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Posted in Mathematics

WILL UPVOTE! Which equation is related to 89 = x + 61? A. x = 150 B. 61 = 89 + x C. x = 28 D. x = 18


C! x = 28. If you use simplification, and then you find the answer and use it in the equation, it would be correct.

Related Questions

Posted in Mathematics

Which ordered pair is a solution of the equation 2x − y = 9 (-4,1) (-2,5) (5,1) (6,-3)

In order to confirm if which ordered pair is a solution of the given equation above, we can just simply plug in the values.
So based on my solution, the correct answer would be the third option: (5,1) 
So let us try to plug in the values.
2(5) - 1 = 9
10 -1 = 9
9 = 9
So this is the correct one. Hope this answers your question.

Posted in Mathematics

What is the range of the function f(x) = 3x2 + 6x – 9

I have a solution here however with a slight change in the equation:

 f(x)=3x^2-6x+1

My solution is:

The domain is all real numbers--there are no restrictions like a square root or variable in the denominator 

this is a U shape parabola and you want to find the bottom point, it is at the vertex 

x=-b/2a =- (-6) /2 (3) =1 
f(1) =3(1)^2 -6(1) +1 =3-6+1 =-2 
the minimum is (1, -2) 
so the range is all real numbers >= -2

By examining my solution, you could just answer the problem on your own! I hope it helps!

Posted in Mathematics

Find the multiplicative inverse of 6 + 2i.

The solution to the problem is as follows:

First thing to do is get rid of the i. Multiplying by 6 - 2i will do this 

( 6 + 2i)(6 - 2i) = 6^2 - (2i)^2 = 36 - 4(-1) = 36 + 4 = 40 

Dividing by 40 gets you 1 

(6 + 2i) (6-2i)/40 = 1 

The answer is (6 - 2i)/40 = (3 - i)/20

I hope my answer has come to your help. God bless and have a nice day ahead!

Posted in Mathematics

Solve the equation for y 2x+6y=13

So here is how we are going to solve for y for the given equation above:
2x+6y=13
Next, transfer 2x to the right side and it will look like this:
6y=13-2x
Now, divide both sides by 6, and it will look like this:
y=13-2x
    --------
       6
So, this is the final answer for y.
Hope this answers your question. Have a great day!

Posted in Mathematics

Which is a factor of 18?

Factors of 18: 1 2 3 6 9 18

hope this helps you

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Posted in Mathematics

What is 1.892 to the nearest tenth?

We need to look at the number after the tenth, called the 'hundredth'. If the hundredth is 5 or above, we must change the hundredth to 0 and make the tenth one higher.

In this case, the hundredth is 9 and is above 5, so it becomes 0 and the tenth moves higher to become 9.

The number will now be 1.9

Posted in Mathematics

The y-coordinate of the y-intercept is the _____ term in the equation of the line.

For the answer to the missing term in the question above, the question is as simple as its answer. The right answer is constant.
I hope my answer helped you. Feel free to ask more questions. Have a nice day!

Posted in Mathematics

What interval includes all possible values of x, where –3(6 – 2x) ≥ 4x + 12? (–∞, –3] [–3, ∞) (–∞, 15] [15, ∞)

The solution to the problem is as follows:

solve for x :

−3(6−2x)≥4x+12

−18+6x≥4x+12

2x≥30

x≥15

So the answer is D ) 15 to +infinity


I hope my answer has come to your help. God bless and have a nice day ahead!

Posted in Mathematics

How to solve this problem 14-6= 10-6=?

I really don't think you wrote the question properly. Or maybe you did, but this question doesn't make any sense! :/

Posted in Mathematics

Algebraic terms are separated by ______. Choose all that apply. 1)= 2)+ 3)x 4)÷ 5)-

Answer

1)=

2)+

5)-

Explanation

When letter or numbers are separated by multiplication or division can be combined to make one term.

In an algebra equation, terms are separated by an addition sign, subtraction sign or an equal sign. For example,

3a + 7b = 21.

This equation have 3 terms.

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Posted in Mathematics

When simplified and written in standard form, which quadratic function is equivalent to the polynomial shown? 2 + 7c – 4c2 – 3c + 4 –4c2 + 4c + 6 –7c2 + 10c + 6 –4c2 + 4c + 8 –7c2 + 7c + 6

Answer:

A) -4c^2 + 4c + 6

Step-by-step explanation:

The given polynomial is 2 + 7c – 4c^2 – 3c + 4

Add the like terms.

2 + 4 + 7c - 3c -4c^2

= 6 + 4c - 4c^2

Write it in a standard form

= -4c^2 + 4c + 6

Answer is A) -4c^2 + 4c + 6

Hope this will helpful.

Thank you.

Posted in Mathematics

What is the ratio of the area of the inner square to the area of the outer square? (a−b)²+b²/a² a²−b²/a² (a−b)²/(a+b)² (ab)²/(a+b)²

The answer is
(a−b)²+b²/a²


proof

if A is the area of the
inner squared, so A= c², and c²= (a−b)²+b²

so the side of the outer must be a-b +b=a, its area is a²

Posted in Mathematics

Arrange the following polynomial into descending order for x, then interpret the degree of the 2nd term. 7x3y3 + 4 − 11x5y2 − 3x2y

For the answer to the question above,  the power of "y" doesn't influence descending order for x even if it is higher than power of x.

Unordered polynomial is 
7x3y3 + 4 - 11x5y2 - 3x2y

Polynomial in descending order  looks like this
-11x5y2 + 7x3y3 - 3x2y + 4

Degree of the second term is 5 ( because of x5 ) 

Posted in Mathematics

The measured weights of 1,000 men in a certain village follow a normal distribution with a mean of 150 pounds and a standard deviation of 15 pounds. Which sentence most closely summarizes the data? About 160 people weigh more than 165 pounds. About 320 people weigh more than 165 pounds. About 320 people weigh less than 165 pounds. About 640 people weigh less than 165 pounds.

Z = (X-Mean)/SD 
z1 = (165 - 150)/15 = +1 
z2 = (135 - 150)/15 = - 1 
According to the Empirical Rule 68-95-99.7 
Mean +/- 1SD covers 68% of the values 
100% - 68% = 32% 
The remaining 32% is equally distributed below z = - 1 and z = +1 
32%/2 = 16% 

Therefore, 

a) Number of men weighing more than 165 pounds = 16% of 1000 = 160 
b) Number of men weighing less than 135 pounds = 16% of 1000 = 160

Posted in Mathematics

Which of the following is a factor of 2x4 + 22x3 + 60x2? 2x3 x4 x + 4 x + 5

The correct answer is Option D, or X+5. I hope I answered this question to your satisfaction Have a nice day!

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Posted in Mathematics

The discriminant of a quadratic equation is negative. One solution is 3+4i . What is the other solution? A.4-3i B.3-4i C.4+3i D.-3+4i

The way you stated the problem, there is an infinity of possibilities for the other solution. 

► For instance, the quadratic equation: 
   x² – (6 + 4i)x + (9 + 12i) = 0 
has for discriminant: 
   Δ = (6 + 4i)² – 4(9 + 12i) = 36 – 16 + 48i – 36 – 48i = -16 
which is indeed negative. 
Its solutions will then be: 
   x₁ = [(6 + 4i) + 4i]/2 = 3 + 4i 
   x₂ = [(6 + 4i) – 4i]/2 = 3 
And the other solution here is 3. 

► If you are not convinced, the quadratic equation: 
   x² – (6 + 5i)x + (5 + 15i) = 0 
has for discriminant: 
   Δ = (6 + 5i)² – 4(5 + 15i) = 36 – 25 + 60i – 20 – 60i = -9 
which is indeed negative. 
Its solutions will then be: 
   x₁ = [(6 + 5i) + 3i]/2 = 3 + 4i 
   x₂ = [(6 + 5i) – 3i]/2 = 3 + i 
And the other solution here is 3+i. 

► In fact, every quadratic equation of the form: 
   x² – [6 + (4 + α)i]x + (3 + 4i)(3 + αi) = 0 
where α is any real, has for discriminant: 
   Δ = [6 + (4 + α)i]² – 4(3 + 4i)(3 + αi) 
      = 36 – (4 + α)² + 12(4 + α)i – 36 + 16α – 12(4 + α)i 
      = 16α – (4 + α)² 
      = 16α – 16 – 8α – α² 
      = -16 + 8α – α² 
      = -(α – 4)² 
WILL be negative. 
Their solutions will then be: 
   x₁ = [ [6 + (4 + α)i] – (α – 4)i ]/2 = 3 + 4i 
   x₂ = [ [6 + (4 + α)i] + (α – 4)i ]/2 = 3 + αi 
And the other solution will then be is 3+αi. 

Since α can take any real value, you'll obtain an infinity of solutions of the form 3+αi. 

► So conclusively: 
If the discriminant of a quadratic is negative AND one of the solutions is 3+4i, the only thing we can say about the other solution is that its real part must be 3. 

Posted in Mathematics

Let P be a point between points S and T on 2004-01-01-02-00_files/i0120000.jpg. If ST = 21, SP = 3b – 11, and PT = b + 4, solve for b. A. –7 B. 7 C. 14 D. 32

The best and most correct answer among the choices provided by your question is the third choice or letter C.

If ST = 21, SP = 3b – 11, and PT = b + 4, the value of b would be 14.


I hope my answer has come to your help. God bless and have a nice day ahead!

Posted in Mathematics

If np >5 and nq>5 estimate P (fewer than 4) with n=13 p=0.4 by using normal distribution as an approximate to the binomial distribution if np <5 or nq< then state that the normal approximation is not suitable.

The Normal approximation to the binomial 

is as follows

mean=13(.5)=6.5 
variance=6.5(.5)=3.25 
Pr[fewer than 4]= 
Pr[N<=3] Apply the continuity correction 
Pr[N<=3.5]~=Pr[Z<3.5-6.5/sqrt(3.25)]= 

Pr[Z<-1.66]=0.048457226

I hope my answer has come to your help. God bless and have a nice day ahead!

Posted in Mathematics

Which polynomial expression represents the area of the outermost square tile, shown below? A square shaped tile with length x plus three is shown x2 + 6x + 6 x2 + 9x + 6 x2 + 6x + 9 x2 − 6x + 9

I believe the correct answer from the choices listed above is the third option. The polynomial expression that represents the area of the outermost square tile would be x^2 + 6x + 9. The area of a square is calculated by the square of its side and the side of this square is given as x+3.

A = (x+3)^2 = x^2+6x+9

Posted in Mathematics

What is the additive inverse of the polynomial 9xy^2 + 6x^2y – 5x^3? A.9xy2 – 6x2y + 5x3 B. 9xy2 – 6x2y – 5x3 C. 9xy2 + 6x2y + 5x3 D. 9xy2 – 6x2y + 5x3

Are you sure that you wrote all your choices right?
Because for so solving the additive inverse of 9xy² + 6x²y - 5x³

-1(9xy² + 6x²y - 5x³)  then it will turn to this ⇒ (-1)(9xy²) + (-1)(6x²y) + (-1)(-5x³)

-9xy² - 6x²y + 5x³ is the additive inverse of the given polynomial.

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Posted in Mathematics

6 times the square root of 2.25 and then minis 4.23 =

The answer is: 4.77.
________________

6√(2.25)  - 4.23 = ?
__________________
6√(2.25)  - 4.23 = 
______________________
6*(1.5)  - 4.23 = 
_______________
9 - 4.23 =
_______________
4.77

Posted in Mathematics

What is the equation in point slope form of the line that passes through the point (–2, 4)(–2, 4) and has a slope of 5?

Point-slope formula: y-y1=m(x-x1) 
Now we'll plug in the numbers they give us into the formula:

y-4= 0(x+2).

Posted in Mathematics

Solve for x. round to nearest tenth if needed. 1. 7r-7=2r+18 a.r=-5 b.r=5 c.r=2.2 d.r=1.2 2. 2x+12=18-x a.x=3 b.x=10 c.x=6 d.x=2 3. 8x-3=15x+18 a.x=-3 b.x=3 c.x=2.1 d.x=0.9 4. 6y-6=4y+16 a.y=2.2 b.y=-2.2 c.y=11 d.y=5 5. 3(x-4)=5(x+2) a.x=11 b.x=-11 c.x=1 d.x=-1

1)  The answer is: [B]: r = 5 .
__________________________
Explanation:
__________________________ 
Given: 7r − 7 = 2r + 18 ; Round your answer to the nearest tenth, if necessary.
____________________________
Since "r" is the only variable given, let us assume we want to solve for "r" (instead of "x").
___________________________
→ Subtract "2r" from EACH SIDE of the equation; and & add "7" to EACH SIDE of the equation:
_____________
→ 7r − 7 − 2r + 7 = 2r + 18 − 2r + 7 ;  to get: → 5r = 25 ;
_____________
→ Now, divide EACH SIDE of the equation by "5"; to isolate "r" on one side of the equation; and to solve for "r" :
______________
→ 5r / 5 = 25 / 5 → r = 5 → which is: "Answer choice: [B]".
_________________
Let us check our answer, by plugging in "5" for "r" in the original equation:
_________________
 → 7r − 7 = 2r + 18 ;  →  7(5) − 7 =? 2(5) + 18? ;
______________________
→ 35 − 7 =? 10 + 18 ?;     → 28 =? 28? Yes!
______________________
 2) The answer is: [D]: x = 2 .
_____________
Explanation: 
_____________
Given: 2x + 12 = 18 − x ; Solve for "x" (round to nearest tenth, if necessary).
_______________
→ Add "x" to EACH SIDE of the equation, & subtract "12" from EACH SIDE of the equation:  → 2x + 12 + x − 12 = 18 − x + x − 12 ; 
______________
→ To get: 3x = 6 ;  → Divide EACH SIDE of the equation by "3";
to isolate "x" on one side of the equation; and to solve for "x":
_____________
→ 3x / 3 = 6 / 3 ; → x = 2 ; which is: "Answer choice: [D]".
______________
Let us check our answer, by plugging in "2" for "x" in the original equation:
________________
→ 2x + 12 = 18 − x ; → 2(2) + 12 =? 18 − 2 ?
________________
→ 4 + 12 =? 18 − 2 ? ;   → 16 =? 16?  Yes!
________________________________
3)  The answer is: [A]: x = -3 . 
_____________
Explanation:
________________
Given:  8x − 3 = 15x + 18 ; Solve for "x". Round your answer to the nearest tenth, if necessary.
_________________
→ Subtract "8x" from EACH SIDE of the equation, & add "3" to EACH SIDE of the equation:
_______________
→ 8x − 3 − 8x + 3 = 15x + 18 − 8x + 3 ; to get:
_______________
→ 0 = 7x + 21 ; → Subtract "21" from EACH SIDE of the equation;
_______________
→ 0 − 21 = 7x + 21 − 21 ; to get:
_______________
→  -21 = 7x ; Now divide EACH SIDE of the equation by "7";
    to isolate "x" on one side of the equation; & to solve for "x":
_______________
→ = -21 / 7 = 7x / 7 ; →  -3 = x ; which is "Answer choice: [A]."
_________________
Let us check our answer, by plugging in "-3" for "x" in the original equation:
________________
→  8x − 3 = 15x + 18 ;  → 8(-3) − 3 =?  15(-3) + 18 ?;
________________________
→ -24 − 3 =?  -45 + 18 ? ;   →  -27 =? -27?  Yes!
___________________________
4)  The answer is: [C]: y = 11 .
_____________
Explanation:
____________
Given: 6y − 6 = 4y + 16 ; Solve for "y"; Round to the nearest tenth, if necessary.
____________
(Note: Since "y" is the only variable given; assume we are to solve for "y" instead of "x").
____________
→ Subtract "4y" from EACH SIDE of the equation, & add "6" to EACH SIDE of the equation; → 6y − 6 − 4y + 6 = 4y + 16 − 4y + 6 ; to get:
_______________
→ 2y  = 22 ; Now, divide EACH SIDE of the equation by "2"; to isolate "y" one side of the equation; and to solve for "y" ;
_______________
→ 2y / 2 = 22 / 2 ; →  y = 11 → which is "Answer choice: [C]".
_______________________________
Let us check our answer, by plugging in "11" for "y" in the original equation:
___________________
→  6y − 6 = 4y + 16 ; → 6(11) − 6 =? 4(11) + 16 ?
_______________________
→ 66 − 6  =? 44 + 16 ?  → 60 =? 60 ?  Yes!
__________________
5)  The answer is: [B]: x = -11 .
_____________________
Explanation:
_________________
Given: 3(x − 4) = 5(x + 2) ; Solve for "x". Round to the nearest tenth, if necessary.
___________
→Note the "distributive property of multiplication": 
_____________
a*(b + c) = ab + ac ;  and: a*(b − c) = ab − ac ;
_______________
→ Let us expand EACH SIDE of our given equation.
→Start with the "left-hand side":
____________
3(x − 4) = (3*x)  − (3*4) = 3x − 12;
______________________________
→Now let us expand the "right-hand side" of the given equation:
____________
→  5(x + 2) = (5*x) + (5*2) = 5x + 10 ;
______________
→Now, we can rewrite the original equation:
_______________
→ 3(x − 4) = 5(x + 2) ; by substituting the expanded values for EACH SIDE of the question:   →  3x − 12 = 5x + 10 ;
__________________
→ Subtract "3x" from EACH SIDE of the equation; and add "12" to EACH SIDE of the equation: →  3x − 12 − 3x + 12 = 5x + 10 − 3x + 12 ; to get:
________________
→  0 = 2x + 22;  → Now subtract "22" from EACH SIDE of the equation:
______________
→  0 − 22 = 2x + 22 − 22 ; to get:  →  -22 = 2x ;
__________
→ Divide EACH SIDE of the equation by "2"; to isolate "x" on one side of the equation; & to solve for "x" ;
_____________
→  -22 / 2 = 2x /2 ;  →  -11 = x ; which is "Answer choice: [B]".
______________
Let us check our answer, by plugging in "-11" for "x" in the original equation:
___________
→ 3(x − 4) = 5(x + 2) ; →  3(-11 − 4) =? 5(-11 + 2) ? ; 
_______________________
→3(-15) =? 5(-9) ? ; → -45 =? -45 ?  Yes!
_____________________________________________
Hope these answers and explanations are helpful. Best of luck!

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Posted in Mathematics

Solve for w. 2w=12-4w Simplify your answer as much as possible.

So we have an equation:
2w=12-4w
Firstly, let's simplify, and divide all terms by 2:
w=6-2w
Now, we add 2w over to the other side:
3w=6
And finally, we divide both sides by 3:
w=2
Hope this helps!

Posted in Mathematics

Round 89,891 to the nearest ten-thousands place.

The ten thousands digit is the 8 to the left edge.

You need to increase this digit because the thousands digit is greater than zero.


The answer is 90,000.

Posted in Mathematics

Calculate the moments Mx, My, and the center of mass (x bar, y bar) of a lamina with the given density p=5 and the shape:

M x = 1/2 p ∫ ( f ( x )² - g ( x )² ) d x
f ( x ) = √( 1 - x²),  g ( x ) = - 2
M x = 1/2 * 5  \int\limits^1_{-1} (- x^{2} -3)\, dx= \\ =-5/2 * [ x^{3}/3 + 3 x]^1 _{-1} = \\ =-5/2 * (1/3+3+1/3+3)=
= - 50/3
My = p ∫ x * ( f ( x ) ) dx
My = p ∫ x ( √(1+x²)) dx
Substitution: 1 - x² = u,  x dx = - du/2
M y = 5 *  \int\limits^0_0 { \sqrt{u} } \, du = 0
M x = - 50/3, M y = 0
M = 5 *  \int\limits^1_{-1}  { (\sqrt{1+ x^{2} }+2)} \, dx  = \\ &#10;=5* [1/2  \sqrt{1+ x^{2} }  *x + 2 x + 1/2 *sinh ^{-1} x]^1_{-1}
M ≈ 5 * 6.3 ≈ 31.2  
x = M y / M = 0 / 31.5 = 0
y = M x / M =  -50/3 : 31.5 ≈ - 0.529
The center of mass is ( 0, -0.529 )


Posted in Mathematics

Mrs. Donley's math class has a total of 25 students. On Friday, the class was given an eight question quiz on fractions. The number of incorrect answers given by the students is shown below. Incorrect Answers Number of Students 0 5 1 7 2 4 3 6 4 2 5 1 What is the relative frequency of students that missed 1 question on the quiz? A. 0.28 B. 0.48 C. 0.35

You need to find the amount of students who missed one question, and divide that by the total number. If you sum all the students, you find that there are 25 students. From the chart, 7 missed 1 question, therefore the solution would be 7/25, which is 0.28, or A.

A. 0.28

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