A storage container leaks water at a rate of 15 gallons every 30 days.

What is the unit rate in gallons per week?

Enter your answer as a mixed number in simplest form in the box.

Answer: i think you should label it with numbers first

maybe??

Step-by-step explanation:

Answer:

  (a)  (2x +7), (x -4)

  (b)  (-7/2, 0), (4, 0)

Step-by-step explanation:

When looking for integer factors of a quadratic of the for ax² +bx +c = 0, it is useful to start by looking for factor pairs whose product is a·c and whose sum is b.

Here, that means you're examining the factors of 2·(-28) = -56, and looking for a pair that have a sum of -1. We can start by examining the ways that -56 can be factored:

  -56 = -56(1) = -28(2) = -14(4) = -8(7)

Sums of these factor pairs are -55, -26, -10, -1, so it is the last pair we're interested in.

At this point, you can rewrite the x-term using these factors and then factor the quadratic by pairs.

  2x² -8x +7x -28 = 0 . . . . . . . use -x = -8x+7x

  (2x² -8x) +(7x -28) = 0 . . . . group into pairs of terms

  2x(x -4) +7(x -4) = 0 . . . . . . factor each pair of terms

  (2x +7)(x -4) = 0 . . . . . . . . . the factored equation

The factors of this equation are (2x +7) and (x -4).

__

The x-intercepts are the values of x that make the factors zero.

  2x +7 = 0 . . . looking for x that makes the first factor zero

  2x = -7 . . . . . subtract 7

  x = -7/2 . . . . divide by the coefficient of x

__

  x -4 = 0 . . . . looking for x that makes the second factor zero

  x = 4 . . . . . . add 4

The x-intercepts are x = -7/2 and x = 4.

[tex]\orange{••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

[tex]\huge\bold\orange{QUESTIONS:}[/tex]

3. Given this quadratic equation, 2x²-x-28= 0.

(a) List the factors of this equation.

(b) Determine the x-intercepts

[tex]\orange{••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

[tex]\huge\bold\orange{ANSWER:}[/tex]

(a) (x-4) and (2x+7)

(b) x=4 and x=-7/2

[tex]\orange{••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

[tex]\huge\bold\orange{SOLUTION:}[/tex]

[tex]\orange{••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

#CarryOnlearning

Using the arrangements formula, it is found that there are 720 words that can be formed.

The number of possible arrangements of n elements is the factorial of n, that is:

[tex]A_n = n![/tex]

In this problem:

[tex]T = 6 \times 5! = 6! = 720[/tex]

There are 720 words that can be formed.

To learn more about the arrangements formula, you can take a look at https://brainly.com/question/24648661

Answer:

$37,396

Step-by-step explanation:

take 2388.5x4 since there are 4 weeks = $9554

then you subtrct since the portfolio fell.

So $46,950-9554 = $37,396

Answer:

$0.35

Step-by-step explanation:

A gallon is equal to 16 cups, so the 3-gallon jug is equal to 48 cups. You when then divide $16.80 by 48, to get $0.35 or the price per cup! Hope this helps :)

Answer:

0.35

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given:

y1 = 5.2

y2 = 1

x1 = 0

x2 = -1.5

Solution:

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

m = ( 1 - 5.2 ) / ( -1.5 - 0 )

m = -4.2 / -1.5

m = 2.8

then

y - y1 = m ( x - x1 )

y - 5.2 = 2.8 ( x - 0 )

y - 5.2 = 2.8x - 0

y = 2.8x + 5.2

Answer:

Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.

Step-by-step explanation:

The total number of cars both the student and the teacher made is 49

let

total cars = x

cars made by student = s

cars made by teacher = t

Total = student + teacher

x = s + t

s = 2/7x

So,

x = 2/7x + t

x - 2/7x = t

t = (7x - 2x) / 7

t = 5/7x

Similarly,

s = t - 21

s = 5/7x - 21

equate both s equation

2/7x = 5/7x - 21

2/7x - 5/7x = -21

(2x - 5x) / 7 = -21

- 3/7x = -21

x = -21 ÷ -3/7

= -21 × - 7/3

= (-21 × -7) / 3

= 147/3

x = 49

Therefore, the total number of cars both the student and the teacher made is 49

Learn more about fractions:

https://brainly.com/question/11562149

Answer:

People who bought tickets = 100%

                                             = 8000

People who bought their tickets in person = (100%-60%-15%) × 8000

                                                                       = 2000

The number of tickets sold online is 4800, by phone is 1200, and in person is 2000.

The Percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that there were 8000 people at the festival. people bought their tickets online, by phone, or in person. based on a random sample of people at the festival, 60% bought their tickets online, and 15% bought their tickets by phone.

The number of the tickets will be calculated as below:-

Total tickets = 8000

Online tickets = 60% of 8000 = 8000 x 0.6 = 4800

By phone = 15% of 8000 = 8000 x 0.15 = 1200

In-person = 25% x 8000 = 0.25 x 89000 = 2000

Therefore, the number of tickets sold online is 4800, by phone is 1200, and in person is 2000.

To know more about percentages follow

https://brainly.com/question/24304697

#SPJ2

Answer:

A(0,3)

Step-by-step explanation:

the line crosses y-axis so its x-coordinates must be zero,

so we subistitute by x=0 in the equation of the line, from this we get y=3

then the coordinates of point A will be (0,3)

The cost of the 6 books if you buy the set is $11.75 less.

The given parameters:

The total cost of the 6 books when bought separately is calculated as follows;

Cost = 6 x $38.25

Cost = $229.5

The difference in price is calculated as follows;

= $241.25 - $229.5

= $11.75

Thus, the cost of the 6 books if you buy the set is $11.75 less.

Learn more about cost price here: https://brainly.com/question/19104371

Answer:

D

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Answer:

13 cm

Step-by-step explanation:

The scale of the drawing was 1 centimeter : 4 meters.

x cm : 52 m   Divide by 4

13 cm : 52 m

Answer:

45

Step-by-step explanation:

I think so i dont know

Answer:

45

Step-by-step explanation:

Just do the regular number sequence (1-44) but add 1 since this specific sequence starts with 2.

Answer:

Figure a) 2

figure b) 4

figure c) 5

Step-by-step explanation:

Answer:

heart

Step-by-step explanation:

Answer:

  heart

Step-by-step explanation:

The 36th shape will be the last shape in the 12th repeat of the sequence.

The 35th shape is next-to-last: heart.

Answer:

To prove: The equation x2+px−1=0 has real and distinct roots for all real values of p.

Consider x2+px−1=0

Discriminant D=p2−4(1)(−1)=p2+4

We know p2≥0 for all values of p

⇒p2+4≥0 (since 4>0)

Therefore D≥0

Hence the equation x2+px−1=0 has real and distinct roots for all real values of p

The expression [tex]\rm \dfrac{15}{x-6}+\dfrac{7}{x+6}[/tex] is equivalent to  [tex]\dfrac{22x+48}{x^2-36}\\\\[/tex]  and it can be determined by using LCM and fraction.

[tex]\rm \dfrac{15}{x-6}+\dfrac{7}{x+6}[/tex]

If no denominator equals zero,

Which expression is equivalent to the given expression?

Expression;

[tex]\rm \dfrac{15}{x-6}+\dfrac{7}{x+6}[/tex]

If no denominator equals zero,

To determine the equivalent relation of the given equation following all the steps given below.

                   [tex]\rm= \dfrac{15}{x-6}+\dfrac{7}{x+6}\\\\=\dfrac{15(x+6) + 7(x-6)}{(x-6) (x+6)}[/tex]

                   [tex]\rm=\dfrac{15(x+6) + 7(x-6)}{(x-6) (x+6)}\\\\= \dfrac{15x+90 + 7x-42}{x(x+6) -6 (x+6)}\\\\= \dfrac{22x+48}{x^2+6x -6 x-36}\\\\= \dfrac{22x+48}{x^2-36}\\\\[/tex]

Hence, The expression [tex]\rm \dfrac{15}{x-6}+\dfrac{7}{x+6}[/tex] is equivalent to  [tex]\dfrac{22x+48}{x^2-36}\\\\[/tex] .

For more details about Expression refer to the link given below.

https://brainly.com/question/14610993

Answer:

(6 + n) - 8

Hope this helps.

Pls mark brainliest. :D

Answer:x < 2

Step-by-step explanation: 6+x < 8

x < (8-6)

x < 2

a) Since the corresponding y-value is -0.6, hence the point (-0.8, -0.6) is a solution to the system of  equations

b) since  the corresponding x-value is not 1/3, hence the point (1/3, 2) is not a solution to the system of  equation

In order to show if the given point corresponds to the given function, we will have to substitute the value of x into the function to see if we will have its corresponding y-value

For the point (-0.8, -0.6), substitute x = -0.8 into both functions as shown:

f(x)  = 2x + 1

f(-0.8) = 2(-0.8) + 1

f(-0.8) = -1.6  + 1

f(-0.8) = -0.6

Simiarly;

y = -3(-0.8)- 3

y = 2.4 - 3

y = -0.6

Since the corresponding y-value is -0.6, hence the point (-0.8, -0.6) is a solution to the system of  equations

For the point (1/3, 2), substitute x = 1/3 into both functions as shown:

x = (y+2)/2

x = (2+2)/2

x = 4/2

x = 2

Simiarly;

x + 2 = 3

x = 3-2

x = 1

Since the corresponding x-value is not 1/3, hence the point (1/3, 2) is not a solution to the system of  equations

Learn more on systems of equation here: https://brainly.com/question/847634

Answer:

697.19248074 is the answer

Answer:62

Step-by-step explanation:

2 times 5=10-5=5

8 times 7=56+7= 63-6=57+5=62!

No solution. hope this helps

Step-by-step explanation:

(note: I'm only answering the ones I know vs giving you wrong answers for the others!)

1. ROS=Obtuse (larger then ninty degrees)

2. octagon has 8 angles (octo means eight, after all!)

3. If a figure has three sides, it is a triagle (not positive on this one)

4. symmetric property of congruence (this one's a simple search :p )

5. N/A (although I believe its angle BEC=124 degrees, as every other choice Is proven to be true)

6. congruent complements theorem (this is because we are given that 3 is a suppliment of 4. we are also given that 2=4. Based on this, then 1=3 is congruent based on 1 being suppliment of 2, 2=4, and 3 being a suppliment of 4)

7. N/A

8. N/A (the picture is too fuzzy for me to make any ideas)

I'm sorry I couldn't solve them all, but I hope this at least gets you somewhere! Have a great day!

Answer:

y= 0.75x + -0.50

A or B is what im guessing

Answer:

24cm

Step-by-step explanation:

because 6 x 4 = 24 centimeters

As the distance from the lighthouse, LH, increases, the angle of elevation,

reduces.

Reasons:

The distance of point A from the light house = 968 feet

Angle of elevation from point A to the lighthouse = 7°

Angle of elevation from point B to the lighthouse = 3°

Required:

The distance from point A to point B.

Solution:

[tex]\displaystyle tan(\theta) = \frac{Opposite \, side \, to\, angle}{Adjacent\, side \, to\, angle} = \mathbf{\frac{Height \ from \ sea \ to \ the \ light \ house }{Horizontal \ from \ boat \ to \ the\ LH}}[/tex]

Which gives;

[tex]\displaystyle tan(7^{\circ}) = \mathbf{\frac{Height \ from \ sea \ to \ the \ light \ house }{968 \ feet}}[/tex]

Height to the lighthouse = tan(7°) × 968 feet  ≈ 118.86 feet

From point B, we have;

[tex]\displaystyle tan(3^{\circ}) = \mathbf{ \frac{118.86 \ feet }{Horizontal \ distance \ from \ point \ B\ to \ LH}}[/tex]

Therefore;

[tex]\displaystyle Horizontal \ distance \ from \ boat \ to \ LH = \frac{118.86 \ feet }{tan(3^{\circ})} \approx \mathbf{2237.9 \, feet}[/tex]

Therefore;

Distance from A to B = D

D = Horizontal distance from B to LH - Horizontal distance from A to LH

Distance from A to B = 2237.9 feet - 968 feet ≈ 1269.9 feet

The distance from point A to point B, D ≈ 1,269.9 feet

Learn more about trigonometric ratios here:

https://brainly.com/question/16577559

https://brainly.com/question/9107775

Answer:

The answer is C, y = 2/3x -2

Step-by-step explanation:

Use the rise over run strategy on linear functions such as this one

Answer:

Hopefully this explains o_O, also Merry Christmas!

Step-by-step explanation:

9 x 10^2 = 9 x 100 = 900

3 x 10^-2 = 3 x 1/100 = 0.03

Ratio of 900:0.03

The first one is 30000 bigger than the second