What is the value of r? What is the length of EB?

Answer:

x=17

Step-by-step explanation:

7x and 2x+27 are supplementary meaning they add up to be 180 degrees.

so, 7x + 2x + 27 = 180

9x + 27 =180

9x = 153

x = 17

hope this helped

Answer:

-24

Step-by-step explanation:

g(-2) = 2(-2)

g(-2) = -4

h(4) = 4² + 4

h(4) = 16 + 4

h(4) = 20

g(-2) - h(4)

-4 - 20

= -24

Answer:

Step-by-step explanation:

g(x) = 2x

To find g( -2) substitute - 2 into g(x)

That's

g( -2) = 2(-2) = - 4

h(x) = x² + 4

To find h(4) substitute 4 into h(x)

That's

h(4) = (4)² + 4 = 16 + 4 = 20

So

g(-2) - h(4) is

- 4 - 20

= - 24

Hope this helps you

Answer:

2x-11

Step-by-step explanation:

2 x X = 2x + 11

Answer:

C

Step-by-step explanation:

0.1(x - 100)² + 250

0.1[(x - 100)(x - 100)] + 250

0.1(x² -200x + 10000) + 250

0.1x² - 20x + 1000 + 250

0.1x² - 20x + 1250

0.1x² - 25x + 5x + 1250

0.1x(x - 250) + 5(x + 250)

∴ (0.1x + 5)(x - 250) or (0.1x + 5)(x + 250)

Answer:

A(ABCD) ≈ 17.285 cm²

Step-by-step explanation:

A = √s(s - a)(s - b)(s - c)

s = (a + b + c)/2

a ; b ; c = the sides of the triangle

s = (AB + BC + AC)/2 = (5cm + 4.5cm + 6.5cm)/2 = 16cm/2 = 8 cm

A(ABC) = √8(8 - 5)(8 - 4.5)(8 - 6.5)

= √8×3×3.5×1.5

= √126

≈ 11.225 cm²

     2. A(ACD) = √s(s - AC)(s - CD)(s - AD)

s = (AC + CD + AD)/2 = (6.5cm + 3.5cm + 4cm)/2 = 14cm/2 = 7 cm

A(ACD) = √7(7 - 6.5)(7 - 3.5)(7 - 4)

= √7×0.5×3.5×3

= √36.75

≈ 6.060 cm²

     3. A(ABCD) = 11.225cm² + 6.060cm² = 17.285 cm²

Answer:

D. 1.3

Step-by-step explanation:

Perimeter (square) = 4*side

4 = 4*side

side = 1

We have triangle QVR. QV is a hypotenuse.

If we look at the triangle QTR, QT is a hypotenuse.

QV should be less than QT.

Let's find QT using Pythagorean theorem.

c² = a² + b²

QT² = QR² + RT² = 1² + 1² = 2

QT = √2 ≈ 1.4

QV < QT

QV < 1.4

We have 1.3 and 1 that are less than 1.4, but 1 is a length of a leg of the triangle, so 1 is impossible.

Answer D. 1.3

Answer:

Step-by-step explanation:

To find the sales tax on a purchased or sold item, first convert the sales tax percentage into the equivalent decimal fraction.  If the sales tax rate is 5.5%, then the desired decimal fraction is 0.055.  Next, multiply the selling price of the purchased or sold item by this decimal fraction.  If, for example, the selling  price is $100, the sales tax is 0.055($100) = $5.50

Answer:

Total amount received by Mrs Khanna will be 182.5 Rs.

Step-by-step explanation:

Cost of the potatoes = 25 Rs per kg

Cost of [tex]2\frac{1}{2}[/tex] kg potatoes = Weight of the potatoes × Per kg cost of the potatoes

= 2.5 × 25

= 62.5 Rs

Cost of onions = 30 Rs per kg

Cost of 3 kg onions = 3 × 30

                                 = 90 Rs

Per kg cost of Peas = 70 Rs

Cost of [tex]1\frac{1}{2}[/tex] kg Peas = 1.5 × 70

                               = 105 Rs

Per kg cost of Carrots = 40 Rs

Cost of [tex]1\frac{1}{2}[/tex] kg Carrots = 1.5 × 40

                                   = 60 Rs

Total amount of the vegetables = 62.5 + 90 + 105 + 60

                                                     = 317.5 Rs

Since she gave a note of 500 Rs

Balance amount she got = 500 - 317.5

                                         = 182.5 Rs

Therefore, total amount received by Mrs Khanna will be 182.5 Rs.

Answer:

8

Step-by-step explanation:

Let's denote the number of members ordered chicken a, the number of members ordered beef b.

We have:

a + b = 12 (total number of members is 12)

10a + 14b = 136 (the chicken costs 10$, the beef costs 14$)

a + b = 12 => a = 12 - b

Substitute a into second equation, we have:

10(12 - b) + 14b = 136

=> 120 - 10b + 14b = 136

=> 4b = 16

=> b = 4

=> a = 12 - b = 12 - 4 = 8

=> Number of members ordered chicken: a = 8

Answer:

( 4,-2)

Step-by-step explanation:

y + 2 = -3 (x - 4)

We are given y = -2

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

0 = -3(x-4)

Divide by -3

0 = x-4

Add 4 to each side

4 = x-4+4

4 =x

Answer:4

Step-by-step explanation:

Answer:

D. 19

Step-by-step explanation:

because they are parallel bases you can compare

63/57 = 21/x

x = 19

Answer: D. 19

Let x by the length of CG. Since the two bases are parallel, we can create the following equation using proportions:

[tex]\dfrac{63}{21}=\dfrac{57}{x}[/tex]

Simplify left side of equation

[tex]3=\dfrac{57}{x}[/tex]

Multiply both sides by x

[tex]3x=57[/tex]

Divide both sides by 3

[tex]x=19[/tex]

Let me know if you need any clarifications, thanks!

Answer:

no

Step-by-step explanation:

there is no factor to convert one into the other.

moreover, 19 is prime and 9 is not, so no way.

Step-by-step explanation:

[tex]4(x-7)=0.3(x+2)+2.11\\\\Distribute\\\\4x+28=0.3(x+2)+2.11\\\\Distribute\\\\4x+28=0.3x+0.6+2.11\\\\Combine\\like\\terms\\\\4x+28=0.3x+2.71\\\\Subtract\\\\3.7x+28=2.71\\\\Subtract\\\\3.7x=-25.29\\\\Divide\\\\x=\tex{ about }6.83513514[/tex]

Hope it helps <3

Answer:

x = 83/10=8^3/10=8.3

Step-by-step explanation:

4(x − 7) = 0.3(x + 2) + 2.11

Use the distributive property to multiply 4 by x−7.

4x−28=0.3(x+2)+2.11

Use the distributive property to multiply 0.3 by x+2.

4x−28=0.3x+0.6+2.11

Add 0.6 and 2.11 to get 2.71.

4x−28=0.3x+2.71

Subtract 0.3x from both sides.

4x−28−0.3x=2.71

Combine 4x and −0.3x to get 3.7x.

3.7x−28=2.71

Add 28 to both sides.

3.7x=2.71+28

Add 2.71 and 28 to get 30.71.

3.7x=30.71

Divide both sides by 3.7.

x= 3071/370

Expand  3.7/30.71≈8.3 by multiplying both numerator and the denominator by 100.

x = 83/10

24 and 16

Step-by-step explanation:

let's assume two part be x and (40 - x)

According to Question,

[tex] x\dfrac{1}{4} = (40 - x) \dfrac{3}{8} [/tex]

[tex] x= \dfrac{3(40 - x)}{2} [/tex]

[tex]2 \times x = 120 - 3x [/tex]

[tex]2x + 3x = 120[/tex]

[tex]5x = 120[/tex]

[tex] \cancel{5}x= \cancel{120}[/tex]

[tex]x = 24[/tex]

Hence one part is 24 and other is (40 - 24) = 16 .

Answer: 24 and 16

Step-by-step explanation:

Answer:

Step-by-step explanation:

Due to the '+1', the graoph of x^2 is shifted 1 unit to the left.  The '+9' results in the entire graph being shifted downward 9 units.

Answer:In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. An example of a polynomial of a single indeterminate, x, is x2 − 4x + 7.

Step-by-step explanation:

might help

Answer:

Step-by-step explanation:

[tex] \mathrm{9 \div \frac{2}{3} }[/tex]

To divide by a fraction, multiply by the reciprocal of that fraction

[tex] \mathrm{ = 9 \times \frac{2}{3} }[/tex]

Calculate the product

[tex] \mathrm{ = \frac{27}{2} }[/tex]

Hope I helped!

Best regards!!

Answer:

[tex]\boxed{13\frac{1}{2} }[/tex]

Step-by-step explanation:

[tex]9 / \frac{2}{3}[/tex]

Changing "division" into "multiplication" and inverting the term after it:

[tex]9 * \frac{3}{2}[/tex]

[tex]\frac{9*3}{2}[/tex]

[tex]\frac{27}{2}[/tex]

=> [tex]13\frac{1}{2}[/tex]

Answer:

The first and last answer.

Step-by-step explanation:

If you look closely at the triangles you can tell which ones are the same and which differ.

Hope this helps!! <3

Answer:

first option

Step-by-step explanation:

Given

- 3x - 2y = 1 → (1)

- x + y = 3 → (2)

Rearrange (2) by adding x to both sides, that is

y = x + 3

Substitute y = x + 3 into (1)

- 3x - 2(x + 3) = 1 ← is the equation to be solved for x

Answer:

14%

Step-by-step explanation:

If the percentage of boys wearing polo shirts were boys, then the rest has to be girls. So 100%-80%=20%. However, we are not done here.

We have only figured out the percentage of girls out of the total number of people wearing polo shirts. We want to find the percentage of girls wearing polo shirts out of the whole school. To do that, we multiply 20% by 70%, since 20% of the polo shirt wearers were girls, and 70% of the entire student body is wearing a polo shirt.

Multiplying those two together gets you 14%.

Answer:

14%

Step-by-step explanation:

Answer:

84 squared units.

Step-by-step explanation:

In order to find the surface area of the pyramid, you use the following formula:

[tex]S=b^2+\frac{1}{2}ps[/tex]           (1)

b: base of the pyramid = 6

p: perimeter of the base = 6*4 = 24

s: slant height

Then, you first calculate the slant height, by using the Pythagoras' theorem:

[tex]s=\sqrt{(5)^2-(\frac{6}{2})^2}=4[/tex]

Thus, you replace the values of b, p and s in the equation (1):

[tex]S=(6)^2+\frac{1}{2}(24)(4)=84[/tex]

The surface area of the pyramid is 84 squared units.

Answer:

Step-by-step explanation:

wrong

Answer:

-6x + 8(-x+6) = 6

Step-by-step explanation:

x+y = 6 => y = 6-x  ..............(1)

Substitute y (1) in

-6x+8y = 6 .......................(2)

to get

-6x + 8(6-x) = 6

or equivalently

-6x + 8(-x+6) = 6

Answer:53 dresses

Step-by-step explanation:

First of all..if one kid required 2 1/4m of cloth,what about 119 1/4m of cloth?

So u take 119 1/4m of cloth and divide it by 2 1/4m of cloth.

Then change the mixed numbers into improper fractions.

So the question will be 477/4 m divided by 9/4 m.

The second improper fraction (9/4)m will be reciprocated to be (4/9)m.

Afterwards,take 477/4 m and multiply it by 4/9 m.

The result will be 53 dresses.

Answer: x = 2

Step-by-step explanation:

First, Distribute

-2+8x=3x+8

Then, Subtract 3x

-2 + 5x=8

Then, Add 2

5x=10

Then, Divide by 5

x=2

Hope it helps <3

Answer:

-2(1-4x)=3x+8

distributive property

-2+8x=3x+8

subtract 8 on both sides

-2-8+8x=3x=-10+8x

now subtract 8x on both sides which equal: -10=-5x

now it part of the step and divide -5 on both sides to leave x or solve for x

-10/-5=x=2=x

x=2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Probability is the likelihood or chance that an event will occur.

Probability = expected outcome of event/total outcome of event

Given the total amount of chocolate in a box = 39chocolates

Amount of nuts = 16

Mount of caramel = 13

Amount of solid chocolate = 10

If he randomly selects a nut chocolate and eat, the probability of selecting a nut chocolate = Amount of nuts/total chocolate in the box = 16/39

IF he selects a seconnd piece (caramel chocolate) and eat, the probability of selecting a caramel chocolate = Amount of caramel/total chocolate in the box = 13/39 = 1/3

The probability of selecting a nut chocolate followed by a caramel chocolate will be 16/39*1/3 = 16/117

Answer:

[tex]2+i[/tex]

Step-by-step explanation:

Given the expression:

[tex]\dfrac{4+\sqrt{16-(4)(5)}}{2}[/tex]

To find:

The expression of above complex number in standard form [tex]a+bi[/tex].

Solution:

First of all, learn the concept of [tex]i[/tex] (pronounced as iota) which is used to represent the complex numbers. Especially the imaginary part of the complex number is represented by [tex]i[/tex].

Value of [tex]i =\sqrt{-1}[/tex].

Now, let us consider the given expression:

[tex]\dfrac{4+\sqrt{16-(4)(5)}}{2}\\\Rightarrow \dfrac{4+\sqrt{16-(4\times 5)}}{2}\\\Rightarrow \dfrac{4+\sqrt{16-20}}{2}\\\Rightarrow \dfrac{4+\sqrt{-4}}{2}\\\Rightarrow \dfrac{4+\sqrt{(-1)(4)}}{2}\\\Rightarrow \dfrac{4+\sqrt{(-1)}\sqrt4}{2}\\\Rightarrow \dfrac{4+\sqrt4i}{2} \ \ \ \ \ (\because \sqrt{-1} =i) \\\Rightarrow \dfrac{4+2i}{2}\\\Rightarrow 2+i[/tex]

So, the given expression in standard form is [tex]2+i[/tex].

Let us compare with standard form [tex]a+bi[/tex] so we get [tex]a =2, b =1[/tex].

[tex]\therefore[/tex] The standard form of

[tex]\dfrac{4+\sqrt{16-(4)(5)}}{2}[/tex]

is: [tex]\bold{2+i}[/tex]

Answer:

19

Step-by-step explanation:

The zebra is the 10th fastest, so there are 9 zebras that are faster.

It's also the 10th slowest, so there are 9 zebras that are slower.

The total number of zebras is therefore 9 + 1 + 9 = 19.

Answer:

- (x - 3y)(3x + y)

Step-by-step explanation:

Given

(x + 2y)² - (2x - y)² ← expand both parenthesis using FOIL

= x² + 4xy + 4y² - (4x² - 4xy + y²) ← distribute

= x² + 4xy + 4y² - 4x² + 4xy - y² ← collect like terms

= - 3x² + 8xy + 3y² ← factor out - 1 from each term

= - 1(3x² - 8xy - 3y²) ← factor the quadratic

Consider the factors of the product of the coefficient of the x² term and the coefficient of the y² term which sum to give the coefficient of the xy- term.

product = 3 × - 3 = - 9 and sum = - 8

The factors are - 9 and + 1

Use these factors to split the xy- term

3x² - 9xy + xy - 3y² ( factor the first/second and third/fourth terms )

= 3x(x - 3y) + y(x - 3y) ← factor out (x - 3y) from each term

= (x - 3y)(3x + y)

Thus

(x + 2y)² - (2x - y)² = - (x - 3y)(3x + y)

Answer:

[tex]\boxed{\sf 43.35 \ cm}[/tex]

Step-by-step explanation:

Apply formula for the circumference of a circle.

[tex]\sf C=\pi d[/tex]

The diameter [tex]\sf d[/tex] is 13.8 cm.

[tex]\sf C=\pi (13.8)[/tex]

[tex]\sf C= 43.3539786195...[/tex]

[tex]\sf{C} \approx \sf{43.35}[/tex]

Answer:

43.4 cm

Step-by-step explanation:

Circumference of the circle = 2πr

r = radius, π = [tex]\frac{22}{7}[/tex]

f = diameter÷2

 =13.8 ÷ 2

 = 6.9

circumference = [tex]2 * \frac{22}{7} * 6.9\\[/tex]

                        = [tex]\frac{303.6}{7}[/tex]

                        = 43.37 cm or 43.4 cm