how do you solve this problem ? 4(-3x+1)-3x=71

Answer:

4 1/4 <_ 2K

Step-by-step explanation:

The inequality that represents the situation is k ≥ 2.125 hours.

Inequality is the statement where two algebraic expressions are equated using an inequality operator, <, >, <> etc.

Karissa takes k time to complete the project.

Oliver takes ≤ 2k

The time spent by Oliver is 4 1/4 = 17/4 = 4.25 hours

2k ≥ 4.25

k ≥ 2.125 hours

Therefore, the inequality that represents the situation is k ≥ 2.125 hours.

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Answer:

Hey there!

We can write a equations here:

3x+y=180

Also, since all of the angles have 3x on the outside, then y must be constant.

3y=180

y=60

Thus, for x, we have 3x+60=180, 3x=120, x=40.

2x+6y

2(40)+6(60)

80+360

440.

Let me know if this helps :)

Answer:

Malcom's maximum speed = 200 km/h

Ravi's maximum speed = 320 km/h

Step-by-step explanation:

Let m = Malcom's maximum speed

Let r = Ravi's maximum speed

Average of their maximum speed would be represented as [tex] \frac{m + r}{2} = 260 [/tex]

[tex] m + r = 520 [/tex].

Make m the subject of the formula by subtracting r from both sides:

[tex] m = 520 - r [/tex]. Let this be equation 1.

Given that Malcom's speed (m), when doubled is 80 km/h more than that of Ravi (r). This can be expressed as: [tex] 2m = r + 80 [/tex]. This is equation 2.

Plug in (520 - r) into equation 2 to replace m:

[tex] 2(520 - r) = r + 80 [/tex]

[tex] 1040 - 2r = r + 80 [/tex]

Solve for r. Subtract 1040 from both sides:

[tex] 1040 - 2r - 1040 = r + 80 - 1040 [/tex]

[tex] - 2r = r - 960 [/tex]

Subtract r from both sides

[tex] - 2r - r = r - 960 - r [/tex]

[tex] - 3r = - 960 [/tex]

Divide both sides by -3

[tex] \frac{-3r}{-3} = \frac{-960}{-3} [/tex]

[tex] r = 320 [/tex]

To find m, plug in the value of r into equation 1.

[tex] m = 520 - r [/tex]. =>Equation 1

[tex] m = 520 - 320 [/tex]

[tex] m = 200 [/tex].

Malcom's maximum speed = m = 200 km/h

Ravi's maximum speed = r = 320 km/h

Answer:

Apartment 207 is a second floor apartment in Building 2.

Step-by-step explanation:

Since one building has four first floor apartments, then I'd think all buildings have 4 apartments per floor. Since one building has first floor apartment numbers 109, 110, 111, and 112, then I'd think there is a building with first floor apartment numbers 101, 102, 103, and 104, and another building with first floor apartment numbers 105, 106, 107, 108.

Building 1 First floor: 101, 102, 103, 104

Building 2 First floor: 105, 106, 107, 108

Building 3 First floor: 109, 110, 111, 112

Building 2 Second floor: 205, 206, 207, 208

Apartment 207 is a second floor apartment in Building 2.

[tex]t=\sqrt{\dfrac{ab-s}{r+ak}}\\\\t^2=\dfrac{ab-s}{r+ak}\\\\rt^2+akt^2=ab-s\\\\akt^2-ab=-rt^2-s\\\\a(kt^2-b)=-(rt^2+s)\\\\a=-\dfrac{rt^2+s}{kt^2-b}\\\\a=-\dfrac{rt^2+s}{-(b-kt^2)}\\\\a=\dfrac{rt^2+s}{b-kt^2}[/tex]

Answer:

slope = - [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

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

with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (3, 1)

m = [tex]\frac{1-2}{3-0}[/tex] = - [tex]\frac{1}{3}[/tex]

Answer:

First, an asymptote means that the function "tends to go" to a value, bt actually never reaches it.

The functions here are:

A.f(x) = 2 + 1

B.f(x) = x^2 + 1

c.f(x) = x^2 - 1

D.f(x) == +1

The functions are really poorly written, but i will try to answer this.

first:

"a root at x = -1"

Means that f(-1) = 0,

The only function that is zero when x = -1, is the option c.

f(-1) = (-1)^2 - 1 = 1 - 1 = 0.

Now, if we want to have a vertical asymptote at x = 2, then we should have a function like:

[tex]f(x) = \frac{something}{x - 2}[/tex]

So we want to have a quotient, where the denominator is equal to zero when x = 2, this will lead to a vertical asymptote.

I can not see this in the options provided, so i guess that the functions are just not well written.

For a horizontal asymptote, we have something like:

[tex]f(x) = \frac{something}{x} + 1[/tex]

So as x starts to grow, the first term in the function will start to decrease, until it becomes really close to zero (but is never equal to zero) so in that case we have an horizontal asymptote to f(x) = 1.

Answer:

x = 5

Step-by-step explanation:

x² - 5x = 0

(x² - 5x) /x = 0/x

x²/x - 5x/x = 0

x - 5 = 0

x = 5

Check:

x² - 5x = 0

5² - 5*5 = 0

25 - 25 = 0

The solution to the equation is:

x = 0 or x = 5

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.

We have:

x²-5x = 0

We can solve the equation as follow:

x²-5x = 0

Factorize:

x(x - 5) = 0

x = 0 or (x -5) = 0

x = 0 or x = 5

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Answer:

Freedom is any case,

is only possible

by constantly

struggling for it.

Albert Einstein

Answer:

B

Step-by-step explanation:

area of the full piece of pie. π(8)²*60/360 (we know 60°, because it's an equilateral triangle)

32π/3

now subtract the area of the triangle

1/2(8)(4√3) = 16√3

32π/3 - 16√3

====================================================

Explanation:

A drawing may be helpful to see what's going on. Check out the diagram below. This is one way of drawing out the two triangles. The locations of the points don't really matter, and neither does the the orientation of how you rotate things. What does matter is we have the right points connected to form the segments mentioned.

----------

For now, focus on triangle TIP only. In order to have this be isosceles, we must make TP = 5 or TP = 7.

If TP = 5, then it's the same length as TI.

If TP = 7, then it's the same length as PI.

In either case, we have exactly two sides the same length (the other side different) which is what it means for a triangle to be isosceles.

----------

Let's consider triangle TOP. For it to be isosceles, we must have two sides the same length. We already locked in TP to be either 5 or 7 in the previous section above. So there's no way that TP could be 11 units long to match up with PO = 11.

If TP = 5, then OT must also be 5 units long so that triangle TOP is isosceles.

If TP = 7, then OT = 7 for similar reasoning.

Either way, TP only has two choices on what it could be.

----------

In short, we basically just write the first two values given to us to get the two triangles to be isosceles. We can't use TP = 11 as it would make triangle TIP to be scalene (all sides are different lengths).

Answer:

So we all cheat AOPS huh

Step-by-step explanation:

Answer:

684

Step-by-step explanation:

19 x 24 = 456    

456 divided by 8 = 57

57 x 12 = 684

The total amount of magnesium, in grams, that the plant gets is 1.08 g

We know that a plant gets 54 milligrams of magnesium each week for a total of 20 weeks.

Then the total amount that the plant gets, in milligrams, is:

T = 20*54 mg

T = 1,080 mg

And we want to find the total amount in grams, we know that:

1000mg = 1g

Then we can do a change of units to get:

T = (1,080/1000)g

T = 1.08 grams

That is the total amount.

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Answer:

[tex]SU=18[/tex]

Step-by-step explanation:

The segments ST and TU make up the line segment SU. Add the values to find SU:

[tex]ST+TU=SU\\\\13+5=18[/tex]

The length of SU is 18.

The length of SU is 18 units.

We have a point T is between S and U.

We have to determine the length SU.

According to the question -

ST = 13 units

TU = 5 units

Now -

SU = ST + TU = 13 + 5 = 18 units

Hence, the length of SU is 18 units.

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Answer:

oyo archer comes here in answer your real answer it is 7 divided by 7 divided / 2 / to the answer X to other words if you're into Google with answers in churches of students

Answer:

A. No real solution

B. 5 and -1.5

C. 5.5

Step-by-step explanation:

The quadratic formula is:

[tex]\begin{array}{*{20}c} {\frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}} \end{array}[/tex], with a being the x² term, b being the x term, and c being the constant.

Let's solve for a.

[tex]\begin{array}{*{20}c} {\frac{{ 5 \pm \sqrt {5^2 - 4\cdot1\cdot11} }}{{2\cdot1}}} \end{array}[/tex]

[tex]\begin{array}{*{20}c} {\frac{{ 5 \pm \sqrt {25 - 44} }}{{2}}} \end{array}[/tex]

[tex]\begin{array}{*{20}c} {\frac{{ 5 \pm \sqrt {-19} }}{{2}}} \end{array}[/tex]

We can't take the square root of a negative number, so A has no real solution.

Let's do B now.

[tex]\begin{array}{*{20}c} {\frac{{ 7 \pm \sqrt {7^2 - 4\cdot-2\cdot15} }}{{2\cdot-2}}} \end{array}[/tex]

[tex]\begin{array}{*{20}c} {\frac{{ 7 \pm \sqrt {49 + 120} }}{{-4}}} \end{array}[/tex]

[tex]\begin{array}{*{20}c} {\frac{{ 7 \pm \sqrt {169} }}{{-4}}} \end{array}[/tex]

[tex]\begin{array}{*{20}c} {\frac{{ 7 \pm 13 }}{{-4}}} \end{array}[/tex]

[tex]\frac{7+13}{4} = 5\\\frac{7-13}{4}=-1.5[/tex]

So B has two solutions of 5 and -1.5.

Now to C!

[tex]\begin{array}{*{20}c} {\frac{{ -(-44) \pm \sqrt {-44^2 - 4\cdot4\cdot121} }}{{2\cdot4}}} \end{array}[/tex]

[tex]\begin{array}{*{20}c} {\frac{{ 44 \pm \sqrt {1936 - 1936} }}{{8}}} \end{array}[/tex]

[tex]\begin{array}{*{20}c} {\frac{{ 44 \pm 0}}{{8}}} \end{array}[/tex]

[tex]\frac{44}{8} = 5.5[/tex]

So c has one solution: 5.5

Hope this helped (and I'm sorry I'm late!)

Answer:

10.35 miles per hour

Sam's rate as stated is 63,756 feet per 70 minutes

Divide by 5,280 feet

Divide by 60 minutes

Step-by-step explanation:

1. Find how many feet Sam ran in one minute

63,756 ÷ 70 = 910.8 ft.

2. Find how many feet he ran in one hour

910.8 · 60 = 54,648 ft.

3. Convert the feet to miles

54,648 ÷ 5280 = 10.35

Step 2: There are 5280 feet in one mile. Therefore, you would divide by 5280 feet to convert feet per minute into miles per minute.

Step 3: There are 60 minutes in one hour. Therefore, you would divide by 60 minutes to convert miles per minute to miles per hour.

Answer:

1: 63,756 and 70 mins

2: 1 mile and 5,280 feet

3: 60 mins and 1 hour

4: 10.35

Answer:

D. m = 43

Step-by-step explanation:

Answer: D. m=43

Step-by-step explanation:

Answer:

Movies cost $2.50 and video games cost $5.50

Step-by-step explanation:

Let the rental cost of movies be x and the rental cost of video games y

12x + 2y = 41

3x + 5y = 35

Solve by substitution

Answer:

Movie price: $2.5

Video game price: $5.5

Step-by-step explanation:

First month

12 movies ([tex]m[/tex]);

2 video games ([tex]v[/tex]);

Cost: $41

Second month

3 movies ([tex]m[/tex]);

5 video games ([tex]v[/tex]);

Cost: $35

[tex]$\left \{ {{12m+2v=41} \atop {3m+5v=35}} \right.$[/tex]

[tex]$\left \{ {{12m+2v=41} \atop {3(-4)m+5(-4)v=(-4)35}} \right.$[/tex]

[tex]$\left \{ {{12m+2v=41} \atop {-12m+-20v=-140}} \right.$[/tex]

[tex]-18v=-99[/tex]

[tex]v=5.5[/tex]

[tex]12m+2(5.5)=41[/tex]

[tex]12m+11=41[/tex]

[tex]12m=30[/tex]

[tex]m=2.5[/tex]

Answer:

3.03 • 10⁻³ is scientific notation

0.00303 is decimal form

Answer:

  70, 140, 280, 350

Step-by-step explanation:

Obviously, it must have the factors 2, 5, 7 as a minimum, so the smallest value is 2×5×7 = 70.

Any of these primes can be added to the product. In increasing order, the smallest additional factors will be 2, 4, 5, 7, 8, 10, ...

So, the four smallest numbers with prime factors of 2, 5, and 7 are ...

  70 = 2·5·7

  140 = 2²·5·7

  280 = 2³·5·7

  350 = 2·5²·7

===================================================

Work Shown:

[tex]33^{-1} \equiv 77 \text{ (mod 508)}\\\\(3*11)^{-1} \equiv 77 \text{ (mod 508)}\\\\3^{-1}*11^{-1} \equiv 77 \text{ (mod 508)}\\\\3*3^{-1}*11^{-1} \equiv 3*77 \text{ (mod 508)}\\\\11^{-1} \equiv 231 \text{ (mod 508)}\\\\[/tex]

Notice how 33*77 = 2541 and 11*231 = 2541

[tex]2541 \equiv 1 \text{ (mod 508)}[/tex] since 2541/508 has a remainder of 1.

So effectively [tex]33*77 \equiv 1 \text{ (mod 508)}[/tex] and [tex]11*231 \equiv 1 \text{ (mod 508)}[/tex]

Answer:

25,886.01 in²

Step-by-step explanation:

The area of shaded region = Area of the outter circle (the larger circle) - area of the inner circle (the smaller circle)

Area of a circle = πr²

Radius of larger circle = PO = 93.4 in

Area of the larger circle = 3.14*93.4² = 27,391.98 in²

Radius of smaller circle = PO - RQ = 93.4 - 71.5 = 21.9

Area of smaller circle = 3.14*21.9² = 1,505.97 in²

Area of shaded region = 27,391.98 - 1,505.97 = 25,886.01 in²

Answer:

the answer

Step-by-step explanation:

D) 0.13 (325)

HOPE THIS HELPS!

do you need the workout?

Answer:

5.83142789

Step-by-step explanation:

did it on a graphing calculator, hope this helps

Answer:

-3

Step-by-step explanation:

When g(0), it means that x=0.

So, if we use 0 instead of x, the answer becomes:

-3

Answer:

-3

Step-by-step explanation:

g(0) = (-2(0)^2) -3

as anything multiplied with 0 is 0,

g(0) = 0 - 3

= - 3

Answer:

f(-2)=13

Step-by-step explanation:

We are given the function:

f(x)= 5-4x

and asked to evaluate f(-2). We want to find what f(x) is when x is equal to -2.

We must substitute -2 in for each x.

f(-2)= 5 - 4(-2)

Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

First, multiply 4 and -2.

⇒ 4 * -2 = -8

f(-2) = 5 - -8

Two negative signs in a row become a positive sign.

f(-2)= 5+8

Finally, add 5 and 8.

f(-2)= 13

The function f(x)= 5-4x evaluated for f(-2) is 13.

Answer:

The factorized expression is (-5) × (t - 2.747) ×(t - 1.747)

Step-by-step explanation:

The given expression is -5·t² + 5·t + 24

To factorize the expression by completing the square method, we equate the expression to zero to get;

-5·t² + 5·t + 24 = 0

WE divide by -5 to get;

t² - t - 24/5 = 0

t² - t = 24/5

t² - t + 1/4 = 24/5 + 1/4

(t - 1/2)² = 5.05

t - 1/2 = ±√5.05

t = 1/2 + √5.05, 1/2 - √5.05

The factorized expression becomes;

(t - 1/2 + √5.05) and (t - 1/2 - √5.05)

Which gives;

(t - 2.747) ×(t - 1.747)

The factorized expression is (-5) × (t - 2.747) ×(t - 1.747).

Answer:

the answer is 14

Step-by-step explanation:

you first add both side to 4 and get x=14

Answer: x = 14

Explanation: Our only step in solving the equation is to add 4 to both sides and the reason that we can add the same quantity to both sides of an equation is based on the addition property of equality.

So the solution to this equation is x = 14.