Find the equation of the line that is perpendicular to y = – 1 4 x – 8 and passes though the point (2, –4).

Solution:

The surface area of cube is given as:

[tex]Surface\ area = 6a^2[/tex]

Where, "a" is the length of side of cube

Given that, surface area = 486 square centimeter

[tex]486 = 6a^2\\\\a^2 = \frac{486}{6}\\\\a^2 = 81\\\\a = 9[/tex]

Find the volume of cube:

[tex]volume\ of\ cube = a^3\\\\volume\ of\ cube = 9^3\\\\volume\ of\ cube = 9 \times 9 \times 9\\\\volume\ of\ cube = 729[/tex]

Thus volume of cube is 729 cubic centimeter

Answer:

NO.

Step-by-step explanation:

If it is a right triangle then by the Inverse of the Pythagoras Theorem:

40^2 = 35^2 + 15^2

Testing:

40^2 = 1600

35^2 + 15^2 = 1225 + 225 = 1450

So the answer is NO>

Answer:

Step-by-step explanation:

If a ≤ b ≤ c are sides of a triangle, then a + b > c.

We have a = 15, b = 35, c = 40.

Check:

15 + 35 = 50 > 40           CORRECT

These sides can be the sides of a triangle.

If a ≤ b ≤ c are sides of a triangle, then

if a² + b² = c², then it's a right triangle

if a² + b² < c², then it's an obtuse triangle

if a² + b² > c², then it's an acute triangle

Check:

15² + 35² = 225 + 1225 = 1450

40² = 1600

1450 < 1600 ⇒ 15² + 35²  < 40²

Therefore it's  an obtuse triangle

Answer:

$195P00*0.0055(1+0.0055)^360

____________________________

           (1+0.0055)^360-1

To find the values that are not restrictions on the variable in a rational expression, we need to evaluate the expression for the given values. By substituting the values -1, 0, -5, 1, and 5 into the expression, we can determine if they result in a zero denominator or not. The values 0 and 5 are not restrictions on the variable.

The rational expression is given by [tex](2y^2 + 2) / (y^3- 5y^2+ y - 5)[/tex]. To identify the values that are not restrictions on the variable, we need to determine which values of y make the denominator equal to zero. To find these values, we can set the denominator [tex](y^3-5y^2+ y - 5)[/tex] equal to zero and solve for y using synthetic division or factoring. By substituting the given values of -1, 0, -5, 1, and 5 into the expression, we can determine whether they result in a zero denominator or not. If the denominator is not zero for a particular value of y, then that value is not a restriction on the variable.

Let's check:

For [tex]y = -1: (2(-1)^2 + 2) / (-1^3 - 5(-1)^2 + (-1) - 5) = (-2 + 2) / (-1 + 5 - 1 - 5) = 0 / -2 = 0[/tex]

For [tex]y = 0: (2(0)^2 + 2) / (0^3 - 5(0)^2 + (0) - 5) = (2 + 2) / (0 - 0 + 0 - 5) = 4 / -5 ≠ 0[/tex]

For [tex]y = -5: (2(-5)^2 + 2) / (-5^3 - 5(-5)^2 + (-5) - 5) = (2(25) + 2) / (-125 + 125 - 5 - 5) = (50 + 2) / -10 \ne 0[/tex]

[tex]For y = 1: (2(1)^2 + 2) / (1^3 - 5(1)^2 + (1) - 5) = (2 + 2) / (1 - 5 + 1 - 5) = 4 / -8 = -0.5 \ne 0 For y = 5: (2(5)^2 + 2) / (5^3 - 5(5)^2 + (5) - 5) = (2(25) + 2) / (125 - 125 + 5 - 5) = (50 + 2) / 0 \ne 0[/tex]

From the calculations, we can determine that the values 0 and 5 are not restrictions on the variable because they do not result in a zero denominator. Therefore, the correct answer is 0 and 5.

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Answer:

-1,0,-5,1

Step-by-step explanation:

The value of y is 3 when x is 6.

Solution:

The given table is the amount of cheese in ounces and the cost price.

Let x represents the amount of cheese and y represents the cost price.

The formula which derived from the table is y = x ÷ 2.

That is [tex]$y=\frac{x}{2}[/tex].

To find the value of y when x is 6:

[tex]$y=\frac{x}{2}[/tex]

Substitute x = 6 in the formula, we get

[tex]$y=\frac{6}{2}[/tex]

y = 3

Hence the value of y is 3 when x is 6.

Answer:

90⁰

Step-by-step explanation:

The diagonal of the rectangles forms two angles with the sides, about 32 degrees and 58 degrees respectively. These are found using the Pythagorean theorem to find the length of the diagonal, and then the arctan function to find the angles.

To find the angle that the diagonal makes with the sides of the rectangle, first calculate the length of the diagonal which can be found using the Pythagorean Theorem. In a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. We can write this as: c² = a² + b². In this case, the length and width of the rectangle are the two sides (a and b) and the diagonal is the hypotenuse (c).

So a = 68 inches, b = 42 inches. Plugging these into our formula gives: c² = 68² + 42², so c = √[(68²) + (42²)] which approximates to 80 inches.

Next, calculate the angles using the inverse tangent (or arctan) function: θ = arctan(opposite/adjacent). In this case, the angles are = arctan(42/68) and arctan(68/42). This gives us angles of approximately 32 degrees and 58 degrees.

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Yo sup??

by the property of log we can say that

laga+logb=logab

log4+log5=log4*5

=log20

Hope this helps

Final answer:

The probability of drawing two green marbles consecutively without replacement from a bag containing 3 green and 3 red marbles is 1/5 or 20%.

Explanation:

The probability that both marbles drawn consecutively from an opaque bag without replacement will be green is calculated by multiplying the probability of the first event by the probability of the second event. Here, we have 3 green marbles out of a total of 6 marbles. So, the probability of drawing the first green marble is 3/6 or 1/2. After drawing one green marble, there are now 2 green marbles left out of 5 total marbles. Therefore, the probability of drawing a second green marble is now 2/5. To find the combined probability, we multiply these two probabilities together: (1/2) × (2/5) which equals 1/5 or 0.2. Hence, there is a 20% chance that both marbles drawn will be green.

Answer:

84 minutes

HOPE THIS HELPS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Step-by-step explanation:

An hour is 60 minutes

60 x 2/5 = 24

24 minutes plus an hour (60 minutes)

= 84

Answer:

1900 ft

Step-by-step explanation:

To find the area where roses will be planted, find the area of the 2 triangles. 60×38 divided by 2 = 1140ft. 40×38 divided by 2 = 760. 760+1140=1900

Answer:

[tex]6x-6y=30[/tex]

Step-by-step explanation:

The complete options are

a) x - 2y = 30

b) 4x - 3y = 30

c) 3x - 4y = 30

d) 6x - 6y = 30

The given equation is

[tex]x-y=5[/tex]

Verify option d

we have

[tex]6x-6y=30[/tex]

Divide by 6 both sides

[tex](6x-6y)/6=30/6[/tex]

[tex]\frac{6x}{6}-\frac{6y}{6}=\frac{30}{6}[/tex]

[tex]x-y=5[/tex]

therefore

[tex]x-y=5[/tex]  and [tex]6x-6y=30[/tex] are equivalent

Answer:

3x -4y = 30

Step-by-step explanation:

Length of the rectangle is 150 m.

Step-by-step explanation:

Step 1:

Let the width of the rectangle be x. Then the length = 3x. Given that perimeter = 400 m, find the length.

Perimeter of the rectangle = 2 (length + breadth)

400 = 2 (3x + x)

400 = 8x

∴ x = 400/8 = 50

⇒ Width is 50 m

∴ Length = 3x = 150 m

Answer:

A. 0.60

Step-by-step explanation:

make a proportion so

36 over 60 = x over 100

36*100= 3600

3600/60

60

.60

The probability that the student attended the jazz concert is 0.60. The correct answer is option A.

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favorable outcomes / Number of sample

It is given from the table that the student who attended the jazz concert is 36 out of 60 students. Then the probability that the student attended the jazz concert is calculated as below:-

Probability = Number of favorable outcomes / Number of sample

Probability = 36 / 60

Probability = 0.60

Therefore, the probability that the student attended the jazz concert is 0.60. The correct answer is option A.

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Answer:

x = 9.25

y = 13.5

Step-by-step explanation:

area = 33

let length be y and width be x

2x - 5 = y

area of rectangle = length * breadth

(2x-5)(x)=33

2x²-5x=33

2x²-5x-33=0

solving quadratic equation

x = 9.25

y = 13.5

Answer:

8,420.43 meters higher im pretty sure

Step-by-step explanation:

If you do 8,844.43-424.3, you get 8,420.83

Answer:

9,268.73 meters higher

Step-by-step explanation:

Add the elevation of Mt.Everest to the absolute value of the elevation of the Dead Sea. That equation looks like: 8,844.43 + |-424.3| = 9,268.73

Mt.Everest was 9,268.73 meters higher than the Dead Sea in 2005.

(1/3) × the cone's volume = The cylinder's volume.

Step-by-step explanation:

Step 1:

The volume of any cone is obtained by multiplying [tex]\frac{1}{3}[/tex] with π, the square of the radius ([tex]r^{2}[/tex]) and the height ([tex]h[/tex]).

So the volume of the cone, [tex]V=\pi r^{2} \frac{h}{3}[/tex].

Step 2:  

The cylinder's volume is nearly the same as the cone but instead by multiplying [tex]\frac{1}{3}[/tex] we multiply with 1.

So the cylinder's volume is determined by multiplying π with the square of the radius of the cylinder ([tex]r^{2}[/tex]) and the height of the cylinder ([tex]h[/tex]).

So the the cone's volume, [tex]V = \pi r^{2} h[/tex].

Step 3:

Now we equate both the volumes to each other.

The cone's volume : The cylinder's volume = [tex]\pi r^{2} \frac{h}{3}: \pi r^{2} h[/tex] = [tex]\frac{1}{3} : 1[/tex].

So if we multiply the cone's volume with [tex]\frac{1}{3}[/tex] we will get the cylinder's volume with the same dimensions.

5

CE=AE-AC=4

CD=CE-DE=4-1.5=2.5

BC=BD-CD=7.5-2.5=5

Answer:?

Step-by-step explanation:

Answer:

1. True

2. False

3.True

4.False

Answer:

length of an arc = 1unit

Step-by-step explanation:

given that the circumference of a circle = 6

central angle = 60

length of the arc =?

recall that the circumference of a circle = 2πr

6 = 2πr

r = 6/2π

now to calculate the length of an arc

recall,

length of an arc = 2πr(Ф/360)

length of an arc = 2π(6/2π) × 60/360

length of an arc = 6 × 60/360

length of an arc = 360/360

length of an arc = 1unit

therefore the length of the arc whose circumference is 6 and arc angle is 60° is evaluated to be 1unit

Answer:

Noah should buy a ladder of length greater than 28.1 ft to reach at least 22 feet height.

Step-by-step explanation:

Given:

Noah has to reach at least 22 ft height.

Angle made by the base of ladder with the ground = 51.5°

To find the length of the ladder.

Solution:

On drawing the situation, we get a right triangle. The hypotenuse of the triangle represents the length of the ladder.

In triangle ABC.

∠C = 51.5°

AB = 22 ft

Applying trigonometric ratio to find AC (length of the ladder).

[tex]\sin\theta = \frac{Opposite\ side}{Hypotenuse}[/tex]

[tex]\sin C=\frac{AB}{AC}[/tex]

Plugging in values.

[tex]\sin 51.5\°=\frac{22}{AC}[/tex]

Multiplying AC both sides.

[tex]AC\sin 51.5\°=\frac{22}{AC}\times AC[/tex]

[tex]AC\sin 51.5\°=22[/tex]

Dividing both sides by [tex]\sin 51.5\°[/tex]

[tex]\frac{AC\sin 51.5\°}{\sin 51.5\°}=\frac{22}{\sin 51.5\°}[/tex]

[tex]AC=\frac{22}{\sin 51.5\°}[/tex]

[tex]AC=28.1\ ft[/tex]

Thus, Noah should buy a ladder of length greater than 28.1 ft to reach at least 22 feet height.

Answer:

center(8x,12y) radius 3

Step-by-step explanation:

If i am doing this correct

Answer:

19.3 degrees

Step-by-step explanation:

The diagonal AC of the rectangle can be found using the Pythagorean Theorem.

8^2 + 3^2 = 73

The square root of 73 = 8.544...

Using this length and the length of FA (which is 3 cm), we can use the inverse of tangent to find the angle.

tangent of the angle = 3 cm/8.544 cm

inverse tangent of (3/8.544) = 19.347...

Hope this helps!

The volume of the prop is calculated to be 2,712.96 cubic inches.

Step-by-step explanation:

Step 1:

The prop consists of a cone and a half-sphere on top. We will have to calculate the volumes of the cone and the half-sphere separately and then add them to obtain the total volume.

Step 2:

The volume of a cone is determined by multiplying  [tex]\frac{1}{3}[/tex] with π, the square of the radius (r²) and height (h). Here we substitute π as 3.14. The radius is 9 inches and the height is 14 inches.

The volume of the cone :  [tex]V=\pi r^{2} \frac{h}{3}[/tex] = [tex]3.14 \times 9^{2} \times \frac{14}{3}[/tex] = 1,186.92 cubic inches.

Step 3:

The area of a half-sphere is half of a full sphere. The volume of a sphere is given by multiplying  [tex]\frac{4}{3}[/tex] with π and the cube of the radius (r³).

Here the radius is 9 inches. We take π as 3.14.

The volume of a full sphere =  [tex]V=\frac{4}{3} \pi r^{3}[/tex] =  [tex]\frac{4}{3} \times 3.14 \times 9^{3}[/tex] = 3,052.08 cubic inches.

The volume of the half-sphere =  [tex]\frac{3,052.08}{2}[/tex] = 1,526.04 cubic inches.

Step 4:

The total volume = The volume of the cone + The volume of the half sphere,

The total volume = 1,186.92 + 1,526.04 = 2,712.96 cubic inches.

Answer:

$102.30

Step-by-step explanation:

Answer:

2600

The gross pay $2,600 if $572 is the tax amount.

Step-by-step explanation:

To estimate 52% of 71, you can use either the proportion method or the multiplication method by setting up a proportion or multiplying 0.52 by 71.

To estimate 52% of 71, you can use either proportion or multiplication. Here's how:

Using the proportion method:

52/100 = x/71

71 * 52 = 100 * x

x = 36.92 (rounded to 37)

Using the multiplication method:

0.52 * 71 = 36.92 (rounded to 37)

Answer:

A =36 pi

or approximately

A =113.04

Step-by-step explanation:

To find the area of a circle, we use the formula

A = pi r^2, where r is the radius

A = pi (6)^2

A = 36 pi

We can approximate pi as 3.14

A = 36 (3.14)

A is approximately 113.04

Answer: 113.1 unit^2

Step-by-step explanation:

A=πr^2

=π(6)^2

=113.0973355 unit^2

Final answer:

Roshanda bought the same amount of roast beef as ham, 0 pounds.

Explanation:

To find out how much more roast beef Roshanda bought compared to ham, we need to subtract the weight of the ham from the weight of the roast beef. Roshanda bought 1 pound of ham and 1 pound of roast beef, so the difference is 1 pound minus 1 pound, which equals 0 pounds. Therefore, Roshanda did not buy more roast beef than ham, they bought the same amount.

Roshanda bought 1/4 pound more roast beef than ham.

To find out how much more roast beef Roshanda bought compared to ham, we need to subtract the amount of ham from the amount of roast beef.

Given:

Ham = 5/8 pound

Roast beef = 7/8 pound

To find the difference:

Roast beef - Ham

= (7/8) - (5/8)

To subtract fractions, we need a common denominator, which is 8 in this case.

= (7/8) - (5/8)

= (7 - 5)/8

= 2/8

Now, simplify the fraction:

2/8 = 1/4

So, Roshanda bought 1/4 pound more roast beef than ham.

Question

Roshanda bought 5/8 pound of ham and 7/8 pol 11 d of roast beef. How much more roast beef than ham did she buy? Write in simplest form.

The value of b is 5.4

Explanation:

Given that ABC is a triangle.

It is also given that [tex]a=12[/tex] , [tex]\angle B=25^{\circ}[/tex] and [tex]\angle C=45^{\circ[/tex]

We need to find the value of b.

The value of b can be determined using the law of sine formula, which is given by

[tex]\frac{a}{sin A} =\frac{b}{sin B} =\frac{c}{sin C}[/tex]

First, we shall find the angle of A.

Since, ABC is a triangle and all the angles in a triangle add up to 180°

Thus, we have,

[tex]\angle A+\angle B+\angle C=180[/tex]

  [tex]\angle A+25+45=180[/tex]

          [tex]\angle A+70=180[/tex]

                  [tex]\angle A=110^{\circ}[/tex]

Thus, the value of angle A is 110°

Let us substitute these values in the law of sine formula.

Hence, we get,

[tex]\frac{12}{sin \ 110^{\circ}} =\frac{b}{sin \ 25^{\circ}}[/tex]

Simplifying, we get,

[tex]\frac{12}{0.9397} =\frac{b}{0.423}[/tex]

Multiplying both sides of the equation by 0.423, we get,

[tex]\frac{12\times 0.423}{0.9397} =b[/tex]

Simplifying, we get,

[tex]\frac{0.5076}{0.9397} =b[/tex]

Dividing, we have,

[tex]5.4=b[/tex]

Thus, the value of b is 5.4