If 1/2 is subtracted from four times the reciprocal of a number, the result is 0. Find the number.

Answer:

x=10/3, y=14/3. (10/3, 14/3).

Step-by-step explanation:

2x+2y=16

10x-2y=24

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

x+y=8

10x-2y=24

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

x=8-y

10(8-y)-2y=24

80-10y-2y=24

80-12y=24

12y=80-24

12y=56

y=56/12=14/3

x=8-14/3=24/3-14/3=10/3

x=10/3, y=14/3.

Final answer:

Reasonable estimates for the number of students per grade when there are 472 students total are 50, 80, or 100 students per grade.

Explanation:

The student's question asks for reasonable estimates for the number of students in each grade if there are 472 students in different grades with about the same number of students in each grade.

Let's examine the options given:

Therefore, reasonable estimates for the number of students per grade are 50 students, 80 students, and 100 students.

16, 32, 48, 64

16 = 16x1

32 = 16x2

48 = 16x3

64 = 16x4

Answer:

C

Step-by-step explanation:

Answer:

4 more gallons of paint

Step-by-step explanation:

Answer:

For the given expression -3( y + 3 ) = 2 y + 3  the value of  y = -2.4.

Step-by-step explanation:

Here, the given expression to be simplified : -3( y + 3 ) = 2 y + 3

Now, by DISTRIBUTIVE PROPERTY:

A (B +C)  = AB + AC

Simplifying the given expression:

-3( y + 3 ) = 2 y + 3  ⇒  -3 ( y) - 3 ( 3)  = 2 y + 3

or, -3y - 9 =  2y + 3

⇒ 3  y +  2 y = -3  -  9

or, 5 y  = -12   ⇒   y = -12/5  = -2.4

⇒ y = - 2.4

Hence,for the given expression -3( y + 3 ) = 2 y + 3  the simplified value of  y = -2.4

Answer:

x = -12

Step-by-step explanation:

Set logs up on both sides-

log 16^x = log 64^x+4

The variable goes behind because of the exponent log property (exponents are permitted to go behind the log to multiply)-

x * log 16 = x + 4 * log 64

Divide both logs out-

log 64/log 16 = 1.5

Simplify-

x = x+4(1.5)

1.5x + 6 = x

Remove 1.5-

1 - 1.5 = -.5x

Simplify-

-.5x = 6

Divide both sides-

6/-.5x = -12

Hence, the answer would be -12

[tex]\bf (\stackrel{x_1}{6}~,~\stackrel{y_1}{1})~\hspace{10em} \stackrel{slope}{m}\implies -3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{-3}(x-\stackrel{x_1}{6})[/tex]

Answer:

1       18

2       36

3       54

4       72

Step-by-step explanation:

18 m/s every second means you multiply the time by rate (to get the distance traveled in 2 seconds, multiply 18m/s by 2 to get 36)

Answer:

$132 in ratio of 2:3:6 is $24, $36 and $72.

Step-by-step explanation:

Dividing $132 in ratio of 2:3:6

Let share of first be = [tex]2x[/tex]

Share of second will be = [tex]3x[/tex]

Share of third will be = [tex]6x[/tex]

Adding the shares

⇒ [tex]2x+3x+6x=11x[/tex]

Total value = $132

So we have,

[tex]11x=132[/tex]

Dividing both ides by 11.

[tex]\frac{11x}{11}=\frac{132}{11}[/tex]

[tex]x=12[/tex]

∴ First share = [tex]2\times 12=\$24[/tex]

∴ Second share = [tex]3\times 12=\$36[/tex]

∴ Third share = [tex]6\times 12=\$72[/tex]

Answer:

he volunteered 140 hours

Step-by-step explanation:

20*7=140

Answer:

The correct answer would be 15.

Step-by-step explanation:

30-15=15

45-2(15)=15

Answer: B

4x^{6} - 2x^{5} + 4x^{3} -x^{2} +4x

Step-by-step explanation:

3x⁵ - 2x³ + 4x  + 4x⁶ - 5x⁵ + 4x³ - x² =

= 4x⁶ + 3x⁵ - 5x⁵ - 2x³ + 4x³ - x² + 4x

= 4x⁶ - 2x⁵ + 2x³ - x² + 4x

Answer: seven hundred seventy six and seven thousand thirty two thousandths

Step-by-step explanation:

Answer:

seven hundred and seventy six and seven hundred thirty two thousandths

Answer:

20 m long,

each piece of cloth for $10

Step-by-step explanation:

Let x m be the length of the piece of cloth.

Original cloth:

Length = x m

Cost = $200

Cost per meter [tex]\dfrac{\$200}{x}[/tex]

Changed cloth:

Length = x + 5 m (5 m longer)

Cost = $200

Cost per meter [tex]\dfrac{\$200}{x}-\$2[/tex] (each metre of cloth was $2 less)

Hence,

[tex]\left(\dfrac{200}{x}-2\right)\cdot (x+5)=200[/tex]

Multiply the equation by x:

[tex](200-2x)(x+5)=200x\\ \\200x+1,000-2x^2-10x=200x\\ \\-2x^2-10x+1,000=0\\ \\x^2+5x-500=0\\ \\D=5^2-4\cdot(-500)=25+2,000=2,025\\ \\x_{1,2}=\dfrac{-5\pm\sqrt{2,025}}{2}=\dfrac{-5\pm 45}{2}=-25,\ 20[/tex]

The length cannot be negative, so x = 20 m, each metre for $10.

Answer:

The piece is 20 m long and costs $10 per meter

Step-by-step explanation:

The total cost of the cloth in $ can be expressed as

C = xu

Where x is the length of the cloth in m, and u is the unit cost in $/m

The problem states that if the length was 5 meters more and the unit cost was $2 less, the cost would not change, that is

C = (x+5)(u-2)

Operating:

C = xu-2x+5u-10

Since C = xu, then

-2x+5u=10         [1]

We also know that

xu=200        [2]

Isolating u in [1] we get

[tex]u=\frac{10+2x}{5}[/tex]

Replacing into [2]

[tex]x\frac{10+2x}{5}=200[/tex]

Simplifying

[tex]10x+2x^2=1000 \\=> x^2+5x-500=0[/tex]

Factoring

(x-20)(x+25)=0

Which gives x=20, x=-25. We can only use the positive value of x, so

x=20 m  and therefore

u=200/20=10$

So the piece is 20 m long and costs $10 per meter

Answer:

10) Supplementary; 11) Supplementary; 12) Complementary

Step-by-step explanation:

Sum of supplementary angles equals 180° while sum of complementary angles equals 90°.

For question 10

x + 70° = 180° (sum of straight lines)

x = 180° - 70° = 110°

Hence, 70° and 110° are supplementary angles.

For question 11,

x + 85° = 180° (sum of straight lines)

x = 180° - 85° = 95°

Hence, 85° and 95° are supplementary angles.

For question 12,

x + 32° = 90° (sum of right angles)

x = 90° - 32° = 58°

Hence, 32° and 58° are complementary angles.

Final answer:

The theorems about parallelograms are used in mathematics to find unknown sides or angles and to prove properties of figures. When dealing with vectors, the parallelogram rule for vector addition helps find the resultant by constructing a parallelogram with the vectors as sides and the diagonal as the resultant.

Explanation:

To use theorems about parallelograms to solve problems, we often apply these principles to find unknown sides or angles or to prove certain properties about the figures we are dealing with. For example, one theorem states that opposite sides of a parallelogram are congruent, which can be useful when you need to find the length of a missing side.

Regarding vector addition, the parallelogram rule is applied. According to this rule, if we are adding two vectors, say vector A and vector B, we place them tail to tail, draw the vectors such that they form adjacent sides of a parallelogram, and then the resultant vector is represented by the diagonal of the parallelogram that starts from the common tail of the two vectors.

Similarly, if we need to find the resultant of three or more vectors, we use the parallelogram rule iteratively. We first find the resultant of the first two vectors and then add the third vector to this resultant using the same rule. This process is based on the associative and commutative properties of vector addition.

Answer:

$70

Step-by-step explanation:

it is between both. I hope this helps

Answer:

$65 ≤ x ≤ $135

It can also be written as $65 ≤ x AND x ≤ $135

Step-by-step explanation:

Now, one should know the meaning of compound inequality. A compound inequality is the inequality which simply combines the two simple inequalities.

Now, in an inequality, three relations are performed, equal to, less than and greater than. You can combine 'equal to' with 'less than' or 'greater than' according to situation given.

Notice that in given sign

≤

the value at left side or the pointed side will be small or lesser than the value at right side. Also notify that if inverted, like this ≥

Value of left side will be greater. Means the value at pointed side will always be smaller. The lower bar is sign of equal to

if this is written

x ≤ 3

It means that x can be equal to three or any value less than 3 means 2,1,0,-1 etc.

Now in question given, it is stated that money should be not less than $65 means it can either be $65 or more but not less than it. Lets assume 'x' as the amount required,

So one inequality is

$65 ≤ x

For second condition which is amount should be no more than $135, means it can be $135 or less, so inequality is

x ≤ $135

Remember that we use AND in the answer because both statements of inequality are need to be fulfilled or satisfied.

Answer:

50

Step-by-step explanation:

200/2=100

100/2=50

A quarter of something is just another word for a fourth of something (1/4th).

We can solve this using two different ways.

Solution #1:

1/4 = 0.25

200 * 0.25 = 50 (quarter of 200)

Solution #2:

200 / 4 = 50 (quarter of 200)

______

Best Regards,

Wolfyy :)

Answer:

20/48

Step-by-step explanation:

Answer:

I think it would be 1/4+1/6

Step-by-step explanation:

2/8 can be simplified by 2 because 2 goes into 2 once so 1 and 2 goes into 8, 4 times so that equals 1/4 and I believe the 1/6 is already simplified.

Answer:

(18 + 6) + y = 18 + (6 + y)

Step-by-step explanation:

Answer:

the answer is (18 + 6) + y = 18 + (6 + y )

Step-by-step explanation:

i did the quiz and got it right!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

hope this helps!!!!!!!!!!!!!!!!!!!11

Step-by-step explanation:

[tex]\text{If is}\ \dfrac{3}{5}^4,\ \text{then}\ \dfrac{3}{5}^4=\dfrac{3\cdot3\cdot3\cdot3}{5}=\dfrac{81}{5}=16\dfrac{1}{5}\\\\\text{If is}\ \left(\dfrac{3}{5}\right)^4=\left(\dfrac{3}{5}\right)\left(\dfrac{3}{5}\right)\left(\dfrac{3}{5}\right)\left(\dfrac{3}{5}\right)=\dfrac{3\cdot3\cdot3\cdot3}{5\cdot5\cdot5\cdot5}=\dfrac{81}{625}[/tex]

Answer:

Using [tex]\pi =3.14[/tex] the volume of the cylinder is [tex]1471.875\ m^{3}[/tex]

Step-by-step explanation:

We are using [tex]\pi =3.14[/tex].

We know that volume of a cylinder is [tex]\pi (r)^2h[/tex]

For this we have

Height of the cylinder is given that is [tex]18.75\ m[/tex]

And the radius of the cylinder is unknown,

But there is a hint in which we can see that the diagonal,height and diameter forms a right angled triangle (or a cone).

Where [tex]21.25\ m[/tex] is the hypotenuse.

Using Pythagoras formula.

[tex](Hypotenuse)^2=(base)^2+(perpendicular)^2[/tex]

We can find the value of diameter which is the base over here.

So,

[tex]d=\sqrt{(21.25)^2-(18.75)^2}=\sqrt{(451.56-351.56)}=\sqrt{(100)}=10\ m[/tex]

Then radius [tex]\frac{diameter}{2} =\frac{10}{2}=5\ m[/tex]

Now using the above values and plugging it on to the formula.

Volume [tex]=\pi (r)^2h=(3.14)(5)^2\times 18.75=1471.875\ m^3[/tex]

So the volume of the cylinder is [tex]1471.875\ m^3[/tex]

Answer:

a. 127 pots

b. 2,943 cubic inches

Step-by-step explanation:

To find the amount of pots of soil can be filled, you can use the equation given. s = 3456 in part a

a.

s = 27p

3456 = 27p

divide 3456 by 27 to isolate p

p = 127 pots

Instead of substituting for s like in part a, you can now substitute for p, since you know that you need to fill 109 pots.

b.

s = 27 * 109

s = 2943 cubic inches

The gardener can fill 128 pots with the 3456 cubic inches of soil available. If the gardener needs to fill at most 109 pots, they will require 2943 cubic inches of soil.

To solve both parts of the question, we will use the function s = 27p, where s represents the amount of soil (in cubic inches) and p represents the number of pots.

Part a: Calculating the Number of Pots

The gardener has a bag containing 3456 cubic inches of soil. To find out how many pots can be filled from the bag, we need to divide the total amount of soil by the amount needed per pot:

p = 3456 cubic inches / 27 cubic inches per pot = 128 pots

Part b: Soil Needed for a Maximum Number of Pots

If the gardener needs to fill at most 109 pots, the total amount of soil required can be calculated using the provided function:

s = 27 cubic inches per pot * 109 pots = 2943 cubic inches of soil

Answer:

[tex]f(x)=16\, (\frac{3}{2} )^{x-1}[/tex]

Step-by-step explanation:

Since we are given the common ratio (3/2), all we need to find to define the geometric sequence, is its multiplicative factor ([tex]a[/tex]) that corresponds to the first term of the sequence - remember that all consecutive terms will be generated by multiplying this first value repeatedly by the common ratio (3/2) as shown below:  

[tex]f(1)=a\\f(2)=a\,*\,(\frac{3}{2} )\\f(3)=a\,*\,(\frac{3}{2} )^2\\f(4)=a\,*\,(\frac{3}{2} )^3\\f(5)=a\,*\,(\frac{3}{2} )^4[/tex]

Since we are given the information that [tex]f(5)=81[/tex] we can use this to find the value of the first term:

[tex]f(5)=\,a\,*\,(\frac{3}{2} )^4\\81=\,a\,*(\frac{81}{16} )\\a\,*\,81=\,81\.*\,16\\a\,=\,16[/tex]

Notice as well that the first term doesn't contain the common ratio, the second term contains the common ration (3/2) to the power one, the third one contains the common ratio to the power two, the fourth one contains it to the power three, and so forth. So the exponent at which the common ratio appears is always one unit less than the order (x) of the term in question. This concept helps us finalize the expression for the sequence's formula:

[tex]f(x)=16\,*\,(\frac{3}{2} )^{x-1}[/tex]

Answer:

B

The other answer was too long.

y= mx+b slope intercept form

slope is also m

b is the y-intercept

y-intercept= -3

slope=1/5

answer:

D. y = 1/5x - 3

Answer:

x = π - sin^(-1)(3/2) + 2 π n_1 for n_1 element Z

or x = 2 π n_2 + sin^(-1)(3/2) for n_2 element Z

Step-by-step explanation:

Solve for x:

sin(x) = 1.5

1.5 = 3/2:

sin(x) = 3/2

Take the inverse sine of both sides:

Answer:  x = π - sin^(-1)(3/2) + 2 π n_1 for n_1 element Z

or x = 2 π n_2 + sin^(-1)(3/2) for n_2 element Z

Answer:

(3.6 × 10^-5) + (3.5 × 10^-5) = 7.1 × 10^-5

Answer:

20%

Step-by-step explanation:

5000 - 4000 = 1000

[tex]\frac{1000}{5000}[/tex] × 100

[tex]\frac{1}{5}[/tex] × 100

0.2 × 100 = 20%

Check:

5000 - 20% of 5000

5000 - 2/10 × 5000

5000 - 1000

= 4000

Answer:

20% decrement

Steps:

➥5000-x% of 5000=400

➥5000-x% × 5000=4000

➥5000-4000=x% × 5000

➥1000=x% × 5000

➥x%=1000/5000

➥x%=0.2

➥x%=20/100

➥x%=20%

Answer:

The question has been presented in a complicated manner. I am answering the question based on my understanding. Line AB will never lie in plane R. The correct option among all the options that are given in the question is the third option.

hope I helped you answer your question:)

Answer:

never

Step-by-step explanation:

Answer:

the slope is -3

m=-3

i tried my best :(