what is the rule for the reflection?

Answer:

The length is 10 inches, and the width is 4 inches.

By creating a quadratic equation using the known facts and algebra, we can determine that the dimensions of the rectangle with an area of 40 square inches are length= 10 inches and width= 4 inches.

This problem is a classic example of using algebra to solve for unknown dimensions. Given that the area (A) of a rectangle equals its length (L) times its width (W), written as A = L x W, you can substitute the given values into this formula. You're told the length is 6 inches longer than the width, which you can denote in algebra as L = W + 6. Secondly, you're given that the area is 40 square inches. Substituting these values gives us the following equation: 40 = W(W + 6).

Solving this equation will give us the width, and substituting the width into the formula L = W + 6, gives us the length.

First, distribute the width on the right side of the equation to get 40 = W^2 + 6W. Re-arranging terms gives W^2 + 6W - 40 = 0. Factoring this quadratic equation yields (W - 4)(W + 10) = 0. Setting each factor equal to zero and solving for W gives W = 4 and W = -10. Because a width cannot be negative, the width of the rectangle is 4 inches. Substituting W = 4 into the length equation results in L = 4 + 6 = 10 inches. Hence, the dimensions of the rectangle are Length = 10 inches and Width = 4 inches.

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This is an exponential growth problem.

The formula is y = a(1+r)^x

Y would be the final answer

a is the starting value

r is the percent of growth

x is the amount of time ( number of weeks)

The equation is:

y(x) = 92(1.06)^x

For 14 weeks replace x with 14:

y(14) = 92(1.06)^14 = 208 pounds.

Answer: W(n) = 92lb*1.06^n

and W(14) = 92lb*1.06^14 = 208lb

Step-by-step explanation:

We know that at the beginning the baby elephant weighs 92Lbs, and for each week it augments by a 6% (or 0.06 in decimals)

Then, at the end of the first week, the weight is:

92lb*1.06 = 97.52lb

at the end of the second week:

(92lb*1.06)*1.06 = 103.37lb

and so on, so you can see that the pattern is:

W(n) = 92lb*1.06^n

where n is the number of weeks after the birth

W(0) = 92lb

W(1) =  97.52lb

...

And we want to know the weight at the end of the 14th week, so we must find:

W(14) = 92lb*1.06^14 = 208lb

Answer:

The simplest form of the expression is 3² ⇒ 3rd answer

Step-by-step explanation:

- The expression is 3 power 3 multiplied by 3 power 3 over 3 power 4

∵ 3 power 3 = 3³

∵ multiplied by 3 power 3 = × 3³

∵ over 3 power 4 = ÷ [tex]3^{4}[/tex]

- Lets write all of them in one expression

∴ The expression = [tex]\frac{3^{3}*3^{3}}{3^{4}}[/tex]

- All the numbers in the expression is 3 to the power

∴ The expression have the same base 3

- Remember: if we have numbers of same base multiplied then we

 add their powers and if divided then we subtract their powers

 [tex]\frac{a^{m}*a^{n}}{a^{q}}=a^{m+n-q}[/tex]

- Lets use this rule to simplify the expression

∵ The expression = [tex]\frac{3^{3}*3^{3}}{3^{4}}[/tex]

- Use the rule of the same base above

∴ [tex]\frac{3^{3}*3^{3}}{3^{4}}[/tex] = [tex]3^{3+3-4}=3^{6-4}=3^{2}[/tex]

∴ The simplest form of the expression is 3²

Answer:

3 to the 2nd power.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Let's see...

It's a cube, so the total volume will be one length cubed or 10^3 which is 1000.

(2500 g)/(1000 cm^3) = [tex]2.5 g/cm^3[/tex]

I'm pretty sure the answer is A because it's the only one with correct scientific notation.

Answer:

m∠MHJ = 50°

========================

Step-by-step explanation:

Best explanation is as shown in the attached figure.

As shown in the figure:

x + 15 = 2x - 20  ⇒ vertex angles are congruent

solve for x ⇒ ∴ x = 35°

So, ∠MHJ =  2x - 20 = 2*35 - 20 = 50°

========================================

The measure of all angles will be:

∠MHJ = 2X - 20° = 2 * 35 - 20 = 50°

∠JHK = 180° - ∠MHJ = 180 - 50 = 130°

∠KHL = X + 15° = 35° + 15° = 50°

∠LHM = ∠JHK = 130°

Answer:

B 50 degrees

Step-by-step explanation:

Answer:

there were 2 doctors. first doctor saw 89 patient. Second doctor saw the twice of first doctor. calculate how much patient did second doctor saw

Answer:

$96.51

Step-by-step explanation:

529.57 - 126.08 = 403.49

500 - 403.49 = 96.51

The possible amount you deposit into your account by the ed of the month to avoid paying the service fee would be $96.51

Answer:

$96.51

Step-by-step explanation:

Answer:

6(9x+5)

Step-by-step explanation:

6*9x = 54x

6*5 = 30

The expression should be 6(9x+5)

The equation is 54x + 30

A polynomial represents an expression that comprises of indeterminates and coefficients, which includes only the operations of addition, subtraction, multiplication, and a non-negative integer.

So,

= 54x + 30

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Answer:

(5 + √115)/15 or (5 - √115)/15

Step-by-step explanation:

4/5x+4/3 = 2x

Multiply each term by the least common multiple of the denominators (15x)

12 + 20x = 30x²

Move all the terms to the left-hand side.

-30x² + 20x + 12 = 0

Multiply each term by -1

30x² - 20x - 12 = 0

Remove the common factor (2)

15x² - 10x - 6 = 0

Solve by using the quadratic formula

a = 15, b = -10, c = -6

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\= \frac{-(-10)\pm\sqrt{(-10)^2-4(15)(-6)}}{2(15)}\\\\= \frac{10\pm\sqrt{100 + 360}}{30}\\\\= \frac{10\pm\sqrt{460}}{30}\\\\= \frac{10\pm\sqrt{4\times115}}{30}\\\\= \frac{10\pm2\sqrt{115}}{30}\\\\= \mathbf{\frac{5\pm\sqrt{115}}{15}}[/tex]

x = (5 + √115)/15 or x = (5 - √115)/15

Answer:

The measure of segment AC is 36 units

Step-by-step explanation:

- The mid-point divides the segment into two equal parts in length

- B is the mid point of segment AC

- That means B divides segment AC into two equal parts in length

∴ AB = BC

∵ AC = 5x - 9

∵ AB = 2x

- The two parts AB and BC are equal in length

∴ BC = 2x

∵ AC = AB + BC

- Substitute the values of AB and BC in the expression of AC

∴ AC = 2x + 2x

∴ AC = 4x

∵ AC = 5x - 9

- Equate the two values of AC

∴ 5x - 9 = 4x

- Add 9 to both sides

∴ 5x = 4x + 9

- Subtract 4x from both sides

∴ x = 9

- Substitute the value of x in any expression of AC

∵ AC = 4x

∵ x = 9

∴ AC = 4(9) = 36

* The measure of segment AC is 36 units

Answer:

-3

Step-by-step explanation:

-(-3) = 3

-(-6) = 6

-3 - (-6) = 3

-c - d

c = -3

-3 - d

d = -6

-3 - (-6)

=-3+6

=3

Answer:

Step-by-step explanation:

-3 - (-6) = x  (u would use Keep Change Flip [KCF] to solve)

-3 + 6 = x

3=x

so the answer is 3

Hope this helps!!

To factorise fully the expression 5x-15, we must search for the greatest common factor (GCF) that can be taken out of both terms. The expression 5x - 15 can be factorised fully by finding the greatest common factor, which is 5. So the expression factorised fully is 5(x - 3).

To factorise fully the expression 5x-15, we must search for the greatest common factor (GCF) that can be taken out of both terms.

The GCF of 5x and 15 is 5. Thus, we can pull 5 outside of the equation and divide each term by 5.

The equation becomes: 5(x - 3).

So, the expression 5x - 15 factorised fully is 5(x - 3).

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Answer:

See explanation

Step-by-step explanation:

Let x be the number of simple arrangements and y be the number of grand arrangements.

1. The florist makes at least twice as many of the simple arrangements as the grand arrangements, so

[tex]x\ge 2y[/tex]

2. A florist can make a grand arrangement in 18 minutes [tex]=\dfrac{3}{10}[/tex] hour, then he can make y arrangements in [tex]\dfrac{3}{10}y[/tex] hours.

A florist can make  a simple arrangement in 10 minutes [tex]=\dfrac{1}{6}[/tex] hour, so he can make x arrangements in [tex]\dfrac{1}{6}x[/tex] hours.

The florist can work only 40 hours per week, then

[tex]\dfrac{3}{10}y+\dfrac{1}{6}x\le 40[/tex]

3. The profit on the simple arrangement is $10, then the profit on x simple arrangements is $10x.

The profit on the grand arrangement is $25, then the profit on y grand arrangements is $25y.

Total profit: $(10x+25y)

Plot first two inequalities and find the point where the profit is maximum. This point is point of intersection of lines [tex]x=2y[/tex] and [tex]\dfrac{3}{10}y+\dfrac{1}{6}x=40[/tex]

But this point has not integer coordinates. The nearest point with two integer coordinates is (126,63), then the maximum profit is

[tex]\$(10\cdot 126+25\cdot 63)=\$2,835[/tex]

To maximize profit, the florist should produce 1 grand arrangement and 2 simple arrangements. The maximum profit is $45.

To maximize profit, the florist should produce a combination of grand and simple arrangements. Let's assume the florist makes x grand arrangements and at least twice as many simple arrangements, which would be 2x or more. Given that the florist can work only a total of 40 hours per week, we can set up the following equation:

18x + 10(2x) ≤ 40

Now, we solve for x to find the number of grand arrangements.

Simplifying the equation, we have 18x + 20x ≤ 40

Combining like terms, we get 38x ≤ 40

Dividing both sides by 38, we find that x ≤ 1.05

Since we can't have a fraction of an arrangement, the florist should produce 1 grand arrangement. From the given information, we know that the florist must produce at least twice as many simple arrangements as grand arrangements. Therefore, the florist should produce at least 2 * 1 = 2 simple arrangements.

The florist's maximum profit can be calculated by multiplying the profit per arrangement by the number of corresponding arrangements.

The profit for the grand arrangement is $25, so the total grand arrangement profit is 1 * $25 = $25. The profit for the simple arrangement is $10, so the total simple arrangement profit is 2 * $10 = $20. Therefore, the maximum profit is $25 + $20 = $45.

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Answer:

They bought 0 ticket of closest section and 7 tickets of other section

Step-by-step explanation:

- Callie and Madison went to buy concert tickets for themselves and

  their five friends

- That mean they are 7

- Tickets for the closest section were $45 each

- Tickets for other section were $30 each

- They  ended up spending a total of $210

- Assume that they buy x tickets for closest section and y tickets for

 the other section

∵ They want 7 tickets

∴ x + y = 7 ⇒ (1)

∵ The cost of the closest section ticket was $45

∵ The cost of the other section ticket was $30

∵ They spent $210 on them

∴ 45x + 30y = 210

- All terms have common factor 15, then divide them by 15

∴ 3x + 2y = 14 ⇒ (2)

* Now we have a system of equations to solve

- Multiply equation (1) by -2 to eliminate y

∴ -2x - 2y = -14 ⇒ (3)

- Add equations (2) and (3)

∴ x = 0

- substitute the value of x in equation (1) to find y

∴ 0 + y = 7

∴ y = 7

∵ x represents the number of tickets of the closest section and y

  represents the number of tickets in the other section

∴ They bought 0 ticket of closest section and 7 tickets of other

   section

Answer:

81x^2 + 12x + 4

Step-by-step explanation:

This expression doesn't factor

let's keep in mind that we have denominators of 2, 4 and 2, and thus we can use their LCD of 4, and multiply both sides by that LCD to do away with the denominators, let's proceed,

[tex]\bf \cfrac{1}{2}n+\cfrac{3}{4}n=\cfrac{1}{2}\implies \stackrel{\textit{multipying both sides by }\stackrel{LCD}{4}}{4\left( \cfrac{1}{2}n+\cfrac{3}{4}n \right)=4\left( \cfrac{1}{2} \right)}\implies 2n+3n=2 \\\\\\ 5n=2\implies n=\cfrac{2}{5}[/tex]

Answer:

x = -1 , y = -4

Step-by-step explanation by elimination:

Solve the following system:

{8 y - 5 x = -27 | (equation 1)

7 y - 8 x = -20 | (equation 2)

Swap equation 1 with equation 2:

{-(8 x) + 7 y = -20 | (equation 1)

-(5 x) + 8 y = -27 | (equation 2)

Subtract 5/8 × (equation 1) from equation 2:

{-(8 x) + 7 y = -20 | (equation 1)

0 x+(29 y)/8 = (-29)/2 | (equation 2)

Multiply equation 2 by 8/29:

{-(8 x) + 7 y = -20 | (equation 1)

0 x+y = -4 | (equation 2)

Subtract 7 × (equation 2) from equation 1:

{-(8 x)+0 y = 8 | (equation 1)

0 x+y = -4 | (equation 2)

Divide equation 1 by -8:

{x+0 y = -1 | (equation 1)

0 x+y = -4 | (equation 2)

Collect results:

Answer:  {x = -1 , y = -4

Answer:

there is an 88% chance it will land on teal, because if you do 16/18, you get 0.8 repeating. then, you multiply by 100 and get 88%

Step-by-step explanation:

The measure of angle y is 62°.

I solve this by

We know: Measures of interior angles in a triangle add up to 180°.

Therefore we have the equation:

60° + 58° + y = 180°

118° + y = 180°         subtract 118° from both sides

118° - 118° + y = 180° - 118°

y = 62°

The measure of angle x is 122°.

I solve this by

Angles 58° and x are supplementary angles.

Supplementary angles add up to 180°.

Therefore we have the equation:

x + 58° = 180°            subtract 58° from both sides

x + 58° - 58° = 180° - 58°

x = 122°

Answer:

6<x>54 ASK YOUR TEACHER

Step-by-step explanation:

Answer:

-26

Step-by-step explanation:

Answer:

The volume of the sphere is [tex]V=288\pi\ m^3[/tex]

Step-by-step explanation:

The question in English is

Calculate the volume in m^3 of the sphere in which the area of one of its maximum circles is 36pi m^2

we know that

The radius of the maximum circle in the sphere is equal to the radius of the sphere

Step 1

Find the radius of the maximum circle

The area of the circle is

[tex]A=\pi r^{2}[/tex]

we have

[tex]A=36\pi\ m^2[/tex]

substitute and solve for r

[tex]36\pi=\pi r^{2}[/tex]

Simplify

[tex]36=r^{2}[/tex]

take the square root both sides

[tex]r=6\ m[/tex]

Step 2

Find the volume of the sphere

The volume of the sphere is

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

substitute the value of r

[tex]V=\frac{4}{3}\pi (6)^{3}[/tex]

[tex]V=288\pi\ m^3[/tex]

Total amount of what?

$8.75 * 7.5

about $65.63

Forgive me if I'm wrong

Hope this helps!

x/4 >= -8

Multiply both sides by 4.

x >= (-8)(4)

x >= -32

The value of X is greater than or equal to -32.

To solve the inequality X/4 ≥ -8, we need to isolate the variable X. Firstly, we can multiply both sides of the inequality by 4 to get rid of the denominator: X ≥ -32. This means that the value of X is greater than or equal to -32. In interval notation, we can represent this as (-32, ∞).

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Answer:

Complementary angles

Step-by-step explanation:

Complementary angles sum to 90°, that is

x + 90 - x = 90°

Thus x and (90 - x) are complementary angles

Answer:

see explanation

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h. k) are the coordinates of the vertex and a is a multiplier

here (h, k) = (- 6, - 1), thus

y = a(x + 6)² - 1

To find a substitute one of the roots into the equation

Using (- 3, 0), then

0 = a(- 3 +6)² - 1

0 = 9a - 1 ( add 1 to both sides )

1 = 9a ( divide both sides by 9 )

a = [tex]\frac{1}{9}[/tex], thus

y = [tex]\frac{1}{9}[/tex](x + 6)² - 1 ← in vertex form

Expand factor and simplify

y = [tex]\frac{1}{9}[/tex] (x² + 12x + 36) - 1 ← distribute

y = [tex]\frac{1}{9}[/tex] x² + [tex]\frac{4}{3}[/tex] x + 4 - 1

  = [tex]\frac{1}{9}[/tex] x² + [tex]\frac{4}{3}[/tex] x + 3 ← in standard form

Answer:

The value of the digit 2 in the number 12,600 is 2,000

Step-by-step explanation:

we have the number 12,600

Rewrite the number in expanded form (write the number in its digits value)

[tex]12,600=10,000+2,000+600[/tex]

so

The value of the digit 1 in the number is 10,000

The value of the digit 2 in the number is 2,000

The value of the digit 6 in the number is 600

Answer:

The inverse property of addition.

Step-by-step explanation:

The number  6 is added to its inverse -6.

The property of real numbers (-6) + 6 = 0 will be Inverse property of addition. Then the correct option is D.

Any of the many numerical laws governing how values are added.

Some Addition properties are as follows:

Associative property of addition – The total is unchanged when the order of the sub-blocks is changed.

For example, (2 + 3) + 4 = 2 + (3 + 4)

Commutative property of addition – No matter how the addends are arranged, the result remains constant.

For example, 4 + 2 = 2 + 4

Identity property of addition – The integer is that summation of 0 and that value.

For example, 0 + 4 = 4

Inverse property of addition – Zero is the result of adding any integer to its inverse.

For example, a + (-a) = 4

The property of real numbers -6+6=0 will be Inverse property of addition.

Then the correct option is D.

More about the properties of the Addition link is given below.

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