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3 years ago

Helpmeeeeee pleaseeeeeee

Mathematics

1 answer:

Aleksandr [31]3 years ago

3 0

The answer is C i believe

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James used a substitution to solve this system of equations. Which equation could be a result of his first step? 2x+3y=12 y=x+1.

Blizzard [7]

Answer:

x = 1.5

y = 3

Step-by-step explanation:

to solve this system of equation using the substitution methods we say let

2x+3y=12................................... equation 1

y=x+1.5..................................... equation 2

substitute equation 2 into equation 1

2x+3y=12................................... equation 1

2x + 3( x + 1.5) = 12

2x + 3x + 4.5 = 12

5x + 4.5 = 12

collect the like terms

5x = 12 - 4.5

5x = 7.5

divide both sides by the coefficient of x which is 5

5x/5 = 7.5/5

x = 1.5

put x = 1.5 into equation 2

y=x+1.5..................................... equation 2

y = 1.5 + 1.5

y = 3

therefore the value of x = 1.5 and y = 3 respectively.

5 0

3 years ago

Find the face value of the 20-year zero-coupon bond at 4.4%, compounded semiannually, with a price of $8,375.

umka21 [38]

<u>Given</u>:

Time,

t = 20 years

Rate,

r = 4.4%

Price

= $8,375

Now,

The yield will be:

= $\frac{4.4}{2}$

= $1.1$ (%)

Time will be:

= $20\times 2$

= $40 \ periods$

As we know the formula,

⇒ $Price \ of \ bond = \frac{Face \ value}{(1+\frac{r}{2} )^{n\times 2}}$

By substituting the values, we get

$8375=\frac{Face \ value}{(1+\frac{0.044}{2} )^{20\times 2}}$

$8375=\frac{Face \ value}{(1.022)^{40}}$

$8375=\frac{Face \ value}{2.3880083}$

The face value will be:

$Face \ value = 2.3880083\times 8375$

$=20,000$ ($)

Learn more about face value here:

brainly.com/question/14862802

5 0

3 years ago

Sterile fruit flies are used in an experiment where the proportion that survives at least days is given by . if the experiment b

Nana76 [90]

Answer:

Number of fruit flies after 14 days is equal to 1880.

Step-by-step explanation:

given,

fruit flies at the beginning of the experiment = 200 fruit flies

rate of increase of fruit flies = 5 per hour

to calculate the number of flies after 14 days.

time = 14 days = 14 × 24 = 336 hours

flies after 14 days = initial number of flies + rate of increase × time

= 200 + 5 × 336

= 1880 fruit flies.

hence,Number of fruit flies after 14 days is equal to 1880.

4 0

3 years ago

Use calculus to find the first order conditions. Use solver then to solve the first order conditions. Show your work for the fir

DaniilM [7]

The values of x and y are 70/22 and 30/22 respectively by using the first-order condition of differential calculus.

<h3>What is the first-order condition in differential calculus?</h3>

A first-order differential equation is represented by the equation $\mathbf{ \dfrac{dy}{dx} =f (x,y) }$ with 2 variables x & y, including its function f(x,y) specified on a xy-plane.

Given that:

$\mathbf{f(x,y) =-22x^2+22xy-11y^2+110x-40y-23}$

Let us first differentiate the above equation with respect to x, we have:

$\mathbf{\dfrac{\partial f(x,y) }{\partial x} = -44x +22y -0+110-0-0=0}$

$\mathbf{\implies -44x +22y+110=0}$ (multiply by -1)

44x - 22y = 110 ------ (equation 1)

Now, differentiating with respect to y, we have:

$\mathbf{\dfrac{\partial f(x,y) }{\partial y} =0 +22x-22y +0-40-0=0}$

$\mathbf{\implies 22x-22y -40=0}$

22x - 22y = 40 ----- (equation 2)

Now, we have a system of equations:

44x - 22y = 110

- ---- ( subtracting equation 2 from 1; elimination method)

<u />

x = 70/22

Replacing the value of x into equation (1), we have:

44x - 22y = 110

44(70/22) - 22y = 110

140 - 22y = 110

140 - 110 = 22y

30 = 22y

y = 30/22

Learn more about the first-order conditions in differential calculus here;

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#SPJ1

4 0

2 years ago

Can someone answer these as well worth lots of points. Only Appropriate Answers Pls :).

Rashid [163]

1. To solve this we are going to find the distance of the three sides of each triangle, and then, we are going to use Heron's formula.
- For triangle RTS:
S (2,1), T (1,3) and R (5,5). Using a graphic tool or the distance formula $d= \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}$ we realize that ST=2.2, SR=5, and TR=4.5. Now we are going to find the semi-perimeter of our triangle:
$s= \frac{ST+SR+TR}{2}$
$s= \frac{2.2+5+4.5}{2}$
$s= \frac{11.7}{2}$
$s=5.85$
Now we can use Heron's formula:
$A= \sqrt{s(s-ST)(s-SR)(s-TR)}$
$A= \sqrt{5.85(5.85-2.2)(5.85-5)(5.85-4.5)}$
$A=4.9$ square units
We can conclude that the area of triangle RTS is 4.9 square units.

- For triangle MNL:
M (2,-4), N (-2,-3), and L (0,-1). Once again, using a graphic tool or the distance formula we get that MN=4.1, ML=3.6, and NL=2.8.
Lets find the semi-perimeter of our triangle to use Heron's formula:
$s= \frac{4.1+3.6+2.8}{2}$
$s=5.25$
$A= \sqrt{5.25(5.25-4.1)(5.25-3.6)(5.25-2.8)}$
$A=4.9$ square units
We can conclude that the area of triangle MNL is 4.9 square units.

2. To find the volume of our pyramid, we are going to use the formula for the volume of a rectangular pyramid: $V= \frac{lwh}{3}$
where
$l$ is the length of the rectangular base
$w$ is the width of the rectangular base
$h$ is the height of the pyramid
From our picture we can infer that $l=15$ , $w=10$ , and $h=12$ , so lets replace the values in our formula:
$V= \frac{lwh}{3}$
$V= \frac{(15)(10)(12)}{3}$
$V=600$ cubic units

To find the volume of the cone, we are going to use the formula: $V= \pi r^2 \frac{h}{3}$
where
$r$ is the radius
$h$ is the height
From our picture we can infer that the diameter of the cone is 9; since radius is half the diameter, $r= \frac{9}{2} =4.5$ . We also know that $h=12$ , so lets replace the values:
$V= \pi r^2 \frac{h}{3}$
$V= \pi (4.5)^2 \frac{12}{3}$
$V=254.5$ cubic units
We can conclude that the volume of the pyramid is 600 cubic units and the volume of the cone is 254.5 cubic units

3. To find $y$ , we are going to use the tangent trigonometric function:
$tan( \alpha )= \frac{opposite.side}{adjacent.side}$
$tan(53)= \frac{4cm}{y}$
$y= \frac{4cm}{tan(53)}$
$y=3.01cm$
and to the nearest whole number:
$y=3cm$
We can conclude that $y=3cm$

4. To solve this, we are going to find the volume of the cube first; to do it we are going to use the formula for the volume of a cube: $V=a^3$
where
$a$ is the edge of the cube
Since the sphere fits exactly in the cube, the edge of the cube is equal to the diameter of the sphere; therefore, $a=12$ . Lets replace the value in our formula:
$V=(12)^3$
$V=1728$ cubic units
Next, we are going to use the formula for the volume of a sphere: $V= \frac{4}{3} \pi r^3$
where
$r$ is the radius of the sphere
We know form our problem that the diameter of the sphere is 12 units, since radius is half the diameter, $r= \frac{12}{2} =6$ . Lest replace the value in our formula:
$V= \frac{4}{3} \pi r^3$
$V= \frac{4}{3} \pi (6)^3$
$V=904.8$ cubic units
Now, to find the volume of the empty space in the cube, we just need to subtract the volume of the sphere form the volume of the cube:
$V_{empty}=1728-904.8=823.2$ cubic units
We can conclude that the volume of the empty space in the cube is 823.2 cubic units

4. To solve this, we are going to use the arc length formula: $s= \frac{ \alpha}{360} 2 \pi r$
where
$s$ =mBC
$s$ is the length of the arc
$r$ is the radius of the circle
Lets, find $x$ first. From the picture we can infer that:
$x+2x+x=180$
$4x=180$
$x= \frac{180}{4}$
$x=45$
Since BE is the diameter of the circle, AB is its radius; therefore $r=AB$ . Lets replace the values in our formula:
$s= \frac{ \alpha}{360} 2 \pi r$
$s= \frac{45}{360} 2 \pi AB$
$s= \frac{ \pi }{4} AB$
$mBC= \frac{ \pi }{4} AB$
We can conclude that $mBC= \frac{ \pi }{4} AB$

3 0

3 years ago