What is the formula for the volume of a cylinder, V= πr²h , solved for h ?
(F) h= r²πV (G) h= πV/r² (H) h= V/πr² (I) h= πr²/V

Answer:

Step-by-step explanation:

Let,  

For English = x min.

For Biology= (x+30) min.

For Math= 3(x+30) min.

2 hours= 2*60 = 120 min.

Now,  x+(x+30)+3(x+30)=120

Or, x=  0 min.

For English = 0 min.

For Biology= 30 min.

For Math= 90 min

Hello,

[tex]f(x) = 4 {x}^{2} - 9[/tex]

[tex]g(x) = 4 {x}^{2} - 9 + 8 = 4 {x}^{2} - 1[/tex]

Answer: S=6x²+25x+14

Step-by-step explanation:

[tex]\displaystyle\\S=S_1+2S_2\\S_1=(2x+7)(x+3)\\S_1=(2x)(x)+(7)(x)+(2x)(3)+(7)(3)\\S_1=2x^2+7x+6x+21\\S_1=2x^2+13x+21\\\\S_2=\frac{(\frac{2x+7)}{2})(4x-2) }{2} \\\\S_2=\frac{(2x+7)(4x-2)}{(2)(2)} \\\\S_2=\frac{(2x)(4x)+(7)(4x)+(2x)(-2)+(7)(-2)}{(2)(2)} \\\\S_2=\frac{8x^2+28x-4x-14}{(2)(2)} \\\\S_2=\frac{8x^2+24x-14}{(2)(2)} \\\\S_2=\frac{(2)(4x^2+12x-7)}{(2)(2)} \\\\S_2=\frac{4x^2+12x-7}{2} \\Hence,\\S=2x^2+13x+21+2*\frac{4x^2+12x-7}{2} \\S=2x^2+13x+21+4x^2+12x-7\\S=6x^2+25x+14[/tex]

Answer: 11

Step-by-step explanation:

[tex]\angle GFE=33^{\circ}[/tex] (linear pair)

[tex]\angle FEB=180^{\circ}-4x[/tex] (linear pair)

[tex]33+180-4x+x=180[/tex] (sum of angles in a triangle)

[tex]33+180-4x+x=180\\\\33-3x=0\\\\x=11[/tex]

Answer: (x-2)(x+7)

Step-by-step explanation:

Answer: (x+7)(x-2)

Step-by-step explanation:

[tex]x^2+5x-14=\\x^2+7x-2x-14=\\x(x+7)-2(x+7)=\\(x+7)(x-2)[/tex]

Answer:

I got 6

Step-by-step explanation:

Hope this is correct :)

Answer:

1. Top left and top right. Middle right

2. 43/24

3. B(42.5%)

4. A(3.25)

Step-by-step explanation:

2. Get the denominators the same(denominator in this case would be 24), and then make an improper fraction.

3. Convert the fraction 17/40 to a percentage(42.5%)

4. 6 hours x 60 minutes= 360 minutes

1170/360 = 3.25 laps per minute

Hope this helps! <3

Answer:

slope: 7

Y-int: -100

Step-by-step explanation:

Basically just solve for y

The solution of x in the equation 3^(x -4) = 6 is x = 5.63

The equation is given as

3^(x -4) = 6

Apply the law of indices on the expression 3^(x -4) to rewrite it

So, we have

3^x/3^4 = 6

The above equation becomes

3^x = 6 * 3^4

Evaluate the product

So, we have

3^x = 486

Take the logarithm of bot sides

xlog(3) = log(486)

Divide both sides by log(3)

x = log(486)/log(3)

Evaluate

x = 5.63

Hence, the solution of x in the equation 3^(x -4) = 6 is x = 5.63

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Answer:

41957

Step-by-step explanation:

39429

2293

235

_______

41957

set as brainliest

The solution to the equation 7(x + 2) + 4x = 6(2x - 4) gives the result x = 38

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the equation:

7(x + 2) + 4x = 6(2x - 4)

Opening the bracket gives:

7x + 14 + 4x = 12x - 24

Collecting like terms:

x = 38

The solution to the equation 7(x + 2) + 4x = 6(2x - 4) gives the result x = 38

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The equation of the line in standard form passing through the point (3 , 1) with slope equal to 0 is y = 1.

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).

Using the point slope form, plug in the values of the slope and the point to set up the equation.

(y - y1) = m(x - x1)

where m = 0 and (x1 , y1) = (3 , 1)

(y - 1) = 0(x - 3)

y - 1 = 0

y = 1

Since the variable(s) is already isolated at one side and the constant on the other side, the equation is y = 1 already in standard form.

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The inequality to model this situation is given by x>60 .

Inequality is defined as the relationship between a variable and a constant or two variables which can be written in the form of an equation using the notations < , > , ≤ or ≥ .

Let us consider the number of bags of lettuce bought be x.

Therefore amount needed to buy x bags from Val's veggies is :

250 + 1.5 x

And the amount needed to buy x bags from Sally's Salads is :

100 + 4 x

Now it is given that Val's Veggies need to be cheaper than Sally 's.

a) Therefore we will write an inequality and solve it for x:

∴ 250 + 1.5 x < 100 + 4 x

moving the variables and constants together

or, 1.5 x - 4 x < 100 - 250

or, - 2.5x < -150

or, x > 60

b) Therefore from the inequality we can conclude more than 60 bags of lettuce needs to be purchased for Val's cost to be cheaper.

c) Set notation: {x ∈ Z | x>60}

interval notation : x∈(60.∞)

Therefore from the inequality , the number of bags to be purchased must be more than 60.

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Answer:

1 1/2 ÷ 1/2 = 3/2 ÷ 1/2 = 3/2 × 2 = 3

Answer:        0= negative 6

Step-by-step explanation:

Answer:

Step-by-step explanation:

We can do this as a normal problem on the left.

(-7)x2+9 we do the multiplication first, then add. (Multiplication and division always happen before addition and subtraction, unless brackets are being used.)

->    -14+9=-5

Now that we know the left side of the equation is equal to -5, we must find which answer is GREATER than -5, because instead of an equal sign, there is a < meaning greater than.

4+[3x(-2)] for this one we do the multiplication first

4+(-6)=-2. -2> -5

Thus, it is the first answer, because that is the one that is greater than -5.

The equation of the line is y = -3/4x + 5

The equation of a line is expressed as;

y = mx + c

Where;

To determine the intercept, we have;

2= -3/ 4(8) + c

2 = -24/8 + c

2 = -3 + c

Make 'c' the subject of formula

c = 2 + 3

c = 5

The equation of the line is y = -3/4x + 5

Thus, the equation of the line is y = -3/4x + 5

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Answer:

17

Step-by-step explanation:

put the point on 17 on the number line

Answer:

17

Step-by-step explanation:

12-(-5) = 12+5. Two negatives create a positive. 12+5=17

The score which is needed on the fourth test so that as average score of 90 is earned as required in the task content is; 93.

According to the task content, it follows that the score needed so that an average score of 90 is earned on all four tests is to be determined.

Since, The average is the ratio of the sum of all scores to the number of scores; we have;

90 = (88 + 92 + 87 + x)/4

Multiply both sides by 4 so that we have;

360 = 88 + 92 +87 + x

Isolate x on one side of the equation;

x = 360 -88 -92 - 87

x = 93.

Ultimately, The score which is needed on the fourth test so that as average score of 90 is earned as required in the task content is; 93.

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The measure of the angle ADB is 65 degrees

The angles are given as

Angle ADB = (7x + 2) degrees

Angle CDB = (3x - 2) degrees

The angles are complementary angles

This means that they add up to 90 degrees

So, we have:

ADB + CDB = 90

This gives

7x + 2 + 3x - 2 = 90

Evaluate

10x = 90

Divide by 10

x = 9

Substitute x = 9 in Angle ADB = (7x + 2) degrees

Angle ADB = (7 x 9 + 2) degrees

Evaluate

Angle ADB = 65 degrees

Hence, the measure of the angle ADB is 65 degrees

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By substitution, the solution of the system of equations, 4x + 2y = 7 and y = 5x, is (1/2 , 5/2).

A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.

There are three methods that can be used to solve system of linear equations.

1. Elimination

2. Substitution

3. Graphing

Using substitution method, given two linear equations in x and y,

4x + 2y = 7     (equation 1)

y = 5x     (equation 2)

Since the second equation is already expressed in y in terms of x, substitute the second equation to the first equation.

4x + 2y = 7     (equation 1)

4x + 2(5x) = 7

4x + 10x = 7

Combining all terms containing the variable x on one side and the constants on the other side of the equality, and solving for x.

4x + 10x = 7

14x = 7

x = 1/2

Substitute the value of x in the second equation and solve for y.

y = 5x

y = 5(1/2)

y = 5/2

Hence, the solution of the given system of equations is (1/2 , 5/2).

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Answer:

D - 59

Step-by-step explanation:

All the options are even except from D which is odd

Hope this helps :)

Answer:

Step-by-step explanation:

2 2/3

Answer: x=2   DS=10   SE=10   DE=20

Step-by-step explanation:

[tex]7x-4=16-3x\\7x-4+3x=16-3x+3x\\10x-6=16\\10x-4+4=16+4\\10x=20\\[/tex]

Divide the equation by 10:

[tex]x=2[/tex]

Hence,

[tex]DS=(7)(2)-4\\DS=14-4\\DS=SE=10\\DE=DS+SE\\DE=10+10\\DE=20[/tex]

The sum of 5,238 and 2,794 is 8,032.

In math, addition is the process of adding two or more numbers together. Addends are the numbers that are added, while the sum refers to the result of the operation.

Given: 5,238 + 2,794

To add the estimate, we place the given 4-digit number 2794 below the given 4-digit number 5238, and then group the numbers into columns according to their places, such as once, tens, hundreds, and thousands.

The numbers are now added column-by-column. First, we add the number in the one's column (8+4=12), then in the tens column after carrying 1 (9+3+1=13), in the hundreds column carrying 1(2+7+1=10) and in the thousands column carrying 1 again (5+2+1=8).

So the final result of the addition is 8,032.

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If the ratios of the measures of the three angles is 4: 5: 11 then the measures of the three angles in a triangle is 84°, 30° and 66° respectively.

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.

The ratios are 4: 5: 11 then

Angle A = 14, Angle B = 5, Angle C = 11

Total ratio = 14 + 5 + 11 = 30

The total angle in a triangle = 180°

Angle A

= 14 / 30 × 180°

= 0.4666666666666 × 180°

= 84°

Angle B

= 5/30 × 180°

= 0.1666666666666 × 180°

= 30°

Angle C

= 11/30 × 180°

= 0.3666666666666 × 180°

= 66°

Therefore, the measures of the three angles in a triangle is 84°, 30° and 66° respectively.

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The measures of the angles in each triangle are 36°, 45°, and 99.°

Angle A = 4

Angle B = 5

Angle C = 11

Total ratio = 4 + 5 + 11

                 = 20

The total angle in a triangle = 180°

Angle A = 4 / 20 × 180°

             = 36°

Angle B = 5/20 × 180°

             = 45°

Angle C = 11/20 × 180°

             = 99°

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Answer: Option A

Step-by-step explanation:

(-3,0) is an x intercept because y is equal 0

1. x intercept of the graph of k is -3

Step-by-step explanation:

2. zeros can be found by setting the function to zero

function is y = 2x + 6

y = 2x + 6 -> 0 = 2x + 6

x would need to be -3 to get the zero of k

3. its not the third option : the slope is 2

4. if you graph it, it doesnt pass thru -1,-8

Two rational expressions that simplify to (x+1) / (x-5) are equals to

(x+1)²/ (x+1) (x-5) and (x+1)(x-5) / (x-5)².

As given in the question,

Simply rational expression is given by (x+1) /(x-5)

Two rational expressions that simplify to given expression are as follow:

        (x+1)²/ (x+1) (x-5).

   2.  Multiply (x-5) to the numerator and denominator of the given rational                      

        expression

        (x+1)(x-5)/ (x-5)².

Therefore, two rational expressions that simplify to (x+1) / (x-5) are equals to  (x+1)²/ (x+1) (x-5) and (x+1)(x-5) / (x-5)².

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The cost of the MP3 player in the year 2013 will be $83.99

If the trend continues, that means the drop in price at the same rate each year

In 2003 it was $499

In 2009 it was $249.99

Price drop each year (from 2003 to 2009) :

= 499 - 249.99 / 2009 - 2003

= 249.01 / 6

Therefore, the price drop each year  = $41.50

Similarly, Price drop each year (from 2009 to 2013) :

(2013 - 2009) x 41.5 = $166

Thus, 249.99 - 166 = 83.99

Therefore, cost of the MP3 player in the year 2013 will be $83.99

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Using proportions, the coordinates of C are given as follows: (60,41).

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

Point B partitions AC in the ratio 1:3, hence:

B - A = 1/4(C - A)

The x-coordinate of C is found as follows:

12 + 4 = 1/4(x + 4)

16 = 1/4(x + 4)

x + 4 = 64.

x = 60.

The y-coordinate of C is found as follows:

5 + 7 = 1/4(y + 7)

12 = 1/4(y + 7)

y + 7 = 48

y = 41.

The coordinates of C are given as follows: (60,41).

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Answer:

Step-by-step explanation: