if k is a positive two-digit integer, what is the tens digit of k ? (1) the sum of the tens digit of k and the units digit of k is 5. (2) the tens digit of k 6 is 3.

In the graph the letter "J" has a height of 17 units.

What is a graph?

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.

According to the graph the distance from A to B is horizontal, so it need not be counted.

From B to C the distance is = 3 units

Again from C to O the distance is horizontal, so it need not be counted.

From O to D the distance is = 10 units

From D to E the distance is = 4 units

From E to F the distance is horizontal, so it need not be counted.

The distance from F to N need not be counted as it will be the repetition of the total height.

So, the total height is = 3 + 10 + 4 = 17 units

Therefore, the total height on the graph is 17 units.

To learn more about graph from the given link

https://brainly.com/question/19040584

#SPJ1

The possible number of the right triangle is 6. Hence option A is the correct option.

What is the right triangle?

A right triangle or right-angled triangle, or more formally an orthogonal triangle, formerly known as a rectangle triangle, is a triangle with one right angle, i.e. two perpendicular sides. Trigonometry is founded on the relationship between the sides and other angles of a right triangle.

Given that △ABC is a right triangle.

The legs of the △ABC are a and b which are integers. The hypotenuse is b+1. Since b is an integer thus b+1 is an integer.

Pythagorean theorem:

The sum of the square of the legs of a right triangle is the square of the hypotenuse.

According to Pythagorean theorem,

a² + b² = (b+1)²

Applying the algebraic formula (a+b)² = a² + b² + 2ab

a² + b² = b² + 2b +1

Cancel out b² from both sides:

a² = 2b + 1

2b is always a positive number since 2 is multiplied with b. Thus 2b+1 is an odd number.

Since a² = 2b + 1, thus a² is an odd number.

The square of an odd number is an odd number. Thus a is an odd number.

Again given that,

b<100

2b < 200

2b + 1< 201

Putting 2b + 1 = a²:

a² < 201

Now putting a=1 in a² < 201:

1² < 201 (true)

Now putting a=3 in a² < 201:

3² < 201 (true)

Now putting a=5 in a² < 201:

5² < 201 (true)

Now putting a=7 in a² < 201:

7² < 201 (true)

Now putting a=9 in a² < 201:

9² < 201 (true)

Now putting a=11 in a² < 201:

11² < 201 (true)

Now putting a=13 in a² < 201:

13² < 201 (true)

Now putting a=15 in a² < 201:

15² < 201 (false)

If a = 1, 2b+1 = 1 which implies b = 0. The length of a side of a triangle is never zero. Therefore a ≠ 1.

Thus the possible values of a are 3,5,7,9,11,13.

To learn more about the sides of a right triangle, click on the below link:

https://brainly.com/question/9446948

#SPJ1

The value of d = 26.

A mathematical statement that maintains the equality of two expressions that are joined by the equals sign "=" is known mathematically as an equation.

A mathematical equation can be solved by adding or subtracting the same number on both sides or multiplying or dividing the same number into both sides.

Here we have

1/4(d-2) = 6    

Solve the above equation as follows

=> 1/4(d-2) = 6      

Multiply by the same number on both sides

=> 4[ 1/4 (d - 2) ] = 4 × 6  

=> (d - 2) = 24

Add '2' on both sides

=> (d - 2) + 2 = 24 + 2

=> d = 26

Therefore,

The value of d = 26

Learn more about Equation problems at

https://brainly.com/question/20745180

#SPJ1

With the help of equations we can say that the shark is 18 years old.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

We have LHS = RHS (left hand side = right hand side) in every mathematical equation.  To determine the value

To determine the value A statement is not an equation if it has no "equal to" sign.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation.

Hence, the shark is 18 years old.

learn more about equations click here:

brainly.com/question/2972832

#SPJ4

A race car driver is 3.79 km away from where she started.

Assume that a race car driver turns southwest, at an angle of  45 degrees.

Also she turns East making another 45 degree angle.

So, we get a right triangle.

Let ABC be right triangle with A = 90°, B = 45° and C = 45°

For right triangle ABC, a = 2.75km, b = y km and c = x km (the distance she has traveled east before crossing her northern path)

Consider the sine of angle B

sin(B) = Opposite side of angle B / Hypotenuse

sin(45) = x / 2.75

x = 1.94

sin(C) = Opposite side of angle C / Hypotenuse

sin(45) = y/2.75

y = 1.94

So, the distance to north before paths crossed would be,

N = 4.69 - y

N = 3.31

And the distance after she passed her northern path.

E = 3.89 - x

E = 1.85

Let m be the distance from Starting Point to End Point.

Using Pythagoras theorem,

m² = N² + E²

m² = (3.31)² + (1.85)²

m = 3.79 km

Learn more about the Pythagoras theorem here:

https://brainly.com/question/343682

#SPJ4

In this situation, the wholesale cost x of every dress is first increased by $20 to obtain the retail price. This is represented by the function f(x) = x + 20.

Then, during a sale, every dress is sold for 75% of the retail price. This is represented by the function g(x) = 0.75x.

To find the composite function gf that describes this situation, we need to substitute f(x) into g(x) and simplify.

gf = g(f(x)) = g(x + 20) = 0.75(x + 20) = 0.75x + 0.75(20) = 0.75x + 15

Therefore, gf = 0.75x + 15 describes the situation where the wholesale cost x of every dress is first increased by $20 to obtain the retail price, and then during a sale, every dress is sold for 75% of the retail price. So, the final cost of the dress is (0.75x + 15)

So, the composite function gf = 0.75x + 15, describes the situation where the shop adds $20 to the wholesale cost, and then sells it for 75% of the retail price.

Learn more about mathematical functions here:

brainly.com/question/12195089

#SPJ4

Answer:

please open the following image for the answer

The domain of a function is the set of all possible input values (x-values) for which the function produces a valid output (y-value). The range of a function is the set of all possible output values (y-values) that the function can produce.

When working with inequalities, the domain and range can be found by analyzing the inequality and the context of the problem.

To find the domain of an inequality function, we need to identify any restrictions or limitations on the input values (x-values) that would make the inequality invalid.

For example, if the inequality contains a denominator that cannot be equal to zero, we need to exclude those values of x from the domain.

To find the range of an inequality function, we need to identify the set of all possible output values (y-values) that would make the inequality true.

For example, if the inequality is in the form y > x, we know that all values of y that are greater than x will satisfy the inequality.

In summary, finding the domain and range of inequalities of a function involves identifying any restrictions or limitations on input values and the set of possible output values that would make the inequality true.

Learn more about the domain at

https://brainly.com/question/28135761

#SPJ4

Therefore , the solution of the given problem of  surface area comes out to be  unused space is equal to 2π - (5π/6 + √3/2) m² .

Its surface area serves as a proxy for how much overall space it occupies. The whole environment of a three-dimensional shape is taken into account when calculating its surface area. The overall size of something is its surface area. The volume of water in a cuboid can be determined by summing the face on each of the six rectangular sides. To determine the box's measurements, apply the following formula: For 2lh, 2lw, & 2hw, the surface is exactly the same (SA). The region is represented by the surface area of the muti form.

Here,

Given:

AB = D = 4 m (R = 2 m)

The size of the AB semicircle is:

=> Area = πr²/2

=>A = 2π

The dimensions of the little semicircle are a=5/6 + 2/3/2 m2 and a=5/6 + 3/2 m2.

The remainder area is therefore equal to A- a.

= 2π - (5π/6 + √3/2) m²

The unused space is equal to 2π - (5π/6 + √3/2) m²

Therefore , the solution of the given problem of area comes out to be  unused space is equal to 2π - (5π/6 + √3/2) m² .

To know more about surface area visit:

https://brainly.com/question/2835293

#SPJ4

Since the graph of a straight line passing through the origin represents two variables in direct variation, with the slope as the coefficient of proportionality,

what was the original temperature, in degrees Fahrenheit, of the cup of hot water?

To learn more about temperature refers to:

https://brainly.com/question/12293537

 #SPJ1

The mean, median, and mode of the heights of 20 people belonging to the same group were found to be 160.95 cm, 160 cm, and 160 cm respectively.

Mean:

Add all the heights together:

160 + 160 + 170 + 180 + 160 + 160 + 175 + 170 + 160 + 160 + 160 + 160 + 160 + 160 + 160 + 175 + 160 + 160 + 170 + 160 = 2605

Divide the sum by the number of data points (20):

2605 / 20 = 160.95

Median:

Arrange the data in numerical order:

160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 170, 170, 175, 175, 180

The median is the middle value, which is 160.

Mode:

The mode is the most common value, which is 160.

The mean, median, and mode of the heights of 20 people belonging to the same group were calculated by adding all the heights together and dividing the sum by the number of data points (20). The mean was found to be 160.95 cm. The data was then arranged in numerical order and the median was found to be the middle value, which was 160 cm. Lastly, the mode was determined to be the most common value, which was also 160 cm.

Learn more about median here

https://brainly.com/question/28060453

#SPJ4

To put it simply, any outlier with a high or low value has the same impact on the data set. The standard deviation goes down when the outlier is taken out.

Outliers are data points that deviate from the distribution's typical pattern. a value that is "outside" of the record's typical range (either significantly lower or substantially greater).

The standard deviation increases when the outlier's value is higher than the average of the data, compared to when it doesn't exist. When the outlier is eliminated, the mean decreases if the outlier was lower than the majority of the data, and the standard deviation is once more higher than it would be without the outlier. What makes it different is that, as opposed to a fall in the mean, the removal of the outlier would cause an increase.

To put it simply, any outlier with a high or low value has the same impact on the data set. The standard deviation goes down when the outlier is taken out.

To know know more about outlier visit:

https://brainly.com/question/26958242

#SPJ4

a) The slope of the line is given as follows: 0.5.

b) The meaning of the slope is that the volume increases by 0.5 gallons per minute.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

For which the parameters are given as follows:

From the graph, when x increases by 8, y increases by 4, hence the slope m is obtained as follows:

m = 4/8 = 0.5.

As x is the time in minutes and y is the volume in gallons, the meaning of the slope is that the volume increases by 0.5 gallons per minute.

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

Answer: hoped this help. bye.:)

Answer:

You cut the question out so it is impossible to tell but i can guess that

W is the midpoint or something, so WR = 136.8/2 = 68.4

This is just a guess, i can't tell properly as i don't know the question.

Answer:

C) [tex]x^{3} + 3x^{2} + 3x - 1[/tex]

Step-by-step explanation:

We have our equations. So, we will substitute them in our last equation, giving us:

[tex](x + 1) * (x^{2} + 2x - 1) + 2x[/tex]

Opening the parentheses gives us:

[tex]x^{3} + 2x^{2} - x + x^{2} + 2x - 1 + 2x[/tex]

Combining like terms:

[tex]x^{3} + 2x^{2} + x^{2} + 2x - x + 2x - 1[/tex]

Then, we combine:

[tex]x^{3} + 3x^{2} + 3x - 1[/tex]

So, your answer is C) [tex]x^{3} + 3x^{2} + 3x - 1[/tex].

Hope this helped!

Please give brainliest if possible!

The equation representing the polynomials are D = x³ + 3x² + 3x - 1

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as D

Now , the value of D is

Substituting the values in the equation , we get

A = x + 1

B = x² + 2x - 1

C = 2x

The value of AB + C = D

And , AB = ( x + 1 ) ( x² + 2x - 1 )

On simplifying the equation , we get

AB = x ( x² + 2x - 1 ) +  ( x² + 2x - 1 )

AB = x³ + 2x² - x + x² + 2x - 1

AB = x³ + 3x² + x - 1

And , D = x³ + 3x² + x - 1 + 2x

D = x³ + 3x² + 3x - 1

Hence , the equation is D = x³ + 3x² + 3x - 1

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ5

On solving the provided question, we can say that the fraction =5/12 = 0.4166666667  rounding off = 0

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

here,

the fraction is

7/12 - 2/12

=5/12

= 0.4166666667

rounding off = 0

To know more about fraction visit:

https://brainly.com/question/10354322

#SPJ4

As per the concept of the normal distribution and the central limit theorem, the probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50.

The term normal distribution is defined as a symmetrical plot of data around its mean value, where the width of the curve is defined by the standard deviation.

Here we have given that  agency will select a random sample of 500 voters from one region, Region A, of the city and here we also know that The proportion is of 0.47.

Then the mean and the standard deviation are 0.47 and 0.0223 respectively.

Here the probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50 is 1 subtracted by the p-value of Z when X = 0.5 is calculated as,

=> Z = (0.5 - 0.47) / 0.0223

=> Z = 1.34

Then by using the Z table we have identified the value of P as 0.9099.

To know more about Probability here.

https://brainly.com/question/11234923

#SPJ4

The length of the straw is equal to the length of the space diagonal of  rectangular box, that is 11.6 inches.

The length of the straw is equal to the space diagonal of the rectangular box. Space diagonals are three-dimensional diagonals.

If the length of the sides of the box is a, b, and c, then the space diagonal can be computed by applying the Pythagorean Theorem.

D = √(a² + b² + c²)

Substitute the following dimensions:

a = 10 inches

b = 3 inches

c = 5 inches

Then,

D = √(10² + 3² + 5²)

D = √(100 + 9 + 25)

D = √134 = 11.6 inches

Hence, the length of the straw is 11.6 inches.

Learn more about diagonal here:

https://brainly.com/question/12516815

#SPJ4

This two options I am going to include in my explanation

a) There is a unique solution.

d) The system is independent and consistent.

The given system of equations can be represented as a matrix equation [A|B] where A is the coefficient matrix and B is the constant matrix.

|1 1 1 | 0 |

|2 -1 3 | 0 |

|3 2 -1 | 0 |

The above system of equation can be written as AX=B, where X=[x,y,z] and A,B are as above.

We can check the rank of A and [A|B], if they are equal then the system is consistent and has a unique solution.

Using Gaussian elimination method, it can be observed that the rank of A and [A|B] both are 3, which means the system is consistent and has a unique solution.

Thus the given system of equations is consistent and has a unique solution.

Learn more about Gaussian elimination method

brainly.com/question/12090959

#SPJ4

The Complete Question  is -

Consider the following system of equations:

x + y + z = 0

2x - y + 3z = 0

3x + 2y - z = 0

Which of the following statements are true about this system of equations?

a) There is a unique solution.

b) The solution is x = 0, y = 0, and z = 0.

c) The system intersects at one point.

d) The system is independent and consistent.

Please check all of the box that apply.

Answer: If one of the roots of the equation 2x^2-bx-20=0 is -2.5, then by Vieta's Formulas, the other root is x = (20 + b)/4.

Step-by-step explanation:

Answer:

x=4

Step-by-step explanation:

Given equation: 2x^2 - bx - 20 = 0

We are also given one of the solutions, which is -2.5.

We can start off by substituting -2.5 in place of x, in the given equation.

This is what it will look like:

2 * (2.5) ^2 - b (-2.5) - 20 = 0

After simplifying, the equation will now look like this:

12.5 + 2.5b - 20 = 0

Now, move all of the similar terms to one side of the equation:

2.5b = 20 - 12.5, which is basically 2.5b = 7.5

b = 7.5/2.5, which is b = 3

Now that we know what the value of "b" is, let's go back to the given equation (2x ^2 - bx - 20 = 0), and substitute "3" in place of "b".

It will look like this:

2x^2 - 3x - 20 = 0

We can now apply the Quadratic formula. The formula looks like this:

(-b ± √b^2 -4ac)

          2a

Substitute the values from the new equation into the formula:

3 ± √9 + 160

         4  

Simplify that:

3 ± 13

   4

You should now have two solutions:

x1 = 3 + 13,   which is x1 = 16/4 = 4            

         4

x2 = 3 - 13 , which is x2=-10/4, = -2.5

        4

Now, the root that was given to us at the start of the problem was -2.5, so the other solution is 4, which we just solved for.

I hope this helps!!

Answer:

i think its A=12BH+12BiH

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

The least common denominator of the given fractions, can be found to be 72.

The least common denominator of two or more fractions, is the least common multiple of the denominators of the fractions.

With the given fractions of 3 / 8 and 5 / 18 therefore, the least common denominator would be the least common multiple of 8 and 18.

The least common multiple of 8 and 18 is the value of 72 so this must be the least common denominator for the fractions.

Find out more on least common denominator at https://brainly.com/question/19249494

#SPJ1

When the person has been dead for 2 minutes and comes back their experience of 2 minutes dead then we call that the person is suffering from Lazarus Syndrome .

What is Lazarus Syndrome ?

The Lazarus syndrome is referred as to your blood circulation returning spontaneously after your heart stops beating and it fails to restart despite providing  cardiopulmonary resuscitation (CPR).

In Simple words it can be called as returning to life after it appears that the person has  died.

So, if the person comes back to life after experience of 2 minutes of dead , then we say that the person has Lazarus Syndrome and got a heart attack .

Learn more about Cardiopulmonary Resuscitation (CPR) here

https://brainly.com/question/10318934

#SPJ4

The probability that x + y <1/3 is 1/18, the probability that x + y < 3/2 is 0.875 and the algebraic expression for F(u) is: F(u) = 0, if u < 0; F(u) = 0.5u^2, if 0 <= u <= 1; F(u) = 1 - 0.5(2 - u)^2, if 1< u < 2; F(u) = 1, if u >= 2.

(a) The set of points (x,y) in the unit square S for which x+y < 1/3 is a triangle with vertices at (0,0), (1/3,0), and (0,1/3).

The area of this triangle is

0.5(1/3)^2 = 1/18

Therefore, the probability that a point (x,y) chosen from the unit square using the uniform probability law is in this triangle is 1/9.

(b) The set of points (x,y) in the unit square S for which x+y < 3/2 is a polygon with vertices at (0, 0), (1, 0), (1, 0.5), (0.5, 1) and (0, 1) as S = [0,1]×[0,1] refer figure for clarity.

The area is

1*1 - 0.5*0.5²

= 1 - 0.125

= 0.875

Therefore, the probability that a point (x,y) chosen from the unit square using the uniform probability law is in this triangle is 0.875

(c) To find an algebraic expression for F(u), we need to consider different cases for the value of u:

if u < 0, then the set of points (x,y) for which x+y <= u is empty, so F(u) = 0

if 0 <= u < 1, then the set of points (x,y) for which x+y <= u is a triangle with vertices at (0,0), (u,0), and (0,u). The area of this triangle is u^2, so

F(u) = 0.5u^2

if 1 <= u < 2, then the set of points (x,y) for which x+y <= u is a polygon with vertices at (0,0), (1,0) (1, u-1), (u-1, 1) and (0, 1). The area can be obtained by subtracting the area of triangle with vertices (1, u-1), (u-1, 1) and (1, 1), from area of square, that is 1 sq units.

F(u) = 1 - 0.5(2 - u)²

if u >= 1, then the set of points (x,y) for which x+y <= u is the entire unit square, so

F(u) = 1.

To know more on uniform probability law

https://brainly.com/question/14854212

#SPJ4

The area of the sector is 113.14 square cm.

Step1:

Given, central angle, θ = 120°

Radius of circle, r = 21 cm

We have to find the area of a sector of the circle.

Area of sector = πr²θ/360°

= π(21)²(120°)/360°

= π(21)²(1/3)

= (22/7)(21)(21)(1/3)

= (22/7)(21)(7)

= (22)(21)

= 462 square cm.

Step2:

Therefore, the area of the sector is 462 square cm.

the area of a sector of circle of radius 12 cm and central angle 90°.

central angle, θ = 90°

Radius of circle, r = 12 cm

We have to find the area of a sector of the circle.

Area of sector = πr²θ/360°

= π(12)²(90°/360°)

= (22/7)(12)(12)(1/4)

= (11/7)(6)(12)

= 113.14 square cm

Therefore, the area of the sector is 113.14 square cm.

To learn more about area of sector refers to;

https://brainly.com/question/29973659

#SPJ1

Answer:

10.75 miles

Step-by-step explanation:

[tex]\frac{40}{100}[/tex]×x=4.3

40x=430

x=10.75