Which is the simplified form?

Answer:

No solution is possible from the information provided

Step-by-step explanation:

you didn't include the function.

Answer:

10

Step-by-step explanation:

d = √(x2  -x1)² + (y2 - y1)²

√(-6 - 0)² + [1 - (-7)]²

√(-6)² + (8)²

√(36) + (64)

√100

= 10

Answer:

2&3

Step-by-step explanation:

Answer:

Mean= 44.2

Median=45

Mode=6

Range=50

Step-by-step explanation:

Mean= (10x1 +30x2 + 40x3 +50x2 +60x4)/12

= 530/12

=44.17

=44.2

Median= 40+50 /2

=45

Mode= 6

Range= 60-10

=50

Answer:

Perimeter = 30

Area = 30

Step-by-step explanation:

[tex](x+8)^2 -x^2 = 12^2[/tex]

[tex]x^2 +16x +64 - x^2 = 144[/tex]

[tex]16x+64=144[/tex]

[tex]16x = 80[/tex]

[tex]x = 5[/tex]

Double check:

[tex]\sqrt{12^2 + 5^2} = (5+8)\\\sqrt{12^2 + 5^2} = 13\\13 = 13[/tex]

Perimeter:

[tex]12+5+13=30[/tex]

Area([tex]\frac{1}{2}bh[/tex]):

[tex]\frac{1}{2}[/tex] × 12 × 5 = 30

According to Pythagorean theorem,

Δ  (Hypotenuse)² = (1st Leg)² + (2nd Leg)²

⇒  (x + 8)² = x² + 12²

⇒  x² + 64 + 16x = x² + 144

⇒  16x = 80

⇒ x = 5

Hypotenuse = (x + 8) = (5 + 8) = 13

1st Leg = 5

2nd Leg = 12

We know that : Perimeter is the Sum of all sides of the Triangle

⇒  Perimeter = Hypotenuse + 1st Leg + 2nd Leg

⇒  Perimeter = 13 + 5 + 12

⇒  Perimeter = 30

We know that :

[tex]\bigstar \ \ \boxed{\sf{\textsf{Area of a Triangle is given by} : \dfrac{1}{2} \times Base \times Height}}[/tex]

Base = 1st Leg

Height = 2nd Leg

[tex]\implies \sf{\textsf{Area of the Triangle} = \dfrac{1}{2} \times 5 \times 12}[/tex]

[tex]\implies \sf{\textsf{Area of the Triangle} = 30}[/tex]

Answer: the 23rd term of the arithmetic sequence=91

Step-by-step explanation:

The nth term of an arithmetic sequence is given as

an=a+  (n-1) d

Given common difference , d=4 and

first term is a^1 = 3.

We have that

a₂₃=3+  (23-1) 4

a₂₃=3+  (22) 4

a₂₃=3+  88

a₂₃=91

the 23rd term of the arithmetic sequence=91

Step-by-step explanation:

[tex]8 log_{5}( {x}^{5} ) = 8 \times 5 log_{5}(x) \\ = 40 log_{5}(x) [/tex]

Answer:

(105 | 35)

the x-component (how much to the side) is left, the y-component right (how high)

The ordered pair that best estimates the time and cost at which the two stores charge the same amount is (110,35).

A graph can be defined as a pictorial representation of statistical data in graphical form. The points on the graph often represents the relationship between two or more things. The points are plotted in x-axis and y-axis respectively.

For the given situation,

The graph shows the time in x-axis and cost in y-axis.

Ordered pairs are often used to represent two variables.

The number which corresponds to the value of x is called the x-coordinate and the number which corresponds to the value of y is called the y-coordinate.

From the graph, the point of intersection of x-axis and y-axis gives the the time and cost at which the two stores charge the same amount.

Thus the point of intersection is x at 110 and y at 35.

⇒ [tex](x,y)=(110,35)[/tex]

Hence we can conclude that the ordered pair that best estimates the time and cost at which the two stores charge the same amount is (110,35).

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Answer:

See Explanation

Step-by-step explanation:

Given two variables (say x and y); the constant of proportionality is the ratio between these to variables.

Illustration; y is directly proportional to x

The above statement can be represented as:

[tex]y\ \alpha\ x[/tex]

When converted to an equation, you get

[tex]y\ =k x[/tex]

k, in the above equation, represents the constant of proportionality

Divide both sides by x to solve for k

[tex]k = \frac{y}{x}[/tex]

Take for instance: [tex]y = 3x[/tex]

Divide both sides by x

[tex]\frac{y}{x} = 3[/tex] --- 3 is the constant of proportionality

Answer:

A two-column proof uses a table to present a logical argument and assigns each column to do one job, and then the two columns work in lock-step to take a reader from premise to conclusion.

Step-by-step explanation:

Basically in simple terms, one side is the statements, and the otherside is the reasoning

Answer:

35square meters

Step-by-step explanation:

5×7=35

Answer:

[tex]AB = 21.3[/tex]

Step-by-step explanation:

Given

[tex]\sin(25) = \frac{9}{c}[/tex]

See attachment

Required

Find AB

We have:

[tex]\sin(25) = \frac{9}{c}[/tex]

Make c the subject

[tex]c = \frac{9}{\sin(25)}[/tex]

[tex]c = 21.3[/tex]

From the attached triangle;

[tex]AB = c = 21.3[/tex]

Hence:

[tex]AB = 21.3[/tex]

Answer:

-3

Step-by-step explanation:

This is a quadratic equation. Therefore, one way we can solve this is by using the quadratic formula, [tex]\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex] and [tex]\frac{-b-\sqrt{b^2-4ac} }{2a}[/tex].

a, b, and c represent the coefficients in our equation [tex]x^2-5x-24=0[/tex]. a represents the coefficient of the term with degree of 2, which is 1. b represents the coefficient of the term with degree of 1, which is -5. c represents the coefficient of the term with degree of 0, which is -24.

Let us plug them in the equation! Let us start with this one: [tex]\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex]

[tex]\frac{5+\sqrt{(-5)^2-4*1*(-24)} }{2} =\\\frac{5+\sqrt{25+96} }{2} =\\\frac{5+\sqrt{121} }{2} =\\\frac{5+11}{2} =\\\frac{16}{2} =\\8[/tex]

Oops! We are looking for the other solution. Let us plug in the values in this equation instead: [tex]\frac{-b-\sqrt{b^2-4ac} }{2a}[/tex]

[tex]\frac{5-\sqrt{(-5)^2-4*1*(-24)} }{2} =\\\frac{5-\sqrt{25+96} }{2} =\\\frac{5-\sqrt{121} }{2} =\\\frac{5-11}{2} =\\\frac{-6}{2} =\\-3[/tex]

I hope this helps! Let me know if you have any questions :)

Answer:

Hi, there the answer is -1

Step-by-step explanation:

Answer:

ummmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm   and i Oop

Step-by-step explanation:

Answer:

Solution given:

letA=(10,-4)

B=(-2,-4)

centre[C](h,k)=[tex]\frac{10-2}{2},\frac{-4-4}{2}=(+4,-4)[/tex]

radius=[tex]\sqrt{(4-10)²+(-4+4)²}=6[/tex]units

we have

Equation of a circle is;

(x-h)²+(y-k)²=r²

(x-4)²+(y+4)²=36

or.

x²-8x+16+y²+8y+16=36

x²-8x+8y+y²=36-32

x²-8x+8y+y²=4

The equation is (x-4)²+(y+4)²=36 or x²-8x+8y+y²=4.

Answer:

[tex] \rm\displaystyle (x - 4) ^{2} + {(y + 4)}^{2} = 36[/tex]

Step-by-step explanation:

the given points are the diameter points of circle because notice that in the both points y coordinate is the same therefore it's a horizontal diameter

since (10,-4),(-2,-4) are the diameter points of the circle the midpoint of the diameter will be the centre of the circle

remember midpoint formula,

[tex] \displaystyle M = \left( \frac{x _{1} + x_{2} }{2} , \frac{ y_{2} + y_{2}}{2} \right)[/tex]

let,

thus substitute:

[tex] \rm\displaystyle M = \left( \frac{10 + ( - 2)}{2} , \frac{ - 4 + ( - 4)}{2} \right)[/tex]

simplify addition:

[tex] \rm\displaystyle M = \left( \frac{8}{2} , \frac{ - 8}{2} \right)[/tex]

simplify division:

[tex] \rm\displaystyle M = \left( 4, - 4 \right)[/tex]

so the centre of the circle is (4,-4)

since it's a horizontal diameter the the redious will be the difference between the x coordinate of the Midpoint and the any x coordinate of the given two points but I'll use (-2,-4) therefore the redious is

[tex] \displaystyle r = 4 - ( - 2)[/tex]

simplify which yields:

[tex] \displaystyle\boxed{ r =6}[/tex]

recall the equation of circle

[tex] \displaystyle (x - h) ^{2} + {(y - k)}^{2} = {r}^{2} [/tex]

we acquire that,

therefore substitute:

[tex] \rm\displaystyle (x - 4) ^{2} + {(y - ( - 4))}^{2} = {6}^{2} [/tex]

simplify:

[tex] \rm\displaystyle (x - 4) ^{2} + {(y + 4)}^{2} = 36[/tex]

and we are done!

also refer the attachment

(the graph is web resource of desmos)

Answer:

I think 180

Step-by-step explanation:

I think 180 because it looks like M+n are supplimetary angles.

Sorry if this is wrong.

Answer:

choose B is the greatest variablity

Answer:

a =9  b=0 c=6

Step-by-step explanation:

6+9x^2

Rewrite

9x^2 +0x+6

This is in the form

ax^2+bx+c

a =9  b=0 c=6

Answer:

48

Hope this helps!

Answer:

the third option

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

to much working out but just as a summary section of working out

3*15=45

300+45=$345(1st year)

345+300=645

6.45*15=96.75

645+96.75=$741.75(2nd year)

keep on doing that until you beat 2 in list and use common sense to realise that (d) is too big, and (b, a) is too small so (c) is the correct amount. (this is quicker than actually doing all 20 years)

The total money with Lin after 20 years will be $4910.   

The formula for compound interest -

[tex]$A = P(1 + \frac{r}{n}) ^{nt}[/tex]

Given is that Lin is saving $300 per year in an account that pays 15% interest per year, compounded annually.

We can write the total money with Lin after 20 years as -

[tex]$A = P(1 + \frac{r}{n}) ^{nt}[/tex]

A = 300(1 + 0.15/1)²⁰

A = 300(1 + 0.15)²⁰

A = 300 x (1.15)²⁰

A = 300 x 16.37

A = 4910

Therefore, the total money with Lin after 20 years will be $4910.   

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Step-by-step explanation:

The Triangle Sum Theorem states that the interior angles of a triangle add up to 180 degrees. A square for an angle symbolizes that the angle is 90 °, as is the case with angle ∠ACB.

Therefore, as ∠CAB = 2x and ∠ABC = 3x, and angles ∠ACB, ∠CAB, and ∠ABC make up the interior angles of the triangle, we can say that ∠ACB + ∠CAB + ∠ABC = 180, so 90 + 2x + 3x = 180

90 + 2x + 3x = 180

90 + 5x = 180

subtract 90 from both sides to separate the x and its coefficient

5x = 90

divide both sides by 5 to separate the x

x = 18

(a) ∠CAB = 2x = 18(2) = 36

(b) ∠ABC = 3x = 18(3) = 54

(c) Any triangle with a 90° angle is called a right triangle. This has a 90° triangle, and is therefore a right triangle. Similarly, a 90° angle in a triangle is called a right angle.

Answer: 4) The center is located at (1, 3), and the radius is 6

Step-by-step explanation:

Solve the general equation of the circle.

x^2 -2x +1+ y^2-6y+9= 26+1+9 (x-1)^2+(y-3)^2=36=6^2

Hence, the coordinates of the center (1,3) And the radius will be 6

The center is located at (1,3) and the radius is 6.

"The center is the point from which all of the points on the circle are the same distance."

"The radius is the exact distance from the center to any point on the circle."

We have

[tex]x^{2} -2x+y^{2}-6y = 26\\[/tex]

Add 1 and 9 on both sides of equation

⇒[tex]x^{2} -2x+1+y^{2}-6y+9 = 26+1+9[/tex]

⇒[tex](x-1)^{2} +(y-3)^{2}= 36[/tex]

⇒[tex](x-1)^{2}+(y-3)^{2}=6^{2}[/tex].......(1)

We know the Standard form of equation of the circle

[tex](x-h)^{2}+(y-k)^{2} =r^{2}[/tex]

By comparing the standard form and equation (1)

Center (h, k) = (1, 3) and radius is 6

Hence, The center is located at (1,3) and the radius is 6.

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Answer:

The maximum angle is 84.3 degree.

Step-by-step explanation:

Sides of a triangle is

a = 6 , b = 11, c = 12

The maximum angle is opposite to c.

So,

[tex]a =6, b =11, c = 12 \\\\cos C =\frac{a^2+b^2-c^2}{2 ab}\\\\cos C =\frac{36+121-144}{2\times 6\times 11}\\\\cos C = \frac{13}{132}\\\\cos C = 0.0985\\\\C =84.3^o[/tex]

Answer:

The person above got it wrong its 84

Step-by-step explanation:

got it wrong on edge

Answer:

Red: 13/41

Yellow: 19/41

Blue: 9/41

Answer:

[tex] \displaystyle d)\frac{d ^{2} y}{d{x}^{2} } = 2 + \frac{ 42}{ {x}^{4} }[/tex]

Step-by-step explanation:

we would like to figure out the second derivative of the following:

[tex] \displaystyle y = \frac{ {x}^{4} + 7}{ {x}^{2} } [/tex]

we can rewrite it thus rewrite:

[tex] \displaystyle y = {x}^{2} + 7 {x}^{ - 2} [/tex]

take derivative in both sides:

[tex] \displaystyle \frac{dy}{dx} = \frac{d}{dx}( {x}^{2} + 7 {x}^{ - 2} )[/tex]

by sum derivation we obtain:

[tex] \displaystyle \frac{dy}{dx} = \frac{d}{dx}{x}^{2} + \frac{d}{dx} 7 {x}^{ - 2}[/tex]

by exponent derivation we acquire:

[tex] \displaystyle \frac{dy}{dx} = 2{x}^{} - 14 {x}^{ - 3}[/tex]

take derivative In both sides once again:

[tex] \displaystyle \frac{d ^{2} y}{d{x}^{2} } = \frac{d}{d x } (2{x}^{} - 14 {x}^{ - 3})[/tex]

use difference rule which yields:

[tex] \displaystyle \frac{d ^{2} y}{d{x}^{2} } = \frac{d}{d x } 2{x}^{} - \frac{d}{dx} 14{x}^{ - 3}[/tex]

use exponent derivation which yields:

[tex] \displaystyle \frac{d ^{2} y}{d{x}^{2} } = 2 + 42{x}^{ - 4}[/tex]

by law of exponent we get:

[tex] \displaystyle \frac{d ^{2} y}{d{x}^{2} } = 2 + \frac{ 42}{ {x}^{4} }[/tex]

hence, our answer is d)

Answer:

y-8x+7=0

Step-by-step explanation:

slope(m)=8

using slope intercept form of equation of staright line we get

y=mx+b

y=8*x+b

y-8x=b ................  eq(i)

since the line include the point (2,9) it satisfies the euation,

here x=2 and y=9

equation: y-8x=b

9-8*2=b

9-16=-b

-7=b

substituting the value of b in eq(i) we get

y-8x=-7

y-8x+7=0   is a required equation of the line.