Find the values of a, b if the parabola
y = a (x + b)² - 8:
a. Has tangent y = 2x at the point P(4,8)
b. Has normal x - 2y = 17 at the point Q(-1,-9)
c. Has a common tangent with y = 2-x² at the point A(1,1) ​

The left Riemman sum approximation for f(x) = x^5, between x = 0 and x = 5, considering 5 intervals, is given as follows:

5.3248.

First we must obtain the Delta value, which is the difference between the bounds of the integral, divided by the number of integrals, thus:

[tex]\Delta_x = \frac{b - a}{n} = \frac{2 - 0}{5} = 0.4[/tex]

Then the values of x at which the numeric values are calculated are obtained as follows:

[tex]x_i = a + \Delta_x(i - 1)[/tex]

Thus the values of x are of:

The numeric values are given as follows:

Then the Riemann sum approximation for the integral is given as follows:

[tex]\sum_{i = 1}^{n} \Delta_x f(x_i)[/tex]

Thus:

0.4(0 + 0.01024 + 0.32768 + 2.48832 + 10.48576) = 5.3248.

More can be learned about Riemann sum approximation at https://brainly.com/question/7229305

#SPJ1

Answer:

C.

Step-by-step explanation:

To find the equation of the line that goes through the points (5, 3) and (-1, 2), we can use the point-slope form of a linear equation. The point-slope form is given by:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line, and m is the slope of the line.

To find the slope of the line, we can use the following formula:

m = (y2 - y1)/(x2 - x1)

Plugging in the coordinates of the two points, we get:

m = (2 - 3)/(-1 - 5) = -1/6

Substituting this value of m and the coordinates of one of the points into the point-slope form, we get:

y - 3 = -1/6(x - 5)

This simplifies to:

6x + y - 13 = 0

Therefore, the equation of the line is:

6x + y - 13 = 0

Answer:

Step-by-step explanation:

You want the cost of each item when person A buys 10 granola bars and 6 cups of yogurt for $18, and person B buys 5 granola bars and 4 cups of yogurt for $9.50.

The equations describing the relations can be written ...

  10g +6y = 18 . . . . . . . person A's purchase

  5g +4y = 9.50 . . . . . . person B's purchase

Subtracting half of the first equation from the second, we find ...

  (5g +4y) -1/2(10g +6y) = (9.50) -1/2(18)

  y = 0.50 . . . . . . . . . . simplify

Substituting this into the first equation gives ...

  10g +6(0.50) = 18

  10g = 15 . . . . . . . . . . subtract 3

  g = 1.50 . . . . . . . . . divide by 10

Each granola bar costs $1.50; each cup of yogurt costs $0.50.

__

Additional comment

The attachment shows the solution found using a calculator to find the reduced row-echelon form of the augmented coefficient matrix. The variable values are in the right column of the reduced matrix. This tells us granola bars are $1.50, and yogurt cups are $0.50, as we found above.

The number of mole O₂ is 2. Since the subscript of oxygen denotes the number of moles.

What is a diatomic element?

Diatomic molecules—so named because they only contain two atoms of the same or different chemical elements—are molecules that are made up of two atoms. A diatomic molecule is considered to be homonuclear if it contains two atoms of the same element, such as oxygen (O₂) or hydrogen (H₂).

One mole consists of an Avogadro number of atoms. If you are aware of the mole quantity, you can convert a mole into grams.

The mole (symbol: mol) is the unit of material quantity used by the International System of Units. The amount of a substance determines how many elementary entities of that substance are present in an object or sample. The mole must contain precisely 6.02214076×10²³ elementary entities.

The subscript part of a chemical compound represents the number of moe of the chemical compound. The subscipt of O₂ is 2. Thus the number of mole is 2.

To learn more about moles, click on the below link:

https://brainly.com/question/29095152

#SPJ4

Answer:0.23

Step-by-step explanation:

Answer:

multiply the original price ($299) by the first markup percentage (150%)

299*1.50= $448.50

that is markup price!

then you have to do the sale % (25%)

so you'll multiply your (25%) by your new price ($448.50)

448.50*.25= $112. 125

then you will subtract the sale price ($112.125) by the upcharged price ($448.50)

448.50-112.125= 336. 375

= $336. 38(round off)

to get the slope of any straight line, we simply need two points off of it, let's use those two in the picture below.

[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{3}-\stackrel{y1}{(-4)}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{(-2)}}} \implies \cfrac{3 +4}{4 +2} \implies {\large \begin{array}{llll} \cfrac{7 }{ 6 } \end{array}}[/tex]

The price that maximize the profit is $10 or $22.

What is maximum profit?

In economics, profit maximization is the short run or long run process by which a firm may determine the price, input and output levels that will lead to the highest possible total profit.

Given:

f(p) = -50p^2 + 1600p - 11000

Now to find velocity point

[tex]-\frac{b}{2a} = \frac{-1600}{2(-50)} = \frac{1600}{100} = 16[/tex]

So for the price p = 16 that generates maximum profit.

Now

f(16) = -50(16)^2 + 1600(16) - 11000 = 1800

The maximum profit is 1800.

At breakeven, f(p) = 0

So,

[tex]-50p^2 + 1600p - 11000 = 0\\p = \frac{-1600 + -\sqrt{(1600)^2 - 4(-50)(-11000)} }{2(-50)} \\p = \frac{-1600 + - \sqrt{2560000 - 2200000} }{-100} \\p = \frac{-1600+-\sqrt{360000} }{-100} \\p = \frac{-1600+-600}{100}\\ p = 10, 22[/tex]

So p = $10   or  p = $22

Hence, the price that maximize the profit is $10 or $22.

To know more about maximum profit, click on the link

https://brainly.com/question/15697949

#SPJ4

The graph of the line y = 4x + 3 is shown below.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

y = 4x + 3

When x = 0, y = 3

When x = 1, y = 4 + 3 = 7

When x = 2, y = 11

Similarly for negative x values, we get,

x = -1, y = -4 + 3 = -1

x = -2, y = -8 + 3 = -5

So on......

So we must get the following coordinates:

(-1, -1), (-2, -5), (0, 3), (1, 7), (2, 11),, ........

Thus,

The graph is shown below.

Learn more about coordinates here:

https://brainly.com/question/13118993

#SPJ1

Answer:

if u feel like u find the value that is correct but if u didn't find it it can be 1 the power of x can be 1

Answer:

B.9

all done  hope it help

Answer:

The value of t is 19.04

Step-by-step explanation:

[tex]7e^{0.1t} = 47\\[/tex]

[tex]e^{0.1t} = \frac{47}{7}[/tex]

take log both sides :

[tex]ln(e^{0.1t}) = ln(\frac{47}{7}) \\0.1t = 1.9042\\t = \frac{1.9042}{0.1}\\t = 19.04[/tex]

Yes, the lines intersect at the point (5, -2) so it is the solution to the system.

Now, According to the question:

Let's know:

Solution to a System of Linear Equations:-

A system of linear equations consists of the equations of two lines. The solution to a system of linear equations is the point which lies on both lines. In other words, the solution is the point where the two lines intersect. To verify whether a point is a solution to a system or not, we will either determine whether it is the point of intersection of two lines on a graph or we will determine whether or not the point lies on both lines algebraically.

Let's determine whether the given points are a solution to the systems of equations below.

Is the point (5, -2) the solution of the system of linear equations shown in the graph below?

Yes, the lines intersect at the point (5, -2) so it is the solution to the system.

Learn more about Linear Equation at:

https://brainly.com/question/11897796

#SPJ4  

Answer: The greatest of the three is 10.

Step-by-step explanation:

27/3=9 so the numbers will be around nine.

8+9+10=27

Answer:

Let x represent the value of the smallest of the three consecutive integers.

Then, the value of the middle integer is x+1, and the value of the greatest integer is x+2.

Since the sum of the three integers is 27, we have:

x + (x+1) + (x+2) = 27

Combining like terms, we have:

3x + 3 = 27

Subtracting 3 from both sides, we have:

3x = 24

Dividing both sides by 3, we have:

x = 8

Therefore, the value of the smallest integer is 8, the value of the middle integer is 8+1 = 9, and the value of the greatest integer is 8+2 = 10.

Thus, the value of the greatest integer is 10.

Step-by-step explanation:

Answer:

5% of 120 is 6, so you would add that 6 to 120.

120 + 6 = 126.

The total cost will sales tax would be $126.00.

Step-by-step explanation:

Hope it helps! =D

Slope of the line AB is 7/6.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

From the given graph the coordinates of A are (4, 3) and B is (-2, -4)

Slope AB=-4-3/-2-4

=-7/-6

Slope=7/6

Hence, slope of the line AB is 7/6.

To learn more on slope of line click:

https://brainly.com/question/14511992

#SPJ1

bring the variable to the left side and bring all the remaining values to the right side.

Image search results for Write the inequality and solve it. -17 -14 ■ -21 -2 -9 -15

To fix an inequality, use these steps:

Step 1: Remove fractions by multiplying all terms by the fractions’ least common denominator.

Step 2 Simplify the inequality by merging like words on either side.

Step 3 Subtract or add amounts to get the unknown on one side and the digits on the other.

In algebra, the letter “x” is frequently used to represent an unknown value. It is referred to as a “variable” or “unknown” at times. X is a variable in x + 2 = 7, but we can deal with it.

To learn more about inequality to refer:

https://brainly.com/question/28823603

#SPJ1

Answer:

x = 2,187

Step-by-step explanation:

27×27×27+27×27×27+27×27×27 =27x

19,683+19,683+19,683 =27x

59,049 = 27x

divide both sides by the coefficient of x ( 27 )

59,049 / 27 = 27x / 27

x = 2,187

The answer is no, we would not be surprised if the sample mean housebroken age for the small breed dogs is at least 3 months more than the sample mean housebroken age for the large breed dogs, as the probability of this happening is very small, 2.28%.

    z = (3-2) / 0.5 = 2

Learn more about Probability here:

https://brainly.com/question/11234923

#SPJ4

The amount of money that the business will receipt is $44.

given:

Small business makes bottles of lemonade today they have 528 oz of lemonade to the bottle each bottle holds 24 oz of lemonade they sell each bottle for $2 how much money will the business receipt

From the above question:

24oz of Lemonade = 1 bottle

528 oz of Lemonade = x

Cross Multiply

24 × x = 528

x = 528/24

x = 22 bottles

We are told that: they sell each bottle for $2

Hence:

1 bottle = $2

22 bottles = y

Cross Multiply

y = 22 × $2

y = $44

Therefore, the amount of money that the business will receipt = $44

Learn more about equations at:

https://brainly.com/question/2972832

#SPJ1

An inequality that represents the number of signatures Ali needs to collect in each of the remaining weeks so that he will have enough signatures to submit the petition: 520 + 6m ≥ 1000

and the minimum number of signatures he needs to collect = 80

Given that Ali wants to collect the same number of signatures each week.

Assume that Ali collects m number of signatures each week.

He has 6 weeks to collect the remaining signatures he needs.

So, by unitary method in 6 weeks the number of signatures he would collect:

6 × m

He currently has 520 signatures and he needs a total of at least 1,000 signatures before he can submit the petition.

so, we get an inequality.

520 + 6m ≥ 1000

We solve above inequality.

6m ≥ 1000 - 520

m ≥ 480/6

m ≥ 80

Ali needs to collect at least 80 signatures, so that he will have enough signatures to submit the petition.

Learn more about an inequality here:

https://brainly.com/question/19003099

#SPJ4

An effective sampling method is not cast doubt on the usefulness of the sample

The effective sample is a calculation of the approximate sample size needed to obtain the same degree of accuracy as a simple random sample. It is denoted mathematically by the formula n/D, where n represents the sample size and D denotes the design effect. It is employed as a means of condensing the volume of data.

Effective sample size calculations are mostly used for qualitative analyses of the sample size. The sample size calculates the total number of measurements or observations made during an experiment or survey. The effective sample size—rather than the actual sample size—is utilized in this assessment since it is thought that a sample size of 30 is necessary for an analysis to be valid.

To know more samples at:

https://brainly.com/question/27829028

#SPJ4

The function that describes the depth of the soil is h(x) = -(1/2)x + 8.

Where x is the number of bags of soil.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Depth of the soil = 8 inches

One bag of soil increases by 1/2 of an inch.

Now,

The function denotes the depth of the soil.

h(x) = -(1/2)x + 8

Where x is the number of bags of soil

Thus,

The function is h(x) = -(1/2)x + 8.

Learn more about functions here:

https://brainly.com/question/28533782

#SPJ1

The value should be added will be [tex]y = -4x^{2} +9x+6[/tex]

Now, According to the question:

Let the value y be added to  [tex]7x^2-5x+1[/tex] to give [tex]3x^2+4x+7[/tex]

y =  [tex]3x^2+4x+7[/tex] - ( [tex]7x^2-5x+1[/tex])

y = [tex]3x^{2} +4x+7-7x^{2} +5x-1[/tex]

Combine like terms:

y = [tex]3x^{2} -7x^{2} +4x+5x+7-1[/tex]

Calculate the subtraction and addition.

[tex]y = -4x^{2} +9x+6[/tex]

Hence, The value should be added will be [tex]y = -4x^{2} +9x+6[/tex].

Learn more about Addition at:

https://brainly.com/question/24289893

#SPJ4

The complete question is this:

What should be added to  [tex]7x^2-5x+1[/tex] to get [tex]3x^2+4x+7[/tex] ?

The probability that Andre, Olivia, and zack all win gift cards that are at least $25 is 1/4. Hence option C is the correct option.

What is an event?

An event is a collection of experiment results (a subset of the sample space) to which a probability is ascribed in probability theory.

The wheel consists of 8 equal sections. Each section contains the price of a gift card. 4 sections contain a $5 gift card, 2 sections contain a $5 gift card, one section contains a $25 gift card, one section contains a $50 gift card.

To win at least $5, they have to get either $25 or $50.

Thus the number of outcomes of favorable event is 2.

Total number of outcomes is 8.

The probability to win at least $25 is 2/8

Divide denominator and numerator by 2:

2/8 = 1/4

To learn more about probability, click on the below link:

https://brainly.com/question/743479

#SPJ4

Answer:

24 + x + 24

X is 0

Answer: substract 24 from both sides

then x = 0

Step-by-step explanation:

The equation to find the original price of the charging chord is 0.15x + 0.15y = 4.20 and the original price of the charging cord is $10.

Let the price of the phone case is x.

And the price of the charging cord is y.

Discounted price for phone case:  15% of x = 0.15x

Discounted price for charging cord = 0.15y

Now, according to the question, the total discount is $4. 20

⇒0.15x + 0.15y = 4.20

⇒0.15 * 18 + 0.15y = 4.20

⇒2.7 + 0.15y = 4.20

⇒0.15y = 4.2 - 2.7

⇒y = 1.5/0.15

⇒y = $10

Therefore the equation to find the original price of the cord is 0.15x + 0.15y = 4.20 and the original price of the charging cord is $10.

To know more about original price, here

https://brainly.com/question/731526

#SPJ4

Mathematical statements are called expressions if they have at least two words that are related by an operator and contain either numbers, variables, or both.

For a square whose side are 2 units long is :

= 2 + 2 x 2 + 2

= ( 2 + 2 ) x 2

= 2 x 4

= 2 x 3 + 2 = 8

Learn more about expressions refer to ;

https://brainly.com/question/1859113

#SPJ4

Step-by-step explanation:

bhshshssf just use some time and fouries and fouries and I don't have a car but who wants the French