The length of the base of an isosceles triangle is 49.96 meters. Each base angle is 31.43°. Find the length of each of the two equal sides of the triangle. Round to the hundredths place.

The error interval for the combined mass (m) of the car and the person is 2047.7 ≤ m < 2049.7

An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments (symbols):

The error interval for the mass of car is given by:

Mass of car = 1990 ± 0.5;

Mass of car = 1990 + 0.5 = 1990.5

Mass of car = 1990 - 0.5 = 1989.5

The error interval for the mass of a person is given by:

b = 1990 ± 0.5;

b = 58.7 + 0.5 = 59.2

b = 58.7 - 0.5 = 58.2

For the value of a and b, we have:

a = 1989.5 + 58.2 = 2047.7

b = 1990.5 + 59.2 = 2049.7

Next, we would calculate the combined mass (m):

m = 1990 + 58.7

m = 2048.7

Now, we can write the error interval for the combined mass (m) of the car and the person as follows:

a ≤ m < b

2047.7 ≤ m < 2049.7

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If the width of larger full size pickup truck is 10.0 in. then its height is equal to 12inches.

As given in the question,

Side mirror of a small pick up truck is similar to larger full size pick up truck.

Smaller truck has rectangular side mirror

Width = 5.0 in.

Height = 6.0 in.

Larger mirror

Width = 10.0 in.

Let h be the height of the larger mirror

Both the mirrors are similar and rectangular in shape.

Hence, sides are in proportion

5 /6 = 10 /h

⇒h = (6 ×10) / 5

⇒ h = 12 in.

Therefore, if the width of larger full size pickup truck is 10.0 in. then its height is equal to 12inches.

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Answer:

The variable x represents the number of fish tanks he/she sells.

Explanation:

Given that Eric's base salary is still $1400, but now he makes a commission of

$100 for each fish tank that he sells and Nancy now gets a base salary of $500 per month, but her commission has stayed the same at $250 per fish tank.

Eric's total income would be;

$1400 plus $100 times the number of fish tanks he sells.

and Nancy's total income would be;

$500 plus $250 times the number of fish tanks she sells.

Therefore, the variable x represents the number of fish tanks he/she sells.

The number of fish tanks each of them sells will determine the total commission and also determines their total income.

The required equation for the line is  y =  x + 4 that perpendicular to y = -x + 4 and passes through the point (1, 5).

The required equation is y = 2x + 7 that parallel to y = -3x+7 passes through the point (0, 7).

The slope of a line is defined as the angle of the line. It is denoted by m

Slope m = (y₂ - y₁)/(x₂ -x₁ )

The equation of the line which is given as

2x + 3y = 18

3y = -2x + 18

y = -2x/3 + 6

Here the slope of the line, m = -1/3

Let the required line would be as

⇒ y₀ - y₁ = m₀ (x₀ - x₁ )

The required line passes through the point (1, 5)

Here x₁ = 1 and y₁ = 5 and m₀ = 1/3 (Since required line perpendicular)

The equation of the line is obtained by substituting these values into the above equation;

⇒ y - 5 = 1 (x - 1)

⇒ y = x - 1 + 5

⇒ y =  x + 4

Therefore, the required equation for the line is  y =  x + 4 that perpendicular to y = -x + 4 and passes through the point (1, 5).

The equation of the line which is given as

y = 2x + 6

Here the slope of the line, m = 2

The given coordinates of the line;

points on the line (0, 7)

Let the required line would be as

⇒ y - y₁ = m (x - x₁ )

Here x₁ = 0 and y₁ = 7 and m = 2

The equation of the line is obtained by substituting these values into the above equation;

⇒ y - 7 = 2 (x - 0)

⇒ y - 7 = 2x

⇒ y = 2x + 7

Therefore, the required equation is y = 2x + 7 that parallel to y = -3x+7 passes through the point (0, 7).

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The value of the given expression x^6 -5x^4 - 5 + x simplified as;  x^4(x^2 - 5) - (5 + x)

The statement is given as ;

Factor: [tex]x^6 -5x^4 - 5 + x[/tex]

From the given expression, we have

[tex]x^6 -5x^4 - 5 + x[/tex]

Group the expression in two part;

So, we have;

[tex]x^6 -5x^4 - 5 + x = (x^6 - 5x^4) - (5 + x)[/tex]

Now Factorize each group of the expression;

[tex]x^6 -5x^4 - 5 + x = x^4(x^2 - 5) - (5 + x)[/tex]

The given expression cannot be further simplified.

Hence, the value of [tex]x^6 -5x^4 - 5 + x is x^4(x^2 - 5) - (5 + x)[/tex]

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Lets assume that the input values are x values and the output values are y values.

Then you will have pairs of coordinate values as shown;

(-1,7) , (0,2) , (1,-3) , (2,-8), (3,-13), (4,-18)

Using the coordinates find the slope a;

(-1,7) and (0,2) ---------slope is change in y-values/ change in x-values , (2-7) /(0--1)

= -5/ 1 = -5

Do the same for the next pair of coordinates ,(0,2) and (1,-3) , (-3-2) / (1-0) = -5/1 = -5

If you continue the procedure to the next pair which is (1,-3) and (2,-8) to get the slope as : (-8- -3) / (2-1) = -5/1 = -5

This means that the slope is -5

The relation will be represented by the equation y= mx + c where m is the slope and c is the y-intercept

First plot the points to visualize the graph

From the plot, you notice that when the points are joined, a straight graph is formed sloping to the negative side and intersecting the y-axis at point (0,2).

So to determine the rule, we apply the equation y= mx + c with m= -5 and c =2

This gives y= -5 x + 2

The rule is f(x) = -5x +2 -----------answer

To write this in standard form, we need to look at the power of 10. In this case, it's a 7. Then, we need to shift the decimal point 7 places to the right:

We can see that behind the 1 (where was the decimal point before) now there are 7 numbers, then what we do is correct.

Volume of a cone =

From the question;

r= 4 h=7

π is a constant and it is equal to 22/7

substitute the values into the formula;

Answer:

80.58

Step-by-step explanation:

do you need an explanation or will this be fine?

The system of equations given has infinitely number of solutions.

A system of equations is a set of two or more equations with the same variables. A solution to a system of equations is a set of values for the variable that satisfy all the equations simultaneously.

system of equations, or simultaneous equations, In algebra, two or more equations to be solved together (i.e., the solution must satisfy all the equations in the system). For a system to have a unique solution, the number of equations must equal the number of unknowns.

In the given question, we can solve for the equation given;

[tex]y = 4x + 5\\-8x + 2y = 10\\[/tex]

Solving for both x and y;

The solution of the equation is y = 4x + 5

The system has infinitely many solutions;

In the second system of equations;

y = 0.5x + 3, x = 2y = -16

This equation is not correct.

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Answer:

-3

Step-by-step explanation:

the 'y- intercept ' is  ACTUALLY the 'y-axis intercept'.......this is where the graph crosses the y - axis    ....for this graph this is -3

We know that

• The earnings are $7,592.

• The time is 16 years.

• The annual interest rate is 9.04%.

This problem is about simple interest, its formula is

Where A = 7,592, r = 9.04, t = 16, and P is the principal.

Let's replace each value.

Notice that 9.04% is equivalent to 0.0904.

Now, we solve it for P.

a) The required down payment is $47,800.

b) The mortgage loan is $191,200.

c) The amount for the three points at closing is $5,736, which is 3% of the mortgage.

d) The monthly payment (excluding escrowed taxes and insurance) is $-1,677.92.

e) The total interest cost for the mortgage over its 30-year period is $412,850.06.

The down payment is an upfront payment required to reduce the mortgage loan and assure the financier that the mortgagee is financially ready to engage in the mortgage transaction.

The price of a dream house = $239,000

Down payment = 20% = $47,800 ($239,000 x 20%)

Mortgage loan = $191,200 ($239,000 - $47,800)

Three points at closing = 3% of $191,200

= $5,736

N (# of periods) 360 months (30 years x 12)

I/Y (Interest per year) = 10%

PV (Present Value) = $191,200

FV (Future Value) = $0

Results:

PMT = $-1,677.92

Sum of all periodic payments = $-604,050.06

Total Interest = $412,850.06

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Answer:7464

Step-by-step explanation:

90 is the score to get

let c represent correct and w represent wrong

if they get 134 points for it being correct, we can look at it like 134c

if they get -14 points for it being incorrect, we can look at it like -14w

now to put this in the right sense we fill in those letters with how many they got right and wrong : 134(58) -14(22)

This would get 7772 -308

after subtracting these two you'd get: 7464

The volume of a rectangular prism can be calculated with the following formula:

Where "l" is the length, "w" is the width and "h" is the height.

In this case, you can set up that:

The centre of mass of 40g, (1,3); 30g, (2,-1); 70g, (0,0) and 50g (0,-2) is located at (10/19,-1/19).

The formula to find the coordinates (X,Y) of centre of mass of a discrete particles system is,

X = (m₁x₁+m₂x₂+m₃x₃+m₄x₄)/(m₁+m₂+m₃+m₄)

Y = (m₁y₁+m₂y₂+m₃y₃+m₄y₄)/(m₁+m₂+m₃+m₄)

As we know,

m = 40

m = 30

m = 70

m = 50

Putting all the values in the formula,

for X coordinate,

X = [(40×1)+(30×2)+(70×0)+(50×0)]/(40+30+70+50)

X =(40+60+0+0)/(190)

X = 100/190

X = 10/19

For Y coordinate,

Y = [(40×3)+(30×-1)+(70×0)+(50×-2)]/(40+30+70+50)

Y= (120-30+0-100)/(190)

Y = -10/190

Y = -1/19

So, the centre of mass of the discrete particle system is at (10/19,-1/19)

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Answer:

I really don't understand much about math sometimes I need help

The statement which best describes Mike's error is that: D) While the graph does pass through the origin, it is not a straight line.

A graph can be defined as a type of chart that's commonly used for the graphical representation of data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

In Mathematics, the graph of any proportional relationship is characterized by a straight line with the points passing through the origin (0, 0) because as the values on the x-coordinate (x-axis) decreases or increases, the values on the y-coordinate (y-axis) decreases or increases simultaneously.

In this context, we can reasonably infer and logically deduce that even though Mike's graph passes through the origin, his error is that it is not a straight line.

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we have the following:

standard form

Therefore:

A = 0

B = 5

C = -8

Answer:

The sequence cannot be arithmetic.

Explanation:

Given the sequence: 6,12,24,48

We want to determine if the sequence is arithmetic.

An arithmetic sequence is a sequence made in which the next term is obtained by the addition of a constant term called the common difference.

In the given sequence:

The difference between the terms is not constant.

Therefore, the sequence cannot be arithmetic.

The equation for the function after the transformation is f'(x) = 2x^2 - 3

The initial equation is given as

f(x) = x²

The above represents the parent function

The sequence of transformations is given as

The rules of the above sequence of transformations are

When the rules are applied, we have

Hence, the equation in its final position is f'(x) = 2x^2 - 3

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From the fact that the sum of the angle measures of a triangle must be equal to 180º and that two angles have measures of 40º and 70º, we can deduce that the third angle must have a measure of 70º.

Therefore, this was a deductive argument.

Point = (8,-4)

When coordinate points (x,y) are rotated by 90° the image became (y,-x)

So, for this case:

Image: (-4,-8)

The number written in scientific notation is 1.12 × 10⁻² .

Scientific notation can be used to describe values that are either too large or too little to be conveniently presented in decimal form (typically would result in a long string of digits).

The given number is 4.501795324E⁻⁶

So simplifying we get :

4.501795324E⁻⁶  =  1.11588350 × 10⁻²

Therefore the number written in scientific notation is 1.12 × 10⁻² .

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Given:

Sum of two numbers-6

Difference of two numbers-12

Required:

To calculate the number

Explanation:

Consider first number-9

Consider second number--3

Sum =9+(-3)=9-3=6

Difference=9-(-3)=12

Required answer:

Option B

The Factors of x² - 5x + 6 are (x-3) (x-2)

Step 1: Add the constant term to the first term's coefficient. i.e (6 x 1) = 6

Step 2:Find the two factors of 6 whose total matches the middle term's coefficient., i.e -5.

Thus, the factors are -3 and -2 as,

-3 × (-2) = 6 (Product)

-3 + (-2) = -5 (Sum)

The polynomial may be expressed as follows after dividing the middle term by the two components, -3 and -2:

x² - 3x - 2x + 6 = 0    

⇒ x(x-3) -2(x-3) = 0

⇒ (x-3)(x-2) = 0  

Thus, the Factors of x² - 5x + 6 are (x-3) (x-2).

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We are asked to determine the equation of a line that is parallel to:

Two lines are parallel if their slopes are in the following relationship:

Therefore, if m1 is the slope of the given line and m2 is the slope of the parallel line we may determine the value of the slope of the parallel line by replacing it in the relationship. Let's remember that when a line is written in the form:

Where "m" is the slope. Therefore, m1 is -2/3. Replacing in the relationship we get:

Now, we go back to the general form of a line equation and replace the value of the new slope:

The value "b" is the y-intercept and can be found using the point through which the line passes:

Now we solve the operations:

Subtracting 21/2 from both sides:

Solving the operations:

Now we replace in the line equation:

And thus we get the equation of the parallel line.

The value of the set  (A∪C)'∩B is {9 , 12} .

A subfield of mathematical logic called set theory examines sets, which are essentially collections of objects.

The given sets are:

U ={1,2,3,4,5,6,7,8,9,10,11,12,13}

A = {3,7,11,13}

B = {3,6,9,12,13}

C = {2,3,5,6,7,8}

Now B' = {1,2,4,5,7,8,10,11}

b) B'∩C = {2,5,7,8,}

c) A∪C = {2,3,5,6,7,8,11,13}

(A∪C)' = {1,4,9,10,12}

(A∪C)'∩B = {9 , 12}

Hence the value of the set (A∪C)'∩B is {9 , 12} .

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The amount of space taken by 39 of these pictures is 117 megabytes.

The unitary approach is a problem-solving process that begins by identifying the value of a single unit and then multiplying that value by the needed value.

Given:

Number of pictures downloaded by Kelly from her cell phone to her computer = 195

Amount of space taken by the pictures = 585 megabytes

Now, an equal amount of space is taken by each picture.

To determine, the megabytes taken by 39 of these pictures.

By the unitary method,

195 pictures = 585 megabytes

39 pictures = ? megabytes

Divide 585 megabytes by the number of pictures 195 and then multiply it by 39.

= (585/195) × 39

= 117 megabytes

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