Question 1
Which equation represents the relationship shown in the table
at the right?

Answer:

g(-3)= 40

Step-by-step explanation:

g(-3) simply means that where there is X, Substitute -3 into the original equation to find the value.

[tex]g( - 3) = 3( - 3) {}^{2} - 4( - 3) + 1[/tex]

[tex]g( - 3) = 27 + 12 + 1[/tex]

=40.

Answer:

40

Step-by-step explanation:

g(x)=3x^2-4x+1 

g(-3)=3x^2-4x+1 

g(-3)=3(-3)^2-4(-3)+1 

g(-3)=27+12+1 

g(-3)= 40

Yes, 73 is a mirror prime number.

A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. Prime numbers play an important role in number theory and have many applications in mathematics and computer science.

A "mirror prime" or "emirp" is a prime number that remains prime when its digits are reversed. For example, the number 73 is prime, but if we reverse its digits, we get 37, which is also prime, so 73 is a mirror prime.

Mirror primes are relatively rare, and finding them requires a lot of computation power. They have been studied in number theory and have been found to have some interesting properties, for example, some researchers have found that the density of mirror primes are similar to the density of regular primes.

In the case of 73, it is a prime number, and it's not a "mirror prime" because when its digits are reversed, 37 is not a prime number, it is divisible by 37.

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The estimates for the requested shaded parts for 1 fourth is to divide the beaker into four parts and shade an area and 1 third, divide by three parts and shade one part as shown in the diagram.

A fraction is a portion of a larger whole. The number is expressed in arithmetic as a quotient, which is the numerator divided by the denominator. Both are integers in a simple fraction. A complex fraction contains a fraction in either the numerator or the denominator. A proper fraction has a numerator that is less than the denominator.

Proper fractions, improper fractions, and mixed fractions are the three types. Fractions are terms that have a numerator and a denominator. We define its types based on these two terms. One third is considered one part of 3 that makes a whole, one fourth, one part of 4 that makes a whole and so on.

The complete question is:

A beaker is considered full when the liquid reaches the fill line showing near the top estimate the amount of water in the beaker by shading The drawing as indicated The first one is done for you

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Let [tex]d[/tex] be the number of dimes and [tex]q[/tex] be the number of quarters.

[tex]\begin{cases} 0.10d=4.00 \\ d+q=25 \end{cases}[/tex]

Answer:

$24.46

Explanation:

$6.85÷7= 1 pint

you times the answer by 25 = $24.46

Answer:

Hi!

We will solve this using proportions, like this:

4 pints cost 10,08

30 pints cost x

__________________

x = (30 * 10,08)/4

x = 302,4/4

x = 75,6

30 pints of ice cream cost 75,6$.

Hope this helps!

Step-by-step explanation:

Abby can make 26 tie-dyed T-shirts.

We can start by setting up a linear equation to represent the total cost of making the tie-dyed T-shirts.

What is a linear equation?

First-order equations include linear equations. In the coordinate system, linear equations are defined for lines. A linear equation in one variable is one in which there is a homogeneous variable of degree 1 (i.e., just one variable).

Multiple variables may be present in a linear equation. Linear equations with two variables, for example, are used when a linear equation contains two variables.

Let x be the number of T-shirts Abby makes

The cost for each T-shirt is $3.95 + $0.50 = $4.45

The cost of the two boxes of salt is $4.50 * 2 = $9

So the total cost for x T-shirts is $4.45x + $9

We know that the total cost is 124.70 and we want to find the value of x, so we can set up the equation as:

$4.45x + $9 = 124.70

Solving for x:

$4.45x = 115.70

x = 115.70 / 4.45

x = 26

Therefore, Abby can make 26 tie-dyed T-shirts.

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Answer: Teo is 9 years old and Richard is 27 years old.

Step-by-step explanation:

First of all, create expressions which represents Teo's and Richard's age:

x = Teo's Age

2x + 9 = Richard's Age

Now create an equation which can be used to find Teo's age and Richard's Age:

(x) + (2x)+9 = 33

(x) + (2x) = 24

3x = 24

x = 9

From this, we can conclude that Teo is 9 years old.

Now substitute 9 into Richard's Age expression which is 2x+9

2*9+9 = 27

From this, we can conclude that Richard is 36 years old.

4 real solutions does the system x² + y² = 25 and xy = 10 have.

The main distinction between an ideal solution and a non-ideal solution (real solutions) is that in an ideal solution, all molecules interact uniformly, but in a non-ideal solution, there are various forces acting on the molecules of the solute and solvent.

A real solution is one that has all the necessary constituent particles in the right ratio and has undergone the necessary dissolution. A solution is therefore referred to as a real solution.

Given that,

x² + y² = 25 .......... (i)

xy = 10 ............(ii)

or, y = 10/x

Now, putting the value of x in equation (i) we get-

x² + (10/x)² = 25

or, x⁴ + 100 = 25 x²

or, x⁴ - 25 x² + 100 = 0

or,  x⁴ - 20 x² - 5 x² + 100 = 0

or, x² (x² - 20) - 5 (x² - 20) = 0

or, (x² - 20) (x² - 5)

therefore, x = ±√20 and ±√5

Thus, there are 4 real solutions of these systems.

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Insurance companies use math in several ways to help them assess and manage risk, price their products, and make financial decisions. Some examples include:

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The relation {(3, 2),(6, 4),(9, 6),(12, 8)} is a function.

The relation {(2, 3),(2, 5),(3, 6),(9, 4)} is not a function.

The relation {(2, 4),(6, 3),(4, 8),(6, 6)} is not a function.

The relation {(3, 4),(5, 2),(6, 8),(6, 4)} is not a function.

A relation between a set of inputs having one output each is called a function.

Now,

In first option,

The relation is,

⇒ {(3, 2),(6, 4),(9, 6),(12, 8)

Clearly, Every inputs having one output each.

Hence, It is a function.

In second option,

The relation is,

{(2, 3),(2, 5),(3, 6),(9, 4)}

Clearly, Two Outputs 3 and 5 have same input 2.

Hence, It is not a function.

In third option,

{(2, 4),(6, 3),(4, 8),(6, 6)}

Clearly, Two Outputs 3 and 6 have same input 6.

Hence, It is not a function.

In fourth option,

{(3, 4),(5, 2),(6, 8),(6, 4)}

Clearly, Two Outputs 8 and 4 have same input 6.

Hence, It is not a function.

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The degree value, when rounded to the nearest decimal, is 6. Therefore, the slope's angle of 1 in 10 is 6 degrees.

1 in 10 in geometry refers to the ratio of one unit of vertical drop or rise for every ten units of horizontal distance crossed. This slope's value is calculated using the angle of tan. Let x represent the tan-using angle.

tan x = horizontal distance/vertical distance

tan x = 1/10

tan x = 0.1

Now taking the inverse

x = [tex]\tan^{-1}(0.1)[/tex]

x = 5.71 degree

The degree value, when rounded to the nearest decimal, is 6.

Therefore, the slope's angle of 1 in 10 is 6 degrees.

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The right question is:

How many degrees angle is a 1 in 10 slope?

The value of x, in the triangle shown is: C. 5.25.

In the image given, the triangles shown are similar to each other, which means that their corresponding side lengths are proportional to each other.

Therefore, we would have the following proportion:

x / 2 = 16.8 / 6.4

Cross multiply:

6.4 * x = 16.8 * 2

6.4x = 33.6

6.4x/6.4 = 33.6/6.4

x = 5.25

The correct value of x is: C. 5.25.

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The probability of selecting a bird would be = 2/15

Probability is defined as the ability of an outcome to occur by chance or not.

The formula that can be used to calculate the outcome of an event= P(E) = number of favorable outcomes/Total number of outcomes

Where, P(E) is the probability of any event.

Let E be an event of selecting an insect.

According to the given question

We have

Total number of insects = 10

Total number of trees = 8

Total number of flowers = 8

Total number of birds = 4

Now, the total number of outcomes = 10 + 8 + 8 + 4 = 30

Total number of favorable outcomes(birds) = 4

Therefore,

The probability of selecting a bird = 4/30 = 2/15

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Complete question:

A stack of 30 science flashcards includes a review card for each of the

following: 10 insects, 8 trees, 8 flowers, and 4 birds.

What is the probability of randomly selecting a bird.

The greatest common factor (GCF) of 14 and 21 is 7.

So we can write 14 and 21 as the product of 7 and their corresponding quotients:

14 = 7 * 2

21 = 7 * 3

Now we can apply the distributive property and combine them:

14 + 21 = 7 * 2 + 7 * 3 = 7 * (2 + 3) = 7 * 5 = 35

The final answer is 35.

Answer:

7(2 + 3)

Step-by-step explanation:

The Greatest Common Factor of 14 & 21 is 7

So, the answer is

7(2 + 3)

The value of 'k' for the given system of equation kx−y=2, 6x−2y=3 has :

a. no solution is k = 3.

b. Infinitely many solution : no such value of 'k' exist.

As given in the question,

Given system of equations are :

kx−y=2

6x−2y=3

Standard form of system of equations are:

a₁x + b₁y + c₁ = 0

a₂x + b₂y + c₂ =0

a. Condition for the no solution is given by :

( a₁ /a₂ ) = (b₁ / b₂) ≠  (c₁ /c₂ )

(k/6) = ( -1/-2)≠( -2/-3)

⇒k/6 = 1/2

⇒k = 3

b. For infinitely many solution:

( a₁ /a₂ ) = (b₁ / b₂) =  (c₁ /c₂ )

⇒(k/6) = ( -1/-2)=( -2/-3)

We know that ( 1/2 ) ≠ ( 2/3)

Condition does not hold true.

No such value of 'k' exist.

Therefore, the value of 'k' for the given system of equation is given by :

a. no solution is k = 3.

b. Infinitely many solution : no such value of 'k' exist.

The above question is incomplete , the complete question is :

Find the value of k for which the system of equations

kx−y=2

6x−2y=3

has no solution. Is there a value of k for which the system has infinitely many solution?

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The predicted population would be 5,250,00 in the year 2011.

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

The population in Austin is growing at a rate of 5% per year in 2010 the population was 500,000.

The exponential function for the prediction of the population can be written as:

ABˣ

Where A represents the population in 2010, B is a growth factor, and x is the year

As per the question, we have

(500,000)(1.05)¹

5,250,00

This is the predicted population in the year 2011.

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The question seems to be incomplete the correct question would be:

The population in Austin is growing at a rate of 5% per year in 2010 the population was 500,000. what would be the predicted population year in 2011?

Therefore , the solution to the given problem of linear equation comes out to be  x = -2.9.

Any function that can be expressed algebraically as y=mx+b is referred to as linear. The slope is B, and the y-intercept is m. The previous statement is sometimes referred to as a two-variable equation system because both y and x are factors. Bivariate equations are linear equations with two variables. There are numerous uses for linear equations, two of which are x + z = 2 and 3z - y + z = 3. A mathematical equation is said to be linear if its formula is y=mx+b, where m denotes the slope and b the y-intercept. Y=mx+b is how the equation is written, where m stands for the slope and b for the y-intercept.

Here,

Given : 8x-4 = -27.2

To find the x value

We do,

=>8x-4= -27.2

=> 8x = -27.2 +4

=>8x = -23.2

=> x = -23.2/8

=> x = -2.9

Therefore , the solution to the given problem of linear equation comes out to be  x = -2.9.

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The equation for the slant asymptote of the given function is y = 2x - 4.

Option (B) is correct.

What is the slant asymptote of the function?

A slant asymptote of a function is a line that the function approaches, but never touches or crosses. It is a type of asymptote that occurs when the degree of the numerator of a rational function (a function that can be written as the ratio of two polynomials) is greater than the degree of the denominator.

To determine the equation for the slant asymptote of a rational function (a function that can be written as the ratio of two polynomials), we need to look at the degree (the highest power of x) of the numerator and the degree of the denominator.

The function g(x) = (2x^2 + 4x + 6) / (x + 4)

The degree of the numerator is 2 and the degree of the denominator is 1, since the x^2 is the highest power of x in numerator and x is the highest power of x in denominator.

Since the degree of the numerator is greater than the degree of the denominator, the slant asymptote will have the same degree as the numerator, which is 2.

To find the equation of the slant asymptote, we divide the numerator by the denominator using the long division method and get

2x + 2 - (x + 2)/(x + 4)

The equation of the slant asymptote will be the result of the long division, which is 2x - 4

Hence, the equation for the slant asymptote of the given function is y = 2x - 4

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Answer:

Step-by-step explanation:

20 = 20 more than

5×9 = 9 times more than 5

So a proper response for a written word expression in a numerical or algebraic expression such as this one here would be:

A number is equal to 20 more than 9 times 5.

Answer: (x-2)(x+3)^2(x^2-16)

Step-by-step explanation:

(x+3)^2(x-2)

(x+3)(x^2-16)

(x+3)(x^2-16)=(x+3)(x+4)(x-4)

(x+3)^2(x-2)=(x+3)(x+3)(x-2)

LCM: (x+3)^2(x-2)(x^2-16)

The statement about adolescence that is false, is D. Teens focus on how to contribute to the world.

Young people will navigate puberty and the end of their growth during adolescence. They will also assume sexually dimorphic body shapes, develop new cognitive skills (including the ability to think abstractly), clarify their personal and sexual identities, and reach a certain level of emotional, personal, and financial maturity.

As a result, they can assume bigger responsibilities in the home and community, think through the effects of their choices, and develop their problem-solving and decision-making skills.

They do not focus on contributing to the world just yet.

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Options for this question include:

The separation of two numerical values, regardless of whether they are positive or negative. Thus, the absolute difference offers little insight into the relative magnitude.

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[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$800\\ r=rate\to 3.8\%\to \frac{3.8}{100}\dotfill &0.038\\ t=years\dotfill &4 \end{cases} \\\\\\ A = 800[1+(0.038)(4)] \implies A = 921.6[/tex]

Answer:

The line parallel to y=2x +3 is

y=2x + k---(1)

Since,st.line (1) passes through point (5,-4) then,

-4=2(5)+k

or,k=-4-10

:.k= -14

Putting value of k in eqn(1) we get

y=2x -14

Hence, y=2x -14 is the line parallel to y=2x +3 and passes through point (5,-4)

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The equivalent expressions are  (b+3c)+(b+3c) and 2(b)+2(3c) or 2b+6c. Options B and C

An algebraic expression is simply described as an expression consisting of variables, coefficients, terms, constants, and factors.

Algebraic expressions are also made up of mathematical operations, such as;

Given the expression;

2(b+3c)

expand the bracket

2(b)+ 2(3c)

2b + 2×3×c

Multiply the values, we get;

= 2b +6c

It can also  be written as the sum of b+3c as (b+3c)+(b+3c)

Hence, the expressions are (b+3c)+(b+3c) and 2(b)+2(3c) or 2b+6c

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The complete question:

Which expressions are equivalent to 2(b+3c)2(b+3c)2, left parenthesis, b, plus, 3, c, right parenthesis ?

Choose all answers that apply:

A 3(b+2c)3(b+2c)3, left parenthesis, b, plus, 2, c, right parenthesis

B (b+3c)+(b+3c)(b+3c)+(b+3c)left parenthesis, b, plus, 3, c, right parenthesis, plus, left parenthesis, b, plus, 3, c, right parenthesis

C 2(b)+2(3c)2(b)+2(3c)2,

Answer:

[tex]8y^3+32y[/tex]

Step-by-step explanation:

[tex]8y(y^2+4)\\= (8y)(y^2)+(8y)(4)\\= 8y^3 + 32y[/tex]

Reason:

An increase of 95% will involve the multiplier 1.95

Think of it like saying 100% + 95% = 1 + 0.95 = 1.95

Therefore,

1.95*3.50 = 6.825 = 6.83 dollars

Answer:

ttt

Step-by-step explanation:

By using the correlation coefficients, it is found that the two conclusions which the researcher can make from the given data are:

The correlation coefficient is a statistical measure of the strength of a linear relationship among two variables. Its assuming values can range from -1 to 1. If it is positive, the relation is positive, which is, they are direct proportional. And if it is negative, they are inverse proportional. If the absolute value of the correlation coefficient is greater than 0.6, it means the relationship is strong.

In this case, since the correlation is 0.486, thus, the conclusion is that the relation among the variables is positive, that means the higher the proportion of calories from sweeteners in the diets, the higher the mortality. And the other conclusion is that the relationship between the variables is not strong enough.

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Although part of your question is missing, you might be referring to this full question: A researcher found a study relating the mortality rates for women aged 65 to 74, y, to the proportion of calories from sweeteners in their diets, x. When researchers looked at the association of x and y, they found that the coefficient of determination was r squared equals 0.486. Select two conclusions that the researcher can make from this data.

The ratios do not form a proportion. The cross-products are not equal.

To find ratios 8 : 4 and 12 : 8 are proportional or not, we are using cross products.

First, we write an equation with the ratios given:

[tex]\frac{8}{4}[/tex] = [tex]\frac{12}{8}[/tex]

Next, we cross-multiply the equation to find the cross products:

8×8 = 12×4

Simplifying both sides we get:

64 ≠ 48

we get our cross products 64 and 48 which are not equal. Thus the ratios 8 : 4 and 12 : 8 are not in proportion.

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