Find the two values x can have if [tex]x^{2}[/tex] - 14=50

Answer:

x = 241 1/3
    ————
      5 1/3

Step-by-step explanation:

Answer:

x = ^3(square root )of 18075   or 5.24875253...

     -----------------------

              5

Step-by-step explanation:

isolate the variable by deviding each side by factors that dont contain the variable

hope this helped have a good day ^^

1.9 × 10^3  is 215 times smaller than 4.085 × 10^5.

The basic formula for the area of ​​a rectangle is length x width, but the basic formula for volume is length x width x height. The calculation does not change depending on how you refer to different measurements. For example, you can use depth instead of height.

Every 3D object occupies a certain space. This space is measured by its volume. Volume is defined as the space occupied within the bounds of an object in three-dimensional space. Also called the capacity of the object. The volume of an object is the amount of space it fills. Large capacity is measured in cubic meters m3. Smaller volumes are measured in cubic centimeters cm3 or cubic millimeters mm3.

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Answer:

4 : 5

Explanation:

We are told that 20 students saw the movie and 5 didn't, meaning there were in total 20 + 5 = 25 students; therefore, the ratio is

To simplify the ratio, we divide both the numerator and the denominator by 5. This gives

Hence, the ratio of the students who saw the movie to the total number is 4 : 5.

The perimeter of the semi circle is 56.54 cm

The perimeter of a figure is the sum of the whole sides of the figure.

The perimeter of  the semi circle is the sum of the whole sides of the semi circle.

Therefore,

perimeter of the semi circle = 2πr / 2 + 2r

perimeter of the semi circle = πr + 2r

where

perimeter of the semi circle = 3.14 × 11 + 2r

perimeter of the semi circle = 34.54 + 2(11)

perimeter of the semi circle = 34.54 + 22

Therefore,

perimeter of the semi circle = 56.54 cm

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As per the compound inequality, the possible values for the number of pop tabs that need to be collected during the third and final week of the competition in order to win the contest is 83 ≤ (82 + 84 + n)/3 ≤ 87; 83 ≤n ≤ 95.

Compound inequality:

A compound inequality is an inequality that merges two inequalities either by using "and" or "or".

Given,

In the recycling contest, you must collect between 83 and 87 pop tabs each week, inclusive for winning.

And suppose you collected 82, and, 84 pop tabs during the first two weeks of competition.

Here we nee to find the possible values for the number of pop tabs that need to be collected during the third and final week of the competition in order to win the contest.

Let us consider n be the number of pop tabs.

So, it can be written using the compound inequality,

=> 83 ≤ (82 + 84 + n) /3 ≤ 87

To cancel the fraction we have to multiply 3 with all of them, then we get,

=> 83 x 3 ≤ (82 + 84 + n) ≤ 87 x 3

=>  249 ≤ (166 + n) ≤ 261

To find the value of n we have to subtract 166, then we get,

=>  249 - 166 ≤  n ≤ 261 - 166

=> 83 ≤ n ≤ 95

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The determinant of a is the product of the pivots in any echelon form u of​ a, multiplied by ​(​1)r​, where r is the number of row interchanges made during row reduction from a to u is False.

Given:

The determinant of a is the product of the pivots in any echelon form u of​ a, multiplied by ​(​1)r​, where r is the number of row interchanges made during row reduction from a to u.

Definition of det A:

det A = (-1)^r * (product of pivots in echelon form) if A is invertible or 0 when A is not invertible.

From definition of det A we can simply say the given statement is false - This can only hold if A is an invertible matrix, but the problem does not state this.

Reduction to an echelon form may also include scaling a row by a nonzero constant, which can change the value of the determinant.

Therefore the determinant of a is the product of the pivots in any echelon form u of​ a, multiplied by ​(​1)r​, where r is the number of row interchanges made during row reduction from a to u is False.

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Answer:214.29

Step-by-step explanation:600 divided by 2.8

possibly the answer

The value represents the climber's change in elevation during the first minute of the training session is  1/5.

Given,

During the second minute of a two-minute training session, a rock climber completed a 12-meter ascent up the wall. The climber returned to the identical location she had been in at the beginning of the two-minute session.

Let x be the distance climbed by the climber is x m

During the first minutes(60 seconds): distance climbed =[tex]\frac{x}{60}[/tex]

In the 2nd minute, they climbed 12 m higher than in the 1st minute.

Now, the distance climbed by the climbed in the Second minute = [tex]\frac{x+12}{60}[/tex]

Now, the change in the elevation during the first minute of the training session= [tex]\frac{x+12}{60}-\frac{x}{60} = \frac{12}{60}=\frac{2}{10}=\frac{1}{5}[/tex]

Hence, the value represents the climber's change in elevation during the first minute of the training session is [tex]\frac{1}{5}[/tex]

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Answer:

y = 3(x - [tex]\frac{4}{3}[/tex] )² + [tex]\frac{23}{3}[/tex]

Step-by-step explanation:

the equation of a parabola in vertex form is

y = a(x - h)² + k

given

y = 3x² - 8x + 13

using the method of completing the square

the coefficient of the x² term must be 1 so divide first 2 terms by 3

y = 3(x² - [tex]\frac{8}{3}[/tex] x) + 13

add/subtract ( half the coefficient of the x- term )² to x² - [tex]\frac{8}{3}[/tex] x

y = 3(x² + 2(- [tex]\frac{4}{3}[/tex] )x + [tex]\frac{16}{9}[/tex] - [tex]\frac{16}{9}[/tex] ) + 13

  = 3(x - [tex]\frac{4}{3}[/tex] )² + 3(- [tex]\frac{16}{9}[/tex] ) + 13

  = 3(x - [tex]\frac{4}{3}[/tex] )² - [tex]\frac{16}{3}[/tex] + [tex]\frac{39}{3}[/tex]

  = 3(x - [tex]\frac{4}{3}[/tex] )² + [tex]\frac{23}{3}[/tex] ← in vertex form

because, the quotient has an integer in its denominator

Explanation

A rational number is a number that is expressed as the ratio of two integers

hence

for

we can solve the root in the denominator, so we have

so, as the number can be expressed as the ratio of two integers ( 20 and 4) we can conclude

because, the quotient has an integer in its denominator

I hope this helps you

hello

let's get the functions out first

Answer:

8.5 and 10.5

Step-by-step explanation:

add your x1 and x2 coordinate and divide them by 2 to get your x.

and for the y add your y1 and y2 coordinate and divide them by 2 to get your y.

The x1, x2, y1, and y2 in this situation would be (5,14) (being the bridge)

and (12,7) being the castle.

x1 = 5

x2 = 12

y1 = 14

y2 = 7

The slope intercept form of the each situation is given by

a) y = 3x + 0

b) y = 14x + 8

c) y = 54x + 8

d) y = 2x + 3

What is slope intercept form?

Slope intercept form- The equation of the line in slope-intercept form is given by:

y = mx + c

Here,

(x, y) = Every point on the line

m = Slope of the line

c = y-intercept of the line

a) In situation one

slope of the line = 3 and y- intercept = 0 =c

The equation becomes y = 3x+ 0

y = 3x

b) slope of the line = 14 and y intercept = 8

y = 14x + 8

c) slope of the line = 54 and y- intercept = 2

y = 54x + 2

d)  slope of the line = 2 and y- intercept = 3

y = 2x + 3

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Using the normal distribution, it is found that:

a) 1.39% of teenagers use their phone less than 5 hours per day.

b) 3.59% of teenagers use their phone more than 10 hours per day.

c) 49.85% of teenagers use their phone between 6 to 8 hours per day.

d) The 75th percentile of the distribution is of 8.59 hours.

The z-score of a measure X of a variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by the fraction presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation of the daily amounts they use their phone are given as follows:

[tex]\mu = 7.75, \sigma = 1.25[/tex]

The proportion that use their phone for less than 5 hours a day is given by the p-value of Z when X = 5, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (5 - 7.75)/1.25

Z = -2.2

Z = -2.2 has a p-value of 0.0139.

Thus the percentage is of 1.39%.

The proportion that use their phone for more than 10 hours a day is one subtracted by the p-value of Z when X = 10, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (10 - 7.75)/1.25

Z = 1.8

Z = 1.8 has a p-value of 0.9641.

1 - 0.9641 = 0.0359 = 3.59% (percentage).

The proportion between 6 and 8 hours a day  is the p-value of Z when X = 8 subtracted by the p-value of Z when X = 6, hence:

X = 8:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (8 - 7.75)/1.25

Z = 0.2

Z = 0.2 has a p-value of 0.5793.

X = 6:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (6 - 7.75)/1.25

Z = -1.4

Z = -1.4 has a p-value of 0.0808.

0.5793 - 0.0808 = 0.4985 = 49.85% (percentage).

The 75th percentile is X when Z = 0.675, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

0.675 = (X - 7.75)/1.25

X - 7.75 = 0.675 x 1.25

X = 8.59 hours.

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Answer:

4.2

Step-By-Step explanation:

12.5+1.5=14

14 times 3= 42

42/10= 4.2

distanceSolution:

Given that a toy car placed on the floor travels at a constant acceleration for 3 seconds reaching a velocity of 4v m/s, we have

It slows down with a constant deceleration of 0.5 m/s² for 4 seconds before hitting a wall and stopping. This is as shown below:

Thus, the velocity-time graph for the toy car is as shown below:

The total distance traveled by the toy car is evaluated by calculating the area of the triangle ABC. Thus,

Hence, the

The statements are true about the given expressions include the following:

In order to determine whether these expressions are equivalent, we would evaluate the two expressions based on each of the statements:

"When x = 2, both expressions have a value of 18"

7x + 4 = 7(2) + 4 = 14 + 4 = 18.

3x + 5 + 4x - 1 = 3(2) + 5 + 4(2) - 1 = 6 + 5 + 6 - 1 = 18.

"The expressions are only equivalent for x = 4 and x = 6." is false has demonstrated above.

"The expressions have equivalent values for any value of x." is true.

Let x = 1;

7x + 4 = 7(1) + 4 = 7 + 4 = 11.

3x + 5 + 4x - 1 = 3(1) + 5 + 4(1) - 1 = 3 + 5 + 4 - 1 = 11.

Let x = 10;

7x + 4 = 7(10) + 4 = 70 + 4 = 74.

3x + 5 + 4x - 1 = 3(10) + 5 + 4(10) - 1 = 30 + 5 + 40 - 1 = 74.

"The expressions should have been evaluated with one odd value and one even value." is false because all values of x are solutions.

"When x = 0, the first expression has a value of 4 and the second expression has a value of 5." is false because the two expressions are equivalent expressions.

In conclusion, "The expressions have equivalent values if x = 8." is true because the two expressions are equivalent expressions.

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The most appropriate choice for equation of line in slope intercept form will be given by

Unit price of apple in store A  = $4

Unit price of apple in store A  = $2

Unit price of apple in store A  = $3

What is equation of line in slope intercept form?

Equation of line in slope intercept form is given by y = mx + c

Where, m is the slope of the line and c is the y intercept of the line

The distance from the origin to the point where the line cuts the x axis is called x intercept

The distance from the origin to the point where the line cuts the y axis is called y intercept

Slope of a line is the tangent of the angle which the line makes with the positive direction of x axis

If [tex]\theta[/tex] is the angle which the line makes with the positive direction of x axis, then slope of the line is given by [tex]tan\theta[/tex]

If the line passes through ([tex]x_1,y_1[/tex]) and ([tex]x_2, y_2[/tex])

slope = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]

Unit price of apple in store A = [tex]\frac{12}{3}[/tex] = $4

For store B

Putting x = 1

y = [tex]2 \times 1[/tex]

y = 2

Unit price of apple in store B = $2

For  store C

From the graph,

At x= 1, y = 3

Unit price of apple in store C = $3

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Complete Question

The graph has been attached

x = -12

Given the following equation

We are to find the variable x. To do that, we will multiply both sides by -2 as shown:

This shows that the value of x for the equation to be true is -12

Check

If x = -12, on substiituting;

Since the result is equivalent to 6, this shows that the solution x = -12 is correct.

The dimensions that maximize the area are, 96cm and 84cm.

What is area?

The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

Let the height of poster be h and breadth be b,

bh = 15630cm square........(1)

Height of the printed area=h-10-10 = h - 20

(decrement of 10 from top and bottom)

the breadth of the printed area b-6-6 = b-12

(decrement of 9 from both sides)

for maximum printed area:

A=(h-20)(b-12) should be maximum

[tex]A = (h - 20)(\frac{15360 }{h}-12)[/tex]

From equation (1)  

[tex]A = 15360-12h-\frac{307200}{h} +240[/tex]

A = 15600 - 12h - (307200/h)

differentiate with respect to h (it should be=0)

[tex]\frac{dA}{dh}= 0-12 + \frac{307200}{h^2}[/tex]

[tex]12 = \frac{307200}{h} \\h = 160 cm[/tex]

from equation (1),

[tex]bh = 15630cm^2\\b = 96cm[/tex]

dimension of printed area,

= h - 20

= 160 - 20

= 140 cm

= b - 12

= 96 - 12

= 84 cm

Therefore, the dimensions that maximize the area are, 96cm and 84cm.

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The following proof of complementary angle is given below:

it is given that <1 and <2 are complementary and <2 and <3 are complementary. By the definition of complementary angle , m<1 + m<2 = 90 degrees and m<2 + m<3 =90 degrees. By the substitution property, m<1 + m<2 = m<2 + m<3.

Then, m<1 = m<3 by the subtraction property. Therefore, <1 congruent <3 by the complementary angle.

Complementary angle is a pair of angles that sum to a right angle. A right angle is half of the angle formed by a single straight line which is equivalent to 90 degrees.

Given: <1 and <2 are complementary and <2 and <3 are complementary.

prove: <1 congruent <3

The proof of <1 congruent <3 is m<1 + m<2 = m<2 + m<3 by substitution effect and m<1 = m<3 by Subtraction effect

Therefore, the proof of <1 congruent <3 is given by <1 and <2 are complementary and <2 and <3 are complementary.

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[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-4)}}} \implies \cfrac{6 +3}{2 +4} \implies \cfrac{ 9 }{ 6 } \implies {\Large \begin{array}{llll} \cfrac{ 3 }{ 2 } \end{array}}[/tex]

The position where where angle, θ would be located is at: angle F (∠F).

A right angle can be defined as a type of angle that is formed by the intersection of two (2) straight lines at 90 degrees. This ultimately implies that, a right angle has a measure of 90 degrees.

Additionally, all right angles are are formed as a linear pair and they are marked with a right angle symbol.

In conclusion, the measure of the angle in this right angle triangle would be calculated by using the tangent function as follows:

Tanθ = Opposite side/Adjacent side

Tanθ = 6/4

Angle, θ = tan⁻¹(6/4)

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Answer: C, D

Step-by-step explanation:

Answer C is correct because 2/5 is 0.4 and 0.55 is greater than 0.4.

Answer D is correct because 2/5 is 0.4 and 3/4 is 0.75 therefore 0.75 is greater than 0.4.

Answer:

C and D

Step-by-step explanation:

On the number line, the first point is 2/5. 2 divided by 5 gets you .4, so that's why it's at .4. .55 is the next point. .55 is a bigger number than .4, so it would be an answer.

3 divided by 4 gets you .75. 3/4=.75. 2/5=.4. .75 is greater than .4. 3/4 is greater than 2/5

Step1: Write the area of the circular Rug

The area of the circle is

From the question the diameter is 25feet, hence the radius is

Step2: substitute the value into the formula

Hence the area of the circular rug is 491.07 square feet

The will take approximately 491square feetyou

The value of expression |2x+5| - 8y is -89 when x = -6 and y =12

Expression is a combination of numbers, variables and Operators.

The given expression is mod two x plus 5 minus eight y.

|2x+5| - 8y

This expression has addition, subtraction and multiplication operators.

Given value of x is minus six and y is equal to twelve.

x=-6 and y=12

plug in values of x and y in expression

|2(-6)+5|-8(12)

|-12+5|-96

|-7|-96

The value in mod will be always taken as positive

7-96

-89

Hence the value of expression |2x+5| - 8y is -89 when x = -6 and y =12.

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Remember that

If the sum of two angles is equal to 180 degrees, then the angles are supplementary

so

In this problem

Let

x ----> the missing angle

x+34.6 =180 degrees -----> by form a linear pair (supplementary angles)

solve for x

x=180-34.6

Answer:

I litteraly have the same problem and no clue how to do I

Step-by-step explanation: