what is 3/8 of 1/4??

Answer:

  (g, f) = (-1, 2)

Step-by-step explanation:

The equation can be put into standard form:

  (x^2 +2gx) +(y^2 +2fy) = 15

  (x^2 +2gx +g^2) +(y^2 +2fy +f^2) = 15 +g^2 +f^2

  (x +g)^2 +(y +f)^2 = 15 +g^2 +f^2 . . . . equation in standard form

The point (3, 2) is on the circle, so one of the equations we have is ...

  (3+g)^2 +(2 +f)^2 = 15 +g^2 +f^2

  9 +6g +g^2 +4 +4f +f^2 = 15 +g^2 +f^2

  6g +4f = 2 . . . . . . . subtract g^2 +f^2 +13

  3g +2f = 1 . . . . . . . divide by 2

__

A line through the center of the circle is perpendicular to the tangent at the point of tangency. That line will have a slope that is the negative reciprocal of the tangent's slope: m = -1/(-1/2) = 2. Then in point-slope form the equation of the line through the center is ...

  y -2 = 2(x -3)

  2x -y = 4 . . . . rearrange to standard form

The point at the center of the circle, (-g, -f), satisfies this equation, so we have another relation for f and g:

  2(-g) -(-f) = 4

  2g -f = -4 . . . . . . multiply by -1

Adding twice this equation to the one above, we have ...

  2(2g -f) +(3g +2f) = 2(-4) +(1)

  7g = -7 . . . . . . . . . simplify

  g = -1 . . . . . . . . . . divide by 7

  f = 2g +4 = 2(-1) +4 = 2 . . . find the corresponding value of f

The values of f and g are: f = 2 and g = -1.

To determine when the total cost of each health club will be the same, we can set up an equation and solve for the number of months.

Let's assume the number of months is represented by 'x'.

For Club A, the total cost is given by:

Total cost of Club A = $13 (one-time fee) + $28x (monthly fee)

For Club B, the total cost is given by:

Total cost of Club B = $19 (one-time fee) + $27x (monthly fee)

To find the number of months when the total cost is the same, we set the two equations equal to each other:

$13 + $28x = $19 + $27x

Simplifying the equation, we get:

$28x - $27x = $19 - $13

$x = 6

Therefore, after 6 months, the total cost of each health club will be the same.

To find the total cost for each club after 6 months, we substitute the value of 'x' back into the equations:

Total cost of Club A after 6 months = $13 + $28(6) = $13 + $168 = $181

Total cost of Club B after 6 months = $19 + $27(6) = $19 + $162 = $181

So, the total cost for both Club A and Club B will be $181 after 6 months.

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The solution to the given inequality is x < 10c

Inequality are expression that are not separated by an equal sign. Given the inequality expression

x/2<5c

We are to determine the value of x from the inequality as shown;

Given

X/2<5c

Multiply both sides buy 2 to have:

X/2(2)<5c(2)

x < 5(2c)
x < 10c

Hence the solution to the given inequality is x < 10c

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Approximately 95% of housing prices are between a low price of $133,000 and a high price of $161,000.

These approximate percentages are defined by the Empirical Rule, for a normally distributed variable.

Hence the prices within two standard deviations of the mean are given as follows:

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Answer:

  (c)  y = 3^x

Step-by-step explanation:

A function is described as exponential if the independent variable is found in the exponent.

  y = x^(1/2) . . . a square root function, not exponential

  y = 2x^3 . . . . a cubic (polynomial) function, not exponential

  y = 3^x . . . . . an exponential function

Answer:

P = 126; A = 927

Step-by-step explanation:

Enlarging by a scale factor means multiplying each number by the given. 6 x 4.5 = 27; 8 x 4.5 = 36. 2(27) + 2(36) = 126; 27 x 36 = 927.

Answer:

Hey there!

Original Width: 6

New Width: 27

Original Length: 8

New Length: 36

Perimeter: 36+36+27+27, or 126

Area: 36(27), or 972.

Hope this helps :)

Answer:

Step-by-step explanation:

hello :

the arc length formula is : s = 2πr(θ/360°)

given : s = 4m , r = 13m

2(3.14)(13)(θ/360°)=4 solve for : θ

θ =(4)(360°) /2(3.14)(13)

θ = 1440/81.64

θ =17.7°

Answer:

4/13 rad

Step-by-step explanation:

correct

The method you would use to prove the two triangles are congruent include the following: B. ASA.

In Mathematics and Geometry, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Additionally, the lengths of corresponding sides are proportional to the  lengths of corresponding altitudes when two (2) triangles are similar.

In Mathematics and Geometry, ASA is an abbreviation for Angle-Side- Angle and it states that when two (2) angles and their included side in two (2) triangles are congruent, then the triangles are said to be congruent.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

you did not provide enough information to answer the question

Answer:

\(0.04 = 4 \div 100 \)

Answer:

12

Step-by-step explanation:

The figure is a right triangle with hypotenuse = QS

The  base from the graph = 4 units
(or you can just subtract the x-coordinates 2 - (-2) = 4)

The height from the graph is 3 units
(Or you can subtract the y-coordinates: 1 - (-2) = 3)

Since this is a right triangle the square of the hypotenuse = sum of squares of the other two sides

QS² = 3² + 4² = 9 + 16 = 25

QS, the hypotenuse = √25 = 5

The perimeter = sum of the sides = 3 + 4 + 5 = 12 units

The linear equation is y = $25 + $10*w, and its graph is on the image at the end.

Here we know that he started with $25 He adds $10 to the cookie jar each week. Then we can model this with a linear equation:

y = $25 + $10*w

Where w is the number of weeks.

Now we want to graph this, to do so, we just need to find two points on the line.

if w = 0

y = $25 + $10*0 = $25

if w = 6

y = $25 + $10*6 = $85

So we need to graph the points (0, 25) and (6, 85) and connect them witha  line.

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Step-by-step explanation:

x²+12x=40

(x+6)²-6²-40=0

(x+6)²-76 = 0

The relationship between segment AC and segment A double prime C double prime is AC = A''C'' /2.

The ratio by which the new image is bigger or smaller than the original image is the scale factor.

It is given that

Triangle A″B″C″ is formed using the translation (x + 0, y + 2)

and the dilation by a scale factor of 2 from the origin.

coordinate plane with triangle ABC at A (- 3,  3), B (1, - 3), and C (- 3, -3).

segment AC is equal to A''C'' over 2

Scale factor = 2

The coordinates are

A (- 3,  3), B (1, - 3), and c (- 3, -3) is translated using  (x + 2, y + 0),

new coordinates

A'(- 1,  3), B'(3, - 3), and C'(- 1, -3).

The dilation by a scale factor of from the origin

A″ (-2, 6), B″ (6, -6) and C″(-2, -6)

By the distance formula

AB = \(\rm \sqrt {52}\)

A''B'' = \(\rm \sqrt{ 8^2 + 12^2}\\\) = 2 \(\rm \sqrt {52}\)

Therefore

AB = A''B'' /2

Similarly AC = A''C'' /2

The relationship between segment AC and segment A double prime C double prime is AC = A''C'' /2.

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Answer:

z(max) = 650 $

x₁ = 10 units

x₂ = 15 units

Step-by-step explanation:

That is a linear programming problem, we will use a simplex method to solve it

Formulation:

Let´s call  x₁  number of chairs   and x₂ number of tables then :

Item              (in hours)     cutting       assembly      finishing        Profit ($)

Chairs (x₁)                              1                   2                     1                      20

Tables (x₂)                              2                   1                      1                      30

Availability                           40                 42                   25

Objective Function

z  =  20*x₁   +  30x₂   ( to maximize) subject to:

x₁  +  2x₂   ≤  40

2x₁  + x₂    ≤  42

x₁ + x₂     ≤    25

x₁  ,   x₂  >= 0

Using excel or any other software we find:

z(max) = 650

x₁ = 10

x₂ = 15

The chairs and tables manufactured by the factory is an illustration of linear programming, where the maximum revenue is 674

Let x represent chairs, and y represent tables

So, the given parameters are:

Cutting:

So, the constraint is:

\(\mathbf{x + 2y \le 40}\)

Assembly:

So, the constraint is:

\(\mathbf{2x + y \le 42}\)

Finishing:

So, the constraint is:

\(\mathbf{x + y \le 25}\)

The unit profit on the items are:

So, the objective function to maximize is:

\(\mathbf{Max\ z = 20x + 30y}\)

And the constraints are:

\(\mathbf{x + 2y \le 40}\)

\(\mathbf{2x + y \le 42}\)

\(\mathbf{x + y \le 25}\)

\(\mathbf{x,y \ge 0}\)

Using graphical method (see attachment for graph), we have the following feasible points:

\(\mathbf{(x,y) = \{(10,15),\ (17,8),\ (14.67, 12.67)\}}\)

Calculate the objective function using the feasible points.

\(\mathbf{z = 20 \times 10 + 30 \times 15}\)

\(\mathbf{z = 650}\)

\(\mathbf{z = 20 \times 17 + 30 \times 8}\)

\(\mathbf{z = 580}\)

\(\mathbf{z = 20 \times 14.67+ 30 \times 12.67}\)

\(\mathbf{z = 673.5}\)

Approximate

\(\mathbf{z = 674}\)

Hence, the maximum revenue is 674

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The total distance of the obstacle course can be calculated by finding the distance between each pair of consecutive points and adding them up. The distance between two points (x1, y1) and (x2, y2) can be calculated using the formula: distance = sqrt((x2 - x1)^2 + (y2 - y1)^2).

Using this formula, we can calculate the distances between each pair of consecutive points as follows:

Start to Tire Race: distance = sqrt((-40 - (-40))^2 + (-30 - (-10))^2) = 20 yards

Tire Race to Rope Climb: distance = sqrt((40 - (-40))^2 + (-30 - (-30))^2) = 80 yards

Rope Climb to Monkey Bars: distance = sqrt((40 - 40)^2 + (20 - (-30))^2) = 50 yards

Monkey Bars to Finish: distance = sqrt((10 - 40)^2 + (20 - 20)^2) = 30 yards

Adding up all these distances, we get a total distance of 20 + 80 + 50 + 30 = 180 yards for the obstacle course.

Answer:

D

Step-by-step explanation:

If the triangles are congruent, that means the angles are congruent also. If the angles are congruent so are the sides and the area

Answer:

D

Step-by-step explanation:

they are the same triangle, they are just rotated differently

The maximum value of f(x) = x^a(5 − x)^b on the interval 0 ≤ x ≤ 5 is  0 ≤ x ≤ 5 is 5^b.

Generally, To find the maximum value of a function on a given interval, it is generally helpful to find the critical points (points, where the derivative is equal to zero or the function, is undefined) and the endpoints of the interval, and then evaluate the function at these points to find the maximum value.

The d/dx f(x) is given by:

f'(x) = ax^(a-1)(5-x)^b - bx^a(5-x)^(b-1)

Setting this equal to zero and solving for x, we find that the critical points are x = 0, x = 5, and x = (5b)/(a+b).

We can then evaluate the function at these points to find the maximum value. At x = 0, f(x) = 0^a*(5-0)^b = 5^b.

At x = 5, f(x) = 5^a*(5-5)^b = 0.

At x = (5b)/(a+b),

f(x) = [(5b)/(a+b)]^a*(5-[(5b)/(a+b)])^b.

Since a and b are positive, the maximum value must occur at either x = 0 or

x = (5b)/(a+b).

To determine which of these points gives the larger value of f(x), we can compare the values of

5^b and [(5b)/(a+b)]^a*(5-[(5b)/(a+b)])^b.

The expression [(5b)/(a+b)]^a*(5-[(5b)/(a+b)])^b is equal to [(5b)/(a+b)]^a*[(a+b-5b)/(a+b)]^b.

Since a and b are positive, [(5b)/(a+b)]^a and [(a+b-5b)/(a+b)]^b are both greater than or equal to 1, so the expression [(5b)/(a+b)]^a*[(a+b-5b)/(a+b)]^b is greater than or equal to 1.

Therefore, the maximum value of f(x) is 5^b, which occurs at x = 0.

Thus, the maximum value of f(x) = x^a(5 − x)^b on the interval 0 ≤ x ≤ 5 is 5^b.

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Answer:

0.16 I think............

Answer:

0.16666666666

You would expect to pay $90 each month for electricity based on an average usage of 120 KWHs per month.

To calculate the monthly cost of electricity, you can multiply the average number of kilowatt-hours (KWH) used per month by the cost per KWH.

Given:

Cost per KWH: $0.75

Average monthly usage: 120 KWHs

To find the monthly cost, you can multiply the cost per KWH by the average monthly usage:

Monthly Cost = Cost per KWH * Average monthly usage

Plugging in the values, we have:

Monthly Cost = $0.75/KWH * 120 KWHs

Calculating the result:

Monthly Cost = $90

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The expression that could be used to calculate the amount Trina was charged in interest for the billing cycle is  (APR / 365) x 30 days x adjusted balance.

The adjusted balance method is one of the methods for computing the finance charge (interest and other fees) for credit cards.

The adjusted balance is the ending balance determined after adjusting the opening balance with purchases and payments.

Credit card interest method = adjusted balance method

Beginning balance = $780

Purchase = $170

Payment = $210

Adjusted balance, AB = $740 ($780 + $170 - $210)

APR = 17% = 0.17 (17/100)

The interest charged = (APR / 365) x 30 days x adjusted balance

= $10.34 [(0.17/365) x 30 x $740]

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1. We know that 1 feet = 12 inches

let x be a number of inches, which when added to 18 inches will give 7 feet

18 inches + x inches = 7 feet

18 inches + x  inches = 84 inches                       [1 feet = 12 inches]

x inches = 84 inches - 18 inches

x inches = 66 inches

2. We know that 1 mile = 1760 yards

let x be the number of yards, when added to 2000 yards will be equal to 2 miles

2000 yards + x yards = 2 miles

2000 yards + x yards = 3520 yards

x yards = 1520 yards

3. We know that 1 feet = 12 inches

Number of feet = Given number of inches / 12

Number of feet = 108 / 12

Number of feet = 9 ft.

4. We know that 1 mile = 5280 feet

let x be the number of feet, when added to 8800 feet. will be equal to 8 miles

8800 feet + x feet = 8 miles

8800 feet + x feet = 42240 feet             [1 mile = 5280 feet]

x feet = 42240 - 8800

x feet = 33440 ft.

5. We know that 12 inches = 1 feet

let x be the number of inches, when added to 37 inches, will be equal to 5 feet

37 inches + x inches = 5 feet

37 inches + x inches = 60 inches         [12 inches = 1 feet]

x inches = 23 inches

6. We know that 1 yard = 3 feet

So, (number of yards)*3 = (number of feet)

Number of yards = number of feet / 3

Number of yards = 73 / 3 = 24.33 yards

7. We know that 1 yard = 3 feet

let x be the number of feet added to 15 feet to make 9 yards

15 feet + x feet  = 9 yards

15 feet + x feet = 27 feet       [1 yard = 3 feet]

x feet = 12 ft

8. We know that 1 mile = 1760 yards

let x be the number of yards remaining to reach 4 miles

3000 yards + x yards = 4 miles

3000 yards + x yards = 7040

x yards = 4040 yards

9. We know that 1 yard = 3 feet

So, number of yards * 3  = number of feet

replacing the values:

number of yards*3 = 114

number of yards = 114/3

number of yards = 38 yards

10. We know that 1 mile = 5280 feet

let x be the number of feet that must be added to 9000 feet to make 3 miles

x feet + 9000 feet = 3 miles

x feet + 9000 feet = 15840 feet

x ft = 6840 ft

11. We know that 12 inches = 1 feet

let x be the number of inches that must be added to 46 inches to get a length of 9 feet

46 inches + x inches = 9 feet

46 inches  + x inches = 108 inches

x inches = 108 - 46 inches

x inches = 62 inches

12. We know that 1 mile = 1760 yards

let x be the number of yards that must be added to 3500 yards to make 2 miles

3500 yards + x yards = 2 miles

3500 yards + x yards = 3520 yards

x = 20 yards

13. We know that 1 ft = 12 inches

So, number of feet * 12 = number of inches

number of feet = number of inches / 12

number of feet in 252 inches

Number of feet = 252/12

Number of feet = 21 ft

14. We know that 1 mile = 5280 feet

let x be the number of feet, when added to 6500 feet, will be equal to 2 miles

x ft + 6500 ft = 2 miles

x ft + 6500 ft = 10560 ft

x ft = 4060 ft

15. We know that 1 mile = 5280 feet

let x be the number of feet, when added to 4500 feet, will be equal to 1 mile

x ft + 4500 ft = 1 mile

x ft + 4500 ft = 5280 ft

x ft = 780 ft

we have two sides and a known angle, then we use the following formula for area

where a = 8. b = 12 and C = 62°, so

answer: 42.4 m^2

HELLO THERE

3 and 4 is the answer

I hope I helped

Answer:

by using formula a+b+c .....

Answer:

Then use Hero's Formula

Step-by-step explanation:

Answer:

Let's say that x is sam's age and y is Amy's age

x=y-4

and five years ago:

x-5=(y-5)/2

y-4-5=(y-5)/2

2y-18=y-5

y=13

x=9

then:

sam's age is 9 and Amy's age is 13

Answer:

Sam: 9, Amy: 13

Step-by-step explanation:

So five years ago, lets say Sam was 4, and Amy was 8. That would be half Amy's age. If we add on 5 to Sams age, as it says, Amy would then be 13, and Sam would be 9. This is also four years apart. Thus, the answers are Sam: 9 and Amy: 13

Answer:

7.5 meters

Step-by-step explanation:

Stay safe!!! Stay 6 feet!!

Answer:

its 7.5

i got it right

The equation of remaining chocolate C  in terms of t is C = 30 - 3t.

A mathematical statement called an equation demonstrates the balance or equality of two expressions. It contains of variables, integers, and mathematical operations and is denoted by the equal symbol (=). Equations may be solved to determine unknown values and are used to express relationships between various quantities. To solve for x in the equation 2x + 3 = 7, for instance, remove 3 from both sides, which gives 2x = 4, then divide both sides by 2, which gives x = 2.

Given that,

Initial number of chocolates in box = 30

Also given that after 8 nights, number of remaining chocolates = 6

Implies that,

In 8 nights, 24 chocolates were treated.

In 1 night, 3 chocolates were treated.

The equation of remaining chocolate C  in terms of t can be written as

C = 30 - 3t.

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Answer:

Step-by-step explanation:

15+5x=20x

   -5x  -5x  => Subtract 5x from each side

You get

15 = 15x

Divide both sides by 15

1=x

Answer:

I'd say the order from youngest to oldest, would be B A C.

Step-by-step explanation:

My reason is that, A is younger than C or in other words C is older than A. Also B is NOT older than A, so therefore B must be younger than A.

So from youngest to oldest, B is younger than A, A is younger than C, and that means C is the absolute oldest out of the three children.

Hope this helps you :)

Sorry if it didn't though.