O EQUATIONS AND INEQUALITIESSolving a word problem using a quadratic equation with rationa...

Answer:

15

Step-by-step explanation:

6.65:5=1.33

1.33х15=19.95$

we need to around the 19.95 and we get a 20$

have a nice day

Step-by-step explanation:

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15.. . is an arithmetic progression with a common difference of 2.

Arithmetic progression is S = 1/2n[2a+(n-1)d]

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In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

Geometric progression is Uₙ = arⁿ ⁻ ¹

Answer:

x ≥ 97

Step-by-step explanation:

Average = Sum of values divided by the amount of numbers in a data set

Data Set: {75, 82, 94, 77, ?}

75 + 82 + 94 + 77 + ? = ? ÷ 5 = 85

85 x 5 = 425

75 + 82 + 94 + 77 + ? = 425 ÷ 5 = 85

75 + 82 + 94 + 77 = 328

425 - 328 = 97

Ray must score greater than or equal to 97, or x ≥ 97 in order to have an average of at least 85.

The volume of the given rectangular prism is V = 5x⁵ + 4x⁴ + x³ cubic units.

What is the volume of the rectangular prism?
Four rectangular faces and two parallel rectangular bases make up a rectangular prism. We are aware that a rectangular prism's cross section is a rectangle. The term "Cuboid" is another name for the rectangular prism.
Therefore, the following formula is provided to determine a rectangular prism's volume: Volume = l*b*h cubic units.

Given, the length of the rectangular prism = l = x
Also, the width of the rectangular prism = w = x²
Again, the height of the rectangular prism = h = 5x² + 4x + 1
Volume of the rectangular prism = l*w*h = x*(x²)*(5x² + 4x + 1)
= x³(5x² + 4x + 1) = 5x⁵ + 4x⁴ + x³
Thus, the volume of the given rectangular prism is V = 5x⁵ + 4x⁴ + x³ cubic units.

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Answer:

Step-by-step explanation:

Given a transversal crossing parallel lines and supplementary angles (x+8°) and (2x-5°), you want to find the measures of angles L and O, supplementary to each of these.

Where a transversal crosses parallel lines, consecutive interior angles are supplementary. Using the given expressions, this means ...

  (x +8°) +(2x -5°) = 180°

  3x +3° = 180° . . . . . . . . . simplify

  x +1° = 60° . . . . . . . divide by 3

  x = 59°  . . . . . . subtract 1°

Then the acute angle is ...

  x+8° = 59° +8° = 67°

and the obtuse angle is ...

  2x -5° = 2(59°) -5° = 113°

Angle L corresponds to angle (2x-5°), so is congruent:

  ∠L = 113°

Angle O is an alternate interior angle with respect to angle (x+8°), so is congruent:

  ∠O = 67°

The absolute value function graphed in this problem is given as follows:

A. y = |x - 5| - 4.

An absolute value function of vertex (h,k) is defined as follows:

y = a|x - h| + k.

The leading coefficient a does not influence the vertex of the absolute value function.

The vertex of the graph is the turning point, hence it is given as follows:

(5, -4).

Hence, considering a leading coefficient 1, h = 5 and k = -4, the equation is given as follows:

y = |x - 5| - 4.

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Answer: 26

Step-by-step explanation:

[tex]f(-2)=-2(-2)^2 -(-2)+3=13\\\\2f(-2)=2(13)=26[/tex]

Answer:

> -24.32 I hope that help so it is a on your screen

It depends on the number of decimal points of the values from which we get the average.

Normally it must be rounded to the nearest tenth, 17.3

Answer:

y to the power of -8

:) hope this help

Answer: y^8

Step-by-step explanation:

You see that the equation has two negative numbers, so it will become positive.

(y^-2)^-6 = y^8

The base of it will cancel each other out and left with y^8

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Answer:

A D

Step-by-step explanation:

An A is 90% to 100% A B is 80% to 89% A C is 70% to 79% A D is 60% to 69%

if we replace y for -3 in the given equation and then we despejate x, we wiil going to have a values for the ordered pair that satisfy the equation:

then

the ordered pair woul be (4,-3)

The polynomial with zeros of −3, −1, and 2, and passes through the point (3,11) is:

P(x) = (11/24)*(x + 3)*(x + 1)*(x - 2)

We know that the zeros are −3, −1, and 2, so if we define the leading coefficient as A, the polynomial can be written as:

p(x) = A*(x + 3)*(x  + 1)*(x - 2)

Now we want this to pass through the point (3, 11), then we get:

p(3) = 11 = A*(3 + 3)*(3 + 1)*(3 - 2)

         11 = A*6*4*1

         11 = A*24

         11/24 = A

Then the polynomial is:

P(x) = (11/24)*(3 + 3)*(3 + 1)*(3 - 2)

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Given the expression:

using the distributive property we get the following:

therefore, the simplified expression is 0

The equation of line is y = -x + 6

What is Equation of line ?

A straight line's general equation is y = mx + b, where m denotes the gradient and y = b denotes the point at which the line crosses the y-axis. On the y-axis, this value b is referred to as the intercept.

The given point are (5, 1) and (7, 11)

We know, the equation of line is,

y = mx + b

where, m = slope

            b = y-intercept

First, find slope i.e m

we know the formula of slope (m) = (y2 - y1) / (x2 - x1)

The points, (x1, x2) = (5, 1) and,

                   (y1, y2) = (7, 11)

put these values in slope formula,

m = (11 -7) / (1 - 5)

   = 4 / -4

m = -1

we get the slope is -1

Next, find y-intercept i.e 'b'

for that, take any one point I'm taking (5, 1) and put these in equation ,

y = mx + b

1 = -1 * 5 + b

1 = -5 + b

b = 6

Now, put slope (m) and y-intercept (b) value in ,

y = mx + b

we get,

y = -x + 6

Hence, the equation of line is y = -x + 6

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Answer: Solve 5x=(2x+3)

Step-by-step explanation:

The perimeter of the triangle is 46.4 and the length of a triangle's boundary taken as a whole is referred to as its perimeter.

Calculate the perimeter of a triangle:

Perimeter of a triangle = a +b + c

Therefore, the triangle's perimeter is 46.4, and the whole length of a triangle's boundary is referred to as the triangle's perimeter.

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Marsha must claim for itemized deductions.

Given,

Last year's gross income is $56,800.

Medical expenses = $4900

State and local income taxes paid = $3100

The mortgage interest paid = $1940

Charitable contributions = $530

Non-reimbursed work expenses = $1200

Standard deduction = $5700

The sum of all the expenses of last year = $4900 + $3100 + $1940 + $530 + $1200 = $11,670

And the Standard deduction is $5700.

Which is, $11,670 - $5700 = $5970 lesser.

Therefore, Marsha must claim for itemize deductions rather than the standard deductions.

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The percentage of red pins in total pins ordered by Eric is 30%.

According to the question,

We have the following information:

Eric received 70 pins in all.

21 of the pins are red.

Now, we will find the percentage of red pins:

Percentage of red pins = (Number of red pins*100/total number of pins)

Percentage of red pins = (21*100)/70

Percentage of red pins = 2100/70

Percentage of red pins = 30%

(In the same way, we can also find the number and percentage of yellow pins from the total pins.)

Hence, the percentage of red pins in total pins ordered by Eric is 30%.

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The factor pairs which matches the number of tents to sleep exactly 40 boys with each tent having an equal number of boys are;

Since 40 students are to be equally distributed in each of the number of tents arrangement.

It follows that first, one must list the integer pairs whose products yield 40 as follows;

Hence, we have;

Hence, the factor pairs for each scenario of number of tents are as listed in the answer section above.

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The line given passes through two points. These are (-6,0) and (0,-8).

Remember that two lines are perpendicular if the product of their slopes is -1. So, the first thing we're going to do is to find the slope of the line given.

The slope between two points (x1,y1) and (x2,y2) can be found using the formula:

If we replace our values:

To find other perpendicular line to this one, we have to find a number which multiplication with -4/3 is -1.

This number is clearly 3/4. Because

Therefore, the slope of the perpendicular line must be 3/4, and the original slope is -4/3.

If we graph this:

Answer:

Step-by-step explanation:

The time interval of interest is 6 hours

There is an average of 18 trains per 24 hours or 18/(24/6)=49/12 trains per 6 hours.

The probability can be found using the Poisson distribution with parameter

λ=49/12

Answer:

245

Step-by-step explanation:

6 - 42

35 - x

cross multiply

6x = 35 × 42

6x = 1470

x = 1470 ÷ 6

x = 245

You have to convert the following number into a fraction:

This is a periodic decimal number, which explicitely is 0.68888888....

In order to convert this number to a fraction you proceed as follow:

You put 0.68 and not 0.688 because to do the convertion you need only the first periodic number (that is, only the first 8). The key is to put in the numerator the complete number as whole number, that is, 68. To this number you subtract the whole part of the decimal number, this whole part is 0 because of the 0.688. Then, in the numerator you have 68 - 0. In the denominator you write a number composed only by 9's. The number of 9 numbers is determined by the number of digits of the first number in the numerator. That is two 9 numbers

The expression to simplify is

We will simplify by combining like terms.

• There are FIVE x's and TWENTY-SIX more x's. We add.

5x + 26x = 31 x

• There is 1 constant, NEGATIVE THIRTEEN. No combining required so leave it as is.

•

• There is 1 term with y, which is SEVEN y. No combining required, so we leave it as is.

The final expression is

a) The linear regression equation is y = 1.360x + 6.540

b) The linear regression equation is y = -0.8909x + 37.59

Given,

a) The data;

Time in years, x ; 1, 1.5, 3, 5, 6, 7, 8.5, 10

Price, y ; 8, 9.75, 10.25, 11.80, 13.90, 17, 18, 20.75

We have to find the linear regression equation to the above given data.

We can use regression calculator ;

There are 8 xy pairs.

The linear regression equation is;

y = 1.360x + 6.540

b) The data

Time in years, x ; 1, 1.5, 3, 5, 6, 7, 8.5, 10

Price, y ; 32.5, 35, 37.3, 36.4, 35.7, 32.4, 29, 25

We have to find the linear regression equation to the above given data.

We can use regression calculator ;

There are 8 xy pairs.

The linear regression equation is;

y = -0.8909x + 37.59

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a) the maximum error in surface area  and  the relative error  is 25.4 cm² and 1.25%

b) the maximum error in the volume and  the the relative error  is 162.1 cm³ and 1.875%

As we know  the  formula for surface area is

                                    Surface Area , S= 4*π*r^2.

So  differentiating both sides we get

                                     dS/dr = 8*π*r .....1

and  the  formula for  the circumference is :2*π*r

, so the error on the circumference will be respect to radius

=> Δc = 2*π*Δr  

=> Δr = ΔC / (2*π)

substituing the value ofΔr in  the equation 1, we get

The maximum error in surface area which is :

ΔS = 8*π*r*Δr = 4*r*Δc

      = (2/π)*c*Δc.

    = 25.4

where for the relative error

                 ΔS/S = 4*r*Δc/(4*π*r^2)

                          = Δc/(π*r)

                          = 2*Δc/c

                        = 1.25%

Now Since  the formula for  the volume of a sphere  is :

                                       V = 4/3*π*r^3

dofferentiating both sides we get ,

                           => dV/dr = 4*π*r^2.

So,  the   the maximum error in the calculated volume  will be :

ΔV = 4*π*r^2*Δr

       = 2*r^2*Δc

       = 1/(2*π^2)*c^2*Δc

      =162.1

Where as the relative error for the volume will be

ΔV/V = 3*Δr / r = 3*ΔC/C = 1.875%

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