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2 years ago

7

PLEASE HELP WITH GRADE 11 MATH. Make sure you show the formula. Substitute values and show all mathematicall operations! show yo

ur work. please!

1 answer:

Degger [83]2 years ago

5 0

3x+y

x

=−3

=−y+3

The second equation is solved for xxx, so we can substitute the expression -y+3−y+3minus, y, plus, 3 in for xxx in the first equation:

\begin{aligned} 3\blueD{x}+y &= -3\\\\ 3(\blueD{-y+3})+y&=-3\\\\ -3y+9+y&=-3\\\\ -2y&=-12\\\\ y&=6 \end{aligned}

3x+y

3(−y+3)+y

−3y+9+y

−2y

y

=−3

=−3

=−3

=−12

=6

Plugging this value back into one of our original equations, say x = -y +3x=−y+3x, equals, minus, y, plus, 3, we solve for the other variable:

\begin{aligned} x &= -\blueD{y} +3\\\\ x&=-(\blueD{6})+3\\\\ x&=-3 \end{aligned}

x

x

x

=−y+3

=−(6)+3

=−3

The solution to the system of equations is x=-3x=−3x, equals, minus, 3, y=6y=6y, equals, 6.

We can check our work by plugging these numbers back into the original equations. Let's try 3x+y = -33x+y=−33, x, plus, y, equals, minus, 3.

\begin{aligned} 3x+y &= -3\\\\ 3(-3)+6&\stackrel ?=-3\\\\ -9+6&\stackrel ?=-3\\\\ -3&=-3 \end{aligned}

3x+y

3(−3)+6

−9+6

−3

=−3

=

?

−3

=

?

−3

=−3

Yes, our solution checks out.

Example 2

We're asked to solve this system of equations:

\begin{aligned} 7x+10y &= 36\\\\ -2x+y&=9 \end{aligned}

7x+10y

−2x+y

=36

=9

In order to use the substitution method, we'll need to solve for either xxx or yyy in one of the equations. Let's solve for yyy in the second equation:

\begin{aligned} -2x+y&=9 \\\\ y&=2x+9 \end{aligned}

−2x+y

y

=9

=2x+9

Now we can substitute the expression 2x+92x+92, x, plus, 9 in for yyy in the first equation of our system:

\begin{aligned} 7x+10\blueD{y} &= 36\\\\ 7x+10\blueD{(2x+9)}&=36\\\\ 7x+20x+90&=36\\\\ 27x+90&=36\\\\ 3x+10&=4\\\\ 3x&=-6\\\\ x&=-2 \end{aligned}

7x+10y

7x+10(2x+9)

7x+20x+90

27x+90

3x+10

3x

x

=36

=36

=36

=36

=4

=−6

=−2

Plugging this value back into one of our original equations, say y=2x+9y=2x+9y, equals, 2, x, plus, 9, we solve for the other variable:

\begin{aligned} y&=2\blueD{x}+9\\\\ y&=2\blueD{(-2)}+9\\\\ y&=-4+9 \\\\ y&=5 \end{aligned}

y

y

y

y

=2x+9

=2(−2)+9

=−4+9

=5

The solution to the system of equations is x=-2x=−2x, equals, minus, 2, y=5y=5y, equals, 5.

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What is the sum of an infinite geometric series if the first term is 81 and the common ratio is 2⁄3?

Marrrta [24]

C

the sum to infinity of a geometric series = $\frac{a}{1-r}$

where a is the first term and r the common ratio

= $\frac{81}{\frac{1}{3} }$ = 81 × 3 = 243

4 0

3 years ago

In Triangle PQR, PQ = 9, QR = 10, and RP = 12. What is the smallest angle of this triangle?

KatRina [158]

Answer:

R

Step-by-step explanation:

8 0

3 years ago

5y-30=-5y+30 and also can you show the steps :}

KatRina [158]

5y-30=-5y+30

add 30 to both sides

5y = -5y+60

add 5y to both sides

10y = 60

divide both sides by 10

y = 6

<em>hope this helps!</em>

8 0

3 years ago

Bob and Doug are both 100-meter sprinters. Bob's sprint time is normally distributed with a mean of 10.00 seconds and Doug's spr

alexdok [17]

Answer:

The standard deviation (σ) = 0.05

Step-by-step explanation:

The question is to find the standard deviation.

STEEP 1: FIND THE MEAN

(10+9.9) ÷ 2 = 9.95

STEP 2: SQUARE THE DIFFERENCE BETWEEN SPRINT TIME AND MEAN

10-9.95= 0.05

0.05^2 = 0.0025

9.9 - 9.95= -0.0025

-0.0025^2 = 0.0025

STEP 3: FIND THE VARIANCE

0.0025+0.0025= 0.005

0.005/2= 0.0025

STEP 4: FIND THE STANDARD DEVIATION (σ )

√variance

√0.0025 = 0.05

Therefore

σ = 0.05.

From the standard deviation, the percentage probability of the higher value to occurs is

0.05×100= 5%

That means Doug has 95%

And Bob has 5%

3 0

3 years ago

Kendra dives off a diving board into the water and then comes back up to the surface. Her dive can be modeled by the equation: ,

MAVERICK [17]

Answer:

1. 6 feet

2. 6.25 feet

3. 1 feet

4. 6 feet

Step-by-step explanation:

The equation is : $h(x)=x^2-7x+6$

1. The diving board is where Kendra dives off. Here, the horizontal distance, x from the diving board is 0.

So, substituting x = 0 in the equation, we get

$h(0)=0^2-7(0)+6$

$=0-0+6$

$=6$

So, the diving board is 6 feet above the surface of the water.

2. From the equation, we known that it is a parabola and the vertex is minimum.

It is the minimum height which represents the depth Kendra dives into the water.

So the $x$ coordinate of the vertex is = $\frac{-b}{2a}$

Here, a and b are the coefficients of linear term and the quadratic terms in the equation. Therefore,

a = 1 and b = -7

∴ x coordinate = $\frac{-(-7)}{2 \times 1}$

$\frac{7}{2}=3.5$

Now substituting to find f(x),

$h(3.5)=(3.5)^2-7(3.5)+6$

= -6.25

Therefore, the diver dives 6.25 feet below the water surface.

3. The horizontal distance from the board the diver enters into the water.

This is the y-intercept and it is the value of x when h(x)=0.

∴ $0=x^2-7x+6$

Factorizing, we get $(x-1)(x-6)=0$

∴ $x=1 \text{ or}\ x=6$

So there are two solutions that are the two x intercepts of the function. Here at x = 1 shows the horizontal distance from the board from where Kendra dives into the water.

4. We know that the equation given has $\text{two}$ x intercepts. These two x intercepts are the points where the parabola crosses the x-axis, which is the height $h(x)=0$ . The height is the water surface level.

The first x intercept represents the points where Kendra dives into the water.

And the second x intercept is the point where Kendra comes out of the water surface. This this is $x=6$ for $h(x)=0$ .

Thus Kendra dives out of the water surface at 6 feet from the board.

3 0

3 years ago