X, Y and Z form the vertices of a triangle, where
∠
YXZ = 57°,
∠
YZX = 47°, and XZ = 7.2cm.
Calculate the length of YZ rounded to 1 DP

The value of c is 72.

What is a quadratic equation?

A quadratic equation is a type of polynomial equation that has the form of ax^2 + bx + c = 0, where x is the variable, and a, b, and c are coefficients. The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b and c are constants. The solutions of a quadratic equation are given by the quadratic formula: x = (-b ± √(b^2-4ac)) / 2a

The equation x^2-17x+c=0 is a quadratic equation where a=1, b=-17 and c=c

To find c, we can use the difference of the two solutions of the equation, which is 1.

The two solutions of the equation are given by the quadratic formula

x = (-b ± √(b^2-4ac)) / 2a

x = (-(-17) ± √((-17)^2-41c)) / 2*1

x = (17 ± √(289-4c)) / 2

The difference of the two solutions is (17 + √(289-4c))/2 - (17 - √(289-4c))/2 = 1

we can solve for c:

(17 + √(289-4c))/2 - (17 - √(289-4c))/2 = 1

√(289-4c) = 1

289-4c = 1

4c = 288

c = 72

Hence, the value of c is 72.

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The numbers that can be formed using the  condition is [tex]20^n[/tex]

When a positive integer has n digits and the first digit is 2, all of the digits are prime, the probability that any two successive digits added together are prime is. Numbers from the set {1,3,5,7,9} must be used in the n odd locations, and numbers from the set {2,4,6,8} must be used in the n even spots.

We cannot include 0 in even positive integers because it is neither positive nor negative.

Order matters and repetitions are permitted.

So, here we are

possibilities are

[tex]5^n \times 4^n =20^n[/tex]

where n is the integral value

Therefore, the number of positive integers with digits and the specified restriction is [tex]20^n[/tex]

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So, the coordinates of the images S', R', T' under the translation are (11,9), (-4,-6) and T'(h+4,k-5) respectively.

a) For the point S(7,14), we are given the translation defined by (x,y) -> (x+4, y-5). This means that for any point (x,y), we add 4 to the x-coordinate and subtract 5 from the y-coordinate to find the image of that point. Applying this transformation to the point S(7,14) gives us the image point S'(7+4, 14-5) = S'(11,9). So the coordinates of the image S' is (11,9)

b) For the point R(-8,-1), we are given the same translation defined by (x,y) -> (x+4, y-5). Applying this transformation to the point R(-8,-1) gives us the image point R'(-8+4,-1-5) = R'(-4,-6). So the coordinates of the image R' is (-4,-6)

c) For the point T(h,k), we are given the same translation defined by (x,y) -> (x+4, y-5). Applying this transformation to the point T(h,k) gives us the image point T'(h+4,k-5).

Here h and k are variables and we can't say the coordinates of image point T' without specific values of h and k. But we can say the transformation of point T as T'(h+4,k-5)

So, we have found the coordinates of the images S', R', T' under the translation defined by (x,y) -> (x+4, y-5) as (11,9), (-4,-6) and T'(h+4,k-5) respectively.

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Answer:

4ft by 7 ft

Step-by-step explanation:

4*7=28 and 7-4=3 so the dimensions are 4ft by 7ft

The dimensions of the rectangle are 7 ft by 4 ft.

What is the area of the rectangle?

The area of a rectangle is defined as the product of the length and width.

Let x be the length of the rectangle.

The width of the rectangle is 3 less than the length, so the width can be represented as x-3.

The area of a rectangle is the length multiplied by the width, so:

Area = Length * Width

Area = x × (x-3)

Area = x² - 3x

We know that the area of the rectangle is 28 ft², so we can set the equation equal to 28 and solve for x:

x² - 3x = 28

x² - 3x - 28 = 0

Now we can use the quadratic formula or factoring method to find the solutions of x:

x = (3 ± √(3² - 41-28))/(2*1)

x = (3 ± √(9+112))/2

x = (3 ± √121)/2

x = (3 ± 11)/2

x = -4 or 7/2

The dimensions of the rectangle can't be negative, so the only valid solution is x = 7/2, which means the length of the rectangle is 7/2 ft and the width is (7/2 - 3) ft = -1/2 ft.

The width can't be negative, this answer is incorrect. So we have to check the other solution x = 7.

Therefore, the dimensions of the rectangle are 7 ft by 4 ft.

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Answer:

  CD = 3/√2 in

Step-by-step explanation:

You want the measure of altitude CD in isosceles right triangle ACB with the right angle at C.

All of the isosceles right triangles in this figure are similar, and all have sides in the ratio 1 : 1 : √2.

In ∆BCD, side BC is the longest, given as 3 in. That means the other two sides of that triangle are ...

  CD = BD = CB/√2

  CD = 3/√2 in

__

Additional comment

Often, we like to rationalize the denominator of expressions involving roots. That would make the expression for CD be ...

  CD = 3/√2 = (3/2)√2 = 1.5√2

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The number of pencils that he bought will be 21 pencils.

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

Karani bought 4 pencils and 6 biro pens for $66 and Mary bought 2 pencils and 5 biro pens for $51.

Let 'x' be the cost of pencils and 'y' be the cost of biro pens. Then the equations are given as,

4x + 6y = 66         ...1

2x + 5y = 51

4y + 10y = 102      ...2

From equations 1 and 2, then we have

10y - 6y = 102 - 66

4y = 36

y = 9

Then the value of 'x' is given as,

2x + 5(9) = 51

2x + 45 = 51

2x = 6

x = 3

Ondieki spent $228 to buy the same type of pencils and biro pens. If the number of biro pens he bought was 4 more than the number of pencils.

Let 'm' and 'n' be the number of pencils and biro pens, respectively.

3m + 9n = 288          ...3

n = m + 4                   ...4

From equations 3 and 4, then we have

3m + 9(m + 4) = 288

12m + 36 = 288

12m = 252

m = 21

Then the value of 'n' is given as,

n = 21 + 4

n = 25

The number of pencils that he bought will be 21 pencils.

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The third side of the right angle triangle is x = 15 ft.

What is right angle triangle?

A right triangle is a triangle with one angle at a right angle, meaning that two of its sides are perpendicular. It is also known as a right-angled triangle, an orthogonal triangle, or more commonly as a rectangled triangle. Trigonometry's foundation is the right triangle's relationship between its sides and other angles.

We have to find the measure of third side of given right triangle.

The two sides of right triangle are 9 ft and 12 ft.

Let the side of third side is x.

By using the Pythagoras theorem,

(9)^2 + (12)^2 = x^2

       81 + 144 = x^2

             225 = x^2

                  x = 15

Hence, the third side of the right angle triangle is x = 15 ft.

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The minimum number of 1 point foul shots that your team must make to win the game is given as follows:

20.

The expression for this problem is defined as follows:

3p + 2f + s.

In which the variables are given as follows:

The opponent made these following shots:

Hence the number of points of the opponent is given as follows:

8 x 3 + 12 x 2 + 11 = 59.

Your team made these following shots:

Hence the number of points of your team is given as follows:

10 x 3 + 8 x 2 + x = 40 + x.

The team wins when:

40 + x > 59

x > 19

Hence the minimum number is of 20, as the number of one point shots is a discrete amount.

Your basketball team made 10 three-pointers, 8 two-point field goals, and x one-point foul shots.

Your opponents made 8 three-pointers, 12 two-point field goals, 11 one-point foul shots.

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In the given scenario the pairing is natural pairing, hence the samples are dependent because there is a natural pairing between the two samples.

A pairing function in mathematics is a technique to convert two natural numbers into one natural number while maintaining their uniqueness. Insets and rational numbers share the same attributes as natural numbers, which may be shown in set theory using any pairing function.

In the given situation, the pairing between the prior drug sample and later drug sample are conducted in the same men. The results will thus, be dependent as same men will be required for the research to be conducted, and the effect of the drug before will also be taken into consideration.

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the ratio of the line segment joining the points (-3, 1) and (-8, 9) is 5:4. The ratio of the line segment joining the points (-3, 1) and (-8, 9) is calculated by subtracting the x-coordinates and y-coordinates of the two points.

5:4

Given two points, (x1, y1) and (x2, y2)

The ratio of the line segment joining the points is:

(x2 - x1) : (y2 - y1)

Therefore, the ratio of the line segment joining the points (-3, 1) and (-8, 9)

The ratio of the line segment joining the points (-3, 1) and (-8, 9) is calculated by subtracting the x-coordinates and y-coordinates of the two points. Specifically, the ratio is given by the expression (x2 - x1) : (y2 - y1). In this case, the x-coordinates are -3 and -8, and the y-coordinates are 1 and 9. By substituting these values into the expression, we get ( -8 - (-3)) : (9 - 1) which simplifies to ( -5 ) : ( 8 ). Therefore, the ratio of the line segment joining the points (-3, 1) and (-8, 9) is 5:4.

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Yes, a function can have 3 roots. This means that the function has 3 values of x where the y value is equal to 0. A polynomial of degree 3 or higher can have 3 roots.

Yes, a function can have 3 roots. A root of a function is a value of x for which the y value of the function is 0. This means that when a function has 3 roots, it has 3 values of x for which the y value of the function is 0. To have 3 roots, the function must be a polynomial of degree 3 or higher. A polynomial of degree 3 is usually written in the form ax^3 + bx^2 + cx + d = 0. This equation can be solved using the quadratic formula to find the 3 roots, which will be the 3 values of x for which the y value of the function is 0. The roots of the polynomial can also be found graphically by plotting the polynomial and finding where it intersects with the x-axis. This will be the 3 roots of the function.

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The amount of money Ryan will have in his account in 6 years is $3668.71.

Compound interest is calculated using the exponential formula y = P(1+r)ⁿ. P is for "Present" or Principal value; r stands for interest rate; n stands for time (in years), and y stands for future value after the amount compounds annually

Given:

Principal Amount = $2500

Rate of interest = 6.25%

Time = 6 years

The exponential equation can be given as:

y = P(1+r)ⁿ where n is the number of years.

y = 2500(1 + 0.0625)ⁿ

The money Ryan will have in his account in 6 years can be calculated as by putting n's value as 6 years.

y = 2500(1 + 0.0625)⁶

y = $3668.71

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3:7 are the odds in favor of choosing a book of poetry

given that

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. [note 1] [1] [2] The likelihood that an event will occur increases with its probability. A straightforward illustration is tossing a fair (impartial) coin. The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half

the probability of randomly picking out a book of poetry from a bookshelf is 3/10

now, we need to find what are the odds in favor of choosing a book of poetry

P(poerty) = 3/10

P(non-poerty) = 1 - 3/10 = 7/10

number of odds = P(poerty) /P(non-poerty)

                          = 3/10/7/10

                          = 3/7

                          = 3:7

3:7 are the odds in favor of choosing a book of poetry

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Solving the provide question, we can say that frequency distribution 70 years or older is 0.1333, 4/30, or 13.3% younger than 40 years old is 8/30, 0.2666, or 0.4000. (there are 12 under 50 out of 30 altogether).

In order to make the information easier to understand, frequencies are organized into frequency distributions, which are visual displays. The frequencies displayed in a frequency distribution can be absolute or relative, like ratios or percentages. Both a graph and a table of frequencies can be used to represent a frequency distribution. Both the exact number of observations and the proportion of observations falling within each range can be displayed in a frequency distribution.

Here,

A relative frequency distribution is the name given to the distribution in the latter scenario. The frequency of an observation is the frequency with which it appears in the data.

The frequency of the number 9 in the following list of numbers, for instance, is 5. (because it occurs 5 times). 1, 2, 3, 4, 6, 9, 9, 8, 5, 1, 1, 9,

70 years or older is 0.1333, 4/30, or 13.3% younger than 40 years old is 8/30, 0.2666, or 0.4000. (there are 12 under 50 out of 30 altogether).

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The complete question is "The following data represents the age of 30 lottery winners .Given the frequency distribution for the data,

Each column (left to right) is as follows: Age, Frequency, Relative Frequency, Cumulative Relative Frequency

[20,29] 1 0.0333 0.0333

[30,39] 7 0.2333 0.2666

[40,49] 4 0.1333 0.3999

[50,59] 5 0.1667 0.5666

[60,69] 9 0.3 0.8666

[70,79] 3 0.1 0.9666

[80,89] 1 0.0333 0.9999

What is the frequency of lottery winners of age between 19 and 40?

"

Answer:

  see attached

Step-by-step explanation:

You want to fill in the blanks to complete the description of writing a number in scientific notation.

A number written in scientific notation can be described as a coefficient times a power of ten (2nd attachment). Different terminology is used by different authors to describe these parts.

Sometimes the entire coefficient is also called the "mantissa." Sometimes, the term "mantissa" is used to refer to the fractional part of the coefficient, the digits to the right of the decimal point. Your curriculum calls the coefficient the "first factor."

The power of ten is chosen so that the first factor is always a number greater than or equal to 1, but less than 10.

The power of 10 has an exponent, also called the "characteristic". Your curriculum calls the combination of base (10) and exponent the "second factor." The exponent is equal to the exponent of the place value multiplier of the most-significant digit when the number is written in standard form (3rd attachment).

The filled-in description is shown in the first attachment. You will notice that its wording helps you fill in the blanks. It asks you how many parts there are to the number, then refers to them as the "first part" and the "second part." It asks you what the parts are called, then refers to the first one as the "first factor."

The given example in scientific notation is ...

  [tex]2.54\times10^6[/tex]

The exponent of 6 corresponds to the 6 little left-arrows in the figure in your problem statement. It is the power of 10 that represents "millions," the place-value multiplier of the most-significant digit of the number two million five hundred forty thousand.

The equation of the least square regression line mated closely with the given data: y = 5.5x + 52.

For the given data:

Option:  y = 5.5x + 52.

Put x = 2,

y = 5.5(2) + 52

y = 63

Put x = 4,

y = 5.5(4) + 52

y = 74

Thus, the equation of the least square regression line mated closely with the given data: y = 5.5x + 52.

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Answer:

(6x + 15y) / x

Step-by-step explanation:

(2x + 5y) * 3/x =

3 * (2x + 5y) / x =

(3 * 2x + 3 * 5y) / x  ==> distribute 3 to 2x and 5y

(6x + 15y) / x ==> simplify

Answer: y=-33.25 or -33.3

Step-by-step explanation:

2x=88

x=44

the triangle has 180 total angle

4y+(5x+5)+2x=180

substituting the numbers

4y+(5(44)+5)+2(44)=180

4y+(220+5)+88=180

4y+225+88=180

4y+313=180

(-313)

4y=-133

(divide by 4)

y=-33.25 or -33.3

The numbers are 4.5 and 13.5.

The ratio of two numbers = 1:3

Let the numbers be x and 3x.

After increasing each number by 9, the numbers will be x + 9 and 3x + 9.

Now, According to the question, after increasing each number by 9 the ratio becomes 3:5

Hence,         [tex]\frac{x + 9}{3x + 9}[/tex]  = [tex]\frac{3}{5}[/tex]

                  5x + 45 = 9x + 27

                  9x - 5x =  45 - 27

                     4x     = 18

                       x     = 18 / 4

                              = 4.5

if x = 4.5, then 3x = 4.5 * 3 = 13.5

So, the numbers are 4.5 and 13.5.

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Answer:

the ratio of n to m is 5 : 7

5m = 7 n

n : m = 5 : 7

$45.38 and $46.42 is the  interval can the branch manager be 95% certain that the sample mean will fall within

Using the Central Limit Theorem, the branch manager can be 95% certain that the sample mean will fall within $1.034 of the mean.

What does the Central Limit Theorem state?

It states that the sampling distribution of sample means of size n has standard deviation .

By the Empirical Rule, 95% of the sample means fall within 2 standard errors of the mean.

In this problem, we have that the standard deviation and the sample size are given as follows:

Hence the standard error is given by:

[tex]s = \frac{10.34}{\sqrt{400}} = 0.517.

Two standard errors is represented by:

2 x 0.517 = $1.034.

Hence, the branch manager can be 95% certain that the sample mean will fall within $1.034 of the mean.

$45.38 and $46.42 is the  interval can the branch manager be 95% certain that the sample mean will fall within

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Answer:

Step-by-step explanation:

The answer is C. 5x + 15 because the 5 outside the parentheses () is supposed to multiply by what's inside the parentheses. So multiply 5 and x and 5 and 3 (5 * X = 5x) (5 * 3 = 15).

The distribution used to obtain the critical value in this situation is the Student's t-distribution.

Critical value is a statistical value used to determine whether a hypothesis test result is statistically significant or not. It is the value that is compared to the test statistic to determine whether the null hypothesis should be rejected or not. The critical value is determined by the level of significance chosen for the study, the sampling distribution of the test statistic, and the degrees of freedom.

The Student's t-distribution is a symmetric probability distribution that is used when the population standard deviation is unknown. It is used in situations where there is a small sample size (less than 30) and the sample is drawn from a normally distributed population. In this case, the owner is interested in developing a 90% confidence interval estimate, so the critical value will be obtained from the Student's t-distribution.

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There are two types of systems in mathematics: discrete systems, which are composed of distinct, separate elements, and continuous systems, which are composed of elements that are connected and can take on any value over a range.

1. Discrete systems: A system with distinct, separate elements, such as a set of integers or a graph.

2. Continuous systems: A system with elements that are connected and can take on any value over a range, such as a line or a curve.

1. Discrete systems: A discrete system is a system with distinct, separate elements. Examples include a set of integers, a graph, or a network of nodes. Discrete systems are usually studied using discrete mathematics.

2. Continuous systems: A continuous system is a system with elements that are connected and can take on any value over a range. Examples include a line, a curve, a function, or a surface. Continuous systems are usually studied using calculus.

There are two types of systems in mathematics: discrete systems, which are composed of distinct, separate elements, and continuous systems, which are composed of elements that are connected and can take on any value over a range. Discrete systems are studied using discrete mathematics, while continuous systems are studied using calculus.

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If two sides of a triangle have lengths 13.2 and 21.5, then the third side length be less than 34.7.

When a triangle's two sides are given lengths of 13.2 and 21.5, we must determine what the third side's length should be.

The sum of the lengths of any two sides of a triangle can always be more than the length of the third side.

The length difference between any two triangle sides will never be greater than the length of the triangle's third side.

13.2 and 21.5 add up to 34.7, and their difference equals 8.3.

The above condition must not be violated, and the length of the third side must be greater than 8.3 and less than 34.7.

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X=5times (root2)/2

Step-by-step explanation:

Sin45=x/5

x=5sin45

x=5 times root2/2

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A number or algebraic expression is said to be in its simplest radical form and to be an nth root if it lacks any elements that are perfect nth powers under the radical.

The term "simplest radical form" refers to the most basic representation of a number or algebraic expression. When a number or algebraic expression contains no elements that are perfect nth powers under the radical, it is said to be in its simplest radical form and be an nth root.

When all of a radical expression's perfect squares, cubes, etc. are eliminated from the radical, the radical is in its simplest form. A radical is a phrase containing a root, most frequently a square or cube root.

Simply put, simplifying a radical eliminates the need to find any more square roots, cube roots, fourth roots, etc. when expressing it in its simplest radical form. Additionally, it entails eliminating any radicals from the denominator of a fraction.

Sin45 = x/5

x = 5 sin 45

x = 5 × (√2)/2

Therefore, the value of x be x = 5 × (√2)/2

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Answer:

The bottom most option

Step-by-step explanation:

Lets divide 3 2/5 and 3 1/6

3 2/5 = 17/5 and 3 1/6 = 19/6

17/5/(19/6) = 17/5  x 6/19 = 102/95 = 1 7/95 or the last option.

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The value of (AB)² is 15.

A circle is a two-dimensional figure formed by a set of points that are at a constant or at a fixed distance (radius) from a fixed point (center) on the plane. The fixed point is called the origin or center of the circle and the fixed distance of the points from the origin is called the radius. Two circles can be called congruent if they have the same radius. Equal chords are always equidistant from the center of the circle. The perpendicular bisector of a chord passes through the center of the circle. When two circles intersect, the line connecting the intersecting points will be perpendicular to the line connecting their center points. Tangents drawn at the endpoints of the diameter are parallel to each other.

Equation of first circle:

(x - 2)² + (y + 1)² = 4²

Equation of secnd circle:

(x - 2)² + (y - 5)² = (√10)²

Solve for (x - 2)² :

(x - 2)² + (y + 1)² = 4²   ==>   (x - 2)² = 16 - (y + 1)²

(x - 2)² + (y - 5)² = (√10)²   ==>   (x - 2)² = 10 - (y - 5)²

Then,

16 - (y + 1)² = 10 - (y - 5)²

16 - (y ² + 2y + 1) = 10 - (y ² - 10y + 25)

15 - 2y - y ² = -15 + 10y - y ²

30 - 12y = 0

12y = 30

y = 30/12 = 5/2

Thus, the y coordinate of A and B is 5/2.

Then solve for x :

(x - 2)² = 16 - (5/2 + 1)²

(x - 2)² = 15/4

x - 2 = ± √(15/4) = ±√15/2

x = 2 ± √15/2

Thus, the x coordinates for either A or B are 2 +√15/2 or 2- √15/2.

The intersections points are A = (2 - √15/2, 5/2) and B = (2 + √15/2, 5/2). Thus, the squared distance between them:

(AB)² = [(2 - √15/2) - (2 + √15/2)]² + (5/2 - 5/2)²

(AB)² = (-√15)² + 0²

(AB)² = 15

Thus, the value of (AB)² is 15.

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