Find the value of the variable(s) in each figure. Explain your reasoning. Thank you in advance

The sum of the interior angles is 1260°

When stone hits the ground, it's height will be zero, and since we're finding the time that's required for the stone to hit the ground, we can set h = 0 and solve for t.

The time required for the stone to hit the ground[tex]v(9)=-288,a(9)=-32[/tex].

What is the equation?

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Here given that,

A stone is dropped of a [tex]1296[/tex]-ft-cliff. The height of the stone above the ground is given by the equation [tex]h=-16t^2+1296[/tex], where [tex]h[/tex] is the stone’s height in feet, and [tex]t[/tex] is the time in seconds after the stone is dropped.

So,

[tex]h=-16t^2+1296\\\\v(t)=\frac{ds}{dt}=-32t+0\\\\=-32t\\\\\\a(t)=\frac{dv}{dt}=-32[/tex]

When [tex]s(t)=0[/tex] now solve it for [tex]t[/tex] so,

[tex]-16t^2+1296=0\\\\t^2=\frac{1296}{16}\\\\t^2=81\\\\t=\sqrt{81}\\\\t=9seconds[/tex]

When [tex]t=9[/tex] so,

[tex]v(9)=-32(9)\\\\v(9)=-288[/tex]

nd

[tex]a(9)=-32[/tex]

Hence, the time required for the stone to hit the ground[tex]v(9)=-288,a(9)=-32[/tex].

To know more about the equation

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Answer:

Step-by-step explanation:

Answer:

1. No 2. No 3. Yes 4. Yes

Step-by-step explanation:

Compare the value of each digit from the leftmost digit.

Answer:

4x+8 +3x - 6 + 3x

10x + 8 - 6

10x + 2

Answer:

128/3

Step-by-step explanation:

The sequence follow the rule (1/6)*(4)^(n-1). The 5th term will be (1/6)*(4)^4=128/3

Answer:

128/3

Step-by-step explanation:

1/6, 2/3, 8/3, . . .

1/6, 4/6, 16/6

We are multiplying by 4 each time

1/6 *4 = 4/6

4/6 * 4 = 16/6

This is a geometric sequence with the common ratio of 4

an = a1 (r)^(n-1)

an = 1/6 (4) ^(n-1)

Let n = 5

a5 = 1/6 (4)^(5-1)

a5 = 1/6 (4)^4

a5 = 1/6 * 256

a5 =128/3

Answer:

Total area = [tex](54+\frac{9\sqrt{3} }{2})[/tex] square inch

Step-by-step explanation:

Total area of the prism = Area of the rectangular sides (lateral sides) + area of the triangular bases

Area of the rectangular sides = 3 × (length × width)

                                                 = 3 × (3 × 6)

                                                 = 54 square inch

Area of the triangular bases = 2 × (Area of an equilateral triangle)

                                               = 2 × [tex]\frac{\sqrt{3}}{4}(\text{Side})^2[/tex]

                                               = [tex]\frac{\sqrt{3}}{2}(\text{Side})^2[/tex]

                                               = [tex]\frac{\sqrt{3}}{2}(3)^2[/tex]

                                               = [tex]9(\frac{\sqrt{3} }{2})[/tex]

                                               = [tex]\frac{9\sqrt{3}}{2}[/tex] square inch

Total surface area = (54 + [tex]\frac{9\sqrt{3}}{2}[/tex]) square inch

Hey there!

A right pyramid with a square base just means that it isn't slanted all funny. If you create a triangle with a point on one of the edges of the base, the center of the base, and the top of the pyramid, it would be a right triangle.

To find the volume of a right pyramid, you just take the base area, multiply it by the height, and then divide by three.

However, we are looking for the height. We have been given, so we will just go backwards.

252×3=756 (multiply instead of divide)

6×6=36 (base is a square, so you just square 6. This is our base area)

756/36=21

So, the vertical height of the pyramid is 21 cubic centimeters.

Have a wonderful day! :D

Answer:

B = 25050

Step-by-step explanation:

S=n/2(2a1+(n-1)d)

Answer:

  x = s, y = t, z = -6 -s -t

Step-by-step explanation:

These are dependent equations. For some values s and t, the solution is ...

  x = s, y = t, z = -6 -s -t

Answer:

  36

Step-by-step explanation:

Each cut creates a triangular face where the corner used to be. That face adds three edges to the figure. The 8 cuts add a total of 8×3 = 24 edges to the 12 edges the prism already had.

The new figure has 12+24 = 36 edges.

Answer:

60 cm^3

Step-by-step explanation:

The equation to find the volume for a rectangular prism is length times width time height.

So just multiply 5 times 3 times 4

V=(5)(3)(4)

V=60

Answer:

60cm^3

Step-by-step explanation:

w=3cm

h=4cm

l=5cm

[V=whl]

V=3×4×5=60

Answer:

(-2,-7)

Step-by-step explanation:

because it's reflected across the x-axis, only the y-intercept will change

Answer:

(-2,-7)

Step-by-step explanation:

All you have to do is draw a graph and draw the point across the x axis in the same row and same distance from the x axis.The distance is 7 so you just change it to -7.

Answer:

Step-by-step explanation:

First lets focus on, y is no greater than 4,

y < 4

Now we focus on, more than –2,

y > -2

Combining these inequalities get us,

-2 < y < 4

Answer:

-2<y≤4

Step-by-step explanation:

Answer:

B.368

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

[tex]|R_n (x)| \leq \dfrac{|x - \dfrac{\pi}{2}|^{n+1}}{(n+1)!}[/tex]

Step-by-step explanation:

From the given question; the objective is to show that :

[tex]\lim_{n \to \infty} R_n (x) = 0[/tex] for all x in the interval of convergence f(x)=cos x, a= π/2

Assuming for the convergence f the taylor's series , f happens to be the derivative on an open interval I with a . Then the Taylor series for the convergence of f , for all x in I , if and only if  [tex]\lim_{n \to \infty} R_n (x) = 0[/tex]  

where;

[tex]\mathtt{R_n (x) = \dfrac{f^{(n+1)} (c)}{n+1!}(x-a)^{n+1}}[/tex]

is a remainder at x and c happens to be between x and a.

Given that:

a= π/2

Then; the above equation can be written as:

[tex]\mathtt{R_n (x) = \dfrac{f^{(n+1)} (c)}{n+1!}(x-\dfrac{\pi}{2})^{n+1}}[/tex]

so c now happens to be the points between π/2 and x

If we recall; we know that:

[tex]f^{(n+1)}(c) = \pm \ sin \ c \ or \ cos \ c[/tex] (as a result of the value of n)

However, it is true that for all cases that  [tex]|f ^{(n+1)} \ (c) | \leq 1[/tex]

Hence, the remainder terms is :

[tex]|R_n (x)| = | \dfrac{f^{(n+1)}(c)}{(n+1!)}(x-\dfrac{\pi}{2})^{n+1}| \leq \dfrac{|x - \dfrac{\pi}{2}|^{n+1}}{(n+1)!}[/tex]

If [tex]\lim_{n \to \infty} R_n (x) = 0[/tex]   for all x and x is fixed, Then

[tex]|R_n (x)| \leq \dfrac{|x - \dfrac{\pi}{2}|^{n+1}}{(n+1)!}[/tex]

Answer:

1.691

Step-by-step explanation:

Standard error of the mean is expressed as SEM = S/√n

S is the population standard deviation

n is the sample size (number of observation)

Given S = 27 and n = 255

SEM = 27/√255

SEM = 27/15.97

SEM = 1.691

Hence the standard error of the mean is 1.691

Answer:

3x^2+x+2

Step-by-step explanation:

Let's simplify step-by-step.

2x2+3x−1+x2−2x+3

=2x2+3x+−1+x2+−2x+3

Combine Like Terms:

=2x2+3x+−1+x2+−2x+3

=(2x2+x2)+(3x+−2x)+(−1+3)

Answer:

9: tens place

4: tenths place

Step-by-step explanation:

Answer:The probability Val will win is 1/5 or 10/50 or 2/10

Step-by-step explanation:

Answer:

A. True

Step-by-step explanation:

Stepwise regression is a variable-selection method for independent variables.

Stepwise regression  helps us to recognize and choose the most handy descriptive variables from a list of several reasonable independent variables.

It entails a series of steps that is drafted to locate the most handy X-variable to incorporate in a regression model. During each step of the course of action or method, each X - variable is estimated by applying a set criterion to determine if it is meant to exist in the model.

The basis for selection can be choosing a variable which satisfies the stipulated criterion or removing a variable that least satisfies the criterion. A typical illustration of such criterion is the t value.

Answer:  [tex]\dfrac{(x+9)^2}{225}-\dfrac{(y+7)^2}{49}=1[/tex]

Step-by-step explanation:

The equation for a horizontal ellipse is: [tex]\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1[/tex]  where

Given: major axis (diameter on x) is 30 --> x-radius (a) = 15  -->  a² = 225

           minor axis (diameter on y) is 14 --> y-radius (b) = 7   --> b² = 49

           center (h, k) is (-9, -7)

Input those values into the equation for a horizontal ellipse and simplify:

  [tex]\dfrac{(x-(-9))^2}{15^2}-\dfrac{(y-(-7))^2}{7^2}=1\\\\\\\large\boxed{\dfrac{(x+9)^2}{225}-\dfrac{(y+7)^2}{49}=1}[/tex]  

Answer:

Hello,

Answer : 1400 and 1575

Step-by-step explanation:

Let's say a and b the ywo numbers

[tex]HCF(a,b)=a\vee b=175=5^2*7\\LCM(a,b)=a\wedge b=12600\\\\a*b=(a\vee b)*(a\wedge b)=(2^3*3^2*5^2*7)*(5^2*7)=2^3*3^2*(5^2*7^2)^2\\\\Both\ numbers\ are\ greater\ than\ their HCF\\a=175*k_1\\b=175*k_2\\\\k_1=2^3\ and\ k_2=3^2\\\\a=175*2^3=1400\\b=175*3^2=1575\\\\[/tex]

Answer:

108.50

Step-by-step explanation:

First find the wages

11* 6 = 66 dollars

Then figure the commission

10% of 425

.10 * 425

42.5

Add the two amounts together

42.5+66

108.50

Answer:

[tex]f(3x)=9x^2-3[/tex]

Step-by-step explanation:

One is given the following function:

[tex]f(x)=x^2-3[/tex]

One is asked to evaluate the function for ([tex]f(3x)[/tex]). Substitute ([tex]3x[/tex]) in place of ([tex]x[/tex]) then simplify. Remember that a number raised to an exponent is the same as that number times itself the number of times that the exponent indicates. One can apply this logic here while simplifying,

[tex]f(x)=x^2-3[/tex]

[tex]f(3x)=(3x)^2-3[/tex]

[tex]f(3x)=(3x*3x)-3[/tex]

[tex]f(3x)=(9x^2)-3[/tex]

[tex]f(3x)=9x^2-3[/tex]

Answer:

16

Step-by-step explanation:

[tex]\frac{8}{2} x (2+2) = \frac{8}{2} x 4 = \frac{8 x 4}{2} = \frac{32}{2} = 16[/tex]

Answer: 16

PEMDAS

P: Parenthesis

E: Exponents

M: Multipcaction

D: Divison

A: Addition

S: Subtraction

PEMDAS can be also known as Please Excuse My Dear Aunt Sally

P: (2+2)

E: N/A (There are no exponents)

M: 4×4

D: 8÷2

A: 2+2

S: N/A (There is nothing to subtract)

How did we get 4×4? We divided 8÷2 which got us 4. Then we added 2+2 and we also got 4. Then we multiplied 4×4 which got us 16. That's how 16 is our answer.

[tex] 24 = 3 \cdot 2^3 [/tex]

[tex]96=3\cdot 2^5 [/tex]

[tex] 384=3\cdot2^7[/tex]

hence it is a geometric progression, with a multiplied constant [tex]3[/tex]

Sum of G.P. of [tex]n[/tex] terms [tex] S_n = a\dfrac{r^n-1}{r-1}\quad \text{where } r \text{ is the common ratio and } a \text{ is the first term} [/tex]

and [tex] r=-2^2=-4[/tex]

Note that the constant should be separated, so

[tex] a= -8 [\tex]

after plugging the values, you'll get the answer

[tex] -26216 \times 3 [/tex]

which option C

Answer:

C

Step-by-step explanation:

-24+96-384+...

a=-24

r=96/(-24)=-4

[tex]s_{7}=a\frac{1-r^7}{1-r} \\=-24\frac{1-(-4)^7}{1-(-4)}\\=-24\frac{1+4^7}{1+4} \\=-24\frac{1+16384}{5} \\=-24\frac{16385}{5} \\=-24 \times 3277\\=-78648[/tex]

Answer:

5x+4f-1(x)=3 this is short answer

Step-by-step explanation:

Hi, there!!!

It's so simple..

Let me clear you, alright.

Here, On the fig line, OE is just a confusing line. If you look it in simple way,

AB and CD are interested at a point O.

so, angle AOD and angle COB are equal.{ because they are vertically opposite angle}

so, angle AOD= angle COB

or, 4x°=45°+15°

or, 4x°= 60°

or, x= 60°/4

Therefore, x= 15°.

Hope it helps....

Answer:

44-d

Step-by-step explanation:

Take the total number of cookies and subtract the number eaten.  That is the number remaining

44-d