FInd the slope of a line

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:

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:

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.

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:

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 unit rate, r, per day to keep the dog at the kennel is $14.25.

Explanation:

To find the unit rate, we need to divide the total cost by the number of days. In this case, Gene paid $171 to keep his dog at the kennel for 12 days. So the unit rate, which represents the cost per day, is calculated as:

Unit rate = Total cost / Number of days

Unit rate = $171 / 12

Unit rate = $14.25 per day which is the required answer

Therefore, unit rate to keep the dog at the kennel is $14.25 per day.

Answer:

b) 6

Step-by-step explanation:

Since this is an isosceles triangle, the two sides are equal and the two angles are equal.

That means  

5x-3 = 2x+15

Subtract 2x from each side.

5x-2x-3 = 2x-2x+15

3x-3 = 15

Add 3 to each side.

3x-3+3 = 15+3

3x =18

Divide each side by 3

3x/3 = 18/3

x =6

Answer: the answer to this question is A because the angle is acute angle and when you solve (5x-3) it equals up to 18 when you finish figureing it out.

Step-by-step explanation:

Answer:

BC - 54 units

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

∠C = 180° - (∠A + ∠B) = 180° - (80 + 50)° = 180° - 130° = 50°

Since ∠B = ∠C = 50° then the base angles of the triangle are equal hence the triangle is isosceles with

AB = AC, that is

4x - 4 = 2x + 16 ( subtract 2x from both sides )

2x - 4 = 16 ( add 4 to both sides )

2x = 20 ( divide both sides by 2 )

x = 10

⇒ BC = 5x + 4 = (5 × 10) + 4 = 50 + 4 = 54

Answer:

5/36

Step-by-step explanation:

Answer:

you add 11 inches each day

Step-by-step explanation:

To find the markup from cost to sale price, calculate the original sale price by dividing the selling price by (1 - discount percentage) which is 230

To find the markup from cost to sale price, we first need to calculate the cost price.

The item is marked down by 20% from the selling price of $440.

So, the original sale price before the discount would be $440 / (1 - 0.20) = $550.

Since the sale price is still marked up from the cost of $320, we can calculate the markup as:

$550 - $320 = $230.

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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

--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:

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:

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: There are 6 sections of  [tex]8\frac{1}{4}\ inches[/tex]  of rope Mario can cut from the rope .

Step-by-step explanation:

Since we have given that

Length of the rope for the tent = 7 feet

As we know that

[tex]1\ feet=12\ inches\\\\7\ feet=12\times 7=84\ inches[/tex]

Length of rope is used to tie a tarp on top of the tent = 34.5 inches

Remaining length of rope is given by

[tex]84-34.5=49.5\ inches[/tex]

According to question, the remaining rope should be cut into

[tex]8\frac{1}{4}\ inches\\\\=\frac{33}{4}\ inches[/tex]

So, Number of  [tex]8\frac{1}{4}\ inches[/tex] sections of rope Mario can cut from the rope is given by

[tex]\frac{49.5}{8\frac{1}{4}}\\\\=\frac{49.5}{\frac{33}{4}}\\\\=\frac{49.5\times 4}{33}\\\\=6[/tex]

Hence, there are 6 sections of [tex]8\frac{1}{4}\ inches[/tex] rope Mario can cut from the rope .

Answer:

6

Step-by-step explanation:

Mario has 7 feet of rope.  Since there are 12 inches in every foot, this means he has

7(12) = 84 inches of rope.

34.5 inches of the rope must be used to tie the tarp to the top; this leaves Mario with

84-34.5 = 49.5

This remaining rope will be cut into 8 1/4 inch sections.  We can also write 8 1/4 as 8.25.  To find the number of sections this length he can cut, we divide:

49.5/8.25 = 6

He can cut 6 sections this length.

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]

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]

41.848/3.4=12.308

The actual building is 12.306 times larger than the model.

Answer:

2/3

Step-by-step explanation:

A six-sided number cube labeled from 1 to 6 is rolled.

Total outcomes = 1,2,3,4,5,6= 6 outcomes

multiple of 2  are 2,4,6 so 3 outcomes

multiple of 3 are 3,6 so 2 outcomes

multiply of 2 or 3  are 2,4,3,6 so 4 outcomes

the probability of getting a multiple of 2 or a multiple of 3

= possible outcomes / total outcomes

= 4/6

now reduce the fraction, divide by 2 on both sides

the probability of getting a multiple of 2 or a multiple of 3 = 2/3

Tthe probability of rolling a multiple of 2 or a multiple of 3 on a six-sided die is [tex]\(\frac{5}{6}\)[/tex].

To find the probability of getting a multiple of 2 or a multiple of 3 when rolling a six-sided number cube, we can list out the possible outcomes and identify which ones satisfy our conditions.

The possible outcomes when rolling six-sided die are: 1, 2, 3, 4, 5, and 6:

Multiples of 2 on the die are: 2, 4, 6.

Multiples of 3 on the die are: 3, 6.

We can see that there is an overlap with the number 6, which is both a multiple of 2 and a multiple of 3. To avoid counting this outcome twice, we use the principle of inclusion-exclusion.

First, we add the number of multiples of 2 to the number of multiples of 3

- There are 3 multiples of 2.

- There are 2 multiples of 3.

So, without considering the overlap, we would have [tex]\(3 + 2 = 5\)[/tex] favorable outcomes.

However, since the number 6 has been counted twice, we subtract one instance of it from our total:

[tex]\(5 - 1 = 4\) unique favorable outcomes (2, 3, 4, 6)[/tex]

Since there are 6 possible outcomes in total when rolling a six-sided die, the probability of rolling a multiple of 2 or a multiple of 3 is the number of favorable outcomes divided by the total number of possible outcomes [tex]\(\frac{4}{6}\)[/tex].

This fraction simplifies to [tex]\(\frac{2}{3}\)[/tex]. However, we have overlooked the fact that every number on a six-sided die is a multiple of 1, and since 1 is neither a multiple of 2 nor of 3, it does not contribute to  favorable outcomes. Therefore, the only outcome that is not a multiple of 2 or 3 is number 1.

Thus, the correct probability is [tex]\(1 - \frac{1}{6} = \frac{5}{6}\)[/tex], since there is only 1 unfavorable outcome out of 6 possible outcomes.

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 :)

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: 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.

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:

<4 and <3

Step-by-step explanation:

The remote interior angles are  the two angles that are inside the triangle and away from the angle adjacent to the exterior angle.

5 is adjacent to 1

so 3 and 4 are the remote interior angles

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:

$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:

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: