1. Which one of the following is a solution of 5x + 3y = 11?
A. (-1, 2)
B. (2, -1)
C. (2, 1)
D. (1, 2)
E.(1/5,3)

Therefore , the solution of the given problem of triangle comes out to be the relationship between s,t and u is u²= t²+s².

Given that it has three sides and three vertices, a triangle qualifies as a polygon. It is a fundamental geometric figure. Triangle ABC is the term used to refer to a triangle containing the vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are discovered. Triangles are polygons because they have three sides and three corners. The points where the three sides of the triangle converge are referred to as the triangle's corners. Three triangle angles are multiplied to yield 180 degrees.

Here,

Given : Triangle STU is a right triangle.

Thus,

We find :

sides s,t and u

the relationship between them is :

As it is a right triangle

So,

According to the pythagoras theorem,

=>u²= t²+s²

Therefore , the solution of the given problem of triangle comes out to be the relationship between s,t and u is u²= t²+s².

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The unit rate of the beef if it cost $14.40 for 4.5 pounds of beef is $3.2 per pound

The unit rate is the cost of each unit of an item at a particular time.

Cost of 4.5 pounds of beef = $14.40

Unit rate of beef = Total cost / Total pounds

= $14.40 / 4.5

= $3.2 per pound

Check:

Cost of 4.5 pounds of beef = unit cost of beef × pounds of beef

= $3.2 × 4.5

= $14.4

In conclusion, the unit rate of beef is given as $3.2 per pound.

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Answer:

r<9

Step-by-step explanation:

r/3 + 5 < 8

Subtract 5 from each side

r/3 + 5-5 < 8-5

r/3 < 3

Multiply each side by 3

r/3 *3 <3*3

r<9

The algebraic expression for this problem is given as follows:

2C - D = -2x² + 2x + 11.

The definition for C in this problem is given as follows:

C = x + 3.

We applying the distributive property to multiply by 2 as follows:

2C = 2(x + 3) = 2x + 6.

The definition for D in this problem is given as follows:

D = 2x² - 5.

The subtraction is then obtained as follows:

2C - D = 2x + 6 - (2x² - 5)

2C - D = 2x + 6 - 2x² + 5

2C - D = -2x² + 2x + 11.

Meaning that the second option is correct.

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Given the system of equations:

we can solve it using elimination by directly adding both equations to get the following:

now that we have that x=3, we can find y using this value on any of the two equations:

therefore, the solution of the system is (3,0)

Answer:

5.7

Step-by-step explanation:

Creating the point into a triangle, both sides a 4.

As the Pythagorean theorem goes, a^2+b^2=c^2

4^2+4^2=

16+16=

32

The square root of 32 is about 5.7

The distance between the points is about 5.7 units

The function which represents the cost to drive a car from this agency miles x a day is :

C(x) = 15, if 0 ≤ x ≤ 200

      = 15 + 0.05x, if x > 200

Given that,

A car rental agency charges $15 a day for driving a car 200 miles or less.

The function can be written as,

C(x) = 15 if 0 ≤ x ≤ 200

If a car is driven over 200 miles, the renter must pay $0.05 for each mile over 200 driven.

C(x) = 15 + 0.05x, if x > 200

Hence the correct option is D.

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if i'm correct its 7x

Answer:

Domen is [ -2 , infinitely) or can be written as

-2 < x < infinitely in inequality form.

Step-by-step explanation:

if (x+2) is negative than function will be imaginary so to be real function (x+2) should be positive

hence answer is : Domen = -2 < x < infinitely or can be written as [ -2 , infinitely )

The histogram provided shows the ages of the players in an adult volleyball league. From the histogram, it is clear to see that the number of players in the league decreases with each increasing age group.

This can be seen with the highest number of players being in the 20-25 age group, followed by the 30-35 age group, and so on. Therefore, the statement that the older the age group, the greater the number of players, is false. Additionally, the histogram shows that there are only 5 players between the ages of 50 and 55, so the statement that there must be 5 players between those ages is true. Finally, the histogram shows that there are 30 players between the ages of 20 and 25, making the statement that there are 30 players between those ages also true.

The histogram provided shows the ages of the players in an adult volleyball league. It is evident that the number of players in the league decreases with each increasing age group. Therefore, the statement that the older the age group, the greater the number of players, is false. Additionally, the histogram shows that there are only 5 players between .the ages of 50 and 55, and 30 players between the ages of 20 and 25, making those statements true.

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The factored form of \(f(x) =4x^3 - 23x^2 + 46x + 13\) as a product of linear factors is:

\(f(x) = (x^2 - 6x + 13)(x - t)\)

Given that the polynomial f(x):  \(f(x)=4x^3-23x^2+46x+13\)

And  \((3 + 2i)\)  is zero of the given polynomial.

Since,  \((3 + 2i )\) is zero of the given polynomial then its conjugate, 3 - 2i, must also be a zero.

To factorise f(x) use these zeros,  write it as a product of linear factors:

f(x) = (x - r)(x - s)(x - t)

where r, s, and t are the zeros of the polynomial.

f(x) = (x - (3 + 2i))(x - (3 - 2i))(x - t)

f(x) = (x - 3 - 2i)(x - 3 + 2i)(x - t)

Since,  \((x - a)(x + a) =(x^2-a^2)\)

Therefore,

\(f(x) = ((x - 3)^2 - (2i)^2)(x - t)\\f(x)= ((x - 3)^2 - 4i^2)(x - t)\\f(x)= ((x - 3)^2 - 4i^2)(x - t)\\f(x)= ((x - 3)^2 + 4)(x - t)\\f(x) = ((x^2 - 6x + 9) + 4)(x - t)\\f(x)= (x^2 - 6x + 13)(x - t)\)

Therefore, the factored form of\(f(x) = 4x^3 - 23x^2 + 46x + 13\)  as a product of linear factors is:

\(f(x) = (x^2 - 6x + 13)(x - t)\)

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Answer:

HJ = LK

HI=MK

JI=ML

ML=6 units

Hope this helps!

Answer:

D

Step-by-step explanation:

The triangles CDA and ADB are similar, thus the ratios of corresponding sides are equal, that is

\(\frac{CD}{AD}\) = \(\frac{DA}{DB}\) , substitute values

\(\frac{13}{x}\) = \(\frac{x}{3}\) ( cross- multiply )

x² = 39 ( take square root of both sides )

x = \(\sqrt{39}\) → D

Answer:

D is the answer

Step-by-step explanation:

The alternative hypothesis (H1) would be that the mean of the bottles of cream is not equal to 8 ounces, indicating that the containers are being filled incorrectly. It can be written as: H1: μ ≠ 8 ounces where μ represents the population mean of the bottle cream fillings.

In the given scenario, the null hypothesis would be that the bottles of cream are being filled correctly with a mean of 8 ounces. The alternative hypothesis would be that the bottles of cream are not being filled correctly, meaning the true mean of the population is different from 8 ounces. However, the specific form of the alternative hypothesis would depend on the direction of the problem. If we are interested in knowing whether the mean filling amount is greater than or less than 8 ounces, we would use a one-tailed alternative hypothesis. If we are interested in determining whether the mean filling amount is simply different from 8 ounces, we would use a two-tailed alternative hypothesis.

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The average velocity from t = 2s to t = 4s would be - 48 ft/s.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that an object is thrown upward with initial velocity of 48 feet per second from a high of 120 feet. The height of the object t seconds after it is thrown is given by h(t) = - 16t² + 48t + 120.

Average rate of change of velocity with time is called average velocity. Mathematically -

v{avg.} = Δx/Δt                                                         .... Eq { 1 }

Δx = x(4) - x(2)

Δx = - 16(4)² + 48(4) + 120 - {- 16(2)² + 48(2) + 120}

Δx = - 96

Δt = 4 - 2 = 2

So -

v{avg.} = Δx/Δt = -96/2 = - 48 ft/s

Therefore, the average velocity from t = 2s to t = 4s would be - 48 ft/s.

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Answer:

Step-by-step explanation:

a = 1935 / 5 is the change

b = 1960 / 10 is the change

c = 1950 / 20 is the change

They are all increasing i'd assume they all went threw a positive change

Answer:

Harry has a loan of $9000 in total. Harry obtained a loan from the bank. Explanation Harry's remaining debt, expressed in dollars, is modeled as a function of time t, expressed in months, by the function D(t). The role is played by, This function can be used to determine that $200 is being subtracted each month from the function, meaning Harry is paying $200 toward his loan. Harry has not yet made any payments, therefore we may set t=0 to obtain the total amount of his solo. Therefore, the value of D(t) will reveal the loan's net amount. Harry's borrowing, therefore, equals to $9000.

Answer:

It is not. A multiplicative inverse is the reciprocal for a number. For a fraction, the form would change from a/b to b/a. In this case the multiplicative inverse of 7/8 would be 8/7.

Answer:

the number of answer is 2.25

Answer:

Equation- p-6= -14

Answer- p=-8

Step-by-step explanation:

The mode is the most appropriate measure of center to represent the data in the graph because it reflects the most common value(s) observed in the dataset. In this case, the mode is 3.

The most appropriate measure of center to represent the data in the given line plot is the mode.

The mode is the value or values that occur most frequently in a dataset. In this case, we can observe the frequencies of the data points on the line plot:

There is one dot above 2, 4, 8, and 9.

There are two dots above 6 and 7.

There are three dots above 3.

Based on this information, the mode(s) of the dataset would be the values that have the highest frequency. In this case, the mode is 3 because it appears most frequently with a frequency of three. The other data points have frequencies of one or two.

The mode is particularly appropriate in this scenario because it represents the most common or frequently occurring value(s) in the dataset. It is useful for identifying the central tendency when the data is discrete and there are distinct peaks or clusters.

While the median and mean are also measures of center, they may not be the most appropriate in this case. The median represents the middle value and is useful when the data is ordered. However, the given line plot does not provide an ordered arrangement of the data points. The mean, on the other hand, can be affected by outliers and extreme values, which may not accurately represent the central tendency of the dataset in this scenario.

Therefore, the mode is the most appropriate measure of center to represent the data in the graph because it reflects the most common value(s) observed in the dataset. In this case, the mode is 3.

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What is the equation of this line?

slope = 2 and y-intercept = 0 so:

y = 2x

Answer:

1.false

2.true

3.true

4.true

5.120

6.105

7.85

8.100

9.115

10.40

11.13

12.30

13.36

14.65

15.35

16.75

Answer:

yes it is.....................

Step-by-step explanation:

9.5 = 19/2

So it is a rational number (and so is not irrational)

Answer:

When a= -8, the equation 3(2x-a) = 2(3x+12) has infinitely many solutions

Step-by-step explanation:

Given:

3(2x-a) = 2(3x+12)

6x - 3a = 6x + 24

Subtract 6x from both sides

6x - 3a - 6x = 6x + 24 - 6x

-3a = 24

Divide both sides by -3

a= 24 / -3

a = -8

Substitute a= -8 into the equation

3(2x-a) = 2(3x+12)

3{2x -(-8)} = 2(3x+12)

3(2x + 8) = 2(3x +12)

6x + 24 = 6x + 24

6x - 6x = 24 - 24

0 = 0

When a= -8, the equation 3(2x-a) = 2(3x+12) has infinitely many solutions

Answer:

aops question smh

Step-by-step explanation:

Based on the information provided, it is most likely that Professor Anderson's focus on studying how family relationships change over time aligns with the field of developmental psychology.

Based on the given information, Professor Anderson's focus on studying how family relationships change over time and conducting longitudinal surveys with the same group of participants, it is most likely that Professor Anderson is a developmental psychologist. Developmental psychologists study human development and changes that occur across the lifespan, including familial relationships and their dynamics. They are interested in how individuals grow, change, and interact with others over time.

Developmental psychology is a branch of psychology that focuses on studying human development and changes that occur throughout a person's life span. Developmental psychologists are interested in understanding how individuals grow, change, and develop in various aspects such as physical, cognitive, emotional, and social domains.

In the given scenario, Professor Anderson's research interest revolves around tracking and surveying the same group of participants over a period of two decades to investigate the changes in their relationships with their parents and siblings. This longitudinal approach allows for the examination of how these family relationships evolve over time and provides insights into the developmental processes that influence familial dynamics.

By studying the patterns, trajectories, and factors that contribute to changes in family relationships, Professor Anderson can gain a deeper understanding of human development within the context of family dynamics. This knowledge can have implications for various aspects of individuals' lives, including their mental and emotional well-being, interpersonal relationships, and overall development.

Therefore, according to the information given, Professor Anderson's interest in researching how family connections change over time is most likely in line with the discipline of developmental psychology.

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The dot product of the vectors (3,3) and (-5,1) is -12.

The component form of vector g is approximately (-1.5, -3.9).

The magnitude of vector o is 2.

The dot product of the vectors (3,3) and (-5,1) is given by:

(3,3) · (-5,1) = 3(-5) + 3(1) = -12

Therefore, the dot product of the two vectors is -12.

Vector g is from the red jet ski to green, and its magnitude is √26.

The direction angle of vector g is 248.7°.

To write the component form of vector g, we can use the formula:

g = (|g| cos θ, |g| sin θ)

where |g| is the magnitude of vector g, and θ is the direction angle of vector g.

Substituting the given values, we get:

g = (√26 cos 248.7°, √26 sin 248.7°)

Using a calculator, we can evaluate:

g ≈ (-1.5, -3.9)

Therefore, the component form of vector g is approximately (-1.5, -3.9).

Given that the dot product of two vectors o · o is 4, we can use the formula for the magnitude of a vector:

|o| = √(o · o)

Substituting the given value, we get:

|o| = √4 = 2

Therefore, the magnitude of vector o is 2.

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well, let's move like the crab, backwards, let's start with b), then we'll do a)

b)

\({\Large \begin{array}{llll} y=ab^x \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=2\\ y=75 \end{cases}\implies 75=ab^2 \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=5\\ y=9375 \end{cases}\implies 9375=ab^5\implies 9375=ab^{2+3}\implies 9375=ab^2 b^3\)

\(\stackrel{\textit{substituting from the 1st equation}}{9375=\underset{ab^2}{(75)} b^3}\implies \cfrac{9375}{75}=b^3\implies 125=b^3 \\\\\\ \sqrt[3]{125}=b\implies \boxed{5=b}\hspace{5em}\stackrel{\textit{we know that}}{75=ab^2}\implies 75=a5^2\implies 75=25a \\\\\\ \cfrac{75}{25}=a\implies \boxed{3=a}\hspace{5em} {\Large \begin{array}{llll} y = 3(5^x) \end{array}}\)

a)

\(\begin{cases} x=0\\ y=j \end{cases}\implies j=3(5^0)\implies j=3(1)\implies j=3 \\\\\\ \begin{cases} x=4\\ y=k \end{cases}\implies k=3(5^4)\implies k=3(625)\implies k=1875\)