Solve for 'x' in both of the following problems. Show all your work/explanations on your own paper and then submit a picture of your work and answers in the dropbox below.

Answer:

a = [tex]\frac{13}{5}[/tex]

Step-by-step explanation:

Given

a = [tex]\frac{3x+2y}{3x-2y}[/tex]  , substitute y = 4 , x = 6

a = [tex]\frac{3(6)+2(4)}{3(6)-2(4)}[/tex] = [tex]\frac{18+8}{18-8}[/tex] = [tex]\frac{26}{10}[/tex] = [tex]\frac{13}{5}[/tex]

Answer:

c(1) = -15

c(n) = c(n - 1) + 4

Step-by-step explanation:

Given arithmetic sequence is,

-15, -11, -7, -3...........

Common difference between each successive and previous term is,

d = -11 - (-15)

  = -11 + 15

  = 4

Since recursive formula of the arithmetic sequence is represented by,

a₁ = First term of the sequence

a(n) = a(n - 1) + d

where a(n) is the nth term and a(n-1) is the previous term of the nth term.

Form the given sequence,

c₁ = -15

c(n) = c(n - 1) + 4

Answer:

45

Step-by-step explanation:

(

3

√

5

)

2

9

√

5

2

Rewrite

√

5

2

as

5

.

9

⋅

5

Multiply

9

by

5

.

45

Answer:

2187

Step-by-step explanation:

I'm guessing you meant ^ as squared? Therefore, our equation is [tex]3^23^5[/tex]. We can simplify using the rule of exponents, giving us [tex]3^7[/tex]. [tex]3^7=2187[/tex].

Answer:

10. x is 15; y is \sqrt104. 11. \sqrt5

Step-by-step explanation:

for 10:

first we find the face on the left side; which according to the pythagorean theorem x is 144 + 81 =225 = x = 15. and y is 11^2 + y^2 = 225 = 225 - 121 = y^2 = y = the square root of 104.

for 11:

144 + y^2 = 169 = y^2 = 25 = y = 5. because the two sides are equivalent, the base is also 5 for the left part of the triangle. therefore, 5^2 + 5^2 = x^2 which means x is the square root of 5.

Answer:

(4x-7)(4x+7)

Step-by-step explanation:

This is called the Difference of Two Squares (DOTS).

These are the conditions that must be met for DOTS to work:

•There must be 2 terms.

•They must be separated by a negative sign.

•Each term must be a perfect square.

First, you have to find 2 square numbers that times together to make 16.

4×4=16

As we want 16x², you just need to make the 4 become 4x:

4x times 4x equals 16x²

Then, find 2 squares that times together to make 49.

7×7=49

You can put the two squares into a bracket with the x variable first, then the number:

(4x-7)(4x+7)

In the brackets, you always put the negative sign in the first one and then the plus sign in the second one.

You can double check your answer by expanding it back out again using FOIL:

F-First

O-Outer

I-Inner

L-Last

Times the First two in the two brackets:

4x times 4x equals 16x²

Times the Outer two:

4x times 7 equals 28x

Times the Inner two:

-7 times 4x equals -28x

Times the Last two:

-7 times 7 equals -49

Form an equation:

16x²+28x-28x-49

The 28x cancel out to leave:

16x²-49

Hope this helps :)

Answer:

could u take a picture of the angles please

Step-by-step explanation:

Question

In circle L, arc MNOP is 120° and the radius is 5 units. Which statement best describes the length of arc MNOP?

• one half the area of circle L

• one third the area of circle L

• one half the circumference of circle L • one third the circumference of circle L

Answer:

• one third the circumference of circle L

Step-by-step explanation:

In the question, we are told that:

In circle L, arc MNOP is 120° and the radius is 5 units.

We are asked to find the statement amongst the options that describes the arc length MNOP of Circle L

Step 1

Find the Area of circle

Area of a circle = πr²

r = 5 units

Area of a circle = π × 5²

Area of a circle = π × 25

Area of a circle = 78.53981634 square units

Step 2

Find the arc length of a circle

Arc length = 2πr × θ /360

r = 5 units

θ = 120°

Arc length = 2 × π × r × 120/360

Arc length = 2 × π × r × (1/3)

Arc length = 2 × π × 5 × (1/3)

Arc length = 10.47198 units

Step 3

Circumference of a circle = 2πr

= 2 × π × 5

= 31.415926536 units

Since the Circumference of a circle = 2πr

Arc length of the circle for the above calculation, = 2πr × 1/3

Therefore, the statement that best describes the arc length MNOP of Circle L is:

" the arc length MNOP is one third the circumference of circle L"

Answer:

the arc length MNOP is one third the circumference of circle L

Step-by-step explanation:

i fishie yupo

Answer:

7 weeks

Step-by-step explanation:

b​=95+(10+9​)w

Combine like terms

b​=95+(19​)w

Let b = 220

220 = 95 + 19w

Subtract 95 from each side

220-95 = 19w

125 = 19w

Divide each side by 19

125/19 = w

6.578947368

Round up

After 7 week

2a , 1st exp= a2 + ab

= a(a+b)

2nd exp = a2-b2

= (a+b) (a-b)

HCF = (a+b)

b, 1 st exp= (a+b)2

= (a+b)(a+)

2 nd exp = a2-b2

= (a+b) ( a-b)

HCF = (a+b)

c, 1 st exp= (a-1)2

= (a+1) (a-1)

2nd exp= a2-1

= (a+1)(a-1)

HCF = (a-1)

d, 1st exp= (x-2)(x-3)

= x(x-3)-2(x-3)

= x2 - 3x - 2x + 6

= x2- 5x+ 6

= x2 - (3+2)x + 6

=x2 -3x-2x+ 6

= x(x-3) -2(x-3)

=(x-3)(x-2)

2 nd exp = (x+2) (x-3)

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

= x2 - 3 x+ 2x -6

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

=(x-3) ( x+ 2)

HCF = (x-3)

Answer:

68 words

Step-by-step explanation:

To find how many words Gordon types per minute :

1972 ÷ 29 = 68 #

Answer:

Step-by-step explanation:

Given that Top Hat Soda has 300,000 millilitres of cola to bottle and,

a bottle is 500 millilitres in capacity.

To find the amount of bottles that will fill the Top Hat Soda,

we have to divide Top Hat Soda by the 500 millilitres bottle

we have:

Number of bottles needed to fill Top Hat Soda=  300,000/500 = 600 bottles.

Hence 600 bottles will fill the Top Hat Soda

Greetings from Brasil...

As stated in the statement:

HEIGHT = CONSTANT ÷ WIDTH

H = C ÷ W

so, isolating the variable C....

C = H · W

choosing any point on the graph...

(2; 30)  ⇒ W = 2 and H = 30

C = H · W

C = 30 · 2

The value of the constant in the equation shown in the figure would be, 60. Hence option C is true.

Given that,

The graph is the relation between Height and width.

As is given in the graph:

Height = Constant / Width

We observe that the graph passes through (2,30), (5,12), (10,6), (30,2)

So, by using any one point we may get the value of constant( since it is a fixed quantity)

Hence, using the point (2,30)

Width = 2

And, Height = 30

So, we get:

Constant = 2 × 30

= 60

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[tex]\\ \sf\longmapsto 20°+2p=70[/tex]

[tex]\\ \sf\longmapsto 2p=70-20[/tex]

[tex]\\ \sf\longmapsto 2p=50[/tex]

[tex]\\ \sf\longmapsto p=\dfrac{50}{2}[/tex]

[tex]\\ \sf\longmapsto p=25[/tex]

Answer:

3d + f -2

Step-by-step explanation:

= 4f+4+3d-6-3f

= f+3d-6

= 3d+ f - 6

Answer:

Joan's older sister weighs 90 pounds

Step-by-step explanation:

x = older sister

x - 10 = Joan

(x + (x-10))/2 = 85

2x - 10 = 170

2x = 180

x = 90

Answer:

90 pounds

Step-by-step explanation:

We can set up an equation to find their weights.

Let's start by naming Joan's weight x.

Her sister's weight would then be x+10, since Joan weighs 10 pounds less.

To find the average between 2 numbers, you need to add them together, then divide by 2.

So we can set up the following equation:

(x+x+10)/2=85

Now let's isolate x.

We can first multiply both sides by 2.

x+x+10=170

Combine like terms.

2x+10=170

Subtract 10 from both sides.

2x=160

Subtract both sides by 2.

x=80

Joan weighs 80 pounds.

x+10 is her sister's weight.

80+10=90

Joan's older sister weighs 90 pounds.

Answer:

The correct option is;

a. 12 pie cm

Step-by-step explanation:

Cavalieri's principle states that if the cross-sectional area of two or more figures of the same altitude are the same at each level of the figures, then the volumes of the figures are also the same;

Given that the base area of the square based prism and the cylinder are the same, and that the square based prism and the cylinder have equal height of 4 cm, then by Cavalieri's principle, their volumes are the same

The volume of the square based prism = 452 cm³

Therefore, the volume of the cylinder (of equal base area) = 452 cm³

The formula for the volume of square based prism = Area of base × Height

∴ The volume of square based prism, 452 cm³ = Area of base × 4 cm

Which gives;

Area of the base of the square based prism  = 452/4 = 113 cm²

The area of the base of the cylinder [tex]A_c[/tex]  = The area of the base of the square based prism = 113 cm²

The area of the base of the cylinder,[tex]A_c[/tex]  is given by the following equation;

[tex]A_c[/tex] = π×r² = 113 cm²

r = √(113/π) = √35.97 ≈ √36  = 6 cm

The circumference of the base of the cylinder,[tex]C_c[/tex]  is given by the following equation

[tex]C_c[/tex] = 2×π×r ≈ 2×π×6 = 12×π cm

The correct option is 12 pie cm.

Answer:

Step-by-step explanation:

[tex]-8+4x-12=-4\left(2x-8\right)\\\\\mathrm{Group\:like\:terms}\\\\\mathrm{Subtract\:the\:numbers:}\:-8-12=-20\\\\4x-20=-4\left(2x-8\right)\\\\\mathrm{Expand\:}-4\left(2x-8\right):\quad -8x+32\\4x-20=-8x+32\\\\\mathrm{Add\:}20\mathrm{\:to\:both\:sides}\\4x-20+20=-8x+32+20\\\\Simplify\\\\4x=-8x+52\\\\\mathrm{Add\:}8x\mathrm{\:to\:both\:sides}\\\\4x+8x=-8x+52+8x\\\\\mathrm{Simplify}\\\\12x=52\\\\\mathrm{Divide\:both\:sides\:by\:}12\\\\\frac{12x}{12}=\frac{52}{12}\\\\x=\frac{13}{3}[/tex]

Answer:

Step-by-step explanation:

-8+4x-12 =-8x+32

4x+8x=32+8+12

12x=52

x=52\12

x=41.3

Answer:

20 meters

Step-by-step explanation:

The track is circular so it means that after Patrick raced the entire track he is back at the starting point. In other words, every 440 meters he is back to the beginning.

So we would have that, if he races round the track twice, he would run 440(2) = 880 meters and he would be back at the starting point.

The problem asks us how far is he from the starting point at the 900 meter mark. If at 880 meters he is at the starting point, then at 900 meters he would be [tex]900-880=20[/tex] meters from the starting point.

Answer:

84 square inches is the correct answer.

Step-by-step explanation:

I am 100% sure of that.

Hope this helps....

Have a nice day!!!!

Answer:

[tex]\huge\boxed{BD = 12\ units}[/tex]

Step-by-step explanation:

If AB = 5 , then AE = 5 [Radii of the same circle]

So,

AC = AE + EC

AC = 8+5

AC = 13 units

Now, Using Pythagorean theorem to find the missing side i.e. BD because tangent strikes the circle at 90 degrees making the triangle a right angled triangle

[tex]c^2=a^2+b^2[/tex]

Where c = AC , a = BD and b = AB

[tex]13^2 = BD^2+5^2[/tex]

169 = BD² + 25

Subtracting 25 to both sides

169 - 25 = BD²

BD² = 144

Taking square root on both sides

BD = 12 units

Answer:  is 762 meters

Step-by-step explanation:

One foot is equal to 0.3048 meters so multiply 2500 by 0.3048 to find how many meters there are.

2500 * 0.3048 = 762

Answer:762.5 meters

Step-by-step explanation:

1 foot =0.305 m

Hence,0.305×2500=762.5 metres as the answer.

Answer:

So the quotient of [tex]\frac{x^{2} + x - 6}{x^{2} -6x + 5} X \frac{x^{2} + 2x - 3}{x^{2} -7x + 10}[/tex] has (x + 3)² in the numerator and (x + 5)² in the denominator.

Step-by-step explanation:

[tex]\frac{x^{2} + x - 6}{x^{2} -6x + 5} X \frac{x^{2} + 2x - 3}{x^{2} -7x + 10}[/tex]

Factorizing the expressions we have

[tex]\frac{x^{2} + 3x -2x - 6}{x^{2} -x - 5x + 5} X \frac{x^{2} + 3x - x - 3}{x^{2} -2x -5x + 10}[/tex]

[tex]\frac{x(x + 3)- 2(x + 3)}{x(x -1) - 5(x - 1)} X \frac{x(x + 3) - 1(x + 3)}{x(x - 2) - 5(x - 2)}[/tex]

[tex]\frac{(x + 3)(x - 2)}{(x - 5)(x - 1)}X\frac{(x + 3)(x - 1)}{(x - 2)(x - 5)}[/tex]

Cancelling out the like factors, (x -1) and (x - 2), we have

[tex]\frac{(x + 3)(x + 3)}{(x - 5)(x - 5)}[/tex]

= [tex]\frac{(x + 3)^{2} }{(x + 5)^{2} }[/tex]

So the quotient of [tex]\frac{x^{2} + x - 6}{x^{2} -6x + 5} X \frac{x^{2} + 2x - 3}{x^{2} -7x + 10}[/tex] has (x + 3)² in the numerator and (x + 5)² in the denominator.

The length of the side can be both 5 and 9.

An Isosceles Triangle is a triangle that has two equal sides.

The length of the sides of an isosceles triangle is given as 5 and 9

To determine the third side, the property of Triangle Inequality will be used

According to the property, the sum of any pair of a triangle’s sides is always greater than the third side.

If the third side is 5 then

5+5 > 9

10 >9

true

if the third side is 9 then

5+9 > 9

14>9

Therefore, the length of the side can be both 5 and 9.

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Answer:

C. X-Y X-Y

Step-by-step explanation:

The question asks to identify the least amount of discount on the conference registration. If the registration discount is at least half of the possible saving of ROB then all attendees will stay within the block. X is the block rate and Y is the non block rate. The saving for staying two nights outside the block is 2 (X-Y)

Answer:

$6,291.70

Step-by-step explanation:

You're given the equation and you're given an x-value; 75,834. Just plug it in to get m = 2500 + 0.05(75,834) = 2500 + 3791.70 = 6,291.70.

Answer:

$6,291.70

Step 1:

To find the monthly salary for somebody who sells $75,834 in cars, we need to first multiply that by 0.05, or 5%, since 0.05 has to get multiplied by s (sales) in the equation they provide us. We don't do anything with $2,500 (yet).

[tex]75,834*0.05=3791.70[/tex]

One of the options for our answer shows 3,791.7, but we are not finished with solving this problem, so 3,791.7 is not our answer.

Step 2:

After completing step 1, Superb Auto already provides new salespeople with $2,500. This means that whatever they sell (or don't sell), they would still get that $2,500. In step 1, we found out that our first number that replaces 0.05s is 3791.7, so we just have to add that to 2,500 to get our final answer.

[tex]3791.7+2500=6291.7[/tex]

Our final answer is $6,291.70, and that is the third option on our list of choices.

Answer:

Answer:

associative

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

0/7 = 0

We can divide 0 by a non zero number

5/0 = undefined

We cannot divide by 0

Answer:

5

Step-by-step explanation:

-4 = x - 9

Answer:

5

Step-by-step explanation:

5 - 9 = -4

Answer:

Step-by-step explanation:

The shaded regions consist of a triangle and a semicircle

Area of shaded regions = Area of Triangle + Area of semicircle

Area of Triangle = (h x b) ÷ 2

Height, h = 10 cm

Base, b = 8 cm

Are of the triangle component = (10 x 8) ÷ 2

= 80 ÷ 2

= 40 cm^2

 Area of semicircle = πr^2 ÷ 2

Diameter, D = 8 cm

Radius, r = 8 cm ÷ 2 = 4 cm

Are of the semicircle component = [π(4^2) ÷ 2)

= 16π ÷ 2

= 16π cm^2

 Total area of shaded regions

= (40+16π) cm^2

= 8 (5 +2π) cm^2

Answer:

[tex]\boxed{\sf Area = 8\pi + 40\ cm^2}[/tex]

[tex]\boxed{\sf Perimeter = 4\pi + 22\ cm}[/tex]

Step-by-step explanation:

Area of the figure:

Firstly: Area of semicircle:

[tex]\sf \frac{\pi r^2}{2} \\Where\ r = 4 \ cm\\\frac{\pi (4)^2}{2} \\\frac{16 \pi}{2}\\8 \pi \ cm^2[/tex]

Then Area of Triangle

[tex]\sf 1/2 (Base)(Height)\\1/2(10)(4)\\10*2\\20\ cm^2[/tex]

Area of Figure = Area of Semicircle + 2(Area of triangle)

=> 8π + 2(20)

=> 8π + 40 cm²

Perimeter of Semicircle:

Firstly, we'll have to find the hypotenuse

[tex]\sf c^2 = a^2+b^2\\c^2 = 4^2+10^2\\c^2 = 16+100\\c^2 = 116\\c = 11\ cm[/tex]

Then, Perimeter of the semi-circle:

=> πr

Where r = 4 cm

=> 4π

Now, the perimeter of the whole figure:

=> 4π + 2(11)

=> 4π + 22 cm

Answer:

Step-by-step explanation:

Answer:

The polygon formed through points A, D, C, and E is a quadrilateral. The sum of the interior angle measures for any quadrilateral is 360°.

Step-by-step explanation: