A number is 5 more than 3 times another number. The sum of the two numbers is 33. As an equation, this is written x + 3x + 5 = 33, where x represents the smaller number. Plug in the numbers from the set {3, 5, 7, 9} to find the value of x.

The value of x that holds true for the equation is blank . So, the smaller number is blank and the larger number is blank .

Answer:

see below

Step-by-step explanation:

x + 7/5 = 10

Subtract 7/5 from each side

x+7/5 -7/5 = 10 -7/5

x  = 10-7/5

Get a common denominator

x = 50/5 - 7/5

x = 43/5

As a mixed number

x = 8  3/5

Or if the equation was

(x+7)/5 = 10

Multiply by 5

(x+7)/5 *5 = 10*5

x+7 = 50

Subtract 7 from each side

x+7-7 = 50-7

x = 43

Answer:

x = 43/5

Step-by-step explanation:

Subtract 7/5 from both sides.

x + 7/5 - 7/5 = 10 - 7/5

x= 43/5

Answer:

65

Sorry if im wrong

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.

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:

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:

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: 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:

251.33yd

Step-by-step explanation:

Answer:

251

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

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: You can simply find out the percentage of the calories from the sugar with this formula :

165/250 x 100%  

You will find out that the percentage would be 66 %

hope this helps!

Step-by-step explanation:

Answer:

3√2

Step-by-step explanation:

√18 = √9 x √2 = 3√2

Start by making a factor tree for 18.

18 factors as 6 x 3 and 6 factors as 2 x 3.

Look for pairs of factors that are the same.

In this case, the 3's match up.

So a 3 will come out of the radical.

Whatever does not pair up stays inside.

In this case, the 2 goes inside.

So our answer is 3√2.

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:

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:

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

To find the perimeter of a rectangle you can multiply the length by 2 and the width by 2, or you can add the four sides together.

The wrong equation is w + 3w = 90 because it only has one width and one length, which would be half the total perimeter.

Final answer:

The equation that does not correctly represent the width w of Sanjay's rectangular garden given the total fence length and length-width relationship is w + 3w = 90, as it simplifies to 4w = 90, which is not the correct equation for this context.

Explanation:

The question asks to identify which equation does not correctly represent the width w of Sanjay's rectangular garden, given that the total length of the fence is 90 meters and that the length l of the garden is three times its width w. We know the perimeter P of a rectangle is given by P = 2l + 2w, where l is the length and w is the width.

We can substitute l = 3w into the perimeter formula to get P = 2(3w) + 2w, which simplifies to P = 6w + 2w or P = 8w. Given that P = 90, the correct equation is 8w = 90. Now, let's examine the provided equations:

w + 3w = 90 simplifies to 4w = 90.

w + 3w + w + 3w = 90 simplifies to 8w = 90, which is the correct equation.

2 · w + 2 · 3w = 90 simplifies to 2w + 6w = 90 which simplifies to 8w = 90, which is also correct.

2 · (3w + w) = 90 simplifies to 2 · 4w = 90 which simplifies to 8w = 90, which is again correct.

Thus, the equation that does not give the correct value for w is w + 3w = 90.

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:

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:

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)

Learn more about Polynomial here:

https://brainly.com/question/1286778

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:

- 77

Step-by-step explanation:

To evaluate, substitute x = 4 into g(x) then substitute the value obtained into f(x).

g(4) = 4² + 3 = 16 + 3 = 19

f(19) = (- 4 × 19) - 1 = - 76 - 1 = - 77

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:

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]

Start with

[tex]-2z+10+7z=16z+7[/tex]

Simplify the left hand side by summing like terms (the one involving z):

[tex]5z+10 = 16z+7[/tex]

Subtract 5z from both sides:

[tex]10 = 11z+7[/tex]

Subtract 7 from both sides

[tex]3 = 11z[/tex]

Divide both sides by 11:

[tex]z = \dfrac{3}{11}[/tex]

The equation has one solution and the solution is z = 3/11.

Simplification of an equation is the process of writing an equation in the most efficient and compact form without affecting the value of the original equation.

For the given situation,

The equation is -2z+10+7z=16z+7

The equation can be simplified as

⇒ [tex]-2z+10+7z=16z+7[/tex]

⇒ [tex]-2z+7z-16z=7-10[/tex]

⇒ [tex]-11z=-3[/tex]

⇒ [tex]z=\frac{-3}{-11}[/tex]

⇒ [tex]z=\frac{3}{11}[/tex]

Hence we can conclude that the equation has one solution and the solution is z = 3/11.

Learn more about simplification of an equation here

https://brainly.com/question/11444405

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ANSWER

[tex]37.53units[/tex]

EXPLANATION

From the given right angle triangle the known angle is 47°

The side length which is x units is opposite to the known angle.

We also know a side length 35 units which is adjacent to the given angle.

We use the tangent ratio to obtain,

[tex] \tan(47 \degree) = \frac{opposite}{adjacent} [/tex]

[tex]\tan(47 \degree) = \frac{x}{35} [/tex]

[tex]x = 35\tan(47 \degree) = 37.53 \: units[/tex]

Answer:

x = 37.53 units

Step-by-step explanation:

Points to remember

Trigonometric ratios

Sin θ  = Opposite side/Hypotenuse

Cos θ = Adjacent side/Hypotenuse

Tan θ = Opposite side/Adjacent side

From the figure we can see a right angled triangle with one angle is 47° and adjacent  side length of that angle is 35

To find the value of x

From the figure we can write,

Tan 47 =  Opposite side/Adjacent side

 = x/35

x = 35 * Tan 47

 = 37.53 units

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:

c

Step-by-step explanation:

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: -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.