Evaluate the expression for the given value of the variable. 34 + 1/6r, r = -1/2

The measure of each of the acute angles of the right triangle is 32° and 58°.

A right triangle is a kind of triangle which has a right angle (90°) and two acute angles (less than 90°).

Let x = measure of one of the acute angles

If the measure of one acute angle of a right triangle is 6 less than twice the measure of the other acute angle, then

measure of the other acute angle = 2x - 6

The sum of all the angles of any triangle is equal to 180°. Hence,

90° + x + 2x - 6 = 180°

Solve for the value of x.

3x = 96

x = 32

Solve for the measure of the other acute angle.

2x - 6 = 2(32) - 6 = 58

Hence, the two angles are 32° and 58°.

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In standard form the answer would be -6a+35b+48c.

Answer: 1/4

Step-by-step explanation:

We know the equation is a/b, and a = 6 when b=24, so we just need to plug the number in the spot of the variable.

6/24 = 1/4

Answer:

(a + 7)(a² + 15a + 59) + 0 = a³ + 15a² + 59a + 12

Step-by-step explanation:

To solve this problem, we can use the long division method.

First, we need to divide the first term of the dividend, which is a³, by the first term of the divisor, which is a. This gives us a quotient of a² with a remainder of 0. We write this as follows:
a³ + 15a² + 59a + 12

a + 7 |

—————

a²  | 0

Next, we multiply the divisor by the quotient and subtract it from the dividend, giving us a new dividend of 15a² + 59a + 12. We write this as follows:

a³ + 15a² + 59a + 12

a + 7 |

—————

a²  | 0

 -  |

a²  | 15a² + 59a + 12

Next, we divide the first term of the new dividend, which is 15a², by the first term of the divisor, which is a. This gives us a quotient of 15a with a remainder of 0. We write this as follows:
a³ + 15a² + 59a + 12

a + 7 |

—————

a²  | 0

 -  |

a²  | 15a² + 59a + 12

   |

   | 15a | 0

Next, we multiply the divisor by the quotient and subtract it from the dividend, giving us a new dividend of 59a + 12. We write this as follows:

a³ + 15a² + 59a + 12

a + 7 |

—————

a²  | 0

 -  |

a²  | 15a² + 59a + 12

   |

   | 15a | 0

    -  |

   15a | 59a + 12

Finally, we divide the first term of the new dividend, which is 59a, by the first term of the divisor, which is a. This gives us a quotient of 59 with a remainder of 0. We write this as follows:
a³ + 15a² + 59a + 12

a + 7 |

—————

a²  | 0

 -  |

a²  | 15a² + 59a + 12

   |

   | 15a | 0

    -  |

   15a | 59a + 12

      |

      | 59 | 0

Since the remainder is 0, this means that the expression (a³ + 15a² + 59a + 12) is divisible by (a + 7). Therefore, the quotient is:

a³ + 15a² + 59a + 12

a + 7

—————

a² + 15a + 59

We can check our answer by multiplying the divisor by the quotient and adding the remainder (which is 0), and verifying that the result is equal to the original dividend
(a + 7)(a² + 15a + 59) + 0 = a³ + 15a² + 59a + 12

The equation of a line whose slope is 3/6 and passes through (8, 4) is y- 4 = 3/6(x -8).

The equation of a line:

The equation of a line is an algebraic form of representing the set of points, which together form a line in a coordinate system. The numerous points which together form a line in the coordinate axis are represented as a set of variables x, and y to form an algebraic equation, which is referred to as an equation of a line.

Here we have to find the equation of a line.

Data given:

The slope (m) = 3/6

The point = (8,4)

The general formula for the equation of a line:

y - y1 = m( x - x1)

Where (x1, y1) is the point on the line.

As it is given that the point is ( 8, 4) and the slope is 3/6, so we have,

y - 4 = 3/6(x - 8)

Therefore the equation of a line is y-4 = 3/6(x -8).

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On rolling a standard die , the probability of getting a even number and less than 4 is  1/6 .

In the question ,

it is given that ,

a standard die is rolled ,

the total outcomes is {1 , 2 , 3 , 4 , 5 , 6} .

the even numbers are {2,4,6} .

and the outcome that are less than 4 is only {2} .

so , the number of favorable outcome is only 1 .

and total number of outcome is 6 ;

So , the probability is = (favorable outcome)/(total outcome)

Substituting the value from above ,

we get ,

probability is = 1/6 .

Therefore , the required probability is  1/6 .

The given question is incomplete , the complete question is

You roll a standard die. What is the probability of getting a even number and less than 4 ?

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To solve the scale drawing, use the equation of scale factor = The dimension of the new shape / The original size of the shape

The scale factor is the ratio of the new size of the object to the original size of the object

The equation will be

The scale factor = The dimension of the new shape / The original size of the shape

If the the dimensions of the drawing and the scale factor is given

To find the actual size of the object multiply the dimensions of the drawing with the scale factor

The equation will be

The actual size = The scale factor × The dimensions of the drawing

Therefore, to solve the scale drawing we have to use the equation of scale factor

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The roots of the quadratic equation x² - 8x + 16 = 0 are real and equal which is 4.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The quadratic equation is given below.

x² - 8x + 16 = 0

The value of the discriminant is given as,

D = b² - 4ac

D = (-8)² - 4(1)(16)

D = 64 - 64

D = 0

The roots of the equation are calculated as,

x² - 8x + 16 = 0

x² - 4x - 4x + 16 = 0

x(x - 4) - 4(x - 4) = 0

(x - 4)(x - 4) = 0

x = 4, 4

The roots of the quadratic equation x² - 8x + 16 = 0 are real and equal which is 4.

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Answer:

1.963%

Step-by-step explanation:

Use the equation for compound interest

[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]

[tex]5400 = 4800(1 + \frac{r}{365})^{(365)(6)}\\5400/4800 = 4800(1 + \frac{r}{365})^{(365)(6)}/4800\\1.125 = (1 + \frac{r}{365})^{2190}\\\sqrt[2190]{1.125} = \sqrt[2190]{ (1 + \frac{r}{365})^{2190}} \\1.0000537836544 = 1 + \frac{r}{365} \\1.0000537836544 -1 = 1 + \frac{r}{365} -1\\.0000537836544 = \frac{r}{365}\\(.0000537836544)(365) = ( \frac{r}{365})(365)\\.019631 = r[/tex]

Answer:

false

Step-by-step explanation:

5²+6²=61.

>

Square root of 61 is 7.81 and not 12 so the points will not meet

Answer:

1428.33333 yards

Step-by-step explanation:

1 foot = 0.33333 yards

4285 feet = 4285*0.33333 = 1428.33333 yards

The solution is Option C.

Number of squares n in a size number s is given by the equation n = 4s + 1

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is given by

Let the number of squares be = n

Let the size number be = s

Now ,

Figure 1 :

The size number s = 1

The number of squares in the figure 1 is = 5 squares

So , the equation will be n = 4s + 1

n = 4 x 1 + 1 = 5 squares

Figure 2 :

The size number s = 2

The number of squares in the figure 2 is = 9 squares

So , the equation will be n = 4s + 1

n = 4 x 2 + 1

n = 8 + 1 = 9 squares

Figure 3 :

The size number s = 3

The number of squares in the figure 2 is = 13 squares

So , the equation will be n = 4s + 1

n = 4 x 3 + 1

n = 12 + 1 = 13 squares

Hence , The equation is given by n = 4s + 1 , where n is the number of squares and s is the size number

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Answer

Step by step explanation

Answer:

Step-by-step explanation:

Train D I believe

Answer:

     [tex]\frac{16}{25}[/tex]

Step-by-step explanation:

[tex]\frac{5*(\frac{4}{5})^{2}*\frac{3}{5} }{3}[/tex]

= [tex]\frac{\frac{5}{1} *\frac{16}{25}*\frac{3}{5} }{3}[/tex]

= [tex]\frac{\frac{5*16*3}{1*25*5} }{3}[/tex]

= [tex]\frac{\frac{240}{125} }{3}[/tex]

= [tex]\frac{\frac{48}{25} }{3}[/tex]

= [tex]\frac{48}{25} /\frac{3}{1}[/tex]

= [tex]\frac{48}{25} *\frac{1}{3}[/tex]

= [tex]\frac{48*1}{25*3}[/tex]

= [tex]\frac{48}{75}[/tex]

= [tex]\frac{16}{25}[/tex]

Answer:

Mode) 7

Median) 6

Mean) 5.2

Range) 7

Step-by-step explanation:

Let's start with what we have:

3, 7, 2, 4, 7, 5, 7, 1, 8, 8

a) The first part of the question we have to do is figure out the mode. The mode of a group of numbers is the number most repeated, which in this case is:

Mode) 7

b) The median of a data set is the number in the middle when ordered from least to greatest. When reordering it, we get:

1,2,3,4,5,7,7,7,8,8

So the number in the middle is...

There is no number in the middle so we have to find the mean of the middlemost numbers which are 5 and 7. Calculating (5 + 7)/2 we get 6, so.

Median) 6

c) The mean of a data set is when we add up all the numbers and then divide by the number of numbers, in this case, is 10. The sum of the numbers is 52. When dividing 52 by 10 we get:

Mode) 5.2

d) The range of a data set is the difference between the greatest number and the smallest number. When subtracting 1 from 8 we get:

Range) 7

According to the given statement, there were 58 children, 29 adults and 64 students.

Algebraically speaking, an equation is indeed a statement that establishes the equivalence of two mathematical equations.

Let there be x number of children, y number of students and x/2 number of adults. Forming the first equation based on number of students -

x + y + x/2 = 151 : Equation 1

Multiply equation 1 with 2

2x + 2y + x = 302 : Equation 2

3x + 2y = 302 : Equation 3

y = (302 - 3x)/2 : Equation 4

Forming second equation based on cost -

5x + 7y + 12x/2 = 1086 : Equation 5

Rewriting this equation

5x + 7y + 6x = 1086 : Equation 6

11x + 7y = 1086 : Equation 7

Keep the value of y from equation 4 in equation 7

11x + 7(302 - 3x)/2 = 1086

11x + (2114 - 21x)/2 = 1086

22x + 2114 - 21x = 2172

x = 2172 - 2114

x = 58

Now,

y = (302 - 3x)/2

y = (302 - 3×58)/2

y = 128/2

y = 64

Number of adults = 58/2

Number of adults = 29

Thus, there were 58 children, 29 adults and 64 students.

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Answer:

Step-by-step explanation:

i got 72

Answer: 112.64 mL

Step-by-step explanation:

     To find the number of milliliters of liquid in the beaker then, we will add all of the given values together.

      79.89 mL + 32.7 mL + 0.05 mL = 112.64 mL

Answer:

The shape of a distribution is described by its number of peaks and by its possession of symmetry, its tendency to skew, or its uniformity.

The y - intercept of a linear function is (0, -4).

What is intercepts?

A y-intercept, also known as a vertical intercept, is a point in analytical geometry where the graph of a function or relation intersects the y-axis of the coordinate system, using the convention that the horizontal axis represents a variable x and the vertical axis represents a variable y. Thus,

x = 0 is satisfied at these points.

y - intercept is the point which crosses the y - axis.

Since y - intercept is when x = 0

From the table the first point is x = 0.

Hence, the y - intercept of a linear function is (0, -4).

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The amount of rabbits produced is 6, 18, 54, 162, and 486.

A permutation is an orderly arrangement of the items or numbers.

Combinations are a means to choose items or numbers from a collection or set of items without regard for the items' chronological sequence.

There are 3 pairings if there are 6 children, 3 of which are male and 3 of which are female.

18 will result from 6 children from each pair.

Thus, there are now 9 pairs.

That equates to either 27 pairs or 54 rabbits.

There would be 162 offspring if each of the 27 pairs had 6 kids.

81 breeding pairs would be left after this, and so on.

Consequently, the following number of rabbits will be produced.

6 for first year

18 for second year

54 for third year

162 for the 4th year

For year five, 486

The amount of rabbits produced is 6, 18, 54, 162, and 486.

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Answer: a

Step-by-step explanation:

10/2 = 5

5-6=-1

Answer: c, 84

Step-by-step explanation:

A function is a mathematical expression that describes the relationship between an input and an output.

The function table is a visual, graded table with cells for input and cells for output that are organized into rows and columns.

Function tables have three variables components. There is the input, the function and the output. Function tables are created so that one of the three components is unknown and the other two serve as the clues to solving the table.

The rule of a function table is the mathematical operation that describes the relationship between the input and the output. The rule must be consistently applied to all input/output parts.

A traditional function table is made using two rows, with the top row being the input cells and bottom row being the ouput celss. Each column represents a signal input/output relationship.

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The transformations that map the strip pattern onto itself is a horizontal translation, a reflection across a vertical line, a reflection across a horizontal line, a glide reflection, and a 180°. Option A is the correct option.

The strip pattern can be mapped onto itself in two different ways.

Hence, the transformations that map the strip pattern onto itself can be achieved through a horizontal translation, a reflection across a vertical line, a reflection across a horizontal line, a glide reflection, and a 180°.

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The value of the function f(-2) is (a) -1

From the question, we have the following parameters that can be used in our computation:

f(x) = [x³,  x < -3

        | 2x² - 9, x > -3

        { 5x+4, x ≥ 4

To calculate the function f(-2), we make use of the domain

x > -3

This is because

-2 > -3

So, we have

f(x) = 2x² - 9

Substitute the known values in the above equation, so, we have the following representation

f(-2) = 2(-2)² - 9

Evaluate

f(-2) = -1

Hence, the function is (a) -1

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The equivalent fraction is defined below and the few equivalent fractions of 1/2 are 2/4 , 3/6... .

In the question ,

it is given that the fraction is 1/2 .

The Equivalent Fractions are defined as the fractions that have different numerators and denominators but are equal to same value  and

A fraction is a part of the whole ; Equivalent fractions represent the same portion of that whole.

the fraction is 1/2 ,

to find the equivalent fraction , we multiply numerator and denominator by 2 ,

we get , 2/4

on multiplying by 3 , we get

= 3/6 .

Therefore , the equivalent fractions of 1/2 are 2/4 , 3/6 ...

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