g(t) = (t 1)2 = 20.25
1) What are the zeros of the function?
Write the smaller t first, and the larger t second.

Answer:

a) SPAZ is equilateral.

b) Diagonals SA and PZ are perpendicular to each other.

c) Diagonals SA and PZ bisect each other.

Step-by-step explanation:

At first we form the triangle with the help of a graphing tool and whose result is attached below. It seems to be a paralellogram.

a) If figure is equilateral, then SP = PA = AZ = ZS:

[tex]SP = \sqrt{[4-(-4)]^{2}+[(-2)-(-4)]^{2}}[/tex]

[tex]SP \approx 8.246[/tex]

[tex]PA = \sqrt{(6-4)^{2}+[6-(-2)]^{2}}[/tex]

[tex]PA \approx 8.246[/tex]

[tex]AZ =\sqrt{(-2-6)^{2}+(4-6)^{2}}[/tex]

[tex]AZ \approx 8.246[/tex]

[tex]ZS = \sqrt{[-4-(-2)]^{2}+(-4-4)^{2}}[/tex]

[tex]ZS \approx 8.246[/tex]

Therefore, SPAZ is equilateral.

b) We use the slope formula to determine the inclination of diagonals SA and PZ:

[tex]m_{SA} = \frac{6-(-4)}{6-(-4)}[/tex]

[tex]m_{SA} = 1[/tex]

[tex]m_{PZ} = \frac{4-(-2)}{-2-4}[/tex]

[tex]m_{PZ} = -1[/tex]

Since [tex]m_{SA}\cdot m_{PZ} = -1[/tex], diagonals SA and PZ are perpendicular to each other.

c) The diagonals bisect each other if and only if both have the same midpoint. Now we proceed to determine the midpoints of each diagonal:

[tex]M_{SA} = \frac{1}{2}\cdot S(x,y) + \frac{1}{2}\cdot A(x,y)[/tex]

[tex]M_{SA} = \frac{1}{2}\cdot (-4,-4)+\frac{1}{2}\cdot (6,6)[/tex]

[tex]M_{SA} = (-2,-2)+(3,3)[/tex]

[tex]M_{SA} = (1,1)[/tex]

[tex]M_{PZ} = \frac{1}{2}\cdot P(x,y) + \frac{1}{2}\cdot Z(x,y)[/tex]

[tex]M_{PZ} = \frac{1}{2}\cdot (4,-2)+\frac{1}{2}\cdot (-2,4)[/tex]

[tex]M_{PZ} = (2,-1)+(-1,2)[/tex]

[tex]M_{PZ} = (1,1)[/tex]

Then, the diagonals SA and PZ bisect each other.

Step-by-step explanation:

Use the compound interest formula:

A = P( 1 + r/n)^nt

A is the amount at the end

P is the principal or original amount.

R is annual rate as a decimal (you have to convert)

N is the # of compounding periods in a year (quarterly means 4)

T is time in years

A = 500( 1 + 0.0475/4)^(4×20)

This would be $1285.64 when fully computed.

Answer:

We are given

We are also given  and , which allows us to rewrite the equation as

(I substituted every "b" with "a" and every "c" with "9").

The solutions to this quadratic equation are -25 and 7. We discard -25 because a side with negative length would make no sense.

The required measure of side a of the rectangular prism is a = 9.3 meters.

The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.

Here,
SA = 2ab + 2bc + 2ac
434 = 2a² + 14a + 14a
434 = 2a² + 28a
2a² + 28a - 434 = 0
a² + 14a - 217 = 0
a² + 14a + 49 - 49 - 217 = 0
(a + 7)² = 266
a = 9.3 or a = -23.3

Since the negative measure of length can be neglected.
a = 9.3 = b

Thus, the required measure of side a of the rectangular prism is a = 9.3 meters.

Learn more about the surface area here: https://brainly.com/question/2835293

#SPJ5

Answer: 20.77%

Step-by-step explanation:

There are 52 cards in a standard deck. Out of these cards, there are 12 face cards. Thus, the probability of drawing a face is 12/52.

On a 20-sided dice, there are 20 options of numbers to roll. Out of these 20 numbers, 18 of the numbers are greater than or equal to 3, making the probability 18/20, or 9/10.

To find the probability of two events, you need to multiply the probabilities together. Thus, you need to multiply 12/52 by 9/10.

(12/52) * (9/10) = 27/130

27/130 is about equal to 0.2077, or a 20.77% probability.

Answer:

x=5

Step-by-step explanation:

substitute y to the first expression

4x-5(x-6)=25

4x-5x+30=25

-x=25-30

-x=-5

times left and right hand side with minus youll get

x=5

Answer:

m = 1

Step-by-step explanation:

We can use the x & y intercepts.

Rise = 2

Run = 2

m = Rise/Run = 2/2 = 1

Answer:

Q

Step-by-step explanation:

X has constant value

x'-x = 0

m =(y'-y)/(x'-x)  --> undefined

Answer:

R

Step-by-step explanation:

A vertical line has a slope that is "undefined". Line R is the vertical line on your graph

___________

The slope of a vertical line is "undefined" because of the way slope is defined. Slope is the vertical change divided by the horizontal change. When the line is vertical, there is no horizontal change, so the computation of slope involves division by zero. The result of division by zero is "undefined."

answer:

- 3   3/5

7/5-5/1 = 18/5

18/5 = - 3  3/5

Answer:

B.56

Step-by-step explanation:

Answer:

Step-by-step explanation:

I know because I just did it on an assignement and it said these were the right answers.

In this exercise we have to use knowledge of direction and congruent lines to identify which objects have these characteristics, so we can say that:

Rectangular Prism

Cube

Cylinder

Triangular pyramid

First we have to remember the definition of congruent lines, such as:

From this we can now identify these figures as:

See more about congruent at brainly.com/question/24887947

Answer:

A general line is written as:

y = a*x + b

where:

a is the slope

b is the y-intercept.

a) y-intercept = 2 and slope = 7.

This line is:

y = 7*x + 2

b) y-intercept =  -1 and is parallel to y= 5x - 7.

Now, if two linear equations are parallel if they have the same slope and different y-intercept. Then if we want a line parallel to  y= 5x - 7, this means that the slope of this line must also be equal to 5.

y = 5*x + (-1)

c) y-intercept 2 and is inclined at 45° to the x- axis. ​

When we have an inclination of A degrees from the x-axis, the slope of the equation is given by: a = Tan(A)

In this case, we have A = 45°

Then the slope is a = Tan(45°) =  1

Then the equation of this line is:

y = 1*x + 2

Answer:

2

Step-by-step explanation:

2

Answer:

28 gallons.

Step-by-step explanation:

1/5 is 20% of the container's full capatcity.

7/10 is 70% of the container's full capatcity.

20% - 70% = 50%

By adding 14 gallons of water, the container's water went up by 50%.

If we multiply 14 by 2, we will know what the container can hold at 100% capatcity.

14 x 2 = 28

9514 1404 393

Answer:

  ∠16 = 47°

Step-by-step explanation:

Vertical and corresponding angles are congruent. The remainder are supplementary to those.

∠1≅∠4≅∠5≅∠7≅∠10≅∠12≅∠13≅∠15 = 133°

∠2≅∠3≅∠6≅∠8≅∠9≅∠11≅∠14≅∠16 = 47°

Answer:

its the second one

Step-by-step explanation:

it's the only one where the x number dosent repeat

Answer:

abcdefghijklmnopqrstuvwxyz

Answer:

0A and C

Step-by-step explanation:

Please mark me brainlist

Answer:

[tex]\boxed {\boxed {\sf About \ 28.36 \ meters }}[/tex]

Step-by-step explanation:

Assuming the tree is perpendicular to the ground, we can use the right triangle trigonometric ratios to find the tree's height.

Now, let's draw a diagram. We know Aiko is 5 meters from the base of the tree. From there, the angle to the top of the tree is 80 degrees. We are looking for x, the tree's height. The diagram attached is not to scale.

We base the sides off of the angle. x is opposite of 80 degrees and 5 is adjacent. Therefore we must use tangent.

[tex]tan(\Theta)=\frac{opposite}{adjacent}[/tex]

Substitute in the known variables.

[tex]tan(80)=\frac{x}{5 \ m }[/tex]

We want to find x, the height of the tree. Therefore we need to isolate that variable.

x is being divided and the inverse operation is multiplication. Multiply both sides of the equation by 5 meters.

[tex]5 \ m* tan(80)=\frac{x}{5 \ m }* 5 \ m[/tex]

[tex]5 \ m* tan(80)=x[/tex]

[tex]5 \ m *5.67128182=x[/tex]

[tex]28.3564091 \ m = x[/tex]

The question asks for an approximation, so let's round to the nearest hundredth.

The 6 in the thousandth place tells us to round the 5 to a 6.

[tex]28.36 \ m \approx x[/tex]

The tree is about 28.36 meters tall.

Answer:

down below

Step-by-step explanation:

k) 1 and 22/48

l)124/26

m)68/20

n)2 and 5/10

o)2 and 18/19

please give me brainliest!!!<3

Answer:

Step-by-step explanation:

Do you mind telling me what grade you are in? Oh and can you take a better picture?

Answer:

4 dollars a pound

Step-by-step explanation:

4x 10 = 40

Answer:

I think it's D:)

Step-by-step explanation:

Answer:

£36

Step-by-step explanation:

3kg = 54

÷ 3

1kg = 18

18 × 2 = 36

hope this helps...

9514 1404 393

Answer:

  a6 = -196,608

Step-by-step explanation:

The general term of a geometric sequence with first term a1 and common ratio r is given by ...

  an = a1·r^(n-1)

For a1 = 6, r = -8, and n = 6, we find the 6th term to be ...

  a6 = 6·(-8)^(6-1)

  a6 = -196,608

Answer:10000

Step-by-step explanation:

Remember that log x and 10^x are inverse functions.

If you have log x = 4 and want the value of x, write this out:

log x 4

10 = 10

This simplifies to:

x = 10^4, and so the fourth answer choice is the correct one.

Answer:

1

Step-by-step explanation: