Which expression is missing from step 7?
OA.(d- e)²
OB. -2de
OC. (A+B)2
OD. A²+ B²

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

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:

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.

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:

Answer: The triangle is not possible.

Step-by-step explanation:

1) Find the missing angle

62+59+x=180

x=59

2) Use the Law of Sine to check if the triangle sides are the same.

The Law of sine means that Sine the angle and divide with the side across it will equal to same.

[tex]\frac{sin(x)}{x} =\frac{sin(y)}{y}[/tex]

Substitute the numbers.

[tex]\frac{sin(59)}{10} =\frac{sin(62)}{10}[/tex]

0.0636 = -0.0739

3) Solve

Since the decimals aren't the same, the triangle is not possible.

Answer:

[tex]y=x-5[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{4.4cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ \\are two points on the line.\\\end{minipage}}[/tex]

Given points:

Substitute the given points into the slope formula to find the slope of the line:

[tex]\implies m=\dfrac{-2-(-1)}{3-4}=\dfrac{-1}{-1}=1[/tex]

[tex]\boxed{\begin{minipage}{5cm}\underline{Point-slope Formula}\\\\$y-y_1=m(x-x_1)$\\\\where $m$ is the slope and\\ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]

Substitute the found slope and the point (4, -1) into the point-slope formula to create the equation of the line:

[tex]\implies y-(-1)=1(x-4)[/tex]

[tex]\implies y+1=x-4[/tex]

[tex]\implies y+1-1=x-4-1[/tex]

[tex]\implies y=x-5[/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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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;

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

and therefore the radius is

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:

One solution.

Explanation:

Let us try to solve the equation and see how many solutions it has.

The first step in solving the equation is to first simplify both the right-hand and the left-hand sides. This means adding all the like terms.

Next, we add 7 to both sides. This gives

dividing both sides by 3 gives

which is exactly one solution!

Therefore, our equation had one solution.

Using simple interest, the rate of interest on the amount that Samantha borrowed to buy the law equipment is 11.75%.

A simple interest system does not accumulate (compound) interest on both the principal and interest, unlike compound interest.

The simple interest uses the following formula, Interest = Principal x Rate x Period.

This simple interest formula can be reversed to find either the principal, rate, or period, as the case may be.

The loan amount = $800

Period of loan  = 9 months

Total interest paid = $70.50

Rate of interest = (Interest × 100)/(Principal × Time)

= 11.75% ($70.50 x 100)/($800 x 9/12)

Check:

Interest = $70.50 ($800 x 11.75% x 9/12)

Thus, Samantha's interest rate on the loan is 11.75%.

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Answer:

the anser is 1.09

Step-by-step explanation:

9.81 divided by 9 = 1.09

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

3/5 of the T-shirts of the shop are on sale

5/8 of those on sale are blue

1/3 of the blue shirts on sale are medium size.

First calculate how many of the shirts on sale are blue:

25/24 of the shirts on sale are blue

Then divide that number by three to know how many are medium size:

25/72 are blue and medium size

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:

hey bro listen

Step-by-step explanation:

you can't always

get the answers

here try to

do yourself and

see your potential.

Explanation

Given the expression

We are asked to find the remainder. We can use the remainder theorem. This can be seen below.

According to this theorem, if we divide a polynomial P(x) by a factor ( x – a); that isn't essentially an element of the polynomial; you will find a smaller polynomial along with a remainder.

All we need to do is to substitute the value of (a) in the numerator to get the remainder. a is represented in the denominator.

Therefore, we will have;

Answer:

Explanation:

Let x represent unknown side length

We can go ahead and find x using the Pythagorean Theorem as seen below;

Let's find sin A as seen below;

Let's find cos A as seen below;

Let's find sin B as seen below;

Let's find cos B as seen below;

Answer:

12

Step-by-step explanation:

Alicia has 3 sisters.

Connor has twice as many sisters.

Twice means "two times".

Connor has 2×3, that is 6 sisters.

Carly has twice (two times) as many sisters as Connor.

Carly has 2×6, or 12 sisters.

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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The required graph below which represents the given equation of the ellipse is (x +7)²/49 + (y-5)²/25 = 1. Which is the correct answer would be option (C).

An ellipse can be defined as a shape that looks like an oval circle.

The equation of the ellipse is (x +7)²/49 + (y-5)²/25 = 1 which is given in the question.

An asymptote is a line that a curve approaches, but never touches. Find the horizontal, vertical, and oblique asymptotes.

Center of the ellipse : (−7,5)

Vertex 1: (0,5)

Vertex 2: (−14,5)

We have attached the required graph below which represents the given

equation of the ellipse is (x +7)²/49 + (y-5)²/25 = 1.

Hence, the correct answer would be an option (C).

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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

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

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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Solution:

Given:

When the cardboard is folded to become a box (cuboid), it will have the following dimensions after the cut of squares from each corner;

The volume of a cuboid is given by;

Solve the quadratic equation by factorization;

Hence, the dimension of the original piece of cardboard is;

Therefore, the dimensions of the original piece of cardboard are 26 in by 22in

Solution:

Given the graph;

(a) The domain of a function is the set of values for which the function is real and defined. Thus, the domain D is;

The range is;

The zeros of the function are the points y=0;

(b) The equation of a parabola in vertex form is;

Thus, the equation is;

(c) Using the graph below;

The graph of g(x) has its intercept at (0,0).

The transformation goes as;

Vertical stretch 2units, reflection over the x-axis, horizontal shift to the the right 3 units, vertical shift up 8 units

Using (5,0);

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 equation that calculates the total pay of Madeline when she sells 'x' number of computers is "P = 20x + 80".

So, the equation for P will be:

Now, the equation can be:

(Refer the table attached below)

Therefore, the equation that calculates the total pay of Madeline when she sells 'x' number of computers is "P = 20x + 80".

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