, 5, 8, 10, 16, 20, 40 and 80.

Which can be 2, 2, 2, 2, and 5 (these numbers would go into all the factor completely without any reminder.)

This leaves us with two numbers 2 and 5

If the highest common factor (H.C.F) of both numbers is 8

And the lowest common multiple (L.C.M) = 80

Multiply the numbers by the highest common factor (H.C.F)

2 × 8 = 16

5 × 8 = 40

The numbers are 16 and 40

Answer:

A is correct

Step-by-step explanation:

What we need to do here is to multiply all the roots together

The roots are;

3, √5 and -√5

Let’s have them in form of a sum

if x = 3, then the root is x-3

If x = √5, then the root is x-√5

If x = -√5, then the root is x+ √5

Now we need to multiply all these together to arrive at the original polynomial

Let’s start by using the roots

(x-√5)(x+ √5)

we can use the difference of 2 squares here and we arrive at (x^2 -5)

So finally, the polynomial would be;

(x^2-5)(x-3)

= x(x^2-5) -3(x^2-5)

= x^3-5x-3x^2+15

By rearranging, we have;

x^3-3x^2-5x+15

Answer:

The common difference = 2.

Step-by-step explanation:

An AP can be written as  a1,  a1 + d,  a1 + 2d,  a1 + 3d,  a1 + 4d,  a1 + 5d, a1 + 6d , a1 + 7d.    

 where a1 = first term and d is the common difference.

Here first term = a1 = 8

3rd term = a1 + 2d = 8 + 2d

5th term = a1 + 4d = 8 + 4d

8th term = 8 + 7d

First 3 terms of a GP are  a , ar and ar^2

So from the given information:

a = 8 + 2d

ar = 8 + 4d

ar^2= 8 + 7d

Dividing the second equation by the first  we have

r = (8 + 4d)/(8 + 2d)

Dividing the third by the second:

r = (8 + 7d) / (8 + 4d)

Therefore, eliminating r we have:

(8 + 4d)/(8 + 2d)  =   (8 + 7d)/(8 + 4d)

(8 + 4d)^2 = (8 + 2d)(8 + 7d)

64 + 64d + 16d^2 =  64 + 72d^ + 14d^2

2d^2 - 8d  = 0

2d(d^2 - 4) = 0

2d = 0 or d^2 = 4, so

d =  0, 2.

The common difference can't be zero so it must be 2.

Answer:

Hey there!

Angles in a quadrilateral add to 360 degrees, so we have 56+78+90+x=360

Solving, we see that the missing angle, x, is 136 degrees.

Hope this helps :)

Answer:

Hey.... Ans is 154°

The mate who ans before me HAVE TO FIND x TOO

Step-by-step explanation:

For example take a quadrilateral ABCD (refer to the pic)

Then solution is...

In quadrilateral ABCD

            Sum of all sides of a quadrilateral= 360°

           =angle A + angle B+ angle C+ angle D=

Given,

          Angle A= 56° + angle B=78° + angle C=90° + angle D=x

        =56° + 78° + 90° + x.            (add all the numbers)

         x+226=360°                           (56+78+90=226)

         x=360° - 226°

         x=154°

Therefore the largest angle = x = 154°

Hope it helped u!!

Answer:

The largest integer that belongs to the interval (-∞, 31] is 31

Step-by-step explanation:

The given interval is (-∞, 31], from which the round bracket indicates that the number next to the bracket is not included in the inequality while the square [] (closed) bracket indicates that the number next to the bracket is included in the inequality

Therefore, 31 is inclusive in the inequality while -∞ is excluded.

The find the largest integer that belongs to the interval (-∞, 31] the numbers are arranged on the number line as follows

The numbers presented in number line form -∞, .....-1, 0, 1, 2,..., 31

Giving 31 as the largest integer in the inequality

Answer:

(1.4, 2.5)

Step-by-step explanation:

[tex]y = x + 1[/tex] ... equ 1

[tex]y =3x - 2[/tex] ... equ 2

subtract equ 1 from 2, we'll have

[tex]0 = 2x - 3[/tex]

[tex]2x = 3[/tex]

[tex]x= 3/2 = 1.5[/tex]

substitute the value of [tex]x[/tex] in equ 1, we'll have

[tex]y = 1.5 +1[/tex]

[tex]y = 2.5[/tex]

therefore, solution to the system of the equation is (1.5, 2.5)

the closest in your option is (1.4, 2.5)

Answer:

The Answer Is C The fist poster is the proper representation, because find the areas compare the paintings to the first poster it is 360 to 3240 which shows the poster is 9x bigger but compared to the second one it is out of proportion for the painting and first poster

Answer: A) 2.95 units

Step-by-step explanation:

The diameter of a circle is twice the radius.  Thus, simply do 5.9/2 to get that the radius is 2.95 units long.

Hope it helps <3

Answer:

your answer would be A-2.95

5.9/2=2.95

Step-by-step explanation:

Answer:

1. Cash flow statements; the investing section

Step-by-step explanation:

The cash flow statements is a useful document that shows where the company receives funds and uses it. Thus, it shows both incoming and outgoing cash flow.

The investment section of the cash flow statement is where all the amount of cash paid for acquisitions of property and equipment is imputed. Usually the transactions are written as capital expenditure.

Answer: S = 8.9 or just 9

Step-by-step explanation:

Answer:

Hamish's earning = $20

Harry's earning = $26

Step-by-step explanation:

Given the following :

Let Harry's earning per hour = x

Let Hamish earning per hour = y

Harry earns a dollar more than more than 5/4 the amount hamish earns per hour;

Therefore,

x = 5/4y + 1

x - 5/4y = 1 - - - - (1)

the amount Harry earns per hour is $2 less than 7/5 the amount Hamish earns per hour

x = 7/5y - 2 - - - - (2)

Substituting (2) into (1)

7/5y - 2 - 5/4y = 1

7/5y - 5/4y = 1 + 2

7/5y - 5/4y = 3

Taking the L. C. M

(28y - 25y) / 20 = 3

28y - 25y = 60

3y = 60

y = 20

Substitute y = 20 into (1)

x - 5/4(20) = 1

x - 100/4 = 1

x - 25 = 1

x = 1 + 25

x = 26

y = Hamish's earning = $20

x = Harry's earning = $26

Answer:

Option A is the correct option.

Step-by-step explanation:

Let the points be A and B

A ( 2 , 2 ) ------> ( x1 , y1 )

B ( 3 , 5 ) -------> ( x2 , y2)

Now, let's find the mid-point :

Midpoint = [tex] (\frac{x1 + x2}{2} \:, \frac{y1 + y2}{2} )[/tex]

plug the values

[tex] = ( \frac{2 + 3}{2} \: , \frac{2 + 5}{2} )[/tex]

Calculate the sum

[tex] = \: ( \frac{5}{2} \:, \frac{7}{2} )[/tex]

Hope this helps..

Best regards!!

Answer:

x=-2 and y=-1

Step-by-step explanation:

If x = -2 then:

y = -(-2)-3

y = 2-3

so y = -1

I hope this helps! And plz mark me brainliest!!!

Answer:

(-2,-1)

Step-by-step explanation:

Well if x is -2 we can plug it in to find y,

y = -(-2) - 3

y = 2 - 3

y = -1

(-2, -1)

Thus,

the solution is (-2,-1)

Hope this helps :)

Answer:

Megan hired the canoe for 2 hours

Step-by-step explanation:

Given:

Cost(h) = 6h+15 = 27

Solution

6h+15 = 27

6h = 27-15 = 12

h = 2

The correct answer is C) The initial population at the time of the estimation

Explanation:

A mathematical function represents the relationship between two variables by showing how one increases or decreases as the other changes. In the case presented, the variables are the time in years represented by x and the population represented by f (x). In this context, the value 160.000 in column f(x) represents the population on the year 0, this means the current population or initial population when the function or estimation is created. On the other hand, other values represent the population in the future, for example, the value 173189 represents the population in 4 years.

Answer:

yes the 3ed answer in correct on ENG 2022

Answer: -1

Step-by-step explanation:

[tex]5t-3=3t-5[/tex]

Add 3 to both sides.

[tex]5t=3t-2[/tex]

Subtract 3t from both sides.

[tex]2t=-2[/tex]

[tex]t=-1[/tex]

Hope this helps!

Answer: t=-1

Step-by-step explanation:

1) add 3 to both sides

2) subtract 3t from both sides

3) Divide both sides by 2

Answer:   y ≤ x² + 8x + 7  

Step-by-step explanation:

x ≤ -7     --> x + 7 ≤ 0

x ≥ -1      --> x + 1 ≥ 0

        y = (x + 7)(x + 1)

        y = x² + 8x + 7

        The quadratic is positive so it is U-shaped

        x ≤ -7    and    x ≥ -1    

       means the outside of the U-shaped parabola is shaded

        so we need to use the ≤ symbol

Note: if the inequality symbols were reversed, the shading would be inside the U-shaped parabola so we would use the ≥ symbol.

Answer:

74°

Step-by-step explanation:

A rhombus is a quadrilateral that has its opposite sides to be parallel to be each other. This means that the two interior opposite angles are equal to each other. Since the sum of the angles of a quadrilateral is 360°.

According to the triangle, since one of the acute angle is 32°, then the acute angle opposite to this angle will also be 32°.

The remaining angle of the rhombus will be calculated as thus;

= 360° - (32°+32°)

= 360° - 64°

= 296°

This means the other two opposite angles will have a sum total of 296°. Individual obtuse angle will be 296°/2 i.e 148°

This means that each obtuse angles of the rhombus will be 148°.

To get the unknown angle m°, we can see that the diagonal cuts the two obtuse angles equally, hence one of the obtuse angles will also be divided equally to get the unknown angle m°.

m° = 148°/2

m° = 74°

Hence the angle measure if m(1) is 74°

Answer:

10x1.4^6

Step-by-step explanation:

Answer:

m(m-3)=108

Step-by-step explanation:

Complete question below:

Two positive integers are 3 units apart on a number line. Their product is 108.

Which equation can be used to solve for m, the greater integer?

m(m – 3) = 108

m(m + 3) = 108

(m + 3)(m – 3) = 108

(m – 12)(m – 9) = 108

Solution

On the number line,

Let

m= larger integer

The integers are 3 numbers apart on the number line, so

m-3=smaller integer

The product (×) of the larger and smaller integers=108

(m)*(m-3)=108

m(m-3)=108

Therefore, the equation that can be used to solve for m, the larger integer is:

 m(m – 3) = 108 

Answer:

its a

Step-by-step explanation:

XD

Answer:

i) Estimate the value of the population proportion = 0.8

ii) 95% confidence interval for the population proportion

(0.7214 , 0.8784)

iii)    Lower bound = 0.7214

     upper bound = 0.8784

Step-by-step explanation:

Step(i):-

Given sample size 'n' = 100

Given data  he surveys 100 customers and finds that 80 paid at the pump

sample proportion

                     [tex]p = \frac{x}{n} = \frac{80}{100} = 0.8[/tex]

Step(ii):-

95% confidence interval for the population proportion is determined by

[tex](p^{-} - Z_{\alpha } \sqrt{\frac{p(1-p)}{n} } , p^{-} + Z_{\alpha } \sqrt{\frac{p(1-p)}{n} })[/tex]

Level of significance  

∝ =0.05

Z₀.₀₅ = 1.96

[tex](0.8 - 1.96 \sqrt{\frac{0.8 X 0.2)}{100} } , 0.8 + 1.96 \sqrt{\frac{0.8 X 0.2}{100} })[/tex]

On calculation , we get

(0.8 - 0.0784 , 0.8 + 0.0784)

(0.7214 , 0.8784)

Conclusion:-

95% confidence interval for the population proportion

(0.7214 , 0.8784)

Answer:

Step-by-step explanation:

( x² + 3 ) ( x³ - x² + 4 )

Multiply the second parentheses by each term from the first parentheses

x² ( x³ - x² + 4 ) + 3 ( x³ - x² + 4 )

Distribute x through the parentheses

x⁵ - x⁴ + 4x² + 3 ( x³ - x² + 4 )

Distribute 3 through the parentheses

x⁵ - x⁴ + 4x² + 3x³ - 3x² + 12

Collect like terms

x⁵ - x⁴ + x² + 3x³ + 12

Use the commutative property to reorder the terms

x⁵ - x⁴ + 3x³ + x² + 12

Hope this helps..

Best regards!!

Answer:

x^5-x^4+3x^3+x^2+12

Step-by-step explanation:

Mulitply each term:

x^5-x^4+4x^2+3x^3-3x^2+12

Now simplify.

x^5-x^4+3x^3+x^2+12

I hope this helps....

Please mark me brainliest!!

Answer:

Distance between balloon and a is = 383.67 m

Step-by-step explanation:

The given situation can be represented as the given diagram as attached in the answer area.

cd = 384 m

cb = 200 m

[tex]\angle adb = 33^\circ[/tex]

To find:

Distance between balloon and a i.e. side ad = ?

Solution:

First of all, let us consider the right angled [tex]\triangle bcd[/tex].

We know the trigonometric identity that:

[tex]tan\theta = \dfrac{Perpendicular}{Base}[/tex]

[tex]tan\angle cbd =\dfrac{cd}{cb}\\\Rightarrowtan\angle cbd =\dfrac{384}{200}\\\Rightarrowtan\angle cbd =1.92\\\Rightarrow \angle cbd = tan^{-1}(1.92) = 62.49^\circ[/tex]

Now, using the external angle property for the external [tex]\angle cbd[/tex] for the [tex]\triangle abd[/tex]:

(External angle is equal to the sum of two opposite angles of the triangle.)

[tex]\angle cbd = \angle adb+\angle a[/tex]

[tex]\Rightarow \angle a =62.49-33 =29.49^\circ[/tex]

Now, let us consider the right angled [tex]\triangle acd[/tex].

We have the value of [tex]\angle a[/tex] and perpendicular dc.

We have to find the hypotenuse ad.

Let us use the sine identity:

[tex]sin\theta =\dfrac{Perpendicular}{Hypotenuse}\\\Rightarrow sin\angle a =\dfrac{cd}{ad}\\\Rightarrow sin(29.49^\circ) =\dfrac{384}{ad}\\\Rightarrow ad = \dfrac{384}{0.49}\\\Rightarrow \bold{ad = 783.67\ m}[/tex]

So, the answer is:

Distance between balloon and [tex]\bold{a}[/tex] is = 383.67 m