In a pet shop, there are 3 hamsters for every 2 guinea pigs, and there are 2 giant cloud rats for every 3 guinea pigs. If n is the total number of hamsters, guinea pigs, and giant cloud rats, and n>0, then what is the smallest possible value of n?

Answer:

log[3(x+4)] is equal to log(3) + log(x + 4), which corresponds to choice number three.

Step-by-step explanation:

By the logarithm product rule, for two nonzero numbers [tex]a[/tex] and [tex]b[/tex],

[tex]\log{(a \cdot b)} = \log{(a)} + \log{(b)}[/tex].

Keep in mind that a logarithm can be split into two only if the logarithm contains the product or quotient of two numbers.

For example, [tex]3(x + 4)[/tex] is the number in the logarithm [tex]\log{[3(x + 4)]}[/tex]. Since [tex]3(x + 4)[/tex] is a product of the two numbers [tex]3[/tex] and [tex](x + 4)[/tex], the logarithm [tex]\log{[3(x + 4)]}[/tex] can be split into two. By the logarithm product rule,

[tex]\log{[3(x + 4)]} = \log{(3)} + \log{(x + 4)}[/tex].

However, [tex]\log{(x + 4)}[/tex] cannot be split into two since the number inside of it is a sum rather than a product. Hence choice number three is the answer to this question.

Answer:

c

Step-by-step explanation:

Answer:

(0, 3 , -2)

Step-by-step explanation:

X-y+2z=-7  ------------------ equ 1

y+z=1            ------------------ equ 2

x-2y-3z=0      ------------------ equ 3

 equ 1                   X -  y + 2z = -7

equ 3                    x - 2y - 3z = 0

                           -     + __+_____

equ 1 - equ 3 ⇒      y    + 5z = -7  -------------- equ 4

equ 2                 y + z   = 1      

equ 4                 y + 5z = -7

                          -   -      = +

equ 2 - equ 4       -4z =8

                                z = 8/ -4 = -2

Put z = -2 in equ 2,

                            y + z   = 1      

                            y - 2 = 1

                               y = 1 + 2 =3

                          y = 3

Put z = -2 & y = 3 in equ 1

                     X -  y + 2z = -7

                x  - 3 + 2* (-2) = -7

                       x  - 3 - 4  = -7

                              x -7   = -7

                                    x  = -7 + 7  =0

                   x = 0

To solve the system of equations, you can use the method of substitution or elimination. Let's use the method of substitution to find the solution. First, solve for y in the second equation and substitute this value into the other equations. Simplify and solve the resulting equations to find the values of x and z.

To find the solution to the given system of equations:

x - y + 2z = -7

y + z = 1

x - 2y - 3z = 0

You can use the method of substitution or elimination to solve the system. Let's use the method of substitution.

https://brainly.com/question/29050831

#SPJ3

Answer:

The answer is B. 20in.

Step-by-step explanation:

The parallel sides have to be the two bases (b1 and b2) = 80in.  

h = height or altitude.  

h = 2(800)/b1+b2  

h = 1600/80  

h = 20 in.

Answer:

The height of the Trapezoid is 20 inches

Step-by-step explanation:

Given Parameters

Shape: Trapezoid

Area of the Trapezoid = 800in²

Sum of opposite parallel sides = 80 in

Required: Height of the Trapezoid...

Are of trapezoid is calculated using the following formula:

A = ½(a + b) * h

Where a + b = sum of the opposite parallel sides

h = height.

A = Area.

By comparison, we have that

A = 800 in²

a + b = 80 in

By substituton, we have that

A = ½(a + b) * h becomes

800 = ½(80)h

800 = ½ * 80 * h

800 = 40 h---- divide through by 40

800/40 = 40h/40

20 = h --- reordsr

h = 20in

Hence, the height of the Trapezoid is 20 inches

Answer:

(5,7)

Step-by-step explanation:

4x+y=27

5x-y=18

Since we want to solve this by elimination we need the lines to be in the same form, and a column with opposite variables or same variables. We actually have both of these.

Both equations are in the form ax+by=c.

The column that contains the y's, we have opposites there. That is the opposite of y is -y.  When you add opposites, you get 0.

So we just add vertically now.

4x+y=27

5x-y=18

--------------Add

9x+0=45

9x    =45

Divide both sides by 9:

x      =45/9

Simplify:

x       =5

Now to find y, you just need to use one of your equations (just pick one) along with x=5.

I guess I will choose 4x+y=27 with x=5.

4x+y=26 with x=5

4(5)+y=27

20+y=27

Subtract 20 on both sides:

y=27-20

y=7

So the solution (x,y) is (5,7).

Answer:

Prime

Step-by-step explanation:

x² + 25 is prime (unfactorable).

Here's what the other options come out to:

(x + 5)(x + 5) = x² + 10x + 25

(x + 5)(x − 5) = x² − 25

(x − 5)(x − 5) = x² − 10x + 25

The correct option is option D: x²+25 is prime.

The algebraic expressions are factorized by taking common factors from the terms and using algebraic properties like a²-b²=(a+b)(a-b), (a+b)²=a²+2ab+b², etc.

The expression which can not be factorized is called prime i.e. unfactorizable.

Here x²+25 is unfactorizable so it is prime.

Also by checking each option

Therefore x²+25 is prime.

Learn more about factorization

here: https://brainly.com/question/25829061

#SPJ2

Answer:

(-1, -1)

Step-by-step explanation:

[tex]\boxed{midpoint=(\frac{x_{1} +x_{2} }{2} ,\frac{y_{1}+y_{2} }{2}) }[/tex]

Midpoint of line segment

[tex]= (\frac{1-3}{2},\frac{-6+4}{2} )\\= (\frac{-2}{2},\frac{-2}{2})\\= (-1, -1)[/tex]

Answer:

13

Step-by-step explanation:

(f∘g)(4) is another way of writing f(g(4)).

First, find g(4).

g(x) = 2x − 3

g(4) = 2(4) − 3

g(4) = 5

Now substitute into f(x).

f(x) = 4x − 7

f(g(4)) = 4g(4) − 7

f(g(4)) = 4(5) − 7

f(g(4)) = 13

[tex](f\circ g)(x)=4(2x-3)-7=8x-12-7=8x-19\\\\(f\circ g)(4)=8\cdot4-19=13[/tex]

Answer:

-77 if I understand correctly

Step-by-step explanation:

If the domain is really {-4} and you have the function f(x)=-5x^2+3.

The range is just whatever the result of f(-4) is...

f(-4)=-5(-4)^2+3

f(-4)=-5(16)+3

f(-4)=-80+3

f(-4)=-77

So again if the question is really "The function f(x)=-5x^2+3 is defined over the domain {-4}, what is the range?"... then the answer is just {-77}

Answer:

[tex]\large\boxed{y-5=-4(x-3)}\\\boxed{y-8=\dfrac{1}{2}(x+1)}[/tex]

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

[tex]m=-4,\ (3,\ 5)\\\\y-5=-4(x-3)[/tex]

[tex]m=\dfrac{1}{2},\ (-1,\ 8)\\\\y-8=\dfrac{1}{2}(x-(-1))\\\\y-8=\dfrac{1}{2}(x+1)[/tex]

Answer:

[tex]\large\boxed{m=\dfrac{49}{8}}[/tex]

Step-by-step explanation:

[tex]\dfrac{7}{8}:m=\dfrac{1}{7}\\\\\dfrac{7}{8}\cdot\dfrac{1}{m}=\dfrac{1}{7}\\\\\dfrac{7}{8m}=\dfrac{1}{7}\qquad\text{cross multiply}\\\\(8m)(1)=(7)(7)\\\\8m=49\qquad\text{divide both sides by 8}\\\\m=\dfrac{49}{8}[/tex]

Final answer:

The algebraic expression for the reduced price of the game system is p - $99, where p represents the original price in dollars.

Explanation:

To express the reduced price of the game system algebraically, we start with the original price, represented by the variable ( p ), and subtract the reduction amount of $99. Mathematically, this can be represented as p - $99.

This expression signifies that we are taking the original price ( p ) and reducing it by $99 to find the new price after the discount. It's essential to understand that algebraic expressions provide a concise and general way to represent mathematical relationships.

In this case, the expression p - $99 encapsulates the idea of reducing the original price by $99, allowing us to calculate the reduced price for any given original price represented by the variable ( p ). This algebraic representation is flexible and can be applied to various scenarios involving discounts or reductions.

Answer:

It is 132 just took it

Step-by-step explanation:

Each of the pairs of opposite angles made by two intersecting lines is called a vertical angle. The measure of ∠AOE is 132°. The correct option is B.

Each of the pairs of opposite angles made by two intersecting lines is called a vertical angle.

In circle O, AD and BE are diameters. Also, the measure of ∠EOD and ∠AOB will be equal because the two angles are vertically opposite angles. Therefore,

∠EOD = ∠AOB = 3x

As it is given that the measure of ∠AOC is 90°. Therefore, we can write,

∠AOC = ∠AOB + ∠BOC

90 = 3x + 0.5x + 34

56 = 3.5x

x = 16

Now, the measure of ∠EOD will be,

∠EOD = 3x

∠EOD = 3(16°)

∠EOD = 48°

Further, we can write,

∠AOD = ∠AOE + ∠EOD

180° = ∠AOE + 48°

∠AOE = 132°

The complete question is mentioned in the below image.

Learn more about Vertical Angles:

https://brainly.com/question/24460838

#SPJ2

Answer:

Answer in factored form (3x+10)(2x+6)

Answer in standard form 6x^2+38x+60 ( I bet you they want this answer)

Step-by-step explanation:

The assumption is this is a rectangle.

If you have the dimensions of a rectangle are L and W, then the area is equal to L times W.

So here we just need to multiply (3x+10) and (2x+6).

The answer in factored form is (3x+10)(2x+6).

I bet you they want the answer in standard form.

So let's use foil.

First: 3x(2x)=6x^2

Outer: 3x(6)=18x

Inner: 10(2x)=20x

Last: 10(6)=60

----------------Add up!

6x^2+38x+60

The area of the window is 3x² + 19x + 30

The dimension of the window are  3x + 10 and 2x + 6.

The area of the window can be calculated as follows;

area = lw

Therefore,

area = (3x + 10)(2x + 6)

area = 6x² + 18x + 20x + 60

area = 6x² + 38x + 60

area  = 3x² + 19x + 30

read more: https://brainly.com/question/3518080?referrer=searchResults

Answer:

12 pounds

Step-by-step explanation:

After trimming:

50 − 0.40 (50) = 0.60 (50) = 30

After cooking:

30 − 0.60 (30) = 0.40 (30) = 12

Answer:

C III

Step-by-step explanation:

The rate of change of a linear function is the slope.

f(x) = mx + b is the equation of a linear function whose graph is a straight line. m is the slope.

I f(x) = 4x - 3;   m = slope = 4

II f(x) = 1/2 x + 5;   m = slope = 1/2

III We can use two points to find the slope.

Let's use points (1, 6) and (2, 12).

m = slope = (y2 - y1)/(x2  x1) = (12 - 6)/(2 - 1) = 6/1 = 6

The three slopes are 4, 1/2, 6.

The greatest rate of change is 6, so the answer is C III.

as you may already know, the inverse of a function has the same exact x,y pairs but backwards, namely f(x)'s domain is f⁻¹(x)'s range.

[tex]\bf \stackrel{f(x)}{\begin{array}{|cc|ll} \cline{1-2} \stackrel{domain}{x}&\stackrel{range}{y}\\ \cline{1-2} 3&4\\ 4&3\\ -2&6\\ \cline{1-2} \end{array}}~\hspace{10em} \stackrel{inverse~of~f(x)}{\begin{array}{|cc|ll} \cline{1-2} \stackrel{domain}{x}&\stackrel{range}{y}\\ \cline{1-2} 4&3\\ 3&4\\ 6&-2\\ \cline{1-2} \end{array}}[/tex]

Answer:

By 2.

Step-by-step explanation:

You need to eliminated the x-terms, so the first step is to focus only in those terms.

So yo have 4x and -2x, since you are thinking in eliminate then you have this equation>

[tex]4-2*K=0[/tex]

Note that we dont put the x variable, since we are studying its coefficients in the equations system.

Solving for K, Gives us that K=2

So.

Multiplying the second equation by 2 results in

[tex]-4x+6y=8[/tex]

When you put them together, it gives you the following

[tex]4x-9y -4x+6y- 7+8[/tex]

and the final equation is

[tex]-3y=15\\[/tex]

giving you the answer for y, that is [tex]y=-5[/tex]

Answer: 2 and 3.

Step-by-step explanation:

Answer:

12 and 8

Step-by-step explanation:

set two numbers as x and y

mean of 10   →   x+y/2=10

range of 4    →   x-y=4

     x+y=20

+    x-y=4

____________

      2x=24, x=12  

      12-y=4, y=8        

Answer:

the answer is 8 and 12 hope it helps

Step-by-step explanation:

Answer:

Plane B was farthest away from the airport

Step-by-step explanation:

This question requires you to visualize the run way as the horizontal distance to be covered, the height from the ground as the height gained by the plane after take of and the distance from the airport as the displacement due to the angle of take off.

In plane A

The take-off angle is 44° and the height gained is 22 ft.

Apply the relationship for sine of an angle;

Sine Ф°= opposite side length÷hypotenuse side length

The opposite side length is the height gained by plane which is 22 ft

The angle is 44° and the distance the plane will be away from the airport after take-off will be represented by the value of hypotenuse

Applying the formula

sin Ф=O/H where O=length of the side opposite to angle 44° and H is the hypotenuse

[tex]Sin44=\frac{O}{H} \\\\\\Sin44=\frac{22}{H} \\\\\\H=\frac{22}{sin44deg} \\\\\\H=31.67[/tex]

31.67 miles

In plane B

Angle of take-off =40°, height of plane=22miles finding the hypotenuse

[tex]sin40deg=\frac{O}{H} \\\\\\sin40deg=\frac{22}{H} \\\\\\H=\frac{22}{sin40deg} \\\\\\H=34.23miles[/tex]

34.23miles

Solution

After take-off and reaching a height of 22 ft from the ground, plane A will be 31.67 miles from the airport

After take-off and reaching a height of 22 ft from the ground, plane B will be 34.23 miles away from the airport.

Answer:

9.33 (flvs)

Step-by-step explanation:

i took the test

Answer:  The correct option is (A) SAS.

Step-by-step explanation:  We are given to select the method that would be used to prove that the two triangles are congruent.

Let us name the given triangles as ABC and EBD as shown in the attached figure below.

Then, according to the given information, we have

[tex]AB=BD\\\intertext{and}\\BC=EB.[/tex]

Also, ∠ABC and ∠EBD are vertically opposite angles, so they must have equal measures.

That is,

[tex]m\angle ABC=m\angle EBD.[/tex]

So, in triangles ABC and EBD, we have

[tex]AB=BD,\\\\BC=EB\\\\\intertext{and}\\m\angle ABC=m\angle BED.[/tex]

That is, two sides and the included angle of one triangle are congruent to the corresponding two sides and the included angle of the other triangle.

Therefore, by side-angle-angle postulate, the two triangles are congruent.

Thus,

ΔABC ≅ ΔEBD (SAS postulate).

Option (A) is CORRECT.

Answer:

2/12

Step-by-step explanation:

Rolling a 5 on one die the probability is 1 out of 6 or 1/6 so when you add the second die the probability increases as well as the number of outcomes so you have 1/6+1/6 or 2/12. hope this helps

Answer:

1/36

Step-by-step explanation:

A cube has six sides.  On number cubes (also called dice), the sides are numbered 1 through 6.  So the probability of rolling a 5 on either cube is 1/6.  The probability of rolling a 5 on both cubes is:

P(A and B) = P(A) × P(B)

P(A and B) = 1/6 × 1/6

P(A and B) = 1/36

Answer:-11x+6

Step-by-step explanation:

(-7x+1)-(4x-5)

collect the like terms and then calculate the sum

-7x+1-4x+5

-11x+1+5

-11x+6

Answer:

-11x +6​

Step-by-step explanation:

(- 7x + 1) - (4x - 5)​

Distribute the minus sign

(- 7x + 1) - 4x + 5

Combine like terms

-11x +6​

Answer:

C.  6√2.

Step-by-step explanation:

Since this is a right angled isosceles triangle bot legs are 6 units long

So h^2 = 6^2 + 6^2 = 72

h = √72 = 6√2.

Answer:

The correct option is C) 6√2.

Step-by-step explanation:

Consider the provided triangle.

The provided triangle is a right angle triangle, in which two angles are 45° and one is 90°.  

As both angles are equal there opposite side must be equal.

Thus, the leg of another side must be 6.

Now find the hypotenuse by using Pythagorean theorem:

[tex]a^2+b^2=c^2[/tex]

Substitute a = 6 and b = 6 in [tex]a^2+b^2=c^2[/tex].

[tex](6)^2+(6)^2=(c)^2[/tex]

[tex]36 + 36=(c)^2[/tex]

[tex]72=(c)^2[/tex]

[tex]6\sqrt{2}=c[/tex]

Hence, the length of the hypotenuse in the right triangle is 6√2.

Therefore, the correct option is C) 6√2.

Check the picture below.

let's recall that the "gray" angle of depression is equals to its alternate interior angle of elevation in "blue".

make sure your calculator is in Degree mode.

Answer:

[tex]\large\boxed{3.\ y-(-7)=-2(x-2)}[/tex]

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

Let [tex]k:y=m_1x+b_1,\ l:y=m_2x_b_2[/tex].

[tex]l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\if m_1=m_2[/tex]

================================================

We have the equation of the line:

[tex]y=\dfrac{1}{2}x-5\to m_1=\dfrac{1}{2}[/tex]

Therefore

[tex]m_2=-\dfrac{1}{\frac{1}{2}}=-2[/tex]

Put it and coorinates of the point (2, -7) to the equation of a line

in the point-slope form:

[tex]y-(-7)=-2(x-2)\\\\y+7=-2(x-2)[/tex]

Answer:

The wheels make 512 revolutions per minute

Step-by-step explanation:

Diameter of truck = 36 in

Speed = 55 mi/h

Revolutions per minute =?

Radius r = diameter / 2

r = 36/2

r = 18 inches

Speed = 55 mi/h

1 mile = 63360 inches

55 miles = 55*63360 inches

55 miles = 3484800 inches

1 hr = 60 minutes

Speed = 3484800 inches/60 minutes

Speed = 58,080 inches/min

The formula used to calculate the revolutions per minute is:

revolutions = speed/Circumference

revolutions = 58,080 / 2*3.14*18

revolutions = 58,080 /113.4

revolutions = 512.16

revolutions = 512 revolutions per minute

So, The wheels make 512 revolutions per minute

[tex]-8(5x+5)+9x(10x+9)=20\\-40x-40+90x^2+81x-20=0\\90x^2+41x-60=0\\\\\Delta=41^2-4\cdot90\cdot(-60)=1681+21600=23281\\\\x=\dfrac{-41\pm \sqrt{23281}}{2\cdot90}=\dfrac{-41\pm \sqrt{23281}}{180}[/tex]

You already did. That is a true statement.

32 > 29 [and vice versa]

I am joyous to assist you anytime.

The inequality 29 < 32 is true.

After calculating 36 - 7 which equals 29, we compare this result to 32. The inequality 29 < 32 holds true, so the original inequality 36 - 7 < 32 is correct.

The student has asked to solve the inequality 36 - 7 < 32. To solve this inequality, we need to perform the subtraction on the left side of the inequality first.

When we calculate 36 - 7, we get 29. Now we can compare this result to 32 to determine if the inequality holds true.

Since we are dealing with an inequality, we know that if a value a is less than a value b, then a is indeed smaller in quantity or value compared to b. Here, 29 is indeed less than 32. Therefore, the inequality 29 < 32 is true.

[tex]\huge{\boxed{\text{9,000 meters}}}[/tex]

There are 1,000 meters in each kilometer, so multiply to find the daily number of meters.  [tex]3*1000=3000[/tex]

Multiply this by 3 to find the number of meters Rowena walks in three days.  [tex]3000*3=\boxed{9000}[/tex]