A circuit contains three resistors rated at 100 Ω, 200 Ω, and 300 Ω that are connected in parallel. What's the total resistance of the circuit?

Answer:

(3a-1)(3a+1)

Step-by-step explanation:

This is the difference of two squares so we can factorise using the rules

x^2-y^2 = (x-y)(x+y)

In this case x = 3a and y = 1 since (3a)^2 = 9a^2 and 1^2 = 1

The answer is:

The total surface area of the pyramid is:

[tex]TotalSurfaceArea=192ft^{2}[/tex]

To calculate the surface area of a square pyramid, we need to use the following formula:

[tex]TotalSurfaceArea=\frac{1}{2}pl+BaseArea[/tex]

Where,

p, is the perimeter of the base.

l, is the slant of the pyramid.

Base area, is the area of the square base.

Now, from the statement we know that the base has a length of 6 feet, and the height of a face (slant) is 13 feet.

So, calculating, we have:

[tex]BaseArea=BaseLength^{2}=(6ft)^{2} =36ft^{2}[/tex]

[tex]Perimeter=4*side=4*6feet=24feet[/tex]

The total surface area will be:

[tex]TotalSurfaceArea=\frac{1}{2}l+BaseArea[/tex]

[tex]TotalSurfaceArea=\frac{1}{2}*24ft*13ft+36ft^{2}[/tex]

[tex]TotalSurfaceArea=156ft^{2}+36ft^{2}=192ft^{2}[/tex]

Hence, we have the total surface area of the pyramid is:

[tex]TotalSurfaceArea=192ft^{2}[/tex]

Have a nice day!

Check the picture below.  So let's use those two points on the line.

[tex]\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{3}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{3-0}{3-0}\implies \cfrac{3}{3}\implies 1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-0=1(x-0)\implies y=x \\\\\\ -x+y=0\implies \stackrel{\textit{standard form}}{x-y=0}[/tex]

bearing in mind that the standard form is also a general form.

standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

Answer:

B. x - y = 0

Step-by-step explanation:

For this case we must solve each of the equations proposed:

A) [tex]m ^ 2 + 9 = 58[/tex]

Subtracting 9 from both sides of the equation we have:

[tex]m ^ 2 = 49[/tex]

Applying root to both sides of the equation:

[tex]m = \sqrt {49}\\m = \pm7[/tex]

B) [tex]7e ^ 2 = 28[/tex]

We divide between 7 on both sides of the equation:

[tex]e ^ 2 = \frac {28} {7}\\e ^ 2 = 4[/tex]

We apply root to both sides of the equation:

[tex]e = \pm \sqrt {4}\\e = \pm2[/tex]

C) [tex]d ^ 2 + 6 = 70[/tex]

Subtracting 6 on both sides of the equation:

[tex]d ^ 2 = 64[/tex]

We apply root to both sides of the equation:

[tex]d =\pm \sqrt {64}\\d = \pm8[/tex]

D) [tex]\frac {1} {2} n ^ 2-10 = 62[/tex]

We add 10 to both sides of the equation:

[tex]\frac {1} {2} n ^ 2 = 72[/tex]

We multiply by 2 both sides of the equation:

[tex]n ^ 2 = 144[/tex]

We apply root to both sides of the equation:

[tex]n = \pm \sqrt {144}\\n =\pm12[/tex]

Answer:

[tex]m = \pm7\\e = \pm2\\d = \pm8\\n = \pm12[/tex]

Answer:

Solutions: (2,10), (4,5)

Not solutions: (1,12), (6,10), (12,8), (18,6)

Step-by-step explanation:

Let x be the number of packages of pasta and y be the number of jars of pasta sauce. If pasta costs $1 for a 1-pound package, then x packages of pasta cost $x and weigh x pounds. If pasta sauce costs $3 for a 1.5 pound jar, then y jars cost $3y and weigh 1.5y pounds.

1. Tyler has $36, then

[tex]x+3y\le 36.[/tex]

2. Tyler can carry up to 20 pounds of food in his backpack, then

[tex]x+1.5y\le 20.[/tex]

You get the following system of inequalities:

[tex]\left\{\begin{array}{l}x+3y\le 36\\ x+1.5y\le 20\end{array}\right.[/tex]

Now substitute the coordinates of each point:

(1,12):

[tex]\left\{\begin{array}{l}1+3\cdot 12=37> 36\\ 1+1.5\cdot 12=19\le 20\end{array}\right.[/tex]

False, because first inequality doesn't hold.

(2,10):

[tex]\left\{\begin{array}{l}2+3\cdot 10=32\le 36\\ 2+1.5\cdot 10=17\le 20\end{array}\right.[/tex]

True, both inequalities hold.

(4,5):

[tex]\left\{\begin{array}{l}4+3\cdot 5=19\le 36\\ 4+1.5\cdot 5=11.5\le 20\end{array}\right.[/tex]

True, both inequalities hold.

(6,10):

[tex]\left\{\begin{array}{l}6+3\cdot 10=36\le 36\\ 6+1.5\cdot 10=21> 20\end{array}\right.[/tex]

False, because secondt inequality doesn't hold.

(12,8):

[tex]\left\{\begin{array}{l}12+3\cdot 8=36\le 36\\ 12+1.5\cdot 8=24> 20\end{array}\right.[/tex]

False, because second inequality doesn't hold.

(18,6):

[tex]\left\{\begin{array}{l}18+3\cdot 6=36\le 36\\ 18+1.5\cdot 6=27> 20\end{array}\right.[/tex]

False, because second inequality doesn't hold.

Convert the decimal number to a fraction by placing the decimal number over a power of ten. So convert the mixed number which is 2 1 /4 into an improper fraction first by multiplying the denominator which is (4)(4) by the whole number part which is (2)(2) and add the numerator (1)(1) to get the new numerator.

Place the new numerator (9)(9) over the old denominator (4)(4).94

Answer:

linear:  slope =10,y-intercept=25

Step-by-step explanation:

Yes, a linear equation can be used to model the situation because for any two given pints, there is a constant value of 10 for change in (p) over change in (n).

The slope is given by:

[tex]m=\frac{Change\:in\:p}{Change\:in\:n}[/tex]

Using (1,35) and (5,75) from the table, we have:

[tex]m=\frac{75-35}{5-1}[/tex]

[tex]m=\frac{40}{4}=10[/tex]

Therefore the slope is 10.

Using the formula

[tex]y=mx+b[/tex], and the point (1,35) we have:

[tex]35=10(1)+b[/tex]

[tex]\implies 35-10=b[/tex]

[tex]\implies 25=b[/tex]

Therefore the y-intercept is 25.

Answer:

(a) What is the probability that you roll a 6?

1/6

(b) What is the probability that you either roll a 6 or do not roll a 6?

1

(c) What is the probability that you don't roll a 6?

5/6

Step-by-step explanation:

(a) What is the probability that you roll a 6?

In a 6- sided cube, a 6 occurs only once. That is only one face is labelled 6. Therefore, the probability that you roll a 6 is;

(number of faces labelled 6)/(totals number of sides) = 1/6

(b) What is the probability that you either roll a 6 or do not roll a 6?

The probability of rolling a 6 was found to be, 1/6.

On the other hand, the probability of not rolling a 6 is;

(number of faces not labelled 6)/(totals number of sides) = 5/6

Therefore, the probability that you either roll a 6 or do not roll a 6 is;

1/6 + 5/6 = 1

These two events are mutually exclusive and exhaustive.

(c) What is the probability that you don't roll a 6?

The probability of not rolling a 6 is;

(number of faces not labelled 6)/(totals number of sides) = 5/6

We have 5 faces not labelled 6 out of 6 possible faces or outcomes

Answer:

[tex]x = 20[/tex] or [tex]x = -5[/tex]

Step-by-step explanation:

To solve the quadratic equation we must factor the expression

Look for 2 numbers that when you multiply them, obtain the result -100 and when you add them, obtain the result -15.

You can verify that these numbers are -20 and 5

[tex]-20 +5 = -15\\\\-20 * 5 = -100[/tex]

Then the polynomial factors are

[tex](x-20) (x + 5) = 0[/tex]

 The zero product property says that if two terms [tex]a * b = 0[/tex] then

[tex]a = 0[/tex] or [tex]b = 0[/tex]

So

[tex](x-20) = 0[/tex] or [tex](x + 5) = 0[/tex]

[tex]x = 20[/tex] or [tex]x = -5[/tex]

Answer:

x = -5 or x = 20

Step-by-step explanation:

There fore the answer is C

Answer:

[tex] x + 2 = \pm \sqrt{4} [/tex]

Step-by-step explanation:

(x + 2)^2 - 9 = -5

Add 9 to both sides.

(x + 2)^2 = 4

Take the square root of both sides.

[tex] x + 2 = \pm \sqrt{4} [/tex]

Answer:

A

Step-by-step explanation:

ed 2020

Answer:

3x+24 more widgets

Step-by-step explanation:

A company owns two manufacturing plants:

To find how many more items the first plant produces daily than the second plant, we have to subtract from the number of widgets the first plant produces the second plant produces. So,

[tex](8x+17)-(5x-7)\\ \\=8x+17-5x+7\ [\text{Eliminate brackets}]\\ \\=(8x-5x)+(17+7)\ [\text{Combine the like terms}]\\ \\=3x+24[/tex]

Answer:

3x + 24

Step-by-step explanation:

The question simply requires us to find the difference between the daily production levels of the two plants;

The first plant produces 8x + 17

The second plant produces 5x - 7

The difference between these two expressions will be our required solution;

(8x + 17) - ( 5x - 7) = 8x + 17 - 5x + 7

= 8x - 5x +17 + 7 = 3x + 24

Answer:

Step-by-step explanation:

[tex]x^2+5x+6=0\\\\x^2+2x+3x+6=0\\\\x(x+2)+3(x+2)=0\\\\(x+2)(x+3)=0\iff x+2=0\ \vee\ x+3=0\\\\x+2=0\qquad\text{subtract 2 from both sides}\\x=-2\\\\x+3=0\qquad\text{subtract 3 from both sides}\\x=-3[/tex]

Answer: 1.25

Step-by-step explanation:

Because...

All you have to do is divide the length value by 3

and your answer will be 1.25.

* Hopefully this helps:) Mark me the brainliest:)!!!

Answer:

1.25yd

Step-by-step explanation:

couted through table

for z the fraction value is 1/26 and for other letters then Z is 25/26

Answer:

Step-by-step explanation:

Eliminate the last two possible answers immediately, because their constants are negative.  A perfect square trinomial MUST have a positive constant.

If we factor the first answer choice, we get (3x - 2)(3x - 2) = 9x^2 - 12x + 4.  This is a perfect square trinomial.

Looking at the second answer choice:  (4x - 3)(4x - 3)  = 36b² - 24x + 9.  This is also a perfect square trinomial.

Please note:  Please use " ^ " to indicate exponentiation:

9x^2 is correct; 9x2 is incorrect.                                            

Answer:

its C 16x2 + 24x + 9

Step-by-step explanation:

Answer:

Final answer is 10.5 gallons of water.

Step-by-step explanation:

Given that Joe is filling the washing machine to wash clothes. After one minute, there are 1.75 gallons of water in the washing machine. After two minutes, there are 3.5 gallons of water in the machine. After three minutes, there are 5.25 gallons in the machine. Now we need to determine If this pattern continues then about how many gallons of water will be in the washing machine after six minutes.

Look at the pattern of volume of the water at given minutes.

We see that 1.75 is added each minute.

then required equation of volume is

V=1.75t

So for t=6 minutes, volume is given by

V=1.75*6=10.5

Hence final answer is 10.5 gallons of water.

The amount of water in the washing machine after six minutes can be determined using an arithmetic sequence formula. The machine fills at a constant rate of 1.75 gallons per minute, so after six minutes, there will be 10.5 gallons of water in the machine.

The question provided concerns a pattern of water filling a washing machine, which falls under the subject of arithmetic sequences in mathematics. To determine how many gallons of water will be in the washing machine after six minutes, we need to recognize the sequence and apply the appropriate formula.

To solve this problem, we note that the washing machine fills at a constant rate of 1.75 gallons per minute because the amount of water increases by 1.75 gallons with each passing minute (1.75 gallons at minute one, 3.5 gallons at minute two, which is 1.75 x 2, and 5.25 gallons at minute three, which is 1.75 x 3).

Mathematically, this can be represented as an arithmetic sequence with the first term a1 = 1.75 gallons and the common difference d = 1.75 gallons. The nth term of an arithmetic sequence is given by the formula an = a1 + (n - 1)d. So, to find the amount of water after six minutes, substitute 6 for n, which yields:

a6 = 1.75 + (6 - 1) times 1.75

a6 = 1.75 + 5 times 1.75

a6 = 1.75 + 8.75

a6 = 10.5 gallons

Therefore, after six minutes, there will be 10.5 gallons of water in the washing machine if the pattern continues.

Rel. Max:

-1 , x=0

Rel. Min:

-6 ,x=5

Increasing in the interval(s)

(-infinty ,0) U (5, infinity)

[ i doubt the above answer]

Decreasing in the interval(s)

(0,5)

Domain

it could be R

Range

R

Step-by-step explanation:

Look at the picture.

The function has a realtive maximum of -1 at x = 0.

The function has a realtive minimum of -6 at x = 5.

The function is increasing on the intervals: (-∞, 0> and <5, ∞).

The function is decreasing on the interval: <0, 5>.

The domain of the function is: (-∞, ∞) = R

The range of the function is: (-∞, ∞) = R

[tex]\bf y=\cfrac{2}{3}x\stackrel{\stackrel{b}{\downarrow }}{-3}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf 6x-7y=21\implies -7y=-6x+21\implies y=\cfrac{-6x+21}{-7}\implies y=\cfrac{6x-21}{7} \\\\\\ \stackrel{\textit{distributing the denominator}}{y=\cfrac{6x}{7}-\cfrac{21}{7}}\implies y=\cfrac{6}{7}x\stackrel{\stackrel{b}{\downarrow }}{-3}[/tex]

y=mx+b

b=y intercept

get into this form with no coefficient to y

Original: yint: -3

1)x+4y=12

4y=-x+12

y=-.25+3

b=3

2)2/3x+3y=-3

3y=2/3x-3

y={doesn't matter}x-1

b=-1

3)-2/3x+3y=6

3y=-2/3x+6

y={doesn't matter} +2

b=2

4) 6x-7y=21

-7y=-6x+21

y=6/7-3

b=-3

4 is the answer

Answer:

$16.50/hr

Step-by-step explanation:

Current pay is 1.00($15/hr).

Current pay plus a 10% raise is 1.10($15/hr) = $16.50/hr

After receiving a 10% raise on a $15 per hour wage, you would be earning $16.50 per hour.

If you are currently making $15 per hour and you receive a 10% raise, you can calculate your new hourly wage by first determining the amount of the raise and then adding it to your current wage. To find the raise amount, you multiply your current wage by the raise percentage expressed as a decimal. In this case:

Amount of raise = Current hourly wage  imes Raise percentage

Amount of raise = $15 per hour  imes 0.10 (since 10% = 0.10)

Amount of raise = $1.50 per hour

Now, you add this raise to your current hourly wage to find your new hourly wage:

New hourly wage = Current hourly wage + Amount of raise

New hourly wage = $15 per hour + $1.50 per hour

New hourly wage = $16.50 per hour

To give an example for comparison, if your job pays $10 per hour and your boss gives you a $2 per hour raise, that is a 20% increase because the percentage change is calculated as $2/$10 = 0.20 or 20%. In your case, the 10% raise increases your wage by $1.50, making it $16.50 per hour after the raise.

Hello There!

Answer Is In Image Provided.

Answer:

1.27, -6.27 to the nearest hundredth,

or if you require it in exact form,

-2.5 + √14.25,   -2.5 - √14.25.

Step-by-step explanation:

x^2 = -5x + 8

x^2 + 5x  = 8

Competing the square:

(x + 2.5)^2 - 6.25 = 8

(x + 2.5) = 14.25

x + 2.5 = +/-√14.25

x = -2.5 + √14.25,   -2.5 - √14.25

x = -2.5 + 3.77,  -2.5 - 3.77

= 1.27, -6.27.

Pythagorean Theorem

[tex]7^2 + 24^2 = x^2[/tex]

[tex]49 + 576 = x^2[/tex]

[tex]x^2=625[/tex]

[tex]x = 25[/tex]

Circumference

1. Since the diameter is 25 the formula to find the circumference is [tex]c = d\pi[/tex]

2. Plug in 25 into the formula

3. [tex]c = 25\pi[/tex]

Answer

[tex]25\pi[/tex]

The circumference of the circle is approximately 78.54 cm.

To find the circumference of the circle, we first need to find the length of the hypotenuse (which is also the diameter of the circle) using the Pythagorean theorem. Then, we can use the formula for the circumference of a circle, which is C = π * d, where C is the circumference and d is the diameter.

Let's calculate it step by step:

Step 1: Find the length of the hypotenuse using the Pythagorean theorem:

[tex]a^2 + b^2 = c^2[/tex]

where a and b are the lengths of the chords (24 cm and 7 cm, respectively), and c is the length of the hypotenuse (diameter).

[tex]24^2 + 7^2 = c^2\\\\576 + 49 = c^2\\\\625 = c^2[/tex]

c = √625

c = 25 cm

Step 2: Calculate the circumference using the formula C = π * d:

C = π * 25 cm

C ≈ 78.54 cm

The circumference of the circle is approximately 78.54 cm.

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Answer:

0.64 seconds.

Step-by-step explanation:

When it hits the ground h(t) = 0.

0 = -16t^2 + 4t + 4

-4(4t^2 - t -1) = 0

t = [-(-1) +/- sqrt (1 - 4*4*-1)] / 8)

t = 0.64, -0.39

answer is 0.64 seconds.

it will take the baseball 0.64 seconds to hit the ground.

The equation representing the height is:

h = -16t² + 4t + 4

When the baseball hits the ground, the height will be 0. That is,h =0

Substitute h =0 into the equation above

0 = -16t² + 4t + 4

Rearrange the given equation to be:

16t² - 4t - 4 = 0

Solving the quadratic equation above:

t = -0.39 and 0.64

Since time cannot be negative, it will take the baseball 0.64 seconds to hit the ground.

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Given:

f(x)=4x-3

f(x) +g(x) =9x +4

To find:g(x)

Solution:

f(x) + g(x) =9x +4

Replacing f(x) with its value.

4x -3 +g(x) = 9x +4

=> g(x) = 9x+ 4 -(4x-3)

=> g(x) = 9x+4 -4x +3

=> g(x) = 5x +7

Hence;

Option A g(x)=5x+7 is the answer.

Hope it helps...

Regards;

Leukonov/Olegion.

Its a bit late, but i wish someone would had answered so

Step 3:  

✔ B

Step 5:  

✔ D

Step 6:  

✔ A

Step 8:  

✔ C

:)

The first incorrect step in the given sequence is Step 3, where the equation is divided by 'a' on both sides instead of factoring it out and grouping the terms.

The quadratic formula is derived by completing the square on the general quadratic equation ax^2 + bx + c = 0. The first incorrect step in the given sequence is Step 3. In Step 3, the equation ax^2 + bx + c = 0 is divided by a on both sides, which results in the equation x^2 + (b/a)x + (c/a) = 0. However, the correct next step should be factoring out the leading coefficient a and grouping the terms.

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Answer :

1. -3x + 6 = -9

-3x = -9 - 6

-3x = -15

x = -15 / -3

x = 5

2. 5m + 4m = 72

9m = 72

m = 72 / 9

m = 8

3. 6d - 10d = 40

-4d = 40

d = 40 / -4

d = -10

4. 2(x + 4) = 30

2x + 8 = 30

2x = 30 - 8

2x = 22

x = 22 / 2

x = 11

5. 78 = -2(m + 3) + m

78 = -2m - 6 + m

78 = -m - 6

78 + 6 = -m

84 = -m

m = -84

Answer:

Each shirt cost $7  and each pair of shorts cost $17 .

Step-by-step explanation:

let shirts be represented as x

let shorts be represented as y

Younger brother spent $79 on 4 new shirts and 3 pairs of shorts.

4 x + 3 y = $79    .......equation 1

Older brother purchased 7 new shirts and 8 pairs of shorts and paid a total of $185.

7 x + 8 y = $185  .......equation 2

multiply equation 1 by 7 and equation 2 by -4 and add both equations to get the value of y.

7 × (4 x + 3 y = $79)     ⇒             +28 x + 21 y = $553

-4 × (7 x + 8 y = $185)  ⇒             -28 x - 32 y = - $740

                                                          0   - 11 y   = - $187     ⇒  -11 y   = - $187

y = [tex]\frac{- $187}{- 11}[/tex]   ⇒   y = $17

shorts = y = $17

put value of y in equation 1

4 x + 3 ( $17 ) = $79  ⇒    4x + $51 = $79   ⇒   4x = $79 - $51

4x = $28   ⇒  x = [tex]\frac{$28}{4}[/tex]   ⇒   x = $7

Shirts = x = $7

Answer:

y = 3x - 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, - 3) and (x₂, y₂ ) = (1, 0) ← 2 points on the line

m = [tex]\frac{0+3}{1-0}[/tex] = 3

The line crosses the y- axis at (0, - 3) ⇒ c = - 3

y = 3x - 3 ← equation of line

The equation of line l will be;

⇒ y = 3x - 3

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (1, 0) and (0, -3).

Now,

Since, The equation of line passes through the points (1, 0) and (0, -3).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (- 3 - 0) / (0 - 1)

m = - 3 / - 1

m = 3

Thus, The equation of line with slope 3 is,

⇒ y - 0 = 3 (x - 1)

⇒ y  = 3x - 3

Therefore, The equation of line passes through the points (1, 0) and

(0, -3)  will be;

⇒ y = 3x - 3

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Answer: (x - 3) (2x-1)

Answer:

(x+3)(2x+1)

Step-by-step explanation:

I got it right on khan academy.

Answer:

x= 36

(it is positive since 78 is larger than 42, everything else is correct)

Step-by-step explanation: