The functions f and g are defined as follows. f(x)=-3x-3,g(x)=2x^(3)+2 Find f(7) and g(-4) Simplify your answers as much as possible.

The coordinates of the point D that partitions the segment in ration 1:2 is D = (4. 3).

The line segment is divided into two pieces by a point, which may or may not be equal. If we know the coordinates of the point, we may calculate the ratio by which the supplied line segment is divided. Also, if we are aware of the ratio that the line segment connecting two places has produced, we may locate the point of division. The two may be accomplished using a section formula from coordinate geometry.

The position of a point that splits a line segment connecting two points into two portions with a length ratio of m:n is found using the section formula.

The coordinates of the point A and B from the given figure is:

A = (1, 3) and B = (10, 3)

The section formula is given as:

(x, y) = (mx2 + nx1 / m+n , my2 + ny1 / m+n)

Substitute the values of m = 1 and n = 2, and the coordinates of the point A and B.

(x, y) = ((1)(10) + (2)(1)/ 3 , (1)(3) + (2)(3) 3)

D(x,y) = (4, 3)

Hence, the coordinates of the point D that partitions the segment in ration 1:2 is D = (4. 3).

Learn more about section formula here:

https://brainly.com/question/30242641

#SPJ1

The cytoskeletal structure composed of actin and involved in regulating cell shape, cell movement, and muscle contraction is called the actin cytoskeleton.

The actin cytoskeleton is a fundamental component of the cytoskeleton, a network of protein filaments within cells that provides structural support and plays essential roles in cellular processes. Actin filaments, also known as microfilaments, are polymers of actin protein subunits and form the main component of the actin cytoskeleton.

The actin cytoskeleton is involved in various cellular functions. It plays a crucial role in determining cell shape by providing structural support and contributing to the maintenance of cell integrity. Actin filaments are also responsible for generating the forces required for cell movement, including crawling, amoeboid movement, and migration of cells during processes such as wound healing.

Learn more about functions here:

https://brainly.com/question/31062578

#SPJ11

This is an exponential growth function so

Our base number is 3.

For statement 2 as explained, it is a growth function.

As far we get in X-axis higher is the value.

For statement 3 the Y interception is (0,2) as sowed below.

For statement 4 The purple line in the graph is a Horizontal asymptote and it has an equation 1.

For statement 5 The domain of the function is all real numbers.

For statement 6 The range of the function is all the real numbers >1. Because we do not include the asymptote.

Answer:

Step-by-step explanation:

Distance formula:

d = rt

where d = distance, r = average speed and t = time travelled.

They told us that an object travels 30 meters in 20 seconds.

So we can say d = 30 and t = 20

If you put these values back into the distance formula you get:

d = rt

30 = r times 20

30 = 20 r

So now we want to find what "r" (average speed) is.

Divide both sides by 20.

20 r = 30

r =  \(\frac{30}{20}\) = 1.5 meters per second.

Answer: 234 degrees

Step-by-step explanation:

Angle formed by a chord and a tangent has half the measure as the arc formed by the chord

The value of measure of arc DEF is,

⇒ 234 degree

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

Given that;

Line t is tangent to the circle.

Hence, We know that;

The angle formed by a chord and a tangent is equal to 1/2 the measure of the intercepted arc.

Thus, The value of measure of arc DEF is,

⇒ 2 x 117 degree

⇒ 234 degree

Learn more about the angle visit:;

https://brainly.com/question/25716982

#SPJ2

Answer: 3

10x+475≥755

Answer:

the 3rd one

Step-by-step

i think its right, i hope :)

Special Product are the result of binomials being multiplied, or simplified further, and can be solved with ease using the First Last Inner Outer method. this product is not a special product.

Special Product (a+b) (a+b) = aa + ab + ab + bb = \(a^{2} + 2ab + b^{2}\).

we can use this formula anytime we are multiplying a binomial of the form a + b.

Factor as a Difference of Squares

factoring:  \(81a^{2} b^{4} - c^{6}\) = \((3^{4}a^{2} . b^{4}) - c^{6}\)

A difference of two perfect squares, \(A^{2} - B^{2}\) can be factored into

\((A+B)(A-B)\\A^{2} - AB + BA - B^{2}\\ A^{2} - AB + AB -B^{2}\\ A^{2} -B^{2}\)

AB = BA is he commutative property of multiplication from the expression.

-AB+BA equal zero and is therefore eliminated from the expression.

81 is the square of 9

\(a^{2}\) is the square of \(a^{1}\)

\(b^{4}\) is the square of \(b^{2}\)

\(c^{6}\) is the square of \(c^{3}\)

Factorization is \((9ab^{2}+c^{3}) . (9ab^{2}-c^{3} )\)

Factoring: \((9ab^{2}+c^{3})\)

A sum of perfect cubes, \(a^{3} + b^{3}\) can be factored into :\((a+b).(a^{2}-ab+b^{2})\\a^{3}-a^{2}b+ab^{2}-b^{2}a+b^{3}\\ a^{3}+(a^{2}b-ba^{2})+(ab^{2}-b^{2}a)+b^{3}\\ a^{3}+b^{3}\)

9 is not a cube(Binomial can not be factored as the difference of two perfect cubes)

Factoring: \((9ab^{2}-c^{3} )\)

A difference of two perfect cubes, \(a^{3} - b^{3}\) can be factored into

\((a-b).(a^{2}+ab+b^{2})\\a^{3}+a^{2}b+ab^{2}-ba^{2}-b^{2}a-b^{3}\\ a^{3}+(a^{2}b-ba^{2})+(ab^{2}-b^{2}a)-b^{3}\\ a^{3}-b^{3}\)

9 is not a cube(Binomial can not be factored as the difference of two perfect cubes)

Hence, 81a2b4 - c6 this solution deals with factoring binomials as the sum or difference of cubes.

Learn more about Special Product here https://brainly.com/question/13647939

#SPJ9

(a) Construct confidence intervals are : 90%: [428.95, 444.05], 95%: [427.13, 445.87], 99%: [423.67, 449.33].

(b) The 99% confidence interval has the widest interval.

(a) To construct confidence intervals for the mean breaking strength of the wool fibers, we shall use the given formula:

Confidence interval = sample mean ± (critical value * standard error)

The critical value here will depends on the level of confidence. For a 90% confidence level, the critical value is 1.645 (from the standard normal distribution). For a 95% confidence level, the critical value is 1.96, and for a 99% confidence level, the critical value is 2.576.

Standard error is obtained by dividing the sample standard deviation by the square root of the sample size.

Plugging in the values, we can calculate the confidence intervals:

90% confidence interval:

Lower bound = 436.5 - (1.645 * (11.9 / √20))

Upper bound = 436.5 + (1.645 * (11.9 / √20))

95% confidence interval:

Lower bound = 436.5 - (1.96 * (11.9 / √20))

Upper bound = 436.5 + (1.96 * (11.9 / √20))

99% confidence interval:

Lower bound = 436.5 - (2.576 * (11.9 / √20))

Upper bound = 436.5 + (2.576 * (11.9 / √20))

(b) The width of a confidence interval depends on both the critical value and the standard error. When aiming for a higher level of confidence, the interval becomes wider as it requires a larger critical value. Consequently, it can be concluded that among the given confidence intervals, the one with a 99% confidence level will have the broadest range.

To learn more about confidence intervals visit : https://brainly.com/question/20309162

#SPJ11

Answer:

X = -2 or X = 8

Explanation:

Numerical variables can be subdivided into two types: discrete variables and continuous variables.

Discrete Variables: Discrete variables are numeric variables that take on a finite or countable number of distinct values. These values are typically whole numbers or integers. For example, the number of students in a classroom, the count of items in a store inventory, or the number of cars in a parking lot are all examples of discrete variables. Discrete variables cannot have values between the defined data points.

Continuous Variables: Continuous variables are numeric variables that can take on any value within a specified range or interval. They can be measured to a high degree of precision. Continuous variables are often obtained through measurements or observations and can have decimal values. Examples of continuous variables include height, weight, temperature, time, and distance. Continuous variables can have an infinite number of possible values within the given range.

To know more about Numerical variables:

https://brainly.com/question/30527805

#SPJ4

Answer:

The equation of the straight line in point-slope form

                            \(y - 4 = \frac{7}{9} (x-0)\)

The equation of the straight line

                         7x -9y +36 =0

Step-by-step explanation:

Step(i):-

Given that the points (0,4) and (-9,-3)

The slope of the line

         \(m = \frac{y_{2} - y_{1} }{x_{2}- x_{1} } = \frac{-3-4}{-9-0} = \frac{7}{9}\)

Step(ii):-

    Equation of the straight line passing through the point (0,4) and having slope m = 7/9

          \(y - y_{1} = m (x-x_{1} )\)

         \(y - 4 = \frac{7}{9} (x-0)\)

      9 y - 36 = 7x

              9y = 7x + 36

          \(y = \frac{7x}{9} +\frac{36}{9}\)

Slope - intercept form  

                            \(y = \frac{7x}{9} +4\)

Final answer:-

The equation of the straight line in point-slope form

                            \(y - 4 = \frac{7}{9} (x-0)\)

The equation of the straight line

                         7x -9y +36 =0

Answer:

pppp

Step-by-step explanation:

ppppp

Answer:

1680

Step-by-step explanation:

subtract the 310 words and then multiply 524 by 2 then add the answer of the subtraction to what you got in the multiplication

Answer:

14.5

Step-by-step explanation:

\( \frac{2}{7} = \frac{5}{m + 3} \)

\(2(m + 3) = 7 \times 5\)

\(2m + 6 = 35\)

\(2m = 35 - 6\)

\(2m = 29\)

\(m = 14.5\)

Answer:

m = 14.5

Step-by-step explanation:

\(\frac{2}{7}\) = \(\frac{5}{m+3}\) ( cross- multiply )

2(m + 3) = 35

2m + 6 = 35 ( subtract 6 from both sides )

2m = 29 ( divide both sides by 2 )

m = 14.5

Answer:

60 miles per hour

Step-by-step explanation:

We need to simply divide the total distance he traveled by the total time it took him.

At 10:00 AM, he is 200 miles from New York.

At 12:00 PM, he is 80 miles from New York.

This means that 2 hours has elapsed and the distance he has traveled is:

200 - 80 = 120 miles

Therefore, his average speed is:

120 / 2 = 60 miles per hour

Answer:

-0.5, -0.4,-0.3,-0.2,-0.1 and 0.1

Step-by-step explanation:

We have to calculate 6 rational number between -2/3 and 1/2

So,

\(\frac{-2}{3} =-0.6\\\frac{1}{2} =0.5\)

Now,

Rational numbers between -2/3 and 1/2 will be -0.5, -0.4,-0.3,-0.2,-0.1 and 0.1

Answer:

Step-by-step explanation:

two

Volume of beach ball or the amount of air will the beach ball hold is 2304π in³.

Formula

Volume of Sphere is 4/3πr³

The volume, V, of a sphere with radius r is  4/3πr³

By employing a technique that roughly represents the surface area of a sphere using square pyramids, it is possible to obtain the formula for the volume of a sphere using the formula for its surface area, which is 4πr^2.

Where r is the radius of the sphere .

As given

12 inches is the radius of a beach ball.

r = 12 in

Substitute the r in above volume equation,

V =4/3πr³

V=4/3π(12)³

V= 2304π in³

Therefore, the amount of air will the beach ball hold is 2304π in³.

To learn more about Volume of Sphere click here:

brainly.com/question/11234923

#SPJ4

Answer: 625 miles

Step-by-step explanation:

100-40=60

so she has 60% for her distance so lets munis 40 from it and add 250 to 250

250+250=500

60-40=20

20 is half of 40 so whats half of 250? its 125

so she drove 625 miles for her road trip 2 and 1/2 a day

In the first question, the statement "Using logarithmic differentiation we obtain that the derivative of the function y = x² satisfies the equation y = 4x log x + 2x" is true.

In the first question, using logarithmic differentiation on the function y = x², we differentiate both sides, apply the product rule and logarithmic differentiation, and simplify to obtain the equation y = 4x log x + 2x, which is correct.

In the second question, the statement is false. When using logarithmic differentiation on the function y = (1+x²)²(1 + sin x)²/(1-x²), the derivative is calculated correctly, but the equation given is incorrect. The correct equation after logarithmic differentiation should be y' = (4x/(1 + x²)(1 + sin x))(1-x²) - (2x(1+x²)²(1 + sin x)²)/(1-x²)².

In the third question, the product z²w is calculated correctly as 30-10%.

It is important to accurately apply logarithmic differentiation and perform the necessary calculations to determine the derivatives and products correctly.

Learn more about Logarithmic differentiation: brainly.com/question/30881276

#SPJ11

9514 1404 393

Answer:

  9.  ±1, ±2, ±3, ±6

  11.  ±1, ±2, ±3, ±4, ±6, ±12

Step-by-step explanation:

The possible rational roots are (plus or minus) the divisors of the constant term, divided by the divisors of the leading coefficient.

Here, the leading coefficient is 1 in each case, so the possible rational roots are plus or minus a divisor of the constant term.

__

9. The constant is -6. Divisors of 6 are 1, 2, 3, 6. The possible rational roots are ...

  ±{1, 2, 3, 6}

__

11. The constant is 12. Divisors of 12 are 1, 2, 3, 4, 6, 12. The possible rational roots are ...

  ±{1, 2, 3, 4, 6, 12}

_____

A graphing calculator is useful for seeing if any of these values actually are roots of the equation. (The 4th-degree equation will have 2 complex roots.)

The equation describing Linda's Age and Liam's age will be: Liam's Age(Baby Brother) + 3 = Linda Age.

An equation means the formula that expresses the equality of two expressions by connecting them with the equals sign =.

Here, let us denote Linda's age as L and Liam's age as B. We are given that Linda is 3 years older than Liam, so we can write the equation as L = B + 3

This equation states that Linda's age (L) is equal to Liam's age (B) plus 3 years. Therefore, Linda's age can be determined by adding 3 years to Liam's age.

Read more about equation

brainly.com/question/9482924

#SPJ1

Answer:

If she didn't spend any additional money and finished the week with 41 how much is Masie weekly paycheck. 1. See answer.

he number of ways the friends can choose seats without sitting next to each other is 7! - 4! = 5040

If there are 5 seats open in a row and no restrictions on the seating arrangement, each friend can choose one seat independently. Therefore, the total number of ways the friends can choose seats is 5 factorial (5!) which is equal to 5 × 4 × 3 × 2 × 1 = 120.

(b) If there are 7 seats open in a row and no restrictions on the seating arrangement, each friend can choose one seat independently. Therefore, the total number of ways the friends can choose seats is 7 factorial (7!) which is equal to 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040.

(c) If two friends are required to sit next to each other, we can treat them as a single entity. This reduces the problem to arranging four entities (three individual friends and one pair of friends) and three empty seats. The total number of ways the friends can choose seats is then 4 factorial (4!) which is equal to 4 × 3 × 2 × 1 = 24.

(d) If two friends are required to not sit next to each other, we can count the complement of the situation in part (c). There are 7 factorial (7!) total seating arrangements without any restrictions. From part (c), we found that there are 4 factorial (4!) seating arrangements where the two friends sit next to each other. - 24 = 5016.

Know more about arrangement here:

https://brainly.com/question/28406752

#SPJ11

Answer:

Step-by-step explanation:

You got this

Answer:

Step-by-step explanation:

l6 x 7l = 42

l-2l = 2

= 42 : 2 = 21

Answer:

Let $x$ be the measure of the included angle. We can use the formula for the area of a triangle to find an equation in terms of $x$.

The area of a triangle is given by $\frac{1}{2}bh$, where $b$ is the length of the base and $h$ is the length of the altitude from the base to the opposite vertex. In this case, the base is 87 and the altitude is the length of the line segment from the vertex opposite the included angle to the base, which we can find using the Law of Sines:

$$\frac{h}{\sin x} = \frac{19}{\sin(180^\circ-x)}$$

$$h = \frac{19\sin x}{\sin(180^\circ-x)}$$

Substituting this expression for $h$ into the formula for the area of the triangle, we get

$$\frac{1}{2}bh = \frac{1}{2} \cdot 87 \cdot \frac{19\sin x}{\sin(180^\circ-x)} = 474$$

Solving this equation for $x$ is somewhat difficult, but we can use a calculator or computer to approximate the value of $x$. Using a calculator, we find that $x \approx 31.4^\circ$. Rounding to the nearest tenth of a degree, the measure of the included angle is $\boxed{31.4^\circ}$.

Step-by-step explanation:

Using a 35-bag sample with a mean of 406.0 grams, a known standard deviation of 25.0 grams, and a level of significance of 0.05, you can perform a one-tailed Z-test to determine whether to reject or fail to reject the null hypothesis.

To test if the potato chip manufacturer's bag filling machine is working correctly at the 411.0-gram setting, we will state the hypotheses using the given terms.

Null Hypothesis (H0): The machine fills bags correctly, with a mean weight of 411.0 grams (µ = 411.0 grams)
Alternative Hypothesis (H1): The machine is underfilling bags, with a mean weight less than 411.0 grams (µ < 411.0 grams)

To learn more about standard deviation, refer here:

https://brainly.com/question/23907081#

#SPJ11

The fraction which should go into the boxes marked A and B in their simplest form is 3/4 and 1/4 respectively.

Total number of fruits Amy has = 10

Number of Apples = 7

Number of Oranges = 3

First random pieces of fruits chosen:

Probability of choosing Apples = 6/9

Probability of choosing Oranges = 3/9

Second random pieces of fruits chosen:

Probability of choosing Apples = 6/8

= 3/4

Probability of choosing Oranges = 2/8

= 1/4

Therefore, the probability of choosing Apples or oranges as the second piece is 3/4 or 1/4 respectively.

Read more on probability:

https://brainly.com/question/251701

#SPJ1