Simplify.

4(x − 5) + 2(y + 6) − 10


A) 4x + 2y − 18
B) 4x + 2y + 18
C) 4x + 2y − 9
D) 6xy − 15

Answer:

l = 2.5 feet

Step-by-step explanation:

A = lb

8.5 = l * 3 2/5

8.5 = l * 3.4

l = 8.5 / 3.4

l = 2.5 feet (Always remember to put the units, otherwise you may not get points.)

Please give a rating and a thanks.

Thank you.

Answer:

l = 2 1/2 ft

Step-by-step explanation:

Area is given by the formula

A = l*w

We know the area is 8 1/2  

Changing this to an improper fraction  8 1/2 = (2*8 +1)/2 = 17/2

The width is 3 2/5  as an improper fraction  = (5*3+2)/5 = 17/5

A = l*w

17/2 = l* 17/5

Multiply each side by 5/17

17/2 * 5/17 = l* 17/5 * 5/17

5/2 = l

2 1/2 = l

Answer:

a and e

Step-by-step explanation:

Answer:

$9,936.47

Step-by-step explanation:

Similarly to the other problem I helped you with we have:

[tex]A_{final}=A_{initial}(1+r)^t[/tex]

Where A is amount, r is rate and t is time.

In this case A=12000, r=9%=0.09 and 9% in decimals is 0.09 (9÷100=0.09), and t=7 since 2025 -2018 = 7 years. So how much is this investment worth in 7 years? Let's plug those values in and we obtain:

[tex]A_{final}=12000(1+0.09)^7=12000(1.09)^7=21936.47[/tex]

So the investment will be worth $21,936.47.  Now we must calculate how much more will this precious mineral be worth so we get the difference of the final amount and the initial amount the mineral was worth and so:

[tex]A_{final}-A_{initial}=21936.47-12000=9936.47[/tex]

And so the mineral will be worth $9,936.47 more than it originally was worth after 7 years.

Answer:

2144.66cm I think

Step-by-step explanation:

Answer:

x = 10

Step-by-step explanation:

the area of a square = s² ( s is the side length )

s² = (4x + 3)² ( take the square root of both sides )

s = [tex]\sqrt{(4x+3)^2}[/tex] = 4x + 3

perimeter = 4s = 172, that is

4(4x + 3) = 172 ( distribute left side )

16x + 12 = 172 ( subtract 12 from both sides )

16x = 160 ( divide both sides by 16 )

x = 10

Answer:

$192.20

Step-by-step explanation:

8 x 5=40  48.32x40=192.20                                                                                                          

Answer:

You will make $1929.20 this summer.

Step-by-step explanation:

You have just accepted a jab at Wonders Day Camp for the summer.

The camp will pay for each day for 8 weeks = $48.23

You work 5 days each week.

So total days of work = 8 × 5 = 40 days

You earn $48.23 for one day.

For 40 days you will earn = 40 × 48.23 = $1,929.20

You will make $1929.20 this summer.

Answer:

B

Step-by-step explanation:

There isn't any number that x can't be. Start with a graph to show how this could be so.

It is easy to see that x > 0 gives a line that goes very near the x axis. It is not quite so easy to see that it never touches the x axis. But if you recreate the graph in  Desmos, you will see that is true if you spread the x's out.

It is not quite so easy to see that when x<0 the graph tips upward very quickly but again if you move the values of the axis around you will see there is no value that x cannot be.

Answer:

B:All real numbers

Answer:

D[tex]_o[/tex] of Y = (-3/2, -1)

Step-by-step explanation:

We are given three points on the graph:

X (4, 0)

Y (3, 2)

Z (2, 2)

and the scale factor of dilation which is [tex]-\frac{1}{2}[/tex].

Given that, we are to find the coordinates of Y after dilation. To find that, we will multiply the coordinates of the point Y with the scale factor.

Y =  [tex](-\frac{1}{2}[/tex] × [tex]3[/tex] , (-\frac{1}{2}[/tex] × [tex]2)[/tex]

Y = [tex](-\frac{3}{2} , -1)[/tex]

[tex]\left\{\begin{array}{ccc}2x+y=1&|\text{subtract 2x from both sides}\\4x+2y=-1\end{array}\right\\\\\left\{\begin{array}{ccc}y=-2x+1&(*)\\4x+2y=-1&(**)\end{array}\right\\\\\text{substitute}\ (*)\ \text{to}\ (**):\\\\4x+2(-2x+1)=-1\qquad\text{use distributive property}\\\\4x+(2)(-2x)+(2)(1)=-1\\\\4x-4x+2=-1\\\\2=-1\qquad\text{FALSE}\\\\Answer:\ \boxed{NO\ SOLUTION}[/tex]

[tex]\dfrac{b}{2q}=h+7\qquad\text{multiply both sides by 2q}\neq0\\\\b=2q(h+7)\qquad\text{use distributive property}\\\\b=(2q)(h)+(2q)(7)\\\\\boxed{b=2hq+14q}[/tex]

Answer:

x=6 ; y=1

Step-by-step explanation:

Let 'y' stand for the speed of the wind and 'x' stand for the speed of Santa. We will use the general equation (distance)=(rate)(time) to write two equations from the given information:

With the wind:

35=(x+y)(5)

Against the wind:

35=(x-y)(7)

Now we have two equations and two unknowns so we can solve for x and y. We get:

x=6 miles/min

y=1 miles/min

Answer:  25 miles

Step-by-step explanation:

Since, the total distance = 31 miles.

Let he walks x miles at the rate of 4 miles per hour.

⇒ he walks remaining (31-x) miles at the rate of 50 miles per hour.

According to the question,

[tex]\frac{x}{4} + \frac{31-x}{50} = 2[/tex]

⇒ [tex]\frac{25x}{100} + \frac{62-2x}{100} = 2[/tex]

⇒  [tex]\frac{25x+62-2x}{100}= 2[/tex]

⇒  [tex]\frac{23x+62}{100}= 2[/tex]

⇒ [tex]23 x + 62 = 200[/tex]

⇒ [tex]23 x = 200 - 62[/tex] ( by subtracting 62 on both sides )

⇒  [tex]23 x = 138[/tex]

⇒ [tex]x=\frac{138}{23}[/tex] ( Dividing both sides by 23 )

⇒ [tex]x = 6[/tex]

Thus, the distance he pays to the cab driver = 31-x= 31 - 6 = 25 miles.

Therefore, He pays to the cab driver for 25 miles.

Distance that must be paid to the taxi = 25 miles

Linear motion consists of 2: constant velocity motion with constant velocity and uniformly accelerated motion with constant acceleration

• At constant velocity motion:

the speed of vo = v = constant

acceleration = a = 0

An equation of constant velocity motion

[tex]\large {\boxed {\bold {x = v \times \: t}}}[/tex]

x = distance = m

v = speed = m / s

t = time = seconds

so

[tex]\rm t=\dfrac{x}{v}[/tex]

A mountain path is 31 miles long

The distance traveled by tourists = x1

The distance traveled taxi = x2, such that

x1 + x2 = 31

x1 = 31-x2

total travel time (t) = 2 hours

tourist speed = v1 = 4 mph

taxi speed = v2 = 50 mph

time taken by tourists = t1

[tex]\rm \dfrac{x1}{v1}=\dfrac{x1}{4}[/tex]

the time taken by taxi = t2

[tex]\rm \dfrac{x2}{v2}=\dfrac{x2}{50}[/tex]

total time = t1 + t2

[tex]\rm 2=\dfrac{x1}{4}+\dfrac{x2}{50}\\\\2=\dfrac{25x1+2x2}{100}\\\\200=25(31-x2)+2x2\\\\200=775-25x2+2x2\\\\575=23x2\\\\x2=\boxed{\bold{25~miles}}[/tex]

The distance of the elevator

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resultant velocity

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the average velocity

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Answer:

(-3x+30)

Step-by-step explanation:

We first distribute: 4(x+7) = 4x+28

Then, we bring it down.

4x+28-7x=2

Combine like terms.

4x+(-7x) = -3x ... 28+2 = 30.

Combine both results.

-3x+30

Answer:

[tex]-3x+30[/tex]

Step-by-step explanation:

We have been given an expression [tex]4(x+7)-7x+2[/tex]. We are asked to simplify our given expression.

Using distributive property [tex]a(b+c)=ab+ac[/tex], we will get:

[tex]4*x+4*7-7x+2[/tex]

[tex]4x+28-7x+2[/tex]

Combine like terms:

[tex]4x-7x+2+28[/tex]

[tex]-3x+30[/tex]

Therefore, the simplified form of our given expression would be [tex]-3x+30[/tex].

none of the above

This question wants you to see that the radical can be simplified because it is ...

[tex]f(x)=\sqrt{(x+6)^2}[/tex]

The answer choices show you are expected to simplify this to ...

... f(x) = x +6

Then

... f(x)·g(x) = (x+6)(x³ -12) = x⁴ +6x³ -12x -72 . . . . . matches choice C

_____

However,

... f(x) = |x+6| . . . . . . . √(x^2) = |x|, the positive root regardless of sign of x

so the product f(x)·g(x) only matches selection C for x≥ -6. It matches the opposite of selection C for x ≤ -6.

The attached graph shows this. It graphs f(x), g(x), f(x)·g(x) (as a purple curve), and selection C (as orange dots).

Answer:

(-4.0,-6.2) and (0.6,5)

Step-by-step explanation:

We have been given the system of equations

[tex]

2.4x-y=-3.5........(1)\\x^2+x+y=6 .....(2)[/tex]

Let us graph these equation on the xy-plane.

The intersection point of these two curves will give us the solution of the system of equations.

Equation 1 represents a parabola and equation (2) represents a straight line.

The graph is shown in the attached file.

The intersection points of the parabola and the line are (0.622,4.992) and (-4.022, -6.152)

Therefore, the solutions rounded to nearest tenth are

(-4.0,-6.2) and (0.6,5)

Answer:

B.  (–4, –6.2) and (0.6, 5)

Step-by-step explanation:

Hope this helps!! Have a great day!!   : )

Answer:

x^2=12y

**C on edge

The equation of a parabola with its vertex at (0,0) and directrix at y=-3 is y = 1/12 x².

To write the equation of a parabola, we are given that its vertex is at (0,0) and its directrix is y=-3. The equation of a parabola with the vertex at (0,0) and the focus at (0,p) or a directrix at y=-p is given as y = 1/4p x². Considering the distance from the vertex to the directrix is the same as the distance from the vertex to the focus, the value of p in this case will be 3. Therefore, the equation of this parabola is y = 1/12 x².

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Answer:

6400 people.

Step-by-step explanation:

If 640 is 10%. You multiply 640 by 10 to get 6400 or 100% of the people.

B. 72 + 78 + 70 + x > 289

Simplify 2/3 + n + 6 to n + 20/3

n + 20/3 = 3/4

Subtract 20/3 from both sides

n = 3/4 - 20/3

Simplify 3/4 - 20/3 to - 71/12

n = -71/12

Answer: Full price of Drug Y = $98.793

Step-by-step explanation:

Cost of 500 tablet = $425

28% markup = 425 * 28/100

= $119

Cost + markup = $425 + $119 = $544

Cost + markup + dispensing fee = $544 + $4.85 = $548.85

Full price of 500 tablet = $548.85

Full price of 1 tablet = $548.85/500

=$1.0977

Full price of 90 tablet = $1.0977 * 90

= $98.793

Answer:

There are four different possible outcomes: both coins are heads, the red coin is heads and the blue coin is tails, the red coin is tails and the blue coin is heads, or both coins are tails. Each outcome has equal probability. So the probability of both being heads is 1/4.

Step-by-step explanation:

Answer:

15 4/9 inches long

Step-by-step explanation:

5 4/9 × 3

When lining them vertically the 3 ends up under 5 in which you multiply and transfer the 4/9 next to the product of 15. Hope that helped!

The king size chocolate bar is three times as long as the regular bar, so given that the regular bar is 5 4/9 inches long, the king size bar is 16 1/3 inches long.

The problem involves a regular size chocolate bar that is 5 4/9 inches long and a king size bar that is three times as long. Given the length of the regular bar, our objective is to find out how long the king size bar is.

We start by converting the mixed number 5 4/9 into an improper fraction which gives us 49/9 inches. We then multiply 49/9 by 3 to get the length of the king size bar which is 147/9 inches. Converting this improper fraction back into a mixed number, we get 16 1/3 inches. Therefore, the king size bar is 16 1/3 inches long.

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[tex]8x^2-12x-8=4(2x^2-3x-2)=4(2x^2-4x+x-2)\\\\=4[2x(x-2)+1(x-2)]=4(x-2)(2x+1)\\\\\boxed{ 8x^2-12x-8 =4(x-2)(2x+1)}[/tex]

Answer:

4(2x+1)(x-2)

Step-by-step explanation: I just did it

Answer:

50 sq. units

Step-by-step explanation:

The length of the base and the height of a triangle are numerically equal.

Let us assume that, the length and height as x.

So the area of the triangle will be,

[tex]\text{Area}=\dfrac{1}{2}\cdot \text{Base}\cdot \text{Height}=\dfrac{x^2}{2}[/tex]

As their sum is 30 less than the number of units in the area of the triangle, so

[tex]\Rightarrow x+x=\dfrac{x^2}{2}-30[/tex]

[tex]\Rightarrow 2x=\dfrac{x^2}{2}-30[/tex]

[tex]\Rightarrow 4x=x^2-60[/tex]

[tex]\Rightarrow x^2-4x-60=0[/tex]

[tex]\Rightarrow x^2-10x+6x-60=0[/tex]

[tex]\Rightarrow x(x-10)+6(x-10)=0[/tex]

[tex]\Rightarrow (x+6)(x-10)=0[/tex]

[tex]\Rightarrow (x+6)=0,(x-10)=0[/tex]

[tex]\Rightarrow x=-6,x=10[/tex]

Neglecting negative roots,

[tex]\Rightarrow x=10[/tex]

Hence, the base and height of the triangle is 10 units, so the area will be,

[tex]\text{Area}=\dfrac{1}{2}\cdot \text{Base}\cdot \text{Height}=\dfrac{1}{2}\cdot 10\cdot 10=50\ unit^2[/tex]

6x+y=4x+11

y=4x+11-6x

y=-2x+11

[tex]\(y = 11 - 2x\)[/tex] is the rearranged equation with [tex]\(x\)[/tex] as the independent variable.

To rearrange the equation [tex]\(6x + y = 4x + 11\)[/tex] so that (x\) is the independent variable and (y) is dependent, we need to isolate (y) on one side of the equation.

Start with the given equation: [tex]\(6x + y = 4x + 11\)[/tex].

Subtract (4x) from both sides to move all terms involving (y) to one side: [tex]\(6x - 4x + y = 11\).[/tex]

Simplify the left side by combining like terms: 2x + y = 11.

To isolate y, subtract 2x from both sides: 2x + y - 2x = 11 - 2x.

Simplify: [tex]\(y = 11 - 2x\)[/tex].

So, the rearranged equation with (x) as the independent variable is y = 11 - 2x.

Detailed calculation:

Starting equation: (6x + y = 4x + 11)

Subtract (4x) from both sides:

[tex]\(6x - 4x + y = 4x - 4x + 11\)[/tex]

[tex]\(2x + y = 11\)[/tex]

Subtract (2x) from both sides:

[tex]\(2x + y - 2x = 11 - 2x\)[/tex]

[tex]\(y = 11 - 2x\)[/tex]

Therefore, [tex]\(y = 11 - 2x\)[/tex] is the rearranged equation with [tex]\(x\)[/tex] as the independent variable.

Elimination Method

[tex]\left\{\begin{array}{ccc}36x+45y=123&\text{divide both sides by (-3)}\\46x+15y=23\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}-12x-15y=-41\\46x+15y=23\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad34x=-18\qquad\text{divide both sides by 34}\\.\qquad\qquad x=-\dfrac{18}{34}\to\boxed{x=-\dfrac{9}{17}}\\\\\text{Put the value of x to the second equation.}\\\\46\left(-\dfrac{9}{17}\right)+15y=23[/tex]

[tex]-\dfrac{414}{17}+15y=\dfrac{391}{17}\qquad\text{add}\ \dfrac{414}{17}\ \text{to both sides}\\\\15y=\dfrac{805}{17}\qquad\text{divide both sides by}\ 15\\\\y=\dfrac{805}{255}\\\\\boxed{y=\dfrac{161}{51}}\\\\Answer:\ \boxed{x=-\dfrac{9}{17}\ and\ y=\dfrac{161}{51}}[/tex]

Answer:

Length = 6 cm and width = 4 cm.

Step-by-step explanation:

Let the width be x, then the length is x + 2 cm and its area = x(x + 2).

The new width and length are x + 4 and x + 6, and the new area is

(x + 4)(x + 6).

So we have the equation:-

(x + 6)(x + 4) = x(x + 2) + 56

x^2 + 10x + 24 = x^2 + 2x + 56

10x - 2x = 56 - 24

8x = 32

x = 4 cm = width

and length = 4 + 2 = 6 cm

Answer:

your answers are 2,and 18

Step-by-step explanation:

46 × 12 = 46 × (10 + 2)  =

= (46 × 10 ) + (46 × 2)  

= 460 + 92

= 552