Which term describes a fraction that has a variable or variable expression in its numerator, its denominator, or both?

A florist is filling a large order for a client. The client wants no more than 300 roses in vases. The smaller vase will contain

d1i1m1o1n [39]

Answer:

$8x+12y\leq 300$

$x\geq 6$

$y\leq 12$

$x\geq 2y$

Step-by-step explanation:

We are given that

x=Number of small vases

y=Number of large vases

Total number of roses not more than 300 in vases.

Number of roses in small vase atleast=8

Number of roses in large vase not more than =12

We have to find the constraints are placed on the variables in the given situation.

According to question

$8x+12y\leq 300$

$x\geq 6$

$y\leq 12$

$x\geq 2y$

4 0

3 years ago

Please don't answer wrong.

Tamiku [17]

Answer:

<u />

<u>Equation of a circle</u>

$(x-a)^2+(y-b)^2=r^2$

where:

(a, b) is the center
r is the radius

Given equation: $x^2+y^2=6.25$

Comparing the given equation with the general equation of a circle, the given equation is a <u>circle</u> with:

center = (0, 0)
radius = $\sqrt{6.25}=2.5$

To draw the circle, place the point of a compass on the origin. Make the width of the compass 2.5 units, then draw a circle about the origin.

Given equation: $x+y=1.5$

Rearrange the given equation to make y the subject: $y=-x+1.5$

Find two points on the line:

$x=-2 \implies -(-2)+1.5=3.5\implies (-2,3.5)$

$x=2 \implies -(2)+1.5\implies-0.5\implies (2,-0.5)$

Plot the found points and draw a straight line through them.

The <u>points of intersection</u> of the circle and the straight line are the solutions to the equation.

To solve this algebraically, substitute $y=-x+1.5$ into the equation of the circle to create a quadratic:

$\implies x^2+(-x+1.5)^2=6.25$

$\implies x^2+x^2-3x+2.25=6.25$

$\implies 2x^2-3x-4=0$

Now use the quadratic formula to solve for x:

$x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0$

$\implies x=\dfrac{-(-3) \pm \sqrt{(-3)^2-4(2)(-4)}}{2(2)}$

$\implies x=\dfrac{3 \pm \sqrt{41}}{4}$

To find the coordinates of the points of intersection, substitute the found values of x into $y=-x+1.5$

$\implies y=-\left(\dfrac{3 + \sqrt{41}}{4}\right)+1.5=\dfrac{3-\sqrt{41}}{4}$

$\implies y=-\left(\dfrac{3 - \sqrt{41}}{4}\right)+1.5=\dfrac{3+\sqrt{41}}{4}$

Therefore, the two points of intersection are:

$\left(\dfrac{3 + \sqrt{41}}{4},\dfrac{3-\sqrt{41}}{4}\right) \textsf{ and }\left(\dfrac{3 - \sqrt{41}}{4},\dfrac{3+\sqrt{41}}{4}\right)$

Or as decimals to 2 d.p.:

(2.35, -0.85) and (-0.85, 2.35)

6 0

2 years ago

The sum of the digits of a three digit number is 19. The second digit is one more than the first digit. The third

Oxana [17]

Answer:

D. 568

Step-by-step explanation:

Let the number is in the form of xyz

Sum of the digits is 19

x + y + z = 19

The second digit is one more than the first digit

y = x + 1

The third digit is two more than the second digit

z = y + 2 = x + 1 + 2 = x + 3

<u>Substitute the values of y and z</u> into the first equation and solve for x

x + x + 1 + x + 3 = 19
3x + 4 = 19
3x = 15
x = 5

<u>Find the value of y and z</u>

y = 5 + 1 = 6
z = 5 + 3 = 8

The number is 568

5 0

2 years ago

Perform the operation and, if possible, simplify<br> 21/20 - 4/15

Kazeer [188]

Answer:

47/60

Step-by-step explanation:

Find the LCM and multiply to get there.

LCM is 60

63/60-16/60

47/60

8 0

3 years ago

Find the measure of each angle.

Galina-37 [17]

<u>Given</u>:

Given that the isosceles trapezoid JKLM.

The measure of ∠K is 118°

We need to determine the measure of each angle.

<u>Measure of ∠L:</u>

By the property of isosceles trapezoid, we have;

$\angle K+\angle L=180^{\circ}$

$118^{\circ}+\angle L=180^{\circ}$

$\angle L=62^{\circ}$

Thus, the measure of ∠L is 62°

<u>Measure of ∠M:</u>

By the property of isosceles trapezoid, we have;

$\angle L \cong \angle M$

Substituting the value, we get;

$62^{\circ}=\angle M$

Thus, the measure of ∠M is 62°

<u>Measure of ∠J:</u>

By the property of isosceles trapezoid, we have;

$\angle J \cong \angle K$

Substituting the value, we get;

$\angle J =118^{\circ}$

Thus, the measure of ∠J is 118°

Hence, the measures of each angles of the isosceles trapezoid are ∠K = 118°, ∠L = 62°, ∠M = 62° and ∠J = 118°

4 0

3 years ago