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algebra 2 word problem

15% answered swimming.

39 people said swimming, so 39 people is 15% of the total people surveyed.

To find the total number of people, divide 39 by 15%:

39 / 0.15 = 260

There were 260 total people surveyed.

Answer:

y = (5/2)x

Step-by-step explanation:

A proportional relation can be written as ...

y = kx

Solving for k, you divide by x to get ...

y/x = k

The contant of proportionality is the ratio of y to x. Any pair of x and y will do for computing k. The first pair requires no reduction in the fraction that results:

5/2 = k

So, your equation is ...

y = (5/2)x

Answer:

The constant of proportionality is

✔ 2.5

The equation that represents this proportional relationship is

✔ y = 2.5x

Step-by-step explanation:

hope this helps:)

Answer:

B) L ∪ (M ∩ N)={0,10,20,40,80,100}

Step-by-step explanation:

The given sets are;

L = {0, 20, 40, 80, 100}

M = {5, 10, 15, 20, 25}

and

N = {10, 20, 30, 40, 50}

(M ∩ N) are elements in set M and set N

(M ∩ N) ={10,20}

The elements in L ∪ (M ∩ N)  are elements in L or M ∩ N or both

L ∪ (M ∩ N)={0,10,20,40,80,100}

The correct choice is B.

Answer:

B

Step-by-step explanation:

L ∪ (M ∩ N)  means take "common" between M and N and take "sum of that and L".

Let's find (M ∩ N) (common between M and N):

We know

M = {5, 10, 15, 20, 25} , and

N = {10, 20, 30, 40, 50}

Thus, the common elements are 10 & 20, thus (M ∩ N) = {10,20}

Now we have:

L = {0, 20, 40, 80, 100}

(M ∩ N) = {10,20}

So sum of L and (M ∩ N)  are all the unique elements of both the sets. They are 0, 10, 20, 40, 80, 100, or Option B

Answer:

-1, 4

Step-by-step explanation:

factor out common term 4

4(x^2 - 3x - 4)        find factors of -4      1 (-4)= -4  (c term)  also 1 - 4 = -3  (b term)

4(x+1)(x-4)  = 0

zeros are -1, 4

Answer:

[tex]\large\boxed{x=-1\ or\ x=4}[/tex]

Step-by-step explanation:

[tex]y=4x^2-12x-16\\\\\text{the zeros are for}\ y=0:\\\\4x^2-12x-16=0\qquad\text{divide both sides by 4}\\\\x^2-3x-4=0\\\\x^2+x-4x-4=0\\\\x(x+1)-4(x+1)=0\\\\(x+1)(x-4)=0\iff x+1=0\ \vee\ x-4=0\\\\x+1=0\qquad\text{subtract 1 from both sides}\\\boxed{x=-1}\\\\x-4=0\qquad\text{add 4 to both sides}\\\boxed{x=4}[/tex]

For this case we must indicate the value of the following expression, expressed in scientific notation:

[tex](1.2 * 10^{-3}) * (1.1 * 10^{8}) =[/tex]

We have that for multiplication properties of powers of the same base, the same base is placed and the exponents are added:

[tex]a ^ n * a ^ m = a ^ {n + m}[/tex]

Then, rewriting the expression we have:

[tex](1.2 * 1.1) * 10 ^{- 3 + 8} =\\1.32 * 10 ^ 5[/tex]

Answer:

[tex]1.32 * 10 ^ 5[/tex]

❤️Hello!❤️ The answer is 11.31 feet                                                                    arc length = radius * central angle (in radians)

arc length = 12.6 * 2*PI/7

arc length = 25.2 * PI/7  

arc length = 11.31 feet ☯️Hope this helps!☯️  ↪️ Autumn ↩️

Answer:

11.31 ft is the arc length.

Step-by-step explanation:

We have given the radius r = 12.6 ft and arc intercept by central angle

Ф = 2π/7.

We have to find the arc length.

We know the formula to find the arc length that is:

L = rФ

Putting the values we get,

 L= 12.6 × 2π/7

L = 25.2 π/7

L = 11.31 ft  is the answer.

11.31 ft is the arc length.

The value of x in Problem 1 is 11 degrees. The measures of angles EFO and EFD in Problem 2 are 28 degrees and 84 degrees respectively.

In both problems, we're dealing with geometric principles related to circles and angles.

https://brainly.com/question/27802544

#SPJ12

1. The value of x is 11

2. angle EFO = 28°

3. angle EFD = 90°

In geometry, the central angle of a circle's arc is equal to the subtended arc's measure.

The relationship is given by

Central Angle = Arc Measure

Central Angle=Arc Measure in degrees. This property is fundamental in circular geometry.

1. Since arc EF = 2x + 10

2x + 10 = 32( angle at the centre equal measure of arc it intercept)

2x = 32 - 10

2x = 22

x = 11

Since FE = 56

EFO = 1/2 × 56 ( angle at the center is 2× angle at the circumference)

EFO = 28°

angle EFD = 90° ( angle substended from the diameter of a circle to the circumference is 90°)

Center (-1,1), radius 5 so

[tex](x - -1)^2 + (y - 1)^2 = 5^2[/tex]

[tex](x+1)^2 + (y-1)^2 = 25[/tex]

Third choice

Answer:

○ (x + 1)² + (y - 1)² = 25

Step-by-step explanation:

According to one of the Circle Equations, (X - H)² + (Y - K)² = R², all the negative symbols give the OPPOSITE terms of what they really are, so be EXTREMELY careful inserting the center into the formula with their CORRECT signs. Then in the end, square the radius.

The radius is five, so squaring this will give you twenty-five.

I am joyous to assist you anytime.

Answer:

C. A(7) = 800·(1 +0.03)^(7-1)

Step-by-step explanation:

Note that the times are described as "the beginning of year 1" and "the beginning of year 7." If you consider the formula to be the one marked (choice D), you find the general case is ...

A(n) = 800·1.03^n

When you put in 1 for n, you see it gives you ...

A(1) = 800·1.03^1 = 824 . . . . . . . incorrect value for "the beginning of year 1"

The exponent of 1.03 needs to be the difference in year numbers: 7-1, as in choice C.

The appropriate formula is ...

A(7) = 800·(1 +0.03)^(7-1)

Answer:

  300 square units

Step-by-step explanation:

Let M be the midpoint of BC. Then AM =20 is the altitude. Let x represent the length BM=MC, and let y represent the length AB=AC. Then the perimeter is ...

  2x +2y = 80

  x +y = 40 . . . . divide by 2 . . . . . [eq A]

The Pythagorean theorem tells us ...

  x^2 + 20^2 = y^2 . . . . . . . y is the hypotenuse of right triangle AMC

Rearranging, we have ...

  y^2 -x^2 = 400

  (y -x)(y +x) = 400

  (y -x)·40 = 400

  y -x = 10. . . . . . . . . [eq B]

Subtracting [eq B] from [eq A], we find ...

  (x +y) -(y -x) = (40) -(10)

  2x = 30

  x = 15

The area of interest is 20x, so is ...

  A = 20·x = 20·15 = 300 . . . . square units

Answer: 6(x-2)

Step-by-step explanation:

(x·2-8)-(2x·2+4)

(2(x-4))+2x·2-4

2(x-4)+2x·2-4

2(x-4)+4x-4

2(x-4+2x-2)

2(3x-4-2)

2(3x-6)

2·3(x-2)

6(x-2)

Answer:

3x^2-12

Step-by-step explanation:

Just took it on USATestPrep, if that's where the question came from! ;)

Answer:

EI=6 units

LJ=8 units

ST=9 units

Step-by-step explanation:

step 1

we know that

The triangle ELT is a circumscribed triangle

so

EI=ES

LI=LJ

TS=TJ

EL=EI+LI ------> 14=EI+LI -----> 14=EI+LJ -----> equation A

LT=LJ+TJ----> 17=LJ+TJ ----> 17=LJ+TS ----> equation B

ET=ES+TS ---> 15=ES+TS----> 15=EI+TS ----> equation C  

Subtract equation A from equation C

15=EI+TS

14=EI+LJ

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

15-14=TS-LJ

TS=1+LJ ------> equation D

substitute equation D in equation B and solve for LJ

17=LJ+(1+LJ)

17=2LJ+1

2LJ=17-1

LJ=8

Find the value of TS

TS=1+LJ -----> TS=1+8=9

Find the value of EI

14=EI+LJ ------> 14=EI+8 ----> EI=14-8=6

therefore

EI=6 units

LJ=8 units

ST=9 units

Answer:

28 Gallons

Step-by-step explanation:

This one is really easy, so i want you to look at my steps:

1. Gather all given information, container is 3/4, 7 gallons are poured out to make it 1/2 full.

2. Find a common denominator for the fractions 1/2 and 3/4, this would be 4.

3. Make them both the same denominator, 2/4 and 3/4.

4. Subtract the remaining amount from the original amount to see how much 7 gallons made up, 3/4 - 2/4 = 1/4

5. Now that you know that 7 gallons made up 1/4 of the container, you can just multiply 7 by 4 to get the total amount of gallons that can fit in the container.

7 * 4 = 28 gallons is the max that the container can hold.

Answer:

28 gallons

Step-by-step explanation:

Got it right on test

Answer:

A) 8 kilograms

Step-by-step explanation:

"kilo-" is a prefix meaning 1000. So, 8 kilo-grams = 8 thousand grams = 8,000 grams.

To convert 8,000 grams to kilograms, divide by 1,000, resulting in 8 kilograms. Therefore, an object that weighs 8,000 grams would indeed weigh 8 kilograms, which is option A.

If an object weighs 8,000 grams and you want to convert it to kilograms, you need to know the conversion between grams and kilograms. In the metric system, one kilogram is equal to 1,000 grams. So, to convert grams to kilograms, you divide the number of grams by 1,000.

To calculate the weight of the object in kilograms from grams:

Therefore, an object that weighs 8,000 grams would weigh 8 kilograms, which corresponds to option A.

Answer:

The lateral area of the cylinder is [tex]24 \pi\ units^{2}[/tex]

Step-by-step explanation:

we know that

The lateral area of the cylinder is equal to

[tex]LA=2\pi rh[/tex]

step 1

Find the radius of the base of the cylinder

The area of the base is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]A=36 \pi\ units^{2}[/tex]

so

substitute and solve for r

[tex]36 \pi=\pi r^{2}[/tex]

Simplify

[tex]r=6\ units[/tex]

step 2

Find the lateral area

we have

[tex]r=6\ units[/tex]

[tex]h=2\ units[/tex]

substitute the values

[tex]LA=2\pi (6)(2)=24 \pi\ units^{2}[/tex]

Answer:

  6y -8

Step-by-step explanation:

Use the distributive property. It tells you the product can be simplified to the product of the outside factor and each of the individual terms in parentheses:

  2(3y - 4) = 2·3y + 2·(-4) = 6y -8

Answer:

x = 1/14

Step-by-step explanation:

You can work it as is by subtacting ln(14), then taking antilogs:

ln(x) = -ln(14)

x = 14^-1

x = 1/14

___

Or you can rewrite to a single log and then take antilogs:

ln(14x) = 0

14x = 1

x = 1/14 . . . . . divide by the coeffient of x

Answer:

  see below

Step-by-step explanation:

This is solved by simplifying each expression and identifying the column heading it matches.

1. (6 x^2/(x^2 - 7 x + 10)) / (2 x)/(x - 5))

= (6 x^2/(x^2 - 7 x + 10)) · (x -5)/(2 x) . . . . invert and multiply

= (6x^2)/(2x) · (x -5)/((x -2)(x -5)) . . . . . . . factor so common factors can cancel

= 3x/(x -2) . . . . matches column 1

__

2. (x - 4) (x + 2)/(x^2 + 5 x + 6) + (-3 x^2 + 24 x - 20)/((x + 3) (4 x - 5))

= (x -4)(x +2)/((x +3)(x +2)) + (-3x^2 +24x -20)/((x +3)(4x -5)) . . . factor

= (x -4)/(x +3) + (-3x^2 +24x -20)/((x +3)(4x -5)) . . . . cancel common factor

= ((x -4)(4x -5) +(-3x^2 +24x -20))/((x +3)(4x -5)) . . . . use common denominator

= (4x^2 -21x +20 -3x^2 +24x -20)/((x +3)(4x -5)) . . . expand product

= (x^2 +3x)/((x +3)(4x -5)) . . . . . . collect terms

= (x)(x +3)/((x +3)(4x -5)) . . . . . . factor numerator

= x/(4x -5) . . . . . . . . . . . . . . . . . . cancel common factor ... matches column 2

__

3. 3 x^2/(x + 3) · (2 x + 6)/(2 x^2 - 4 x)

= 3·2·x·(x +3)/((x +3)(2·x)(x -2)) = 3/(x -2) . . . . matches column 1

__

4. 3 x/(4 x - 5) - 4 x^2/(8 x^2 - 10 x)

= 3x/(4x -5) - 4x^2/(2x(4x -5)) = (3x -2x)/(4x -5) = x/(4x -5) ... matches col 2

__

5. 5 x^2/(x - 2) · (2 x + 6)/(8 x^2 - 4 x) . . . . no match (has a denominator factor of 2x-1 that doesn't cancel any numerator factors)

__

6. -x/(4 x - 5) - 4 x^2/(16 x^2 - 22 x)

In order to match one of the columns, the term on the right must reduce to 2x/(4x-5), which it does not, or must have a denominator factor of x-2, which it also does not. no match.

Answer:

a=216.

Step-by-step explanation:

What you do is you need to get a by itself.

a/6-11=25. You first add 11 to both sides.

a/6=36. Next you will times 6 on both sides to get

a=216 as your answer.

Answer:

  C. not similar, dilations are involved

Step-by-step explanation:

For geometric figures, such as triangles, we generally study a couple of kinds of transformations.

One is the "rigid transformation" which lets us move, rotate, or reflect the figure any way we like, but we keep it the same size—as though it were cut from cardboard or anything else that holds its shape and size. Any figures transformed by a rigid transformation are congruent.

Another is very much like the "rigid transformation", but dilation is involved. That is, the figure is allowed to be stretched or shrunk uniformly (by the same factor in every direction). Figures transformed in this way are similar, but are not congruent.

In this diagram, your triangle has been reflected and changed in size by a different factor horizontally than vertically. Hence dilation is involved (answer choices A or C), but because the factors are different, the figures are not similar (answer choice C).

_____

Comment on the answer choices

Rotations may be involved in similarity transformations, too. For some reason, that possibility was left off of choices A and C. (On the other hand, rotation is equivalent to a suitable set of reflections.)

i jus want some point bro

Answer:

the correct answer is the 3rd one

Answer:

the third option is correct

Step-by-step explanation:

Answer:

  (2a +b)·(13a^2 -5ab +b^2)

Step-by-step explanation:

The factorization of the difference of cubes is a standard form:

  (p -q)^3 = (p -q)(p^2 +pq +q^2)

Here, you have ...

so the factorization is ...

  (3a -(a -b))·((3a)^2 +(3a)(a -b) +(a -b)^2) . . . . substitute for p and q

  = (2a +b)·(9a^2 +3a^2 -3ab +a^2 -2ab +b^2) . . . . simplify a bit

  = (2a +b)·(13a^2 -5ab +b^2) . . . . . . collect terms

Example:

 a) mutually exclusive

 b) not mutually exclusive

 c) not mutually exclusive

Your Turn:

 a) not mutually exclusive

 b) not mutually exclusive

 c) not mutually exclusive

 d) mutually exclusive

Events are mutually exclusive if they cannot both occur together. Otherwise, they are not mutually exclusive.

Example

 a) the winner cannot be both a junior and a senior — mutually exclusive

 b) the winner could be a female sophomore — not mutually exclusive

 c) the winner could be a male freshman — not mutually exclusive

___

Your Turn

 a) the card could be the ace of clubs — not mutually exclusive

 b) the number could be divisible by both 5 and 10 — not mutually exclusive

 c) the card could be the 5 of hearts — not mutually exclusive

 d) the result cannot be both 6 and 7 — mutually exclusive

The perimeter of a triangle is just adding all the sides.

So, (2x)+(4x-2)+(3x-1)= 9x-3

So, the answer is D, 9x-3

Answer:

D.

Step-by-step explanation:

The perimeter = the sum of the 3 sides.

Perimeter = 2x + 4x - 2+ 3x - 1

=  9x - 3.

Answer:

t ≤ -3

Step-by-step explanation:

5t ≤ -15

You are solving for t. That means you want t alone on the left side. t is being multiplied by 5. To get rid of a multiplication by 5, you do the opposite operation, and you divide by 5. You must do the same operation to both sides of an inequality, so you must divide both sides by 5.

5t/5 ≤ -15/5

t ≤ -3

Answer:

The equation of the line is y = 3/2x + 5/2

Step-by-step explanation:

To find the equation of this line, start by using the two points with the slope formula to find the slope.

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

m = (4 - 1)/(1 - -1)

m = 3/(1 + 1)

m = 3/2

Now that we have the slope, we can use that and either point in point-slope form to find the equation.

y - y1 = m(x - x1)

y - 4 = 3/2(x - 1)

y - 4 = 3/2x - 3/2

y = 3/2x + 5/2

Answer:

i also need the answer to this question

Step-by-step explanation:

Answer:

y= 8x +18

Step-by-step explanation:

The probability that the arrow will land on any of them once is 1/4.

The probability that the arrow will land on any of them twice is 1/4 * 1/4. This is because the probability of Event A and Event B is P(B) * P(A).

Based on this:

[tex]P(a\cap b\cap c\cap d) = \frac{1}{4}\times \frac{1}{4}\times\frac{1}{4}\times\frac{1}{4}\\\\=\frac{1}{4\times4\times4\times 4}\\=\frac{1}{256}[/tex]

1/256

Hope this helps, let me know if I missed anything!

Answer:

1/256 or 2/512

Step-by-step explanation:

Answer:

  90

Step-by-step explanation:

The total number of "ratio units" is 9+6 = 15, so each one must stand for 225/15 = 15 people. Then 6·15 = 90 people were snowboarders who bought season passes.