Four times a number, increased by 10, is -2
what is the number?

Answer:

  33. $5.75

  34. 15 ft

  35. 8

  36. 32

Step-by-step explanation:

These questions pretty much cover the sorts of things you're supposed to learn in an Algebra course. If you don't get any of it, you may have a problem with follow-on courses.

__

You are expected to understand this question gives you two relations in two unknowns. The first step is to assign a variable to each of the unknowns. We can use ...

The given relations have to do with the prices of different quantities of these:

  2x +3y = 26.25 . . . . . . cost of 2 shakes and 3 sundaes

  4x +2y = 29.50 . . . . . . cost of 4 shakes and 2 sundaes

These two equations in two unknowns can be solved several ways. Here, it is convenient to use the method of "elimination", because the coefficients of x are related by a small integer. Subtracting the second equation from 2 times the first eliminates the x-variable (hence the name of the method).

  2(2x +3y) -(4x +2y) = 2(26.25) -(29.50)

  4y = 23.00 . . . . . . simplify

  y = 5.75 . . . . . . . . . divide both sides by 4

The cost of an ice cream sundae is $5.75.

We can substitute this value into either equation and solve for x. We would find the cost of a shake to be x=4.50. However, the question only asks for the price of a sundae.

__

There are formulas for the perimeter, area, and volume of various geometric figures of a generally circular or rectangular shape. You might find it convenient to memorize them. Here, you need the formulas for the volume of a cylinder and of a cone. You also need to know that the diameter of a circle is 2 times the radius of the circle, since most of the circle-related formulas are in terms of the radius.

Volume of a cone of radius r and height h: V = 1/3πr²h

Volume of a cylinder of radius r and height h: V = πr²h

It can be convenient to remember that a cone has 1/3 the volume of a cylinder the same height.

The relation of interest here is the volume of the silo is the sum of the volumes of the bottom cylinder and the top cone.

  V = π(20 ft)²(60 ft) + 1/3(20 ft)²(x ft) = 26000π ft³

  V = 24000π ft³ +(400/3)x·π ft³ = 26000π ft³ . . . . simplify a bit

  400/3·x = 2000 . . . . . . . divide by π ft³, and subtract 24000

  x = 2000(3/400) = 15 . . . . multiply by 3/400

The height of the top portion is 15 feet.

__

This has to do with understanding the meaning of a table and of an expression relating table values. The expression f(a) = g(b) means you're looking for table entries such that the number in the f(x) column is equal to the number in the g(x) column.

We find the only common function value to be -1, so f(-6) = -1 = g(1). Comparing this to f(a) = g(b), we see that a=-6.

The question asks for |g(a)|. The table tells us g(-6) = -8. Its absolute value will be the value without the negative sign:

  |g(-6)| = |-8| = 8 = |g(a)|

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This is a polynomial division problem. It tells you the quotient of the quadratic, divided by (ax +2), is (3x -4) with a remainder of 66. We're concerned with the leading coefficient of the divisor, 'a'.

Polynomial long division is much simpler than numerical long division, because each quotient term is the leading dividend term divided by the leading divisor term. Here, that means ...

  96x²/(ax) = 3x

Multiplying by ax gives ...

  96x² = 3ax²

Dividing by 3x², we see that ...

  (96x²)/(3x²) = (3ax²)/(3x²)

  96/3 = a = 32

The value of 'a' is 32.

Option D is correct, the value of the rational expression when x = –3 is undefined.

An expression is combination of variables, numbers and operators.

The given expression is x/x²-9

x divided by x square minus nine.

Now let us find the value of the expression when x is minus three,

Plug in x as -3 in the above expression.

-3/(-3)²-9

-3/9-9

-3/0

Anything divided by zero then the value is undefined.

Hence, Option D is correct, the value of the rational expression when x = –3 is undefined.

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What is the value of the rational expression x/x2-9 when x = –3?

A. -1/12

B. 0

C. 1/6

D. Undefined

Answer: B

Step-by-step explanation: Hope this helps :)

Step-by-step explanation:

We will use the LHS to find the RHS.

Step 1: Expand the LHS by multiplying through the brackets and simplify

(sinx + cosx)(1 − sinx cosx) ≡  sinx + cosx - (sinx + cosx (sinx cosx))

                                             ≡  sinx + cosx - sin²x cosx - sinx cos²x

Step 2: Use the identity sin²x + cos²x = 1, to rewrite the equation

                                           ≡ sinx + cosx - cosx (1 - cos²x) - sinx (1 - sin²x)

Step 3: Simplify the equation by adding like terms

                                           ≡ sinx + cosx - cosx + cos³x - sinx + sin³x

                                           ≡ sin³x + cos³x                 [QED]

Reminder:

Answer:

ok good morning

have a nice day

Step-by-step explanation:

#toxicsquad

Answer:

i think its 7, but you should probably check that...

The equation that represents this situation is 8 + 3t = 25.50.

Let the sales tax for each book be represented as t.

Since Orion buys 3 books for a total of 25.50 and he pays $8 plus sales tax for each book. This will be illustrated as:

Cost of book + Tax = Total amount

8 + (3 × t) = 25.50

8 + 3t = 25.50

Collect like terms

3t = 25.50 - 8.

3t = 17.50

Divide

t = 17.50 / 3

t = 5.83

The sales tax is $5.83.

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Answer:

see below

Step-by-step explanation:

You're doing well!  The parts of the table you've done are correct.

For x = 1, you switch to the second part of the function rule (because that part says to use it if [tex]x \ge 1[/tex].

x =1 :   6 - 2(1) = 4   (1, 4)

x = 2:  6 - 2(2) = 2   (2, 2)

x = 3:  6 - 2(3) = 0   (3, 0)

x = 4:  6 - 2(4) = -2  (4, -2)

Each of the parts of the function rule graph as pieces of straight lines.  The first part will be a straight line through points (-4, 1), (-3, 0), (-2, 1), (0, 3) but that part of the graph stops at point (1, 4).  Point (1, 4) is on BOTH parts of the graph, so the two lines connect at that point.

Answer:

Step-by-step explanation:

Hello!

Remember y=mx+b.

m is the slope and b is the y intercept.

So

the slope is 7 and the y intercept is 4.

Hope this helps!

~Just a felicitous teen

#CarryOnLearning

[tex]SIlentNature[/tex]

Answer:

slope: 7

y-intercept:4

Step-by-step explanation:

-10 and -8????

I believe because -10 + -8 = -18 and they are both consecutive

Answer:

if the units is in m/s

Step-by-step explanation:

first work out using this triangle.

distance= speed x by time

so if we're trying to find out the speed we reaarange the triangle to :

   distance

---------------------

speed x   time

so speed = distance divided by time

distance = 45cm

divided by time = 90 seconds

But the units are cm and should be metres per second

change 45cm to m

that is 45cm = 45/ 100 = 0.45

0.45/ 90= 0.005cm

answer = 0.005 metres per second( m/s)

plz say thanks + rate !

Answer: f 500 Ft./sec

Step-by-step explanation:

By evaluating the derivate of the distance in t = 10s, we will see that at t =  10s the distance is changing at a rate of 464.2 ft/s

We can think of the situation as in a right triangle, one cathetus is equal to 2000ft, and the other cathetus increases at a rate of 500ft/sec.

The hypotenuse would be the distance between the radar and the rocket.

Then the distance function is:

[tex]D(t) = \sqrt{(2000ft)^2 + (500ft/s*t)^2}[/tex]

Now we need to get the rate of change, this is given by:

[tex]\frac{dD(t)}{dt} = (1/2)*\frac{2*(500ft)^2*t}{\sqrt{(2000ft)^2 + (500ft/s*t)^2} }[/tex]

Now we evaluate this in t = 10s to get:

[tex]\frac{dD(10s)}{dt} = (1/2)*\frac{2*(500ft/s)^2*10s}{\sqrt{(2000ft)^2 + (500ft/s*10s)^2} } = 464.2 ft/s[/tex]

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Answer:

-3 is less and -5 is greater

Step-by-step explanation:

Answer:

less than

Step-by-step explanation:

because -5 would be less than -3 because it is bigger

Hi there! :)

A geometric sequence is a sequence where we use multiplication or division to get to the next term.

We use multiplication in the third sequence (we multiply by -5)

So the answer is Option C

Hope it helps

~Just a gloomy teen who misses her best friend

#CarryOnLearning

[tex]SilentNature[/tex]

Answer:

Set an equation x+47+48= 136

solve for x

x+95=136

x= 40

so they need to score a 40

Answer:

y = -7x + 3/11

Step-by-step explanation:

Answer:

m is the slope of line and x1, y1= 2,5 , and x2, y2= -4, 5

m = 5-2/-4-5 = -1/3

Step-by-step explanation:

        With this in mind,

                 x + y = -3

                 x * y = -18

        Then we will think about which ones could add up to 3

                 1 & 18, 2 & 9, 3 & 6 are factors of 18 (one being negative results in -18)

                 Well 1 and 18 cannot make 3, same for 2 and 9, that leaves us with 3 and 6.

        You can see our test shows this solution works!

                 -6 + 3 = -3

                 -6 * 3 = -18

Have a nice day!

  I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer:

m = 2/5

Step-by-step explanation:

2x - 5y = 52

-5y = -2x + 52

y = 2/5x - 52/5

The slope of the line with equation 2x−5y=52 is 2/5.

The given equation of line is 2x−5y=52.

The slope formula is used to calculate the inclination or steepness of a line. It finds application in determining the slope of any line by finding the ratio of the change in the y-axis to the change in the x-axis.

The given equation 2x−5y=52 can be rewritten as

2x-52=5y

⇒ y = 2x/5-52/5

Now, compare y = 2x/5-52/5 with the standard form of an equation y=mx+c

So, m=2/5

Therefore, the slope of the line with equation 2x−5y=52 is 2/5.

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Answer:

i think you need to add all that up

Step-by-step explanation:

Answer:

The number of hours Jenny babysits

Step-by-step explanation:

Since we know that the 10 is the fixed fee for the babysitting services and 5 represents the amount charged per hour, it is safe to say x represents the number of hours Jenny babysits.

Ex.: Let us say she baby sits for 3 hours. 3 would take the place of the x

   5(3)+10. This means Jenny will charge the person she babysat for a total of  

   $15 just for the hours alone.

Hope this helps! :)

Answer:

x represent the number of hours Jenny Babysits

Step-by-step explanation:

since she charges $5 per hour, then X is always how many hours

Answer:

  £225

Step-by-step explanation:

The relationship between the cost price (cp) and the selling price (sp) is ...

  cp + 5% × cp = sp

  cp(1.05) = sp . . . . . . collect terms

  cp = sp/1.05 . . . . . . divide by 1.05

  cp = £236.25/1.05 = £225

The original wholesale price was £225.

We have

If,

Putting value:

➡ (-1×2 + 2×1)² - 2×-1²×2²×1

➡ (-2 + 2)² - 2×1×4×1

➡ (0)² - 8

➡ 0 - 8 = -8,answer

Answer:

1.

1.5 litre carton for $2.35 is the cheapest way since it's the cheapest out of all the other options.

2.

a. 1.25 / 0.5 = $2.50 per L

2.35 / 1.5 = $1.57 per L

3.25 / 2 = $1.63 per L

b. 2.50 x 8 = $20.00 per 8 L

1.57 x 8 = $12.56 per 8 L

1.63 x 8 = $13.04 per 8 L

Step-by-step explanation:

find unit rate (cost / quantity)

Answer:

56

Step-by-step explanation:

Answer:

11 Julie's and 5 East Indians

Answer:

-251

Step-by-step explanation:

Following BEDMAS/PEMDAS

6*2/(-1)4*5-(8+3); first simplify the brackets/parenthesis

= 6*2/(-1)4*5-11; now do divisons and multiplications going from left to right

= 12/(-1)4*5-11 = -12*4*5-11 = -48*5-11 = -240-11

= -251

Answer:

Step-by-step explanation:

Given table:

Use two pairs of points to work out the equation of the line y = mx + b:

Find the slope:

Use one pair to find the y-intercept:

The line is:

m = (-9 - 3)/(2 + 2) = -12/4 = -3 ==> (x)

3 = (-3)•(-2) + b

3 = 3•2 + b

3 = 6 + b

b = -3 ==> (a)

Soo :

Answer:

infinity solution

solution:

-x-3y=-6

x+3y=6

Answer: $6322

114800.8806 - 108478.6929

= 6322.1877

Rounded to the nearest dollar = $6322

Answer:6761

Step-by-step explanation:

Answer:

skew

skew

parallel

parallel

Step-by-step explanation:

First see the below figure to understand parallel and skew lines

As you can see parallel lines lie on the same plane

skew lines lie on different plane and do not intersect

1)AB and GF

AB lies on ABCD plane

GF lies on EFGH plane

and they will never meet / intersect

so skew

2)DH and BF

DH lies on ADHE plane

BF lies on BCGF plane

they seem parallel but they are on different plane, so skew

3)EF and HG

EF and HG both lie on the same plane EFGH

and they both are parallel

4)for this see the second picture

both these planes are parallel

Hope this helps!