Determine the number of x-intercepts that appear on a graph of each function. f(x)= (x-6)^2(x+2)^2

Answer:

8 yards

Step-by-step explanation:

This can be illustrated from drawing it. (Attachment)

Scale-  Real : Map

          10 yard : 1 cm

        150 yard : 15 cm

        145 yard : 14.5 cm

Step 1: Draw a 7.5 cm line from origin to Point A

Step 2: Form a 2 degree angle from the origin

Step 3: Draw a 7.25 cm line 2 degree angle from the origin to Point B

Step 4: Measure the distance in cm from Point A to Point B

Step 5: Convert the distance from Point A to Point B in yards.

Therefore, the ball is 8 yards far from the goal.

!!

Answer:

The ball is 7.176 yards away from the center of the goal.

Step-by-step explanation:

Given distance between the center goal and Mark is AB = 150 yards

Distance traveled by ball at angle 2 degree off to the right from Mark is

AC = 145 yards

We have to find the distance BC in triangle ABC

Using cosine rule

[tex]BC^{2}=AB^{2}+AC^{2}-2AB\times AC\times \cos \Theta[/tex]

=>[tex]BC^{2}=[150^{2}+145^{2}-2\times 150\times 145\times \cos (2^{\circ})] yards^{2}[/tex]

=>BC^{2}=51.5 yards^{2}

=>[tex]BC=\sqrt{(51.5 yards^{2})}=7.176yards[/tex]

Thus the ball is 7.176 yards away from the center of the goal.

Answer: (1,3,5) & (2,2)

Step-by-step explanation:

Answer:

< 8, 4 >

Step-by-step explanation:

Consider the coordinates

x- coordinate A - 3 → A' 5 → that is + 8

y- coordinate A 1 → A' 5 → that is + 4

Hence T = < 8, 4 >

or (x, y) → (x + 8, y + 4)

The translation T is given by:

                        T(x,y)=(x+8,y+4)

i.e. it shifts the point 8 units to the right and 4 units up.

The translation is the transformation that changes the location of points of the figure but there is no change in the shape as well as size of the original figure.

It is given that:

The translation T maps point A(-3,1) onto point A'(5,5).

so, if the translation rule that is used is:

(x,y) → (x+h,y+k)

Here

(-3,1) → (5,5)

i.e.

-3+h=5    and  1+k=5

i.e.

h=5+3   and   k=5-1

i.e.

h=8   and   k=4

Hence, the translation is 8 units to the right and 4 units up.

(9 - 4i)(2 + 5i)

To solve this question you must FOIL (First, Outside, Inside, Last) like so

First:

(9 - 4i)(2 + 5i)

9 * 2

18

Outside:

(9 - 4i)(2 + 5i)

9 * 5i

45i

Inside:

(9 - 4i)(2 + 5i)

-4i * 2

-8i

Last:

(9 - 4i)(2 + 5i)

-4i * 5i

-20i²

Now combine all the products of the FOIL together like so...

18 + 45i - 8i - 20i²

***Note that i² = -1; In this case that means -20i² = 20

18 + 45i - 8i + 20

Combine like terms:

38 - 37i

^^^This is your answer

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

9x²y¹⁴

Step-by-step explanation:

[tex]\tt (3xy^4)^2(y^2)^3\\\\=3^2x^2y^{4\cdot2}\cdot y^{2\cdot3}\\\\=9x^2y^{8}\cdot y^{6}\\\\= 9x^2y^{8+6}\\\\= 9x^2y^{14}[/tex]

Answer:

D. if we are describing how to get from y=x^2 to y=x^2+8.

Step-by-step explanation:

If we are describing how to get from y=x^2 to y=x^2+8, then the transformation is just a translation of 8 units up.

If the equation was y=x^2-8, it would have been down 8 units.

If the equation was y=(x-8)^2, it would have been right 8 units.

If the equation was y=(x+8)^2, it would have been left 8 units.

Answer:

The x-coordinate of the solution is x=3

Step-by-step explanation:

we have

[tex]y=-x+5[/tex] ------> equation A

[tex]y=x-1[/tex] ------> equation B

Solve the system of equations by substitution

Substitute equation B in equation A and solve for x

[tex]x-1=-x+5[/tex]

[tex]x+x=5+1[/tex]

[tex]2x=6[/tex]

[tex]x=3[/tex]

Find the value of y

[tex]y=x-1[/tex]  ------> [tex]y=3-1=2[/tex]

The solution of the system of equations is the point (3,2)

therefore

The x-coordinate of the solution is x=3

Answer:

x = 3

Step-by-step explanation:

i did the same test and got it right

Answer:

7/20 m^2

Step-by-step explanation:

A = l*w

   =3/5 * 7/12

Multiplying the numerators

3*7 =21

Multiplying the denominators

5*12= 60

Putting the numerator over the denominator

21/60

Divide the top and bottom by 3

7/20

Answer:

7/20

Step-by-step explanation:

Answer:

(2,2)

Step-by-step explanation:

Step-by-step explanation:

¼ pizza is to 5 dollars as x pizza is to 8 dollars.

¼ / 5 = x / 8

Cross multiply:

5x = 2

Divide:

x = ⅖

You can buy ⅖ of a pizza.

Step-by-step explanation:

I have answered ur question

To make y the subject, distribute and simplify the equation, then isolate y on one side by performing the necessary operations.

To make y the subject of the equation X = 5y + 4/2y - 3, we need to isolate y on one side of the equation.

Therefore, y = (X + 1)/5 is the solution.

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Answer:

[tex]\large\boxed{C.\ y=2+x^4}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of linear function:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

============================

[tex]A.\\\\9y+3=0\qquad\text{subtract 3 from both sides}\\\\9y=-3\qquad\text{divide both sides by 9}\\\\y=-\dfrac{3}{9}\\\\y=-\dfrac{1}{3}\to m=0,\ b=-\dfrac{1}{3}[/tex]

[tex]B.\\\\y-4x=1\qquad\text{add}\ 4x\ \text{to both sides}\\\\y=4x+1\to m=4,\ b=1[/tex]

[tex]C.\\\\y=2+x^4\qquad\text{nonlinear, because}\ x\ \text{is in fourth power}[/tex]

[tex]D.\\\\x-2y=7\qquad\text{subtract}\ x\ \text{from both sides}\\\\-2y=-x+7\qquad\text{divide both sides by (-2)}\\\\y=\dfrac{1}{2}x-\dfrac{7}{2}\to m=\dfrac{1}{2},\ b=-\dfrac{7}{2}[/tex]

[tex]E.\\\\\dfrac{x}{y}+1=2\qquad\text{subtract 1 from both sides}\\\\\dfrac{x}{y}=1\to y=x\to m=1,\ b=0[/tex]

Answer:

graph c

Step-by-step explanation:

there is no slope since it doesn't go up/down by anything or over by anything. meaning there is no increase or decrease.

[tex]13 - |3x-9| = 2\\|3x-9|=11\\3x-9=11\vee 3x-9=-11\\3x=20 \vee 3x=-2\\x=\dfrac{20}{3} \vee x=-\dfrac{2}{3}[/tex]

TWO

Answer:

2

Step-by-step explanation:

[tex]13-|3x-9|=2[/tex]

Subtract 13 on both sides.

[tex]-|3x-9|=2-13[/tex]

Simplify right hand side.

[tex]-|3x-9|=-11[/tex]

Take the opposite of both sides (also known as multiply both sides by -1).

[tex]|3x-9|=11[/tex].

Let u=3x-9.

Since we have |u|=positive, we will have two solutions for x.

If we had |u|=negative, we will have no solutions for x.

If we had |u|=0, we would have one solution for x.

Answer:

1980.

Step-by-step explanation:

John was born in  1995 - 40 = 1955.

His father was born in 1995 - 65 = 1930.

Let x  be Johns age and his father 2x

1955 + x = 1930 + 2x

1955 - 1930 = 2x - x

x =  25

So the year is 1955 + 25 = 1980..

In that year John was 25 and his father was  50.

Answer:

[tex]3r^{4}s^{5}\\-r^{4}s^{6}[/tex]

Step-by-step explanation:

The standard form of a polynomial is when its term of highest degree is at first place.

In this case, we have two variables. The grade of each term is formed by the sum of its exponents. That means both given terms have a degree of six. So, the right answers must have a higher degree.

Therefore, the right answers are the second and third choice, because their degrees are 9 and 10 respectively.

Answer:

Vertices of hyperbola: (2,0) and (-2,0)

Foci of hyperbola: (8,0) and (-8,0)

Step-by-step explanation:

The given equation is:

[tex]\frac{x^2}{4}-\frac{y^2}{60}=1[/tex]

The standard form of equation of hyperbola is:

[tex]\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1[/tex]

Center of hyperbola is (h,k)

Comparing given equation with standard equation

h=0, k=0

so, Center of hyperbola is (0,0)

Vertices of Hyperbola

Vertices of hyperbola can be found as:

The first vertex can be found by adding h to a

a^2 - 4 => a=2, h=0 and k=0

So, first vertex is (h+a,k) = (2,0)

The second vertex can be found by subtracting a from h

so, second vertex is ( h-a,k) = (-2,0)

Foci of Hyperbola

Foci of hyperbola can be found as

The first focus of hyperbola can be found by adding c to h

Finding c (distance from center to focus):

[tex]c=\sqrt{a^2+b^2}  \\c=\sqrt{(2)^2+(2\sqrt{15})^2}\\c=8[/tex]

So, c=8 , h=0 and k=0

The first focus is (h+c,k) = (8,0)

The second focus is (h-c,k) = (-8,0)

Answer:

[tex]2(x-1)^{2}=4[/tex]

Step-by-step explanation:

we have

[tex]2x^{2} -4x-2=0[/tex]

This is the equation of a vertical parabola open upward

The vertex is a minimum

Convert the equation into vertex form

Group terms that contain the same variable and move the constant to the other side

[tex]2x^{2} -4x=2[/tex]

Factor the leading coefficient

[tex]2(x^{2} -2x)=2[/tex]

[tex]2(x^{2} -2x+1)=2+2[/tex]

[tex]2(x^{2} -2x+1)=4[/tex]

Rewrite as perfect squares

[tex]2(x-1)^{2}=4[/tex] -----> this is the answer

The vertex is the point (1,-4)

Answer:

F. 10

Step-by-step explanation:

She had 15 flowers today

So if she had 5 more than yesterday

You subtract the 5 to get how much she had yesterday

15-5=10

Answer:

F. 10

Step-by-step explanation:

Today: 15 flowers

          : 5 more than yesterday

more than means add

15 = 5+ yesterday

Subtract 5 from each side

15-5 = 5+ yesterday -5

10 = yesterday

Neither of those two graphs do the trick, but if I saw the rest of the answer choices, then I would be happy to assist you.

Answer:

Trey earns a base pay of $47,300 plus 15% for each car sold.

The equation that represets Trey's total pay in dollars is:

y = $47,300 + 0.15x

Where $47,300 represents the base pay, and 0.15x represents the money he earn for the total cars sold.

Answer:

[tex]y=47,300+0.15x[/tex]

Step-by-step explanation:

Let x represent total sales in dollars.

We have been given that Trey earns base pay of $47,300 and was paid  commission of 15% for each car he sold.

Since Trey is paid 15% for each car he sold and total sales were x dollars, this means his commission would be 15% of x that is [tex]\frac{15}{100}x=0.15x[/tex].

The total salary of Trey would be base salary plus commission: [tex]y=47,300+0.15x[/tex]

Therefore, the equation [tex]y=47,300+0.15x[/tex] represents Trey's total pay in dollars.

Answer:

The answer is B, given the module of a number has always a positive value

Answer:

Answer is B.

SECOND NUMBER LINE

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

Let's identify some points here that are on the graph:

(0,0), (pi/2,-1), (pi,0).

Let's see if this is enough.

We want to see which equation holds for these points.

Let's try A.

(0,0)?

y=cos(x-pi/2)

0=cos(0-pi/2)

0=cos(-pi/2)

0=0 is true so (0,0) is on A.

(pi/2,-1)?

y=cos(x-pi/2)

-1=cos(pi/2-pi/2)

-1=cos(0)

-1=1 is false so (pi/2,-1) is not on A.

The answer is not A.

Let's try B.

(0,0)?

y=cos(x)

0=cos(0)

0=1 is false so (0,0) is not on B.

The answer is not B.

Let's try C.

(0,0)?

y=sin(-x)

0=sin(-0)

0=sin(0)

0=0 is true so (0,0) is on C.

(pi/2,-1)?

y=sin(-x)

-1=sin(-pi/2)

-1=-1 is true so (pi/2,-1) is on C.

(pi,0)?

y=sin(-x)

0=sin(-pi)

0=0 is true so (pi,0) is on C.

So far C is winning!

Let's try D.

(0,0)?

y=-cos(x)

0=-cos(0)

0=-(1)

0=-1 is not true so (0,0) is not on D.

So D is wrong.

Okay if you do look at the curve it does appear to be a reflection of the sine function.

Answer:

C

step-by-step explanation:

you just have to subtract them 9/16-1/4=8/12

Answer:

A

Step-by-step explanation:

A function can't have the same number more than once, so the answer is A since there are no repeating numbers.

Answer:

1) [tex]3 a^3 + 8 a^2 b - b^3[/tex]

2) 93 inches

Step-by-step explanation:

1) We know that the lenghts are given by these expressions:

[tex]2ab(a - b)\\\\3a^2(a + 2b)\\\\b^2(2a - b)[/tex]

Then, we need to add them in order to find the expression that represents the total length of the rope:

- Apply Distributive property.

- Add the like terms.

Then:

[tex]=2ba^2-2ab^2+3a^3+6ba^2+2ab^2-b^3\\\\=3 a^3 + 8 a^2 b - b^3[/tex]

2) Knowing that:

[tex]a=2in\\\\b=3in[/tex]

We must substitute these values into [tex]3 a^3 + 8 a^2 b - b^3[/tex] in order to caculate the total lenght of the rope. This is:

 [tex]3 (2in)^3 + 8 (2in)^2 (3in) - (3in)^3=93in[/tex]

Answer:

w=12

l=20

Step-by-step explanation:

The area can be found using the following equation:

[tex]A=lw[/tex]

Given the information provided, we are also told the following:

[tex]l=w+8[/tex]

Therefore, we can plug in our length and our area:

[tex]240=w(w+8)\\240=w^2+8w\\\\w^2+8w-240=0[/tex]

We can solve by using the quadratic formula.

[tex]w=\frac{-8+\sqrt{8^2-4(1)(-240)} }{2(1)}=12 \\\\[/tex]

w=12, so w+8=20.

Step-by-step explanation:

Just graph it and see if the descriptions fit the graph

(see attached)

A. We can see from the graph that the possible x-values are -∞ ≤ x ≤ +∞ . Hence limiting to domain to x≤ -2 this is obviously not true.

B. We can see from the graph that the vertex is y = 6 and that the entirety of the graph is under this point, hence range y<6 is true

C. We can see that the vertex is located at x=-2. Every part of the graph to the left of this point has a positive slope, hence the function is increasing for negative infinity to this point x=-2 is true

D) We can see that for the interval -4<x<∞, the graph actually increases between -4<x<-2, and then decreases after that. Hence this statement is not true.

E. it is obvious that the y intercept is y=2 which is positive. Hence this is true.

The graph of F(x)=-x^2-4x+2 is a downward-opening parabola with its vertex serving as the local and global maximum. There are no asymptotes for this quadratic function. The shape of the graph is best understood by examining its behavior over a range of x-values and by sketching it with the vertex and axis of symmetry.

The graph of the function F(x) = -x^2 - 4x + 2 represents a parabola opening downward because the coefficient of x^2 is negative. To understand the nature of the graph, we evaluate its characteristics by identifying the vertex, the axis of symmetry, and whether it has local or global extrema. The vertex of this parabola can be found using the formula -b/2a, which gives us the x-coordinate, and by substituting that back into the function for the y-coordinate. The axis of symmetry will be a vertical line passing through the vertex's x-coordinate.

Since this is a quadratic function, it does not have asymptotes because it extends indefinitely in both the positive and negative directions of the y-axis. Instead, the parabola will have a maximum point at the vertex, which is a local and global maximum because the parabola opens downward. Moreover, we should evaluate the function for a range of x-values to understand its behavior for large negative x, small negative x, small positive x, and large positive x.

Sketching the graph of this function would involve plotting the vertex, drawing the axis of symmetry, and selecting a few points around the vertex to determine the shape of the parabola.

Answer:

Part A)

[tex]P=\$8,500\\ r=0.052\\n=4[/tex]  

Part B) [tex]S(7)=\$12,203.47[/tex]  

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]S(t)=P(1+\frac{r}{n})^{nt}[/tex]  

where  

S is the Future Value  

P is the Present Value  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

Part A)

in this problem we have  

[tex]P=\$8,500\\ r=5.2\%=5.2/100=0.052\\n=4[/tex]  

Part B) How much money will Marcus have in the account in 7 years?

we have

[tex]t=7\ years\\ P=\$8,500\\ r=0.052\\n=4[/tex]  

substitute in the formula above  

[tex]S(7)=8,500(1+\frac{0.052}{4})^{4*7}[/tex]  

[tex]S(7)=8,500(1.013)^{28}[/tex]  

[tex]S(7)=\$12,203.47[/tex]  

In this problem, we find that Marcus should use the values P = $8,500, r = 0.052 and n = 4 for the given savings account. After calculating, we conclude that Marcus would have approximately $11,713.69 in the account after 7 years.

This problem involves the concept of compound interest in mathematics. Let's break it down:

We use the formula S(t)=P(1+rn)^(nt):

S(7) = 8500(1 + 0.052/4)^(4*7)

By calculating the above, we find the balance after seven years to be approximately $11,713.69 when rounded to the nearest penny.

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Answer:

[tex]\large\boxed{\dfrac{1}{36a^4b^{10}}}[/tex]

Step-by-step explanation:

[tex]\left(\dfrac{\left(2a^{-3}b^4\right)^2}{\left(3a^5b\right)^{-2}}\right)^{-1}\qquad\text{use}\ a^{-1}=\dfrac{1}{a}\\\\=\dfrac{\left(3a^5b\right)^{-2}}{\left(2a^{-3}b^4\right)^2}\qquad\text{use}\ (ab)^n=a^nb^n\\\\=\dfrac{3^{-2}(a^5)^{-2}b^{-2}}{2^2(a^{-3})^2(b^4)^2}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=\dfrac{3^{-2}a^{(5)(-2)}b^{-2}}{4a^{(-3)(2)}b^{(4)(2)}}=\dfrac{3^{-2}a^{-10}b^{-2}}{4a^{-6}b^8}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}[/tex]

[tex]=\dfrac{3^{-2}}{4}a^{-10-(-6)}b^{-2-8}=\dfrac{3^{-2}}{4}a^{-4}b^{-10}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\=\dfrac{1}{3^2}\cdot\dfrac{1}{4}\cdot\dfrac{1}{a^4}\cdot\dfrac{1}{b^{10}}=\dfrac{1}{36a^4b^{10}}[/tex]

Answer:

1 / 36a^4 b^10

Step-by-step explanation: