Find an equation of the circle whose diameter has endpoints ( −1,−4) and (3,2) .

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.

To learn more about function here

https://brainly.com/question/13581879

#SPJ2

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.

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.

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.

The slope of a line perpendicular to another line has a slope which is the negative reciprocal of that line or:

m1 = -1/m2

First, we convert the given equation into slope-intercept form of a line: y = mx + b

8x + 15y = 12

15y = -8x + 12

y = (-8/15) x + 0.8

m1 = -8 / 15

Therefore the slope of the perpendicular line is:

m2 = 15 / 8

Since the perpendicular line crosses the point (11, 17), therefore using the slope formula:

m = (y2 – y1) / (x2 – x1)

15 / 8 = (y2 – 17) / (x2 – 11)

1.875 (x2 – 11) = y2 – 17

1.875 x2 – 20.625 = y2 – 17

y2 = 1.875 x2 – 3.625

y = (15/8) x – 3.625

multiplying both sides by 8:

8y = 15x – 29

rewriting in standard form:

15x – 8y = 29                (ANSWER)

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.

area = PI x r^2

 r = 20/2 = 10

3.14 x 10^2 = 314 square units

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.

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.

Learn more about factors here:

https://brainly.com/question/24182713

#SPJ2

4 * 1.5 = 6 cm <== Because this is the answer.

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

 5/13 = 20/X

x=52 LBS

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 guarantee two pairs, a player must pick at least 14 cards from a deck of 52 playing cards without replacement. For three of a kind, a minimum of 16 cards is required. This is an example of sampling without replacement, where each selection affects subsequent draws.

To determine the minimum number of cards one must pick from a standard deck of 52 playing cards to guarantee getting two pairs, consider the worst-case scenario where you pick one card of each rank before getting any pair. Since there are 13 different ranks, picking 13 single cards wouldn't guarantee a pair, but the 14th card will definitely match one of the previously drawn ranks, thus forming a pair. To ensure two pairs, you could go through another 13 cards without getting a match to your first pair, so the 15th card would be the second pair. Therefore, you must pick at least 14 cards to guarantee two pairs.

For three of a kind, you pick sequentially from the different ranks. After picking one card of each of the 13 ranks, the 14th card will form a pair, and the 15th card could potentially be of a new rank. However, the 16th card drawn must either create a pair with another rank or a 'three of a kind' with the rank that already has two. Thus, the minimum number of cards one must pick to guarantee a three of a kind is 16.

In sampling without replacement, drawn cards are not returned to the deck, making each draw dependent on the previous ones. This contrasts with sampling with replacement, where each draw is independent since cards are returned to the deck and reshuffled after each pick.

Mr. Brown should increase the monthly rent by $2.25 to cover the additional annual property tax caused by the tax rate increase from $25 to $28 per $1000 assessed valuation on a $9000 house.

The student is asking for a calculation of how much the monthly rent of a house should be increased to cover the additional property tax imposed when the tax rate was increased from $25 to $28 per $1000 assessed valuation. The house is valued at $9000.

First, we calculate the initial annual tax by multiplying the assessed valuation by the initial tax rate:

Initial annual tax = $9000 / 1000 times $25 = $225

Then we calculate the new annual tax with the increased rate:

New annual tax = $9000 / 1000 times $28 = $252

The increase in the annual tax amount is:

Increased tax amount = New annual tax - Initial annual tax = $252 - $225 = $27

To find the monthly increase, we divide by 12:

Monthly rent increase = Increased tax amount / 12 = $27 / 12 = $2.25

Therefore, the monthly rent should be raised by $2.25 to absorb the increase in that year's taxes.