What is the distance between the points (3,_5) (-2,7) ?

Answer:

y = [tex]\frac{12-2x}{5}[/tex]

Step-by-step explanation:

Given

2x + 5y = 12

Isolate the term in y by subtracting 2x from both sides

5y = 12 - 2x ( divide both sides by 5 )

y = [tex]\frac{12-2x}{5}[/tex]

The equation for y is y = [tex]-\frac{2x}{5}+\frac{12}{5}[/tex]. The given equation is solved for y by applying simple operations like subtraction and division.

To isolate a variable in an equation,

The equation is 2x + 5y =12

Step 1: Subtract 2x from both the sides

⇒ 2x + 5y -2x = 12 - 2x

⇒ 5y = -2x + 12

Step 2: Dividing by 5 on both sides

⇒ 5y/5 = -2x/5 + 12/5

⇒ y = -2x/5 + 12/5

Therefore, the equation is y = -2x/5 + 12/5.

Learn more about the solving for other variables in an equation here:

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Answer:

We have the following function:

F(x) = x^2 + 3x - 2

Factorizing, we have: F(x) = (x+ 3.562)(x -0.562)

Then, the solution to the system of equation is:

x1 = -3.562

x2 = 0.562

Now, let's work with F(x - 1) = (x-1)^2 + 3(x-1) - 2

F(x - 1) = (x+2.562)(x-1.562)

Then, the solution to the equation is:

x1 = -2.562

x2 = 1.562

answer :  

we have the following function  

F(x) = x^2 + 3x - 2

Factorizing, we have: F(x) = (x+ 3.562)(x -0.562)

Then, the solution to the system of equation is:

x1 = -3.562

x2 = 0.562

Now, let's work with F(x - 1) = (x-1)^2 + 3(x-1) - 2

F(x - 1) = (x+2.562)(x-1.562)

Then, the solution to the equation is:

x1 = -2.562

x2 = 1.562

Answer:

C) 2

Step-by-step explanation:

1/x+ 1/y= 1/4 and 1/x-1/y=3/4

Add  the two equations together

1/x+ 1/y= 1/4

1/x-1/y=3/4

---------------------------

2/x = 4/4

2/x =1

Multiply each side by x

2/x *x = 1x

2 =x

Answer:

The last one.

Step-by-step explanation:

The grouping of factors are x(x² + 5) - 9(x² + 5).

An algebraic expression known as a polynomial requires that all of its exponents be whole numbers. Any polynomial must have variable exponents that are non-negative integers. Constants and variables are components of a polynomial.

We have equation

x³ - 9x² + 5x - 45.

Now, factories the equation as

x² (x-9) + 5(x-9)

= (x² + 5)(x-9)

1. x²(x - 9) - 5(x - 9) ⇒ x³ - 9x² - 5x + 45 (False)

2. x²(x + 9) - 5(x + 9) ⇒ x³ + 9x² - 5x - 45 (False)

3. x(x² + 5) - 9(x² + 5) ⇒ x³ + 5x - 9x² - 45 (True)

4. x(x² - 5) - 9(x² - 5) ⇒ x³ - 5x - 9x² + 45 (False)

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Hello There!

The temperature at 10 am in the morning was 1 degree below zero.

First, we know at 8 am that the temperature was 3 degrees below zero so that number is -3 and it’s our starting number.

Next, it says an hour later the temperature has gone up 6 degrees so we have -3 + 6 and we get a sum of positive 3.

Finally, at 9 am the temperature dropped again but this time 4 degrees so 3 - 4 = -1

The temperature at 10 am in the morning was 1 degree below zero.

Answer:

The correct answer is:

16˚F

Step-by-step explanation:

The correct answer is:

-14˚F + 10˚F = -4 ˚F

10˚F x 2 = 20˚F

-4˚F + 20˚F = 16˚F

Answer:

[tex]\large\boxed{-11,325}[/tex]

Step-by-step explanation:

First simplify:

[tex]-1-(n-1)=-1-n-(-1)=-1-n+1=-n[/tex]

Therefore we have:

[tex]\sum\limits_{n=1}^{150}[-1-(n-1)]=\sum\limits_{n=1}^{150}(-n)=(-1)+(-2)+(-3)+...+(-150)\\\\-1,\ -2,\ -3,\ -4,\ ...,\ -150-\text{it's the arithmetic sequence}\\\text{with the common difference d = -1.}\\\\\text{The formula of a sum of terms of an arithmetic sequence:}\\\\S_n=\dfrac{a_1+a_n}{2}\cdot n\\\\\text{Substitute}\ n=150,\ a_1=-1,\ a_n=-150:\\\\S_{150}=\dfrac{-1+(-150)}{2}\cdot150=(-151)(75)=-11,325[/tex]

Answer:

C.)

Step-by-step explanation:

Answer:

2x - 3y = 19

Step-by-step explanation:

The equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers

Given

y + 1 = [tex]\frac{2}{3}[/tex](x - 8)

Multiply all terms on both sides by 3 to eliminate the fraction

3y + 3 = 2(x - 8)

3y + 3 = 2x - 16 ( subtract 3y from both sides )

3 = 2x - 3y - 16 ( add 16 to both sides )

19 = 2x - 3y, that is

2x - 3y = 19 ← in standard form

Answer:

see explanation

Step-by-step explanation:

Solve the inequality

x + 5 > 3 ( subtract 5 from both sides )

x > - 2

solution set is { x : x > - 2 }

Answer: Acute

Step-by-step explanation: Right triangle has an angle of 90, and obtuse is more than 90, acute is less then 90 so there you go, hope this helps!

Answer:

acute

Step-by-step explanation:

In matrix form, the system is

[tex]\begin{bmatrix}1&2&-1\\1&2&1\\-1&-1&2\end{bmatrix}\begin{bmatrix}x_1\\x_2\\x_3\end{bmatrix}=\begin{bmatrix}-4\\2\\6\end{bmatrix}[/tex]

Solving this "using matrices" is a bit ambiguous but brings to mind two standard methods.

Compute the inverse of the coefficient matrix using the formula

[tex]\mathbf A^{-1}=\dfrac1{\det\mathbf A}\mathbf C^\top[/tex]

where [tex]\mathbf A[/tex] is the coefficient matrix, [tex]\det\mathbf A[/tex] is its determinant, [tex]\mathbf C[/tex] is the cofactor matrix, and [tex]\top[/tex] denotes the matrix transpose.

We compute the determinant by a Laplace expansion along the first column:

[tex]\det\mathbf A=\begin{vmatrix}1&2&-1\\1&2&1\\-1&-1&2\end{vmatrix}[/tex]

[tex]\det\mathbf A=\begin{vmatrix}2&1\\-1&2\end{vmatrix}-\begin{vmatrix}2&-1\\-1&2\end{vmatrix}-\begin{vmatrix}2&-1\\2&1\end{vmatrix}[/tex]

[tex]\det\mathbf A=5-3-4=-2[/tex]

The cofactor matrix is

[tex]\mathbf C=\begin{bmatrix}5&-3&1\\-3&1&-1\\4&-2&0\end{bmatrix}\implies\mathbf C^\top=\begin{bmatrix}5&-3&4\\-3&1&-2\\1&-1&0\end{bmatrix}[/tex]

which makes the inverse

[tex]\mathbf A^{-1}=\begin{bmatrix}-5/2&3/2&-2\\3/2&-1/2&1\\-1/2&1/2&0\end{bmatrix}[/tex]

Finally,

[tex]\begin{bmatrix}x_1\\x_2\\x_3\end{bmatrix}=\mathbf A^{-1}\begin{bmatrix}-4\\2\\6\end{bmatrix}\implies\boxed{x_1=1,x_2=-1,x_3=3}[/tex]

Take the augmented matrix

[tex]\begin{bmatrix}1&2&-1&-4\\1&2&1&2\\-1&-1&2&6\end{bmatrix}[/tex]

Subtract row 1 from row 2, and -(row 1) from row 3:

[tex]\begin{bmatrix}1&2&-1&-4\\0&0&2&6\\0&1&1&2\end{bmatrix}[/tex]

Multiply row 2 by 1/2:

[tex]\begin{bmatrix}1&2&-1&-4\\0&0&1&3\\0&1&1&2\end{bmatrix}[/tex]

The second row tells us that

[tex]x_3=3[/tex]

Then in the third row,

[tex]x_2+x_3=2\implies x_2=-1[/tex]

Then in the first row,

[tex]x_1+2x_2-x_3=-4\implies x_1=1[/tex]

Answer:

1

-1

3

Step-by-step explanation:

j did it on edge

Answer:

1/5 squared

Step-by-step explanation:

Answer:

Fraction 1 over 5 whole squared m²

Step-by-step explanation:

We know that,

The area of a square,

[tex]A=s^2[/tex]

Where, s is the side of the square,

Here,

[tex]s=\frac{1}{5}\text{ meters}[/tex]

Thus, the area of the square,

[tex]A=(\frac{1}{5})^2\text{ square meters}[/tex]

= Fraction 1 over 5 whole squared m²

Answer:

400 m^3

Step-by-step explanation:

volume of cylinder = area of the base * height

volume of cylinder = 100 m^2 * 12 m

volume of cylinder = 1200 m^3

The cylinder is 1/3 filled with water, so the volume of the water is 1/3 the volume of the cylinder.

volume of water = 1/3 * 1200 m^3

volume of water = 400 m^3

Answer:

The answer is 8.

Step-by-step explanation:

64^3/6

=3/6= ½

=64= 8^2

=(8^2)^1/2

According to exponent rule (a^b)^c = a^b^c

=8^2^1/2

=8

Answer:

8

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Let total number of vegetables be y and number of carrots be x

x+3x=y

4x=y

the smallest whole number is 1

x=1

y=4

Answer:

x = 150

Step-by-step explanation:

Answer:

[tex]\boxed{x=150}\checkmark[/tex]

The answer should have a "POSITIVE SIGN ONLY!"""

Step-by-step explanation:

First, you do is switch sides.

[tex]\frac{x}{5}=30[/tex]

Then, you multiply by 5 from both sides.

[tex]\frac{5x}{5}=30*5[/tex]

Finally, you solve and simplify.

[tex]30*5=150[/tex]

So, the final answer is x=150.

I hope this helps you!

Have a nice day! :)

Answer:

I have two problems and I put both of the answers in (x,v) form.

(-11/4,-3/14) for 2x+7v=-7 and -4x-30=-19

OR

(-343/32 ,  33/16) for 2x+7v=-7 and -4x-30v=-19

Step-by-step explanation:

I will solve the system as is ... but I'm not sure if you want your answer as (x,v) or (v,x)...

Let's go!

The second equation contains only one variable so I'm going to solve it first!

I'm going to solve -4x-30=-19 for x.

-4x-30=-19

Add 30 on both sides

-4x     =11

Divide both sides by -4

  x      =11/-4  or -11/4

So the 1st equation 2x+7v=-7 we are going to use our x=-11/4 to solve for v.

                              2(-11/4)+7v=-7

                               -22/4 +7v=-7

                               -11/2   +7v=-7

                                           7v=-7+11/2

                                           7v=-3/2

                                             v=-3/14

So (x,v) is (-11/4,-3/14).

Now I will also pretend you meant:

2x+7v=-7

-4x-30v=-19

I will do this by elimination.

Multiply the first equation by 2 and your x's will be opposites... And everyone knows when you add opposites you get 0 :).

4x+14v=-14    (I had multiply 2x+7v=-7 by 2 on both sides)

-4x-30v=-19

---------------------- I will now add the equations:

0-16v=-33

   -16v=-33

         v=33/16

Now to find x... Use one of the equation, doesn't matter which.... Replace v with 33/16 and solve for x.

So I'm going to use 2x+7v=-7  with v=33/16

                                2x+7(33/16)=-7

                                2x+231/16=-7

                                2x            =-7-231/16

                                2x            =-343/16

                                 x              =-343/32

So the solution in the form (x,v) is (-343/32 ,  33/16)

Answer:

Case 1  

The solution is: [tex](-\frac{343}{32}, \frac{33}{16})[/tex]

Case 2

The solution is: [tex](-\frac{11}{4},-\frac{3}{14})[/tex]

Step-by-step explanation:

Case 1

Assuming you want to write the following

[tex]2x+7v= -7[/tex]

[tex]-4x -30v= - 19[/tex]

----------------------------

Multiply the first equation by 2 and add it to the second equation

[tex]4x+14v= -14[/tex]

        +

[tex]-4x -30v= - 19[/tex]

------------------------------------

[tex]-16v=-33[/tex]

[tex]v=\frac{33}{16}[/tex]

Then

[tex]2x+7(\frac{33}{16})= -7[/tex]

[tex]2x+\frac{231}{16}= -7[/tex]

[tex]2x= -7-\frac{231}{16}[/tex]

[tex]2x=-\frac{343}{16}[/tex]

[tex]x=-\frac{343}{32}[/tex]

The solution is: [tex](-\frac{343}{32}, \frac{33}{16})[/tex]

Case 2

Assuming you want to write the following

[tex]2x+7v= -7[/tex]

[tex]-4x -30= -19[/tex]

Then solve the second equation for the variable x and then replace the value of x in the first equation

[tex]-4x -30= -19[/tex]

[tex]-4x= -19+30[/tex]

[tex]-4x= 11[/tex]

[tex]x= -\frac{11}{4}[/tex]

Then wehave that:

[tex]2(-\frac{11}{4})+7v= -7[/tex]

[tex]-\frac{11}{2}+7v= -7[/tex]

[tex]7v= -7+\frac{11}{2}[/tex]

[tex]7v= -\frac{3}{2}[/tex]

[tex]v= -\frac{3}{14}[/tex]

The solution is: [tex](-\frac{11}{4},-\frac{3}{14})[/tex]

Answer:

Elimination isn't exactly the easiest for this situation. But since the equations are in the same form and not solved for the same variable, I would go with elimination.  (If they were solved for the same variable, I would go with substitution.) It would require me to make a manipulation on both equations.

I would multiply first equation by 5 and second equation by -2.  The reason I would do this is because the y's would have opposite coefficients and when you add opposites you get 0.

The new set of equations would look like this:

20x+10y=45

-14x-10y=2

But I will slope here since we aren't asked to solve it.

Some texts use the term linear combination instead of elimination. They are the same.

Answer:

75 degrees

Step-by-step explanation:

sum of all angles in a triangle is=180 degrees

180 degrees -70 degrees- 35 degrees=75 degrees

mark me as brainliest plz

Answer:

B 75

Step-by-step explanation:

The three angles of a triangle add to 180 degrees.

35+70+x = 180

Combine like terms

105+x =180

Subtract 105 from each side

105-105+x = 180-105

x = 75

Answer:

x=17

Step-by-step explanation:

Distributive property: A(B+C)=AB+AC

Expand.

3(x+11)=3x+33

5x-1=3x+33

Add by 1 from both sides of equation.

5x-1+1=3x+33+1

Simplify.

5x=3x+34

Subtract by 3x from both sides of equation.

5x-3x=3x+34-3x

Simplify.

2x=34

Divide by 2 from both sides of equation.

2x/2=34/2

Simplify, to find the answer.

34/2=17

x=17 is the correct answer.

I hope this helps you, and have a wonderful day!

Answer:

x=17

Step-by-step explanation:

5x-1=3x+33

5x-3x=33+1

2x=34

x=34/2

x=17

just 1 solution

Answer:

3x+9

Step-by-step explanation:

Hope this helped!

Answer:

3x+9

Step-by-step explanation:

Remember that like terms can combine. 7x and -4x are like terms, and they combine to get 3x. 12 and -3 are like terms, and they combine to get 9. Therefore, the simplified expression is 3x+9.

Answer:

251.33yd

Step-by-step explanation:

Answer:

251

Step-by-step explanation:

ANSWER

[tex]2 \sqrt{42} +7 \sqrt{2}- 6- \sqrt{21}[/tex]

EXPLANATION

The given product is:

[tex]( \sqrt{14} - \sqrt{3} )( \sqrt{12} + \sqrt{7} )[/tex]

We expand using the distributive property to obtain:

[tex]\sqrt{14}( \sqrt{12} + \sqrt{7}) -\sqrt{3}( \sqrt{12} + \sqrt{7} )[/tex]

Extract the perfect squares to get:

[tex]\sqrt{14}(2 \sqrt{3} + \sqrt{7}) -\sqrt{3}( 2\sqrt{3} + \sqrt{7} )[/tex]

Expand further to get;

[tex]2 \sqrt{42} +7 \sqrt{2}- 2(3) - \sqrt{21} [/tex]

This simplifies to,

[tex]2 \sqrt{42} +7 \sqrt{2}- 6- \sqrt{21} [/tex]

1. First, let us write out the formula for the volume of a cylinder:

V = πr^(2)h

Now, given that the cylinder has a volume of 321 cubic units, we can rewrite the above formula with this new information:

321 = πr^(2)h

2. The volume of a cone is given by the following formula:

V = (1/3)πr^(2)h

Now, we can substitute 321 = πr^(2)h into the formula above to find the volume of the cone (this will work as the cone and cylinder have the exact same radius and height). Thus we get:

V = (1/3)πr^(2)h

V = (1/3)*321

= 107 cubic units

Note that there is another method that is perhaps more intuitive and can be used quite effectively in multiple choice questions, where working isn't required. What you should notice from the general formulas for the volume of a cone and a cylinder is that the volume of a cone is actually 1/3 of the volume of a cylinder (given that they have the same radius and height). Thus, if we know that the cone in our situation has the exact same radius and height as the cylinder, we can use this method as such:

Volume of cone = (1/3)*Volume of cylinder

Volume of cone = (1/3)*321

= 107 cubic units

All of the above.

To check if an ordered pair is a solution to the inequality, plug in the ordered pair into the inequality and see if the inequality checks out.

[tex]y<x+12[/tex]

(-2,5)

[tex]5<-2+12[/tex]

[tex]5<10[/tex]

So this ordered pair works.

(0,1)

[tex]1<0+12[/tex]

[tex]1<12[/tex]

So this ordered pair works as well.

(15,0)

[tex]0<15+12[/tex]

[tex]0<27[/tex]

So this ordered pair works.

(-5,0)

[tex]0<-5+12[/tex]

[tex]0<7[/tex]

So this ordered pair works as well.

Answer:it’s a function

Step-by-step explanation:

By using a graph of f(x), one can establish y-values for corresponding x-values. Graphs are visual representations of the relationship between x and y. The type of graph used depends on the variables and their relationships.

To evaluate the given expression using the graph of f(x), locate the necessary y-values for the suitable x-values from the graph. The values for y are the functional values of f(x) at any given point x. For instance, given the points (1,5), (2,10), (3,7), and (4,14) in your table, these represent the values of f(x) = y at x = 1, 2, 3, and 4 respectively. Therefore, use the graph to find the y-values for the specific x-values required.

Remember that graphs are visual representations of a function and the relationship between variables x and y. In a graph, the rise or fall of the line tells us how the two quantities being compared are changing relative to each other.

The types of graphs largely depends on the types of variables and the relationship between them. For instance, Line graphs are used when both variables are numerical and the data is continuous. Bar graphs are used when comparing the quantity, frequency, or other measure for different categories or groups. Pie chart is used when you are trying to compare parts of a whole.

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Answer:

8 : 343

Step-by-step explanation:

Given 2 similar figures

ratio of sides = a : b, then

ratio of volumes = a³ : b³

Here the ratio of edges = 2 : 7, hence

ratio of volumes = 2³ : 7³ = 8 : 343

Answer: It's the first one because their slope it's correct y over x in this case it's 4 over 3!

Yes, because both lines have a slope of 4/3.

you just have to find the rise/run of the two lines. If both answer are the same, in this case it is, then the lines are parallel. but if one of the slopes were 8/6 remember to simply and you'd get the correct answer!

Answer: -3 ≤  -2c

Step-by-step explanation:

First multiply C by -2, and make sure it's not less than -3. It can be -3, but it can't be less than.

To find the answers, we can put the numbers as x.

A) f(x)= -2x+7, when f(3)

f(3) = -2(3)+7

=-6+7

=1

Therefore f(3) = 1

B) f(x)= -2x+7, when f(-5)

f(-5)= -2(-5)+7

=10+7

=17

Therefore f(-5) = 17

Hope it helps!

Answer: 5 lbs each

Step-by-step explanation:

Create a table such that you multiply across and add down (first and last column only). Then solve the equation that develops in the last row.

[tex]\begin{array}{l|c|c||l}&\underline{Qty(lbs)}&\underline{Price(\$)}&\underline{\qquad Price \times Qty\qquad}\\Almonds&x&3.75&\qquad 3.75(x)=3.75x\\\underline{Cashews}&\underline{10-x}&\underline{6.72}&\underline{6.72(10-x)=67.2-6.72x}\\Mixture&10&5.22&\qquad 3.75x+67.2-6.72x\end{array}\\\\\\.\qquad \qquad \qquad \qquad 5.22(10)=3.75x+67.2-6.72x\\.\qquad \qquad \qquad \qquad \qquad 52.2 =-2.97x+67.2\\.\qquad \qquad \qquad \qquad \quad -15.0=-2.97x\\.\qquad \qquad \qquad \qquad \qquad \ 5.0=x[/tex]

If x = 5,

then 10 - x = 10 - 5 = 5

To determine the amount of almonds and cashews needed, we set up a system of equations using the costs per pound and the desired total cost for a combined weight of 10 pounds. By solving the equations, we find the pounds of each type of nut required to make the mixture.

To solve this problem, we use a system of equations to determine how many pounds of almonds and cashews are needed to produce a 10-pound mixture that sells for $5.22 per pound.

If done correctly, the solution will give you the exact pounds of almonds and cashews needed for the 10-pound mixture.