I’m confused. Please help?

Answer:

Step-by-step explanation:

For the equation ...

  y = a(x -h)² +k

you can find the x-intercepts by setting y=0 and solving for x.

  0 = a(x -h)² +k

  -k = a(x -h)² . . . . . . subtract k

  -k/a = (x -h)² . . . . . divide by a

  ±√(-k/a) = x -h . . . . take the square root

  h ± √(-k/a) = x . . . . add h . . . . this is the general solution

__

So, for each of your problems, fill in the corresponding numbers and do the arithmetic. If (-k/a) is a negative number, the square root gives imaginary values, so there is "no solution".

1.  x = 5 ± √9 = {5 -3, 5 +3} = {2, 8} . . . . the x-intercepts are 2 and 8

2.  x = -3 ± √(-2) . . . . . . no solution; the roots are complex

3.  x = 5 ± √(-8/4) . . . . . no solution; the roots are complex

Answer:

Step-by-step explanation:

These are all done the exact same way.  I'll do the first one in its entirety, and you can do the rest, following my example.

Finding x-intercepts means that you find the places in the polynomial where the graph of the function goes through the x-axis.  Here, the y-coordinates will be 0.  To find these x-intercepts, you have to set y equal to 0 and then factor.  First, though, we need to know exactly what the polynomial looks like in standard form.  The ones you have are all in vertex form.  We find the standard form by first expanding the binomial, like this:

[tex]0=(x-5)(x-5)-9[/tex]

FOIL those out to get

[tex]x^2-10x+25-9=0[/tex]

Combine like terms to get

[tex]0=x^2-10x+16[/tex]

Now we have to factor that.  I'll use regular old factoring, although the quadratic formula will work also.

In our quadratic, a = 1, b = -10 and c = 16

The product of a * c = 16.  The factors of 16 are:

1, 16

2, 8

4, 4

Some combination of those factors will give us a -10, the b term.  2 and 8 will work, as long as they are both negative.  -2 + -8 = -10.  Fit them into the polynomial with the absolute value of the largest number named first:

[tex]x^2-8x-2x+16=0[/tex]

Now we group them by 2's without ever changing their order:

[tex](x^2-8)-(2x+16)=0[/tex]

and then factor out the common thing in each set of parenthesis.  The common thing in the first set of parenthesis is an x; the common thing in the second set is a 2:

[tex]x(x-8)-2(x-8)=0[/tex]

Now the common thing is (x - 8), so we factor that out and group together in a separate set of parenthesis what's left over:

[tex](x-8)(x-2)=0[/tex]

By the Zero Product Property, either x - 8 = 0 or x - 2 = 0.  Solving the first one for x:

x - 8 = 0 so x = 8

Solving the second one for x:

x - 2 = 0 so x = 2

The 2 solutions are x = 2 and x = 8, choices a and d.

Answer:

  a) J, K, W

  b) any of X, Y, or P

  c) 1 line

Step-by-step explanation:

a) The figure shows points J, K and W on line m.

b) Any points in the diagram other than J, K, and W are not on line m. Those include points X, Y, and P. Your answer will be one or more of these.

c) Two points define 1 line. There is only one line through any given pair of points. It can be named many ways, but it is still the same (one) line.

Answer:

 1) J, K, W

 2) any of X, Y, or P

 3) Only one line  (pyx)

Step-by-step explanation:

1) The figure shows points J, K and W on line m.

2) All points in the diagram except for j, w, and k are not on line m. These include points x, y, and p. Your answer should be one or more of these.

3) Three points define 1 line. There is only one line through any given group of points. It can be named many ways, but it will remain (one) line. The line would run through the points p, y, and x.

Hope this helps

- Que

Answer:

  y = (7/4)(x -4) +12

Step-by-step explanation:

The rate of growth is ...

  (19 in -12 in)/(8 wk -4 wk) = 7/4 in/wk

Using this slope in a point-slope form of the equation for a line, we get ...

  y = m(x -h) +k . . . . . line with slope m through point (h, k)

  y = (7/4)(x -4) +12 . . . . . line with slope 7/4 through the point (4 wk, 12 in)

Answer:

[tex]\large\boxed{|5x-2|\leq8}[/tex]

Step-by-step explanation:

[tex]-1.2\leq x\leq2\qquad\text{multiply all sides by 5}\\\\-6\leq5x\leq10\qquad\text{subtract 2 from both sides}\\\\-8\leq5x-2\leq8\iff|5x-2|\leq8[/tex]

Answer:

The triangles are similar

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional

step 1

In the right triangle FED

Find the length of side FD

Applying the Pythagoras Theorem

[tex]FD^{2}=FE^{2}+DE^{2}[/tex]

substitute the given values

[tex]FD^{2}=3^{2}+4^{2}[/tex]

[tex]FD^{2}=25[/tex]

[tex]FD^{2}=5\ units[/tex]

step 2

In the right triangle BUG

Find the length of side GU

Applying the Pythagoras Theorem

[tex]BG^{2}=BU^{2}+GU^{2}[/tex]

substitute the given values

[tex]10^{2}=6^{2}+GU^{2}[/tex]

[tex]GU^{2}=100-36[/tex]

[tex]GU^{2}=8\ units[/tex]

step 3

Find the ratio of its corresponding sides

If the triangles are similar

[tex]\frac{FD}{BG}=\frac{FE}{BU}=\frac{DE}{GU}[/tex]

substitute the given values

[tex]\frac{5}{10}=\frac{3}{6}=\frac{4}{8}[/tex]

[tex0.5=0.5=0.5[/tex] -----> is true

therefore

The triangles are similar

Answer:

The last choice is the one you want.

Step-by-step explanation:

Use the 5th row of Pascal's Triangle.  Since you have a 4th degree polynomial, there will be 5 terms in it.  The 5 coefficients, in order, are:

1, 4, 6, 4, 1

We will use these coefficients only up to and including the third one, since that is the one you want.  Binomial expansion using Pascal's Triangle looks like this:

[tex]1(3x)^4(y^3)^0+4(3x)^3(y^3)^1+6(3x)^2(y^3)^2+...[/tex]

That third term is the one we are interested in.  That simplification gives us:

[tex]6(9x^2)(y^6)[/tex]

Multiply 6 and 9 to get 54, and a final term of:

[tex]54x^2y^6[/tex]

The third term of the given binomial expansion is [tex]54(x^{2})(y^{5})\\[/tex]

The binomial expansion is based on a theorem that specifies the expansion of any power [tex](a+b)^{m}[/tex] of a binomial (a + b) as a certain sum of products [tex]a^{i} b^{i}[/tex], such as (a + b)² = a² + 2ab + b².

The given term is [tex](3x + y^{3}) ^{4}[/tex]

The third term in the expansion will be

[tex]4C_{2}(9x^{2})(y^{3})^{2}\\ = 54(x^{2})(y^{5})\\[/tex]

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the first one

the degree of the polynomial in the numerator is 2.

the degree of the polynomial in the denominator is 2.

when the top and bottom have the same degree, like in this case, the horizontal asymptotes that that can afford us is simply the value of their coefficients.

[tex]\bf \cfrac{x^2-16}{x^2+2x+1}\implies \cfrac{1x^2-16}{1x^2+2x+1}\implies \stackrel{\textit{horizontal asymptote}}{y=\cfrac{1}{1}\implies y=1}[/tex]

for the second one

well, the degree of the numerator is 3.

the degree of the denominator is 2.

when the numerator has a higher degree than the denominator, there are no horizontal asymptotes, however, when the degree of the numerator is exactly 1 degree higher than that of the denominator, the rational has an oblique or slant asymptote, and its equation comes from the quotient of the whole expression, check the picture below, the top part.

for the third one

this one is about the same as the one before it, the numerator has exactly one degree higher than the denominator, so we're looking at an oblique asymptote, check the picture below, the bottom part.

Answer:

the expected value is if your sum is odd because half of the values you could roll are odd witch means you have 50% chance to get odd

because their are not high odds of getting something good

Answer:

Option D (As the x-values go to negative infinity, the function's values go to positive infinity).

Step-by-step explanation:

The graphed function shows a curve which has two turning points and three x-intercepts, which means it is a cubic polynomial. To check which statement is true, we will check all the statements one by one.

Option A) The graph shows that after the second turning point, the function starts to increase. Which means that as x-values increase, the function values will approach positive infinity. Therefore, option A is incorrect.

Option B) This option is incorrect because the graph explicitly shows that f(0) = 0, which means that when x = 0, the function value is also 0.

Option C) This option is incorrect because the function value is 0 at the x-value = 0, as shown in the graph. It can be also seen that As the x-values go to negative infinity, the function's values go to positive infinity since the value of the function decreases as the value of x decreases. Hence Option D is the correct answer!!!

Answer:

The correct option is D.

Step-by-step explanation:

Consider the provided graph of the function.

As the x values go to positive infinity or negative infinity the function value increase or goes to positive infinity.

The end behavior of the function is,

[tex]f(x)\rightarrow +\infty, as x\rightarrow -\infty[/tex]

[tex]f(x)\rightarrow +\infty, as x\rightarrow +\infty[/tex]

Now consider the provided options.

Option A is incorrect because As the x-values go to positive infinity, the function's values go to positive infinity.

Option B is incorrect because As the x-values go to zero, the function's values doesn't go to positive infinity.

Option C is incorrect because As the x-values go to negative infinity, the function's values are not equal to zero.

Option D is the correct option because As the x-values go to negative infinity, the function's values go to positive infinity.

Therefore, the correct option is D.

Answer:

  -4432.5 m

Step-by-step explanation:

Displacement is measured in meters, so will be the product of velocity in m/s and time in s.

  (-98.5 m/s)×(45.0 s) = -4432.5 m

___

If you're concerned with significant figures, you can round this to -4430 m, which has the required 3 significant figures.

Answer:

-4432.5 m

Step-by-step explanation:

distance (or displacement) = rate times time.

Here, the displacement is

                                             (-98.5 m/s)(45.0 s) = -4432.5 m

Answer:

  Yes

Step-by-step explanation:

The law of cosines relates the three sides of a triangle with the cosine of the angle opposite one of them. It is useful for finding an angle of the triangle when only the side lengths are given, as here.

Answer:

  Your work is correct as far as it goes. Now eliminate the terms that are zero.

Step-by-step explanation:

Multiplying anything by zero gives zero. Adding zero is like adding nothing. Zero is called the "additive identity element" because ...

  a + 0 = a

Adding zero doesn't change anything. You can (and should) drop the zero if your goal is to simplify the expression.

[tex]a. \quad x_{f}=v_{0}\\\\b. \quad x_{f}=v_{0}t\\\\c. \quad v_{f}^2=v_{0}^2[/tex]

The correct option is C. Never The product of (a - b)(a - b) is always equal to a² - 2ab + b².

The product of (a - b)(a - b) can be expanded using the distributive property:

(a - b)(a - b) = a(a) - a(b) - b(a) + b(b)

Simplify by multiplying the terms:

= a² - ab - ab + b²

Combine like terms:

= a² - 2ab + b²

As you can see, the product of (a - b)(a - b) is a² - 2ab + b², not a² - b².

However, there is a well-known algebraic identity called the difference of squares, which states that a² - b² can be factored as (a + b)(a - b). So, the correct statement is:

(a - b)(a - b) is equivalent to a² - 2ab + b², not a² - b².

Therefore, the answer is C. Never the product of (a - b)(a - b) is always equal to a² - 2ab + b².

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Answer: OPTION D.

Step-by-step explanation:

The vertex form of a quadratic function is:

[tex]y= a(x - h)^2 + k[/tex]

Where (h, k) is the vertex of the parabola and "a" is the coefficient of the squared in the parabola's equation.

We know that the vertex of this parabola is at (5,5) and we also know that when the x-value is 6, the y-value is -1.

Then  we can substitute values into  [tex]f (x) = a(x - h)^2 + k[/tex] and solve for "a". This is:

[tex]-1= a(6- 5)^2 + 5\\\\-1=a+5\\\\-1-5=a\\\\a=-6[/tex]

Answer:

D

Step-by-step explanation:

Answer:

0.37

Step-by-step explanation:

we have given that emails arrives at the server at the rate of 10 per hour means [tex]\frac{10}{60}=0.166[/tex]  per minute

we have to find the probability that the time difference between the two email is more than 2 minute

so probability [tex]P\left ( X> 2 \right )=e^{-2\lambda }=e^{-2\times 0.166}=0.7166[/tex]

The probability that the time between two consecutive emails arriving at the server is more than two minutes is 0.72 (or 72%).

Given:

- Average rate of email arrivals [tex](\( \lambda \))[/tex] = 10 per hour

1. Understanding the Poisson Process:

  - In a Poisson process, the time between events (in this case, email arrivals) follows an exponential distribution.

  - If [tex]\( \lambda \)[/tex] is the average rate of events per unit time (here, per hour), the time between events (interarrival time) T follows an exponential distribution with parameter [tex]\( \lambda \)[/tex].

2. Parameter Conversion:

  - Since [tex]\( \lambda = 10 \)[/tex] emails per hour, we convert this to the rate per minute:

 [tex]\[ \lambda_{\text{minute}} = \frac{10}{60} = \frac{1}{6} \text{ emails per minute} \][/tex]

3. Probability Calculation:

  - We are interested in the probability that the time between two consecutive emails is more than two minutes.

  - Let X denote the time between two consecutive emails. X follows an exponential distribution with rate [tex]\( \lambda_{\text{minute}} = \frac{1}{6} \)[/tex].

[tex]\[ P(X > 2) = e^{-\lambda_{\text{minute}} \cdot 2} \][/tex]

  Substitute [tex]\( \lambda_{\text{minute}} = \frac{1}{6} \)[/tex]:

 [tex]\[ P(X > 2) = e^{-\frac{1}{6} \cdot 2} \] \[ P(X > 2) = e^{-\frac{1}{3}} \][/tex]

4. Calculating the Probability:

  - Use a calculator to find [tex]\( e^{-\frac{1}{3}} \)[/tex].

[tex]\[ e^{-\frac{1}{3}} \approx 0.7165 \][/tex]

  Therefore, the probability that the time between two consecutive emails is more than two minutes is approximately 0.72 (rounded to two decimal places).

This result aligns with the characteristics of a Poisson process with an average arrival rate of 10 emails per hour.

The intersection of plane GFL and a plane that contains points A and C can be any plane that passes through those two points.

In mathematics, an intersection of two planes is the set of points that are common to both planes.

In this case, we want to find the intersection of plane GFL and a plane that contains points A and C.

Since both points A and C lie on the same plane, any plane that contains both points A and C would intersect plane GFL at those points.

Therefore, any plane that passes through points A and C would be an intersection of plane GFL and a plane that contains points A and C.

Examples of planes that contain points A and C are:

A plane that contains the line segment AC

A plane that is perpendicular to line AC at point A

A plane that is perpendicular to line AC at point C

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Answer:

  573.6 ft

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relationship of right triangle sides and angles:

  Tan = Opposite/Adjacent

This tells us ...

  tan(61°) = (height)/(distance to first point)

or

  distance to first point = height/tan(61°)

Likewise, ...

  distance to second point = height/tan(32°)

Then the difference of the distances is ...

  distance to second point - distance to first point

     = height/tan(32°) -height/tan(61°)

  600 ft = height × (1/tan(32°) -1/tan(61°))

Dividing by the coefficient of height, we have ...

  height = (600 ft)/(1/tan(32°) -1/tan(61°)) ≈ (600 ft)/(1.04603) ≈ 573.6 ft

Answer:

574

Step-by-step explanation:

Answer:

Base of the original triangle is 12 cm.

Step-by-step explanation:

Let base of triangle be x  

two equal legs  of triangles by y

therefore perimeter of triangle

                       x+y+y = 50 or x+2y =50

according to the question

 if base is x+3 and leg is y-4

then both are equal

   that is x+3 = y-4

            y-x = 7 or y =x+7

   x+2y =50

   x+2(x+7) = 50

    x+2x +14 =50

     3x +14 =50

     3x = 50 -14

      3x = 36

      x = 12

therefore base of the original  triangle is 12 cm                    

Answer: Adjacent Angles

A pair of angles which share a common side and vertex is called adjacent angles.

When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.

Given:

A pair of angles which share a common side and vertex.

If two angles share a side and a vertex, they are said to be adjacent in geometry.

In other words, adjacent angles do not overlap and are placed precisely next to one another.

Therefore, the right definition is adjacent angles.

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Answer:

  7 6/7

Step-by-step explanation:

Parallel segment BD creates triangle BDC similar to triangle AEC. The sides and segments of similar triangles are proportional:

  x/11 = 5/7

  x = 55/7 = 7 6/7 . . . . . multiply by 11

Step-by-step explanation:

3x3-2x2

3(-2)3-2(-2)2

-6×3+4×2

-18+8

-10

I hope it will help you!

Answer:

-10

Step-by-step explanation:

Yes. All you have to remember is that double negatives result in POSITIVES.

I am joyous to assist you anytime.

Answer:

Step-by-step explanation:

Let the other leg = x

x^2 + 4^2 = (3x)^2

x^2 + 4^2 = 9x^2

4^2 = 9x^2 - x^2

16= 8x^2

16/8 = x^2

x^2 = 2

x = sqrt(2)

The lengths of the sides

x = sqrt(2)      

other side =4

hypotenuse = 3*sqrt(2)

x = 1.4

other side= 4

hypotenuse = 3*1.4142

hypotenuse = 4.2

Answer:

4 feet, 1.4 feet, 4.2 feet

Step-by-step explanation:

We are looking for the lengths of the three sides of a right triangle. We are given that one leg has length 4ft. Let x be the length of the other leg. Since the hypotenuse of the right triangle is three times the length of this leg, we can represent the hypotenuse as 3x. This is a right triangle, so we can use the Pythagorean Theorem to find x.

42+x216+x2=(3x)2=9x2

Subtracting x2 from both sides, then dividing by 8 to isolate the x, we have

8x2x2x=16=2=±2–√

Considering only the positive value for x, the lengths of the three sides of the triangle are approximately 4 feet, 2–√≈1.4 feet, and 32–√≈4.2 feet.

Answer:

(a) The expression for the average cost per pair of shoes is [tex]A(x)=\frac{12000}{x}+19[/tex] and equation for the situation is [tex]\frac{12000}{x}+19-(\frac{12000}{x+1000}+19)=0.43[/tex].

(b) x=[tex]x\approx 4806[/tex]

(c) The average function is not defined for x=0, so the domain of the function is all real numbers except 0.

(d) The reasonable domain is all natural numbers.

Step-by-step explanation:

The cost in dollars to manufacture x pairs of shoes is given by

[tex]C(x)=12000+19x[/tex]

where, x is the pairs of shoes.

(a)

The expression for the average cost per pair of shoes.

[tex]A(x)=\frac{C(x)}{x}[/tex]

[tex]A(x)=\frac{12000+19x}{x}[/tex]

[tex]A(x)=\frac{12000}{x}+19[/tex]

This month, the manufacturer produced 1000 more pairs of shoes than last month. The average cost per pair dropped by $0.43.

[tex]A(x)-A(x+1000)=0.43[/tex]

[tex]\frac{12000}{x}+19-(\frac{12000}{x+1000}+19)=0.43[/tex]

Therefore the expression for the average cost per pair of shoes is [tex]A(x)=\frac{12000}{x}+19[/tex] and equation for the situation is [tex]\frac{12000}{x}+19-(\frac{12000}{x+1000}+19)=0.43[/tex].

(b)

On solving the above equation we get

[tex]\frac{12000}{x}-\frac{12000}{x+1000}=0.43[/tex]

[tex]\frac{12000000}{x^2 + 1000 x} = 0.43[/tex]

[tex]12000000=0.43(x^2 + 1000 x)[/tex]

[tex]12000000=0.43x^2 + 430x[/tex]

[tex]0=0.43x^2 + 430x-12000000[/tex]

Using graphing calculator we get

[tex]x\approx -5806.31,4806.31[/tex]

The pair of shoe can not be native and decimal value.

[tex]x\approx 4806[/tex]

Therefore the solution is [tex]x\approx 4806[/tex].

(c)

The average cost function is

[tex]A(x)=\frac{12000}{x}+19[/tex]

The function is not defined if the denominator is 0.

The above function is not defined for x=0, so the domain of the function is all real numbers except 0.

(d)

In the average function x represents the number of pair of shoe.

It means the value of x must be a positive integer.

Since the average function is not defined for x=0, So the reasonable domain of average function is

Domain={x : x∈Z⁺, x≠0}

Domain=N

Therefore the reasonable domain is all natural numbers.

Answer:

Step-by-step explanation:

The base of the exponential function is 1 + r.

The initial value is P.

The exponent is t.

The base of the exponential function is 1 + r

exponent is t, and

initial value is P

The mathematical expression for an exponential function is f (x) = a ˣ, where “x” denotes a variable and “a” denotes a constant. This constant is referred to as the base of the function and should be greater than zero. The most common use exponential function is with base e

Given A coin formula V(t) = P(1+r)^t

to find the initial value put t = 0

V(0) = P(1+r)⁰

V(0) = P

P is the initial value

and exponent is the term which is in the power of any exponential function

here t is exponent and (1+r) is base function

Hence according to coin formula The base of the exponential function is 1 + r; exponent is t;  and initial value is P.

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Answer:

2

Step-by-step explanation:

The degree of the vertex B is 2 because from vertex B there are 2 line segments coming out of it.

Another example, C has degree 4 because from it there are 4 line segments coming from it.

Answer:

y = 5x - 11

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 )

here slope m = 5, hence

y = 5x + c ← is the partial equation

To find c substitute (1, - 6) into the partial equation

- 6 = 5 + c ⇒ c = - 6 - 5 = - 11

y = 5x - 11 ← equation of line

[tex]\bf ~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$2500\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ t=years\dotfill &5 \end{cases} \\\\\\ A=2500e^{0.03\cdot 5}\implies A=2500e^{0.15}\implies A\approx 2904.59[/tex]

Answer:

C. $2904.59

Step-by-step explanation:

Compounded continually means that the principal amount is constantly earning interest and the interest keeps earning on the interest earned.

The formula to apply is

[tex]A=Pe^{rt}[/tex]

where A is the amount, P is the principal, r is rate of interest, t is time in years and e is the mathematical constant

Taking

e=2.7183, P=$2500,  r=3% and t=5 years

[tex]A=Pe^{rt} \\\\\\A=2500*2.7183^{0.03*5} \\\\\\A=2500*1.1618\\\\\\A=2904.59\\\\A=2904.59[/tex]

Answer:

  [tex]\cos{A}=\pm\sqrt{\dfrac{1+\cos{x}}{2}}[/tex]

Step-by-step explanation:

[tex]\cos{A}=\cos{\frac{x}{2}}=\pm\sqrt{\dfrac{1+\cos{x}}{2}}[/tex]

Apparently, you're supposed to recognize that the formula tells you the value of cos(x/2).