What does it mean when you substitute a value into an equation and the result is a true statement?

Answer:

x=5/2 and x=0

Step-by-step explanation:

To solve this equation, we first need to get all the terms on one side of the equation by subtracting 3x from both sides:

4x^2 - 7x - 3x = 24

Simplifying, we get:

4x^2 - 10x = 24

Now, we can factor out the GCF (Greatest common factor) on the left side of the equation:

2x(2x-5) = 24

Now we can divide both sides of the equation by 2x(2x-5) to get the solutions for x:

x = 5/2 , x = 0

So the solutions of the equation 4x^2 - 7x = 3x + 24 are x=5/2 and x=0

The line y = -3/2(x) + 3 has a slope of negative three halves and a y-intercept of 3.

The correct option is C.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

Given:

We have a graph that has a slope of negative three halves and a y-intercept of 3.

If a line passes through two points (x₁ ,y₁) and (x₂, y₂),

then the equation of line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁).

A). Line passing through the points (0, 2) and (3, 0).

y - 2 = 2/3(x)

y = 2/3(x) + 2.

This is not a required line.

B). Line passing through the points (0, 2) and (2, -1).

y - 2 = -3/2(x)

y = -3/2(x) + 2.

This is not a required line.

C).  Line passing through the points (0, 3) and (2, 0).

y - 3 = -3/2(x)

y = -3/2(x) + 3.

This is a required line.

D). Line passing through the points (0, 3) and (3, 1).

y - 3 = -2/3(x)

y = -2/3(x) + 3.

This is not a required line.

Therefore, y = -3/2(x) + 3 is a required line.

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Answer:

The line y = -3/2(x) + 3 has a slope of negative three halves and a y-intercept of 3.

The correct option is C.

Step-by-step explanation:

The value of x in (8^x/5) (8^x/4)=8^4 is 80/9

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

Given;

The equation;(8^x/5) (8^x/4)=8^4

LHS=(8^x/5) (8^x/4)

=(8^x/5) (8^x/4)

=8^(x/5+x/4)

=8^((4x+5x)/20)

=8^(9x/20)

Now, by comparing LHS to RHS

We will get;

9x/20=4

9x=80

x=80/9

Therefore the answer of the equation will be 80/9

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It is not a triangle.

Does given feet is a triangle or not?

The Triangle Inequality theorem states that in a triangle, , where  and  are shorter side lengths and  is the longest side length.

Given that  5+9<15, the given side lengths do not compose a valid triangle.

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The possible side length of the third side is 16 inches

It is important to note that the Pythagorean theorem states that the square of the hypotenuse side is the sum of the square of the other two sides, they are the opposite and adjacent sides.

This is represented as;

a² = b² + c²

Given that;

Note: 1 feet = 12 inches

Substitute the values into the formula, we get;

20² = 12² + c²

Find the squares

400 = 144 + c²

collect like terms

c² = 256

Find the square root

c = 16 inches

Hence, the value is 16 inches

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The apothem of a regular pentagon exists [tex]$4.6797 \mathrm{~cm}$[/tex], and the perimeter exists [tex]$34 \mathrm{~cm}$[/tex]. The area equals [tex]$79.55 \mathrm{~cm}^2$[/tex].

It is a regular pentagon if all of its sides and angles are equal in size. It is not normal if not. Each angle inside the regular pentagon is 108°, while each angle outside is 72°. There are 5 equal sides in an equilateral pentagon.

Five congruent sides (sides of identical length), five congruent inner angles (each measuring 108°), and five congruent outer angles of 72° are necessary for a regular pentagon to exist.

If a polygon's sides and angles are equal, it is said to be regular. As a result, an equilateral triangle is a regular triangle, and a regular quadrilateral is a square.

Therefore, the correct answer is option c) The apothem of a regular pentagon is [tex]$4.6797 \mathrm{~cm}$[/tex], and the perimeter is [tex]$34 \mathrm{~cm}$[/tex]. The area equals [tex]$79.55 \mathrm{~cm}^2$[/tex].

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If value of Kensington's car decreases in Value according to the exponential decay function "V = Pe^(-0. 12t)" , then value of Kensington car after 8 years is = $7658     .

The value of the Kensington car is decreasing according to the function ;

the exponential decay function is : V = Pe^(-0. 12t) ;

the purchase Price(P) of the car is = $20000  ;

we have to find the value of Kensington's car in 8 years ;

So , we substitute the value of P = 20000 and t = 8 years in the exponential decay function ,

we get ;

V  = 20000 × e^(-0. 12 × 8)

V = 20000 × e^(-0.96)

V = 20000/e^(0.96)

Simplifying further ,

V = 7657.8577 ,

V ≈ $7658 .

Therefore , the value of the car after 8 years is $7658  .

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Answer:

5

Step-by-step explanation:

(1) last season, the new york yankees played 160 games

(2) last season, the new york yankees scored

4 runs per game in exactly 1/5 of their games,  1/5*160 =32 games

5 runs per game in exactly 3/4 of their games, 3/4*160 =120 games

9 runs per game in exactly 1/20th of their games 1/20*160 = 8 games

total runs 4*32+ 5*120 + 9 *8 = 128+600+72 =800

total games 160

average: 800/160 =5

The mean is 24.2 and the standard deviation is 8.7.

The mean amount of revenue each car generates can be calculated by multiplying the mean number of hours parked by the cost per hour. To find the mean number of hours parked, we need to multiply each possible number of hours by its probability and add them up.

E(X) = (1 * 0.229) + (2 * 0.113) + (3 * 0.114) + (4 * 0.076) + (5 * 0.052) + (6 * 0.027) + (7 * 0.031) = 4.84 hours

So, the mean revenue is 4.84 * 5 = 24.2 dollars

The standard deviation of the revenue can be calculated by finding the standard deviation of the number of hours parked and then multiplying by the cost per hour.

SD(X) = sqrt( (1^2 * 0.229) + (2^2 * 0.113) + (3^2 * 0.114) + (4^2 * 0.076) + (5^2 * 0.052) + (6^2 * 0.027) + (7^2 * 0.031) - (4.84)^2) = 1.74 hours

So, the standard deviation of the revenue is 1.74 * 5 = 8.7 dollars.

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Answer:

A function is concave downward if its second derivative is negative. To find the values of x for which the graph of y = x^4 - 6x^2 + x is concave downward, we need to find the values of x for which the second derivative of y is negative.

The second derivative of y = x^4 - 6x^2 + x is y'' = 12x^2 - 12x

To find the values of x for which y'' is negative, we need to find the roots of the equation 12x^2 - 12x = 0.

We can factor the equation as: 12x(x-1) = 0

which gives us x = 0 and x = 1 as the roots.

Now, we need to test the sign of the second derivative in the intervals between the roots.

In the interval (0,1)

y'' = 12x^2 - 12x is positive, therefore the function is not concave downward in this interval.

In the interval (-infinity,0)

y'' = 12x^2 - 12x is negative, therefore the function is concave downward in this interval.

In the interval (1,infinity)

y'' = 12x^2 - 12x is negative, therefore the function is concave downward in this interval.

Therefore, the values of x for which the graph of y = x^4 - 6x^2 + x is concave downward are all values of x less than 0 or greater than 1.

The result of an average of more than 100% in a survey of tenants on cleaning chores in shared apartments is likely due to social desirability bias.

The average tenant response of more than 100% in a study about cleaning duties in shared apartments is probably the product of social desirability bias. Social desirability bias occurs when respondents give answers that they think are socially acceptable or desirable, rather than their true opinions or behavior.

In this case, tenants may have overstated their contribution to cleaning the apartment, in order to appear more helpful or responsible, leading to an average percentage higher than 100%.

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If Neil uses 41-cent stamps and 6-cent stamps to mail a gift card to a friend , then the number of 41 cent stamp used is 3  and number of 6 cent stamps used is 12 .

Let number of 41 cents stamps used be = x ;

and let number of 6 cents stamps used be = y ;

converting amount 41-cents in dollars is = $0.41  ;

and converting amount 6-cents in dollars is = $0.06  ;

the amount for which Neil used 41-cent stamps , 6-cent stamps is = $1.95 ;

this situation in equation form is written as ⇒ 0.41x + 0.06y = 1.95

Multiplying on both sides by 100 , we get

⇒ 41x + 6y = 195  ;

⇒ y = (195 - 41x)/6 ;

We will test this equations for values of x and y , the number of stamps must be whole numbers .

If x = 1 , then value of y is = 25.66

If x = 2 , then value of y is = 18.833

If x = 3 , then value of y is = 12

If x = 4 , then value of y is = 5.166 .

the only value of x and y which shows a whole number as an output is : If x = 3 , then y = 12 .

Therefore , Neil used "3" 41-cents stamps and "12" 6-cent stamps .

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Jennifer's monthly gross pay will be $4,589.08

Figures used to determine Jennifer's monthly gross compensation

Calculate the overall tax percentage deductions as a first step.

Using this equation

State tax + City tax + Social Security + Medicare = Total tax percentage deductions

Let's enter the formula.

Total tax deductions as a percentage equal: 3.5% + 2.5% + 6.2% + 1.45%

Total tax deductions as a percentage equal 13.65%

Now let's calculate the monthly gross pay

Total tax percentage deductions = 2.5% +1.2% +6.2% +1.45%

Total tax percentage deductions = 11.35%

Now let's calculate the monthly gross pay

Monthly gross pay= ($3,981.22 +87)/(1-11.35%)

gross pay= ($3,981.22 +87)/0.8865

Monthly gross pay=$4,068.22/0.8865

Monthly gross pay= $4,589.08'

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The cost of each raffle ticket is thus $14.50, and the cost of 90 tickets is $1305.

In multiplication, the numbers being multiplied are referred to as factors, and the end result is referred to as the product. In division, the dividend is the number being divided, the divisor is the number dividing it, and the quotient is the outcome of the division.

Given that the equation to find the cost of a single ticket is:

1218 ÷ 84 = x

x = 14.5

The cost of each raffle ticket is thus $14.50.

The cost of 90 tickets is given by:

90 × 14.50 = y

y = 1305.

Hence, the cost of 90 tickets is $1305.

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The only option that is true for the function g is; Option D: g(3) = 18

The function, g, has;

Domain; -1 ≤ x ≤ 4

Range: 0 ≤ g(x) ≤ 18

g(-1) = 2 and g(2) = 8

Then the following properties must hold to be true;

The value(s) of x must be between -1 and 4

The values of g(x) must be between 0 and 18.

We consider the options and state why they are true or otherwise.

Option A: g(5) = 12

When x = 5, g(5) = 12. This contradicts property 1 stated above and as such it is not true.

Option B: g(1) = -2

When x = 1,  g(x) = -2. This contradicts property 2 stated above and as such, it is not true.

Option C: g(2) = 4

When x = 2, g(2) = 4. However by property 4 stated above, g(2)=9. Therefore, we can say that it is not true.

Option D: g(3) = 18

When x =3 means that its domain lies between -1 and 4 and its range  lies between 0 and 18.

Therefore, Option D is true.

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The missing options are;

A) g(5)=12

B) g(1) = -2

C) g(2) = 4

D) g(3) = 18

The correct option regarding the median of each data-set is given as follows:

The median of the number of hours spent volunteering by each student in Sophia's homeroom is less than the median of the number of hours spent volunteering by each student in the tenth-grade class.

The median of a data-set is the middle value of a data-set, the value of which 50% of the measures are less than and 50% of the measures are greater than. Hence, the median also represents the 50th percentile of a data-set.

For Sophia's Homeroom, the total number of students is given as follows:

4 + 9 + 3 + 7 = 23.

Hence the median is the 12th element, which is on the interval 10-19.

For the Tenth Grade class, the total number of students is given as follows:

42 + 38 + 65 + 40 = 185.

Hence the median is the element at the position (185 + 1)/2 = 93, which is on the interval 20-29.

Hence the median is the 12th element, which is on the interval 10-19.

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The simplest polynomial function having integer coefficients with the given zeros is: x⁴ -2x³ + 14x² - 32x - 48

The polynomial is of degree 4

We have the values as 4i, 3 , -1

Hence we would have the following in brackets

for 4i = (x - 4i) (x + 4i)

for 3 = (x - 3)

for - 1 = (x + 1)

We would have to multiply these

(x - 4i) (x + 4i) (x - 3) (x + 1)

f(x) = x² + 4ix - 4ix (-4i)² (x² + x - 3x - 3)

f(x) = (x²  + 16)(x² - 2x - 3)

This can also be expanded to standard form if you wish

x⁴ - 2x³ - 3x² + 16x² - 32x - 48

properly arrange

x⁴ -2x³ + 14x² - 32x - 48

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where A is a real integer and A ≠ 0.

f(x) = A(x2 + 16)(x - 3)(x + 1)

The domain of the function is the set of all real numbers

From the question, we have the following parameters that can be used in our computation:

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

Express properly

So, we have the following representation

f(x) = ∛(x + 2) - 2

The above function is a cubic function

A cubic function has no restriction on its input value

This implies that the domain is the set of all real numbers

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Answer: 77 degrees

Step-by-step explanation:

Ratio of the angles = 5 : 7 : 9 = 5x : 7x : 9x

5x + 7x + 9x = 21x

180 = 21x

x = 180/21

Largest angle = 9x,

= 9 * 180/21

= 540/7

540/7 = 77.14285...

Which is rounded to 77 degrees :>

This suggests that the translation vector [tex]$\mathbf{t}$[/tex] has a component of -1 in the y-direction. Therefore, we have:

t=(3,−1)

To find the translation vector that maps quadrilateral ABCD to quadrilateral $A"B"C"D"$, we can subtract the coordinates of corresponding vertices. Let $\mathbf{t}$ be the translation vector. Then:

[tex]$$ \begin{align*}\\\mathbf{A}" - \mathbf{A} &= \langle -3 - t_x, -3 - t_y \rangle - \langle -3, -2 \rangle \\\&= \langle -3 - t_x + 3, -3 - t_y + 3 \rangle \\\&= \langle -t_x, -t_y \rangle\end{align*} $$[/tex]

Similarly, we have:

Since [tex]$\mathbf{D}"$[/tex] is not given, we cannot use it to solve for the components of [tex]$\mathbf{t}$[/tex]. However, note that the x-coordinate of [tex]$\mathbf{A}"$[/tex] is -3, which is 3 less than the x-coordinate of [tex]$\mathbf{A}$[/tex]. This suggests that the translation vector [tex]$\mathbf{t}$[/tex] has a component of 3 in the x-direction. Similarly, the y-coordinate of [tex]$\mathbf{B}"$[/tex] is -1, which is 1 more than the y-coordinate of [tex]$\mathbf{B}$[/tex]. This suggests that the translation vector [tex]$\mathbf{t}$[/tex] has a component of -1 in the y-direction. Therefore, we have:

t=(3,−1)

which means that the correct answer is [tex]$\boxed{\langle 3, -1 \rangle}$[/tex]

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Answer:

12

Step-by-step explanation:

Assuming that $300 and $50 are the respective cost(s) of the premium and discount tickets, if we didn't buy any premium tickets, we could afford to buy 12 discount tickets at $50 because 12($50) = $600 

Hi There!

Your Answer could be 8 don't trust me i might be wrong

Answer:

c. non-linear and increasing

Step-by-step explanation:

At a large museum, there are 60 people in each tour group. so that the ordered pairs are 1 - 60 peoples, 2 - 120 peoples, 3 - 180 peoples, 4 - 240 peoples, 5 - 300 peoples, 6 - 360 peoples etc.

An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence.

In order to understand a point visually, it can be helpful to position it on the Cartesian plane.

An ordered pair's numerical values may be fractions or integers.

Given that, at a large museum, there are 60 people in each tour group.

In 1 group there are 60 peoples.

In 2 group there are 2 * 60 = 120 peoples.

In 3 group there are 3 * 60 = 180 peoples.

like this the correct ordered pairs are 1 - 60 peoples, 2 - 120 peoples, 3 - 180 peoples, 4 - 240 peoples, 5 - 300 peoples, 6 - 360 peoples etc.

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The length of x in the triangle is 8 units.

A midsegment is the line segment connecting the midpoints of two sides of a triangle.

The midsegment theorem states that a line segment connecting the midpoints of any two sides of a triangle is parallel to the third side of a triangle and is half of it

Therefore, DE is the mid segment of the triangle ABC. The value of x can be found as follows:

Using the mid segment principle,

BE = EC

BD = DA

Therefore,

x = 8 units

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Answer:

z=1.4

Step-by-step explanation:

honestly, I'm not that smart so i just looked it up.

but Im pretty sure thats the right answer.

The graph would be a line, where the x-axis represents the distance in miles running, and the y-axis represents the time spent on the treadmill. The points on the graph would be (0,90), (2,78), (4,66), (3,72).

(a) If Annalise only walks on the treadmill, she would spend 15 minutes per mile walking. Since she does a total of 6 miles, she would spend 15 minutes/mile * 6 miles = 90 minutes on the treadmill.

(c) Here are three other combinations for running and walking times on the treadmill:

2 miles running and 4 miles walking: 2 miles * 9 minutes/mile running + 4 miles * 15 minutes/mile walking = 18 minutes + 60 minutes = 78 minutes

4 miles running and 2 miles walking: 4 miles * 9 minutes/mile running + 2 miles * 15 minutes/mile walking = 36 minutes + 30 minutes = 66 minutes

3 miles running and 3 miles walking: 3 miles * 9 minutes/mile running + 3 miles * 15 minutes/mile walking = 27 minutes + 45 minutes = 72 minutes

(d) The graph would be a line, where the x-axis represents the distance in miles running, and the y-axis represents the time spent on the treadmill. The points on the graph would be (0,90), (2,78), (4,66), (3,72).

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