I need help with my math practice problems
\( - \frac{1}{8} = \frac{7}{4} + \frac{3}{2} z\)
​

y/x is equivalent to a constant and is equal to [m].

The general equation of a straight line is -

y = mx + c

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

Other possible equations of lines are -

(y - y₁) = m(x - x₁)                                {Point - slope form}

(y - y₁) = (y₂ - y₁) × (x - x₁)/(x₂ - x₁)      {Two point - slope form}

x/a + y/b = 1                                        {intercept form}

x cos(β) + y sin(β) = L                          {Normal form}

We have a relationship that is proportional when the ratio of [y] over [x].

The equation of a straight line -

y = mx + c

can be used to represent proportional relationship when [c] = 0. Now -]

y = mx

m = y/x

Now, y/x is equivalent to a constant and is equal to [m].

Therefore, y/x is equivalent to a constant and is equal to [m].

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Answer:

The U.S. pays $630,000,000 (or six hundred thirty million dollars) in FUTA taxes annually.

Step-by-step explanation:

First, we must find 6% of $7,000 to find the annual taxes per employee.

7,000 x 0.06 = $420

Therefore, each employee gets $420 in taxes per year.

Since there are 1.5 million employees, we need to multiply $420 by 1.5 million.

1,500,000 x 420 = $630,000,000

Therefore, the U.S. pays $630,000,000 in FUTA taxes annually.

Hope this helps! :D

Tax paid to FUTA annually by 1.5 million employee is $630000000.

Percent is the ratio or a fraction in which the whole is always taken as 100.

To convert a percentage to decimal, we follow the following step

According to the given question

Tax 6.0% on the first $7,000 an employee earn each year.

⇒ 6% of $7000 = \(\frac{6}{100}\)× $7,000 = $420

⇒ The tax of $420 an employee pay each year.

Therefore, the tax paid by 1.5 million of employees = 1500000 ×$420 = $630000000.  (1million = 1000000)

Hence, tax paid to FUTA annually by the 1.5 million employee will be $630000000.

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1. Using Radicals the number √17 has a value of 4.123.

2. √510 =260100.

3. √4x = 2√x.

Simply multiply or divide the numbers at each point where it makes sense to multiply or divide a function. If the functions are specified by formulas, you can simply multiply or divide the formulas (inserting numbers before or after is irrelevant).

When multiplying or dividing, it is standard practise for the final result to contain the same number of significant figures as the number with the fewest significant figures. The division of two numbers can be calculated using the following formula: Dividend Divisor = Quotient + Remainder. The number that is being divided in this case is known as the dividend.

The number that divides the number (dividend) into equal parts is known as the divisor.

1. \(\sqrt{17}\\\) = 4.123 (The values of the number √17 is 4.123.)

2.  √510

= 510^2

=(500+10)^2

=500^2+10^2+2×500×10

=250000+100+10000

=260100.

3. √4x = 2√x.

because 4 = 2*2

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Answer:

C.

Step-by-step explanation:

A. 5/8=0.625

B. 4/16=0.25

C. 15/6=2.5

D. 10/12=0.83

Answer:

Step-by-step explanation:

Here is your workings

(3x)^3  Apply the rule of exponents

Step 2

(3x)^3=3^3x^3  Simplify

Step 3

3^2=27  Solve

27x^3

Step-by-step explanation:

I think it's 2√61............................

here u can use distance formula

Answer:

\(\sqrt[5]{4}\)  + \(\sqrt[10]{3}\)

Step-by-step explanation:

We sure can write 2^2/5+ 3^1/10 as \(2^{\frac{2}{5} } + 3^{\frac{1}{10} }\)

// use the \(a^{\frac{m}{n} } =\sqrt[n]{a^{m} }\) to transform the expression

Convert \(2^{\frac{2}{5} }\) to \(\sqrt[5]{2^{2} }\) = \(\sqrt[5]{4}\)                        (here a = 2, n = 5, m = 2)

Then convert  \(3^{\frac{1}{10} }\) to \(\sqrt[10]{3^{1} }\) = \(\sqrt[10]{3}\)             (here a = 3, n = 10, m = 1)

Now we get  \(2^{\frac{2}{5} } + 3^{\frac{1}{10} }\) = \(\sqrt[5]{4}\)  + \(\sqrt[10]{3}\) . This is the simplified form, which is the answer.

We are given an economy with two goods and Leontief consumers who have utility functions that depend on the minimum of the two goods. The initial endowments of the consumers are positive, and we are assuming that the aggregate endowment of the economy has more of the first good than the second. If a price system p=(p1,p2) is an equilibrium with market clearing, we need to show that p1=0 and p2>0.

We start by considering the demand function for a Leontief consumer, which is given by xi1(p) = xi2(p) = (p1 + p2)mi/pi, where mi represents the initial endowment of consumer i and pi represents the price of good i.

Since the aggregate endowment ω=(ω1,ω2) of the economy satisfies ω1 > ω2, we know that the total supply of the first good is greater than the total supply of the second good.

Now, if p1 > 0, then for any positive value of p2, the demand for the second good xi2(p) will be positive for all consumers. This implies that the total demand for the second good will be greater than the total supply, leading to a market imbalance.

To achieve market clearing, where total demand equals total supply, we must have p1 = 0. This is because if p1 = 0, the demand for the first good xi1(p) will be zero for all consumers, and the total supply of the first good will match the total supply. Additionally, p2 must be positive to ensure positive demand for the second good.

Therefore, we have shown that in an equilibrium price system with market clearing, p1 = 0 and p2 > 0, given the initial endowment condition ω1 > ω2.

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Answer:

Step-by-step explanation:

3 gallons because 3/4 of a gallon covers 1/4 of a wall so you multiply the amount of gallons used for a wall times 4 which is 12/4 (keep the denominator the same ) and then divide 12 by 4 which is 3 gallons

Vertical Angles are the angles opposite each other when two lines cross.

In our question, we have to opposite angles. For this reason the answer is letter B.

The Hectora's rate of work in part per hour is 18 hours

Given the following parameters:

Taking the sum of the reciprocals of the time taken;

1/6 = 1/9 + 1/r

1/r = 1/6 - 1/9

1/r = 9-6/54

1/r = 3/54

Cross multiply

3r = 54

r = 54/3

r = 18 hours

Hence the Hectora's rate of work in part per hour is 18 hours

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Answer:

Step-by-step explanation:

1/9

The simplest form expression for the addition of the fractions given using the lowest common multiple of the denominator is 2/3.

A fraction is a numerical value that is a part of a whole. It is evaluated by dividing a whole into a number of parts.In Mathematics, a fraction is defined as a part of the whole thing.  For example, ½ represents half of a whole number or a thing

Given the fractions :

1/4 + 5/12

The lowest common multiple of the denominator ;

A lowest common multiple of 4 and 12 = 12

1/4 + 5/12 = (3 + 5) / 12

1/4 + 5/12 = 8/12

Expressing in simplest form :

8/12 = 2/3

Therefore, the simplest form expression of the addition is 2/3

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Answer: 0.06

27/50

1/64

I am not sure but I think it is 1/36

3⁵

Idaho has the smallest population.

0.000857

 1.414213562..

1.5 x 10⁸

.16

3/32

6.2

 29/30

I am not sure

-1/6

4/9

2.25

.265

Step-by-step explanation:

Graphs are used to represent functions.

Sara's mistakes are:

Graph A

When a graph is plotted, the intervals on both axes must be uniform.

In Sara's graph, the intervals on the y-axis do not follow a uniform pattern (i.e. 0, 1, 2, 4, 8)

Instead, she could have used 0, 2, 4, 6, 8.....

Graph B

The origin of a graph is always 0

In Sara's graph, the origin is at -1.

This means that, the wrong origin was used, and the actual origin is wrongly placed.

See attachment for the correction of graph A

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Daniel's method is incorrect, as the interquartile range is given by the difference between the third quartile and the first quartile.

The interquartile range of a data-set is by the difference of the 75th percentile(Q3) by the 25th percentile(Q1) of the data-set.

The quartiles are described as follows:

From this, we get that the quartiles are related to the median of the set, that is, neither is given by the highest and by the lowest values, hence the interquartile range is given by the difference between the third quartile and the first quartile.

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The math topics covered in the grade 6 math worksheets are algebra,geometry,measurement, number operation.

1. Number sense and operations: This includes understanding numbers, fractions, decimals, and integers, as well as performing operations with them.

2. Algebra: This includes understanding algebraic expressions and equations, and using them to solve problems.

3. Geometry: This includes understanding basic geometric concepts, such as lines, angles, and shapes, and using them to solve problems.

4. Measurement: This includes understanding measurement concepts, such as length, area, and volume, and using them to solve problems.

5. Data analysis and probability: This includes understanding basic concepts of statistics, such as mean, median, and mode, and using them to analyze data and make predictions.

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The capital includes :

Any financial contribution made to a business to assist in achieving and advancing its commercial goal is referred to as a capital investment. The phrase may also refer to a long-term purchase made by a company, such as one for land, equipment, businesses, etc.

When a corporation issues securities to equity investors and debt to bondholders, the total amount of debt and capital lease obligations are added to the amount of stock given to investors to determine the overall amount of money raised. This amount is referred to as invested capital. The balance sheet of the business does not include an item for invested capital because debt, capital leases, and stockholders' equity are all stated separately.

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The theorem that proves that the two triangles are similar is the SAS Similarity Theorem. The theorem states that if two sides of one triangle are proportional to two sides of another triangle, and the included angle between these sides is the same in both triangles, then the two triangles are similar.

In this case, the ratio of the corresponding sides of the two triangles are:

AB/DE = 3/18 = 1/6

BC/EF = 7/42 = 1/6

Since the ratio of corresponding sides is equal, and the included angle between them (angle B and angle E) is the same, the two triangles are similar by the SAS Similarity Theorem.

The interest rate on the account is 9.79%.

To determine the interest rate on the account, we can use the formula for compound interest:

A = P(1 + r/n\()^{(nt)\)

In this case, we have:

P = $4,000.00

A = $8,850.00

t = 9 years

n = 12 (compounded monthly)

Substituting the values into the formula, we have:

$8,850.00 = $4,000.00(1 + r/12)^(12*9)

Divide both sides by $4,000.00:

8,850/4,000 = (1 + r/12)^(12*9)

2.2125 = (1 + r/12)^(108)

Take the logarithm (base 10) of both sides to remove the exponent:

log(2.2125) = log[(1 + r/12\()^{(108)\)]

log(2.2125) = 108 x log(1 + r/12)

log(2.2125)/108 = log(1 + r/12)

0.008147 = log(1 + r/12)

1\(0^{(0.008147)\) = 1 + r/12

1\(0^{(0.008147)\) - 1 = r/12

12 (1\(0^{(0.008147)\) ) - 1) = r

r ≈ 0.0979

r ≈ 9.79%

Therefore, the interest rate on the account is 9.79%.

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Answer:

x=-5

Step-by-step explanation:

x+2=-3

x+2-2=-3-2

x=-5

im in algebra two so you can trust my answer. happy holidays and stay safe!

Answer:

y = 3x - 1

Step-by-step explanation:

In order for lines to be parallel, they must have the same slope.

The slope of y = 3x - 8 is 3.

Now, we can solve it using point-slope form. Remember that m = 3, x₁ = -2 and y₁ = -7:

y − y₁ = m(x − x₁)

y - (-7) = 3(x - (-2))

y + 7 = 3(x + 2)

Distribute 3 and isolate y:

y + 7 = 3x + 6

y = 3x - 1

The balanced chemical equations for the given reactions are as follows:

a. Ca(CH3COO)2 + 2NH4OH → Ca(OH)2 + 2CH3COONH4

b. 2K + 3Mg3(PO4)2 → 6KPO4 + Mg

In reaction (a), Ca(CH3COO)2 reacts with NH4OH. The reactants are calcium acetate (Ca(CH3COO)2) and ammonium hydroxide (NH4OH). The products formed are calcium hydroxide (Ca(OH)2) and ammonium acetate (CH3COONH4). The equation is balanced by ensuring that the number of atoms on both sides of the equation is the same.

In reaction (b), potassium (K) reacts with magnesium phosphate (Mg3(PO4)2). The reactants are potassium and magnesium phosphate, while the products are potassium phosphate (KPO4) and magnesium.

The equation is balanced by adjusting the coefficients in front of each compound to ensure the conservation of atoms.

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The mean of the sampling distribution will be 3.54. Thus, the correct option is C.

The population means is equal to the mean of the sampling distribution for all feasible samples of size 4. In this instance, 3.54 pounds is shown as the population means.

This suggests that the mean weight of the population of banana bunches will be 3.54 pounds if we pick several random samples of size four, compute the mean weight for each sample, and then average those sample means.

The Central Limit Theorem, which asserts that the sampling distribution of the sample means approaches a normal distribution centered on the population mean as the sample size grows, is a fundamental idea in statistics.

Thus, the correct option is C.

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Answer:

y = -2x - 4

Step-by-step explanation:

Formula is y = mx + b where m is the slope and b is the y-intercept

(1, -6) (-3, 2)

\(\frac{-6-2}{1-(-3)}=\frac{-8}{4} =-2\)

The slope is -2

y = -2x + b

So let's find b, insert 2 for y and -3 for x to find b

2 = -2(-3) + b

2 = 6 + b

Subtract 6 from both sides to get b alone

-4 = b

We found what b equals (the y-intercept), which is -4

So, the equation is y = -2x - 4

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Answer:

11 & 12 = 19⁰

13 = 71⁰

14, 15, 16 & 17 = 90⁰

18 & 20 = 78⁰

19 = 12⁰

Step-by-step explanation:

14,15,16 and 17 are formed from perpendicular lines. They are not counted as angles for the kite because, the are in the middle of the kite, not at the side...

You can easily find the angles using the triangle angles formula...to find 12,

180 - 90 - 71 = 19

To find 20 & 18, with the same method,

180 - 90 - 12 = 78

Answer:

\(100x^2-4\pi x^2\)

Also can be said as:

\(4x^2(25-\pi )\)

Step-by-step explanation:

The question is asking you, "how much is left over."

In this scenario, you're going to have to subtract the area of the pool (P) from the total area of the backyard (B), which will leave you with the remaining area of the backyard (x).

This means your equation to solve this question is:

\(x=B-P\)

The value of B is the area of the backyard.

We are told that the backyard is a rectangular shape. So, we can use the formula of finding the area of a rectangle.

The formula is \(B=L*W\), where L is the length and W is the width.

Both the length and width are 10x, so we must plug that into this equation.

We end up getting:

\(B=10x*10x\)

Which can be simplified to:

\(B=100x^2\)

The value of P is the area of the pool.

The pool is a circular shape. So, to get the area of it, we must use the formula of finding the area of a circle.

The formula is \(P=\pi r^2\), where r is the radius.

Plugging in the radius of 2x, we get:

\(P=\pi (2x)^2\)

By solving this out, we end up with:

\(P=4\pi x^2\)

From the scenario, we have the equation:
\(x=B-P\)

And from steps 1 and 2, we have the values:

\(B=100x^2\) and \(P=4\pi x^2\)

Now we just plug those values in to get:

\(x=100x^2-4\pi x^2\)

And finally, the amount of the backyard remaining is:

\(100x^2-4\pi x^2\)

This answer may be simplified to:

\(4x^2(25-\pi )\)

The points on the x-axis that are at a distance of 25‾√ from point P(2, -3, -1) are x = 2 + (√585)/2 and x = 2 - (√585)/2.



To find the points on the x-axis that are at a distance of 25‾√ from point P(2, -3, -1), we need to consider the coordinates of the points on the x-axis.

Since we are dealing with the x-axis, the y and z coordinates of the points will be zero. Let's assume the coordinates of the points on the x-axis as (x, 0, 0).

The distance between two points can be calculated using the distance formula:Distance = √((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2)

In this case, the coordinates of point P are (2, -3, -1) and the distance is given as 25‾√. Plugging these values into the distance formula, we get:

25‾√ = √((x - 2)^2 + (-3 - 0)^2 + (-1 - 0)^2)

Simplifying further:

625/4 = (x - 2)^2 + 9 + 1

625/4 = (x - 2)^2 + 10

Solving for x:

(x - 2)^2 = 625/4 - 10

(x - 2)^2 = 625/4 - 40/4

(x - 2)^2 = 585/4

Taking the square root of both sides:

x - 2 = ±√(585/4)

x = 2 ± (√585)/2

Therefore, the points on the x-axis that are at a distance of 25‾√ from point P(2, -3, -1) are x = 2 + (√585)/2 and x = 2 - (√585)/2.

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Answer:

A = 210 cm²

Step-by-step explanation:

Perimeter of the triangle = the sum of the sides of the triangle.

70 = (3x - 1) + (4x + 1) + (3x)

70 = 10x  

7 = x     The length of the sides of the triangle are 3x - 1 = 20;  4x + 1 = 29 and                

             3x = 21.

 Looking at the given information, this triangle is a special type of triangle because the area of a triangle is Area = 1/2 bh and you do not know which side is the base and height of the triangle.

Trying a² + b² = c² to see if it is a right triangle.   20² + 21² = 29 ² ; yes it is a right triangle and now we know that the base and height is 20 and 21.   The longest side is the hypotenuse in a right triangle

A = 1/2bh

A = 1/2 (20)(21)

A = 10 · 21

A = 210 cm²