The figure below shows a triangular prism that Tasha is
using for a science experiment.
Tasha's Prism
-
-
5 cm
12 cm
6 cm
What is the volume of Tasha's prism?
242 cm3
324 cm3
360 cm
180 cm3

Answer:

Blank 1: 3

Blank 2: 6

Step-by-step explanation:

When doing the X method, the numbers on the sides(3 and 6) have to add up to the number on the bottom (9) and multiply to get the number on the top(18)

Answer:

7 minutes

Step-by-step explanation:

the trip takes 7 mins

Pilar puts the boat in a lake that travels 400 meters at a constant speed. The time. On the return, the speed was the same for 2 minutes and then increase by 10m/min. The time boat takes in return back = 8 minutes

The given information states that the away distance the boat traveled = 400 m

The time traveled at the same initial speed, v₁, by the boat on the way back = 2 minutes.

The increase in speed of the boat by Pilar =  10 m/min

The new speed, v₂ = v₁ + 10

The time for the return trip, t₂ = 60 seconds (1 minute) faster than the time for the trip, t₁

[tex]t_2 = t_i - 1[/tex]

Therefore we have;

[tex]v_i\times t_i = v_i \times 2 + v_2 \times (t_2-2) \\= 400\\v_i \times 2 + (v_i + 10) \times (t_2-2) = 400\\(v_i + 10) \times t_2 - 20 = 400\\[/tex]

but

[tex]v_i = \frac {400}{t} = \frac{400)}{t_2+ 1}[/tex]

Which gives;

[tex]\frac{(400) }{(t₂ + 1} + 10) \times t_2 - 20 = 400\\10\times ( t_2²+ 36·t_2-2)/(t_2+1) = 40010 \times t_2^²+ 10 \times t_2-420 = 0[/tex]

[tex]t_2^2+ t_2-42 = 0[/tex]

[tex](t_2 - 7)(t_2 + 6) = 0[/tex]

[tex]t_2 = 7[/tex] minutes or [tex]-6[/tex] minutes

Given that t₂ is a natural number, we have,

t₂ = 7 minutes

Whereby, [tex]t_2 = t_i - 1[/tex], we have;

[tex]7 = t_i - 1[/tex]

[tex]t_{i} = 1 + 7 = 8[/tex] Minutes

The trip normally takes 8 minutes

Learn more about speed and distance:

https://brainly.com/question/4931057

Answer:35350

Step-by-step explanation:

its easy 32,550 - 34,150 it gives 1600 then divide by for because it id 4 years from 3 to 7 you get 400 thats your yearly raise then multiply by 3 because 7 to 10 is 3 years you get 1200 add ton 34150 and you get 35350

Answer:

Nolan is right.

Step-by-step explanation:

14 seats initially so thats your starting number, the +14 has to be there. He is right in saying +3n because it adds 3 every succeeding row. It would be 3 ×2 if its the second row, so 6 plus 14 equals 20 for example

Answer: Yes there is an outlier.

Step-by-step explanation: 51 is the outlier.

Answer:

The missing step in that proof is E

Answer:

C and A

Step-by-step explanation:

Part 1.

The area of a trapezoid is base 1 + base 2 divided by 2 times height.

Base 1 is 38, base 2 is 14, and the height is 16.

38 + 14 = 52, 52 / 2 = 26, and 26 x 16 = 416.

The answer is C, 416.

Part 2.

The area of a kite is diagonal 1 times diagonal 2 divided by 2. The length of diagonal 1 is 12 (on the left) + 12 (on the right) = 24. The length of diagonal 2 is 10 (on the top) + 18 (on the bottom) = 28.

28 x 24 / 2 = 336.

The answer is A, 336

Answer:

336

Step-by-step explanation:

In the figure, there are four triangles

Total Area = sum of four triangles areas

0.5(12*18)*2+0.5(12*10)*2=336

Answer:

1.Polygon

Step-by-step explanation:

Notice that

1. A triangle is a Polygon.

2. The triangle can be classified into Right, Obtuse, and Acute triangles.

3. An acute triangle is a triangle in which each angle is a acute angle. All acute triangle angles are less than 90 degrees. For example, an equilateral triangle is always acute, since all angles( which are 60) are all less than 90.

Taking into account the above, we have that the concept map can be filled.

Then, the unlock code is PTROAE

9514 1404 393

Answer:

  parallelogram

Step-by-step explanation:

A shape with two pairs of parallel sides is a parallelogram. If an angle is something other than 90°, then the figure is not a rectangle.

(f+g-k)(x) means to add the equations f(x) and g(x) then subtract k(x)

2x^2 + 3x + 4x - 9 = 2x^2 +7x -9

2x^2 + 7x - 9 - x^2 -7x = x^2 -9

The answer is : x^2 - 9

The answer I got is x^3 + 14x - 9x

Answer:

v = -5

Step-by-step explanation:

Answer:

v=-5

Step-by-step explanation:

-3 times -5= 15

Answer:

$65?

Step-by-step explanation:

Answer:

10π

Step-by-step explanation:

Length for arc = θ/360 × πd

Where,

θ = 180°

d = 20

Length of the given arc = 180/360 × π × 20.

= 10π

Step-by-step explanation:

Standard form is

[tex] {x}^{2} + {y}^{2} + ax + by + c = 0 \\ [/tex]

[tex] {x}^{2} + {y}^{2} - 18y + 5 = 0[/tex]

Answer:

125 cm^3

Step-by-step explanation:

The volume of a cube is given by length*width*height. In a cube, all sides are the same. Therefore, you can put in (5cm)*(5cm)*(5cm) and get 125 cm^3

Answer:

As we know the formula for "Circumference of circle": Since we have also mentioned that there is 2 feet wide circular track for a camera dolly. Therefore, A wheel on the outer rail travel 12.57 ft more than a wheel on the inner rail of the track.

Step-by-step explanation:

i hope it helped

Answer:

it has no real roots.

and the 2nd answer is correct.

Step-by-step explanation:

Answer:

this quadratic equation has two roots:

x = (2+i√(2))/3 , (2-i√(2))/3

Steps:

3x²-4x+2​=0

x = (4±√((-4)²-4×3×2))/2×3

x = (4±√(16-24))/6

x = (4±√(-8))/6

x = (4±√(-2×4))/6

x = (4±√(-2)×√(4))/6

x = (4±i√(2)×2)/6

x = (2±i√(2))/3

x = (2+i√(2))/3 , (2-i√(2))/3

Answer:

96

Step-by-step explanation:

16 * 6 = 96

Answer:

1.65 meters

Step-by-step explanation:

11.55 meters divided by 7 is 1.65 meters

Answer:

1.65 metres per girl

Step-by-step explanation:

Divide 11.55 (length) of ribbon by 7 girls (11.55/7). You get 1.65 metres.

Answer:

Distance = 10.77 unit (Approx.

Step-by-step explanation:

Given:

Coordinate of Jenna's house = (2,4)

Coordinate of Zac's house = (-2,-6)

Find:

Distance

Computation:

Distance = √(X1 - X2)² + (Y1 - Y2)²

Distance = √(2 + 2)² + (4 + 6)²

Distance = √(2 + 2)² + (10)²

Distance = √16 + 100

Distance = √116

Distance = 10.77 unit (Approx.

Answer:

i dont know

Step-by-step explanation:

SA = (5 × 4) + (5 × 12) + (4 × 12)

= 20 + 60 + 48

= 128

Step-by-step explanation:

[tex] \frac{4}{ \sqrt{5} + \sqrt{2}} - \frac{3}{ \sqrt{5} - \sqrt{2} } = \\ = \frac{4( \sqrt{5} - \sqrt{2} ) - 3( \sqrt{5} + \sqrt{2} ) }{( \sqrt{5} + \sqrt{2} )\times ( \sqrt{5} - \sqrt{2} )} = \\ = \frac{4 \sqrt{5} - 4 \sqrt{2} - 3 \sqrt{5} - 3 \sqrt{2} }{5 - \sqrt{10} + \sqrt{10} - 2 } = \\ = \frac{ \sqrt{5} - 7 \sqrt{2} }{3} [/tex]

Answer:

The first term is -6 and common difference is 3

Step-by-step explanation:

The nth term of an arithmetic progression is expressed as;

Tn = a + (n-1)d

T3 = a+2d

T4 = a + 3d

If the third term of an arithmetic sequence less than the fourth term by three

T3 = T4 - 3

a+2d = a+3d - 3

2d - 3d = -3

-d  = -3

d = 3

Similarly;

T7 = a+6d

T5 = a+4d

If the seventh term  is two times the fifth term, the;

T7 = 2T5

a+6d = 2(a+4d)

a+6d = 2a+8d

Since d = 3

a + 6(3) = 2a + 8(3)

a+18 = 2a + 24

a-2a = 24 - 18

-a = 6

a = -6

Hence the first term is -6 and common difference is 3

Answer:

3/4 to 9/6

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

25% of 80=20

9514 1404 393

Answer:

Step-by-step explanation:

Factoring is taking apart products. It helps immensely if you are familiar with how products are formed. That is, it helps to be familiar with your multiplication tables and the rules of divisibility. It also helps to have  thorough understanding of the distributive property and the forms produced by the multiplication of binomials.

The first step is to look for any factors that are common to all of the terms you are factoring. Next steps include ...

__

1.1.1 4x -x^2

There is only one constant, so no constant factors. The variable x appears in all terms, with a lowest power of 1, so x^1 = x is a factor.

  = x(4 -x) . . . . . . . cannot be factored further

__

1.1.2 x² -8y³ . . . . we assume this is the intended expression. (It helps to use appropriate (and consistent) exponent presentation: x^2 -8y^3, or x² -8y³.

There are no common numerical factors, no common variable factors, and the form is not the difference of squares or cubes. This expression cannot be factored.

__

1.1.3 x² +15x -54

This is a trinomial in a single variable (x), so may be factorable as the product of two binomials. The product of binomial factors will have the form ...

  (x -p)(x +q) = x² +(q-p)x -pq

This means we are looking for two factors of 54 that have a difference of 15. Here is where your familiarity with numerical factoring is helpful.

  54 = 54×1 = 27×2 = 18×3 = 9×6

Differences of the factors are 54-1=53, 25, 15, 3. The factor pair we're looking for is 18×3. Comparing that to the above form, we see that q=18 and p=3, so the factorization is ...

  = (x -3)(x +18)

__

1.1.4 6x²y -10xy +15x -25

There are no numerical or variable factors that are seen in all terms. However, we notice that pairs of terms have common factors. Factoring those out gives ...

  = (2xy)(3x -5) +5(3x -5)

At this point, we notice that (3x -5) is a factor of both of these terms, so we can factor it out. This gives the complete factorization ...

  = (2xy +5)(3x -5)

_____

Additional comment

Many methods are promoted for factoring trinomials. It is helpful to understand that the product of factors looks like ...

  (ax +b)(cx +d) = acx² +(ad+bc)x +bd

That is to say, the product of the x² coefficient and the constant term (ac·bd) will have factors (ad, bc) that have a sum equal to the linear term coefficient. Once you realize this, finding the factorization is not so difficult. You look at the factor pairs of abcd in the same way we looked at factor pairs of -54 in problem 1.1.3 above.

Answer:  Second choice

Step-by-step explanation:  Think of it as "folded on" x axis insted of "reflected on" to help visualize.