what is 7 less than the product of 5 and a number?

Answer:

Positive discriminant = 2 real solution

x= -5,-40

Step-by-step explanation:

The discriminant is used to see how many solutions an equation has. If it is negative, the equation has no real solutions, if =0 the equation has 1, and if it is positive, the equation has two real solutions.

The discriminant is the part of the quadratic formula inside the square root:

[tex]b^{2}-4ac[/tex]

Every quadratic formula has the structure:

[tex]ax^{2} +bx+c=0[/tex]

So first, in order to meet this structure we need to add 200 to both sides so the equation is equal to 0. This gives us:

[tex]x^{2} +45x+200=0[/tex]

Our a=1, b=45 and c=200

Now we can substitute these values into the discriminant:

[tex](45)^{2} -4(1)(200)[/tex]

Solve:

[tex]2025-800=1225[/tex]

The discriminant is a positive number which means this equation will have 2 real solution. Now we just need to plug in our values into the quadratic formula to solve this equation. Quadratic formula:

[tex]x=\frac{-+/-\sqrt{b^{2}-4ac} }{2a} \\x=\frac{-45+/-\sqrt{1225} }{2}[/tex]

(Same discriminant value)

[tex]x=\frac{-45+/-35}{2}[/tex]

Now to find the two solutions, we use both signs in the equation. Solution 1:

[tex]x=\frac{-45+35}{2}[/tex]

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

Our first solution is -5, now for the second:

[tex]x=\frac{-45-35}{2}\\\\ x=\frac{-80}{2}=-40[/tex]

The two solution to this equation are -5 and -40.

Hope this helped!

Answer:

Wonka bars=3 and  Everlasting Gobstoppers=24

Step-by-step explanation:

let the wonka bars be X

and everlasting gobstoppers be Y

the objective is to

maximize 1.3x+3.2y=P

subject to constraints

natural sugar

4x+2y=60------1

sucrose

x+3y=75---------2

x>0, y>0

solving 1 and 2 simultaneously we have

4x+2y=60----1

x+3y=75------2

multiply equation 2 by 4 and equation 1 by 1 to eliminate x we have

 4x+2y=60

 4x+12y=300

-0-10y=-240

10y=240

y=240/10

y=24

put y=24 in equation 2 we have'

x+3y=75

x+3(24)=75

x+72=75

x=75-72

x=3

put x=3 and y=24 in the objective function we have

maximize 1.3x+3.2y=P

1.3(3)+3.2(24)=P

3.9+76.8=P

80.7=P

P=$80.9

Answer:

wonka bars=3 and  Everlasting Gobstoppers=24

Step-by-step explanation:

Answer:

6 y^5 - 8 y^4 - 10 y^3 + 36 y^2 - 28 y

Step-by-step explanation:

Expand the following:

(3 y^3 + 2 y^2 - 7 y) (2 y^2 - 4 y + 4)

| | | | 3 y^3 | + | 2 y^2 | - | 7 y | + | 0

| | | | | | 2 y^2 | - | 4 y | + | 4

| | | | 12 y^3 | + | 8 y^2 | - | 28 y | + | 0

| | -12 y^4 | - | 8 y^3 | + | 28 y^2 | + | 0 | + | 0

6 y^5 | + | 4 y^4 | - | 14 y^3 | + | 0 | + | 0 | + | 0

6 y^5 | - | 8 y^4 | - | 10 y^3 | + | 36 y^2 | - | 28 y | + | 0:

Answer: 6 y^5 - 8 y^4 - 10 y^3 + 36 y^2 - 28 y

9514 1404 393

Answer:

  9x -10y = 75

Step-by-step explanation:

The least common denominator is the least common multiple of the denominators. Here, that is 5×3 = 15. Multiplying both sides of the equation by that gives ...

  15(3/5x -2/3y) = 15(5)

  9x -10y = 75

Answer:

[tex]x[/tex]-intercept is [tex](68.5,0)[/tex]

[tex]y[/tex]-intercept is [tex](0,44.2)[/tex]

Step-by-step explanation:

Let [tex]x[/tex] denotes time denoted (in minutes) by a person in jogging.

Let [tex]y[/tex] denotes time denoted (in minutes) by a person in running.

A person is wanting to burn 500 calories a day through exercise. They know that they burn 7.3 calories a minute jogging and 11.3 calories a minute running.

So, equation becomes [tex]7.3x+11.3y=500[/tex]

For [tex]x[/tex]-intercept, put [tex]y=0[/tex]

[tex]7.3x+11.3(0)=500\\7.3x=500\\x=68.5[/tex]

So, [tex]x[/tex]-intercept is [tex](68.5,0)[/tex]

For [tex]y[/tex]-intercept, put [tex]x=0[/tex]

[tex]7.3(0)+11.3y=500\\11.3y=500\\y=44.2[/tex]

So, [tex]y[/tex]-intercept is [tex](0,44.2)[/tex]

Differentiate equation [tex]7.3x+11.3y=500[/tex] with respect to [tex]x[/tex]

[tex]7.3+11.3y'=0\\y'=\frac{-7.3}{11.3}\\ y'=-0.65[/tex]

[tex]x-[/tex]intercept means that a person spends 68.5 minutes in jogging and no time in running.

[tex]y-[/tex]intercept means that a person spends 44.2 minutes in running and no time in jogging.

Answer:

The table that starts with (-3, -1)

Step-by-step explanation:

For a table to represent a function the x value has to be different number. Such as, the other tables one has two -5, two -2, two -4 and etc. Do you get it

Answer: the first box

-3       -1

0         0

-2         -1

8          1

Step-by-step explanation:  the x value can not repet it self but the y value can

Answer:

2,1

Step-by-step explanation:

Answer:

295

Step-by-step explanation:

After 9 years, Alexander will have $295 in his bank account.

This is a type of interest that is compounded after time period it is said to be compounded. After that particular period, the interest is calculated and then added with the principle. For the next duration, the interest is calculated on the sum.

Here, to find the amount of money after n years, we need to use the formula S = P(1 + r)ⁿ.

For Alexander, S = sum of money after the total period of investment.

P = Principle = $240, r = rate of interest = 2.3% compounded annually, n = time period = 9 years.

Now, S = $240(1 + 2.3/100)⁹= $240(1 + 0.023)⁹ = $240(1.023)⁹ = $294.5

≈ $295

Hence, after 9 years, Alexander will have $295 in his bank account.

Learn more about compound interest here: brainly.com/question/25857212

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Answer:

85% of 19 = 16.15

Step-by-step explanation:

9514 1404 393

Answer:

  16 inches

Step-by-step explanation:

The sum of length and width is half the perimeter, so is 36 inches.

The width is 4/(4+5) = 4/9 of the total of length and width, so is ...

  (4/9)(36 inches) = 16 inches

The width of the rectangle is 16 inches.

Answer:

x = -6

Step-by-step explanation:

I hope this helps!

Answer:

x= -6

Step-by-step explanation:

3/2x+8-8=-1-8

3/2 x= -9

2. 3/2x=2(-9)

3x= -18

3x/3 = -18/3

x= -6

Density of fresh egg = 1.2 g/cm³.

Density of spoiled egg = Density of fresh egg   - 0.3 g/cm³.

Density of spoiled egg =( 1.2 - 0.3 ) g/cm³ = 0.9 g/cm³.

Now, it is given that any object with density less than 1 g/cm³ will float on water.

To tell whether an egg is spoiled or not using water. We should drop egg in water if it float then it is spoiled else it is fresh.

Hence, this is the required solution.

Answer:

x=19

Step-by-step explanation:

x=25-6

x=19

Answer:

x=19

Step-by-step explanation:

Step 1: Subtract 6 from both sides.

x+6−6=25−6

x=19

Answer:

27.20seconds

Step-by-step explanation:

hope this helped,brainliest?

Sum of 5th & 8th terms of an AP = 37

11th term = 32

A.P

We know that,

nth term of an AP – an = a + (n - 1)d

Hence,

⟹ a₅ + a₈ = 37

⟹ a + (5 - 1)d + a + (8 - 1)d = 37

⟹ 2a + 4d + 7d = 37

⟹ 2a + 11d = 37 -- equation (1)

Similarly,

⟹ a₁₁ = 32

⟹ a + (11 - 1)d = 32

⟹ a + 10d = 32

⟹ a = 32 - 10d

Substitute the value of a in equation (1).

⟹ 2(32 - 10d) + 11d = 37

⟹ 64 - 20d + 11d = 37

⟹ 64 - 37 = 20d - 11d

⟹ 27 = 9d

⟹ 27/9 = d

⟹ 3 = d

Substitute the value of d in equation (1).

⟹ 2a + 11(3) = 37

⟹ 2a + 33 = 37

⟹ 2a = 37 - 33

⟹ 2a = 4

⟹ a = 4/2

⟹ a = 2

Now,

General form of an ap = a , a + d , a + 2d...

⟶ Required AP = 2 , 2 + 3 , 2 + 2(3)...

⟶ Required AP = 2 , 5 , 2 + 6...

⟶ Required AP = 2 , 5 , 8...

I hope it will help you.

Regards.

Answer:

→ md - 2nd + 3md = 2 * [ a + (n - 1)d ]

→ 4md - 2nd = 2 * [ a + (n - 1)d ]

→ 2(2md - nd) = 2 * (a + nd - d)

→ 2md - nd - a + d = nd

→ 2md - nd - (md - 2nd) + d = nd

[ From equation (1) ]

→ 2md - nd - md + 2nd + d = nd

→ md + nd + d = nd

→ (m + n + 1)d = n * d

→ (m + n + 1) = n

Step-by-step explanation:

Answer: x=-3, y=2

Step-by-step explanation: -2x+y=8 + -3x-y=7 and you get x=-3 then you put that in to x and pick one of the beginning equations i chose to put -3 in to -2(-3)+y=8 and got 6+y=8 then you subtract the 6 on both sides and should get y=2

Answer:

(-3,2)

Step-by-step explanation:

You can solve it by various methods. These two equations can be solved simultaneously or by matrix method, or even by graphing

Simultaneous is easier so lets get started.

1st equation  : [tex]-2x+y=8[/tex]

2nd equation: [tex]-3x-y=7[/tex]

We solve it by using the substitution method which means there are two variables x and y and we substitute one variable in form of another variable.

Like, take the 1st equation

[tex]-2x+y=8\\y=8+2x[/tex]

the equation is arranged in a different manner but its the same thing.

This new equation becomes our new third equation and now we simply put our third equation in our 2nd equation. Like this, take the 2nd equation and substitute it with our 3rd third equation

[tex]-3x-y=7\\-3x-7=y\\-3x-7=8+2x\\-3x-2x=8+7\\-5x=15\\x=-3[/tex]

we get x=-3 and then we put the value of x and in our third equation to get the value of y or we can simply put it in any equation 1st , 2nd , 3rd it will give the same answer. I chose third.

[tex]y=8+2x\\y=8+2(-3)\\y=8-6\\y=2[/tex]

The solution set of our system of linear equations is

(-3,2)

Answer:

(2x-6)+4(x-3)

2x-6+4x-12

6x-18

6(x-3)

Answer:

1. For a rotation of 270° counterclockwise about the origin the coordinates of J' is (1, -2)

2. For a rotation of 180° counterclockwise about the origin the coordinates of K' is (-7, -1)

3. For a rotation of 90° counterclockwise about the origin the coordinates of L' is (3, 6)

4. For a rotation of 90° counterclockwise about the origin the coordinates of M' is (3, 1)

Step-by-step explanation:

The coordinates of the vertices of the parallelogram are given as follows;

J(2, 1), K(7, 1), L(6, -3), M(1, -3)

1. We have, for a rotation of 270° counterclockwise about the origin we have

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

Therefore, we have for the vertices;

f(J(2, 1)) = J'(1, -2)

Therefore, we have the coordinates of J' as (1, -2);

2. We have, for a rotation of 180° counterclockwise about the origin we have

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

Therefore, we have for the vertex point K;

f(K(7, 1)) = K'(-7, -1)

3. We have, for a rotation of 90° counterclockwise about the origin we have

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

Therefore, we have for the vertex point L;

f(L(6, -3)) = L'(3, 6)

4. We have, for a rotation of 90° counterclockwise about the origin we have

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

Therefore, we have for the vertex point M;

f(M(1, -3)) = M'(3, 1)

Answer:

d) 1/2 ÷ 4 = 1/2 • 4/1

Step-by-step explanation:

when dividing fractions use keep change flip (keep the first fraction, change the sign to multiplication, flip the second fraction)

when multiplying just multiply straight across

Answer:

You can exempt a A, C, and D because the greatest number out of the group is 4/5 which means 4/5 should be at the end of the list since it's going for least to greatest.

B is the answer

Answer:

25%

6.5%

35%

Step-by-step explanation:

Given the invoice :

Bill for a pair of Jean

Jeans ______39.99

Discount ___ - 10.00

Subtotal ____ 29.99

Sales tax ____ 1.95

Total _______ 31.94

A) % of discount to the nearest %

Discount amount = % discount * price

10 = x% * 39.99

10/39.99 = x%

0.2500625 = x%

x = 0.2500625 * 100%

% discount = 25%

% of sales tax:

Sales tax amount = % tax * Subtotal

1.95 = x% * 29.99

1.95/29.99 = x%

0.06502 = x%

x = 0.06502 * 100%

x = 6.5%

Markup before discount = 60%

Markup after discount = (60 - 25)% = 35%

Answer:

a...................

Answer:

Yes, the point lies on the line.

Step-by-step explanation:

 Given coordinate of the locus = (1,2)

  Equation of the line  2x+4y = 10

Unknown:

Does the given coordinate lie on the line?

Solution:

The equation given is that of a straight line. To solve this problem, we simply plug the coordinates of the point back into the equation and check if solves it.

   x  = 1 and y = 2;

   2x+4y = 10

 So;

    2(1) + 4(2) gives 2 + 8 = 10

Yes, the point lies on the line.

Answer:

[tex]y=-4x+6[/tex]

Step-by-step explanation:

If you are looking for a parallel line with just the equation then look for an equation with the same slope and different Y intercept. After you find that just check and see if it passes the coordinate.

[tex]2=-4(1)+6[/tex]

[tex]2=-4+6[/tex]

[tex]2=2[/tex]

If it works you have your answer!

The equation of the line parallel to y = -4x - 6 and passing through (1, 2) is

y = -4x + 6.

The slope of y = -4x - 6 is -4.

passing through the point (1, 2)

the new line is parallel to the original line, it will have the same slope (-4).

Use the point-slope form of a linear equation to write the equation of the new line. The point-slope form is y - y1 = m(x - x1), where m is the slope, and (x1, y1) is the given point.

substituting values,

y - 2 = -4(x - 1)

y - 2 = -4x + 4

y = -4x + 6

learn more about slope here

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Answer:

35502

Step-by-step explanation:

The product will be 35502, 183x100+183x90+183x4=18300+16500+732=35502. Hope it helps!

Answer:

The second answer

Step-by-step explanation:

Because if you subtract a negative from an equation you get positive (two negatives make a positive)

Answer: $0.14 per fluid ounce.

Step-by-step explanation: $4.48 divided by 32 = $0.14