50=50-10a It is for 2 step equations

Answer:

1st one 6.4

Step-by-step explanation:

C^2= a^2 +b^2

C^2 = 5^2 + 4^2

C^2 = 25 + 16

C^2= 41

Root of 41 is 6.4

Step-by-step explanation:

option A ... that is 6.4 is the right answer

Answer: $30 + $10h > $140.

Step-by-step explanation: Currently Cassie has $30, so that is the fixed amount of money she has. She needs $140 dollars, so this will be on the left side of your inequality with a "greater than symbol". Cassie can earn $10 an hour, use the variable "h" to represent the number of hours she will work. Set your inequality like this:

$30 + $10h > $140.

The reason why we use a "greater than" sign (>) is that the amount of money Cassie earns needs to be greater than the price of the calculator to be able to buy it.

The slope equals the rise divided by the run: Slope =riserun Slope = rise run . You can determine the slope of a line from its graph by looking at the rise and run. One characteristic of a line is that its slope is constant all the way along it.

hope this help!

5. In the given scenario, we have;Mode = $25,000 Median = $50,000Mean = $47,500As there are different measures of central tendency, the best measure of the center would be the median.6.                

Explanation of the answer:In statistics, the central tendency is the way of defining a single value that characterizes the whole set of data. This central tendency can be measured using different statistical measures such as mean, mode, median, etc.The given data represents the annual earnings of 300 workers at a factory. We are given that the mode is $25,000 and occurs 150 times out of 301, the median is $50,000, and the mean is $47,500.The mode is the value that occurs the most number of times in a data set. In this case, the mode is $25,000 and it occurs 150 times out of 301, which is less than half of the data. Therefore, the mode is not the best measure of center in this case.The mean is the sum of all the values in a data set divided by the number of values. The mean is sensitive to outliers, so if there are extreme values in the data set, the mean will be affected. The mean for this data set is $47,500.The median is the value in the middle of a data set. It is not affected by outliers, so it gives a better measure of central tendency than the mean. The median for this data set is $50,000, which is the best measure of center.  

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The length of ARC CB is (A) 7.75m.

The arc length is the separation between two points along a section of a curve. Curve rectification is the technique of replicating an irregular arc section using connected line segments in order to measure its length. A rectifiable curve can be divided into a finite number of segments.

To calculate the length of an arc, a section of the entire circle is taken. For instance, an arc with a center angle of 45 degrees would have a radius of 45/360 degrees. The length of the arc can be found by counting the circle's circumference, or 45 of its 360 degrees.

A segment of a curve, particularly a segment of a circle's circumference.

The length of the Arc is equal to 4 × 180 × r.

Where r is the radius and A is the angle at the center in degrees. According to the given figure, r-3 m

A=148°

So by substituting in the formula we will get

L = 148 × 3.14 180 × 3

L = 7.75m

Therefore the length of ARC CB is 7.75m.

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Answer:

x=6, y=-6. (6, -6). I used elimination method.

Step-by-step explanation:

-4x-2y=-12

4x+8y=-24

-------------------

6y=-36

y=-36/6

y=-6

-4x-2(-6)=-12

-4x+12=-12

-4x=-12-12

-4x=-24

4x=24

x=24/4

x=6

Answer:

x=0 or x=6

Step-by-step explanation:

Step 1: Divide both sides by -4.

−4(|−2x+6|)

−4

=

−24

−4

|−2x+6|=6

Step 2: Solve Absolute Value.

|−2x+6|=6

We know either−2x+6=6or−2x+6=−6

−2x+6=6(Possibility 1)

−2x+6−6=6−6(Subtract 6 from both sides)

−2x=0

−2x

−2

=

0

−2

(Divide both sides by -2)

x=0.

We can rewrite\(2log3(x) - log3(y)\)as a single logarithm, which is\(log3(x²/y)\).

Rewriting of \(2log3(x) - log3(y)\)as a single logarithm:We can use the quotient rule of logarithm to rewrite \(2log3(x) - log3(y)\) as a single logarithm.

According to the quotient rule of logarithm ,\(logb (m/n) = logb m - logb n.\)

Therefore,\(2log3(x) - log3(y) = log3(x²) - log3(y).\)

Using the quotient rule of logarithm again, we can simplify\(log3(x²) - log3(y) as log3(x²/y)\).Therefore,\(2log3(x) - log3(y) = log3(x²/y).\)

Thus, the  answer to the question is log3(x²/y).

We can rewrite \(2log3(x) - log3(y)\) as a single logarithm, which is \(log3(x²/y).\)

In logarithm, the quotient rule is used to divide two numbers that are in the form of logarithms. In simple terms, it is used to simplify the logarithmic expression when the logarithms of two numbers are subtracted. It states that the logarithm of the quotient of two numbers is equal to the difference of the logarithm of the two numbers. The formula is given by: \(logb (m/n) = logb m - logb n.\)

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Answer:

(1,0) and (-3,0)

Step-by-step explanation:

Answer: The surface area of the rectangular box = the amount of wrapping paper needed to cover the rectangular box = 394.24 in.²

Step-by-step explanation:

Surface area = 2(wl + hl + hw).

Volume = Length x Width x Height

Given the following:

Volume = 476.16 in.³

Length = 4.8 in.

Width = 8 in.

Find the height (h) using the volume formula:

476.16 = 4.8 × 8 × h

476.16 = 38.4 × h

476.16/38.4 = h

h = 12.4 in.

Surface area = 2(wl + hl + hw) = 2(8 × 4.8 + 12.4 × 4.8 + 12.4 × 8) = 394.24 in.²

The amount of wrapping paper needed to cover the rectangular box = Surface area = 394.24 in.²

The real values of $c$ for which $4x² + 14xc + c$ is the square of a binomial are $c = 0$ and $c = \frac{4}{49}$.

To determine the real values of $c$ for which the expression $4x² + 14xc + c$ is the square of a binomial, we need to find the conditions under which it can be factored as $(ax + b)²$, where $a$ and $b$ are constants.

Expanding $(ax + b)²$, we have $(ax + b)² = a²x² + 2abx + b²$. Comparing this with $4x² + 14xc + c$, we can set up the following equations:

$a² = 4$ (equating the coefficients of $x²$)

$2ab = 14c$ (equating the coefficients of $x$)

$b² = c$ (equating the constant terms)

From the first equation, we find that $a = \pm 2$. Substituting this value into the second equation, we have:

$2(\pm 2)b = 14c$

$\Rightarrow \pm 4b = 14c$

$\Rightarrow b = \pm \frac{14c}{4}$

$\Rightarrow b = \pm \frac{7c}{2}$

Finally, substituting the values of $a$ and $b$ into the third equation, we get:

$\left(\pm \frac{7c}{2}\right)² = c$

$\Rightarrow \frac{49c²}{4} = c$

$\Rightarrow 49c² = 4c$

$\Rightarrow 49c² - 4c = 0$

$\Rightarrow c(49c - 4) = 0$

Now, we can solve this equation to find the values of $c$:

$c = 0$: This is one possible solution.

$49c - 4 = 0 \Rightarrow 49c = 4 \Rightarrow c = \frac{4}{49}$: This is another possible solution.

Therefore, the real values of $c$ for which $4x² + 14xc + c$ is the square of a binomial are $c = 0$ and $c = \frac{4}{49}$.

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The result of the equation 25.8 - 14 / 2, rounded to the nearest one decimal place, is 18.8.

To solve the equation 25.8 - 14 / 2, we need to perform the division first, and then subtract the result from 25.8.

Division: 14 divided by 2 equals 7.

Subtraction: 25.8 minus 7 equals 18.8.

Rounding to one decimal place: The answer, 18.8, rounded to the nearest one decimal place, remains as 18.8.

Therefore, the result of the equation 25.8 - 14 / 2, rounded to the nearest one decimal place, is 18.8.

Following the order of operations (PEMDAS/BODMAS), we prioritize the division operation before subtraction. Thus, we divide 14 by 2, resulting in 7. Then, we subtract 7 from 25.8 to obtain 18.8. Since no rounding is necessary for 18.8 when rounded to one decimal place, the answer remains as 18.8.

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Based on the number of years in a century, we can calculate that the 4 centuries before 1965 was 1565.

A century refers to a period of 100 years.

If we are looking for a period of 4 centuries therefore, this would be:

= 4 x 100

= 400 years

4 centuries before 1965 would therefore be:

= 1965 - 400

= 1565

In conclusion, the answer is 1565.

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Answer :59.9

Step-by-step explanation:

Answer:

Annalise is correct because the outputs are closest when x = 1.35

Step-by-step explanation:

The solution to the equation 1/(x-1) = x² + 1 means the one x value that will make both sides equal. If we look at the table, notice how when x = 1.35, f(x) values are closest to each other for both equations, signifying that x = 1.35 is approximately the solution. Thus, Annalise is correct.

Answer:

y=6

Step-by-step explanation:

y=4x-2

y=4(2)-2

y=8-2

y=6

Hope it helped!

The evaluated integral using the substitution method is 5x^2 - 7x - 86 + C.

The integral can be evaluated using the substitution method to find the antiderivative and then simplifying the result.

Let's break down the given integral step by step. We are given:

∫(6x^2 - 2x) du

To evaluate this integral, we can use the substitution method. Let's choose u = 2x + 7. Differentiating u with respect to x gives du/dx = 2.

Now, we can rewrite the integral in terms of u:

∫(6x^2 - 2x) du = ∫(6(u-7)/2 - u/2)(du/2)

Simplifying further:

= ∫(3u - 21 - u/2) du

= ∫(5u/2 - 21) du

Now, we can integrate term by term:

= (5/2)∫u du - 21∫du

= (5/2)(u^2/2) - 21u + C

Finally, we substitute u back in terms of x:

= (5/2)((2x + 7)^2/2) - 21(2x + 7) + C

Simplifying and combining terms:

= (5/4)(4x^2 + 28x + 49) - 42x - 147 + C

= 5x^2 + 35x + 61 - 42x - 147 + C

= 5x^2 - 7x - 86 + C

Therefore, the evaluated integral using the substitution method is 5x^2 - 7x - 86 + C.

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The statistics z is -1.878 and the p value is 0.0302

Given,

Number of random sample selected, n = 6967

Number of surveys returned, x = 1331

Estimated proportion of return rate;

p = 1331/6967 = 0.192

Significance level, ∝ = 0.01

z would represent the statistic

We investigate the assertion that the return rate is less than 20%, and the following hypotheses are tested:

Null hypothesis, p₀ ≥ 0.2

Alternative hypothesis, p₀ < 0.2

The statistics, z = (p - p₀) / √(p₀(1 - p₀)/n)

That is,

z = (0.191 - 0.2) / √(0.2(1 - 0.2)/6967) = -1.878

Using the alternative hypothesis and the following probability, we can now get the p value:

p value  = p(z < - 1.878) = 0.0302

We fail to reject the null hypothesis when the p value exceeds the significance level of 0.01 and there is insufficient evidence to support the conclusion that the return rate is less than 20% at 1% of significance.

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The alien's total distance traveled are Total Distance Traveled: 19 kilometers.

Distance is the separation between two points or things. It can be measured in a number of different units, including feet, meters, kilometers, and others. In addition to physical distance, time between two sites can also be considered, including days, hours, and minutes. In physics, mathematics, and geography, distance is a crucial notion. Utilizing additional formulas or the Pythagorean theorem, one can determine distance. Distance can be used to gauge an object's speed, the length of a journey, or the size of an area.

Displacement = final point - initial point

= (5 - 0 )km

5 kilometers

Total Distance Traveled: 12 + 7 = 19 km

19 kilometers are of 12 kilometers to the crater and 7 kilometers back to the spaceship.

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Answer:

a

Step-by-step explanation:

\(a_{1} = -6\\\\a_{n}=\frac{1}{2}a_{n-1} - n\\\\a_{2}=\frac{1}{2}a_{1}-2\\\\ = \frac{1}{2}*(-6)-2\\\\ = -3 - 2\\\\= -5\\\\a_{3}=\frac{1}{2}a_{2}-3\\\\= \frac{1}{2}*(-5)-3\\\\=\frac{-5}{2}-3\\\\= \frac{-5}{2}-\frac{3*2}{1*2}\\\\=\frac{-5}{2}-\frac{6}{2}\\\\=\frac{-11}{2}\)

Answer:

x = 5

Step-by-step explanation:

Well all you have to do is use this formula

75 + 36x -3 = 180

How did I figure that out?? Well I know that the angle next to 75 is the same as 36x-3 becuase that are alternate interior angles and 75 and 36x-3 would be a linear pair meaning that the product of the them would be 180, Thus making the formula

Now all you have to do is combine like terms:

75 -3 = 72

72 + 36x = 180

subtract 72 from both sides

72 -72 = 0

180- 72 = 108

36x = 108

divide both sides by 36

X= 5

The house is 0 miles east of the center of the town.

To determine how far east of the center of the town the house is located, we need more information about the shape of the cell tower's coverage. However, we can make an estimation based on the given information.

Since the house lies on the boundary of the cell tower's coverage, we can assume that the cell tower's coverage area is circular.

Let's consider the following scenario: if the center of the town is the origin of a coordinate system, and the cell tower is located at (0,0), with the house 6 miles north of the town's center, we can represent the house's location as (0,6).

Assuming the cell tower's coverage area is circular, the house must lie on the circumference of this circle. In this case, the radius of the circle is 6 miles (since the house is located 6 miles north of the town's center).

Now, if we want to find the eastward distance of the house from the center of the town, we need to find the x-coordinate of the house. Since the house is directly east of the cell tower, the x-coordinate will be 0.

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The price that Maura sell each scarf would be =$33. Maura sells each scarf for $33. That is option A.

To calculate the amount of money that Maura spends on each scarf the following is carried out.

The amount of money that she spends on the scarf material = $5.50

The percentage selling price of each scarf = 600% of $5.50

That is ;

= 600/100 × 5.50/1

= 3300/100

= $33.

Therefore, each price that is sold by Maura would probably cost a total of $33.

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Answer:

r=6

Step-by-step explanation:

Proportions

We know M is directly proportional to \(r^3\)

This can be written as

\(M=kr^3\)

Where k is the constant of proportionality which will be determined knowing that when r = 4, M= 160. Substituting in the equation above:

\(160=k\cdot 4^3\)

\(160=k\cdot 64\)

Solving for k:

\(k=\frac{160}{64}=2.5\)

The equation is:

\(M=2.5\cdot r^3\)

Now find r when M=540:

\(540=2.5\cdot r^3\)

Dividing by 2.5:

\(216=r^3\)

Taking cube roots:

\(r=\sqrt[3]{216}\)

r=6

Answer:

Light + carbon dioxide → glucose + oxygen.

Step-by-step explanation:

A is the right one.

...

.

Richard's net pay for the week, considering Social Security, Medicare, and FIT deductions, can be calculated by subtracting the total deductions from his gross earnings.

First, let's determine the amount deducted for Social Security. The Social Security rate is 6.2%, and the maximum earnings subject to this deduction are $118,500. Since Richard is $1,000 below the maximum level, the amount subject to Social Security deduction is $1,000. Therefore, the Social Security deduction is 6.2% of $1,000.

Next, we calculate the Medicare deduction. The Medicare rate is 1.45%, and it is applied to the entire earnings of $1,700.

To calculate the FIT deduction, we need additional information about Richard's taxable income, tax brackets, and exemptions. Without this information, we cannot provide an accurate calculation for the FIT deduction.

Finally, we subtract the total deductions (Social Security, Medicare, and FIT) from Richard's gross earnings of $1,700 to obtain his net pay for the week.

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Answer:

0.6 is equivalent

Answer:

60/100=6/10=4/5

0.6

Step-by-step explanation:

these are all equivalent

To find (the derivative of \( y \) with respect to \( x \)) from the given function \( y = \ln(x^2) + \ln(x+3) - \ln(2x+1) \), we can apply the rules of logarithmic differentiation.

First, we can rewrite the function using logarithmic properties:

\(\( y = \ln(x^2) + \ln(x+3) - \ln(2x+1) = \ln(x^2(x+3)) - \ln(2x+1) \).\)

Now, using the rules of logarithmic differentiation, we can differentiate \( y \) with respect to \( x \) as follows:

\( \frac{dy}{dx} = \frac{1}{x^2(x+3)} \cdot (2x(x+3)) - \frac{1}{2x+1} \).

Simplifying further:

\(\( \frac{dy}{dx} = \frac{2x(x+3)}{x^2(x+3)} - \frac{1}{2x+1} \).\( \frac{dy}{dx} = \frac{2x^2 + 6x}{x^2(x+3)} - \frac{1}{2x+1} \).Thus, \( \frac{dy}{dx} = \frac{2x^2 + 6x}{x^2(x+3)} - \frac{1}{2x+1} \) is the derivative of \( y \) with respect to \( x \)\) for the given function.

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a. We can form the change of coordinates matrix P as: P = [b₁]c b₂]c   =  [2, 8]  [0, 5]  [-5, 0]

Therefore, [x]c is the column vector [-20, -1] representing the coordinates of x with respect to the basis C.

b. We have x = 2b₁ - 3b₂ = 2(2c₁ - 5c₂) - 3(8c₁ + 5c₂) = (-22c₁ - 37c₂) Therefore, we need to find [x]

c. We compute this as follows:

[x]c = [a, b]

= [(-22)(2) + (-37)(0), (-22)(0) + (-37)(5)]

= [-44, -185]

Therefore, [x]c is equal to [-44, -185].

To find the change-of-coordinates matrix from B to C, we need to express the basis vectors of B (b1, b2) in terms of the basis vectors of C (c₁, c₂).

Given that b₁ = 2c₁ + 7c₂ and

b₂ = 8c₁ + 5c₂, we can write the change-of-coordinates matrix P as:

P = [b₁ | b₂]

= [2c₁ + 7c₂ | 8c₁ + 5c₂]

= [2 8]

[7 5]

This matrix P represents the linear transformation that maps coordinates relative to basis B to coordinates relative to basis C.

b. To find [x]c for x = 2b₁ - 3b₂, we can use the change-of-coordinates matrix P obtained in part (a).

First, we express x in terms of the basis vectors of C:

x = 2b₁ - 3b₂

= 2(2c₁ + 7c₂) - 3(8c₁ + 5c₂)

= 4c₁ + 14c₂ - 24c₁ - 15c₂

= -20c₁ - c₂

Next, we can express x as a linear combination of the basis vectors of C:

[x]c = [-20 | -1]

Therefore, [x]c is the column vector [-20, -1] representing the coordinates of x with respect to the basis C.

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