Which expressions represent a quadratic expression in factored form? Select all the correct answers.
x^2 − x − 72
(x + 3)(x − 7)
-8(x + 56)
(x + 1)(x − 2)
(x − 2) + (x + 3)

Answers

Answer 1

The expressions that represent a quadratic expression in factored form is (x + 1)(x − 2).

What is quadratic expression?

Quadratic expression  can be described as the mathematical expression that posses  the variable which have highest power of 2.

It should be noted that the quadratic equation is usually expressed in the form ax^2 + bx + c where the abc are the known numbers in the equation  that will be used in the calculation of the factors of the equation and in the quadratic equation the number a will not be equal to zero in the equation.

Therefore, option C is correct.

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Related Questions

I’ve been trying to figure out how to solve this and was wondering how to do this correctly!

Answers

SOLUTION

To solve this we will use the form for exponential growth to determine the formula to use.

Exponential growth has the form

[tex]\begin{gathered} P=P_0e^{rt} \\ P=\text{population after timer t} \\ P_0=\text{ initial population growth } \\ r=\text{ percent growth rate} \end{gathered}[/tex]

Now the frogs tripple in population after 9 days. Initially they were 21. So in 9 days they become

[tex]21\times3=63\text{ frogs }[/tex]

Applying the formula, we have

[tex]\begin{gathered} P=P_0e^{rt} \\ 63=21e^{9r} \\ 3=e^{9r} \\ \text{taking ln of both sides } \\ \ln 3=\ln e^{9r} \\ \ln 3=9r \\ r=\frac{\ln3}{9} \end{gathered}[/tex]

The time for the frogs to get to 290 becomes

[tex]undefined[/tex]

Rick buys a $4,500 stove with an installment plan that requires 12% down. How much
is the down payment?
O $540
O $375
O $250
O $125

Answers

Answer: 540

Step-by-step explanation: 12% of 4500 is 540

Ronda ate 2/5 of the pie. Connor ate .375 of the pie. How much did they eatcombined? (Express your answer either as a fraction or decimal)

Answers

[tex]\begin{gathered} \text{Ronda ate }\frac{2}{5}\text{ of the pie} \\ \text{Connor ate 0.375 of the pie} \\ We\text{ can either convert Ronda's part to a decimal or} \\ we\text{ can convert Connor's part to a fraction.} \\ \text{Let us now convert Ronda's part to a decimal;} \end{gathered}[/tex]

To convert 2/5 to a decimal;

[tex]undefined[/tex]

Robin is saving money to buy a 720$ phone. she has 105$ saved, and each week she adds 30$ to her savings. write an equation to find the number of weeks (w) until she has enough savings to buy the phone.

Answers

Let call w the number of weeks she has been saving.

Then, we can write the expression for her saving in function of the number of weeks as:

[tex]S(w)=105+30\cdot w[/tex]

We now have to find the number of weeks it will take for her savings to reach $720.

We can find it by calculating w for S(w)=720:

[tex]\begin{gathered} S(w)-105+30w=720 \\ 105+30w=720 \\ 30w=720-105 \\ 30w=615 \\ w=\frac{615}{30} \\ w=20.5\approx21 \end{gathered}[/tex]

Answer: it will take her 21 weeks to have enough savings.

Permutation/combination In how many ways can five people line up to get on a bus? (Hint: all 5 people are lining up)

Answers

We have to calculate in how many ways can five people line up to get on a bus.

This is a permutation of 5 in 5 without repetition, so it can be calculated as:

[tex]P(5,5)=5!=120[/tex]

Answer: in 120 ways.

A reflection across which line(s) carries the trapezoid onto itself?

Answers

If we reflect about x =2, it is a mirror image on each side ( left and right). There is no other line where we can have a mirror image on each side.

Factor the expression. 12y + 14

Answers

Answer:

2(6y+7)

Explanation:

To factor the expression:

[tex]12y+14[/tex]

First, find the greatest whole number that divides 12 and 14.

The number = 2, therefore:

[tex]\begin{gathered} 12y+14=2\mleft(\frac{12y}{2}+\frac{14}{2}​\mright) \\ =2(6y+7) \end{gathered}[/tex]

160 is what percent of the sum of 100 and 120 and 160

Answers

42.105%

1) Let's first add thosse numbers up: 100 +120+160 =380

2) Now we can write out the following ratio, to find out what percentage is equivalent to 160 out of that 380:

[tex]\begin{gathered} 160----x \\ 380----100 \\ \frac{160}{380}=\frac{x}{100} \\ 380x=16000 \\ \frac{380x}{380}=\frac{16000}{380} \\ x=42.105\% \end{gathered}[/tex]

Note that we had to cross multiply that.

3) Hence, the answer is 160 is approximately 42.105% of 380

7 singles, 13 fives, 4 twenties, and 3 hundred dollar bills are all placed in a hat. If a player is to reach into the hat and randomly choose one bill, what is the fair price to play this game?

Answers

So,

The probability to obtain one bill of the four, is 1/4.

So, the expected value is:

[tex]\begin{gathered} \frac{1}{4}(7)+\frac{1}{4}(13)+\frac{1}{4}(4)+\frac{1}{4}(3) \\ \\ =6.75 \end{gathered}[/tex]

Therefore, the fair price to play this game is 6.75.

Real numbersA stock lost 8 and 3/8 on Monday, 1 and 5/8 points on Tuesday. On Wednesday, it gained 13 points. What was the net gain or loss of the stocks for these three days?

Answers

Answer: The net gain was 3 stocks for these three days.

Explanation

Given

• Monday: lost 8 and 3/8.

,

• Tuesday: lost 1 and 5/8 points.

,

• Wednesday: gained 13 points.

Procedure

To calculate the net gain, we have to add all the values we are giving, considering that the stock lost will have a negative sign:

[tex]\text{Net gain}=Gains-losses[/tex]

0. Calculating the losses

We have to mixed numbers, for which we can add the whole numbers and the fractions separately.

• Whole numbers

[tex]-8-1=-9[/tex]

• Fractions

[tex]-\frac{3}{8}-\frac{5}{8}=-\frac{8}{8}=-1[/tex]

At last, we add both results and we get the losses:

[tex]losses=-9-1=-10[/tex]

2. Calculating the gains

As we only have one quantity, there is no need for calculations:

[tex]Gains=13[/tex]

3. Calculating net gain

Finally, we put both quantities in the formula:

[tex]\text{Net gain}=13-10=3[/tex]

What is the greatest common factor of 9 and 72?

Answers

The Greatest Common Factor of 9 and 72 is: 9

SOLUTION

Problem Statement

The question asks us to find the greatest common factor of 9 and 72.

Method

In order to solve this question, we just need to follow these steps:

1. Write out the prime factors of 9 and 72

2. Choose the common factors from both expressions.

3. Multiply the common factors.

Implementation

1. Write out the prime factors of 9 and 72:

[tex]\begin{gathered} 9=1\times3\times3 \\ \text{The common factors of 9 are: 3 and 3} \\ \\ 72=1\times2\times2\times2\times3\times3 \\ \text{Common factors of 72 are: 1,2, 2, 2 and 3, 3} \end{gathered}[/tex]

2. Choose the common factors from both expressions.:

We need to examine the two expressions for 9 and 72 above. Choose the common values.

[tex]\begin{gathered} 3\times3\text{ is common to both 9 and 72} \\ i\mathrm{}e\text{.} \\ 9\text{ is common to both 9 and 72} \\ 3\text{ is common to both 9 and 72 as well} \\ 1\text{ is also common to both 9 and 72} \end{gathered}[/tex]

3. Multiply the common factors.:

[tex]\begin{gathered} \text{Thus, choosing the greatest values from 1,3 and 9.} \\ \therefore\text{The Greatest Common Factor = 9} \end{gathered}[/tex]

Final Answer:

The Greatest Common Factor of 9 and 72 is: 9

determine whether the given by binomial is a factor of the polynomial p(x) . If so, find the remaining factors of p(x).

Answers

The given binomial is a factor of the polynomial p(x) with remaining factors of (x + 1)(x - 1).

What is termed as the factors of polynomial?Factorisation is the process of determining the factors of a given value as well as mathematical expression. Factors are integers which are multiplied together to create the original number.

For the given question.

The polynomial is given as; x³ + 2x² -x - 2.

The binomial is given as; (x +2).

The, to get the remainder, divide the polynomial with the binomial.

= (x³ + 2x² - x - 2)/ (x +2)

Taking x² common from the first two terms of the numerator and (-1) from the last two terms.

= x²(x + 2) - (x + 2)/ (x +2)

Taking (x + 2) common from two terms.

= (x + 2)(x² - 1)/(x + 2)

Cancel (x + 2) from both.

= (x² - 1)

Now use the identity to open the square.

(a²  + b² ) = (a + b) (a - b)

= (x + 1)(x - 1).

Thus, the given binomial is a factor of the polynomial p(x) with remaining factors of (x + 1)(x - 1).

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The correct question is-

Determine whether the given binomial is a factor of the polynomial p(x).

If so, find the remaining factors of p(x).

p(x) = x³ + 2x² -x - 2 ; (x +2)

Answer:

a

Step-by-step explanation:

The area (in square inches) of a rectangle is given by the polynomial function A(b)=b^2 +9b+18. If the width of the rectangle is (b+3) inches what is the length?

Answers

As given by the question

There are given that area of rectangle and width of a rectangle

[tex]\begin{gathered} \text{Area}=A(b)=b^2+9b+18 \\ \text{Width}=(b+3) \end{gathered}[/tex]

Now,

From the formula of area of a rectangle:

[tex]\text{Area}=\text{length}\times width[/tex]

Then,

Put the value of an area and width into the above formula

So,

[tex]\begin{gathered} \text{Area}=\text{length}\times width \\ b^2+9b+18=length\times(b+3) \end{gathered}[/tex]

Then,

[tex]\begin{gathered} b^2+9b+18=length\times(b+3) \\ (b+3)(b+6)=\text{length}\times(b+3) \\ \text{length}=\frac{(b+3)(b+6)}{(b+3)} \\ \text{length}=(b+6) \end{gathered}[/tex]

Hence, the value of length is ( b + 6 ).

Four more than three times a number, is less than 30. Which of the following is not a solution?61278

Answers

Solution

- To solve the question, we simply need to interpret the question line by line.

- Let the number be x.

- "Four more than three times a number" can be written as:

[tex]\begin{gathered} \text{ Three times a number is: }3x \\ \text{ For more than three times a number becomes: }4+3x \end{gathered}[/tex]

- "Four more than three times a number is less than 30" can be written as:

[tex]4+3x<30[/tex]

- Now, we can proceed to solve the inequality and find the appropriate range of x. This is done below:

[tex]\begin{gathered} 4+3x<30 \\ \text{ Subtract 4 from both sides} \\ 3x<30-4 \\ 3x<26 \\ \text{ Divide both sides by 3} \\ \frac{3x}{3}<\frac{26}{3} \\ \\ \therefore x<8\frac{2}{3} \end{gathered}[/tex]

- This means that all correct solutions to the inequality lie below 8.666...

- This further implies that any number greater than this is not part of the solutions of the inequality.

- 12 is greater than 8.666

Final Answer

The answer is 12

I really need help solving thisIt’s from my trig prep bookIt asks to answer (a) and (b)

Answers

Answer:

The sum in summation notation is:

[tex]\sum ^4_{r\mathop{=}0}(-1)^r(4Crx^{4-r}y^r)[/tex]

The expansion is:

[tex]81x^{20}-12x^{15}y^3+\frac{2}{3}x^{10}y^6-\frac{4}{243}x^5y^9+\frac{1}{6561}y^{12}[/tex]

Explanation:

Given the expression:

[tex](3x^5-\frac{1}{9}x^3)^4[/tex]

In summation notation, this can be written as:

[tex]\sum ^4_{r\mathop=0}(-1)^r(4Crx^{4-r}y^r)[/tex]

The simplified terms of the expression is:

[tex]\begin{gathered} 4C0(3x^5)^{\mleft\{4-0\mright\}}(\frac{1}{9}y^3)^0-4C1(3x^5)^{\mleft\{4-1\mright\}}(\frac{1}{9}y^3)^1+4C2(3x^5)^{\mleft\{4-2\mright\}}(\frac{1}{9}y^3)^2-4C3(3x^5)^{\mleft\{4-3\mright\}}(\frac{1}{9}y^3)^3+4C4(3x^5)^{\mleft\{4-4\mright\}}(\frac{1}{9}y^3)^4 \\ \\ =(3x^5)^4-4(3x^5)^3(\frac{1}{9}y^3)+6(3x^5)^2(\frac{1}{9}y^3)^2-4(3x^5)^{}(\frac{1}{9}y^3)^3+(\frac{1}{9}y^3)^4 \\ \\ =81x^{20}-12x^{15}y^3+\frac{2}{3}x^{10}y^6-\frac{4}{243}x^5y^9+\frac{1}{6561}y^{12} \end{gathered}[/tex]

Andy spent 1/3 of his money on pastries and 3/4 of his remaining money on 2 pies. Each pie costs 6 times as much as each pastry. if all pastries cost the same how many did he buy

Answers

3/4 x 2/3 = 6/12 = 1/2 so he spend 1/2 of his money on 2 pies
This means he originally had enough money to buy 4 pies or 24 pastries
1/3 of his money would buy 8 pastries

Four friends had dinner at a restaurant. The bill was $45.40, and they added a 20% tip. The 4 friends shared the total cost equally. How much money did each person pay?

Answers

Answer:

$13.62

Step-by-step explanation:

To find the tip of 20%, multiply 45.40 by 0.20, and you get 54.48.

Now, since there are 4 friends, divide the amount by 4.

54.48/4=13.62

So each person would pay $13.62.

Hope this helps! :D

Question
Find the values for x and y .

Answers

Step-by-step explanation:

6x+3=75° ( being alternate angle )

6x = 72°

x=12

75+45+y= 180

y= 60°

I’ve already done this problem, but I’m being told it’s wrong and I need to simplify but I don’t know how to do it with this question.

Answers

[tex]\begin{gathered} y=x^2-3 \\ For\text{ (1,2)} \\ x=1,\text{ y=2} \\ y=1^2-3 \\ y=1-3 \\ y=-2,\text{ -2}\ne2,\text{ hence} \\ \text{ this pair doesnt satisfy the equation }y=x^2-3 \\ \text{For (}4,13\text{)} \\ x=4,y=13 \\ y=4^2-3 \\ y=16-3 \\ y=13,\text{ 13=13, hence} \\ \text{This pair satisfies the equation }y=x^2-3 \\ \text{for (}-3,-9\text{)} \\ x=-3,\text{ y=-9} \\ y=(-3)^2-3 \\ y=9-3 \\ y=6,\text{ -9}\ne6,\text{ hence} \\ \text{ this pair doesnt satisfy the equation }y=x^2-3 \\ \text{For (}-5,22\text{)} \\ x=-5,\text{ y=22} \\ y=(-5)^2-3 \\ y=25-3 \\ y=22,\text{ 22=22, hence} \\ \text{This pair satisfies the equation }y=x^2-3 \end{gathered}[/tex]

It goes from -1 to 1 on the x axis.

Answers

ANSWER :

EXPLANATION :

3 A free diver can dive at a rate of -0.75 meters per second. About how long would it take to reach a depth of -145 meters?

Answers

Answer:193.33s or 3.2 mins

Step-by-step explanation:

Here the diver dives at -0.75 constant velocity. So we can use the formula s = vt

from there we can find out the time when s = -145 m and v = -0.75m/s

in the graph below line k,y = -x makes a 45 degree angle with the X and Y axes complete the following

Answers

The point with a coordinate of (2,5) will be translated into y=-x line.

The transformation for y=-x would be:

1. x'= -y

2. y'= -x

For x=2 and y=5 would be:

x'= -y

x'= -5

y'= -x

y'= -2

The translated coordinate would be: (-5, -2)

I need help to know how to solve graphing a system of inequalities2x - 3y > -12x + y ≥ -2

Answers

Answer

2x - 3y > -12 (in red ink)

x + y ≥ -2 (in black ink)

The solution region is the region that the two shaded regions have in common.

Explanation

When plotting the graph of linear inequality equations, the first step is to first plot the graph of the straight line normally, using intercepts to generate two points on the linear graph.

If the inequality sign is (< or >), then the line drawn will be a broken line.

If the inequality sign is (≤ or ≥), then the line drawn is an unbroken one.

Step 1

For this question, we easily see that the first inequality will have a broken line and the second one will have an unbroken line.

To plot each of the lines, we will use intercepts to obtain the coordinates of two points on each line

Recall, we will first plot the lines like they are equations of a straight line.

To plot the graph

2x - 3y = -12

when x = 0,

2(0) - 3y = -12

-3y = -12

Divide both sides by -3

(-3y/-3) = (-12/-3)

y = 4

First point on the line is (0, 4)

when y = 0

2x - 3(0) = -12

2x = -12

Divide both sides by 2

(2x/2) = (-12/2)

x = -6

Second point on the line is (-6, 0)

For the second line,

To plot the graph,

x + y = -2

when x = 0

0 + y = -2

y = -2

First point on the line is (0, -2)

when y = 0

x + 0 = -2

x = -2

Second point on the line is (-2, 0)

So, for the plotting, we connect the two points for each of the lines.

Step 2

The shaded region now depends on whether the inequality sign is facing y or not.

If the inequality sign is facing y, it means numbers above the line plotted are the wanted region and the upper part of the graph is shaded.

If the inequality sign is not facing y, it means numbers below the line plotted are the wanted region and the lower part of the graph is shaded.

2x - 3y > -12

Can be rewritten as

-3y > -2x - 12

Divide through by -3 (this changes the inequality sign)

y < (2x/3) + 4

Here, we see that the inequality sign is not facing y, hence the numbers below the broken line plotted are the shaded region (in red ink)

x + y ≥ -2

We can rewrite this as

y ≥ -x - 2

Here, we see that the the inequality sign is facing y, hence, the numbers above the unbroken line plotted are the shaded region (in black ink)

The graph of this system of inequalities is presented above under 'Answer'

Hope this Helps!!!

If f (x) = 4x^3 - 25x^2 – 154x+ 40 and (x - 10) is a factor, what are the remaining factors?

Answers

[tex]f(x)=4x^3-25x^2-154x+40[/tex][tex]f(x)=4\cdot(\frac{1}{4})^3-25(\frac{1}{4})^2-154(\frac{1}{4})+40[/tex][tex]f(x)=\frac{1}{16}-\frac{25}{16}-\frac{77}{2}+40[/tex][tex]f(x)=0[/tex]

There are 39 chocolates In a box call identically sheet dear 16 off filled with nuts 13 with caramel and 10 are solid chocolate you randomly select one piece eat it and then select a second piece find the probability of selecting to solid in a row

Answers

The probability of selecting two solid chocolates in a row is 0.0607 .

In the question ,

it is given that

there are total 39 chocolates in the box .

number of chocolates filled with nuts = 16

number of chocolates filled with caramel = 13

number of chocolates filled with solid = 10

Probability of selecting first chocolate as a solid is  10/39.

Now , there are 38 chocolates , with 9 solid chocolates ,

hence the probability of selecting second chocolate as a nut is = 9/38

So, the probability of selecting two solid chocolates in a row = 10/39×9/38

= 90/1482

= 0.0607

Therefore , the probability of selecting two solid chocolates in a row is 0.0607 .

The given question is incomplete , the complete question is

There are 39 chocolates in a box, all identically shaped. There 16 are filled with nuts, 13 with caramel, and 10 are solid chocolate. You randomly select one piece, eat it, and then select a second piece. Find the probability of selecting 2 solid chocolates in a row.

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X) *11.4.14 Find the volume of the cylinder in terms of it and to the nearest tenth. 2 in 1 in The volume in terms of it is V= in3

Answers

We can calculate the volume of the cylinder as the product of the area of the base and the height of the cylinder.

[tex]V=A_b\cdot h[/tex]

The area of the base is equal to:

[tex]A_b=\pi r^2=\pi\cdot2^2=4\pi[/tex]

Then, the volume becomes:

[tex]V=A_b\cdot h=4\pi\cdot1=4\pi\approx12.6\text{ in}^3[/tex]

Answer:

The volume in function of π is V = 4π in^3.

The volume rounded to the nearest tenth is 12.6 in^3.

Laverne created a painting with an area of 72 square inches and a length of 9 inches. They create a second painting with an area of 56 square inches. It has the same width as the first painting. What is the length of the second painting?​

Answers

Answer: 7

Step-by-step explanation:

As our first step, we can divide 72 by 9 to discover the width of the first AND second painting. 72÷9=8

Now that we have discovered the width of the second painting, we will now solve the mathematical expression 56÷8.

Because 56 divided by 8 equals 7, the length of the second painting is 7 inches.

Sean johnson 1. The angles of a triangle are described as follows: angle A is the largest angle: its measure is twice the measure of angle B. The measure of angle C is 2 less than half the measure of angle B. Find the measures of the three angles in degrees.

Answers

Explanation

Let

angle A is the largest angle

[tex]m\measuredangle A=m\measuredangle A[/tex]

its measure is twice the measure of angle B,( in other words you have to multiply angle b by 2, to get angle A)

[tex]2(m\measuredangle B)=m\measuredangle A[/tex]

there are 14 square and 18 rectangles. what is the simplest ratio of squares to rectangles?

Answers

The simplest ratio of squares to rectangles can be obtained as follows:

There are 14 squares and 18 rectangles. The ratio of squares to rectangles is:

[tex]\frac{14}{18}=\frac{7}{9}[/tex]

Then, the simplest ratio is 7/9 because 7 is a prime number and the ratio cannot be simplified any more. To obtain 7/9 we divided the numerator by 2 and the denominator also by 2.

A buoy oscillates in simple harmonic motion as waves go past. At a given time it is noted that the buoy moves a total of 3.9 feet from its low point to its high point, and that it returns to its high point every 16 seconds

Answers

Concept

What is a simple harmonic motion ?

Repetitive movement back and forth through an equilibrium, or central, position, so that the maximum displacement on one side of this position is equal to the maximum displacement on the other side. The time interval of each complete vibration is the same

a) y= 1.95ftcos(π/2)

b) v(t)= -0.76sin(π/5t)

Part a

Since the buoy oscillates in simple harmonic motion the equation to model this is given by: y=  A cos(ωt+θ)

For this case from the info given we know that:

2A= 3.9 , A= 3.9/2= 1.95ft

It returns to its high point every 16 seconds. That means period = 16 , and the angular frequency can be founded like this:

ω=2π/16

= π/8

Assuming that the value for the phase is (θ=0°) our model equation is given by

y= 1.95ftcos(π/2)

Part b

From definition we can obtain the velocity with the derivate of the position function and if w calculate the derivate we got this,

dy/dt= v(t)= -1.95ft(π/8)sin(π/8t)

v(t)= -0.76sin(π/8t)

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A. It is the chief Security Officer for the Court and they make all decisions for Court Safety.B. It is the system used to determine the rank and order of the Judges from top to bottom and allows everyone to know who is in charge.C. It is the title given to the first decision made by the court on a specific subject and is used to help determine all future rulings on that subject.D. It is the primary system used to build Laws and it impacts all citizens. 23 < y - 2 solve the inequality of y and simplify your answer as much as possible. which disorder causes purulent drainage from the auricle and ear canal? a. otitis externa b. otitis media c. otitis interna d. ruptured tympanic membrane What is the Places and events in Louisiana ? an important first step before running a regression model is to compile a comprehensive list of potential predictor variables. how can we reduce the list to a smaller list of predictor variables? what is divided government and how does it affect the relationship between congress and the president Find The distance DB from Cassini yo Tethys when AD is tangent to the circular orbit. Round to the nearest kilometer When auscultating the heart sounds of a client, a nurse notes that the s2 is louder than the s1. How should the nurse describe s2?. In a survey, 12 people were asked how much they spent on their child's last birthday gift. The results wereroughly bell-shaped with a mean of $39.1 and standard deviation of $17.4. Estimate how much a typical parentwould spend on their child's birthday gift (use a 99% confidence level). Give your answers to 3 decimal places.Express your answer in the format of + Error.$ $ For, you see, so many out-of-the-way things had happened lately, that Alice had begun to think that very few things indeed were really impossible.There seemed to be no use in waiting by the little door, so she went back to the table, half hoping she might find another key on it, or at any rate a book of rules for shutting people up like telescopes: this time she found a little bottle on it, ("which certainly was not here before," said Alice,) and round the neck of the bottle was a paper label, with the words "DRINK ME," beautifully printed on it in large letters.It was all very well to say "Drink me," but the wise little Alice was not going to do that in a hurry. "No, I'll look first," she said, "and see whether it's marked 'poison' or not"; for she had read several nice little histories about children who had got burnt, and eaten up by wild beasts and other unpleasant things, all because they would not remember the simple rules their friends had taught themWhich of the following lines implies that Alice is cautious?A. For, you see, so many out-of-the-way things had happened lately, that Alice had begun to think that very few things indeed were really impossible.B. It was all very well to say "Drink me," but the wise little Alice was not going to do that in a hurry.C. There seemed to be no use in waiting by the little door, so she went back to the table, half hoping she might find another key on itD this time she found a little bottle on it, ("which certainly was not here before," said Alice) When resistors are put in series next to each other, their overall resistance isA. Larger than that of any individual resistorB.the same as the resistance of one of the resistorsC. Smaller than the resistance of any of the resistors 24. The base of a 13-foot ladder stands 5 feet from a house. Sketch a drawing to model this situation. How many feet up the side of the house does the ladder reach? Explain how drawing the picture helped you solve the problem. which of the following statements is consistent with a given (i.e., fixed) lm curve? a) a reduction in the interest rate causes investment spending to increase. b) a reduction in the interest rate causes money demand to decrease. c) a reduction in the interest rate causes an increase in the money supply. d) an increase in output causes an increase in demand for goods. e) an increase in output causes an increase in money demand. Lola needs 2/3 cup of lemon-lime soda for every 2 cups of punch. Find ____ cups of soda/cup of punch Which is most directly contributed to the decision in philadelphia referenced in the excerpt to build a specific meeting house for the new preachers? Which fraction equals \dfrac{4}{7} + \dfrac{3}{8} 74 + 83 ?