Identify the hypothesis and conclusion of conditional statement.
If you are a teenager, then you are at least 13 years old.

Answer: The answer is D

Step-by-step explanation:

The distance between X(5,4) and Y(2,1) is 4.24 rounded to the nearest tenth.

Let's consider we have two points (x₁, y₁) and (x₂, y₂) the distance between these two points is given by the formula;

[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]

The distance between two points (x₁, y₁) and (x₂, y₂)  is given by ;

[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]

So,

Distance between X(5,4) and Y(2,1)

[tex]d = \sqrt {\left( {5 - 2 } \right)^2 + \left( {4 - 1 } \right)^2 }[/tex]

d = √18 = 4.242640687

Roud to nearest tenth ⇒ 4.24 units.

Hence "The distance between X(5,4) and Y(2,1) is 4.24 rounded to the nearest tenth".

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Answer:

Step-by-step explanation:

The missing values from area model will be  48, 240.

An area model is a rectangular diagram or model used in mathematics for problems involving multiplication and division, where the length and breadth of the rectangle are determined by the factors, quotient, and divisor.

Write the enlarged form of each component first. Next, sketch your model. To get the area of each smaller rectangle, multiply next. To determine the entire area, add those items last.

The area model will be -

                    60                        6

8                   480                      48

40                2400                    240

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The value of x if D bisects A and B is 6

The given parameters are

D bisects A and B.

Length AD = 2x - 2

Length DB = x + 4

This means that

AD =DB

So, we have

2x - 2= x + 4

Evaluate the like terms

x = 6

Hence, the value of x if D bisects A and B is 6

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Bruce's principle is $140.

The interest that Bruce earned is $9.80

The interest rate that Bruce savings account is 7%.

Simple interest is the interest that that is earned a certain amount over a period of time given a principal and the number of years.

Simple interest = amount deposited x time x interest rate.

A graph can be described as a pictorial representation of data. A graph has a y-axis and the x-axis. The y-intercept is a point where the graph touches the y-axis. The y-intercept represents the initial amount that is deposited. The principle is $140.

The slope of the graph represents the rate at which the amount invested increases in value.

Interest Bruce earned after 1 year : change in the slope

149.80 - 140 = $9.80

Interest rate = Interest / (principle x time)

9.80 / (140 x 1) = 0.07 = 7%

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The distance from the line x=4 to the given point (-2,5) is 6 units .

Distance formula from line to point :

The distance from the line ax+by+c=0 to the point (u,v) is given by the formula

[tex]distance=\frac{|au+bv+c|}{\sqrt{a^{2} +b^{2} } }[/tex]

In the given question

the equation of the line is [tex]x=4[/tex]

taking all the terms to Left side we get

[tex]x-4=0[/tex]

[tex]1.x+0.y-4=0[/tex]

given the points (-2,5)

From above values we the values as a=1 , b=0 , c=-4 , u=-2 , v=5 .

Substituting the values in the distance formula we get

[tex]d=\frac{|1*(-2)+0*(5)-4|}{\sqrt{1^{2} +0^{2} } }[/tex]

[tex]=\frac{|-2+0-4|}{1} \\ \\ =|-6|\\ \\ =6[/tex]

Therefore , the distance from the line x=4 to the given point (-2,5) is 6 units.

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Answer:

x=4

Step-by-step explanation:

Answer:

x=4

Step-by-step explanation:

2x-2=6

Okay, first we need to create the inverse of this equation.

The inverse of subtraction is addition.
2(x)-2=6


2x = 6+2

Now, we solve the right-hand side.

2x = 8

Then, divide both sides by the greatest common factor.

We get x by itself.

2x = 8
/2     /2
x = 4

Answer:

8136366271773737i228882ywhw

The proof is completed and showed that < 2 ≅ < 3 as required.

Given data

<1 and <2 are linear pair

<1 + <3 = 180 degrees

required to proof <2 ≅ <3

linear pair implies mathematically that the sum of the two angles are 180 degrees, hence we have:

< 1 + < 2 = 180 degrees    equation 1

also given that,

< 1 + < 3 = 180 degrees    equation 1

equating equation 1 and equation 2 gives

< 1 + < 2 = < 1 + < 3

< 2 = < 3

Hence the required proof

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The standard form of the given equation is; x + (-y) = -5

We are given the equations;

x + 6 = 0  -----(1)

y - 3 = 4   -----(2)

Add 4 to both sides of equation 2 to get;

y - 3 + 4 = 0

y + 1 = 0    -----(3)

Put y + 1 for 0 in eq 1 to get;

x + 6 = y + 1

The standard form of an equation is expressed in the form;

Ax + By = C

Thus;

x + 6 = y + 1 can be rewritten as;

x + (-y) = 1 - 6

x + (-y) = -5

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Distance between the points A and B are equal to distance between points B and C.

So, The given triangle is isosceles.

And, . By using distance formula we have to write an expression for BC as,

⇒ [tex]D_{BC} = \sqrt{4a^2+b^2}[/tex]

Here,

The vertices of a triangle are A (0, 0), B (2a, b) and C (4a, 0)

We have to check the triangle is isosceles.

And, Write an expression for BC.

What is Isosceles triangle?

When two sides of a triangle are equal then the triangle is said to be isosceles triangle.

Now,

The vertices of a triangle are A (0, 0), B (2a, b) and C (4a, 0)

We have to check the triangle is isosceles.

For this we use distance formula and prove that the two sides of triangle are equal.

Distance between the points A (0, 0) and B (2a, b) is;

[tex]D_{AB} = \sqrt{(2a-0)^2 + (b-0)^2} = \sqrt{4a^2+b^2}[/tex]

And, Distance between the points B (2a, b) and C (4a, 0) is;

[tex]D_{BC} = \sqrt{(4a-2a)^2 + (0-b)^2} = \sqrt{4a^2+b^2}[/tex]

Hence, Distance between the points A and B are equal to distance between points B and C.

So, The given triangle is isosceles.

c. By using distance formula we have to write an expression for BC as,

⇒ [tex]D_{BC} = \sqrt{(4a-2a)^2 + (0-b)^2} = \sqrt{4a^2+b^2}[/tex]

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Answer:

13 cups of milk I think

Step-by-step explanation:

yes, actually it is possible. The mathematical expression f(x)=exp or ex denotes the exponential function.

The mathematical expression f(x)=exp or ex denotes the exponential function. The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, though it can be extended to the complex numbers or adapted to other mathematical objects like matrices or Lie algebras. When the input variable x appears as an exponent in the formula f(x) = axe, an exponential function is indicated. The exponential curve is influenced by both the exponential function and the value of x.

One of the key mathematical operations is the exponential function (though it would have to admit that the linear function ranks even higher in importance). We allow the exponent to be the independent variable to create an exponential function. The formula f(x)=2x is a straightforward example.

Hence, yes, actually it is possible.

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Option C: The value of m ∠3 is 30° (C).

As per the question, ∠4 and ∠5 form a linear pair. Therefore the sum of ∠4 and ∠5 is 180° so, so the sum of the remaining m∠1,m∠2, and m∠3 angles is 180°.

So, m∠1 + m∠2 + m∠3 + m∠4 + m∠5 = 360° (as the total angle is 360°).

Now, m∠4 + m∠5 = 180°(∠4 and ∠5 form a linear pair). (∴ m∠1 + m∠2 + m∠3 = 180°). Now we will put the given values and will try to find out the value of x.

2x + (3x-20) + (x-4) = 180

[m ∠1 = 2 x, m ∠2 = 3 x-20, and m ∠3 = x-4]

or,

6x-24=180

or,

6x = 180+24

or,

6x = 204

or, x = 204/6

or. x = 34

As per the question we have to find out the value of m ∠3.

m ∠3 = 34° - 4° = 30° (as x = 30°)

So, m ∠3 is 30°.

If ∠4 and ∠ 5 form a linear pair. And, m ∠1=2 x, m ∠2=3 x-20, and m ∠3=x-4, the value of ∠3 is 30°. Therefore, Option C is the correct answer.

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Answer: number 1. 4 number2. 7

Step-by-step explanation:

I hope this helps!

Answer:

the answer is 2 upon 10 ndnznnznznzjzjzj

The principal of the car loan is $23,400, the interest rate of the car loan is 1.60% and the monthly payment is $375.

Given that, balance after 3 months = 22,275 and balance after 12 months = 18,900.

Average payment rate means, for any date of determination, the sum of the monthly payment rates for the prior three monthly periods divided by three.

Now, the difference of payment = 22,275 - 18,900

= $3,375

The difference of time = 12 - 3 = 9 months

So, the payment per month = 3,375 / 9

= $375 per month.

Now, 375 x 12 = $4,500

Principal amount = 4,500 + 18,900

= 23,400

Rate = 375 / 23400 × 100

= 0.016 × 100 = 1.60%

Therefore, the principal of the car loan is $23,400, the interest rate of the car loan is 1.60% and the monthly payment is $375.

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The cost function will be of the form f(x) = x + 29.

A function have a set of dependent variable for the given or specified independent variable.

According to the given question Recycled​ CDs, Incorporated, offers a choice of 5 used CDs for ​29 dollars with each additional CD costing a dollar.

We have to write a function for purchasing 5 or more CDs where x represents the no. of CDs over 5.

Let f(x) represents the cost of CDs.

∴ f(x) = x + 29.

Here the constant 29 dollars represents the cost of 5 CDs and x represents no. of CD's over 5.Put x = 0 and the cost for 5 CDs will be 29 and for any more value of x we will get our desire result.

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The given lograthimic expression 7log p + 2logq can be written as log(p^7q^2).

According to the given question.

We have a lograthimic expression.

7log p + 2logq

As we know that, a logarithmic expression is an expression that involves the logarithm of an expression containing a variable.

Also according to the product  and power rule we know that

log(mn) = logm + logn

log(x^y) = ylogx

Therefore, the given lograthimic expression 7log p + 2logq can be written as

7log p + 2logq

= log p^7 + log q^2

= log(p^7q^2)

Hence, the given lograthimic expression 7log p + 2logq can be written as log(p^7q^2) as log(p^7q^2).

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Answer:

Step-by-step explanation:

First Number : x - 5

Second Number : x

x + ( x - 5) = 31

     2x - 5 = 31

            2x = 31 + 5

           2x/2 = 36/2

               x = 18

Then plugin x= 18 into First numer X - 5

   x - 5

  18 - 5 = 13

18 + 13 = 31

so .....

First Number is 13

Second number is 18

Answer:

infinite number of solutions

Step-by-step explanation:

3(n + 11) - 5n = - 2(n - 12) + 9 ← distribute parenthesis on both sides

3n + 33 - 5n = - 2n + 24 + 9 , that is

- 2n + 33 = - 2n + 33

since the expressions on both sides are the same then any value of n will make the equation true.

thus the equation has an infinite number of solutions

Answer:

Any real value. Infinite no. of solutions.

Step-by-step explanation:

Let's open the bracket first. Multiply the term outside the bracket with each term inside the bracket.

[tex]\Rightarrow[/tex] 3(n+11)-5n = -2(n-12)+9

[tex]\Rightarrow[/tex] 3n + 33 - 5n = -2n + 24 + 9

Now simplify the n terms on both sides

[tex]\Rightarrow[/tex] -2n + 33 = -2n + 33

Here both LHS and RHS are same. And the terms gets canceled. Any real value of n satisfy the above equation.

The price of a rake and a shovel is $22 and $25 respectively.

Let's assume the price of a rake is x and the cost of a shovel is y.

Now, Theresa purchased 10 rakes and 15 shovels for $595.

10x + 15y = $595                                                                      -------------------(1)

Taking 5 common out from each side of the equation,

5( 2x + 3y) = 5( 119)

2x + 3y = 119                                                                             ------------------(2)

Brett purchased 8 rakes and 20 shovels for $676.

8x + 20y = $676                                                                       ------------------(3)

Multiply equation (2) by 4 and subtract from equation (3),

8x + 20y - ( 8x + 12y ) = 676 - 476

8x + 20y - 8x - 12y = 200

8y = 200

y = $25

Therefore,

10x + 15y = 595

10x + 15(25) = 595

10x + 375 = 595

10x = 595 - 375

10x = 220

x = $22

Hence, the price of a rake and shovel is $22 and $25 respectively.

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The value of h(g(t))(-6) is 24.

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Functions are ubiquitous in mathematics and are essential for formulating physical relationships in the sciences.

An example of this would be y=x².

If you put in anything for x, you get one output for y. We would say that y is a function of x since x is the input value.

Given:

g(t) = t² + 4t

h(t) = 2t

h(g(t))

=h( t² + 4t)

=2( t² + 4t)

And, h(g(t)) (-6)

=2( (-6)² + 4(-6))

=2(36-24)

=2*12

=24

Hence, the value of the function is 24.

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I) There are 8.76* 10³ hours in 1 year.

II) The exact number of hours in one year is 8.76582*10³ hours.

Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.

Given:

1 hour=3600 seconds

1 year = 31556952 seconds.

Now,

I)  Use scientific notation to estimate the number of hours in one year.

1 day = 24 hours

1 year = 365 days

So, number of hours in one year is given by,

=24*365

=8760

=8.76* 10³

So, there are 8.76* 10³ hours in 1 year.

II) 1 year = 31556952 seconds.

1 hour = 3600 seconds

In one year the number of hour is given by,

=31556952/3600

=8765.82

=8.76582*10³

So, the exact number of hours in one year is 8.76582*10³ hours.

III)

The exact numbers of hours using 365 days is 8760 which is written as  in scientific notation but using the given data we get  hours.

Comparing these answers the first one has only 3 significant figures and the second answer has six significant figures.

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The formula for an arithmetic series  -5,-3.5,-2,-0.5,1, is An = A1 + (n-1)d

See the pattern

-5-(-3.5)= -1.5

-3.5-(-2)= -1.5

The formula for an arithmetic series  -5,-3.5,-2,-0.5,1, is  An = A1 + (n-1)d

An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.

Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.

An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.

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Each angle to draw a pie chart a, b, c, d, and e will be 116°, 36°, 96°, 64°, and 48°, respectively.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

Workers in an office of 90 staff were asked their favorite type of takeaway. The results are summarised in the table.

Take-away             Frequency            Angle

   Pizza                         29                       a

   Curry                          9                        b

Fish & chips                 24                        c

  Kebab                        16                        d

   Other                         12                       e

The angles on the pie chart are calculated by multiplying the table by 4. Then the angles will be

∠a = 4 x 29 = 116°

∠b = 4 x 9 = 36°

∠c = 4 x 24 = 96°

∠d = 4 x 16 = 64°

∠e = 4 x 12 = 48°

Each angle to draw a pie chart a, b, c, d, and e will be 116°, 36°, 96°, 64°, and 48°, respectively.

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