MATHEMATICS HIGH SCHOOL

Simplify. (15/x-5)-5 = (21/x-6)-7

Answers

Answer 1

Answer:

Answer:

x = 2

Step-by-step explanation:

To simplify the given equation:

(15/x - 5) - 5 = (21/x - 6) - 7

First, let's simplify the algebraic expressions within the parentheses.

(15/x - 10) = (21/x - 13)

Now, let's multiply both sides of the equation by the common denominator, which is x.

x * (15/x - 10) = x * (21/x - 13)

This simplifies to:

15 - 10x = 21 - 13x

Next, let's combine like terms.

-10x + 15 = -13x + 21

Adding 10x to both sides of the equation:

15 = -3x + 21

Now, subtract 21 from both sides of the equation:

15 - 21 = -3x

-6 = -3x

Finally, divide both sides by -3 to solve for x:

x = -6 / -3

Simplifying the expression, we find:

Related Questions

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Find the value of F(5) for each function.f(a) = 3(a + 2) - 1
Which is greater, 0.5 or 2/3??
What’s the potential difference across a 5.0 resistor that carries a current of 5.0A
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a potato chip company packages chest by stacking them into a tall cylindrical K which units are most appropriate for measuring the thickness of an individual chip

Answers

Answer:

MIllimeters

Step-by-step explanation:

Its simple who measures this in inches or centimeters, or meters or anything else

Find the vertex, focus, and directrix. y = 1/24(x+1)² - 3.

Answers

$y = (1)/(24)(x+1)^2 - 3\n\ny+3 =(1)/(24)(x+1)^2\ \ / *24\n\n (x+1)^2 = 24(y+3)$

This is an equation of a parabola that opens upwards.

$Its \ standard \ form: \n(x-h)^2=4p(y-k)\n (h,k)=(x,y) \ coordinates \ of \ the \ vertex\n\ (h,k)=(-1,-3) \n\naxis \ of \ symmetry: \ x= -1\n \n4p=24\ \ /:4\np=6$

$focus:(h,k+p)=(-1,-3+6)=(-1,3) \n \ndirectrix: \ y=k-p=-3-6=-9$

$the\ equation\ in\ the\ form\ (x-h)^2=4p(y-k)\ is \ a\ parabola\nwith\ a\ vertex\ at\ \ (h,\ k), \na\ focus\ at\ \ (h,k+p)\n\ and\ a\ directrix\ \ y = k - p \n\n y = 1/24(x+1)^2 - 3\ \ \ \ \Rightarrow\ \ \ y+3 = 1/24(x+1)^2\ /\cdot24\n\n 24\cdot(y+3)=(x+1)^2\n\n(x+1)^2=4p(y+3)\ \ \Rightarrow\ \ 4p=24\ \ \Rightarrow\ \ p=6\ \ \ and\ \ \ h=-1,\ k=-3\n\nthe\ vertex:\ \ \ (h;\ k)=(-1;\ -3)\n\nthe\ focus:\ \ \ (h;\ k+p)=(-1;\ -3+6)=(-1;\ 3)\n\nthe\ directrix:\ \ \ y=k-p\ \ \ \Rightarrow\ \ \ y=-3-6=-9$

A candy jar contains 120 pieces of candy, including 45 red candies. If the ratio of red candies to the total number of candies in the jar remains the same, how many red candies would there be in a jar containing 200 pieces of candy?

Answers

Answer:

75 red candies

Step-by-step explanation:

200 candies divided by 120 = 1.666666666666667

Simply times 45 by 1.666666666666667

For each pair of mathematical expressions, determine if the expressions have equal values. Select each pair of expressions that came out to be equal.Please note, not all pairs will come out to the same value. We want you to determine if the expressions in each answer option have the have the same value.

Question options:

36÷3+3 and 22+2
36
÷
3
+
3

a
n
d

2
2
+
2

−(23)2and 49
-
(
2
3
)
a
n
d

4
9

8(−9) and −12−60
8
(
-
9
)

a
n
d

-
12
-
60

1+24 and 1−14

Answers

this doesn’t make sense you can really see the options

Mr. Wilk is a high school math teacher whose salaryis $33,660 for this school year, which has 180 days.In Mr. Wilk’s school district, substitute teachers are paid $85 per day. If Mr. Walker takes a day off without payand a substitute teacher is paid to teach his classes. How much less does the school district pay in salary by payinga substitute teacher instead of Mr. Wilk for this particukar day?

Answers

Mr. Wilk's salary for 180 days = $33,660
Mr. Wilk's salary for 1 day = $?
By unitary method:
Days Salary
180 $33,660
1 ?
By cross-multiplication:
1*33660/180
33660/180 = $187
Mr. Wilk's salary per day = $187
Substitute teacher's salary per day = $85
Difference in salary = 187-85
= $102
The school district pays $102 less to the substitute teacher.

Can you show us how to find the discriminant of the quadratic x^2 + 2x -2 =0

Answers

Step #1:
Make sure the equation is in the form of [ Ax² + Bx + C = 0 ].

Yours is already in that form.
A = 1
B = 2
C = -2

Step #2:
The 'discriminant' for that equation is [ B² - 4 A C ].
That's all there is to it, but it can tell you a lot about the roots of the equation.

-- If the discriminant is zero, then the left side of the equation is a perfect square,
and both roots are equal.

-- If the discriminant is greater than zero, the the roots are real and not equal.

-- If the discriminant is less than zero, then the roots are complex numbers.

The discriminant of your equation is [ B² - 4 A C ] = 2² - 4(1)(-2) = 4 + 8 = 12

Your equation has two real, unequal roots.

$the\ discriminant\ of\ the\ quadratic\ ax^2+bx+c=0\n\n\Delta=b^2-4\cdot a\cdot c\n-------------------------\n\n x^2 + 2x -2 =0\n\n\Delta=2^2-4\cdot1\cdot(-2)=4+8=12\n\ndiscriminant=12$

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