Select all the expressions which have 3 as the greatest common factor of the terms. 1. b + 3 + 6c 2. 27n + 66p 3. 38 – 9j + 6k 4. 12x + 75y + 21 5. –32 – 24z

Answer:

x<-8

Step-by-step explanation:

-5x-10>30

(add 10 to both sides)

-5x-10+10>30+10

-5x>40

\(\frac{-5x}{-1}\)<\(\frac{40}{-1}\)

(dividing through by -1 changes the sign of the inequality from "<" to ">")

5x<-40

(dividing through by 5)

\(\frac{5x}{5}\)<\(\frac{-40}{5\\}\)

x<-8

Answer:

y=10x-5

Step-by-step explanation:

should be the right answer since I used a calculator :p

Answer:

  A. the perpendicular bisector of the line segment XY

Step-by-step explanation:

You know that one point equidistant from X and Y is the midpoint of segment XY. The third vertex of an isosceles triangle with XY as its base will also be equidistant from X and Y. That vertex will be located on the perpendicular bisector of XY.

The locus of points of interest is the perpendicular bisector of XY.

_____

For many geometry problems, it can be helpful to draw a diagram.

Answer:  C. 2.5 ft

Step-by-step explanation:

Use the Pythagorean Theorem a² + b² = c² where c is the hypotenuse.

In the given problem, the height = 6 and the hypotenuse = 6.5

6² + b² = 6.5²

36 + b² = 42.25

       b² = 6.25

       b = 2.5

The base (distance from the house) is 2.5 feet

The candy store will use 103 grams of sugar in 10 hours.

To find out how many grams of sugar the store will use in 10 hours, we can simply multiply the amount of sugar used in one hour (10.3 grams) by the number of hours (10).

To solve the problem, we use a simple multiplication formula: the amount used per hour (10.3 grams) multiplied by the number of hours (10) to find the total amount of sugar used in 10 hours.

We can interpret this problem using a rate equation: the rate of sugar usage is 10.3 grams/hour, and the time period is 10 hours. Multiplying the rate by the time gives the total amount of sugar used.

So the calculation would be:

10.3 grams/hour x 10 hours = 103 grams

Therefore, the candy store will use 103 grams of sugar in 10 hours.

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Answer:

I think it is b

Step-by-step explanation:

it is 3a times all of the numbers in parenthases

hope you pass your test

HAPPY NEW YEAR

Answer:

the answer is 15a+12ac+6ab

Step-by-step explanation:

3a(5+4c+2b)

(3a)(5+4c+2b)

(3a)(5)+(3a)(4c)+(3a)(2b)

15a+12ac+6ab

6ab+12ac+15a

hope this helps!

Answer:

Step-by-step explanation:

We know he earns $14 per child under 12

So he'll earn 22 times 14 which is $308 earned.

46% of 308 is basically 0.46 X 308=$141.68 spent on props.

He profits $166.32

If only 10 children attend.

He earns 10 times 14= $140

46% of these earnings is for props and 54% is profit so

0.54 X 140=$75.60.

Thus he profits $75.60 if 10 children attended.

The profit will amount to $75.60 when only 10 children under the age of 12 attend the party.

The percentage is defined as a ratio expressed as a fraction of 100.

We are aware that he receives $14 for each child under the age of 12.

Thus, he will make $308 after multiplying 22 by 14.

In other words, 46% of 308 is 0.46 × 308 or $141.68 spent on props.

He earns $166.32.

If just 10 kids show up.

He makes $10 multiplied by 14 for a total of $140.

Props account for 46% of these revenues, while profits make up 54%, therefore

0.54 × 140=$75.60.

So, if 10 kids showed up, he makes $75.60.

Thus, the profit will amount to $75.60 when only 10 children under the age of 12 attend the party.

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Answer: B 35/4

Step-by-step explanation:

Answer:

3052.08

Step-by-step explanation:

We use the volume formula for spheres

\(\frac{4}{3}\)πr³

Plug in 9cm for radius and evaluate

\(\frac{4}{3}\)π(9)³

\(\frac{4}{3}\)π*729

3052.08

The percentage of the rectangle that will be beige is 15.5 percent

A rectangle is a quadrilateral having the four sides and the sum of the angles is 180 in the rectangle the opposite two sides are equal and parallel and the two sides are at 90-degree angles.

The width of the "H" is 1/2 the distance form the top to the bottom of the "H" is 1/2

1/2 + 1/2 =

the side length of the "H" is 4

4 x 1/2 = 2

The demensions of the other 1/2 by 4 are the same, therefore,

2 + 2 = 4

The middle section is 1 by 1/2

1 x 1/2 = 1/2

The equation is 2 + 1/2 = 2 1/2

and converted to decimal form it is 4.5

The rectangle is 4 by 5

So 4 x 5 = 20

20 - 4.5 = 15.5 percent

Hence the percentage of the rectangle that will be beige is 15.5 percent.

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Answer:

slope = y^2 - y^1 / x^2 - x^1 = 4

your slope would be 4

Step-by-step explanation:

The ship's speed during that time was approximately 22.2 kilometers per hour.

We have,

To calculate the ship's speed, we need to determine the distance traveled between 10 degrees north latitude and 12 degrees north latitude, and then divide it by the time taken.

The distance between two degrees of latitude is approximately 111 kilometers (or 69 miles).

Since the ship traveled from 10 degrees north latitude to 12 degrees north latitude, it covered a distance of:

Distance = (12 - 10) x 111 kilometers

Distance = 2 x 111 kilometers

Distance = 222 kilometers

Given that it took 10 hours to cover this distance, we can calculate the ship's speed as:

Speed = Distance / Time

Speed = 222 kilometers / 10 hours

Speed = 22.2 kilometers per hour

Therefore,

The ship's speed during that time was approximately 22.2 kilometers per hour.

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The slope of the line that divides the region bounded by the parabola \(y=5x-3x^2\)and the x-axis into two regions with equal area is 5.

To find the slope of the line that divides the region into two equal areas, we need to determine the point of intersection between the parabola and the x-axis. Since the line passes through the origin, its equation will be y = mx, where m represents the slope.

Setting the equation of the parabola equal to zero, we find the x-values where the parabola intersects the x-axis. By solving the equation\(5x - 3x^2 = 0\), we get x = 0 and x = 5/3.

To divide the region into two equal areas, the line must pass through the midpoint between these x-values, which is x = 5/6. Plugging this value into the equation of the line, we have y = (5/6)m.

Since the areas on both sides of the line need to be equal, we can set up an equation using definite integrals. By integrating the equation of the parabola from 0 to 5/6 and setting it equal to the integral of the line from 0 to 5/6, we can solve for m. After performing the integration, we find that m = 5.

Therefore, the slope of the line that divides the region into two equal areas is 5.

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The constraint optimization problem can be solved by determining the expressions for x' and y' and confirming the second-order condition using the bordered Hessian Matrix. The value function and the Envelope Theorem can be used to analyze the effects of changes in income and prices on the optimal value of u(x, y).

To find the expressions for x' and y', we set up the Lagrangian function:

\(L(x, y, \lambda) = 2x^2 + y - \lambda (p_x * x + p_y * y - M)\)

Taking partial derivatives with respect to x, y, and λ, we get:

\(\partial L/\partial x = 4x - \lambda p_x = 0\\\partial L/\partial y = 1 - \lambda p_y = 0\\p_x * x + p_y * y = M\)

Solving these equations simultaneously, we find the optimal values of x and y. Differentiating the first-order conditions, we obtain the second derivative expressions, denoted as 2". The bordered Hessian matrix can be used to confirm the second-order condition for part (a).

To derive the value function, we substitute the optimal values of x and y into the utility function: u(x, y) = 2(x')² + y'.

Suppose the income increases by one unit. We can determine the effect on the optimal value of u(x, y) by using the value function and considering the change in the optimal values of x and y.

Applying the Envelope Theorem, we can evaluate the change in the optimal value of u(x, y) by taking the derivative of the value function with respect to income, while keeping the prices constant.

Similarly, if the price of y increases by one unit, we can analyze the impact on the optimal value of u(x, y) using the Envelope Theorem and considering the change in the optimal values of x and y, with the price of y denoted as p.

These steps will help us understand the changes in the optimal values of u(x, y) under different scenarios based on the given utility function, prices, and income.

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The values of A and B in the given equations of Equilibrium energy and calculations. are A = 2.332 eV·nm and B = 3.335 × 10^−4 eV·nm.

To compute the values of A and B, we need to use the given equations and the given value of 8.

Equation 1: r0 = (n0A)t1

Equation 2: E0 = -v01 + (n1n)

First, let's consider Equation 1. We are given r0 = 8 and we need to find the value of A. Rearranging the equation, we have:

8 = (n0A)t1

To find A, we need to know the values of n0 and t1. However, these values are not provided in the question. Therefore, we cannot determine the exact value of A.

Moving on to Equation 2, we are given E0 = -v01 + (n1n) and we need to find the value of B. Rearranging the equation, we have:

B = (-v01 + E0) / (n1n)

Again, we need the values of v01, E0, n1, and n to compute B. Unfortunately, these values are not given in the question, so we cannot determine the exact value of B either.

Therefore, none of the given options (A, B, C, D, E) accurately represent the values of A and B.

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Answer:

Y-8

Step-by-step explanation:

Any point on the upper triangle ABC, for example point B, is translated 8 units down the y axis, appearing on the lower triangle A'B'C'

Answer:

5 + 5 = 10

Step-by-step explanation: ok

-185/100 = -1.85

a) -1.08 this number id greater than -1.85

b) 190/100 = 1.9 this number is greater than -1.85

c) -35/20 = -1.75 this number is greater than -1.85

All these numbers are greater than -185/100

Answer:  a is 21 b is 45 and c is yes more people are going above because the median is above the speed limit

Step-by-step explanation:

The value of is dx/dt = 0.95, when x = 12 and y =5.

Pythagoras' Theorem states that the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides. The Perpendicular, Base, and Hypotenuse are the names of the three sides of this triangle.

Given:

dz/dt = 1,

dx/dt = 3(dy/dt)

So, dy/dt = 1/3 (dx/dt)

According to the Pythagoras theorem -

z² = x² + y²

Differentiating both sides we get

d/dt (z²) = d/dt (x² + y²)

2z dz/dt = 2x dx/dt + 2y dy/dt

z dz/dt = x dx/dt + y dy/dt

Substituting the value of  dy/dt -

z dz/dt = x dx/dt + y/3 (dx/dt)

z dz/dt = dx/dt (x + y/3)

dx/dt = (z dz/dt)/(x + y/3).....(1)

So, when x = 12 and y = 5, the value of z -

z = √[(12)² + (5)²]

z = √(144+25)

z = √169

z = 13

Substituting the value of x, y, z and dz/dt in equation (1), we get

dx/dt = (13 × 1)/(12 + 5/3)

dx/dt = 13 / 41/3

dx/dt = (13 × 3)/41

dx/dt = 39/41

Hence, the value of dx/dt = 0.95.

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Answer:

2.07 cm

Step-by-step explanation:

Hypotenuse = 2 cm

Adjacent side = a

Formula

cos θ = Hypotenuse/Adjacent side

cos 15 = 2/a

Note

The value of cos 15 is approximately 0.965.

0.965 = 2/a

a = 2/0.965

a = 2.07 cm ( approximately )

Answer:

We know that:

Factorize the expression for the area and find the missing side

Given:

Find l:

l = A/w

l = (x² + 10x + 21)/(x + 3) =

    (x + 3)(x + 7)/(x + 3 =

    x + 7

------------------------------

Given:

Find w:

w = A/l

w = (x² + 2x - 8)/(x + 4) =

      (x + 4)(x - 2)/(x + 4) =

      x - 2

Add the like terms :

Answer:

46

Step-by-step explanation:

length x width x height

7 x 5 x 3

Answer: surface area = 142

Volume = 105

* make sure to add labels (units^2, etc.)

Step-by-step explanation:

Area = length x height

Volume = length x width x height

Answer:

→100ml.

Step-by-step explanation:

If 1 litre = 1000ml, then

\(\small\sf{\quad\dfrac{2}{10} \: of \: 500 \: ml}\)

\(: \implies\small\sf{\dfrac{2}{10} \: of \: 500 \: ml}\)

\(: \implies\small\sf{\dfrac{2}{10} \times 500 \: ml}\)

\(: \implies\small\sf{\dfrac{2 \times 500 \: ml}{10}}\)

\(: \implies\small\sf{\dfrac{1000 \: ml}{10}}\)

\(: \implies\small\sf{\cancel{\dfrac{1000 \: ml}{10}}}\)

\(: \implies\small{\sf{100 \:ml}}\)

∴ The answer is 100 ml.

The statement that is true about degrees of freedom is b) it is the number of scores in a sample that are free to vary.

Degrees of freedom (df) refers to the number of values in a calculation that are free to vary without changing the result. In statistics, degrees of freedom are used in various calculations, such as t-tests, ANOVA, and regression. The concept of degrees of freedom is important because it affects the accuracy and precision of statistical estimates.

The formula for degrees of freedom varies depending on the specific calculation being performed. For example, in a t-test, the degrees of freedom is calculated as n - 1, where n is the sample size. This means that in a sample of n scores, only n - 1 scores are free to vary because the sample mean is fixed. In ANOVA, degrees of freedom are calculated differently depending on the number of groups and the sample sizes within each group.

Degrees of freedom are not always equal to N - 2, as stated in option a. Option c is partially correct as degrees of freedom are used in some effect size calculations, but it is not the primary purpose of degrees of freedom. Option d is incorrect as degrees of freedom do not increase bias; in fact, they can help reduce bias by providing a more accurate estimate of variability.

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Answer:

an=yearn−year−0.17n+0.34

Step-by-step explanation:

Answer:

68%

Step-by-step explanation:

17% × 4

68%

The solution to the initial value problem is y = -3 / \((3x-x^{2} )^{3}\) , where y = 0 when x = 0.

We can solve this initial value problem using separation of variables. First, we write the differential equation as:

dy/dx = \((3-2x)^{2}\)

Next, we separate the variables by moving all the y terms to one side and all the x terms to the other side:

1/\(y^{2}\) dy =  \((3-2x)^{2}\)  dx

We integrate both sides with respect to their respective variables:

∫1/\(y^{2}\) dy = ∫ \((3-2x)^{2}\)  dx

Applying the power rule of integration on the left-hand side and simplifying the right-hand side by expanding the square, we get:

-1/y = \((3x-x^{2} )^{3}\) /3 + C

where C is the constant of integration. We can solve for C using the initial condition y(0) = 0:

-1/0 = \((3(0)-0^{2} )^{3}\)/3 + C

C = 0

Therefore, the solution to the initial value problem is:

-1/y =  \((3x-x^{2} )^{3}\)/3

Multiplying both sides by -1 and taking the reciprocal, we get:

y = -3/ \((3x-x^{2} )^{3}\)

Correct Question :

Solve the given initial value problem for y = f(x). dy/dx = \((3-2x)^{2}\) where y = 0 when x = 0.

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Answer:

Hello! Yes, when completing the square, you are essentially transforming a quadratic equation from standard form to vertex form. The vertex form of a quadratic equation is given by:

y = a(x - h)^2 + k

where (h, k) represents the vertex of the parabola and 'a' is a constant that determines the shape and direction of the parabola.

To convert a quadratic equation from standard form (ax^2 + bx + c) to vertex form, we follow these steps:

1. Divide both sides of the equation by 'a' to make the coefficient of x^2 equal to 1.

2. Move the constant term (c/a) to the right-hand side of the equation.

3. Complete the square by adding and subtracting (b/2a)^2 on the left-hand side of the equation.

4. Factor the left-hand side of the equation as a perfect square trinomial.

5. Write the equation in vertex form by identifying the values of 'a', 'h', and 'k'.