Solve the inequality 7(2x + 5) < 3(4x – 1). Write your solution in algebraic form, interval notation, and graphed on a number line.

The graph could be the graph of f(x) which is the correct answer would be option (B).

A graph can be defined as a pictorial representation or a diagram that represents data or values.

We are given the degree of the polynomial function f(x) to be 3; and

the roots of the equation f(x) to be 0 are -1, 0, and 4.

So we will put these values in the polynomial function of degree 3 to get:

f(x) = (x  -(-1))(x-0)(x-4)

f(x) = (x  + 1)x(x-4) = x³ - 3x² - 4x

According to this, the x-intercepts of this function on the graph will be:

(0, 0)

(-1, 0)

(4, 0)

So we will look for a graph that intercepts the x-axis at these points.

Therefore, the graph of the option (B) at the bottom right satisfies the conditions and is the graph of f(x).

Learn more about the graphs here:

brainly.com/question/16608196

#SPJ1

Using Pythagorean theorem, the side of the ladder will reach 22.45 ft far up now.

Pythagorean theorem describes the relationship between the sides of a right triangle. It states that the square of the hypotenuse is equal to the sum of the squares of the two other side.

c² = a² + b²

If a 45 foot ladder is set up against the side of a house so that it reaches up 27 feet, then the distance between the base of the ladder and the base of the side of the house is the difference between the square of the two values.

c = 45 ft

a = 27 ft

b² = c² - a²

b² = (45 ft)² - (27 ft)²

b² = 2025 - 729

b² = = 1296

b = 36 ft

If Latanya grabs the ladder at its base and pulls it 3 feet farther from the house, then the distance becomes b + 3 = 39 ft.

Using Pythagorean theorem, determine how far up the ladder is on the side of the house.

c = 45 ft

b = 39 ft

a² = c² - b²

a² = (45 ft)² - (39 ft)²

a² = 2025 - 1521

a² = 504

a = 6√14

a = 22.45 ft

Learn more about Pythagorean theorem here: https://brainly.com/question/9125970

#SPJ4

Answer:

0.1 == -0.1

1/7 == -1/7

10 == -10

-7 == 7

Step-by-step explanation:

I took the test

The opposite of the numbers 0.005, 12, 0, -2 are -0.005, -12, 0, 2 after changing the sign of the number.

A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.

It is given that:

The numbers are:

0.005, 12, 0, -2

As we know, from the definition of the number, a number is a mathematical entity that can be used to count, measure, or name things.

The opposite of any number can be obtained by changing the sign of the number.

The opposite of the number 0.005 is -0.005

The opposite of the number 12 is -12

The opposite of the number 0 is 0

The opposite of the number -2 is 2

Thus, the opposite of the numbers 0.005, 12, 0, -2 are -0.005, -12, 0, 2 after changing the sign of the number.

Learn more about the number here:

brainly.com/question/17429689

#SPJ5

Answer:46kg

Step-by-step explanation:

23+2=25

50/25=2

2x23=46kg

Answer:

46 kg

Step-by-step explanation:

Ratio of copper to tin in the bronze alloy is 23:2

That means, as a ratio of the entire brass mass, the copper content is in the ratio of 23/(23 + 2) = 23/25

Since the mass of the bronze statue is 50 kg, the mass of copper in it must be 50  x  23/25 = 46 kg

The remaining kg (2/25 of 50 kg) is tin

Answer: The common factors of 14 and 35 are 7, 1, intersecting the two sets above. In the intersection factors of 14 ∩ factors of 35 the greatest element is 7. Therefore, the greatest common factor of 14 and 35 is 7.

Step-by-step explanation:

Answer:

first equation: Incorrect

second equation: Correct

Step-by-step explanation:

first equation:

[tex]-1 + (\frac{1}{-1}) = 1[/tex]

[tex]-1 + (-1) = 1[/tex]

[tex]-2 = 1[/tex]

negative 2 isn't the same as positive 1 which isn't true so the answer is incorrect.

second equation:

[tex](\frac{-1}{1} ) = -1[/tex]

[tex](-1) = -1[/tex]

negative 1 is the same as negative 1 so the answer is correct

Four siblings whose ages are consecutive odd integers. If the sum of their ages is 112 then The eldest sibling is 31, followed by siblings 29, 27, and 25.

What is consecutive integers ?

Consecutive means in order.  Integers are a collection of whole integers and their antipodes, such as -3, -2, 1, 0, 1, 2, 3, etc.

Let x = the 1st sibling

Let x -2 = the second sibling

Let x -4 = the third sibling

Let x-6 = the fourth sibling.

If you add the four siblings together they equal 112

(x) +(x-2)+(x-4)+(x-6) = 112  Combine like terms

4x - 12 = 112

add 12 from both sides

4x - 12 + 12 = 112 + 12

4x = 124

divide 4 both side :

x = 31

The eldest sibling is 31, followed by siblings 29, 27 and 25

To learn more about consecutive integers visit:

brainly.com/question/1767889

#SPJ1

Answer:

[tex]y=-\frac{1}{4}x+2[/tex]

Step-by-step explanation:

Perpendicular lines have slopes thst are negative reciprocals, so the slope of the line to be found is -1/4.

Substituting into point-slope form, the equation is [tex]y-4=-\frac{1}{4}(x+8)[/tex].

Rearranging into slope-intercept form,

[tex]y-4=-\frac{1}{4}(x+8) \\ \\ y-4=-\frac{1}{4}x-2 \\ \\ y=-\frac{1}{4}x+2[/tex]

Answer:

See below

Step-by-step explanation:

x = amount at  9.2 %             interest = .092 x

(9500 -x) = amount at 9%     interest = .09 ( 9500-x)    summed, they = 870

.092x + .09 ( 9500-x)  = 870

x = 7500   then the other amount at 9 % is 2000

Answer:

65 feet

Step-by-step explanation:

[tex]3705=57h \\ \\ h=\frac{3705}{57}=65[/tex]

Answer:

yes correct ^ ^

Step-by-step explanation:

This question is a bit confusing

Answer:

[tex]g(h(x))=−6x−17

[/tex]

Step-by-step explanation:

given:

[tex] g(x) = 15 - 4x \\ h(x) = \frac{3}{2 } x + 8[/tex]

To find g(h(x)) substitute h(x) instead of every x in g(x)

therefore:

[tex]g(h(x)) = 15 - 4( \frac{3}{2} x + 8) \\ [/tex]

simplify

[tex]g(h(x)) = 15 - 6x - 32 \\ g(h(x)) = - 6x - 17[/tex]

Answer:

A 2√6

Step-by-step explanation:

- Split the value under root into divisions of factors of 24

[tex]{ \sf{ \sqrt{24} = \sqrt{6 \times 4} }} \\ \\ { \sf{ \sqrt{24} = \sqrt{6} \times \sqrt{4} }} \\ \\ { \sf{ \sqrt{24} = \sqrt{6} \times 2 }} \\ \\ { \boxed{ \sf{ \: \sqrt{24} = 2 \sqrt{6} }}}[/tex]

3633 is the difference of these numbers.

To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference. We frequently employ subtraction in our daily lives. Subtraction is used, for instance, to determine how much money was spent on the products we purchased, how much money is still in our possession, or how much time is left to complete a task.

Subtraction can be applied in a variety of real-world situations. Assume you had five apples and your friend had three. We may calculate the quantity of remaining apples by subtracting: 5 - 3 = 2.

Given Data

9832 - 6199

Subtracting,

= 9832 - 6199

= 3633

3633 is the difference of these numbers.

To learn more about subtraction, visit:

https://brainly.com/question/20348406

#SPJ9

The given expression -3x²-6x+9 is quadratic expression and it is trinomial.

Classification of polynomials are given below:

A) 2x²

Degree = 2, so it is quadratic expression

Name using number of terms=monomial

B) -2

Degree = 0, it is constant

Name using number of terms=monomial

3) 3x-9

Degree = 1, so it is linear expression

Name using number of terms=monomial

4) -3x²-6x+9

Degree = 2, so it is quadratic expression

Name using number of terms=trinomial

Therefore, the given expression -3x²-6x+9 is quadratic expression and it is trinomial.

To learn more about an expression visit:

https://brainly.com/question/28170201.

#SPJ1

Answer:

Its C

Step-by-step explanation:

The rate of change for the height of the ice cream is [10 - (2π / 3) · (1 / 14) · h] / [(π / 3) · r²] units per second.

The volume of an ice cream cone (V), in cubic units, is described by the following formula:

V = (1 / 3) · (π · r²) · h                                     (1)

Where:

The rate of change for the height of the cone is derived from differentiating (1) with respect to time:

V' = (1 / 3) · (2π · r) · h · r' + (1 / 3) · (π · r²) · h'

V' = (2π / 3) · h · r' + (π / 3) · r² · h'

h' = [V' - (2π / 3) · h · r'] / [(π / 3) · r²]

Where:

If we know that V' = 10 and r' = 1 / 14, then the rate of change for the height of the cone is:

h' = [10 - (2π / 3) · (1 / 14) · h] / [(π / 3) · r²]

The height of the ice cream cone changes at a rate of [10 - (2π / 3) · (1 / 14) · h] / [(π / 3) · r²] units per second.

To learn more on rates of change: https://brainly.com/question/11606037

#SPJ1

The discrete data might consist of number of legs, number of teeth. The continuous data might consist the length of tail, and the height of dog.

The discrete data is a data whose value is obtained by counting and they can be described by an integer value. Those random variables, who take only distinct values, are called discrete random variables.

Consider the provided information; Something that will never change

So, the discrete data might consist of number of legs, number of teeth.

A continuous data is defined as a variable whose value is obtained by measuring.

The continuous data might consist the length of tail, and the height of dog.

The continuous variables are random variables, who take any value from a given continuous interval of real numbers.

Learn more about the discrete;

https://brainly.com/question/14353704

#SPJ1

Answer: The price of the apartment lies in the range of $1300 to $1800

Step-by-step explanation: Because Carlos doesn't exactly know how much  he'll make at his new job but he knows the range will be between 3000$ and 4000$ we will use inequality to solve this problem.

Let the rent on the new apartment = r

let monthly pay of Carlos = x

Given, apartment related fees = 200$

Given he is willing to use half of his monthly pay for rent and apartment related fees combined.

∴rent + apartment related fees = Monthly pay / 2

⇒[tex]r + 200 = \frac{x}{2}[/tex]

⇒[tex]x=2*(r+200)[/tex]

⇒[tex]x=2r+400[/tex]                                                (1)

Given Carlos' monthly pay is in the range of $3000 to $4000

∴[tex]3000\leq x\leq 4000[/tex]

⇒[tex]3000\leq (2r+400)\leq 4000[/tex]                             (from equation (1))

⇒[tex]3000-400\leq 2r+400-400\leq 4000-400[/tex]     (subtracting 400)

⇒[tex]2600\leq 2r\leq 3600[/tex]

⇒[tex]\frac{2600}{2}\leq \frac{2r}{2}\leq \frac{3600}{2}[/tex]                                           (dividing by 2)

⇒[tex]1300\leq r\leq 1800[/tex]                                           (2)

ANS: The apartment lies in the price range of $1300 to $1800 as given by equation (2)

here is a problem solved using inequality

https://brainly.com/question/13618639

#SPJ4

The expression of (f+g)(x) from the functions  f(x)=−2x2+4x and g(x)=3x+3 is (f+g)(x) = (-2x^3+7x^2 +3x ).

From the question we were given the functions that is expected to be simplified as :

f(x)=−2x^2+4x

g(x)=3x+3

And we were told to find the function  (f+g)(x) which can be written as :

(f+g)(x) = [(−2x^2+4x )+(3x+3)]x

This can be further expressed as :

(f+g)(x) = (-2x^2+4x +3x+3 )x

This can be further simplified as :

(f+g)(x) = (-2x^2+7x+3 )x

This can be further simplified as :

(f+g)(x) = (-2x^3+7x^2 +3x )

Therefore, the expression of the function (f+g)(x) is (f+g)(x) = (-2x^3+7x^2 +3x ).

Read more about functions here:

https://brainly.com/question/1415456

#SPJ1

The missing part:

Find (f+g)(x).

The following data table for two distinct linear functions utilizing identical x values for both functions is displayed:

[tex]\begin{tabular}{|c|c|c|}$\mathrm{x}$ & $\mathrm{y}=2 \mathrm{x}+7$ & $\mathrm{y}=-\mathrm{x}+4$ \\$-3$ & $2(-3)+7=-6+7=1$ & $-(-3)+4=3+4=7$ \\$-2$ & $2(-2)+7=-4+7=3$ & $-(-2)+4=2+4=6$ \\$-1$ & $2(-1)+7=-2+7=5$ & $-(-1)+4=1+4=5$ \\0 & $2(0)+7=0+7=7$ & $-(0)+4=0+4=4$ \\1 & $2(1)+7=2+7=9$ & $-(1)+4=-1+4=3$ \\2 & $2(2)+7=4+7=11$ & $-(2)+4=-2+4=2$ \\3 & $2(3)+7=6+7=13$ & $-(3)+4=-3+4=1$\end{tabular}[/tex]

The table demonstrates that the function y = 2x + 7 and the function y = -x + 4 both have values of 5 for x = -1.

As a result, the two functions' graphs will intersect at (1, 5)

First of all, we create 2 LINEAR function, i created the function f(x)=2x+5 and the function h(x)=3x+2, both are linear(without a quadratic term). Then

Choose a group of x values before creating the table. Add each x value from the left side column to the equation. To find the y value, evaluate the equation (middle column). Since the table of values really only contains x and y pairs, you can choose to omit the middle column from your table as an optional step.

you replace the x for a number:

Table 1 (F(X)=2X+5)                                 Table 2 (H(X)=3X+2)

X=1----->Y=2+5=7                                     X=1------>Y=3·1+2=5

X=2---->Y=2·2+5=9                                  X=2----->Y=3·2+2=8

X=3---->Y=3·3+5=11                                  X=3----->Y=3·3+2=11

With both tables of data we can see that in the X=3/Y=11 point this two linear functions will intersect so the answer is that the two functions will intersect at (3,11)----->(X,Y)

To learn more about functions visit:https://brainly.com/question/12431044

#SPJ1

The slope of the line passing from the two points is found as infinity.

For the given question;

The two passing points of the line is given as;

(x1, y1) = (-4, 6)

(x2, y2) = (-4, 18)

The formula for calculating the slope is;

Slope  = m = (y2 - y1)/(x2 - x1)

Put the values.

m = (18 - 6)/ (- 4 + 4)

m = 12/0

m = ∞

It means, the line is parallel to the x axis.

Thus, the slope of the line passing from the two points is found as infinity.

To know more about the slope of the line, here

https://brainly.com/question/28912703

#SPJ10

g ≥ 1.8 is  the number of hours of running per day in inequality .

What are the mathematical inequalities?

Atleast means the number would be greater than or equal to given number.

g ≥ 1.8

Learn more about inequalities

brainly.com/question/20383699

#SPJ9

hey you man what are you going here go to there

The range of the error will be [3.65,3.75.

The accuracy range or limit where a number is rounded off or truncated is known as the error interval. This range merely depicts the possible range before rounding.

Given that :A number, x, rounded to 1 decimal place is 3.7

The mistake will be half of 0.1, which is[tex]\frac{0.1}{2} = 0.05[/tex], since the number is rounded to the nearest 0.1 unit.

3.7-0.05=3.65 will then be the lower limit of the error interval.

The error interval's upper limit will be 3.7 + 0.05 = 3.75.

The error will be 3.65≤x<3.75 milliseconds.

If the second decimal unit is more than 5, the first decimal unit will be 6, since we are rounding the first decimal unit. Similar to this, the first decimal unit will be 7 if the second decimal unit is less than 5.

The figures below, when rounded, result in 3.7.

3.65 ,3.66,3.67 ,3.68,3.69,3.70,3.71,3.72,3.73,3.74

As a result, the error range will be [3.65,3.75).

To Learn more about error intervals visit :

brainly.com/question/23923516

#SPJ9

[tex]~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] ~\dotfill\\\\ \left( 4^{\frac{2}{5}} \right)^{\frac{1}{4}}\implies 4^{\frac{2}{5}\cdot \frac{1}{4}}\implies 4^{\frac{1}{10}}\implies \sqrt[10]{4^1}\implies {\Large \begin{array}{llll} \sqrt[10]{4} \end{array}}[/tex]

Answer:

[tex]y=-\frac{k}{-4+k}; k \neq 4[/tex]

Step-by-step explanation:

2y + k = 6y - ky; solve for y

2y = 6y - ky - k (Subtraction Property of Equality)

2y - (6y - ky) = 6y - ky - k - (6y - ky)  (Subtraction Property of Equality)

-4y + ky = -k (Simplify)

y(-4 + k) = -k (Factor)

[tex]\frac{y(-4+k)}{-4+k}=\frac{-k}{-4+k}: k\neq 4[/tex] (Division Property of Equality)

   [tex]y=-\frac{k}{-4+k}; k \neq 4[/tex] (Simplify)

The value of y is k/ (4- k).

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them. Variables are the name given to these symbols because they lack set values. We frequently observe constant change in specific variables in our day-to-day situations. But the need to depict these shifting values is ongoing. These values are frequently represented in algebra by symbols such as x, y, z, p, or q, and these symbols are known as variables. In order to determine the values, these symbols are also subjected to different addition, subtraction, multiplication, and division arithmetic operations.

Given:

2y + k = 6y - ky

Now, solving for y

2y -6y + ky = -k

-4y + ky= -k

y( k-4) = -k

y = -k/(k -4)

y= k/ (4- k)

Hence, the value of y is k/ (4- k).

Learn more about algebra here:

https://brainly.com/question/24875240

#SPJ2

The rational numbers - 5 / 6 and - 7 / 10 are equivalent to - 25 / 30 and - 21 / 30, respectively. Then, the relationship is that - 5 / 6 is the less than - 7 / 10 as - 25 < - 21.

Rational numbers are real numbers of the form m / n, where m and n are integers and n is not zero. In this problem we need to determine the relationship between two rational numbers, this can be done by amplifying the two rational numbers to a form with the same denominator and then compare the two numerators.

First, find the least common multiple of the two denominators:

6 = 2 × 3

10 = 2 × 5

L.C.M. = 2 × 3 × 5 = 30

Second, amplify each rational number:

- (5 × 5) / (6 × 5) = - 25 / 30

- (7 × 3) / (10 × 3) = - 21 / 30

Third, compare the numerators of the fraction found in the previous step:

Since - 25 < - 21, then - 5 / 6 < - 7 / 10.

To learn more on rational numbers: https://brainly.com/question/17450097

#SPJ1