Jim and Krutika win some money and share it in the ratio 2:3. Jim gets £10. How much did Krutika get?

Answer: l = 60 ft and w = 30 ft

P = 2(l + w)

180 = 2(l + w)

Let x = width of his yard

Let 2x = length of his yard

[tex]180=2(2x+x)[/tex]

[tex]\frac{180}{2}=\frac{2(2x+x)}{2}[/tex]

[tex]90=3x[/tex]

[tex]\frac{90}{3} =\frac{3x}{3}[/tex]

[tex]x=30ft[/tex]

l = 2x = 30(2) = 60 ft

Check:

180 = 2(l + w)

180 = 2(60 + 30)

180 = 2(90)

180 = 180

LS = RS

Answer:

If x=7 that means that if 7 substitute r which is 7^2 and 7*7=49 and 49/4

=12 1/4

So the remainder is 1

Step-by-step explanation:

To solve this system of equations by addition, our first goal is to cancel

out one of the variables by adding the two equations together.

However, if we add these two equations together right away, nothing

will cancel so we need to set things up so a variable will cancel.

Notice that we have an 2x in our second equation.

If we had a -2x in our first equation, then the x's would cancel out.

In order to create a -2x in the first equation, we simply

multiply both sides of the first equation by -2.

So we have (-2)(x - 2y) = (-4)(-2) which can be rewritten as -2x + 4y = 8.

Now rewrite both equations, as shown below.

Now when we add the equations together, the x terms

will cancel out and we're left with 5y = 15.

Dividing both sides by 5, y = 3.

To solve for x, plug a 3 in for y in either one of our 2 original equations.

So let's go with our second equation.

Plugging a 3 in for y, we get 2x + (3) = 7.

Now subtract 4 from both sides to get 2x = 4.

Dividing both sides by 2, we fid that x = 2.

Since x = 2 and y = 3, our answer is the ordered pair (2, 3).

Answer:

It's 144 square units

Step-by-step explanation:

The pyramid has a square base with 8 sides and a slant height of 5

a=8

l=5

The total are of the square base pyramid is

A= [tex]a^{2}[/tex]+2al

a is side length of square and l is slant height

A= [tex](8)^{2}+2[/tex] x 8 x 5

A=64+80

A=144

Answer:

Hey I know!

1.10 euro

Answer:

397.5 :)

Step-by-step explanation:

Step-by-step explanation:

I would suggest that she studies or do a cost analysis of what it will cost her to transport to the library to request for the book and return it, if it is not expensive as compared to the cost of the book she should travel down to request for it. else she should purchase the book

Or

Fareeda can simply check if the second library has a distant library services so that the book can be either

1. Sent to her home or placement address, or

2.Scans of book chapters and articles be emailed to her.

Answer:

0.73

Step-by-step explanation:

Data obtained from the question include the following:

Length (L) of square = x

Base (b) of triangle = (3x – 2)

Height (h) of triangle = (2x + 4)

Area of square = L²

Area of square = x²

Area of triangle = ½bh

Area of triangle = ½(3x – 2) (2x + 4)

Expand

½ [3x(2x + 4) –2(2x + 4)]

½[6x² + 12x – 4x – 8]

½[6x² + 8x – 8]

3x² + 4x – 4

Area of triangle = 3x² + 4x – 4

Now, to find the value of x which makes the area of the two figures the same, we simply equate both areas as shown below:

Area of triangle = area of square

Area of triangle = 3x² + 4x – 4

Area of square = x²

Area of triangle = area of square

3x² + 4x – 4 = x²

Rearrange

3x² – x² + 4x – 4 = 0

2x² + 4x – 4 = 0

Solving by formula method

a = 2, b = 4, c = –4

x = – b ± √(b² – 4ac) / 2a

x = – 4 ± √(4² – 4×2×–4) / 2×2

x = – 4 ± √(16 + 32) / 4

x = – 4 ± √(48) / 4

x = (– 4 ± 6.93)4

x = (– 4 + 6.93)4 or (– 4 – 6.93)4

x = 0.73 or –2.73

Since the measurement can not be negative, the value of x is 0.73.

Answer: 92

Step-by-step explanation:

Formula : Sum of first n numbers = Average x n

Given: Average score on first 6 tests= 84

A score on all 8 tests = 86

Then, Sum of first 6 numbers = 84 x 6 = 504

Sum of first 8 numbers = 86 x 8 = 688

Sum of two last numbers = (Sum of first 8 numbers) - (Sum of first 6 numbers)

= 688-504

=184

Average of last two numbers = (Sum of two last numbers )÷2

= 184÷2

= 92

Hence,  the average of your last two test scores = 92.

Answer:

Hey there!

Discrete Data is the number of friends you invited to your last birthday party.

Hope this helps :)

Answer:

a) The number of friends you invited to your last party.

Step-by-step explanation:

Let’s take a step back what is discrete, and what continuous?

Discrete

This is the type of data with certain whole numbers not 2.36 only 2 or 3.

Continuous

This is the data being specific like 1.373.

So a)

The is discrete because you can only have like 5 friends not 7.49 friends.

b)

This is continuous because height can be 5.26 feet.

c)

Time is continuous because there can be 4.3739 minutes.

d)

Weight is also continuous it can be 6339.373 pounds.

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:

1/4

1/2

3/4

Step-by-step explanation:

Given:

Types of colors in the spinner

Yellow 1

Red 2

Blue 1

Total:4

Successful outcome of Yellow:1

Successful outcome of Red:2

Successful outcome of Blue:1

Required:

Probability of the

Formula:

Probability= successful outcome ÷ possible outcome

Solution

Probability=1 ÷ 4

Probability= 2÷4

Probability= 3÷4

Hope this helps ;) ❤❤❤

Answer:

Ones: 91

Hundredths: 91.20

Step-by-step explanation:

All numbers that comprises the digits, 91.20, have place value.

The 9 in the digit has a place value of tens, i.e. 9*10 = 90.

The 1 has a place value of one's, i.e. 1*1 = 1

The 2, after the decimal point to the right, has a place value of tenth, i.e. 1*10-¹ = ⅒ = 0.1

While the zero has a place value of hundredth.

Therefore, the digits, in the ones place = 91

In the hundredths place = 91.20

Answer:3.82

Step-by-step explanation: Find 80% of 4.50 (4.50 x 0.8=3.60) then find 6% of 3.6 (0.06 x 3.6= 0.216) add 0.216 + 3.6= 3.816 but in money you have to round so the answer is 3.82

Answer:

1.8

Step-by-step explanation:

$4.50-%20=3.6

3.6- %9=1.8

Answer:

The data that we have is:

f(x) = x + 5

g(x) = x^2 + 1

p(x) = g(x) + f(x) = (x^2 + 1) + (x + 5) = x^2 + x + 6.

q(x) = g(x) - f(x) =  (x^2 + 1) - (x + 5) = x^2 - x - 4

We want to find  p(x)*q(x)

well, we can replace:

p(x)*g(x) = (g(x) + f(x))*(g(x) - f(x))

Now, you can recall the relationship:

a^2 - b^2 = (a + b)*(a - b)

then we have that:

(g(x) + f(x))*(g(x) - f(x)) = g(x)^2 - f(x)^2

now we can replace g(x) and f(x) by the expressions that we know:

g(x)^2 - f(x)^2 = (x^2 + 1)^2 - (x + 5)^2

now we can simplify this:

(x^2 + 1)^2 - (x + 5)^2 = (x^4 + 2*1*x + 1^2) - (x^2 + 2*5*x +5^2)

= x^4 + 2*x + 1 - x^2 - 10x - 25

= x^4 - x^2 - 8*x - 24

p(x)*q(x) = x^4 - x^2 - 8*x - 24

Answer:

x^4+x^2-10x-24

Step-by-step explanation:

Answer: 40 inches

Step-by-step explanation:

The woman weight and the seat will be: 145lb + 5lb = 150lb,

her son weight and the seat will be: 95lb + 5lb = 100lb

her daughter weight and the seat will be: 70lb + 5lb = 75lb

Given that the woman is on the left side of the seesaw, 60 inches from the fulcrum. The moment of the woman will be 150 × 60 = 9000

The daughter and son both get on the right side.

If the son sits 60 inches from the fulcrum, his moment will be:

100 × 60 = 6000

The sum of the moment of the son and daughter must be equal to the moment of their mother.

Let the position of the daughter = X

The moment of the daughter will be:

75 × X = 75X

Equate the moment of the mother to the sum of the moment of her children

9000 = 6000 + 75X

Collect the like terms

75X = 9000 - 6000

75X = 3000

X = 3000/75

X = 40

The position the daughter should sit to balance the seesaw is 40 inches away from seasaw to the right.

Answer: A) 21.25 ≤ x ≤ 22.75

Step-by-step explanation:

Given, Average weight of basketballs = 22 ounces

It is possible for its weight to vary at most 0.75 ounces from this average.

Let x denotes the weight of the basket ball.

Then, the required range  for a basketball's weight:

Average-0.75 ≤ x ≤ Average+0.75

⇒22-0.75 ≤ x ≤ 22+0.75

⇒21.25 ≤ x ≤ 22.75

Hence, the range for a basketball's weight: 21.25 ≤ x ≤ 22.75 .

Correct option: A) 21.25 ≤ x ≤ 22.75

Answer:

Construction II

Step-by-step explanation:

Construct 3 perpendicular bisectors of the triangles sides; where they intersect is the point of concurrency. The distance from the point of concurrency to one of the vertices is the radius.

Answer:

The salary of the governor of state A is $171,575 and the salary of the governor of state B is $117,830.

Step-by-step explanation:

If the governor of state A's salary is "x" and the governor of state B's salary is "y", then:

[tex]x = y + 53,745[/tex]

If the total of their salaries is $289,405, then the sum of x and y should be equal to that number.

[tex]x + y = 289,405\\[/tex]

Applying the first expression on the second allows us to solve for y as shown below.

[tex]y + 53745 + y = 289405\\2y = 289405 - 53745\\2y = 235660\\y = 117830[/tex]

Using this data on the first expression allows us to solve for the first governo's salary.

[tex]x = 117830 + 53745 = 171575[/tex]

The salary of the governor of state A is $171,575 and the salary of the governor of state B is $117,830.

Answer:

.32 or 32%

Step-by-step explanation:

The area of the circle is about 50.27

Given this you can use this to find the area of the triangle and find the precent  of the circle that is shaded:

The area of the triangle is 16

you can divide 16 by 50.27 to see the precntage or propability for the answer

Answer:

-9.6

Step-by-step explanation:

[tex]2\frac{2}{5} =2.40\\-\frac{1}{4} =-0.25[/tex]

If change them into decimals it looks like that.

Then all you have to do is use standard calculator to find the answer.

[tex]\frac{2.40 }{-0.25} =-9.6[/tex]

Answer:9 and 3/8  

Step-by-step explanation:

you have to make 2 and 2/5 into an improper fraction then make the -1/4 into a -4/1 then multiply across to make 48/5 then you have to reduce down to 8 and 8/5. but that cant happen so you reduce again and get 9 and 3/8.

Answer:

1 3/4

Step-by-step explanation:

5/4 + 1/2

Get a common denominator of 4

5/4 * 1/2 *2/2

5/4 + 2/4

7/4

Rewriting as a mixed number

4/4 + 3/4

1 3/4

Answer:

You get 12$ per B and 15$ per A.  Thus, the answer is A) $282

Step-by-step explanation:

4A+4B=108

Divide by 4

A+B=27

Subtract B

A = 27 - B

3A+5B=105

Substitution

3(27-B)+5B = 105

Distribute

81-3B+5B=105

Combine like terms

81+2B=105

Subtract 81

2B=24

Divide by 2

B = 12

A = 15

14(15)+6(12)=x

210+72=x

282=x

Hope it helps <3

Answer:

D

Step-by-step explanation:

Apply rule : [tex]-(-a)=+a[/tex]

Negative times negative is positive.

The expression turns into a sum of fractions.

Answer:  19)  117°                    20) 53°

               21)  229°                   22) 119°

               23) 155°                    24) 323°

Step-by-step explanation:

Use Pythagorean Theorem to find r:     x² + y² = r²

19) x = [tex]-\sqrt{17}[/tex] ,  y = 8,    r = 9

     [tex]\cos \theta=\dfrac{x}{r} \rightarrow \quad \cos \theta =\dfrac{-\sqrt{17}}{9} \rightarrow \quad \theta = cos^{-1}\bigg(\dfrac{-\sqrt{17}}{9}\bigg)\rightarrow \quad \theta = \large\boxed{117^o}[/tex]

20) x = 3,   y = 4,   r = 5

      [tex]\cos \theta=\dfrac{x}{r} \rightarrow \quad \cos \theta =\dfrac{3}{5} \rightarrow \quad \theta = cos^{-1}\bigg(\dfrac{3}{5}\bigg)\rightarrow \quad \theta = \large\boxed{53^o}[/tex]

21) x = [tex]-\sqrt7[/tex],   y = -3,   r = 4

    [tex]\sin \theta=\dfrac{y}{r} \rightarrow \quad \sin \theta =\dfrac{-3}{4} \rightarrow \quad \theta = sin^{-1}\bigg(\dfrac{-3}{4}\bigg)\rightarrow \quad \theta = \large\boxed{229^o}[/tex]    

22) x = [tex]-\sqrt{15}[/tex],   y = 7,   r = 8

     [tex]\tan \theta=\dfrac{y}{x} \rightarrow \quad \tan \theta =\dfrac{7}{-\sqrt{15}} \rightarrow \quad \theta = tan^{-1}\bigg(\dfrac{7}{-\sqrt{15}}\bigg)\rightarrow \quad \theta = \large\boxed{119^o}[/tex]

23) x = -13,   y = 6,   r = [tex]\sqrt{205}[/tex]

     [tex]\tan \theta=\dfrac{y}{x} \rightarrow \quad \tan \theta =\dfrac{6}{-13} \rightarrow \quad \theta = tan^{-1}\bigg(\dfrac{6}{-13}\bigg)\rightarrow \quad \theta = \large\boxed{155^o}[/tex]

24) x = 4,    y = -3,   r = 5

     [tex]\sin \theta=\dfrac{y}{r} \rightarrow \quad \sin \theta =\dfrac{-3}{5} \rightarrow \quad \theta = sin^{-1}\bigg(\dfrac{-3}{5}\bigg)\rightarrow \quad \theta = \large\boxed{323^o}[/tex]

For the point [tex](-\sqrt{17},8)[/tex], [tex]cos\theta=0.4581[/tex]

For the point [tex](3,4)[/tex], [tex]cos\theta=0.6[/tex]

For the point [tex](-\sqrt7,-3)[/tex], [tex]sin\theta=-0.75[/tex]

For the point [tex](-\sqrt{15},7)[/tex], [tex]tan\theta=-1.807[/tex]

For the point [tex](-13,6)[/tex], [tex]tan\theta=-0.4615[/tex]

For the point [tex](4,-3)[/tex], [tex]sin\theta=-0.6[/tex]

For ratios [tex]sin\theta[/tex] and [tex]cos\theta[/tex], we need to calculate the hypotenuse of the right-angled triangle. For the ratio [tex]tan\theta[/tex], we can directly make use of the coordinate points.

For the point [tex](-\sqrt{17},8)[/tex]

[tex]r=\sqrt{17+8^2}=9[/tex]

[tex]cos\theta=\dfrac{x}{r}\\\\=-\dfrac{\sqrt{17}}{9}\approx0.4581[/tex]

For the point [tex](3,4)[/tex]

[tex]r=\sqrt{3^2+4^2}=5[/tex]

[tex]cos\theta=\dfrac{x}{r}\\\\=\dfrac{3}{5}=0.6[/tex]

For the point [tex](-\sqrt7,-3)[/tex]

[tex]r=\sqrt{7+(-3)^2}=4[/tex]

[tex]sin\theta=\dfrac{y}{r}\\=-\dfrac{3}{4}=-0.75[/tex]

For the point [tex](-\sqrt{15},7)[/tex]

[tex]tan\theta=\dfrac{y}{x}\\=-\dfrac{7}{\sqrt{15}}=-1.807[/tex]

For the point [tex](-13,6)[/tex]

[tex]tan\theta=\dfrac{y}{x}\\=-\dfrac{6}{13}=-0.4615[/tex]

For the point [tex](4,-3)[/tex]

[tex]r=\sqrt{4^2+(-3)^2}=5[/tex]

[tex]sin\theta=\dfrac{y}{r}\\=-\dfrac{3}{5}=-0.6[/tex]

Learn more about trigonometry here: https://brainly.com/question/23686339

Answer:

isosceles

Step-by-step explanation:

Answer:

clay sphere gives more clay for less money

Step-by-step explanation:

Volume of cone=1/3πr^2h

=1/3*3.14*(9^2)*12

=1/3*3.14*81*12

=3,052.08/3

=1017.36 inches^3

Volume of a cyclinder=πr^2h

=3.14*(9^2)*12

=3.14*81*12

=3,052.08 inches^3

Volume of a sphere=4/3πr^3

=4/3*3.14*(9^3)

=4/3*3.14*(9^3)

=4/3*3.14*729

=9,156.24 / 3

=3,052.08 inches^3

Clay cone=$12

Clay cyclinder=$30

Clay sphere=$28

Which is the best to buy

Comparing volume

Volume of sphere=3,052.08 inches^3

Volume of cyclinder=3,052.08 inches^3

Volume of cone=1017.36 inches^3

Sphere and cyclinder both have the same volume which is 3 times more than volume of a cone

Clay sphere cost $28 which is cheaper than clay cyclinder at the same volume.

Therefore, clay sphere gives more clay for less money

Answer:

Step-by-step explanation:

7x² - 4x - 3 = 0

Rewrite - 4x as a difference

That's

7x² - 7x + 3x - 3 = 0

Factorize the expression

7x( x - 1) + 3 ( x - 1) = 0

(7x + 3)( x - 1 ) = 0

7x + 3 = 0 x - 1 = 0

7x = - 3 x = 1

x = -3/7

The solutions are

x = - 3/7 or x = 1

Hope this helps you

Answer:

[tex]$\arcsin\left(\frac{129\sqrt{2}}{250}\right)\approx 0.8179$[/tex]

Step-by-step explanation:

[tex]\alpha \text{ and } \beta \text{ in Quadrant I}[/tex]

[tex]$\tan(\alpha)=\frac{1}{7} \text{ and } \sin(\beta)=\frac{1}{\sqrt{10}}=\frac{\sqrt{10} }{10} $[/tex]

Using Pythagorean Identities:

[tex]\boxed{\sin^2(\theta)+\cos^2(\theta)=1} \text{ and } \boxed{1+\tan^2(\theta)=\sec^2(\theta)}[/tex]

[tex]$\left(\frac{\sqrt{10} }{10} \right)^2+\cos^2(\beta)=1 \Longrightarrow \cos(\beta)=\sqrt{1-\frac{10}{100}} =\sqrt{\frac{90}{100}}=\frac{3\sqrt{10}}{10}$[/tex]

[tex]\text{Note: } \cos(\beta) \text{ is positive because the angle is in the first qudrant}[/tex]

[tex]$1+\left(\frac{1 }{7} \right)^2=\frac{1}{\cos^2(\alpha)} \Longrightarrow 1+\frac{1}{49}=\frac{1}{\cos^2(\alpha)} \Longrightarrow \frac{50}{49} =\frac{1}{\cos^2(\alpha)} $[/tex]

[tex]$\Longrightarrow \frac{49}{50}=\cos^2(\alpha) \Longrightarrow \cos(\alpha)=\sqrt{\frac{49}{50} } =\frac{7\sqrt{2}}{10}$[/tex]

[tex]\text{Now let's find }\sin(\alpha)[/tex]

[tex]$\sin^2(\alpha)+\left(\frac{7\sqrt{2} }{10}\right)^2=1 \Longrightarrow \sin^2(\alpha) +\frac{49}{50}=1 \Longrightarrow \sin(\alpha)=\sqrt{1-\frac{49}{50}} = \frac{\sqrt{2}}{10}$[/tex]

The sum Identity is:

[tex]\sin(\alpha + \beta)=\sin(\alpha)\cos(\beta)+\sin(\beta)\cos(\alpha)[/tex]

I will just follow what the question asks.

[tex]\text{Find the value of }\alpha+2\beta[/tex]

[tex]\sin(\alpha + 2\beta)=\sin(\alpha)\cos(2\beta)+\sin(2\beta)\cos(\alpha)[/tex]

[tex]\text{I will first calculate }\cos(2\beta)[/tex]

[tex]$\cos(2\beta)=\frac{1-\tan^2(\beta)}{1+\tan^2(\beta)} =\frac{1-(\frac{1}{7})^2 }{1+(\frac{1}{7})^2}=\frac{24}{25}$[/tex]

[tex]\text{Now }\sin(2\beta)[/tex]

[tex]$\sin(2\beta)=2\sin(\beta)\cos(\beta)=2 \cdot \frac{\sqrt{10} }{10}\cdot \frac{3\sqrt{10} }{10} = \frac{3}{5} $[/tex]

Now we can perform the sum identity:

[tex]\sin(\alpha + 2\beta)=\sin(\alpha)\cos(2\beta)+\sin(2\beta)\cos(\alpha)[/tex]

[tex]$\sin(\alpha + 2\beta)=\frac{\sqrt{2}}{10}\cdot \frac{24}{25} +\frac{3}{5} \cdot \frac{7\sqrt{2} }{10} = \frac{129\sqrt{2}}{250}$[/tex]

But we are not done yet! You want

[tex]\alpha + 2\beta[/tex] and not [tex]\sin(\alpha + 2\beta)[/tex]

You actually want the

[tex]$\arcsin\left(\frac{129\sqrt{2}}{250}\right)\approx 0.8179$[/tex]

Answer:

ok bye guy................

Answer:

i think its option b but im not sure

Answer:  No they are not inverses.

Step-by-step explanation:

If they are inverses,  then the inverse of f(x) will equal g(x).

[tex]y=\dfrac{1}{x+4}-9\\\\\\\text{Swap the x's and y's:}\\x=\dfrac{1}{y+4}-9\\\\\\\text{Solve for y:}\\x+9=\dfrac{1}{y+4}\\\\y+4=\dfrac{1}{x+9}\\\\y=\dfrac{1}{x+9}-4[/tex]

f⁻¹(x) ≠ g(x) so they are not inverses