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2 years ago

How can I solve these problems

Mathematics

2 answers:

telo118 [61]2 years ago

8 0

For the first 6 problems you need to know that all the angles in a triangle are equal to 180°.

for example: #1

60 + 75 + x = 180
x = 180 - (60 + 75)
x = 180 - 135
x = 45°

for numbers 7 and 8, you just need to know that vertical angles are equal to each other.

for example: #7

3x = 45°
x = 45 ÷ 3
x = 15°

for number 9, you need to know that those to angles add up to give you 180° because lines are 180°.

for example: #9

5x + 12 + 68 = 180°
5x + 80 = 180
5x = 180 - 80
5x = 100
x = 100 ÷ 5
x = 20°

I really hope that this made sense to you and that this actually helped you.

KATRIN_1 [288]2 years ago

4 0

Answer:

Step-by-step explanation:

Easy the three angles of a triangle equal 180 degrees

so 60+75 = 135 --> 180-135=

1) 145

2) 35

3) no since the tops a 100 and its a Isosceles triangle two corners left it be 40 for each corner

4) 34 for both x's cause 34+34+112. = 180

5) 180- 120= 60- 10 = 50/4 is (12.5)= x

6) x = 15 cause it be 120- 60 to get 60

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A population has the following characteristics. (a) A total of 75% of the population survives the first year. Of that 75%, 25% s

Artemon [7]

Answer:

$= \left[\begin{array}{ccc}1344\\84\\28\end{array}\right] \left \begin{array}{ccc}{0 \ \leq age \leq 1 }\\{ 1 \ \leq age \leq 2 }\\{2 \ \leq age \leq 3}\end{array}\right$

i.e after the first year ;

there 1344 members in the first age class

84 members for the second age class; and

28 members for the third age class

Step-by-step explanation:

We can deduce that the age distribution vector x represents the number of population members for each age class; Given that in each class of age there are 112 members present.

The current age distribution vector is as follows:

$x = \left[\begin{array}{ccc}1&1&2\\1&1&2\\1&1&2\end{array}\right] \left[\begin{array}{ccc}{0 \ \leq age \leq 1 }\\{ 0 \ \leq age \leq 2 }\\{0 \ \leq age \leq 3}\end{array}\right]$

Also , the age transition matrix is as follows:

$L = \left[\begin{array}{ccc}3&6&3\\0.75&0&0 \\0&0.25&0\end{array}\right]$

After 1 year ; the age distribution vector will be :

$x_2 =Lx_1 = \left[\begin{array}{ccc}3&6&3\\0.75&0&0 \\0&0.25&0\end{array}\right] \left[\begin{array}{ccc}1&1&2\\1&1&2\\1&1&2\end{array}\right]$

$= \left[\begin{array}{ccc}1344\\84\\28\end{array}\right] \left \begin{array}{ccc}{0 \ \leq age \leq 1 }\\{ 1 \ \leq age \leq 2 }\\{2 \ \leq age \leq 3}\end{array}\right$

6 0

2 years ago

Mike just hopped on the edge of a merry-go-round. What are his linear and angular speeds if the diameter of the merry-go-round i

dsp73

Step-by-step explanation:

Given that,

The diameter of the merry-go-round, d = 14 feet

Time taken, t = 6 seconds

Radius, r = 7 feet

The linear speed of the merry-go-round is given by :

$v=\dfrac{2\pi r}{t}\\\\v=\dfrac{2\pi \times 7}{6}\\\\=7.33\ m/s$

Also,

$v=r\omega$

Where

$\omega$ is the angular speed

So,

$\omega=\dfrac{v}{r}\\\\\omega=\dfrac{7.33}{7}\\\\=1.04\ rad/s$

Hence, his linear and angular speeds are 7.33 m/s and 1.04 rad/s.

8 0

3 years ago

Y=2x-1<br> y=1/2x+4<br> find the solution to the system equations

Evgesh-ka [11]

Answer:

x=10/3 y=17/3

Step-by-step explanation:

Use substitution to solve your equation. Plug in y=2x-1 into y=1/2x+4. This makes (2x-1)=1/2x+4. Simplify this to get 3/2x-1=4. Simplify it again to get 3/2x=5. No one likes fractions so multiply both sides by 2 to get 3x=10. Simplify this and get x=10/3. Plus 10/3 into one of the equations. You can pick anyone but I picked y=2x-1. Because you know x=10/3, you put y=2(10/3)-1. Simplify this and get y=20/3-1. Convert 1 into a fraction and get y=20/3-3/3. Simplify this and get y=17/3.

Therefore,

x=10/3 y=17/3

Hoped this helps you

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3 years ago

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Using the distributive property method on 6x32 and 7x29

Maru [420]

$6\cdot32=6(30+2)=(6)(30)+(6)(2)=180+12=192\\\\7\cdot29=7(30-1)=(7)(30)-(7)(1)=210-7=203$

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3 years ago

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A company manufactures running shoes and basketball shoes. The total revenue (in thousands of dollars) from x1 units of running

Alborosie

Answer:

$x_1 =2 , x_2=7$

Step-by-step explanation:

Consider the revenue function given by $R(x_1,x_2) = -5x_1^2-8x_2^2 -2x_1x_2+34x_1+116x_2$ . We want to find the values of each of the variables such that the gradient( i.e the first partial derivatives of the function) is 0. Then, we have the following (the explicit calculations of both derivatives are omitted).

$\frac{dR}{dx_1} = -10x_1-2x_2+34 =0$

$\frac{dR}{dx_2} = -16x_2-2x_1+116 =0$

From the first equation, we get, $x_2 = \frac{-10x_1+34}{2}$ .If we replace that in the second equation, we get

$-16\frac{-10x_1+34}{2} -2x_1+116=0= 80x_1-2x_1+116-272= 78x_1-156$

From where we get that $x_1 = \frac{156}{78}=2$ . If we replace that in the first equation, we get

$x_2 = \frac{-10\cdot 2 +34}{2}=\frac{14}{2} = 7$

So, the critical point is $(x_1,x_2) = (2,7)$ . We must check that it is a maximum. To do so, we will use the Hessian criteria. To do so, we must calculate the second derivatives and the crossed derivatives and check if the criteria is fulfilled in order for it to be a maximum. We get that

$\frac{d^2R}{dx_1dx_2}= -2 = \frac{d^2R}{dx_2dx_1}$

$\frac{d^2R}{dx_{1}^2}=-10, \frac{d^2R}{dx_{2}^2}=-16$

We have the following matrix,

$\left[\begin{matrix} -10 & -2 \\ -2 & -16\end{matrix}\right]$ .

Recall that the Hessian criteria says that, for the point to be a maximum, the determinant of the whole matrix should be positive and the element of the matrix that is in the upper left corner should be negative. Note that the determinant of the matrix is $(-10)\cdot (-16) - (-2)(-2) = 156>0$ and that -10<0. Hence, the criteria is fulfilled and the critical point is a maximum

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3 years ago

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