Please help this is my last tutorial in this subject.......

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:

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:

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:

f(8) = 8.25(1.1)^7; f(8) = 16.077

Step-by-step explanation:

In order to calculate the explicit formula we need to look at the y coordinates. All the options list the formula of a Geometric Sequence, so we will find which sequence defines the given coordinates:

The sequence is:

8.25, 9.075, 9.9825, 10.98075

f(1) = First term of the Sequence = 8.25

r = Common Ratio = Ratio of two consecutive terms = [tex]\frac{9.075}{8.25}[/tex] = 1.1

The explicit formula for a geometric sequence is:

[tex]f(n)=f(1)(r)^{n-1}[/tex]

Using the values, we get:

[tex]f(n)=8.25(1.1)^{n-1}[/tex]

For 8th term, we have to replace n by 8:

[tex]f(8)=8.25(1.1)^{8-1}\\\\ f(8)=8.25(1.1)^{7} \\\\ f(8)=16.077[/tex]

So, second option gives the correct answer: f(8) = 8.25(1.1)^7; f(8) = 16.077

Answer:

B // f(8) = 8.25(1.1)^7; f(8) = 16.077

Step-by-step explanation:

I'm Pretty Sure She's Got It ^^^

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:

60 nickles and 30 dimes

Step-by-step explanation:

60 $0.05=3.00

30 $.10=3.00

60+30=90

In the box, there are 30 dimes and 60 nickels, as determined by solving a system of equations based on the total number of coins and their value.

The box contains both dimes and nickels, totaling an amount of money of $6.00. Because a dime is worth $0.10 and a nickel is worth $0.05, we can set up a system of equations to solve this problem.

Let's denote the number of dimes as x and the number of nickels as y. Thus, our equations are x + y = 90 (since the total number of coins is 90) and 0.10x + 0.05y = 6 (since the total value of the coins is $6.00).

Solving these equations will give us the number of dimes and nickels in the box. Doubling the second equation gives us 0.20x + 0.10y = 12. We can subtract the first equation from this to solve for x, giving us x = 30. Substituting x=30 into the first equation, y = 90 - 30, so y = 60. So, there are 30 dimes and 60 nickels in the box.

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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:

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:

The perimeter of the triangle is equal to 36 cm

Step-by-step explanation:

we know that

The inscribed circle contained in the triangle BCA is tangent to the three sides

we have that

BF=BH

CF=CG

AH=AG

step 1

Find CG

we know that

CF=CG

so

CF=7 cm

therefore

CG=7 cm

step 2

Find AG

we know that

CA=AG+CG

we have

CA=15 cm

CG=7 cm

substitute

15=AG+7

AG=15-7=8 cm

step 3

Find AH

Remember that

AG=AH

we have

AG=8 cm

therefore

AH=8 cm

step 4

Find BF

Remember that

BF=BH

BH=3 cm

therefore

BF=3 cm

step 5

Find the perimeter of the triangle

P=AH+BH+BF+CF+CG+AG

substitute the values

P=8+3+3+7+7+8=36 cm

The perimeter of  ΔBCA (triangle BCA) is 36 cm

The perimeter of a triangle is the sum of the length of the three sides.

The inscribed circle contained in the triangle BCA is tangent to the three sides

Therefore,

BF = BH = 3 cm

CF = CG = 7 cm

AH = AG = 15 - 7 = 8 cm

Therefore,

perimeter = CA + BC + BA

perimeter = 15 + 3 + 7 + 3 + 8

Therefore,

perimeter = 15 + 10 + 11

perimeter = 15 + 21

perimeter = 36 cm

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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:

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:

[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:

385.5 USD

Step-by-step explanation:

If an average car is sold for 25,700 USD, and the sales person gets 1.5% commission of it, we can easily get to the amount of money that the sales person managed to get from each sale.

The 25,700 should be divided by 100, as that is number of total percentage:

25,700 / 100 = 257

So we have 1% being 257 USD, but we need 1.5%, so we should multiple the 257 USD by 1.5%:

257 x 1.5 = 385.5

So we get a result of 385.5 USD, which is the amount the sales person makes from commissions on average per sold car.

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.

(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

[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:

(2,2)

Step-by-step explanation:

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:

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:

C

step-by-step explanation:

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

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: (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.

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:

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]\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:

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.

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

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:

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