A diagonal of a rectangle splits the rectangle into two 300-60 •-90° triangles. If the diagonal of the rectangle is 21 in, what is the length and width of the rectangle. Find the area

The roots of the quadratic equation 6x²-2x=8 are x=4/3 and x=-1.

Given that,

The equation is 6x²-2x=8

To find : The roots of the quadratic equation 6x²-2x=8

Any equation that can be rearranged in standard form as where x represents an unknown value, and a, b, and c represent known values, where a 0, is referred to as a quadratic equation in algebra (from Latin quadratus, "square"). The equation is linear, not quadratic, if a = 0 and b 0. The coefficients of the equation are the numbers a, b, and c, which can be separated by naming them, respectively, the quadratic coefficient, the linear coefficient, and the constant coefficient or free term.

We know that,

The solutions are x1 and x2  = -b±√b²-4ac/2a

Here b = -2 ,a = 6 and c= -8

No substitute those values in the formula,

= -b±√b²-4ac/2a

= -(-2) ± √(-2²)-4(6)(-8) / 2(6)

x = 4/3 and x =-1

So, The roots of the quadratic equation 6x²-2x=8 are 4/3 and -1

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The system has no solution when h is not equal to ( 18x+7 )/( -6x)

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

− 6(hx + 2) = 3(x − 3) + 2(x + 2) +13x

-6hx-12=3x-9+2x+4+13x

=>  -6hx-12= 18x-5

=> -6hx = 18x-5 +12

=>  -6hx = 18x+7

=> h = ( 18x+7 )/( -6x)

The system has no solution when h is not equal to ( 18x+7 )/( -6x)

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x/sin 45 = 4√22/sin 90

CB = 4√22/sin 90 × sin 45

CB = 4√11

or

CB = √(4√22)²-(4√11)²

= 4√11

Answer:

CB = AC = 4√11

Step-by-step explanation:

We know that the sum of the angles of a triangle is 180°. If angle A = 45° and C = 90°, then angle B = 180° - 90° - 45° = 45°. This shows us that the triangle is isosceles and the leg AC is equal to the leg CB.

Consequently: CB = AC = 4√11

If we didn't know the length of AC, then it can be calculated from the hypotenuse:

AC² + CB² = AB²
2 * CB² = (4√22)²
CB² = (4√22)² / 2
CB² = 16 * 22 / 2
CB = √(16 * 11)
CB = 4√11

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The range is the spread of the values of the output of a function.

To Find : The Range of a Function ,Consider a function y = f(x)

The spread of all the y values from minimum to maximum is the range of the function. In the given expression of y, substitute all the values of x to check whether it is positive, negative or equal to other values. Find the minimum and maximum values for y. Then draw a graph for the same.

The range of a function is a set of all its possible outputs.

Example: Let’s consider a function ƒ: A⇢A, where A = {1,2,3,4}.

The elements of the set Domain, are called pre-images, and elements of the set Co-Domain which are mapped to pre-images are called images. The range of a function is a set of all the images of elements in the domain. In this example, the range of the function is {2,3}.

The range is the spread of the values of the output of a function. If we are able to calculate the maximum and the minimum values of the function, we can get an idea of the range of the function.

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Amelia cut a 168 inch long ribbon into 6 equal part. Patrick cut a 14 foot long ribbon into 7 equal piece.

Amelia's ribbon pieces were 28 inches long each. Patrick's ribbon pieces were 2 feet long each.

Amelia's ribbon:

To calculate how long each piece of ribbon is, we need to divide 168 inches (the total length of the ribbon) by 6 (the number of pieces).

168 ÷ 6 = 28

Therefore, Amelia's ribbon pieces were 28 inches long each.

Patrick's ribbon:

To calculate how long each piece of ribbon is, we need to divide 14 feet (the total length of the ribbon) by 7 (the number of pieces).

14 ÷ 7 = 2

Since 1 foot is equal to 12 inches, we can convert 2 feet to 24 inches.

Therefore, Patrick's ribbon pieces were 2 feet (or 24 inches) long each.

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Answer:

x = 5

Step-by-step explanation:

Angles on a straight line add up to 180, so add up the angles and equate to 180:

9x + 85 + 10x = 180

Now we can solve for x by simplifying further:

19x + 85 = 180

Subtract 85 on both sides:

19x + 85 - 85 = 180 - 85

19x = 95

Divide 19 on both sides which cancels out the 19 on the left:

x = 95/19 = 5

The range of the data with the outlier is 7 and without is 2

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

0, 3; 1, 3; 2, 2; 3, 1; 8, 1.

The range without the outlier

The range is calculated as

Range = Highest - Least

Without the outlier, we have

Range = 3 - 1

Range = 2

The range with the outlier

The range is calculated as

Range = Highest - Least

With the outlier, we have

Range = 8 - 1

Range = 7

Hence, the range are 2 and 7

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Step-by-step explanation:

The answer is gotten by 5% of 70

5/100 × 70/1

= 35/10

= 3.5

Answer: $73.50

Step-by-step explanation:

First, we need to find what is 5% worth of 70 bucks. We would divide 5 by 100 since percents are based on 100 which gets us 0.05. Next do 0.05 * 70 = 3.5. Means that she'll pay $3.50 on top of the 70 bucks, so add the two together, common sense: $73.50. Have a good day ;)

If the historical data says that the number of road bikes sold is 9 and the number of stationary bikes sold is 3, out of a total of 60 bikes, then  the probability that the next customer purchase a stationary bike is 1/20.

A probability based on historical data is referred to as empirical probability or experimental probability. In other words, empirical probability depicts the probability of an occurrence occurring based on past data.

Empirical probability is also known as the relative frequency.

Formula for the empirical probability is:

Empirical probability = times of event A occurs / total number of trials

In the problem, there are two kinds of bike: road bike and stationary bike.

The historical data:

sales of road bike = 9

sales of stationary bike = 3

total bikes = 60

Hence, the probability that the next customer will buy a stationary bike is:

P(stationary) = sales of stationary bike / total bikes

P(stationary) = 3/ 60 = 1/20

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The complete table would look like this:

Number of loaves    Number of Bananas

1                                    2 1/2

2                                   5                            

4                                    10

What is a number line?

A number line is a visual representation of a continuous range of numbers, usually represented as a straight line. Numbers are represented by points along the line, and the distance between two numbers corresponds to the difference between their numerical values. The numbers are usually represented by evenly spaced marks or tick marks on the line, and they can be positive or negative numbers, integers or fractions, or real numbers. The number line is used to represent various mathematical concepts such as inequalities, absolute values, and intervals. It is also used to help students understand concepts such as addition, subtraction, and ordering of numbers.

So the first one was easy because it already said it in the number line.

For the second one you simply multiply 2x 2 1/2

For the third one, you multiply 4x 2 1/2.

Hence, The complete table would look like this:

Number of loaves    Number of Bananas

1                                    2 1/2

2                                   5                            

4                                    10

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Answer:

[tex]y=-\frac{6}{5} x[/tex]

Step-by-step explanation:

[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

[tex]\frac{7-(-5)}{-5-5}[/tex]

[tex]\frac{7+5}{-10}[/tex]

[tex]-\frac{12}{10}[/tex]

[tex]y=-\frac{6}{5} +b[/tex]

[tex]-5=-\frac{6}{5} (5)+b[/tex]

- 5 = - 5 + b

b = 0

[tex]y=-\frac{6}{5} x[/tex]

Since b and g are the numbers of boys and girls in class b + 3g is equal to [tex]b^3 - 3b^2 + 5g^2 - 3g + 2b[/tex]

We can use the concept of combination to determine the value of b + 3g.

The number of ways to choose 3 boys from b boys and 2 girls from g girls is:

(b choose 3) x (g choose 2) = (b! / (3!(b-3)!) ) x (g! / (2!(g-2)!) ) = (b x (b-1)(b-2))/(321) x (g(g-1))/(2 x 1)

We know that this is equal to 168, so we can set up the equation:

(b x (b-1)(b-2))/(321) x (g(g-1))/(2 x 1) = 168

We can solve this equation to find the value of b + 3g. Since b and g are the numbers of boys and girls in the class, we know that b + g is the total number of students in the class.

So we can simplify the equation as:

(b x (b-1)(b-2)) x (g(g-1)) = 32121 x 168

and rearrange it to:

[tex](b^3 - 3b^2 + 2b) * (g^2 - g) = 1008[/tex]

[tex]= b^3 - 3b^2 + 2b = 1008 / (g^2 - g)b + 3g \\= (b^3 - 3b^2 + 2b) + 3(g^2 - g) \\= b^3 - 3b^2 + 2b + 3g^2 - 3g \\= b^3 - 3b^2 + 5g^2 - 3g + 2b[/tex]

So we can see that b + 3g is equal to b^3 - 3b^2 + 5g^2 - 3g + 2b. However, the exact value cannot be determined without the specific values of b and g.

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Answer: We can use the formulas for conditional probability to calculate the percentage of people in the village who speak both French and English.

P(French and English) = P(French) x P(English|French)

We know that P(French) = 64% and P(English|French) is the probability of someone speaking English given that they already speak French, which is 58%. So we can plug these values into the formula:

P(French and English) = 64% x 58% = 37.12%

Therefore, 37.12% of the inhabitants of the village on the Nigerian border speak both French and English.

Note that this is an estimation since this formula assumes independence and the real probabilities might be different.

Step-by-step explanation:

This problem may be simplified by substituting the number seven into the original equation. The result will then be obtained by solving the given expression.

Put the supplied value of h, which is seven, in the given phrase to begin solving this problem. Then, using the BODMAS rule, the bracket will be solved first, followed by the addition, from which this can be solved yielding a result of 50.

This may be resolved as follows:

For h=7, in 5 x ( h + 3 )

= 5 x ( 7 + 3 )

= 5 x ( 10 )

= 50

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The following triangles are congruent.

Yes AAA

Answer:

-2+4=2

Step-by-step explanation:

All you need to do is count 4 spaces from -2 on the number line. See in image.

-Hope this helped

The total number of miles Reuben biked last year and this year is the sum of the miles he biked last year and this year.

You can represent the total number of miles he biked as:

Total miles = 496 + m

Where 496 is the number of miles biked last year and m represents the number of miles biked this year.

So the expression for the total number of miles he biked is 496 + m

There are 364 solutions to the given inequality: x1 + x2 + x3 <= 11.

To get the solution of the inequality x1 + x2 + x3 <= 11, we first need to include an additional variable in the inequation to write in as an equation.

Therefore, let the additional variable be x4.

Thus, equation is x1 + x2 + x3 + x4 = 11

The number of solutions of an equation can be calculated by the formula,

[tex]( \left \ {{n+ r - 1} \atop {n}} \right.)[/tex], where n is the constant value of the equation and r is the number of variables in the equation.

In this case, n = 11 and r = 4

Therefore,

[tex]( \left \ {{n+ r - 1} \atop {n}} \right.)[/tex] = [tex]( \left \ {{11+ 4 - 1} \atop {11}} \right.)[/tex] = [tex]( \left \ {{14} \atop {3}} \right.)[/tex]

= 14 * 13 * 12 * 11!/(3 * 2 * 1 * 11!)

=2184/6 = 364

Therefore, there are 364 possible solutions of the inequality.

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Answer: It's the same process to get the variable by itself. But once found depending on how you are required to represent the solution, the final answer may vary. You need to also keep in mind that with negatives when multiplying and dividing you have to flip the inequality sign.

Step-by-step explanation:

Ex. 2x>4

x>2

but if

-2x>4

x<-2

The process of dividing the two digit numbers without a calculator is solved by using the dividend, divisor, quotient and remainder.

Division in math is defined as the process to distribute the whole thing to a group in equal parts or make equal parts.

Here we need to find he way to divide two digit numbers without a calculator.

As per the definition of division, here we have to divide the first number of the dividend or the two first numbers if the previous step took another digit by the first digit of the divisor.

And then we have to write the result of this division in the space of the quotient.

Finally we have to multiply the digit of the quotient by the divisor, then write the result beneath the dividend and subtract it.

This process is repeated until we get zero as remainder.

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The length of EF, to the nearest tenth of a foot is found to be 14.3 ft.

In rDEF, DE = 90°, DF = 81°, and DE = 14. 6 ft,

Because the given triangle is a right angled triangle, we can use the concepts of trigonometry in order to solve the given problem.

Using the trigonometric relation,

sin A = P/H

Where,

P is perpendicular and H is the hypotenuse.

We have, A = 81°,

It is given that the value of DE is 14.6 ft.

We know, sin(81°) = 0.98

So, the length of EF, to the nearest tenth of a foot is,

0.98 = EF/14.6

EF = 14.3 ft.

So, the length of the EF is 14.3 ft.

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Complete Question - In ΔDEF, ∠E = 90°, ∠F = 81° and DE = 14.6ft. Find the length of EF, to the nearest tenth of a foot.

The distance between the pair of points with the coordinates ( 3, 4 ) and (0, 0) is given by 5 units.

As given in the question,

Given pair of points with the coordinates are as follow :

( x₁ , y₁ ) = ( 3,4 )

( x₂ , y₂ ) = ( 0, 0 )

General formula to determine the distance between two pair of points with the coordinates is :

= √( y₂ - y₁ )² + (x₂ - x₁ )²

Now, substitute the values of the coordinates to find the distance between two pair of points :

= √ ( 0 - 4 )² + ( 0 - 3 )²

= √4² + 3²

= √16 + 9

= √25

= 5 units.

Therefore, the distance between the given pair of points with the coordinates is equal to 5 units.

The above question is incomplete , the complete question is:

What is the distance between the pair of points (3, 4) and (0, 0) ?

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Answer:

88.50

Step-by-step explanation:

0.12x400=48 dollars +the 40.50 dollars answer 88.50

Answer:

The equation x2+6x+9 = 0 has roots of 3+i and 3-i. By the fundamental theorem of algebra, this equation has three roots, two of which may be equal. The standard quadratic equation using the given set of solutions {3+i,3-i} is y=x2+6x+9.

In the given arithmetic sequence, the First term is -74, 2nd term is -81 3rd term is -88 and 4th term is -95.

There are two ways to define an arithmetic sequence. It is a "sequence where the differences between every two successive terms are the same" (or) In an arithmetic sequence, "each term is obtained by adding a fixed number (positive or negative or zero) to its preceding term." The following is an arithmetic sequence where each term is obtained by adding 4 to the term before it.

We know that arithmetic sequence is:

[tex]a_{n}=a_{1}+(n-1)d[/tex]

Given

a = -74, d = -7

[tex]a_{1} = -74 + (1 - 1)(-7)[/tex]

[tex]a_{1} = -74 + (0)(-7)[/tex]

[tex]a_{1} = -74[/tex]  (First term)

[tex]a_{2} = -74 + (2 - 1)(-7)[/tex]

[tex]a_{2} = -74 + (1)(-7)[/tex]

[tex]a_{2} = -81[/tex] (2nd term)

[tex]a_{3} = -74 + (3- 1)(-7)[/tex]

[tex]a_{3} = -74 + (2)(-7)[/tex]

[tex]a_3 = -88[/tex] (3rd term)

[tex]a_{4} = -74 + (4- 1)(-7)[/tex]

[tex]a_{4} = -74 + (3)(-7)[/tex]

[tex]a_3 =-95[/tex] (4th term)

Thus, In the given arithmetic sequence, the  First term is -74, 2nd term is -81 3rd term is -88 and 4th term is -95.

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The slope of a line is determined by the formula:

(y2 - y1) / (x2 - x1)

So for the points (9, 5) and (21, -5), the slope would be:

(-5 - 5) / (21 - 9) = -10 / 12 = -5/6

So the slope of the line that passes through the points (9, 5) and (21, -5) is -5/6 in simplest form.

The distance between two points (2, 3) and (5, 7) is 5 units.

Therefore the answer is 5.

To find the distance between the points (2, 3) and (5, 7), we can use the distance formula:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

where (x₁, y₁) = (2, 3) and (x₂, y₂) = (5, 7)

Substituting the coordinates of the two points into the formula:

d = √((5 - 2)² + (7 - 3)²)

d = √((3)² + (4)²)

d = √(9 + 16)

d = √(25)

d = 5

So the distance between the points (2, 3) as well as (5, 7) will be  5 units by solving the above expression.

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The value of x as shown in the straight line is 32

An equation is an expression showing the relationship between numbers and variables.

An angle is formed when two lines intersect at a point. The sum of angles in a straight line is 180 degrees.

From the diagram:

(3x - 4) + (3x - 8) = 180° (sum of angle in a straight line)

3x + 3x - 4 - 8 = 180

6x - 12 = 180

6x = 192

x = 32

The value of x is 32

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