Simplify square root of 540 Radical way

ANSWER

EXPLANATION

We want to differentiate y given:

To differentiate fractions as this, we first spllit the numerator and denominator as:

U = x

V = 4x - 5

Now, differentiate them separately.

dU/dx = 1

dV/dx = 4

Now, use formula:

So, let us put those values in there:

That is the answer

Answer:

(17, -12)

Explanation:

The system of equations is

7x +5y = 59

3x - 9y = 159

An ordered pair satisfies the system if it satisfies both equations. So, for each option we need to replace the ordered pair on the given equations.

For (x, y) = (-17, -12)

7x +5y = 59

7(-17) + 5(-12) = 59

-119 - 60 = 59

-179 = 59

The equality is not satisfied, so (-17, -12) is not a solution to this system

For (x, y) = (-17, 12)

7x +5y = 59

7(-17) + 5(12) = 59

-119 + 60 = 59

-59 = 59

The equality is not satisfied, so (-17, 12) is not a solution to this system

For (x, y) = (17, -12)

7x +5y = 59

7(17) + 5(-12) = 59

119 - 60 = 59

59 = 59

3x - 9y = 159

3(17) - 9(-12) = 159

51 + 108 = 159

159 = 159

Since both equations are satisfied, so (17, -12) is a solution to the system of equations

Therefore, the answer is (17, -12)

Deceleration is the term used to describe a decrease in speed as the body moves away from the beginning place. The opposite of acceleration is deceleration. It is written as. Negative acceleration is another name for deceleration.

As she climbs a slope, a bicycle slows from 40 km/h to 10 km/h in 10 seconds. How quickly does she brake?

When motion changes, the term acceleration is used to describe it. It is customary to refer to accelerating as going faster and decelerating as going slower.

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The required cost of the bushes is $23 and the cost of the tree is $45.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,

Let the prices of bushes are x and prices of tress are y,
According to the question,
13x + 4y = 487 - - - - -  -(1)
6x +2y = 232  - - - - - -  -(2)

From equation 2
y = 116 - 3x - - - -  -(3)
Put this y in equation 1
13x + 4(116 - 3x) = 487
13x + 464 - 12x = 487
x = 487 - 464
x = 23
Now put this x in equation 3
y = 116 - 3(23)
y = 116 - 69
y = 45

Thus, the required cost of the bushes is $23 and the cost of the tree is $45.

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The diameter of circular field is 290ft .

The area of circular field is

It is given that 1 lb of grass seed covers about 400 square feet of field.

The smallest number of bags he should buy is

(x + 8)(x + 8)

factors of 64 whose sum gives 16: +8 and +8

factorise:

Hence, the factorised form:

(x + 8)(x + 8)

Answer:

yes

Step-by-step explanation:

The final answer would be -126<-105

79 degree

Explanation:

When typing tan^-1 (5), click on the function that allows you to access the tan^-1 (generaly above the tan option),

Info given

We have the following info given

x. y

3. 12

5. 20

6. 24

9. 36​

Solution

In order to see if the two quantites are prportional we can check the following:

k=y/x

If we analyze the first pair of values we have:

k= 12/3=4

And for the next pairs we have:

k= 20/5=4

k= 24/6=4

k=36/9=4

So then as we can see the value of k is the same so then we can say that x and y are proportional since for each unit that x increase y increase 4 units

downloading about 35%

Solution:

Given:

The graph of the above equation is shown below:

The critical values points are

The simplified mixed number upon evaluation is [tex]3\frac{11}{27}[/tex].

Given:

a = −3/5 and b = −6.75

We have to determine the value of (2a−1/3) ÷ b/15.

Substituting the values of a and b in the expression, we get

(2(−3/5)−1/3) ÷ (−6.75)/15

⇒ (-6/5 - 1/3) ÷ (-0.45)

⇒ (-23/15) ÷ (-0.45)

⇒ 23/15 × 100/45

⇒ 92/27

⇒ [tex]3\frac{11}{27}[/tex]

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Answer:

The intercept points are:

The vertex is:

Step-by-step explanation:

To find the intercept points, we equal the function to zero and solve for x, as following:

Now, we know that the intercept points have an x-value of -3 and -2. Since we're talking about intercepts, the y-values will be 0.

Therefore, we can conlcude that the intercept points are:

The vertex of any given quadratic function in the form:

is:

This way, for the given function, we'll have that the vertex point is:

14 = -2c - 6 - 3c

14 + 6 = -2c - 3c

20 = -5c

c = 20/-5

c = -4

The x and y intercepts of the graph - 2x + 3y = - 6 are  (3, 0) and (0, -2).

We know to find the x-intercept of a graph we have to substitute y = 0 in the given equation and to find the y-intercept we have to substitute x = 0 in the given equation.

The graph of the equation is - 2x + 3y = - 6.

Now at y = 0, the equation becomes

- 2x + 3(0) = -6.

- 2x = - 6.

2x = 6.

x = 3.

Now at x = 0, the equation becomes

- 2(0) + 3y = - 6.

3y = - 6.

y = - 2.

∴ The x and y intercepts of the graph are (3, 0) and (0, -2).

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Answer:

176 feet of shadow

Step-by-step explanation:

Since 5 feet cast 40 feet, that means that 1 foot casts 8 feet. 22*8 = 176.

We can start solving the solution to the polynomial given by factoring out 2x, getting:

The expression inside the parenthesis is a quadratic equation. By methods of factoring, we can rewrite this as:

Solving for the value of x that satisfies the polynomial given, we have:

Hence, the solutions to the polynomial given are x = -5, 0, 3.

Answer: x = -5, 0, 3

The measures of the numbered angles are as follows:

3.

4.

When parallel lines are cut by a transversal line, angle relationships are formed such as alternate angles, corresponding angles, linear angles, vertically opposite angles etc.

Therefore, line a and b are parallel to each other. The transversal line t cut the parallel lines.

Hence,

3.

m∠1 = 180 - 41 = 139° (angles on a straight line)

m∠2 = 41° (vertically opposite angles)

Vertically opposite angles are congruent.

m∠3 = 139° (vertically opposite angles)

m∠4 =  180 - 41 = 139° (same interior angles)

Same interior angles are supplementary.

m∠5 = 41° (same interior angles)

m∠6 = 139° (vertically opposite angles)

m∠7 = 41° (vertically opposite angles)

4.

m∠1 = 117° (alternate exterior angles)

Alternate exterior angles are congruent

m∠2 = 180 - 117 = 63° (sum of angles on a straight line)

m∠3 = 117° (vertically opposite angles)

m∠4 = 63° (vertically opposite angles)

m∠5 = 117° (vertically opposite angles)

m∠6 = 180 - 117 = 63° (sum of angles on a straight line)

m∠7 = 63° (vertically opposite angles)

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Given the numbers: 4, -2, and 10.​

We want to create three different expressions that are each equal to 20.

First Expression

Second Expression

Third Expression

(a) We need to find the number of combinations of selecting 3 courses of a group of 5 courses.

The number of combinations of n things chosen r at a time is found using:

Substituting with n = 5 and r = 3, we get:

The 10 possible combinations are:

• 669, 644, 679

• 669, 634, 644

• 669, 679, 656

• 669, 634, 656

• 634, 644, 679

• 634, 644, 656

• 669, 644, 656

• 634, 679, 656

• 669, 634, 679

• 644, 679, 656

(b) There is a 1 in 10 chance that these courses will be selected

The measure of the angles are given below.

What is an angle?

An angle is a symbol in Euclidean space made up of two arcs that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are on the plane where the rays are located. The meeting of 2 dimensions ultimately creates angles. We refer to these as dihedral angles. The angle formed by the rays lying perpendicular to the two crossing curves at the point of junction is another property of intersecting curves. Angle can also refer to the length of a rotation or an angle. This metric represents the relationship between a circular arc's length and radius. The arc is centered when there is a geometric angle.

Answer 2

angle 1 = angle 6 = angle 9 = angle 14 = 97°

angle 4 = angle 7 = angle 12 = angle 15 = 114°

angle 2 = angle 5 = angle 10 = angle 13 = 180° - 97° = 83°

angle 3 = angle 8 = angle 11 = angle 16 = 180° - 114° = 66°

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The student whose name is Joy has described the function correctly as the line is horizontal line.

What are the coordinates ?

Coordinates are a set of values which helps to show the exact position of a point in the coordinate plane.

The given coordinates of the linear function f(x) are (-9, 4) and (6,4).

The y-coordinates for both of these points will be the same if we plot them on the graph.

Additionally, if the y-coordinates on the graph are the same, then the line connecting these points is horizontal in nature.

So , we can conclude that , Joy is saying correct by saying it is a horizontal line.

Therefore , the student whose name is Joy has described the function correctly as the line is horizontal line.

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The quadratic equations solved using the square root property is;

a. x = -3 and 7

b. x = 3 and -11

Given the quadratic equation as;

(x -2)² - 11 = 14

To determine the roots, we have to take the following steps;

expand the bracket

(x-2)(x-2) - 11 = 14

x² -2x -2x + 4 - 11 =1 4

collect like terms

x² - 2x - 2x + 4 -11 - 14 = 0

Add or subtract like terms

x² - 4x - 21 = 0

Factorize the equation

x² - 7x + 3x - 21 = 0

factorize further

x(x - 7) + 3(x - 7) = 0

Then. x = - 3, x = 7

x² + 8x + 16 = 49

collect like terms

x² + 8x + 16 - 49 = 0

x² + 8x - 33 = 0

Factorize further

x² + 11x - 3x - 33 = 0

x( x + 11) - 3(x + 11) = 0

Then, x = 3 and x = -11

Hence, the values are -3 and 7 and 3 and -11 respectively.

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Solution:

Given:

Let the washer be represented by w.

Let the dryer be represented by d.

Hence,

Substituting the equation (2) into equation (1);

Hence, the cost of the dryer is $425 and the cost of the washer is $480.

Therefore, the cost of the dryer is $425.

To answer this question we will set the equation y=f(x), then we will solve the equation for x, and finally, we will exchange x and y.

Setting y=f(x) we get:

Subtracting 12 from the above equation we get:

Multiplying the above equation by 4/3 we get:

Exchanging x and y in the above equation we get:

Therefore the inverse function of h(x) is:

Answer:

1) Simplifying this product, using the distributive property

(-3h -4)(4h-3)

-12h²+9h-16h+12

-12h²-7h +12

2) Inserting the table, or better making a similar one, multiplying the row by the column number:

_____|4h | -3 |

-3h | -12h² | 9h |

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

-4 | -16h | 12

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

-12h² +9h -16h +12

-12h² -7h +12

3) So the answer is -12h²-7h +12

Answer:

Chau served 63 orders.

Elsa served 16 orders.

Felipe served 21 orders.

Step-by-step explanation:

Given information:

Define the variables:

Create a system of equations from the given information and defined variables:

[tex]\begin{cases}e+c+f=100\\c=3f\\e=f-5\end{cases}[/tex]

Substitute the second and third equations into the first equation and solve for f:

[tex]\implies e+c+f=100[/tex]

[tex]\implies (f-5)+3f+f=100[/tex]

[tex]\implies 5f-5=100[/tex]

[tex]\implies 5f=105[/tex]

[tex]\implies f=21[/tex]

Substitute the found value of f into the second equation and solve for c:

[tex]\implies c=3f[/tex]

[tex]\implies c=3(21)[/tex]

[tex]\implies c=63[/tex]

Substitute the found value of f into the third equation and solve for e:

[tex]\implies e=f-5[/tex]

[tex]\implies e=21-5[/tex]

[tex]\implies e=16[/tex]

Therefore:

Let us assume that,

→ Elsa = x

→ Felipe = x + 5

→ Chau = 3x + 15

Now the required value of x,

→ x + x + 5 + 3x + 15 = 100

→ 5x + 20 = 100

→ 5x = 100 - 20

→ x = 80/5

→ [ x = 16 ]

Then the orders each serve is,

→ Elsa = x = 16

→ Felipe = x + 5 = 16 + 5 = 21

→ Chau = 3x + 15 = 48 + 15 = 63

Hence, the above one is correct.

Answer:

(0,9)

Step-by-step explanation: