The measure of one of the small angles of a right triangle is 45 less than twice the measure of the other small angle. Find the measure of both angles. ​

Answer:

isosceles acute

Step-by-step explanation:

sum of angles in a triangle = 180

to find third angle, subtract 72 & 36 from 180 and you get 72

72, 36, and 72 are all less than 90 so it will be an acute triangle

It will also be isosceles bc there are 2 angles of the same measure

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Answer:

Step-by-step explanation:

The linear speed 12 mi/h translates to inches per minute as follows:

  (12 mi/h) × (5820 ft/mi) × (12 in/ft) ÷ (60 min/h) = 12,672 in/min

The relationship between arc length and angle is ...

  s = rθ

For a constant radius, the relationship between linear speed and angular speed is ...

  s' = rθ'

  θ' = s'/r = (12,672 in/min)/(12 in) = 1056 rad/min

There are 2π radians in one revolution, so this is ...

  (1056 rad/min) ÷ (2π rad/rev) = 168.068 rev/min

Answer:

x = 150°

Step-by-step explanation:

Interior angle of a hexagon = 120° and interior angle of a square = 90°

so remaining angle, 360-120-90 = 150°

Answer:

x > - 8

Step-by-step explanation:

4x - 8 > - 40

4x > - 40 + 8

4x > - 32

Divide 4 on both sides,

4x / 4 > - 32 / 4

x > - 8

Using the shell method, the volume integral would be

[tex]\displaystyle 2\pi \int_0^2 x(256-x^8)\,\mathrm dx[/tex]

That is, each shell has a radius of x (the distance from a given x in the interval [0, 2] to the axis of revolution, x = 0) and a height equal to the difference between the boundary curves y = x ⁸ and y = 256. Each shell contributes an infinitesimal volume of 2π (radius) (height) (thickness), so the total volume of the overall solid would be obtained by integrating over [0, 2].

The volume itself would be

[tex]\displaystyle 2\pi \int_0^2 x(256-x^8)\,\mathrm dx = 2\pi \left(128x^2-\frac1{10}x^{10}\right)\bigg|_{x=0}^{x=2} = \boxed{\frac{4096\pi}5}[/tex]

Using the disk method, the integral for volume would be

[tex]\displaystyle \pi \int_0^{256} \left(\sqrt[8]{y}\right)^2\,\mathrm dy = \pi \int_0^{256} \sqrt[4]{y}\,\mathrm dy[/tex]

where each disk would have a radius of x = ⁸√y (which comes from solving y = x ⁸ for x) and an infinitesimal height, such that each disk contributes an infinitesimal volume of π (radius)² (height). You would end up with the same volume, 4096π/5.

The volume of the solid formed by revolving the region bounded by y=x^8 and y = 256 in the first quadrant about the y-axis is 4096π/5 cubic units.

It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.

We have a function:

[tex]\rm y = x^8[/tex]   or

[tex]x = \sqrt[8]{y}[/tex]

And  y = 256

By using the vertical axis of rotation method to evaluate the volume of the solid formed by revolving the region bounded by the curves.

[tex]\rm V = \pi \int\limits^a_b {x^2} \, dy[/tex]

Here a = 256, b = 0, and [tex]x = \sqrt[8]{y}[/tex]

[tex]\rm V = \pi \int\limits^{256}_0 {(\sqrt[8]{y}^2) } \, dy[/tex]

After solving definite integration, we will get:

[tex]\rm V = \pi(\frac{4096}{5} )[/tex]  or

[tex]\rm V =\frac{4096}{5}\pi[/tex] cubic unit

Thus, the volume of the solid formed by revolving the region bounded by y=x^8 and y = 256 in the first quadrant about the y-axis is 4096π/5 cubic units.

Learn more about integration here:

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Answer:

$275 a month

Step-by-step explanation:

Let x represent how much each friend is paying.

The amount Jane pays can be represented by 2x, since she is paying double than her friends.

Add together these terms and set them equal to 550. Then, solve for x:

x + x + 2x = 550

4x = 550

x = 137.5

So, each friend is paying $137.50. Double this to find how much Jane is paying:

137.5(2)

= 275

So, Jane is paying $275 a month

Answer:

7/12

Step-by-step explanation:

There are 12 roses - 5 white = 7 pink

7 pink / 12 total

Answer:

c.) in the correct answer

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Answer:

  9

Step-by-step explanation:

If x is the number of 10-inch stones, then (x-1) is the number of 5-inch stones, and the total width is ...

  10x +5(x-1) = 130

  15x -5 = 130 . . . . . . . eliminate parentheses

  15x = 135 . . . . . . add 5

  x = 9 . . . . . . . divide by 15

Wesley will need 9 10-inch stones for one row.

Answer:

7x is monomial according to question.

answer:

another number is -47/22

explanation:

let one number be x and the other be y

-11/21 × y = 47/42

y = -47/22

Answer:

- [tex]\frac{47}{22}[/tex]

Step-by-step explanation:

let n be the other number , then

- [tex]\frac{11}{21}[/tex] × n = [tex]\frac{47}{42}[/tex] ( divide both sides by - [tex]\frac{11}{21}[/tex] )

n = [tex]\frac{\frac{47}{42} }{-\frac{11}{21} }[/tex]

   = [tex]\frac{47}{42}[/tex] × - [tex]\frac{21}{11}[/tex] ( cancel 21 and 42 )

   = [tex]\frac{47}{2}[/tex] × - [tex]\frac{1}{11}[/tex]

   = - [tex]\frac{47}{22}[/tex]

Answer:

[tex]{ \tt{y = 3x + 7}}[/tex]

Step-by-step explanation:

General equation of a line:

[tex]{ \boxed{ \bf{y = mx + c}}}[/tex]

m is the slope, and c is the y-intercept:

m = 3, and c = 7

Given:

d = 2

f = 4

To find:

Value of  [tex]\frac{14(7)-d}{2f}[/tex]

Steps:

we need to substitute and then find the value,

[tex]= \frac{14(7)-2}{2(4)}\\ \\=\frac{98-2}{8} \\\\=\frac{96}{8}\\\\=12[/tex]

Therefore, the answer is option C) 12

Happy to help :)

If you need help, feel free to ask

Answer:

The Bison is faster by 10 miles per hour.

Step-by-step explanation:

The Bison runs at 3520 ft / min

= 3520/ 5280 miles / minute

= (3520/ 5280) * 60 miles per hour

= 40 miles per hour

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Answer:

Step-by-step explanation:

The reduced side ratios, shortest to longest are ...

  AC : AT : CT = 8 : 9 : 15

  OD : OG : DG = 5 : 6 : 10

These are different ratios, so the triangles are not similar.

Answer:

A - L = O

Step-by-step explanation:

A = L + O

Subtract L from each side

A-L = L + O - L

A - L = O

The way that the given formula A = L + O can be rewritten to solve for O is; O = A - L

We are given the formula to find A as;

A = L + O

Now, to make O the subject of the formula, let us use subtraction property of equality to subtract L from both sides to get;

A - L = L + O - L

O = A - L

Thus, the way the formula can be rewritten to solve for O is;

O = A - L

Read more about Subject of Formula at; https://brainly.com/question/10643782

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According to the given information, we build the equation for the cost. After we build the equation, the equation that relates these measures is:

[tex]C = 0.99 + xy + 0.2z[/tex]

Cost:

0.3 kilograms of tomatoes, at 3.30 dollars per kilogram.

Thus, the cost starts at:

[tex]C = 0.3*3.3 = 0.99[/tex]

y kilograms of cucumbers, at x dollars per kilogram.

Considering this, the cost will now be of:

[tex]C = 0.99 + xy[/tex]

0.2 kilograms of carrots, at z dollars per kilogram:

Now, we have to consider this for the cost, so:

[tex]C = 0.99 + xy + 0.2z[/tex]

A similar example is given at https://brainly.com/question/14544759

Step-by-step explanation:

2., 3., 4., 5.

yes, you had the right idea to calculate the half distances between the coordinates. just create the absolute values of the full distance before cutting it in half.

you need to remember : we have to go this half distance from one point to the other (meaning adding our subtracting the half distance to/from the starting point).

2.

(-4, 6) to (10, -10)

in x the distance is 10 - -4 = 14. half is 7.

in y the distance is |-10 - 6| = |-16| = 16. half is 8.

so the midpoint is

(-4 + 7, 6 - 8) = (3, -2)

remember, to go the half distance in the direction towards the second point (so we have to choose properly, when to use "+" and "-" depending on the change of the coordinate : from -4 to 10 we have to add, from 6 to -10 we have to subtract, of course).

3.

(-3, -8) to (-6.5, -4.5)

in x distance : -3 - -6.5 = 3.5. half is 1.75

in y distance : -8 - -4.5 = |-3.5| = 3.5. half is 1.75

midpoint is

(-3 - 1.75, -8 + 1.75) = (-4.75, -6.25)

4.

(3, 7) to (-8, -10)

x : 3 - -8 = 11. half is 5.5

y : 7 - -10 = 17. half is 8.5

midpoint is

(3 - 5.5, 7 - 8.5) = (-2.5, -1.5)

5.

(-6, -13) to (-6.4, -3.8)

x : -6 - -6.4 = 0.4. half is 0.2

y : -13 - -3.8 = |-9.2| = 9.2. half is 4.6

midpoint is

(-6 - 0.2, -13 + 4.6) = (-6.2, -8.4)

6.

(-1, 7) to (5, 1)

x : -1 - 5 = |-6| = 6. 1/3 is 2.

y : 7 - 1 = 6. 1/3 is 2.

1/3 from C to D

(-1 + 2, 7 - 2) = (1, 5)

7.

2/3 of the way from D to C is the same point as in 6. (1/3 from C to D).

again

(1, 5)

8.

2/3 of the way from C to D.

so, we need to double what we added in 6.

(-1 + 4, 7 - 4) = (3, 3)

9.

1/3 of the way from D to C is the same point as in 8. (2/3 of the way from C to D).

again

(3, 3)

10.

exactly. Pythagoras.

the square root of the sum of the squares of the coordinate differences.

distance = sqrt((x1 - x2)² + (y1 - y2)²)

11.

(6, 8) to (-1, 8)

distance = sqrt((6 - -1)² + (8 - 8)²) = sqrt(49) = 7

12.

(5, -6) to (5, 6)

sqrt((5-5)² + (-6-6)²) = sqrt(144) = 12

13.

(-2, 0) to (11, 0)

sqrt((-2 - 11)² + (0-0)²) = sqrt(169) = 13

14.

(1, -5) to (9, 1)

sqrt((1-9)² + (-5 - 1)²) = sqrt(64 + 36) = sqrt(100) = 10

15.

ST and MT are basically the same equation.

MT is half of ST.

ST equation based on 2 points :

y – yS={(yT – yS)/(xT – xS)}(x – xS)

M = (xS + (xT - xS)/2, yS +(yT - yS)/2)

so, let's put that into the general equation :

y - yM={(yT - yM)/(xT - xM)}(x - xM)

y - (yS +(yT - yS)/2) = {(yT - (yS +(yT - yS)/2))/(xT - (xS + (xT - xS)/2))}(x - (xS + (xT - xS)/2))

16.

the two corners farthest away are (5, 10) and (9, 6).

what distance from (0, 0) is now bigger ?

since it is (0, 0), we can skip the 0s and just sum up the squares of the coordinates.

5² + 10² = 125

9² + 6² = 117

so, the corner (5, 10) is the farthest away.

Answer:

x1 = 3

Step-by-step explanation:

first set up the proportion (write as fractions):

(y1/x1) = (y2/x2)

then fill in the variables:

4/x1 = 8/6

now cross multiply:

8 • x1 = 6 • 4

simple algebra:

8 • x1 = 24

x1 = 24/8

x1 = 3

If y1 = 4, x2 = 6, and y2 = 8, then the value of x1 is 3 which we can solve using ratios.

In a directly proportional relationship, the ratios between the corresponding values of two variables remain constant. This constant ratio is often referred to as the "proportionality constant."

In this problem, you have two pairs of values: (x1, y1) and (x2, y2). We're given that the ratios are directly proportional, which means:

x1 / y1 = x2 / y2

Plugging in the given values:

x1 / 4 = 6 / 8

Now, cross-multiply to solve for x1:

x1 * 8 = 4 * 6

x1 = 24 / 8

x1 = 3

Therefore, the value of x1 is 3.

Learn more about ratios here:

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Answer:

This depends whether you want to make the fraction bigger or smaller.

Step-by-step explanation:

If you want to the the fraction into something smaller than it already is, you would use division because when you divide something, you get a smaller number.

However, if you want to make the fraction bigger, then you would multiply.

Hope this helps! :)

Answer:

Because 7 is a prime number which means it can only divide by itself and one so you cannot divide seven but you can divide 15.

Step-by-step explanation:

Answer:

Selling price=rs.600.

Profit of rs=100.

Step-by-step explanation:

C.P=500; profit%=20%

S.P.=100+profit%×C.P/100

S.P=120×500/100

=rs.600

S.P>C.P

Profit S.P-C.P

600-500=100

he gained for rs.100.

Answer:

(m-6+2root3)(m-6-2root3)

Step-by-step explanation:

m^2 - 12m +36 -12

= (m-6)^2 - 12

= (m-6+2root3)(m-6-2root3)[root 12 = 2root3]

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Answer:

  43

Step-by-step explanation:

Put the value where t is and do the arithmetic.

  h = 50 -t/5

  h = 50 -35/5 = 50 -7 = 43

The output, h, is 43 when the input is 35.

Answer:

43

Step-by-step explanation:

The answer is 43 on Khan :)

Answer:

...

Step-by-step explanation:

seeee the above picture

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Answer:

  $7641.24

Step-by-step explanation:

The amortization formula tells the payment amount.

  A = P(r/n)/(1 -(1 +r/n)^(-nt))

where principal P is paid off in t years with n payments per year at interest rat r.

Using the given values, we find ...

  A = $7000(0.165/12)/(1 -(1 +0.165/12)^-12) = $7000×0.01375/(1 -1.01375^-12)

  A = $636.77

The total of 12 such payments is ...

  $636.77 × 12 = $7641.24

You will pay a total of about $7641.24.

_____

Additional comment

Since the payment amount is rounded down, the actual payoff will be slightly more. Usually, the lender will round interest and principal to the nearest cent on each monthly statement. The final payment will likely be a few cents more than the monthly payment shown here.

We have,

[tex]a:b=3:6,a+b=96[/tex]

Introduce variable [tex]x[/tex] such that [tex]a=3x,b=6x[/tex]

The sum [tex]a+b=96[/tex] is therefore [tex]9x=96\implies x=10.\overline{6}[/tex]

So,

[tex]a=3\cdot10.\overline{6}=\boxed{32}[/tex] (sadia's age)

[tex]b=6\cdot10.\overline{6}=\boxed{64}[/tex] (father's age)

Hope this helps :)

Answer:

6b=18

b=18/6

b=3

.

.

.

.

.

.

Answer:

6b=18

b=18/6

b=3

.

Step-by-step explanation:

Answer:

35 lbs is the final weight

Step-by-step explanation:

20 +23 = 43 lbs

Then they had to remove 8 lbs

43 - 8 =35

35 lbs is the final weight

Answer:

A≈795.77ft²

Step-by-step explanation:

C=100ft

Area of circle=C^2/4pie

100/4×22/7≈795.77472ft²

Answer:

D. [tex]3x\sqrt{2x}[/tex]

Step-by-step explanation:

The problem gives on the following equation:

[tex]\sqrt{32x^3}+-\sqrt{16x^3}+4\sqrt{x^3}-2\sqrt{x^3}[/tex]

Alongside the information that ([tex]x\geq0[/tex]).

One must bear in mind that the operation ([tex]\sqrt[/tex]) indicates that one has to find the number that when multiplied by itself will yield the number underneath the radical. The easiest way to find such a number is to factor the term underneath the radical. Rewrite the terms under the radical as the product of prime numbers,

[tex]\sqrt{2*2*2*2*2*x*x*x}-\sqrt{2*2*2*2*x*x*x}+4\sqrt{x*x*x}-\sqrt{2*x*x*x}[/tex]

Now remove the duplicate factors from underneath the radical,

[tex]2*2*x\sqrt{2x}-2*2*x\sqrt{x}+4x\sqrt{x}-2x\sqrt{x}[/tex]

Simplify,

[tex]4x\sqrt{2x}-4x\sqrt{x}+4x\sqrt{x}-x\sqrt{2x}[/tex]

[tex]3x\sqrt{2x}[/tex]