A sector of a circle of radius 14cm containing
an angle 60° is folded to forma cone
Calculate the radius of the base of the circle
}

Answer:

x is 90°

y is 56°

Step-by-step explanation:

Concepts used :

The angle subtended by a diameter inside the circle is always 90° .

Sum of interior angles of a triangle is 180°.

Here x is the angle subtended by the diameter of the circle therefore ,

x is 90°.

let the end points of diameter  as A , B

and the point where the it subtends the 90° angle be C

using interior angle property on the triangle  ΔABC

90° + 62° + ∠A = 180°

152° + ∠A = 180°

∠A = 180° - 152°

∠A  =  28°

now let he midpoint of diameter as D

as the sides DC and DA are radius of circle  and therefore equal

so using isosceles triangle property which states that angle opposite to equal sides are equal

so the angle ∠ACD = 28°

now using exterior angle property on ΔADC

y = 56°

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[tex]\boldsymbol{Answer:}[/tex] 10 and -8 ✅

[tex]\boldsymbol{Step-by-step\;explanation:}[/tex]

Hii, do you need to know the co-efficients in the expression [tex]"\boldsymbol{2+6+10b-8a}"[/tex]? No problem! (:

A "co-efficient" is a number that comes before a variable.

Here there are only two such numbers: "10" and "-8"; 10 comes before b, and -8 comes before a. 2 and 6 don't come before any variables at all, so they are not co-efficients.

Voila! There's our solution, cheers! (:

--

Hope that this helped! Best wishes.

[tex]\it Reach\;far.\;Aim\;high.\;Dream\;big.[/tex]

[tex]\bigstar\underbrace[/tex]

--

Answer:

-8c+6

Step-by-step explanation:

2(-6c+3)+4c = -12c+6+4c = -8c+6

Answer:

Area of Quadrilateral = 289.57 sq.cm

Step-by-step explanation:

First of all, let us understand what is a Quadrilateral?

A quadrilateral is a polygon with four sides. A quadrilateral is a closed two-dimensional figure formed by joining the four points among which three points are non-collinear points.

Given,

Length of sides :

AB = 7.5 cm

BC = 11.7 cm

CD = 15.6 cm

AD = 18 cm

and given , the Angle between BCD is 90 degrees and the angle between BAD is 90 degrees.

It implies that the TRAINGLES BCD and BAD are Right angled triangles

So, the length of BD can be found using Pythagorean theorem

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.

From the Triangle of BCD,

a= BC

b=CD and

c= BD

Therefore, The length of BD =

c=[tex]\sqrt[2]{(11.7^{2})+(15.6 x^{2}) }[/tex]

c = [tex]\sqrt{380.25}[/tex]

c = 19.5 cm

Hence, c= BD=19.5 cm

Now, Area of Quadrilateral =

1/2*(diagonal)*(sum of height of two triangles)

Here, Diagonal = Length of BD = 19.5 cm

Height (h1) = BC = 11.7 cm

Height ( h2) = AD = 18 cm

Therefore, Area = 1/2*19.5*(11.7+18)

                           = 289.57 sq.cm

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Answer:

29.5

Step-by-step explanation:

Use PEDMAS

P - Paraenthesis

E -Exponents

D - Divsion

M - Multiplication

A and S - Addition and subtraction respectively.

First multiply 4.2 and 7 as they are inside the parenthesis

Then find 2² which 4

(4.2 *7) - 10.4 *2² + 2.9*3 - 6 = 29.4 - 10.4 ÷2² + 2.9*3 - 6   {Parenthesis}

                                              = 29.4 - 10.4÷4 + 2.9*3 - 6   {Exponents}

                                               = 29.4 - 2.6 + 2.9*3 - 6    {Division}

                                              = 29.4 - 2.6 + 8.7 - 6   {Multiplication}

                                              = 29.5

Answer:

x=115⁰

z=27⁰

Step-by-step explanation:

65+x=180 -> Due to same side interior being equal to 180 degrees

x= 115

x = 3z + 34 -> opposite interior being equal

115 = 3z + 34

81 = 3z

divide by 3 on both sides

z=27

Answer:

-5=m

Step-by-step explanation:

-3/4m-1/2=2+1/4m

-2/4m-1/2=2

-2/4m=2 1/2

m=-5

(i) Monthly installment is $21.53 approximately.

(ii) Total amount man has to pay is $3716.8

(iii) Extra money he had to pay for buying the computer on hire is $516.8

Given,

Initial price of the computer(p) = $3200

Down payment = $480

Time period = 2 yrs

rate percent = 9.5%

(i) Monthly installment = ?

monthly installment =(capital amount × interest rate)/time in months

down payment to be paid = 3200 ₋ 480

                                         = 2720

therefore, monthly payment = 2720 × 9.5 × 1/ 12

                                            = $21.53

(ii) Total amount man has to pay = ?

                                           = down payment ₊ remaining amount ₊                                                                                                                                                 (remaining amount × t × r)                                          

                                           = 480 ₊ 2720 ₊ 2720 × 9.5 × 2

                                           = $3716.8

(iii) If he buys the computer on hire then how much more he has to pay = ?

= total amount ₋ initial cost

= 3716.8 ₋ 3200

= $516.8

Hence the man has to pay $21.23 as a monthly installment, $3716.8 as a total cost of the computer system and $516.8 as an extra amount if he buys it on hire.

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An expression is defined as a set of numbers, variables, and mathematical operations. The male cheetah's average speed for the last month is 20 mph.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

A.) Let the male cheetah's average speed for the last month be represented by x.

Given the male cheetah runs at a speed of 26 mph, that is 30% faster than his average last month.

x + 30% of x = 26 mph

1.30x = 26

x = 20 mph

Hence, the male cheetah's average speed for the last month is 20 mph.

B.) Sadie makes 1.5 liters of iced tea. She pours a liter into a pitcher to take to her neighbor. Her sister drinks the remaining iced tea. Therefore,

Iced tea Sadie's sister drink  = 1.56 liters - 1 liter = 0.56 liter

Hence, the amount of tea Sadie’s sister drinks is 0.56 liters.

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7978978

Step-by-step explanation:

Answer:

The sum of the polynomials is a 7th degree polynomial.

The difference of the polynomials is a 7th degree polynomial.

Step-by-step explanation:

Janie's polynomial is a 3rd degree with only x terms. Maybe she wrote:

f(x) = x^3

or maybe she was fancy and wrote:

f(x) =

x^3 + 2x^2 - 7x + 4

could be anything really, but the biggest exponent is 3.

Then Max does like:

g(x) = x^7

or

g(x) = x^7-x^4-3x+2

Whatever he made up, but the biggest exponent is 7.

So if they add or subtract their two polynomials, there's no x^7 in Janie's to add with the x^7 in Max's. MAYBE Max put some x^3 or x^2 or x or constants that might combine with the terms in Janie's.

Either way, anything that Max put in his polynomial that is a bigger power than 3 (4th, 5th, 6th, or 7th power) is just going to end up in the sum or difference.

Answer:

Step-by-step explanation:

[tex]|x+2| > 2\iff x+2 > 2\ \vee\ x+2 < -2[/tex]

subtract 2 from both sides

[tex]x > 0\ \vee\ x < -4[/tex]

ABCD is a quadrilateral that has been translated 2 units to the right and 7 units down. The length of side AB will not change following the translation. Option C is correct.

Each point in a figure is moved the same distance in the same direction using a sort of transformation known as translation.

The complete question is

"Quadrilateral ABCD has translated 7 units down and 2 units to the right.

The length of side AB of the original quadrilateral is_____ units. After the translation, the length of side AB will___________ .

2

3

3.5

4

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

Increase

Decrease

Remain the same"

Quadrilateral ABCD has translated 7 units down and 2 units to the right.  After the translation, the length of side AB will remain the same.

Hence option C is correct.

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Using translation concepts, it is found that this transformation can be described as a reflection across the x-axis.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, considering the vertices of quadrilateral 1 and quadrilateral 2, the transformation from quadrilateral 1 to quadrilateral 2 has the following format:

(x,y) -> (x, -y).

Which means that it can be described as a reflection across the x-axis.

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Answer:

d(v) =2.15v^/25.116

Step-by-step explanation:

Answer:

first 1  is .39
second one is C

Step-by-step explanation:

The total distance if Pete walks from A to B to C is 40 yards, the direct distance from A to C is more than 10 yards, and an inequality w < 30

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

We have:

Points A, B, and C, form a triangle. The distance between point A and point B is 15 yards. The distance between point B and point C is 25 yards.

Total distance if Pete walks from A to B to C:

= 15 + 25 = 40 yards

As we know in the triangle the sum of the two sides is greater than the third side.

25 + 15 > AC

The direct distance from A to C is more than 10(25-15) yards.

The inequality w < 30 represents the distance, w, that Pete might save by taking the direct path.

Thus, the total distance if Pete walks from A to B to C is 40 yards, the direct distance from A to C is more than 10 yards, and an inequality w < 30

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Answer:

40 yards, 10 yards, and 30 yards.

Was correct for me on edge 2023

Answer:

Step-by-step explanation:

[tex]log_{b}a=c = > b^c=a\\ln(a) = > log_{e}a=c = > e^c=a\\log(a) = > log_{10}a=c = > 10^c=a[/tex]

[tex]log(1000) = 3 = > =10^3 =1000\\ log_{5}(25)=2 = > 5^2=25\\log_{12}144=x = > 12^x=144\\ln(12) =x = > e^x=12[/tex]

The solution has a positive answer (True).

Arithmetic operators are those signs such as addition, subtraction, multiplication, and division that are used to solve mathematical expressions such as fractions and linear equations.

1.

The solution to the expression:

= (-1)(1)(-1)(-1)(1)(-1)(-1)(-1)(-1)(1)(-1)(1)

= 1

Thus, the solution has a positive answer(True)

2.

The solution to the improper fraction:

[tex]\mathbf{\dfrac{5}{7}+(-\dfrac{2}{7})= \dfrac{3}{7} }[/tex]

3.

= -52.31 -(-7.44)

= -52.31 + 7.44

= -44.87

= - 4487/100

4.

The solution to the improper fraction is:

[tex]\mathbf{\dfrac{3}{5}\div -\dfrac{6}{15}=-\dfrac{3}{2} }[/tex]

5.

The given equation is:

-(-6.6) (-20) = 132  which is incorrect.

The correct solution is:

-(-6.6) (-20) = -132

Eric's mistake is that he forgot to multiply by -1 first.

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Answer:

9

Step-by-step explanation:

2 + 1 + 4 + 3 + 5 + 7 + 4 + 2 + 2 + 1 + x = 40

x = 40 - (2 + 1 + 4 + 3 + 5 + 7 + 4 + 2 + 2 + 1)

x = 40 - (3 + 7 + 12 + 6 + 3)

x = 40 - (10 + 18 + 3)

x = 40 - 31

x = 9

Answer:

x = 136

Step-by-step explanation:

x = 180 - 22 - 22

  = 136

The functions shown in the table below are exponential functions, will be g(x) and k(x). Then the correct option are B and D.

The complete question is attached below.

Let a is the base and x is the power of the exponent function and b is the y-intercept.

The exponent is given as

y = aˣ + b

Checking for g(x), then we have

g(x) = 5ˣ

Then the function g(x) satisfies all the condition.

Checking for k(x), then we have

k(x) = 4⁻ˣ

Then the function k(x) satisfies all the condition.

Then the correct option are B and D.

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An inequality that can be used to describe the possible values of x is; C. 0 < x < 14

From the given image, let us first use sine rule to find the angles in the triangle with sides 12, 6 and 7 and angle 120°. Thus;

7/sin α = 12/sin 102

sin α = (7/12) * sin 102

sin α = 0.570586

α = sin⁻¹0.570586

α = 34.8°

We know that sum of angles in a triangle is 180°. Thus;

34.8° + 90° + (7x + 4) = 180°

124.8 + 7x + 4 = 180

7x = 180 - 128.4

x = 51.6/7

x = 7.37

Looking at the given options, x cannot be negative and that rules out the first option. x is greater than 8/7 and that rules out the second option but x is greater than 0 and less than 14 and so option C is correct.

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:Domain : \fbox{-3}\leqslant x \leqslant \fbox{-1}[/tex]

[tex]\qquad \tt \rightarrow \:Range :\:\:\fbox{-4}\leqslant x \leqslant \fbox{-3}[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

Domain = All possible values of x for which f(x) is defined

[ generally the extension of function in x - direction ]

Range = All possible values of f(x)

[ generally the extension of function in y - direction ]

[tex] \large\textsf{For the given graph : } [/tex]

[tex]\qquad \tt \rightarrow \: domain : \fbox{-3}\leqslant x \leqslant \fbox{-1}[/tex]

[tex]\qquad \tt \rightarrow \: range : \:\:\fbox{-4}\leqslant x \leqslant \fbox{-3}[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

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

Step-by-step explanation:

first ,let’s calculate the number of bags made by the company that have both buttons and zips :

150-(43+38+34)

=35

a bag that has buttons : either has buttons but no zips  or  has both buttons and zips

Then

The number of the bags that have buttons is :

43+35 = 78

………………………

Conclusion:

the probability that the bag has buttons is :

[tex]=\frac{75}{150} = \frac{1}{2}[/tex]

Answer:

[tex]45[/tex]

Step-by-step explanation:

[tex]\tan 45^{\circ} = \dfrac{\sin 45^{\circ}}{ \cos 45^{\circ} }\\\\\\~~~~~~~~~~=\dfrac{\sin 45^{\circ}}{\sin\left(90^{\circ} - 45^{\circ} \right)}\\\\\\~~~~~~~~~~=\dfrac{\sin 45^{\circ}}{\sin 45^{\circ}}\\\\\\~~~~~~~~~~=1[/tex]

Answer:200 minutes

Step-by-step explanation:

1 minute = 60 seconds.

6/3 = 2 (20 seconds) 1 photo every 20 seconds.

600x20 = 12000. seconds.

12000/60 = 200 (200 minutes)

Answer:

200 photos

Step-by-step explanation:

1 min = 3 photos

X min = 600 photos

3 X = 600

X = 600/3

X = 200

Answer:

$17,506.73

Step-by-step explanation:

Continuous Compounding Formula

[tex]\large \text{$ \sf A=Pe^{rt} $}[/tex]

where:

Given:

Substitute the given values into the formula and solve for A:

[tex]\sf \implies A=10000e^{(0.07 \times 8)}[/tex]

[tex]\sf \implies A=10000e^{0.56}[/tex]

[tex]\implies \sf A=17506.725...[/tex]

Therefore, the value of the account after 8 years is $17,506.73 to the nearest cent.

Answer:

11

Step-by-step explanation: