Find the area of the triangle below.
Be sure to include the correct unit in your answer.

Complete question is:An orange is shot up into the air with a catapult. The function h given by h(t) = 15 + 60t - 16t² models the orange’s height, in feet, t seconds after it was launched.

Select all the true statements about the situation.

Options:

1. The domain of function h only contains values greater than or equal to 0.

2. The orange is at the same height 1 second after launch and 2 seconds after launch.

3. After 3 seconds, the orange has hit the ground.

4. The orange is 15 feet above the ground when it is launched.

5. The value t = 10 does not belong to the domain of h.

Answer:

Option 1 - True

Option 2 - False

Option 3 - False

Option 4 - True

Option 5 - True

Step-by-step explanation:

Looking at the options,

-The domain is the x or t value and it is time. Now, time can only be positive or greater than or equal to zero i.e. t ≥ 0. Thus, option 1 is true.

- At t = 1 second;

h = 15 + 60(1) - 16(1)²

h = 15 + 60 - 16 = 59 ft

Also, at t = 2 seconds;

h = 15 + 60(2) - 16(2)²

h = 15 + 120 - 64 = 71 ft

So,value of h is not the same at t = 1 and t = 2. Thus, option 2 is not true.

- The orange will hit the ground when h(t) = 0.

However, at t = 3;

h(t) = 15 + 60(3) - 16(3)²

h(t) = 51 ft

h(t) is not equal to zero at t = 3, so option 3 is false

- when the orange is launched it is at time t = 0.

Thus,

h(0) = 15 + 60(0) - 16(0)²

h(0) = 15 ft

So option 4 is true.

- At t=10, h(t) = 15 + 60(10) - 16(10)²

h(10) = -985

This means the orange would be below ground level and thus doesn't belong to the domain of h, so option 5 is true.

Answer:

1 true 4 true and 5 true the rest are false

Step-by-step explanation:

Answer:

a=  initial amount

r= rate of growth/decay

t= time

Step-by-step explanation:

Answer:

y = 1/3X - 6

Step-by-step explanation:

Answer:

The order from top is

8 - 3

1 - 35

3 - 50

7 - 3/5

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

Step-by-step explanation:

c=36+g

c:g:s=5:2:1

The ratio gives us two equations so that's three equations in three unknowns.  Actually we're after the total t; let's put that in to solve for directly.

c:g:s:t = 5 : 2 : 1 : 5+2+1

We turn the ratio to fraction equations.  s has the one; let's write everything in terms of s.

c/s = 5/1,  g/s = 2/1, t/s = 8/1

Clearing the fractions,

c = 5s, g = 2s, t = 8s

Our other equation is

c = 36 + g

Substituting in for c and g,

5s = 36 + 2s

Solving,

3s = 36

s = 12

That's right; let's just get the total t.

t = 8s = 72

Answer: 72

Answer: There are 10 two points and 16 five points questions.

Step-by-step explanation:

This is the detailed question:

A language arts test is worth 100 points. There are a total of 26 questions. There are spelling word questions that are worth 2 points each and vocabulary word questions worth 5 points each. How many of each type of question is there?

Let y = the number of 2 points questions

Let z = the number of 5 points questions

y + z = 26 ......... i

2y + 5z = 100 ........ ii

Multiply equation i by 2

Multiply equation ii by 1

2y + 2z = 52 ......... iii

2y + 5z = 100 ....... iv

Subtract iv from iii

-3z = -48

z = 48/3

z = 16

Since y + z = 26

y = 26 - 16

y = 10

y = 10 two points questions

z = 16 five points questions

There are 10 two points and 16 five points questions.

We have been given that in ΔRST, s = 93 inches, ∠S=123° and ∠T=28°. We are asked to find the length of r to the nearest 10th of an inch.

We will use law of sines to solve for side r.

[tex]\frac{a}{\text{Sin}(a)}=\frac{b}{\text{Sin}(B)}=\frac{c}{\text{Sin}(C)}[/tex], where a, b and c are corresponding sides to angles A, B and C respectively.

Let us find measure of angle S using angle sum property of triangles.

[tex]\angle R+\angle S+\angle T=180^{\circ}[/tex]

[tex]\angle R+123^{\circ}+28^{\circ}=180^{\circ}[/tex]

[tex]\angle R+151^{\circ}=180^{\circ}[/tex]

[tex]\angle R+151^{\circ}-151^{\circ}=180^{\circ}-151^{\circ}[/tex]

[tex]\angle R=29^{\circ}[/tex]

[tex]\frac{r}{\text{sin}(R)}=\frac{s}{\text{sin}(S)}[/tex]

[tex]\frac{r}{\text{sin}(29^{\circ})}=\frac{93}{\text{sin}(123^{\circ})}[/tex]

[tex]\frac{r}{\text{sin}(29^{\circ})}\cdot \text{sin}(29^{\circ})=\frac{93}{\text{sin}(123^{\circ})}\cdot \text{sin}(29^{\circ})[/tex]

[tex]r=\frac{93}{0.838670567945}\cdot (0.484809620246)[/tex]

[tex]r=110.889786233799179\cdot (0.484809620246)[/tex]

[tex]r=53.7604351[/tex]

Upon rounding to nearest tenth, we will get:

[tex]r\approx 53.8[/tex]

Therefore, the length of r is approximately 53.8 inches.

Answer:

580 cm^2

Step-by-step explanation:

H = Height

L = length

W = width

2(HL)+2(WH)+2(WL)

= 2(20*10)+2(3*20)+2(3*10)

= 2(200)+2(60)+2(30)

= 400+120+60

= 580

Answer:

D. Tossing a coin 50 times and recording the number of times it lands on heads

Step-by-step explanation:

It is best to analyze each option and see if it meets the conditions of a binomial experiment or not, the most important thing is that the binomial distribution can be used when the results of each experiment / trace in the process are yes / no or success / failure .

A. Drawing one marble from a bag containing 12 red and 8 blue marbles (replacing after each draw) until you have drawn 5 blue marbles

Does not meet the conditions, although there are two options, The tests are not independent of each other. The result of one test does affect the results of subsequent tests. because there is a replacement.

B.  Asking 25 students how tall they are and recording their answers

There are not two options

C.  Rolling a single number cube until you get a 5

There are not two options

D.   Tossing a coin 50 times and recording the number of times it lands on heads

Yes there are two options and they are events are independent of each other, therefore it is the correct answer.

Answer:

D. Tossing a coin 50 times and recording the number of times it lands on heads

Step-by-step explanation:

A P 3 X

Answer: 3 feet by 10 feet rectangle

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

Explanation:

Assuming this garden is a rectangle, it has dimensions L and W which are the length and width respectively.

perimeter of rectangle = 2*(length+width)

P = 2*(L+W)

26 = 2(L+W) ... plug in given perimeter

26/2 = L+W .... divide both sides by 2

13 = L+W

13-W = L  .... isolate L by subtracting W from both sides

L = 13-W

------

Area of rectangle = Length*Width

A = L*W

A = (13-W)W .... replace L with 13-W

A = W(13-W)

A = 13W - W^2 ..... distribution

30 = 13W - W^2 .... plug in given area A = 30

W^2 - 13W + 30 = 0 ... get everything to one side

(W - 10)(W - 3) = 0 ...... factor

W-10 = 0 or W-3 = 0 ...... zero product property

W = 10 or W = 3

----------

If the width is W = 10, then

L = 13-W

L = 13-10

L = 3 is the length

Or if the width is W = 3, then

L = 13-W

L = 13-3

L = 10 is the length

Either way, this is a 3 ft by 10 ft rectangle

--------

Check:

Area = length*width = 10*3 = 30 square feet

perimeter = 2(length+width) = 2*(10+3) = 2*13 = 26 feet

or you could say

perimeter = L+W+L+W = 10+3+10+3 = 13+13 = 26 feet

we get the correct area and perimeter, so this confirms our answer.

Answer: 15 Gray or white Marbels!

Step-by-step explanation:

Answer:

x=9

Step-by-step explanation:

If two chords intersect in a circle, the product of the lengths of the segments of one chord equal the product of the segments of the other.

x* (x+1) = 10*9

Distribute

x^2 +x = 90

Subtract 90 from each side

x^2 +x-90 =0

Factor

(x-9)(x+10) =0

Using the zero product property

x-9=0  x+10=0

x=9  x=-10

Since we cannot have a negative length

x=9

The circle is made up of 2 lines, this means that they will equal each other.

x(x + 1) = 10 * 9

~Simplify

x² + x = 90

~Subtract 90 to both sides

x² + x - 90 = 90 - 90

~Simplify

x² + x - 90 = 0

~Factor out

(x - 9)(x + 10) = 0

~Set both factors to equal 0

x - 9 = 0

x + 10 = 0

~Solve for x in [ x - 9 = 0 ]

x - 9 + 9 = 0 + 9

x = 9

~Solve for x in [ x + 10 = 0 ]

x + 10 - 10 = 10 - 10

x = -10

Since -10 is negative, we can't use it.

Therefore, x = 9

Best of Luck!

Answer:

The slope-intercept is [tex]y = 2x -2[/tex] .

Step-by-step explanation:

-First, you need to find the slope by using the slope formula:

[tex]m =\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

-Second, use both points (6, 10) and (1, 0) for the formula:

[tex]m =\frac{0-10}{1-6}[/tex]

-Third, you solve:

[tex]m =\frac{0-10}{1-6}[/tex]

[tex]m = 2[/tex]

-Fourth, after you found the slope, you need to use the Point-slope form equation:

[tex]y - y_{1} = m (x -x_{1})[/tex]  (where [tex]m[/tex] represents the slope, and [tex](x_{1},y_{1})[/tex] represents the first coordinate or the first point).

-Fifth, use the slope 2 and the first point (6, 10) for the Point-slope form equation:

[tex]y - 10= 2 (x -6)[/tex]

-Sixth, you solve the equation to get the slope-intercept form:

[tex]y - 10= 2 (x -6)[/tex]

[tex]y -10 = 2x -12[/tex]

[tex]y -10 +10 = 2x -12 +10[/tex]

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

So, therefore, the slope-intercept is [tex]y = 2x -2[/tex] .

Answer:I think it’s a

Step-by-step explanation:

Answer:

2π|b| 2 π | b

Step-by-step explanation:

Answer: option C.

Step-by-step explanation:

If city X is in the point (0,0)

Now, we can use that a displacement of L in distance with an angle A, gives us that the components of the displacement are:

X = L*cos(A)

Y = L*sin(A)

So we know that the city Y is located in:

(40m*cos(40°), 40m*sin(40°))

Now, from this point he moves other 40m with an angle of 140°.

The new position is

(40m*cos(40°) + 40m*cos(140°), 40m*sin(40°) + 40m*sin(140°))

this is:

40m*(cos(40°) + cos(140°), sin(40°) + sin(140°)) = 40m*( 0, 1.28)

the new position is (0, 51.2m)

This means that for a new displacement L and angle A we have:

X = L*cos(A) = 0

Y = L*sin(A) = 51.2m

Cos(A) is only 0 when A = 90° or 270°,

and we know that sin(90°) = 1 and sin(270°) = -1

As we have a positive number in the Y equation, we can conclude that A must be 90°.

Then

Y = L*sin(90°) = L = 51.2m

Here we finded that the bearing of Z from city X is 90°

Answer:

13p

Step-by-step explanation:

because the P it have 1 hidden there

12p + 1p = 13p

Answer:

okay so u have a graph

u go to the center 0,0

u go up 2 places

then up 3 ove to the left 5

the repeat that step

u get it

Step-by-step explanation:

The formula to calculate the area of a trapezoid is as follow:

4 * (8 + 16) * 1/2

Answer:

trapezoid area :(a+b)/2 ×h

(16+ 8)/2 ×4

=48

Answer: it's around 40

Step-by-step explanation:

Answer:

x=2

Step-by-step explanation:

2x = 4  and your multiplying 2 times x so x would have to be equal to 2 time blank which equals 4

Hope it helps!

Answer:

120

Step-by-step explanation:

You need to move the triangle (on the right) to the left side so you can make a rectangle. Then, you do bxh and get 120

The area of a given parallelogram is 120m^2.

We have given parallelogram,

A=bh

Where b is the base and

h is the height.

In the given figure we have b=15m and h=8m.

A=15(8)

A=120m^2

The area of a given parallelogram is 120m^2.

To learn more about the area of the parallelogram visit:

https://brainly.com/question/970600

#SPJ2

Answer:

infinitely many solutions

Step-by-step explanation:

Reduce the second equation by dividing all three terms by 3:  y + 1 = 2x.  Then compare this result to the first equation 2x - y = 1.  Noe that these two equations are identical.  Thus, the two lines coincide.  There are "infinitely many solutions."

Answer:

20

Step-by-step explanation:

u have to look at the 9 after the decimal and if it is 5 or above then it goes up

Answer:

20

Step-by-step explanation:

the 9 would move the 19 up to a 20. Hope that this helps you and have a great day :)

Answer:

h ≈ 2.64ft

Step-by-step explanation:

A = 2πrh + 2πr2

h= A /2πr﹣r = 240 /2·π·5﹣5 ≈ 2.63944ft

Kono Dio Da!!

Answer:

Step-by-step explanation:First you apply the distributive property to create equivalent expressions, then you use algebra tiles to write equivalent expressions, and finally you verify that two different values of the variable yield the same value for each expressions, then the expressions are equivalent .

Answer:

$5,368,709.12

Step-by-step explanation:

Kono Dio Da!!

Answer:

5368709.12

Step-by-step explanation:

i just did this earlier