Find the area of this triangle.
8 m
14 m
A = [?] m2

Answer:

-40

Step-by-step explanation:

[tex] \sqrt{5} \times - 4 \sqrt{20} [/tex]

Multiplication is commutative.

[tex] - 4 \sqrt{20} \times \sqrt{5} [/tex]

Apply Profuct Rule

[tex] - 4 \sqrt{100} [/tex]

Simplify sqr root of 100

[tex] - 4 \times 10 = - 40[/tex]

Hi ;-)

√5 · (-4√20) = -4√(5 · 20) =

= -4√100 = -4 · 10 = -40

The simplified expression for the perimeter of the rectangle is 16x - 4. The perimeter of a rectangle is given by the formula: P = 2 * (length + width).In this case, the length of the rectangle is given as 7x + 1, and the width is given as x - 3.

So, the perimeter can be expressed as: P = 2 * (7x + 1 + x - 3)

Now, let's simplify this expression: P = 2 * (8x - 2)

P = 16x - 4

Therefore, the simplified expression for the perimeter of the rectangle is 16x - 4.

A rectangle is a type of quadrilateral with specific properties that distinguish it from other shapes. Here are some key properties of a rectangle:

Opposite Sides are Equal in Length: In a rectangle, the opposite sides are always equal in length. This means that the length of one pair of parallel sides is the same as the length of the other pair.

Opposite Angles are Equal: The opposite angles in a rectangle are equal in measure. This property makes all angles in a rectangle right angles (90 degrees).

Consecutive Angles are Supplementary: Consecutive angles in a rectangle are supplementary, meaning that the sum of any two consecutive angles is 180 degrees. This property is a consequence of the fact that opposite angles are equal, making each pair of consecutive angles form a linear pair.

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Answer:

A) y=-7

Step-by-step explanation:

we talking about the better pond right?

Answer:

(0.5, -1)

Step-by-step explanation:

Answer:

600

Step-by-step explanation:

if SP>CP,  

It is profit [SP - CP = Profit]

if CP>SP,  

It is loss  [CP - SP = Loss]

Here in the question CP>SP so,  

loss = CP - SP  

      =2500 - 1900  

      = 600

Answer:

24

Step-by-step explanation:

C.P=2500

S.P=1900

Here,

Cp>Sp

So,

Loss= cp-sp

---------- ×100%

cp

=2500-1900

----------------- ×100%

2500

= 600

------- ×100 %

2500

= 24.

Answer:

i would say true

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

a. solution

Area = 50 m^2

Area of square = l^2

or, 50 m^2 = l^2

or, √50m^2 = l

or, 5√2 m= l

Hence, The exact length of the playground is 5√2 m.

Answer:

$127.875

Step-by-step explanation:

cost of 3 pizzas= $15*3

cost of 3 pizzas=$45

cost of 15 drinks=$1.50*15

cost of 15 drinks=$22.5

cost of 6 nachos=$5.80*6

cost of 6 nachos=$34.8

Total cost = pizza cost+ drinks+nachos

total cost=$45+$22.5+$34.8

total cost=$102.3

Now ,

Tip cost=$102.3*20%

=$20.46

tex cost=$102.3*5%

=$5.115

Bill which all friends pay=total cost+ tip cost+tex cost

= $102.3+$20.46+$5.115

=$127.875

Answer:

The coordinates of a point are a pair of numbers that define its exact location on a two-dimensional plane.

⇛ -12 + 8

⇛ -4

‌

‌

‌

[tex] \: [/tex]

Hey there!

The word “sum” simply means “to add” or “addition” in mathematical terms

So, we have to ADD -12 from 8 from each other.

Positives are on the RIGHT side of the number line whereas negatives are on the LEFT side of the number line

Start at -12 and go UP 8 spaces to the right.

-12 + 8

= -4

Answer: -4

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

infinite solutions, true for all x

Step-by-step explanation:

-6 - 8x = -2(4x + 3)

Distribute

-6-8x =-8x-6

Add 8x to each side

-6-8x+8x = -8x-6+8x

-6 =-6

Since this is always true, the equation is true for all x

-6-8x = -2(4x+3)

-6-8x = -8x-6

-8x+8x = -6+6

0=0

infinite solution

THANK YOU

Step-by-step explanat

(g) 3[(3)²-2]+4=3(9-2)=3×7=21+4=25

Answer:

[tex]\displaystyle \lim_{x\rightarrow 0^{+}} \frac{x\ln x}{\tan x}=-\infty\implies \text{B. Nonexistent (best answer)}[/tex]

Step-by-step explanation:

Recall L'Hopital's rule:

[tex]\displaystyle \lim_{x\rightarrow c}\frac{f(x)}{g(x)}=\lim_{x\rightarrow c}\frac{f'(x)}{g'(x)}[/tex]

First derivative of [tex]x\ln x[/tex]:

Recall the product rule:

[tex](f\cdot g)'=f'\cdot g+g'\cdot f[/tex]

[tex]\displaystyle \frac{d}{dx} (x\ln x)=\frac{d}{dx}(x)\cdot \ln (x)+\frac{d}{dx}(\ln x)\cdot x[/tex]

Note that:

[tex]\displaystyle \frac{d}{dx}(x)=1,\\\frac{d}{dx}(\ln (x))=\frac{1}{x}[/tex]

Simplifying, we get:

[tex]\displaystyle \frac{d}{dx} (x\ln x)=1\cdot \ln x+\frac{1}{x}\cdot x,\\\frac{d}{dx}(x\ln x)=\ln x+1[/tex]

First derivative of [tex]\tan x[/tex]:

[tex]\displaystyle \frac{d}{dx}(\tan x)=\sec^2 x[/tex]

Therefore, we have:

[tex]\displaystyle \lim_{x\rightarrow 0^{+}}\frac{x\ln x}{\tan x}=\lim_{x\rightarrow 0^{+}}\frac{\ln x+1}{\sec^2{x}}[/tex]

By definition, [tex]\cos x=\frac{1}{\sec x}[/tex]. Therefore,

[tex]\displaystyle \lim_{x\rightarrow 0^{+}}\frac{x\ln x}{\tan x}=\lim_{x\rightarrow 0^{+}}\frac{\ln x+1}{\sec^2{x}}=\lim_{x\rightarrow 0^{+}}\cos^2x(\ln x+1)[/tex]

Note:

[tex]\displaystyle \lim_{x\rightarrow 0^{+}}\cos^2x=1,\\\lim_{x\rightarrow 0^{+}}\ln x+1=-\infty[/tex]

Substitute:

[tex]\displaystyle \lim_{x \rightarrow0^{+}} \cos^2x(\ln x+1)=1\cdot (-\infty)=-\infty[/tex]

Therefore, we have:

[tex]\displaystyle \lim _{x\rightarrow 0^{+}}\frac{x\ln x}{\tan x}=-\infty \text{}[/tex], which best corresponds with [tex]\boxed{\text{B. Nonexistent}}[/tex]

*Commentary:

Technically speaking, a limit exists only if it is equal to a real number. By proper definition, infinity is not a number. With that being said, you will see limits expressed as infinity or negative infinity.

Here's what I will say about this specific problem.

The problem is stipulating that we approach [tex]x[/tex] from the right side. Because of this condition, it may be unorthodox to say this limit doesn't exist. However, if the problem just asked for [tex]\displaystyle \lim_{x\rightarrow 0}\frac{x\ln x}{\tan x}[/tex], it is common and preferred to say this limit does not exist, since [tex]\displaystyle \lim_{x\rightarrow 0^{-}}\frac{x\ln x}{\tan x}\neq \displaystyle \lim_{x\rightarrow 0^{+}}\frac{x\ln x}{\tan x}[/tex].

For example, [tex]\displaystyle \lim_{x\rightarrow 0}\frac{1}{x}=\text{DNE}[/tex], because [tex]\displaystyle \lim_{x\rightarrow 0}\frac{1}{x}[/tex] diverges. In other words, [tex]\displaystyle \lim_{x\rightarrow 0^{-}}\frac{1}{x}=-\infty \neq \displaystyle \lim_{x\rightarrow 0^{+}}\frac{1}{x}=\infty[/tex].

But again, the problem is asking for the limit as [tex]x[/tex] approaches from the right, in which case [tex]\displaystyle \lim _{x\rightarrow 0^{+}}\frac{x\ln x}{\tan x}=-\infty }[/tex]. It's really a pedagogical choice whether to say a limit equal to infinity or negative infinity exists or not since infinity implies there is no limit, so saying the limit of something is infinity becomes an oxymoron. In this case, the person who wrote the answer choices chose to express a limit of infinity as nonexistent, but it is worth mentioning that someone else solving this problem might express [tex]-\infty[/tex] as the answer, and they would be just as, if not more, correct.

Without resorting to L'Hopital's rule, recall that

[tex]\displaystyle \lim_{x\to0}\frac{\sin(ax)}{ax} = 1[/tex]

for a ≠ 0. Then

[tex]\displaystyle \lim_{x\to0^+} \frac{x \ln(x)}{\tan(x)} = \lim_{x\to0^+}\frac x{\sin(x)} \times \lim_{x\to0^+}\cos(x) \times \lim_{x\to0^+}\ln(x)[/tex]

The first two limits exist and are equal to 1, but the last limit is -∞.

9514 1404 393

Answer:

  3 in

Step-by-step explanation:

Ratios of corresponding sides are equal, so we have the proportion ...

  x/(5 in) = (6 in)/(10 in)

  x = (5 in)(6/10) = 3 in

The missing side (x) is 3 in.

Answer:

Step-by-step explanation:

P ___15cm______T____10cm______B

As shown above,

PB is a line segment and point T in it forming - PT = 15 and TB = 10

So,

PB = PT + TB

= 15 + 10

= 25 (Ans)

Answer:

answer is 16380

Step-by-step explanation:

answer is 16380

Answer:

Step-by-step explanation:

We can see that:

Use the following identity:

Substitute the values to get:

Answer:

2，3

Step-by-step explanation:

for number 1

Answer: f(g) = 895 + 30g

-----------------------------------------------------------------

He paid $2065. Number of games he played:

-----------------------------------------------------------------

2065 = 895 + 30g

30g = 2065 - 895

30g = 1170

g = 39

-----------------------------------------------------------------

Answer: He played 39 games.

Step-by-step explanation:

Number of games anton played is 39; the equation is 2065 = 895 + 30G

An equation usually consists of equality of two mathematical expressions. Let it be

A = B

. If we take them to be equal to third variable, then:

A = B = C

type of equation is obtained.

We can then take it as system of two equations as:

A = C\\ B=C

Solution to this system will give us the solution to the considered equation.

Solution to an equation is finding values of the variable included in the considered equation for which the equation considered evaluates to be true.

The equation will be f(g) = 895 + 30G

Amount anton paid = $2065.

Number of games he played;

2065 = 895 + 30G

30g = 2065 - 895

30g = 1170

G = 39.

Therefore, the solution of the equation os 39

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Answer:

The current temperature would be 64°F

Step-by-step explanation:

first

55°F-13°F = 42°F

Now,

42°F + 22°F

= 64°F

9514 1404 393

Answer:

  (c)  symmetric property

Step-by-step explanation:

The symmetric property of equality lets you swap sides of the equal sign.

__

Reflexive: A = A

Substitution: if A=B and A=C, then C=B

Symmetric: A = B  ⇔  B = A

Transitive: if A = B and B = C, then A = C.

  note that the substitution and transitive properties are almost indistinguishable.

Answer:

The most basic question I have ever seen lol

XY = 9*3 = 27

Answer:

y = c1 e^-x + c2 e^(3x)

Step-by-step explanation:

Review linear DE's

(D-3)(D+1)y = 0

Step-by-step explanation:

z = 5y/8

x = 3y/8

2x + 3y - z = 50

6y/8 + 3y - 5y/8 = 50

6y/8 + 24y/8 - 5y/8 = 50

25y/8 = 50

25y = 400

y = 16

x = 3y/8 = 3×16/8 = 3×2 = 6

z = 5y/8 = 5×16/8 = 5×2 = 10

Answer:

25d + 100

Step-by-step explanation:

I will call "d" the days passed

25d + 100

Answer:

Step-by-step explanation:

10 dozen is equal to 120 so ratio is 800/120 or 80/12

same ration on the other side but 200/x.Cross multiply and u get 3

PEMDAS- Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

Answer= -91