Ethan bought 4 packages of pencils. After he gave 8 pencils to his friends, he had 40 pencils
left over. How many pencils were in each package? Use the drop-down menus to solve the
problem arithmetically and algebraically.

Answer:

51

Step-by-step explanation:

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

The reference angle has AC = 12.3 as the opposite side and BC = 8.4 as the adjacent side. The tangent ratio ties the opposite and adjacent sides together.

--------

tan(angle) = opposite/adjacent

tan(theta) = AC/BC

tan(theta) = 12.3/8.4

theta = arctan(12.3/8.4)

theta = 55.6697828044967

theta = 55.7 degrees approximately

--------

arctan is the same as inverse tangent which is written as [tex]\tan^{-1}[/tex]

make sure your calculator is in degree mode

Answer:

x= -11

Step-by-step explanation:

the coefficient is variable that appears before a number . bearing this in mind, the coefficient of x is therefore 2 .

the value of x is:

>32+2x=10

>2x=10-32

>2x= -22

>x= -11

Answer:

Step-by-step explanation:

Coefficient of x = 2

32 + 2x  = 10

Subtract 32 from both side

32 + 2x -32 = 10 - 32

              2x =  - 22

Divide both sides by 2

            2x/2 = -22/2

x = -11

Answer:

She swam 2 kilometers

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given an angle θ₁ located on in the first quadrant and sinθ₁ = 1/2, we are required to calculate the value of cosθ₁.

Firstly, we need to find the value of the angle θ₁ from the expression sinθ₁ = 1/2.

Given sinθ₁ = 1/2

Take the arcsin of both sides

arcsin(sinθ₁) = arcsin(1/2)

The arcsin will cancel out the sin at the left hand side to have only θ₁. Hence;

θ₁  = arcsin(1/2)

Using the calculator, θ₁ = 30°

Since we are to find the value of cosθ₁

cosθ₁ = cos30°

cos30° = √3/2

Hence the value of cosθ₁ is √3/2

Answer:

60/61

Step-by-step explanation:

60/61

khan. #gayrights

Answer:

b

Step-by-step explanation:

the answer is b because b have the greatest spread for the middle 50%

I hope this was helpful

Answer:

[tex]\Large \boxed{(5^{-2})^{-3}}[/tex]

Step-by-step explanation:

Applying the law of exponents : [tex](a^b)^c=a^{bc}[/tex]

[tex](5^4)^2 = 5^{4 \times 2} = 5^{8}[/tex]

[tex](5^{-2})^{-3}=5^{-2 \times -3}=5^6[/tex]

[tex](5^1)^5 =5^{1 \times 5}=5^5[/tex]

Answer:

[tex]\huge\boxed{Option \ B}[/tex]

Step-by-step explanation:

[tex]5^6[/tex] is equivalent to

=>   [tex](5^4)^2 = 5^{4*2} = 5^ 8[/tex]

=> [tex](5^{-2})^{-3} = 5^{-2*-3} = 5^6[/tex]          ← Correct

=> [tex](5^1)^5 = 5^{1*5} = 5^5[/tex]

Answer:

A.  [tex]Claire = 20250[/tex]

B.   [tex]Richard = 9350[/tex]

C.    Height = 3.2 feet

D. Charges = $760

Step-by-step explanation:

Given

[tex]Claire = 50x^2 + 250[/tex]

[tex]Richard = 40x^2 + 350[/tex]

Solving (a): Claire's 20ft charges

In this case, x = 20

Substitute 20 for x in [tex]Claire = 50x^2 + 250[/tex]

[tex]Claire = 50(20)^2 + 250[/tex]

[tex]Claire = 50(400) + 250[/tex]

[tex]Claire = 20000 + 250[/tex]

[tex]Claire = 20250[/tex]

Solving (b): Richard's 15ft charges

In this case, x = 15

Substitute 20 for x in [tex]Richard = 40x^2 + 350[/tex]

[tex]Richard = 40(15)^2 + 350[/tex]

[tex]Richard = 40(225) + 350[/tex]

[tex]Richard = 9000 + 350[/tex]

[tex]Richard = 9350[/tex]

Solving (c): Height which they both charge the same;

This implies that

[tex]50x^2 + 250 = 40x^2 + 350[/tex]

Solving for x [Collect Like Terms\

[tex]50x^2 - 40x^2 = 350 - 250[/tex]

[tex]10x^2 = 100[/tex]

Divide both sides by 10

[tex]x^2 = 10[/tex]

Take square roots of both sides

[tex]x = \sqrt{10}[/tex]

[tex]x = 3.2ft[/tex]  (Approximated)

Hence; Height = 3.2 feet

Solving (d): How much they charge when the charge the same amount.

Substitute 3.2 for x in any of the given equation

[tex]Claire = 50x^2 + 250[/tex]

[tex]Claire = 50(3.2)^2 + 250[/tex]

[tex]Claire = 50*10.24 + 250[/tex]

[tex]Claire = 512 + 250[/tex]

[tex]Claire = 762[/tex]

[tex]Richard = 40x^2 + 350[/tex]

[tex]Richard = 40(3.2)^2 + 350[/tex]

[tex]Richard = 40 * 10.24 + 350[/tex]

[tex]Richard = 409.6 + 350[/tex]

[tex]Richard = 759.6[/tex]

The reason for the difference is due to approximation

Hence, they both charge approximately 760

Answer:

1/7 is left

Step-by-step explanation:

What is left to read after the first week

1 - 3/7

7/7 - 3/7

4/7

He read 3/4 of this the second week

4/7 * 3/4

3/7 was read

4/7 - 3/7 is what is left

1/7 is left

Answer:

The correct answer is

Step-by-step explanation:

1/7 of the book is left to read.

Hope this helps....

Have a nice day!!!!

Answer: HIJK is a parallelogram because the midpoint of both diagonals is (1,0) , which means the diagonals bisect each other.

Step-by-step explanation:

Given: The coordinates of parallelogram H I J K as

H is at (- 2, 2), point I is at (4, 3), point J is at (4, - 2), and point K is at (- 2, - 3).

Diagonals : HJ and IK  [join opposite vertices]

Mid point of HJ = [tex](\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})[/tex]

[tex]=(\dfrac{-2+4}{2},\dfrac{2+(-2)}{2})=(1,0)[/tex]

i.e. Mid point of HJ = (1,0)

Mid point of IK = [tex](\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})[/tex]

[tex]=(\dfrac{4+(-2)}{2},\dfrac{3+(-3)}{2})=(1,0)[/tex]

i.e. Mid point of IK = (1,0) =Mid point of HJ

When mid points of both diagonals are equal then that means the diagonals bisect each other.

Thus, HIJK is a parallelogram because the midpoint of both diagonals is (1,0) , which means the diagonals bisect each other.

Answer:

(1,0)

Step-by-step explanation:

Answer:

Step-by-step explanation:

We have that

A = 51°, b = 14, c = 6

step 1

find the value of a

Applying the law of cosines

a²=c²+b²-2*c*b*cos A

a²=6²+14²-2*6*14*cos 51-------> 126.27

a=11.2

we know that

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

we have

a=11.2

b=14

c=6

so

(a+b) > c-------------> (11.2+14)=25.2

25.2 > 6-----> is not correct

therefore

the answer is the option

a. No triangles possible

I don't know if i am right sorry if this is wrong

Answer:

15%

Step-by-step explanation:

profit=sp -cp

cp=sp-profit

=17250-2250

=15000

profit%= profit amount/cp *100%

=2250/15000×100

= 15

Answer:

Step-by-step explanation:

Given,

SP ( Selling price ) = Rs 17250

Profit ( P ) = Rs 2250

CP ( Cost price ) = Rs 17250 - Rs 2250 = Rs 15000

Now, let's find the profit / gain percentage :

Profit % = [tex] \sf{ \frac{profit}{cost \: price} \times 100\%}[/tex]

plug the values

⇒[tex] \sf{ \frac{2250}{15000} \times 100\%}[/tex]

Calculate

⇒[tex] \sf{15\%}[/tex]

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

▪[tex] \underline{ \underline{ \sf{ \blue{What \: is \: the \: formula \: to \: find \: profit \: percent \: and \: loss \: percent?}}}}[/tex]

We know that , profit and loss are calculated on cost price ( CP ). So, profit percent and loss percent can be calculated by using the following formula :

[tex] \boxed{ \sf{Loss\% \: = \frac{cp - sp}{cp} \times 100\%}}[/tex]

[tex] \boxed{ \sf{ \bold{Profit\% \: = \: \frac{sp \: - \: cp}{cp} \times 100}}}[/tex]

Hope I helped!

Best regards!!

Answer:

3.0 miles

Step-by-step explanation:

Using the conversion 1 mile equals 1.6093 km to convert 4.9 kilometers to miles, round to the nearest tenth of a mile.

1 mile = 1.6093 km

Convert 4.9km to mile

We can use cross multiplication :

Let the number of miles = m

1 mile = 1.6093 km

'm' miles = 4.9 km

Cross multiply :

m × 1.6093 = 4.9 × 1

m = 4.9 / 1.6093

m = 3.0448020 miles

Rounding 3.0448020 to the nearest tenth :

3.0 miles

Answer:

AB = 3π

Step-by-step explanation:

The formula for the circumference of a circle is:

C = 2πr

By substituting 27 for r:

C = 2π(27)

C = 54π

The whole circumference is 54π. A circle is 360º around. We can set up a proportion to find the length of the 20º arc:

[tex]\frac{360}{54p}[/tex] = [tex]\frac{20}{x}[/tex]

Cross-multiply:

360x = 1080π

Divide both sides by 360:

x = 3π

AB = 3π

Answer:

AB = 3π

Step-by-step explanation:

The arc AB can be calculated as

AB = circumference of circle × fraction of circle

The central angle is equal to the measure of arc AB = 20° , thus

AB = 2πr × [tex]\frac{20}{360}[/tex]

     = 2π × 27 × [tex]\frac{1}{18}[/tex] ( cancel 18 and 27 by 9 )

     = 2π × 3 × [tex]\frac{1}{2}[/tex] = 6π × [tex]\frac{1}{2}[/tex] = 3π

Answer:

1) Please find attached the graph sowing the line of symmetry

The symmetry line is a vertical line passing through (2, -9)

2) The x-intercept are (5, 0) and (-1, 0)

The y-intercept is (0, -5)

The vertex is (2, -9)

Step-by-step explanation:

The given function is;

f(x) = x² - 4·x - 5

The data values are generated as follows;

x,          f(x)

-1,         0

-0.8,    -1.16

-0.6,    -2.24

-0.4,    -3.24

-0.2,    -4.16

0,         -5

0.2,      -5.76

0.4,      -6.44

0.6,     -7.04

0.8,     -7.56

1,         -8

1.2,      -8.36

1.4,      -8.64

1.6,      -8.84

1.8,      -8.96

2,        -9

2.2,     -8.96

2.4,      -8.84

2.6,     -8.64

2.8,     -8.36

3,        -8

3.2,     -7.56

3.4,     -7.04

3.6,     6.44

3.8,     -5.76

4,        -5

4.2,      -4.16

4.4,     -3.24

4.6,     -2.24

4.8,      -1.16

5,           0

The minimum is found from differentiating the function, f(x), with respect to x and looking for the zeros of the result  as follows;

f'(x) = 2·x -4

f'(x) = 0 = 2·x -4

x = 2

The y-coordinate gives; f(2) = 2² - 4×2 - 5 = -9

Therefore, the symmetry line is a vertical line passing through (2, -9)

The x-intercept is the point at which y = 0, therefore, from f(x) = x² - 4·x - 5, we have;

0 = x² - 4·x - 5 = (x - 5)·(x + 1)  

Therefore, the x-intercept are x = 5 or -1

The x-intercept are (5, 0) and (-1, 0)

The y-intercept occur at the point where the x value = 0, therefore, we have;

The y-intercept occur at y = f(0) = 0² - 4·0 - 5 = -5

The y-intercept is (0, -5)

Re-writing the  equation in vertex form y = a(x - h)² + k gives;

f(x) = x² - 4·x - 5 = 1·(x - 2)² - 9

Therefore, the vertex is (2, -9)

Answer:

see attached graph

The x-intercept are (5, 0) and (-1, 0)

The y-intercept is (0, -5)

The vertex is (2, -9)

Step-by-step explanation:

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

Explanation:

We're conducting a one proportion Z test.

The hypothesized population proportion is p = 0.53, which is not to be confused with the p-value (unfortunately statistics textbooks seem to overuse the letter 'p'). Luckily this problem is not asking for the p-value.

The sample population proportion is

phat = x/n = 41/79 = 0.518987 approximately

The standard error (SE) is

SE = sqrt(p*(1-p)/n)

SE = sqrt(0.53*(1-0.53)/79)

SE = 0.056153 approximately

Making the test statistic to be

z = (phat - p)/(SE)

z = (0.518987 - 0.53)/0.056153

z = -0.19612487311452

z = -0.196

Which is approximate and rounded to 3 decimal places.

Answer:

Step-by-step explanation:

d is directly proportional to the square of a speed v

d = av²

5 = a•10²

5 = 100a

a = 0.05

d = 0.05v²

d = 0.05•70²

d = 0.05•4900

d = 245

Answer:

see below (I hope this makes sense!)

Step-by-step explanation:

Constants, as the name suggest, stay constant, meaning that their value never changes. For example, 2 will always be 2 and 9.4 will always be 9.4. On the other hand, the values of variables can change. Take, for example, the variable 2x. When x = 1, 2x = 2 and when x  =2, 2x = 4 so the value of 2x can change depending on what x is. You can't combine constants and variables because they are not like terms, basically, one can change and the other can't and you cannot combine terms that are not like each other.

Answer:

area of cube = a^2  ( a is side)

2.4^2 = 5.76 cm^2

Answer:

5.76 cm^2

Step-by-step explanation:

Hey there!

Well if the side length is 2.4 cm then the area would be,

A = l•l

A = 2.4 • 2.4

A = 5.76cm^2

Hope this helps :)

Answer:

[tex]AC=20[/tex]

Step-by-step explanation:

The line segment AC is the entire length of the line. Within this segment, point  B is found.

Point B, in a way, splits the segment into two, creating the segments AB and BC.

To find the length of AC, add the lengths of the lines AB and BC together:

[tex]AB=11\\BC=9\\AB+BC=AC\\11+9=AC\\20=AC[/tex]

The length of AC is 20.

:Done

Answer:

20 units.

Step-by-step explanation:

Segment AC is broken into two parts by point B. That means that the length of segment AB plus the length of segment BC equals the length of segment AC.

If BC = 9, and AB = 11, AC = 9 + 11 = 20 units.

Hope this helps!

Answer:

Step-by-step explanation:

Given the function [tex]G(x)= -\dfrac{x^2}{4} + 7[/tex], the average rate of change of g(x) over the interval [-2,4], is expressed as shown below;

Rate of change of the function is expressed as g(b)-g(a)/b-a

where a - -2 and b = 4

[tex]G(4)= -\dfrac{4^2}{4} + 7\\G(4)= -\dfrac{16}{4} + 7\\G(4)= -4 + 7\\G(4) = 3\\[/tex]

[tex]G(-2) = -\dfrac{(-2)^2}{4} + 7\\G(-2)= -\dfrac{4}{4} + 7\\G(-2)= -1 + 7\\G(-2)= 6[/tex]

average rate of change of g(x) over the interval [-2,4] will be;

[tex]g'(x) = \frac{g(4)-g(-2)}{4-(-2)}\\ g'(x) = \frac{3-6}{6}\\\\g'(x) = -3/6\\g'(x) = -1/2[/tex]

Answer:

w = 5

Step-by-step explanation:

Hey there!

Cross multiply,

84 = 12w + 24

-24 to both sides

60 = 12w

Divide both sides by 12

w = 5

Hope this helps :)

Answer:

3.  Intersect at exactly one point.  ( (2/3), (-2/3) )

Step-by-step explanation:

To make the comparison of these lines easier, let's rewrite the 2nd equation into slope-intercept form, as the 1st equation is in slope-intercept form.

[1] y = 2x - 2

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

[2] 6x + 3y = 2 ==> 3y = 2 - 6x ==> y = -2x + (2/3)

[2] y = -2x + (2/3)

So now that we have both equations in slope-intercept form, we can see that the two equations are both linear, have different slopes, and have different y-intercepts.

Since these equations have both different slopes and different y-intercepts, we know that the lines will cross at least one point.  We can confirm that the lines only cross at a single point using the fact that both equations are linear, meaning there will only be one point of crossing.  To find that point, we can simply set the equations equal to each other.

y = 2x - 2

y = -2x + (2/3)

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

4x = (8/3)

x = (8/12) = (2/3)

And plug this x value back into one of the equations:

y = 2x - 2

y = 2(2/3) - 2

y = (4/3) - (6/3)

y = (-2/3)

Thus these lines only cross at the point ( (2/3), (-2/3) ).

Cheers.

Answer:

I don't understand the question

Answer:

Ok, we know that the driving accuracy is of 71%.

Then the first step is to get a spinner that is enumerated from 1 to 100 (in such way that each number is equispaced)

Now, we can mark a section between numbers 1 and 71. (this regio represents the cases where the shot lands in the fairway) and the unmarked region represents the cases where the shot does not land in the fairway.

Now, for each shot, we can spin our spinner next to a fixed pencil, depending on the section of the spinner that is marked by the pencil when the spinner fully stops, we can guess if the shot landed or not in the fairway.

In this way the shot has the region from 1 to 71 (71%) to land in the fairway

and the region from 72 to 100 to not land in the fairway.

If you want to simulate Sorenstam’s performance in a round of golf where she attempts 15 drives, you need to spin the spinner 15 times, and record the oucomes.

Answer: x=32

Step-by-step explanation:

[tex]\frac{1}{8}x+8=12[/tex]

subtract 8 on both sides

[tex]\frac{1}{8}x+8-8=12-8[/tex]

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

multiply 8 on both sides

[tex]8\cdot \frac{1}{8}x=4\cdot \:8[/tex]

[tex]4\cdot8=32[/tex]

[tex]x=32[/tex]

Answer:

False

Step-by-step explanation:

We can simplify this equation and then solve for x.

[tex](x+3)^3-4=0\\\\x^2+6x+9-4=0\\\\x^2+6x+5=0\\\\(x+2)(x+3)=0\\\\x=-3\\x=-2[/tex]

As you can see, the solutions are not x=-1 and x=-5.

Therefore, the answer is false.

Answer:

True

Step-by-step explanation:

Given

(x + 3)² - 4 = 0 ( add 4 to both sides )

(x + 3)² = 4 ( take the square root of both sides )

x + 3 = ± [tex]\sqrt{4}[/tex] = ± 2 ( subtract 3 from both sides )

x = - 3 ± 2

Thus

x = - 3 - 2 = - 5

x = - 3 + 2 = - 1

Answer:

[tex]\boxed{\sf 6.4 \ seconds}[/tex]

Step-by-step explanation:

t = time (s) ⇒ ?

d = distance falling (m) ⇒ 200 (m)

a = acceleration due to gravity ⇒ 9.8 (m/s²)

The time in seconds is not given. Solve for time using the formula.

[tex]t=\sqrt{\frac{2(200)}{9.8} }[/tex]

[tex]t=\sqrt{\frac{400}{9.8} }[/tex]

[tex]t= 6.388766...[/tex]

Round answer to nearest tenth of a second.

[tex]t \approx 6.4[/tex]

Answer:

Step-by-step explanation:

expression = (x + 4) / 3

x = 5

(5 + 4) / 3

= 9/3

= 3

Hope this helps

plz mark as brainliest!!!!!!

Answer:

Option (4)

Step-by-step explanation:

By the theorem of inscribed angles and the intercepted arc,

"In a circle, angles subtended by the same arc always measure the same and the arc measures the double of the inscribed angle."

If an inscribed angle in a circle measures 75° then all inscribed angles by the same arc will measure 75°.

In addition to this, measure of arc subtended by these inscribed angle will measure double of the inscribed angle (150°)

Therefore, Option (4) will be the answer.

Answer:

   your choice is correct

Step-by-step explanation:

The magnitude of the difference between the target amount and the actual amount will be no greater than the allowed error.

  |x -34| ≤ 0.25