What is the area, in square inches, of the isosceles trapezoid below?
17.9 in
18 in
8.3 in

Answer:

Step-by-step explanation:

yo

The number of cows is 54 and the number of chickens is 27 if the cows and the chickens, there are 162 eyes and 270 feet.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have:

A farmer was asked how many cows and chickens she has. The farmer replied, "between the cows and the chickens, there are 162 eyes and 270 feet.

Let x be the number of cows and y be the number of chickens.

2x + 2y = 162 (there are 162 eyes)

4x + 2y = 270 (there are 270 feet)

From the first equation take the value of x and plug it into the equation second.

2y = 162 - 2x

y = 81 - x

4x + 2(81 - x) = 270

4x + 162 - 2x = 270

2x = 108

x = 54

y = 27

Thus, the number of cows is 54 and the number of chickens is 27 if the cows and the chickens, there are 162 eyes and 270 feet.

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Answer: x= 5 and y= -2

Step-by-step explanation:

Given: The area of a square field is 841 sq.m

Since side of square = √Area

So, side of square field = [tex]\sqrt{841} =29[/tex]

Thus , side of square field = 29 m

Perimeter of square = 4( side) = 4(29) = 116 m

Let x be the breadth of rectangle then 2x be the length

Perimeter of rectangle = 2 (length+breadth) = 2(2x+x)= 2(3x)=6x

As per question, perimeter of rectangle=  Perimeter of square

[tex]\Rightarrow\ 6x=116\\\\\Rightarrow\ x=\dfrac{116}{6}=\dfrac{58}{3}\ m[/tex]

Length : [tex]2x =2\dfrac{58}{3}=\dfrac{116}{3}\ m[/tex]

Area of rectangle =  length x breadth

[tex]=\dfrac{116}{3}\times\dfrac{58}{3}=\dfrac{6728}{9}\\\\=747\dfrac{5}{9}\ m^2[/tex]

Area of rectangle = [tex]747\dfrac{5}{9}\ m^2[/tex]

Answer:

Step-by-step explanation:

The total surface area of the sphere = 2πr²

Total surface area of the cylinder = 2πr²+2πrh

Total surface area of the solid = 4πr²+2πrh

r is the radius of the sphere and the cylinder

h is the height of the cylinder

Total surface area of the solid = 2πr(r+h)

If the total height of the solid is 18 cm, then r+h = 18cm

Given the Total surface area of the solid = 205π cm

205π = 2πr(r+h)

205π = 2πr(18)

205π = 36πr

205 = 36r

Divide both sides by 36

205/36 = 36r/36

r = 5.69cm

Since  r+h = 18cm

5.69+h = 18

h = 18-5.69

h = 12.31cm

Answer:

19. Opposite of a Difference     ↔    E. -(8 - 3·m) = 3·m - 8

20. Opposite of a sum               ↔    A.  -[(-r) + 2p] = -(-r) - 2p

21. Opposite of an Opposite     ↔   F. -1[ -1(9 - 2w)] =  9 - 2w

22. Multiplication by 0               ↔   B.  160 - (3d + 2)(0) = 160 - 0

23. Multiplication by                   ↔   D. -1 -(4r + 3s) + t = (-1)(4r + 3s) + t

21. Distributive property             ↔   C.  5(2 - x) = 10 - 5x

Step-by-step explanation:

19. Opposite of a difference is the difference of the opposites

20. Opposite of a sum is the sum if the opposites

21. Opposite of an opposite is the original number

22. Multiplication by 0- The result of multiplication by 0 is 0

23. Multiplication by -1 results in the change in sign of a number

24. Distributive property - Multiplying the sum or difference of two numbers  by a number, will have the same result as multiplying each each of the addends by the number individually and adding the product together.

Answer:

[tex]\huge \boxed{\mathrm{5^{3+2} \ \ \ \ 5^5 }}[/tex]

Step-by-step explanation:

5³ × 25

25 can be written as a base of 5.

5³ × 5²

We need expressions with fewest number of bases possible.

Apply exponent rule : [tex]a^b \times a^c = a^{b+c}[/tex]

[tex]5^{3+2}[/tex]

Add exponents.

[tex]5^5[/tex]

Answer:

The answer is easy its 53 times 2 and 52 times 2

Step-by-step explanation:

Answer:

x+3y-6=0

Step-by-step explanation:

given eqn is y=3x-2 which is 3x-y-2=0

the eqn of line perpendicular to given eqn is -x+3y+k=0

it passes through (6,4)

-6+3*4+k=0

or,. -6+12+k=0

or, k= -6

therefore, the eqn of line perpendicular to given eqn is x+3y-6=0

Answer:

any x value would work

Step-by-step explanation:

4(x+4)

4*x=4x

4*4=16

4x+16=4(x+4)

Answer:

[tex]\boxed{y=\frac{c}{b}-\frac{ax}{b}}[/tex]

Step-by-step explanation:

[tex]ax+by=c\\\\ax-ax+by=c-ax\\\\by=c-ax\\\\\frac{by=c-ax}{b}\\\\\boxed{y=\frac{c}{b}-\frac{ax}{b}}[/tex]

Hope this helps.

Answer:

Step-by-step explanation:

For us to write a math expression for the problem, we will use the formula for calculating speed.

Speed is the change of distance of a body with respect to time.

Mathematically, Speed =  Distance/Time

Distance = Speed * Time

If  Lumpy drove for h hours at 50 mph, then Lumpy speed =  50mph and time = h hours.

Substituting the given parameters into the formula to get the distance;

Distance = 50mph * h hours

Distance = 50h miles

Hence the math expression that modeled how far Lumpy drive is 50h miles

Answer:

$6.50

Step-by-step explanation:

Create a system of equations, where s represents the price of a stuffed animal and t represents the price of a toy train:

4s + 7t = 75

6s + 5t = 74

Solve by elimination by multiplying the top equation by 3 and the bottom equation by -2:

12s + 21t = 225

-12s - 10t = -148

11t = 77

t = 7

Plug 7 in as t to find s:

4s + 7t = 75

4s + 7(7) = 75

4s + 49 = 75

4s = 26

s = 6.5

= $6.50 for a stuffed animal

Answer:

The first option.

Step-by-step explanation:

Domain is anything less than or equal to 2, but anything greater than or equal to -4

Range is anything greater than or equal to -4, but also less than or equal to 4

Answer:

-6

Step-by-step explanation:

We are given x=- 3 , y= 6 and z= -4.

We are also given the expression:

-15 + (-x) +y

Substitute -3 in for x and 6 in for y.

-15 + (- -3) + 6

2 negative signs creates a positive sign

-15 + (+3) +6

-15 + 3+ 6

Add -15 and 3.

(-15+3) +6

-12 +6

Add -12 and 6.  

-6

-15+(-x)+y evaluated at x= -3 and y=6 is equal to -6.

Answer: QN = 12

Step-by-step explanation: This quadrilateral is a paralelogram because its 2 opposite sides (NP and MQ) are parallel and the other 2 (MN and PQ) are congruent.

In paralelogram, diagonals bisect each other, which means QR = RN.

If QR = RN:

QR = 6

Then,

QN = QR + RN

QN = 6 + 6

QN = 12

The diagonal QN of quadrilateral MNPQ is QN = 12.

Answer:

a= 1,2,4 b= 1,2,3,6 c=1,2,4 d=1,2,5,10 e=1,2,3,4,6,12 H.C.F of all the pairs= 2

Step-by-step explanation:

Factors of:

a. 8=1,2,4,8

12=1,2,3,4,6,12.

common factor=1,2,4

b. 12=1,2,3,4,6,12

18=1,2,3,6,9,18

common factor=1,2,3,6

c. 16=1,2,4,16

24=1,2,3,4,6,8,12,24

common factor=1,2,4

d. 20=1,2,4,5,10,20

30=1,2,3,5,6,10,15,30

common factor=1,2,5,10

e. 24=1,2,3,4,6,8,12,24

36=1,2,3,4,6,9,12,18,36

common factor=1,2,3,4,6,12

HIGHEST COMMON FACTOR (H.C.F)=

The factor common to the whole pairs

which is 1 and 2

therefore 1 multiplied by 2 which is equal to 2

(and in Mathematics means multiplication)

Answer:

-6, 0, 15

Step-by-step explanation:

You just replace x with the given number.

g(-2)= 3(-2)

=-6

g(0)=3(0)

=0

g(5)=3(5)

=15

The required evaluated values of g(x) = 3x would be -6, 0, 15 respectevily when substitute the values x = -2, 0, and 5.

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

We have been the given expression:

g(x) = 3x

To determine the evaluated values of  g(x) = 3x when x= -2, 0, and 5

We have to substitute x with the given number.

⇒ g(x) = 3x

Substitute the value of x = -2 in the g(x) = 3x

⇒ g(-2) = 3(-2)

⇒ g(-2) = -6

Substitute the value of x = 0 in the g(x) = 3x

⇒ g(0) = 3(0)

⇒ g(0) = 0

Substitute the value of x = 5 in the g(x) = 3x

⇒ g(5) = 3(5)

⇒ g(5) = 15

Hence, the required evaluated values of g(x) = 3x would be -6, 0, 15 respectevily when substitute the values x = -2, 0, and 5.

Learn more about the algebraic expression here :

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Answer:

f(4) = 23

Step-by-step explanation:

[tex] f(x) = x^2 + 7[/tex]

Plug x = 4

[tex] f(4) = 4^2 + 7[/tex]

[tex] f(4) = 16 + 7[/tex]

[tex] f(4) = 23[/tex]

Answer: f(4) = 23

Step-by-step explanation: Notice that f is a function of x.

So we want to find f(4).

We find f(4) by plugging 4 in for x, everywhere that x appears in the function.

So we have f(4) = (4)² + 7.

(4)² is 16 so we have 16 + 7 which is 23.

So f(4) is 23.

Answer:

900 grams.

Step-by-step explanation:

1 kg = 1000 grams.

0.9 kg = 1000 * 0.9

= 900 grams.

Answer:

900 grams is the answer

1 cartons of juice = $4.20

3 single cartons = 4.20 * 3 =  $12.60

1 pack = $9.45

He saved 12.60 - 9.45 = $3.15

So, he saved $3.15, compared to the total ($12.60)

To calculate the percentage, we will do a proportion:

3.15 (money saved) : 12.60 (total of 3 single cartons) = x (how much percentage) : 100 (total)

3.15 : 12.6 = x : 100

To calculate x, we will moltiplicate the ends (where we have known numbers) than divide all per 12.6

So

x = (3.15 * 100) / 12.60 = 315 / 12.6 = 25

So the percentage saving is 25%

Answer:

The correct option is;

B. This equation is not considered to be a quadratic equation because it is not in the form a·x² + b·x + c = 0

Step-by-step explanation:

A. The given equation, x² - c = 0, can be presented in the form of the difference of two squares as follows;

(x + √c)·(x - √c) = 0

B. The equation x² - c = 0, is a quadratic equation because it is a polynomial equation of degree 2

C.  The equation x² - c = 0 can always be factored as (x + √c)·(x - √c) = 0

D. Where c > 0, the equation x² - c = 0 can by the square root property as follows;

x² - c = 0

x² = c

x = √c

Answer:

6.47 gal

Step-by-step explanation:

cost of gas per gallon = $2.78

rate of change is cost of gas per gallon as cost to buy gas changes with the change in quantity of gallon.

Total cost for x gallons = cost of gas per gallon*x = 2.78x

Given that total money paid by him is $18

2.78x = 18

x = 18/2.78 = 6.47

Answer:

6.47 gallons

Step-by-step explanation:

18 divided by 2.78 = 6.47

Answer:  20 liters

Step-by-step explanation:

The mixture is 60 liters. The ratio is 2 : 1   (2 parts to one part)

60 ÷ (2 + 1) = one part

60 ÷ 3 = 20

Therefore, the ratio of 2 : 1 means 2(20) liters milk to 1(20) liters water

If we change it to a ratio of 1 : 2, then we have 1(20) liters milk to 2(20) liters water.

2:1 ratio has 20 liters water

1:2 ratio has 40 liters water

The amount of water added is 40 - 20 = 20 liters

Answer:

Component form of the vector will be (-1, 2).

Step-by-step explanation:

When [tex]P(x_1, y_1)[/tex] translates to [tex]P'(x_2,y_2)[/tex] vector V formed after the translation will be,

V = [tex]<(x_2-x_1), (y_2-y_1)>[/tex]

If we draw this vector on a graph,

Vector will start from origin and the terminal point will be at [tex][(x_2-x_1), (y_2-y_1)][/tex]

Therefore, component form of the vector that translates from P(-3, 6) and P'(-4, 8) will be,

V = [tex]<(-4+3),(8-6)>[/tex]

V = [tex]<(-1,2)>[/tex]

Translation involves changing the position of a point

The vector that translates P to P' is [tex]\mathbf{ <-1,2>}[/tex]

The points are given as:

[tex]\mathbf{P = (-3,6)}[/tex]

[tex]\mathbf{P' = (-4,8)}[/tex]

The translation rule is calculated as:

[tex]\mathbf{(x,y) = P' - P}[/tex]

So, we have:

[tex]\mathbf{(x,y) = (-4,8) - (-3,6)}[/tex]

Combine

[tex]\mathbf{(x,y) = (-4+3,8-6)}[/tex]

[tex]\mathbf{(x,y) = (-1,2)}[/tex]

Express as vectors

[tex]\mathbf{<x,y> = <-1,2>}[/tex]

Hence, the vector that translates P to P' is [tex]\mathbf{ <-1,2>}[/tex]

Read more about translations at:

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Answer: The coordinate of L is 4.

Step-by-step explanation:

Let's say you were to plot the point on a number line and find the distance between P and G.

P is -6 on the number and G is 18 on the number so to find the distance between them we will need to find the different between the number and find its absolute value.

-6- 18 = -24  and the absolute value of -24 is 24.

In other words to get from -6 to 18 on the number line you need to move 24 units to the right.

Now to answer the question, we know that the distance between the two numbers is 24 and and it says that L is 1/6 of the distance.

We can represent that by the equation,

L = [tex]\frac{1}{6} * 24[/tex]

L =  4

Answer:

im pretty sure the answer is b. im not 100% though

Step-by-step explanation:

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{n = 1}}}}}[/tex]

Step-by-step explanation:

[tex] \sf{2 - 4n = 2 - 4(3 - 2n)} [/tex]

Distribute 4 through the parentheses

⇒[tex] \sf{ 2 - 4n = 2 - 12 + 8n}[/tex]

Move 8n to left hand side and change it's sign

⇒[tex] \sf{2 - 4n - 8n = 2 - 12}[/tex]

Collect like terms

⇒[tex] \sf{2 - 12n = 2 - 12}[/tex]

Move 2 to right hand side and change it's sign

⇒[tex] \sf{ - 12n = 2 - 12 - 2}[/tex]

Calculate

⇒[tex] \sf{ - 12n = - 12}[/tex]

Divide both sides of the equation by -12

⇒[tex] \sf{ \frac{ - 12n}{ - 12} = \frac{ - 12}{ - 12} }[/tex]

Calculate

⇒[tex] \sf{n = 1}[/tex]

Hope I helped!

Best regards!!

Hey there! I'm happy to help!

To find the area of a trapezoid, you add the lengths of the two bases, divide by two, and then multiply by the height.

We add our two bases.

483+207=690

We divide by 2.

690/2=345

We multiply by the height.

345(320)=110,400

Therefore, Hien can estimate that the area of Nevada is 110,400 square miles.

Have a wonderful day! :D

The formula for area of a trapezoid is [tex](b_{1} + b_{2})*\frac{1}{2} h=A[/tex]

b=base

h=height AKA altitude.

A=area.

Base 1 is 483.

Base 2 is 405.

483+405=888

888×320 (h) = 284160

284160 × [tex]\frac{1}{2}[/tex] = 142080

The approximate area of Nevada is 142080 square miles.

♡ Hope this helps! ♡

❀ 0ranges ❀

Answer:

Total time when cost are equal = 600 minutes

Total cost = 104

Step-by-step explanation:

Given:

Plan A = costs 8 plus an additional 0.16 for each minute

Plan B = costs 20 plus an additional 0.14 for each minute

Find:

Total time when cost are equal

Computation:

Assume total time = x minutes

Plan A = 8 + 0.16x

Plan B = 20 + 0.14x

Plan A = Plan B

8 + 0.16x =  20 + 0.14x

0.02x = 12

x = 600 minutes

Total time when cost are equal = 600 minutes

Total cost = 8 + 0.16x

Total cost = 8 + 0.16(600)

Total cost = 104