Juan had 138 Lego bricks. He also had two containers and divided them equally between the two. He had 14 bricks left over. How many Lego bricks did each container hold?

Answer:

the ans is 6.4

Step-by-step explanation:

using the distance formula

d^2= (x2-x1)^2 + (y2-y1)^2

d^2= (8-4)^2 + (8-3)^2

d^2= (4)^2 + (5)^2

d^2= 16+ 25

d^2= 41

d= sqrt of 41*

d= 6.4units

The rate at which the height of the water in the trough is changing when the water's height is 1 meter is approximately 0.0833 meters per minute.

Let's denote the height of the water in the trough as 'h' (in meters) and the time as 't' (in minutes). We are given that the trough is 18 meters long and its ends have the shape of isosceles triangles with a top width of 8 meters and a height of 3 meters.

The volume of the trough can be calculated using the formula for the volume of a triangular prism: V = (1/2) * base * height * length. In this case, the base of the triangle is 8 meters, the height is h, and the length is 18 meters. Therefore, the volume V of water in the trough is V = (1/2) * 8 * h * 18 = 72h.

We are given that the water is being drained from the trough at a rate of 12 m³/min. Therefore, the rate of change of volume with respect to time (dV/dt) is -12 m³/min. To find the rate at which the height of the water is changing, we need to calculate dh/dt. We can use the chain rule of differentiation:

dV/dt = dV/dh * dh/dt

We know that dV/dt = -12 m³/min, and we can differentiate V = 72h with respect to h to find dV/dh, which is 72.

-12 = 72 * dh/dt

Simplifying the equation, we find:

dh/dt = -12/72 = -1/6 = -0.1667 m/min

So, when the height of the water is 1 meter, the rate at which the height of the water is changing is approximately 0.0833 meters per minute.

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Answer:

1,2,4,5,10 and 20

Step-by-step explanation:

Answer

20y-25 i think

Step-by-step explanation:

15 + 4(5y - 10)

15 + 20y - 40

20y - 25

The solution is: simplification of the linear expression 15 +4(5y-10) is

20y - 25.

Here, we have,

given that,

the linear expression is: 15 +4(5y-10).

now, we have to simplify this.

so, we have,

15 + 4(5y - 10)

withdrawing the bracket and multiplying 5y - 10 by 4 => 20y - 40,

we get,

=15 + 20y - 40

now, adding or subtracting the like terms, we get,

=20y - 25

Hence, The solution is: simplification of the linear expression 15 +4(5y-10) is 20y - 25.

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The root of the equation sinx = 2x-3 is 0.8401 (approx).

Given equation is sinx = 2x-3

We need to solve this equation using false position method.

False position method is also known as the regula falsi method.

It is an iterative method used to solve nonlinear equations.

The method is based on the intermediate value theorem.

False position method is a modified version of the bisection method.

The following steps are followed to solve the given equation using the false position method:

1. We will take the end points of the interval a and b in such a way that f(a) and f(b) have opposite signs.

Here, f(x) = sinx - 2x + 3.

2. Calculate the value of c using the following formula: c = [(a*f(b)) - (b*f(a))] / (f(b) - f(a))

3. Evaluate the function at point c and find the sign of f(c).

4. If f(c) is positive, then the root lies between a and c. So, we replace b with c. If f(c) is negative, then the root lies between c and b. So, we replace a with c.

5. Repeat the steps 2 to 4 until we obtain the required accuracy.

Let's solve the given equation using the false position method.

We will take a = 0 and b = 1 because f(0) = 3 and f(1) = -0.1585 have opposite signs.

So, the root lies between 0 and 1.

The calculation is shown in the attached image below.

Therefore, the root of the equation sinx = 2x-3 is 0.8401 (approx).

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The given signal, \(x(t) = 5cos(\omega t+\pi/3)+ 7cos(\omegat-5\pi/4)+3cos(\omega t)\), can be expressed in the form x(t)=Acos(ωt+ϕ), where A represents the amplitude and ϕ represents the phase.

To express the given signal x(t) in the form x(t)=Acos(ωt+ϕ), we need to combine the cosine terms and simplify the expression. Let's start by rewriting the given signal:

\(x(t) = 5cos(\omega t+\pi/3)+ 7cos(\omegat-5\pi/4)+3cos(\omega t)\)

Using the trigonometric identity cos(a+b)=cos(a)cos(b)−sin(a)sin(b), we can simplify the expression:

\(x(t) = 5cos(\omega t+\pi/3) - 5sin(\omega t)sin(\pi/3) + 7cos(\omegat-5\pi/4)-7sin(\omega t)sin(-5\pi/4)+3cos(\omega t)\)

Simplifying further:

\(x(t) = (5cos(\pi/3)+7cos(\omegat-5\pi/4)+3)cos(\omega t) - (5sin(\pi/3) +7sin(-5\pi/4))sin(\omega t))\)

We can rewrite the constants as

\(A=5cos(\pi/3)+7cos(-5\pi/4)+3\) and \(\theta= -arctan(\frac{5sin(\pi/3)+7sin(-5\pi/4)}{5cos(\pi/3)+7cos(-5\pi/4)+3})\)

Therefore, the given signal x(t) can be expressed in the form x(t)=Acos(ωt+ϕ), where A is the amplitude and ϕ is the phase.

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JL, LK, JK are the smallest angle of a triangle is located across from its smallest side. The biggest side is on the other side of the biggest side.

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Answer:

Positive

Step-by-step explanation:

Positive / positive = positive

positive / negative = negative

negative / negative = positive

negative/ positive = negative

Sign of -4 divided by -8 we get positive expression.

Here we have to find the sing of expression,

When -4 divided by -8

Since we know that,

Dividing two fractions is equivalent to multiplying the first fraction by its reciprocal. The first step in splitting fractions is to get the reciprocal of the second fraction (reverse the numerator and denominator). Then, multiply the numerators.

We can write it,

-4 divided by -8  = -4/-8

                            = (4/8)x(-1/-1)

                            =  1/2    its a positive number.

Hence,

-4 divided by -8  = 1/2

Hence we get positive expression.  

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Answer:

Step-by-step explanation:

(3x + 1)/x = 1/(x -3)                Cross multiply

(3x + 1)(x - 3) = x                   Remove the brackets. Use FOIL

f:3x*x = 3x^2

o:3x*(-3) = -9x

i:1*x = x

L : 1 * - 3 = -3

FOIL: 3x^2 -9x +x - 3

FOIL: 3x^2 - 8x - 3

3x^2 - 8x - 3 = x                  Subtract x from both sides

3x^2 - 8x -x - 3 = 0             Combine

3x^2 - 9x - 3 = 0                 Factor

It's rather ugly. I had to use the quadratic equation

a = 3

b = - 9

c = - 3

x1 = 3.3

x2 = - 0.3

The product of the given expression is -3ed + 3e^2 showing that they contain two terms and the product has a degree of 2.

Equations are expressions separated by an equal sign.

Given the following expression

(–d + e)(4e + d).

We are to take the product of both expressions.

Expand to have:

(–d + e)(4e + d) = -4ed - d^2 + 4e^2 + de

(–d + e)(4e + d) = -3ed + 3e^2

Hence, there are two terms in the solution and the product is degree 2.

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Answer:

B and E

Step-by-step explanation:

ANSWER

4/5

EXPLANATION

The slope of a line is given by,

In this roof, the rise is the height of the roof, 12ft, and the run is half the width of the roof, 15ft,

Hence, the pitch is 4/5.

The cheaper cost that should be chosen is $3000 to make 500 apple pies a week.

From the information, the manager of Best Bakery finds it costs $3000 to make 500 apple pies a week. The cost per pie will be:

= Total amount / Number of pie

= $3000 / 500

= $6

Also, it cost $2300 to make 325 apple pies a week. The cost per apple pie will be:

= $2300 / 325

= $7.08

Therefore, the cheaper option is $3000 to make 500 apple pies a week.

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Complete question

The manager of Best Bakery finds it costs $3000 to make 500 apple pies a week or $2300 to make 325 apple pies a week. Which is cheaper?

square root(3) * ((125 / 5) - 8) =

29.44

that's the final answer.

if possible please give me a brainliest. tnx good day

To determine the equation of the tangent plane and normal line of the given curve at the point P(2, -3, 18), we need to find the partial derivatives of the function f(x, y, z) = x^2 + y^2 - 2xy - x + 3y - z - 4.

Taking the partial derivatives with respect to x, y, and z, we have:

fx = 2x - 2y - 1

fy = -2x + 2y + 3

fz = -1

Evaluating these partial derivatives at the point P(2, -3, 18), we find:

fx(2, -3, 18) = 2(2) - 2(-3) - 1 = 9

fy(2, -3, 18) = -2(2) + 2(-3) + 3 = -7

fz(2, -3, 18) = -1

The equation of the tangent plane at P is given by:

9(x - 2) - 7(y + 3) - 1(z - 18) = 0

Simplifying the equation, we get:

9x - 7y - z - 3 = 0

To find the equation of the normal line, we use the direction ratios from the coefficients of x, y, and z in the tangent plane equation. The direction ratios are (9, -7, -1).Therefore, the equation of the normal line passing through P(2, -3, 18) is:

x = 2 + 9t

y = -3 - 7t

z = 18 - t

where t is a parameter representing the distance along the normal line from the point P.

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Answer:

All of them can be helpful

Step-by-step explanation:

The index form of the expression is 5^-1m

Note that index form means in a power form

We have that;

= 4m/20m

Find the similar factor

= 1/5m

The inverse of a number, is that number to the power of -1

Then,

1/5m = 5^-1m

Thus, the index form of the expression is 5^-1m

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Answer:

56 degrees

Step-by-step explanation:

Answer:

56 degrees

Step-by-step explanation:

When two lines cross eachother, the angles opposite eachother are equal.

Answer:

x equals 14

Step-by-step explanation:

If u plug in 14 as X. The equation would equal 180.

Answer:

a line of symmetry is a line divide an object in to two equal parts. answer is A

Answer:

6/7

Step-by-step explanation:

First, cancel out 16 and 56 by a common factor of 8. The resulting expression is -2/5*-15/7. Then, simply 5 and 15 by a common factor of 5. Then, you will get: -2*(-3/7). The negatives cancel out, so the answer is 6/7.

None of the given numbers (-8, 0, 542, 1/2) are irrational. They are all rational numbers.

In the given numbers:

-8: -8 is a rational number because it can be expressed as the ratio of two integers (-8/1).

0: 0 is a rational number because it can be expressed as the ratio of two integers (0/1).

542: 542 is a rational number because it can be expressed as the ratio of two integers (542/1).

1/2: 1/2 is a rational number because it can be expressed as the ratio of two integers (1/2).

None of the given numbers (-8, 0, 542, 1/2) are irrational.

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Answer:

7+8+9/7*8*9 = 24/504 or 0.0476

Step-by-step explanation:

Answer:

1/10

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

x is the favorite number

x÷\(\frac{1}{x}\) = 10x (flip the fraction and multiply)

\(x^{2}\)=10x (divide both sides by x)

x=10

In the following question, Jordan needs 2200 square centimetres of carpet to cover the surface of the post, including the bottom.

To find the surface area of the scratching post, we need to add up the surface areas of all the sides.

The scratching post has a rectangular prism shape with dimensions of 10 cm x 10 cm x 90 cm. The bottom is also a 10 cm x 10 cm square.

So the surface area of the post, including the bottom, is:

2(10 cm x 10 cm) + 2(10 cm x 90 cm) + 2(10 cm x 10 cm) = 200 cm^2 + 1800 cm^2 + 200 cm^2 = 2200 cm^2

Therefore, Jordan needs 2200 square centimetres of carpet to cover the surface of the post, including the bottom.

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Angle of the ladder with the floor is 74.5°.

We have given that,

base of the ladder from the wall, x₀ = 2.70 m

top of the ladder above the floor y = 5.13 m

speed of the spaceship = 0.85 c

and we have to find the angle ladder makes with the floor, θ.

From the given information we will construct a diagram.

From the diagram,

tanθ = y/x₀

tanθ = y / x₀√(1- V^2 / c^2)

we will substitute all the values,

tanθ = 5.13 / 2.70√(1-((0.85c)^2 / c^2))

        = 5.13 / 2.70√(1-(0.85^2))

        = 5.13 / 2.70√(1 - 0.7225)

        = 5.13 / 2.70√0.2775

        = 5.13 / 1.4223

tanθ = 3.606

    θ = tan⁻¹(3.606)

    θ = 74.5°

Therefore angle the ladder makes with the floor is 74.5°.

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Answer:

$30 but the number depends on the bucket of balls used

Step-by-step explanation:

$12 + $6b =

$12 + $6(3) =$30

b= bucket of balls

I used 3 bucket of balls for this clinic

Answer:

Grapes=19.51

Step-by-step explanation:

Apples=$2.19 per pound

Grapes=$2.60 per pound

Apples+Grapes=20 pounds

A+G=20

A=20-G

Equation is

PaA+PgG=35.80

2.19A+2.60G=35.80

2.19(20-G)+2.60G=35.80

43.8-2.19G+2.60G=35.80

43.8-0.41G=35.80

-0.41G=35.80-43.8

-0.41G=-8

Divide both sides by 0.41

G=19.51 pounds

Recall

A=20-G

A=20-19.51

A=0.49 pounds

They ordered 19.51 pounds of grapes.

let us say they ordered 'x' pound of grapes.

so, the quantity of apples ordered = (20-x) pound

it is given that

cost of the apple= $2.19 per pound

cost of the grapes= $2.60 per pound

according to the given scenario,

total cost = $35.80

the total cost will be the sum of the cost of apples as well as grapes.

2.60x + 2.19(20-x) =35.80

-0.41x = 8

x = -19.51 pounds

therefore, they ordered 19.51 pounds of grapes.

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Answer:

Z+12a−z+8+12−+8

Step-by-step explanation:

Z+8−6(z−2a)+5z

+8−6(−2)+5

Z+8−6(−2a+z)+5z

+8−6(−2+)+5

Z+8−6(−2a+z)+5z

+8−6(−2+)+5

Z+8+12a−z+8+12−

Answer:

Z + 8 + 12a − z

12a + 8

Step-by-step explanation: