what is the area of this triangle​

Answer:

Step-by-step explanation:

Answer:

[tex]\displaystyle A = \frac{32}{3}[/tex]

General Formulas and Concepts:

Calculus

Integrals

Integration Rule [Reverse Power Rule]:                                                                   [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:                                        [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:                                                             [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration Property [Addition/Subtraction]:                                                           [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Area of a Region Formula:                                                                                       [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

Identify

Curve: x³ + 2x² - 3x

Interval: [-3, 1]

Step 2: Find Area

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Book: College Calculus 10e

Answer:

24 , 12x12 = 144. , 144/6 =24

Answer:

[tex]{ \bf{0.35{ \bar{2}}}} = { \bf{0.352222222....}} \\ = \frac{317}{900} [/tex]

Answer:

Step-by-step explanation:

Area of circle:

Distance between x and y is same as r, so:

Then the area is:

Answer:

Step-by-step explanation:

Answer:

1.1 gallons of paint

Step-by-step explanation:

The wall measures;

21 foot by 17 foot

Thus, area of wall = 21 × 17 = 357 ft²

Circular area has a radius of 5 ft.

Thus;

Area of circle = πr² = π × 5² = 78.54 ft²

Total area covered = 357 + 78.54 = 435.54 ft² ≈ 436 ft²

A gallon of paint can cover 400 ft²

Thus gallons Muhammad would need = 436/400 = 1.09 gallons ≈ 1.1 gallons

Answer:

The dryer costs $325.

Step-by-step explanation:

Let w represent the cost of the washer and d represent the cost of the dryer.

They cost $587 combined. In other words:

[tex]w+d=587[/tex]

The washer costs $63 less than the dryer. Therefore:

[tex]w=d-63[/tex]

Thus, we have the system of equations:

[tex]\displaystyle \begin{cases} w+d = 587 \\ w=d-63\end{cases}[/tex]

We can solve it using substitution. Substitute the second equation into the first. Hence:

[tex](d-63)+d=587[/tex]

Combine like terms:

[tex]2d-63=587[/tex]

Add 63 to both sides:

[tex]2d=650[/tex]

And divide both sides by two. Hence:

[tex]d=325[/tex]

The dryer costs $325.

Further Notes:

And since the washer is $63 less, the washer costs:

[tex]w=(325)-63=262[/tex]

The washer costs $262.

Answer:

A. It acts perpendicular to an object

Answer:

A

Step-by-step explanation:

slope=(1-0)/(5-4)=1

eq. of line through (4,0) with slope 1 is

y-0=1(x-4)

put y=f(x)

f(x)=x-4

Answer:

a) 120°

Step-by-step explanation:

i think this is the right answer

5x - 3y = -4

-3y = -5x - 4

3y = 5x + 4

Y = (5/3)x + (4/3)

The slope of the line is (5/3).

(Its y-intercept is 4/3 but we don't need that.)

Any line parallel to it has same slope. (5/3)

Any line perpendicular to it has slope that is the negative reciprocal of 5/3. (-3/5)

Answer:

137

Step-by-step explanation:

Since angle Z and the angle of 43° are supplementary, the sum of them must equal 180. Therefore,

∠Z + 43 =180

∠Z = 137°

Answer:

137 degrees

Step-by-step explanation:

First thing, we know y is 43 because 43 degrees and y are vertical angles meaning they are congruent. (This is just a small part doesn't really do much though.)

Straight lines add up to 180 so simply just subtract 43 from 180.

180 - 43 = 137.

Therefore,

z =  137 degrees

Answer:

The last one is the answer

Answer: For each hour that Michelle drove, she travelled an additional 50 miles.

Step-by-step explanation:

Test each option to see its accuracy

Calculate the slope:

[tex](x_{1}, y_{1}) = (7, 0)\\(x_{2}, y_{2}) = (0, 350)\\ \\\frac{y_{2}-y_{1}}{x_{2}-x_{1}} =\frac{350-0}{0-7} =\frac{350}{-7} =-50[/tex]

This means that Michelle drove 50 miles per hour.

The other three options are wrong because if you bring in:

into your function- y = -50x + 350, you would not get the stated miles.

Answer:

[tex](13 + 29 - 2) \div 2 \\ (42 -2 ) \div 2 \\ 40 \div 2 \\ = 20[/tex]

Answer:

hope it helps.

Answer:

[tex]8x^2y-18y^3[/tex]

[tex]=8x^2y-18yy^2[/tex]

[tex]=4\cdot \:2x^2y+9\cdot \:2yy^2[/tex]

[tex]=2y\left(4x^2-9y^2\right)[/tex]

[tex]=2y\left(2x+3y\right)\left(2x-3y\right)[/tex]

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

Hope it helps...

Have a great day!!

Answer:

1500

Step-by-step explanation:

The area of the regtangular floor is 360m². The floor is going to be retired with tiles having area of 240cm² . We need to find the number of times . Therefore ,

[tex]\implies 360m^2 = 360 \times 10^4 \ cm^2 [/tex]

And , the number of tiles required will be ,

[tex]\implies n =\dfrac{Area \ of \ floor}{Area \ of \ a \ tile }\\\\\implies n =\dfrac{ 360 \times 10^4 \ cm^2}{240 cm^2} \\\\\implies \underline{\underline{ n = 1,500 }}[/tex]

Hence the required answer is 1500 .

Answer:

All options are correct.

Step-by-step explanation:

We have to find the expression which are in the simplest form.

A.[tex]x^{-3}+y^3[/tex]

The expression cannot solve further.

Therefore, the given expression is in the  simplest form .

B.[tex]\frac{1}{x^4}[/tex]

The expression cannot solve further.

The given expression is in the  simplest form.

C.[tex]\frac{w^7}{x^2}[/tex]

[tex]x^2[/tex] cannot divide [tex]w^7[/tex].

The expression cannot solve further.

Hence, the given expression is in the  simplest form.

D.[tex]a^{-9}[/tex]

The expression cannot solve further.

The given expression is in the  simplest form.

E.[tex]\frac{1}{a^2}+b^2[/tex]

The expression cannot solve further.

Hence, the given expression is in the  simplest form.

F.[tex]\frac{1}{b^5}[/tex]

The expression cannot solve further.

Hence, the given expression is in the  simplest form.

Hence, all options are true.

Answer: y = 25 - 2x

Step-by-step explanation:

y = mx + b

y = -2x + 25

Answer:

9x

Step-by-step explanation:

(x² + 2x) - (x² - 7x) ← distribute parenthesis

= x² + 2x - x² + 7x ← collect like terms

= 9x

Answer:

9x

Step-by-step explanation:

( x ² + 2 x ) - ( x² - 7 x )

Simply the expression

Remove unnecessary parantheses

combine like terms

Answer:

RV = 18

Step-by-step explanation:

The diagonals of a parallelogram bisect each other, then

RV = [tex]\frac{1}{2}[/tex] RT = [tex]\frac{1}{2}[/tex] × 36 = 18

Answer:

[tex]slope = \frac{ - 1 - 4}{0 - 2} \\ = \frac{ - 5}{ - 2} \\ = { \tt{ \frac{5}{2} }}[/tex]

Answer:

[tex]\frac{6}{5}[/tex] of an hour = 1 1/5 hour = 72 minutes

Step-by-step explanation:

[tex]\frac{1}{3} h + \frac{1}{2}h = 1\\\\\frac{2}{6} h + \frac{3}{6}h = 1\\\\\\\frac{5 }{6} h =1\\\\h=\frac{6}{5}[/tex]

It would take Ted and Jacob 6/5 or 1.2 hours to clear the field together.

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

Let's use the formula for the work rate:

Ted's work rate = 1/3 of the field per hour

Jacob's work rate = 1/2 of the field per hour

Together, their work rate.

= (1/3 + 1/2) of the field per hour

Now,

We can simplify the equation for the combined work rate by finding a common denominator:

(1/3 + 1/2)

= (2/6 + 3/6)

= 5/6 of the field per hour

Now we can use the formula for the work rate to solve the time it would take them to clear the field together:

(5/6)t = 1

(where t is the time in hours)

Solving for t:

(5/6)t = 1

t = 6/5

Therefore,

It would take Ted and Jacob 6/5 or 1.2 hours to clear the field together.

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ7

Answer:

(-3,2)

Step-by-step explanation:

The given Equations of lines are ,

[tex]\implies x + 3 = 0 [/tex]

[tex]\implies y -2 = 0 [/tex]

On plotting the graph of the given two equations we will get that the two lines will intersect each other at a point and that point will be the solution of the system of equation. On drawing a graph ,

On looking at graph , Point P will be ,

[tex]\implies Solution = P(-3,2) [/tex]

Answer:

53 degrees

Step-by-step explanation:

Angle N = angle E

because angle made by joining end points of same chord on circumference are always equal.

so angle E = 37

Angle D = 90 ( because angle made by diameter on circumference is 90 degrees)

Now in Triangle DEC. Sum if all the angles of triangle us 180

Angle D + angle E + ? = 180

37 + 90 + ? = 180

127 + ? = 180

? = 180 - 127

? = 53 degrees

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Explanation:

Let r be the common ratio. Also, we'll make r nonzero, i.e. [tex]r \ne 0[/tex]

Multiplying this common ratio by any term gets us the next term of the geometric sequence.

16/9 is the first term, so that makes (16/9)*r the second term

Since (16/9)r is the second term, the third term is (16/9)r*r = (16/9)r^2

Set this equal to 1 and solve for r.

(16/9)r^2 = 1

r^2 = 1*(9/16)

r^2 = 9/16

r = sqrt(9/16) or r = -sqrt(9/16)

r = 3/4 or r = -3/4

Now that we know what r is, we can determine the second term

If r = 3/4, then,

(16/9)*r = (16/9)*(3/4) = 4/3

Or if r = -3/4, then,

(16/9)*r = (16/9)*(-3/4) = -4/3

So the second term is either 4/3 or -4/3 depending on which r value you go for.

The equation will be:

25 + d = t

where t is total money