I need help please.

Answer:

[tex]\large\boxed{D.\ \dfrac{-27w^{15}}{c^9}}[/tex]

Step-by-step explanation:

[tex](-3c^{-3}w^5)^3\qquad\text{use}\ (ab)^n=a^nb^n\\\\=(-3)^3(c^{-3})^3(w^5)^3\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=-27c^{-3\cdot3}w^{5\cdot3}=-27c^{-9}w^{15}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\=-27\left(\dfrac{1}{c^9}\right)w^{15}=\dfrac{-27w^{15}}{c^9}[/tex]

Final answer:

To simplify (-3c⁻³w⁵)³, you must distribute the power of 3 to each factor inside the parenthesis and apply the rule for negative exponents to end up with -27w¹⁵/c⁹, which is answer choice D.

Explanation:

The expression to simplify is  (-3c⁻³w⁵)³. We will apply the rule for exponents to simplify the expression. When applying this rule and the negative exponent rule which states that a⁻ⁿ = 1/aⁿ, we get:

The correct answer is D.  -27w¹⁵/c⁹.

The distance from point A to A' after translation is 2 sqrt(13).

The given points are A(-6,-5) and A' is obtained by translating A using the transformation T: (x,y) -> (x + 4, y + 6).

So the coordinates of A' are (-6 + 4, -5 + 6) which is (-2,1).

To find the distance from A to A', we can use the distance formula.

Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the coordinates of A and A' into the formula, we get Distance = sqrt((-2 - (-6))^2 + (1 - (-5))^2).

Calculating the distance, we get Distance = sqrt((4)^2 + (6)^2) = sqrt(16 + 36) = sqrt(52) = 2 sqrt(13).

Answer:

727.29 − 248.50 + x ≥ 500; x ≥ $21.21

Step-by-step explanation:

Write down all the data given :

Beginning amount : $727.29

Balance to be maintained : $ 500

Check : $248.5

Current balance = 727.29 - 248.5 = $478.79

Tony must maintain a balance of $500 so he should have at least $21.21 more (500-478.79)

727.29 - 248.5 + 21.21 = 500

500=500

x can be 21.21 or greater than that which would maintain the balance of $500 or more.

Therefore the third statement is correct.

727.29 − 248.50 + x ≥ 500; x ≥ $21.21

!!

Answer:

x = 44 − y

Step-by-step explanation:

x is the number of glasses of iced tea, and y is the number of glasses of lemonade.  The sum is 44, so:

x + y = 44

Solving for x:

x = 44 − y

Answer: 44-y represents the number of glasses of ice tea she can serve.

Step-by-step explanation:

Since we have given that

Let x be the number of glasses of iced tea.

Let y be the number of glasses of lemonade.

Total number of glasses = 44

According to question,

[tex]x+y=44[/tex]

So, the number of glasses of ice tea she can serve is given by

[tex]x=44-y[/tex]

Hence, 44-y represents the number of glasses of ice tea she can serve.

There are 16 different ways Sarah can top her sundae, considering no toppings, 1 topping or 2 toppings out of 5 available at the restaurant.

The subject of this question is in the field of combinatorics, a branch of mathematics. We are asked to find the number of ways Sarah can top her sundae with at most 2 toppings out of 5 available. The answer will be the number of ways she can pick no topping, or 1 topping, or 2 toppings.

The number of ways to pick no toppings is 1 (just the ice cream), to pick 1 topping out of 5 is 5 (assuming all toppings are different), and to pick 2 toppings out of 5 is represented by a combination formula '5 choose 2', which means: 5! / ((5 - 2)! * 2!) = 10, where '!' denotes factorial.

So by summing these possibilities (1+5+10), we come to the conclusion that Sarah can top her sundae in 16 different ways if she is restricted to at most 2 toppings.

https://brainly.com/question/39347572

#SPJ12

Sarah can top her sundae in 6 different ways if she is restricted to at most 2 toppings.

To calculate the number of ways or combinations, Sarah can top her sundae with at most 2 toppings, we can consider two cases. In the first case, she chooses 0 toppings. In the second case, she chooses 1 topping.

The total number of ways would be the sum of these two cases.

In the first case, she has only one choice, which is not to choose any topping.

In the second case, she can choose any one of the 5 toppings. So, the total number of ways would be 1 + 5 = 6.

Therefore, Sarah can top her sundae in 6 different ways if she is restricted to at most 2 toppings.

https://brainly.com/question/33904163

#SPJ12

Answer:

A) -0.3 of an inch per second

Step-by-step explanation:

You'll have to put (2, 8.4) and (4, 7.8) into the slope formula.

It's represented as (∆y)/(∆x) = m

(y1 + y2)/(x1 + x2) = m

You subtract both y's in the numerator and subtract both x's in the denominator.

Like this:

(8.4-7.8)/(2-4) = m

(0.6)/(-2) = m

-0.3 = m

Answer:

y = (-0.3 in/sec)x + 9.0 in

Step-by-step explanation:

(2, 8.4) and (4, 7.8) are points on a linear graph.

As we go from  (2, 8.4)  to  (4, 7.8), x increases by 2 and y decreases by 0.6.

Thus, the slope of the line is m = rise / run = -0.6 / 2, or m = -0.3 inches/sec

Let's use the slope-intercept form of the equation of a straight line, with m = -0.3 in/sec and one point being (2, 8.4).

Then y = mx + b becomes 8.4 = (-0.3 in/sec)(2) + b, or

8.4 = -0.6 + b.  Thus, b = 9.0, and the desired equation is thus:

y = (-0.3 in/sec)x + 9.0 in

Answer:

x=(-3+-sqrt15)/2

Step-by-step explanation:

Without using calculatorsoup,

we can use the quadratic formula for x^2+3x-3=0

using it we find:

x=(-b+-sqrtb^2-4ac)/2a

x=(-3+-sqrt3-4*1*-3)/2

x=(-3+-sqrt15)/2

For this case we must resolve the following expression:

[tex]x ^ 2 + 3x-3 = 0[/tex]

The roots will be given by:

[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}[/tex]

We have to:

[tex]a = 1\\\b = 3\\c = -3[/tex]

So:

[tex]x = \frac {-3 \pm \sqrt {3 ^ 2-4 (1) (- 3)}} {2 (1)}\\x = \frac {-3 \pm \sqrt {9 + 12}} {2}\\x = \frac {-3 \pm \sqrt {21}} {2}[/tex]

We have two roots:

[tex]x_ {1} = \frac {-3+ \sqrt {21}} {2} = 0.7913\\x_ {2} = \frac {-3- \sqrt {21}} {2} = - 3.7913[/tex]

Answer:

[tex]x_ {1} = \frac {-3+ \sqrt {21}} {2} = 0.7913\\x_ {2} = \frac {-3- \sqrt {21}} {2} = - 3.7913[/tex]

Answer:

The graphical is radical function sqrt(x) shifted 3 units left

Step-by-step explanation:

The argument of the radical function is x+3, this means, that if x=-3, then y=0 since sqrt(0)=0

The parent function y=sqrt(x), something simmilar ocurrs, y=0 when x=0

This is the key difference between the two given functions.

Answer:

B. 12ft

Step-by-step explanation:

Area of kite is 2 times the area of triangle

= 2[(1/2)(4)AC] = 48, ie., AC = 12 ft

Answer:

So we have

[tex](fg)(x)=3x^3+x^2-18x-6[/tex]

[tex](f \circ g)(x)=3x^2-17[/tex]

Step-by-step explanation:

I'm going to do two problems just in case.

We are given [tex]f(x)=3x+1[/tex] and [tex]g(x)=x^2-6[/tex].

[tex](fg)(x)=f(x)g(x)=(3x+1)(x^2-6)[/tex]

Multiply out using foil!

First:  3x(x^2)=3x^3

Outer: 3x(-6)=-18x

Inner: 1(x^2)=x^2

Last: 1(-6)=-6

-------------------Add together:

[tex]3x^3+x^2-18x-6[/tex]

[tex](f \circ g)(x)=f(g(x))=f(x^2-6)=3(x^2-6)+1=3x^2-18+1=3x^2-17[/tex]

Answer:

-3 , 21

Step-by-step explanation:

RS = R + S = 12

S lies on 9

There are 12 spaces in between R & S, so you can add and subtract 12 from S:

9 - 12 = -3

9 + 12 = 21

R can be located on either -3 or 21.

~

Answer:

1.609344 kilometers

Step-by-step explanation:

Step-by-step explanation:

[tex]slope=\dfrac{rise}{run}=\dfrac{\Delta y}{\Delta x}\\\\\text{We have}\ m=0.5=\dfrac{1}{2}\to\Delta y=1,\ \Delta x=2\\\\\text{From given point (y-intercept: (0, 2), run 1 unit up and 2 units to the right.}\\(x+2,\ y+1)\to(0+2,\ 2+1)=(2,\ 3)\\\text{Mark new point.}\\\text{Plot the line passes throught given points.}\\\\======================\\\\\Delta x > 0-\text{run to the right}\\\Delta x<0-\text{run to the left}\\\Delta y>0-\text{run up}\\\Delta y<0-\text{run down}[/tex]

Answer:

D the last one

Answer:

Explanation contains answer.

Step-by-step explanation:

Question 1:

I would perfer to solve the first equation for y because there is only one operation to perform on both sides and it is subtraction of 2x on both sides.

The other equation requires two steps to isolate y; subtracting 3x on both sides then multiplying both sides by -1.

So basically solving the first one for y because it has coefficient 1.

Question 2:

They solved the 2nd equation for y and plugged into itself instead of plugging it into 1st equation.

Answer:

Step-by-step explanation:

If we divide 9,795 by 7 we get:

=1399.28571429

Rounding to the nearest hundredth:

Underline the hundredths place: 1399.28571429

Look to the right. If it is 5 or above 5 then we give it a shove.

If it is 4 or less than 4, we let it go.

In our case it is 5. We will add 1 in 8, then it will become 9. 28 will be rounded off as 29.

Therefore the answer after rounding off to the nearest hundredth is 1399.29....

Answer:

A(1,1)

Step-by-step explanation:

the system is :

2x-y=1

x+2y=3

so :

y = 2x-1  .....the line color : red

y= (-1/2)x+3/2......the line color : blue

the pair solution is the intersection point for this line : A(1 ; 1)

Answer: (5x-2)(3^2-5)

Step-by-step explanation:

So using the commutative property, we can change the equation 15x^3-6x^2-25x+10 into 15x^3-25x -6x^2+10

Let’s split that into two sections so it’s easier to see:

(15x^3-25x) - (6x^2+10)

Next let’s look at what 15x^3 and -25x have in common. They have 5x in common.

Factoring out 5x, we get this: 5x(3^2-5)

Next let’s look at what -6x^2and 10 have in common. They only have 2 in common, so we factor out 2.

2(-3^2+5) we can write this as -2(3^2-5)

So the end result will be : 5x(3^2-5)-2(3^2-5)

And the complete factorization will be (5x-2)(3^2-5)

Answer:

136

Step-by-step explanation:

The perimeter of the triangle is about 136

Firstly , let us learn about trigonometry in mathematics.

Suppose the ΔABC is a right triangle and ∠A is 90°.

There are several trigonometric identities that need to be recalled, i.e.

[tex]cosec ~ A = \frac{1}{sin ~ A}[/tex]

[tex]sec ~ A = \frac{1}{cos ~ A}[/tex]

[tex]cot ~ A = \frac{1}{tan ~ A}[/tex]

[tex]tan ~ A = \frac{sin ~ A}{cos ~ A}[/tex]

Let us now tackle the problem!

This problem is about Sine Rule.

First of all, we will calculate the ∠C :

∠A + ∠B + ∠C = 180°

72° + 16° + ∠C = 180°

∠C = 180° - 72° - 16°

∠C = 92°

Next, we will use the Sine Rule to find the length of the other side of the triangle.

[tex]\frac{c}{\sin \angle C} = \frac{b}{\sin \angle B}[/tex]

[tex]\frac{61}{\sin 92^o} = \frac{b}{\sin 16^o}[/tex]

[tex]b \approx \boxed {16.82}[/tex]

[tex]\frac{c}{\sin \angle C} = \frac{a}{\sin \angle A}[/tex]

[tex]\frac{61}{\sin 92^o} = \frac{a}{\sin 72^o}[/tex]

[tex]a \approx \boxed {58.05}[/tex]

Finally, we can find the perimeter of a triangle with the following formula

[tex]\text{Perimeter of the triangle} = a + b + c[/tex]

[tex]\text{Perimeter of the triangle} = 58.05 + 16.82 + 61[/tex]

[tex]\text{Perimeter of the triangle} \approx \boxed {136}[/tex]

Grade: College

Subject: Mathematics

Chapter: Trigonometry

Keywords: Sine , Cosine , Tangent , Opposite , Adjacent , Hypotenuse  

Answer:

So angle G has measurement 127 degrees.

Step-by-step explanation:

     E                       F

H                     G

I had to write it out the parallelogram so I could have a better visual.

F and G are consecutive angles in a parallelogram (not on opposite sides).

This means they add to be 180 degrees.

F+G=180

(3x-10)+(5x+22)=180

(3x+5x)+(-10+22)=180

8x       +12=180

Subtract 12 on both sides:

8x           =180-12

Simplify:

8x           =168

Divide both sides by 8:

x              =168/8

x              =21

If x=21 and want the measurement of angle G, then

(5x+22)=(5*21+22)=127.

So angle G has measurement 127 degrees.

Answer: [tex]127^{\circ}[/tex]

Step-by-step explanation:

Given : In parallelogram EFGH, the measure of angle F is (3x − 10)° and the measure of angle G is (5x + 22)°.

We known that in a parallelogram , the sum of two adjacent angles is 180° .

Therefore , we have

[tex]3x -10+5x + 22=180\\\\\Rightarrow\ 8x+12=180\\\\\Rightarrow\ 8x=180-12\\\\\Rightarrow\8x=168\\\\\Rightarrow\ x=21[/tex]

Now, the measure of angle G =[tex](5x + 22)^{\circ}=(5(21)+22)^{\circ}=127^{\circ}[/tex]

Hence, the measure of angle G = [tex]127^{\circ}[/tex]

Answer:

It would be 5 liters because you gave 5 liter to C

Step-by-step explanation:

Hope this helped! :3

Tank C now has 5 more liters of water than tank A.

Assume the initial amount of water in tank C is "x" liters.

Given that:

Tank A originally had 10 more liters of water than tank C,

The initial amount of water in tank A is "x + 10" liters.

When five liters of water were poured from tank A into tank B,

The amount of water in tank A is reduced to "(x + 10) - 5" liters,

The amount of water in tank A  =  "(x + 5)" liters.

When ten liters of water are poured into tank C

So, the amount of water in tank C=  "x + 10" liters.

The amount of  extra water in tank C is calculated as;

Difference = (Amount of water in tank C) - (Amount of water in tank A)

Difference = (x + 10) - (x + 5)

Difference = x + 10 - x - 5

Difference = 10 - 5

Difference = 5

Tank C now has 5 more liters of water than tank A by 5 liters.

Learn more about liters here:

https://brainly.com/question/30983451

#SPJ5

Answer:

Step-by-step explanation:

we have

[tex]18 > -5x+2 > -48[/tex]

This is a compound inequality

Remember that

A compound inequality i can divide in a system of two inequalities

so

[tex]18 > -5x+2[/tex] -----> inequality A

[tex]-5x+2 > -48[/tex] ---> inequality B

step 1

Solve the inequality A

[tex]18 > -5x+2[/tex]

Multiply by -1 both sides

[tex]-18< 5x-2[/tex]

[tex]-18+2< 5x[/tex]

[tex]-16< 5x[/tex]

Divide by 5 both sides

[tex]-3.2< x[/tex]

Rewrite

[tex]x > -3.2[/tex]

The solution of the inequality A is the interval ----> (-3.2,∞)

step 2

Solve the inequality B

[tex]-5x+2 > -48[/tex]

Multiply by -1 both sides

[tex]5x-2 < 48[/tex]

[tex]5x < 48+2[/tex]

[tex]5x < 50[/tex]

Divide by 5 both sides

[tex]x < 10[/tex]

The solution of the inequality B is the interval ----> (-∞, 10)

step 3

Find the solution of the compound inequality

(-3.2,∞) ∩ (-∞, 10)=(-3.2,10)

All real numbers greater than -3.2 and less than 10

The graph in the attached figure

Answer:

B

Step-by-step explanation:

Given

x + 10 = 15 ( subtract 10 from both sides )

x = 5 → B

Answer:

f(x)=a(x-h)^2+k =f(x)=5(3-2)^(2)-4 and f(x)=1

Step-by-step explanation:

i really hope this helps im sorry if it doesnt

Answer:

m=15

Step-by-step explanation:

-7 + m = 8

=>m=8+7

=>m=15

Answer: 658

Step-by-step explanation:

If Winslow wants to plant 12 vegetables and has 34 seeds of each kind of vegetable, then she has 12*34 seeds.

12*34=408

If a neighbor giver her 10 more packets, each with 25 seeds, she has 10*25 more seeds.

10*25=250

Then we add 408+250 to get 658 seeds

Answer:

(1, - 6 )

Step-by-step explanation:

Under a reflection in the x- axis

a point (x, y ) → (x, - y )

The point J has coordinates (0, 3 ), hence

J'(0, - 3 ) ← after reflection in x- axis

A translation (x, y ) → (x + 1, y - 3 )

Means add 1 to the x- coordinate and subtract 3 from the y- coordinate

J'(0, - 3 ) → J''(0 + 1, - 3 - 3 ) → J''(1, - 6 ) ← final image

Answer:

f (gx) = 1/ -2(1/x^2+6x+10) + 9

Step-by-step explanation:

f (gx) = 1/ -2(1/x^2+6x+10) + 9

Answer:

The domain is all real numbers where

[tex](f \circ g)(x)=\frac{x^2+6x+10}{9x^2+54x+88}[/tex]

Step-by-step explanation:

[tex](f \circ g)(x)=f(g(x))[/tex]

So g(x) must exist before plugging it into f(x).

Let's find where g(x) doesn't exist.

[tex]x^2+6x+10[/tex] is a quadratic expression.

[tex]b^2-4ac[/tex] is the discriminant and will tell us if [tex]x^2+6x+10=0[/tex] will have any solutions.  I'm trying to solve this equation because I want to figure out what to exclude from the domain.  Depending on what [tex]b^2-4ac[/tex] we may not have to go full quadratic formula on this problem.

[tex]b^2-4ac=(6)^2-4(1)(10)=36-40=-4[/tex].

Since the discriminant is negative, then there are no real numbers that will make the denominator 0 here.  So we have no real domain restrictions on g.

Let's go ahead and plug g into f.

[tex]f(g(x))[/tex]

[tex]f(\frac{1}{x^2+6x+10})[/tex]  

I replaced g(x) with (1/(x^2+6x+10)).

[tex]\frac{1}{-2(\frac{1}{x^2+6x+10})+9}[/tex]  

I replaced old input,x, in f with new input (1/(x^2+6x+10)).

Let's do some simplification now.

We do not like the mini-fraction inside the bigger fraction so we are going to multiply by any denominators contained within the mini-fractions.

I'm multiplying top and bottom by (x^2+6x+10).

[tex]\frac{1}{-2(\frac{1}{x^2+6x+10})+9} \cdot \frac{(x^2+6x+10)}{(x^2+6x+10)}[/tex]  

Using distributive property:

[tex]\frac{1(x^2+6x+10)}{-2(\frac{1}{x^2+6x+10})\cdot(x^2+6x+10)+9(x^2+6x+10)}[/tex]

We are going to distribute a little more:

[tex]\frac{x^2+6x+10}{-2+9x^2+54x+90}[/tex]

Combine like terms on the bottom there (-2 and 90):

[tex]\frac{x^2+6x+10}{9x^2+54x+88}[/tex]

Now we can see if we have any domain restrictions here:

[tex]b^2-4ac=(54)^2-4(9)(88)=-252[/tex]

So again the bottom will never be zero because [tex]9x^2+54x+88=0[/tex] doesn't have any real solutions.  We know this because the discriminant is negative.

The domain is all real numbers where

[tex](f \circ g)(x)=\frac{x^2+6x+10}{9x^2+54x+88}[/tex]

Answer:

(12, 3.2) would be the max amount of gas he could buy.  (11.25, 3) for an even gallon amount.

Step-by-step explanation:

Answer:

(3.2, 12)

Step-by-step explanation:

Total cost for gas = $12

Cost per gallon = $3.75

Letting total cost of gas be y and number of gallons be x, maximum number of gallons of gas he can buy would be ;

Total cost of gas/ cost per gallon = 12 / 3.75 = 3.2 gallons

Therefore , the coordinate pair (x, y) = (3.2, 12)

Answer:

x = 2 or x = -5

Step-by-step explanation:

It s given that,  (x – 2)(x + 5) = 0

To find the solution of given equation

Let  (x – 2)(x + 5) = 0

From this we get

either  (x – 2) = 0 or (x + 5) = 0

If (x - 2) = 0  then x = 2

If (x + 5) = 0 then x = -5

Therefore the solutions of given equation  (x – 2)(x + 5) = 0  are,

x = 2 or x = -5

Answer: X = 2 or X = -5

Step-by-step explanation:

(X - 2) x ( X - 5) = 0

X - 2 = 0 or X - 5 = 0

Therefore X=2 or X=5

Answer:

d) $130

Step-by-step explanation:

Average means you add up the numbers and divide by the number of numbers.

We want our average to be 131.

We have 128,135, and the next pay check amount.

So let's average the three numbers together.

[tex]\frac{128+135+x}{3}[/tex]

[tex]x[/tex] represent the amount on the next pay check.

We want this average to equal 131 so we have this equation to solve:

[tex]\frac{128+135+x}{3}=131[/tex]

First step: Add 128 and 135:

[tex]\frac{263+x}{3}=131[/tex]

Second step: Multiply both sides by 3:

[tex]263+x=3(131)[/tex]

Third step: Multiply 3 and 131:

[tex]263+x=393[/tex]

Fourth step: Subtract 263 on both sides:

[tex]x=393-263[/tex]

Fifth step: Subtract 393 and 263:

[tex]x=130[/tex]

d. 130

D). $130

In this question, we're trying to figure out what would be the lowest amount of money he earned on his next paycheck in order for his income to be an average of $131.

To do this, we would need to use some important information in the question.

Important information:

With the information above, we can use that to get the answer to the question.

We know that he made $128 and $135 on his recent paychecks, but we need to find on how much he needs to make on his next paycheck in order to reach his goal average.

We would be solving for x:

128, 135, x

131,  131,  131

We would add the numbers:

128, 135, x = 263 + x

131,  131,  131 = 393

We will now solve.

[tex]393 = 263+x\\\\\text{Subtract 263 on both sides}\\\\130=x[/tex]

When you're don solving, you should get 130. This means that Cal needs to make $130 on his next paycheck in order to have an average of $131.

We can check to see if it's right by adding up all of the numbers and divide by how many there are (3).

[tex]128+130+135=393\\\\393\div3=131[/tex]

Now, we can confirm that D). $130 would be the correct answer.