Which of the following sets of angles of a triangle represents an acute triangle?

30°, 60°, 90°
60°, 65°, 55°
40°, 40°, 100°
45°, 40°, 95°


I think it's B, but I think i am wrong. Please explain...

Answer:

Step-by-step explanation:

a)

i)

Time taken at the first part:

ii)

Time taken at the second part:

b)

If time is 3 hours and 15 minutes = 3 1/4 hours = 13/4 hours, the equation is:

c)

Solve the equation:

d)

Answer:

see below

Step-by-step explanation:

Let t = time (in hours)

a) i)  First 105 km of journey

[tex]\mathsf{speed=\dfrac{distance}{time}}[/tex]

[tex]\implies x=\dfrac{105}{t_1}[/tex]

[tex]\implies t_1=\dfrac{105}{x}[/tex]

ii) Rest of journey

distance = 190 - 105 = 85 km

speed = [tex]x+12[/tex] km/h

[tex]\mathsf{speed=\dfrac{distance}{time}}[/tex]

[tex]\implies x+12=\dfrac{85}{t_2}[/tex]

[tex]\implies t_2=\dfrac{85}{x+12}[/tex]

b)  3 hours 15 minutes = 3.25 hours

[tex]\implies[/tex]  total time = [tex]t_1+t_2=3.25[/tex]

[tex]\implies \dfrac{105}{x}+\dfrac{85}{x+12} =3.25[/tex]

[tex]\implies \dfrac{105(x+12)+85x}{x(x+12)} =3.25[/tex]

[tex]\implies 105(x+12)+85x =3.25x(x+12)[/tex]

[tex]\implies 105x+1260+85x =3.25x^2 +39x[/tex]

[tex]\implies 3.25x^2-151x-1260=0[/tex]

multiply by 4:

[tex]\implies 13x^2-604x-5040=0[/tex]

c)

[tex]\textsf{quadratic formula} \ x=\dfrac{-b \pm\sqrt{b^2-4ac} }{2a}}[/tex]

[tex]\implies x=\dfrac{604 \pm\sqrt{(-604)^2-4(13)(-5040)} }{2(13)}}[/tex]

[tex]\implies x=\dfrac{604 \pm\sqrt{626896} }{26}}[/tex]

[tex]\implies x = 53.68, x=-7.22[/tex]

(to 2 decimal places)

d) time ≥ 0, therefore, x = 53.68 only

Substitute x = 53.68 into the expression for [tex]t_1[/tex] and solve for [tex]x[/tex]:

[tex]\implies t_1=\dfrac{105}{53.68}=1.955912... \textsf{hours}=\textsf{1 hr 57 min}[/tex]

Answer: a minute and a half

Step-by-step explanation:

3/4 +3/4 is 6/4 which is 1 1/2 or 1 2/4

Total pounds=1lbs

Total mins:-

Answer:

14 ft²

Step-by-step explanation:

To find the area of a rectangle you multiply the length and width. Sense the length is 10 feet but 3 feet was removed it is now 7 feet. Now you multiply that 7 feet by the width of 2 feet to get

7×2=

Area= 14 ft²

Answer:

12

Step-by-step explanation:

30% of 40=12

I think you mean the circles

x² + y² = 4

(x - 2)² + (y - 2)² = 4

Notice that both have radius 2, but the first one is centered at the origin (0, 0) while the second one is centered at (2, 2). The two circles intersect at the points (2, 0) and (0, 2), which means the bounded region between them is contained entirely in the first quadrant.

If we solve both equations above for y, we would find two solutions in each case:

x² + y² = 4   ⇒   y = ± √(4 - x²)

(x - 2)² + (y - 2)² = 4   ⇒   y = 2 ± √(4 - (x - 2)²)

The positive/negative root corresponds to the upper/lower semicircle the make up the full circle. The semicircles we're interested in are

y = + √(4 - x²)

y = 2 - √(4 - (x - 2)²)

that is, the upper half of the circle centered at the origin, and the lower half of the circle centered at (2, 2).

So, in standard Cartesian coordinates, the bounded region (call it R) is the set

[tex]R = \left\{(x, y) : 0 \le x \le 2 \text{ and } 2-\sqrt{4-(x-2)^2} \le y \le \sqrt{4-x^2} \right\}[/tex]

and the area is given by the double integral

[tex]\displaystyle \iint_R dA = \boxed{\int_0^2 \int_{2-\sqrt{4-(x-2)^2}}^{\sqrt{4-x^2}} dy \, dx}[/tex]

Answer:

83.33 or 83.3 feet per second

Step-by-step explanation:

250 feet/3 seconds = 83.33 ft per second

Answer:

  Plant B grows 3 times as fast as Plant A

Step-by-step explanation:

Both plants start at 0 height on Day 1 and grow the same amount each day. Plant A grows 2 cm each day; Plant B grows 6 cm each day. The growth rate of Plant B is 3 times the growth rate of Plant A.

Answer:

Leonard’s balance is −$8.00.

Step-by-step explanation:

Answer:x=125

Step-by-step explanation:

180-55=125

Answer:

Step-by-step explanation:

x+55=180[Sum of linear pair]

x=180-55

x=125

Answer:

A ,D , F

Step-by-step explanation:

A) x-3=0 , x=3

B 1+x=2 , x=2-1=1 , x=1

C 9-x=3 , x=9-3=6 , x=6

D) 6=2x , x=6/2=3 , x=3

E (1/5)x=3 , x=3*5=15 , x=15

F) x^2=9 x=√9 , x=3

Answer:187

Step-by-explanation: width multiply by height

=11 times 17

=187

The principal of a loan is the amount of money they took out as a loan.

Principal = $35,000

Answer:

24

Step-by-step explanation:

(4 times 2 to the third power) - (64 divided by 8) = 4*(2^3) - 64/8

= 4*8 - 8 = 32 - 8 = 24

The answer is 24

Hope this helps :)

Have a great day!

Answer:

22

Step-by-step explanation:

180-90-68=22

Answer:

180 - (90+68) = 22

B =22

Hope this helps!

Answer:

1.0 inch

Step-by-step explanation:

Round the 9 in 0.955, this turns it into 1.0, Since you said an inch, the value will be in inches.

Answer:

1.0in is your answer!

Step-by-step explanation:

the person above me explained it good enough

Answer:

what event there is no picture or words to tell me please explain

Step-by-step explanation:

Answer:

7.7.7.7 and 7^4 and seven to the fourth power

Step-by-step explanation:

They all equal 2401.

They are all the same but in different forms:

(7.7.7.7- expression)

(7^4 - exponential form)

(seven to the fourth power-word form of exponent)

Answer:

x = 20, angle B = 92 and angle c = 40

Step-by-step explanation:

3 angles in a triangle adds up to 180, and since A is 48, we have B + C = 132

6x - 28 + 2x = 132
=> 8x - 28 = 132
=> 8x = 160 and x = 20

B = 6 x 20 - 28 = 92
C = 2 x 20 = 40

Answer:

Step-by-step explanation:

We know that sine and cosine are equal when angles are complementary.

sin and cos are equal when their sum is 90°

So

Answer:

x² + 6x + 9

Step-by-step explanation:

(x + 3)² = (x + 3)(x + 3)

Each term in the second factor is multiplied by each term in the first factor , that is

x(x + 3) + 3(x + 3) ← distribute parenthesis

= x² + 3x + 3x + 9 ← collect like terms

= x² + 6x + 9

Answer:

8.23 cm

Step-by-step explanation:

A circle is given to us and we need to find out the length of the bolded arc . The arc subtends an angle of 118° at the centre . And the radius of the circle is 4cm .As we know that , length of the arc is given by ,

[tex]\longrightarrow Length_{arc}= \dfrac{\theta}{360}\times 2\pi r [/tex]

Here ,

On substituting the respective values,

[tex]\longrightarrow Length_{arc}=\dfrac{118^o}{360^o}\times 2(3.14)(4cm) [/tex]

Simplify ,

[tex]\longrightarrow Length_{arc}= 0.3277 \times 25.18 \ cm [/tex]

Multiply ,

[tex]\longrightarrow \underline{\underline{Length _{arc}= 8.23 \ cm}} [/tex]

This is the required answer!

Answer:

-21

Step-by-step explanation:

the y intercept is when x=0.

you can see that this is a linear equation where each increase in x results in  an increase of 4 onto the y value.

so if when x=1, y=-17, subtract 4 to find what y equals when x is 0.

-17 -4=-21

good luck :)

Answer:

$13.56 is 80% of $16.95.

Answer:

Yes

Step-by-step explanation:

Yes; Dividing by 2 is the same as multiplying by [tex]\frac{1}{2}[/tex].

Answer:

In y = kx, where k is the constant of proportionality.

Answer:

k is the constant

Step-by-step explanation:

Direct variation is simply explained as when a number is directly proportional to another number. For example, when 8 is directly proportional to 4 then it will result to

=> 8= k4, where k is the constant

=> divide both sides by 4 to get k

=> k= 2

Answer:

African American and women

Step-by-step explanation:

Mary Eliza Mahoney was eager to encourage greater equality for African Americans and women

hope this helps!