The two legs of a right triangle are 9 and 7. Find the hypothesis of the triangle. Draw a Picture! Leave your answer in radical form.

Answer: x=13°

Step-by-step explanation: We know total amount of degrees in a triangle is 180°. We also know two of the angles' degrees: 39° and 90°. Now, with this info, we set up an equation: (3x+12)+39+90=180. We add 39 and 90 to get 129; then we subtract 129 on both sides of the equation. Our equation should now look like this: 3x+12=51. Subtract 12 on both sides to get: 3x=39. Lastly, divide 3 on both sides to find the value of x.

It will take them 36 minutes to drive 24 miles.

A problem can be solved using the unitary method by first determining the value of a single unit, and then multiplying that value to determine the required value. A single or distinct unit is referred to by the word unitary. Because of this, the goal of this method is to determine values in reference to a single unit. For instance, we can use the unitary technique to determine how many kilometers a car will go on one liter of gas if it travels 44 km on two liters of fuel.

Given Data

Tim and his sister drove 18 miles in 27 minutes.

They drove 1 mile in :

18 mile = 27 minutes

1 mile = [tex]\frac{27}{18}[/tex] minutes

1 mile = 1.5 minutes

For 24 miles,

1 mile = 1.5 minutes

24 miles = 1.5(24) minutes

24 miles = 36 minutes.

It will take them 36 minutes to drive 24 miles.

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Answer:

y + 9 = [tex]\frac{1}{7}[/tex](x+4)

Step-by-step explanation:

Point slope form: y − y1 = m(x − x1)

First, we find the slope (m):

m = [tex]\frac{y2-y1}{x2-x12} = \frac{-8-(-9)}{3-(-4)} = \frac{1}{7}[/tex]

Now insert your points and slope into the form:

y + 9 = [tex]\frac{1}{7}[/tex](x+4)

Answer:

6 and 9.

Step-by-step explanation:

The representation of the number is 1.998 multiplied by 10^27

The expression is given as

1.998 x 10^27

The above mathematical representation is a number in scientific form and is already in its most simplified form

This means that the scientific form cannot be further simplified

However, the scientific number can be rewritten as a mathematical statement

Recall that, we have

1.998 x 10^27

The pronunciation of the above expression is:

1.998 multiplied by 10^27

And it is evaluated by

Moving the decimal point 27 places to the right.

This gives

1998000000000000000000000000

See that the above result does not have a proper representation compared to 1.998 x 10^27

Hence, the representation of the scientific number given as 1.998 x 10^27 is the 1.998 multiplied by 10^27

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The Stem plot is displayed below of eighteen faculty members in a college math department range in age from 32 to 68.

How do you make a stem plot?

On the left hand side of the page, write down the thousands, hundreds or tens (all digits but the last one). These will be your stems. Draw a line to the right of these stems. On the other side of the line, write down the ones (the last digit of a number).

A Stem Plot is a chart for demonstrating the distribution of numeric variables .

It is used to analyze the shape of the distribution.

The data provided is as follows:

S = {32,48,99,40,35,69,53,47,89,96,38}

The Stem plot is displayed as follows:

3 | 2  5   8

4 | 0  7  8

5 | 3

6 | 9

8 | 9

9 | 6  9

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Answer:

137°

Step-by-step explanation:

Given: ∠2 = 43°

Find: ∠1 = ?

Solution:

∠1 + ∠2 = 180°

∠1 = 180° - ∠2

∠1 = 180° - 43°

∠1 = 137°

He can find out by using mathematical operation - subtraction.

An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands.

Binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, are the operations that are most frequently studied. A constant is an operation with arity zero, often known as a nullary operation. An example of an operation of arity 3, sometimes known as a ternary operation, is the mixed product.

The arity is typically assumed to be limited. Even yet, infinitary operations are occasionally taken into account, in which case the "typical" operations of finite dimensionality are referred to as finiteary operations.

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Answer:

Option 1

Step-by-step explanation:

[tex]|x-2|<14 \\ \\ x-2<-14, x-2>14 \\ \\ x<-12, x>16[/tex]

Answer:

4 outfits

Step-by-step explanation:

So to find out how much he has left after all his purchases to buy new biking outfits we can add:

9.54 x 3 = 28.62

22.01 + 28.62 + 322.09 = 372.72

Now we subtract his budget by how much he has already spent:

620 - 372.72 = 247.28

He has $247.28 left for outfits so we can divide 247.28 by $61.82 (the amount per outfit) to find how many he can buy:

247.28 / 61.82 = 4

Adrian can buy 4 outfits.

Answer:

Step-by-step explanation:

Answer:

2x(2x + 7)(3x - 1).

Step-by-step explanation:

12x^3 + 38x^2 - 14x

= x(12x^2 + 38x - 14)

= 2x(6x^2 + 19x - 7)

To factor the expression in the parentheses we need 2 numbers whose product is (6 * -7) = - 42 and whose sum = +19.

These are +21 and - 2.

So, we write:

6x^2 - 2x + 21x - 7

= 2x(3x - 1) + 7(3x - 1)

= (2x + 7)(3x - 1)

So, the answer is 2x(2x + 7)(3x - 1).

Answer:

[tex]2x(3x-1)(2x+7)[/tex]

Step-by-step explanation:

[tex]12x^3+3x^2-14x\\[/tex]

Factor out common factor: (2x)

[tex]=2x(6x^2+19x-7)[/tex]

Factor [tex]6x^2+19x-7[/tex]

[tex]= 2x(3x-1)(2x+7)[/tex]

Hope this helps! :) Sorry for the late reply

Answer:

Method 2, a monthly base salary of $1,500 with a 3% commission on sales over $7,500, will earn more money.

Step-by-step explanation:

given -

method 1 - he can choose to earn only a 10% commission on sales each month,

method 2-earn a monthly base salary of $1,500 with a 3% commission on sales over $7,500.

also, he has an average sales of $16,000 each month.

according to the question;

method 1 earning =>

10% of $16,000 =>(10/100)*$16,000=$16,00.

method 2 earning =>

$1,500+(3/100)*($16000-$7500)=$1755.

in method 2, a monthly base salary of $1,500 with a 3% commission on sales over $7,500. he will earn more.

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Rational fraction is a fraction where a and/or b are fractions and b is not equal to 0.

Any function that can be expressed mathematically as a rational fraction—an algebraic fraction in which both the numerator and the denominator are polynomials—is referred to as a rational function. The polynomials' coefficients don't have to be rational numbers; they can be found in any field K. Any function that can be expressed as a polynomial divided by a polynomial is said to be rational. The domain of a rational function is the set of all numbers except the zeros of the denominator since polynomials are defined everywhere.

Given Data

a_____________ is a fraction where a and/or b are fractions and b is not equal to 0.

A rational fraction is a fraction where a and/or b are fractions and b is not equal to 0.

Example 1. f(x) =[tex]\frac{x}{x-3}[/tex]

The denominator has only one zero, x = 3.

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Based on the vectors given, the sum of the vectors can be found to be (44, 4)

When given two vectors such as (15, −41) (29, 37) and you are required to add them, the sum of the vectors can be found by the formula:
= (a1 + b1, a2 + b2)

Where the vectors are:
(a1, a2) (b1, b2)

The sum of the vectors (15, −41) (29, 37) is therefore:

= (a1 + b1, a2 + b2)

= (15 + 29, -41 + 37)

= (44, -41 + 37)

= (44, 4)

In conclusion, the sum of the vectors are (44,4).

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The value of c in the equation 7c - cy = 10x will give a line with slope +5 is -2.

We can rewrite the equation as:-

-cy = 10x - 7c

y = (-10/c) x + 7

Now the equation is in slope-intercept form which is given by:-

y = mx + b

Where,

m represents the slope of the line

b represents the y-intercept of the line

(x,y) represents ordered pair of each point of the line

Comparing both the equations, we get

m = -10/c

b = 7  

We have to get m = +5

Hence, equating both the values of m, we get

5 = -10/c

c = -10/5

c = -2

Hence, the value of c is -2.

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The formula for q will be q = p*logm/(logK - logt)

Logarithm

A logarithm is defined as the power to which a number must be raised to get some other values. It is the most convenient way to express large numbers. A logarithm has various important properties that prove multiplication and division of logarithms can also be written in the form of logarithm of addition and subtraction.

Given equation:

[tex]K=tm^{(\frac{p}{q} )}[/tex]

We have to find a formula for q.

Raising the whole equation to the power of q, we get

[tex]K^q=t^qm^{p}[/tex]

We can rewrite it as,

[tex]\frac{K^q}{t^q}=m^p[/tex]

[tex](\frac{K}{t})^q=m^p[/tex]

Operating with logarithm on both sides, we get,

q*log(K/t) = p*logm

q = p*logm/log(K/t) = p*logm/(logK - logt)

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Answer:

y = √25 - x

y = -√25 - x

Step-by-step explanation:

x + y² = 25

-x                -x

----------------------

y² = -x + 25

√y² = √-x + 25

y = √25 - x

y = -√25 - x

I hope this helps!

The most appropriate choice for linear equation will be given by -

Length of the rectangle is 80 inches

What is linear equation?

At first it is important to know about equation

Equation shows the equality between two algebraic expressions by connecting the two algerbraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Here,

Let the length of the pegboard be l inches

Width of the pegboard = [tex]\frac{1}{2}l - 8[/tex]

Perimeter =

                   [tex]2(l + \frac{1}{2}l - 8 )\\2(\frac{3l}{2} - 8)\\[/tex]

                    [tex](3l - 16)[/tex] inches

But the problem,

[tex]3l - 16 = 224\\3l = 224 +16\\3l = 240\\l = \frac{240}{3}\\[/tex]

[tex]l = 80[/tex] inches

The length of the rectangle is 80 inches.

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Answer:

5000 students

Step-by-step explanation:

Let total number of students appeared in the exams is x.

20% of x have failed in both maths and science.

Here,in maths 60% of students passed.

%ag of students failed in maths= 40%

%ag of students failed in math — % of students failed in both maths and science = students passed in science but failed in maths i.e. 40–20 = 20%.

Likewise as 70% of students passed science

So 30% failed in science.

And Students failed in science only but passed in maths= %ag of students failed in science- % of students failed in both maths and science.

i.e. 30–20= 10%.

Given 2500 number of students passed in both maths and science = 100–(students failed in both maths and science+ students failed only in maths and passed in science+ students failed only in science but passed in maths)%

= 100–(20+20+10)= 50% of students passed both.

50% of x = 2500

50x/100= 2500

=> x= 5000.

So total number of students appeared in exam is 5000 in number

Reflection and rotation preserve length , so the perimeter of ΔABC is equal to the perimeter of ΔXYZ. A possible set of values for AB, BC and AC is  7,9 and 10 units.

A rotation is a transformation that occurs when a figure is turned a preset number of degrees around a fixed point (referred to as the center of rotation).

The given figure is a triangle ABC such that it is transformed by a rotation of 90 °and reflection about y=-5.

The image thus formed will be congruent to the object and will have same sides and perimeter.

Hence the perimeter will be 26 units and the possible length of AB,BC and AC will be 7,9 and 10 units which is the only possible option as a triangle cannot have sides 2 , 14  and 10.(2+10<14)

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Using Binomial probability distribution,

X = 20, 0.15

P (X ≤ 3) =[tex]20 C_{0} (0.15)^{0} (1-0.15)^{20} + 20C_{1} (0.15)^{1} (1-0.15)^{19} + 20C_{2} (0.15)^{2} (1-0.15)^{18} + 20C_{3} (0.15)^{3} (1-0.15)^{17}[/tex]

P(X ≤ 3) = 0.648

P (X ≥ 3) = 1 - P(X ≤ 3) = 1 - 0.648

P ( X ≥ 3) = 0.352

Therefore, thee required probability is 0.352.

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There are 28 ways in which a couple can choose the name of the baby for its name.

If we need to choose objects from two groups of x and n objects so that one object from each group is chosen, we can do so by calculating the combinations possible by:  

= ˣC₁  ×  ⁿC₁

Let 'x' be the set of first name = 7

Let 'n' be the set of second name = 4

Putting the values in formula;

= ⁷C₁ × ⁴C₁

= 7 × 4

= 28

Thus, there are 28 ways in which a couple can choose the name of the baby for its name.

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The complete question is-

A couple has narrowed down the choices of a name for their new baby to 7 first names and 4 second names.

How many different first- and second-name arrangements are possible?

The value of the limit of piece wise function is 2k.

For the given question;

The piece wise function is defined as a;

f(x) = (x² - k²)/(x - k) , x ≠ k

f(x) = 4 - k , x = k

For the value of lim (x → k⁻) f(x);

Use function for  x ≠ k, as the left hand limit of the functions is to be evaluated.

=  lim (x → k⁻) f(x)

Let x = k - h, put in the function.

=  lim (h → 0)  ((k-h)² - k²)/(k - h - k)

= lim (h → 0) h(h - 2k)/-h

=  lim (h → 0) 2k - h

Pu h = 0

= 2k

Thus, the  value of the limit of piece wise function is 2k.

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:B. \:\: - \dfrac{1}{18} [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

The given equation of a line is in its slope intercept form, that is :

[tex]\qquad \tt \rightarrow \: y = mx + c[/tex]

The original equation is :

[tex]\qquad \tt \rightarrow \:y = 18x + 5[/tex]

by comparing the two equations we get slope (m) of this line equal to 18

we need to find the slope (n) of line perpendicular to this.

By the property of perpendicular lines, we know :

[tex]\qquad \tt \rightarrow \:m \times n = - 1[/tex]

[tex]\qquad \tt \rightarrow \:18 \times n = - 1[/tex]

[tex]\qquad \tt \rightarrow \:n = - \cfrac{1}{18} [/tex]

So, slope of required line is -1/18

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer: -1/18

Step-by-step explanation:

Let y=k₁x+b1 be the line. Given the perpendicularity of lines, the equation of the line perpendicular to the given line has the form:

                                       [tex]\displaystyle\\y=-\frac{1}{k}x+b_1[/tex]

[tex]\displaystyle\\So,\ y=18x+5\\\\\Rightarrow\ -\frac{1}{18}[/tex]

The rate at which the x-coordinate is changing is 3√3 units per second .

In the question ,

it is given that

the equation of the particle moving in the circular orbit is x²+y²=16

given the y coordinate decreases at 3units per second

So, dy/dt = -3.

to find the rate at which the x-coordinate is changing , we will differentiate the given equation.

Differentiating the equation  x²+y²=16 with respect to t , we get

d/dt(x²+y²) = d/dt(16)

2x(dx/dt) + 2y(dy/dt) = 0

2x(dx/dt) =  -2y(dy/dt)

Dividing both sides by 2 ,

we get ,

x(dx/dt) =  -y(dy/dt)

[tex]\frac{dx}{dt} =\frac{-y(\frac{dy}{dt}) }{x}[/tex]

As the particle is passing through the point (2,2√3) , So, the point will satisfy the equation.

Substituting the value of x=2 , y=2√3 and dy/dt= -3 ,

we get ,

dx/dt = ((-2√3)*(-3))/2

= (6√3)/2

= 3√3

Therefore , the rate at which the x-coordinate is changing is 3√3 units per second .

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To find:

The midpoint of the line segment with the endpoints P1(11/2,3/8) and P2 (-7/2,5/8).

Solution:

The midpoint formula is:

Put the values:

Thus, the midpoint is (1, 1/2).