01
5. Solve the polynomial by typing it into a graphing calculator and identifying the zeros. Round to the nearest tenth.
5x^4-7x^3-5x^2+5x+1=0

Let [tex]x,y,z[/tex] denote the amounts (in liters) of the 20%, 30%, and 60% solutions used in the mixture, respectively.

The chemist wants to end up with 72 L of solution, so

[tex]x+y+z=72[/tex]

while using twice as much of the 60% solution as the 30% solution, so

[tex]z = 2y[/tex]

The mixture needs to have a concentration of 35%, so that it contains 0.35•75 = 26.25 L of pure acid. For each liter of acid solution with concentration [tex]c\%[/tex], there is a contribution of [tex]\frac c{100}[/tex] liters of pure acid. This means

[tex]0.20x + 0.30y + 0.60z = 26.25[/tex]

Substitute [tex]z=2y[/tex] into the total volume and acid volume equations.

[tex]\begin{cases}x+3y = 72 \\ 0.20x + 1.50y = 26.25\end{cases}[/tex]

Solve for [tex]x[/tex] and [tex]y[/tex]. Multiply both sides of the second equation by 5 to get

[tex]\begin{cases}x+3y = 72 \\ x + 7.50y = 131.25\end{cases}[/tex]

By elimination,

[tex](x+3y) - (x+7.50y) = 72 - 131.25 \implies -4.50y = -59.25 \implies \boxed{y=\dfrac{79}6} \approx 13.17[/tex]

so that

[tex]x+3\cdot\dfrac{79}6 = 72 \implies x = \boxed{\dfrac{65}2} = 32.5[/tex]

and

[tex]z=2\cdot\dfrac{79}6 = \boxed{\dfrac{79}3} \approx 26.33[/tex]

Answer: 3 1/4

Step-by-step explanation: you started with 8 1/4 subtract the 1/4 now ur left with 8-3 which equals 5

By Euler's method the numerical approximate solution of the definite integral is 4.189 648.

In this problem we must make use of Euler's method to estimate the upper bound of a definite integral. Euler's method is a multi-step method, related to Runge-Kutta methods, used to estimate integral values numerically. By integral theorems of calculus we know that definite integrals are defined as follows:

∫ f(x) dx = F(b) - F(a)     (1)

The steps of Euler's method are summarized below:

The table for x, f(xₙ, yₙ) and y is shown in the image attached below. By direct subtraction we find that the numerical approximation of the definite integral is:

y(4) ≈ 4.189 648 - 0

y(4) ≈ 4.189 648

By Euler's method the numerical approximate solution of the definite integral is 4.189 648.

To learn more on Euler's method: https://brainly.com/question/16807646

#SPJ1

The arc length of the circle is 5π/9 units

From the question, we have the following parameters

Angle, ∅ = 5π/9

Radius, r = 1 unit

The arc length (x) is calculated as

x = r∅

Substitute the known values in the above equation

x = 5π/9 * 1

Evaluate the product

x = 5π/9

Hence, the arc length of the circle is 5π/9 units

Read more about arc lengths at:

https://brainly.com/question/2005046

#SPJ1

Answer:0.08333333....

Step-by-step explanation:

Answer:

4x²

Step-by-step explanation:

Normally you would use the exponent → roots rule, but this one simplifies easier without that

[tex](8x)^{\frac{2}{3} }[/tex]

8 = 2³

so [tex](8x)^{\frac{2}{3} } = (2^{3}x)^{\frac{2}{3}}[/tex]

then the threes cancel, since one is a 3 and the other one is [tex]\frac{1}{3}[/tex]

so [tex](8x)^{\frac{2}{3} } = (2^{3}x)^{\frac{2}{3}} = (2x)^2[/tex]

then just square the 2 and the x

[tex](8x)^{\frac{2}{3} } = (2^{3}x)^{\frac{2}{3}} = (2x)^2 = 4x^2[/tex]

Answer:

Step-by-step explanation:

parallel lines are the same so they dont touch u-u

perpendicular lines do touch eachother and intersect

The required two differences between constructing parallel lines and constructing perpendicular lines are,
1) Constructing parallel lines never intersect each other while perpendicular lines intersect each other.
2) Constructing Perpendicular lines make an angle of 90° with each other at the point of the intersection. while parallel lines do not have angles with each other.

Parallel lines are defined as the pair of lines in which points on both the lines are equidistant from each other, and the line never intersects each other.

The differences between constructing parallel lines and constructing perpendicular lines are as follows.

1) Constructing parallel lines never intersect each other while perpendicular lines intersect each other.
2) Constructing Perpendicular lines make an angle of 90° with each other at the point of the intersection. while parallel lines do not have angles with each other.

Learn more about parallel lines here,

https://brainly.com/question/16701300
#SPJ2

there are two expressions that can represent the length of the rectangle, these two expressions are:

L = x

or

L = (4x + 12)

Remember that for a rectangle of length L and width W, the area is given by:

A = L*W

In this case, we know that the area is:

[tex]A = 4x^2 + 12x[/tex]

We can factorize that expression into:

[tex]A = x*(4x + 12)[/tex]

So there are two expressions that can represent the length of the rectangle, these two expressions are:

L = x

or

L = (4x + 12)

If you want to learn more about rectangles:

https://brainly.com/question/17297081

#SPJ1

The simplification of the algebraic fraction equation given as 3a³ - 5b³ + (3/a) + b³ is; (3/a)(a⁴ + a) - 4b³

We want to solve the algebraic fraction equation given as;

3a³ - 5b³ + (3/a) + b³

Rearranging the algebra to get;

(3a³ + (3/a)) + b³ - 5b³

Factorizing out 3/a and simplifying gives;

(3/a)(a⁴ + a) - 4b³

This is the final part for the simplification of the given algebraic fraction. Thus, we can conclude that the simplification of the algebraic fraction equation given as 3a³ - 5b³ + (3/a) + b³ is; (3/a)(a⁴ + a) - 4b³

Read more about Algebraic Fractions at; https://brainly.com/question/11875858

#SPJ1

Answer:

X-intercepts:

[tex] (\frac{3}{7} ,0)[/tex]

Y-intercepts:(0,3)

Step-by-step explanation:

Hello!

given expression

[tex]y = - 7x + 3[/tex]

x-intercept is the point on the graph where y=0

solve

[tex] - 7x + 3 = 0 \\ - 7x = - 3 \\ x = \frac{3}{7} [/tex]

Thus, x-intercept

[tex]( \frac{3}{7} ,0)[/tex]

y-intercept is the point on the graph where x=0

solve

[tex]y = - 7(0) + 3 \\ y = 0 + 3 \\ y = 3[/tex]

Thus, y-intercept (0,3)

Hope it helps!

By using the linear function which models the data in the given table, the cost of a textbook with 402 pages is equal to $47.4478.

A scatter plot can be defined as a type of graph which is used for the graphical representation of the values of two variables, with the resulting points showing any association (correlation) between the data set.

A linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.

By critically observing the graph (see attachment) which models the data in the given table, we can infer and logically deduce that the linear function is given by:

y = 0.1057x + 4.9564

If x = 402, then y is given by:

y = 0.1057(402) + 4.9564

y = 42.4914 + 4.9564

y = $47.4478.

Read more on scatterplot here: brainly.com/question/6592115

#SPJ1

The graph is shown in the attached image.

Comparing A and B we find the value of the variables as

x = radius

Centre (-2,0)

Radius 2

The sketch of the image is attached below

Generally, the equation for is mathematically given as

x = -4 cos -(i)

Multiply -(i) both sides by & we

x^2= -4xcos\theta

We know that and

x= x cos\theta

y = rsino

x² + y² = x² (cos²∅ + sin²∅).

x² + y² = x² ....sin² ∅ + cos 2∅=1

so, putting rates in (ii) we get

x²+y² = -4x

x²+4²  +4 + y²=4

(2 + 2)² + y² =4

The rectangular form of

x = -4cos∅  is (x + 2)² + y² = 4 ---- A

We can see that A is a graph of circles. The general equation of a circle is

= (x-h)² + (y)² = x² ----B

where (h, k) = centre

Comparing A and B we find

Read more about rectangular form

https://brainly.com/question/1553696

#SPJ1

Answer:

C

Step-by-step explanation:

sin^4x as a product of two squared terms is sin^2(x) * sin^2(x)

The sine expression is given as

sin^4x

The above means

sin x raised to the power of 4

This in other words, the expression is represented as

(sin(x))^4

Express 4 as 2 + 2

(sin(x))^(2 + 2)

Apply the law of indices

(sin(x))^2 * (sin(x))^2

This gives

sin^2(x) * sin^2(x)

Hence, sin^4x as a product of two squared terms is sin^2(x) * sin^2(x)

Read more about products at:

https://brainly.com/question/10873737

#SPJ1

The correct answer is the option A because in one-to-one functions, each y value corresponds to only one x value.

Since the Dilating polygon WXYZ will alter the side lengths of the polygon. The correct option is option  (b) the slope of WX is 3/4, and the length of W'X' is 15.

The coordinates in the question were:

(3,2), and  (7,5).

Then the slope of WX is:

[tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

So m   = [tex]\frac{{5} - 2 }{7-3} }[/tex]

    =3/4

The length of WX is calculated by:

[tex]WX = \sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1}) ^ 2}[/tex]

[tex]\sqrt{(7-3)^2 + (5-2)^2} \\\\= \sqrt{25} \\\\= 5[/tex]

Since, The scale factor is  =  3.

Hence, WX = 3 x 5 = 15

Therefore, Since the Dilating polygon WXYZ will alter the side lengths of the polygon. The correct option is option  (b) the slope of WX is 3/4, and the length of W'X' is 15.

Learn more about vertex from

https://brainly.com/question/25336437

#SPJ1

Answer:    slope 3/4 and length 15

Step-by-step explanation: plato

Answer:

A = 8000

B = 4000

C = 12000

Step-by-step explanation:

$24000 = A,B and C

A = 2B

B = 1/3C

solve for the letter that gets described the most

that letter is B

A =2B

B = 1/3C -> C = 3B

24000 = A + B + C

24000 = 2B + B + 3B

24000 = 6B

B = 4000

A =2B = 8000

C = 3B = 12000

Using a calculator, the critical value for the t-distribution, with a confidence level of 99%, a sample size n = 20 and a two-tailed test is of Tc = 2.8609.

It is found using a calculator, with three inputs, which are given by:

In this problem, the inputs are given as follows:

Hence, using a calculator, the critical value is of is of Tc = 2.8609.

More can be learned about the t-distribution at brainly.com/question/27125917

#SPJ1

The conclusion for p, from the confidence interval, using an absolute value inequality is:

[tex]|p - 0.27| \leq 0.019[/tex]

A confidence interval is given by the estimate plus minus the margin of error. As an inequality, we have that the absolute value of the difference between the proportion and the estimate is of at most the margin of error, that is:

[tex]|p - E| \leq M[/tex]

For this problem, the estimate and the margin of error are:

E = 0.27, M = 0.019.

Hence the inequality is:

[tex]|p - 0.27| \leq 0.019[/tex]

More can be learned about confidence intervals at https://brainly.com/question/25890103

#SPJ1

Using the probability concept, we have that:

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, there are 35 people, out of which 17 are female and 5 are male that prefer mint chocolate chip, hence:

p = (17 + 5)/35 = 22/35 = 0.6286.

There is a 0.6286 = 62.86% probability that a randomly selected person is female or prefers mint chocolate chip.

Out of the same 35 people, 11 people prefer cookie and cream and 2 people prefer vanilla, hence:

p = (11 + 2)/35 = 13/35 = 0.3714

There is a 0.3714 = 37.14% probability that a randomly selected person prefers cookie and cream or vanilla.

More can be learned about probabilities at https://brainly.com/question/14398287

#SPJ1

Answer:

9/25 or -1/11

Step-by-step explanation:

2 outcome

1; 7x-5=18x-4

2;-(7x-5)=18-4

The domain of the functions are:

The domain of a function is the set of input values the function can take i.e. the set of values the independent variable can assume?

Function 1

The function is given as:

f(x) = √4x + 6

Set the radicand greater than 0

4x + 6 > 0

Subtract 6 from both sides

4x > -6

Divide by 4

x > -3/2

Express as interval notation

[-3/2, ∞)

Hence, the domain of f(x) = √4x + 6 is [-3/2, ∞) or x >-3/2

Function 2

The function is given as:

g(x) = -4√-20x - 6

Set the radicand greater than 0

-20x - 6 > 0

Add 6 to both sides

-20x > 6

Divide by -20

x < -6/20

Simplify

x < -3/10

Express as interval notation

(-∞, -3/10]

Hence, the domain of g(x) = -4√-20x - 6 is (-∞, -3/10] or x < -3/10

Function 3

The function is given as:

f(x) = 15 + √5x - 16

Set the radicand greater than 0

5x - 16 > 0

Add 16 to both sides

5x > 16

Divide by 5

x > 16/5

Express as interval notation

[16/5, ∞)

Hence, the domain of f(x) = 15 + √5x - 16 is [16/5, ∞) or x >16/5

Function 4

The function is given as:

p(x) = √20x + 6

Set the radicand greater than 0

20x + 6 > 0

Subtract 6 from both sides

20x > -6

Divide by 20

x > -6/20

Simplify

x > -3/10

Express as interval notation

(-3/10, ∞]

Hence, the domain of p(x) = √20x + 6 is (-3/10, ∞] or x > -3/10

Read more about domain at:

https://brainly.com/question/10197594

#SPJ1

The number line with the points 3/6, 3/4, and 3/12 graphed on it is attached.

When fractions are represented on a number line, we can plot them on a number line just like we do with whole numbers and integers. Parts of a whole are represented by fractions. As a result, fractions on the number line are represented by splitting a whole into equal parts, ranging from 0 to 1, and the number of those equal parts would match the denominator of the fraction.

To graph the given fractions on the number line, we first convert them to like fractions.

3/6, 3/4, and 3/12

= 6/12, 9/12, and 3/12, which are like fractions.

Now we divide the number line with the minimum mark as 1/12, the least fraction, with 12 as denominator.

Now, we can mark the points 6/12, 9/12, and 3/12, as shown.

Thus, the number line with the points 3/6, 3/4, and 3/12 graphed on it is attached.

Learn more about the number line at

https://brainly.com/question/14878277

#SPJ1

By the 30 - 60 - 90 theorem the right options of the multiple choice question is:

A. The hypotenuse is twice as long as the shorter leg.

D. The longer leg is √3 times as long as the shorter leg.

In this problem we must look for the right choices in a multiple choice question. According to the Euclidean geometry, 30 - 60 - 90 have the following properties:

Thus, the right options of the multiple choice question is:

A. The hypotenuse is twice as long as the shorter leg.

D. The longer leg is √3 times as long as the shorter leg.

To learn more on right triangles: https://brainly.com/question/6322314

#SPJ1

Answer:

x = 15°

Step-by-step explanation:
165 and x are on a straight line which means they are supplementary.
Set up the equation and solve for x:

165 + x = 180

x = 180 - 165

x = 15

Answer:

[tex]52\sqrt{3}[/tex]

Step-by-step explanation:

[tex]\frac{1}{2}(11+15)(4\sqrt{3})=52\sqrt{3}[/tex]