Lucien is going to move to a new house he needs to figure out how much each packing box will hold which formula can lucien use to figure out how much the box will hold h=40cm w=45cm l=70 cm NEED HELP PLEASE QUICK GOOD AMOUNT OF POINTS!!!!!!!!!!

x = 4; y = 9; length of a side = 5

Here, you're expected to use the fact that all of the sides of a square are the same length.

The left and right sides both have different expressions only in y, so it is convenient to equate them.

... y -4 = 2y -13

... 0 = y -9 . . . . . subtract the left side

... 9 = y . . . . . . . add 9

This tells us the side of the square (s) is ...

... s = y -4 = 9 -4

... s = 5

And we can use this to find x.

... 5 = 2x -3 . . . . equate the x-expression to the square side length

... 8 = 2x . . . . . . add 3

... 4 = x . . . . . . . . divde by the coefficient of x

x and y are 4 and 9; the square side length is 5.

The values of x and y are not given, so the length of the square cannot be determined.

To find the side lengths of the square, we first need to determine the values of x and y. However, the provided information does not give any equations or context to solve for x and y. Without additional information, it is not possible to find the values of x and y, and therefore, we cannot calculate the length of the square. If you have any additional information or equations, please provide them so that we can assist you further.

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[tex]\dfrac{13x+10}{2x^2-5x-25}[/tex]

Multiply the first fraction by (x-5)/(x-5) and the second by (2x+5)/(2x+5). Now, you have both fractions with the common denominator (2x+5)(x-5).

[tex]\dfrac{3}{2x+5}+\dfrac{5}{x-5}=\dfrac{3(x-5)}{(2x+5)(x-5)}+\dfrac{5(2x+5)}{(2x+5)(x-5)}\\\\=\dfrac{3(x-5)+5(2x+5)}{(2x+5)(x-5)}=\dfrac{3x-15+10x+25}{2x^2-5x-25}\\\\=\dfrac{13x+10}{2x^2-5x-25}[/tex]

Answer:

The side lengths are 4, 5, and 6.

Step-by-step explanation:

Each midsegment is half the length of the parallel side, so the side lengths of ΔMNK are 4, 5, and 6.

It isn't clear which point is the midpoint of what segment. If it is true that ...

then ...

Answer:

4, 5, 6

Step-by-step explanation:

Answer:

18 cm

Step-by-step explanation:

The length of the median is the average of the two base lengths:

... (24 cm + 12 cm)/2 = 18 cm

(x, y) = (6, -6)

Divide the first equation by 2 to get equal and opposite coefficients for x.

... -2x -y = -6

Add this to the second equation to eliminate x.

... (2x +4y) +(-2x -y) = (-12) +(-6)

... 3y = -18 . . . . . . . . simplify

... y = -6 . . . . . . . . . . divide by 3

Substitute this vaue into any of the equations to find x. We choose to use the reduced first equation above.

... -2x -(-6) = -6

... -2x = -12 . . . . subtract 6

... x = 6 . . . . . . . divide by -2

The solution to the system is (x, y) = (6, -6).

1. If f(x) and g(x) are inverse functions, then f(g(x)) = g(f(x)) = x. Finding the composite of the two functions will tell you if they are inverses.

2. To find the inverse of a function, swap x and y, then solve for y.

... x = 3y

... x/3 = y . . . . . matches f(x) = x/3

3. A function will pass the vertical line test. If its inverse is also a function, that, too, will pass the vertical line test. Since the inverse of a function is that function reflected across y=x, any inverse function that passes the vertical line test corresponds to an original function that passes the horizontal line test. (A vertical line reflected across y=x is a horizontal line.)

4. See 2.

... x = 3(y -2)³

... (x/3) = (y -2)³ . . . . divide by 3

... ∛(x/3) = y -2 . . . . .take the cube root

... 2+∛(x/3) = y . . . . .add 2

... f(x) = 2+∛(x/3) . . . . is the inverse

5. See 2.

... x = 2y -3

... x+3 = 2y . . . . . add 3

... (x+3)/2 = y . . . .divide by 2

... f(x) = (x+3)/2 . . . .  is the inverse

A composite function is the combination of multiple functions.

The correct answers are:

1. Test for inverse function

To test if two functions are inverse of one another, we simply find their composites.

Assume the functions are g(x) and h(x).

We simply test for [tex]g(h^{-1}(x))[/tex] and [tex]h(g^{-1}(x))[/tex]

If they are equal, then both functions are inverse functions

2. Inverse of f(x) = 3x

Rewrite as:

[tex]y = 3x[/tex]

Swap y and x

[tex]x = 3y[/tex]

Make y the subject

[tex]y = \frac x3[/tex]

Hence, the inverse function is: [tex]f'(x) = \frac x3[/tex]

3. True statements

A function has unique ordered pairs; so, it will pass the vertical line test.

Because it has unique ordered pairs, the inverse function will pass the vertical line tests, and the horizontal line tests.

Hence;

(b) All answers are correct

4. Inverse of [tex]f(x) = 3(x - 2)^3[/tex]

Rewrite as:

[tex]y = 3(x - 2)^3[/tex]

Swap x and y

[tex]x = 3(y - 2)^3[/tex]

Solve for y: Divide both sides by 3

[tex](y -2)^3 = \frac x3[/tex]

Take cube roots of both sides

[tex]y -2 = \sqrt[3]{\frac x3}[/tex]

Add 2 to both sides

[tex]y =2 + \sqrt[3]{\frac x3}[/tex]

Hence, the inverse function is: [tex]f^{-1}(x) =2 + \sqrt[3]{\frac x3}[/tex]

5. The inverse of [tex]f(x) =2x - 3[/tex]

Rewrite as:

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

Swap x and y

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

Solve for y: Add 3 to both sides

[tex]2y = x + 3[/tex]

Divide both sides by 2

[tex]y = \frac{x + 3}{2}[/tex]

Hence, the inverse function is: [tex]f^{-1}(x) = \frac{x + 3}{2}[/tex]

Read more about inverse functions at:

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A point belongs to the x axis if its y coordinate equals zero.

The points on a graph are in the form [tex] (x,f(x)) [/tex], so these points are on the x axis if and only if [tex] f(x)=0 [/tex]

In this case, we have

[tex] f(x) = 0 \iff x^2+14x+49=0 [/tex]

You can observe that your expression is actually a squared binomial: using

[tex] (a+b)^2 = a^2+2ab+b^2 [/tex]

you can notice that

[tex] (x+7)^2 = x^2+14x+49 [/tex]

So, you have

[tex] x^2+14x+49=0 \iff (x-7)^2 = 0 \iff x=7 [/tex]

Now, how we decide if this function "touches" or "passes through" the x-axis at x=7? Well, since our function is a square, it is never negative. So, this graph can't cross the x-axis, but rater touch it from above. The parabola has a U shape, and the point of minimum lies on the x axis.

So, the graph touches the x axis at x=7.

The graph of the function f(x)=x^2+14x+49 is a parabola that touches the x-axis at -7, it does not pass through it because the root of the equation -7 is of multiplicity 2.

The function f(x)=x^2+14x+49 is a quadratic function, which when factorized becomes f(x) = (x+7)^2. This means that the graph of the function touches the x-axis at -7, but does not pass through it because the root of this equation -7 is of multiplicity 2. Hence, the correct answer is B: The graph touches the x-axis at -7.

To visualize this, remember that a quadratic function like this one forms a parabola. The point where the parabola intersects or touches the x-axis corresponds to the solution(s) of the equation. In this case, because there's only one solution (x=-7), the parabola just touches the x-axis at this point, but doesn't cross it.

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What is 45% of 36 feet?

To find the percent of a number, you have to change the percent into a decimal or a fraction and multiply by the number.

DECIMAL

To change a percent into a decimal, remove the percent sign and move the decimal point 2 places to the left.

[tex]45 \% \rightarrow 0.45[/tex]

Now that you have your decimal, multiply by 36:

[tex]0.45 \times 36 = 16.2[/tex]

ANSWER = 16.2 feet

FRACTION

To change a percent into a fraction, make the percent number as the numerator(top number) and 100 as the denominator(bottom number) since fractions are out of 100.

[tex]45 \% \rightarrow \frac{45}{100}[/tex]

Now that you have your fraction, multiply by 36:

[tex]\frac{45}{100} \times 36 = \frac{1620}{100} \rightarrow 16.2[/tex]

ANSWER = 16.2 feet

If you have any questions, feel free to ask in the comments! :)

Answer:

Step-by-step explanation:

36feet=100%

18feet=50%

48.2=45%

Answer:

4

Step-by-step explanation:

The formula for a rectangle is base times height so if one side is 7 inches then you need to figure out what times seven equals 28, which would be four.

If one pair of sides is 7 inches and the area is length times width then the answer would be whatever you multiple by 7 to get 28, so it would be 4 inches for each of the other two sides.

1:00 a.m. (and 3:00 a.m., and 5:00 a.m.)

The problem is to find the least common multiple (LCM) of the barking intervals. One way to find the LCM is to find the product of the factors of the numbers.

... 5 = 5 . . . . a prime number

... 8 = 2³

... 12 = 2²×3

The factor 2³ is a multiple of the factor 2², so we only need 2³ in our final product.

The LCM is then ...

... 2³×3×5 = 120 . . . . minutes

The dogs will all bark together every 120 minutes (2 hours).

2 hours after 11 p.m. is 1 a.m.

_____

The problem statement doesn't say whether Ms. Li was awakened multiple times. The dogs will bark together again at 3 a.m., 5 a.m. and (possibly) 7 a.m.

The time when Ms. Li was awakened by the dogs Lola, Patch and Lady barking together was calculated using the concept of least common multiple (LCM). The LCM of the intervals the dogs bark (5, 8, and 12 minutes) is 120 minutes or 2 hours. Therefore, Ms. Li was awakened at 1:00 am.

This problem is a least common multiple (LCM) problem in Mathematics. The dogs Lola, Patch, and Lady started barking together at 11:00 pm. Lola barked every 5 minutes, Patch every 8 minutes, and Lady every 12 minutes. The number that is divisible by all of 5, 8, and 12 is their LCM.

To find the LCM of 5, 8, and 12, list the multiples of each number. The LCM is the smallest number that occurs in each list. In this case, the LCM is 120.

So they all barked together 120 minutes, or 2 hours, after 11:00 pm. Therefore, Ms. Li was awakened at 1:00 am.

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Answer:

8,800

Step-by-step explanation:

400 km

1 cm

=

d

22 cm

Each of these sequences goes into the classification box above it.

If the difference of terms is a constant, it is arithmetic.

... (3 -(-1)) = 4 = (7 -3), so the first sequence is arithmetic

If the ratio of terms is a constant, it is geometric.

... 12/36 = 1/3 = 4/12, so the second sequence is geometric

The third sequence has neither constant differences nor constant ratios, so is neither arithmetic nor geometric.

Answer:

A=6

B=8

Step-by-step explanation:

The hypotenuse QR is twice the length of BC, so PQ will be twice the length of AB, 2·3 = 6; and PR will be twice the length of AC, 2·4 = 8.

In similar triangles PQR and ABC:

Side PQ (a) is 40/3 units.

Side PR (b) is 50/3 units.

To find the unknown side lengths in similar triangles PQR and ABC, we can use the properties of similar triangles. Two triangles are similar if their corresponding angles are congruent, and their corresponding sides are in proportion.

In this case, we have triangles PQR and ABC:

PQR:

RQ = 10

QP = a

RP = b

ABC:

AB = 3

AC = 4

BC = 5

Since the triangles PQR and ABC are similar, the ratios of corresponding sides must be equal. Specifically, the ratio of the sides in triangle PQR to the sides in triangle ABC should be the same. We can set up proportions to solve for a and b:

RQ / AB = QP / AC = RP / BC

10 / 3 = a / 4 = b / 5

Now, we can solve for a and b separately.

From the first part of the proportion:

10 / 3 = a / 4

Cross-multiply:

10 * 4 = 3 * a

40 = 3a

Now, divide by 3 to solve for a:

a = 40 / 3

From the second part of the proportion:

10 / 3 = b / 5

Cross-multiply:

10 * 5 = 3 * b

50 = 3b

Now, divide by 3 to solve for b:

b = 50 / 3

So, the unknown side lengths are:

a = 40/3

b = 50/3

Therefore, in similar triangles PQR and ABC:

Side PQ (a) is 40/3 units.

Side PR (b) is 50/3 units.

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Answer:

a. Infinitely many solutions

Step-by-step explanation:

The given equations are  2x - y = 3

4x = 6 + 2y

We can use substitution method to solve these system of equations.

2x - y = 3

y = 2x - 3

Now plug in y = 2x - 3 in the second equation, we get

4x = 6 + 2(2x - 3)

4x = 6 + 4x  - 6

4x = 4x

Here we get infinitely many solution.

Both the equations are the same.

Thank you.

Answer:

208

Step-by-step explanation:

basically you can plug this into a calculator, just by pressing 160 + 30(then the percent sign), followed by the equal sign. or you can do it on paper by dividing 160 by 100, which gives you 1.6. then you multiply that by 30, with leaves you with 48. and because 48 is 30% of 160, you do 48 + 160 equals 208.

Answer:

13.8–14.2 inches

Step-by-step explanation:

If you assume the "symmetrical and bell-shaped" distribution is a normal distribution, then 95% of observations will lie within 2 standard deviations of the mean:

... 14 in ±2×(0.1 in) = 13.8 in to 14.2 in

Answer:

1/8

Step-by-step explanation:

When there are two possiblities for each of 3 positions, the number of possible codes is 2^3 = 8. Your code is one of those, so its probability of occurrence is 1/8.

_____

CCC, CCP, CPC, CPP, PCC, PCP, PPC, PPP

Answer: [tex]\dfrac{1}{8}[/tex]

Step-by-step explanation:

Given: A three-character code uses the letters C and P.

If repetition is allowed then the total number of ways to make the three letter character code using two letters C and P is given by :-

[tex]2\times2\times2=8[/tex]

Since the PCP is one of the character code, therefore , the probability of the code PCP is given by :-

[tex]\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}\\\\=\dfrac{1}{8}[/tex]

Hence, the probability of the code PCP = [tex]\dfrac{1}{8}[/tex]

The answer, I believe, is an Equilateral triangle.

In geometry, an equilateral triangle is a triangle in which all three sides are equal. In the familiar Euclidean geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each other and are each 60°.

Answer:

[tex]\sqrt{3}[/tex] :1

Step-by-step explanation:

Ratio of height of two cylinders are 3:1

Let C2 has the height x

then height of C1 is 3x

Let r1 is the radius of C1

and r2 is the radius of C2

As given that volume of both are equal

Also we know that formula for the volume of the cylinder is

V= π r²h

for C1

V= π (r1)²h

for C2

V=π (r2)²h

As volume of both are same so equating them

π (r1)²h1 = π (r2)²h2

as h1 =3x and h2=x

putting values

π (r1)²(3x) = π (r2)²(x)

cancelling out π and x from both side of the equation

3(r1)²= (r2)²

Taking square root of both sides give

[tex]\sqrt{3(r1)^{2} }=\sqrt{(r2)^{2} }[/tex]

r1 ( [tex]\sqrt{3}[/tex]) = r2

or

r1 : r2 =  [tex]\sqrt{3}[/tex]  :1

Question

classify what type of angle this is

Answer:

Step-by-step explanation:

2 equal side and 2 equal angles, it is an isosceles.

Answer:

y = 5x+15

Step-by-step explanation:

The cost per calculator is 5

The shipping cost is 15

Let y = total cost

Let x = number of calculators

y = 5x+15

Answer: The answer is c)5

Answer:

c) 5

Step-by-step explanation:

Answer:

A. 1⁄2 < 3⁄4

Step-by-step explanation:

1/2   vs 3/4

Get a common denominator of 4

1/2 *2/2   vs 3/4

2/4   vs 3/4

2 is less than 3

2/4 < 3/4

1/2 < 3/4

1

The given angle is opposite the longest given side, so there will be exactly one solution.

_____

The number of solutions may be 0, 1, or 2 when the given angle is opposite the shortest given side.

Cos(y-z) = Cos(z-24)

You have two equations in three unknowns, so no solution for the unknowns is possible.

The tangent equation tells you ...

... tan(z -24) = tan(y -z)

... z -24 = y -z . . . . . . take the arctangent

... cos(y -z) = cos(z -24) . . . . take the cosine

Equilateral

An equilateral triangle has medians that are also angle bisectors that are also altitudes.

12%

Her discounted price was 100% - 20% = 80% of the original price. The service fee made it be 100% + 10% = 110% of that, so her final price was ...

... 110% × 80% = 88%

of the original ticket price.

This represents a discount of 100% - 88% = 12% from the original.

Answer:

k = -3

Step-by-step explanation:

Simplify, divide by 9, add the opposite of the constant.

0 = 9k -9·2/3 +33

0 = 9k +27

0 = k +3

-3 = k

Answer:

See below

Step-by-step explanation:

The values in the table change by $3.80 from one line to the next. Since each change from line to line changes in number of photos by 20, the average cost per photo is $3.80/20 = $0.19. There is apparently a $5.80 -3.80 = $2.00 shipping charge for numbers of photos in the range shown in the table.

Thus, the piecewise function has 3 pieces:

for x < 100: $2.00 + 0.19x

for x < 200: $4.50 + 0.17x

for x ≥ 200: $0.15x

This could be written as ...

[tex]C(x)=\left\{\begin{array}{rcl}\$2.00+0.19x&\text{for}&0\le x<100\\\$4.50+0.17x&\text{for}&100\le x<200\\\$0.15x&\text{for}&x\ge 200\end{array}\right.[/tex]