What is the measure of the base of the rectangle if the area of the triangle is 28 ft?

Given:

f(x)=6x+3

Required:

To calculate the average rate

Explanation:

Required answer:

30

Explanation

The quotient is the number obtained by dividing one number by another

for example:

the quotient of a and b is

so

Step 1

Let

number 1=23x

number 2=15 t

so, the quotient would be

therefore, the answer is C:

I hope this helps you

Given:

To Determine: The identity that is equivalent to the given tangent

Note that, the identity rule below would be applied

Also,

And also,

From the given tangent, we can re-write it as below:

Therefore:

Also:

And also,

It can be observed from the option provided, the correct options is

I and III only

The property of a rhombus regarding the two diagonals states that they bisect each other at right angles.

Hence, option D is the correct answer.

Recall the following trigonometric identities. If the legs of the right triangle have lengths a and b, the hypotenuse has length c, and the side a is adjacent to an angle θ, then:

Then, for the given right triangle:

Then, x and y are given by the expressions:

Therefore, the answers are:

The given data  is incorrect, k does not constitute a constant, but rather y does not varies directly to x.

We may have 11=7k for the initial point, implying that k=11/7.

Again for second point, we'd have 13=8k, which means k=13/8.

Using proportions, we can see that 11/7 doesn't really equal 13/8: cross multiply and you get 11*8=7*13, or 88=91.

Thus, this is incorrect, k does not constitute a constant, but rather y does not varies directly to x.

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The complete question is-

Determine whether y varies directly with x. If so, find the constant of variation k and write the equation.

x y

7 11

8 13

9 15

10 17

Answer:

the anser is 1.09

Step-by-step explanation:

9.81 divided by 9 = 1.09

Answer

Explanations:

The product of two integers using the partial product is expressed using the distributive law as shown:

Expanding the result using the distributive law as shown;

SOLUTION

Given the question on the question tab;

Explanation:

Final answer:

The philosophy of dilation is to resize uniformly the figure in question. Under this intuitive idea, dilation is the answer. Now, what does uniformly mean here?

It means that, as can be seen in the figure, the length of every side of the right triangle can be calculated by multiplying its corresponding side in the left ("small") triangle by a constant. However, this can be done from the right triangle to the left triangle; that's why I put a bidirectional arrow.

Finally, I want to give you some motivation for this concept: Every time you are resizing an image on your phone or in your computer, you're applying this concept.

The expression that can complete the blank is 6y^3

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

2/y^2=_/3y^5

Replace the blank with x

So, we have

2/y^2 = x/3y^5

Multiply both sides of the equation by 3y^5

So, we have

x = 3y^5 * 2/y^2

Evaluate the products

x = 6y^3

This means that the blank is 6y^3

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The number of red beads obtained from the jar is 12 beads.

The number of red beads that can be obtained from the jar is the ratio of red beads to the total number of beads multiplied by the total number of beads picked at random.

 Number of red beads obtained = (number of red beads / total number of beads) x number of beads picked

Total number of beads = 65 + 154 + 70 = 289

Number of red beads obtained = (65 / 289) x 54 = 12.14 ≈ 12 beads

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Explanation:

Length of green line = length of black line

Length of green line = 26

Total length of black line = h + h + *

Total length of black line = 2h + 8

Equate the two expressions

26 = 2h + 8

Collect the like terms

26 - 8 = 2h

18 = 2h

Isolate h by dividing both sides by 2

18/2 = 2h/2

h = 18/2

h = 9

The equation is 26 = 2h + 8

of the circumference is 21.2, we get that the diameter is

and therefore the radius is

Answer:

-6/5

Step-by-step explanation:

[tex]5x-6y=30 \\ \\ 6y-5x=-30 \\ \\ 6y=5x-30 \\ \\ y=\frac{5}{6}x-5[/tex]

Perpendicular lines have negative reciprocal slopes, so the answer is -6/5.

The first step is to simplify both sides of the equation. The equation can be written as

y^3 - 3^3 = 9y(y - 3)

For the left hand side, we would apply the difference of two cubes formula. it is expressed as

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

By comparing with the left hand side of the equation,

x = y and y = 3. It becomes

(y - 3)(y^2 + 3y + 3^2)

= (y - 3)(y^2 + 3y + 9)

The equation becomes

(y - 3)(y^2 + 3y + 9) = 9y(y - 3)

If we divide both sides of the equation by (y - 3), it becomes

(y - 3)(y^2 + 3y + 9)/(y - 3 = 9y(y - 3)/(y - 3)

y^2 + 3y + 9 = 9y

y^2 + 3y - 9y + 9 = 0

y^2 - 6y + 9 = 0

We would solve the quadratic equation by applying the method of factorisation. We would find two terms such that their sum or difference is - 6y and their product is 9y^2. The terms are - 3y and - 3y. The equation becomes

y^2 - 3y - 3y + 9

y(y - 3) - 3( y - 3) = 0

(y - 3)(y - 3) = 0

y - 3 = 0 twice

y = 3 twice

What is the LCM of 9 and 15? ​

we know that

9=(3^2)

15=(3)(5)

so

the LCM=(3^2)(5)=45

the answer is

Answer:

Step-by-step explanation:

Given that,

To find the standard form of the equation of the parabola with a focus at (0, 9) and a directrix y = -9.

What is a parabola?

A parabola is a cross-section cut out of the cone and represented by an equation

Focus of the prabola = (h , k + F ) =  (0, 9)

Since the directrix, y =  -9

F = -9

k + F = 9

k = 0

Vertex of the parabola = (h,  k  )

                                    =  (0, 0)

Standard equation of the parabola

( y - k ) = 4a (x - h)²

( y - 0 ) = 4a (x - 0)²

y = 4 * 9 x²

y = 36 x²

Thus, the required expression for the parabola with focus at (0, -9) and a directrix y = 9 is y = 36x².

.

A piece-wise function is a function that changes its value, based on the input

That is a function its range depends on the domain.

The correct answer is the third option

The scientific notation is [tex]5.72 * 10^{6}[/tex]

Factor out 1 of the powers of 10

[tex]= (5.5 * 10^{6}/10^{6} + 2.2 * 10^{5}/10^{6}) * 10^{6}[/tex]

Perform division of exponents:

[tex](5.5 * 10^{0} + 2.2 * 10^{-1}) * 10^{6}[/tex]

Convert Scientific notations to real numbers:

[tex]= (5.5 + 0.22) * 10^{6}[/tex]

Combine real numbers:

[tex]= (5.72) * (10^{6})[/tex]

Convert to proper Scientific notations:

[tex]= 5.72 * 10^{6}[/tex]

Manually check answer

= (5.5 x 1000000) + (2.2 x 100000)

= 5500000 + 220000

= 5720000

[tex]= 5.72 * 10^{6}[/tex]

What are Scientific notations?

Scientific notation is a way to display extremely big or extremely small numbers in a more understandable way. We are aware that full numbers can go on forever, but we are unable to write such enormous figures on paper. Additionally, a simpler method of representation was required for the numbers that appear at the millions place following the decimal. This makes it challenging to express a small number of integers in their enlarged form. We thus employ scientific notations. Learn general forms for numbers as well.

Rules for Scientific Notation

We must adhere to the following rule in order to calculate the power or exponent of 10:

The base must always be 10.

Exponents that are non-zero integers must be either positive or negative in order to be used.

The coefficient's absolute value is more than or equal to 1, but it must be less than 10.

Positive and negative numbers, including whole and decimal values, can be coefficients.

The remaining significant digits of the number are represented by the mantissa.

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The term in the AP whose value is 201 / 2 is 71.3.

The first term of an arithmetic progression is 5 and the common difference is - 3/2.

The formula of the arithmetic progression can be described as follows:

nth term = a + (n - 1)d

where

Therefore, using the arithmetic progression formula,

a = 5

d = 3 / 2

nth term = 201 / 2

let's find the term(n)

Therefore,

- 201 / 2 = 5 + (n - 1) - 3 / 2

- 201 / 2 = 5  - 3 / 2 n  + 3 / 2

- 201 / 2  - 3 / 2 - 5 =  - 3 / 2 n

- 107  =  -3 / 2 n

-3n = - 214

n = 214 / 3

n = 71.3

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ANSWER

EXPLANATION

We want to find the equation of the perpendicular bisector of the line segment with the given endpoints.

To do this, we first have to find the slope of the given line, since the slope of a line perpendicular to a given line is the negative inverse of the slope of the line.

Then, we have to find the midpoint of the given line since the line is a bisector, it passes through the midpoint of the given line segment.

To find the slope of the line, apply the formula for the slope of a line:

where (x1, y1) and (x2, y2) are the two endpoints of the line segment

Hence, the slope of the line is:

The negative inverse of this is:

To find the midpoint of the endpoints, apply the formula for midpoint:

Hence, the midpoint of the given endpoints are:

Now, we have the slope and an endpoint of the perpendicular bisector.

To find the equation of the line, we have to apply the point-slope method:

Therefore, the equation of the perpendicular bisector of the line segment is:

1. The decrease in dollars, based on a 7.5 percent decrease, is $615.

2. The balance in the account at the end of last year was $7,585.

A percentage is a ratio or proportion of a variable in another.

For instance, the percentage decrease in the investment account was 7.5%, which in dollar terms amounts to $615.

The percentage reference gives an idea of the investment status and the fractional effect that the decrease had on it.

Initial investment = $8,200

Decrease in investment = 7.5%

Decrease in dollars = $615 ($8,200 x 7.5%)

Balance = $7,585 ($8,200 - $615)

Thus, Tammy's investment account decreased to $7,585 by $615, representing a 7.5% decrease.

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Answer:

[tex]\textsf{The quotient is $\boxed{10}\;x+\boxed{16}$}[/tex]

[tex]\textsf{The remainder is $\boxed{28}\:x^2+\boxed{10}\:x+\boxed{22}$}[/tex]

Step-by-step explanation:

Definitions

Dividend: The polynomial which has to be divided.

Divisor: The expression by which the dividend is divided.

Quotient: The result of the division.

Remainder: The part left over.

Long Division Method of dividing polynomials

Given:

[tex]\textsf{Dividend}: \quad 10x^4-14x^3-10x^2+6x-10[/tex]

[tex]\textsf{Divisor}: \quad x^3-3x^2+x-2[/tex]

Therefore:

[tex]\large \begin{array}{r}10x+16\phantom{)}\\x^3-3x^2+x-2{\overline{\smash{\big)}\,10x^4-14x^3-10x^2+6x-10\phantom{)}}}\\{-~\phantom{(}\underline{(10x^4-30x^3+10x^2-20x)\phantom{-b)}}\\16x^3-20x^2+26x-10\phantom{)}\\-~\phantom{()}\underline{(16x^3-48x^2+16x-32)\phantom{}}\\28x^2+10x+22\phantom{)}\\\end{array}[/tex]

Solution:

[tex]10x+16+\dfrac{28x^2+10x+22}{x^3-3x^2+x-2}[/tex]

[tex]\textsf{The quotient is $\boxed{10}\;x+\boxed{16}$}[/tex]

[tex]\textsf{The remainder is $\boxed{28}\:x^2+\boxed{10}\:x+\boxed{22}$}[/tex]

ANSWER

YES, the base is 4 ......option B

Answer:

Equation of line is given as y = mx + c, where m is the gradient and c is the y-intercept.

First find the gradient. Formula for gradient is given as (y2-y1)÷(x2-x1) or (y1-y2)÷(x1-x2).

Gradient = (2-0)÷(0-4) = -1/2

Equation of line is y = -1/2x + c

Substitute either one of the points into the equation to find c.

0 = -1/2(4) + c

c = 2

Hence, the equation of the line is y = -1/2x + 2.

Answer:

6

Step-by-step explanation:

Using the intersecting chords theorem,

[tex]x^2=36 \\ \\ x=6 (x>0)[/tex]

Applying the Pythagorean Theorem, the ladder's height from the ground is: 24.3 ft.

If we know any two sides of a right triangle, the Pythagorean Theorem can be used to find the length of the third side, c, if c is the longest side, and a and b are the shorter sides of the right triangle, we ill have the equation:

c² = a² + b².

The ladder forms a right triangle with the wall of the building. Therefore:

Substitute

25² = 6² + b²

b = √(25² - 6²)

b = 24.3 ft.

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We will have the following:

First, we find the slope:

So, the equation that represents the line is:

So:

***Explanation***

We are given the points (-2, 1) & (2. 1).

From this we cans see that the line passes both times through y = 1.

We also know that the slope (m) is given by:

So the slope for this line will be:

Now, we also know that the equation of the line in general form is given by:

So, the equation of the line will be given by:

So the function is a constant value, thus a horizontal line.

***Explanation for the general form of a line***

The general form of a line is given by:

Here "x" & "y" are two variables; "x1" & "y1" are the component of a point that belongs to that lline and "m" is the slope of that line. We remember that (x1, y1) can be any point that belongs to the line.

So, we simply replace the values, in our case I willl solve for (-2, 1), but we could also use (2, 1), the solution at the end will be the same.

So: