Five times the sum of a number and 27 is greater than or equal to six times the sum of that number and 26. What’s the solution set of this problem?

Answers

Answer 1

First, let's translate each part of the question into an equation. We'll use x to represent the unknown number:
5(x+27) ≥ 6(x+26)

Now, expand the terms:
5x+135 ≥ 6x+156

Solve for x:
135-156 ≥ 6x-5x
(-21) ≥ x

x ≤ (-21)

Answer 2

Answer:

B (-∞, -21]

Step-by-step explanation:

edge

Related Questions

2x+y=25. 3y=2x-13 solve by elimination

Answers

what are you trying to find X or Y ?

When matter changes state, what two things are always conserved?

Answers

Even though matter changes state, there are two things which are always conserved: they are mass and chemical composition. Just because the state has changed, it does not mean that any new molecules are either created or have been destroyed. The Law of Conservation of mass explains this concept.

In a change of state, mass and energy are the two things that are always conserved, in accordance with the law of conservation of matter and the first law of thermodynamics, respectively.

When matter changes state, the two things that are always conserved are mass and energy. This is explained by the law of conservation of matter, which states that the total mass of the products must equal the total mass of the reactants in a chemical reaction, and the law of conservation of energy, often referred to as the first law of thermodynamics.

In any given closed system, neither mass nor energy is created or destroyed, but can be transformed from one form to another. For example, when a substance burns, its matter is not lost but is instead transformed into other substances with the same total mass. Likewise, energy can be moved or transformed, but the total amount of energy remains constant. These principles apply to both living and non-living systems, keeping the total quantity of matter and energy fixed in the universe.

The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of 3 cm/s. when the length is 20 cm and the width is 10cm, how fast is the area of the rectangle increasing

Answers

Let l = length of the rectangle,
b = breadth of the rectangle,
a = area of the rectangle,
t = time,

So, [tex] \frac{dl}{dt} [/tex] = 8 cm/s &
[tex] \frac{dw}{dt} [/tex] = 3 cm/s

Area of the rectangle, a = l × w

Differentiate the equation with respect to t,

[tex] \frac{da}{dt} [/tex] = l × [tex] \frac{dw}{dt} [/tex] + w × [tex] \frac{dl}{dt} [/tex]

[tex] \frac{da}{dt} [/tex] = 20 × 3 + 10 × 8

[tex] \frac{da}{dt} [/tex] = 60 + 80

[tex] \frac{da}{dt} [/tex] = 140 [tex] cm^{2} [/tex]/s

Therefore, the correct answer is 140 [tex] cm^{2} [/tex]/s.

The information that is given:
dl/dt = 8 (rate of length increasing)
dw/dt = 3 (rate of width increasing)
l = 20 (when the length is 20)
w = 10 (when the width is 10)

The unknown is dA/dt (the rate the area is increasing)

Start with the formula for the area of a rectangle
A = w*l
Find the derivative of it
d/dt(A) = d/dt(w*l) Use the multiplication rule
dA/dt = w(dl/dt) + l(dw/dt)
Substitute in what is known from above
dA/dt = 10(8) + 20(3) = 80+60 = 140
The area is increasing 140 square centimeters per second

What is the exact value of
Tan 17pi/12

Answers

i think it should be 2+√3 correct me if im wrong or dont since you asked but i hope i helped! :)

Find the angular velocity of a wheel that makes 30 revolutions in 10 seconds.

1.5π rad/sec
3π rad/sec
6π rad/sec

Answers

30 revolutions = 30 * 2pi = 60 pi radians

angular velocity in rads / sec = 60pi / 10 = 6pi Answer

The angular velocity of the wheel is 6π rad/sec.

What is angular velocity?

Angular velocity is the speed at which the angle between two bodies changes as an item rotates or revolves around an axis.

In one revolution,

The angular velocity is 2π rad/sec.

In 30 revolutions,

The angular velocity is 2π x 30 rad/ 10sec.

The angular velocity is 60π rad/sec.

The SI unit of angular velocity is radians per second.

Hence, The wheel's angular velocity is 6 rad/sec.

To learn more about the angular velocity:

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Thomas paid $5 for a multicolor file folders. There were 100 folders in the box .what was the cost of each folder?

Answers

Thomas paid $5 for 100 folders, to find cost of each folder:

5/100 = $0.05

Therefore, the cost of each folder was $0.05

Hope I helped :)

5 divided by 100, since there were 100 folders n total is 5

0.05

:))

The town Atlanta needs $14,000 for a new playground Lanzetta Elementary school raise $5358 Lantana middle school race $2834 Atlanta high school raised eig The town Atlanta needs $14,000 for a new playground Lanzetta Elementary school raise $5358 Lantana middle school race $2834 Atlanta high school raised $4132 about how much more do they need to raise choose the best estimate

Answers

Lanzetta Elem. raised 5358....round to 5,000
Lantana Mid. Sch raised 2834....round to 3,000
Atlanta High Sch. raised 4132...round to 4,000

they need 14,000...they have (5,000 + 3,000 + 4,000) = 12,000....so they will need (14,000 - 12,000) = 2,000 more....keep in mind, these are estimates...not exact answers

To find out how much more money is needed for the Atlanta playground, add the amounts raised by each school and subtract from the total amount needed. The schools have raised $12,324, so they still need about $1676. Therefore, $1676 more is required to meet the goal.

Let's calculate how much money the schools have already raised:

Lanzetta Elementary School raised $5358Lantana Middle School raised $2834Atlanta High School raised $4132

First, add these amounts together:

$5358 + $2834 + $4132 = $12,324

Next, subtract the total amount raised from the total money needed:

$14,000 - $12,324 = $1676

Therefore, the town of Atlanta still needs to raise about $1676 for the new playground.

What is 12.7, 12 3/5 and 12 3/4 form greatest to least

Answers

12.7 , 12 3/4, 12 3/5

Hope this helps!

12 3/5,12.7, 12 3/4

convert 12 3/5 and 12 3/4 into decimals
12 3/5=12.6
12 3/4=12.75

One number is 4 less than a second number. twice the second number is 19 less than 5 times the first. find the two numbers.

Answers

the answer is because i know so

The exchange rate is £1 = €1.12 how many £ would I get for €336

Answers

1€ = 1/1.12 £
so 336€ = 336/1.12£ = 300£

PLEASE HELP!!! Will give brainliest!

Answers

The correct answer would be 24, I don't know how to show the work but you can go on youtube.

Hope this helps!

Kevin picked 13 more apples than Andy. if Kevin picked 30 apples, how many did Andy pick ? Let A= the apples sandy picked

Answers

Andy picked 17 apples
30-13=17

A-13=how many apples Andy Picked

Steven wants to buy a $500 bicycle. Steven has no money saved, but will be able to deposit $45 into a savings account when he receives his paycheck each Friday. However, before Steven can buy the bike, he must give his sister $85 that he owes her. For how many weeks will Steven need to deposit money into his savings account before he can pay back his sister and buy the bike?

Answers

The answer is 13 weeks

Math is not my forte, so correct me if I am wrong.

If he first has to pay back $85 to his sister, then he'd be able to do that by the second week. 45+45 is 90 so he will have $5 once he pays back his sister. In 3 weeks, He'll have 50 dollars. In four weeks, he'll have 95 dollars. In five weeks, he'll have 140 dollars. In six weeks, he'll have 185 dollars. In several weeks, he'll have 230 dollars. In eight weeks, he'll have 275 dollars. I think you get the gist by now. I calculated that in 13 weeks he will have enough money to pay back his sister and buy his bike.

write in graphing form please! A parabola that opens down with no stretch factor that has a vertex of (-6,5)

Answers

If it has no stretch factor, then there will be no coefficient. Meaning this is a lot easier. So, we equation is

(x+6)^2 + 5

Hope this helps!

1) Which statement about 5y = 2x is true?

A) The equation represents a direction variation whose consent of variations is 5/2.

B) The equation represents a direct variation whose consent of variations is 2/5.

C) The equation does not represent a direction variation.

D) The equation does not represent a line through the origin.

2) What is the equation of the graph of y = |x| shifted 3 units up?

A) y = |x| – 3

B) y = |x| + 3

C) y = |x + 3|

D) y = |x – 3|

3) Two parallel lines form an inconsistent system of equations that has no solution.

True
or
False

Answer all and Show or Explain your answer :)

Answers

1) B you can divide both sides of the equation by 5 and it will be of the form y = kx which is direct variation

2) B f(x) + k is a vertical shift up k units

3) True Because parallel lines have the same slope and different y - intercepts they do not touch thus called inconsistent. Since they do not touch they will not have a solution.

A displacement vector with a magnitude of 20. meters could have perpendicular components with magnitudes of

Answers

To find the magnitude of the resultant vector, the formula is written as:

R² = x² + y²,
where
x and y are the perpendicular vectors along x and y axes, respectively.

So, any pair of x and y must satisfy the given equation. There are a lot os possibilities. Let's say, if x = 12, then,

20² = 12² + y²
y = 16

One answer would be a horizontal x vector equal to 12 m, and a vertical y vector equal to 16 m.

Final answer:

To find the perpendicular components of a displacement vector with a magnitude of 20 meters, use trigonometry and the Pythagorean theorem.

Explanation:

The question asks for the perpendicular components of a displacement vector with a magnitude of 20 meters. Perpendicular components of a vector can be determined using trigonometry. Let's assume the vector has components Ax and Ay.

Using the Pythagorean theorem, Ax^2 + Ay^2 = 20^2. Since the components are perpendicular, we can set up a right triangle and solve for the components using the sine and cosine functions. For example, if one component is Ax = 10 meters, the other component Ay can be calculated using Ay = sqrt(20^2 - 10^2) = 10*sqrt(3) meters. Similarly, if one component is Ay = 10 meters, the other component Ax can be calculated using Ax = sqrt(20^2 - 10^2) = 10*sqrt(3) meters.

Learn more about perpendicular components here:

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It is given that a+b=6 and ab=7. Find the value of a^2 + b^2.

Answers

Use the identity:-

a^2 + b^2 = (a + b)^2 - 2ab

Plugging in the given values;-

a^2 + b^2 = 6^2 - 2*7 = 36-14 = 22 Answer

Billie and Toni are driving from Chicago to Phoenix. The first day they drove 420 miles. They want to drive at 65 miles per hour for the rest of their trip. a. Write an algebraic expression to represent the situation. b. If they drive 8 hours a day for the next two days, how far have they traveled by the end of the third day?

Answers

A. We are given that they already drove 420 miles and an additional of 65 miles per hour. Therefore distance covered is:

d = 420 + 65 t

where d is distance and t is time

B. If they drove 8 hours per day for 2 days, then total time is t = 16 hours, hence:

d = 420 + 65 * 16

d = 1460 miles

stella writes 1/7 of a page in 1/5 of a minute. how many minutes doesn’t it take her to write a full page?

Answers

It takes Stella 1.4 minutes to write a full page, calculated by setting up a proportion based on her rate of writing [tex]\frac{1}{7}[/tex] of a page in 1/5 of a minute.

Stella writes [tex]\frac{1}{7}[/tex] of a page in [tex]\frac{1}{5}[/tex] of a minute. To calculate how many minutes it takes her to write a full page, we can set up a proportion. Since 7/7 would make a full page, we'd need Stella to write seven times as much as she does in 1/5 of a minute. So, the math to find the time for a full page looks like this:

[tex]\frac{1}{7}[/tex] page : [tex]\frac{1}{5}[/tex] minute = 7/7 page : x minutes

Now multiply both sides by (1/5) minutes to isolate x:

[tex]\frac{1}{7}[/tex] / [tex]\frac{1}{5}[/tex] = 1/x

Cross multiply to solve for x:

[tex]\frac{1}{7}[/tex] * x = [tex]\frac{1}{5}[/tex]

x = [tex]\frac{1}{5}[/tex] / [tex]\frac{1}{7}[/tex]

x = [tex]\frac{1}{5}[/tex] * (7/1)

x = 7/5 minutes

x = 1.4 minutes

Therefore, it takes Stella 1.4 minutes to write a full page.

A right triangle has one angle that mesures 23. The adjacent leg measures 27.6 cm and the hypotenuse measures 30cm.

What is the approximate area of triangle? Round to the nearest tenth

Area of the triangle =1/2bh

A:68.7cm^2
B.161.7cm^2
c.381.3cm^2
D450.cm^2

Answers

you can start by finding the height or altitude ("alt" = vertical side touching hypotenuse and bottom base):
tangent (23) = opposite/adjacent (TOA), where opposite is altitude and adjacent is base
So tangent (23) = alt/27.6cm
alt = 27.6×tan23 = 27.6×0.424
alt = 11.72cm
So now area = 1/2 (b)(h), where h=alt
area = 1/2 (27.6cm)(11.72cm) = 161.7cm^2
[tex] 161.7{cm}^{2} [/tex]
So the correct answer is [B.]

What is the perimeter of a polygon with vertices at (−2, 1) , (−2, 4) , (2, 7) , (6, 4) , and (6, 1) ?

Answers

The perimeter is 24 units.

If EG=25 and point F is 2/5 of the way between E and G, find the value FG. The drawing is not to scale.

a. 12.5
b. 10
c. 20
d. 15
d. 7

Answers

First find 2/5 of 25.
This can be done by multiplying the two numbers.
2/5 × 25 = 10

10 is the distance from E to F.
So now that you have EF and know the overall length of EG (25), you can easily find FG.
25 - 10 = 15

The answer is:
d. 15

Consider the equation 2x-3(2x-1)=3-4x. solve the equation for x. for each step, identity the property used to write an equivalent equation.

Answers

First, you expand it.

2x - 6x + 3 = 3 - 4x

Now, simplify.

-4x + 3 = - 4x

Cancel out the double "4x"

3 = 3

Since both side have an equal answer, there in an infinite number of answers.

Hope this helps! ☺♥

Joe bought a length of timber for his fence. He uses 1/5 of the wood for the first garden and 3/8 for the second garden. What fraction of the wood remains for the third garden

Answers

1/5 + 3/8 = 8/40 + 15/40 = 23/40 40/40 -23/40 = 17/40

17/40 of the wood remains for the third garden.

HOPE THIS HELPS!!!

Joe used 1/5 of the timber for the first garden and 3/8 for the second garden. After converting these fractions to have a common denominator, we found that 23/40 of the timber was used. Therefore, 17/40 of the timber remains for the third garden.

The student is asking how much of the timber remains after Joe has used some for two gardens. Joe uses 1/5 of the wood for the first garden and 3/8 for the second garden. To solve this, we first add the fractions of wood used for both gardens to find out the total used fraction:

1/5 + 3/8

To add these fractions, we first need to find a common denominator, which in this case is 40. So we convert the fractions:

8/40 + 15/40} = 23/440

Now we subtract the used fraction from the total amount of timber, which is 1:

1 - 23/40 = 40 / 40 - 23 / 40= 17 / 40

Thus, 17/40 of the wood remains for the third garden.

Se implicit differentiation to find an equation of the tangent line to the curve at the given point.7x2 + xy + 7y2 = 15, (1, 1) (ellipse)

Answers

F'(x, y) = 14x +xydy/dx + 14ydy/dx = 0
(xy+14y)|dy/dx = -14x
dy/dx = -14x /(xy+14y)
dy/dx |(x=1,y=1) : -14(1) / (1+14) = -14/15

using
y-y1=/x-x1 = -14/15
y-1/x-1 = -14/15
15y-15 = -14x+14
15y+14x -15-14=0
14x +15y = 29

A warehouse is packing materials to ship out to a customer. A small box has the dimensions of x inches, (x+ 2) inches and (2x) inches. Where x is the length in inches of width. A large box has the dimensions of (x+5) inches, (x + 7) inches and (3x) inches.

*Recall that Volume = (Length)(Width)(Height)

Part 1: Write an expression that represents the dimensions of the small box.

Part 2: Write an expression that represents the dimensions of the large box.

Part 3: What is the difference in the volumes of the two boxes? Show or explain or work.

Answers

did you ever figure it out? I have that question on my test thats due tomorrow and i need it
I ended up finding the first 2
vsmall=x(x+2)(2x)
vlarge=(x+5)(x+7)(3x)
I found those on answers . com
V=volume...
I just need #3

1. The expression that represents the dimensions of the small box is (2x³ + 4x²).

2. The expression that represents the dimensions of the large box is (3x³ + 36x² + 105x).

3. The difference in the volumes of the two boxes is (x³ + 32x² + 105x)

What is the volume of the box?

Small box:

x inches,

(x+ 2) inches and

(2x) inches

Volume = length × width × height

= x × (x + 2) × (2x)

= (x² + 2x) × 2x

= 2x³ + 4x²

Large box:

(x+5) inches,

(x + 7) inches and

(3x) inches.

Volume = length × width × height

= (x + 5) × (x + 7) × (3x)

= 3x³ + 36x² + 105x

Difference in volume = Large box - Small box

= (3x³ + 36x² + 105x) - (2x³ + 4x²)

= 3x³ + 36x² + 105x - 2x³ - 4x²

= x³ + 32x² + 105x

Therefore, x³ + 32x² + 105x is the expression which represents the volume of the box.

Answers

first convert feet to inches:
18 ft × (12in/1ft)= 216 in
15 ft × (12 in/1ft)= 180 in

divide each side of the room by 9 inches to get number of white tiles per a wall

wall 1(18ft): 216in/9in= 24 white tiles
wall 2(15ft): 180in/9in= 20 white tiles
wall 3(18ft): 216in/9in= 24 white tiles
wall 4(15ft): 180in/9in= 20 white tiles

Lastly, add up all the white tiles and subtract 4 (the tiles that we counted twice because they were the corner tiles and touched both walls)

24+20+24+20-4= 84 white tiles total

The scale drawing of a flower bed has the dimensions of 3 inches by 7 inches. The dimensions of the actual flower bed are 36 inches by 84 inches.

What is the scale factor used to find the dimensions of the drawing?

Answers

i believe it is 12*12

Final answer:

The scale factor used to find the dimensions of the scale drawing is 1/12. This is found by dividing the dimensions of the drawing by the dimensions of the actual flower bed, confirming both scale factors for length and width are equal.

Explanation:

The student is asking about determining the scale factor used to create a scale drawing from the actual dimensions of an object, which in this case is a flower bed. To find the scale factor, we compare the dimensions of the drawing with those of the actual object. For the given dimensions of the drawing, which are 3 inches by 7 inches, and the actual dimensions being 36 inches by 84 inches, we can find the scale factors for the length and width separately and confirm they are the same.

For the length, the scale factor is calculated as:
Scale factor for length = Length of drawing / Length of actual object
Scale factor for length = 3 inches / 36 inches = 1/12

For the width, the scale factor is calculated as:
Scale factor for width = Width of drawing / Width of actual object
Scale factor for width = 7 inches / 84 inches = 1/12

Thus, the scale factor for the scale drawing is 1/12. This means that each unit of measurement in the drawing represents 12 units in the actual flower bed.

Solve for x: −3 |x + 7| = −12

Answers

[tex]-3|x + 7|=-12\quad |:(-3)\\\\|x+7|=4\\\\\\x+7=-4\qquad\vee\qquad x+7=4\\\\x=-4-7\qquad\vee\qquad x=4-7\\\\\boxed{x=-11\qquad\vee\qquad x=-3}[/tex]

first you divide both sides by -3
then you get |x + 7| = 4
what you do now is make two separate equations
drop the absolute value signs
x + 7 = 4 OR x + 7 = -4
subtract 7 from both sides AND BOTH EQUATIONS
x = -3 OR x = -11

lets check it!

-3 |-3 + 7| = -12 -3 |-11 + 7| = -12
-3 |4| = -12 -3 |-4| = -12
-3 (4) = -12 -3 (4) = -12

yep! your answers are x = -3 OR x = -11

i hope this helps!!

A sports club is holding a fundraiser dinner. The function graphed models the profit, y, in dollars, from selling x tickets.

Select True or False to describe each statement.

Answers

Let

x-------> the number of tickets

y------> the profit in dollars

Let

[tex]A(0,-400)\ B(40,0)[/tex]

Find the slope of the linear equation

The slope is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute

[tex]m=\frac{0+400}{40-0}[/tex]

[tex]m=10\frac{\$}{ticket}[/tex]

the linear equation is

[tex]y=10x-400[/tex]

Statements

case A) The y-intercept represents the cost per ticket

The statement is false

The cost per ticket represent the slope of the linear equation

The y-intercept is the value of the profit for a number of tickets equal to zero

In this problem the y-intercept is the point [tex](-400,0)[/tex]

case B) The slope represents the money spent before the sale of the first ticket

The statement is False

The slope represents the cost per ticket

the money spent before the sale of the first ticket is the y-intercept

case C) The sports club must sell more than [tex]40[/tex] tickets to make a profit

The statement is True

Because

we know that

For [tex]x=40\ tickets[/tex]

the value of the function is

[tex]y=0[/tex]

in the linear equation

[tex]y=10x-400[/tex]

For [tex]x>40\ tickets[/tex]

the profit will be

[tex]y > 0[/tex] --------> see the graph

therefore

the answer is

The sports club must sell more than [tex]40[/tex] tickets to make a profit

Answer:

the first 2 are false and the last one is true.

Step-by-step explanation:

I took the test :)

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