A triangle has an area of 48 square feet. The height of the triangle is 8 ft. What is the length of the base of the triangle?

Answer:

x=8

Step-by-step explanation:

Answer:

The system is of equations is:

[tex]\left\{ \begin{array}{ll} 10g+15r=725 & \quad \\ g+r=60 & \quad \end{array} \right.[/tex]

Where g is the amount of general tickets and r is the amount of reserve tickets.

35 general tickets and 25 reserve tickets were sold.

Step-by-step explanation:

Let general tickets be represented by g and reserved tickets be represented by r.

Each general ticket sells for $10 each and reserved tickets $15 each. Dave collected a total of $725. Thus:

[tex]10g+15r=725[/tex]

And a total of 60 tickets were sold. Hence:

[tex]g+r=60[/tex]

Our system of equations is:

[tex]\left\{ \begin{array}{ll} 10g+15r=725 & \quad \\ g+r=60 & \quad \end{array} \right.[/tex]

We can solve by substitution. First, divide both sides of the first equation by 5:

[tex]2g+3r=145[/tex]

Next, we can subtract a variable (r in this case) from the second equation:

[tex]g=60-r[/tex]

Substitute:

[tex]2(60-r)+3r=145[/tex]

Distribute:

[tex]120-2r+3r=145[/tex]

Simplify:

[tex]120+r=145[/tex]

Subtract:

[tex]r=25[/tex]

Using the previous equation:

[tex]g=60-r[/tex]

Substitute and evaluate:

[tex]g=60-(25)=35[/tex]

So, 35 general tickets and 25 reserve tickets were sold.

Answer:

i

Step-by-step explanation:

Answer:

12 feet

Step-by-step explanation:

use the pythagorean theorem to figure out what the hypotenuse is

3.5^2+3.5^2=x^2

12.25+12.25=x^2

25=x^2

x=5

now that you know the hypotenuse, you can find the perimeter by adding up all the sides

3.5+3.5+5=12

x > 3

(adding extra characters so its over 20)

Answer:

[tex]\frac{dA}{A} = -\frac{1}{70} dt[/tex]

A(t) = [tex]40 e^{-\frac{t}{70}}[/tex]

Step-by-step explanation:

Given - A tank contains 350 liters of fluid in which 40 grams of salt is dissolved. Pure water is then pumped into the tank at a rate of 5 L/min; the well-mixed solution is pumped out at the same rate. Let the A(t) be the number of grams of salt in the tank at time t.

To find - Find the rate at which the number of grams of salt in the tank is changing at time t.

Find the number A(t) of grams of salt in the tank at time t.

Proof -

Given that,

Total fluid in the tank = 350 litres

Total salt = 40 grams

Rate in flow = 5 L/min

Rate out flow = 5 L/min

Concentration in = 0

Concentration out = (Amount of salt at time t )/ (Solution in tank at time t)

Now,

Total solution in the tank at time t = Total fluid in the tank + (Rate in flow - Rate out flow )t

                                                        = 350 + (5 - 5)t

                                                        = 350

⇒Solution in the tank at time t = 350

⇒Concentration out = [tex]\frac{A(t)}{350}[/tex]

Now,

Rate of change in the tank at time t = [tex]\frac{dA}{dt}[/tex]

                                                           =  (Rate in flow )( Concentration In) - (Rate out flow )( Concentration out)

                                                           = 5(0) - 5([tex]\frac{A(t)}{350}[/tex])

                                                           = 0 - [tex]\frac{A(t)}{70}[/tex]

                                                           = [tex]-\frac{A(t)}{70}[/tex]

⇒[tex]\frac{dA}{dt}[/tex] = [tex]-\frac{A(t)}{70}[/tex]

⇒[tex]\frac{dA}{A} = -\frac{1}{70} dt[/tex]

Integrate both sides , we get

ln(A) = [tex]-\frac{1}{70}t + C[/tex]

⇒A(t) = [tex]e^{-\frac{t}{70}+ C}[/tex]

         = [tex]e^{-\frac{t}{70}}*e^{C}[/tex]

         = [tex]C_{1} e^{-\frac{t}{70}}[/tex]

⇒A(t) = [tex]C_{1} e^{-\frac{t}{70}}[/tex]

Now,

Given that,

Initially, the tank has 40 grams of salt

⇒A(0) = 40

⇒C₁ = 40

⇒A(t) = [tex]40 e^{-\frac{t}{70}}[/tex]

Answer:

y=3x^2 -15x-42

Step-by-step explanation:

Answer:

y = -x +2

Step-by-step explanation:

First let's find the slope.

(-1,3) and (4,-2)

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

Slope = -1

Now let's use slope intercept form:

y1-y2=m(x1-x2)

Let's plug in our slope for m.

y1-y2= -1 (x1-x2)

And now let's substitute y2 and x2 for one of our points, I'll use (4,-2)

y1+2 = -1(x1- 4)

y= -x + 4 -2

y = -x +2

Answer:

B, C, D

Step-by-step explanation:

Those are the equivalent ratios, look where the umbers are placed in the question to where they are placed in the ratio

Step-by-step explanation:

Per our conceptual understanding, when two parallel lines are cut by a transversal line then their corresponding angles are equal.

So, If PQ and RS are two parallel lines and line L1 as shown is the transversal line then the corresponding angles are equal.

Hence, ∠1 = ∠2Or, c0 = 1800 – c02c = 180c = 90°

Therefore, if we get c = 90° then PQ and RS are parallel else PQ and RS are not parallel,

With this understanding, let us now analyse the individual statements.

Step 3: Analyse Statement 1

“b = 2a”

Per conceptual understanding, the sum of all the angles of a triangle is 180.

Hence, a + b + c = 180a + 2a + c = 1803a + c = 180

However, from the above equation, we can get many values of a and c.

Hence, statement 1 is not sufficient to answer the question.

Step 4: Analyse Statement 2

“c = 3a”

a + b + c = 180a + b + 3a = 180b + 4a = 180

However, from the above equation, we can get many values of a and b.

Hence, statement 2 is not sufficient to answer the question.Step 5: Combine Both Statements Together (If Needed)

From statement 1:

3a + c = 180

From statement 2:

c = 3a

Combining both the statements:

3a + 3a = 180.

From the above equation, we can find the value of a. Then we can find c.

Since we could find the answer by combining both the statements, option C is the correct answer.

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Answer:

x>36

Step-by-step explanation:

Hope this helps and good luck

Answer:

it is C.

Step-by-step explanation:

we know,

14+17= 31

so if we subtarct 17 from 31 we get 14

and if we subtract 14 from 31 we get 17

Answer:

(a) 19%

(b) 5:6

Step-by-step explanation:

Given: Gh 258,000

salaries Gh 49,020

training Gh 72,000

housing Gh 60,000

entertainment Gh 12,000

exigencies Gh 23,020

(a) Percentage of the income spent on salaries = [tex]\frac{amount of salaries}{total income}[/tex] x 100

                           = [tex]\frac{49020}{258000}[/tex] x 100

                           = 0.19 x 100%

                           = 19%

The percentage of the income spent on salaries is 19%.

(b) Ratio of amount for housing to amount for training = [tex]\frac{amount for housing}{amount for training}[/tex]

                                = [tex]\frac{60000}{72000}[/tex]

                                = [tex]\frac{5}{6}[/tex]

The ratio of the amount for housing to the amount for training is 5:6

Answer:

She can invite 66 people so 66 x 5 = $330 + 120 = $450

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

if you can't use calculator, you must know that after a number being square root, it MUST be in positive

for the negative answer will be false

so for the rest of the answer you need to try it

3² = 9 < 10 so it's true

4² =16 > 10 so it's false

the only answer is 3

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Any 3 digit number can be expressed in the form of:

[tex](a*100)+(b*10)+(c*1)[/tex]

Where [tex]a, b, c[/tex] represent any natural number from 0 to 9.

We are told the hundreds number (this means [tex]a*100[/tex] in the expression above) is equal to the value of 40 tens, 40 tens is 400. Then, we know the digit in the tens is greater then 6, this means [tex]b>6[/tex] in the expression above.

So, there are multiple numbers the room number could be, namely:

[tex]400+(b*10)+(c*1)\\[/tex]

where [tex]b[/tex] can be 7, 8, or 9; and [tex]c[/tex] can be  0, 1, 2, 3, 4, 5, 6, 7, 8, or 9. So, there's 30 possible room numbers Lydia may be.

Answer:

20

Step-by-step explanation:

add 3ft+3ft+11ft+3ft and that's your answer

Answer:

-21

Step-by-step explanation:

GIven data

We are given the equation of a line as

Y=-2x-21

let us compare this with the general equation of a line

y=mx+c

from the comparison, we can see that the intercept is -21

Therefore, the intercept is -21

Answer:

$69.75

Step-by-step explanation:

$9 x 7 = $63

45 min/60 min = 0.75

$9 x 0.75 = $6.75

$63 + $6.75 = $69.75

Answer:

$69.75

Step-by-step explanation:

$9 x 7 hours = $63

$9 x 3/4 = $6.75

$63 + $6.75 = $69.75

I hope this helps :)

Answer:

31-9

Step-by-step explanation:

hers is 31 so if marcos is 9 in taller you just subtract it to get the height of his

Answer:

A) x = -3

Step-by-step explanation:

|3(-3) + 9| = 0

|-9 + 9| = 0

|0| = 0

0 = 0

Answer:

A)x=−3

Step-by-step explanation:

Step 1: Add -6 to both sides.

|3x+9|+6+−6=6+−6

|3x+9|=0

Step 2: Solve Absolute Value.

|3x+9|=0

We know 3x+9=0

3x+9=0(Possibility 1)

3x+9−9=0−9(Subtract 9 from both sides)

3x=−9

3x /3 = −9 /3

(Divide both sides by 3)

x=−3

Answer:

go everything youve learnt from grade 3 come right up

Step-by-step explanation:

sometimes its knowing the simply formulas thatll get you through

Answer:

The answer would be D

Step-by-step explanation:

Why? because as the temperature increases the amount of lemonade sold increases by 2

This is represented in 2(x) if that makes sense

For every 1-degree increase in high temp of the day, sales decrease by 2 glasses of lemonade. Then the correct option is D.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The function is given below.

f(x) = 2(x – 65) + 12

f(x) = 2x – 130 + 12

f(x) = 2x – 118

For every 1-degree increase in high temp of the day, sales increase by 2 glasses of lemonade. Then the correct option is D.

More about the linear equation link is given below.

https://brainly.com/question/11897796

#SPJ2

The missing options are given below.

a) for every 65-degree decrease in high temp of the day, lemonade sales increase by 1 glass of lemonade

b) for every 1-degree increase in high temp of the day, sales increase by 2 glasses of lemonade

c) for every 65-degree decrease in high temp of the day, sales decrease by 1 glass

d) for every 1-degree increase in high temp of the day, sales decrease by 2 glasses of lemonade

Answer:

852 students walking to school

Step-by-step explanation:

Lets start with a simple example so you can get it

if 60% of 100 students walk to school that means

60 students walk to school... right??

so lets simplify it more that means you have multiplied 100 (students) by 60%

or [tex]\frac{60}{100}[/tex]  (note: you can say that 60% is equal to [tex]\frac{60}{100}[/tex] )

so the problem told 60% of 1420 students walk to school that means we should

do this:     [tex]1420*\frac{60}{100} = 852[/tex]

Answer:

852 walk to school

Step-by-step explanation:

i got this because i divided the 1420 into 10 which became a 142, multiply by 6 and you get 852

also you could

it is really simple also, all you have to do is multiply the number of student, S times the precent of students who walk, so s times w, which is 60 precent turend into .6 precent so 1420 x .6