What is the volume of the triangular prism below?
20 ft
18 ft
15 ft
СА
B
1, 280 ft
1, 320 ft
2, 700 ft
5, 400 ft
OD

Answer:

[tex]a^3 + 1 = 0[/tex]

Step-by-step explanation:

We start with the equation:

[tex]a + \frac{1}{a} = 1[/tex]

We want to find the value of:

[tex]a^3 + 1 =[/tex]

We can start with our previous equation and multiply both sides by a:

[tex](a + \frac{1}{a})*a = 1*a\\a^2 + 1 = a[/tex]

Now we can rewrite our initial expression as:

[tex]a = 1 - \frac{1}{a}[/tex]

Replacing that in the right side, we get:

[tex]a^2 + 1 = a = 1 - \frac{1}{a}[/tex]

Now again, let's multiply both sides by a

[tex]a*(a^2 + 1) = a*(1 - \frac{1}{a} )\\a^3 + a = a - a/a\\a^3 + a = a - 1\\a^3 = -1\\a^3 + 1 = 0[/tex]

So we can conclude that:

[tex]a^3 + 1 = 0[/tex]

Answer:

Step-by-step explanation:

the square of x-5 given by

[tex] \displaystyle (x - 5) ^{2} [/tex]

use (a-b)²=a²-2ab+b² to simplify so we obtain:

[tex] \displaystyle {x}^{2} - 10x + 25[/tex]

hence

our answer is 2)

to find:

[tex]f(x) - g(x)[/tex]

substitute the value of f(x) and g(x):

[tex] \rm \displaystyle{6x}^{2} + 8x - 5 - ( {2x}^{2} - 4x + 4)[/tex]

remove parentheses and change its sign:

[tex] \rm \displaystyle{6x}^{2} + 8x - 5 - {2x}^{2} + 4x - 4[/tex]

combine like terms:

[tex] \rm \displaystyle{6x}^{2} + 12x - 5 - {2x}^{2} - 4[/tex]

collect like terms:

[tex] \rm \displaystyle{4x}^{2} + 12x -9[/tex]

hence,

our answer is 3)

given Polynomial:

[tex] \displaystyle {5x}^{3} + 2 {x}^{2} + 7[/tex]

substitute the value of x:

[tex] \displaystyle {5.(10}^{3}) + 2 ({10}^{2}) + 7[/tex]

simplify squares:

[tex] \displaystyle 5(1000) + 2 (100) + 7[/tex]

simplify multiplication:

[tex] \displaystyle 5000 + 2 00 + 7[/tex]

simplify addition:

[tex] \displaystyle 5207 [/tex]

hence our answer is 1)

given:

notice that,

every time there's a GCF of 4x²y

hence our answer is 4)

Answer:

[tex]81[/tex]

Step-by-step explanation:

The average of a set of [tex]n[/tex] values is equal to the sum of the values in that set divided by [tex]n[/tex].

Therefore, the average of your 5 scores is equal to [tex]\frac{73+86+91+88+67}{5}=\boxed{81}[/tex]. Since evidently your grade is represented by the average of all your scores, your new grade is 81.

Answer:

[tex]9^{3/2}-3\times 5^0-(\dfrac{1}{81})^{-1/2}=15[/tex]

Step-by-step explanation:

The given expression is :

[tex]9^{3/2}-3\times 5^0-(\dfrac{1}{81})^{-1/2}=15[/tex]

We need to prove that LHS is equal to RHS.

Taking LHS,

[tex]=9^{3/2}-3\times 5^0-(\dfrac{1}{81})^{-1/2}[/tex]

[tex]=(3)^{2\times\dfrac{3}{2}}-3-(\dfrac{1}{9})^{2\times \dfrac{-1}{2}}\\\\=27-3-9\\\\=15\\\\=RHS[/tex]

Hence, LHS = RHS.

Answer:

Step-by-step explanation:

Answer:

12.75

Step-by-step explanation:

c = π x d

40.035= 3.14 x d

40.035/3.14 = 12.75

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Answer:

x + y = 60

Step-by-step explanation:

[tex]2x + 2y + 60 = 180 \\ 2x + 2y = 180 - 60 \\ 2x + 2y = 120 \\ \frac{2x + 2y}{2} = \frac{120}{2} \\ x + y = 60 \\ [/tex]

Answer:

A   y ≥ (1/2)x + 5

Step-by-step explanation:

The shaded area is above the solid line

the correct symbol is ≥

Answer:

165 cm

Step-by-step explanation:

We solve using the rule

Shadow of ruler/Length of ruler = Shadow of the girl /Length of the girl

Shadow of ruler = 20cm

Length of ruler = 30cm

Shadow of the girl = 110cm

Length of the girl = x

Hence:

20/30 = 110/x

Cross Multiply

20x = 30 × 110

x = 30 × 110/20

x = 165 cm

Therefore, Sierra(the girl) is 165cm tall

Answer:

It would be 9π

Step-by-step explanation:

(x-1)²π

(x-1)(2x-4)

Answer:

(a+b)/2(a-b)

Step-by-step explanation:

Explained in the paper

Goodluck

Answer:

366

Step-by-step explanation:

A garden table and bench cost 816 when combined together

The garden table cost 84 less than the bench

Therefore the price of the bench can be calculated as follows

x + (x+84)= 816

2x+84= 816

2x= 816-84

2x= 732

Divide both sides by 2

x= 732/2

= 366

Hence the price of the bench is 366

Answer:

x=-20

Step-by-step explanation:

x=-10•2

• means multipled

Answer:

[tex]\displaystyle y=-\frac{1}{6}x-\frac{1}{2}[/tex]

Step-by-step explanation:

We want to write the equation of a line that passes through the point (3, -1) and is perpendicular to the line:

[tex]y=6x-4[/tex]

Remember that the slopes of perpendicular lines are negative reciprocals of each other.

The slope of the given equation is 6.

So, the slope of our perpendicular line is the negative reciprocal of 6, which is -1/6.

Next, we are given that it passes through the point (3, -1). Since we are given a point and know the slope, we can use the point-slope form. Point-slope form is given by:

[tex]y-y_1=m(x-x_1)[/tex]

Where m is the slope and (x₁, y₁) is a point.

We will substitute -1/6 for m and (3, -1) for (x₁, y₁). Hence:

[tex]\displaystyle y-(-1)=-\frac{1}{6}(x-(3))[/tex]

Simplify:

[tex]\displaystyle y+1=-\frac{1}{6}(x-3)[/tex]

Our answer is valid as it as, but we can simplify this into slope-intercept form. Distribute:

[tex]\displaystyle y+1=-\frac{1}{6}x+\frac{1}{2}[/tex]

And subtract one from both sides. Therefore, our equation is:

[tex]\displaystyle y=-\frac{1}{6}x-\frac{1}{2}[/tex]

Answer:

this two graph is not same because they have different slopes for this they are not same

Answer:

2×2-3×-5=0

Step-by-step explanation:

(2×2-3×)- 5=0

Answer:

x = 2

Step-by-step explanation:

In a vertical line, all x-coordinates are the same.

x = 2

Answer:

x =2

Step-by-step explanation:

A vertical line means the x value remains constant

The x value is 2

x =2

Answer:

91.7%

hope I helped

Answer:

f(0) = g(0)

Step-by-step explanation:

The functions intersect at x =0, which means they have the same y value at x=0

f(0) = g(0)

Answer:

8x.

Step-by-step explanation:

coordinates: (3,10) (5,26)

use slope formula (y2 - y1/x2-x1)

26-10/5-3

16/2

= 8

Answer:Its  the last one to the left up

Step-by-step explanation:

Answer:

78.5 square feet

option b

Step-by-step explanation:

area = pi*r^2

a = 3.14*5^2

a = 3.14*25

a = 78.5

Answer:

Angle F

Step-by-step explanation:

=====================================================

Explanation:

We see that angle A = angle E as shown by the arc marking. The tickmark says that side AB is the same length as side EF.

In the letter sequences "AB" and "EF", erase the first letters A and E to be left with B and F. This is one way to show how angle B pairs with angle F, and that is enough to show the two angles are congruent.

Answer:

2, 5, 6

Step-by-step explanation:

The volume of a rectangular prism is given by [tex]V=l\cdot w\cdot h[/tex], where all variables to the right are dimensions of the prism.

Therefore, we're looking for three numbers that multiply to be 60.

Since the question stipulates that no side length may be 10, we have:

[tex]2\cdot 5\cdot 6=60[/tex]

Answer:

Step-by-step explanation:

sin A = [tex]\frac{opposite side}{Hypotenuse}[/tex]

Sin 29 = [tex]\frac{y}{500}[/tex]

0.4848 * 500 = y

y = 242.4 ft

Answer:

Y=242.4

Step-by-step explanation:

due to the association property the angle at the bottom left is 29 degrees

since sine property is oposite over hypothesis we get

sine(29)=y/500

500sin(29)=y

Y=242.4

Answer: Hi the Range is 4

Step-by-step explanation: The range of a data set in statistics is the difference between the largest and the smallest values. While range does have different meanings within different areas of statistics and mathematics, this is its most basic definition, and is what is used by the provided calculator. Using the same example:

18, 16, 19, 15, 17

19,18,17,16,15

19-15= 4

Answer:

1/6

Step-by-step explanation:

A dies has six sides

1,2,3,4,5,6

There is 1 three

P(3) = number of threes/ total numbers

      = 1 / 6