Seven less than one-fourth of a number is 2. What is the number?

The two numbers whose sum is 7500 and whose product  is a maximum value are 3750 and 3750.

Let the two numbers be x and y.

Since their sum equals 7500,

x + y = 7500  (1)

Their product f(x,y) = xy  (2)

We desire to maximize the product.

From (1), x = 7500 - y

Substituting x into (2), we have

f(x,y) = xy

f(x,y) = (7500 - y)y

f(y) = 7500y - y²

To maximize the product, we find the value of y that maximizes f(y), we differentiate f(y) and equate it to zero.

So, df(y)/dy = d(7500y - y²)/dy

f'(y)/dy = d(7500y)/dy - dy²/dy

f'(y)/dy = 7500 - 2y

Equating it to zero, we have

7500 - 2y = 0

7500 = 2y

y = 7500/2

y = 3750

To determine if this gives a maximum for f(y), we differentiate f'(y) with respect to y.

So, f"(y) = d(7500 - 2y)dy

f"(y) = 0 - 2

f"(y) = -2 < 0.

So, y = 3750 gives a maximum for f(y) = f(x, y)

Since x = 7500 - y

Substituing y = 3750 into the equation, we have

x = 7500 - 3750

x = 3750

So, the two numbers whose sum is 7500 and whose product is a maximum product are 3750 and 3750.

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Answer:

B. [tex]\frac{\pi }{4} Rad>30^{0}[/tex]

Step-by-step explanation:

[tex]\frac{\pi }{4} Rad=(180/4)^{0} =45^{0}[/tex]

Hope this helps

Answer:

He works until 5:30.

Step-by-step explanation:

ok so first, every day don would take a total of 7 hours and 30 minutes on mon-Thurs. If we subtract his lunch from that total it would be 7 hours so next we do 7 hours times 9.75 which is 68.25$. Now that we know how much he makes per day, we times that by 4 since mon-thurs is 4 days. This would be 273$. Now we need to get to 360.75 so we subtract that. This would be 87.75$. Now if a normal day is 68.25$ and friday is 87.75, we find the diffrence which is 19.50. which is also 9.75(an hour) x 2 resulting in 2 hours extra. Therefore, he works 9 hours and 30 minutes on fridays (until 5:30). Thanks for putting in the work to understand and have a nice day!

Don must work approximately 9 additional hours on Friday to have a total pay of $360.75 for the week.

Don works from 8:00 AM to 3:30 PM Monday through Thursday. Let's calculate his total work hours for these four days:

Total work hours from Monday to Thursday:

(3:30 PM - 8:00 AM) - 0.5 hours (lunch break)

= 7.5 hours - 0.5 hours

= 7 hours (per day)

Total work hours for the week (Monday to Thursday):

4 days x 7 hours/day = 28 hours

Total pay for the week = Hourly rate x Total work hours + Additional hours on Friday

$360.75 = $9.75 x 28 hours + Additional hours on Friday

Additional hours on Friday = ($360.75 - $9.75 x 28) / $9.75

Additional hours on Friday = ($360.75 - $273) / $9.75

Additional hours on Friday = $87.75 / $9.75

Additional hours on Friday ≈ 9 hours (rounded to the nearest hour)

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Answer:

(1/2)x + 4 - 4 = 10 - 4

2(1/2)x = 6 * 2

x = 12

Answer:

y = 0.4 x

Step-by-step explanation:

Answer:

Step-by-step explanation:

A relation is only a function if ALL the x-values (the first number in the pairs) ONLY have one partner.

Check that -1

At first that -1 is paired up with a 5 in the ordered pair (-1, 5) but then later... that -1 is down there hanging out with a 1 in the last ordered pair (-1, 1).

This means that this relation (all the pairs lumped together) is NOT a function. Just because of that -1 pairing up with more that one partner.

Answer:

This a vector addition problem and you need to know the law of cosines and law of sines to solve this problem.

Two vector forces of 80lbs and 70 lbs act on an object at 40 degree angle between them.

The magnitude of the resultant force can be found by applying the law of cosines:

c2 = a2 + b2 - 2abcos140°

where a = 80, b = 70 and c is the resultant force vector you are asked to find

Once you find the magnitude of the resultant force, then you can find the angle it makes wrt the 70lb force using the law of sines:

sinα/a = sin140°/c

where α is the angle opposite side a, or the angle between the resultant and the 70lb vector that you are asked to find. so it would be 140lbs

Step-by-step explanation

Answer:

Definetly t = 4n

use this equation:

b+t+3+4

Answer:

D şıkkı iyi dersler hadi

Answer:

C: [tex](2x+5)(4x^2-10x+25)[/tex]

Step-by-step explanation:

First of all, you need to be able to recognize the two terms as cubes, and what they are cubes of. In this case, [tex]8x^3 = (2x)^3[/tex] and [tex]125=5^3[/tex].

Then you have to find a way you like to remember the formula for how to factorize. The way I do it is by saying "the binomial has the same zero as the original, so [tex]x^3+a^3=(x+a)(...)[/tex] and [tex]x^3-a^3 = (x-a)(...)[/tex] and the whole expression has one minus sign attached to the second term of either factor. In the sum of cubes first parenthesis has a plus, so the second term of the other parentesis has to take that minus: [tex]x^3+a^3=(x+a)(x^2-ax+a^2)[/tex] while in the difference of cubes you already used a minus, so everything else goes plus: [tex]x^3-a^3=(x-a)(x^2+ax+a^2)[/tex]

Or you commit the two formulas to memory.

Answer:

Step-by-step explanation:

x value of M is 1 - (-3) = 4 units to the right of A

B will be another 4 units to the right of M or x = 1 + 4 = 5

y value of M is -4 - (-6) = 2 units above A

B will be another 2 units above M or y = -4 + 2 = -2

B = (5, -2)

[tex]|m| -54\\\\\text{When}~ m=45,\\\\|45| -54 = 45 -54 = -9[/tex]

[tex]\huge\textbf{Hey there!}\\\\\\\\\\\\\\\huge\boxed{\mathbf{|m| - 54 = }}\\\huge\boxed{\rightarrow \mathbf{|45| - 54 = }}\\\huge\boxed{\mathbf{\rightarrow 45 - 54}}\\\\\huge\text{Start at 45 and go back 54 to the left.}\\\huge\text{You should be left on \boxed{\bf -9}}\\\\\\\huge\textbf{Therefore, your answer is: \boxed{\mathsf{-9}}}\checkmark\\\\\\\\\\\\\\\huge\textbf{Good luck on your assignment \& enjoy}\\\huge\textbf{your day!}\\\\\\\\\\\\\\\frak{Amphitrite1040:)}[/tex]

Answer:

[tex]-37\frac{3}{4}[/tex]

Step-by-step explanation:

0.75 is equivalent to three quarters, or (3/4).

3/4 would be the fraction. -37 would be the whole number.

[tex]-37.75 = \boxed{-37\frac{3}{4}}[/tex]

Hope this helps.

Answer:

- 37 3/4

Step-by-step explanation:

Answer:

8/3

Step-by-step explanation:

x equals 8/3

7x_2_4x_6=0

3x=8 ÷3 in both sides

Answer:

Which of the following graphs is described by the function given below?

y = 2x2 + 6x + 3

-A. Graph A

The function y = 2x^2 + 6x + 3 is a quadratic function that has a vertex of (-1.5,-1.5)

The equation of the function is given as:

y = 2x^2 + 6x + 3

Differentiate

y' = 4x + 6

Set to 0

4x + 6 = 0

This gives

4x = -6

Divide by 4

x = -1.5

Substitute x = -1.5 in y = 2x^2 + 6x + 3

y = 2(-1.5)^2 + 6(-1.5) + 3

Evaluate

y = -1.5

This means that the function y = 2x^2 + 6x + 3 has a vertex of (-1.5,-1.5)

See attachment for the graph of y = 2x^2 + 6x + 3

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Step-by-step explanation:

the surface area of that object consists of

2 triangles (one left, one right)

1 rectangle at the top

1 rectangle at the bottom

1 rectangle in the back

so, we need to calculate the area of each of these 5 areas and sum them up. that's it.

the area of such a triangle is

6×8/2 = 24 m²

we have 2 such triangles, so in total they are 48 m².

the rectangle at the top

10×12 = 120 m²

the rectangle at the bottom

12×8 = 96 m²

the rectangle in the back

12×6 = 72 m²

so the total surface area is

48 + 120 + 96 + 72 = 336 m²

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let "n" be the second odd number in the sequence

(n - 2) + n + (n + 2) + (n + 4) + (n + 6) = 135

                                              5n + 10 = 135

                                                      5n = 125

                                                        n = 25

23 + 25 + 27 + 29 + 31 = 135

Answer: 1 1/3 miles

Step-by-step explanation:

Since we know that an hour is 60 minutes, and 60 divided by 15 = 4, then we can multiply 1/3 times 4 to get the total number of miles in 60 minutes.

1/3 X 4 = 4/3

4/3 = 1 1/3

Therefore, the answer is 1 1/3 miles.

Therefore, in an hour, a person will walk 4/3 mile.

Hoped this helped.

[tex]BrainiacUser1357[/tex]

Answer:

3 1/5

Step-by-step explanation:

The improper fraction 16/5 is called improper because the top number(the numerator) is bigger than the bottom number(the denominator) we "fix" this by dividing and creating a mixed number (it is called mixed because there is a whole part and a fraction part):

As 16÷5 >>> doing this division gives you 3 wholes and 1/5 leftover. We write this as

3 1/5 (in handwriting the three is big and the 1/5 is a fraction, it is the mixed number they are asking you for)

Answer:

LCM is [tex]72[/tex]

GCF is [tex]1[/tex]

Step-by-step explanation:

LCM is least common multiplier

LCM of

[tex]8,9=8\times 9\\\\=72[/tex]

GCF is greatest common factor

Factors of [tex]8=1,2,4,8[/tex]

Factors of [tex]9=1,3,9[/tex]

Greatest common factor is [tex]1[/tex]

GCF is [tex]1[/tex]

Answer:

60

Step-by-step explanation:

Formula:

We know that

nth term of the AP is Tn = a+(n-1)d

Where, a = First term

d = Common difference

n = number of terms

Now,

Given that

pth term of the A.P. = Tp = q

⇛a + (p-1)d = q

⇛(p-1)d = q - a

⇛d = (q-a)/(p-1) →→→→(i)

and

qth term of the A.P. = Tq = p

⇛a + (q-1) d = p

⇛ (q-1)d = p-a

⇛ d = (p-a)/(q-1) →→→→(ii)

From Eqn(i) and Eqn(ii)

⇛(q-a)/(p-1) = (p-a)/(q-1)

On applying cross multiplication then

⇛(q-a)×(q-1) = (p-a)×(p-1)

⇛q²-q-aq+a = p²-p-ap+a

⇛q²-q-aq = p²-p-ap

⇛ap-aq = p²-p+q-q²

⇛a(p-q) = (p²-q²)-(p-q)

⇛a(p-q) = (p+q)(p-q)-(p-q)

⇛ a(p-q) = (p-q){(p+q)-1}

On cancelling (p-q) both sides then

⇛a = (p+q-1) →→→→Eqn(iii)

On Substituting the value of a in Eqn(ii) then

⇛ d = [p-(p+q-1)]/(q-1)

⇛d = (p-p-q+1)/(q-1)

⇛d = (-q+1)/(q-1)

⇛d = -(q-1)/(q-1)

⇛d = -1

We have,

a = p+q-1 and d = -1

Now, rth term of the AP

⇛ Tr = a + (r-1)d

⇛Tr = (p+q-1)+(r-1)(-1)

⇛ Tr = p+q-1+(-r+1)

⇛ Tr = p+q-1-r+1

⇛ Tr = p+q-r

Therefore, Tr = p+q-r

Answer: rth term of the given A.P. is p+q-r

Answer:

rth=q+p+qxp

Step-by-step explanation:

rth= 3 of the T and Tq added together and joined.

Answer:

[tex]-\frac{1}{3}[/tex]

Step-by-step explanation:

If we take points [tex](1,1)[/tex] and [tex](4,0)[/tex] from the line, we can determine the slope:

[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{0-1}{4-1}=\frac{-1}{3}=-\frac{1}{3}[/tex]

Therefore, the slope of the line is [tex]-\frac{1}{3}[/tex]

Answer:

W = 10

Step-by-step explanation:

W / 5 + 20 = 22

W / 5 - 20 = 22 - 20

W / 5 = 2

W * 5 = 2 * 5

W = 10

Step-by-step explanation:

[tex] \frac{w}{5} + 20 = 22 \\ \\ \frac{w}{5 } = 22 - 20 \\ \\ \frac{w}{5} = 2 \\ \\ w = 5 \times 2 \\ \\ w = 10[/tex]

Therefore, the solved inequality is z > -4.

Hoped this helped.

[tex]BrainiacUser1357[/tex]