Find the x and y intercepts of 10x-15y=30

Leah should stretch for 25 minutes during a 50-minute dance class, as she stretches for 5 minutes for every 10 minutes of dancing.

Leah stretches for 5 minutes for every 10 minutes of dancing. To calculate how much time she should be stretching during a 50-minute dance class, we need to apply a simple ratio. For every 10 minutes of dance, she stretches for 5 minutes, which is half the time spent dancing. We can set up the proportion as follows: 5 minutes of stretching / 10 minutes of dancing = X minutes of stretching / 50 minutes of dancing.

Now, solving for X gives us 5/10 = X/50, which simplifies to X = (5/10) × 50 = 25 minutes. Therefore, Leah should stretch for 25 minutes during her 50-minute dance class.

Answer: The required value of [tex]\log_{100}75[/tex] is 0.9375.

Step-by-step Explanation: Given that [tex]\log 75=1.875.[/tex]

We are to find the value of the following logarithm :

[tex]log_{100}75.[/tex]

We will be using the following properties of logarithm :

[tex](i)~\log_ba=\dfrac{\log a}{\log b}\\\\\\(ii)~\log a^b=b\log a.[/tex]

Therefore, we have

[tex]\log_{100}75\\\\\\=\dfrac{\log 75}{\log100}\\\\\\=\dfrac{1.875}{\log10^2}\\\\\\=\dfrac{1.875}{2\times\log10}\\\\\\=\dfrac{1.875}{2}~~~~~~~~~~~[since~\log10=1]\\\\\\=0.9375.[/tex]

Thus, the required value of [tex]\log_{100}75[/tex] is 0.9375.

The rate of change of the base of a triangle, given an increase of the altitude at 1 cm/min and an increase in area at 2 cm2/min, when the altitude is 10 cm and the area is 100 cm2, is 4 cm/min.

The subject of this question is related to the field of calculus, specifically dealing with determining the rate of change, or the derivative, of a function. We're asked to determine the rate at which the base of the triangle is changing when the altitude is 10 cm and the area is 100 cm2, given that the altitude of the triangle is increasing at a rate of 1 cm/ min and the area of the triangle is increasing at a rate of 2 cm2 / min.

We know that the area of a triangle is given by the formula 1/2 * base * height. When it comes to rates, we can differentiate this with respect to time t to get dA/dt = 1/2 * (base * dh/dt + height * db/dt) where dA/dt is the rate of change of the area, dh/dt is the rate of change of the height, and db/dt is the rate of change of the base.

Given that dA/dt = 2 cm2/min and dh/dt = 1 cm/min, and we are finding db/dt when the height is 10 cm and the area is 100 cm2, we substitute these values to solve for db/dt. This simplifies to find that the base is increasing at a rate of 4 cm/min.

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The value of given function f(7) is -1.8.

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range.

According to the given problem,

f(x) = [tex]\frac{3}{x + 5}- \sqrt{x - 3}[/tex]

At x = 7,

⇒ f(7) = [tex]\frac{3}{7 + 5} - \sqrt{7-3}[/tex]

⇒ f(7) = [tex]\frac{1}{4} - 2[/tex]

⇒ f(7) = [tex]-\frac{7}{4}[/tex]

⇒ f(7) = - 1.75

          ≈ -1.8

Hence, we can conclude, the value of function f(7) is -1.8.

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we have

[tex](x + 2)^{2}-9=-5[/tex]

Adds [tex]9[/tex] both sides

[tex](x + 2)^{2}-9+9=-5+9[/tex]

[tex](x + 2)^{2}=4[/tex]

square root both sides

[tex](x+2)=(+/-)\sqrt{4}\\(x+2)=(+/-)2\\x1=2-2=0 \\x2=-2-2=-4[/tex]

therefore

the answer is

the resulting equation is [tex](x+2)=(+/-)2[/tex]

Answer:  [tex](x+2) = \pm 2[/tex]

Step-by-step explanation:

If the given expression is,

[tex](x + 2)^2 - 9 = -5[/tex]

For solving this expression, By adding 9 on both sides,

[tex](x+2)^2 = 4 [/tex]

By taking square root on both sides,

[tex]\sqrt{(x+2)^2} = \sqrt{4}[/tex]

[tex]({(x+2)^2)^{\frac{1}{2} = \pm 2[/tex]                    [tex]( \text{ Because, }\sqrt{4} = \pm 2 \text { and }\sqrt{x} = x^{\frac{1}{2}})[/tex]

[tex]{(x+2)^{2\times \frac{1}{2} = \pm2[/tex]              [tex]((a^m)^n=a^{m\times n})[/tex]

[tex](x + 2) = \pm2[/tex]

Which is the required next step.

Equation, because Addison's candy is equal to 15 less than Ronny's candy.

i hope this help you

Answer:

Equation, because Addison's candy is equal to 15 less than Ronny's candy.

Step-by-step explanation:

After factored out a common factor in each term. Factor the simplified trinomial. Option c) is correct.

Step after the the third step when factoring the trinomial ax^2+bx+c to be determine.

Factors is are the sub multiples of the value.

Here,
After factored out a common factor in each term. The next step come is to factor the simplified term which implies taking common and kept in parenthesis.

Thus, after factored out a common factor in each term. Factor the simplified trinomial.

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The age of Mikhail's is 24 years old.

To find Mikhail's age, let's denote Mikhail's age as ( x ) and Gabrielle's age as ( 2x ) (since Gabrielle is twice as old as Mikhail). We know the sum of their ages is 72. We can set up an equation to represent this information:

[tex]\[ x + 2x = 72 \][/tex]

Step 1: Combine like terms

Combine the (x) terms on the left side of the equation:

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

So, the equation simplifies to:

[tex]\[ 3x = 72 \][/tex]

Step 2: Solve for ( x )

To find the value of ( x ), divide both sides of the equation by 3:

[tex]\[ x = \frac{72}{3} \][/tex]

[tex]\[ x = 24 \][/tex]

Therefore, Mikhail's age is 24 years old.

Mikhail's age is 24. Gabrielle is 48.

Let's solve it step by step:

1. Let's represent Gabrielle's age as [tex]\( G \)[/tex] and Mikhail's age as [tex]\( M \)[/tex].

2. According to the given information, Gabrielle's age is two times Mikhail's age, so we can express this as an equation:

  [tex]\[ G = 2M \][/tex]

3. We also know that the sum of their ages is 72, which can be expressed as another equation:

  [tex]\[ G + M = 72 \][/tex]

4. Now, we have a system of two equations:

  [tex]\[ G = 2M \][/tex]

  [tex]\[ G + M = 72 \][/tex]

5. Substitute the value of [tex]\( G \)[/tex] from the first equation into the second equation:

  [tex]\[ 2M + M = 72 \][/tex]

  [tex]\[ 3M = 72 \][/tex]

6. Divide both sides by 3 to solve for [tex]\( M \)[/tex]:

  [tex]\[ M = \frac{72}{3} \][/tex]

  [tex]\[ M = 24 \][/tex]

7. So, Mikhail's age is 24 years.

Now, to verify, we can find Gabrielle's age using the first equation:

[tex]\[ G = 2M \][/tex]

[tex]\[ G = 2(24) \][/tex]

[tex]\[ G = 48 \][/tex]

Gabrielle's age is indeed 48 years.

So, to recap, Mikhail's age is 24 years.

The method that can be used to find the volume of the house is:

 Add the volume of a rectangular prism to the volume of the triangular prism.

In order to find the volume of the house we need to find the volume of the bottom part of the house which in the shape of a rectangular prism or cuboid  and volume of the top of the house which is in the shape of a triangular prism.

        Hence, the total volume of the house is:

  Volume of rectangular prism+Volume of triangular prism.

Answer:

Option D is correct.

Step-by-step explanation:

Given Equation of plane is 7x + 2y + 3z = 42

We need to find ordered triplet where plane cuts the x-axis.

To find point of x-axis when plane cuts it. we put other coordinates equal to 0.

So, put y = 0 and z = 0 in equation plance to get x-coordinate of the required ordered triplet.

7x + 2 × 0 + 3 × 0 = 42

7x + 0 + 0 = 42

7x = 42

[tex]x=\frac{42}{7}[/tex]

x = 6

⇒ ordered triplet = ( 6 , 0 , 0 )

Therefore, Option D is correct.

To find and classify critical points of a two-variable function, calculate and set the first partial derivatives to zero to find critical points. Then, use the second derivatives to classify these points. The determinant of the Hessian matrix, made up of the second derivatives, contributes to this classification.

To find the critical points of the function F(x,y)=e^8x - x^2 + 8y - y^2, you first need to find the partial derivatives F_x and F_y and set them both equal to zero.

F_x = 8e^8x - 2x and F_y = 8 - 2y. By setting these equal to zero and solving for x and y, you will find the critical points.

Once the critical points are found, we classify them using the second derivative test. This involves computing the second partial derivatives F_xx, F_yy, and F_xy, and evaluating them at the critical points.

Finally, we calculate the determinant D of the Hessian matrix, composed of the second derivatives, at the critical points. The signs and values of these results and the determinants help classifying the critical points.

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since cone B is bigger it needs to weigh more than 20 lbs.

 5/13 = 20/X

x=52 LBS

Final answer:

The volume of a right circular cone with a radius of 4 inches and a height of 12 inches is calculated using the formula V = (1/3)πr²h, resulting in a volume of 64π cubic inches.

Explanation:

The question asks to find the volume of a right circular cone with a specific radius and height. To calculate the volume of a cone, you use the formula V = (1/3)πr²h, where V is the volume, r is the radius, and h is the height of the cone. Since we're given the radius as 4 inches and the height as 12 inches, we substitute these values into the formula: V = (1/3)π(4²)(12).

Carrying out the calculation, we have V = (1/3)π(16)(12) = (1/3)π(192) = 64π inches³. Therefore, the volume of the cone is 64π cubic inches.

area = PI x r^2

 r = 20/2 = 10

3.14 x 10^2 = 314 square units