For each of the following system of linear equations, state the number of solutions without solving the system. a) -x+3y=9, -4x+12y=12 b) 2x-y-4=0,6x=3y+12

Answer:

[tex] y = 9.1 [/tex]

Step-by-step explanation:

Use the Law of sines to find y in ∆WXY, given:

m < Y = 106°

m < X = 58°

WY = x = 8

WX = y = ?

Therefore,

[tex] \frac{y}{sin(Y)} = \frac{x}{sin(X)} [/tex]

[tex] \frac{y}{sin(106)} = \frac{8}{sin(58)} [/tex]

[tex] \frac{y}{0.961} = \frac{8}{0.848} [/tex]

[tex] \frac{y}{0.961} = 9.434 [/tex]

Multiply both sides by 0.961 to solve for y

[tex] \frac{y*0.961}{0.961} = 9.434*0.961 [/tex]

[tex] y = 9.434*0.961 [/tex]

[tex] y = 9.1 [/tex] (to nearest tenth)

Answer:

See the answer below.

Step-by-step explanation:

We know that:  [tex]d=S\times t[/tex]

So, using the given data, we can write an equation for the total distance travelled as:

[tex]3\times S+4\times (S+10)=335\\\\\Rightarrow S\approx 42.1\:Km/h[/tex]

Best Regards!

Answer:

I have:

33 - 3N/44   marbles

N = marbles of Nicole

Step-by-step explanation:

Nicole + me = 44 marbles

m = 44 - N

m = me

N = Nicole

if i lose 1/4 of my marbles

4/4 - 1/4 = 3/4

i have left:

3/4 of my marbles

then:

m = 3(44-N)/4

m = 3*44/4 + 3*-N/44

m = 33 - 3N/44

I have finally:

33 - 3N/44

To find the vertex, you need to find the axis of symmetry first.

In order to find the axis of symmetry we have to do -b/2a.

In our case, the b is -8 and the a is 1.

Plug it in.

-(-8)/2(1)

8/2 = 4

Our axis of symmetry is 4.

Now, we plug it into the equation to find the rest of the vertex.

y = 4^2 - 8(4) + 1

y = 16 - 32 + 1

y = -16 + 1

y = -15

Put it together.

Our vertex is (4,-15).

Answer:

25x  ²−49y ²

Step-by-step explanation:

We need to find product of (5x+7)(5x−7y)

By using identity (a+b)(a−b)=a −b  ²

We have a=5x,b=7y

Thus (5x+7y)(5x−7y)=(5x)  ²−(7y)  

let me know if it was helpful

25x² - 49y²

Step-by-step explanation:

To Find:

The product of (5x - 7y)(5 x + 7)

How to solve:

Just need to use the formula of a² - b² = (a+b)(a-b)

let's assume a = 5x and b = 7x

Solution:

(5x - 7y)(5 x + 7) = (5x)² - (7y)²

= 25x² - 49y²

Hence required answer is 25x² - 49y².

Answer:

[tex]\large \boxed{\sf \ \ \dfrac{x^2}{x^4+1}=\dfrac{1}{7} \ \ }[/tex]

Step-by-step explanation:

Hello,

We know that (let's assume that x is different from 0 as we cannot divide by 0)

   [tex]x+\dfrac{1}{x}=3[/tex]

and we want to estimate

   [tex]\dfrac{x^2}{x^4+1}[/tex]

Let's take the square.

[tex]9=3^2=(x+\dfrac{1}{x})^2=x^2+2\cdot x \cdot \dfrac{1}{x}+\dfrac{1}{x^2}=x^2+2+\dfrac{1}{x^2}=\dfrac{x^4+1}{x^2}+2[/tex]

So, we can write

[tex]\dfrac{x^4+1}{x^2}=9-2=7 \\ \\\\\text{*** let's take the inverse ***} \\ \\\dfrac{x^2}{x^4+1}=\dfrac{1}{7}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

315943/12683

Step-by-step explanation:

Well -9 2/7 * -10 3/7 is 315943/12683

Answer:

540/49

Step-by-step explanation:

Work on the brackets first: (-10✖️3/7)=-30/7

-30/7✖️2/27=-60/49

-60/49✖️-9=540/49

Answer: $77.84

Step-by-step explanation:

First multiply 8.5*6 to get 51.  Thus, she made 51 dollars from her first job.

Then multiply 9.21*4 to get 26.84.  Thus, she made 26.84 dollars from her second job.

Then add her first and second jobs(51+26.84) to get $77.84

Hope it helps <3

Answer:

260%

Step-by-step explanation:

For the coffee;

cost price ([tex]C_{P}[/tex]) = $5/kg

selling price ([tex]S_{P}[/tex]) = $18/kg

Percentage profit (%P) = [tex]\frac{S_P - C_P}{C_P} * 100%[/tex] %

Substitute the right values into the above;

%P = [tex]\frac{18 - 5}{5} * 100%[/tex] %

%P = [tex]\frac{13}{5} * 100%[/tex] %

%P = 260%

Therefore, the percentage profit compared to the original cost of the coffee is 260%

The largest x that satisfies

[tex]3x^2+17x+15=5[/tex]

is the largest solution to

[tex]3x^2+17x+10=0[/tex]

We have

[tex]3x^2+17x+10=(3x+2)(x+5)=0[/tex]

[tex]\implies x=-\dfrac23\text{ or }x=-5[/tex]

and so the largest value of x we want is -2/3.

Let A, B, and C denote the sets of students that have taken calculus, sociology, and Spanish, respectively.

We're given that [tex]A\cup B\cup C[/tex] consists of 187 students.

We want to find the size of [tex]A\cap B\cap C[/tex], given that

• A has 61 students;

• B has 78;

• C has 72;

• [tex]A\cap B[/tex] has 15;

• [tex]A\cap C[/tex] has 20; and

• [tex]B\cap C[/tex] has 13.

Using the inclusion/exclusion principle, we have

[tex]|A\cup B\cup C|=|A|+|B|+|C|-(|A\cap B|+|A\cap C|+|B\cap C|)+|A\cap B\cap C|[/tex]

where |X| denotes the size of the set X. Plug in all the known sizes:

[tex]187=61+78+72-(15+20+13)+|A\cap B\cap C|[/tex]

[tex]\implies|A\cap B\cap C|=24[/tex]

so 24 students have taken all three classes.

Answer:

2 hours

Step-by-step explanation:

Let's denote the amount of time we need to find out, t.

=> 600 + 50t < 500 + 100t

or 600 - 500 < 100t - 50t

or 100 < 50t

or 100/50 < t

or t > 2

=> After 2 hours, company B will be cheaper option than company A

Answer:

Step-by-step explanation:

This is more physics than math, but since "The book of nature is written in the language of mathematics"...

Anyway, the one-dimesional motion equation you want to use here resembles the quadratic we use to model parabolic motion. It is

[tex]v^2=v_0^2+2a[/tex]Δx

where v is the final velocity of the firefighter, v₀ is the initial velocity of the firefighter, a is -9.8 m/s/s (negative because the motion is in the downward direction), and Δx is -34 m. This is also negative because where the firefighter lands is below the point at which he started. This is important, because if you leave the 34 as positive, you end up with a negative radicand...and that's not gonna work. Filling in the formula:

[tex]v^2=(7.5)^2+2(-9.8)(-34)[/tex]

Paying close attention to significant digits here is important (at least it is when I teach physics in school!). Since there are 2 significant digits in 7.5, we need 2 in the product. 7.5 squared is 56.25 which will round to 56. Then on the right side of the plus sign, we need 2 significant digits as well since the number 2 is part of the equation. We don't count it as significant if it is part of the equation. 2(-9.8)(-34) = 666.4 but that will round to 670. NOW, since the rules for significant digits are different in multiplication and addition, you have to round each first, then take the square root of the sum, rounding at the end. In this case we will round to the place that holds the least significance between the 2 numbers. In our case that is the tens place, since the tens place is less significant than is the 1's place. The number 7 is in the tens place. (Following that rule is super tricky, and also quite maddening!)

What we have here is

[tex]v^2=56+670[/tex] and

[tex]v=\sqrt{56+670}[/tex]

That leaves us with

v = 26.94438j

But don't forget we round that to the tens place which comes out in the end, finally, to

v = 30 m/s

Hey there!

We see that the first factor is 82.17, which is about 80. Then, we have 7.32, which is about 7.

80 times 7 is just doing 8 times 7 but putting a zero on the end!

So, 80 times 7 is 560, so our best estimate is A.560

Have a wonderful day!

Answer:

Hey there!

On on a graph, find the point of intersection of two lines; the first line has y-intercept = 5 and slope = -3, and the second line has y-intercept = 2 and slope =  1.

Hope this helps :)

Answer:

yes

Step-by-step explanation: i agree its 3

Answer:

36 : 6 and -6

12 = [tex]2\sqrt{3} , -2\sqrt{3}[/tex]

1.96 =1.4 and -1.4

0.64 : 0.8 and -0.8

400 : 20 and -20

25/36 = 5/6 and -5/6

Step-by-step explanation:

we know that

(-x)^2 = x^2

ALSO

(x)^2 = x^2

thus, square of both negative and positive number is same positive number.

_________________________________________________

36 = 6*6

36 = -6*-6

hence

square roots of 36 is both -6 and 6

12 = 4*3 = [tex]2^2*\sqrt{3} *\sqrt{3}[/tex]

[tex]\sqrt{12} = 2\sqrt{3}[/tex]

also

12 = [tex]-2\sqrt{3} *-2\sqrt{3}[/tex]

[tex]\sqrt{12} = -2\sqrt{3}[/tex]

___________________________________

1.96 = 196/100 = (14/10)^2

1.96 = 196/100 = (-14/10)^2

hence

[tex]\sqrt{1.96} = 14/10 \ or -14/10[/tex]

_______________________________

0.64 = 64/100 = (8/10)^2 = 0.8^2

0.64 = 64/100 = (-8/10)^2 = (-0.8)^2

Thus, square root of  0.64 = 0.8 and -0.8

_________________________________

400 = 20^2

400 = (-20)^2

[tex]\sqrt{400} = 20\\\sqrt{400} = -20\\[/tex]

__________________________________

25/36 = (5/6)^2

25/36 = (-5/6)^2

[tex]\sqrt{ 25/36} = 5/6 \\\sqrt{ 25/36} = (-5/6[/tex]

Answer:

23.75

Step-by-step explanation:

IM GANNA HELP FOR THE SECOND ONE CUZ THE FIRST QUESTION DOESNT HAVE SOME VALUES AND THE THIRD IS KINDA HARD

BUT I HOPE I HELPED

the question:

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. At the farmers market, Nathaniel buys two dozen oranges at $3.50 per dozen, four kilograms of apples at $3.25 per kilogram, two kilograms of carrots at $1.90 per kilogram, and one kilogram of potatoes for $1.20. He received a 5% discount off his total bill. How much money did Nathaniel spend on fruits and vegetables at the farmers market? Nathaniel spent $______ at the farmers market.

nathaniel got 2 dozen so 7$ for the oranges

4 kg  so 13$ for apples

2 kg so 3.8$ for carrots

1 kg so 1.2$ for potatoes

LETS ADD IT TOGETHER

25$ TOTAL

DISCOUNT=5%

5% OF 25 IS 1.25

SO 25-1.25=23.75

SO NATHANIEL SPENT 23.75$ IN ALL

HOPE I HELPED

PLS MARK BRAINLIEST

DESPERATELY TRYING TO LEVEL UP

  ✌ -ZYLYNN JADE ARDENNE

JUST A RANDOM GIRL WANTING TO HELP PEOPLE!

                                 PEACE!

Answer:

C

Step-by-step explanation:

Before expressing as a ratio the quantities must have the same denomination

$2 = 200 cents, thus

40 cents : $2

= 40 cents : 200 cents ( divide both parts by 40 )

= 1 : 5 → C

Answer:

x>4

Step-by-step explanation:

x+3>19-3x

x+3x>19-3

4x>16

x>4

Answer:

x > 4

Step-by-step explanation:

Solution set:

Solution set as set builder notation:

Answer:

2.625 cups or 21 ounces

Step-by-step explanation:

Ava needs 3/4 cup of blue paint for every 1 cup of white paint. So, the ratio is 0.75 : 1.

She has 28 ounces of white paint. But, you have to convert ounces to cups.

1 cup = 8 ounces

28 ounces ÷ 8 ounces/cup = 3.5 cups

Now set up a ratio.

[tex]\frac{0.75}{1} = \frac{x}{3.5}[/tex]

X (how much blue paint is needed) is over 3.5 cups (the amount of white paint she has)

Cross multiply and divide.

[tex]\frac{0.75}{1} = \frac{x}{3.5}[/tex]

x = 0.75 × 3.5

x = 2.625 cups

To convert to ounces, multiply by 8.

2.625 cups × 8 ounces = 21 ounces

Therefore, Ava needs 2.625 cups or 21 ounces of blue paint.

Hope that helps.

Answer:

Step-by-step explanation:

According to Question,

[tex] {x}^{2} = 46[/tex]

Squaring on both sides

[tex] \sqrt{ {x}^{2} } = \sqrt{46} [/tex]

Calculate

[tex]x = 6.79[/tex]

Let's check :

If we multiply 6.79 by itself, then the result will be approximately 46.

Hope this helps..

Best regards!!

Answer:

The third option is correct

Step-by-step explanation:

We can rule out the first option because systems of equations CAN have decimal answers (this certain question cannot because of the domain) Same for the second option.

The last option says that all the numbers of forks knives and spoons must be equal but the question never specified that, in fact it looks like that is impossible since the variables have different coefficients.

The only logical answer is number 3

Answer:

The mean and variance are known as the parameters of a distribution.

Step-by-step explanation:

The mean and the variance are parameters of a distribution. Parameters are constantly estimated in Statistics using samples of values of a population because they are often unknown.

They characterize a quantitative aspect of a probability distribution, and completely determined the distribution. For example, in the normal distribution, the mean, [tex] \\ \mu[/tex],  and the variance, [tex] \\ \sigma^{2}[/tex], determined this distribution.

Most of the time, the standard deviation, [tex] \\ \sigma[/tex], is more used than the variance because is in the same units that the mean.

In this way, we can say that these parameters "tell us" where the central point of the distribution is (this is the case for the mean), and also, how spread the values of a probability distribution are (the case for variance or the standard deviation).

Answer:

Step-by-step explanation:

a = 8

b  = 10

a^3 =8^3 = 512

b^3= 10^3 =1000

a^3 + b^3 = 1512

a^2 = 64

-ab = - 80

b^2 = 100

a + b=18

(a + b) (64 -  80+ 100)

18 * (84)

1512'

Answer:

[tex] A = 350\pi \approx 1100 [/tex]

Step-by-step explanation:

The shaded area is a sector with a central angle of 45 deg.

The total measure of the central angle of a full circle is 360 deg.

The central angle of the unshaded sector is

360 deg - 45 deg = 315 deg

The area of a sector of a circle with a central angle of n degrees and a radius r is

[tex] A = \dfrac{n}{360}\pi r^2 [/tex]

[tex] A = \dfrac{315}{360}\pi \times 20^2 [/tex]

[tex] A = 350\pi \approx 1100 [/tex]

Answer:

3 1/3 km or 3.33 km (to the hundredth)

Step-by-step explanation:

Using the given formula,

estimated distance = v.t  = velocity * time,

velocity = 5 km/h

time = 40 minutes = [tex]\frac{40}{60}[/tex] hours = [tex]\frac{2}{3}[/tex]  hours

Therefore

distance = 5 km/h * [tex] \frac{2}{3} [/tex]  hours = 10/3 km

= 3.33 km approximately

Answer:

[tex]\boxed{Distance = 3.33\ km}[/tex]

Step-by-step explanation:

Given:

Time = t = 40 min = 40/60 = 0.67 hours

Speed = v = 5 km/hr

Required:

Distance = S = ?

Formula:

Distance = Speed × Time

Solution:

Distance = 5 × 0.67

Distance = 3.33 km

Work Shown:

area of base = 18*17 = 306 square yards

V = volume of pyramid

V = (1/3)*(area of base)*(height)

V = (1/3)*(306)*(15)

V = 1530 cubic yards

Answer:1530

Step-by-step explanation: length*width*height* divided by 3

Answer:

$3,500

Step-by-step explanation:

First, Lets analyze the problem.

LeBron buys 500 shares for $10 a share. So he buys 500 shares for $5,000.

Now the price drops to $3, he had 500 stocks, the stocks are now only worth $1500.

5000-1500=3,500

He has lost $3,500 in the Tiger Corporation shares.