use the substitution method to solve the system of equations

3x+2y=13

y=x-1

Answers:  x = 1 and y = -1

Explanation:

Start where your teacher left off, which is -3y = 3.

We solve for y by dividing both sides by -3

That turns -3y = 3 into y = -1

Then we use this y value to find x

x - 5y = 6

x - 5(-1) = 6

x + 5 = 6

x = 6-5

x = 1

The solution is (x,y) = (1, -1)

Answer:

-1,1

Step-by-step explanation:

Answer:

Obviously B

Step-by-step explanation:

Answer:

88%

Step-by-step explanation:

to initial price (100%) was increased by 10% (resulting in 110% of the initial price).

then these 110% were decreased by 20%.

so, the final price is actually 80% of 110% of the initial price

20/100 = 1/5

80/100 = 4/5

so, the customer pays only 4/5 of the 110% price.

110 × 4/5 = 22 × 4 = 88%

so, the final price was 88% of the initial price

Answer:

you do length times width then add them

Answer:

Number of fish in 2006 = 845 fishes (Approx.)

Step-by-step explanation:

Given;

Number of fish in 2000 = 1,150 fishes

Decreasing rate = 5% per year

Find:

Number of fish in 2006

Computation:

Exponential decay function:

F = P[1-r]ⁿ

Number of year = 2006 - 2000

Number of year =  6 year

Number of fish in 2006 = 1,150[1-5%]⁶

Number of fish in 2006 = 1,150[1-0.05]⁶

Number of fish in 2006 = 1,150[0.95]⁶

Number of fish in 2006 = 1,150[0.735]

Number of fish in 2006 = 845.25

Number of fish in 2006 = 845 fishes (Approx.)

Answer:

∠3 = 142°

Step-by-step explanation:

L // M

∠2 = 38°    {Corresponding angles are congruent}

∠2 + ∠3 = 180   {Linear pair}

38 + ∠3 = 180

       ∠3 = 180 - 38

∠3 = 142°

the answer is 142 degrees, get 180 degrees from a straight lines and subtract the acute angle from 180 to get the answer, 180-38

Answer:

Dilated pupils

Long periods of wakefulness

Loss of appetite

Overconfidence

Over-excitement

Paranoia

Runny nose or frequent sniffles

White powder around nostrils

Legal issues

Missing or being late to work

Financial problems

Mood swings

Irritability

Depression

Answer:

64.0655322 miles is maybe the answer

Answer:

13

Step-by-step explanation:

Distance between points (1, 3) and (6, 15) is 13

Answer:

option b is correct

tag me as brilliaiest

Answer:

75% probability

Step-by-step explanation:

calculating the total ratio and percentage

Answer:

h = 2 and k = 1.5

Step-by-step explanation:

The solution is, Solve of the system of equations. using elimination,

6h=2k+9 & 3h+4k=12 is, h = 2 & k=3/2.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

given that, the system of equations.

6h-2k=9.......(1)

3h+4k=12 ...........(2)

now, for solving, multiply (1) by 2 & add with  (2),

we get,

12h - 4k = 18

3h + 4k = 12

---------------------

15h = 30

i.e. h = 2

from (1), we get, k = 3/2

Hence, The solution is, Solve of the system of equations. using elimination,

6h=2k+9 & 3h+4k=12 is, h = 2 & k=3/2.

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Answer:

(a) 52°

(b) 322°

Step-by-step explanation:

(a) The details of the circle are;

The diameter of the circle = AOC

The center of the circle = Point O

The point the line AT cuts the circle = Point B

The point the tangent PT touches the circle = Point C

Angle ∠COB = 76°

We have that angle AOB and angle COB are supplementary angles, therefore;

∠AOB + ∠COB = 180°

∠AOB = 180° - ∠COB

∴ ∠AOB = 180° - 76° = 104°

∠AOB = 104°

OA = OB = The radius of the circle

Therefore, ΔAOB  =  An isosceles triangle

∠OAB = ∠OBA by base angles of an isosceles triangle are equal

∠AOB + ∠OAB + ∠OBA = 180° by angle summation property

∴ ∠AOB + ∠OAB + ∠OBA = ∠AOB + ∠OAB + ∠OAB = ∠AOB + 2×∠OAB = 180°

∠OAB = (180° - ∠AOB)/2

∴ ∠OAB = (180° - 104°)/2 = 38°

∠TAC = ∠OAB = 38° by reflexive property

AOC is perpendicular to tangent PT at point C, by tangent to a circle property, therefore;

∠TCA = 90° and ΔTCA = A right triangle

∠TAC + ∠ATC + ∠TCA = 180° by angle sum property

∠ATC = 180° - (∠TAC + ∠TCA)

∴ ∠ATC = 180° - (38° + 90°) = 52°

Angle ATC = 52°

(b) In ΔABC, ∠ABC = Angle subtended by the diameter = 90°

∴ ΔABC = A right triangle

∠ABC and ∠TBC are supplementary angles, therefore;

∠ABC + ∠TBC = 180°

∠TBC = 180° - ∠ABC

∴ ∠TBC = 180° - 90° = 90°

∠TCB = 180° - (∠TBC + ∠ATC)

∴ ∠TCB = 180° - (90° + 52°) = 38°

The bearing of B from C = (360° - 38°) = 322°.

Answer:

About Points

S = (x,y)        searched point (it will be in the third quadrant )

M = (-2,0)      Midpoint | SP |

P = (3,5)        one end of the segment | SP |

You have to draw Cartesian.

we set in a point M and P. We both points by a simple and we extend it for the third quarter of the system. Compass measure the distance from the point M to the point P. From the point M we set a compass point S. Figure attached. Received point S = ( -7 , -5 ) . It sought a point that calculate .

We use the information that | SM | = | MP |

Answer : S = (-7,-5)

Step-by-step explanation:

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ P(\stackrel{x_1}{3}~,~\stackrel{y_1}{5})\qquad \underline{Q}(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{x+3}{2}~~,~~\cfrac{y+3}{2} \right)=\stackrel{M}{(-2,0)}\implies \begin{cases} \cfrac{x+3}{2}=-2\\[1em] x+3=-4\\ \boxed{x = -7}\\[-0.5em] \hrulefill\\ \cfrac{y+3}{2}=0\\[1em] y+3=0\\ \boxed{y=-3} \end{cases}[/tex]

Answer:

2units

Step-by-step explanation:

Given the coordinates D(6,−1), E(-4,-1), using the distance formula

DE = √(x2-x1)²+(y2-y1)²

DE = √(-1-(-1))²+(4-6)²

DE = √(-1+1)²+(-2)²

DE = √0+4

DE = √4

DE = 2units

Hence the length od DE in units is 2units

Answer:

Added

Step-by-step explanation:

For example, take the arithmetic sequence of 3, 5, 7, 9...

Here, the number that gets us from the first number to the second (from 3 to 5), is 2. Meaning, we need to add 2 to 3 in order to get 5. I believe that makes "addition" or "added" the answer. Please let me know if I misunderstood and I will change my answer! Thank you!

Answer:

added or subtracted

Step-by-step explanation:

Answer:

[tex]-\sqrt{2} \le m \le \sqrt{2}[/tex] would ensure that at least one real root exists for this equation when solving for [tex]x[/tex].

Step-by-step explanation:

Apply the Pythagorean identity [tex]1 - \sin^{2}(x) = \cos^{2}(x)[/tex] to replace the cosine this equation with sine:

[tex](1 - \sin^{2}(x)) - (m^2 - 3)\, \sin(x) + 2\, m^2 - 3 = 0[/tex].

Multiply both sides by [tex](-1)[/tex] to obtain:

[tex]-1 + \sin^{2}(x) + (m^2 - 3)\, \sin(x) - 2\, m^2 + 3 = 0[/tex].

[tex]\sin^{2}(x) + (m^2 - 3)\, \sin(x) - 2\, m^2 + 2 = 0[/tex].

If [tex]y = \sin(x)[/tex], then this equation would become a quadratic equation about [tex]y[/tex]:

[tex]y^{2} + (m^2 - 3)\, y + (- 2\, m^2 + 2) = 0[/tex].

However, [tex]-1 \le \sin(x) \le 1[/tex] for all real [tex]x[/tex].

Hence, the value of [tex]y[/tex] must be between [tex](-1)[/tex] and [tex]1[/tex] (inclusive) for the original equation to have a real root when solving for [tex]x[/tex].

Determinant of this quadratic equation about [tex]y[/tex]:

[tex]\begin{aligned} & b^{2} - 4\, a\, c \\ =\; & (m^{2} - 3)^{2} - 4 \cdot (-2\, m^{2} + 2) \\ =\; & m^{4} - 6\, m^{2} + 9 - (-8\, m^{2} + 8) \\ =\; & m^{4} - 6\, m^{2} + 9 + 8\, m^{2} - 8 \\ =\; & m^{4} + 2\, m^{2} + 1 \\ =\; &(m^2 + 1)^{2} \end{aligned}[/tex].

Hence, when solving for [tex]y[/tex], the roots of [tex]y^{2} + (m^2 - 3)\, y + (- 2\, m^2 + 2) = 0[/tex] in terms of [tex]m[/tex] would be:

[tex]\begin{aligned}y_1 &= \frac{-b + \sqrt{b^{2} - 4\, a\, c}}{2\, a} \\ &= \frac{-(m^{2} - 3) + \sqrt{(m^{2} + 1)^{2}}}{2} \\ &= \frac{-(m^{2} - 3) + (m^{2} + 1)}{2} = 2\end{aligned}[/tex].

[tex]\begin{aligned}y_2 &= \frac{-b - \sqrt{b^{2} - 4\, a\, c}}{2\, a} \\ &= \frac{-(m^{2} - 3) - \sqrt{(m^{2} + 1)^{2}}}{2} \\ &= \frac{-(m^{2} - 3) - (m^{2} + 1)}{2} \\ &= \frac{-2\, m^{2} + 2}{2} = -m^{2} + 1\end{aligned}[/tex].

Since [tex]y = \sin(x)[/tex], it is necessary that [tex]-1 \le y \le 1[/tex] for the original solution to have a real root when solved for [tex]x[/tex].

The first solution, [tex]y_1[/tex], does not meet the requirements. On the other hand, simplifying [tex]-1 \le y_2 \le 1[/tex], [tex]-1 \le -m^{2} + 1 \le 1[/tex] gives:

[tex]-2 \le -m^{2} \le 0[/tex].

[tex]0 \le m^{2} \le 2[/tex].

[tex]-\sqrt{2} \le m \le \sqrt{2}[/tex].

In other words,  solving [tex]y^{2} + (m^2 - 3)\, y + (- 2\, m^2 + 2) = 0[/tex] for [tex]y[/tex] would give a real root between [tex]-1 \le y \le 1[/tex] if and only if [tex]-\sqrt{2} \le m \le \sqrt{2}[/tex].

On the other hand, given that [tex]y = \sin(x)[/tex] for the [tex]x[/tex] in the original equation, solving that equation for [tex]x\![/tex] would give a real root if and only if [tex]-1 \le y \le 1[/tex].

Therefore, the original equation with [tex]x[/tex] as the unknown has a real root if and only if [tex]-\sqrt{2} \le m \le \sqrt{2}[/tex].

Answer:

Wasim has enough money.

Step-by-step explanation:

1. find the area of the garden path:

600 cm x 120 cm = 72,000 sq. cm

2. find the area of each stone:

it is a square of 30 cm by 30 cm, so:

30 cm x 30 cm = 900 sq. cm

3. find how many stones can fit in the path:

72,000 / 900 = 80 stones

4. multiply that by the price of each stone:

80 stones x $2.50 = $200

Wasim's budget is $220 and the stones will only cost $200, so it is within the budget

Answer:

1/8 of an hour

Step-by-step explanation:

3/4 x 1/6 = 3/24 = 1/8

Hope this helps!

Answer:

441 miles

Step-by-step explanation:

Rate of the Car: 819/13 = 63mph

Miles Driven in 7 Hours: 63*7 = 441 miles

Answer:

441 miles

Step-by-step explanation:

* means multiply

819/13 = x/7

13 * x = 819 * 7

13x = 5733

x = 5733 ÷ 13

x = 441

Answer:

12.

Step-by-step explanation:

6x10 = 60.

60 divided by 12 =5.

Answer:

12

Step-by-step explanation:

5x = 60

x  = 12

Answer:

ok so the probility of gettting one white fish is

13/23

and if we take out one white fish the problity is

12/22

so we just multiply

12/22*13/23=0.30830039525

so the problity is 0.30 if you choose two fish you will get white for both

Answer: The Answer is A

Step-by-step explanation:

Answer:

only Y

Step-by-step explanation:

all the others have for at least 1 value of x more than one different y values defined.

but a function must be clear about the association between an x unit value and the corresponding result.

many different input values can have the same functional result. but there can be only one defined result per input value. otherwise it is not a function.

you cannot say 1+1 = 2 or 3. it is either 2 or 3, but you need to define what. you can't leave it open.

The function is given by the table Y

x = { -3 , 2 , 0 , 3 } and y = { 1 , 1 , 1 , 1 }

The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Given data ,

Let the function be represented as A

Now , the value of A is

Let the x values of the function be represented as

x = { -3 , 2 , 0 , 3 }

Now , the y values of the function is

y = { 1 , 1 , 1 , 1 }

From the table , we can see that for every different values of x there are range of values of y

No two same values of ranges have the same domain

Therefore , it is a function

Hence , the function is table Y

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Answer:

B

Step-by-step explanation:

[tex]2xy + 3xt - 7yt = 0[/tex]

[tex]3xt - 7yt = - 2xy[/tex]

Factor out t

[tex]t(3x - 7y) = - 2xy[/tex]

Divide by 3x-7y

[tex]t = - \frac{2xy}{3x - 7y} [/tex]

But since x and y are positive, the answer is positive

[tex]t = \frac{2xy}{3x - 7y} [/tex]

Answer:

Charity is more correct

Step-by-step explanation:

Flight time = 6.94 hours

Charity estimation = 7 hours

Her sister's estimation = 6.9 hours

Charity is more correct if we are to round to the nearest whole hour

6.94 hours is approximately 7 hours

Her sister is only correct if we are to round up to 1 decimal place

6.94 hours is approximately 6.9 hours to 1 decimal place

Answer:

The correct answers are:

The variable p is the independent variable.

The number of hours spent reading causes a change in the number of pages read.

The variable p is the dependent variable.

Step-by-step explanation: Hope this helps :)))

These two statements are correct and applicable

(1) The number of hours spent reading causes a change in the number of pages read.

(2) The variable p is the dependent variable.

"A Variable is a quantity that may change within the context of a mathematical problem or experiment. Typically, we use a single letter to represent a variable. The letters x, y, and z are common generic symbols used for variables."

"A dependent variable is the variable that changes as a result of the independent variable manipulation."

"A Line graph is a graphical display of information that changes continuously over time. A line graph may also be referred to as a line chart. Within a line graph, there are points connecting the data to show a continuous change. A Line graph has two axes(X- axis and Y-axis)"

We have,

Kelvin read 35 pages per hour

According to the question,

Number of hours increasing, number of pages also increasing

∵ The table data shows linear graph

We can clearly say that from a line graph definition,

These two are correct and applicable to Kelvin's situation

(1) The number of hours spent reading causes a change in the number of pages read.

(2) The variable p is the dependent variable.

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