1) Which line is perpendicular
to y = 4x+5?

The volume of a rectangular prism would be 100 cubic cm.

Since we know that rectangular prism is a three-dimensional shape that has two at the top and bottom and four are lateral faces.

The volume of a rectangular prism=Length X Width X Height

We are given that base of a rectangular prism is 20 cm sq. . If the height of the prism is 5 cm, then;

Base area = 20 cm sq.

Height = 5 cm

Volume of a rectangular prism=Length X Width X Height

Volume of a rectangular prism= Base area  X Height

Volume of a rectangular prism= 20 x 5

= 100

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The simplified form of trigonometric functions by trigonometric formulas are listed below:

Case 1: 0.5√(2 - √3)

Case 2: (0.5√2) / (1 + 0.5√2)

Case 3: sin 6x

Case 4: sin θ

In this problem we must simplify and evaluate trigonometric functions by means of trigonometric formulas. The first two expressions must be simplified and evaluated by of half angle formulas:

Case 1

sin 15° = √[(1 - cos 30°) / 2]

sin 15° = √[(1 - √3 / 2) / 2]

sin 15° = √[(2 - √3) / 4]

sin 15° = 0.5√(2 - √3)

Case 2

tan 22.5° = sin 45° / (1 + cos 45°)

tan 22.5° = (0.5√2) / (1 + 0.5√2)

The last two expressions are simplified and evaluated by double angle formulas:

Case 3

2 · sin 3x · cos 3x

sin 6x

Case 4

2 · sin 0.5θ · cos 0.5θ

sin θ

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Answer: im pretty sure the answer is in the pdf, when you scroll down. its 126 cm^2

Step-by-step explanation:

Answer:2.7

Step-by-step explanation:

Formula, divide the value in centimeters by 100 so 1 meter equals 100 centimeters

So 270 centimeters = 270/100 = 2.7

The volume of the prism will be 88 cubic units. Then the correct option is B.

Given that:

Length, L = 4 units

Width, W = 4 units

Height, H = 5.5 units

The volume of the prism is given as,

V = L x W x H

The volume of the prism is calculated as,

V = 4 x 4 x 5.5

V = 88 cubic units

The volume of the prism will be 88 cubic units. Then the correct option is B.

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The complete question is given below.

The measurements of the cylindrical (round and hollow) drum that minimize the fetched of development are roughly 10.19 yards by 2.46 yards.

Let's expect that the round and hollow drum includes a stature of h and a span of r.

The volume of a barrel is given by: V = πr^2h.

We know that the drum includes a capacity of 806 cubic yards, so able to compose:

πr^2h = 806

We need to play down the taken a toll of building the drum, which is given by the entirety of the fetched of the beat, foot, and side divider.

The zone of the beat and foot of the drum is given by: A = πr^2.

The fetched of fabric for the beat and foot is $2 per square yard, so the taken a toll of the best and foot is:

C_topbottom = 2A = 2πr^2

The cost of fabric for the side divider is $17 per square yard, and the region of the side divider is given by:

A_side = 2πrh

The whole fetched of building the drum is in this manner:

C = C_topbottom + C_side = 2πr^2 + 17(2πrh) = 2πr^2 + 34πrh

Presently we are able utilize the condition for the volume of the drum to kill h from the fetched condition:

h = 806/(πr^2)

Substituting this expression for h into the taken a toll condition, we get:

C = 2πr^2 + 34πr(806/(πr^2)) = 2πr^2 + 27404/r

To discover the least fetched, we got to take the subordinate of the fetched condition with regard to r and set it rise to to zero:

dC/dr = 4πr - 27404/r^2 =

Fathoming for r, we get:

r = (27404/(4π))^(1/3) ≈ 10.19 yards

Substituting this esteem of r back into the expression for h, we get:

h = 806/(π(10.19)^2) ≈ 2.46 yards

Hence, the measurements of the round and hollow drum that minimize the fetched of development are roughly:

Span: 10.19 yards

Stature: 2.46 yards

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Applying the leg rule, the length of BC in simplest radical form is: x = x = √390

The leg rule is used to find missing lengths in a right triangle when an altitude intersects the hypotenuse and form segments.

The leg rule is given as:

Hypotenuse / leg = leg / part

Thus, using the image given, we have:

Hypotenuse (AC) = 65

Part (DC) = 6

Leg = x

Plug in the values:

65 / x = x / 6

Cross multiply:

x * x = 6 * 65

x² = 390

x = √390

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The values of AB and BC are equal and equal to

Information given in the problem includes

DE bisects AC at point B

AC = a + 23

AB = 3a + 4

From  the definition of a bisector, point B divides AC into two equal sides, this means that

AB = BC = (1/2) * AC

Substituting the value of AC and AB

AB = 3a + 4 = (1/2) * (a + 23)

3a + 4 = (1/2) * (a + 23)

solving for a

2 * (3a + 4) = a + 23

6a + 8 = a + 23

6a - a  = 23 - 8

5a = 15

a = 3

Then we have that:

AB = 3a + 4 = 3(3) + 4 = 9 + 4 = 13

and, AB = BC

so BC = 13

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The amount of flour that will be needed for 38 cakes is 912 grams therefore Johan does not have enough amount of flour

A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation.

360 grams is needed for 15 small cakes

therefore for 1 small cake, 369/15 = 24grams will be needed

therefore for 38 small cakes = 38× 24 = 912 grams of flour will be needed.

Johan has 0.85 kg of flours which is equivalent to 0.85 × 1000grams = 850 grams of flour.

Since 912 grams will be needed for 38 small cakes , it shows that Johan does not have enough amount of flour for 38 small cakes.

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The perimeter of the regular nonagon will be; 840.7 units

The in-radius of the regular nonagon is given as:

Radius, r =17

The perimeter is then calculated by:

P = 18r/Tan(π/9)

Substitute 17 for r;

P = 18(17)/Tan(π/9)

Evaluate the product of 18 and 17;

P =  306/Tan(π/9)

Evaluate the quotient

P =  840.7

Hence, the perimeter of the regular nonagon = 840.7 units

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Answer:

angle m∠WXY intercepts the diameter WY.

Then,

m∠WXY  =  90°

(13x - 1)°  =  90°

13x - 1  =  90

Add 1 to each side.

13x  =  91

Divide each side 13.

x  =  7

Step-by-step explanation:

HOPE THIS HELPSSS

Answer:

The answer would be 3.5 in decimal form.

Answer:

The answer is 55/12

Step-by-step explanation:

8-41/12

(8×12+1×(-41))/12

(96-41)/12

55/12

The three different values of n to demonstrate that 2n + 3n is equivalent to 5n are 1, 4 and 10.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = 2n + 3n

On simplifying the equation , we get

A = 5n

when n = 1 , we get

2n + 3n = 2(1) + 3(1) = 2 + 3 = 5

5n = 5(1) = 5

Therefore, both expressions give the same result of 5.

when n = 4 , we get

2n + 3n = 2(4) + 3(4) = 8 + 12 = 20

5n = 5(4) = 20

Again, both expressions give the same result of 20.

when n = 10 , we get

2n + 3n = 2(10) + 3(10) = 20 + 30 = 50

5n = 5(10) = 50

Hence , the equation is solved

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Answer: Answer choice C: -1.3 and 1.3.

Step-by-step explanation:

We can start by using the formula for the distance, D, between the two trains as a function of time, T:

D = 55(T + 2.25) - 120T

Simplifying this equation, we get:

D = 55T + 123.75 - 120T

D = -65T + 123.75

To find the two values of T for which D = 40, we can set this equation equal to 40 and solve for T:

40 = -65T + 123.75

-85 = -65T

T = 1.31

Plugging this value back into the original equation, we can see that D is equal to 40:

D = -65(1.31) + 123.75

D = 40.0375

Therefore, one solution is T = 1.31. To find the other solution, we can plug D = 40 into the equation and solve for T:

40 = -65T + 123.75

-83.75 = -65T

T = 1.29

Plugging this value back into the original equation, we can see that D is equal to 40:

D = -65(1.29) + 123.75

D = 40.0375

Therefore, the two values of T for which D = 40 are approximately 1.3 and 1.3, which rounds to answer choice C: -1.3 and 1.3.

The surface area of the triangular prism is 191 cm².

The surface area (SA) of a triangular prism is given by the formula:

SA = 2A + Ph

where A is the area of the base, P is the perimeter of the base, and h is the height of the prism.

First, we need to find the area of the triangular base.

Using the formula for the area of a triangle:

A = (1/2)bh = (1/2)(5 cm)(4 cm) = 10 square centimeter

Next, we need to find the perimeter of the base:

P = 5 cm + 6 cm + 8 cm = 19 cm

Now we can use the formula for the surface area of a triangular prism:

SA = 2A + Ph

= 2(10 cm²) + (19 cm)(9 cm)

= 20 cm²+ 171 cm²

= 191 cm²

Therefore, the surface area of the triangular prism is 191 cm².

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answer

a. 5,8

explanation

use numbers in each answer choice

+5 * -8 = - 40

+5 -8 = -3

Consider the form [tex]x^2+bx+c[/tex]. Find a pair of integers whose product is [tex]c[/tex] and whose sum is [tex]b[/tex]. In this case, whose product is -40 and whose sum is -3.

[tex]\longrightarrow\boxed{\bold{(-8,5)}}[/tex]

Write the factored form using these integers.

[tex](x-8) \ (x+5)[/tex]

Answer:

4.   30°

Step-by-step explanation:

Sum of interior angles of a triangle = 180

y° + ∠XYZ + ∠YZX = 180

y° = 180 - 90 - 60 = 30°

The total amount of FICA tax that was deducted from the executive's paychecks for the year 2018 is $10,860.80.

The FICA tax is imposed on both employees and employers to fund Social Security and Medicare which are federal programs that provide benefits for retirees, the disabled and children of deceased workers.

The Social Security tax will be calculated on the maximum taxable earnings of $128,400:

= $128,400 x 6.2%

= $7,961.20

The Medicare tax will be calculated on the entire earnings:

= $200,000 x 1.45%

= $2,900.

The total FICA tax will be:

= Social Security tax + Medicare tax

= $7,960.80 + $2,900

= $10,860.80.

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1. The lateral surface area of the prism is 200 units²

2. The lateral surface area of the cylinder is 125.6 cm²

The lateral surface area is the area of the lateral surface.

The lateral surface area of a prism is expressed as;

LSA = (a+b+c)h

or perimeter of the base × height

LSA = (6+12+7)8

= 25 × 8

= 200 units²

The lateral surface area of a cylinder

= 2πrh

r = 4cm and h = 5cm

LSA = 2 × 3.14 × 4 × 5

LSA = 40 × 3.14

= 125.6cm²

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The triangles are classified according to their sides as:

1. equilateral 2. Scalene   3. and 4. Isosceles   5. equilateral     6. and 7. scalene triangle.      8. Isosceles   9. and 10. Equilateral

Recall the following:

A triangle is equilateral if all three sides are equal.

It is isosceles if it has two equal sides.

A triangle is scalene if all three sides are of different lengths.

1. The triangle is equilateral because all sides are equal.

2. Scalene

3. and 4. Isosceles (two sides are equal)

5. All sides are equal, so it is an equilateral triangle.

6. and 7. The three sides have different lengths, therefore, it is a scalene triangle.

8. Isosceles

9. and 10. Equilateral

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The equation for the relationship between the number of bracelets made and the number of beads is y = 21x.

First, the rate of change

= (483 - 210) / (23 - 10)

= 273 / 13

= 21

So, the equation for the relationship between the number of bracelets made and the number of beads used.

(y - 210) = 21 (x-  10)

y - 210 = 21x - 210

y = 21x

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Answer:

C. (4, 0)

Step-by-step explanation:

(x, y)

a. (4, 3)

y = 12 - 3x

3 = 12 - 3(4)

3 = 12 - 12

3 = 0  false

b. (-4, 4)

y = 12 - 3x

4 = 12 - 3(-4)

4 = 12 + 12

4 = 24  false

c. (4, 0)

y = 12 - 3x

0 = 12 - 3(4)

0 = 12 - 12

0 = 0  true

d. (0, 4)

y = 12 - 3x

4 = 12 - 3(0)

4 = 12 - 0

4 = 12  false.

Answer:   C   (4, 0)

Step-by-step explanation:

your function y = 12 - 3x

They are asking which of those points are on the line

(x, y)   this is a format of a point where you can plug in x for x and y for y.

a.  (4, 3)  x=4  y=3  substitute and see if your answer is true

   3 = 12 -3(4)

   3 = 0   this is not true so (4, 3) is not a solution

b. (-4,4) x= -4 y=4

  4 = 12 - 3(-4)

  4 = 24  not true

c.  (4, 0)  x=4  y=0

  0 = 12-3(4)

  0 = 0  true      (4,0) is a solution

d. (0, 4)

4 =  12 - 3 (0)

4=12

Area of rectangular prism: Base x Height.

so 3x1/3x2/5=0.4 0r 2/5

Step-by-step explanation:

( 11 * x ) + 2     where 'x' is a number

The equivalent area of the parallelogram is 44.4m^2

The formula for finding the area of a parallelogram is expressed as:

Area = base * height

Given the following parameters

Base = 12m

Height = 3.7m

Substitute the given parameters into the formula to have:

Area = 12m * 3.7m

Area of the parallelogram = 44.4m^2

Hence the area of the parallelogram given is 44.4m^2

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The different committees possible are 10,584. Option A is the answer.

Тhe number оf wаys tо choosе 4 men out оf 9 is givеn by 9C4, which is:

9C4 = (9!)/(4!5!)

= 126

Similаrly, the number оf wаys tо choosе 6 wоmen out оf 9 is givеn by 9С6, which is:

9С6 = (9!)/(6!3!)

= 84

So the tоtal number оf wаys tо choosе a committее consisting оf 4 men and 6 wоmen is:

126 * 84 = 10,584

Тherefore, the аnswer is (А) 10,584.

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Answer: The slope is -5/4

m=-5/4

A point that represent a striking deviation in the box plot above include the following: C. P.

In Mathematics and Statistics, a box plot can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.

Based on the information provided about the data set, the five-number summary for the given data set include the following:

In conclusion, we can logically deduce that point P represent a striking deviation in the box plot because it is an outlier (it is significantly far from all of the other data points).

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