Consider a triangle ABC like the one below. Suppose that a =53, b=18, and A=130º. (The figure is not drawn to scale.) Solve the triangle.
Carry your intermediate computations to at least four decimal places, and round
your answers to the nearest tenth.
If no such triangle exists, enter "No solution." If there is more than one solution, use the button labeled "or".

Answer:

135 cubes

Step-by-step explanation:

First, find the volume of the box with the equation V = Bh, where B is the area of the base and h is the height.

V = (2.25)(0.75)(1.25)

V = 2.109375

Next, find the volume of one cube with the side length 1/4 with V = Bh:

V = (0.25)(0.25)(0.25)

V = 0.015625

Then, divide the volume of the box by the volume of one cube:

2.109375 / 0.015625

= 135

Answer:

d. [tex]\angle BIJ \cong \angle CGJ\ and\ \angle BJI \cong \angle CJG[/tex]

Step-by-step explanation:

Here, we are given a diagram in which there are two triangles to be considered:

[tex]\triangle CJG \ and\ \triangle BJI[/tex].

We can consider the whole diagram in the form as attached in the answer area.

To find:

The conditions to prove [tex]\triangle CJG \sim \triangle BJI[/tex].

Solution:

First of all, let us learn about AAA similarity.

AAA stands for Angle Angle Angle.

i.e. when we prove that the all the three corresponding angles of two triangles are equal ,the triangles are similar.

There is one more property of the triangles, that if two angles of two triangles are equal then the third angle of the triangles will also be equal to each other.

So, actually, to prove that [tex]\triangle CJG \sim \triangle BJI[/tex], we need the conditions that two corresponding angles of the triangles are equal to each other, then we can say that third angle will also be equal. Therefore the triangles will be similar to each other.

Let us consider the corresponding angles:

[tex]\angle BIJ \ and \ \angle CGJ\ ,\ \angle BJI \ and \ \angle CJG\ , \ \angle IBJ\ and \ \angle GCJ[/tex]

So, if we are given that any of the two above three pairs are equal/congruent to each other, we can prove [tex]\triangle CJG \sim \triangle BJI[/tex].

Therefore, the correct answer is:

d. [tex]\angle BIJ \cong \angle CGJ\ and\ \angle BJI \cong \angle CJG[/tex]

Answer:

y=x+-5

Step-by-step explanation:

y is x+-5 because as you can see in the graph the difference in everysingle one is -5 so y=x-5

Answer:

y=x+(-5)

Step-by-step explanation:

d=-3-(-4)=-3+4=1

y-(-4)=1(x-1)

y+4=x-1

y=x-1-4

or y=x+(-5)

Answer:

[tex]\boxed{2\pm \frac{\sqrt{2}}{2}}[/tex]

Step-by-step explanation:

[tex]2x^2-8x=-7[/tex]

[tex]\sf Add \ 7 \ on \ both \ sides}.[/tex]

[tex]2x^2-8x+7=-7+7[/tex]

[tex]2x^2-8x+7=0[/tex]

[tex]ax^2 +bx+c=0[/tex]

[tex]\sf Apply \ quadratic \ formula.[/tex]

[tex]a=2 \ \ \ b=-8 \ \ \ c = 7[/tex]

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

[tex]x=\frac{-(-8)\pm\sqrt{(-8)^2-4(2)(7)}}{2(2)}[/tex]

[tex]x=\frac{8\pm\sqrt{64-56}}{4}[/tex]

[tex]x=\frac{8\pm\sqrt{8}}{4}[/tex]

[tex]x=\frac{8\pm2\sqrt{2}}{4}[/tex]

[tex]x=2\pm \frac{\sqrt{2}}{2}[/tex]

Answer:

It would be difficult to see what you are doing if the line segments overlapped, making it easier to make a mistake and harder to check your work.

Answer:

19.9 cm²

Step-by-step explanation:

The following data were obtained from the question:

Angle at the centre (θ) = 150°

Diameter (d) = 7.8 cm

Area of sector =.?

Next, we shall determine the radius.

This can be obtained as illustrated below:

Radius (r) = Diameter (d) /2

r = d/2

Diameter (d) = 7.8 cm

Radius (r) =.?

r = d/2

r = 7.8/2

r = 3.9 cm

Finally, we shall determine the area of the sector as follow:

Angle at the centre (θ) = 150°

Radius (r) = 3.9 cm

Pi (π) = 3.14

Area of sector (A) =.?

A = θ/360 × πr²

A = 150/360 × 3.14 × 3.9²

A = 15/36 × 3.14 × 15.21

A = 19.9 cm²

Therefore, the area of the sector is 19.9 cm²

Answer:

0

Step-by-step explanation:

Hello, do you agree that 25 * 2 = 50 ?

So, we can write that [tex]50 = 25 * \boxed{2} + \boxed{0}[/tex]

the remainder is 0.

Thank you

Answer:

(4x + 1)(2x² - 5)

Step-by-step explanation:

Given

8x³ + 2x² - 20x - 5 ( factor the first/second and third/fourth terms )

= 2x²(4x + 1) - 5(4x + 1) ← factor out (4x + 1) from each term

= (4x + 1)(2x² - 5)

Answer:

blank 1 is -20-5

blank 2 is 4x+1

blank 3 is -5

blank 4 is 2x^2-5

Step-by-step explanation:

Answer:

The total volume of the solid is 1.67 cubic units.

Step-by-step explanation:

Each pyramid with a height of 2 units and a rectangular base with dimensions of 5 units × 0.25 units.

1/3 x (area of base) x height

= 1/3 x (5 x 0.25) x 2= 0.833

Therefore, the volume of each pyramid will be

= cubic units.

So, the total volume of the solid is (2 × 0.833) = 1.67 cubic units. (Answer)

Hope it helped ya!

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Tysmm

The total volume of the solid is 1.67 unit³.

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

Given:

Each pyramid has a height of 2 units.

and the rectangular base with dimensions of 5 units × 0.25 units.

So, the Volume of each Pyramid is

= 1/3 x (area of base) x height

= 1/3 x (5 x 0.25) x 2

= 0.833

and, the total volume of the solid

= (2 × 0.833)

= 1.67 cubic units.

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Answer:

1,4,9,16

Step-by-step explanation:

those are the squares

1 = 1²

4 = 2²

9 = 3²

16 = 4²

Step-by-step explanation:

[tex] {1}^{2} = 1 \times 1 = 1 \\ {2}^{2} = 2 \times 2 = 4 \\ {3}^{2} = 3 \times 3 = 9 \\ {4}^{2} = 4 \times 4 = 16 \\[/tex]

[tex] {5}^{2} = 5 \times 5 = 25 \\ [/tex]

[tex] {10}^{2} = 10 \times 10 = 100[/tex]

[tex] {6}^{2} = 6 \times 6 = 36 \\ {7}^{2} = 7 \times 7 = 49 \\ {8}^{2} = 8 \times 8 = 64 \\ {9}^{2} = 9 \times 9 = 81 \\ [/tex]

[tex] {11}^{2} = 11 \times 11 = 121 \\ {12}^{2} = 12 \times 12 = 144 \\ {13}^{2} = 13 \times 13 = 169 \\ {14}^{2} = 14 \times 14 = 196 \\ [/tex]

[tex] {15}^{2} = 15 \times 15 = 225 \\ {16}^{2} = 16 \times 16 = 256 \\ {17}^{2} = 17\times 17 = 289 \\ {18}^{2} = 18 \times 18 = 324[/tex]

[tex] {19}^{2} = 19 \times 19 = 361 \\ {20}^{2} = 20 \times 20 = 400[/tex]

The value of the unknown number is calculated as - 3

Let the unknown number = y

5  less than the number is written as = y - 5

1 more than three times the number is written as = 1 + 3y

Since the first statement and the second statement are equal, we can equate the two and solve for y.

y - 5 = 1 + 3y

collect similar terms together

y - 3y = 1 + 5

-2y = 6

y = -6/2

y = -3

Therefore, the number is - 3

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Building and solving the expression, it is found that the number is -3.

------------------

They are equivalent, thus:

[tex]x - 5 = 1 + 3x[/tex]

Solving for x.

[tex]3x - x = -5 - 1[/tex]

[tex]2x = -6[/tex]

[tex]x = -\frac{6}{2}[/tex]

[tex]x = -3[/tex]

The number is -3.

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Answer:

1 miles/hour = 1.467·feet/second

Step-by-step explanation:

The given measurement unit are;

88 feet/second = 60 miles/hour

The number of feet per second that is equal to one mile per hour is found as follows;

88 feet/second = 60 miles/hour

To have a unit measure of one mile per hour , we divide both sides of the equation by 60 to get

(88 feet/second)/60 = (60 miles/hour)/60

Which gives;

(88/60 feet/second) = (60/60 miles/hour) = 1 miles/hour

22/15 × feet/second =  1 miles/hour

1.46667·feet/second =  1 miles/hour

Rounding to the nearest thousandth gives;

1.467·feet/second =  1 miles/hour

The number of feet per second that is in 1 mile per hour is 1.467·feet/second.

Greetings from Brasil...

2X/(X + 2) = 6/(X + 4)

2X(X + 4) = 6(X + 2)

2X² + 2X - 12 = 0     ÷2

2X²/2 + 2X/2 - 12/2 = 0/2

Δ = 25

S = {-3, 2}

By using factorization,  [tex]\frac{2x}{x+2} =\frac{6}{x+4}[/tex] , values of x are -2, 3.

Factorization can be defined as the process of breaking down a number into smaller numbers which when multiplied together arrive at the original number. These numbers are broken down into factors or divisors.

Given

[tex]\frac{2x}{x+2} =\frac{6}{x+4}[/tex]

⇒ 2x(x + 4) = 6(x + 2)

⇒ [tex]2x^{2} +8x = 6x + 12[/tex]

⇒ [tex]2x^{2} +8x-6x-12=0[/tex]

⇒ [tex]2x^{2} +2x -12=0[/tex]

Divide above equation by 2, we get

⇒ [tex]x^{2} +x -6=0[/tex]

⇒ [tex]x^{2} +2x-3x-6=0[/tex]

⇒ [tex]x(x+2)-3(x+2)=0[/tex]

⇒ [tex](x+2)(x-3)=0[/tex]

⇒ x = -2, 3

By using factorization,  [tex]\frac{2x}{x+2} =\frac{6}{x+4}[/tex] , values of x are -2, 3.

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Answer:

3.2 cm = h

Step-by-step explanation:

The area of a triangle is

A = 1/2 bh

where b is the base and h is the height

b = 10  and the area is 16

16 =1/2 *10 *h

16 = 5h

Divide each side by 5

16/5 = 5h/5

3.2 cm = h

Answer:

2.7 hours

Step-by-step explanation:

We can use the formula

1/a + 1/b = 1/c

where a and b are the times working alone and c is the time working together

1/8 + 1/b = 1/2

Multiply each side by 8b to get rid of the fractions

8b( 1/8 + 1/b = 1/2)

b + 8 = 4b

Subtract b from each side

b+8-b = 4b-b

8 = 3b

Divide each side by 3

8/3 = 3b/3

2.666666repeating = b

Round to 1 decimal place

2.7 = b

Answer:

2.7 hr

Step-by-step explanation:

2/8 +2/x = 1

2x+16 =8

16/8

x=8/3 =2.7

Answer:

13x3= 39

Step-by-step explanation:

10x3=30

3x3=9

30+9=39

Hope it helps!

Answer:

41.4 kgs

Step-by-step explanation:

Take the number of bags times the weight of each bag

6 * 6.9

41.4 kgs

Answer:

41.4 kilograms of sugar

Step-by-step explanation:

its 41.4 kilograms of sugar because you take the 6 bags and multiply that by the 6.9

Answer: find the answer in the explanation.

Step-by-step explanation:

To increase the time the fireworks stays in the air by 2 seconds to build up the suspense, 2 should be added to the time t.

T + 2 = t

T = t - 2

Substitute T for t in the function g(t)

The company will make this happen without changing the length of the fuse by substituting T for t which will lead to

g(t) = -16(t - 2)^2 + 224(t - 2) + 120

How will this affect the maximum height of the firework?

Initially the function is:

g(t) = -16t2 + 224t + 120

Where the time at maximum height is found by using the formula

t = -b/2a

b = 224, a = -16

Substitutes both into the formula

t = -224/2(-16)

t = -224/-32

t = 7

Substitute 7 for t in the first equation

g(t) = -16(7)^2 + 224(7) + 120

g(t) = -16(49) + 224(7) + 120

g(t) = -784 + 1568 + 120

g(t) = 904 metres

But when the time is delayed by 2 seconds in the air, the maximum height will be

g(t) = -16( 7 - 2 )^2 + 224(7 - 2) + 120

g(t) = -16(5)^5 + 224(5) + 120

g(t) = -16(25) + 224(5) + 120

g(t) = -400 + 1120 + 120

g(t) = 840

The effect will surely reduce the maximum height of the fireworks.

Answer:

20°

Step-by-step explanation:

The measure of the inscribed angle is equal to the half of the arc it sees

Since AC is the diameter the measure of arc ABC is 180°

and since A sees arc BC and C sees the arc AB

A< + C< = 90° so angle C = 20°

Answer:

r = 1

Step-by-step explanation:

6r - 1 + 6r = 11

Adding 6r and 6r (because they're like terms) gives us:

12r - 1 = 11

Adding 1 to both sides of the equation gives us:

12r - 1 + 1 = 11 + 1

12r = 12

Dividing both sides of the equation by 12 gives us:

12r/12 = 12/12

r = 1

Answer:

Perimeter = 8x - 12

Step-by-step explanation:

The perimeter of a square is:

p = 4(side length)

on this case:

p = 4(2x-3)

p = 4*2x + 4*-3

p = 8x - 12

Answer:

12.25

Step-by-step explanation:

73.50 divided by 6 for each shirt is 12.25 a shirt

Average rate of change ... of what?

Given some continuous function [tex]f(x)[/tex] and some interval [tex][a,b][/tex], its average rate of change over the interval is

[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]

Without knowing what your function is exactly, I can only give a symbolic answer,

[tex]\dfrac{f(18)-f(0)}{18}[/tex]

Answer: -5/18

Step-by-step explanation: edg

Answer:

Option A

Step-by-step explanation:

Expression: y = 12h

If h = 15, then:

y = 12(15)

y =  $180

Option A

Answer:

it's true

Step-by-step explanation:

Answer:

1. 38.3 x 10^5

2. 6.67 x 10^9

3. 4.48 x 10^4

Step-by-step explanation:

4.2 X 10 ^6 - 1.2 X 10^5 - 2.5 x 10^5

For the above question, we need to make the exponents equal

=> 42 x 10^5  -  1.2 x 10^5  -  2.5 x  10^5

SInce, all the exponents are equal, we can now add and subtract the normally.

=> (42 - 1.2 -2.5) x 10^5

=> (42 - 3.7) x 10^5

=> 38.3 x  10^5

So, the answer to the 1st question is 38.3 x 10^5

Next question:

=> 3.3 x 10^9 + 2.6 x 10^9 +7.7 x 10^8

=>  we need to make the exponents equal

=> 3.3 x 10^9 + 2.6 x 10^9 + .77 x 10^9

=> All the exponents are equal, we can now add and subtract the normally.

=> (3.3 + 2.6 + .77) x 10^9

=> 6.67 x 10^9

=> So the answer to the 2nd question is 6.67 x 10^9

Next question,

=> 8 X 10^4 - 3.4 x 10^4  - 1.2 x 10^3

=> we need to make the exponents equal

=> 8 x 10^4 - 3.4 x 10^4 - .12 x 10^4

=> All the exponents are equal, we can now add and subtract the normally.

=> (8 - 3.4 - .12) x 10^4

=> 4.48 x 10^4

=> So the answer to the 3rd question is 4.48 x 10^4

The solutions to the expressions are:

[tex]4.2 \times 10^6 - 1.2 \times 10^5 - 2.5 \times 10^5[/tex]=[tex]38.3\times 10^5[/tex]

[tex]3.3 \times 10^9 + 2.6 \times 10^9 + 7.7 \times 10^8[/tex] = [tex]6.67\times 10^9[/tex]

[tex]8.0 \times 10^4 -3.4 \times 10^4 - 1.2 \times 10^3[/tex] = [tex]4.48 \times 10^4[/tex]

[tex]4.2 \times 10^6 - 1.2 \times 10^5 - 2.5 \times 10^5[/tex]

Combine like terms:

[tex]4.2 \times 10^6 - (1.2+2.5) \times 10^5[/tex]

[tex]4.2 \times 10^6 - 3.7 \times 10^5[/tex]

[tex]42 \times 10^5 - 3.7 \times 10^5[/tex]

[tex](42-3.7)\times 10^5[/tex]

[tex]38.3\times 10^5[/tex]

[tex]3.3 \times 10^9 + 2.6 \times 10^9 + 7.7 \times 10^8[/tex]

Convert all terms with same power:

[tex]3.3 \times 10^9 + 2.6 \times 10^9 + 0.77 \times 10^9[/tex]

[tex](3.3+2.6+0.77) \times 10^9[/tex]

[tex]6.67\times 10^9[/tex]

[tex]8.0 \times 10^4 -3.4 \times 10^4 - 1.2 \times 10^3[/tex]

[tex]8.0 \times 10^4 - 3.4 \times 10^4 - 0.12 \times 10^4[/tex]

[tex](8.0-3.4-0.12) \times 10^4[/tex]

[tex]4.48 \times 10^4[/tex]

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Answer:

5/12

Step-by-step explanation:

4√y√y / 3√y

The above equation can be simplified as follow:

4√y√y / 3√y

4√y × √y ÷ 3√y

Recall:

√a = a^1/2

m√a = a^1/m

Therefore,

4√y√y ÷ 3√y

y^1/4 × y^1/2 ÷ y^1/3

Recall:

a^m × a^n = a^(m+n)

Therefore,

y^1/4 × y^1/2 ÷ y^1/3

y^(1/4 + 1/2) ÷ y^1/3

y^3/4 ÷ y^1/3

Recall:

a^m ÷ a^n = a^(m–n)

Therefore,

y^3/4 ÷ y^1/3

y^(3/4 – 1/3)

y^5/12

Comparing the above with y^m, we have

y^5/12 = y^m

m = 5/12

Therefore, the value of m is 5/12

Answer:

(B) A location

Step-by-step explanation:

If you have a point on a graph or number line, it always represents a certain location on the graph.

For instance, if we have a point on the x=3 line and the y=4 line, the point would represent the location (3,4).

Hope this helped!

Answer:

Now solve these two equations.ull get andwer

The original number will be "63".

Let,

The equation will be:

→ [tex]x=y+3[/tex]...(equation 1)

Original number will be:

→ [tex]10x+y[/tex]

then,

→ [tex]2 (10x+y)-\frac{(10y+x)}{2} = 108[/tex]

→ [tex]\frac{4(10x+y)}{1} -(10y+x) = 216[/tex]

→ [tex]40x+4y-10y-x = 216[/tex]

→ [tex]39x-6y=216[/tex]...(equation 2)

By using (equation 1) and (equation 2), we get

→ [tex]39(y+3)-6y=216[/tex]

→ [tex]39y+117-6y=216[/tex]

→                   [tex]33y=99[/tex]

→                       [tex]y = \frac{99}{33}[/tex]

→                          [tex]= 3[/tex]

Now,

[tex]x = y+3[/tex]

  [tex]=3+3[/tex]

  [tex]=6[/tex]

hence,

The original number will be:

= [tex]10x+y[/tex]

= [tex]10\times 6+3[/tex]

= [tex]60+3[/tex]

= [tex]63[/tex]

Thus the above approach is right.

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