Find the range for the measure of the third side of a
triangle given the measures of two sides.
8, 13

Answers

Answer 1

By using properties of triangle, it can be inferred that

The value of c lies between 5 and 21 and also 5 and 21 are not included

What is a triangle?

A triangle is a three sided two dimensional figure. A triangle has three sides and three interior angles. The sum of the interior angles of a triangle is 180°

Let a = 8, b = 13 and let the third side be c

We know sum of two sides of a triangle is always greater than the third side

a < b + c

8 < 13 + c

c > 8 - 13
c > -5, which is obvious

b < c + a

13 < c  + 8

c > 13 - 8

c > 5

c < a + b

c < 8 + 13

c < 21

5 < c < 21

The value of c lies between 5 and 21 and also 5 and 21 are not included

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Related Questions

answer the questions below about the following function
what is the domain of f(x)
what is the range of f(x)
what is the x-intercept of f(x)? enter your answer as an ordered pair. if no x-intercept exists, enter none
what it the equation of the vertical asymptote

Answers

Domain of the function is,  (0, ∞).

Range of the function is, (-∞, ∞).

x - intercept of the function is, (1, 0).

Vertical asymptote of the function is,  None.

What is domain and range?

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x).

A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

First to find the domain of the function,

Since, all input values shown on the x-axis make up a graph's domain.

We can see that values of x values are from 0 to ∞.

Hence, the domain is (0, ∞).

Now to find the range.

Since, the y-axis on a graph represents the possible output values, or range.

The y - axis having the values from -∞ to ∞.

Hence, the range of the function is, (-∞, ∞).

x - intercept is the point where function crosses the x - axis.

Here function crosses x - axis at (1, 0).

Hence, the x - intercept is (1, 0).

A graph's vertical asymptote is the vertical line at x = a where the graph trends toward positive or negative infinity as the inputs go closer to a.

So, the vertical asymptote is x = 0.

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In a shop the price of a radio is reduced by one third. if the original price of the radio is two thousand four hundred naira,what is the reduced price

Answers

If the original price of the radio is 2,400 Naira and it is reduced by one third, then the discounted price is 1,600 Naira.

A store usually provides discount of some items to attract more customers and make greater sales.

Suppose the original price is p, the discount rate is d%, and the discounted price is q, then the discounted price can be calculated as:

q = (1 - d%) x p

Parameters given in the problem:

p = 2,400 Naira

d = 1/3

Hence,

q = (1 - 1/3) x 2400

q = 2/3 x 2400 = 1600

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The system of conics has two solutions.

(x−4)^2 + (y+1)^2 = 9
(x−4)^2/9 + (y+1)^2/81 = 1

What are the solutions to this system of conics?

Answers

The system of equations has its solutions to be (1, -1) and (7, -1)

How to solve the system of equations?

The system of equations is given as

(x−4)² + (y+1)² = 9

(x−4)²/9 + (y+1)²/81 = 1

Make (y + 1)² the subject in the equation (x−4)² + (y+1)² = 9

So, we have

(y+1)² = 9 - (x−4)²

Substitute (y+1)² = 9 - (x−4)² in (x−4)²/9 + (y+1)²/81 = 1

This gives

(x−4)²/9 + [9 - (x−4)²]/81 = 1

Split

(x−4)²/9 + 9/81 - (x−4)²/81 = 1

Collect the like terms

(x−4)²/9 - (x−4)²/81 = 1 - 9/81

Evaluate the like terms

[9(x−4)² - (x−4)²]/81 = 72/81

So, we have

9(x−4)² - (x−4)² = 72

Evaluate the difference

8(x−4)² = 72

Divide by 8

(x−4)² = 9

Take the square roots

x - 4 = ±3

So, we have

x = 4 ± 3

Evaluate

x = 1 or 7

Substitute x = 1 or 7 in (y+1)² = 9 - (x−4)²

(y + 1)² = 9 - (1−4)² or (y + 1)² = 9 - (7−4)²

This gives

(y + 1)² = 0 or (y + 1)² = 0

This gives

y + 1 = 0

Evaluate

y = -1

Hence, the solution is (1, -1) and (7, -1)

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Set up the form for the partial fraction decomposition. Do not solve for A, B, C, and so on.

Answers

Answer:

For part a you would decompose the fraction into two independent fractions with the following form:

() = ()/( x^2+5)(x ^2+3x−4)  = (Ax + B)/(x^2+5) + (Cx + D)/(x ^2+3x−4)

Combining these fractions we get:

((Ax + B)*(x ^2+3x−4) + (Cx + D)*( x^2+5))/( x^2+5)(x ^2+3x−4) = ()/( x^2+5)(x ^2+3x−4)

Thus we can say: (Ax + B)*(x ^2+3x−4) + (Cx + D)*( x^2+5) = ()

You then simplify the equation on the left by combining like terms and solve the system of equations that arise corresponding with ().

You would follow a similar process for part b as well.

Step-by-step explanation:

Give the numerical coefficient of the term.
−7x

The numerical coefficient is _____.

Answers

The numerical coefficient is -7

How to determine the numerical coefficient?

From the question,  the expression is given as

-7x

Considering an expression given as

Ax

The numerical coefficient of the above expression is A

When compared to the expression -7x, we have

The numerical coefficient is -7

So, we can conclude that the numerical coefficient of -7x is -7

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Answer:

-7

Step-by-step explanation:

The numerical coefficient is -7

a box with an open top and a square base is to be constructed to contain 4000 cubic inches. find the dimension that will require the minimum amount of material to construct the box.

Answers

The dimension of the box will be (40 inch × 40 inch × 10 inch).

How to determine the maximum and minimum values of an expression using differentiation?
Any given expression can have both minimum and maximum outcomes for any number in a real world scenario, which can be determined using differentiation; first order differentiation when equated to zero reveals the value that will solute to produce the maximum or minimum and then the upon differentiating the obtained expression again and then substituting the variable in acceptable positions, if the outcome is a positive number then the obtained number in first differentiation suggests a minimum value of the given expression.

Given, the volume of the box described = 4000 inch³
Let the dimension of the base of the box be = 'a' inch × 'a' inch = a² inch²
Therefore, height of the box = (4000 inch³)/(a² inch²) = (4000/a²) inch
Total surface area of the described box = S = a² + [4a×(4000/a²)]
= [a² + 16000/a] inch
For the limiting values of S, dS/da = 0 ⇒ d[a² + 16000/a]/da = 0
⇒ 2a - [16000/a²] = 0 ⇒ 2a = 16000/a² ⇒ a³ = 8000 ⇒ a = ∛8000 = 20
Therefore, the value of a is 20 inch.
Thus, height of the box = 4000/a² = 4000/400 = 10 inch
For S to have the minimum limited value, d²S/da² > 0 for a = 20 inch, which is satisfied by the available value of S.
∴ The minimal surface area = a² + 16000/a = 400 + (16000/400)
= 440 inch²
We are aware that the least amount of material will be needed to build the box when its overall surface area is the smallest.
Thus, to minimize the amount of material in consideration, the dimension of the box will be (40 inch × 40 inch × 10 inch).

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HELPPPP I'm so confused!!! 60 POINTSSSS!!!

Answers

Answer:

que tienes que realizar no se entiende tu pregunta lo siento

The price for a taxi cab in a small city is $4.00 per mile, x, while traveling, and $0.50 every minute, y, while waiting. If you have $40 to spend on a cab ride, the inequality 4,00x+0.50y<=40 represents your situation. Graph this inequality in the first quadrant only.

Use the graphing tool to graph the inequality

Answers

The graph of the linear inequality 4x + 0.5y ≤ 40 is given by the image at the end of the answer.

How to graph the linear inequality?

The first step in graphing the linear inequality is identifying the domain of the situation.

Only numbers in the first quadrant are plotted, hence the first two constrains for the domain are given as follows:

x > 0.y > 0.

The inequality is a linear inequality, hence the next step is identify the intercepts and then trace a line connecting them.

The x-intercept is the value of when y = 0, hence:

4x = 40

x = 40/4

x = 10.

Hence it is represented by point (10,0).

The y-intercept is the value of y when x = 0, hence:

0.5y = 40

2 x 0.5y = 2 x 40

y = 80.

Hence it is represented by point (0,80).

The values less than the inequality are plotted, hence the graph is composed by the points on the first quadrant and below the line 4x + 0.5y = 40, as shown by the image at the end of the answer.

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best ontime airlines: hawaiian airlines topped the list of the most punctual u.s. airlines for full-year 2014, according to data released by the bureau of transportation statistics. the on-time arrival performance was 91.9% another aviation data service believes that this percentage now is even higher. the team of researchers chose 130 randomly selected flights and find that 120 of the flights arrived on time. can a hypothesis test be used to determine whether the proportion of hawaiian airlines flights that arrive on-time is higher than 91.9%? group of answer choices yes, because the sample is random. thus, it is representative of the population of flights for the airlines. yes, because the sample is random and (130)(0.923) and (130)(0.077) are both at least 10. this means the normal model is a good fit for the sampling distribution. yes, because the sample is random and (130)(0.919) and (130)(0.081) are both at least 10. this means the normal model is a good fit for the sampling distribution.

Answers

1.because sample is random and (130)

(0.923) and (130)(0.077) are both at least 10.

This means the normal model is a good fit for the sampling distribution.

Consider the provided information.

130 randomly selected flights and find that

120 of the flights arrived on time.

n=130

The on-time arrival performance was 91.9%

p=0.923 and q=1-0.923=0.077

np = 130 x 0.923

np = 120 ≥ 10

nq = 130 × 0.077

nq = 10 = 10

Hence, Yes, because sample is random and

(130)(0.923) and (130)(0.077) are both at least 10. This means the normal model is a good fit for the sampling distribution.

2.because sample is random and (130)

(0.919) and (130)(0.081) are both at least 10.

This means the normal model is a good fit for the sampling distribution.

Consider the provided information.

130 randomly selected flights and find that

120 of the flights arrived on time.

n=130

The on-time arrival performance was 91.9%

p=0.919 and q=1-0.919=0.081

np = 130 x 0.919

np = 119.5 ≥ 10

nq = 130 × 0.081

nq = 10.5 ≥ 10

Hence, Yes, because sample is random and

(130)(0.919) and (130)(0.081) are both at least 10. This means the normal model is a good fit for the sampling distribution.

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Which of the following statements are true?


Corresponding angles of congruent figures are the same.
Corresponding angles of similar figures are the same.
Corresponding sides of congruent figures are the same.
Corresponding sides of similar figures are the same.

Answers

The statements that are true are:

Corresponding angles of congruent figures are the same.Corresponding sides of congruent figures are the same.

What is Corresponding angles of congruent figures ?

It should be noted that the two figures can be regrdedas as one that are similar in the case whereby their corresponding angles are congruent ,also their ratios of the lengths with respect to their corresponding sides would also be equal.

In conclusion, when two figures are similar then it can be concluded that their  corresponding angles are congruent .

Hence, the second and third options are correct.

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Answer:

Corresponding angles of congruent figures are the same.

The corresponding sides of congruent figures are the same.

Step-by-step explanation:

Write a polynomial of least degree with roots 1 and -9. un Write your answer using the variable x and in standard form with a leading coefficient of 1. ​

Answers

Answer:

  y = x² +8x -9

Step-by-step explanation:

You want the least-degree polynomial with roots 1 and -9, written in standard form.

Factors

Each root p means there is a factor (x-p). The two roots make the factored form of the polynomial be ...

  y = (x -1)(x +9)

Expanding this to standard form, we get ...

  y = x² +8x -9

__

Additional comment

A quadratic that has two roots, p and q, will have the standard form ...

  y = (x -p)(x -q) = x² -(p+q)x +pq

That is, the linear term coefficient is the opposite of the sum of the roots, and the constant is their product. This means you can write down the equation directly from the roots:

  y = x² -(1-9)x +(1)(-9) = x² +8x -9

Please solve the following exponential equation
[tex] \frac{4}{2 {}^{x } } = 64 {}^{x} [/tex]

Answers

x = 2/7

see explanation in image

Write an equation in standard form with an x-intercept of 4 and a y-intercept of 5.

Answers

Equation in standard form with an x-intercept of 4 and a y-intercept of 5 is y = -5/4(x) + 5.

Given:

x - intercept = 4

y - intercept = 5

At x intercept y = 0 and at y intercept x = 0

(4,0) and (0,5)

slope = 5-0/0-4

= 5/-4

m = -5/4

substitute (4,0) and m value,

y = mx+c

0 = -5/4*4 +c

0 = -5 + c

c = 5

y = mx + c

y = -5/4(x) + 5.

Therefore equation in standard form with an x-intercept of 4 and a y-intercept of 5 is y = -5/4(x) + 5.

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Write down the two district properties between parellelograml and trapezium

Answers

Properties of Trapezium

The base of the trapezium is parallel to each other. In the above case, AD // BC.None of the sides, diagonals and angles are equal to each other.

Properties of Parallelogram

The opposite sides of a parallelogram are parallel to one another and are also equal to one another.The angles are also congruent.The adjacent angles are supplementary.The diagonals bisect each other and the diagonal divides the parallelogram into two congruent triangles.If one of the angles in the parallelogram is a right angle, then all the other angles are a right angle.

You can see pic..

Characterize the slope of the line in the graph.
• A. Zero
• B. Negative
• C. Undefined
• D. Positive

Answers

Answer: C Undefined

Step-by-step explanation:

A vertical line never moves left and right, so the run is 0. Because the quotient of a number divided by 0 is undefined, the slope of a vertical line is always undefined.

The slope is positive

D.Positive

A wheel has a radius of 45 millimeters. Below is the table from the previous screen. About how many rotations does the wheel make when it travels 100,000 millimeters?

Answers

The number of revolutions taken by a wheel will be 353.68 millimeters.

What is the Circumference of a circle?

The Circumference of a circle is defined as the product of the diameter of the circle and pi.

C = πd

where 'd' is the diameter of the circle

Given data as:

The radius of the wheel r = 45 millimeters

Circumference of wheel = Circumference of a circle

Circumference of wheel = 2πr =2π(45) = 282.74 millimeters

The distance traveled by wheel = 100,000 millimeters

Now, the number of revolutions taken by a wheel will be

⇒ distance traveled by wheel / Circumference of wheel

⇒ 100,000 / 282.74

⇒ 353.68

Thus, the number of revolutions taken by a wheel will be 353.68 millimeters.

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Karama can paint a staircase banister in 50 minutes. Find the rate per minute at which Karama can paint banisters

Answers

The rate per minute at which Karama can paint banisters is 0.02.

In the given question,

Karama can paint a staircase banister in 50 minutes.

We have to find the rate per minute at which Karama can paint banisters.

Since we have to find the rate per unit. Rate per unit means how much Karama can paint in one minute.

To find the rate per unit we divide 1 by 50.

As we know that Karama can paint one staircase banister in 50 minute.

So we can write it as

50 minute = 1 staircase banister paint

Now in 1 minute.

1 minute = 1/50 staircase banister paint

Simplifying

1 minute = 0.02 staircase banister paint

Hence, the rate per minute at which Karama can paint banisters is 0.02.

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On this assignment I am just writing about what the student did wrong. Please help me. LOOK AT THE PICTURE ABOVE ^^^^^^^^^^^^^^^^^^^^^^^^^

QUESTIONS:

1. What math did Ann do well?? EXPLAIN

2. What mistake has Ann made? EXPLAIN​

Answers

ann made a rectangle with the

right perimeter & area

ann doesn't try any other

rectangles to see if their areas are

different.

splitting the land , ann confuses perimeter and area

mapmathshellorg

a supermarket employee wants to construct an open-top box from a 14 by 30 in piece of cardboard. to do this, the employee plans to cut out squares of equal size from the four corners so the four sides can be bent upwards. what size should the squares be in order to create a box with the largest possible volume?

Answers

The size of the squares should be 3 inches in order to create a box with the largest possible volume.

If squares of equal sizes are to be cut out from the four corners so the four sides can be bent upwards, then the length of these squares will be the height of the box. Also twice of this length subtracted from the initial length and width of the material will be the new length and width of the box, respectively.

let x = length of square to be cut = height of the box

length of the box = 30 - 2x

width of the box = 14 - 2x

The volume of the box, which is a rectangular prism, is the product of the length, height and width.

V = l x w x h

V = (30 - 2x)(14 - 2x)(x)

V = 420x - 88x² + 4x³

To obtain the largest volume possible, the first derivative of the volume should be equal to zero.

V'(x) = 0

V = 420x - 88x² + 4x³

420 - 176x + 12x² = 0

Simplify and solve for the value of x.

12x² - 176x + 420 = 0

3x² - 44x + 105 = 0

(3x - 35)(x - 3) = 0

x = 35/3   ;   x = 3

Check each value.

When x = 35/3 = h

l = 30 - 2x = 20/3

w = 14 - 2x = -28/3 ( length should be positive)

When x = 3 = h

l = 30 - 2x = 24

w = 14 - 2x = 8

Hence, the length of square to be cut  is 3 in.

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Pls help due today!!!!!

Answers

It must be 10 as you need a way to get to 100

Can someone help solve this the first problem is below in the picture. Can you put it in interval notation, regular notation, graph it on a number line, and set builder

Answers

The solution to the system of inequalities is -6 < x [tex]\leq[/tex] -3

What is an Inequality?

Inequality shows the relationship between two values in an algebraic expression that are not equal. Inequality signs can indicate that one variable of the two sides of the inequality is greater than, greater than or equal to, less than, or less than or equal to another value.

The system of linear equations,

x + 4 > -2 or -4x [tex]\geq[/tex] 12

from first inequality,

x + 4 > -2

making x stand alone,

x > -2 -4

x > -6

from second inequality,

-4x  [tex]\geq[/tex] 12

divide both sides bu -4

x [tex]\leq[/tex] 12/-4

x  [tex]\leq[/tex] -3

The combined inequality is -6 < x [tex]\leq[/tex] -3

In conclusion, -6 < x [tex]\leq[/tex] -3 is the solution for the set of inequalities.

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37=18q+1 show work pls

Answers

Answer:

37=18q+1

subtract 1 on both sides

then divide both sides by 18

q=2

Step-by-step explanation:

Answer:

q = 2

Step-by-step explanation:

[tex]\sf 37=18q+1[/tex]

[tex]\sf 18q+1=37[/tex]

Subtract 1 from both sides:-

[tex]\sf 18q+1-1=37-1[/tex]

Simplify:-

[tex]\sf 18q=36[/tex]

Divide both sides by 18:-

[tex]\sf \cfrac{18q}{18}=\cfrac{36}{18}[/tex]

[tex]\sf q=2[/tex]

_____________________

Hope this helps!

Have a great day!

Sam guessess the answer to two questionsfor each question the probability of guessing correctly is 1 in 4.what is the probability that Sam gets only one of the two guessess correct

Answers

The probability that Sam gets only one of the two guessess correct is 3/16.

What's is probability?

Probability is the likelihood of the occurence of an event.

The probability of guessing correctly = 1/4

The probability of guessing incorrectly = 3/4

Therefore, the probability that only one guess is correct will be:

= probability of guessing correctly × probability of guessing incorrectly

= 1/4 × 3/4

= 3/16

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The art teacher gave each student half of a sheet of paper. Then she asked the students to colored one one fourth of their pieces of papper. what do the number represent? what information was given?

Answers

The number 1/8 represent the fraction of full sheet of paper the teacher asked each student to color.

The information given are;

Paper given to each student by the teacherPart the teacher asked each student to color

What fraction of paper did the student colored?

The information given are

The full sheet of paper = xPaper given to each student by the teacher = 1/2x

Part the teacher asked each student to color = one fourth of their pieces of papper

= 1/4 of 1/2x

= 1/4 × 1/2x

= 1/8x

So therefore, the student colored 1/8 of the original piece of paper.

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Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease y=210(1.092)^x

Answers

The change  y=210(1.092)^x represent exponential growth

The percentage rate of increase is 9.2 percent increase

How to determine exponential growth

Exponential functions are functions that consist of three part say c(b)^d

the part that says whether the function is growth or decay is b

b is called the base function and it is used as follows to determine growth or decay function

b < 1 gives a decay functionb > 1 gives a growth function

Comparing with the given function 1.092 > 1 hence a growth function

The percentage is solved as follows

1.092 * 100 = 109.2%

109.2% is also referred to as 9.2 percent increase since it is an increment of 9.2%. this is shown below

100% + 9.2% = 109.2%

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a) Work out the gradient of the line y=5x-3 (1)

Gradient = (Answer here)

b) Work out the gradient of the line 3y-12x+7=0 (1)

Gradient = (Answer here)

Answers

Answer:

5 and 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the gradient and c the y- intercept )

(a)

y = 5x - 3 ← is in slope- intercept form

with gradient m = 5

(b)

3y - 12x + 7 = 0 ( add 12x to both sides )

3y + 7 = 12x ( subtract 7 from both sides )

3y = 12x - 7 ( divide through by 3 )

y = 4x - [tex]\frac{7}{3}[/tex] ← in slope- intercept form

with gradient m = 4

help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

a(x-h)^2+k is vertex form so the vertex is (1,-2) and i think axis of symmetry is x=1

Please help. Will mark brainliest. Please choose one answer

Which of the following is the most reasonable estimate of the correlation coefficient? Image is provided

0.5

0.7

0.9

1.0

Answers

The most reasonable estimate of the correlation coefficient is 0.9

What is the correlation coefficient?

The correlation coefficient gives an estimate of how strong is the linear relationship between two variables.

The correlation coefficient, r, is given by the formula;

[tex]r = \dfrac{\sum(x_i-\overline x)\cdot (y_i-\overline y)}{\sqrt{\sum (x_i-\overline x)^2\sum(y_i-\overline y)^2} }[/tex]

Where;

[tex]x_i[/tex] = The ith x-value

[tex]\overline x[/tex] = The mean (average of the x-values)

[tex]y_i[/tex] = The ith y-value

[tex]\overline y[/tex] = The mean (average of the y-values)

The give points on the scatter plot graph are;

(8, 9), (6, 9), (6, 6), (5, 5), (4, 5), (3, 4), (3, 3), (2, 4), (1, 2), (1, 3)

Plotting the above points on MS Excel gives;

The equation of the regression line is; y = 0.9407·x + 1.3313

The square of the correlation coefficient, = 0.8322

Therefore, R = √(0.8322) ≈ 0.9122

The option that is the most reasonable estimate of the correlation coefficient is therefore; 0.9

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Solve for v. Write your answers in simplified, rationalized form.
64v^3+1=0

Answers

Answer: v=-.25

Step-by-step explanation:

Step 1: Subtract 1 from both sides.

64v^3+1−1=0−1

64v^3=−1

Step 2: Divide both sides by 64.

64v^3 64 = −1 64

v^3= −1 64

Step 3: Take cube root.

v=( −1 64 )^(1/3 )

Step 4: There is no step 4 lol

v=−0.25

Preston goes to the movies with $15 in his wallet. He buys
a ticket for $6.50 and two snacks for $1.75 each. How
much money does he have left?
Select the correct expression.
OA. 15-6.5-1.75
OB. 15-(6.5+ 2.1.75)
O C. 15-2(6.5+ 1.75)
OD. 15-6.5+2.1.75

Answers

Preston left with $5 and correct expression for to find solution is option(B) i.e, 15 - (6.5 + 2 * 1.75)

What is an Algebraic Expression?

An expression constructed using integer constants, variables, and algebraic operations is known as an algebraic expression. For example, 3x² − 2xy + c is an algebraic expression.

Given,

Total money Preston have = $15

He buys the ticket for = $6.50

And, two snacks = $1.75 each

so the cost of two snacks is = 1.75 * 2 = $3.5

Total cost for ticket and snacks = $3.5 + $6.50 = $10

Now, he spent money on snacks and ticket $10 and he have total money $15 so,

Preston left with = $15 - $10

                           = $5

Therefore, Preston left with $5 and correct expression for to find solution is option(B) i.e, 15 - (6.5 + 2 * 1.75)

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