What is the least common multiple of x^2-16 and
x^2+4x-32?

.........................

I will set it up.

Let a = adults

Let s = seniors

The first equation is a + s = 325.

The second equation is 9a + 7s = 2504.

Here is your system of equations:

{a + s = 325

{9a + 7s = 2504

Take it from here.

Answer:

LCM = 2^4 x 5^1 x 7^1 = 560

Step-by-step explanation:

Answer:

75%, or 7

Step-by-step explanation:

100-25=75

75% of 9 is 6.75 (because 9x0.75)

so we can round to 7, unless there's a decapitated reindeer involved

Answer: 6.75

Step-by-step explanation:

for this math problem we need to find the percentage and subtract that from the original number ( 9 ) . . .

what is 25% if 9 ? 2.25

what is 9 - 2.25 ? 6.75

x = 64

since , it is vertically opposite

The given triangles ΔDOA and ΔABC are right triangles that have a

common vertex at point A.

Reasons:

The given parameters are;

The diameter of the circle with center O = AB

DO ⊥ AB (DO is perpendicular to AB)

Required:

Prove that ∠AEC = ∠ODA

A two column proof is presented as follows;

Statement [tex]{}[/tex]                                                 Reason

1. AB is the diameter of circle     [tex]{}[/tex]                 1. Given

2. DO is perpendicular to AB [tex]{}[/tex]                     2. Given

3. ∠DOA = 90° [tex]{}[/tex]                                             3. Definition of DO ⊥ AB

4. ∠BCA = 90°   [tex]{}[/tex]                                             4. Thales theorem

5. ∠BCA ≅ ∠BCA [tex]{}[/tex]                                         5. Reflexive property

6. ΔDOA ~ ΔABC   [tex]{}[/tex]                                        6. AA similarity postulate

7. ∠ABC ≅ ∠ODA   [tex]{}[/tex]                                       7. CASTC

8. ∠ABC = ∠ODA   [tex]{}[/tex]                                        8. Definition of congruency

9. ∠AEC ≅ ∠ABC   [tex]{}[/tex]                                        9. Angles in the same segment

10. ∠AEC = ∠ABC   [tex]{}[/tex]                                       10. Definition of congruency

11. ∠AEC = ∠ODA   [tex]{}[/tex]                                        11. Transitive property of equality

In statement 6, ΔDOA is similar to ΔABC by Angle-Angle, AA, similarity

postulate, therefore, the three angles of ΔDOA are congruent to the three

angles of ΔABC.

Therefore ∠ABC ≅ ∠ODA by Corresponding Angles of Similar Triangles

are Congruent, CASTC.

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If f(n) = f(n - 1) + 4, then

f(n - 1) = f(n - 2) + 4

and substituting this into the first equation gives

f(n) = f(n - 2) + 2•4

Similarly,

f(n - 2) = f(n - 3) + 4

so that

f(n) = f(n - 3) + 3•4

and so on.

Note the pattern:

f(n) = f(n - k) + k•4

so that when k = n - 1, we have

f(n) = f(n - (n - 1)) + (n - 1)•4

or

f(n) = f(1) + 4 (n - 1)

so that

[D] f(n) = -2 + 4 (n - 1)

Answer:

y=log_2 (x)

Step-by-step explanation:

We see that the graph passes though the point (2,1). So we can write:

log_a (2) = 1  => a = 2

So it's a log in base 2.

Stacy sold 15 children tickets and 30 adult tickets.

The tickets are $7 for adults and $4 for children.

She sells twice as many adult tickets as children tickets and bring in a total of $270.

Therefore,

let

number of children ticket sold = x

number of adult ticket sold = 2x

7(2x) + 4(x) = 270

14x + 4x = 270

18x = 270

x = 270 / 18

x = 15

The number of children ticket sold = 15

The number of adult ticket sold = 15 × 2 = 30

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Answer:30 drinks

Step-by-step explanation:

Step-by-step explanation:

we use the law of sine :

sin(A)/a = sin(B)/b = sin(C)/c

with the related angles being opposite of the lines.

so, we have

sin(A)/1 = sin(A) = sin(90)/ sqrt(10) = 1/ sqrt(10) =

= 0.316227766...

cos²(A) + sin²(A) = 1

cos(A) = sqrt(1 - sin²(A)) = sqrt(1 - 0.1)) = sqrt(0.9) =

= 0.948683298...

tan(A) = sin(A)/cos(A) = 0.333333333...

cot(A) = 1/tan(A) = 3

sec(A) = 1/cos(A) = 1.054092553...

csc(A) = 1/sin(A) = 3.16227766...

Answer:

they are the same

Step-by-step explanation:

6x - 2x + 4 ← collect like terms

= 4x + 4

and

4(x + 1) ← distribute parenthesis by 4

= 4x + 4

The 2 expressions are equivalent to 4x + 4

Answer:

No, Jamie is incorrect

Step-by-step explanation:

No, because in the expression 4(x+1)  you will first need to multiply 4 by x, your result is 4x, and then you multiply 4 by 1, you get 4, so the answer will be 4x+4.

Also in the expression 6x-2x+4  ,you will first need to subtract 2x from  6x, your result is 4x ,and then you add 4 , so the answer will be 4x + 4

Our final answer is:

6x-2x+4 = 4x + 4 and 4(x+1) = 4x + 4

The vertices of the feasible region of the constraints is (0,2.5)

The constraints are given as:

x + 3y ≤ 6

4x + 6y ≥ 9

x ≥ 0,  y ≥ 0

Express the inequalities as equations

x + 3y = 6

4x + 6y = 9

Make x the subject in x + 3y = 6

x = 6 - 3y

Substitute x = 6 - 3y in 4x + 6y = 9

4(6 - 3y) + 6y = 9

Expand

24 - 12y + 6y = 9

Evaluate the like terms

-6y = -15

Divide by 6

y = 2.5

Substitute y = 2.5 in x = 6 - 3y

x = 6 - 3 * 2.5

Evaluate

x = -1.5

So, we have:

(x,y) = (-1.5, 2.5)

Recall that: x ≥ 0,  y ≥ 0

This means that the feasible region must have positive coordinates or zero

So, we set x = 0

(x,y) = (0, 2.5)

Hence, the vertices of the feasible region of the constraints is (0,2.5)

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I'll help.

The answer to your question is True!!

Answer:

It's attached

Step-by-step explanation:

y=4/3x-4

is the equation for the line

So you just plot the line.

The equation for the given slope and point is y = 4x/3 - 4

The slope of a line is a number that describes both the direction and the steepness of the line.

Given that, a line that has a slope of 4/3 and contains the point (0,-4)

The slope intercept of a line is y = mx+c, where m is slope,

Here, m = 4/3, x = 0 and y = -4

Finding for c,

-4 = 4/3x0+c

c = -4

Establishing the equation,

y = 4x/3-4

Now plotting the graph,

(Attached)

Hence, the graph will pass through the points (3,0) and (0,-4)

For more references on slope, click;

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its d becuase i used math-way

Step-by-step explanation:

b

=

4

Answer:

Step-by-step explanation:

Given equation:

Add 12 to both sides:

Correct graph is D, where point 4 is marked

Answer:

y = 1/2x + 3

Step-by-step explanation:

Y= mx+b is slope-intercept form, m is for slope, and b is for my y-intercept. Also remember the pitch is the rise over the run or the y-direction over the x-direction.

In our case, they highlight 2 points to calculate the slope; looking at the graph, we can see it rises one and runs two to get to the second highlighted point at (2,4). And my slope is rise over run, so here it 1/2.

My b or y-intercept is simply three because that is where the line passes over or intercepts the Y-axis

Answer: y = 1/2 x + 3

Step-by-step explanation:

Answer:

its 54

Step-by-step explanation:

Answer:

the answer is 6

Step-by-step explanation:

4 to the 3 power is 64

64-4=60

2x5=10

60/10=6

[tex]\text{Given that,}\\\\(x_1,y_1) = (1,-2)~~ \text{and}~~ (x_2,y_2) = (3,-4)\\\\\text{Slope,}~ m= \dfrac{y_2-y_1}{x_2 -x_1} = \dfrac{-4+2}{3-1} = -\dfrac 22 = -1\\\\\text{Equation with given points,}\\\\y-y_1 = m(x-x_1)\\\\\implies y +2 = -1(x-1)\\\\\implies y = -x+1 -2\\\\\implies y = -x-1\\\\\text{This is the slope-intercept form(y =mx+b).}[/tex]

Answer:

y=-x-1

Step-by-step explanation:

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

m=(-4-(-2))/(3-1)

m=(-4+2)/2

m=-2/2

m=-1

y-y1=m(x-x1)

y-(-2)=-1(x-1)

y+2=-x+1

y=-x+1-2

y=-x-1

Pedro has $13.65 in his wallet left.

Pedro had $14.90 in his wallet.

He spent $1.25 on a drink.

How much does he have left: 14+90 - 1.25 = 13.65

Pedro has $13.65 in his wallet left.

The difference is $1.95.

Problem solving is the act of defining a problem; determining the cause of the problem; identifying, prioritizing, and selecting alternatives for a solution; and implementing a solution.

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Answer:

Let x be the number of dimes and y the number of quarters

x +y = 100

a dime is $0.10 and a quarter is $0.25

0.1x + 0.25y = 21.40 multiply by 100 to remove the decimals

10x + 25y = 2140, From the first equation y = 100 - x and plug it in to the second equation.

10x + 25(100 -x) = 2140

10x + 2500 - 25x =2140

2500 - 15x = 2140

360 = 15x x = 24 and y = 76

There are 24 dimes and 76 quarters

Answer:

76 Quarters = $19.00

24 Dimes = $2.40

$19.00 + $2.40 = $21.40

Step-by-step explanation:

Yaga

Answer:

m>15

Step-by-step explanation:

Divide both sides by 2

Hello there! :-)

This is a one-step inequality, which means we can solve it in one step.

The goal is to find m.

To isolate m, we divide both sides by 2:

m>15

Remember to divide both sides by 2.

Therefore, m>15 (this means m is greater than 15)

Hope it helps. Use the comment section to clarify your doubts.

Answered by

~A felicitous teen who helps others :-)

Good luck with your studies. :)

Answer:

rise over run

Step-by-step explanation:

you look at the distance between the 2 points by looking at how many points its goes up or down, and you look at how points it goes from the left to the right or vice versa. but if you don't have a graph to look at, you will want to use the slope formula. look up the slope formula and plug it in.

Answer:

Step-by-step explanation:

From the point one on the graph, you go up (rise) making loops each time you go up (shown in red) then, once you've reached the same hight of point two, you go over (run), making loops once again (shown in blue). Then, you take the rise and put it over the run, so in the image attached it would be 4/3.

Answer: pretty sure -7

Step-by-step explanation:

Answer:

-7

Step-by-step explanation:

(-80) - (-10) is -79

-70 / (+10) = -7

Answer:

b

Step-by-step explanation:

took the test a bit ago

0.99 /3 = 0.33 per peach

0.33 per peach x 5 peaches = 1.65 total

Answer: $1.65

Answer:

1.65

Step-by-step explanation:

Answer:

LQ = 54

Median = 69

UQ = 94

Step-by-step explanation:

This list is already sorted for you, so you don't need to worry about that, otherwise you would need to sort the numbers in ascending order. To find the median, we do [tex]\frac{n+1}{2}[/tex], where n is the amount of numbers. This gives us 4, so the median is at position 4, so the median is 69. The lower quartile is simply [tex]\frac{n+1}{4}[/tex], so 2, so the lower quartile is 54. The upper quartile is [tex]\frac{n+1}{2} X 3[/tex], so 6, so the upper quartile is 94.