What is 1/3 of 1/4 what is 1/3 1/4

Answer:

the area of the rectangle is A=L•W

The length is 3m less than twice its width W: L+ 3m=2W...->, L=2W-3m

A=L-W

27m²=(2W-3m)-W

27m2=2w2-3m-W

2w2-3wm-27m2=0

....use quadratic formula -(-3m)+ (-3m)²-4-2-(-27m²)

W=

2-2

w=(3m± √9m²+216m²)

w=(3m+ √225m²)

W=(3m± 15m...you need only positive root because width cannot be negative

W= 3m+15m

4

W=. 4

18m

W=4.5m ......now find the L

L=2.4.5m-3m

L=9m-3m

L=6m

Answer:

W = 4.5cm

L = 6cm

Step-by-step explanation:

Answer: X, Y, Z are collinear points on the same segment, Then YZ=2.

                                                                                                                                                                                                                                                                                                                                                                                             Step-by-step explanation:

Collinear points are the points that lie on the same straight line or in a single line. If two or more than two points lie on a line close to or far from each other, then they are said to be collinear, in Euclidean geometry.

X, Y, Z are collinear points on the same segment, and Y is between X and Z.

As given Y is between X and Z

We can write,: YZ+XY=XZ

If, XY=11

XZ=13

Replace XY and XZ values in above equation

So, YZ+XY=XZ

YZ+11=13

Solve to get, YZ=13-11

YZ=2

So,  X, Y, Z are collinear points on the same segment, and Y is between X and Z, use the segment  addition postulate, then YZ=2.

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The solution to the given quadratic equation using the completing the square method is t = -5/2 ±√29/4

Given the quadratic equation expressed as;

t^2+5t−1=0

Add 1 to both sides

t^2+5t−1 + 1 = 0+1

t^2 + 5t = 1

Take the square of half of the coefficient of t to have:

t^2 + 5t + (5/2)^2 = 1 + (5/2)^2

(t+5/2)^2 = 1+25/4

(t+5/2)^2 = 29/4

t + 5/2 = ±√29/4

t = -5/2 ±√29/4

Hence the solution to the given quadratic equation using the completing the square method is t = -5/2 ±√29/4

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The solutions of the equations of the situation can be:

z = 1 , y = 5, x = 4

z= 2 , y = 3, x = 5

z=3 , y = 1, x = 6

z = 0 , y = 7, x =3

The question can be expressed as a equation

6 x + 8 y + 10 z = 84

also, x + y + z = 10

⇒ x = 10- y - z

Putting it in first equation,

6(10 - y - z ) +8y + 10z = 84

⇒ 60 +2y + 4z = 84

⇒2(y + 2z ) = 14

⇒ y + 2z = 7

Now putting

z = 1 , we get y = 5,

z= 2 , y = 3

z=3 , y = 1

z = 0 , y = 7

So, only 4 possible solutions.

Therefore, there can only be 4 possible solutions for the equations.

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Answer:

27.5 years old

Step-by-step explanation:

We are given the formula: [tex]P=0.006A^{2} -0.02A+120[/tex] relating a patient's pressure to age.

We are also given the value for pressure (P) as 124 mmHg and need to find age (A). In order to do this, we can substitute the value 124 for P in the equation and solve the quadratic equation to obtain A:

[tex]124=0.006A^{2} -0.02A+120[/tex]

1. Set equation to 0 by subtracting 124 from both sides:

[tex]124-124=0.006A^{2} -0.02A+120-124\\= > 0.006A^{2} -0.02A-4=0[/tex]

2. Solve equation using a calculator:

It should give the solutions: [tex]A= 27.54, -24.2[/tex]

It doesn't really make sense for someone's age to be negative, therefore we can accept the positive solution as our answer.

The man whose normal blood pressure measures 124 mmHg is 27.5 years old.

Hope this helped!

hi

if you call the number  "n"  you have  :    ( 4n)³

The cube formed by the product of 4 and a number is (4 * n)^3.

According to our question ,

Hence we can say that the cube formed by the product of 4 and a number is (4 * n)^3.

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Answer:

x =(2-√52)/6=(1-√ 13 )/3= -0.869

x =(2+√52)/6=(1+√ 13 )/3= 1.535

it has either 0.868 or -1,85

Figure in option A is the figure that represents a rotation of 90° clockwise of the trapezoid

The term rotation refers to the circular movement of an object or something about a point. The point mentioned is also called axis. The movement is circular because it involves turning round.

Rotation may be clockwise or anticlockwise. clockwise is the reverse of anticlockwise, and clockwise involves moving in same direction as the clock is turning,

As regards the trapezium, rotating it clockwise will result to the image depicted by option A

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Given - F(x) = 5 × 3-x

F(-2) refers to x = -2

Therefore 5×3-(-2) = 5× (3+2) = 5×5 = 25

Hence 25 is the value of f(-2)

Step-by-step explanation:

the domain is the interval or set of all valid x values.

as we can see, the function goes continuously from all the way to the left (until all eternity to -infinity) all the way to the right (until all eternity to +infinity).

the domain is

-infinity < x < +infinity

the range is the interval or set of all valid y (function result) values.

we see, the lowest y value is -1. and then the function goes on both sides up, up, up in all eternity to +infinity.

the range is

-1 <= y < +infinity

f(x) is decreasing for

-infinity < x < -1

f(x) is increasing for

-1 < x < +infinity

Answer:  a

Step-by-step explanation: hope it helps.

Answer:

w= 3 feet

h= 5 feet

Step-by-step explanation:

H=height; W=width=2H-7ft

W=2H-7ft

2H+4W=22ft Substitute for W

2H+4(2H-7ft)=22ft

2H+8H-28ft=22ft Add 28 ft to each side.

10H=50ft

H=5 ft ANSWER 1: The bookshelf is 5 feet high.

W=2H-7ft=2(5ft)-7ft=10ft-7ft=3ft

ANSWER 2: the bookshelf is 3 feet wide.

CHECK:

2H+4W=22ft

2(5ft)+4(3ft)=22ft

10ft+12ft=22ft

22ft=22ft

Hope this helps!

Answer:

No, 2 is not a solution

Step-by-step explanation:

x - 5>10  Add 5 to both sides of the equations

x > 10  The solutions are all numbers greater than 10.  Two is not greater than 10.

At this point, the canoe will be under a net force of 51.52 N.

The total mass of a canoe and a paddler is 100.0 kg. A river that runs from east to west is where the canoe is thrown in. The power of the water current on the canoe is 18.0 N. The paddler exerts a force of 36.0 N [E 37.0° N].

The Free Body Diagram is then displayed below.

The canoe's net force would then be indicated as follows:

F = (18 + 36 cos 37°) i + (36 sin 37°) j

F = 46.75 i + 21.67 j

Therefore the force's strength will be

|F| = √(46.75² + 21.67²)

|F| = √2655.15

|F| = 51.52 N

Thus, at this point, the canoe will be under a net force of 51.52 N.

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The possible values for the range of f(x) are given by:

The range of a function f(x) is the set that contains all possible output values for the function. Looking at the graph of the function, the range is composed by the values of y.

In this problem, the function is not given, so I can't give you an exact answer, but since the range is composed by the values of y, the first option is not possible, and the possible values for the range of f(x) are given by:

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An integer to describe 6 meters above the sea level would be [tex]+6[/tex] meters.

As per the question statement, We are supposed to use an integer to describe the following situation "6 meters above sea level".

We assume that sea level is the datum line and anything above that would be positive and below that would be negative.

So 6 meters above the sea level can be described as [tex]=6meters[/tex].

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The graph of the linear equation, x = 6, is shown in the image attached below.

The equation of a vertical line is given as x = b, where b is the x-intercept of the line. That is, b is the point on the x-axis where the line crosses.

Given the equation, x = 6, it means the line is a vertical line. Therefore, on the graph, the line would intercept the the x-axis at 6.

Thus, the graph of the linear equation, x = 6, is shown in the image attached below.

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Answer:

1/8

Step-by-step explanation:

(6m^-1n^0)^-3 =

= (6 × 1/3 × (-5)^0)^-3

= (6/3)^-3

= 2^-3

= 1/2^3

= 1/8

Answer:

A: 0.50

B: 2.70

C: 28.20

D: 3.10

E: 2.40

F: 9.90

G: 15.200

H:  1.40

I: 0.80

J: 39.20

K: 2.50

L: 0.80

Here are the first ones

M: 4

N: 4

O: 23

P: 8

Q: 4

R: 53

S: 3

T: 28

U: 11

V: 17

W: 92

X: 25

Y: 8

Z: 3

These are the last ones

Hope you found these helpful! <3

Answer:

  y = -3

Step-by-step explanation:

You want the solution to the absolute value equation | y-4 | = | y+10 |.

The absolute value function ...

  f(x) = | x |

is piece-wise defined as ...

  [tex]f(x)=\begin{cases}-x&\text{for }x < 0\\x&\text{for }x\ge 0\end{cases}[/tex]

That is, the function is defined differently for argument values less than 0.

The above observation regarding the absolute value function means the nature of the given equation changes where the absolute value arguments are zero. Those values are ...

  y -4 = 0   ⇒   y = 4

  y +10 = 0   ⇒   y = -10

In other words, the points y = -10 and y = 4 divide the domain of the equation into three parts. The behavior will be different in each of those parts.

To solve the equation, we must examine each region of the domain for possible solutions.

When y < -10, both of the absolute value functions change the sign of their argument. Then the equation is ...

  -(y -4) = -(y +10)

Adding y to both sides of this equation gives ...

  4 = -10 . . . . . false

This means there is no solution to the equation in the region y < -10.

When -10 ≤ y < 4, the absolute value function |y -4| changes the sign of its argument, but the other function does not. In this region, the equation becomes ...

  -(y -4) = (y +10)

  -6 = 2y . . . . . . . . . add y-10 to both sides

  -3 = y . . . . . . . . divide by 2. This value is in the region -10 ≤ y < 4.

The solution to the equation is y = -3.

When 4 ≤ y, neither absolute value function changes the sign of its argument. In this region the equation becomes ...

  y -4 = y +10

Subtracting y from both sides of this equation gives ...

  -4 = 10 . . . . . false

This means there is no solution to the equation in the region 4 ≤ y.

__

Additional comment

The first attached graph shows the given equation rewritten as two functions. The solution is where those functions have equal values: the point(s) where the graphs intersect.

We often find it more convenient to rewrite equations like this to the form f(x) = 0. Here, that might mean we define ...

  f(x) = |y -4| -|y +10|

Then the solution is found on the graph at the x-intercepts. The graph in the second attachment shows this solution, and clearly shows the changes in behavior at x = -10 and x = 4.

Using proportions, it is found that the exact value of 41% of 379 is of 155.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

The proportion of 41% of 379 is given as follows:

0.41 x 379 = 155.39.

Since 0.39 < 0.5, the exact value is rounded to 155.

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Answer:

Step-by-step explanation:

create the cartesian system, sign the points, because the new triangle is reflected, so we need to use the straight lines which points on its ends, perpendicular to the x-axis, then we get A(0,-6), B(3,0), C(4,-3)

Split up the interval [1, 3] into 4 intervals of equal length,

[tex]\Delta x = \dfrac{3 - 1}4 = \dfrac12[/tex]

The left endpoint of the [tex]i[/tex]-th interval is

[tex]\ell_i = 1 + \dfrac i2[/tex]

The area under the curve is then approximately

[tex]\displaystyle \int_1^3 f(x) \, dx \approx \sum_{i=1}^4 f(\ell_i)\Delta x \\\\ ~~~~~~~~ = \frac12 \sum_{i=1}^4 \left(1 + \frac i2\right)^3 \\\\ ~~~~~~~~ = \frac12 \sum_{i=1}^4 \left(1 + \frac{3i}2 + \frac{3i^2}4 + \frac{i^3}8\right) = \boxed{27}[/tex]

Answer:

this question is wrong .................

Answer:

39÷(5+(4×5÷2) )

39÷(5+(20÷2) )

39÷(5+10)

39÷15

2.6

Answer: -1/5

Step-by-step explanation:

14/20 - 81/90=

7/10-9/10=       ==> 10 is the GCF of 20 and 90

(7-9)/10=

-2/10=-1/5

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{\dfrac{14}{20} - \dfrac{81}{90}}[/tex]

[tex]\mathsf{= \dfrac{14\div2}{20\div2} - \dfrac{81\div 9}{90\div9}}[/tex]

[tex]\mathsf{= \dfrac{7}{10} - \dfrac{9}{10}}[/tex]

[tex]\mathsf{= \dfrac{7 - 9}{10 - 0}}[/tex]

[tex]\mathsf{= \dfrac{-2}{10}}[/tex]

[tex]\mathsf{= \dfrac{-2\div 2}{10\div2}}[/tex]

[tex]\mathsf{= \dfrac{-1}{5}}[/tex]

[tex]\huge\text{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{-\dfrac{1}{5}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

b

Step-by-step explanation:

Trust me

The equation that could be used to determine, m, is 5m = 55.5 - 19. The correct option is C. m = (55.5 - 19)/5

From the question, we are to determine the equation that could be used to determine, m, the average number of miles she would have to ride to meet her goal

From the given information,

"Arianys wants to ride her bicycle 55.5 miles"

and

"She has already ridden 19 miles"

Thus,

The number of miles she needs to ride more is

55.5 miles - 19 miles

= 36.5 miles

If m is the average number of miles she would have to ride for 5 more days to complete her goal,

Then, we can write that  

m = 36.5/5

OR

m = (55.5 - 19)/5

Hence, the equation that could be used to determine, m, is 5m = 55.5 - 19. The correct option is C. m = (55.5 - 19)/5

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The cordinates of the turning point of the graph of y=f(x) occurs at (1.1) and (5/3, 23/27)

2

(x−2)+1

Now, differentiating w.r.t. x, we get

f

′

(x)=2(x−1)(x−2)+(x−1)

2

=(x−1)[2(x−2)+x−1]

=(x−1)[3x−5]

Hence,

f

′

(x)=0 implies x=1 and x=

3

5

​

Corresponding values of y are y=1 and y=

27

23

​

 respectively.

∴ Co-ordinates of turning point of the graph of f(x) occurs at (1,1) and (

3

5

​

,

27

23

​

)

Now,

f(x)=(x−1)

2

(x−2)+1

=(x

2

−2x+1)(x−2)+1

=x

3

−2x

2

−2x

2

+4x+x−2+1

=x

3

−4x

2

+5x−1

The value of p for which the equation f(x)=p has 3 distinct solutions lies in interval (

27

23

​

,1)

Area enclosed by f(x),x=0,y=1 and x=1 is

A=∫

0

1

​

(1−f(x))dx

⇒∫

0

1

​

(4x

2

−x

3

−5x+2) dx

⇒A=

12

7\

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