Which equation represents a line that passes through (-2, 4) and has a slope of 1/2?

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

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:

12:1

Step-by-step explanation:

12:1Answer:

Step-by-step explanation:

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) The length of an arc between  two consecutive fan blades is 16.76 inches

b) The area of each sector is 67.02 inches²

c) The angular velocity is 4m rad/sec

Step-by-step explanation:

* Lets explain how to solve the problem

- The fan has three thin blades that spin to  produce a breeze

- The diameter of the fan is  16 inches

- The three blades divided the circle into three equal parts

- The circumference of the circle is 2πr

a)

∵ The diameter of the circle = 16 inches

∵ The radius of the circle is half the diameter

∴ The radius (r) = 1/2 × 16 = 8 inches

∵ The length of the circle = 2πr

∴ The length of the circle = 2π(8) = 16π

- The length of an arc between  two consecutive fan blades is 1/3

  the length of the circle

∴ The length of the arc = 1/3 × 16π = 16.76 inches

* The length of an arc between  two consecutive fan blades is

  16.76 inches

b)

- The area of a sector in the circle = [tex]\frac{x}{360}(\pi r^{2})[/tex]

  where x is the central angle of the sector and r is the radius

  of the circle

∵ The angle between each two consecutive blades = 360°/3

∴ x = 360°/3 = 120°

∵ r = 8 inches

∴ The area of each sector = [tex]\frac{120}{360}(\pi )(8^{2})=67.02[/tex]

* The area of each sector is 67.02 inches²

c)

∵ The angular velocity = Ф rad ÷ t, where Ф is the central angle

   with radian measure and t is the time in seconds

∴ ω = Ф/t  radian/second

∵ Ф = 8m radians

∵ t = 2 seconds

∴ ω = 8m ÷ 2 = 4m rad/sec

* The angular velocity is 4m rad/sec

[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]

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!

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:

D

Step-by-step explanation:

The rules we need to simplify this are:

[tex]a^x*a^y=a^{x+y}[/tex]

and

[tex](a^x)^y=a^{xy}[/tex]

Now, let's simplify the problem:

[tex](y^{-7}*y^{-3})^{-1}\\(y^{-10})^{-1}\\y^{10}[/tex]

Answer choice D is y^10, so that's correct.

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]\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: 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:

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:

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

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:

78 and 46

Step-by-step explanation:

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

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:

(-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]

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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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:

1.6 < x < 9.6.

Step-by-step explanation:

Now x cannot be less than  5.6 - 4.0 = 1.6 as a triangle  could not be formed if it were.

In fact x must be greater than 1.6.

Also x must be less than the sum of the other 2 sides.

So x  must be less than 4.0 + 5.6 = 9.6.

Answer:

1.6 < x < 9.6

Step-by-step explanation:

The range of possible sizes for side x is 1.6 < x < 9.6.

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:  

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!

Add all of the numbers together

2+3.5+2+3.5

5.5+5.5

= 11 cm

Answer is 11cm - second time

Answer:

11 cm

Step-by-step explanation:

The perimeter is equal to

P =2(l+w)

P = 2(2+3.5)

  = 2(5.5)

  = 11 cm

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:

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:

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:

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:

[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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