Find the value of a. Then find the angle measures of the polygon.
a =
26
(2aº caº
a
Sum of angle
measures: 360°

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:  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:

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:

900 grams.

Step-by-step explanation:

1 kg = 1000 grams.

0.9 kg = 1000 * 0.9

= 900 grams.

Answer:

900 grams is the answer

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:

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:

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:

https://brainly.com/question/12463306

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:

Step-by-step explanation:

The SI unit of work is Joule.

Further more explanation:

▪️[tex] \blue{ \mathsf{ {What \: is \: Work \: ?}}}[/tex]

⇒Work done by a force acting on a body is defined as the product of force and displacement of the body in the direction of the force.

▪️[tex] \blue{ \bold{ \sf{What \: is \: SI \: unit \: ?}}}[/tex]

⇒The system of units which is agreed by the international convention of scientists held in France in 1960 is called SI unit.

▪️[tex] \blue{ \bold{ \sf{What \: do \: you \: mean \: by \: \: one \: joule \: work \: \: ?}}}[/tex]

⇒One joule is the amount of work done when one Newton force displaces a body through one metre in its own direction.

Hope I helped!

Best regards!

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: 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.

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:

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

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

Answer:

£500,000.00

Step-by-step explanation:

Principal = x

Saving rate  = 2% PA simple

Time = 5 years

Final amount = £550,000

Principal amount is £500,000

Answer:

[tex]\huge \boxed{{x=500,000}}[/tex]

Step-by-step explanation:

[tex]A=P(1+rt)[/tex]

[tex]A[/tex] = amount   ⇒  550000

[tex]P[/tex] = principal amount   ⇒  x

[tex]r[/tex] = rate   ⇒  2%

[tex]t[/tex] = time   ⇒  5

[tex]\displaystyle 550000=x(1+\frac{2}{100} (5))[/tex]

Solve for the brackets.

[tex]\displaystyle 550000=\frac{11}{10}x[/tex]

Multiply both sides of the equation by [tex]\frac{10}{11}[/tex].

[tex]500000=x[/tex]

The value of x (principal amount) is 500,000.

Answer:

32°

Step-by-step explanation:

What we have to notice here is that m∠1 and m∠2 are complementary angles. This means that their angles add up to 90°.

Since we know the measure of m∠1, we can easily find the measure of m∠2 since both add up to 90.

m∠1 is 58, so:

[tex]58 + x = 90[/tex]

[tex]x = 90-58\\\\x=32[/tex]

Hope this helped!

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: 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:

m∠W = 125°

m∠X = 55°

m∠Z = 55°

Step-by-step explanation:

The explanation of angle measures is shown below:-

The shape which is parallelogram WXYZ. m∠Y = 125

A parallelogram represents the shape of quadrilateral in which both opposite sides and opposite angles are similar to each other. One parallelogram diagonals bisect each other. Consecutive angles are also supplementary to a parallelogram.

In WXYZ parallelogram is there

m∠Z + m∠Y = 180° is an angle of Consecutive in a parallelogram is supplementary

m ∠ Z + 125 = 180

m ∠ Z = 180 - 125

m ∠ Z = 55°

m ∠ W which equals to m∠Y where equal angles are Opposite

m∠W = 125°

m ∠ W + m ∠ X = 180°

which is the angle of Consecutive in a parallelogram called supplementary)

m ∠ X + 125 = 180

m ∠ X = 180 - 125

After solving the above equation we will get

m ∠ X = 55°

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:

[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!!

Answer:

11 games

Step-by-step explanation:

17+6=23

23/2=11.5

Victoria can play 11 games. You'd usually round up, but in this case you can't play half a game so she'll play 11 games and have one quarter leftover.

Answer:

Victoria can play 11 games and have 1 quarter left over.

Step-by-step explanation:

17 given quarters +6 found quarters = 23 total quarters.

Since 23 is an odd number and we want to divide by 2, we have to go down to the last even number: 22. (This gives us the left over quarter)

22 quarters/2quarters per game = 11 games

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:

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:

x = 12; m<ABC = 76

Step-by-step explanation:

The two angles whose measures are given form a linear pair. Therefore, they are supplementary angles, and their measures add up to 180 degrees.

8x - 20 + 116 - x = 180

7x + 96 = 180

7x = 84

x = 12

The angle with measure 8x - 20 and angle ABC are vertical angles. That means that their measures are equal.

m<ABC = 8x - 20 = 8(12) - 20 = 96 - 20 = 76

Answer: x = 12; m<ABC = 76

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.