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Answer:

[tex] \dfrac{a}{a - 4} [/tex]

Step-by-step explanation:

You are subtracting fractions, so as usual with fraction subtraction, you need a common denominator. To get a common denominator, you need to factor each denominator.

[tex] \dfrac{3a}{a + 4} - \dfrac{2a^2 - 16a}{a^2 - 16} = [/tex]

Factor the right denominator. It is a difference of two squares.

[tex] = \dfrac{3a}{a + 4} - \dfrac{2a^2 - 16a}{(a - 4)(a + 4)} [/tex]

The left denominator is (a + 4). The right denominator is (a - 4)(a + 4). The LCD is (a - 4)(a + 4), so multiply the left fraction by (a - 4)/(a - 4).

[tex] = \dfrac{3a}{a + 4} \times \dfrac{a - 4}{a - 4} - \dfrac{2a^2 - 16a}{(a - 4)(a + 4)} [/tex]

[tex] = \dfrac{3a^2 - 12a}{(a - 4)(a + 4)} - \dfrac{2a^2 - 16a}{(a - 4)(a + 4)} [/tex]

Be careful when you do the subtraction of the numerators, 3a² - 12a minus 2a² - 16a. 3a² - 12a - (2a² - 16a). The minus of the subtraction changes each sign inside the parentheses, so you end up with 3a² - 12a - 2a² + 16a. Be especially careful with the +16a.

[tex] = \dfrac{3a^2 - 12a - (2a^2 - 16a)}{(a - 4)(a + 4)} [/tex]

[tex] = \dfrac{3a^2 - 12a - 2a^2 + 16a}{(a - 4)(a + 4)} [/tex]

[tex] = \dfrac{a^2 + 4a}{(a - 4)(a + 4)} [/tex]

[tex] = \dfrac{a(a + 4)}{(a - 4)(a + 4)} [/tex]

[tex] = \dfrac{a}{a - 4} [/tex]

Answer:

88772677020890.30

Step-by-step explanation:

To calculate its volume, we need to know two parameters - the radius (or diameter) and height:

cylinder_volume = π * cylinder_radius² * cylinder_height

Answer:

11852.97

Step-by-step explanation:

is the correct answer took the test on k12

Rewrite : [tex]1500 : (6^{2} +43)[/tex] x 37

Simplify : [tex]1500 : 79[/tex] x 37 = 702.531646...

Round to :
- Nearest whole number : 703
- 1 d.p : 702.5
- 2 d.p : 702.53
- 3 d.p : 702.532

The value of the expression when 1500 divided by (6 squared + 43) x 37 using simplification is 702.531647.

A collection of constants, variables connected using one or more arithmetic operator is called an expression.

The way of writing the complex mathematical problems into simpler forms using certain way is called simplification.

Simplification is solved using BODMAS rule.

The expression 1500 divided by (6 squared + 43) x 37 can be written in mathematical form as:

[tex]\dfrac {1500}{((6)^2 + 43)} \times37[/tex]

This can be simplified as,

[tex]\dfrac {1500}{(36 + 43)} \times37[/tex]

[tex]\dfrac {1500}{79} \times37[/tex]

On further solving, it results to 702.531647.

The value of the given expression is 702.531647.

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Answer:

Step-by-step explanation:

Answer:

ik my head be harding so much

Step-by-step explanation:

like take it out

The quadratic equation that can be used to determine the thickness of the frame will be B. 3x² + 5x - 19.25 = 0

It should be noted that a quadratic equation simply means an algebraic expression of the second degree in x.

In this case, the quadratic equation that can be used to determine the thickness of the frame will be 3x² + 5x - 19.25 = 0

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Answer:

The answer is C. 4x2 + 16x - 4.25 = 0.

Step-by-step explanation:

The chairs in the auditorium illustrates an arithmetic sequence

From the question, we have the following sequence:

Seats: 18, 26, 34

Rewrite as:

26 = 18 + 8

34 = 26 + 8

The above means that:

The number of seats on a row is 8 added to the the number of seats on the previous row.

Hence, the recursive rule is:

an = an-1 + 8; a1 = 26

In (a), we have:

a1 = 26 and d = 8

The explicit rule is calculated using:

an = a1 + (n -1) * d

This gives

an = 26 + (n - 1) * 8

Expand

an = 26 - 8 + 8n

Evaluate the difference

an = 18 + 8n

Hence, the explicit rule is:

an = 18 + 8n

This means that n = 7.

So, we  have:

a7 = 18 + 8 * 7 = 74

Hence, there are 74 seats in the 7th row

We have the maximum number of rows to be 12.

So, the sigma notation would be:

[tex]\sum\limits^{12}_{n=1} {18 + 8n}[/tex]

The total number of seats is:

Sn = n/2(2a + (n -1) * d)

This gives

S12 = 12/2(2 * 26 + (12 -1) * 8)

S12 = 840

Hence, 840 chairs can fit the auditorium

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Answer: 224

Step-by-step explanation:

on the white boards

Answer:

i did it

Step-by-step explanation:

Answer:

5 + i

Step-by-step explanation:

the Fundamental theorem of Algebra states that a polynomial of gegree n has n zeros , some of which may be complex.

A polynomial of degree 3 will therefore have 3 zeros

given x = 1 and 5 - i are two of the zeros

Complex zeros occur as conjugate pairs , then

5 - i is a zero then 5 + 1 is also a zero

the 3 zeros are x = 1 , x = 5 - i and x = 5 + i

Answer:

m∠G = 60°

Step-by-step explanation:

This is a kite, so its angles sum to 360 degrees. Write an equation adding all of the angles and make them equal to 360:

m∠H + m∠F + m∠E + m∠G = 360

90 + 150 + m∠E + m∠G = 360

Since this is a kite, m∠E = m∠G, so the equation can be represented as:

90 + 150 + 2(m∠G) = 360

Finally, solve by isolating m∠G:

2(m∠G) = 120

m∠G = 60°

Answer:

  see attached

Step-by-step explanation:

The given equation is in "point-slope" form:

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

Comparing the equation to the form, you see ...

__

The equation is easily graphed by plotting the point (-1, -3) and then drawing a line through it that has a slope (rise/run) of 3. That is, the line will go up 3 grid squares for each grid square to the right. (The origin is a point on the line.)

Answer:

20 would be the lowest that both 10 and 5 could go into, and that would make the fractions 4/20 and 6/20.

Answer:

10

Step-by-step explanation:

We need to find the lowest common multiple of teh 2 denominator:

So first let's write the first few multiples of 5:

5,10,15,20,25

Now let's write the first few multiples of 10:

10,20,30,40,50

Since 10 is the first number that appears in both lists this is our answer

Ball is sphere

SurfAce area:-

Answer:

Formula

Surface area of a sphere:

[tex]\sf SA=4\pi r^2[/tex]  (where r is the radius)

Given information

[tex]\pi[/tex] = 3.14

r = 16

Final solution

Substitute given values into the equation and solve:

[tex]\sf \implies SA=4 \cdot 3.14 \cdot 16^2[/tex]

            [tex]\sf =3215.36 \ cm^2[/tex]

Answer:

The number would be 90

Step-by-step explanation:

140 + 10 - 90 = 60

90 - 30 = 60

60 = 60

Answer: 90

Step-by-step explanation:

Let's use x as a placeholder to the number we are trying to find

[tex]140+10-x=x-30[/tex]

Now we need to isolate x

Step 1) Simplify both sides

[tex]140+10-x=x-30\\150-x=x-30[/tex]

Step 2) Add 30 to both sides

[tex]150-x+30=x-30+30\\180-x=x[/tex]

Step 3) Add x to both sides

[tex]180-x+x=x+x\\180=2x[/tex]

Step 4) Divide both sides by 2

[tex]\frac{180}{2}=\frac{2x}{2} \\90=x[/tex]

Step 5) Sub our value into the original equation and solve

[tex]140+10-x=x-30\\140+10-90=90-30\\150-90=60\\60=60[/tex]

Answer:

Step-by-step explanation:

Simply divide the numbers, the result is the quotient

The quotient of the given expression when 1,224 divided by 9 is 136.

The quotient is defined as the number obtained on dividing a number with some number.

The number left after the division is called as the remainder.

Example: When 37 is divided by 5, the quotient is 5 and the remainder is 2.

The quotient of the following expression can be calculated as:

When 1224 is divided by 9, it gets divisible in 136 times completely, leaving no remainder.

So, it can be said that 136 is the quotient when 1,224 divided by 9.

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Answer:

[tex] \frac{3}{8} \div \frac{2}{3} - \frac{1}{8} [/tex]

Step-by-step explanation:

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Answer:

= 185 units²

Step-by-step explanation:

the area (A) of a trapezoid is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )

where h is the perpendicular height between the bases and b₁, b₂ the bases

here h = 10 , b₁ = 22 , b₂ = 22 - 7 = 15 , then

A = [tex]\frac{1}{2}[/tex] × 10 × (22 + 15) = 5 × 37 = 185 units²

Answer:

Step 2-3

Step-by-step explanation:

I don't know what's wrong with step 2 but in step 3 the student added the exponent instead of multiplying.

That automatically makes every other step done afterwards wrong but it's not 3-4 because the math is right it's just that step 3 messed up step 4 laws of exponent wise.

Answer:

0

Step-by-step explanation:

•103n+26n = 131n

Combine 103 n and 26 n to get 129n

•129n=131n

Substract 131n from both sides

•129n-131n=0

Combine 129n and -131n to get 2n

•-2n=0

Product of two numbers is equal to 0 if atleast one of them is 0. Since -2 is not equal to 0, n must be 0.

•n=0

Answer:

$6.14.

Step-by-step explanation:

$30.70×20%

there will be after the tax and discount.

Answer:

Both of them are correct because if we simply the fraction of Edwin we will get the fraction of Tony

[tex] \frac{3}{6} [/tex]

[tex] = \frac{1}{2} [/tex]

PLEASE MARK ME BRAINLIEST IF MY ANSWER IS CORRECT PLEASE

Answer:

Step-by-step explanation:

Given equation,

⇒ 5x - 6 = 3x - 8

Subtracting 3x from both sides :

⇒ 5x – 6 – 3x = 3x – 8 – 3x

⇒ 2x – 6 = – 8

Adding 6 to both sides we get :

⇒ 2x – 6 + 6 = – 8 + 6

⇒ 2x = – 2

Dividing both sides by 2 we get :

⇒ 2x/2 = – 2/2

⇒ x = – 1

Therefore,

Answer:

[tex]\sf \boxed{\bold{x=-1}}[/tex]

Solving Stepwise:

[tex]\dashrightarrow \sf 5x-6=3x-8[/tex]

add 6 on both sides

[tex]\dashrightarrow \sf 5x-6+6=3x-8+6[/tex]

simplify

[tex]\dashrightarrow \sf 5x=3x-2[/tex]

subtract both sides by 3x

[tex]\dashrightarrow \sf 5x-3x=3x-2-3x[/tex]

simplify

[tex]\dashrightarrow \sf 2x=-2[/tex]

divide both sides by 2

[tex]\dashrightarrow \sf \dfrac{2x}{2} =\dfrac{-2}{2}[/tex]

simplify

[tex]\dashrightarrow \sf x =-1[/tex]

Check for the answer:

insert x = -1

[tex]\hookrightarrow \sf 5(-1)-6=3(-1)-8[/tex]

[tex]\hookrightarrow \sf -5-6=-3-8[/tex]

[tex]\hookrightarrow \sf -11=-11[/tex]

Answer:

What is the question? Also, your answer looks a bit wrong  1 think t should be 1 oz

Step-by-step explanation:

For every 15 oz potatoes, Garry uses 0.5 oz less cheese than Heather. So Heather's cheesy potatoes have more cheese.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

For Gary's recipe of cheesy potatoes has 15oz of potatoes and 4oz of cheese.

Ratio of potatoes to cheese in Gary's recipe = 15/4

Heather's recipe of cheesy potatoes has 10 oz of potatoes and 3 oz of cheese.

Ratio of potatoes to cheese in Heather's recipe = 10/3

Multiplying with 1.5 in numerator and denominator

Ratio of potatoes to cheese in Heather's recipe = 15/4.5

Thus, for every 15 oz potatoes heather uses 4.5 oz of cheese.

Hence, In Heather's recipe amount of cheese is 0.5 oz more than Garry's recipe per 15 oz. of potatoes.

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Answer:

y=18

x=14.4

Step-by-step explanation:

the answer is 8

8j-5+j=67

8J +j

9J-5=67

    +5  +5

9J=72

  /9    /9

j=8

[tex]\qquad \qquad \huge \pink {\sf{☁Answer☁}} \\ \\ [/tex]

[tex] \large \purple{ \rm{Let's \: solve→}}[/tex]

[tex] \rm{8j - 5 + j = 67} \\ \\ \rm{arranging \: like \: terms} \\ \\ \rm{8j + j = 67 + 5} \\ \\ \rm{9j = 72} \\ \\ \rm{j = \frac{72}{9} } \\ \\ \rm{j = \cancel\frac{72}{9} } \\ \\ \rm{j = 8}[/tex]

[tex]\rule{70mm}{2.2pt}[/tex][tex]\sf{\:мѕнαcкεя\: ♪...}[/tex]

The volume of the trapezoidal prism having side lengths x, (x+2), (x+4) and height of 2x is 2x³+6x² option first is correct.

It is defined as a three-dimensional space enclosed by an object or thing.

We know the volume of the trapezoidal prism can be given:

[tex]\rm V=\frac{1}{2} (a+b)\times h \times L[/tex]

Where V = The volume of the trapezoidal prism:

Length of the trapezoid L = x

Top width  a = (x+2)

Base width  b = (x+4)

Height of the trapezoidal prism  h = 2x

[tex]\rm V=\frac{1}{2} (x+2+x+4)\times 2x \times x[/tex]

[tex]\rm V=\frac{1}{2} (2x+6)2x^2\\\\\rm V= (2x+6)x^2\\\\\rm V= (2x^3+6x^2)[/tex]

Thus, the volume of the trapezoidal prism is  [tex]\rm (2x^3+6x^2)[/tex]

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Answer:

A.

Step-by-step explanation:

right on edge

Answer:

Divide y by x. The answer is 8

For example 252 divided by 30 equals 8.4

Round it out to 8.

Answer:

The answer is A

Step-by-step explanation:

you divide the Y by the X