For which triangle is the length of the hypotenuse an INTEGER?

ANSWER

A. 22 in

EXPLANATION

The volume of a cone is calculated using the formula:

[tex]Volume = \frac{1}{3} \times \pi {r}^{2} h[/tex]

It was given that: the volume is 2,279.64 in³

The height of the cylinder is also given as: h=18 in.

We substitute, the given values into the formula to get:

[tex]2279.64= \frac{1}{3} \times (3.14) \times {r}^{2} \times 18[/tex]

[tex]2279.64= 18.84 {r}^{2} [/tex]

[tex] {r}^{2} = \frac{2279.64}{18.84} [/tex]

[tex] {r}^{2} = 121[/tex]

We take positive square root to get;

[tex]r = \sqrt{121} [/tex]

[tex]r = 11in[/tex]

Therefore the diameter is 2(11) which is equal to 22 inches.

Answer:

24 cubic feet

Step-by-step explanation:

The formula is V = Length x width x height

the first has a length of 2, a width of 2 and a height of 2 = 8 cubic feet

The second has a length of 4, a width of 2 and a height of 2 = 16 cubic feet

8 + 16 = 24 cubic feet

Answer:

the answer is C

Step-by-step explanation:

x2−162x2−9x+42x2+14x+244x+4

=4x3+4x2−64x−644x4+10x3−70x2−160x+96

=2x3+2x2−32x−322x4+5x3−35x2−80x+48

=2(x+1)(x+4)(x−4)(2x−1)(x+3)(x+4)(x−4)

=2x+22x2+5x−3

Answer:

[tex]\large\boxed{L.A.=153\pi\ mm^2}\\\boxed{S.A.234\pi\ mm^2}[/tex]

Step-by-step explanation:

The formula of a lateral area of a cone:

[tex]L.A.=\pi rl[/tex]

r - radius

l - slant height

The formula of a surface area of a cone:

[tex]S.A.=\pi r^2+\pi rl[/tex]

We have r= 9mm and l = 17mm. Substitute:

[tex]L.A.=\pi(9)(17)=153\pi\ mm^2[/tex]

[tex]S.A.=\pi(9^2)+153\pi=81\pi+153\pi=234\pi\ mm^2[/tex]

30^2+43^2= x^2

900 +1849= 2749

sqr root of 2749 = x

the answer is about 52 in.

The size of the TV will be equal to 52 inches.

Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the square of the sum of the other two sides.

Given that the space where you want to put the TV measures 30 inches high and 43 inches wide.

The size of the TV will be calculated as,

30²+43²= x²

900 +1849= 2749

√2749 = x

x = 52 inches

Therefore, the size of the TV will be equal to 52 inches.

To know more about the Pythagorean theorem follow

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Answer:

The area of parallelogram GHTA is [tex]41.568 cm^2[/tex].

Step-by-step explanation:

Given parallelogram GHTA

GH = 8 cm =-AT

GA = 6 cm

∠ GAT =∠ GHT = 60°

To find = Area of parallelogram

Solution:

Draw perpendicular GO on the base AT.

In ΔGOA

[tex]\sin 60^o=\frac{GO}{GA}=\frac{GO}{6 cm}[/tex]

(sin 60°=0.8660)

GO = 5.196 cm

Area of the parallelogram: GO × AT

[tex]=5.196 cm\times 8 cm =41.568 cm^2[/tex]

The area of parallelogram GHTA is [tex]41.568 cm^2[/tex].

The answer would be D 48V3 cm ^2

the v is the root btw

Three sides adds up to 3ft squared.

Answer:18

Step-by-step explanation:I did the question and got it right

The answers are: A and C

Answer:

Option D. [tex]\$6,139.25[/tex]

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=4\ years\\ P=\$5,350\\ r=0.035\\n=1[/tex]  

substitute in the formula above  

[tex]A=\$5,350(1+\frac{0.035}{1})^{1*4}[/tex]

[tex]A=\$5,350(1.035)^{4}=\$6,139.25[/tex]

Final answer:

The future amount of money in the account after 4 years with annual compound interest is approximately $6,139.25, which is option D.

Explanation:

The student's question pertains to the calculation of compound interest over a period of 4 years on a principal amount at a given interest rate. To calculate compound interest, we use the formula A = P(1 + r)^n, where A is the total amount after n periods, P is the principal amount, r is the annual interest rate (as a decimal), and n is the number of years the money is compounded. Applying this formula:

P = $5,350 (the principal amount)

r = 0.035 (since 3.5% as a decimal is 0.035)

n = 4 (compounding for 4 years)

Using the formula:

A = $5,350(1 + 0.035)^4

A = $5,350(1.035)^4

A = $5,350 * 1.14888281

A ≈ $6,139.25

Thus, the amount of money in the account at the end of 4 years, with compound interest, will be approximately $6,139.25, which corresponds to option D.

Answer:

y=15

Step-by-step explanation:

The formula for direct variation is

y = kx

5 =k*2

Solve for k

Divide by 2

5/2 = k

y = 5/2 x

Now we substitute x=6

y = 5/2(6)

y = 15

Answer:

y = 15

Step-by-step explanation:

If the variables are directly proportional, increasing one by a factor of 3 will mean the other one also increases by a factor of 3.

6 is 3 times 2, so the value of y will be 3 times 5, or 15.

___

You can write the relation as a proportion:

y/x = 5/2 = ?/6

Multiplying by 6 gives ...

(5/2)·6 = ? = 15

___

Or, you can bother with an equation relating x and y:

y = kx

5 = k·2 . . . plug in the given values and solve for k

5/2 = k . . . divide by 2

Then ...

y = (5/2)·6 = 15 . . . . same as the proportion, above.

If you rearrange this to y = 5·(6/2) then you see the relation described at the beginning of this solution. The new value of y is the old value multiplied by the factor by which x changes.

Answer:

38°

Step-by-step explanation:

Angles in a triangle add up to 180° and opposite angles are equal, therefore 180°-104°=76°

76°÷2=38°

I think this is correct :)

Answer:

The correct answer is <1 = 38°

Step-by-step explanation:

From the figure we can see a parallelogram.

Opposite  angles of a parallelogram are equal.

To find the measure of <1

From the figure we get <1 + <2 = <3 + <4

<1 = <2

<1 + <2 + <3 + <4 = 360 - (2 * 104)

 = 360 - 208 = 152

<1 + <2 = 152/2 = 76°

<1 = <2 = 76/2 = 38°

Therefore measure of <1 =  38°

Answer:

Step-by-step explanation:

If the polynomial is degree 2, then it has 2, 1 or 0 zeros.

If the polynomial is degree 2 and the zeros are 2 irrational numbers, then they are in the form a + b√c and a - b√c.

Therefore if one of the zero is 2 + √3, then the other zero is 2 - √3.

Answer:

86%

Step-by-step explanation:

Answer:

[tex](x + 3) {}^{2} - 16[/tex]

Step-by-step explanation:

[tex] {x}^{2} + 6x - 7 = (x + 3) {}^{2} - (3) {}^{2} - 7 \\ = (x + 3) {}^{2} - 16[/tex]

The equation x^2 + 6x - 7 can be written in the form (x+a)^2 + b as (x + 3)^2 - 16 by completing the square.

To solve this, we will complete the square for the polynomial x^2 + 6x - 7. The equation (x+a)^2 + b involves squaring a binomial (x+a) and adding a constant. Completing the square can convert x^2 + 6x - 7 to this form.

Step 1: Half of the coefficient of x is (6/2)=3 so a=3. Then we square a to get a^2 = 9.

Step 2: We adjust the original equation by subtracting and adding a^2 within it: (x^2 + 6x + 9) - 9 - 7.

Step 3: Simplify the equation to get (x + 3)^2 - 16, which is the form we desired.

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Answer:

if p(x) is the given polynomial then -p(x) represents its additive inverse.

Step-by-step explanation:

We need to explain about what is the addictive inverse of the polynomial.

We know that additive inverse of a polynomial is basically another polynomial that adds to the given polynomial to give result 0.

which can be done by take opposite sign of each term in the given polynomial.

For example if p(x) is the given polynomial then -p(x) represents its additive inverse.

There’s an app called Socratic it will help u with the steps

Question 1:

For this case we have to simplify the following expression:

[tex]\sqrt {54n ^ 7}[/tex]

We can rewrite the 54 as:

[tex]54 = 9 * 6 = 3 ^ 2 * 6[/tex]

In addition, we have to:

[tex]n ^ 7 = n ^ 6 * n[/tex] (According to the multiplication of powers of the same base)

Also, by definition of properties of powers and roots we have to:

\sqrt [n] {a ^ m} = a ^ (\frac {m} {n})

Then, we can rewrite the expression as:

[tex]\sqrt {3 ^ 2 * n ^ 6 * 6 * n} =\\3n ^ 3 \sqrt {6n}[/tex]

Answer:

Option C

Question 2:

For this case we have by definition, that a perfect square is the result of multiplying a number by itself. Also, the perfect squares are the numbers that have exact square roots.

So:

2 and 10 are not perfect squares.

Answer:

Option A and D

Question 3:

For this case we must simplify the following expression:

[tex]\sqrt {75x ^ 2 * y ^ 4}[/tex]

We can rewrite the 75 as:[tex]75 = 25 * 3 = 5 ^ 2 * 3[/tex]

Also we have that by definition of properties of powers and roots that:

[tex]\sqrt [n] {a ^ m} = a ^ (\frac {m} {n})[/tex]

So, we rewrite the expression:

[tex]\sqrt {5 ^ 2 * x ^ 2 * y ^ 4 * 3} =\\5xy ^ 2 \sqrt {3}[/tex]

Answer:

Option B

8.99 rounded to 1 decimal place is 9.0, since the number after the decimal is 9, which is 5 or over, hence, the rounding up.

In mathematics, rounding means to replace a number with an approximate value that has a shorter, simpler, or more explicit representation. To round the number 8.99 to 1 decimal place, you need to look at the second number after the decimal point. Since that number is 9, which is 5 or over, we round up the first number after the decimal point, which is 8. Thus, 8.99 rounded to 1 decimal place is 9.0.

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Answer:

1.5 times

Step-by-step explanation:

6.75/4.5 = 1.5

To find out how many times longer Mike's ride was than Noah's, you first need to convert the mixed fractions to improper fractions. Then you divide the length of Mike's ride by Noah's ride length. The result is 1.5, meaning Mike’s bike ride was 1.5 times longer than Noah’s.

This problem falls under the category of division of fractions. The question is asking for how many times longer Mike's ride was than Noah's. In order to do this, we must divide the length of Mike's ride by the length of Noah's ride.

First, we convert the mixed fractions to improper fractions. Mike biked 6 3/4 = 27/4 miles, and Noah biked 4 1/2 = 9/2 miles.

To find how many times longer Mike's ride was than Noah's, we divide 27/4 by 9/2. This is equivalent to multiplying 27/4 by the reciprocal of 9/2 (which is 2/9).

When we perform this multiplication, we get (27/4) * (2/9) = (27 * 2) / (4 * 9) = 54 / 36. The result is 1.5, so this means Mike’s bike ride was 1.5 times longer than Noah’s bike ride.

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For this case we must find the inverse of the following function:

[tex]f (x) = - \frac {1} {2} \sqrt {x + 3}[/tex]

We follow the steps below:

Replace f(x) with y:

[tex]y = -\frac {1} {2} \sqrt {x + 3}[/tex]

We exchange the variables:

[tex]x = - \frac {1} {2} \sqrt {y + 3}[/tex]

We solve for "y":

[tex]- \frac {1} {2} \sqrt {y + 3} = x[/tex]

Multiply by -2 on both sides of the equation:

[tex]\sqrt {y + 3} = - 2x[/tex]

We raise both sides of the equation to the square to eliminate the radical:

[tex](\sqrt {y + 3}) ^ 2 = (- 2x) ^ 2\\y + 3 = 4x ^ 2[/tex]

We subtract 3 from both sides of the equation:

[tex]y = 4x ^ 2-3[/tex]

We change y by f ^ {- 1} (x):

[tex]f ^ {- 1} (x) = 4x ^ 2-3[/tex]

Answer:[tex]f ^ {- 1} (x) = 4x ^ 2-3[/tex]

Answer:

[tex]f(x)^{-1}= 4x^{2} -3 [/tex] .

Step-by-step explanation:

Given : [tex]f(x) =-\frac{1}{2}\sqrt{x+3}[/tex].

To find : Find the inverse of the given function.

Solution : We have given

[tex]f(x) =-\frac{1}{2}\sqrt{x+3}[/tex].

Step 1: take f(x) = y

[tex]y =-\frac{1}{2}\sqrt{x+3}[/tex].

Step 2 : Inter change y and x.

[tex]x =-\frac{1}{2}\sqrt{y+3}[/tex].

Step 3 : Solve for y

Taking square both sides

[tex]x^{2} = \frac{1}{4}(y+3)[/tex].

On multiply both sides by 4.

[tex]4x^{2} = (y+3)[/tex].

On subtraction both sides by 3.

[tex]4x^{2} -3 = y[/tex].

Here, [tex]f(x)^{-1}= y[/tex] is inverse of f(x)

[tex]f(x)^{-1}= 4x^{2} -3 [/tex] .

Therefore, [tex]f(x)^{-1}= 4x^{2} -3 [/tex] .

the degree of the polynomial would be 10.

the degree of the above polynomial is (a)10

Answer:

Step-by-step explanation:

In a right angled triangle, we have perpendicular, hypotenuse and base.

The hypotenuse is the longest side and opposite to the right angle. the side having 90 degree angle is perpendicular.

Applying formulas we can find the values:

the formulas are : cos (Ф) = Base / hypotenuse

sin (Ф) = Perpendicular / hypotenuse

tan (Ф) = Perpendicular / Base

11. cos z

cos z = Base / hypotenuse

cos z = 12/15

12. cos C

cos C = base / hypotenuse

cos C = 38/45

13. tan C

tan C = Perpendicular/ Base

tan C = 40/30

14. tan A

tan A = Perpendicular/ Base

tan A = 21/20

15. tan C

tan C = Perpendicular/ Base

tan C = 12/35

16. tan X

tan X = Perpendicular/ Base

tan X = 30/40

17. sin Z

Sin Z = Perpendicular / Hypotenuse

sin Z = 35/37

18. sin z = Perpendicular / Hypotenuse

sin z = 30/50

Answer:

28%

Step-by-step explanation:

78 x .36 = 28.08

Answer:

B. 28%

Step-by-step explanation:

Right on edge.

x^2 = x3

x^2 - 3x = 0

x(x - 3) = 0

x = 0 and x -3 = 0 or x = 3

x cannot equal zero, therefore the answer is three

The numbers that when squared equal to three times themselves are 0 and 3. This is found by solving the quadratic equation x² = 3x, which factors to x(x - 3) = 0.

To express this mathematically, we let 'x' represent the number, so the equation becomes x² = 3x. This is a quadratic equation that can be solved by rearranging the terms and factoring, resulting in x(x - 3) = 0. Applying the Zero Product Property, we have two potential solutions for x: 0 or 3. Therefore, the numbers that fit the condition are 0 and 3.

Answer:

The common ratio for the given geometric sequence is -1/2.

Step-by-step explanation:

The common ratio in a geometric sequence is simply the number that multiplies one term to arrive at the next term. From the sequence given, we can let the common ratio be x and determine its value using any of the following set of equations;

1/2 * x = -1/4

-1/4 * x = 1/8

1/8 * x = -1/16

using the first equation;

1/2 * x = -1/4

we divide both sides by 1/2 to solve for x.

x = (-1/4)/(1/2)

x = -1/4 * 2

x = -1/2

Thus, the common ratio for the given geometric sequence is -1/2.  

Answer:

Common ratio is -1/2

Step-by-step explanation:

Common ratio is the amount between each number in a geometric sequence.

It is called the common ratio because it is the same to each number.

Common ratio is the ratio between two successive numbers in a geometric sequence.

Common is a gotten by either division or multiplication.

Therefore in the case above

1/2 x -1/2 = -1/4 ......

-1/4 x -1/2 = 1/8 ......

1/8 x -1/2 = -1/16 ....etc

Therefore our common ratio is -1/2

Answer:

B. -9+4 1/3

Step-by-step explanation:

If you distribute -1 to -4 1/3 and just bring down the -9, you'd end up with

-9+4 1/3.

The to this question is b I hope this is helpful

Answer:

a=3

Step-by-step explanation:

3x3=9

Answer: a=3

Step-by-step explanation: 3*3=9

Answer:

22x + 99

Step-by-step explanation:

Given

9(2x + 9) + 2(2x +9) ← factor out (2x + 9) from each term

= (2x + 9)(9 + 2)

= 11(2x + 9) ← distribute parenthesis

= 22x + 99

Here's two ways you can solve this exercise: you can expand the multiplications and sum like terms:

[tex]9(2x+9)+2(2x+9) = 18x+81+4x+18 = 22x+99[/tex]

Or you can factor the parenthesis:

[tex]9(2x+9)+2(2x+9) = (2x+9)(9+2) = 11(2x+9) = 22x+99[/tex]

Answer:

B

Step-by-step explanation:

The range is the set of y-values for which the function is defined.

** Attached is the graph of the function

By looking at the graph, we can clearly see that there aren't any y-values that is not permitted in the graph. The function is defined for all y-values. Hence the range is set of all real numbers, or, the range is (-∞, +∞)

Answer choice B is right.

Final answer:

The range of the reciprocal function 1/x is all real numbers except zero, expressed in interval notation as (-∞, 0) ∪ (0, +∞).

Explanation:

The range of the reciprocal function, which is denoted as 1/x, can be understood by considering the behavior of the function as x approaches different values. As x approaches zero from the positive side (x → 0+), the reciprocal 1/x becomes increasingly larger, theoretically 'going to infinity' (∞). Similarly, as x approaches zero from the negative side (x → 0-), 1/x becomes increasingly negative, 'going to negative infinity' (-∞). Thus, the range of the reciprocal function excludes zero, but includes all other real numbers. In interval notation, the range is expressed as (-∞, 0) ∪ (0, +∞).

Answer:

diabeties

Step-by-step explanation:

jfghnfuigbdihgbuneughei

The square root of 104 is approximately 10.198039, which can be confirmed using a calculator. It’s not a perfect square, so rounding it to 10.2 is often sufficient for practical purposes.

To find the square root of 104, we will use a calculator since it's not a perfect square. The square root of 104 is approximately 10.198039.

Here’s a step-by-step approach:

The exact value includes more decimal places, so for most purposes, you can round it to an appropriate value, such as 10.2 for simplicity.

ANSWER

[tex]y-1= \frac{1}{3} (x- 6)[/tex]

EXPLANATION

We want to write the point-slope form of the line that passes through (6, 1) and is perpendicular to a line with a slope of -3.

The slope of this line is negative reciprocal of -3.

[tex]m = - \frac{1}{ - 3} = \frac{1}{3} [/tex]

The point-slope form is given by:

[tex]y-y_1=m(x-x_1)[/tex]

We substitute the point and the slope to get;

[tex]y-1= \frac{1}{3} (x- 6)[/tex]

Answer:

y - 1 = 1/3*(x - 6)

Step-by-step explanation:

point-slope form of a line:

y - y1 = m*(x - x1)

where x1 and y1 are the coordinates of the point included in the line and m is its slope.

Two lines are perpendicular when the multiplication of their slopes is equal to -1. In this case,

m*(-3) = -1  

m = 1/3

Replacing this slope and the coordinates of point (6, 1) we get:

y - 1 = 1/3*(x - 6)