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

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

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

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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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

Answer:

Michelle weighs 120.15 lb. now.

You can calculate it by

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

Answer: Each part of 20.49 cm.

Step by step explanation:

Data :

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

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

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

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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Answer:

ive had this

Step-by-step explanation:

i remember having this its 35ft

Answer: 35ft

Step-by-step explanation: i did this before

The 15th percentile can be found to be 66.5

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

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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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.

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

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

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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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.

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.

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

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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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

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,

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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.

The value of x is obtained as follows:

x = 2.83.

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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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

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).

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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[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]

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

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

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.

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

In this case the proportion used is inverse

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

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

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

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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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

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.

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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