What is the equation of the line that is perpendicular to the given line and passes through the point (2,6)?

Answer:  x = 2, y = 2

Step-by-step explanation:

[tex]y=x^2-3x+4\\x + y = 4\quad \implies y=4-x\\\\\underline{\text{Substitute y (in the first equation) with 4 - x:}}\\4-x=(4-x)^2-3(4-x)+4\\\\\underline{\text{Expand and distribute right-hand side:}}\\4-x=16-8x+x^2-12+3x+4\\\\\underline{\text{Simplify right-hand side:}}\\4-x=8-5x+x^2\\\\\underline{\text{Set left-hand side equal to zero (subtract 4 and add x):}}\\0=4-4x+x^2\quad \implies 0=x^2-4x+4\\\\\underline{\text{Factor and solve for x:}}\\0=(x-2)(x-2)\\0=x-2\\2=x[/tex]

Replace x with 2 in the second equation to solve for y:

x + y = 4

2 + y = 4

     y = 2

Answer:

x = 98

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the two opposite interior angles.

∠x is an exterior angle and

∠GFH and ∠FHG are the 2 opposite interior angles, hence

x = 53 + 45 = 98

The value of x is 98 degree.

If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles

The exterior angle of a triangle is equal to the sum of the two opposite interior angles.

∠GFH and ∠FHG are the 2 opposite interior angles to exterior angle 'x',

x = 53 + 45

x = 98

Hence, the value of x is 98 degree.

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ANSWER

The correct answer is B

EXPLANATION

The given sum is

[tex] \sqrt{ {x}^{2} {y}^{3} } + 2 \sqrt{ {x}^{3} {y}^{4} } + xy \sqrt{y} [/tex]

We need to remove the perfect squares.

[tex]\sqrt{ {x}^{2} \times {y}^{2} \times y } + 2 \sqrt{ {x}^{2} \times ( {y}^{2})^{2} \times x } + xy \sqrt{y} [/tex]

Let us split the radical sign for the factors to get;

[tex]\sqrt{ {x}^{2}} \times \sqrt{ {y}^{2}} \times \sqrt{y} + 2 \sqrt{ {x}^{2} } \times \sqrt{( {y}^{2})^{2}} \times \sqrt{x} + xy \sqrt{y} [/tex]

This simplifies to

[tex]xy \sqrt{y} + 2x {y}^{2} \sqrt{x} + xy \sqrt{y} [/tex]

Group similar terms to get:

[tex]xy\sqrt{y} + xy \sqrt{y} + 2x {y}^{2} \sqrt{x} [/tex]

Combine the similar terms to get:

[tex]2xy\sqrt{y} + 2x {y}^{2} \sqrt{x} [/tex]

The correct answer is B.

Answer: agree

Step-by-step explanation:

5(2)=10•2=20

Answer:

disagree

Step-by-step explanation:

Given

5x² = 20 ( divide both sides by 5 )

x² = 4 ( take the square root of both sides )

x = ± [tex]\sqrt{4}[/tex] = ± 2

x = 2 or x = - 2 are the solutions to the equation

Answer:

[tex]\large\boxed{V=\dfrac{4}{3}\pi R^3=\dfrac{D^3}{6}\pi}\\\\\boxed{V=\dfrac{500\pi}{3}\ in^3\approx523.33\ in^3}[/tex]

Step-by-step explanation:

[tex]\text{The formula of a volume of a sphere:}\\\\V=\dfrac{4}{3}\pi R^3\\\\R-radius\\\\\text{A diameter}\ D=2R\Rightarrow R=\dfrac{D}{2}.\\\\\text{Therefore}\\\\V=\dfrac{4}{3}\pi\left(\dfrac{D}{2}\right)^3=\dfrac{4}{3}\pi\left(\dfrac{D^3}{8}\right)=\dfrac{D^3}{6}\pi[/tex]

[tex]\text{We have the dimater}\ D=10in.\ \text{Substitute:}\\\\V=\dfrac{10^3}{6}\pi=\dfrac{1000}{6}\pi=\dfrac{500\pi}{3}\ in^3[/tex]

For this case we have that by definition, the volume of a sphere is given by:

[tex]V = \frac {4} {3} \pi * r ^ 3[/tex]

Where:

r: It is the radius of the sphere

We are told as data that the diameter of the sphere is 10in, so the radius is 5in:

[tex]V = \frac {4} {3} \pi * 5 ^ 3\\V = \frac {4} {3} \pi * 125\\V = \frac {500} {3} \pi\\V = 523.33in ^ 3[/tex]

Answer:

[tex]V = \frac {4} {3} \pi * 5 ^ 3\\V = \frac {4} {3} \pi * 125\\V = \frac {500} {3} \pi[/tex]

Any of the three given expressions can be used to find the volume of the sphere.

Answer:

(-3,4)

Step-by-step explanation:

That means to reflect the point across the y-axis... If you draw (3,4) on the coordinate plane you should see (-3,4) is the reflection across the y-axis from that point.

Answer:

P' = (- 3, 4 )

Step-by-step explanation:

Under a reflection in the y- axis

a point (x, y ) → (- x, y ), hence

P(3, 4 ) → P'(- 3, 4 )

Answer:

180°

Step-by-step explanation:

(8y+17)°=(6x-7)°

(3x-29)°+(8y+17)°=180°

so,

(3x-29)°+(6x-7)°=180°

To solve the expression (6x-7)+(3x-29), we combine like terms. The 'x' terms (6x + 3x) sum up to 9x and the constants (-7 and -29) sum up to -36. Therefore, the simplified expression is 9x - 36.

The student wants to solve the expression (6x-7)+(3x-29). To do this,  you should combine like terms, which means you should add together the terms that have the same variable.

Step 1: Add the 'x' terms together. This would give us 6x + 3x which equals 9x.

Step 2: Then add the constants together, in this case -7 and -29, you get -36.

So, the simplified result of the expression (6x-7)+(3x-29) is 9x - 36.

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[tex]\left(\dfrac{g}{f}\right)(x)=\dfrac{x^2-6}{3x+1}[/tex]

Answer:

Number of candy received by each kid, [tex]x=\frac{104}{8}=23[/tex]

Step-by-step explanation:

Let x be the pieces of candy each  kid will receive.

Total number of candy left with Carleen = 104

Number of kids for which she is distributing = 8

Number of candy received by each kid, [tex]x=\frac{104}{8}=23[/tex]

23 pieces of candy each kid will receive.​

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

According to the question,

The pieces of candy each  kid will receive will be x

Total number of candy left with Carleen = 104

The number of kids for which she is distributing = 8

The equation will be

[tex]x =\frac{104}{8}[/tex]

[tex]x = 23[/tex]

Here , the number of candies receive by each kid will be 23.

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Answer:

-8

Step-by-step explanation:

Answer:

4 cm.

Step-by-step explanation:

Area of the shape =

136 =  6 * 14 + (h/2)(12 + 14)      where the last part is the area of the trapezoid.

84 +  13h = 136

13h = 138 - 84 = 52

h = 4 (answer).

Answer:

[tex]\large\boxed{x<\dfrac{6}{7}}[/tex]

Step-by-step explanation:

[tex]\dfrac{7x}{3}<2\qquad\text{multiply both sides by 3}\\\\3\!\!\!\!\diagup^1\cdot\dfrac{7x}{3\!\!\!\!\diagup_1}<(3)(2)\\\\7x<6\qquad\text{divide both sides by 7}\\\\x<\dfrac{6}{7}[/tex]

Answer:

x<6/7

Step-by-step explanation:

Multiply by 3 from both sides of equation.

3*7x/3<2*3

Simplify.

7x<6

Divide by 7 from both sides of equation.

7x/7<6/7

Simplify, to find the answer.

x<6/7 is the correct answer.

I hope this helps you, and have a wonderful day!

Answer:

B

Step-by-step explanation:

It is a function because it passes the vertical line test... (There is no vertical line you can draw that will go through 2 or more than 2 points.)

Answer:

-8

Step-by-step explanation:

All you have to do is divide 56/7 and you get -8.

Hope this helps!

Feel free to ask if you have any questions!

When you divide 56 by -7, the result is -8. This means that -8 is the quotient or simplified expression obtained when dividing 56 by -7.

A simplified expression is a mathematical expression that has been reduced or simplified to its most concise or straightforward form. It typically involves combining like terms, applying rules of arithmetic, or simplifying fractions or radicals. Simplifying an expression helps to make it easier to understand and work with.

To simplify the expression 56 ÷ (-7) step by step, you can follow these steps:

Divide 56 by -7:

56 ÷ (-7) = -8

Therefore, the simplified expression is -8.

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Answer:

15/2 or 7.5

Step-by-step explanation:

cos(60)=1/2

so 15(1/2)=15/2 or 7.5

For this case we must evaluate the following expression:

[tex]15 * cos (60)[/tex]

By definition we have that the cosine of 60 degrees is [tex]\frac {1} {2}.[/tex] Then, substituting in the expression we have:

[tex]15 * \frac {1} {2} = \frac {15} {2} = 7.5[/tex]

So, we have:

[tex]15 * cos (60) = 7.5[/tex]

Answer:

[tex]15 * cos (60) = 7.5[/tex]

The first one. x and y only ever appear as first degree terms.

Second one, no y, third one xy isn't linear, fourth one x squared isn't linear.

Answer:

The first one: y - 2 = -5(x - 2)

Step-by-step explanation:

The probability the spinner lands on a prime number is 4/10 or 40%

Answer:

40%

Step-by-step explanation:

Prime numbers less than 10 are 2, 3, 5, and 7.  Assuming the sections are sized equally, then four out of ten sections is 40%.

Answer:

The resulting vector b - a is <-5 , 7>

The resulting vector 2a - b is <8 , -9>

Step-by-step explanation:

* Use the graph to solve the problem

- The vector a is <3 , -2>

- The vector b is <-2 , 5>

* We can add and subtract the vectors

∵ a = <3 , -2>

∵ b = <-2 , 5>

- To find b - a subtract a from b

∴ b - a = <-2 , 5> - <3 , -2> = <(-2 - 3) , (5 - -2)> = <(-5) , (7)>

∴ The resulting vector b - a is <-5 , 7>

* 2a means multiply vector a by 2

∵ a = <3 , -2>

∴ 2a = <(2 × 3) , (2 × -2) = <6 , -4>

* Now lets find the resulting vector 2a - b

- Subtract b from 2a

∵ 2a = <6 , -4>

∵ b = <-2 , 5>

∴ 2a - b = <6 , -4> - <-2 , 5> = <(6 - -2) , (-4 - 5> = <(8) , (-9)> = <8 , -9>

∴ The resulting vector 2a - b is <8 , -9>

Answer:

t = w/(11+r)

Step-by-step explanation:

To solve for t, we need to divide anything that t is multiplied to to get it on the other side of the equal sign.

w = t(11+r)

w/(11+r) = t

Answer:

t = w/(r + 11)

Step-by-step explanation:

Solve for t:

w = t (r + 11)

w = (r + 11) t is equivalent to (r + 11) t = w:

t (r + 11) = w

Divide both sides by r + 11:

Answer: t = w/(r + 11)

Answer:

[tex]\frac { 4 } { 5 } [/tex]

Step-by-step explanation:

We are given the following two points and we are to find the slope of the line which passes through these points:

[tex](3.-1)[/tex] and [tex](-2,-5)[/tex]

The formula of the slope is given by:

Slope = [tex] \frac { y _ 2 - y _ 1 } { x _ 2 - x _ 1 } [/tex]

Substituting the given coordinates in the above formula:

Slope = [tex] \frac { - 5 - ( - 1 ) } { - 2 - 3 } = \frac { 4 } { 5 } [/tex]

Answer:

it would be 7x+12y=140

The required system of equation is that can be used to find number of 7-inch plates and 12-inch plates is:

        [tex]x+y=15\\7x+12y=140[/tex]

Given information:

The plates in a kitchen cabinet = 15

The diameter of each plates is either 7 inch or 12 inch.

The diameter of all 12[tex]x+y=15[/tex] plates combined is 140 inches.

Now, for the system of equation:

According to the question:

The number of 7 inches plates is [tex]x[/tex]

The number of 12 inches plates is [tex]y[/tex]

So, by the information given in the question:

[tex]x+y=15[/tex]

Because, there are 15 plates in the cabinet we can write the above equation.

Now, the sum of diameters of all plates is 140, that is also given in the question.

Hence, we can write the second equation as:

[tex]7x+12y=140[/tex]

Hence, The required system of equation is that can be used to find number of 7-inch plates and 12-inch plates is:

[tex]x+y=15\\7x+12y=140[/tex]

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Answer:

OE. (2,0)

Step-by-step explanation:

Since x is by itself x equals 1 so the x value would be 1/1. The y intercept is 2 which means you began on the y axis 2 and x axis 0 and then you move 1/1 from that spot because of your x value or slope.

Answer:

112

Step-by-step explanation:

Monday=14

Tuesday=2x14=28

Wednesday= 2x28=56

Thursday= 2x56=112

Answer:

The plant increased a total of 4 inches. Week 3 the plant increased 8 inches and week 4 the plant was 12 in, now subtract 12-8= 4

Answer:

The plant increased a total of 4 inches.  

Week 3, the plant was 8in and week 4, the plant was 12in.

To find our solution, subtract 8 from 12

12-8=4

Step-by-step explanation:

For this case we must simplify the following expression:

[tex]\frac {\frac {4t ^ 2-16} {8}} {\frac {t-2} {6}} =[/tex]

Applying double C we have:

[tex]\frac {6 (4t ^ 2-16)} {8 (t-2)} =[/tex]

Simplifying:

[tex]\frac {3 (4t ^ 2-16)} {4 (t-2)} =[/tex]

We take common factor 4 from the parentheses of the numerator:

[tex]\frac {3 * 4 (t ^ 2-4)} {4 (t-2)} =[/tex]

We simplify:

[tex]\frac {3 (t ^ 2-4)} {(t-2)} =[/tex]

We factor the numerator:

[tex]t ^ 2-4 = (t + 2) (t-2)[/tex]

We rewrite the expression:

[tex]\frac {3 (t + 2) (t-2)} {(t-2)} =[/tex]

We simplify:

[tex]3 (t + 2) =\\3t + 6[/tex]

Answer:

[tex]3t + 6[/tex]

Answer:

Step-by-step explanation: 26+2c=312

Now we solve for c.

Subtract 26 on both sides giving 2c=286

So c=143

This is the equation in numbers translated (n is a number)

26 + 2n = 312

We have to find what the number (n) is. This means we must isolate n. To do this you must subtract 26 to both sides

26 - 26 + 2n = 312 - 26

0 + 2n = 286

2n = 286

To further isolate n you must divide 2 to both sides

2n/2 =286/2

n = 143

Check:

26 + 143*2 = 312

26 + 286 = 312

312 = 312

The number is 143

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

C

Step-by-step explanation:

A major arc is an arc that is greater than 180 degrees.

A minor arc is an arc less than 180 degrees.

An acute angle is an angle less than 90 degrees.

A central angle is the angle created in the center of a circle with 2 sides being the radius.

Thus, we can see in the figure that we are talking about the angle so we can eliminate major arc and minor arc.

Now, we clearly see that the angle is greater than 90 degree so it cannot be acute angle.

The correct answer is central angle as it goes with the definition.

Final answer:

AOR or Adjusted Odds Ratio is used in medicine as a measure of association between exposures and outcomes, and it tends to overestimate the RR for common diseases.

Explanation:

The term AOR refers to the Adjusted Odds Ratio, which is a statistical measure used to describe the strength of association or non-independence between two binary data values in epidemiology and other fields. In comparison to the Relative Risk (RR), the AOR is a more complex measure that takes into account additional variables that may affect the outcome. In the context of disease prevalence, when a disease is uncommon (around 5% prevalence or less), the AOR can closely approximate the RR. However, for more common diseases (for example, with a 40% prevalence of hypertension), the odds ratio tends to overestimate the risk compared to the RR, diverging more as the prevalence increases.