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The equation of the line tangent to the graph of g at the point where x = 1 y + 10x + 44 =0.

What is line tangent?

A line that touches a curve at one point is said to be tangent. A point of tangency is the location where a curve and a line intersect. Y = mx + b is the slope-intercept formula for a line, where m is the line's slope. The straight line that "just touches" the curve at a particular location is referred to as the tangent line to a plane curve in geometry. It was described by Leibniz as the path connecting two points on a curve that are infinitely near together.

Given g(x)=f(2x)

Differentiate it on both side with respect to x.

[tex]\begin{aligned}& \frac{d g(x)}{d x}=2 * \frac{d f(2 x)}{d x} \\& \frac{d g(-1)}{d x}=2 * \frac{d f(-8)}{d x}=-5^* 2=-10\end{aligned}[/tex]

Slope =-10

Here x coordinate = -4

g(-4)=f(-8)=-4 = y coordinate

Thus point of tangency on function g is (-4,-4)

Thus equation of tangent is

y + 4= -10(x+4)

y + 10x + 44 =0

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Answer:

  y = 8x -11

Step-by-step explanation:

You want the equation of the line tangent to g(x) = f(2x-6) at x=1, where f is a differentiable function with f(1) = 2, f(-4) = -3, f'(1) = 3, f'(-4) = 4.

The equation of the tangent line at x=1 can be written ...

  y = g'(1)(x -1) +g(1)

The necessary function values are ...

  g(1) = f(2·1 -6) = f(-4) = -3

and

  g'(x) = f'(2x -6)·(2x -6)' = 2f'(2x -6)

  g'(1) = 2f'(2·1 -6) = 2f'(-4) = 8

Then the equation of the line is ...

  y = 8(x -1) +(-3) = 8x -8 -3

  y = 8x -11 . . . . . . tangent to g(x) at x=1

__

Additional comment

The minimum polynomial function f(x) that can have the desired values and derivatives is a cubic. The attached graph shows g(x) and the tangent at x=1 using that cubic for f(x).

The Answers are shown below:

In general, the term "proportion" refers to a part, share, or amount that is compared to a total.

According to the concept of proportion, two ratios are in proportion when they are equal.

A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

Given:

1. 3 x 20= 60

  10 x 6 =60

Yes, it is proportion.

2. 12 x 4 =48

   24 x 2= 48

Yes, it is proportion.

3. 8 x 8= 64

 5 x 16 = 80

No, it is not proportion.

4. 7/5, 21/15 is proportion

5. 16/3, 5/1 is not proportion

6. 12/9, 4/3 is proportion

7. 4/24, 2/6 is not proportion

8. 15/5, 6/2 is proportion

9. 9/3, 27/9 is proportion

10. 25/35, 5/7

or, 5/7, 5/7

The ratio is in proportion.

11. 15/3, 10/2

or, 3/1, 5/1

The ratio not in proportion.

12. 9/3, 12/4

or, 3/1, 3/1

The ratio is in proportion.

13. 2/5, 6/15

or, 2/5, 2/5

The ratio is in proportion.

14. 3.6/200, 1.8/100

The ratio is in proportion.

15. 6/12, 4/8

or, 1/2, 1/2

The ratio is in proportion.

16. 16/ 12 , 96/24

or, 4/3, 4/1

The ratio not in proportion.

17. 3/7, 2/5

The ratio not in proportion.

18. 2/22, 1/11

or, 1/ 11, 1/11

The ratio not in proportion.

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Simple interest analysis reveals that

a) The installment was $321.53 per month.

b) The total amount of the payments is $11,575.

c) Interest was paid of $1,575.

After t years, the amount of simple interest is calculated using:

A(t) = p(1 + rt)

that where:

The initial deposit is known as the primary, or P.

The interest rate in decimal form is r.

In this issue:

Hence, a $10,000 loan.

APR of 5.25%, which equals 3 years, therefore

Item c:

The result is A(3), so:

A(t) = P( 1 + rt)

A(3) = 10000[ 1 + 0.0525(3)]

A(3) = 11575

The total amount of the monthly installments is $11,575.

Item d:

I = A(3)  - P = 11575 - 10000 = 1575

When interest is calculated, the principal is removed, so:

Interest was paid of $1,575.

Item b:

36 payments were made over a period of 3 years, or 3 x 12 months.

Item a:

11575/3 = 321.53

The amount due each month was $321.53.

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1) 18 Quarts of Sparkling water needs to be mixed with 9 quarts grape juice.

2) 15/2 Quarts of grape juice is required for 15/4 quarts of sparkling water.

3) The Quantity of grape juice and sparkling water in 100 quarts of punch are 33 1/3 quarts and 66 2/3 quarts respectively.

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I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!

Answer:

The answer is 6, I am going to give you a explanation just in case you need one.

Step-by-step explanation:

We are going to refer seed packets as SP just to make it more simple. And flowers F this is just to make it easier on ourselves.

Ok since we know that in order to plant 9 F we need 3 SP.

If we do the equation correctly we should get

3 SP × ? = 9

In order to do this there is two ways I am going with the easier one we just have to add 3 to 3 until we get 9 ok so 3 + 3 = 6 so lets add more 3's 6 + 3 = 9 great so this means 3 + 3 + 3 = 9. Now if  you noticed he had three three's which means our equation now is

3 SP × 3 = 9

Now that we are done with the first part it should just get easier from here.

We know that each SP has 3 F to grow and each SP has 9 F to grow we just have to do 9 + 9 which gives us 18.

Therefore the answer is 2 SP needed to plant 18 flowers.

Hope this helped :)

a. The margin of error for this survey is of: 4.85%.

b. The 95% confidence interval for the percentage of teenagers who occasionally smoke cigarettes is of:

(30.15%, 39.85%).

Confidence intervals for proportions are obtained using the z-distribution.

The bounds of the interval are given as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The sample size and the estimate in this problem are given as follows:

[tex]n = 371, \pi = 0.35[/tex]

The margin of error is given as follows:

[tex]M = 1.96\sqrt{\frac{0.35(0.65)}{371}} = 0.0485[/tex]

As a percentage, it is of 4.85%.

Then the bounds of the interval are given by the estimate plus/minus the margin of error, hence:

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Answer:

perimeter is 6 times as long as the width

Step-by-step explanation:

let width be w then length l = 2w

perimeter (P) of a rectangle is calculated as

P = 2(l + w )

  = 2(2w + w)

 = 2(3w)

 = 6w

Perimeter is 6 times as long as the width

The width of the rectangle is (1/6) times long as the perimeter of the rectangle.

The area of a rectangle is given by -

A{R} = Length x Breadth

A{R} = L x B

Given is the length of a rectangle is twice its width.

Assume the width of the rectangle be [x] units. Then, the length will be [2x] units. For the width of the rectangle to be as long as the perimeter of the rectangle -

{P} = 2{L + B} = 2{x + 2x} = 6x

Now -

{w} = x

So, we can write that -

{P} = 6{w}

{w} = {1/6}{P}

Therefore, the width of the rectangle is (1/6) times long as the perimeter of the rectangle.

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Answer:

x = 8

y = 36

Step-by-step explanation:

The triangle shown in the image is an isosceles triangle.

We can find the value of x using the above mentioned information:

∠B = ∠A

5x = 40 divide both sides by 5

x = 8

The sum of interior angles in a triangle is equal to 180°.

Since ∠B and ∠C are both 40°:

40 + 40 + 3y - 8 = 180 add/subtract like terms

72 + 3y = 180 subtract 73 from both sides

3y = 108 divide both sides by 3

y = 36

To be certain of attaining the required result , 5 green balls must be selected.

We are informed that a box contains 90 red balls and 95 green balls.

To ensure that we have the items below, we must find the balls.

One red and one green

Consequently, take away the box's 90 red and 95 green balls.

95-90 = 5

Consequently, 5 green balls must be picked.

The unitary method , in its most basic form, is used to calculate the value of a single unit from a specified multiple. How to determine the value of one pen, for instance, if the cost of 40 pens is Rs. 400. The unitary approach can be used to complete it. Additionally, after determining the value of a single unit, we can multiply that value by the number of units needed to determine the value of the additional units. The concept of ratio and proportion is mostly applied using this way.

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Answer: I think its 10%

Step-by-step explanation: I hope that helps

yes, the periodic interest rate for a loan with an annual interest rate of 15.98% compounded weekly is 0.3073%

The yearly interest rate is divided by the quantity of compounding periods to produce the periodic interest rate. Interest can be earned on or added to interest more frequently when there are more compounding periods.

The interest rate that is levied on a periodic basis, such as monthly or quarterly, is known as the periodic rate. A credit card with an annual percentage rate of 18% has a periodic rate of 1.5 percent per month. The periodic rate is calculated by multiplying it by the number of periods in a year.

according to the formula :

periodic interest rate is annual interest rate divided by the number of times per year interest compounds so,

we have;

Annual interest rate = 15.98%

no.of week in a year= 52

so ;

periodic interest rate=15.98%/52

=0.3073%,

so the given statement is true.

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In 2011 we can predict there will be only 1.13 million VHS movie rentals.

A regression equation is utilized in details to figure out what relationship, if any, exists between sets of information. For instance, assuming that you measure a kid's level consistently you could find that they develop around 3 inches a year. That pattern (growing three inches a year) can be displayed with a regression equation.

The remarkable relapse condition is the dramatic capability that best fits the arrangement of information and it is given in the structure:

y = a · bˣ

where:

a = beginning worth of the model

b = remarkable develop or rot

x = time elapsed all along

For our situation,

y = 9.92 · (0.8208)ˣ

where:

a = 9.92

b = 0.8208

Since 0 < b < 1 we have an outstanding rot, affirming that the quantity of VHS is diminishing with time.

We can then utilize this condition to gather the quantity of VHS motion pictures in 2011.

As something first, compute how long all along (2000) would pass:

x = 2011 - 2000 = 11

Presently, substitute this worth in the situation:

y = 9.92 · (0.8208)¹¹

  = 1.13

Thus, number of vhs movies in 2011 is 1.13 million.

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Answer:pt 1). Oliver is correct

pt 2). The volumes are the same

yw

Answer:

Step-by-step explanation:

-3.45

To make 26 gallons of the shade of green paint, 13 gallons of blue paint is needed.To make 26 gallons of the shade of green paint, 20.8 gallons of yellow paint is needed.

Finding the product of two or more integers is done mathematically through the action of multiplication. It entails adding a number, known as the , known as the multiplier. For instance, adding three to itself four times produces the result of multiplying three by four, which is twelve. In other ways, repeated addition may be expressed using the abbreviation "multiplication." It is frequently used to calculate the overall worth of a set of paint, such as the cost of numerous products in a shopping cart. Finding the area of a rectangle or the volume of a cube are two more more difficult mathematical procedures that employ it.

How to solve?

To make 26 gallons of the shade of green paint, 1/2 * 26 = 13 gallons of blue paint is needed.

To make 26 gallons of the shade of green paint, 4/5 * 26 = 20.8 gallons of yellow paint is needed.

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In given expression constant term is 4, degree of expression is 2, coefficient of second term is 5 and at x=-1 value of expression is 6.

The highest or greatest power of a variable in a polynomial equation is referred to as the degree of the polynomial.

The degree denotes the polynomial's highest exponential power.

A term in an equation with a fixed value that is unaffected by variations in the variable.

A constant is typically represented as c to reflect a fixed value when written as a variable.

The usage of the word "variable" in this terminology may be perplexing, but all it really implies is that c is a variable that may stand in for any fixed value.

Given: p(x)=7x²+5x+4

(a) Constant term is coefficient of [tex]x^{0}[/tex].

So constant term in given equation is 4.

(b) Degree of expression is highest power of x in the expression. For our expression we have two as our highest power.

So, degree of expression is 2.

(c) Coefficient of second term is 5.

(d) On substituting value of x as -1, we get

7× (-1)² +5(-1) +4 = 7-5+4 = 6

So, value of expression at x=-1 is 6.

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The slope of a line parallel to the line 8x - 6y = -24 is 4/3.

The slope-intercept formula is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given the equation of the line.

8x - 6y = -24

First, rewrite in slope-intercept form.

8x - 6y = -24

Solve for y

8x + 24 = 6y

6y = 8x + 24

y = (8/6)x + 24/6

y = (4/3) + 4

Now, from the slope-intercept form;

y = mx + b

Where m is the slope

Slope of the line y = (4/3) + 4 will be

m = 4/3

All line parallel to the line y = (4/3) + 4 must have the same slope.

Hence, the slope of a parallel line to the line y = (4/3) + 4 will be;

m_parallel = 4/3

Therefore, the slope of the parallel line is 4/3.

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The equation that represents the model is 6x + 3 = 27, the solution of the equation is x = 4

Total number of pack of eraser = 6

Number of eraser in one pack = x

Number of erasers in 6 pack = 6x

Add 3 more erasers

Total number of erasers = 6x + 3

Total number of erasers = 27

Then the equation that represents the model will be

6x + 3 = 27

Solve the equation

6x = 27 - 3

Subtract the numbers

6x = 24

x = 24/6

Divide the numbers

x = 4

Therefore, the equation is 6x + 3 = 27, and the solution of the equation x = 4

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Answer:

81/2 is answer.......2/3× 81/ 2 = 27

Answer:

x=40.5

Step-by-step explanation:

2/3x=27

x3.    x3

2x=81

/2 /2

x=40.5

hopes this helps please mark brainliest

The correct option is 1/8 for the given expression.

What is fraction?

In Maths, a fraction is employed to represent the portion/part of the full issue. It represents the equal elements of the full. A fraction has 2 elements, particularly dividend and divisor. the quantity on the top is named the numerator, and therefore the range on the bottom is named the denominator.

Main body:

firstly , the model shows that it is divided into 4 parts

so the fraction becomes 1/4

as one part of 1/4 is divided into half so we can say

half of quarter which can be represented as

1/4*1/2 = 1/8

Hence the correct option is 1/8

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Answer:

x = 2

Step-by-step explanation:

X is the vertical edge

x=2

Answer: x = 2

Step-by-step explanation:

The slope of a vertical line is undefined, so the equation of a vertical line is x = a

In this problem, the only choice that represents a vertical line is x = 2 (where a = 2)

Answer: 50-35

Step-by-step explanation:

Because if you calculate it, 50x70% or 50x0.7 is 35. I multiply bt 70% not 30% because you are trying to find the amount after the 30% decrease, meaning it is 70% of the orginal value.

Answer:

50 to 35

Step-by-step explanation:

[tex]\frac{30}{27} =\frac{100}{y}[/tex]

30y = 2700

y = 90

27 is 90% of 30.

[tex]\frac{50}{35}=\frac{100}{y}[/tex]

50y = 3500

y = 70

35 is 70% of 50.

The equation in point slope form will be -

y - 2 = 2(x - 3).

The general equation of a straight line is -

Other possible equations of lines are -

We have some equations of line as given in the question.

The point slope form is -

(y - y₁) = m(x - x₁)  

The points are -

(3, 2) and (5, 6)

So -

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

m = 4/2

m = 2

Equation will be -

y - 2 = 2(x - 3)

Therefore, the equation in point slope form will be -

y - 2 = 2(x - 3)

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Answer: 28.3 calories

Step-by-step explanation:

From 12 oz down to 2 oz, we divided by 6

So take 170 divided by 6 = 28.33 cal; ground up will be 28.3 cal

The equation that represents the situation will be y = 1.5x.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

From the graph, the y-intercept of the line is zero. Then the equation is given as,

y = mx

The line is passing through (6, 9), then we have

9 = 6m

m = 9 / 6

m = 1.5

Then the equation that represents the situation will be y = 1.5x.

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