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3 years ago

5. Simplify: 3a + b + a - 5

Mathematics

2 answers:

Yuri [45]3 years ago

7 0

Answer:

4a +b -5

Step-by-step explanation:

<h3>Let's simplify step-by-step.</h3>

3a + b + a −5

= 3a + b + a + −5

<h3>Combine Like Terms:</h3>

= 3a + b + a + −5

= (3a + a) + (b) + (−5)

= 4a + b + −5

andriy [413]3 years ago

3 0

Answer: 4a + b - 5

Step-by-step explanation:

We can only simplify the like terms of 3a and a, which add to 4a and we keep the rest the same.

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If you can solve all parts I will give brainliest (also give strategy)

Alexxx [7]

The Halloween conical hat, with given height, circular base and brim

extension has the following calculated parameters;

Part a. The slant height is 18.2 inches

Part b. The volume of the cone is $37\frac{1}{2} \cdot \pi$ in.³

Part c. The area of the brim, A = 36·π in.²

Part d. The area of the brim is found by subtracting the area of the base of the cone from the area covered by the perimeter of the brim

Reasons:

Known parameters;

Height of the conical portion, h = 18 inches

Base circumference, C = 5·π inches

Part a. Slant height of the conical portion; Required

Solution:

The circumference of a circle, C = 2·π·r

Therefore;

$r = \dfrac{C}{2 \cdot \pi}$

Which gives;

$r = \dfrac{5 \cdot \pi}{2 \cdot \pi} = \dfrac{5}{2} = 2.5$

Radius, r = 2.5 inches

According to Pythagoras's theorem, we have; s² = r² + h²

Where;

s = The slant height of the cone

s² = 2.5² + 18² = 330.25

s = √(330.25) ≈ 18.2

The slant height, s ≈ 18.2 inches

Part b. The measure in cubic inches of candy that exactly fills the conical portion of the hat is the volume of the cone.

$Volume \ of \ a \ cone = \dfrac{1}{3} \cdot \pi \cdot r^2 \cdot h$

Therefore;

$V = \dfrac{1}{3} \times \pi \times 2.5^2 \times 18 = 37\frac{1}{2} \cdot \pi$

The volume of the cone, V = $37\frac{1}{2}$ ·π in.³

Part c. The extension of the brim from the base of the cone = 4 inches

The radius of the brim, R = Radius of the base of the cone + 4 inches

∴ R = 2.5 inches + 4 inches = 6.5 inches

Area of the brim, A = Area of the 6.5 inch circle - Area of the circular base of the cone

∴ A = π × 6.5² - π × 2.5² = 36·π

The area of the brim, A = 36·π in.²

Part d. The procedure for solving the question in part c, is described as follows;

The area of the brim can be found by finding the entire area of the circle formed by the perimeter of the brim, then subtracting the area of the base of the cone from that area.

Learn more here:

brainly.com/question/17023854

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2 years ago

Steve wants to buy a new music player. The player he wants costs $279.95. The city he lives charges a 5% sales tax, so for every

Yakvenalex [24]

Ultimately, the question is "What is 5% of $279.95?"

To answer this, multiply 279.95 by 5%, or 0.05 which is 5% in decimal form.

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2 years ago

If parallelogram RSTV has diagonals then RSTV must also be a _______. square and a rectangle rhombus and a rectangle rhombus rec

andrew11 [14]

a rectangle rhombus(parallelogram) since even a parallelogram has diagonals

5 0

3 years ago

An architect makes a model of a new house. The model shows a tile patio in the backyard. In the model, each tile has length 1/4

Semmy [17]

Answer:

The answer is below

Step-by-step explanation:

The model is a tile with length 1/4 in. and width 1/6 in while the actual tile has length 1/6 ft. and width 1/9 ft.

Firstly we have to convert the model length and width from inches to feet.

1 feet = 12 inches

model length = 1/4 in. = 1/4 in * (1/12) ft./in = 1/48 ft.

model width = 1/6 in. = 1/6 in * (1/12) ft./in = 1/72 ft.

Therefore:

Ratio of model length to actual length of tile = (1/48 ft.) / (1/6 ft.) = 1 / 8

Ratio of model length to actual length of tile = (1/72 ft.) / (1/9 ft.) = 1 / 8

Area of model tile = length * width = 1/48 ft. * 1/72 ft. = 1/3456 ft²

Area of actual tile = length * width = 1/6 ft. * 1/9 ft. = 1/54 ft²

Ratio of model area to actual area of tile = (1/3456 ft²) / (1/54 ft²) = 1 / 64

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2 years ago

Solve the following 3 × 3 system. Enter the coordinates of the solution below.

love history [14]

The system is:

i) 2x – 3y – 2z = 4
ii) x + 3y + 2z = –7
iii) –4x – 4y – 2z = 10

the last equation can be simplified, by dividing by -2,

thus we have:

i) 2x – 3y – 2z = 4
ii) x + 3y + 2z = –7
iii) 2x +2y +z = -5

The procedure to solve the system is as follows:

first use any pairs of 2 equations (for example i and ii, i and iii) and equalize them by using one of the variables:

i) 2x – 3y – 2z = 4
iii) 2x +2y +z = -5

2x can be written as 3y+2z+4 from the first equation, and -2y-z-5 from the third equation.

Equalize:

3y+2z+4=-2y-z-5, group common terms:
5y+3z=-9

similarly, using i and ii, eliminate x:

i) 2x – 3y – 2z = 4
ii) x + 3y + 2z = –7

multiply the second equation by 2:

i) 2x – 3y – 2z = 4
ii) 2x + 6y + 4z = –14

thus 2x=3y+2z+4 from i and 2x=-6y-4z-14 from ii:

3y+2z+4=-6y-4z-14
9y+6z=-18

So we get 2 equations with variables y and z:

a) 5y+3z=-9
b) 9y+6z=-18

now the aim of the method is clear: We eliminate one of the variables, creating a system of 2 linear equations with 2 variables, which we can solve by any of the standard methods.

Let's use elimination method, multiply the equation a by -2:

a) -10y-6z=18
b) 9y+6z=-18
------------------------ add the equations:

-10y+9y-6z+6z=18-18
-y=0
y=0,

thus :
9y+6z=-18
0+6z=-18
z=-3

Finally to find x, use any of the equations i, ii or iii:

2x – 3y – 2z = 4

2x – 3*0 – 2(-3) = 4

2x+6=4

2x=-2

x=-1

Solution: (x, y, z) = (-1, 0, -3 )

Remark: it is always a good attitude to check the answer, because often calculations mistakes can be made:

check by substituting x=-1, y=0, z=-3 in each of the 3 equations and see that for these numbers the equalities hold.

3 0

2 years ago

Read 2 more answers