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One leg of a right triangle has a length of 3 m. The other sides have lengths that are consecutive integers. Find these lengths.

The other leg is ___ m.

Answer:

perfect square

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

8 is the digit after 7  and previous to 9

Answer:

[tex]\huge\boxed{\sf x = 14 , y = 10}[/tex]

Step-by-step explanation:

Let the two numbers be x and y

Condition # 1:

Condition # 2:

[tex]\rule[225]{225}{2}[/tex]

Putting Equation # 2 in Equation # 1

2y - 6 + y = 24

3y - 6 = 24

Adding 6 to both sides

3y = 24 + 6

3y = 30

Dividing both sides by 3

y = 10

[tex]\rule[225]{225}{2}[/tex]

Putting y = 10 in Equation # 2

x = 2y - 6

x = 2(10) - 6

x = 20 - 6

x = 14

[tex]\rule[225]{225}{2}[/tex]

The two numbers are 10 and 14.

The sum of 2 numbers is 24.

let the number be x and y . Therefore,

x + y = 24

One is 6 less than twice the other. therefore,

2x - y = 6

Combine the equations

x + y = 24

2x - y = 6

3x = 30

x = 30 / 3

x = 10

x + y = 24

10 + y = 24

y = 24 - 10

y = 14

The 2 numbers are 10 and 14 .

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Answer:

a. -2

b. 3

c. 3

d. -3

e. x=-2

Step-by-step explanation:

When a question asks for f(x), it is basically just asking for what the y-value is at the given point of x. So for example, to solve the first one: f(-4), we see that the x-value is -4. This means it is asking for the y-value at x=-4. As we can see from the graph, where x = -4, the y-value is -2 (along the bottom flat line) therefore f(-4) = -2.

This is the same for the other three, f(0) = 3 because the line at x=0 is crossing at y=3. etc.

Finally e is difference because it is instead asking for the x-value when y=6. To solve this we just need to find a point on the graph where the line is at y=6. This, as we can see is at the top of the highest point and occurs where x=-2.

Hope this helped!

Answer:

35°

Step-by-step explanation:

-5° + 40° = 35°

So the ansWer is 35°

Answer:

12 times.

Step-by-step explanation:

96÷8=12

Answer:

3 + 9i

Step-by-step explanation:

(4 + 2i) - (1 - 7i)

distribute the (-)

(4 + 2i) - 1 + 7i

combine like terms

3 + 9i

Answer:

its an integer

Step-by-step explanation:

Because it has a negative sign

Answer: the answer should be A

if this helps the equation format is y= mx + b your replace the with the slop and the b with the y intercept

the way to find the slope is rise over run

Step-by-step explanation:

To find a decimal that is equavalent to 4/15, all we need to do is divide.

4 / 15 = 0.26666...

Best of Luck!

Answer:

15.6 is the right answer

Step-by-step explanation:

Answer:

30 miles in 2 hours

Step-by-step explanation:

Answer:

A unit rate is a rate where the second quantity is one unit , such as $34 per pound, 25 miles per hour, 15 Indian Rupees per Brazilian Real, etc. Example 1: A motorcycle travels 230 miles on 4 gallons of gasoline. Find the average mileage per gallon.

Step-by-step explanation:

Answer:

50%

Step-by-step explanation:

34+16=50% he or she ate half of the pizza

Answer:

No

Step-by-step explanation:

t the two equations for the lines into slope-intercept form. ...

Set the two equations for y equal to each other.

Solve for x. ...

Use this x-coordinate and plug it into either of the original equations for the lines and solve for y.

Answer:

X=2

Step-by-step explanation:

|2x -12| = -4x

2x-12 = -4x

2x - (-4x) = 12

2x +4x =6x

6x=12

x=12/6

x=2

Answer:

Step-by-step explanation:

2+3+4+5+6=20

20/20=4,000,000

2/20=?

2/20×4,000,000÷20/20=400,000

20/20=4,000,00

3/20

3/20×4000000÷20/20=600,000

20/20=4,000,000

4/20

4/20×4,000,000÷20/20=800,000

20/20=4,000,000

5/20

5/20×4,000,000÷20/20=1,000,000

20/20=4,000,000

6/20

6/20×4,000,000÷20/20= 1,200,000

2:3:4:5:6=400,000 :600,000: 800,000 : 1,000,000: 1,200,000

If 2x+7>=0, x>=-3.5 then |2x+7|=2x+7.

Then the inequality becomes:

2x+7>23, 2x>16, x>8.(which is an acceptable result since we already assumed x>=-3.5)

If 2x+7<0, x<-3.5 then |2x+7|= -(2x+7).

Then the inequality becomes:

-(2x+7)>23, 2x+7<-23, 2x <-30, x<-15.

(which is an acceptable result since we already assumed x<-3.5)

Thus the answer is x<-15 or x>8.

The graph is simple. You draw the line of real numbers and "shadow" all numbers above 8 and all numbers bellow - 15.

Answer:

1 : 20 20 students for every 1 teacher

Step-by-step explanation:

divide both sides by 12

Answer:

Step-by-step explanation:

Given the 2 by 2 matrix [tex]A = \left[\begin{array}{-cc}x&5\\y&-8\\\end{array}\right][/tex] , we are to find the value of x and y for the expression A² = A to be true.

First we need to find A² by multiplying the same matrix together

[tex]A^2 = \left[\begin{array}{-cc}x&5\\y&-8\\\end{array}\right] \left[\begin{array}{-cc}x&5\\y&-8\\\end{array}\right]\\\\ \ we \ normally \ multiply \ the \ rows \ of \ the \ first \ matrix \ with \ the \ column \ of \ the \ second \\\\A^2 = \left[\begin{array}{-cc}x^2+5y&5x-40\\xy-8y&5y+64\\\end{array}\right]\\\\Since \ A^2 = A,\ hence;\\\\\left[\begin{array}{-cc}x^2+5y&5x-40\\xy-8y&5y+64\\\end{array}\right] = \left[\begin{array}{-cc}x&5\\y&-8\\\end{array}\right]\\[/tex]

Equating the first row and second column of both matrices together, we will have;

5x-40 = 5

add 40 to both sides of the equation

5x-40+40 = 5+40

5x = 45

x = 45/5

x = 9

Similarly,  we will equate the second row and second column of both matrices to have;

5y+64 = -8

Subtract 64 from both sdies

5y+64-64 = -8-64

5y = -72

y = -72/5

Hence the value of x is 9 and y is -72/5

Matrices are used to represent data in rows and columns

The values of x and y are 9 and -14.4 respectively.

Matrix A is represented as:

[tex]\mathbf{A = \left[\begin{array}{ccc}x&5\\y&-8\end{array}\right] }[/tex]

Calculate [tex]\mathbf{A^2}[/tex]

[tex]\mathbf{A^2 = \left[\begin{array}{ccc}x&5\\y&-8\end{array}\right] \times \left[\begin{array}{ccc}x&5\\y&-8\end{array}\right] }[/tex]

Recall that [tex]\mathbf{A^2 = A}[/tex]

This means that:

[tex]\mathbf{\left[\begin{array}{ccc}x^2++5y&5x-40\\xy-8y&5y+64\end{array}\right] = \left[\begin{array}{ccc}x&5\\y&-8\end{array}\right] }[/tex]

So, by comparison

[tex]\mathbf{5x - 40 = 5}[/tex]

[tex]\mathbf{5x = 40 + 5}[/tex]

[tex]\mathbf{5x = 45}[/tex]

[tex]\mathbf{x = 9}[/tex]

Similarly

[tex]\mathbf{5y + 64 = -8}[/tex]

[tex]\mathbf{5y =-64 -8}[/tex]

[tex]\mathbf{5y =-72}[/tex]

[tex]\mathbf{y =-14.4}[/tex]

Hence, the values of x and y are 9 and -14.4 respectively.

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Answer:

0

Step-by-step explanation:

-115-(-115)

Subtracting a negative is like adding

-115 + 115

0

The answer is 0

Because they subtract each other

Step-by-step explanation:

The second graph is the right one

Answer:

see below

Step-by-step explanation:

f(x) = -x-7 is of the form

y = mx+b  where m is the slope and b is the y intercept

The line  has a y intercept of (0,-7) and a slope of -1

A slope of -1 means the line goes down from left to right ( down 1 and to the right 1)

Answer:

y = -7

Step-by-step explanation:

3(-4) = y - 5

-12 = y - 5

y = -12 + 5

y = -7

The volume of the right rectangular prism having dimensions  1.5 cm, 0.5 cm and 2. 25 cm. will be V=1.6875 [tex]cm^3[/tex]

Volume is defined as the space covered by any object in the three dimensions having coordinates in all three sides is called as volume.

We know that the volume of the Rectangular prism is given as:

[tex]\rm V=L\times W\times D\\\\\\V=1.5\times 0.5\times 2.25\\\\\\V=1.6875\ \ \ cm^3[/tex]

Hence the volume of the right rectangular prism having dimensions  1.5 cm, 0.5 cm and 2. 25 cm. will be V=1.6875 [tex]cm^3[/tex]

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Answer: B.  |x-100| = 25

Explanation:

Draw out a number line. Mark 75, 100 and 125 on the number line as points A, B, and C in that order. Don't worry about the spacing.

The value of x represents where the train is. So if we had say x = 85, then it would be at location 85 on the number line. Writing |x-100| is the distance from x to 100. The absolute value ensures the distance is never negative. We want this distance to be 25 because after traveling 25 cm, the switch is turned, and the train goes the other way.

The equation which models the movement of the train is represented by |x − 100| = 25. The correct option is B.

One-variable linear equation The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution. For instance, the linear equation 2x+3=8 only has one variable.

The train's location is indicated by the value of x. Therefore, if x were to equal, let's say, 85, it would be at position 85 on the number line.

The distance between x and 100 is expressed as |x-100|. The distance will never be negative thanks to the absolute value. Because the switch is switched after the train has traveled 25 cm in one direction, we need this distance to be 25 cm.

Therefore, the equation which models the movement of the train is represented by |x − 100| = 25. The correct option is B.

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Answer:

Following are the solution:

Step-by-step explanation:

Given equation:

[tex]\frac{dx}{dy}= \frac{y(y-2)}{2}........(a)[/tex]

[tex]\Phi (x) = \frac{2}{1-ce^x}[/tex]

In the question [tex]\Phi (x)[/tex], is a solution of the equation (a) only if when [tex]\Phi (x)[/tex]satisfies equation (a):

let us find [tex]\Phi' (x)[/tex]:-

[tex]\Phi(x) =\frac{d}{dx} \Phi (x)=\frac{d}{dx}(\frac{2}{1-ce^x})[/tex]

                        [tex]= 2 \frac{d}{dx}({1-ce^x}^-1)\\\\= 2 (-1) ({1-ce^x})^{-2} \frac{d}{dx}({1-ce^x})\\\\= -2 ({1-ce^x})^{-2} (-ce^x})\\\\= 2(-ce^x) ({1-ce^x})^{-2} \\\\[/tex]

Now:

[tex]\frac{dy}{dx}=\frac{y(y-2)}{2}\\\\\frac{d}{dx}\Phi (x) =\frac{\Phi (x) (\Phi (x)-2)}{2}\\[/tex]

by subtracting the value of [tex]\Phi (x)[/tex]and [tex]\frac{d}{dx}[/tex][tex]\Phi (x)[/tex],we get:

[tex]\to[/tex][tex]2ce^x(1-ce^x)^-2= \frac{(\frac{2}{1-ce^x})(\frac{2}{1-ce^x})^{-2}}{2}[/tex]

[tex]=2ce^x (1-ce^x)^{-2}=\frac{1}{2}[\frac{2}{1-ce^x}(\frac{2-2(1-ce^x)}{1-ce^x)}]\\\\= \frac{1}{1-ce^x} \times \frac{2ce^x}{1-ce^x}\\\\=\frac{2ce^x}{(1-ce^x)^2}\\\\=2ce^x (1-ce^x)^-2[/tex]

[tex]\bold{2ce^x(1-ce^x)^-2=2ce^x(1-ce^x)^-2}[/tex]

[tex]\Phi (x)[/tex] the solution of the given equation. [tex]\Phi (x)[/tex] has one Parameter Family of

[tex]\frac{dy}{dx}=\frac{y(y-2)}{2}[/tex]

[tex]\Phi (x) =\frac{2}{1-ce^x}\\\\_{when} \ \ \ c= 0 \to \Phi (x) =\frac{2}{1-0\times e^x}=2\\\\_{when} \ \ \ c= 1 \to \Phi (x) =\frac{2}{1-1\times e^x}=\frac{2}{1-e^x}\\\\_{when} \ \ \ c= -1 \to \Phi (x) =\frac{2}{1-(-1)\times e^x}=\frac{2}{1+e^x}\\\\_{when} \ \ \ c= 2 \to \Phi (x) =\frac{2}{1-(-2)\times e^x}=\frac{2}{1-2e^x}\\\\_{when} \ \ \ c= -2 \to \Phi (x) =\frac{2}{1-(-2)\times e^x}=\frac{2}{1+2e^x}\\\\[/tex]

Answer: simply

Step-by-step explanation: Example: 15y= -5x+0 First move -5 to other side of equal sign. So 15y+5x=0 Then simply by dividing by 5. So 5y+x=0

Answer:

No

Step-by-step explanation:

Its 1000

Answer:

C

Step-by-step explanation:

24÷6= 6 Hope this helps.