a. Find the length of the midsegment of an equilateral triangle with side lengths of 12.5 cm.

b. Given that UT is the perpendicular bisector of AB, where T is on AB, find the length of AT given AT = 3x + 6 and TB = 42 - x.

c. Given angle ABC has angle bisector BD, where AB = CB, find the value of x if AD = 5x + 10 and DC = 28 - x.

Answer: There Ya go

Explanation:

Answer:

[tex] \sqrt{\frac{668}{\pi} } [/tex] feet  given the area is 167 ft squared

Step-by-step explanation:

Since our sector as a central angle of 90 degree then it is only a 4th of the whole circle.  The area of a circle is pi*r^2.  We will only be using a 4th of that since are sector is only a 4th of the circle.

So the formula will be using for the area of our sector is A=1/4 *pi*r^2.

We are given the area is 167 so replace A with 167.

167=1/4 * pi *r^2

Multiply both sides by 4.

167*4  =pi * r^2

668=pi * r^2

Divide both sides by pi

668/pi =r^2

Square root both sides

[tex] \sqrt{\frac{668}{\pi} } =r [/tex]

seventy five thousand

Answer:

Step-by-step explanation:

I can't add much to this. The answer is 75 thousand.

Final answer:

The Pythagorean theorem relates the lengths of the legs and hypotenuse of a right triangle. By substituting the given values into the equation, we can solve for x using the theorem. The rounded value of x is 3.6 (B).

Explanation:

The Pythagorean theorem relates the length of the legs of a right triangle, labeled a and b, with the hypotenuse, labeled c. The relationship is given by: a² + b² = c². This can be rewritten, solving for c: c = √(a² + b²).

In this case, we want to find the value of x using the Pythagorean theorem. Let's say that the lengths of the legs are 3 and x. Substituting these values into the theorem, we have:

3² + x² = c²

Now, we can solve for x by rearranging the equation:

x² = c² - 3²

x = √(c² - 3²)

Rounding to the nearest tenth, we can find the value of x to be approximately 3.6 (B).

Final answer:

The Pythagorean theorem allows us to calculate the length of the hypotenuse of a right triangle by squaring the lengths of the other two sides, adding them together, and then taking the square root. To round to the nearest tenth, we calculate and then round the final result accordingly.

Explanation:

To use the Pythagorean theorem to find x and round to the nearest tenth, we need to establish the components of the equation. The theorem states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). The formula is written as a² + b² = c².

However, the problem provided does not include the initial lengths to insert into the equation; hence, we cannot compute the value directly. Nonetheless, I can illustrate with a hypothetical example:

If we have a right triangle with legs of lengths 9 (a) and 6 (b), then the hypotenuse (c) can be found as follows:

c = √(9² + 6²)
c = √(81 + 36)
c = √117
c = 10.82, round off to the nearest tenth would be c = 10.8

In this example, we squared the lengths of the legs, added them together, and took the square root of the result to find the hypotenuse to the nearest tenth. The same steps apply to any right-angled triangle where you are given the lengths of the legs and need to find the hypotenuse using the Pythagorean theorem.

Answer:

The y-intercept is the point (0,2)

see the attached figure                

Step-by-step explanation:

we have

[tex]3y=-5^{x}+7[/tex]

we know that

The y-intercept is the value of y when the value of x is equal to zero

so

For x=0

substitute in the equation and solve for y

[tex]3y=-5^{0}+7[/tex]    

[tex]3y=-(1)+7[/tex]

[tex]3y=6[/tex]

[tex]y=2[/tex]

therefore

The y-intercept is the point (0,2)

using a graphing tool

see the attached figure                      

Answer: For Plato users plot a point on 2 at the y intercept.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let assume that x% = 200,000

Lets assume that 100 %  = 131,000,000 because it is the output value:

Therefore we have two equations:

x% = 200,000

100 %  =131,000,000

Now observe that the L.H.S of both the equations have same unit. So we can write it as:

100%/x% = 131,000,000/200,000

Now just simply solve the values:

Multiply both sides by x

100/x *x = 131,000,000/200,000 *x

100=655x

Now divide both the sides by 655.

100/655 = 655x/655

100/655=x

0.15267175572519=x

Therefore the answer is 200,000 is 0.15267175572519% of 131,000,000 ....

just an addition to the reply above, which is correct, so to the risk of sounding redundant.

if we take 131,000,000 to be the 100%, what is 200,000 off of it in percentage?  Bearing in mind that 1% of 131,000,000 is really 1,310,000, notice we simply chopped off two zeros, but that amount is larger than 200,000 and thus whatever 200,000 is, is less than 1%.

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 131000000&100\\ 200000&x \end{array}\implies \cfrac{131000000}{200000}=\cfrac{100}{x}\implies \cfrac{1310}{2}=\cfrac{100}{x} \\\\\\ 1310x=200\implies x=\cfrac{200}{1310}\implies x\approx 0.1526717557251908[/tex]

Answer:

4

Step-by-step explanation:

a term is simply separated by either a + or a - which means the terms here is 4x,2x,3x and 5

Answer:

4

Step-by-step explanation:

There are 4 terms in the equation 4x+2x(3x-5).

4x,2x,3x and 5

Answer:

see explanation

Step-by-step explanation:

Using the identity

(a + b + c)³ = a³ + b³ + c³ + 3 [ (a + b + c)(ab + bc + ac) - abc ], then

5³ = a³ + b³ + c³ + 3(5 × 10) - 3abc, that is

125 = a³ + b³ + c³ + 150 - 3abc, hence

a³ + b³ + c³ - 3abc = 125 - 150 = - 25

Using the cubic identity equation and the values given in the question, we can prove that if (a+b+c) = 5 and ab+bc+ac = 10, then a³+b³+c³-3abc equals -25.

The equation required to prove is derived from the expansion of the cubic identity (a+b+c)³. The equation is a³+b³+c³-3abc = (a+b+c)[(a+b+c)²-3(ab+bc+ac)]. Let's use the values given in the question which are (a+b+c) = 5 and ab+bc+ac = 10.

Therefore, we have proved that if (a+b+c) = 5 and ab+bc+ac = 10, then a³+b³+c³-3abc indeed equals -25.

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Answer:

3.7

Step-by-step explanation:

Inversely means we are taking the constant and dividing it.

So y varies inversely with x means "y=k/x".

k is a constant.  We can find the constant if they give us a point on this curve.

The constant is a number that doesn't change no matter your input and output.

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

So they actually give us k=8.88 and y=2.4 so let's input this:

[tex]2.4=\frac{8.88}{x}[/tex]

We need to solve this equation for x.  You can do your favorite thing in cross-multiply. But how, Freckles?  Well just slap a 1 underneath that 2.4.  You can do that because 2.4/1 is still 2.4.

[tex]\frac{2.4}{1}=\frac{8.88}{x}[/tex]

Cross-multiply:

[tex]2.4x=8.88(1)[/tex]

[tex]2.4x=8.88[/tex]

Divide both sides by 2.4:

[tex]x=\frac{8.88}{2.4}[/tex]

[tex]x=3.7[/tex] when [tex]y=2.4[/tex].

Answer:

Step-by-step explanation:

11C4 = 11! / (7!*4!) = 11 * 10 * 9 * 8 * 7!/ 7! * 4!

11C4 = 11*10 * 9 * 8 / 24

11C4 = 11*10 * 3

11C4 = 330

========

You can't do the second one. Permutations and Combinations always give an answer greater than 1 and integers.

[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ H(\stackrel{x_1}{2}~,~\stackrel{y_1}{1})\qquad K(\stackrel{x_2}{10}~,~\stackrel{y_2}{7}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{10+2}{2}~~,~~\cfrac{7+1}{2} \right)\implies \left( \cfrac{12}{2}~,~\cfrac{8}{2} \right)\implies (6,4)[/tex]

Answer:

The graph intersect the y-axis at (0,4.5)

The graph intersect the x-axis at (-3.6,0)

Step-by-step explanation:

The equation is;

-4y=-5x-18

Dived every term by -4

[tex]\frac{-4y}{-4} =\frac{-5x}{-4} -\frac{18}{-4} \\\\\\y=\frac{5}{4}x+\frac{9}{2}[/tex]

plot using a graph tool to view the liner graph as below

Answer:

C 8

Step-by-step explanation:

The average rate of change is given by

f(x2) -f(x1)

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

x2-x1

x2 = -3  and x1 = -5

Looking at the graph

f(x2) = f(-3) = 1

f(x1)= f(-5) =-15

Substituting these values into the equation

1 - (-15)

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

-3 - (-5)

1+15

----------

-3 +5

16

----

2

8

Answer: OPTION C.

Step-by-step explanation:

You need to use this formula:

[tex]averate\ rate\ of\ change=\frac{f(b)-f(a)}{b-a}[/tex]

Knowing that we need to find the average rate of change for the given quadratic function, for the interval from [tex]x=-5[/tex] to [tex]x=-3[/tex], we need to find their corresponding y-coordinates.

We can observe in the graph that:

For [tex]x=b=-5[/tex] →  [tex]y=f(b)=-15[/tex]

For [tex]x=a=-3[/tex] → [tex]y=f(a)=1[/tex]

Therefore, substitituting, we get:

 [tex]averate\ rate\ of\ change=\frac{-15-1}{-5-(-3)}=8[/tex]

Answer:

(f-g)(x) = 4x - x^(-5)

Step-by-step explanation:

Please, enclose that negative exponent inside parentheses:  g(x)=x^(-5).  No need to type in the " + " in f(x)=4x^+1.

g(x) is to be subtracted from f(x).  Write f(x):

f(x)=4x

followed by the negative of g(x):  -g(x) = -x^(-5)

and now combine these two results:

 f(x)=4x

-g(x)= -x^(-5)

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

(f-g)(x) = 4x - x^(-5)

The expression for (f-g)(x) is (f-g)(x) = 4x² + 1 - 1/x⁵

A function is a mathematical formula that describes how the dependent variable and independent variable are related. The dependent variable's value varies in the function together with the independent variable's value.

To find (f-g)(x), we need to subtract g(x) from f(x):

(f-g)(x) = f(x) - g(x)

We are given:

f(x) = 4x² + 1

g(x) = x⁻⁵ = 1/x⁵

Substituting these values into the expression for (f-g)(x), we get:

(f-g)(x) = f(x) - g(x) = (4x² + 1) - (1/x⁵)

Simplifying the expression, we can write:

(f-g)(x) = 4x^2 + 1 - 1/x⁵

Therefore, the expression for (f-g)(x) is:

(f-g)(x) = 4x² + 1 - 1/x⁵

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Answer:

The answer would be option B and option C

∠DEF and ∠FED describe an angle with a vertex at E.

The correct answers are option (B) and option (C)

For given question,

We need to find the correct angle with a vertex at E.

We know that the vertex is the common point of the rays of an angle.

It is always written at the middle in an angle.

So, ∠DEF and ∠FED describe an angle with a vertex at E.

The correct answers are option (B) and option (C)

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The kind of symmetry the figures have are horizontal line symmetry and vertical line symmetry

From the question, we have the following parameters that can be used in our computation:

The figures

The figures have horizontal line symmetry and vertical line symmetry

Horizontal line symmetry occurs when a shape can be divided into two identical halves by a horizontal line.

In other words, if you fold the shape in half along the horizontal line, the two halves will exactly overlap.

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Answer:

f[g(6)] = 0

Step-by-step explanation:

f(x) = 6x + 12

g(x) = x - 8

f[g(6)]

First lets find g(6)

g(6) = 6-8 = -2

Then we substitute -2 in for g(6)

Putting -2 into f(x)

f[g(6)] = f(-2) = 6(-2)+12 = -12+12 =0

have you finished this yet? im doing it rn and i need help on some of them. if you havent i can help you with a couple answers

Answer:

Step-by-step explanation:

[tex]16=2^4\\\\8=2^3\\\\16^{2n-3}=8^{4n}\\\\(2^4)^{2n-3}=(2^3)^{4n}\qquad\txt{use}\ (a^n)^m=a^{nm}\\\\2^{(4)(2n-3)}=2^{(3)(4n)}\iff4(2n-3)=12n\qquad\text{use the distributive property}\\\\(4)(2n)+(4)(-3)=12n\\\\8n-12=12n\qquad\text{subtract}\ 8n\ \text{from both sides}\\\\-12=4n\qquad\text{divide both sides by 4}\\\\\dfrac{-12}{4}=\dfrac{4n}{4}\\\\-3=n\to n=-3[/tex]

Answer:

The number is x-6

Step-by-step explanation:

difference of x and a number is 6

Difference means subtract, is means equals

x-n = 6

Add n to each side

x-n+n = 6+n

x = n+6

Subtract 6 from each side

x-6 = n+6-6

x-6 =n

The number is x-6

Answer:

The price of 4 apples is Rs 28

Step-by-step explanation:

The price of 1 dozen apple is Rs 84

12 apples =Rs 84

1 apple = Rs 84÷12

1apple =Rs 7

Again

Price of 4 apples = Rs 7 × 4

= Rs 28 Ans,,

Answer:

130°

Step-by-step explanation:

Since there are 360 degrees is a circle, measure of AXC = 260 means the measure of Arc AC is:

360 - 260 = 100

Now if we were to draw 2 lines, one from A to X and another from C to X, we would have an intercepted angle at X originating from AC.

The theorem is when the intercepted angle is at the opposite side of the circumference, the angle is HALF THAT OF THE ARC.

So, half of 100 is 50.

Angle X and Angle B add up to 180, hence Angle ABC is 180 - 50 = 130

Answer:

The x-intercepts are x = 1 , x = 2 , x = 3

The y-intercept is -6

Step-by-step explanation:

* Lets explain how to solve the problem

- To find the x-intercept of a function substitute f(x) by 0

- To find the y-intercept of a function substitute x by 0

- To find the factors of quadratic function use the long division

* Lets solve the problem

∵ f(x) = x³ - 6x² + 11x - 6

∵ (x - 3) is one of its factors

- Use the long division to find the other factors

∵ x³ - 6x² + 11x - 6 ⇒ dividend

∵ x - 3 ⇒ divisor

# Divide the 1st term in the dividend by the 1st term of the divisor

∵ x³ ÷ x = x²

# Multiply x² by the divisor (x - 3)

∵ x²(x - 3) = x³ - 3x²

# subtract it from the dividend

∵ (x³ - 6x² + 11x - 6) - (x³ - 3x²) = (x³ - x³) + (-6x² + 3x²) +11x - 6

∴ The dividend is -3x² + 11x - 6

# Divide the 1st term in the dividend by the 1st term of the divisor

∵ -3x² ÷ x = -3x

# Multiply -3x by the divisor (x - 3)

∴ -3x(x - 3) = -3x² + 9x

# subtract it from the dividend

∵ (-3x² + 11x - 6) - (-3x² + 9x) = (-3x² - 3x²) + (11x - 9x) - 6

∴ The dividend is 2x - 6

# Divide the 1st term in the dividend by the 1st term of the divisor

∵ 2x ÷ x = 2

# Multiply 2 by the divisor (x - 3)

∴ 2(x - 3) = 2x - 6

# subtract it from the dividend

∴ (2x - 6) - (2x - 6) = (2x - 2x) + (-6 + 6) = 0

∴ (x³ - 6x² + 11x - 6) ÷ (x - 3) = x² - 3x + 2

∴ The factors of f(x) are (x - 3)( x² - 3x + 2)

- The factor (x² - 3x + 2) can factorize into two bracket

∵ The last term is positive and the middle term is negative than the

   two brackets have the middle sign (-)

∵ x × x = x² ⇒ 1st terms in the two brackets

∵ 2 × 1 = 2 ⇒ 2nd terms in the two brackets

∵ 2 × x = 2x

∵ 1 × x = x

∵ 2x + x = 3x

∴  (x² - 3x + 2) = (x - 2)(x - 1)

∴ f(x) = (x - 3)(x - 2)(x - 1)

- To find the x-intercept put f(x) = 0

∴ (x - 3)(x - 2)(x - 1) = 0

- That means each bracket = 0

∵ x - 3 = 0 ⇒ add 3 for both sides

∴ x = 3

∵ x - 2 = 0 ⇒ add 2 for both sides

∴ x = 2

∵ x - 1 = 0 ⇒ add 1 for both sides

∴ x = 1

∴ The x-intercepts are x = 1 , x = 2 , x = 3

- To find the y-intercept put x = 0

∵ f(x) = x³ - 6x² + 11x - 6

∵ x = 0

∴ f(0) = 0 - 0 + 0 - 6 = -6

∴ The y-intercept is -6

Answer:

Option D y=3

Step-by-step explanation:

The question in English is

Which of the following functions is a constant function?

we know that

A constant function is a function whose output value is the same for every input value

so

Verify each case

case A) y=x+1

This is not a constant function, this is a linear equation

Is a function whose output value is different for every input value

case B) y=x+2

This is not a constant function, this is a linear equation

Is a function whose output value is different for every input value

case C) x=y+3

This is not a constant function, this is a linear equation

Is a function whose output value is different for every input value

case D) y=3

This is a constant function

Is a function whose output value is the same for every input value

Answer:

101

Step-by-step explanation:

The theorem to use this is the intercepted arc theorem, which tells us that if we take 2 points on the circumference of a circle and create an angle in the opposite side of the circumference, that angle is HALF that of the ARC intercepted.

If we look at 100 degree angle, we see the ARC intercepted is 99 degree and a degrees. According to theorem, we can say:

99 + a = 2(100)

99 + a = 200

a = 200 - 99

a = 101

Answer:

B

Step-by-step explanation:

The vertex form of an absolute value function is f(x)=a|x-h|+k where (h,k) is the vertex.

a is positive means the absolute value function will face up.

a is negative means the absolute value function will face down.

So looking at the picture we see the vertex is (2,3) and all of the choices have a is 1.

So plugging in 2 for h and 3 for k and 1 for a into f(x)=a|x-h|+k

f(x)=|x-2|+3.

B.

The correct function represent in the graph are,

⇒ y = |x - 2| + 3

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The graph of the function shown in image.

Now, Let the parent function is,

⇒ y = |x|

Clearly, the function is move 2unit left and 3 unit up.

Hence, The correct function represent in the graph are,

⇒ y = |x - 2| + 3

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Answer:

here is

Step-by-step explanation:

Answer:

D. X+5y=7

passes through both coordinates

Answer:

all work is shown and pictured

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\text{x + 5}\ >\huge\text{ 10}[/tex]

[tex]\huge\text{First you'll need to SUBTRACT by 5}[/tex][tex]\huge\text{on each of your sides!}[/tex]

[tex]\huge\text{x + 5 - 5}>\huge\text{ 10 - 5}[/tex]

[tex]\huge\text{Cancel out: 5 - 5 because it equals to 0}[/tex]

[tex]\huge\text{Keep: 10 - 5 because it gives us the result of 5}[/tex]

[tex]\huge\text{x}>\huge\text{5}[/tex]

[tex]\huge\text{It's an (o)(p)(e)(n)(e)(d) circle} \checkmark[/tex]

[tex]\huge\text{Starts off with \#5}\checkmark[/tex]

[tex]\boxed{\boxed{\huge\text{Answer: A.}}}[/tex] [tex]\huge\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

[tex]\Large\textnormal{A. First graph}[/tex]

Step-by-step explanation:

[tex]\Large\textnormal{First, subtract by 5 from both sides of equation.}[/tex]

[tex]\displaystyle x+5-5>10-5[/tex]

[tex]\Large\textnormal{Then, simplify, to find the answer.}[/tex]

[tex]\displaystyle 10-5=5[/tex]

[tex]\Large \boxed{x>5}[/tex], which is our answer.

[tex]\Large\textnormal{The correct answer is A.}[/tex]

Answer:

  50 million

Step-by-step explanation:

You don't need to go to the trouble to find the value of k in e^(kt). Rather, you can use the given ratio directly.

When t = years after 1990, the population of 49 million took 12 years to achieve. The estimate desired is for 16 years after the year 1990. The appropriate exponential formula for the population is ...

  P = 46·(49/46)^(t/12)

Then for t=16, this is ...

  P = 46·(49/46)^(16/12) ≈ 50.04 . . . .  million

The population in 2006 is estimated at 50 million.

_____

The form of the exponential equation we used above is ...

  f(x) = (baseline value)·(ratio to baseline)^(x/(interval corresponding to ratio))