What is the algebraic expression for "the difference between seven times a number and three times that number"?

7 - 3x
7x - 3
7x - 3x

Answer:

[tex]\bf \sin x =\frac{3}{5}[/tex]  

Step-by-step explanation:

Angle x is an acute angle in a triangle.

The measure of cosine angle is given to be :

[tex]\cos x = \frac{4}{5}[/tex]

Now, we need to find the measure of the sine angle for the same triangle.

[tex]\cos x = \frac{Base}{Hypotenuse}[/tex]

⇒ Base = 4 units and Hypotenuse = 5 units

So, Length of perpendicular = 3 units ( By using Pythagoras theorem)

[tex]\sin x=\frac{Perpendicular}{Hypotenuse}\\\\\implies\bf \sin x =\frac{3}{5}[/tex]

Answer:

360 degrees is  sum of the measures of the exterior angles of any convex polygon.

Step-by-step explanation:

Convex Polygon:

Exterior angle sum Property:

The sum of the measures of the exterior angles of any convex

polygon is 360°.

This is the polygon that is the boundary of a convex set and has

all the interior angles to be less than 180°.

The interior angles is 180(n-2) degrees and each exterior angle

is supplementary to its interior angle thereby resulting in the

sum of the exterior angles to be 360°.

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The amount after 15 years is approximately $26,971.67.

To calculate the amount after 15 years, we can use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:

In this case, P = $10,000, r = 0.0625 (6.25% as a decimal), n = 12 (monthly compounding), and t = 15. Substituting these values into the formula:

A = $10,000(1 + 0.0625/12)^(12*15) = $26,971.67 (approximately).

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Option B, [tex]p^{-9} *p^{0} * p^{2} *p^{5}[/tex] is not equal to [tex]p^{2}[/tex].

Here,

We have to find the expression is not equal to p^2.

What is Property of addition in power of number?

This property states that when multiplying two powers with the same base, we add the exponents.

Now,

Let an expression [tex]x^{a} x^{b}[/tex]

Then it can be written as, [tex]x^{a} x^{b} = x^{a+b}[/tex]

So, Option B is given as,

[tex]p^{-9} *p^{0} * p^{2} *p^{5} = p^{-9+0+2+5} = p^{-2}[/tex]

Which is not equal to [tex]p^{2}[/tex].

Similarly, we check all options.

We get only option B is not equal to [tex]p^{2}[/tex].

Hence,

Option B, [tex]p^{-9} *p^{0} * p^{2} *p^{5}[/tex] is not equal to [tex]p^{2}[/tex].

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-5 is in the domain of the function f(x)=5x-7, but not in the domain of the function g(x)√x-2. The domain of a function is the set of all acceptable input values.

The question is asking whether -5 is in the domain of the given functions, f(x)=5x−7 and g(x)√x−2. The domain of a function is the set of all permissible inputs or arguments, i.e. x-values that can be inserted into the function.

In the case of f(x)=5x-7, the domain is all real numbers, as we can substitute any real number into 'x' and obtain a valid result. Hence, -5, indeed, is in the domain of the function f(x). However, for the function g(x)√x-2, the domain is all non-negative real numbers since we can't take the square root of a negative number in the real number system, hence -5 is not in the domain of g(x).

Thus, the statement '-5 is not in the domain' would be true if we are referring to g(x). However, if we are referring to f(x), the statement would be false because -5 is in the domain.

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Answer:

She should deposit $35.00 in her account.

Step-by-step explanation:

The balance in Beth's checking account = $75.00

She must deposit enough money in her account to be able to pay the electric bill, which is = $110.00

So we have to subtract 75 from 110 to get how much more money she needs to deposit the electric bill.

$110.00 - $75.00= $35.00

She should deposit $35.00 in her account.

To find the largest positive integer $n$ such that $rac{(n + 1)^2}{n + 23}$ is an integer, we need to find the largest perfect square that is less than or equal to $n + 23$. The largest such $n$ is $41$.

To find the largest positive integer $n$ such that $rac{(n + 1)^2}{n + 23}$ is an integer, we can start by considering the numerator. The expression $(n + 1)^2$ is a perfect square, so it will always be divisible by $n + 23$ if $n + 23$ is also a perfect square. Therefore, we need to find the largest perfect square that is less than or equal to $n + 23$.

Let's consider some examples. If $n + 23 = 25$, then $n = 2$. If $n + 23 = 36$, then $n = 13$. If $n + 23 = 49$, then $n = 26$. If $n + 23 = 64$, then $n = 41$. Therefore, the largest value of $n$ such that $rac{(n + 1)^2}{n + 23}$ is an integer is $41$.

There are no positive integers $n$ that satisfy the given condition, and we cannot compute the largest such $n$.

To find the largest positive integer $n$ such that $\frac{(n + 1)^2}{n + 23}$ is an integer, we need to consider the factors of the numerator and denominator.

Let's expand the numerator, $(n + 1)^2$, using the binomial expansion formula:

$(n + 1)^2 = n^2 + 2n + 1$

Now, we divide this expression by $n + 23$ and express the result as an integer:

$\frac{n^2 + 2n + 1}{n + 23}$

We can use polynomial long division to divide $n^2 + 2n + 1$ by $n + 23$:

- (n - 21)
__________
n + 23 | n^2 + 2n + 1
- (n^2 + 23n)
_____________
-21n + 1
- (-21n - 483)
_____________
484

We obtain a remainder of 484. In order for the fraction to be an integer, the remainder must be 0. However, in this case, the remainder is not 0, which means that $\frac{(n + 1)^2}{n + 23}$ is not an integer for any positive integer $n$.

Therefore, there are no positive integers $n$ that satisfy the given condition, and we cannot compute the largest such $n$.

Complete question :-

There are exactly four positive integers $n$ such that \[\frac{(n + 1)^2}{n + 23}\] is an integer. Compute the largest such $n$.

Answer:  The correct name is (B) ∠S.

Step-by-step explanation:  We are given to find the correct name for the angle shown in the figure.

We can see in the figure that the rays RS and ST are intersecting at the point S. Therefore, RS and ST are making an angle at the point 'S'.

So, the name of the angle will be ∠S or ∠RST or ∠TSR.

First option is ∠R. This is not correct.

Second option is ∠S. This is the correct option.

Third option is ∠RTS. This is also not correct.

Fourth option is ∠SRT. This is not correct.

Thus, the correct option is (B) ∠S.

Doug can read 33 pages in one hour.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Total pages in a book= 231 pages

Time to read books= 7 hours

so, in 1 hour he can read = 231/7

                                       = 33 pages.

Hence, he can read 33 pages in one hour.

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Answer:

[tex]B=\frac{7A}{3}+25[/tex]

Step-by-step explanation:

We have been given an equation [tex]A=\frac{3}{7}(B-25)[/tex]. We are asked to find the value of B for our given equation.

Upon multiplying both sides of our equation by [tex]\frac{7}{3}[/tex], we will get:

[tex]\frac{7}{3}*A=\frac{7}{3}*\frac{3}{7}(B-25)[/tex]

[tex]\frac{7}{3}*A=B-25[/tex]

[tex]\frac{7A}{3}+25=B-25+25[/tex]

[tex]\frac{7A}{3}+25=B[/tex]

[tex]B=\frac{7A}{3}+25[/tex]

Therefore, the value of B is [tex]\frac{7A}{3}+25[/tex].

The regression models used by Jessica is such that A.) The linear model better represents the situation ... owes is decreasing by about the same amount every 6 months.

The linear regression model is best for a situation where there is a constant rate of change while the exponential model is for situations where change isn't constant.

Jessica's data shows that there is a constant rate of reduction in the amount to repay because the amounts are quite similar to each other as shown by the graph.

In conclusion, option A is correct.

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Answer:

120 ways

Explanation:

Since there are no repeating letters, and there are 5 total letters, there are 5!= 120 ways to arrange them. In other words, there are 5 slots to place the first letter in, then 4 slots for the second letter, 3 for the third, 2 for the fourth, and then the last letter goes in the 1 slot that is left.

I hope this is correct and if it is I hope it helps. I hope you have a great day and remember it doesn't matter what other people say or think about you, you are still and always will be strong, smart, and an amazing person. Have a wonderful day.

I am happy to help with anything.

The correct answer is -1

Graph of the line [tex]y = \frac{2}{3} x+490[/tex] is drawn with slope [tex]m = \frac{2}{3}[/tex] and y-intercept 490 and x-intercept = -735.

"Slope of the line is defined as the ratio of difference in the increment in y coordinates to the difference in increment in x-coordinates."

Formula used

standard equation of line

y = mx + c

m = slope of the line

c = y- intercept

According to the question,

Given equation of line,

[tex]y = \frac{2}{3} x+490[/tex]

Compare it with standard equation of line y = mx + c we get,

Slope [tex]m = \frac{2}{3}[/tex]

y-intercept = 490

Calculate x-intercept by putting y=0

x-intercept = -735

Now plot it on the graph as shown and join the points with slope [tex]m = \frac{2}{3}[/tex]

Hence, graph of the line [tex]y = \frac{2}{3} x+490[/tex] is drawn with slope [tex]m = \frac{2}{3}[/tex] and y-intercept 490 and x-intercept = -735.

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When polygon ABCDE is translated 3 units to the right and 4 units down, its shape and size remain unchanged, but its position on the coordinate plane changes, maintaining the same orientation and angles.

If a polygon ABCDE is translated 3 units to the right and 4 units down, the shape and size of the polygon will remain the same, but its position will change. Each vertex (point) of the polygon will move 3 units to the right on the x-axis and 4 units down on the y-axis. This type of transformation is known as a translation, which is a slide of the entire figure in a specific direction. As a result, the translated polygon will maintain the same orientation and angles; it will simply be in a different location on the coordinate plane.

The value of y when equals -7 would be equal to -7.

An equation represents equality of two or more mathematical expression.

When someone asks you to solve an equation, then they usually mean to find the values of the unknowns for which that equation would be true

Solutions to an equation are those values of the variables involved in that equation for which the equation is true.

We are given the equation as-3x+6y=-21

if x = -7 then we get;

-3x+6y=-21

Substitute;

-3(-7) +6y = -21

21 + 6y = -21

6y = -42

y = -7

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Answer:

The approximate remaining grass area is 144 square feet.

Explanation:

To find the area of the rectangular yard, we use the formula:

Area of rectangle [tex]= \text{length} \times \text{width} \)[/tex]

Given that the length is 20 feet and the width is 8 feet, we have:

Area of Rectangle [tex]= 20 \times 8 = 160 \text{ square feet} \)[/tex]

Next, we find the area of the equilateral triangle. Since we know the length of each side (5 feet) and an equilateral triangle can be divided into two congruent 30-60-90 triangles, we can use the formula for the area of an equilateral triangle:

Area of equilateral triangle [tex]= \frac{\sqrt{3}}{4} \times (\text{side length})^2 \)[/tex]

Plugging in the value of the side length (5 feet), we get:

Area of equilateral triangle  [tex]= \frac{\sqrt{3}}{4} \times (5)^2 \)[/tex]

Area of equilateral triangle  [tex]= \frac{\sqrt{3}}{4} \times 25 \)[/tex]

Area of equilateral triangle  [tex]= \frac{25\sqrt{3}}{4} \text{ square feet} \)[/tex]

Now, to find the remaining grass area after Pythagoras digs up the rose-bed section, we subtract the area of the equilateral triangle from the total area of the rectangle:

Remaining grass area [tex]= \text{Area of rectangle} - \text{Area of equilateral triangle} \)[/tex]

Remaining grass area  [tex]= \ 160 - \frac{25\sqrt{3}}{4} \)[/tex]

Using a calculator, we find:

Remaining grass area [tex]\approx 144.3 \text{ square feet} \)[/tex]

Rounded to the nearest foot, the approximate remaining grass area is 144 square feet.

Answer:

5 ways

Step-by-step explanation:

I got it correct on founders edtell

Answer:

96

Step-by-step explanation:

The area of the shaded triangle will be 96 mm² so option (B) is correct.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

As per the given two inscribed triangles.

The bigger one is the right-angle triangle.

The area of the right-angle triangle will be as,

A = 1/2 x 8 x (6 + 24)

A = 4 x 30= 120 mm².

The area of the smaller right-angle triangle,

a = 1/2 x 8 x 6 = 24 mm²

The area of the shaded triangle = 120 - 24 = 96 mm².

Hence "The area of the shaded triangle will be 96 mm²".

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Answer:

y= -5

Step-by-step explanation:

rewrite as standard form    [tex]4.2(y-(3-))=(x-2)^{2}[/tex]

(h.k) = (2, -3), P=2

y= -3 -P

y= -3 -2

y= -5