Let a and b be rational numbers. Then by definition
a = m/n and b = p/p where m, n, p, and q are integers
xy=m/n × p/q
ng
so xy is the quotient of two integers.
This proof shows that the product of two rational numbers is........
a. an integer
b. irrational
c. rational
d. a whole number ​

Answer:

10 pairs of earrings and 5 necklaces (the maximum profit will be $250)

Step-by-step explanation:

Let x be the number of earrings and y be the number of necklaces Lisa makes.

1.  Lisa only has enough materials to make 15 total jewelry items per week, then

[tex]x+y\le 15.[/tex]

2.  It takes half an hour to make a pair of earrings, so it takes her [tex]\dfrac{1}{2}x[/tex] hours to make x earrings. It takes her 1 hour to make a necklace, so it takes her y hours to make y necklaces. Lisa only has 10 hours a week to make jewelry, thus

[tex]\dfrac{x}{2}+y\le 10[/tex]

3. Lisa makes a profit of $15 on each pair of earrings and $20 on each necklace. In total her profit is

[tex]P=15x+20y.[/tex]

You have to find the maximum value of the function [tex]P=15x+20y[/tex] with respect to inequalities

[tex]x+y\le 15\\ \\\dfrac{x}{2}+y\le 10[/tex]

Draw the solution set on the coordinate plane (see attached diagram). The maximum value of the efunction P is at point (10,5) and is

[tex]P=15\cdot 10+20\cdot 5=150+100=\$250[/tex]

Answer:

[tex]\large\boxed{y=-\dfrac{1}{2}x+\dfrac{3}{2}}[/tex]

Step-by-step explanation:

[tex]\text{Let}\ k:y=_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\============================\\\\\text{We have}\ 2x-y=5.\\\\\text{Convert to the slope-intercept form y = mx + b:}\\\\2x-y=5\qquad\text{subtract 2x from both sides}\\\\-y=-2x+5\qquad\text{change the signs}\\\\y=2x-5\to m_1=2\\\\\text{Therefore}\ m_2=-\dfrac{1}{2}.[/tex]

[tex]\text{The equation of the searched line:}\ y=-\dfrac{1}{2}x+b.\\\\\text{The line passes through }(3,\ 0).\\\\\text{Put the coordinates of the point to the equation.}\ x=3,\ y=0:\\\\0=-\dfrac{1}{2}(3)+b\\\\0=-\dfrac{3}{2}+b\qquad\text{add}\ \dfrac{3}{2} \text{to both sides}\\\\b=\dfrac{3}{2}[/tex]

Answer:

3.6 hours

Step-by-step explanation:

Blake can do work in hours = 9

Blake can do a part of work in 1 hour = [tex]\frac{1}{9}[/tex]

Ned can paint the same room in six hours.

Ned can do a part of work in 1 hour = [tex]\frac{1}{6}[/tex]

They can do a part of work together in 1 hour =  [tex]\frac{1}{9}+\frac{1}{6}[/tex]

                                                                           =  [tex]\frac{5}{18}[/tex]  

Now they can do [tex]\frac{5}{18}[/tex]  part of work in hour = 1

So, they can do whole work in hours =  [tex]\frac{1}{\frac{5}{18}}[/tex]

                                                             =  [tex]3.6[/tex]

Hence it will take 3.6 hours to paint the room if they work together.

Answer:

360

Step-by-step explanation:

f varies directly as g

f = kg  where k is the constant of variation

f varies inversely as h

f = kg/h

We know g = 198 when  h = –11 and f = –6.  Substituting in

-6 = k*198/(-11)

-6 =k*(-18)

Dividing each side by -18

-6/-18 = k*-18/-18

1/3 =k

Our equation is

f = 1/3 g/h

Letting  f = 12 and h = 10

12 = 1/3 g/10

Multiply each side by 10

12*10 =1/3 g/10*10

120 = 1/3 g

Multiply each side by 3

120*3 =1/3 g *3

360 =g

ANSWER

[tex]b \geqslant - 18[/tex]

EXPLANATION

The given inequality is:

[tex] - 18 \leqslant b[/tex]

We can rewrite this as:

[tex]b \geqslant - 18[/tex]

The above two inequalities have the same meaning.

Reading from right to left, the first inequality says, "b is greater than or equal to negative 18."

Reading from left to right, the second inequality says, "b is greater than or equal to negative 18."

Therefore the two inequalities have the same meaning.

Step-by-step Answer:

Many inequalities are possible, for example:

Keeping the less than or equal to sign, we could write

-18-b<=0

or, switching sides,

b>= -18   (just by switching sides)

b+18>=0  (by transposing -18 to the left)

Then again, we can multiply both sides by -1, but we need to change the direction of the inequality:

18>=-b

or equivalently, by transposing 18 to the other side

0>=-b-18

and similarly

b+18>=0  (we already had this above)

Guess time to stop!

Answer:

1) 45 minutes or 0.75 hours

2) 45 minutes or 0.75 hours

Step-by-step explanation:

We are given the graph that shows Miriam's bike ride.

The x-axis represents the time (in minutes) and the y-axis represents the distance traveled in miles.

1) How many hours did Miriam stop to rest?

The graphs stays the same from 45 minutes to 90 minutes, where he took the rest. No distance covered in that time.

Rest time = 90 minutes - 45 minutes = 45 minutes

He took rest for 45 minutes.

In hours, it is 45/60 = 0.75 hours

2) How many hours did it take Miriam to bike the initial 8 miles.

Look at the graph, the graph reached 8 miles when the time was 45 minutes.

It took 45 minutest to reach 8 miles initially.

In hours, it is 45/60 = 0.75 hours

Answer:

C. (5, -2)

Step-by-step explanation:

Midpoint:

x = (x1+x2)/2 = (16-6)/2 = 10/2 = 5

y = (y1+y2)/2 = (5 - 9)/2 = -4/2 = -2

Answer

Midpoint (5, -2)

The midpoint of the graphed line segment is (5, -2)

The correct option is C) (5, -2).

The midpoint formula is expressed as;

Midpoint = ( ( x₁+x₂ )/2, ( y₁+y₂ )/2 )

From the graph:

Point 1 (16, 5)

x₁ = 16

y₁ = 5

Point 2 (-6,-9)

x₂ = -6

y₂ = -9

Plug the coordinates into the above formula and solve for the midpoint:

Midpoint = ( ( x₁+x₂ )/2, ( y₁+y₂ )/2 )

Midpoint = ( ( 16+(-6) )/2, ( 5+(-9) )/2 )

Midpoint = ( ( 16 - 6 )/2, ( 5 - 9 )/2 )

Midpoint = ( 10/2, -4/2 )

Midpoint = ( 5, -2 )

Therefore, the midpoint is (5, -2).

Option C) (5, -2) is the correct answer.

Learn more about the midpoint formula here: https://brainly.com/question/28577846

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Answer:48 red marbles

Step-by-step explanation:

144÷24= 6

6*5= 30 white

6*11= 66 black

6*8= 48 red

Answer:  The number of red marbles in the jar is 48.

Step-by-step explanation:  Given that the number of white, black and red marbles in a jar are in the ratio 5 : 11 : 18. And the total number of marbles in the jar is 144.

We are to find the number of red marbles in the jar.

Let, 5x, 11x and 8x be the number of white, black and red marbles in the jar.

Then, according to the given information, we have

[tex]5x+11x+8x=144\\\\\Rightarrow 24x=144\\\\\Rightarrow x=6.[/tex]

Therefore, the number of red marbles will be

[tex]8x=8\times6=48.[/tex]

Thus, there are 48 red marbles in the jar.

14+38=52

52-38= 14

Answer: 38 and 14.

I think this is the answer.

33 and 19

33+19=52

33-19=14

After distributing the -1, you will find

y+7= -x-6

Finally, isolate y to find your answer in the linear form of

y= -x-13

Answer:

x=35

Step-by-step explanation:

The angles are alternate interior angles.  Alternate interior angles are equal if the lines are parallel.

3x+16 = 5x-54

Subtract 3x from each side

3x -3x+16 = 5x-3x-54

16 = 2x-54

Add 54 to each side

16+54 = 2x-54+54

70 = 2x

Divide each side by 2

70/2 = 2x/2

35 =x

ANSWER

1. No solution

2. 4 and 6

3. 81

EXPLANATION

1. The given quadratic equation is

[tex] {x}^{2} + 1 = 0[/tex]

This implies that:

[tex] {x}^{2} = - 1[/tex]

There is no real number whose square is negative one.

This quadratic equation has no solution.

2. The given quadratic equation is

[tex] {x}^{2} - 10x + 24 = 0[/tex]

We split the middle term with -6,-4 because their product is 24 and their sum is -10

[tex]{x}^{2} - 6x - 4x+ 24 = 0[/tex]

We factor by grouping

[tex]{x}(x - 6)- 4(x - 6)= 0[/tex]

[tex](x - 6)(x - 4)= 0[/tex]

We have x=4 and x=6.

3. The given quadratic equation is

[tex] {x}^{2} - 18x = 7[/tex]

We the square of half the coefficient of x to both sides of the equation.

[tex]( - \frac{18}{2} )^{2} = ( { - 9)}^{2} = 81[/tex]

The correct choice is C.

3 hours equals 195.

5 hours equals 325

9 hours equals 585

10 hours equals 650

To find this I multiplied the hours by 65 pages.

Hope this helps :)

Answer:

70/9

Step-by-step explanation:

multiply the parenthesis

add the constant together then divide

Answer:

70 / 9

Step-by-step explanation:

9(X - 9) = -11

9X - 81 = -11

      9X = -11 + 81

      9X = 70

        X = 70 / 9

[tex] \sqrt{0.81} = (0.9)[/tex]

Answer:

the correct answer is .9

.9 times .9 is .81

blackpink dun dunna dun dun dun dunna

Answer:

C) 50,653

Step-by-step explanation:

y = 1000(3.7)^x

After 3 hours   x=3

y = 1000(3.7)^3

y = 1000(50.653)

y =50653

Answer: OPTION C

Step-by-step explanation:

You know that in the function [tex]y = 1000(3.7^x)[/tex] the variable "y" is the number of bacterias in a petri dish  and the variable "x" is the number of hours.

Then, to answer the question "How many bacteria will there be after 3 hours?", you need to substitute [tex]x=3[/tex] into the function.

Therefore, the number of baterias after 3 hours will be:

[tex]y = 1000(3.7^3)[/tex]

[tex]y = 1000(50.653)[/tex]

[tex]y = 50,653[/tex]

This matches with the option C.

1/3 = 33%

33% * 390 = 118.8

Your answer 118.8 degrees

Answer: 120 degrees

Step-by-step explanation:

Just did it.

Answer:

the answer is 3

Step-by-step explanation:

21/8 simplify is 3

Yeah, The answer is 3

Answer:

The equation [tex]y=x^2+1[/tex] will be a parabola when it is graphed

Answer:

It's a parabola

Step-by-step explanation:

The equation seems to a parabolic function. The parabola is defined as:

[tex]y=Ax^2+b[/tex]

where b is a displacement, we can notice that in our case A=1 and b=1

so it is a parabola with a vertical displacement of one unit.

Answer: [tex](f-g)(x)=-x+10[/tex]

Step-by-step explanation:

Given the function f(x):

[tex]f(x)=3x-1+4[/tex]

And given the function g(x):

[tex]g(x)=4x-7[/tex]

You must subtract both functions is order to find [tex](f-g)(x)[/tex].

You need to remember the multiplication of signs:

[tex](+)(+)=+\\(-)(-)=+\\(+)(-)=-[/tex]

Then:

[tex](f-g)(x)=3x-1+4-(4x-7)[/tex]

Now, you must distribute the negative sign:

[tex](f-g)(x)=3x-1+4-4x+7[/tex]

And finally, add the like terms. Then you get that  [tex](f-g)(x)[/tex] is:

[tex](f-g)(x)=-x+10[/tex]

Answer:30

Step-by-step explanation: V=1/3 Bh, 9x10=90 divide that by 3 for 30

The volume of a triangular pyramid that is 10 inches tall and has a base area of 9 square inches is 30 cubics in.

Take a triangle. This is a base.

Now take 3 triangles such that each of them is connected to the one-one side of the first triangle and when they're taken together, they form a closed object, called a triangular pyramid.

The volume of a triangular pyramid that is 10 inches tall and has a base area of 9 square inches

The volume of a triangular pyramid

V = 1/3 x B x h,

V = 1/3 x 9 x 10

V = 3 x 10

V = 30

Hence, the volume will be 30 cubics in.

Learn more about triangular pyramids here:

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Answer:

The cost of one pack of paper was $0.90 and the cost of one box of pens was $2.00

Step-by-step explanation:

Let

x----> the cost of one pack of paper

y---> the cost of one box of pens

we know that

10x+12y=33 ----> equation A

15x+7y=27.50 ---> equation B

Solve the system of equations by graphing

Remember that the solution of the system of equations is the intersection point both graphs

The solution is the point (0.9,2)

see the attached figure

Therefore

The cost of one pack of paper was $0.90

The cost of one box of pens was $2.00

Answer:

pens = $2

paper = .9

Step-by-step explanation:

p = price of a pack of paper

n =  price of a box of pens

10p + 12n = 33

15p + 7n = 27.50

Multiply the first equation by 3

3(10p + 12n )= 33*3

30p +36n = 99

Multiply the second equation by -2

-2(15p + 7n) = 27.50*-2

-30p -14n = -55

Add the 2 modified equations together

30p +36n = 99

-30p -14n = -55

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

    22n = 44

Divide each side by 22

22n/22 = 44/22

n =2

Each box of pens is $2

Now we can find the price of the paper

10p + 12n = 33

10p +12(2) = 33

10p +24 =33

Subtract 24 from each side

10p+24-24=33-24

10p = 9

Divide by 10

10p/10 =9/10

p = .9

0.5 as a percent is 50%

0.5 to a percent value is 50%

The solution is X=0.4

The answer is the first one

Answer:

5(1248 lb/horse + t lb) ≤ 8000 lb

Step-by-step explanation:

One way to do this is to find the average weight of the 5 horses:

It is:

6,240 lb

---------------- = 1248 lb/horse

  5 horses

and to this, for each horse, we must add t lbs tack.

Thus, 5(1248 lb/horse + t lb) ≤ 8000 lb

would be an appropriate inequality.

Please note that your question mentions "the following inequalities;" that means you are expected to share them!  Please do so next time.  Thanks.

I would say option A best proves it is a parallelogram.

Answer:

hypotenuse = 20

leg = x + 4

other leg = x

From the Pythagorean Theorem we know that

20^2 = (x + 4)^2 + x^2

400 = x^2 + 8x + 16 + x^2

2 x^2 + 8x -384 = 0

Solving the quadratic equation we get

x = 12 and x = -16

x = 12 and so the lengths of the 2 legs are:

12 and 16

Right Triangle Area = (leg1 * leg2) / 2

Right Triangle Area = (12 * 16) / 2

Area = 192 / 2

Area = 96 square centimeters

Step-by-step explanation:

To find the area of the triangle, we used the Pythagorean theorem to solve for the legs, obtaining lengths of 16 cm and 12 cm. The area is then calculated using the formula for the area of a right triangle (1/2 * base * height), resulting in an area of 96 cm².

We are given a right triangle with a hypotenuse of 20 cm and two legs where one leg (let's call it a) is 4 cm longer than the other leg (let's call it b). Using the Pythagorean theorem, we can express the relationship between the legs and the hypotenuse: a² + b² = 20². We know that a = b + 4, so if we substitute a into the equation, we get:

(b + 4)² + b² = 400

b² + 8b + 16 + b2 = 400

2b² + 8b - 384 = 0

Dividing everything by 2, we get:

b² + 4b - 192 = 0

Using the quadratic formula or factoring, we find that b = 12 (b can't be negative). Consequently, a = 16. The area of the triangle is given by 1/2 * base * height, which is:

Area = 1/2 * a * b

Area = 1/2 * 16 * 12

Area = 1/2 * 192

Area = 96 cm²

Answer: Second Option

{x| x< -3 ∪ x > 3}

Step-by-step explanation:

To solve the inequality

[tex]| x | >3[/tex] there are two cases:

Case 1.   [tex]x>0[/tex]

[tex]x > 3[/tex]

Case2. [tex]x<0[/tex]

[tex]-x > 3[/tex]

[tex]x < -3[/tex]

The final solution is the union of the solution of each case

This is:

[tex]x < -3[/tex] or [tex]x > 3[/tex]

{x| x< -3 ∪ x > 3}

2, -1. I think, possibly.

Answer:

3, -1

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

Try the points and see:

(x, y) = (-1, 3) . . . . x + y = -1 + 3 = 2 . . . . yes

(x, y) = (3, -1) . . . . x + y = 3 + (-1) = 2 . . . yes

The remaining points lie on the line connecting these points, so they, too will be on the graph of that line.