AB of rhombus ABCD passes through the point (6, 6) and is perpendicular to the graph of y=3/4x-11. CD is parallel to AB and passes through the point (-6, 10). Select the equation in slope-intercept form of the line that includes CD.
A. y=4/3x+2
B. y=-4/3x+2
C. y=-3/4x+2
D. y=3/4x+2​

Answer:

B. \(B = (4,-2)\)

Step-by-step explanation:

GIven that \(A = (-2, 2)\) and \(M = (1, 0)\), and that point M is the midpoint of AB, the midpoint can be determined as a vectorial sum of A and B. That is:

\(M = \frac{1}{2}\cdot A + \frac{1}{2}\cdot B\)

The location of B is now determined after algebraic handling:

\(\frac{1}{2}\cdot B = M - \frac{1}{2}\cdot A\)

\(B = 2\cdot M -A\)

Then:

\(B = 2\cdot (1,0)-(-2,2)\)

\(B = (2\cdot 1, 2\cdot 0)-(-2,2)\)

\(B = (2,0) -(-2,2)\)

\(B = (4,-2)\)

Which corresponds to option B.

The coordinate of point B will be (4, -2). Then the correct option is B.

Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.

Point A is located at (-2, 2), and point M is located at (1,0).

If point M is the midpoint of AB.

Then the location of point B will be

We know that the mid section formula

\(\rm (x, y) = \left ( \dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2} \right)\)

Then the formula can be written as

x₂ = 2x - x₁ and y₂ = 2y - y₁

Then we have

x₂ = 2 × 1 + 2

x₂ = 4

y₂ = 2 × 0 - 2

y₂ = - 2

Then the coordinate of point B will be (4, -2).

Thus, the correct option is B.

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Answer:

Dependent variable → bacteria cell increase or population

Independent variable → time variable

Step-by-step explanation:

An independent variable has direct effect on the dependent variable. The independent variable can stand on it own and it is not change by the other variable you are trying to measure. The independent variable have direct effect on the dependent variable.

A dependent variable is actually the variable being tested in an experiment. The dependent variable is actually dependent on the independent variable.

The dependent variable in this scenario is the bacteria cell increase or the bacteria cell multiplication.  The bacteria cell increase is dependent on the time . The time variable is the independent  variable as it can stand on it own .

Dependent variable → bacteria cell increase or population

Independent variable → time variable

Answer:

The answer is Yes, No, No, Yes, Yes

Answer:

here,

Step-by-step explanation:

a.No

B.No

C.No

D.Yes

e.Yes

Using an algebraic equation to represent the word problem, the smallest integer is 1

This is a way of representing mathematical problems with words. To solve this, we have to use algebraic equations or expressions.

Let the integers be represented as

We can write an equation from the word problem given as

7 × (x + 2) = 15 + [x + (x + 4)]

7x + 14 = 15 + x + x + 4

7x + 14 = 15 + 2x + 4

collect like terms

7x - 2x = 15 - 14 + 4

5x = 5

Divide both sides by coefficient of x

5x / 5  = 5 / 5

x = 1

The smallest integer is 1

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Translation:

Find the smallest of three consecutive odd integers such that 7 times the middle integer is 15 more than the sum of the first and third integers

The quotient is 2x² - 7 and the remainder is -12.

How to perform polynomial division?

To perform this polynomial division, we use the long division method, where we divide the leading term of the dividend by the leading term of the divisor to obtain the first term of the quotient. Then, we multiply the entire divisor by this term and subtract the result from the dividend. We repeat this process with the new dividend until we obtain a remainder of degree less than the divisor.

Here is the long division:

2x² - 7

--------------------

x² + 1 | 2x⁴ + 0x³ + 0x² - 7x - 12

- (2x⁴ + 0x²)

--------------

-7x² - 7x

+ ( -7x² - 7x)

--------------

-12

Therefore, the quotient is 2x² - 7, and the remainder is -12.

So we can express the division as:

2x⁴ - 7x - 12 = (x² + 1)(2x² - 7) - 12

Hence, the quotient is 2x² - 7 and the remainder is -12.

This is a problem of division.

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Answer:

The linear equation satisfying the given condition is,

\(x=t+15\)

where x is Ravi's age and t is the number of years

(after 10 years (t=10) his age becomes 25)

Step-by-step explanation:

Let x be Ravi's age

Now, his  current age is unknown, but if you add 10 to it, then it becomes 25, so

x + 10 =25

so, his current age is x = 25 =10

x = 15

Now, we find the linear equation satisfying the given condition,

Let t be the number of years that have passed since the present time

so, if 0 years have passed, his age will be 15 years

after 1 year, his age will be 16 years

after 10 years, his age will be 25 years and so on

so

\(x = t + 15\)

this satisfies the given condition, since if we add ten years i.e t = 10,

then we get 25

The equation is:

Work/explanation:

Here's the linear equation for Ravi's age.

Ravi's age is x.

If you add 10 to x you get x + 10.

That gives 25.

So the linear equation is x + 10 = 25.

Answer:

n + (3n)+7 =

4n+7

And that is the answer

Step-by-step explanation:

The person that is correct among the students is Frank who said the pencils are an example of parallel lines.

Parallel lines are lines that can never meet. These are lines that run a direction that is quite opposite to each other as we can see from the image. It is clear that the lines as shown are not able to meet at any point even if they are extended.

Thus, the person that is correct among the students is Frank who said the pencils are an example of parallel lines.

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we can conclude that 2/3 is not equal to 4/5.

To determine if 2/3 is equivalent to 4/5, we can compare the fractions by checking if their ratios are equal. The ratio of 2/3 can be written as 2:3, while the ratio of 4/5 can be written as 4:5.

To check if the ratios are equal, we can cross-multiply and see if the products are equal. Cross-multiplying means multiplying the numerator of the first fraction with the denominator of the second fraction, and the numerator of the second fraction with the denominator of the first fraction.

For 2/3 and 4/5, we have:

2 * 5 = 10

3 * 4 = 12

Since 10 is not equal to 12, we can conclude that 2/3 is not equivalent to 4/5.

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The measure of the hypotenuse of the right-angle triangle is 53.21 feet.

Given that:

Perpendicular, P = 50 feet

Angle, Ф = 70°

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

The measure of the hypotenuse of the right-angle triangle is calculated as,

sinФ = P/H

sin 70° = 50 / x

x = 53.21 feet

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Answer:

x=4

x=2.5

Step-by-step explanation:

2x² - 3x - 20 = 0

assign a, b, and c using ax² + bx + c = 0

so a = 2

b = -3

and c = -20

then you plug that into the quadratic formula which gets you:

\(x=\frac{-(-3)+\sqrt[]{(-3)^{2}-4*2*(-20) } }{2*2}\)

It looks complicated but it's not so bad if you take it one step at a time

a negative negative is a positive, so that -(-3) in the front is just 3

Inside the square roots sign we can evaluate the power: -3 squared is 9

and -4 times 2 is -8 and -8 times -20 is 160

then on the bottom, 2 times 2 is 4

The equation is now

\(x=\frac{3+\sqrt{9+160} }{4}\)

9+160=169, and the square root of 169 is 13

\(x=\frac{3+13}{4}\)

3 + 13 = 16

16 divided by 4 is 4

so your first answer is 4

Now you have to do it again with a subtraction sign in front of the square root. The good thing is all the steps are the same until the last one. (We're not actually changing the contents of the root, just what we do with the result)

so when where we used to have \(x=\frac{3+13}{4}\) its going to be \(x=\frac{3-13}{4}\)

3- 13 = -10

and -10 divided by 4 = -2.5

Using opposite by the same vertex and supplementary angles, it is found that the measure of angle 4 is of 66º.

In this problem, angles 5 and 7 are opposite by the same vertex, hence:

m<7 = m<5 = 114º.

Angles 4 and 5 are supplementary, hence:

m<4 + m<5 = 180º.

m<4 = 66º.

The measure of angle 4 is of 66º.

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Answer:

Add all the digits of the number, then check if that sum is divisible by 9. If yes, we know the number is divisible by 9.

Answer: 4.27% of adults in the USA have stage 2 high blood pressure.

Step-by-step explanation:

Let x be a random variable that denotes a person with high blood pressure .

Given: Average blood pressure: \(\mu=122\)

Standard deviation: \(\sigma=22\)

Someone qualifies as having Stage 2 high blood pressure if their systolic blood pressure is 160 or higher.

The probability that an adult in the USA have stage 2 high blood pressure:

\(P(x\geq160)=P(\dfrac{x-\mu}{\sigma}}\geq\dfrac{160-122}{22})\\\\=P(z\geq1.72)\ \ \ [z=\dfrac{x-\mu}{\sigma}]\\\\=1-P(z<1.72)\\\\=1-0.9573\ \ [By\ p-value\ table]\\\\=0.0427=4.27\%\)

Hence, 4.27% of adults in the USA have stage 2 high blood pressure.

Answer:

Radius = 5 units

Diameter = 10 units

Circumference = 10π units

Area = 25π square units.

Step-by-step explanation:

i choose diameter.

Let's say the diameter of the circle is 10 units.

The radius of the circle can be found by dividing the diameter by 2:

Radius = Diameter / 2 = 10 / 2 = 5 units

The circumference of the circle can be found using the formula:

Circumference = 2πr = 2π * 5 = 10π units

The area of the circle can be found using the formula:

Area = πr^2 = π * 5^2 = 25π square units.

So, for a circle with a diameter of 10 units:

Radius = 5 units

Diameter = 10 units

Circumference = 10π units

Area = 25π square units.

The net area of the paper needed is 4.125 square feet.

A cuboid is a three-dimensional closed figure which has volume along with surface area.

The volume of a cuboid is the product of its length, width, and height.

The total surface area of a cuboid is 2(lw + wh + wl) and the lateral surface area is 2(l + w)×h.

Given, The gift is 1.5 feet tall and one of the bases is 9 inches = 0.75 by 0.5 feet.

Therefore the total surface area is,

= 2(1.5×0.5 + 1.5×0.75 + 0.75×0.5).

= 2(0.75 + 1.125 + 0.375).

= 2(2.25).

= 4.5 square feet.

Now, She left one of the bases uncovered which have an area of 0.375 square feet.

Therefore, the net amount of paper needed is = 4.5 - 0.375.

= 4.125 square feet.

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Answer:

8 < \(\sqrt{71}\) < 9

Step-by-step explanation:

You need to find the perfect squares above and below 71

8*8= 64

9*9 =81

8 < \(\sqrt{71}\) < 9

Answer: No solution/Empty Set

Step-by-step explanation: When you factor the 2(-7+b), you get 2b, which when moved to the other side cancels out the variable

The dimensions of the room are approximately 7 meters by 10.5 meters.

In Mathematics, dimensions are referred to as measures of size such as length, width, and height of an object or a shape. A rectangle has length and width as its dimensions that define the area of a rectangle.

Let's start by using algebra to represent the information given in the problem. Let x be the width of the rectangular room, then the length is 1.5 times the width or 1.5x.

The perimeter of a rectangle is the sum of the lengths of all its sides, which can be expressed as:

\(\text{Perimeter} = 2(\text{length} + \text{width})\)

Substituting the values we have for length and width, we get:

\(\rightarrow35 = 2(1.5\text{x} + \text{x})\)

Simplifying the equation, we get:

\(\rightarrow35 = 2(2.5\text{x})\)

\(\rightarrow35 = 5\text{x}\)

\(\rightarrow\text{x}=\dfrac{35}{5}\)

\(\rightarrow\bold{x\thickapprox7}\)

So the width of the room is 7 meters.

To find the length, we can substitute x into the expression we have for the length:

\(\rightarrow\text{Length} = 1.5\text{x}\)

\(\rightarrow\text{Length} = 1.5(7)\)

\(\rightarrow\bold{Length=10.5}\)

So the length of the room is 10.5 meters.

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Answer:

Step-by-step explanation:

m<9= 126

m<4= 36

m<11= 36

m<14= 144

Answer/Step-by-step explanation:

1. Sin A = opp/hyp

Opp = 3

Hyp = 5

\( sin(A) = \frac{3}{5} \) (substitution)

\( sin(A) = 0.6 \)

2. Sin B = opp/hyp

Opp = 4

Hyp = 5

\( sin(B) = \frac{4}{5} \) (substitution)

\( sin(B) = 0.8 \)

3. Cos Q = adjacent/hypotenuse

Adjacent = 12

Hypotenuse = 13

\( cos(Q) = \frac{12}{13} \) (substitution)

\( cos(Q) = 0.9231 \) (4 decimal places)

4. Cos S = adjacent/hypotenuse

Adjacent = 5

Hypotenuse = 13

\( cos(S) = \frac{5}{13} \) (substitution)

\( cos(S) = 0.3846 \) (4 decimal places)

Answer:

y-1= -1/3(x+3)

Step-by-step explanation:

y-y1=m(x-x1)

y-1=m(x+3)

the slope is rise over run

the slope is -1/3

Answer:

y - 1 = 3/2 (x + 3)

Step-by-step explanation:

To find the equation of a line parallel to the given line and passing through the point (-3, 1), we can use the point-slope form of a linear equation. The point-slope form is given by:

y - y₁ = m(x - x₁)

Where (x₁, y₁) is the given point and m is the slope of the line.

First, let's calculate the slope of the given line using the two points (-2, -4) and (2, 2):

slope = (y₂ - y₁) / (x₂ - x₁)

= (2 - (-4)) / (2 - (-2))

= 6 / 4

= 3/2

Since the line we want to find is parallel to the given line, it will have the same slope. Therefore, the slope (m) of the new line is also 3/2.

Now we can substitute the values into the point-slope form using the point (-3, 1):

y - 1 = (3/2)(x - (-3))

y - 1 = (3/2)(x + 3)

The equation in point-slope form of the line parallel to the given line and passing through the point (-3, 1) is:

y - 1 = 3/2 (x + 3)

Hello, there.

To find the slope of a line, first you need to make sure which points this line passes through:

The slope \(m\) of a line, passing through the points \((x_0,~y_0)\) and \((x_1,~y_1)\) is given by the formula \(m=\dfrac{y_1-y_0}{x_1-x_0}\).

As we can see in the graph, this lines passes through the points \((0,~1)\) and \((1,~3)\), such that we can substitute these values on the formula to find its slope:

\(m=\dfrac{3-1}{1-0}\)

Subtract the values in both numerator and denominator

\(m=\dfrac{2}{1}=2~~\checkmark\)

This is the slope of this line.

Answer:

m=2

Step-by-step explanation:

use

\(y^2/x^2 - y^1/x^1\)

Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

Answer:

y=3x+8

Step-by-step explanation:

First of all, remember what the equation of a line is:

y = mx+b

Where:

m is the slope, and

b is the y-intercept

you find the slope by using this formula:

then we figure out it is 3

then graph to find the y-intercept which is 8

Answer:

y = 3x + 8

Step-by-step explanation:

Below is the image for the formula of the slope.

1. Subtract y values:
17 - 5 - 12
2. Subtract x values:
3 - (-1) = 4
3. Divide y/x
12 / 4 = 3
Therefore, the slope is 3.

Next, you need to find the y-intercept. This is our equation so far:
y = 3x + b
We can substitute any of the points given to us from the problem. I will use the first point: (-1, 5).

When substituting, you get:
5 = 3 ( -1 ) + b
5 = -3 + b
b = 8

Therefore, the equation is y = 3x + 8

Using an exponential function, it is found that:

It is modeled by:

\(y = ab^x\)

In which:

In this problem:

Thus, the equation is: \(y = 5(3)^x\)

16 hours later, the amount is:

\(y = 5(3)^{16} = 215233605\)

After 16 hours, there would be 215,233,605 tribbles.

8 hours later, the amount is:

\(y = 5(3)^{8} = 32805\)

After 8 hours, there would be 32,805 tribbles.

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Answer: $250. Step-by-step explanation: let the amount she need is $x. now. given that. 30℅ of x = $75. so. 30/100 × X = $75.

Usando conceptos de polígonos, se encuentra que la fórmula para el número de diagonales d, en función del número de lados n, viene dada por:

\(d = n - 3\)

---------------------

\(d = n - 3\)

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Answer:

(a) 1/6. One out of six sides will give you the desired result.

(b) 3/6. 3 out of 6 sides will give you the desired result.

(c) 2/3. 4 out of 6 sides will give you the desired result.