In circle H, HJ¯¯¯¯¯ is a radius and JK¯¯¯¯¯ is a tangent segment. Which statement must be true?

A) HJ=JK
B) ∠HJK is an obtuse angle.
C) HJ=HK
D) ∠HJK is a right angle.

To convert 2x + 4y = 12 into slope-intercept form, we must put it into y = mx + b form, where m represents the slope of the line and b is the y intercept of the equation. To begin, we should subtract 2x from both sides so that we can get the variable y alone on the left side of the equation.

2x + 4y = 12

4y = -2x + 12

Next, because there cannot be a coefficient on the variable y in this form, we must divide both sides of the equation by 4.

y = -2/4x + 3

Because 2 and 4 are both divisible by 2, we can divide both the numerator and the denominator by 2 to further simplify the equation.

y = -1/2x + 3

Therefore, the answer is y = -1/2x + 3.

Hope this helps!

To convert the equation 2x + 4y = 12 into slope-intercept form (y=mx+b), you subtract 2x from both sides and then divide by 4 to isolate y, resulting in y = -1/2x + 3, where the slope (m) is -1/2 and the y-intercept (b) is 3.

To convert the equation 2x + 4y = 12 into slope-intercept form (y=mx+b), we need to solve for y. Here's how you can do it step by step:

Now the equation is in slope-intercept form where m (the slope) is -1/2 and b (the y-intercept) is 3. The slope m is defined as the rise over the run of the straight line, and the y-intercept b is the point where the line crosses the vertical axis, which in this case is when x=0 and y=3.

Answer:

The correct option is c.

Step-by-step explanation:

Given information: The measure of arc AXC is 235°. Let the center of the circle be O.

The sum of all disjoint arcs is 360°. So,

[tex]Arc(AXC)+Arc(AC)=360^{\circ}[/tex]

[tex]235^{\circ}+Arc(AC)=360^{\circ}[/tex]

[tex]Arc(AC)=360^{\circ}-235^{\circ}[/tex]

[tex]Arc(AC)=125^{\circ}[/tex]

[tex]\angle AOC=125^{\circ}[/tex]

The measure of arc AC is 125°.

Line BA and BC are tangent on the circle O from the same point, so the sum of opposite angles of the quadrilateral is 180°.

[tex]\angle AOC+\angle ABC=180^{\circ}[/tex]

[tex]125^{\circ}+\angle ABC=180^{\circ}[/tex]

[tex]\angle ABC=180^{\circ}-125^{\circ}[/tex]

[tex]\angle ABC=55^{\circ}[/tex]

The measure of angle ABC is 55°. Therefore the correct option is c.

Answer:

answer is 1 & 3 on edg

Step-by-step explanation:

Final answer:

To calculate the original price of Thomas's backpack, we set up an equation with the information that a 30% discount resulted in a $15 savings, which, when solved, indicates the original price was $50. The correct option is b.)$50

Explanation:

Thomas bought a new backpack at a 30% discount, which saved him $15. To find the original price, we can set up an equation to solve for the original price. Let's denote the original price as 'P'. The equation would therefore be 0.30 * P = $15, meaning 30% of the original price is equal to the $15 discount he received.

First, divide both sides of the equation by 0.30 to isolate 'P':
P = $15 / 0.30
P = $50

Hence, Thomas's backpack originally cost $50 before the discount was applied. Therefore, the correct answer is b.) $50.

The radius of the circle with the equation (x−2)^2+(y−16)^2=169 is 13 units.

The equation of the circle provided is (x−2)2+(y−16)2=169. In the standard form of a circle's equation, (x - h)2 + (y - k)2 = r2, where (h, k) is the center of the circle and r is the radius, we see that 169 represents r2. Hence, to find the radius of the circle, we take the square root of 169.

The radius r is calculated as r = √169 = 13 units. Therefore, the circle's radius is 13 units.

The inverse of the given function y =x+5 is y =x-5.

The given function is:

y =x+5

A function is invertible only if each input has a unique output and each element of the codomain should be mapped.

Step1: check function is invertible i.e. bijective i.e. one-one and onto or not

f(x₁)=x₁+5

f(x₂) = x₂+5

f(x₁) = f(x₂)

x₁+5 =x₁+5

x₁=x₂

So, the function is one-one or injective.

For onto range and codomain should be same.

Step 2: interchange x and y

x=y+5

Step3: bring 5 to the left side of the equation.

x-5 = y

Step4: write in y=f(x) form

y = x-5

Therefore, the inverse of the given function y =x+5 is y =x-5.

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Answer:

The value of lesser root is:

                         x=2

Step-by-step explanation:

We are given  a quadratic equation in terms of variable " x " as:

[tex]x^2-6x+8=0[/tex]

We know that for any quadratic equation of the type:

              [tex]ax^2+bx+c=0[/tex]

The roots of x are calculated as:

[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

Here we have:

      a=1 , b=-6 and c=8

Hence, on solving for roots:

[tex]x=\dfrac{-(-6)\pm \sqrt{(-6)^2-4\times 1\times 8}}{2\times 1}\\\\\\x=\dfrac{6\pm \sqrt{36-32}}{2}\\\\\\x=\dfrac{6\pm \sqrt{4}}{2}\\\\\\x=\dfrac{6\pm 2}{2}[/tex]

Hence, we have:

[tex]x=\dfrac{6+2}{2}\ or\ x=\dfrac{6-2}{2}\\\\x=\dfrac{8}{2}\ or\ x=\dfrac{4}{2}\\\\\\x=4\ or\ x=2[/tex]

Hence, the value of lesser root is:

                             x=2

To begin this problem, we need to use the two points that we are given to find the slope of the line. Slope is defined as the change in y values divided by the change in x values, or rise/run, and is represented by the variable m.

m = (y1-y2)/(x1-x2) = (8-0)/(3-6) = 8/(-3) = -8/3

Now, we can use the slope and one of the points from our given values to create an equation of the line in point-slope form.

y = m(x-h) + k, where a point on the line is (h,k)

y = -8/3(x - 3) + 8

Now, we can distribute our slope and simplify through addition.

y = -8/3x + 8 + 8

y = -8/3x + 16

Therefore, your answer is y = -8/3x + 16.

Hope this helps!

The best linear approximation for f(x) = cos(x) near x = π/2 is L(x) = π/2 - x. This conclusion is reached by finding the slope of the tangent line to the function at x = π/2 (which is the cosine derivative at this point), and then applying the formula for linear approximation.

The linear approximation of a function at a certain point is the line tangent to the function at that point. In this case, we want the linear approximation for f(x) = cos(x) near x = π/2. The slope of the tangent line at a point is equal to the derivative of the function at that point, and the cosine derivative is -sin(x). So at x = π/2, the slope is -sin(π/2) = -1.

Now, we use the formula for the linear approximation, which is L(x) = f(a) + f'(a)(x-a). In this case, a is π/2, so we get L(x) = cos(π/2) - 1(x - π/2). Since cos(π/2)=0, the best linear approximation is L(x) = 0 - 1(x - π/2) = π/2 - x.

We use the

cosine derivative

to find the slope of the tangent line and the

linear approximation formula

to find the equation of the line. We also assume a

small-angle approximation

since we are close to x = π/2.

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Final answer:

The total amount on a $6,500 investment at a 6% annual interest rate compounded yearly for 25 years is approximately $28,353.25, with the interest earned being about $21,853.25.

Explanation:

To calculate the total amount and the amount of interest earned on $6,500 at 6% for 25 years, we need to identify whether the interest is compounded annually, monthly, or if it's simple interest. Since the type of interest isn't specified, we'll assume it's compounded annually, which is common in savings accounts. The formula for compound interest is:

A = P(1 + r/n)nt

Where:

A = the future value of the investment/loan, including interest

P = the principal investment amount ($6,500)

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per year

t = the time the money is invested or borrowed for, in years (25 years)

For this example, since the interest is compounded annually, n = 1. First, convert the interest rate from a percentage to a decimal by dividing by 100: 6% / 100 = 0.06. Now, plug the values into the formula:

A = $6,500(1 + 0.06/1)1*25

A = $6,500(1 + 0.06)25

A = $6,500(1.06)25

Calculating this out, A, which is the total future amount, comes out to:

A = $28,353.25 approximately

To find out the total interest earned, subtract the principal from the final amount:

Total interest = A - P

Total interest = $28,353.25 - $6,500

Total interest = $21,853.25 approximately

The total amount is about $28,353.25 and the amount of interest earned is about $21,853.25.