C (-1,-7), A (1,4), T (5, 1). What kind of triangle is CAT? Calculate the area and the perimeter of CAT.

Answer:

a5 = 122

Explanation:

Given:

Solve:

a1 = 2

a2 = -3a1+2 = -3(2)+2 = -4

a3 = -3a2 + 2 = -3(-4)+2 = 14

a4 = -3a3 + 2 = -3(14) + 2 = -40

a5 = -3a4 + 2 = -3(-40) + 2 = 122

Answer:

a₅ = 122

Step-by-step explanation:

What is a₅ for the sequence defined by:

[tex]\left\{\begin{array}{ccc}a_1=2\\a_n=-3a_{n-1}+2\\\end{array}\right\\\\\\\hrule[/tex]

Letting n=2:

[tex]a_n=-3a_{n-1}+2\\\\\\\\\Longrightarrow a_2=-3a_{2-1}+2\\\\\\\\\Longrightarrow a_2=-3a_{1}+2\\\\\\\\\Longrightarrow a_2=-3(2)+2\\\\\\\\\therefore a_2=-4[/tex]

Letting n=3:

[tex]a_n=-3a_{n-1}+2\\\\\\\\\Longrightarrow a_3=-3a_{3-1}+2\\\\\\\\\Longrightarrow a_3=-3a_{2}+2\\\\\\\\\Longrightarrow a_3=-3(-4)+2\\\\\\\\\therefore a_3=14[/tex]

Letting n=4:

[tex]a_n=-3a_{n-1}+2\\\\\\\\\Longrightarrow a_4=-3a_{4-1}+2\\\\\\\\\Longrightarrow a_4=-3a_{3}+2\\\\\\\\\Longrightarrow a_4=-3(14)+2\\\\\\\\\therefore a_4=-40[/tex]

Letting n=5:

[tex]a_n=-3a_{n-1}+2\\\\\\\\\Longrightarrow a_5=-3a_{5-1}+2\\\\\\\\\Longrightarrow a_5=-3a_{4}+2\\\\\\\\\Longrightarrow a_5=-3(-40)+2\\\\\\\\\therefore \boxed{\boxed{a_5=122}}[/tex]

The data recorded by Ben shows the attendance log of his classmates over a given period of time.

This refers to a simple chart that resembles a histogram that is used to represent small data.

Hence, we can see that because Ben tracked the attendance of the class over a given time period with the frequency on a frequency table, a sample of a dot plot has been provided below,

Read more about dot plots here:

https://brainly.com/question/25957672

#SPJ3

The sign of a times -b/b when a = 0 and b < 0 is neutral neither negative nor positive .

An integer is a whole number (not a fractional number) that can be positive, negative, or zero

As b<0 which means b would be negative.

So, -b/b gives a negative value.

Because if any of the either numerator or denominator is negative then the resulting value also be negative.

and if zero '0' is multiplied and number whether it is positive or negative the resulting value will be zero.

So,  a* (-b/b)= 0* negative= negative zero, but zero is neither negative nor positive .

hence, the sign of a times -b/b is neutral neither negative nor positive .

Learn more about integers here:

https://brainly.com/question/15276410

#SPJ1

The probability distribution for x will be given below.

x              0              1              2              3

P(x)        0.20       0.30        0.40        0.10

The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.

In a particular region, for families with a combined income of $80,000 or more, 20% have no children, 30% have one child, 40% have two children, and 10% have three children.

Let x be the number of children per family.

We have to construct a probability distribution for x from the given information.

x = 0, 1, 2, 3

For x = 0, the probability will be

P(x) = 20 / 100 = 0.20

For x = 1, the probability will be

P(x) = 30 / 100 = 0.30

For x = 2, the probability will be

P(x) = 40 / 100 = 0.40

For x = 2, the probability will be

P(x) = 10 / 100 = 0.10

Then the probability distribution for x will be given as

x              0              1              2              3

P(x)        0.20       0.30        0.40        0.10

More about the normal distribution link is given below.

https://brainly.com/question/12421652

#SPJ1

Answer:

Image attached below.

Step-by-step explanation:

Hello!

First let's isolate y:

This means that we are looking at all the values on the coordinate plane that are above the line y = -15.

The red shaded region is the solution region. Note that -15 is not a solution of y > -15 (the dotted line indicates that).

Answer:

y = 3/2x + 6

Step-by-step explanation:

Equation of the given line

Perpendicular

Using Point-slope equation

The volume of the rectangular prism given its base area and its height is 264 units³.

A rectangular prism is a three-dimensional object that has six faces, 12 sides and 6 vertices.

Volume = length x width x height

base area x height

44 x 6 = 264 units³

To learn more about rectangular prisms, please check: https://brainly.com/question/8890358

#SPJ1

Answer:

[tex]m <U = 80°[/tex]

Step-by-step explanation:

Before we start calculating we have to first note that the angles in a triangle always add up to 180°. Therefore in order to find the missing angle U we have to add both the angles we know, 37° and 63°, then subtract the sum from 180°

[tex]m < U = 180- (37 + 63) \\ \\ m < U = 180 - 100 \\ \\ m< U = 80[/tex]

Answer:

g(x) = a(x − h)2 + k, where a ≠ 0.

Step-by-step explanation:

The parent function of the quadratic family is f(x) = x2. A transformation of the graph of the parent function is represented by the function g(x) = a(x − h)2 + k, where a ≠ 0.

Answer:

A function means that we get one input and one output.  In this example that means for every x-value that we have, we only have one y-value.

Looking at the first option, we can see that there is no x-value that has more than one y-value which means that it is a function.

The rest of the options are seen with at least two values for one x-value in one of the points.  Therefore, they wouldn't be considered a function leaving us with only option A as the solution.

Answer:

559.01 i think that is rounded correctly

Step-by-step explanation:

so it did $615.99 - 9.25% = 559.010925

Hope This Is Good And Helped Sorry If i Did It Worng

Answer:

12 * Answer:
12 x 3 = 36 + 6 = 42,
Step-by-step explanation:

Step-by-step explanation:

Answer:

8.227 then rounded to tenth is 8.2

Step-by-step explanation:

just smart.

please rate good. have a good day.

The equation of the amount charged by Bob will be y = 7.25x.

The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.

Given that:-

The equation will be generated as follow:-

6 hours  =  $  43.50

1 hours   =  $  7.25

9 hours   =  $ 65.2575

1 hours    =  $ 7.25

Let x represent the number of hours Bob works and y represent the amount he charges. The equation will be:-

y  =  7.25x dollars.

Therefore the equation of the amount charged by Bob will be y = 7.25x.

To know more about equations follow

https://brainly.com/question/2972832

#SPJ1

Answer:

Below in bold.

Step-by-step explanation:

a) The rectangle in the middle of the net is 10 cm long.

A = 8

B = 3

C = 6

D = 10

b) Surface area

=  3*6 + 3*10 + 3*8 + 2 * 1/2 + 8 * 6

= 18 + 30 + 24 + 48

= 120 cm^2

[tex]sa = bh + ( b_{1} + b_{2} + b_{3})l[/tex]

[tex]sa = 6(8) + (6 + 8 + 3) \times 10[/tex]

[tex]sa = 48 + (17)(10)[/tex]

[tex]sa = 48 + 170[/tex]

[tex]sa = 220 \: {cm}^{2} [/tex]

Answer:

26.88

Step-by-step explanation:

20%*22.40=4.48

22.40+4.48=26.88

Answer:

15

Step-by-step explanation:

- 360 degrees in a complete circle you divide it by 24

360/24=15

Answer:

C? Not 100% sure

Step-by-step explanation:

Answer:

30° and 60°

Step-by-step explanation:

Let the interior angles be ∠x₁ (smaller) and ∠x₂ (larger), and the exterior angle ∠X.

Making the statements into equations :

Size of an exterior angle of a triangle is the supplement of smaller of two opposite interior angles ⇒ ∠X + ∠x₁ + ∠x₂ = 180° [Equation 1]

Greater of the opposite interior angles exceeds smaller by 30° :

⇒ ∠x₂ = ∠x₁ + 30° [Equation 2]

By exterior angle property :

⇒ ∠x₁ + ∠x₂ = ∠X [Equation 3]

Substituting Equation 3 in Equation 1 :

⇒ ∠x₁ + ∠x₂ + ∠x₁ + ∠x₂ = 180°

⇒ 2 (∠x₁ + ∠x₂) = 180°

⇒ ∠x₁ + ∠x₂ = 90°

⇒ ∠x₂ = 90° - ∠x₁ [Equation 4]

Substituting Equation 4 in Equation 2 :

⇒ 90° - ∠x₁ = ∠x₁ + 30°

⇒ 2∠x₁ = 60°

⇒ ∠x₁ = 30°

Substituting the value of ∠x₁ in Equation 2 :

⇒ ∠x₂ = 30° + 30°

⇒ ∠x₂ = 60°

The measures of the interior angles are 30° and 60°

Answer:

Step-by-step explanation:

4a. yes: 5 = 3(2)-1    5 = 6 - 1      5 = 5

4b.  No: 1 = 3(4) + 1

      1 = 12 + 1

       1 ≠ 13

4c. No; 1 = 3 - 3

            1 ≠ 3

4d. yes; 7 = -3(5) + 22

              7 = -15 + 22

              7 = 7

4e. no; -8 = -2(-4)

             -8 ≠ 8

4f. no; 8 = -2 + 11

           8 ≠ 9

Answer:

sin(t) = 4*sqrt(5) / 21; cos(-t) = 19/21

Step-by-step explanation:

think of a right triangle with an adjacent leg a, opposite leg b, and hypotenuse c.

cos(t) = a/c = 19/21. so we can assume a=19 and c=21.

using Pythagorean's theorem, find b: b = sqrt(21^2 - 19^2) = 4*sqrt(5) or 8.944

since tan(t)> 0, b/a > 0 and a is positive so b must be positive. using this information, we know sin(t) = b/c = 8.944/21 or 4* sqrt(5) / 21

since cos x is an even function, cos(-x) = cos x so cos(-t) = cos(t) = 19/21

Answer:

267.95 cubic meters

Explanation:

volume of sphere: (4/3)π(radius)³

Here given:

Volume:

insert values

simplify

final answer

Answer:

V = 267.95

Step-by-step explanation:

The equation to find the volume of a sphere is:

V = [tex]\frac{4}{3} \pi r^{3}[/tex]

r = radius

In the diagram of the question it shows that the radius is 4 m. Plug this into the equation:

[tex]V=\frac{4}{3} (3.14) (4)^{3}[/tex]

Use a calculator to find the answer and then round to two decimal points:

V = 267.95

Hope this helps!!

The initial value of the function is f(0) = 1 and the graph of the function has been attached.

We are given the function f(x) = (1/4)ˣ

1) Now, the initial value of the function is;

f(0) = (1/4)⁰ = 1

2) The initial value of the function which is the coordinate (0, 1) can be plotted on the attached graph and the point is where the graph crosses the y-axis.

3) f(1) = (1/4)¹ = 1/4

4) The points  (1, 1/4) and (-1, 4)

5) The horizontal asymptote will be a vertical line which will be the value of x when y = 0.

Read more about Function Graphs at; https://brainly.com/question/4025726

#SPJ1

Answer:

g(x) = f(x) - 4.

Step-by-step explanation:

4 down = -4

g(x) = f(x) - 4.

Applying the angle of intersecting secants and tangents theorem, m(KNL) is: A. 264°.

The angle of intersecting secants and tangents theorem states that the angle formed outside a circle has a measure that equals 1/2 the positive difference of the measures of the intercepted arcs.

60 = 1/2(18x - 6 - 5x - 17) [angle of intersecting secants and tangents theorem]

Solve for x

2(60) = 13x - 23

120 = 13x - 23

120 + 23 = 13x

143 = 13x

x = 143/13

x = 11

m(KNL) = (18x - 6 + 5x + 17)

m(KNL) = 23x + 11

Plug in the value of x

m(KNL) = 23(11) + 11

m(KNL) = 264° (option A)

Learn more about the angle of intersecting secants and tangents theorem on:

https://brainly.com/question/1626547

#SPJ1

Answer:

True, (-∞, ∞)      5 ≤ 11

Step-by-step explanation:

−11 ≤ −5                       Add 16 to both sides

−11 + 16 ≤ −5 + 16

5 ≤ 11

The approximate angle that the ladder makes with the ground is 37 degrees

The given question will be solved using the SOH CAH TOA identity.

The given statement will form a right triangle with the following parameters

Hypotenuse = 5m

Height(opposite) .= 3m

Determine the approximate measure of ∠θ

sin ∠θ = opp/hyp
sin ∠θ = 3/5
sin ∠θ = 0.6
∠θ = arcsin(0.6)
∠θ = 37degrees

Hence the approximate angle that the ladder makes with the ground is 37 degrees

Learn more on SOH CAH TOA here: https://brainly.com/question/20734777

#SPJ1

Answer:

Given equation:

[tex]10^{5x-2}=2^{8x-3}[/tex]

Take natural logs of both sides:

[tex]\implies \ln 10^{5x-2}= \ln 2^{8x-3}[/tex]

[tex]\textsf{Apply log Power law}: \quad \ln_ax^n=n\ln_ax[/tex]

[tex]\implies (5x-2)\ln 10=(8x-3) \ln 2[/tex]

Expand brackets:

[tex]\implies 5x\ln 10 - 2\ln 10=8x \ln 2 -3 \ln 2[/tex]

Collect like terms:

[tex]\implies 5x\ln 10 - 8x \ln 2 =2\ln 10-3 \ln 2[/tex]

Factor left sides:

[tex]\implies x(5\ln 10 - 8 \ln 2) =2\ln 10-3 \ln 2[/tex]

[tex]\textsf{Apply log Power law}: \quad \ln_ax^n=n\ln_ax[/tex]

[tex]\implies x(\ln 10^5 - \ln 2^8) =\ln 10^2- \ln 2^3[/tex]

[tex]\textsf{Apply log Quotient law}: \quad \ln_a\frac{x}{y}=\ln_ax - \ln_ay[/tex]

[tex]\implies x\left(\ln\left(\dfrac{10^5}{2^8}\right)\right) =\ln\left(\dfrac{10^2}{2^3}\right)[/tex]

Simplify:

[tex]\implies x\left(\ln\left(\dfrac{3125}{8}\right)\right) =\ln\left(\dfrac{25}{2}\right)[/tex]

[tex]\implies x=\dfrac{\ln\left(\dfrac{25}{2}\right)}{\ln\left(\dfrac{3125}{8}\right)}[/tex]

[tex]\implies x=0.4232297737...[/tex]