Solve the simultaneous equations
2x – 3y = 12
3x + 4y = 1

Answer:

Step-by-step explanation:

The first one gives us everything we need except the radius, which is easy enough to solve for if you're careful with your algebra. The area of a sector of a circle is given as:

[tex]A_s=\frac{\theta}{360}*\pi r^2[/tex] where θ is the measure of the central angle of the circle. For us, that fills in as follows:

[tex]48\pi=\frac{270}{360}*\pi r^2[/tex] and manipulate it as follows:

[tex]r^2=\frac{(360)(48\pi)}{270\pi}[/tex] the π's cancel out, leaving us with simple multiplication and division to get

r = 8. Now for the next one, which is a bit more involved.

In order to find the area of the shaded part, we need to find the area of the right triangle there and subtract it from the area of the sector of the circle. First the area of the sector, which is given as:

[tex]A_s=\frac{\theta}{360}*\pi r^2[/tex] where θ again is the measure of the central angle of the circle, 90°:

[tex]A_s=\frac{90}{360}(3.1415)(10)^2[/tex] which simplifies a bit to

[tex]A_s=\frac{1}{4}(3.1415)(100)[/tex], giving us an area of

[tex]A_s=78.5375m^2[/tex]. Now onto the area of the triangle.

Since this triangle is inscribed in the circle and the circle's radius is 10, tha also gives us both the height and the base measures of the triangle. The area then is:

[tex]A_t=\frac{1}{2}(10)(10)[/tex] which is

[tex]A_t=50m^2[/tex]

Subtract that from the area of the sector to get that the shaded area is 28.5 square meters, choice A.

Answer:

I still think you equations are wrong...

4000/4000 not 400/400

Step-by-step explanation:

2000 A+ 6000B=520

4000A+4000B        =480

~~~~~~~~~~~~~~~~~~~~~

2000 A+ 6000B=520

-2000A - 2000B   =-240  

4000B = 280

B=7%

A=5%

Answer:

none

Step-by-step explanation:

that's not the correct sign

Answer:

m = 2, n = - 3

Step-by-step explanation:

Given the 2 equations

2m + 3n = - 5 → (1)

5m + 3n = 1 → (2)

Subtract (2) from (1) term by term to eliminate n

2m - 5m = - 5 - 1

- 3m = - 6 ( divide both sides by - 3 )

m = 2

Substitute m = 2 into either of the 2 equations and solve for n

Substituting into (1)

2(2) + 3n = - 5

4 + 3n = - 5 ( subtract 4 from both sides )

3n = - 9 ( divide both sides by 3 )

n = - 3

Step-by-step explanation:

2m + 3n = -5

5m + 3n = 1

(Multiply each equation by a suitable number so that the two equations have the same leading coefficient)

6m + 9n = -15

15m + 9n = 3

(Subtract the second equation from the first)

15m- 6m = -15-3

-9m= -18

-9m/-9= -18/-9

m= 2

(Solve this new equation for m)

5(2) +3n = 1

10+3n=1

3n=1-10

3n=-9

3n/3 = -9/3

n= -3

(Substitute m = 2 into either Equation 1 or Equation 2 above and solve for n )

Answer:

option A

Step-by-step explanation:

Let  x = y + y

Now using Pythagoras theorem :

                                    [tex]15^2 = y^2 + 12^2\\225 = y^2 + 144\\225 - 144 = y^2\\81 = y^2\\9 = y[/tex]

Therefore , x = y + y = 18

Answer:

(x/2)²+12² =15²

(x/2)²+144=225

(x/2)²=225-144

x²/4. =81

x² =81×4

x. =√81×4

x. =9×2

x. =18

answer is option A

Answer:

c is the and

no worries thank you to each of the Fourth of that mother you have any other questions please contact me

[tex]\huge\color{purple}\boxed{\colorbox{black}{♡Solution♡}}[/tex]

[tex]8 \: {m}^{2} - 5 \: m + 1[/tex] ✅

Step-by-step explanation:

[tex] \frac{(16 \: {m}^{3} - 10 \: {m}^{2} + \: 2m) }{2 \: m} \\ \\ = \frac {2 \: m \: (8 \: {m}^{2} - 5 \: m + 1)} {2 \: m} \\ \\ = 8 \: {m}^{2} - 5 \: m + 1[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{.}}}}}[/tex]

Answer:

Red can

Step-by-step explanation:

Tonato juice come in different sizes

The red can contains 6 cups

The blue can contains 2 pints

The yellow can contains 32 fluid ounces

Therefore the can that holds the highest juice is the red can with 6 cups if tomato juice

Answer:

perimeter is 35.6 area is 108

Step-by-step explanation:

it helps to draw a picture. first the perimeter of the rectangle is 4x2 +12=20 we wont be needing one of the twelves because it is connected to the triangle the area or the rectangle is 12x4=48. now for the triangle. we will need the Pythagorean theorem to find the sides first split the base in half 12/2=6 now we use the height and the base 6^{2} +5x^{2} =6

2

+5x

2

= 61 the square root of 61 is about 7.8 the perimeter is 7.8+7.8 +12 but we wont need the base because it is attached to the rectangle =15.6 the area of the triangle is like half a square Base times height though 12x5=60

the whole perimeter if 15.6+20=35.6 the area is 60+48=108

wlcm♥️

Answer:

Total number of mug = 14 mugs

Step-by-step explanation:

Given:

Total amount of Clay Leo bought = 50 lbs

Total amount of Clay left = 27.42 lbs

Total amount of Clay used in sculpture = 12.5 lbs

Amount of clay each muh need = 0.72 lbs

Find;

Total number of mug

Computation:

Assume;

Total number of mug = a

So,

Total amount of Clay Leo bought = Total amount of Clay left + Total amount of Clay used in sculpture + (Amount of clay each muh need)(Amount of clay each muh need)

50 = 27.42 + 12.5 + (0.72)(a)

50 = 39.92 + (0.72)(a)

(0.72)(a) = 10.08

a = 14

Total number of mug = 14 mugs

Answer:

(-2,-5)

Step-by-step explanation:

Y=x^2/2 +2x-3

Y=1/2 ×(x+2)^2 -5

a=1/2

h=-2

k=-5

(-2,-5)

The requried vertex of the parabola y = (1/2)x² + 2x - 3 is (-2, -5).

A parabola is a cross-section cut out of the cone and represented by an equation y = 4ax².

To find the vertex of the parabola defined by the equation y = (1/2)x² + 2x - 3, we can use the fact that the vertex is located at the point (-b/2a, f(-b/2a)), where a and b are the coefficients of the quadratic term and the linear term, respectively.

In this case, a = 1/2 and b = 2, so we can substitute these values into the formula to get:

x-coordinate of vertex = -b/2a = -2/(2*1/2) = -2

To find the y-coordinate of the vertex, we can substitute this value of x into the equation and simplify:

y-coordinate of vertex = (1/2)(-2)² + 2(-2) - 3

= 1/2(4) - 4 - 3

= -5

Therefore, the vertex of the parabola y = (1/2)x² + 2x - 3 is (-2, -5).

Learn more about parabola here:

brainly.com/question/4074088

#SPJ2

Answer:

option A

Step-by-step explanation:

[tex]\frac{x^a}{x^b} = x^{a-b}[/tex] , [tex]z^0 = 1[/tex]

So,

[tex]\frac{18x^5 y}{6xy^8z^0} = \frac{18}{6} \times x^{5 -1} \times y^{1-8} = 3 x^4 \times y^{-7} = \frac{3x^4}{y^7}[/tex]

Answer:

x = 1/2

Step-by-step explanation:

y = 7x+5

y = 9x+4

7x+5 = 9x+4

1=2x

x = 1/2 = 0.5

Answer:

1. [tex]x = - \frac{5}{7} [/tex]

2. [tex] x = - \frac{4}{9} [/tex]

Step-by-step explanation:

[tex]y = 7x + 5 \\ 0 = 7x + 5 \\ - 7x = 5[/tex]

[tex]\boxed{Answer:{\boxed{\green{x = - \frac{5}{7}}}}} [/tex]

[tex]y = 9x + 4 \\ 0 = 9 x + 4 \\ - 9x = 4[/tex]

[tex] \boxed{Answer:{\boxed{\green{x = - \frac{4}{9} }}}}[/tex]

Answer:

x = 1 .  Hopefully im reading this correct

Step-by-step explanation:

8x - 5 = 3

8x = 5 + 3

8x = 8

x = 8/8

x = 1

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

x is 1

Step-by-step explanation:

AC =PR

AB =PQ

8x - 5 =3

8x =3+5

8x =8

x=8/8

x=1

Answer:

2 students

Step-by-step explanation:

Given that

There are 48 students out of which 2 by 3 have their speeches and the remaining of 7 by 8 give their speeches

We need to find the no of students who haven't given their speeches

So,

= 48 × 2 ÷ 3

= 32

Now

= (48 - 32) × 7 ÷ 8

= 14

So, the no of students still haven't given their speeches is

= 48 - 32 -14

= 2 students

Answer:

Starting from

2(-x) = 3x - 5

Distribute

-2x = 3x - 5

add 2x to both sides

0 = 5x - 5

Add 5 to both side

5 = 5x

Flip

5x = 5

Answer:

The number itself is 508.231

Step-by-step explanation:

Any multiplying each of the numbers, we will have the specific places

Hundreds

5 * 100 = 500

Tenths

0 * 10 = 0

ones

8 * 1 = 8

Tenths = 2 * 1/10 = 2/10 = 1/5 = 0.2

Hundredths = 3/100 = 0.03

Thousandths = 1/1000 = 0.001

So we simply sum all these to get the number itself as follows

500 + 8 + 0.2 + 0.03 + 0.001 = 508.231

Answer:

2 1/2

Step-by-step explanation:

divide in 5 then divide half in 5 also

Answer:

2,5

Step-by-step explanation:

The length of a piece of wood is:

12 ½ : 5 = 5/2 = 2,5

9514 1404 393

Answer:

  A) r = d/t

  B) 221,760 ft/h

  C) 42 mi/h

  D) miles; the number is more comprehensible

Step-by-step explanation:

A) Given d = rt

Divide by the coefficient of r to solve for r.

  r = d/t

__

B) Fill in the given numbers to find the rate in ft/h.

  r = (665,280 ft)/(3 h) = 221.760 ft/h

__

C) Multiply by the conversion factor (1 mi)/(5280 ft) to convert to miles.

  (221,760 ft/h)(1 mi)/(5280 ft) = 42 mi/h

__

D) For this scenario, miles per hour is a better unit for speed. Many people have seen that speed registered on a speedometer, so have some sense of what it means. Often numbers outside the range of 1 to 1000 are beyond ready comprehension.

Answer:

Step-by-step explanation:

since there is no table included with the question I'm concluding that you need to find values of y using values of x, simply substitute the x values in the equation and you'll get the y value like this

if x = 1 y = 4

Answer:

x - 0 1 2 3 4 5

y - 3 4 5 6 7 8

It is very simple, all you have to do is add three to x every time, for example if x is 153, y will be 156. 3 should be the beginning, the y intercept in graphs, and the beginning means x should be 0.

Answer:

Step-by-step explanation: the second answer im not vary sure but ist kinda resonable

Answer:

Step-by-step explanation:

Step 1

Find the fraction of the money he gave the charity

Let the total amount he had = 1

Bertie won the lottery! He spends 4/5 of his money on a large house. He spends 3/4 of his REMAINING money on a luxury yacht. He spends 2/3 of his remaning money on a trip to space.

Fraction of money he gave to charity =

1 - (4/5 + 3/4 + 2/3)

He gives the remaning $50,000 to a charity. How much did he win?

Both operations in the equation are adding so you would add the numbers from left to right.

The first step would be 33 + 46

Answer: 1. 33 + 46

Given:

Consider the below figure attached with this question.

To find:

The measure of angle 3.

Solution:

According to intersecting secant theorem, if two secants of a circle intersect each other outside the circle, then the angle on the intersection is half of the difference of the intercepted arc.

[tex]\text{Angle on intersection}=\dfrac{1}{2}(\text{Major arc}-\text{Minor arc})[/tex]

Using the intersecting secant theorem, we get

[tex]m\angle 3=\dfrac{1}{2}(m(arcXY)-m(arcWZ))[/tex]

[tex]m\angle 3=\dfrac{1}{2}(85^\circ-25^\circ)[/tex]

[tex]m\angle 3=\dfrac{1}{2}(60^\circ)[/tex]

[tex]m\angle 3=30^\circ[/tex]

Therefore, the measure of angle 3 is 30 degrees.

Answer: 30 degrees

Step-by-step explanation:

need the points

Given:

The table of values of a function.

To find:

The domain and range of the given function.

Solution:

Domain: The set of input values of x-values is known as domain.

Range: The set of output values of y-values is known as domain.

From the given table it is clear that x-values are [tex]-5,0,5,10,15[/tex] and the y-values are [tex]-1,0,1,2,3[/tex]. So,

[tex]Domain=\{-5,0,5,10,15\}[/tex]

[tex]Range=\{-1,0,1,2,3\}[/tex]

Therefore, the correct option is D.

The domain and range of the function represented by the table is as follows:

The domain of a function is the set of input values, x, for which a function is defined. The domain is the input of the function. The domain is the sets of all input value that produces the output value.

The domain are likewise called input . The domain are usually the x values

The set of values the function outputs is termed the range of the function. In a simpler term, the range are the output of the function. The range are usually the y values.

Therefore, the domain and range of the function represented by the table is as follows;

learn more on domain and range here; https://brainly.com/question/25173046

===============================================

To find this answer, you apply the given translation rule to the coordinates of point P(-2,6)

[tex](x,y) \to (x-2, y-16)\\\\(-2,6) \to (-2-2, 6-16)\\\\(-2,6) \to (-4, -10)\\\\[/tex]

We see that point P' has a y coordinate of -10

This translation, aka shifting, rule moved point P 2 units to the left and 16 units down.

Answer:last one D ( -10)

Step-by-step explanation:

edg

Answer:

7x + 8y - 5

Step-by-step explanation:

Like terms are terms with the same variable as well as the same amount of said variable:

Set the expression:

4x + 3y - 4 + 5y + 3x - 1

4x + 3x + 3y + 5y - 4 - 1

Combine like terms:

(4x + 3x) + (3y + 5y) + (-4 - 1)

(7x) + (8y) + (-5)

7x + 8y - 5 is your answer.

~

Answer:

∠D = 56°

∠D = 180° - (35° + 89°) = 56°