Match each quadratic equation with its solution set.
2x²8x+5=0
2x²9x-1=0
2x²10x - 3=0
2x²9x+6=0
2x²8x3=0

Match Each Quadratic Equation With Its Solution Set.2x8x+5=02x9x-1=02x10x - 3=02x9x+6=02x8x3=0

Answers

Answer 1
1. 2x² + 8x + 5 = 0; Solution Set: {-3, -1/2}
2. 2x² + 9x - 1 = 0; Solution Set: {1/2, -1}
3. 2x² + 10x - 3 = 0; Solution Set: {-3/2, 1}
4. 2x² + 9x + 6 = 0; Solution Set: {-3/2, -2}
5. 2x² + 8x - 3 = 0; Solution Set: {3/2, 1}

Related Questions

a concrete block has a volume of 34 cubic meters and the dimensions shown. find the value of X

Answers

The value of x is obtained as follows:

x = 2.83.

How to obtain the volume of the rectangular prism?

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, as follows:

Volume = length x width x height.

Considering the dimensions in this problem, and the volume of 34 cubic meters, the equation is given as follows:

x(2x - 3)(3x - 4) = 34.

x(6x² - 17x + 12) = 34

6x³ - 17x² + 12x - 34 = 0.

Which is a cubic equation with coefficients given as follows:

a = 6, b = -17, c = 12, d = -34.

Using a calculator, the real solution are given as follows:

x = 2.83.

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Michelle is also a contestant. On day 21, she is informed by the wellness team that she has lost 17% of her body weight. Michelle weighed 145 lb. at the start of the competition. How much does she weigh now?

Answers

Answer:

Michelle weighs 120.15 lb. now.

You can calculate it by

145lb x (1-.17) = 145lb x .83 = 120.15lb

Calculate the percentage error to the nearest 1 cm, if the footpath around a building is 400 m long

Answers

Answer:

4000cm

Step-by-step explanation:

1m is equal to 100cm

so 400m is equal to 400 x 10 which is 4000

so 1cm dividided by 400m ks 400m

Suppose that 18 inches of wire cost 72 cents At the same rate, how much (in cents) will 13 inches of wire cost?

Answers

Solution :

So right now in the the given question we use the proportional method

In this case the proportion used is inverse

What is Inverse Proportion ?

In direct proportion, if one quantity is increased or decreased then the other quantity increases or decreases, respectively. But in indirect or inverse proportion, if one quantity increases then other quantity decreases and vice-versa.

Eg: As the variable y decreases the variable x will also decrease

When we apply the given values into a fraction we get

[tex]\frac{18}{72} = \frac{13}{x}[/tex]

Cross Multiplying we get,

[tex]18x = 72X13[/tex]

[tex]18x = 936[/tex]

[tex]x = \frac{936}{18}[/tex]

[tex]x = 52[/tex]

Hence, 13 inches of wire costs 52 cents

Luis has a piece of wood of 102.45 cm if he needs to cut them into 5 equal parts, how much to measure each part?​

Answers

Answer: Each part of 20.49 cm.

Step by step explanation:

Data :

I have = 102.45 cmI need = 5 equal parts

In this problem we have to divide the piece of wood that is 102.45 cm, with 5 equal parts:

[tex]\bf \: \cfrac{ 102.45 }{5} = \boxed{ \bf20.49 \: cm}[/tex]

Rpt: Each part of 20.49 cm.

Answer: 20.49

Step-by-step explanation:

102.45/5=20.49

What is the tangent of the angle shown on the figure?

Answers

The tangent of the given angle shown above would be = 1.43. That is option C.

How to calculate the tangent of an angle?

The formula that is used to calculate the tangent of the given angle ;

Tan θ = opposite/adjacent

Where the opposite = 60ft

the adjacent = 42ft

Tan θ = 60/42

= 1.43°

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Which equation represents the graph of function j?

Answers

The required equation that represents the graph is j(x) =  (-x + 4)¹/². Option D is correct.

What is a parabola?

A parabola is a cross-section cut out of the cone and represented by an equation x = y².

here,
The given graph is of the left parabola,
-x = y²
When we translate the above expression 4 units right we get the graph,
So
-x + 4 = y²

put y = j(x)

-x + 4 = j(x)²
j(x) = [-x + 4]¹/²

Thus, the required equation that represents the graph is j(x) =  (-x + 4)¹/². Option D is correct.

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Help with stem & leaf

Answers

The 15th percentile can be found to be 66.5

How to find the 15 th percentile ?

The value that a specific percentage falls under is known as the percentile. The most typical definition of a percentile is a number below which a predetermined proportion of scores fall.

To find the 15 th percentile, the formula is:

= ( Percentile / 100 )  x Number of values in set

The 15th percentile is therefore:

= 15 / 100 x 117

= 17.55

= 18 th position

The value in the 18th position which is the 15th percentile is 66.5

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someone help i dont get this math much at all- its about compound interest

Answers

[tex]{\Large \begin{array}{llll} y=ab^x \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=5\\ y=7 \end{cases}\implies 7=ab^5 \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=0\\[1em] y=\frac{1}{4} \end{cases}\implies \cfrac{1}{4}=ab^0\implies \cfrac{1}{4}=a(1)\implies \cfrac{1}{4}=a \\\\\\ \stackrel{\textit{substituting on the 1st equation}}{7=\left( \cfrac{1}{4} \right)b^5\implies 28=b^5}\implies \sqrt[5]{28}=b~\hfill \boxed{y\approx \cfrac{1}{4}(1.9473)^x}[/tex]

If a/2-b/3 = 1 what is 2a+3b in terms of b

Answers

If a/2-b/3 = 1, then we can write:

2(a/2-b/3) = 2

Combining like terms, we have:

a - b/3 = 1

Multiply both sides by 3 to get:

3a - b = 3

Now, we can add b to both sides of the equation:

3a = b + 3

Finally, we can divide both sides by 3 to get:

a = (b + 3)/3

Now we can substitute this value of a into the original equation

2a + 3b = 2(b + 3)/3 + 3b = 2b/3 + 6/3 + 3b = 2b + 2 + 3b = 5b + 2

So 2a+3b = 5b + 2 in terms of b

Which statement is true about this function for all values of
x
<
4
?

A nonlinear graph intercepts x-axis at points (2.8, 0) and (5.5, 0) with vertex point at (4, minus 2)

Answers

The function is decreasing, is true about this function for all values of x < 4.

What does the term "graph" mean?

To develop a graph is to make a diagram that depicts the relationship between two or more objects. Make a sequence of bars on graph paper as an example of a graph.

A nonlinear graph can have more than one x-intercept, but it cannot have exactly two x-intercepts for all values of x. The vertex of a nonlinear graph is a special point that occurs when the graph changes from increasing to decreasing or vice versa, but it is not necessarily an x-intercept.

Therefore, the statement that the function intercepts the x-axis at points (2.8, 0) and (5.5, 0) with vertex point at (4, -2) is not true and decreasing for all values of x.

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Complete question:

Which statement is true about this function for all values of x < 4

The function is positive.

The function is decreasing.

The function is increasing.

The function is negative.

It is day 8 and you are getting hungry. Since hunting/fishing have not been successful so far, you decide to eat ants for protein. 100 grams of ants gives enough protein as an egg. How many ants is this if one ant is between 1 - 5 mg? (Give a range of values)

Answers

The range of ants to eat is 20,000-1,00,000 ants.

What is range?

The difference between the highest and lowest values for a particular data collection is the range in statistics. For instance, the range will be 10 - 2 = 8 if the provided data set is 2, 5, 8, 10, and 3.

As a result, the range may alternatively be thought of as the distance between the highest and lowest observation. The range of observation is the name given to the outcome. Statistics' range reflects the variety of observations.

The answer is given below:

If each ant is of 1 mg:

1g = 1000 mg = 1000 ants

100g = 100000 mg = 100000 ants

=> Maximum 105 ants

Now if one ant is of 5 mg:

1g = 1000mg = 1000/5 = 200 ants

100g = 20000 ants

Minimum 20,000 ants

Hence the range of ants to eat is 20,000-1,00,000 ants.

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Which transformations have been performed on the graph of f(x)=x√ to obtain the graph of g(x)=14x+3−−−−√+6? Select each correct answer. Responses reflect the graph over the x-axis reflect the graph over the x -axis translate the graph to the right translate the graph to the right stretch the graph away from the x-axis stretch the graph away from the x -axis translate the graph up translate the graph up compress the graph closer to the x-axis compress the graph closer to the x -axis translate the graph to the left translate the graph to the left translate the graph down

Answers

The transformations have been performed on the graph of f(x) = 3√x to obtain the graph of g(x)=1/4x+3√x+3+6 are respectively,

C. stretch the graph away from the x-axis

E. translate the graph to the left  

G. translate the graph up

What are functions?

Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).

Given that,

Two functions,

f(x) = 3√x,

g(x)=1/4x+3√x+3+6

Graph is attached,

the steps of transformation are,

stretch the graph away from the x-axistranslate the graph to the left  translate the graph up

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Answer:  

compress the graph closer to the x-axis

translate the graph up

translate the graph to the left

Step-by-step explanation:

I took the test on k12 trust me.

A bottle contains 36 tablets. If a client took 1/3 of the tablets. How many tablets are left?

Answers

Answer:

24

Step-by-step explanation:

36 * 1/3 = 12

36 - 12 = 24

Answer:

24

Step-by-step explanation:

36/3 = 12

2/3 of 36 = 24

Venus has an angular diameter of about 0.018° when it is a distance of about 38.5 million km from Earth.
What is its true diameter (physical size)? Round to the nearest hundred km.

Answers

The true diameter of the Venus given the angular diameter of 0.018 is about 39.7 million km.

What is angular diameter?

An angular distance used to describe how big a sphere or circle seems from a certain point of view is known as the angular diameter, angular size, apparent diameter, or apparent size. It is known as the visual angle in the vision sciences and as the angular aperture in optics (of a lens). The angular diameter may also be thought of as the angle that a camera or eye must spin around in order to view from one side of an apparent circle to the other.

Given that the angular diameter of Venus is 0.018 degrees.

The true diameter of the planet is calculate using the following formula:

diameter = distance (angular diameter / 57.3)

Substitute the value of distance = 38.5 million and angular diameter = 0.018 degrees.

diameter = 38.5 * 10^6 (0.018 / 57. 3)

diameter = 39. 7 million

Hence, the true diameter of the Venus given the angular diameter of 0.018 is about 39.7 million km.

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Pizza sales increase by 8% this year then decrease by 4% the following year then your sales are up by what %?

Answers

What is the percentage?

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

Pizza sales increase by 8% this year then decrease by 4%. Then we have

P = [1 - (1 + 0.08) x (1 - 0.04)] x 100

P = [1 - 1.08 x 0.96] x 100

P = [1 - 1.0368] x 100

P = [1 - (1 + 0.0368)] x 100

P = 0.0368 x 100

P = 3.68%

The percentage that your sales are up will be 3.68%.

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Lee has made a nonrefundable deposit of the first month’s rent (equal to $900) on a
apartment lease to 6 months. The same day later Lee finds a different apartment that
he likes just as well, but its monthly rent is cheaper and negotiable. Assume a nominal
rate interest rate of 8% convertible monthly. The rent will be paid monthly and at the
beginning of each month. [8]
(i) Write down the cash flow and compute the present value (to 2 decimal numbers)
of 6 months if Lee rents the first apartment ($900).
(ii) Find the range of the rent (to 2 decimal numbers) of the cheaper apartment such
that Lee would switch to rent the new apartment.

Answers

It would be wiser for the couple to stay in the old apartment and save $1400.

What is  multiplication?

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

Explanation:

If they stay until the end of the lease, total money that will be paid out is $1000 x 6 = $6000,

If they leave, they'll have to forgo $1000.

If they move to their new apartment, they'll pay $900 x 6 = $5400

total expenditure if they move to the new place at the end of the six months period will be, the $1000 that will not be refunded back to them on the old apartment, plus this new $5600 for six month's rent in this new apartment, and that will be a total of $6400.

It would be wiser for the couple to stay in the old apartment and save $1400.

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Please help me ASAP!

Answers

The reflection points of (-7, 8) across the x-axis and y-axis are (-7, -8) and (7, 8).

What is a reflection?

A reflection is a type of transformation that involves flipping a shape, known as the preimage, over a line, known as the line of reflection, to produce a new shape (called the image). You can picture what would happen if you flipped the form over the line in order to graph a reflection.

Given:

A point (-7, 8).

Reflection rule about the x-axis:

(x , y) → (x, -y)

So, (-7, 8) → (-7, -8)

Reflection rule about the y-axis:

(x , y) → (-x, y)

So, (-7, 8) → (7, 8)

Therefore, all the required values are given above.

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Please help me with the following question.

Answers

a) The point estimate of the population mean is given as follows: 3.2.

b) The standard error of the sample mean is given as follows: 0.16.

c) The interpretation of the 95% confidence interval is that we can be 95% confidence that the mean number of children that females would like to have is between 3.04 and 3.36. (option D).

d. It is not plausible that the population mean is of 2, as 2 falls outside of the confidence interval. (option A).

How to obtain the features?

The point estimate of the confidence interval is given by half the sum of the bounds, hence:

(3.04 + 3.36)/2 = 3.20.

The standard error of the sample mean is half the difference between the bounds, hence:

(3.36 - 3.04)/2 = 0.16.

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Simplify the following union [-1,8]∪(8,14)

Answers

the answer should be (-1,8,14)

Write the other side of this equation so it's true for all values of x:
1/2(6x - 10) - x =

write the other side of this equation so it's true for no values of x:
1/2(6x - 10) - x =

Answers

The other side of this equation so it's true for all values of x: 1/2(6x - 10) - x = 2x - 5, and the other side of this equation so it's true for no values of x: 1/2(6x - 10) - x = 2x-5 = 2x+3.

How do equations work?

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

Given that, find the other side of this equation so it's true for all values of x:

1/2(6x - 10) - x

= 6x/2 - 10/2 -x

= 3x-5-2

= 2x-5

Now for, equation so it's true for no values of x:

1/2(6x - 10) - x =

Distribute the parentheses:

1/2(6x - 10) - x =

= 3x -5 -x

= 2x -5

We need to other side to be of the form 2x - constant where the constant is not equal to 5.

2x-5 = 2x+3

Subtract 2x from each side.

-5 =3

This is not true so there is no solution.

Hence, the other side of this equation so it's true for all values of x: 1/2(6x - 10) - x = 2x - 5, and the other side of this equation so it's true for no values of x: 1/2(6x - 10) - x = 2x-5 = 2x+3.

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The scatter plot shows a relationship between the height and width of a tree. Based on this relationship, predict the height of a tree whose width is 10 ft.


Thank you in advance!

Answers

Answer:

ive had this

Step-by-step explanation:

i remember having this its 35ft

Answer: 35ft

Step-by-step explanation: i did this before

Suppose that a study of elementary school students reports that the mean age at which children begin reading is 5.9
years with a standard deviation of 0.8
years.
Step 2 of 2 : If a sampling distribution is created using samples of the ages at which 68
children begin reading, what would be the standard deviation of the sampling distribution of sample means? Round to two decimal places, if necessary.

Answers

The standard deviation of the sampling distribution of sample means will be 0.097.

What is a normal distribution?

The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.

Assume that an investigation of primary school understudies reports that the mean age at which youngsters start perusing is 5.9 years with a standard deviation of 0.8 years.

The standard deviation of the sampling distribution of sample means is given as,

⇒ 0.8 / √68

⇒ 0.8 / 8.246

⇒ 0.097

The standard deviation of the sampling distribution of sample means will be 0.097.

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Find the equation of the line, in slope-intercept form, which has a slope of 2/3 and contains the point (3, -4).

Answers

Answer:

The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.

To find the equation of the line with a slope of 2/3 and passing through the point (3, -4), we can plug in the point and the slope into the equation:

y = 2/3 * x + b

-4 = 2/3 * 3 + b

-4 = 2 + b

b = -6

So the equation of the line is:

y = 2/3 x - 6

A linear equation is graphed

Answers

Answer:

(t,v) =(5,61)

Step-by-step explanation:

re-write expression

v=61

t=5

a posible solution

then check the solution

then the ordered pair is the solution

Is the relationship linear, exponential, or neither? X/-12 -6 0 6 y/9 12 20 40

Answers

Answer: The relationship between the variables x and y in the given data points is linear.

Step-by-step explanation: A linear relationship is one in which the change in the y-value (output) is always the same for a given change in the x-value (input), regardless of the starting point. In other words, the slope of the line is constant.

In this case, the slope of the line can be calculated by finding the difference in y-values for a given difference in x-values between two points. We can pick any two points, for example:

(X: -6, Y: 12) and (X: 6, Y: 20)

The slope can be calculated by:

m = (20 - 12) / (6 - (-6)) = 8/12 = 2/3

This means that for every 1 unit increase in x, y increases by 2/3 units.

This is a linear relationship.

In contrast, in an exponential relationship, the y-value increases (or decreases) at a constantly increasing (or decreasing) rate as the x-value increases.

A ramp is designed with the profile of a right triangle.
The measure of one acute angle is 2 times the measure
of the other acute angle. Find the measure of each
acute angle.

Answers

The measure of each acute angle [tex]30^{0}[/tex]

What is the  acute angle?Angles that are less than 90° are considered acute, and a protractor can be used to measure these angles. Acute, Obtuse, Right, Straight, Reflex, and Full Rotation are the names of the basic angles. Two rays are joined at their ends to create the geometric shape known as an angle. Typically, angles are expressed in terms of degrees. A triangle that has each angle less than 90 degrees is said to be acute.Triangles are not sharp even when one of their angles is 90 degrees. The fact that all angles (60°) in an equilateral triangle are less than 90° ensures that it is always sharp.

If you need to see the algebra, the acute angles in a right triangle are complementary, adding to 90 degrees:

x + 2x = 90

3x = 90

x = 30

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A baker will supply 22 jumbo cinnamon rolls to a cafe at a price of $3.46 each. If she is offered $3.16, then she will supply 2 fewer rolls to the cafe. The cafe's demand for jumbo cinnamon rolls is given by p = D(x) = -0.25x + 6.56. What is the equilibrium point?

Answers

If a baker will supply 22 jumbo cinnamon rolls to a cafe at a price of $3.46 each.   the equilibrium point is: 20 rolls and the price is $4.86.

How to find the price?

The equilibrium point is where the supply and demand curves intersect, representing the price and quantity where the market is in balance.

Let's call the number of rolls the baker supplies x.

At the original price of $3.46 each, she supplies 22 rolls.

When offered $3.16, she will supply 2 fewer rolls, so she supplies x = 22 - 2 = 20 rolls.

We can use the demand equation to find the corresponding quantity demanded for each price:

p = D(x) = -0.25x + 6.56

D(22) = -0.25 * 22 + 6.56 = 4.56

D(20) = -0.25 * 20 + 6.56 = 4.86

The intersection of the two points (22, 4.56) and (20, 4.86) gives us the market equilibrium quantity and price.

So the equilibrium point is:

x = 20 rolls

p = $4.86 each.

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f(x) = 2x + 7 and g(x) = 3x − 2, find f(g((6))

Answers

Answer:

To find f(g(6)), we need to first find g(6) by plugging 6 into the function g(x) and solving for the output:

g(6) = 3x - 2 = 3 * 6 - 2 = 16

Next, we plug the result of g(6), which is 16, into the function f(x) and solve for the final output:

f(g(6)) = f(16) = 2x + 7 = 2 * 16 + 7 = 31

So f(g(6)) = 31.

Order equivalent equations of 2(−3) = 4 2 x - 3 = 4 x to solve for x .

Answers

The missing 3 steps for the given equivalent equation are as follows:

1st step: 2x - 6 = 4x

2nd step: -6 = 2x

3rd step: -3 = x

What are equivalent equations?

Algebraic equations with equivalent solutions or roots are called equivalent equations.

An analogous equation is one that is created by adding or removing the identical quantity or expression from both sides of a given equation.

An equation is equivalent if both sides are multiplied or divided by the same non-zero value.

So, we have the equation:

2(x-3) = 4x

Now, solve further as follows:

2(x-3) = 4x

1st step: 2x - 6 = 4x

2nd step: -6 = 2x

3rd step: -3 = x

Therefore, the missing 3 steps for the given equivalent equation are as follows:

1st step: 2x - 6 = 4x

2nd step: -6 = 2x

3rd step: -3 = x

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Why is carbon an element and not a compound?A. Carbon bonds easily with oxygen, but not helium.B. All carbon atoms have the same number of neutrons.C. All carbon atoms have the same number of protons.D. Carbon is found in all living things. a nurse is teaching a nursing student about the two classes of adrenergic agonist drugs. which statement by the nursing student indicates understanding of the teaching? QUESTION 9Malch the part of the nervous system with its respective function.G. Peripheral nervous systemSomatic nervous systemF.D. Autonomic nervous systemA.B. Sympathetic nervous systemC.Central nervous systemE. Spinal cordParasympathetic nervous systemA. Part of the autonomic nervous system: Helps to calm the body after an emergency Might be called the "peace" systemB. Part of the autonomic nervous system. Increases heart rate when we are afraid. Think of it as the "stress" systemC. Controls all voluntary movements, thoughts, and registration of incoming informationD. Part of the peripheral nervous system that controls the involuntary functions that we are not aware ofE. Main carrier of messages between the brain and the bodyF. Part of the peripherical nervous system that coordinates information from the senses and controls voluntary movementsG. Includes all parts of the nervous system other than the brain and spinal cord In the diagram below, ST is parallel to PQ. If SR = 2.4, PQ = 1.8, RQ = 3,and ST = 1.2, find the length of PR. Figures are not necessarily drawn to scale.PRT Concord Pizza's checkbook balance is $1,799.59. The bank statement has a balance of $2,314.22. Interest earned on the statement was $35.50. With checks outstanding of $504.13 and a monthly service charge of $25.00, the reconciled balance is: Summer of the Mariposas chapter 1-12 Based on the characters development how has your perspective changed or been reassured? Explain. What is the value of x cesium-139 undergoes radioactive decay by one mode and generates barium-139. what mode of decay is consistent with this product? researchers conducted a study and determined that students who carpool have less friends than students who ride the bus to school. can we conclude that carpooling causes students to have less friends? Article "WHY GOOD ADVERTISING WORKS (EVEN WHEN YOU THINK IT DOESN'T) on commonlit Write: What does the author think makes a good advertisement? If a tribe in Africa uses the blood, milk, and fur of their livestock (without killing them) and provides them protection from predators and help finding water and food, this relationship is demonstrative of ______. The Renaissance was a rebirth of these two classical cultures A. France and England B. Greece and Rome C. Ottoman and Mughal D. China and Japan the function of the grand jury is to group of answer choices decide the guilt or innocence of a criminal defendant. decide the liability of a defendant in a civil suit. determine if there is sufficient evidence to decide the case on summary judgment. determine if there is sufficient evidence to bring someone accused of a crime to trial. If 201,000 jobs were added in August, why did the unemployment rate remain unchanged? The unemployment rate remained unchanged because A. the people who were unemployed in July did not have the necessary skills to become employed in the new jobs in August B. all of the jobs went to people who were already employed in other jobs C. people entered the labor force and the percentage increase in the labor force equals the percentage increase in unemployment D. people entered the labor force and the percentage increase in the labor force is greater than the percentage increase in unemployment consider the following statements: a. car owners purchase more gasoline from a gas station that sells gasoline at a lower price than other nearby gas stations. b. banks offer gift cards to open new checking accounts. c. firm produce more of a particular product when its selling price rises. d. households spend less money when the economy is in a recession. which of the above statements demonstrates that economic agents respond to incentives? select all that apply 5. julie heard her friends talking very favorably about a local coffee shop and decided she would go there and try it. for julie, her friends served as a(n) . Discuss with your classmates the types of literature you like to read. Provide reasons for each type of literature you list. What about your choices make them worthy to analyze? In your posting, make sure to give at least three stories and three explanations. Help . rationalize the following observations. a. aerosol cans will explode if heated. b. you can drink through a soda straw. c. a thin-walled can will collapse when the air inside is removed by a vacuum pump. d. manufacturers produce different types of tennis balls for high and low elevations. What is the answer to this equation X-5 let f(x) = 1 x if x < 1 x2 if 1 x < 1 2 x if x 1 . sketch the graph of f.