Suppose logbx = logcx, where b ≠ c. Then the value of x can be

A) 0 only
B) 1 only
C) b^c or c^b only
D) any positive real number

Answer:

d SA /dt = 36  in ^2 / hour

Step-by-step explanation:

Surface area of a cube is  6s^2

We need to take the derivative with respect to t

d SA / dt = ds /dt * 12 s

We know ds /dt is 1.5 inches per hour

   s = 2 for the particular instant we are looking at

d SA / dt =1.5 * 12 *2

d SA /dt = 36  in ^2 / hour

Answer:

-36 inches^2 per hour

Step-by-step explanation:

Answer:

x = 7 and y = 2

Step-by-step explanation:

the denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the value that x cannot be and if the numerator is non-zero for this value then it is a vertical asymptote

solve x - 7 = 0 ⇒ x = 7 is the asymptote

horizontal asymptotes occur as

[tex]lim( x → ± ∞), f(x) → c ( where c is a constant )

divide terms on numerator/ denominator by x

f(x) = (3/x/x/x -7/x ) + 2

as x → ± ∞, f(x) → 0 / 1 - 0 + 2 = 2

y = 2 is the asymptote

Answer: Vertical asymptote is x = 7

              Horizontal asymptote is y = 2

Step-by-step explanation:

The vertical asymptote is the restriction on the domain (x-value).  Since the denominator cannot be zero  ⇒  x - 7 ≠ 0  ⇒  x ≠ 7  so the vertical asymptote is at x = 7.

The horizontal asymptote (H.A.) is the restriction on the range (y-value). There are three rules that determine the horizontal value which compare the degree of the numerator (n) with the degree of the denominator (m):

In the given problem, n = 0 and m = 1  ⇒  n < m  ⇒  H.A. is y = 0

Since there is a vertical shift of +2 units, the H.A. is y = 0 + 2  ⇒  y = 2

Answer:

the answer is d

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

To see if it is a solution substitute x in and see if it works for y

a.  y>= x +2

-4 >= -2+2

-y> = 0 No

b y <= x+2

  -4<=-2+2

-4 <0  True

keep going

y<= x-3

-4 <= -2-3

-4<=-5

No

c  y> x+2

  -4 >-2+2

-4 > 0

True

y< x-3

-4 <-2-3

-4 <-5

NO

d y <= x+2

-4 <= -2+2

-4<=0

True

-4 >= -2-3

-4>=-5

This is the solution

Answer: Daniel has $22 in his savings account balance.

Step-by-step explanation:

Let Daniel's savings account balance be x

and Henry's savings account balance be y, then as given Daniel's savings account balnce is 20 times that of Henry's, We get [tex]x=20y[/tex]...........(1)

And also total amount of both savings account is $462 so we get [tex]x+y=462[/tex] ......(2)

Now by substituting values of x from (1) into (2) we get,

[tex]20y + y=462\\21y=462\\y=22[/tex]

And [tex]x=$440[/tex]

So, Daniel's savings account balance is $440

and Henry's savings account balance is $22

Answer:

Daniel have $440 in his savings account.

Step-by-step explanation:

Given that Daniel's saving account balance is 20 times the amount of Henry's savings account balance.

So, let Henry's saving account balance = x

Therefore, Daniel's saving account balance = 20 x

Given that total amount of money contained in both account is $ 462

    ⇒  20 x + x = 462

         21 x =462 ⇒ x = 22

  Hence, Daniel's saving account balance = 20 x

                                                                      = 20 * 22

                                                                     = $ 440

Answer:

3

Step-by-step explanation:

The 'm' value stands for the slope in the context of a linear equation (y = mx + b). In the provided example, it was determined to be 3, i.e., for each unit movement along the x-axis, there will be a three units movement along the y-axis.

The

value of m

in your diagram is representative of the slope in a mathematical equation, specifically in the context of a linear equation in the form y = mx + b. Here, 'm' describes how much the line on the graph moves up or down on the y-axis along the line's length. This usually means how much 'y' changes for each one-unit change in 'x'. According to the information provided, assuming that the equation is y = mx + b and b is set to 9, the m value has been determined to be 3. This indicates that for every step you move horizontally (along the x-axis), you would move three steps vertically (along the y-axis). Hence, in this case, the value of 'm' is 3.

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Answer:

As long as the numbers are in equal proportion on the spinner, the probabilty of landing on an even number for the first and second spin is 1/4, or 25%.  

Step-by-step explanation:

If there are four numbers on a spinner, all in equal proportion, than the probability of getting an even number (either 4 or 6) on any spin is 2/4, or 1/2, which is also 50%.  Since the results of the first spin do not influence the results of the second spin, then they are independent events.  So, if the likelihood of landing on even each time is 1/2, then we would mutliply 1/2 by 1/2 in order to find the probability that landing on an even number would happen in both spins.  Our result would be 1/4, or 25%.  

Not sure what that dude is even saying. The answer is C- P(A and B)=2/4*2/4

Hope this helped.

Answer:

I) P(cat│dog) = [tex]\frac{0.15}{0.38}[/tex]

II) These events are not independent

III) P(cat or dog)=  0.7

Step-by-step explanation:

Given : Households have  dogs = 38%

           So, P(dog) = 0.38

           Households have  cats = 47%

           So, P(cats) = 0.47

             Households have both dogs and cats  = 15%

           So, P(both dog and cat ) = [tex]P(cat\cap dog)[/tex] = 0.15

solution :

i) By formula P(A│B) =[tex]\frac{P(A\cap B)}{P(B)}[/tex]

P(cat│dog)= [tex]\frac{P(cat\cap dog)}{P(dog)}[/tex]

P(cat│dog) = [tex]\frac{0.15}{0.38}[/tex]

ii)  P(cat│dog)=39.47% = 0.39 and P(cat)=47% = 0.47, are the events not independent

Because condition for independent events in conditional probability is P(A|B)=P(A)

but P(cat│dog) ≠P(cat) i.e. 0.39≠0.47

So, these events are not independent

iii) P(cat or dog) = ?

"or" means union

Formula : [tex]P(A\cup B)= P(A) + P(B)-P(A\cap B)[/tex]

P(cat or dog) = [tex]P(cat\cup dog)= P(cat) + P(dog)-P(cat\cap dog)[/tex]

P(cat or dog)= 0.47 + 0.38 - 0.15

P(cat or dog)=  0.7

Answer:

Step-by-step explanation:

Cats are better (sorry, I just had to say it.)

Answer:

$360

Step-by-step explanation:

So for 2 cases that have 12 packs its $48 which means each case cost $24, so keep that for later now look closely, they need 180 PACKAGES not cases so if there are 12 packages in one case divide 180/12 and you will get 15, so that means you need 15 cases, so take the $24 per case and multiply that by the 15 cases you need and boom...it will cost the company $360 for next months order :)

Answer:

13.2'

Step-by-step explanation:

zip line, tower n finish form right-angle triangle w/

zip line as hypothesis=20' n the distance to finish as one side=15'

the tower height^2 + 15^2 = 20^2

the tower height = sqrt (400-225)

=sqrt(175)

=13.2'

Answer:

Lucy has to climb 13.2 feet.

Step-by-step explanation:

By the Pythagoras theorem, with zip line being the hypothesis and the distance from tower base to finish as one side,

20^2 = 15^2 + Height^2

Height^2 = 400 - 225 = 175

Height = 13.22 feet

Lucy has to climb 13.2 feet.

Answer:

$240 million

Step-by-step explanation:

In 1 year, $ 60 million would be spent

in 4 years,$ (60 x 4) million or $240 million would be spent

Answer:

The total interest after 10 years is $10.

Step-by-step explanation:

Formula

[tex]Simple\ interest = \frac{Principle\times Rate\times Time}{100}[/tex]

As given

when the principal amount is $100, the annual simple interest rate is 1%, and the number of years is 10.

Principle = $100

Rate = 1%

Time = 10 years

Simple interest = T

Put in the formula

[tex]T = \frac{100\times 1\times 10}{100}[/tex]

[tex]T = \frac{1000}{100}[/tex]

T = $10

Therefore the total interest after 10 years is $10.

Final answer:

The equation for calculating the total interest T on a $100 principal at a 1% annual simple interest rate over 10 years is T = $100 x 0.01 x 10, which equals $10 of interest earned.

Explanation:

The equation representing the total interest, T, earned from a principal amount of $100 with an annual simple interest rate of 1% over 10 years can be calculated using the simple interest formula:

Interest (I) = Principal (P) × Rate (R) × Time (T)

Here, Principal (P) is $100, Rate (R) is 1% or 0.01 (when expressed as a decimal), and Time (T) is 10 years. So our equation will be:

T = $100 × 0.01 × 10

Now, we calculate the total interest:

T = $100 × 0.01 × 10 = $10

Thus, the total interest earned after 10 years will be $10.

Answer:

Odd

Step-by-step explanation:

The graph intersects the x-axis three times. These three intercepts are the roots of the function and form the factors or solutions for x. They also represent the degree. This is an odd degree because there are 3 roots and 3 is odd. It is at least 3 but could be higher. All odd degree polynomials have the shape of a sideways s.

If the line MN is the angle bisector of ΔJMK, then it creates two angles of equal measure. Hence, m∠JMN is half of m∠JMK due to the property of an angle bisector.

In the field of geometry, an angle bisector is a line or ray that divides an angle into two equal angles. This is given by the information provided that MN is an angle bisector of ΔJMK.

By definition, if MN is an angle bisector of ΔJMK, then it creates two angles, ∠JMN and ∠NMK, that are equal in measure. So, we have m∠JMN = m∠NMK. This is the definition of an angle bisector, which is the reason you are looking for.

Given this, if you want to find m∠JMN in terms of ∠JMK, keep in mind that MN bisects ∠JMK, creating the two equal angles we just mentioned. Therefore, m∠JMK = m∠JMN + m∠NMK. Since ∠JMN and ∠NMK are equal, m∠JMK = 2m∠JMN. Hence, m∠JMN = 1/2m∠JMK. This would be a consequence of the angle bisector property.

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Answer:

1. Perpendicular

2. Isosceles

3. Never

Step-by-step explanation:

1. AC ⊥ BD because diameter of a square are perpendicular bisector of each other.

2. In Δ AOB , By using pythagoras : AB² = OA² + OB² .......( 1 )

In Δ COB , By using pythagoras : BC² = OC² + OB²  ..........( 2 )

But, OA = OC because both are radius of same circle

So, by using equations ( 1 ) and ( 2 ), We get AB = BC ≠ AC

⇒ ABC is a triangle having two equal sides so ABC is an isosceles triangle.

3. The side can never be equal to radius of circle because the side of the square will be chord for the circle and in a circle chord can never be equal to its radius

Answer:

1. Perpendicular

2. Isosceles

3. Never

Step-by-step explanation:

Final answer:

The new price of the item is $3 after the 85% reduction from the original price of $20.

Explanation:

To find the new price of the item after an 85% reduction, we start with the original price and calculate 85% of that price to know how much is being subtracted. The original price is $20. Now let's calculate 85% of 20 dollars:

0.85 (85%) × $20 = $17

This means an $17 reduction from the original price. We subtract this from the original price to find the new price:

$20 - $17 = $3

The new price of the item is $3 after a reduction of 85%.

Answer:

Since 18 cupcakes are a multiple of 18, simply multiply by 3 times 2 1/2 = 10.5 pounds to bake 18 cupcakes.

Step-by-step explanation:

Final answer:

Hisaki can make 4 1/3 batches of sugar cookies with the amount of sugar he has.

Explanation:

To find out how many total batches of sugar cookies Hisaki can make, we need to divide the total amount of sugar he has (3 1/2 cups) by the amount of sugar needed for one batch (3/4 cup).

We can convert the mixed number 3 1/2 into an improper fraction: 3 1/2 = 7/2.

Now, we divide 7/2 by 3/4: (7/2) ÷ (3/4) = (7/2) x (4/3) = 28/6 = 4 2/6 = 4 1/3.

Therefore, Hisaki can make a total of 4 1/3 batches of sugar cookies with the amount of sugar he has.

Answer:

<A = 67

Step-by-step explanation:

The three angles of a triangle add up to 180 degrees.  We know a right angle is 90 degrees.

<A + <B + <C = 180

3x-8 + 90 + x-2 =180

Combine like terms

4x-10+90 = 180

4x+80 =180

Subtract 80 from each side

4x+80-80=180-80

4x=100

Divide each side by 4

4x/4 = 100/4

x=25

But we want to know <A

<A = 3x-8

 Substitute x=25

    =3(25) -8

    =75-8

   = 67

Answer:

67°

Step-by-step explanation:

In a right triangle, the acute angles are complementary. That means that the sum of their measures is 90 deg.

m<A + m<C = 90

3x - 8 + x - 2 = 90

4x - 10 = 90

4x = 100

x = 25

m<A = 3x - 8

m<A = 3(25) - 8

m<A = 75 - 8

m<A = 67

Answer:

the answer is 3/40

Step-by-step explanation:

Answer:

1  False

b. 4.6 and -1.1

Step-by-step explanation:

A negative answer for x is ok

A negative answer inside the square root is not ok.  A negative answer inside the square root means the answer is not real.  A negative answer just means that x is less than zero.

The quadratic formula is

-b ± sqrt(b^2 -4ac)

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

2a

2x^2 -10= 7x

Lets get the equation in proper form

2x^2 -7x-10 = 7-7x

2x^2 -7x-10 =0

a=2  b=-7 c=-10

7 ± sqrt((-7)^2 -4(2)(-10))

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

2(2)

7 ± sqrt((49 +80)

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

4

7 ± sqrt((129)

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

4

7 ±11.3579

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

4

7 +11.3579             7-11.3579

------------------ and   -------------

4                                  4

4.589  and  -1.089475

Rounding

4.6 and -1.1

Answer:

[tex]x=\frac{-5+ln9}{3}[/tex] which appears to be from the list x=ln9-5/3

Step-by-step explanation:

We take the natural logarithm of both sides as the inverse operation to an exponent on e. This allows us to use log rules to rearrange the problem.

[tex]e^{3x+5}=9\\lne^{3x+5}=ln9 \\(3x+5)lne=ln9[/tex]

We know that as inverse operations, ln e =1.

[tex](3x+5)(1)=ln9\\3x+5=ln9\\3x=-5+ln9\\\frac{3x}{3}=\frac{-5+ln9}{3}[/tex]

[tex]x=\frac{-5+ln9}{3}[/tex]

Answer:

x  = (ln (9)-5) /3

Step-by-step explanation:

e^3x+5=9

First we subtract 5 from each side

e^3x+5-5=9-5

e^3x=(9-5)

Then we take the natural log of each side

ln(e^3x) = ln(9-5)

3x = ln (9-5)

Then we divide by 3 on each side

3x/3  = ln (9-5) /3

x  = ln (9-5) /3

Answer: P =36

Step-by-step explanation:

4.5 + 6 +3 +3 +10.5+ 9= 36

2,3,2,4,7,6                                     2/3=3/a    a=4.5

3,a,3,b,c,d                                      2/3=4/b   b=6

                                                     2/3=7/c   c=10.5

                                                      2/3=6/d    d=9

The perimeter of hexagon is 36 units.

A closed, two-dimensional polygon with six sides is what is known as a hexagon.

Six vertices and six angles make up a hexagon.

The words "hexa" and "gonio" both refer to six.

Regular hexagons have sides that are all the same length. Therefore, a regular hexagon's circumference is six times as long as its longest side.

Given the sides of Hexagon 2, 3, 2, 4, 7, and 6

the perimeter of hexagon is given by sum of all the sides,

and  a similar hexagon with two sides of length 3

the given hexagon have two same sides with length 2 units, so ae can change it by 3 units,

the length of hexagon is 3, a, 3, b, c, and d.

since hexagon are similar so the ratio of their length is also equal,

2/3 = 3/a = 2/3 = 4/b = 7/c = 6/d

solving rati we get a = 4.5, b = 6, c = 10.5 and d = 9

length of new hexagon is 3, 4.5, 3, 6, 10.5, 9

Perimeter = 3 + 4.5 + 3 + 6 + 10.5 +9 = 36 units.

Hence the perimeter is 36 units.

Learn more about hexagon;

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Answer: 70

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

Explanation:

The exterior angles (2x+12) and (2x) have corresponding interior angles 180-(2x+12) and 180-(2x)

Triangle ABC has the following interior angles

A = 112

B = 180 - 2x

C = 180 - (2x+12) = 180-2x-12 = 168-2x

Add up the interior angles for A,B,C and set the result equal to 180. Solve for x

A+B+C = 180

(112)+(180-2x)+(168-2x) = 180

112+180-2x+168-2x = 180

460-4x = 180

-4x = 180-460

-4x = -280

x = -280/(-4)

x = 70

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

Side note:

2x = 2*70 = 140 is the exterior angle for B, so 180-140 = 40 is the interior angle for angle B

2x+12 = 2*70+12 = 152 is the exterior angle for C, so 180 - 152 = 28 is the interior angle for C

Add up the interior angles to find that A+B+C = 112+40+28 = 180, so this helps confirm we have the right x value.

--First we have to simplfy

[tex]\frac{2x-8}{x^2-x-12} -\frac{x-3}{x(x+1)}[/tex]

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

--Cancel common factors

[tex]\frac{2}{(x+3)} -\frac{x-3}{x(x+1)}[/tex]

--Here remember never cancel factors in a subtraction or addition problem

--Now Multiply each side until both denominators are equal to each other

[tex]\frac{2[x(x+1)]}{x(x+3)(x+1)} -\frac{(x-3)(x+3)}{x(x+3)(x+1)}[/tex]

--Simplify

[tex]\frac{2x^2+2x}{x(x+1)(x+3)} - \frac{x^2-9}{x(x+1)(x+3)}[/tex]

--Now that the denominators are the same: subtract!

[tex]\frac{2x^2+2x-(x^2-9)}{x(x+1)(x+3)}[/tex]

[tex]\frac{2x^2-x^2+2x+9}{x(x+1)(x+3)}[/tex]

--And LAST STEP! ......Simplify More.... To get your answer

[tex]\frac{x^2+2x+9}{x(x+1)(x+3)}[/tex]

Answer:

y = 14

Step-by-step explanation:

[tex]50^\circ+50^\circ+(5y+10)^\circ=180^\circ[/tex]

[tex]100^\circ+(5\times y+10)^\circ=180^\circ[/tex]

[tex](5\times y+10)^\circ=180^\circ - 100^\circ=80^\circ[/tex]

[tex]5 \times y=80^\circ-10^\circ=70^\circ[/tex]

[tex]y=\frac{70^\circ}{5} =14^\circ[/tex]

Answer:

[tex]18[/tex] skis and [tex]10[/tex] snowboards were rented.

Step-by-step explanation:

Let the number of skis rented be [tex]x[/tex] and the number of snowboards rented be [tex]y[/tex].

If a total of [tex]28[/tex] people rented on a certain day, then the total number of skis and snowboards rented that particular day is also [tex]28[/tex].

This gives us the equation

[tex]x+y=28...eqn(1)[/tex].

If skis cost $ [tex]16[/tex], then [tex]x[/tex] number of skis cost $ [tex]16x[/tex].

If snowboards cost $ [tex]19[/tex], then [tex]y[/tex] number of snowboards cost $ [tex]19y[/tex].

The total cost will give us another equation,

[tex]16x+19y=478...eqn(2)[/tex]

From equation (1),

[tex]y=28-x...eqn(3)[/tex].

We put equation (3) into equation (2) to get,

[tex]16x+19(28-x)=478[/tex]

We expand the brackets to obtain,

[tex]16x+532-19x=478[/tex]

We group like terms to get,

[tex]16x-19x=478-532[/tex]

This implies that,

[tex]-3x=-54[/tex]

We divide both sides by [tex]-3[/tex] to get,

[tex]x=18[/tex]

We put [tex]x=18[/tex] into equation (3) to get,

[tex]y=28-18[/tex]

[tex]y=10[/tex]

Therefore [tex]18[/tex] skis and [tex]10[/tex] snowboards were rented.

To solve this problem, you can set up a system of equations where one equation represents the total number of skis and snowboards rented, and the other represents the total cost of those rentals. By solving this system, you can determine the number of skis and snowboards rented.

This problem is a classic example of a system of linear equations. Let's denote the number of skis rented as x and the number of snowboards rented as y. From the problem, we know that:

By solving these two equations, we can find the values of x and y which represent the number of skis and snowboards rented respectively.

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6. Answer: y = 5x - 11

Step-by-step explanation:

Parallel means "same slope".  y = 5x - 2 is in the form y = mx + b,

so the slope (m) = 5

Next, input the point (x₁, y₁ = 2, -1) and slope (m = 5) into the Point-Slope formula:

y - y₁ = m(x - x₁)

y - (-1) = 5(x - 2)

y + 1 = 5x - 10

y      = 5x - 11

*******************************************************************

7. Answer: [tex]\bold{y = \dfrac{1}{3}x + 4}[/tex]

Step-by-step explanation:

Perpendicular means "opposite reciprocal slope". y = -3x + 7 is in the form y = mx + b, so slope (m) = -3 ⇒ m⊥ = [tex]\frac{1}{3}[/tex]

Next, input the point (x₁, y₁ = 3, 5) and slope (m = [tex]\frac{1}{3}[/tex] ) into the Point-Slope formula:

y - y₁ = m(x - x₁)

[tex]y - 5=\dfrac{1}{3}(x - 3)[/tex]

[tex]y - 5 =\dfrac{1}{3}x - 1[/tex]

   [tex]y=\dfrac{1}{3}x + 4[/tex]

Answer: B

Step-by-step explanation:

   (x - 6) (x¹⁾²) (x + 3)

= (x¹⁾²) (x² - 3x - 18)

= x⁵⁾² - 3x³⁾² - 18x¹⁾²

= √x⁵ - 3√x³ - 18√x

********************************************

Answer: B

Step-by-step explanation:

[tex]\frac{f(x)}{g(x)} =\frac{(x+1)^{-1}}{x-2} = \frac{1}{(x+1)(x-2)}[/tex]

Since denominator cannot equal zero,

x + 1 ≠ 0     and      x - 2 ≠ 0

 x ≠ -1        and         x ≠ 2

Interval Notation: (-∞, -1) U (-1, 2) U (2, ∞)

Divide both sides by -3, and replace [tex]x^2[/tex] with [tex]y[/tex]. Then

[tex]-3x^4+27x^2+1200=0\iff y^2-9y-400=0[/tex]

Factorize the quadratic in [tex]y[/tex] to get

[tex]y^2-9y-400=(y+16)(y-25)=0\implies y=-16,y=25[/tex]

which in turn means

[tex]x^2=-16,x^2=25[/tex]

But [tex]x^2\ge0[/tex] for all real [tex]x[/tex], so we can ignore the first solution. This leaves us with

[tex]x^2=25\implies x=\pm\sqrt{25}=\pm5[/tex]

If we allow for any complex solution, then we can continue with the solution we ignored:

[tex]x^2=-16\implies x=\pm\sqrt{-16}=\pm i\sqrt{16}=\pm4i[/tex]