Mathematics College

Translate and solve the inequality. “Ten subtracted from the quotient of a number and seven is less than negative six.”

Answers

Answer 1

Given:

The objective is to translate the statement and solve the inequality.

Explanation:

Consider the unknown number as x. The quotient of a number and 7 can be written as,

[tex]Q=\frac{x}{7}\text{ . . . . .. . (1)}[/tex]

By subtracting 10 from the quotient, the value is less than -6.

[tex]Q-10<-6\text{ . . . . .(2)}[/tex]

On substituting the equation (2) in (1),

[tex]\frac{x}{7}-10<6\text{ . . . . . . (3)}[/tex]

To find x :

On solving the equation (3), the value of x can be calculated as,

[tex]\begin{gathered} \frac{x-10(7)}{7}<-6 \\ x-70<-6(7) \\ x<-42+70 \\ x<28 \end{gathered}[/tex]

Hence, the value of x is less than 28.

Related Questions

Which Zeros of the polynomial function partially graphed below have even multiplicity?

Answers

The Zeros of the polynomial function partially graphed below have even multiplicity are x = -3 and x = 3.

What are the Zeros of the Polynomial?

The zeros of a Polynomial graph are simply the points where the graph curve crosses the x-axis.

In simply terms, the Zeros of a function are the values of the independent variable that make the function equal to 0. Multiplicity just refers to how many copies of a given zero exist.

From the given graph, the zeros of the Polynomial function are x = 2 and x = 3 and x = -3

An odd multiplicity means the graph of the function crosses the x-axis at that point. An even multiplicity means the curve contacts the x-axis at that point and backs instead of crossing.

Thus, the odd multiplicity is at x = 3

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What is the volume??

Answers

what is volume answer the volume is your topic for to day

Write an equation of a the line passing through the point (2,-9) that is perpendicular to the line y=x+6
An equation of the line is…..

Answers

The linear function passing through the point (2,-9) that is perpendicular to the line y=x+6 is:

y = -x -7.

How to write the equation of perpendicular linear functions?

A linear function is modeled according to the following rule:

y = mx + b.

The coefficients of the linear function are as follows:

m is the slope, which is the rate of change of the function.b is the y-intercept, which is the numeric value of the function when x = 0.

When two lines are perpendicular, the multiplication of their slopes is of -1.

For this problem, the line is perpendicular to line y = x + 6, which has slope 1, hence:

m = -1.

Then:

y = -x + b.

When x = 2, y = -9, hence we use this to find the intercept b as follows:

-9 = -2 + b

b = -7.

Hence the rule is:

y = -x -7.

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Answer:

Step-by-step explanation:

What is the ratio of blue paint to total paint in the mixture?

Answers

The ratio of blue paint to the total paint in the mixture is 5:8.

How is a ratio calculated?Ratios contrast two figures by ordinarily dividing them. The term "antecedent" refers to the dividend and "consequent" to the divisor. A ratio in mathematics demonstrates how many times one number is present in another.It is a comparison or relationship between two amounts of the same quantity to determine how much larger one number is than the other. Where b is not equal to zero, it is expressed as a/b or a: b.

Given:

In the figure, there are 10 blocks of blue paint and 6 blocks of red paint.

Total paint in the mixture = 10+6 = 16

Ratio of blue paint to total paint = 10/16 = 5/8

Therefore, the required ratio is 5:8.

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Which of the following shows a correct way of simplifying 6+(3-5x)

Answers

Answer: 9 - 5x

Step-by-step explanation:

6 + (3 - 5x) = 6 + 3 - 5x = 9 - 5x

Which is a function?
{(12, 3), (11, 2), (10, 1), (9, 0), (8, 1), (7, 2), (6, 3)}
{(6, 3), (5, 2), (4, 1), (3, 0), (4, –1), (5 ,–2), (6 ,–3)}
{(1000, 10), (1000, 12), (1000, 16), (100, 5), (100, 7), (78, 3), (90, 5)}
{(7, 2), (100, 10), (13, –7), (7, 9), (10, 100), (4, –2), (5, 5)}

Answers

Answer: {(12, 3), (11, 2), (10, 1), (9, 0), (8, 1), (7, 2), (6, 3)}

Step-by-step explanation:

Each value of x corresponds to only one value of y, making the relation a function.

the linear equation 3x- 4y =7 has:
a, unique solution
b, two solutions
c, infinitely many solutions
d,no solution

Answers

The linear equation is 3x+4y=7. The solution to the equation 3x+4y=7 is unique.

Given that,

The linear equation is 3x+4y=7

Any equation with a maximum degree of 1 is said to be linear. No variable in a linear equation, thus, has an exponent greater than 1.The graph of a linear equation is always a straight line.

There are numerous options if x and y are not positive integers (natural numbers), thus it is best if they are.

The x and y are positive integers so it is a unique solution.

Therefore, The solution to the equation 3x+4y=7 is unique.

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What is the congruence, if any , that will prove the given triangles congruent?

Answers

Given:

The triangle FTP and triangle JTA is given.

In the given triangles,

[tex]\begin{gathered} \angle P\cong\angle A \\ \angle F\cong\angle J \\ \angle T\cong\angle T \end{gathered}[/tex]

As only three angles of both triangles are similar we can not say that the given traingles are congruent.

So, Option A is correct.

Wat 8x3 to get a answer

Answers

Answer:

Step-by-step explanation:

24 basically add 8 plus 8 plus 8 three times to get 24 as your answer

Evaluate the expression: No 4m2 when m = 3

Answers

We solve as follows:

[tex]f(3)=4(3)^2\Rightarrow f(3)=36[/tex]

The solution is 36.

PLEASE HELP ME I MISSED CLASS BECAUSE I WAS SICK AND I DONT I UNDERSTAND

Answers

Answer:

see explanation

Step-by-step explanation:

(a)

the angles shown are alternate interior angles and are congruent

(c)

since they are congruent , then

27x - 5 = 130 ( add 5 to both sides )

27x = 135 ( divide both sides by 27 )

x = 5

(d)

then

27x - 5 = 27(5) - 5 = 135 - 5 = 130

The Royal Fruit Company produces two types of fruit drinks. The first type is 65% pure fruit juice, and the second type is 90% pure fruit juice. The company is attempting to produce a fruit drink that contains 70% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 30 pints of a mixture that is 70% pure fruit juice?

Answers

20 of the 65 percent pure fruit juice, 10 of the 90 percent pure fruit juice.

What is percentage ?

A fraction that is parts out of 100 is referred to as a percentage.100% is the totality. The percentages that make up a whole add up to 100%.When representing a percentage as a number, the % symbol is used. A decimal, fraction, mixed number, integer, or other type of number can be used.In a grid of 100 squares, shading can be used to represent a percentage.

First, we define our variables: let x be the number of pints of the first fruit drink (65% pure fruit juice), and y be the number of pints of the second fruit drink (90%pure fruit juice).

We know that there are 30 total pints of the mixture. Thus:

x+y=30

We also know that 90%of those 30 pints will be pure fruit juice, and all of the pure fruit juice will come from xor y.

For x pints of the first juice, there is .65x pure fruit juice. Similarly, for ypints of the first juice, there is .90y pure fruit juice. Thus, we get:

.65x+.90y=30 ×0.7

Now we solve. First I'll get rid of the decimals in the second equation by multiplying by 100:

65x+90y=2100

Multiply the first equation by 65 on both sides to be able to cancel out one of the terms:

65x+65y=1950

Subtract the second equation from the first equation:

25y=250

y=10

Thus, we need 10 pints of the second fruit juice (90%pure fruit juice). This means that we need 30−10=20 pints of the first fruit juice (65% pure fruit juice).

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Tyler was making a meal for his family. For every 3/4 pound of beef, the recipe calls for 9/8 cups of broccoli. How many cups of broccoli would be needed for a pound of beef?

Group of answer choices

1/2 cup of broccoli per beef

1 and ½ cup of broccoli per beef

2/3 pound of broccoli per beef

5/4 cup of broccoli per beef

Answers

Proportionately, the number of cups of broccoli needed for a pound of beef is B. 1 and ½ cups of broccoli per beef.

What is proportion?

Proportion refers to the numerical quantity or relationship of one variable to another, which are set equal to each other.

Proportions, like ratios, use fractional values because they show the quantity of one variable in another.

We state proportions in fractions, decimals, or percentages.

The proportion of 3/4 pound of beef to broccoli = 9/8 cups of broccoli

3/4 pound = 0.75 pound

9/8 cups = 1.125 cups

The number of cups of broccoli for a pound of beef = 1.5 cups (1.125/0.75)

1.5 cups = 1½ cups

Thus, given the proportional relationship presented, for a pound of beef, Tyler would need 1½ cups of broccoli.

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Use inductive reasoning to find a pattern for the answer then use the pattern to guess the result of the final calculation and perform the operations to see if your answer is correct

Answers

Given:

1 = 1²

1 + 3 = 2²

1 + 3 + 5 = 3²

1 + 3 + 5 + 7 = 4²

1 + 3 + 5 + 7 + 9 = 5²

1 + 3 + 5 + 7 + 9 + 11 = ___

Let's find the answer and determine the pattern.

Here, we have:

1 + 3 = 4

Now, write the sum as a perfect square:

4 = 2²

For the third equation:

1 + 3 + 5 = 9

Now, write the sum as a perfect square:

9 = 3²

This means the result will be the sum written as a perfect square.

Thus, we have:

1 + 3 + 5 + 7 + 9 + 11 = 36

Now, let's write the sum (36) as a perfect square:

36 = 6²

Therefore, we have:

1 + 3 + 5 + 7 + 9 + 11 = 6²

• ANSWER:

6²

The line y=kx+4 goes through the point (2,-2)
K=-3
Sketch the graph of the line (need ASAP!!)

Answers

We can see that the value of k is -3, then the line is:

y = -3*x + 4

By finding two points of the line, we can graph the line like in the image you can see below.

How to sketch a graph of the line?

Here we have the following linear equation:

y = k*x + 4

We know that this line goes through the point (2, -2), then we can replace these values in the above equation so we get the value of k.

-2 = k*2 + 4

Solving this, we can find the value of k.

-2 - 4 = k*2

-6 = k*2

-6/2 = k = -3

So the value of k, the slope of the line, is k = -3.

Then the line is:

y = -3*x + 4

If we evaluate in x = 1, we get:

y = -3*1 + 4 = 1

So, at this point we know that the line passes through points (1, 1) and (2, -2).

Now we can draw these two points on a coordinate axis, and then connect them with a line. That will be the graph of the linear equation.

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How can we guarantee that a polynomial is not a perfect square, considering just the constant term? For instance, in 4, the constant term is -121, in 2, the constant term is 36. Which of them cannot be a perfect square and why, based only on the constant term?

Answers

Regarding perfect squares, it is found that:

A negative constant guarantees that the polynomial is not a perfect square.The polynomial with a constant term of -121 is not a perfect square.

Perfect squares

Perfect square expressions are formed with the notable products of the square of the sum or the square of the subtraction, as follows:

(a + b)² = a² + 2ab + b² -> square of the sum.(a - b)² = a² - 2ab + b² -> square of the subtraction.

The constant term of perfect squares, in both cases, is given by:

b².

Since the number is squared, it will always be a positive value, meaning that a negative constant term guarantees that the polynomial is not a perfect square.

The polynomial with a negative constant in this problem has a constant of -121, hence it is not a perfect square.

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Find the coefficient of the x^2 term in the expansion of (5x-2)^6 //Series and sequences precalculus

Answers

We need to expand the term:

[tex](5x-2)^6[/tex]

This seems like a colossal task, we would need to multiply (5x-2) 6 times. However, we can use a useful tool that is called the 'Pascal's triangle'

I'll paste an image of it above

We will use it in this way:

Each one of the rows, represent the n in the term:

[tex](x+y)^n[/tex]

So, if we have the expression (x+y) we will pay attention to the upper row, if we have (x+y)^2 we will need the second row, and so on.

In our case, we need the 6th row.

Now, usually a term of the form

[tex](x+y)^6=ax^6+bx^5y+cx^4y^2+dx^3y^3+ex^2y^4+fxy^5+gy^6[/tex]

As we say, look at the 6th row of the triangle, the numbers a, b, c,..., and g are given there!

[tex]\begin{gathered} a=1 \\ b=5 \\ c=10 \\ d=10 \\ e=5 \\ f=1 \end{gathered}[/tex]

And we need the term that corresponds to x^2, we need the number e=5!

So, after the expansion, the coefficient of the term x^2 will be equal to 5

8. If APTS - APOR, find the value of x.5x + 13TP36306.r - 2R

Answers

The triangles PTS and POR are similar, so we can take the ratios of the side to order

[tex]\frac{PT}{ST}=\frac{PQ}{SQ}[/tex]

[tex]\frac{36}{30}\text{ =}\frac{5x\text{ + 13}}{6x\text{ - 2}}[/tex]

[tex]\begin{gathered} \text{cross multiplying} \\ \\ 30\text{ (6x - 2) = 30 (5x + 13)} \\ \\ \text{Expanding the parenthesis} \\ \\ 30\text{ x 6x - 30 x 2 = 30 x 5x + 30 x 13} \\ \\ 180x\text{ -60 = 150x + 390} \end{gathered}[/tex]

We can then solve for x by collecting like terms

180x - 150x = 390 + 60

30x = 450

Divide both sides by 30

x = 450/ 30

x = 15

Write an expression for the amount of money (in nickels) in n dollars.

PLEASE HELP ITS DUE IN AN HOUR

Answers

An expression for the amount of money (in nickels) in n dollars is 20n nickels.

How many nickels are in a dollar?

A nickel is a five-cent coin produced by the United States Mint that is made of a copper-nickel alloy rather than silver. Because 100 cents equal one dollar and one nickel equals five cents, we conclude that 20 nickels are equivalent to one dollar.

To write an expression for the amount of money (in nickels) in n dollars,

Convert the n dollars to nickels.

1 dollar = 20 nickels

So, n dollars = 20n nickels

The required expression for the amount of money (in nickels) in n dollars is 20n nickels.

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2sinxcosx/sin^2x+cos^2x-1=1

Answers

The simplified equation is sin(2x) = 2

How to determine the value of the trigonometry formula?

The trigonometry ratio is given as

2sinxcosx/sin^2x+cos^2x-1= 1

Rewrite the equation of the trigonometry formula properly