Math Question (10 Points):

Answer:

a - HT = 17

b - ∠T = 62

c - ∠H = 28

Answer:

0.67

Step-by-step explanation:

We have to find out the exchange rate for pounds to dollars

150 pounds divided by 225 dollars

We get 0.6(6) the 6 in parenthesis for the repeating number.

Since we round to the nearest hundred we get 0.67.

Answer:

[tex]x= \sqrt{503}-3[/tex]

Step-by-step explanation:

Hypotenuse = 32 feet

Short leg = x

Long leg = x+6

We will use Pythagoras theorem

[tex]Hypotenuse^2=Perpendicular^2+Base^2[/tex]

[tex]32^2=x^2+(x+6)^2[/tex]

[tex]1024=x^2+x^2+36+12x[/tex]

[tex]2x^2+12x-988=0[/tex]

[tex]x=-3-\sqrt{503}, \sqrt{503}-3[/tex]

Since the distance cannot be negative

So,[tex]x= \sqrt{503}-3[/tex]

Answer:

2 × 5

Step-by-step explanation:

We want to split the number 10 into its prime numbers.

A good way to start is divide the number by 2, if it's even. 10 is even, so we can divide by 2.

[tex]10\div2=5[/tex]

So the current factors are 2 and 5. We would keep going if one of these numbers was composite, but 2 and 5 or both prime numbers, so we can end the factorization here.

Therefore, the prime factorization of 10 is 2 × 5.

Hope this helped!

The prime factorization of 10 is 2 x 5.

Prime factorization is when you figure out the prime numbers that you can multiply together  to get a certain number.

To figure out the prime factors of 10, we begin by dividing it by the lowest prime number, which is 2. Because 10 can be divided evenly by 2, we can say that 10 is equal to 2 multiplied by 5.

The numbers 2 and 5 are special because they can only be divided by 1 and themselves. This makes them prime numbers. The prime factorization of 10 is the result of multiplying the prime factors 2 and 5 together.

Read more about  factorization  here:

https://brainly.com/question/25829061

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Answer:

x = 80

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the opposite interior angles

25+x = 105

Subtract 25 from each side

25+x-25 = 105-25

x = 80

Answer: C) 16

Step-by-step explanation:

A Hexagon has 6 Sides and Since the perimeter is 24, each side has a length of 4.

4 * 4 = 16

ANSWER:

4d shape LOOKS LIKE THIS

Answer:

draw 2 lines and draw 2 circles in the lines with the edge touching the line

Step-by-step explanation:

In between two circles, there might be 0, 1, 2, 3, and 4 tangents are there.

"A tangent line to a circle is a line that touches the circle at exactly one point, never entering the circle's interior.

1. When one circle is in between another and one circle does not touch the other one, then tangent is not possible.

2. When one circle is in between another and one circle touches the other one at a point inside the circle, then only one tangent is possible.

3. When one circle intersects the other one, then two tangents are possible.

4. When one circle touches the other one at a point outside, then three tangents are possible.

5. When one circle neither intersects the other one nor inside the other one, then four tangents are possible.

Learn more about the tangent of a circle here: https://brainly.com/question/393370

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Answer:

Step-by-step explanation:

for each positive integer m, so that la - r2m-ll and la - r2m I are both less than

1 1

Ir2m - r2m-ll .:::: 42(m-l) Ir2 - rll = 24m - 3 ·

It follows that limn--->oo rn = limn--->oo rn-l = a. Taking limits in the recursion in

(d) leads to

1

a=I+--

l+a

which reduces to a 2 = 2. Since rn > 0 for each n, a > O.

Answer:

44

Step-by-step explanation:

1/2m-3/4n=16 , m when n=8

1/2m-3/4n=16

1/2m - 3/4(8) = 16

1/2m - (8 x 3)/4 = 16

1/2m - (24/4) = 16

1/2m - 6 = 16

1/2m = 16 + 6

1/2m = 22

m = 22 x 2

m = 44

Here

Angle R = Angle T

UR = ST

US = SU

So using RHS conguerence criteria Triangle RSU conguerent to Triangle TUS

Answer: C is your answer.

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Answer:

63

Step-by-step explanation:

becuase when you divide 70 by 10, you will get 7 which then when you mutiply it by 9, you will get 63

Answer:

nothing can be further done with this topic. please check the expression entered or submit a picture for futher understanding

Step-by-step explanation:

Answer:

[tex]\boxed{x = 40}[/tex]

Step-by-step explanation:

Hey there!

Well angles like 142 and 2x + 22 equal each other because they are across from each other.

So we can set up the following,

142 = 3x + 22

Single out x

-22 to both sides

120 = 3x

Divide both sides by 3

x = 40

Hope this helps :)

Answer:

x=40

Step-by-step explanation:

142=3x+22

3x+22-22=142-22

3x=120

120/3=40

Answer:

So, 1 point is on (-4, -3)

Other point is on (-4, -7)

Step-by-step explanation:

Slope = y/x - y1/x1

=> -3 / -4 - ? = 1/3

=> -3 / -4  - 1/3 = ?

=> -3 -1 / -4 - 3

=> -4 / -7

So, -3 / -4 - (-4 / -7)

=> -3 +4 / -4 + 7

=> 1/3

So 1 point is on (-4 , -3)

Other point is on (-4, -7)

Answer:no

Step-by-step explanation:

No

Answer:

Step-by-step explanation:

Given two  series A and B;

Series A: 10 + 4 +8/5 + 16/25 + 13/125 + ...

Series B: 1/5 + 3/5 + 9/5 + 27/5 + 81/5 +...

Both series are geometric series since they have the same common ratio. Given the geometric series T₁, T₂, T₃, T₄..., the common ratio r is expressed as [tex]\frac{T_2}{T_1} =\frac{T_3}{T_2} =\frac{T_4}{T_3} = r[/tex].

a) For series A, Given T₁ = 10, T₂ = 4, T₃ = 8/5 and T₄ = 13/125

Its common ratio is expressed as [tex]\frac{4}{10} =\frac{8/5}{4} =\frac{13/125}{8/5} = 2/5[/tex]

Hence the common ratio of series A is 2/5

The sum to infinity of the geometric series will be expressed as [tex]s_\infty = \dfrac{a}{1-r}[/tex]

Note that the sum to infifnity is used since the series is tending to infinity.

a is the first term if the series = 10

r - 2/5

On substituting this values into the formula;

[tex]s_\infty = \dfrac{10}{1-2/5} \\\\s_\infty = \dfrac{10}{3/5} \\\\s_\infty = 10* 5/3\\s_\infty = 50/3[/tex]

Hence the sum of the series is 50/3

b) For the series B;

Series B: 1/5 + 3/5 + 9/5 + 27/5 + 81/5 +...

The common ratio of the series is expressed as shown;

[tex]\frac{3/5}{1/5} =\frac{9/5}{3/5}= \frac{27/5}{9/5 } = r\\ r = (3/5 * 5/1) = 9/5*5/3 = 27/5*5/9 = 3[/tex]

Hence its common ratio is 3.

Sun of the series is expressed similarly as:

[tex]s_\infty = \frac{a}{1-r}\\ s_\infty = \frac{1/5}{1-3}\\\\s_\infty = \frac{1/5}{-2}\\\\[/tex]

[tex]s_\infty = 1/5 * -1/2\\s_\infty = -1/10[/tex]

Hence the sum of series B is -1/10

Answer:

The conjugate is 2+5i and the product is 29.

Step-by-step explanation:

The conjugate of a complex number [tex]a+bi[/tex] is [tex]a-bi[/tex]

Our complex number is 2-5i.

Here, a = 2 and b = -5

Thus, the conjugate of 2-5i is

[tex]2-(-5i)=2+5i[/tex]

Using this rule:

[tex](a+b)(a-b)=a^{2}-b^{2}[/tex]

And the fact that [tex]i^{2} = -1[/tex]

We can find the product of any complex number and its conjugate:

[tex](a+bi)(a-bi)=a^{2} - (bi)^{2}=a^{2} - b^{2} i^{2} = a^{2} + b^{2}[/tex]

As our complex number is [tex]2-5i[/tex], the product with its conjugate will be

[tex]2^{2} + (-5)^{2} =4+25=29[/tex]

The right question is:

[tex]\frac{1}{2}x - 3y = 9[/tex]

[tex]5x + y = 28[/tex]

Answer:

[tex]x = 6[/tex]

[tex]y = -2[/tex]

Step-by-step explanation:

Given

[tex]\frac{1}{2}x - 3y = 9[/tex]

[tex]5x + y = 28[/tex]

Required

Solve for x and y

Make y the subject of formula in the second equation

[tex]y = 28 - 5x[/tex]

Substitute [tex]y = 28 - 5x[/tex] in the first equation

[tex]\frac{1}{2}x - 3(28 - 5x) = 9[/tex]

Open the bracket

[tex]\frac{1}{2}x - 3*28 - 3*- 5x = 9[/tex]

[tex]\frac{1}{2}x - 84 + 15x = 9[/tex]

Collect Like Terms

[tex]\frac{1}{2}x + 15x = 9+ 84[/tex]

[tex]\frac{x}{2} + 15x = 9+ 84[/tex]

[tex]\frac{x+30x}{2} = 93[/tex]

[tex]\frac{31x}{2} = 93[/tex]

Multiply both sides by 2

[tex]2 * \frac{31x}{2} = 93 * 2[/tex]

[tex]31x = 186[/tex]

Divide both sides by 31

[tex]\frac{31x}{31} = \frac{186}{31}[/tex]

[tex]x = \frac{186}{31}[/tex]

[tex]x = 6[/tex]

Recall that [tex]y = 28 - 5x[/tex]

So;

[tex]y = 28 - 5 * 6[/tex]

[tex]y = 28 - 30[/tex]

[tex]y = -2[/tex]

Hence;

[tex]x = 6[/tex] and [tex]y = -2[/tex]

Answer:

g(1)=-72; g(n)=g(n-1)*(1/6)

Step-by-step explanation:

g(1)= -72*(1/6)^(1-1)=-72*(1/6)^0=-72*1=-72

g(2)=-72*(1/6)^(2-1)=-72*(1/6)^1=-72*(1/6)=-12

g(2)=g(1)*(1/6)

g(n)=g(n-1)*(1/6)

Answer:

37.3

Step-by-step explanation:

If you want to solve it.

Cylineder Formula: Volume = π(radius)²(height)

Isolate height by diving πr² on both sides.

height = (volume/πr²)

height = (300/π(1.6^2))

Answer:

h = 36.2 cm

Step-by-step explanation:

lets make it short and simple

vol of cylinder + volume of hemisphere = 300 cu.cm.

Vc + Vh = 300  --- eq.1

cylinder radius = 1.6 cm.

since it says NOT TO SCALE

let the radius of hemisphere is the same as cylinder.

vol of cylinder = πr²h

vol of hemisphere = 2/3 πr³

using eq.1

πr²h + 2/3 πr³ = 300

π (1.6²) h + 2/3 π (1.6³) = 300

h = 36.2 cm

check:

Vc + Vh = 300

π (1.6²) 36.2 +  2/3 π (1.6³) = 300

300 cu.cm = 300 cu.cm.  ----OK

Answer:

31 Pikachu bags were sold.

19 peanut bags were sold.

Step-by-step explanation:

Let's set up an equation of the total revenue of the day, where x is the number of Pikachu's sold.

We know that the number of Peanuts sold is 50-x (as the total needs to be 50)

We know that the total revenue is:

Number of Pikachus * Cost per Pikachus + Number of Peanuts * Cost per Peanuts

Using our definitions above:

Total Revenue = x * $3.68 + (50-x) * $0.76

We know that the revenue needs to be $128.52.

$128.52 = x * $3.68 + (50-x) * $0.76

Let's remove the $ signs.

128.52 = x * 3.68 + (50-x) * 0.76

Multiplying both 50 and -x with 0.76, "expanding" the parenthesis.

128.52 = x*3.68 + 50*0.76 - x*0.76

128.52 = x*3.68 + 38 - 0.76*x

Subtracting 38 from both sides

90.52 = 3.68*x - 0.76*x

We can simplify the right side.

90.52 = 2.92*x

We can divide both sides by 2.92:

31 = x

And flip it:

x = 31

So 31 Pikachus were sold (remember we claled that x), and as we know, the number of peanut bags sold is

50-x = 50-31 = 19

31 Pikachu bags were sold.

19 peanut bags were sold.

[tex] \LARGE{ \boxed{ \rm{ \pink{Solution:}}}}[/tex]

Let the number of peanut bags be x

Then, Number of pikachu bags = 50 - x

Given,

Then,

⇛ Total cost he gets from peanut bag = $0.76 × x

⇛ Total cost he gets from pikachu bag = $3.68(50 - x)

According to question,

⇛ $0.76x+ $3.68(50 - x) = $128.52

Solving this equation,

⇛ 0.76x + 184 - 3.68x = 128.52 (Removed $ symbol)

⇛ 184 - 2.92x = 128.52

⇛ 184 - 128.52 = 2.92x

⇛ 55.48 = 2.92x

Flipping the equation,

⇛ 2.92x = 55.48

⇛ x = 55.48 / 2.92

⇛ x = 19

Then,

⇛ 50 - x = 50 - 19 = 31

[tex] \large{ \therefore{ \boxed{ \rm{ \purple{No. \: of \: peanut \: bags = 19}}}}}[/tex]

[tex] \large{ \therefore{ \boxed{ \rm{ \purple{No. \: of \: pikachu \: bags = 31}}}}}[/tex]

━━━━━━━━━━━━━━━━━━━━

Answer:

40z + 5

Step-by-step explanation:

I'm assuming you need to factor 32z + 4 + 8z + 3 - 4 + 2

Hope this helped

Answer:

The factored expression for the given equation is 4(8z⁴ + 2z³ - z²)

Step-by-step explanation:

In the problem, we a re given an equation.

32z⁴ + 8z³ - 4z²

We can factor out this equation by finding the common factor between all of the coefficients which are 32, 8, and 4.

A common factor between them is 4 because each number can be easily divided by 4. Each number is also a multiple of 4. So, when we are factoring, we will divide each number by 4 because 4 will be on the outside of the parentheses in the final answer.

4(8z⁴ + 2z³ - z²)

So, this is your factored expression from the given equation.

[tex] \cos(2A)=\cos^2 A-\sin^2A=(\cos A+ \sin A)(\cos A-\sin A)[/tex]

substitute the second term in LHS to get

[tex]{ (\cos A - \sin A)^2 \over \cos(2A))}[/tex]

expand the square, [tex] \frac{1-2\sin A \cos A}{\cos 2A}= \sec2A- \tan 2A[/tex]

([tex] \sin (2\theta)=2 \sin\theta\cos\theta[/tex])

Answer:

Both sides can take the same identity

Step-by-step explanation:

Sec 2A - tan 2A

Express with sin and cos

1/cos (2A) - sin (2A)/cos (2A)

= 1 - sin (2A) / cos (2A)

=

1 - sin (x) = 1-sin (x) = 1 - sin^2 ( x ) / 1 + sin (x)  

=

1 - sin ^2 (x) = cos ^2 (x)  

=cos ^2 (2A) / 1+sin (2A)/Cos (2A)

simplified

cos (2A) / 1+sin 2A

identity x used = cos 2x = cos ^2 x - sin ^2 x

= 1 + sin (2x) + (cos (x)) + (sin (x))^2

= cos ^2A - sin ^2A / (cos A - sin A) ^2

= cos A - sin A / cos A +sin A

Both sides are true.

You need to see if it passes the vertical line test, then graph it to see if it is but is a function tho.

Answer:

19.5

Step-by-step explanation:

The Volume of a cone is h/3(r²)[tex]\pi[/tex]

That means, for the larger cone,

66=h/3(3²)([tex]\pi[/tex])

66=h/3*9[tex]\pi[/tex]

66/9[tex]\pi[/tex]*3=h

h=7, so the height of the larger cone is seven

Since the cones are similar, it has to have the same ratio. 7/3 of 2 is 4.6666.  So the height of the smaller cone is 4.66666.

Putting that in the formula,

V=(4.66666/3)(2²)[tex]\pi[/tex]

V=1.555555*4*[tex]\pi[/tex]

V=19.547

Answer:

19.6

Step-by-step explanation:

I have acellus too, and honestly, I typed in 19.5, which didn't work, so I typed in 19.6 and it worked. Hope this helps!

Answer:

B

Step-by-step explanation:

It's domain is side from side and so it can't be c or d. and it range goes to a positive number so it has to be B.