A steady stream of water flows into a partially-filled rectangular tank. After 6 minutes, there are 87 gallons of water in the tank. After 21 minutes, there are 222 gallons. Write an equation to represent the volume of water in the tank y after x minutes. How much water was in the tank to begin?

Answer:

Answer c): write the function in standard form

Step-by-step explanation:

To start with, it is important to write the polynomial in standard form, so as to have the two terms with the dependence in x together:

[tex]6x^2-42\,x+5[/tex]

then you extract 6 as a common factor of just the terms with the variable x:

[tex]6(x^2-7x)+5[/tex]

Then proceed to complete the square in the expression inside the parenthesis:

[tex]6(x^2-7x+\frac{49}{4} -\frac{49}{4})+5[/tex]

[tex]6\,((x-\frac{7}{2} )^2-\frac{49}{4} )+5\\6\,(x-\frac{7}{2} )^2-\frac{147}{2}+5\\6\,(x-\frac{7}{2} )^2-\frac{137}{2}[/tex]

Then, the function can be finally be written as:

[tex]f(x)=6\,(x-\frac{7}{2} )^2-\frac{137}{2}[/tex]

in vertex form

Answer:

C.) Write the function in standard form

Step-by-step explanation:

Answer:

x=3

Step-by-step explanation:

-2x-3=-9

Add 3 to each side

-2x-3+3=-9+3

-2x = -6

Divide by -2

-2x/-2 = -6/-2

x = 3

Answer:

x =3

Step-by-step explanation:

[tex]-2x-3=-9. \\ - 2x = - 9 + 3 \\ - 2x - 6 \\ \frac{ - 2x}{ - 2} = \frac{ - 6}{ - 2} [/tex]

[tex]x = 3[/tex]

Answer:

120

Step-by-step explanation:

12 x 6 = 72

8x(12/2)=48

72+48 =120

Answer:

Option A is the correct option.

Step-by-step explanation:

Let the points be A and B

A ( 2 , 2 ) ------> ( x1 , y1 )

B ( 3 , 5 ) -------> ( x2 , y2)

Now, let's find the mid-point :

Midpoint = [tex] (\frac{x1 + x2}{2} \:, \frac{y1 + y2}{2} )[/tex]

plug the values

[tex] = ( \frac{2 + 3}{2} \: , \frac{2 + 5}{2} )[/tex]

Calculate the sum

[tex] = \: ( \frac{5}{2} \:, \frac{7}{2} )[/tex]

Hope this helps..

Best regards!!

Answer:

1.5 rounded to the nearest tenth

Step-by-step explanation:

To find how much greater WBC are from RBC we do,

3.92 ÷ 2.6

= 1.50769230769

Which is 1.5 rounded to the nearest tenth.

Thus,

there are approximately 1.5 times WBC than RBC.

Hope this helps :)

The 1.5 times greater is the number of red blood cells than white blood cells

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

Adult humans have approximately 2.6 red blood cells and 3.92 white blood cells.

To find the number of times greater is the number of red blood cells than white blood cells:

Use division operation,

3.92 / 2.6

= 1.5076

≈ 1.5 rounded to the nearest tenth.

Therefore, the required number is 1.5 times.

To learn more about the division;

https://brainly.com/question/13263114

#SPJ5

Answer:

There are 200 girls in that school

Step-by-step explanation:

The correct and complete question is as folly;

In a school 3/5 pupils are boys. One day 1/6 of the boys were absent when 250 boys were present. How many girls are in the school?

SOLUTION

Let the total number of students in the school be x students

Since 3/5 are boys , then the number of girls in the school would be 1-3/5 = 2/5

The number of boys are 3/5 * x = 3x/5

The number of girls are 2/5 * x = 2x/5

Now on a particular day, 1/6 of the boys were absent and 250 boys were present.

What this means is that the fraction of boys present is 1-1/6 = 5/6

Now, 5/6 of the total boys population were present.

Mathematically;

5/6 * 3x/5 = 250

3x/6 = 250

x/2 = 250

x = 2 * 250 = 500

So there are 590 students in the school.

The number of girls in the school is ;

2x/5 = 2/5 * 500 = 200 girls

Answer:

x = 1

Step-by-step explanation:

Using the rules of logarithms

log [tex]x^{n}[/tex] ⇔ n log x

[tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]

Given

3[tex]log_{2}[/tex] (2x) = 3

[tex]log_{2}[/tex] (2x)³ = 3

(2x)³ = 2³

8x³ = 8 ( divide both sides by 8 )

x³ = 1 ( take the cube root of both sides )

x = 1

Answer:

x=1 is the correct answer

Step-by-step explanation:

got it right on edge!!!!

Answer: -1

Step-by-step explanation:

[tex]5t-3=3t-5[/tex]

Add 3 to both sides.

[tex]5t=3t-2[/tex]

Subtract 3t from both sides.

[tex]2t=-2[/tex]

[tex]t=-1[/tex]

Hope this helps!

Answer: t=-1

Step-by-step explanation:

1) add 3 to both sides

2) subtract 3t from both sides

3) Divide both sides by 2

Answer:

Step-by-step explanation:

Given the surdic expression [tex]\frac{2}{3\sqrt{5} + 2\sqrt{11}}\\[/tex], to rationalize the expression, we will have to multiply the numerator and denominator of the expression by the conjugate of the denominator as shown;

[tex]= \frac{2}{3\sqrt{5} + 2\sqrt{11}} * \frac{3\sqrt{5} - 2\sqrt{11}}{3\sqrt{5} - 2\sqrt{11}}\\\\= \frac{2(3\sqrt{5} - 2\sqrt{11})}{(3\sqrt{5} + 2\sqrt{11})(3\sqrt{5} - 2\sqrt{11})}\\\\= \frac{6\sqrt{5} - 4\sqrt{11} }{9\sqrt{25}+6\sqrt{55}- 6\sqrt{55}-4\sqrt{121} } \\\\= \frac{6\sqrt{5} - 4\sqrt{11} }{9(5)-4(11) }\\\\= \frac{6\sqrt{5} - 4\sqrt{11} }{45-44 }\\\\= \frac{6\sqrt{5} - 4\sqrt{11} }{1}[/tex]

Comparing the result [tex]\frac{6\sqrt{5} - 4\sqrt{11} }{1}[/tex] with the expression [tex]\frac{A\sqrt{B} + C\sqrt{D}}{E}[/tex], it can be seen that A = 6, B = 5, C = -4, D = 11 and E = 1

A+B+C+D+E = 6+5+(-4)+11+1

A+B+C+D+E = 11-4+12

A+B+C+D+E = 19

Hence the value of A+B+C+D+E is 19

Answer:

The expression is equal to 3,120 when x = -5 and y = 25.

Step-by-step explanation:

In order to obtain the output of the expression when x = -5 and y = 25, we need to apply these numbers in its correct places as shown below. We need to pay close attention to [tex]|x|[/tex] which is the absolute value of "x", this means that if x is positive, then [tex]|x|[/tex] will also be positive, but if x is negative then the result will still be positive.

[tex]\frac{5|x| - y^3}{x}[/tex]

[tex]\frac{5*|-5| - (25)^3}{-5}\\\frac{5*5 - 15625}{-5}\\\frac{25 - 15625}{-5}\\\frac{-15600}{-5} = 3,120[/tex]

The expression is equal to 3,120 when x = -5 and y = 25.

Answer:

Shape - Cube

Area= 864

Step-by-step explanation:

The shape folds to become a cube and all the edges are the same size.

Area of a cube is Length * Width * Height = Area

12*12*12= 864

Answer:

Shape - Cube

Area= 864

Step-by-step explanation:

The shape folds to become a cube and all the edges are the same size.

Area of a cube is Length * Width * Height = Area

12*12*12= 864

Answer:

4c

Step-by-step explanation:

We can say that the maximum number of cars can be represented as:

Maximum number of cars = Total of rows × Number of cars per row

In this particular case, we have 4 rows and the number of cars per row is c, thus, the expression above becomes:

Maximum number of cars = 4c

Answer:

Step-by-step explanation:

In this problem we are going find the natural logarithmic of the numbers involved and solve for x

[tex]ln65-Ln x= 39\\[/tex]

from tables

[tex]4.17-ln x= 39\4.17-39= lnx\\-34.83=lnx\\[/tex]

taking the exponents of both sides we have

[tex]e^-^3^4^.^8^3= x\\x= 7.47[/tex]

Answer:

(Choice B) B It decreases.

Step-by-step explanation:

According to the situation, the solution of the value of the expression is as follows

Let us assume

r         80 -2r

5        80 - 10 = 70

4        80 - 8 = 72

3        80 - 6 = 74

2        80 - 4 = 76

1         80 - 2 = 78

As we can from the above calculation that expression value risen if r value decreased

Therefore the correct option is B.

Answer:

It increases

Step-by-step explanation:

Answer:

Slope = 3

Step-by-step explanation:

Slope is rise (vertical distance) over run (horizontal distance).

Our rise is equal to 3

Our run is equal to 1

So, slope = 3/1 = 3

Answer:

Step-by-step explanation:

( x² + 3 ) ( x³ - x² + 4 )

Multiply the second parentheses by each term from the first parentheses

x² ( x³ - x² + 4 ) + 3 ( x³ - x² + 4 )

Distribute x through the parentheses

x⁵ - x⁴ + 4x² + 3 ( x³ - x² + 4 )

Distribute 3 through the parentheses

x⁵ - x⁴ + 4x² + 3x³ - 3x² + 12

Collect like terms

x⁵ - x⁴ + x² + 3x³ + 12

Use the commutative property to reorder the terms

x⁵ - x⁴ + 3x³ + x² + 12

Hope this helps..

Best regards!!

Answer:

x^5-x^4+3x^3+x^2+12

Step-by-step explanation:

Mulitply each term:

x^5-x^4+4x^2+3x^3-3x^2+12

Now simplify.

x^5-x^4+3x^3+x^2+12

I hope this helps....

Please mark me brainliest!!

Answer:

Slope = -6/7

Step-by-step explanation:

You need to use the formula m = y2 - y1 ÷ x2 - x1

The formula means: slope = the y coordinate of point 2 subtract the y coordinate of point 1, divided by the x coordinate of point 2 subtract the x coordinate of point 1

So,

m = 2 - 5 ÷ 3/2 - (-2)

m = -3 ÷ 7/2

m = -6/7

Hope this helps :)

Answer: w=5

Step-by-step explanation:

Answer:

y = 110°

Step-by-step explanation:

The inscribed angle CHF is half the measure of its intercepted arc CDF

The 3 arcs in the circle = 360°, thus

arc CDF = 360° - 160° - 60° = 140°, so

∠ CHF = 0.5 × 140° = 70°

∠ CHF and ∠ y are adjacent angles and supplementary, thus

y = 180° - 70° = 110°

Answer:

x = 4

Step-by-step explanation:

The midsegment ( median is equal to half the sum of the parallel bases, that is

[tex]\frac{AB+CD}{2}[/tex] = EF, substitute values

[tex]\frac{4x-10+3x+8}{2}[/tex] = 13 ( multiply both sides by 2

7x - 2 = 26 ( add 2 to both sides )

7x = 28 ( divide both sides by 7 )

x = 4

Answer:

Bearing of R from S = S 45° E or 135°

The bearing of R from Q

= S 66.42° w or 246.42°

Step-by-step explanation:

Distance between R and S

RS²= RP²+PS²

RS²= 15²+15²

RS²=225+225

RS= √450

RS= 21.21

Angle at S

21.21= 15/sins

Sin s= 15/21.21

S= sin^-1 15/21.21.

S= 45°

90+45= 135°

Bearing of R from S = S 45° E or 135°

Distance between R and Q

RQ²= PQ²+PR²

RQ²= 35²+15²

RQ²=1225+225

RQ= √1450

RQ= 38.08

RQ= 15/sinQ

SinQ= 15/38.08

SinQ= 0.40

Q=23.58°

90-23.58 = 66.42°

66.42+180= 246.42°

The bearing of R from Q

= S 66.42° w or 246.42°

Answer:

15, 16, 17, 18

Step-by-step explanation:

29-14=15

15, 16, 17, 18 are less than or equal to 18

Answer:

A).300763=+ 67

b) 704969= +87

c)( - 226981)= -61

Step-by-step explanation:

The values of the cube root iyf the given numbers above will be looked up in a calculator and the estimated value will be returned back.

Going through the numbers

A).for 300763

The value of the cube root = +67

B). For 704969

The value of the cube root = +89

C). For ( - 226981)

The value of the cube root= -61

Hey there! I'm happy to help!

There are 31 days in March, so there are 11 days left in March. We add this to the 20 days in April, giving us 31 total days this interest is compounded.

We could calculate the amount compounded each day for 31 total days, but that would take a long time. Instead, there is a formula we can use to calculate compound interest instead.

[tex]Total= P(1+i)^n\\\\P=Principal Amount\\i=interest rate\\\\n=number of times compounded[/tex]

So, let's plug in those numbers! Remember to convert the percent to a decimal so it works in the equation!

[tex]Total=1000(1+0.055)^3^1\\Total=1000(5.258068609)\\Total=5258.068609[/tex]

Now, we subtract the initial amount just to see how much interest was earned.

5258.068609-1000=4258.07 (rounded to nearest cent).

Therefore, the money will have earned $4,258.07 by April 20.

Have a wonderful day!

Answer: 299.5 cycles per second.

Step-by-step explanation:

An inverse variation can be written as:

y = k/x

Where, in this case:

y = frequency

x = length of the string

k = constant.

We know that 410 mm correspond to 515 cps.

then:

515cps = k/410mm

k = 515cps*410mm = 211,150 cps*mm

now, if we use x = 705mm we can find the frequency as:

y = ( 211,150 cps*mm)/705mm = 299.5 cycles per second.

Answer:   y ≤ x² + 8x + 7  

Step-by-step explanation:

x ≤ -7     --> x + 7 ≤ 0

x ≥ -1      --> x + 1 ≥ 0

        y = (x + 7)(x + 1)

        y = x² + 8x + 7

        The quadratic is positive so it is U-shaped

        x ≤ -7    and    x ≥ -1    

       means the outside of the U-shaped parabola is shaded

        so we need to use the ≤ symbol

Note: if the inequality symbols were reversed, the shading would be inside the U-shaped parabola so we would use the ≥ symbol.

Answer:

Hey there!

Angles in a quadrilateral add to 360 degrees, so we have 56+78+90+x=360

Solving, we see that the missing angle, x, is 136 degrees.

Hope this helps :)

Answer:

Hey.... Ans is 154°

The mate who ans before me HAVE TO FIND x TOO

Step-by-step explanation:

For example take a quadrilateral ABCD (refer to the pic)

Then solution is...

In quadrilateral ABCD

            Sum of all sides of a quadrilateral= 360°

           =angle A + angle B+ angle C+ angle D=

Given,

          Angle A= 56° + angle B=78° + angle C=90° + angle D=x

        =56° + 78° + 90° + x.            (add all the numbers)

         x+226=360°                           (56+78+90=226)

         x=360° - 226°

         x=154°

Therefore the largest angle = x = 154°

Hope it helped u!!

Answer: 16 units

Step-by-step explanation:

Given that in triangle ABC, m∠C=90,

it means m∠A +∠B= m∠BAC + m∠ABC = 90

m∠ABC = 90 - m∠BAC

Also given that;m∠BAC = 2m∠ABC

So,

m∠BAC = 2(90 - m∠BAC) = 180 - 2m∠BAC

m∠BAC +2m∠BAC = 180

3m∠BAC = 180

m∠BAC=180/3 = 60

m∠ABC = 60/3 = 30

thus,ΔBAC is a 30-60-90 right triangle, in which the ratio of the side lengths is 1:√3:2AC:BC=1:√3, AC=BC/√3BC=24, So,

AC=24/√3=8√3AL bisects angle A =>m∠LAC=30

ΔALC is a 30-60-90 right triangle, in which the ratio of the side lengths is 1:√3:2AC:AL=√3:2AL=2AC/√3=2x8√3/√3=16

Answer:

[tex]4 \frac{1}{4} [/tex] hours

Step-by-step explanation:

Given,

Time spent in studies : [tex]1 \frac{3}{4} [/tex] hours

Time spent in playing cricket : [tex]2 \frac{1}{2} [/tex] hours

Now, let's find the time that he spent in all:

[tex]1 \frac{3}{4} + 2 \frac{1}{2} [/tex]

Add the whole number and fractional parts of the mixed numbers separately

[tex](1 + 2)( \frac{3}{4} + \frac{1}{2} )[/tex]

Add the numbers

[tex]3 +( \frac{3}{4} + \frac{1}{2} )[/tex]

Add the fractions

[tex]3 + ( \frac{3 + 1 \times 2}{4} )[/tex]

[tex]3 + ( \frac{3 + 2}{4} )[/tex]

[tex]3 + \frac{5}{4} [/tex]

Convert the improper fraction into mixed number

[tex] 3 + 1\frac{1}{4} [/tex]

Write the mixed number as a sum of the whole number and the fractional part

[tex]3 + 1 + \frac{1}{4} [/tex]

Add the numbers

[tex]4 + \frac{1}{4} [/tex]

Write the sum of whole number and the fraction as a mixed number

[tex]4 \frac{1}{4} [/tex] hours

Hope this helps..

Best regards!!

Answer:

4 1/4 hours.

Step-by-step explanation:

1 3/4 + 2 1/2

= 1 + 2 + 3/4 + 1/2

= 3 + 3/4 + 1/2   The LCM of 2 and 4 is 4 so 1/2 = 2/4. and so we have:

3 + 3/4 + 2/4

= 3 + 5/4

= 3 + 1 1/4

= 4 1/4 hours.