Determine whether the following system of equations has one solution, no solution, or an infinite number of solutions. Explain your reasoning.

2x - 4y = 10
7x - 9y = 12

Answer:

12.68

Step-by-step explanation:

76 degrees /2 = 38

Half the width of 15m forms the lower side of the triangle: 7.5 m

sin(38) = 7.5/h

=12.1820

12.18+.5

12.68

Answer:

60

Step-by-step explanation:

Looking at case 1.

a * 10^5 + 2a * 10 ^4= 7200000

a * 10 * 10^4 + 2a *10 ^4 =7200000

[10a + 2a] * 10^4= 7200000

12a= 7200000/ 10000

12a= 720

a= 720/12 = 60

Looking at case 2,

a * 10^5 - a * 10^4 = 5400000

a * 10 * 10^4 - a *10^4 = 5400000

10a* 10^ 4 - a * 10^ 4 = 5400000

[10a- a] *10^4 = 5400000

9a = 5400000/10000

9a= 540

a =540/9

a= 60

Answer:

x=0.885622

Step-by-step explanation:

Dont forget to round

Answer:

0.77

Step-by-step explanation:

7=9x

9x/9

7=x

7/9=0.77777777777

Answer:

Read below.

Step-by-step explanation:

a. reflection over the x-axis, translate 2 units up

b. rotate 90° counterclockwise or 270° clockwise

c. use a scale factor of 2 and translate 3 units down, 3 units left

d. translate 8 units right, 7 units up

I'm not so sure about c since I do not like scale factors.

Answer:

Circle Equation: ( x - 3.8 )^2 + ( y - 7.8 )^2 = 25/36

Step-by-step explanation:

* Knowing a circle equation is in the format (x – h)^2 + (y – k)^2 = r^2, with the center being at the point (h, k) and the radius being "r" *

Let us substitute values into this equation; provided ( 3.8, 7.8 ) is the center:

( x - 3.8 )^2 + ( y - 7.8 )^2 = r^2,

Now substitute value of r, or rather the radius 5/6:

( x - 3.8 )^2 + ( y - 7.8 )^2 = ( 5/6 )^2 ⇒

Circle Equation: ( x - 3.8 )^2 + ( y - 7.8 )^2 = 25/36

* Sorry this wasn't answered earlier *

Answer:

Yes

Step-by-step explanation:

[tex]6^{2}[/tex] + [tex]8^{2}[/tex] = [tex]10^{2}[/tex]

36 + 64 = 100

The Pythagorean theorem is true.

Answer:

x ≈ 2.65(nearest hundredth)

Step-by-step explanation:

Base on your question the triangle is a right angle triangle. This means the triangle should obey the Pythagoras theorem.

Pythagoras theorem says

c² = a² + b²

where

c = hypotenuse of the triangle

a and b are called the legs of the triangle.

The hypotenuse is the longest side of the triangle.

Recall your question says the unknown side x is one of the legs of the triangle. That means the other legs will definitely be 3 since the hypotenuse should be the longest side of the triangle which is 4.

Using Pythagoras theorem

4² = 3² + x²

16 - 9 = x²

7 = x²

square root both sides

x = √7

x = 2.64575131106

x ≈ 2.65(nearest hundredth)

Answer:

[tex]\large \boxed{(-1,-6),(-1,10)}[/tex]

Step-by-step explanation:

Point A must be on a circle with centre at (5,2) and radius 10.

The centre-radius form for the  equation of a circle is  

(x – h)² + (y – k)² = r², where

(h,k) = the coordinates of the centre and

     r = the radius

Thus, the equation for this circle is

(x - 5)² + ( y - 2)² = 10²

Substitute the value for x and solve for  y:

[tex]\begin{array}{rcl}\\(x - 5)^{2} +( y - 2)^{2} &=& 10^{2}\\(-1 - 5)^{2} +( y - 2)^{2} &=& 100\\(-6)^{2} +( y - 2)^{2} &=& 100\\36 +( y - 2)^{2} &=& 100\\( y - 2)^{2} &=& 64\\y - 2 = -8 & \qquad & y - 2 = 8\\y = \mathbf{-6} & \qquad & y = \mathbf{10}\\\end{array}\\\text{The possible coordinates of A are $\large \boxed{\mathbf{(-1,-6),(-1,10)}}$}[/tex]

The figure below shows the circle intersecting the line x = -1 at (-1,-6) and (-1,10).

[tex]\left \{ {{y=2} \atop {x=2}} \right. x^{2} x^{2} x^{2} x^{2} x^{2} x^{2}[/tex]Answer:

A

Step-by-step explanation:

Answer:

13 packages

Step-by-step explanation:

We need to first find the area of the composite figure. We can draw a horizontal line through the figure so that it is broken up into two rectangles.

The top rectangle has dimensions of 9 ft by 2 ft, while the bottom rectangle has dimensions of 3 ft by 7 ft. The area of a rectangle is denoted by: A = lw, where l is the length and w is the width.

Here, the top rectangle has width 9 and length 2, so the area is A = 9 * 2 = 18 square feet. The bottom rectangle has width 7 and length 3, so the area is A = 7 * 3 = 21 square feet. Add these up:

18 + 21 = 39 square feet

We know that each package of tile will cover 3 square feet, so divide 39 by 3 to get the number of packages needed:

39 / 3 = 13

The answer is 13 packages.

Answer:

13

Step-by-step explanation:

Larger rectangle - smaller rectangle

(9×5) - [(5-2)×(9-7)]

45 - (3×2)

45 - 6

39 ft²

1 package : 3 ft²

X packages : 39 ft²

X/1 = 39/3

X = 13 packages

Answer:

Lower Quartile: 23

Median: 30

Upper Quartile: 43

Interquartile range: 20

Answer:

A. 25%

Step-by-step explanation:

If you multiply something by 0.75, you're multiplying it by 75%, and that means you're losing 25% each time, so the rate of decay is 25%

Answer:

A 25%

Step-by-step explanation

the first thing we want to do for this problem is look at the exponential decay formula. its y=a(1-b)^x. "y" represents the final amount, "a" represents the original amount, and "b" represents the decay factor.

in this situation, .75 is the decay factor and our original amount is 1000. so to find out the decay factor, we need to subtract .75 from 1. you would get .25. .25 in percentage form is 25%.

we can double check by putting .25 in the orginal exponential decay formula. y=1000(1-.25)^x. 1-.25 equals .75, so now the equation is the same as our original equation, y=1000(0.75)^x

Answer:

m = 5

b = -6

Step-by-step explanation:

y = mx + b

Answer:

m = 5 and b = -6

Step-by-step explanation:

y = mx + b

y = 5x + (-6)

Answer:

[tex] \cos \bigg( \frac{7\pi}{12} \bigg)= \frac{1 - \sqrt{3} }{2 \sqrt{2} } [/tex]

Step-by-step explanation:

[tex] \cos \bigg( \frac{7\pi}{12} \bigg) \\ \\ = \cos \bigg( \frac{7 \times 180 \degree}{12} \bigg)\\ \\ = \cos \bigg( {7 \times 15 \degree} \bigg)\\ \\ = \cos \bigg( {105 \degree} \bigg)\\ \\ = \cos \bigg( {60\degree + 45 \degree} \bigg) \\ \\ = \cos {60\degree .\cos 45 \degree} - \sin {60\degree .\sin 45 \degree} \\ \\ = \frac{1}{2} . \frac{1}{ \sqrt{2} } - \frac{ \sqrt{3} }{2} .\frac{1}{ \sqrt{2} } \\ \\ = \frac{1}{2 \sqrt{2} } - \frac{ \sqrt{3} }{2 \sqrt{2} } \\ \\ \huge \purple{ \boxed{ \cos \Bigg( \frac{7\pi}{12} \Bigg)= \frac{1 - \sqrt{3} }{2 \sqrt{2} } }}[/tex]

The exact value of cos (7 pi/12) would be,

⇒ cos (7 pi/12) = - 0.2588

We have to given that,

An equation is,

⇒ cos (7 pi/12)

Now, WE can change it into degree as,

⇒ cos (7 pi/12)

⇒ cos (7 × 180 / 12)

⇒ cos (7 × 15)

⇒ cos 105°

⇒ cos (90 + 15)°

⇒ - sin 15°

⇒ - (√3 - 1) / 2√2

⇒ - 0.2588

Thus, The exact value of cos (7 pi/12) would be,

⇒ cos (7 pi/12) = - 0.2588

Learn more about trigonometric ratios at:

brainly.com/question/1836193

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Answer:

Step-by-step explanation:

These are independent events, so we will just multiply the two probabilities together.

1/6 x 1/6 = 1/36

I'm always happy to help :)

The probability should be [tex]1\div 36[/tex].

Since You roll a fair six-sided die twice. The first roll shows a five and the second roll shows a six.

So here the probability should be

[tex]= 1\div 6 \times 1\div 6 = 1\div 36[/tex]

Hence, we can conclude that The probability should be [tex]1\div 36[/tex].

Learn more about probability here: https://brainly.com/question/21909925

Answer:

8.9%

Step-by-step explanation:

Probability of picking a red marble first: [tex]\frac{2}{10}=\frac{1}{5}[/tex]

Probability of picking a blue marble (no replacement): [tex]\frac{4}{9}[/tex]

[tex]\frac{4}{9} *\frac{1}{5} =\frac{4}{45} = 8.8888888888...%[/tex] % ≈ 8.9%

Answer:

.4 yards of fabric were used for each pillow.

Steps:

2/5=0.4 (or [tex]\frac{2}{5}[/tex])

Answer: 113.1

2 π r

2 π 18

113.1 answer not sure if it is right

Step-by-step explanation:

Answer:

The answer is -3.1, or 3 1/10.Since diving a negative and a positive equals a negative, your quotient will be negative. You can start by removing the 0.5, and divide 15 by 5 which is 3. Then with the 0.5 from -15.5, divide it by 5 and you get 0.1. 3 plus 0.1 is 3.1, and since it has to be negative, it's -3.1.

Step-by-step explanation:

i tried, have a nice day (:

Answer: 1/125,000

Step-by-step explanation:

If the lenght of the building is L, the height is H, and the width is W, the volume of the building is V = L*H*W

Then for the model we will have that each measure is 1/50 times the original, this is:

lenght = L/50

height = H/50

widht= W/50

The volume of the scale model is:

V' = (L/50)*(H/50)*(W/50) = L*H*W/50^3

So we have the volume of the actual building divided 50^3

This means that the volume of the scale is 1/50^3 = 1/125,000 times the volume of the actual building.

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4 - x < 9

Subtract 4 from both sides

4 - x - 4 < 9 - 4

Now we have:

- x < 5

Divide both sides by -1

x < -5

When you divide an inequality by -1, the sign flips

Thus, your answer would be:

x > -5

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Step-by-step explanation:

4x - 3 = 4x + 5

4x - 4x = 5 + 3

0 = 8

x is disappear and 2 both sides are not equal

Answer:

If you subtract 4x from both sides there are different numbers so the equation isn't equal so the equation is impossible

4x-4x=3

4x-4x=5

3≠5

Hope this helps

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]V=whl=3*4*2=24units^3[/tex](grey)

[tex]V=whl=6*8*4=192units^3[/tex](green)

They are similar, the green is just double in size so a ratio of 1:2

Answer:

Volume of cone = 314 in³

Step-by-step explanation:

Radius of the cone (r) = 5 in

Height of the cone (h) = 12 in

[tex]Voume \: of \: the \: cone = \frac{1}{3} \pi {r}^{2} h \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{3} \times \pi \times {(5)}^{2} \times 12\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{3} \times \pi \times 25 \times 12\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{3} \times \pi \times 300 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \pi \times 100\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 314 \: {in}^{3} [/tex]

Answer:

M x M / x + y =4​

Step-by-step explanation:

Answer:

It will take him 8 months.

Step-by-step explanation:

If you divide 280 and 35 you get 8, which is the amount of months it takes.

Formula for the perimeter of a quarter circle: C = ((pi x 2 x r) / 4) + r + r

32.13 = (6.28r / 4) + 2r

32.13 = 1.57r + 2r

32.13 = 3.57r

r = 9 yards

Hope this helps! :)