What is the y-intercept of the line with
a slope of 2 that passes through the
point (1, 2)

The length and width of the rectangle with a perimeter of 378ft are 168ft and 21ft respectively.

The formula used in calculating the perimeter of a rectangle is expressed as;

P = 2( l + w )

Where l is length and w is width.

Given the data in the question;

Let 'x' represent the width of the rectangle.

Plug the given values into perimeter formula and solve for x .

P = 2( l + w )

378 = 2( 8x + x )

378 = 2( 9x )

378 = 18x

18x = 378

x = 378/18

x = 21

Now, we find the length and width of the rectangle.

Width of the rectangle w = x = 21ft

Length of the rectangle l = 8x = 8( 21 ) = 168ft

Therefore, the width of the rectangle is 21ft while its length is 168ft.

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The definite integral which represents the area of the region in the fourth quadrant enclosed by r = 10 - cos is A = 210π - 80/8

Given:

the area of the region in the fourth quadrant enclosed by r = 10 - cos

we know that:

A = (limit a to b)∫ r²/2 dθ

we know that area of first quadrant = area of fourth quadrant (by symmetry)

A = (limit θ=0 to π/2)∫ (1-cosθ)²/2 dθ

= (limit θ=3π/2 to 2π)∫ (1-cosθ)²/2 dθ

A = 1/2(limit 0 to π/2)∫ (100 - 20cosθ + cos²θ)dθ

A = 1/2 (limit 0 to π/2)∫ (100 - 20cosθ + 1/2 + cos2θ/2)dθ

= 1/2 (limit 0 to π/2) ∫ (201/2 - 20cosθ + cos2θ/2)dθ

= 1/2 ( 201/2 θ- 20sinθ + sin2θ/4) limit π/2 to 0

= 1/2 ( 201π/4 - 20 + 0)

= 1/2 ( 210π - 80/4)

Hence we get the required answer.

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Answer: b = 11.62

Step-by-step explanation:

We can use this formula to solve for b:

\(b^{2} =\) \(\sqrt{c^{2}-a^{2} }\)

\(b^{2} =\) \(\sqrt{12^{2}-3^2 }\)

\(b^2= \sqrt{144-9}\)

= 11.61895004

We can round that to 11.62.

Hope this helped!

Answer:

(a)

\(\left[\begin{array}{ccc}110\\4\\20\\2\end{array}\right] x+\left[\begin{array}{ccc}130\\3\\18\\5\end{array}\right] y=\left[\begin{array}{ccc}295\\9\\48\\8\end{array}\right]\)

(b)

\(\left[\begin{array}{ccc}110&130&295\\4&3&9\\20&18&48\\2&5&8\end{array}\right]\)

1.5 servings of cheerios and 1 serving of Quaker 100% natural cereal will give the desired mixture.

Step-by-step explanation:

Given the mixture of cereals below:

\(\left|\begin{array}{c|c|c}&$General Mills &$Quaker \\$Nutrient&$Cherrios &100\% $Natural Cereal\\----&---&---\\$Calories&110&130\\$Protein (g)&4&3\\$Carbhydrate (g)&20&18\\$Fat (g)&2&5\end{array}\right|\)

Suppose a mixture of these two portions of cereals is to be prepared that contain exactly 295 calories, 9 g of protein, 48 g of carbohydrate, and 8 g of fat.

(a)Let x be the number of servings of Cheerios

Let y be the number of servings of Natural Cereal

From the table above, we have

\(110x+130y=295\\4x+3y=9\\20x+18y=48\\2x+5y=8\)

Then a vector equation for this problem is:

\(\left[\begin{array}{ccc}110\\4\\20\\2\end{array}\right] x+\left[\begin{array}{ccc}130\\3\\18\\5\end{array}\right] y=\left[\begin{array}{ccc}295\\9\\48\\8\end{array}\right]\)

(b) Next, we obtain an equivalent matrix equation of the data

\(\left[\begin{array}{ccc}110&130\\4&3\\20&18\\2&5\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] =\left[\begin{array}{ccc}295\\9\\48\\8\end{array}\right]\)

This is of the form AX=B. To solve for X we, therefore have an equivalence matrix:

\(\left[\begin{array}{ccc}110&130&295\\4&3&9\\20&18&48\\2&5&8\end{array}\right]\)

Next, we row reduce the matrix using a calculator to obtain the matrix:

\(\left[\begin{array}{ccc}1&0&1.5\\0&1&1\\0&0&0\\0&0&0\end{array}\right]\)

Therefore:

1x+0=1.5

0x+y=1

x=1.5 and y=1

To get the required mixture, we use 1.5 servings of cheerios and 1 serving of Quaker 100% natural cereal.

Answer:

volume=60cm3, surface area=96cm2

Step-by-step explanation:

volume=1/3×(6×6)×5

=60cm3

surface area= 4(1/2×6×5)+(6×6)

=96cm2

Answer:

It would be D.x = -2/3 or x =2

Answer:

B

Step-by-step explanation:

(3x-2) - 5 = -1

⇒(3x-2)-4=0

⇒3x-6=0

⇒3x=6

⇒x=6/3

⇒x=2

When 'x' is 5, the Algebraic  expression 3x - 4 evaluates to 11.

To find the algebraic expression for "4 less than the product of 3 and some number," let's break it down step by step.

First, let's define the unknown number as 'x.' Since the problem states "the product of 3 and some number," we can express this as 3 * x or simply 3x.

Next, we want to subtract 4 from this product. The phrase "4 less than" indicates subtraction, so we subtract 4 from 3x. This can be represented as 3x - 4.

In summary, the algebraic expression for "4 less than the product of 3 and some number" is 3x - 4, where 'x' represents the unknown number.

To calculate the value of this expression for a specific value of 'x,' you substitute that value into the expression and simplify. For example, if 'x' is 5, you would substitute 5 into the expression:

3(5) - 4

This simplifies to:

15 - 4 = 11

So, when 'x' is 5, the expression 3x - 4 evaluates to 11.

In general, the algebraic expression allows us to represent a mathematical relationship between quantities using symbols and operations. By substituting specific values into the expression, we can calculate the corresponding results.

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Note the complete question:

Algebraic expression for 4 less than the product of 3 and some number

What is the algebraic expression for "4 less than the product of 3 and some number?

Please help me understand the meaning of how to calculate.

Answer: A is the answer

Answer: a

Step-by-step explanation:

edge

Answer:

.125

Step-by-step explanation:

I believe that if the time is uniformly distributed, it is equally likely that it will take him  22     23   24   25   26  27   28   or 29 minutes ....each has a 1/8 th probability = .125

Answer:

$119

Step-by-step explanation:

08:00 - 12:15 = 4hrs 15mins

13:00 - 17:15 = 4hrs 15mins

Total hours worked = 8hrs 30 mins

$14/hr

14 × 8 = 112

30 mins is half of an hour so 14/2 = 7

$7 for 30 mins

112 + 7 = 119

$119

hope this helps ^^

Answer:

angle ced is a right ange

so the m angels debate =135 m angle aeb =35

so the answer is 135+35 =170

180 is a all side sim

=180-170=10 answer

Answer:

∠CED is a right angle.

∠CEA is a right angle.

m∠CEB = m∠BEA

m∠DEB = 135°

Answer:

1/2

Step-by-step explanation:

Answer:

15 units

Step-by-step explanation:

Answer:

its a scale factor of 4

Step-by-step explanation:

Answer:

\(h(x) = \frac{1}{2} x+ 5\)

Step-by-step explanation:

To find the inverse of a function, simply switch the 'x' and 'y' variables. Substitute in 'y' in the place of f(x) for this purpose:

y = 2x - 10

Switch positions:

x = 2y - 10

Add '10' to both sides to begin simplifying:

x + 10 = 2y

Divide both sides by 2:

\(y= \frac{x+10}{2}\)

This can be rewritten as:

\(y = \frac{1}{2} x+ 5\)

Therefore, the inverse of the function is:

\(h(x) = \frac{1}{2} x+ 5\)

Find the sum of a number that is 3.7 units to the left of 2.2.

In order to find this number you consider that certain units to the left means subtraction. Thus, you have:

2.2 - 3.7 = 1.5

Find the sum of a number that is 12 units to the left of -6. The same procedure as before:

-6 - 12 = -18

Hence, the searched numbers are 1.5 and -18

To calculate the interest for 1/2 a month over a period of 8 years, we first need to calculate the total number of months in 8 years:

Total number of months = 8 years x 12 months/year = 96 months

Next, we can calculate the interest for half a month:

Interest = Principal x Rate x Time

Where:

- Principal = $90,900.00

- Rate = 8.25% (annual interest rate)

- Time = 0.5/12 years (half a month, expressed in years)

Rate needs to be converted to a monthly rate, so we divide it by 12:

Rate = 8.25% / 12 = 0.6875% (monthly interest rate)

Time needs to be expressed in years, so we divide it by 12:

Time = 0.5/12 years

Now we can calculate the interest:

Interest = $90,900.00 x 0.006875 x 0.0416667

Interest = $25.08 (rounded to the nearest cent)

Therefore, the interest for 1/2 a month on a principal of $90,900.00 with an annual interest rate of 8.25% over a period of 8 years is $25.08.

Answer:

The interest for 1/2 month is $312.47, and the total interest for 8 years is $30, 032.64

Step-by-step explanation:

Make a plan:

Draw the conclusion:

Hope this helps!

To find the value of N, we need the future value of the retirement fund. If you provide the desired future value, I can calculate the exact value of N.

To find the value of N, we need to calculate the number of monthly deposits Sam made for his retirement fund over 20 years.

Sam deposited $1000 every month for 20 years, which is a total of 20 x 12 = 240 deposits. Each deposit has a compounded interest rate of 5% per year, compounded monthly.

The formula to calculate the future value of a series of monthly deposits is given by:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value of the investment,

P is the monthly deposit amount,

r is the monthly interest rate, and

n is the number of deposits.

In this case, P = $1000, r = 5% / 12 = 0.05 / 12 = 0.00417 (monthly interest rate), and FV is the value of the retirement fund after 20 years.

By rearranging the formula, we can solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Plugging in the values, we get:

n = log((FV * 0.00417) / (1000 * 0.00417 + FV)) / log(1 + 0.00417)

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Hello

To solve this question, we were given a particular function and asked to evalute when the function is defined with a particular variable

For f(-6)

For g(-9)

For f(-9) + g(-9)

for g(-6) - f(-9)

For f(-9).g(-7)

For f(-6) / g(-7)

From the calculations above, i believe you must've seen your mistaken and taken the necessary correction.

Therefore the answers are

1 = 27

2 = 297

3 = 336

4 = 87

5 = 6825

6 = 27/175

We have shown that C is the image of A by dilation with center B and ratio 3.

Now, To show that C is the image of A by dilation with center B and ratio 3, we need to follow these steps:

Firstly, Find the vector AB by subtracting the coordinates of B from the coordinates of A:

AB = A - B = (6 - 3, 4 - 7) = (3, -3)

Multiply the vector AB by the dilation ratio of 3:

3 AB = 3 (3, -3)  = (9, -9)

Add the resulting vector to the coordinates of the center B:

BC = B + 3 AB = (3, 7) + (9, -9)

BC = (12, -2)

Hence, Compare the resulting point BC to the coordinates of C to show that they are the same:

BC = (12, -2) = C

Therefore, we have shown that C is the image of A by dilation with center B and ratio 3.

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Answer:

4082

Step-by-step explanation:

Given

The composite object

Required

The volume

The object is a mix of a cone and a hemisphere

Such that:

Cone

\(r = 10cm\) ---- radius (r = 20/2)

\(h = 19cm\)

Hemisphere

\(r=10cm\)

The volume of the cone is:

\(V_1 = \frac{1}{3}\pi r^2h\)

\(V_1 = \frac{1}{3}\pi * 10^2 * 19\)

\(V_1 = \frac{1900}{3}\pi\)

The volume of the hemisphere is:

\(V_2 = \frac{2}{3}\pi r^3\)

\(V_2 = \frac{2}{3}\pi 10^3\)

\(V_2 = \frac{2000}{3}\pi\)

So, the volume of the object is:

\(V = V_1 + V_2\)

\(V = \frac{1900}{3}\pi + \frac{2000}{3}\pi\)

\(V = \frac{3900}{3}\pi\)

\(V = 1300\pi\)

\(V = 1300 * 3.14\)

\(V = 4082\)

Answer:

15

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

f( - 1) with x < 1 , then

f(- 1) = \(\sqrt{-(-1)}\) = \(\sqrt{1}\) = 1

f(1)  with x ≥ 1 , then

f(1) = x + 1 = 1 + 1 = 2

Thus

f(- 1) + f(1) = 1 + 2 = 3 → c

The right response is 400%. In other words, Johnny moves at four times the pace of Jane.

We must compare the speeds of Johnny and Jane in relation to one another in order to get their ratio. According to the issue, Jane moves at a pace that is 1/4 that of Johnny. In other words, Jane moves at a speed that is one-fourth that of Johnny.

We may compare the speeds as a fraction to figure out the ratio:

Johnny's speed divided by Jane's speed equals 4/1.

This indicates that Johnny is moving at a speed that is four times that of Jane. We can express Johnny's speed as 400% of Jane's speed in percentage terms.

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Answer:

The first error in the bill is +8

because when two opposite signs of number are multiplied so the result is always negative.

so,

2 × -4 = -8

instead of 8 their should be -8.

hope this answer helps you dear...take care!

We are asked to determine the perimeter of the figure. The perimeter of any geometrical figure is equivalent to the sum of all of its sides, therefore, the perimeter "P" is:

Replacing we get:

Solving the operation:

Therefore, the perimeter is 634 in.