-0.785714286 as a fraction

Answer:

The answer is down payment.

Step-by-step explanation:

Gerald bought a home for $300,000. His largest up–front cost is 10 percent, or $30,000.

This cost is called down payment.

Down payment is an amount in cash that is given while purchasing a home. This lies between 5% to 20% of the purchase price.

This payment reduces the amount of money you will have to borrow from banks. Each loan requires some sort of down payment.

Final answer:

A linear equation perpendicular to y=5 is a vertical line, expressed as x=c, where c is any real number. For instance, x=2 is perpendicular to y=5.

Explanation:

A linear equation perpendicular to y=5 would need to have an undefined slope, meaning it's a vertical line. Since y=5 is a horizontal line, a perpendicular line will have no slope value that we can put in terms of y=mx+b, where m represents the slope and b represents the y-intercept. Thus, the equation will be of the form x=c, where c is any real number. This represents a vertical line that crosses the x-axis at the point (c,0).

For example, the linear equation x=2 is perpendicular to y=5 and crosses the x-axis at the point (2,0).

Answer:

Step-by-step explanation:

alright, lets get started.

bc and cd will be same as both are radius of the circle.

[tex]bc=cd=3[/tex]

[tex]ac=ad+cd[/tex]

[tex]ac=4+3[/tex]

[tex]ac=7[/tex]

as we know ab is tangent to the circle so, triangle abc will be a right triangle.

Using Pythagorean theorem

[tex]a^2+b^2=c^2[/tex]

[tex]3^2+x^2=7^2[/tex]

[tex]9+x^2=49[/tex]

Subtracting 9 from both sides

[tex]x^2=49-9=40[/tex]

[tex]x=\sqrt{40} =2\sqrt{10}[/tex]

So, the answer is [tex]2\sqrt{10}[/tex]    :   answer

Hope it will help.   :)

Answer:

75

Step-by-step explanation:

The student's clues form the equation 3x + 4 = 22. When solved, this equation reveals that the original number x is 6.

The student is creating an algebraic equation to find an unknown number. Starting with the clues given:

Now, we can solve this equation to find x:

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Final answer:

The volume of a sphere increases by 72.8%, which after calculations, results in a 20% increase in the radius of the sphere.

Explanation:

The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius of the sphere. An increase in volume by 72.8% implies that the new volume V' is equal to 1.728 times the original volume V. To find the percentage increase in the radius, we use the relationship between volume and radius:

V' = (4/3)πr'^3, where r' is the new radius after increase. Since V' = 1.728V, we have:

After taking the cube root of both sides, we obtain:

Thus, the new radius is approximately 120% of the original radius, which means there is a 20% increase in the radius.

Final answer:

To calculate the percentage increase in the radius of the sphere when the volume is increased by 72.8%, we can use the formula for volume and solve for the new radius in terms of the original radius. The percentage increase in radius is then calculated by comparing the new and original radius.

Explanation:

The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius of the sphere. If the volume of the sphere is increased by 72.8%, we can calculate the new volume by multiplying the original volume by 1 + 0.728. Let's denote the original radius as r1 and the new radius as r2.

The formula for volume can be written as V = (4/3)πr³. Substituting r1 and r2 into the formula, we get:

Since the two volumes are related by the percentage increase (1 + 0.728), we can write the equation:

(1 + 0.728)V1 = V2

Now, let's solve for r2 in terms of r1:

(1 + 0.728)V1 = (4/3)πr2³

r2 = ([(1 + 0.728)V1] * (3/4π))^(1/3)

Finally, we can calculate the percentage increase in the radius by comparing r2 to r1:

Percentage increase in radius = (r2 - r1) / r1 × 100%

Answer:

[tex]\frac{5\sqrt[3]{6}}{8}[/tex]

Step-by-step explanation:

We have been given an exponential number. We are supposed to simplify our given number.

[tex](\frac{750}{512})^{\frac{1}{3}[/tex]  

Using fractional exponent rule [tex]x^\frac{m}{n}=\sqrt[n]{x^m}[/tex], w ecan write our given number as:

[tex](\frac{750}{512})^{\frac{1}{3}}=\sqrt[3]{(\frac{750}{512})^1}[/tex]

[tex](\frac{750}{512})^{\frac{1}{3}}=\sqrt[3]{\frac{750}{512}}[/tex]

We can rewrite 512 as [tex]8^3[/tex] and 750 as 125*6.

[tex](\frac{750}{512})^{\frac{1}{3}}=\sqrt[3]{\frac{125*6}{8^3}}[/tex]

We can rewrite 125 as [tex]5^3[/tex]

[tex](\frac{750}{512})^{\frac{1}{3}}=\sqrt[3]{\frac{5^3*6}{8^3}}[/tex]

Using radical rule [tex]\sqrt[n]{a^n}=a[/tex], we will get:

[tex](\frac{750}{512})^{\frac{1}{3}}=\frac{5\sqrt[3]{6}}{8}[/tex]

Therefore, [tex]\frac{5\sqrt[3]{6}}{8}[/tex] is equivalent to our given number.

The solution to the inequality 12 < y(8 - y) is y such that 2 < y < 6.

The solution of the inequality 12 < y(8 - y), you can start by simplifying the expression on the right side: y(8 - y)
Distribute the y on the right side: 8y - [tex]y^2[/tex]
Now, substitute this expression back into the original inequality: [tex]12 < 8y - y^2[/tex]
Rearrange the terms to form a quadratic inequality: [tex]y^2 - 8y + 12 > 0[/tex]

Now, factor the quadratic expression: (y - 2)(y - 6) > 0
To solve for y, set each factor equal to zero and find the critical points: y - 2 = 0 or y - 6 = 0
Solving these equations gives y = 2 and y = 6.

Now, create intervals using these critical points and test a value in each interval:
1. Test y = 1: (1 - 2)(1 - 6) = (-1)(-5) = 5 > 0
2. Test y = 3: (3 - 2)(3 - 6) = (1)(-3) = -3 < 0
3. Test y = 7: (7 - 2)(7 - 6) = (5)(1) = 5 > 0
The solution is y such that 2 < y < 6

The solution to the parts is given below.

Trigonometry is a discipline of mathematics that studies the relationship between the sides of a triangle (right triangle) and their angles. There are six trigonometric functions that define the relationship between sides and angles.

1. Using Trigonometry

sin 60 = P/H

√3/2 = x/ 12

x = 12√3 / 2

x= 6√3

2. Using Trigonometry

sin 60 = P/H

1/√2 = 7√2 / x

x/√2 = 7√2

x = 14 unit

3. Using sine law

sin 75 /11 = sin 54 / x

0.965 / 11 = 0.809 / x

0.0877 = 0.809 / x

x = 9.224 miles

Learn more about Trigonometry here:

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The algebraic expression equivalent to cot(arctan x) is 1 / x, derived by recognizing that cot(θ) is the reciprocal of tan(θ), and tan(θ) = x for θ = tan-1(x)

To find an algebraic expression for cot(arctan x), let's follow a step-by-step transformation using trigonometric identities: cot(arctan x) is denoted as cot(tan-1(x))

Therefore, the algebraic expression equivalent to cot(tan-1(x)) is 1 / x.

Answer:

your answer would be y-65=8(x-5)

For the first question; we have a problem dealing with translations. Our goal is to translate the word problem into an algebraic one. So our numbers are 60, 2, and 5. Our variable, or the letter holding the unknown number's place value,  is N. 

The problem states that 60 is MORE THAN the PRODUCT of 5 and N. Focus on the words I bolded and capitalized. These are your key words that tells you what operations you need to use. Note that 'product' signals the operation of multiplication (Since the answer you get from multiplying numbers is called the 'product'.) and 'more than' signals the operation of addition (Because you are left off with more than you originally had before adding). 

Now that we know that our algebraic expression contains multiplication, addition, letter N and the numbers 2 and 5; we can start plugging the numbers in.

60 = 2 (more than) + (product of) 5N. The answer for the first attachment is B. 

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All we need to do for the AB problem (Question 25 on your material) is solve AB.

Note 1: When a problem has no operation separating two letters or numbers, this means multiplication.

Note 2: A and B are variables. Variables are letters that stand for and hold the place of our unknown quantities. However, the values are not unknown anymore given the fact that the question tells us that A= 42 and B = 2. Thus we substitute A with 42 and B with 2, then work from there. 42 * 2 =84. Answer = A.

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And finally, for question 26, we use PEMDAS. P = parenthesis (), E = exponent x^2, M/D = x or /, A/S means + or subtraction.

According to PEMDAS, we first solve what's parenthesis, which is 77 – 32. Using mental math, 77 – 32 = 45. ( 7 – 3 = 4 and 7 – 2 = 5.). 5/9 * 45 is what we have left. 5 divided by 9 =0.5555555555555556. 0.5555555555555556 * 45 = 25. Answer is D.