A diameter is a line segment whose endpoints are on a circle. It is a special type of chord because it must contain the _____ of the circle HELP!!!!!!!!!!

Answer:

y = - x + 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 1, 2) and (x₂, y₂ ) = (4, - 3)

m = [tex]\frac{-3-2}{4+1}[/tex] = [tex]\frac{-5}{5}[/tex] = -1, hence

y = - x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (- 1, 2), then

2 = 1 + c ⇒ c = 2 - 1 = 1

y = - x + 1 ← equation in slope- intercept form

The equation is y = –x + 1.

To find the slope-intercept form of a line passing through two points, calculate the slope using the given points and then use one point to find the y-intercept. The final equation for the line through the points (–1, 2) and (4, –3) is y = –x + 1.

To write an equation in slope-intercept form for the line passing through the points (–1, 2) and (4, –3), we first need to calculate the slope (m) using the formula
m = (y2 - y1) / (x2 - x1). Plugging in our points gives us m = (–3 – 2) / (4 – (–1)) = –5 / 5 = –1. Now that we have the slope, we can use one of the points to find the y-intercept (b). Using the point (–1, 2) and the slope-intercept formula y = mx + b, we plug in the values to get 2 = (–1)×(–1) + b, simplifying to 2 = 1 + b, which yields b = 1. Thus, the equation is y = –x + 1.

Answer:

She had eaten 15 chocolates.

Step-by-step explanation:

[tex]\frac{5}{8} * 24 = \frac{120}{8} = 15[/tex]

Final answer:

Kelsey ate 15 chocolates out of the 24 after a week, which is 5/8 of the total. Jenny initially had 14 chocolates before eating two and giving half of the remainder to Lisa.

Explanation:

To solve how many chocolates Kelsey has eaten, we have to calculate 5/8 of 24. Since 24 chocolates multiplied by 5/8 equals 15, Kelsey ate 15 chocolates after one week.

Regarding the second question about Jenny and her chocolates:

In summary, the answer to how many chocolates Jenny initially had is 14.

Answer:

The graph in the attached figure

Step-by-step explanation:

we have that

[tex]f(x)=x-4[/tex] ------> For [tex]x < 2[/tex]

[tex]f(x)=-2x+2[/tex] ------> For [tex]x\geq2[/tex]

To graph this piece wise- defined function

In the interval (-∞,2) ----> graph the line [tex]f(x)=x-4[/tex]

In the interval [2,∞) ----> graph the line [tex]f(x)=-2x+2[/tex]

The function is continue -----> the domain is all real numbers

using a graphing tool

see the attached figure

[tex]\bf \cfrac{x^8}{x^{14}}\implies x^8x^{-14}\implies x^{8-14}\implies x^{-6}\implies \stackrel{\textit{using the power rule}}{-6x^{-7}\implies \cfrac{-6}{x^7}}[/tex]

Question 1:

We have the following expression:

[tex]4x ^ {-4}[/tex]

By definition of power properties we have to:

[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]

Then, rewriting the expression:

[tex]\frac {4} {x ^ 4}[/tex]

ANswer:

[tex]\frac {4} {x ^ 4}[/tex]

Question 2:

For this case we have the following expression:

[tex]\frac {x ^ 8} {x ^ {14}} =[/tex]

By definition of power properties of the same base we have:

[tex]x ^ n * x ^ m = x ^ {n + m}[/tex]

Then, we can rewrite the denominator of the expression as:

[tex]\frac {x ^ 8} {x ^ 8 * x ^ 6} =[/tex]

Simplifying terms of the numerator and denominator:

[tex]\frac {1} {x ^ 6}[/tex]

ANswer:

[tex]\frac {1} {x ^ 6}[/tex]

Answer:

60x^3

Step-by-step explanation:

Given:

4/15x^3 and 5/12x^2

finding LCM of denominators (15x^3,12x^2)

for variable x, as x^3 is the heighest power so we'll keep x^3

now for the numeric part

15= 3*5

12=3*4

common factor is 3, so

3*4*5 =60

hence LCD= 60x^3!

Let's solve for x.

−b3+3b2+8−x−5b2−9=5b3+852+17

Step 1: Add b^3 to both sides.

−b3−2b2−x−1+b3=5b3+869+b3

−2b2−x−1=6b3+869

Step 2: Add 2b^2 to both sides.

−2b2−x−1+2b2=6b3+869+2b2

−x−1=6b3+2b2+869

Step 3: Add 1 to both sides.

−x−1+1=6b3+2b2+869+1

−x=6b3+2b2+870

Step 4: Divide both sides by -1.

−x

−1

=

6b3+2b2+870

−1

x=−6b3−2b2−870

Answer:

x=−6b3−2b2−870

Answer:

the answer is the first option -6b^3

Step-by-step explanation:

yup

Answer:  

t2=ar^(2-1)

20=ar

then

t4=ar^(4-2)

45/4=ar.r

45/4=20.r

45/80=r

Answer:

r=±0.75

Step-by-step explanation:

Given:

a2= 20

a4= 45/4

As a geometric sequence has a common ratio and is given by:

an=a1(r)^n-1

where

an=nth term

a1=first term

n=number of term

r=common ratio

Now

a2=20=a1(r)^(2-1)

20=a1(r)^1

20=a1*r

Also

a4=45/4=a1(r)^(4-1)

45/4=a1r^3

(a1*r)r^2=45/4

Substituting value of 20=a1*r

(20)r^2=45/4

r^2=45/4(20)

r^2=0.5625

r=±0.75!

Answer:

Step-by-step explanation:

[tex]C(F)=\dfrac{5}{9}(F-32)[/tex]

The function C(F) represents the temperature of F degrees Fahrenheit converted to degrees Celsius.

The function C(F) represents the temperature of F degrees Fahrenheit converted to degrees Celsius. Temperature conversion is the process of converting between different temperature scales, such as Fahrenheit (°F), Celsius (°C), and Kelvin (K).

Each scale measures temperature differently, so conversions are necessary for various applications. The most common conversion formulas are: Celsius to Fahrenheit: °F = (°C × 9/5) + 32, and Celsius to Kelvin: K = °C + 273.15. These conversions are vital for international communication, weather reports, and scientific calculations.

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The event "not rolling 1, 3, 4, or 5" is the same event as "rolling 2 or 6".

Since the possible outcomes of a number cube have the same probability, the probability of rolling 2 or 6 is given by

[tex]\dfrac{\text{\# of good outcomes}}{\text{\# of possible outcomes}}=\dfrac{2}{6}=\dfrac{1}{3}[/tex]

Answer:

See below in bold.

Step-by-step explanation:

The 50 grams of alloy contains 50 * 0.52 = 26 g of pure copper.

So the amount of copper n the mixture = 78 + 26 = 104 g.

The total mass of the mixture = 78 + 50 = 128 g.

% copper = 104 * 100 / 128

= 81.25%.

Final answer:

The resulting mixture contains 104 grams of copper, which constitutes 81.25% of the mixture.

Explanation:

To find out how many grams of copper are in the resulting mixture of the alloy, we need to calculate the amount of copper from both sources and add them together. The first source is 50 grams of an alloy that is 52% copper, and the second source is 78 grams of pure copper.

Now, add the amounts of copper from both sources:

26 grams (from the alloy) + 78 grams (pure copper) = 104 grams of copper.

To determine what percent of the resulting mixture is copper, we add the total weight of the mixture (50 grams + 78 grams = 128 grams) and then calculate the percentage:

(104 grams copper / 128 grams total) × 100 = 81.25%

So, the resulting mixture contains 104 grams of copper and is 81.25% copper.

Answer:

(-inf,2]

Step-by-step explanation:

[tex](w \circ r)(x)=w(r(x))[/tex]

[tex]w(2-x^2)[/tex] I replaced r(x) with 2-x^2

[tex](2-x^2)-x[/tex] I replace the x in w(x)=x-2 with 2-x^2

[tex]-x^2-x+2[/tex]

You can graph this to find the range.

But since this is a quadratic (the graph is a parabola), I'm going to find the vertex to help me to determine the range.

The vertex is at x=-b/(2a).  Once I find x, I can find the y that corresponds to it by using y=-x^2-x+2.

Comparing ax^2+bx+c to -x^2-x+2 tells me a=-1, b=-1, and c=2.

So the vertex is at x=1/(2*-1)=-1/2.

To find the y-coordinate that corresponds to that I will not plug in -1/2 in place of x into -x^2-x+2.

This gives me

-(-1/2)^2-(-1/2)+2

-1/4 +  1/2  +2

Find a common denominator which is 4.

-1/4 +  2/4  +8/4

8/4

2.

So the highest y value is 2 ( I know tha parabola is upside down because a=negative number)

That mean then range is 2 or less than 2.

So the answer an interval notation is (-inf,2]

[tex]\bf \qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ \stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+6}x\stackrel{\stackrel{c}{\downarrow }}{+9}=0 ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{\underline{one real solution}}~~\textit{\Large \checkmark}\\ positive&\textit{two real solutions}\\ negative&\textit{no solution} \end{cases} \\\\\\ 6^2-4(1)(9)\implies 36-36\implies 0[/tex]

Arc length will be equal to the perimeter divided by 4 since we are talking about quarter circle.

[tex]2\pi r/4=\pi r/2=6\pi/2\approx\boxed{9.42}[/tex]

Hope this helps.

r3t40

Answer:

9.42 inches

Step-by-step explanation:

the cercle length is : 2π×r = 2×3.14 ×6=37.68 inches

the arc length of a quarter circle is : 37.68/4 =9.42 inches

Answer:

A.  True.

Step-by-step explanation:

The value increases by the same amount ($5) every year so it is simple interest.

Answer:True

Step-by-step explanation:

Answer:

22

Step-by-step explanation:

11+22+33=66

66/3

=22

Answer:

22

Step-by-step explanation:

The mean is just another word for average

Add up the three numbers and divide by 3

(11+22+33) /3 = 66/3 = 22

The value of r that satisfies the given area is approximately 5.08 ft, which is closest to 4 ft.

The area of a circle can be calculated using the formula A = πr², where A is the area and r is the radius. In this case, the area of the circle is given as 64 ft². So we can substitute the value of A as 64 ft² in the formula to find the value of r.

64 = πr²

To solve for r, we can divide both sides of the equation by π and then take the square root of both sides.

r² = 64/π

r = √(64/π)

To simplify further, we can approximate the value of π as 3.14.

r = √(64/3.14)

r ≈ 5.08 ft

Based on the given options, the value of r that is closest to 5.08 ft is 4 ft.

Answer:

ITS 8FT

Step-by-step explanation:

Answer:

ship B is going in a straight line north ship A is going diagonal make a straight line where each ship is moving towards and where ever they intersect will be where the ship in distress is located

hope this helped

Answer:

B,D, and E

Step-by-step explanation:

They all label the vertices in the correct order and do not label sides when naming it.

Answer:

B. [tex]\Delta TAX[/tex],

D. [tex]\Delta AXT[/tex]

E. [tex]\Delta XTA[/tex].

Step-by-step explanation:

We have been given a triangle. We are asked to choose the valid names for our triangle from the given choices.

We know that labels of the vertices of the triangle are used to name a triangle. In naming triangle, we can start from any vertex and we should keep the letters in order as we go around the triangle.

We can see that vertices of our given triangle are labeled as A, T and X, therefore, we can get three names for our triangle as:

[tex]\Delta TAX[/tex], [tex]\Delta AXT[/tex] and [tex]\Delta XTA[/tex].

Therefore, options B, D and C are correct choices.

Answer:

77°

Step-by-step explanation:

[tex]\\ T = \frac{1}{2}  (RU - SU)\\ \\ 21 =\frac{1}{2}(119 - SU)\\ \\ 42 = 119 - SU\\ SU=77[/tex]

The measure of mSU from the given diagram is 77 degrees

The half of the difference of the intecepted arc is equal to the measure of the angle at the vertex

Applying this theorem to the given figure, we will havea;

1/2(119 - mSU) = 21

119 - mSU = 2(21)

119 - mSU = 42

Determine the measure of mSU

mSU = 119 -42

mSU = 77degrees

Hence the measure of mSU from the given diagram is 77 degrees

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Answer: 32

Step-by-step explanation: You need to use PEMDAS. First, multiply the two numbers.

3(8) = 24

Then, add 8.

24 + 8 = 32

32 is your answer.

Answer:

The second polynomial is:

[tex]6d^5-2c^3d^2+5c^2d^3-12cd^4+8[/tex]

Step-by-step explanation:

Given

[tex]Sum\ of\ polynomials=S=8d^5-3c^3d^2+5c^2d^3-4cd^4+9\\Polynomial\ 1=A=2d^5-c^3d^2+8cd^4+1\\Polynomial\ 2=B=?\\S=A+B\\B=S-A\\=8d^5-3c^3d^2+5c^2d^3-4cd^4+9-(2d^5-c^3d^2+8cd^4+1)\\=8d^5-3c^3d^2+5c^2d^3-4cd^4+9-2d^5+c^3d^2-8cd^4-1\\=8d^5-2d^5-3c^3d^2+c^3d^2+5c^2d^3-4cd^4-8cd^4+9-1\\=6d^5-2c^3d^2+5c^2d^3-12cd^4+8[/tex]

Answer:

A C D

Step-by-step explanation:

A prime Trinomial is one that cannot be reduced into integer factors. It is easier to define a non prime trinomial first.

x^2 - 4x - 12 can be factored into

(x - 6)(x + 2) -6 and 2 are integers.

So B is not prime.

All of the others are prime. You need to use the quadratic formula to solve them.

B factors into

x^2 - 13x + 42

(x - 7)(x - 6)

Answer:

946

Step-by-step explanation:

To find just the remainder when dividing a polynomial by x-3, you could just plug in 3 into that polynomial.

If you were dividing by x+3, the remainder would just be the polynomial evaluated at x=-3.

Anyways plugging in 3 gives

7(3)^4 + 12(3)^3 + 6(3)^2 - 5(3) + 16

Just put this into your nearest calculator .

It should output 946.

You could use synthetic division or even long.

Synthetic Division.

We put 3 on outside because we are dividing by x-3.

3. | 7. 12. 6. -5. 16

| 21. 99. 315. 930

________________________

7. 33. 105. 310. 946

The remainder is the last number in the last column.

The plugging in and the synthetic division will always work when dividing by a linear expression.

Answer:

Step-by-step explanation:

We know:

1. Diagonals of a rhombus are perpendicular.

2. Diagonals divide the rhombus on four congruent right triangles.

3. The sum of measures of acute angles in a right triangle is equal 90°.

Therefore we have the equation:

(2x + 3) + (3x + 2) = 90           combine like terms

(2x + 3x) + (3 + 2) = 90

5x + 5 = 90               subtract 5 from both sides

5x = 85             divide both sides by 5

x = 17

The value of x is 17. This means that the angles formed by the diagonals of the rhombus are 37 degrees (2 * 17 + 3) and 53 degrees (3 * 17 + 2), and they indeed form congruent right triangles as required in the properties of a rhombus.

To find the value of x in the given equation, we start by understanding the properties of a rhombus and how its diagonals divide it into four congruent right triangles.

Given information:

Diagonals of a rhombus are perpendicular.

Diagonals divide the rhombus into four congruent right triangles.

Let's proceed with the steps to solve for x:

Step 1: Recognize that the angles formed by the diagonals are 2x + 3 and 3x + 2. Since these angles are congruent right angles, their sum is equal to 90 degrees.

Step 2: Set up the equation:

(2x + 3) + (3x + 2) = 90

Step 3: Combine like terms:

5x + 5 = 90

Step 4: Isolate x by subtracting 5 from both sides of the equation:

5x = 85

Step 5: Solve for x by dividing both sides by 5:

x = 85 / 5

x = 17

Hence, the value of x is 17. This means that the angles formed by the diagonals of the rhombus are 37 degrees (2 * 17 + 3) and 53 degrees (3 * 17 + 2), and they indeed form congruent right triangles as required in the properties of a rhombus.

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Answer:

[tex]Pr=\dfrac{45}{208}\approx 0.216.[/tex]

Step-by-step explanation:

You are given the information about students:

In total, there are 45 + 60 + 82 + 21 = 208 students.

Use the definition of the probability:

[tex]Pr=\dfrac{\text{Number of favorable outcomes}}{\text{Number of all possible outcomes}}[/tex]

Number of favorable outcomes = 45

Nomber of all possible outcomes = 208,

hence,

[tex]Pr=\dfrac{45}{208}\approx 0.216.[/tex]

Answer:

12:1

Step-by-step explanation:

12:1Answer:

Step-by-step explanation:

Answer:

[tex]\large\boxed{h^{-1}(x)=\dfrac{3x+4}{2}}[/tex]

Step-by-step explanation:

[tex]h(x)=\dfrac{2x-4}{3}\to y=\dfrac{2x-4}{3}\\\\\text{Exchange x to y and vice versa}:\\\\x=\dfrac{2y-4}{3}\\\\\text{Solve for y:}\\\\\dfrac{2y-4}{3}=x\qquad\text{multiply both sides by 3}\\\\2y-4=3x\qquad\text{add 4 to both sides}\\\\2y=3x+4\qquad\text{divide both sides by 2}\\\\y=\dfrac{3x+4}{2}[/tex]

Answer:

78 and 46

Step-by-step explanation:

Substitution (look it up it's hard to explain lol)

Answer:

178.98 square feet

Step-by-step explanation:

Alright so we need to find two areas here and find the difference to find the area of the path.

The two shapes involved is a smaller circle inside a bigger circle.

Let's look at the smaller circle, the gardening area.

You are given is has a radius of 8 ft.

The area of a circle is [tex]\pi \cdot r^2[/tex] where r is the radius.

So the area of the smaller circle is [tex]\pi \cdot 8^2[/tex].

Now time to look at the bigger area (which will have some overlapping area with the smaller one which will subtract out to find the area of path).

The diameter of the smaller circle was (8+8)=16 feet.

What is the diameter of the bigger one.  The path is 3 ft wide so we have to add a 3 before the diameter of the smaller circle to another 3 after that diameter to get the diameter of the bigger circle.  So the diameter of the bigger circle is (3+16+3)=22 feet.  The radius is half the diameter so the radius is 22/2=11.

The area of the bigger circle is [tex]\pi \cdot 11^2[/tex].

The area of the path=

the area of bigger circle     -      the area of smaller circle=

[tex]\pi \cdot 11^2-\pi \cdot 8^2[/tex]

Type this into your calculator with 3.14 instead of the [tex]\pi[/tex] button.

178.98 square feet

The answer is:

[tex]PathArea=178.98ft^{2}[/tex]

To calculate the are of the path alone, we need to add the width of the path to the radius of the garden in order to know is radius, then, calculate the total  area (using garden radius plus path width) and then, subtract it the area of the circular garden.

We know that the radius of the circular garden is equal to 8 feet, and the circular path has a width of 3 feet, so, the radius of the circular path will be:

[tex]CPath_{radius}=8feet+Path_{width}\\\\Path_{radius}=8feet+3feet=11[/tex]

Now, calculating the areas, we have:

Garden Area:

[tex]CircularGardenArea=\pi *radius^{2}\\\\CircularGardenRadius=\pi *8ft^{2}=3.14*64ft^{2}=200.96ft^{2}[/tex]

Total Area:

[tex]TotalArea=\pi *(8feet+3feet)^{2}=\pi *(11ft)^{2}=3.14*121ft^{2}=379.94ft^{2}[/tex]

Now, calculating the area of the path, we have:

[tex]TotalArea=CircularGardenArea+PathArea\\\\PathArea=TotalArea-CircularGardenArea\\\\PathArea=379.94ft^{2}-200.96ft^{2}=178.98ft^{2}[/tex]

Hence, we have that:

[tex]PathArea=178.98ft^{2}[/tex]

Have a nice day!

Answer:

[tex]f(x) = {2}^{x } \\ f(x) = 8 \\ \\ {2}^{x} = 8 \\ \\ {2}^{x } = {2}^{3} \\ \\ x = 3[/tex]

The value of x when f(x) = 8 is 3 in f(x) = 2^x

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

f(x) = 2^x

To find the value of x when f(x) = 8, we need to solve the equation 2^x = 8.

We can rewrite 8 as 2^3

So, the equation becomes:

2^x = 2^3

Since the bases are the same, we can equate the exponents:

x = 3

Hence, the value of x when f(x) = 8 is 3.

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