Are the fractions 1/4 and 3/12 common denominators?

Answer:

C) Both

Step-by-step explanation:

The given equation is:

[tex]0=(3x+2)(x-4)[/tex]

To solve the given equation, we can use the Zero Product Property according to which if the product A.B = 0, then either A = 0 OR B = 0.

Using this property:

[tex](3x+2) = 0 \Rightarrow \bold{x = -\frac{2}{3}}\\(x-4) = 0 \Rightarrow \bold{x = 4}[/tex]

So, Erik's solution strategy would work.

Now, let us discuss about Caleb's solution strategy:

Multiply [tex](3x+2)(x-4)[/tex] i.e. [tex]3x^2-12x+2x-8[/tex] = [tex]3x^2-10x-8[/tex]

So, the equation becomes:

[tex]0=3x^2-10x-8[/tex]

Comparing this equation to standard quadratic equation:

[tex]ax^2+bx+c=0[/tex]

a = 3, b = -10, c = -8

So, this can be solved using the quadratic formula.

[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

[tex]x=\dfrac{-(-10)\pm\sqrt{(-10)^2-4\times3 \times (-8)}}{2\times 3}\\x=\dfrac{-(-10)\pm\sqrt{196}}{6}\\x=\dfrac{10\pm14}{6} \\\Rightarrow x= 4, -\dfrac{2}{3}[/tex]

The answer is same from both the approaches.

So, the correct answer is:

C) Both

Answer:

Both

Step-by-step explanation:

Answer:

Step-by-step explanation:

Perimeter of a rectangle = 2l + 2w

where

l is the length

w is the width

From the question

Perimeter = 90 inches

The statement

The length of a rectangle is five inches more than four times it’s width is written as

l = 5 + 4w

Substitute this expression into the above formula and solve for the width

That's

90 = 2(5 + 4w) + 2w

90 = 10 + 8w + 2w

10w = 90 - 10

10w = 80

Divide both sides by 10

w = 8

Substitute this value into l = 5 + 4w

That's

l = 5 + 4(8)

l = 5 + 32

l = 37

Therefore we have

Hope this helps you

Answer:

1

Step-by-step explanation:

i²⁵⁶ is the equivalent of (i²)¹²⁸.

(i²)¹²⁸ = (-1)¹²⁸ = 1.

Answer:

[tex]\Huge \boxed{1}[/tex]

Step-by-step explanation:

[tex]i^{256}[/tex]

[tex](i^4)^{64}[/tex]

Apply identity : [tex]i^4 =1[/tex]

[tex]1^{64}=1[/tex]

Answer:

The quantity of the first model is 150 and the second model is 100 that maximize the profit.

Step-by-step explanation:

Let the quantity of first model = x

Let the quantity of second model = y

The cost of the first model = $100

The cost of the second model = $150

Total number of models = 250 units

Total amount to spend on units = $30000

Now form the equations.

x  +  y  = 250

100x + 150y = 30000

Now solve for the x and y.

x = 250 – y

Now insert this value in the 100x + 150y = 30000.

100(250 –y) + 150y = 30000

25000 – 100y + 150y = 30000

50y = 30000 – 25000

50y = 5000

Y = 100

Now insert the Y in x + y = 250

x = 250 – y

x = 250 – 100

x = 150

Therefore, the first model is 150 units and the second model is 100 units that maximize the profit.

Answer:

Should be 10- (-2) lemme know if im wrong

Step-by-step explanation:

The answer is 10-(-2)

Answer:

[tex]y=\frac{5}{3}x-5[/tex]

Step-by-step explanation:

Slope-intercept:

[tex]y=mx+b[/tex]

m is the slope and b is the y-intercept. We know that the line passes through the y-axis at -5, so this is the y-intercept (where x is equal to 0). Insert this into the equation:

[tex]y=mx-5[/tex]

With the given information, we can form two points:

[tex](3,0)(0,-5)[/tex]

The first one is the x-intercept and the second the y-intercept. Use these to find the slope:

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{rise}{run}[/tex]

Rise over run is the change in the y-axis over the change in the x-axis, otherwise known as the slope. Insert the appropriate values:

[tex](3_{x1},0_{y1})\\(0_{x2},-5_{y2})\\\\\frac{-5-0}{0-3}[/tex]

Solve:

[tex]\frac{-5-0}{0-3}=\frac{-5}{-3}[/tex]

Note that both the numerator and denominator are negatives. Two negatives make a positive, so:

[tex]\frac{5}{3}[/tex]

The slope is [tex]\frac{5}{3}[/tex]

Insert into the equation:

[tex]y=\frac{5}{3}x-5[/tex]

:Done

Answer:2y

Step-by-step explanation:

!!!

Answer:

Answer: h(x) = 1/5x

Step-by-step explanation:

6x + y = 4x + 11y

    -y            -y  

6x       = 4x + 10y

-4x        -4x        

2x       =         10y

÷10               ÷10  

1/5x =     y

Since "y" represents h(x), then h(x) =

Answer:

11/5

Step-by-step explanation:

We can use the slope formula

m = (y2-y1)/(x2-x1)

    = (5 - -6)/(-4 - -9)

    = (5+6)/( -4+9)

   = 11/5

Let's find the slope using the graphing method.

First set up a coordinate system like I have done below.

Now, graph each ordered pair.

Let's call (-9, -6) point A and (-4, 5) point B.

Now remember that the slope or m is equal

to the rise over run from point A to point B.

To get from point A to point B, we rise 11 units and run 5 units.

So our slope is 11/5.

Step-by-step explanation:

la 6 es la mejor rspuesta

Answer:

A had 22 mangoes, B had 26 mangoes

Step-by-step explanation:

We can write the following system:

A + 10 = 2(B - 10) -- Equation 1

3(A - 10) = B + 10 -- Equation 2

A + 10 = 2B - 20 → A = 2B - 30 -- Equation 3 (Simplify Equation 1)

3(2B - 30 - 10) = B + 10 -- Equation 4 (Substitute 3 into 2)

3(2B - 40) = B + 10

6B - 120 = B + 10

5B = 130

B = 26 -- (Solve for B in Equation 4)

A = 2 * 26 - 30 = 22 -- (Substitute B = 26 into Equation 3)

Answer

the second value is ten times higher then the refference one

Hope it helped u if yes mark me BRAINLIEST!

Tysm!

Answer:

2 in 32000 is in the thousands place

2 in 26000 is in the ten thousands place

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

3( x+ 2)=2(x+2)​

=>3x+6=2x+4

=>3x-2x=4-6

=>x=-2

-2  is the value of x

Answer:

The answer is

Step-by-step explanation:

3( x+ 2)=2(x+2)

First expand the terms in the bracket

That's

3x + 6 = 2x + 4

Group like terms

Send the constants to the right side of the equation and those with variables to the left side

3x - 2x = 4 - 6

Simplify

We have the final answer as

Hope this helps you

Answer:

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form:

Answer:

The government paid an interest of $41.9, which is 4.19%

Step-by-step explanation:

Given the 189-day, $1,000 U.S Treasury bill is purchased at a discount of 4.19%, this means that:

It was purchased at a discount of:

4.19% of $1000

= (4.19/100) × 1000

= $41.9

Purchase price = $1000 - $41.9 = $958.1

Because the treasure is sold for $1000 on maturity day, that means the government paid an interest of $41.9, which is 4.19%

Answer:

[tex]\huge \boxed{8\sqrt{3}}[/tex]

Step-by-step explanation:

[tex]2\sqrt{48}[/tex]

Simplify [tex]\sqrt{48}[/tex].

[tex]2\sqrt{16} \sqrt{3}[/tex]

[tex]\sqrt{16}=4[/tex]

[tex]2 \times 4\sqrt{3}[/tex]

Apply rule : [tex]a \times b\sqrt{c} =ab\sqrt{c}[/tex]

[tex]8\sqrt{3}[/tex]

Answer: Hi!

The equation given is 5.29 * 10^4.

First, we need to solve the exponent.

10^4 = 10,000

Next, we multiply 10,000 by 5.29.

10,000 * 5.29 = 52,900

Therefore, your answer is a), 52,900.

Hope this helps!

Answer:

A.

Step-by-step explanation:

It is 5.29 x 10,000

= 52,900.

Answer: a constant

Step-by-step explanation:

A constant is a numerical expression like 2, 0,78 etc .

A variable is a alphabetical expression that vary like a,b,c,d,x,y,z.

An expression can consists of both numerical and alphabets and also any arithmetic expression like x, 2abc, 6a+2c etc

A term consist of either numbers and variables multiplied together or only numbers or variable like 2xy, x, 2ab etc.

X is all (a term, a variable , an expression) except a constant because a constant is a numerical expression.

Answer: D, a constant

Step-by-step explanation: A constant is an expression without variables.

Answer:

$-48

Step-by-step explanation:

(-125 + -86 +54 +-35)/4 = -48

Add all the Profits/losses and divide by the number of weeks.

Answer:

true

Step-by-step explanation:

Answer:

The answer is A

Step-by-step explanation:

Step 1: Use Cosine to find ∅

Cos∅=[tex]\frac{4}{5}[/tex]

∅=Cos[tex]^{-1}[/tex]([tex]\frac{4}{5}[/tex])

Therefore the answer is A

Answer:

-96+24= -72   or just -72

Step-by-step explanation:

4(-24+6)

-96+24= -  72

put the values of x,y and z

4(-24+6)

4(-18)

= -72

The domain is the input value of x, which can be any real number.

There is no inequality.

Set notation x | E R. ( all real nUmbers)

Interval. Oration (-infinity, infinity)

Range: set x to 0 and solve:

3(0)^2 + 2 = 2

The lowest value is 2 and goes to infinity.

Inequality is >=

Set notation Y | >= 2

Interval notation : [2, infinity)

End behavior they both go to infinity .

Answer:

  √8106

Step-by-step explanation:

8106 = 2·3·7·193

It has no square factors, so the radical cannot be simplified further.

Answer:

y = -x + 10

Step-by-step explanation:

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Slope-Intercept Form: y = mx + b

Step 1: Find slope m

m = (11 - 9)/(-1 - 1)

m = 2/-2

m = -1

y = -x + b

Step 2: Find y-intercept b

9 = -(1) + b

9 = -1 + b

b = 10

Step 3: Rewrite linear equation

y = -x + 10

Answer:

See below

Step-by-step explanation:

a) line marked a is tangent

b) line marked b is radius

c) line marked c is diameter

d) line marked d is chord

Answer:

y = 2( x-3)^2 +5

Step-by-step explanation:

The vertex form of a parabolic functions is

y = a( x-h)^2 +k

where (h,k) is the vertex

y = a( x-3)^2 +5

Substituting the point into the equation

13 = a( 1-3)^2 +5

13 = a*( -2)^2 +5

13 = 4a +5

Subtract 5

8 = 4a

Divide by 4

8/4 =a

2=a

y = 2( x-3)^2 +5

Answer:

Cups of water she needs to make the punch is 12.

Step-by-step explanation:

Amount of water Carson need to make fruit punch = 3 quarts

2 cups is 1 pint

2  pints is 1 quart

1 pint = 1/2 quarts

2 cups is 1 pint which is 1/2 quarts

So, 1 cup:

1 cup is 1/2 times 2 quarts

1 quart is 1 times 2 times 2 cups equals 4 cups

So, 3 quarts equals 3 times 4 cups which equals 12 cups.

So it is 12 cups.

Cups of water she needs to make the punch is 12.

A unit conversion expresses the same property as a different unit of measurement.

Given that, Carson needs 3 quarts of water to make fruit punch, but has only an l-cup measuring cup.

She knows there are 2 cups in 1 pint, and 2 pints in 1 quart.

Amount of water Carson need to make fruit punch = 3 quarts

2 cups is 1 pint

2  pints is 1 quart

1 pint = 1/2 quarts

2 cups is 1 pint which is 1/2 quarts

So, 1 cup:

1 cup is 1/2 times 2 quarts

1 quart is 1 times 2 times 2 cups equals 4 cups

So, 3 quarts equals 3 times 4 cups, which equals 12 cups.

Hence, she need 12 cups.

For more references on unit conversion, click;

https://brainly.com/question/19420601

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Answer:

[tex]3 \sqrt 5}[/tex]  and [tex]-3 \sqrt 5}[/tex]

Step-by-step explanation:

Given

[tex]x^2 = 45[/tex]

Required

Determine the values of x

[tex]x^2 = 45[/tex]

Take square root of both sides

[tex]\sqrt{x^2} = \±\sqrt{45}[/tex]

[tex]x = \±\sqrt{45}[/tex]

Expand 45 as 9 * 5

[tex]x = \±\sqrt{9 * 5}[/tex]

Split the square root

[tex]x = \±(\sqrt{9} *\sqrt 5}[/tex]

[tex]x = \±3 *\sqrt 5}[/tex]

[tex]x = \±3 \sqrt 5}[/tex]

This can be further split to:

[tex]x = 3 \sqrt 5}[/tex] or [tex]x = -3 \sqrt 5}[/tex]

Hence, the possible values of x are

[tex]3 \sqrt 5}[/tex]  and [tex]-3 \sqrt 5}[/tex]

Answer:

1

Step-by-step explanation:

We can use the slope formula

m = (y2-y1)/(x2-x1)

    = (5-8)/(-8 - -5)

    = -3/(-8+5)

    = -3/-3

   = 1