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Arturiano [62]
3 years ago
5

Use a number line to find the value of the expression -4+4-9 what property can you use to make your calculation easier explain

Mathematics
1 answer:
Bess [88]3 years ago
8 0
You can put the -4 and -9 together and put it at the end to make the new sequence 4-13 which would leave you with -9
You might be interested in
Simplify<br><br> 14 +{ -2 + 3 [ 1 +3 ( -6 -2 ) ] }
gregori [183]
ANSWER: -57
14+{−2+3[1+3(−6−2)]}
= 14+{−2+3[1+3(-8)]}
= 14+{−2+3[1+(-24)]}
= 14+{−2+3[1-24]}
= 14+{−2+3[-23]}
= 14+{−2+[-69]}
= 14+{−2-69}
= 14+(-71)
= 14 - 71
= -57
5 0
2 years ago
Write the equation described in each case.
Lapatulllka [165]

Answer:

The Answer is: y = -1/4x + 6

Step-by-step explanation:

Given point: (4, 5)

Given equation: y = -1/4x - 11

Slope: m = -1/4, a parallel line will have the same slope.

Start with the point slope form and solve for y:

y - y1 = m(x - x1)

y - 5 = -1/4(x - 4)

y - 5 = -1/4x + 1

y = -1/4x + 1 + 5

y = -1/4x + 6

Proof:

f(x) = -1/4x + 6

f(4) = -1/4(4) + 6

= -1 + 6 = 5, giving (4, 5)

Hope this helps!! Have an Awesome day!!! :-)

4 0
3 years ago
How do you solve this using substitution method<br> 17x+7y=20 <br> Y=20x-42
Nutka1998 [239]

Answer:

17 <em>x</em><em> </em>+ 7 y = 20

y =<em>20x</em><em> </em><em>-</em><em> </em><em>4</em><em>2</em>

<em>1</em><em>7</em><em> </em><em>x</em><em> </em><em>+</em><em> </em><em>7</em><em>(</em><em>20x</em><em> </em><em>-</em><em> </em><em>4</em><em>2</em><em>)</em><em> </em><em>=</em><em> </em><em>2</em><em>0</em>

<em>17x</em><em> </em><em>+</em><em> </em><em>140x</em><em> </em><em>-</em><em> </em><em>2</em><em>9</em><em>4</em><em> </em><em> </em><em> </em><em>=</em><em> </em><em>2</em><em>0</em>

<em>1</em><em>5</em><em>7</em><em> </em><em>x</em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em>=</em><em> </em><em>2</em><em>0</em><em> </em><em>+</em><em> </em><em>2</em><em>9</em><em>4</em>

<em>157x</em><em> </em><em>÷</em><em> </em><em>1</em><em>5</em><em>7</em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em>=</em><em> </em><em>3</em><em>1</em><em>4</em><em> </em><em>÷</em><em> </em><em>1</em><em>5</em><em>7</em>

<em>x</em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em>=</em><em> </em><em>2</em>

<em>y</em><em> </em><em>=</em><em> </em><em>20x</em><em> </em><em>-</em><em> </em><em>4</em><em>2</em><em> </em>

<em>y</em><em> </em><em>=</em><em> </em><em>2</em><em>0</em><em> </em><em>(</em><em>2</em><em>)</em><em> </em><em>-</em><em> </em><em>4</em><em>2</em>

<em>y</em><em> </em><em>=</em><em> </em><em>4</em><em>0</em><em> </em><em>-</em><em> </em><em>4</em><em>2</em>

<em>y</em><em> </em><em>=</em><em> </em><em>-2</em>

<em>there</em><em> </em><em>for</em><em> </em><em>x</em><em> </em><em>=</em><em> </em><em>2</em><em> </em><em>and</em><em> </em><em>y</em><em> </em><em>=</em><em> </em><em>-2</em><em> </em><em>is</em><em> </em><em>the</em><em> </em><em>solution</em><em> </em>

4 0
2 years ago
Find the function y1 of t which is the solution of 121y′′+110y′−24y=0 with initial conditions y1(0)=1,y′1(0)=0. y1= Note: y1 is
strojnjashka [21]

Answer:

Step-by-step explanation:

The original equation is 121y''+110y'-24y=0. We propose that the solution of this equations is of the form y = Ae^{rt}. Then, by replacing the derivatives we get the following

121r^2Ae^{rt}+110rAe^{rt}-24Ae^{rt}=0= Ae^{rt}(121r^2+110r-24)

Since we want a non trival solution, it must happen that A is different from zero. Also, the exponential function is always positive, then it must happen that

121r^2+110r-24=0

Recall that the roots of a polynomial of the form ax^2+bx+c are given by the formula

x = \frac{-b \pm \sqrt[]{b^2-4ac}}{2a}

In our case a = 121, b = 110 and c = -24. Using the formula we get the solutions

r_1 = -\frac{12}{11}

r_2 = \frac{2}{11}

So, in this case, the general solution is y = c_1 e^{\frac{-12t}{11}} + c_2 e^{\frac{2t}{11}}

a) In the first case, we are given that y(0) = 1 and y'(0) = 0. By differentiating the general solution and replacing t by 0 we get the equations

c_1 + c_2 = 1

c_1\frac{-12}{11} + c_2\frac{2}{11} = 0(or equivalently c_2 = 6c_1

By replacing the second equation in the first one, we get 7c_1 = 1 which implies that c_1 = \frac{1}{7}, c_2 = \frac{6}{7}.

So y_1 = \frac{1}{7}e^{\frac{-12t}{11}} + \frac{6}{7}e^{\frac{2t}{11}}

b) By using y(0) =0 and y'(0)=1 we get the equations

c_1+c_2 =0

c_1\frac{-12}{11} + c_2\frac{2}{11} = 1(or equivalently -12c_1+2c_2 = 11

By solving this system, the solution is c_1 = \frac{-11}{14}, c_2 = \frac{11}{14}

Then y_2 = \frac{-11}{14}e^{\frac{-12t}{11}} + \frac{11}{14} e^{\frac{2t}{11}}

c)

The Wronskian of the solutions is calculated as the determinant of the following matrix

\left| \begin{matrix}y_1 & y_2 \\ y_1' & y_2'\end{matrix}\right|= W(t) = y_1\cdot y_2'-y_1'y_2

By plugging the values of y_1 and

We can check this by using Abel's theorem. Given a second degree differential equation of the form y''+p(x)y'+q(x)y the wronskian is given by

e^{\int -p(x) dx}

In this case, by dividing the equation by 121 we get that p(x) = 10/11. So the wronskian is

e^{\int -\frac{10}{11} dx} = e^{\frac{-10x}{11}}

Note that this function is always positive, and thus, never zero. So y_1, y_2 is a fundamental set of solutions.

8 0
2 years ago
X an y are proportional. What is the missing value in the table <br>​
Leto [7]

Answer:

X+y

Step-by-step explanation:

6 0
2 years ago
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